P1152-2038.txt

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P 1152 2038

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Clo0027
45303

ASPECTS OF MOLTEN FLUORIDES AS HEAT
TRANSFER AGENTS FOR POWER GENERATION

PROEFSCHRIFT

TER VERKRUGING VAN DE GRAAD VAN DOCTOR IN
DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE
HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR
MAGNIFICUS PROF. DR. IR. F.J. KIEVITS VOOR EEN
COMMISSIE AANGEWEZEN DOOR HET COLLEGE
VAN DEKANEN, TE VERDEDIGEN OP WOENSDAG
14 FEBRUARI 1979 DES MIDDAGS
OM 13.30 UUR

DOOR

0050827
'-'?.%-) QUELENSTR.IUY <
‘() ’

N4

BAUKE VRIESEMA

werktuigkundig ingenieur S b el

geboren te Uithoorn

Dit proefschrift is goedgekeurd door de promotor
PROF.IR. D. G. H. LATZKO

TABLE OF CONTENTS

LIST OF SYMBOLS
ABSTRACT
1. INTRODUCTION

2. FLOW MEASUREMENTS

2.1. Introduction
2.2. Venturi flow meter

2.2.1. Special features
2.2.2. Description of equipment

2.1. The venturi

2.2. The control system
.2.3. Safety

2.4. Instrumentation
es 24 35  ACCUTACY

2.3. Thermal flow measurement

1. Introductory remarks
Description of the method

a3
P
2.3.3. Description of the equipment

il e dids FEODS

.3.3.2. Electronic output adjustment
2.3.4. Accuracy

2.4. Transit time measurement

1. Introductory remarks

2. Description of the method
.3. Description of equipment
4., Accuracy

2.5. Test program for flow measurements
2.6. Experimental results

2.7. Conclusions

3. TURBULENT HEAT AND MOMENTUM TRANSFER

3.1 Introduction
3.2. Heat transfer

3.2.1. Introductory remarks

3.2.2. Description of the test module
3.2.3. Description of the loop

3.2.4. Outline of the method

3.2.5. Instrumentation

3.2.6. Data reduction and processing
Sedsil « CRIIDTALIiON

3.2.8. Accuracy

3:2:9

Test program

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O OO OO0 O U1 LTI WW WN N~ -

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- 0.5 -

3.2.10. Experimental results
3.2.11. Discussion of results

3.3. Momentum transfer

Introductory remarks

. Description of the method

Description of equipment

.1. Test tube
.2. Differential pressure measurement

Test program
Experimental results
Accuracy

Discussion of results

4. BAYONET TUBE STEAM GENERATOR

4.1,

Introduction

4.1.1. General back-ground
4.1.2. The bayonet tube steam generator

4.1.3. Aims and scope of the present investigations

4.1.2.1. Design characteristics
4.1.2.2. Potential interest

4.1.3.1. Steady state behaviour
4.1.3.2. Dynamic behaviour

4.1.
4.1.

3.2.1. Large transients
3.2.2. Stability

4.2. Basis for analysis

4.2.1. General assumptions
4.2.2. Balance equations

.1. Single-phase flow
.2. Two-phase flow

2.2.1. Thermal equilibrium
2.2.2. Thermal non-equilibrium

4.2.2.3. Energy balance of the wall

4.2.3. Empirical relations

4’

- 0.6 -

4.2.3.1. Transition criteria

=
=
=
=
3

. Te

1.1. Preheat-subcooled

1.2. Subcooled-saturation boiling
.1.3. Saturation boiling-mist flow
1.4. Mist flow-superheat

2. Heat transfer correlations

3. Frictional pressure drop correlations
.4. Slip correlations

5. Heat distribution parameter

st facility

Test module

- = O O WO O~d 9 OO0 (o2 T ® 2 BENN “SEREN SN ) [ J T N ST

L I T S S S S SN i S S S S S S S
o

SN
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4.12

4.3.1.1. Heating fluid 4.16
4.3.1.2. Flow pattern 4.16
4.3.1.3. Process conditions 4.17
4.3.1.4. Dimensions Rid?
4.3.2. Water/steam loop 4.17
4.3.2.1. General 4.17
4.3.2.2. Feedwater supply system 4.18
4.3.2.3. Heat sink 4.18
4.3.3. Instrumentation and control 4.18
4.3.3.1. Loop instrumentation and control 4.18
4.3.3.2. Test instrumentation 4.19
4.3.3.2.1. Instrumentation for steady state and 4.19
transient experiments

4.3.3.2.2. Instrumentation for the stability experiments 4.20
4.3.3.2.3. Calibration 4.20
4.3.4. Operational procedures 4.21
4.4. Steady state 4.22
4.4.1. Analysis : _ 4,22
4.4.1.1. Additional assumptions 4.22
4.4.1.2. Modified equations 4.23
4.4.1.3. Solutional procedure 4.24
4.4.2. Experiments 4.24
4.4.2.1. Data acquisition 4.24
4.4.2.2. Test program 4.27
4.4.2.3. Experimental results 4.28
.4.3. Evaluation of results 4.28
4.5. Transients 4.28
4.5.1. Introduction 4.28
4.5.2. Analysis 4,29
4.5.2.1. Modified equations 4.29
4.5.2.2. Solution in Eulerian co-ordinates (DYBRU) 4.30
4.5.2.3. Solution in Lagrangian co-ordinates (DSTS) 4.31
4.5.3. Critique of the methods employed 4.33
4.5.4. Experiments 4.34
4.5.4.1. Data acquisition 4.34
4.5.4.2. Test program 4.36
4.5.4.3. Experimental results 4.36
4.5.5. Evaluation of results 4.37
4.5.5.1. Introductory remarks 4.37
4.5.5.2. Comparison of DYBRU with an experiment 4.37
4.5.5.3. Comparison of DSTS with an experiment 4.37
4.6. Stability 4.37
4.6.1. Analysis &.37

in ¢ o R

Introductory remarks
Identification of characteristic sections

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N -
. .

4,6.1.2.1. Linearized analysis of the total system
4.6.1.2.2. Linearized description of subsystems
d4.6.1.2.3. Stability criteria

4.6.1.3. Analysis in the time domain

1. Introductory remarks

2. Additional assumptions
.3. Modified equations

4. Solutional procedure

4.6.1.4. Analysis in the frequency domain

1. Extensions in the model
2. Modified equations

.3. Solutional procedure

4. Program structure

4.6.2.1. Introductory remarks
4.6.2.2. Experimental procedure and data acquisition
4.6.2.3. Test program

4.6.3. Evaluation of analytical and experimental results

.1. Introductory remarks
.2. Preliminary program verification in the frequency
domain

.1. Eigenvalue analysis
.2. Frequency analysis

1 MW steam generator experiments

B.6:3.3 +h

4.6.3.3.1. Outline of experiments
4.6.3.3.2. Eigenvalue analysis
4.6.3.3.3. Frequency analysis

4.6.3.4. SWISH experiments

6.3.4.1. Outline of experiments
I

4.
4. .2. Frequency analysis
4.6.3.5. Bayonet tube experiments
6.3.5.1. Time domain analysis
.6.3.5.2. Frequency domain analysis
6.3.5.3. Additional remarks

5. CONCLUSIONS AND RECOMMENDATIONS
ACKNOWLEDGEMENTS

REFERENCES

SAMENVATTING

~J

L S N
. . . .
b W
U1 W N N

P S

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

APPENDIX

2A

3A

4A

4B

4C

4E

4F

4G

4H

4J

4K

Thermal conductivity of FLiNakK

Error analysis of the friction pressure drop
measurement

N\

Energy balances for the subcooled region

An adapted version of the Bankoff-Jones slip
correlation

The derivative of the specific mass of two-phase
mixtureswith respect to the mixture enthalpy

Derivation of the equations describing the
total system

Explanation for the existence of predominant
modes ofparallel channel instability

Zero's of H , and IMI

po

Details of discretization, linearization and
substitution steps in the solutional procedure

res

Example of an application of the SLINQ program
for substitution of linear equations

Power method and vector deflaticn as applied for
determining eigenvalues in the CURSSE program

REFERENCES PERTAINING TO APPENDICES

4A.1

4B.1

4c.1

4E.1

4r.1

4G.1

4H.1

4J.1

4K.1

- 0.9 -

LIST OF SYMBOLS
A = area
= coefficient
C = specific heat
D = diameter
E = mathematical expectation
f = friction factor
g = gravity constant
G = mass flux
h = enthalpy
H = transfer function
Im = imaginary part
K = total conductivity
= heat distribution factor
l1,LL = length
M = mass
Nu = 9X2-= Nusselt number
0 = perimeter
P = pressure
¥ = power
Pr = Prandtl number
q = heat flux
Q = heat flow
= radius
R = covariance function
Re = Reynolds number
= Real part
s = Laplace operator
= slip factor
S = gpectral density function
= time
u = internal energy
v = velocity
w = width
X = steam quality
z = axial co-ordinate
Z = impedance

- 0.10 -~

GREEK SYMBOLS

a = heat transfer coefficient J/m? Oc
= void fraction -
6 = small variation -
= small distance \ m
€ = error &
= angle with upward vertical rad
z = pressure loss coefficient : -
n = dynamic viscosity Ns/m?
6,9 = temperature Oc
A = thermal conductivity J/m Oc
= real part of eigenvalue _ -
o) = gpecific mass kg/m3
T = delay time S
= wall shear stress N/m?
@ = mass flow rate kg/s
= heat flow rate J/s
W = angular velocity rad/s

= imaginary part of eigenvalue -

SUBSCRIBTS
b = bulk
c = correction

= cross-sectional

- o = critical
d = delay
Do = dry-out
E = Eulerian
EV = evaporator channel
f = finish
fl = film
S = friction
FL = FLiNaK channel
g = gas
h = heated
inc = inconel
H = header
= hydraulic
1 = liquid
= lower

= 0.11 -

lg = evaporating
= latent

= Lagrangian

[-1
|

m = mass
= measured
P = pressure

= primary (salt) channel

¥ = released
res = resulting
S = start

= steam

= secondary (water/steam) channel

sat = saturated
t = transferred
tf = two-phase

tot = total

u = upper
v = volume
ve = venturi
7 = wall

MISCELLANEOUS

= average value,
mixture property

maximum value

ABSTRACT

The present thesis consists of two distinct parts. The first of these deals
with the potential application of a molten salt mixture as heat transfer
agent at temperatures well beyond 500 0c. The need for such applications,
which exclude more usual low pressure fluids, may arise from new chemical
processes. The fluid in question, the ternary eutectic of the fluorides of
lithium, sodium and potassium known as FLiNaK, is highly corrosive.

Chapter 2 evaluates three different methods for measuring mass flow rates
of such a corrosive liquid at elevated temperatures, based on venturi, "hot
finger" and transit time techniques, respectively. The evaluation was
performed on pilot plant scale in a molten salt loop.

The same loop was then used to establish empirical correlations for heat
transfer and frictional pressure drop. These experiments, using a salt-to-
air heat exchanger and a calibrated tube respectively, are reported in
Chapter 3 together with the resulting correlations.

The second part of the thesis deals with the thermo-hydraulic performance
of bayonet tube steam generators. The relation with the first part is given
by the fact that this design offers the only possibility for subcritical
steam raising plant heated by FLiNaK or other fluoride mixtures because of
the high melting points of these fluids. The need for such steam raising
plant may result from continued development of molten salt thermal breeder
reactors. For each of the three aspects of thermo-hydraulic design covered
in Chapter 4, viz.:

- steady state behaviour (full and part load)
- transient behaviour
- hydro-dynamic stability,

one or more computer programs were developed and subsequently verified by
comparison with experimental results obtained on a single tube test module
with rated steam conditions of 18 MPa/540 Oc.

In the course of developments in the latter area it became clear that a
continuing need existed for a simulation program capable of predicting
operating limits imposed by either parallel channel or loop instability
for once-through steam generators of various geometries. To that end a
modular user-oriented program (CURSSE) was developed in the frequency
domain and verified by comparison with experimental results obtained both
on the above bayonet tube test module and on two different steam generators
tested elsewhere.

The conclusions for both parts of the thesis as presented in Chapter 5

may be summarized as follows:

® FLiNaK appears well suited as heat transfer agent in the 500 - 700 Oc

temperature range .

bayonet tube design present a technically promising, though perhaps

economically questionable, alternative for raising steam in molten

salt breeder reactor systems

® the CURSSE program was proven a flexible and reliable tool for
predicting the stability limits of once-through steam generators of
various geometries.

- 0.13 -

INTRODUCTION

The research project underlying the present thesis originated in 1963 as a
joint undertaking between Euratom Joint Research Center (Petten
Establishment) and Delft University of Technology, Laboratory for Thermal
Power Engineering. The project's aim was to generate knowledge in the
field of heat transfer by molten fluorides, notably regarding:

® heat transfer and heat transport capability, with special reference
to a ternary eutectic mixture of NaF, LiF and KF further to be
referred to as FLiNak

® the technology of a heat transfer system operating in the 500 - 700 O¢c
temperature range at an semi-industrial ( = pilot plant) scale

® special instrumentation capable of reliable service for prolonged
periods in heat transfer systems such as described in the preceding
paragraph.

The Euratom interest in the development of molten salt technology stemmed
from their potential of these fluids as fuel carrier in fluid fuel nuclear
reactors, as demonstrated by the operation of the 10 MWth Molten Salt
Reactor Experiment (MSRE) at Oak Ridge National Laboratory from 1966 to
1970.

The University's interest was mainly focussed on the second objective
mentioned above, bearing in mind that molten salts constitute one of the
two groups of heat transfer agents capable of operation in the 500 - 700 Oc
temperature range at near atmospheric pressures without chemical stability
problems. The fact that the other group, viz. liquid metals, were already
under extensive study both worldwide and in the Netherlands in connection
with the development of fast breeder reactor cooling systems and the fire
hazard associated with their use suggested the study of molten salts as
potential heat transfer agents in high temperature process plant as a
worthwhile object for a technologically oriented university laboratory.
Continuing development work on the molten salt reactor concept at Oak Ridge
made it increasingly apparent that its eventual transition into the
electric power generating stage would require the solution of a number of
difficult problems in connection with the design of a molten salt heated
steam generator.

These problems are mainly due to the high melting point of the heating
salt, combined with the thermal stress problems inherent to high
temperature liquid systems. With the solution of these problems at Oak
Ridge National Laboratory being delayed by budgetary restrictions the
laboratory for Thermal Power Engineering was presented with an opportunity
for active participation in this area by investigating the so-called
bayonet tube design as a possible solution.

The availability of the FLiNaK primary loop made it possikle to construct a
salt-heated steam generator test facility with relatively little effort.
Feasibility of the bayonet tube steam generator was investigated with
respect to three aspects of the thermo-hydraulic design:

- steady state behaviour at various loads
- transient behaviour
- hydrodynamic stability.

The last two aspects appeared of particular interest because of the
extensive work on steam generator dynamics under way for other projects in
the same laboratory.

The present author's association with the above project further to be
referred to as the Delft Molten Salt Project (DMSP), lasted from August
1969 until its termination in Aprll 1978. Accordingly the work described in

1.1 -

this thesis covers both phases of the project. Investigations concerning
the thermo-hydraulic behaviour of FLiNaK and the associated special
measuring techniques form the subjects of Chapter 2 and 3. Analytical and
experimental investigations of the bayonet tube steam generator thermo-
hydraulics are dealt with in Chapter 4.

Any research report covering a period of over 8 years is liable to
contain parts which are either obsolete by the time of publication and/or
make the author realise in hindsight that a different approach or some
supplementary effort might have yielded better results. The latter is
particularly true in the area of steam generator transient analysis,
where the impending termination of the project foreclosed both additional
experiments and further elaboration of simulation codes. It is the
author's hope that the work reported in this area and some of the analyti-
cal work on steam generator stability may prove of sufficiently general
interest for others to extend and improve upon it.

These aspects which have been studied both analytically by computer
simulations and experimentally in the specially designed single tube test
facility are discussed in Chapter 4.

- 1.2 -

FLOW MEASUREMENTS

Introduction.

The availability of a suitable flow measuring device is essential for the
application of any fluid as an industrial heat transfer agent. For most
fluids differential pressure type flow meters (e.g. using a venturi-type
restriction) are entirely adequate; with this type of device a vast amount
of industrial experience has been accumulated over many years.

However, in the case of molten fluorides and similar high melting salts the
very high temperature level (500 - 700 Oc) and the corrosivity of the fluid
exclude the application of such standard flow meters.

Fluids posing similar problems are:

- toxic fluids
- corrosive liquids (acids)
- liquid metals (e.g. sodium)

Especially in the latter case the problems are very similar to those for
molten salts, and considerable efforts have been made for their solution
within the framework of LMFBR development activities.

However, unfortunately for the project under discussion, by far the largest
and most successful part of these efforts has gone into the development of
electromagnetic devices. In these devices a magnetic field is induced in
the flowing liquid at right angles to the magnetic field and to the velo-
CLtY. ;

To pick up this e.m.f. two electrodes are provided in the wall of the tube.
Unless the resistivity of the fluid approximates that of the pipe wall
material, as is the case for liquid metals, the electrodes have to be
electrically insulated from the pipe wall. Up till now no insulated elec-
trodes are available that are leaktight at the molten salt operating
temperature level, thereby excluding application of this method in molten
salt systems.

Of the other flow measuring systems considered by the author the following
two seemed most promising for this latter application:

- transit time flow meter
- thermal flow meter

Their advantages and disadvantages are discussed in detail in TURNER
[2.1-1 ]. In the following only their potential for molten salt flow
measurement will be taken into consideration.

On the other hand it was evident that of the two parts making up a diffe-
rential flow meter, viz.

- the restriction causing the pressure differential
- the differential pressure measurement

only the latter gives rise to serious problems for the application
envisaged here.

Thus two alternative and complementary roads towards a practical and
reliable flow measuring device seemed open to the author:

- development of a diffential pressure transmitter suitable for molten
salts; in practice this meant transforming the pressure of the salt into
that of an other fluid of easier handling characteristics

- investigation of the other measuring principles mentioned above.

The former approach, in addition to adhering to normal industrial practice,
has the major advantage of offering the possibility for reliable analytical
determination of its characteristics, so that calibration of the flow meter

- 2.1 -

13 unnecessary unless a very high accuracy is needed (better than 2%, which
is the maximum accuracy that can be obtained for a venturi, manufactured in
accordance with the V.D.I. DURCHFLUSZMESZREGELN [ 2.2-2 ]).

Where calibration is required, the results obtained in a water system can
be converted for application in any fluid, including molten salts.

On the other hand, transit time flow meters offer the potential of high
long term reliability through a minimum of equipment in the molten salt
environment, while the thermal flow meter, in addition to being also a
relatively simple device, would capatalize on the heat transfer measurement
techniques extensively investigated in the remainder of the project.

Hence both roads were pursued; the results are described in the next
sections.

2.2. Venturi flow meter.

2.2.1. Special features.

The principle of measuring flows through pressure differences across
orifices such as venturi tubes has been successfully applied in industrial
practice for many years. The discussion in the present thesis will there-
fore be restricted to the special features resulting from its application
to molten fluorides at up to 700 Oc.

The high temperature and the corrosivity of the salt make it impossible to
fill the piping to the differential pressure transmitter and the trans-
mitter itself with the fluid to be measured, as is customary in venturi
liquid flow measurements.

This problem can be solved by the application of an intermediate system
filled with a different fluid of easier handling characteristics between
the venturi and the differential pressure meter. _

One possibility is the use of a liquid, separated from the salt by a
membrane. This fluid has to be proof against the operating temperature and
should preferably be in the liquid state at room temperature.

This approach, shown in figure 2.2-1, has been tested in the Oak Ridge
National Laboratory using NaK as intermediate fluid (cf. BRIGGS [2.2.1]).
There are, however, a number of disadvantages to this all-welded design:

- while the dP-meter can be of standard design, it has to be specially
fabricated and filled with Nak

- calibration after installation is not possible

- the instrument proved rather sensitive to temperature changes in the
system

- in case of breakdown replacement of the dP-meter is difficult.

The major advantage of the all-welded design is its complete leaktightness.
An other possibility is the use of a gas as intermediate fluid. This
system was tested in our laboratory. To transform salt pressure into gas
pressure use is made of two small vessels between the venturi and the
differential pressure transmitter, each connected to one of the pressure
taps of the venturi. In these vessels the FLiNaK level is kept at a con-
stant height by adjusting the cover gas (argon) supply to - or release
from - the gas-filled space (cf. figure 2.2-2).

The resulting cover gas pressure difference between the two vessels is the
same as the pressure difference across the two venturi taps.

This transforms the problem of measuring the molten salt pressure differen-
tial into the much simpler one of measuring a differential gas pressure.

- 2o =

2.2.2. Description of equipment.

2.2.2.1. The venturi.

The venturi itself was designed and machined according to the V.D.I.
DURCHFLUSZMESZREGELN [ 2.2-2 ] (cf. figure 2.2-3).

Normally such a venturi does not require calibration. In this case, however,
the dimensions were somewhat below the normal DIN range and a calibration
was therefore considered necessary.

This calibration, performed by the staff of the "Waterloopkundig Laborato-
rium Delft" (VERBEEK [ 2.2-3 ]) using water as the working fluid, resulted
in the following characteristic formula:

<3
¢m = . 1.45% 10, o &p p'£3.2% ku/s (2.2-1)

(Ap in N/m2, p in kg/m3)

The accuracy stated above resulted from the calibration and is valid for
Re-numbers over 1.4 x 10%.

The Re-number for FLiNaK in this venturi in the range of interest is given
in figure 2.2-4 as a function of mass flow and temperature.

2.2.2.2. The control system.

As stated in subsection 2.2-1 the method requires equalization of the salt
levels in the two expansion vessels by adjusting the cover gas pressures
where required.

While it would be sufficient to maintain both levels at the same (varying)
height, this is more difficult to achieve in practice than to keep them
both constant.

Because of the problems encountered in designing a level gauge capable of
continuous level measurement, the idea of applying a continuous control
system was abandoned in favour of a simple on-off control system.

Two alternative control systems based on the above method of level detec-
tion were successively tested. .

The second and final system will be described first. In this system (cf.
schematic diagram figure 2.2-5) the level is detected by three electrodes
making or breaking contact with the fluid in the expansion vessels. These
electrodes are mounted in the upper part of the expansion vessels by means
of a gastight ceramic insulation (figure 2.2-6).

By measuring the electric resistance between the electrode and the vessel
it is possible to detect whether the salt level is above or below the tip
of the electrode.

If the level rises and passes the tip, contact is made and the electrical
resistance drops to a very low value. However, if the level falls and
passes the tip of the electrode contact is maintained until the liquid
column developing under the electrode as a result of capillary forces
(figure 2.2-7) collapses. The maximum height of this FLiNaK column was
found to be about 2.5 mm for an electrode with a flat tip, decreasing as
the tip of the electrode is sharpened. This phenomenon introduces a sort of
dead band in the action of the electrode.

The shortest electrode forms no part of the control, but is part of the
safety system, to be discussed in the next section.

The other two electrodes define a discrete interval in height within which
the level is maintened by the control system. If the level rises above the
tip of the shorter electrode gas is supplied to the gas-filled space in the

- 2.3 -

expansion vessel, thus driving the level down again until contact is broken.
On the other hand, if the level falls below the tip of the longer electrode,
gas is released from the vessel to allow the level to rise again until
contact is re-established.

Under steady state conditions the level remains in the interval between the
ends of the electrodes without any action of the control system; fluctuati-
ons within this interval are discernible as ripples in the output signal of
the flowmeter, as e.g. in figure 2.2-8, showing a change in flow from one
steady state value to another and the reactions of the control system.

The control system described above was developed from an earlier version,
originally thought to be simpler amd more accurate. In that system each
vessel contained only one control electrode (schematic diagram figure
2.2-9). During operation gas was released from the vessels at a constant
rate. If the salt level rose so high that contact was made with the elec-
trode, gas was supplied at a rate exceeding the release rate, thus driving
down the level. As in the previous system the salt column under the elec-
trode introduced a dead band in the system's reaction.

This seemingly simpler system was found to possess a number of
disadvantages:

® although for steady state conditions the maximum deviation of the
level equals the maximum height of the salt column, much greater
deviations could occur under dynamic conditions without being
recognized as excessive by the control system.

® the salt level is never at rest. There is always salt flowing from the
venturi to the vessel or vice versa, causing a frictional pressure
drop across the connecting tube even under steady state conditions.
This pressure drop causes an additional error in the differential
pressure measurement, which in our experiments proved to be greater
than the level deviations proper, as could be deduced from the
response of the control system. This results in a greater total
inaccuracy compared to the system described first.

® an additional inconvenience is the oscillatory behaviour of the
system under steady state conditions as illustrated in figure 2.2-10
which shows a recording of the output signal.

® the "breathing" of the system causes a constant consumption of cover
gas.

In view of these disadvantages the first system is considered preferable.

2223 Safetx.

The third or "alarm" electrode is added for safety. If for any reason an
insufficient amount of gas is supplied to the vessel by the control system
after the fluid has contacted the shortest control electrode, the level
keeps rising and flooding of both expansion vessel and differential
pressure transmitter might result.

To avoid this accident a large flow of cover gas at full pressure (6 bar)
is admitted to the vessel as soon as the rising fluid contacts the alarm
electrode. This ensures that the level is maintained in the vessel, unless
a very large leakage occurs.

A further protective measure in the control systems is made necessary by
mechanical vibrations in the loop, which induce waves on the salt surfaces
in the expansion vessels. These waves can make and break the contact with
the electrode very rapidly, causing rattling of the magnetic valves in the
control system. This rattling - a very ominous sound for the operator - may
result in excessive wear, decreasing the life time of the valves.

- 2.4 -

To avoid this effect a time delay was included in the electronic circuitry
for each electrode in the manner shown diagrammatically in figure 2.2-11.
This device slows down the reaction of the electrode. Contact must be
closed for over 1 sec. before the magnetic valve reacts.

2.2.2.4. Instrumentation.

In addition to the equipment described above the instrumentation specific
for the venturi flow measurements consists of:

® a differential pressure transmitter
® a voltmeter

The differential pressure transmitter used in our experiments is a 613 DM

Foxboro d/p transmitter.

The voltmeter is part of the Hewlett & Packard 2012 D data acquisition
system used for the data handling of all our experiments.

A schematic diagram of this part of the instrumentation is given in
figure 2.2-12.

Lo doBs Accuracy.

In a venturi flow measurement there are two error sources:

® the equipment
® the density of the fluid

The equipment consists of four elements:

® the venturi
The accuracy of the venturi used in our system is 1.2%, as explained
in subsection 2.2.2.1.

® the differential pressure transformer, described in subsection
Lol dn
The simplicity of this system has to be paid for by a less accurate
control action under dynamic conditions: during periods of gas supply
or release (indicated by a signal from the control system) following
flow transients the measurement is unreliable.
Under steady state conditions, however, the additional error caused by
the transformation from differential liquid pressure to differential
gas pressure is very small. In the tested system the difference in
lenght between the two control electrodes which equals the maximum
difference in salt head is 10 mm. The pressure difference across the
venturi taps at maximum flow (10 kg/s) and 650 Oc is 0.037 MN/m?,
equivalent to 1830 mm of salt column.
Thus the accuracy of the pressure transformation at maximum flow is
~ 0.5%. As the absolute error is approximately constant, this
inaccuracy is proportional with the reciproce of the flow.

® the differential pressure transmitter
The accuracy of the Foxboro d/p cell transmitter type G13 DM is 1% of
the span (5000 mm Wc).

® the voltmeter
The Hewlett Packard data logger type 2012 D, used to measure the
output voltage of the d/p cell, has an overall accuracy of 0.015% for
the range used (0 - 100 mV).

- 2,0 =

The fluid density as given in the table shown in figure 2.2-13 for FLiNak,
is known within 5%. According to the Gaussian error law (cf. BEVINGTON
[2.2-4 ]) the above inaccuracies yield a total inaccuracy of:

e =7 (1.22 + 0.5 (12 + 0.52 + 0.0152) + 0.5%52) = 43

of the maximum flow (10 kg/s).

This result may seem rather poor, but it should be noted that this is
mainly due to the inaccuracy of the specific density. Without this factor
the inaccuracy would be less than 1.5%.

2.3. Thermal flow measurement.

2.3.1. Introductory remarks.

Another type of flow measurement potentially suitable for highly corrosive
fluids at high temperatures that has been tested is the so called thermal
flow meter. There are two groups of thermal flow meters, each based on a
different principle (cf. BENSON [ 2.3-1 ]). The first group measures the
flow by adding heat to it. The resulting temperature rise is measured and
related to the flow rate (cf. figure 2.3-1). The amount of heat that has to
be transferred to the flow limits the application of this principle to
small flow rates.

The second group, an example of which is discussed here, is based on the
effect of the flow velocity on the temperature of a heated body inserted in
the fluid. A well-known example of this group is the hot wire anemometer.
The instrument described here was selected for its expected suitability for
plant measurements under severe conditions, where ruggedness and relia-
bility take precedence over high accuracy.

2.3.2. Description of the method.

When a heated probe is inserted in a fluid flow (cf. figure 2.3-2), it will
rise in temperature until a state of equilibrium is reached between the
heat transferred from the probe to the fluid and the heat generated in the
probe.
Assume the total heat release rate to be ¢w . The heat transfer rate is:
4
¢ = a A A6 (2.3-1)

h
Wi

Setting both heat rates equal yields the relation for the equilibrium
temperature difference:

AB = (2.3-2)

The heat transfer coefficient of the fluid depends on the velocity and
hence on the flow rate of the fluid. At a higher flow rate the heat trans-
fer coefficient increases and if the heat release rate is kept constant,
the temperature difference across the boundary layer decreases. This
relationship between flow rate and temperature difference forms the bkasis
of the method descibed. The nature of this relationship depends on the heat
transfer correlation valid for the conditions in the flow meter. As
established in subsection 3.2, a corrected version of the Dittus-Boelter
correlation is valid for FLiNaK. Extending this correlation by a correction
factor for annular flow derived in subsection 2.3.4 one obtains:

- 2.6 -

. b

. 0.8 0,k Di, 5
Nu = 0.020 Re, Pr, { 0.87 (Do) } (2.3-3)

The exponent n in the correction for annular flow depends on the diameter
ratio. A survey of the literature in this field (cf. subsection 2.3.4)
yielded n = 0.23 * 0.05 as the most likely value for the diameter ratio of
the thermal flow meter (Di/Do = 0.51).

Combination of equation (2.3-3) with the continuity equation:

¢m =p vV Ac (2.3-4)

and with equation (2.3-2) yields the following relationship between mass
flow rate and temperature difference across the boundary layer:

¢
w 325 0,251 % . 9
= _Xy1,25 7o me D _D.,o,5 0,25
o A (Ah ) (0.020) xb ( . ) D
P
; B9 4. ¢w %
(0.87 7™ T e - X;E-Ce)- i (2.3-5)
¢
v, AL 98
In this relationship A6 has been replaced by (Aem - -——-Ce) ' ’

where Aem is the temperature difference actually measured by the equipment

described in the next section, which will also contain the explanation for

the correction factor Ce.

This equation shows that the mass flow rate depends not only on the
temperature difference, but also on a number of physical properties of the
fluid and hence on its temperature. The table shown in figure 2.2-13 gives
the relationships between these properties and temperature. While the
density p and the kinematic viscosity v are seen to vary significantly with
temperature, the table indicates that A and ¢ may be considered independent
of temperature for practical purposes.

Figure 2.3-3 compares thermal flow meter readings obtained from equation
(2.3-5) using the data of table 2.2-13 at various temperatures to the
venturi outputs. The temperature dependence evident in the former was found
from a least squares analysis to be adequately described by:

.
£(p) = 5.15 -~ 0.0107 ¢ + 0.63 10 2 + 1.5% - (2.3-6)
where 6 is the FLiNaK temperature (%).
It follows that the mass flow is defined by:
¢

v, 1425
} (2.3-5A)

¢m = cg £(0){

- 2.7 -

2.3.3. Description of the equipment.

2.3.3.1. Probe.

Figure 2.3-4 shows the first prototype of the thermal flow meter. For
design reasons the probe was inserted in a bend of the primary loop in
counterflow direction.

To avoid vibration and to ensure a fixed concentric position, the probe was
provided with three radial fins at the tip.

An electrical resistance element was inserted in the hollow core for
heating the probe. Four thermocouple pairs (1 mm @ sheathed type) were
installed for measuring the temperature difference over the boundary layer,
each pair consisting of one thermocouple for measuring the bulk temperature
of the fluid and another for measuring the wall temperature.

All thermocouples were fixed in grooves in the probe wall, leading from the
measuring point to the passage through the outer tube wall.

This was done by metal spraying the probe until the grooves were completely
filled, followed by milling to obtain a smooth surface.

The wall thermocouples were imbedded in the wall of the probe to ensure
good contact between the couple and the surrounding metal.

In order to avoid distortion of the cilindrical shape of the probe, with
its possible consequences on local heat transfer coefficients and thus on
the temperature differences, the thermocouples had to be located below the
surface of the probe. (cf. figure 2.3-5). This results in larger tempera-
ture differences being measured, due to the additional temperature drop
across the metal layer between the thermocouple and the probe wall surface.
A number of investigators (e.g. MOELLER [ 2.3-2 ]) have studied this problem.
They concluded that if the brazing material used to fasten the thermocouple
in the wall has about the same thermal conductivity as the probe material,
the temperature actually measured by the thermocouple is that which would
occur in the probe at the same location (centerline of the thermocouple) if
no couple were present. Figure 2.3-6 illustrates this conclusion.

In our case we have thermocouples sheated in Inconel-600 and brazed into
the Inconel-600 probe with micro-braze of about the same chemical
composition as Inconel-600, thus satisfying the above condition.

For obtaining the actual temperature difference across the boundary layer
it therefore suffices to decrease the measured temperature difference by a
correction:

o)
pg =28 (2.3-7)

© Ah Ainc

where, xinc is the thermal conductivity of the probe material and § is

the distance between thermocouple centerline and probe surface (cf. figure
2.3-5).

At maximum flow AGC is about 50% of the total temperature difference
measured.

2.3.3.2. Electronic output adjustment.

It is evident from equation 2.3-5 that the output from this type of flow
meter, viz. the temperature difference, is not proportional to the measured
flow. On the contrary, the measured temperature difference decreases with
increasing flow.

For practical applications in power and process plant flow measurement a
linear scale was considered essential, resulting in the need for electronic

= 2.8 =

output adjustment.

Figure 2.3-7 shows the design of an electronic correction device for
linearization.

Another undesirable effect in the output of this flow meter requiring
correction is its temperature dependence, as defined above by equation
(2.3-6). An electronic correction device could also have been applied for
this purpose. Prior to its implementation, however, the development of this
type of flow meter was terminated. A computational correction according to
equation (2.3-6) was applied to the flow meter output instead.

e O Accuracy.

The repeatability of the thermal flow measurement depends both on the
magnitude of the variations in heat release rate and on the repeatability
of the temperature difference measurement.

2
The heat release rate is proportional to %—-where V is the supply voltage

and R is the electrical resistance of the element.

Fluctuations of 10% (200 - 240 Volt) which can appear in the supply voltage
V would cause errors of over 20% in the generated heat.

There are two different types of solution for this problem. Solutions of
the first type control the heat release rate, either by means of an AC
voltage stabilizer or by controlling the electrical power direcly by means
of a thyristor power control system. However, for the power rating of the
thermal flow meter - about 2 kW - both these solutions are rather expen-
sive. The second possibility is to allow the heat release rate to vary, but
to correct the reading of the measurement electronically for these varia-
tions. For this latter method only low current electronics are needed which
are less expensive than the high current electronics applied in the two
former solutions. Besides, an electronic correction device is needed
anyhow, for the reasons stated in subsection 2.3.3.2, hence a power
correction unit could easily be incorporated.

Utilizing standard electronic components such a system, had it been
installed, which was not the case because deficiencies described hereafter
led us to abandon the entire concept, might haved reduced the error

caused by supply voltage fluctuations to less than 1%.

The repeatability of the temperature difference measurement can be divided
into two parts: :

- that of the thermocouple pair
- that of the amplifier and voltage measurement.

For both parts the two aspects "zero" and "gain" have to be considered.
"Gain" is defined for the thermocouples as the ratio between an increase in
temperature difference and the resulting rise in e.m.f. from the thermo-
couples. "Zero" is the e.m.f. measured at the couple pair if both thermo-
couples are at the same temperature. The change in gain is typically within
1% for the thermocouple used. The.zero e.m.f., however, can be substantial
in temperature difference measurements at high temperature levels.

The repeatability of the electronics (amplifier and electronic voltmeter
depends on the quality of the instruments: for the kind of equipment

used here the gain is typically constant within 0.1%. Possible changes

in "zero" of both thermocouples and electronics can be corrected by

a simple online calibration procedure. If the power supply to the
electrical element is cut off, the temperature differences across

the thermocouple pairs become zero. By correcting the level of the

= 2.9 -

amplifier both its own "zero" deviation and that of the thermocouple pair
can be compensated. This brings the total repeatability of the thermal flow
meter within the range of 2%. (two paired couples).

The accuracy of the flow meter can be established in two ways:

- by calibration
- by computation

In the first case the established accuracy equals the repeatability of the
thermal flow meter, increased according to [ 2.2-4 ] with the accuracy of
the standard flow meter used for calibration.

For a full-size flow meter (e.g. tube diameter 500 mm @) where calibration
will be out of the question in most cases, the accuracy will have to be
predicted by computation from the individual variables constituting the
right-hand side of equation (2.3-5).

This relationship, derived in subsection 2.3,2, contains three sources of
inaccuracy:

a) the correlation used for the heat transfer coefficient
b) the material proporties appearing in this correlation
c) the thermocouple measurements

ad a.:

The correlation applied is an adapted version of the well known
Dittus-Boelter correlation, corrected for annular flow. Validation of
this ccorrelation for molten salt heat transfer formed a separate aim
of this project, discussed in section 3.2.

The coefficient 0.020 valid for flow in circular tubes is accurate
within 3%.

However, the accuracy of the correction for annular flow of the usual
form:

Di, -n
C(BBO . (2.3-8)

requires some discussion.

The literature on this subject yields a great number of different
values for both constant C - representing the ratio of the heat
transfer coefficient for flow between two parallel plates and in a
circular tube - and exponent n (cf. [2.3-3 ] through [2.3-9 ]). The
value of 0.87 for the constant C is a theoretical prediction (cf. KAYS
[ 2.3-9 ]) backed by experimental evidence; this value is considered
accurate within 5%. The value of 0.23 chosen for n is the mean of a
cluster of values given by a number of investigators for heat transfer
in an annulus with a diameter ratio of about 0.5 (cf. figure 2.3-8).
The annulus correction given above is valid for an exactly concentric
position of the heating element. This however, is very difficult to
achieve. Therefore the effect of small eccentricities must be
considered in the error analysis. As mentioned in subsection 2.3.3
the temperature difference in equation (2.3-5) is obtained by
averaging the readings of the couple pairs positioned along the
circumference of the heating element.

Thus only the effect of eccentricities on the mean temperature
difference and therefore on the mean heat transfer coefficients has
to be considered. Figure 2.349 shows results of an investigation by
LEE [ 2.3-8 ] giving the effect of eccentricity on the mean heat

= 2,10 ~

transfer coefficient for two different diameter ratios. The maximum
eccentricity of the element is estimated al less than 0.5 mm or 5%
when expressed relative to the gap width. Figure 2.3-9 shows that for

. 2z - G : g
a diameter ratio BS-= 0.5 a relative eccentricity of 0.05 causes a

decrease in average heat transfer coefficient by about 2%.

ad *bs

The table given in figure 2.3-10 lists values for the various
proporties appearing in equation (2.3-5) and their inaccuracies.
Amongst these, the FLiNaK thermal conductivity requires some comment.
As discussed in Appendix 2A the accuracy of this physical property is
insufficiently known. Lacking this information, a maximum error of 10%
was assumed to yield a realistic overall accuracy.

ad. ess

The temperature differences are measured directly by connecting both
thermocouples so that the resulting e.m.f. is the difference of the
e.m.f.'s of the two separate couples. An accuracy of 1% can be
obtained in this way after correction for zero reading errors caused
by slight differences between individual thermocouples. To avoid
effects of drift and of thermo-cycling on the thermocouples each
series of measurements starting at a new temperature level was
preceded by a zero reading calibration.

An error analysis, taking into account the above three sources of in-
accuracy and the inaccuracies mentioned in connection with the repeata-
bility, yields an overall inaccuracy of the mass flow of 15% at the maximum
flow of 10 kg/s.

While this would at first sight seem a rather poor showing, one should keep
in mind that this type of flow measurement has the unusual property of
increasing accuracy with decreasing mass flow, whereas in general the
accuracy of a measurement decreases with the measured value. As discussed
before, this phenomenon is due to the opposite behaviour of the mass flow
rate and the temperature difference related to it.

In conclusion it may be stated that the above error analysis has revealed
two major disadvantages of this method, viz. the great number of physical
properties occurring in equation (2.3-5) and the dependence on the accuracy
of a heat transfer correlation. In combination these disadvantages tend to
result in an unsatisfactory overall accuracy. Hence development of this
type of flow meter was discontinued.

2.4, Transit time measurement.

2.4.1. Introductory remarks.

This method was included in the DMSP test program for two purposes:

® to provide a method entirely independent of physical properties of
the fluid as a reference for the other measurements

® to verify the possibility for using simple temperature sensors in lieu
of more elaborate and hence failure-prone devices for flow measure-
ments in hostile environments.

- 2.11 =~

2.4.2. Description of the method.

The principle of applying correlation techniques to instrument output
signals for the purpose of measuring transit times and hence velocities is
well-known and has been extensively described elsewhere (e.g. ALBERS

[2.4-1 ], BENTLEY [ 2.4-2 ] and RANDALL [ 2.4-3 ]). We shall therefore
restrict ourselves to a brief introductory outline.

As applied in our case the transit time measurement refers to thermal
disturbances in the fluid traveling through a certain part of the DMSP loop
(cf. figure 2.4-1). Two temperature sensors are installed a well-defined
distance apart and the signals of both sensors are recorded. If no
distortion of the temperature profile were to occur in the fluid the signal
recorded from the downstream sensor would be identical to the signal of the
upstream sensor, except for a delay time: the transport time from upstream
to downstream sensor.

However, distortion of signals does occur in practice due to the following
effects:.

® flow disturbance
® eclectrical noise

which exclude determination of the transport times by visual inspection of
the two recorded signals.

Flow disturbances affect the signal in two different ways, a predictable
and a random one.

The predictable effect of such flow disturbances as turbulence and radial
velocity gradients is to smooth the temperature profile present in the
fluid. Several investigators, e.g. TAYLOR [ 2.4-7, 2.4-8 ] and SCHMIDTL
[2.4- %], have shown that the result of these effects on the distribution
of the mean cross-sectional temperature of turbulent flow in tubes can be
described by the diffusion equation:

du 32u
ek (2.4-1)

Where k is the so-called Taylor diffusivity, a pseudo-diffusion coefficient,

comparable with the thermal diffusivity a = lg in conduction heat transfer
The value of k can be approximated by: P

y
k = 10.1 R 59- : (2.4-2)

(cf£. [2.4-8]).

X is a coordinate in a system moving in the direction of the tube axis with
the average fluid velocity. This pseudo diffusivity is predictable and is
part of the process in the tube between the two sensors. Its effect on the
established delay times will be discussed later.

The second effect of the flow disturbances is the occurrence of a tempe-
rature noise superposed on the average temperature in a cross-section. The
presence of these random disturbances requires the application of statis-
tical techniques. Consider the block diagram of a time delay. The input
signal is a random one, the output signal is the delayed input signal.

The cross-covariance function of these two signals, defined as:

f(1) = E{évi(t,g) . Svyo(t + 1,0)} (2.4-3)

has the general shape of curve a in figure 2.4-2.

- 2.12 -

The covariance function f£(t1) is maximum for T = Td » i.e. the delay time.

If the output signal is influenced by some disturbance uncorrelated to the
input signal the statistical technique applied reduces the effect of this
noise. The cross-covariance function maintains its general shape and in
particular the location of the top remains the same. However, if the
correlated components in the signals are so weak that they are drowned in
the thermal and electrical noise (insufficient signal/noise ratio) this
method will also fail.

The cross—-covariance function itself cannot be determined, but it can be
estimated by a time integration:

e

g tf le(t) . 6v2(t + 1)dt
f s S

%(T) =

where ts and tf define a time interval.

In the remainder of this section the term covariance function will be used

both for this function proper and for the estimator f(T1).

Figure 2.4-3 shows a typical cross-covariance function of our test signals.
The top of this function is curved. The "radius" of this curvature depends
on the highest frequency present in the signals. The higher the frequency
the steeper the top, which increases the measuring accuracy of the trans-
port time. A number of investigators (BENTLEY [ 2.4-2 ], RANDALL [ 2.4-3,
2.4-4 ], MUREY [ 2.4-5 ]) have tested this method of flow measurement for
various fluids (air, water, sodium) and for particulate suspensions.

These tests can be divided into two categories:

1. measurement of the local velocity, e.g. for turbulence studies:
the distance between the two sensors is in the order of the channel
diameter.

2. measurement of the mean velocity:
the distance between the two sensors is in the order of ten to one
hundred channel diameters.

A condition for practical applications of the first category is the
availability of fast sensors such as hot wire anemometers with a time
constant small compared to the transport time. The use of normal thermo-
couples as sensors is limited to the second category because of their
relatively large time constant. Even in this case - the one of interest for
the present thesis - there are upper limits to the time constants which
must be observed in order to obtain the desired accuracy.

Excessive time constants would filter the higher frequencies and thus cause
an unfavourable ratio of transport time to width of the top of the cross
correlation function.

The 1 mm thickness of the Inconel-sheathed thermocouples selected for the
present measurements was considered a practical minimum for obtaining an
adequate life time in the highly corrosive molten salts. A typical time
constant of this type of thermocouples is 0.3 sec. (cf. GORDOV [ 2.4-6 ]).
This is sufficiently low to obtain a satisfactory accuracy (cf. subsection
2.4.4.) for the application discussed here.

Furthermore, differences between the response characteristics of the two
sensors must be avoided, as they might introduce a pseudo-delay decreasing
the accuracy of the measurement.

In all the references relevant to measurements of the mean velocity
([2.4.2. ], [2.4.3.]1, [2.4.4.], [2.4.5. ]) the introduction of

w. 2,43 =

artificial temperature disturbances has been found necessary for accurate

measurement, because in practical cases the signal due to natural noise in
the mean temperature is so weak that the correlated signals are drowned in
the noise of the instruments used, in particular where high current devices
for heating are present in the immediate surroundings.

2.4.3. Description of the equipment.

In our case a straight part of the primary loop was selected for the
correlation flow measurement (cf. figure 2.4-5). The shape of the cross-
covariance function is strongly dependent on sensor distance, as borne out
by a comparison between figures 2.4-3 and 2.4-4, showing this function for
our test signals as obtained with sensor spacings of 3200 and 200 mm,
respectively. To determine the optimum distance between the sensing
thermo-couples a series of 7 sensors with increasing spacing was applied
(cf. figure 2.4-6). Each sensor consisted of four 1 mm. thermo-couples
connected as a thermopile (cf. figure 2.4-7) in order to increase the
signal of the sensor and thereby to obtain a higher signal-to-noise ratio.
To obtain a high amplification without overloading the amplifier it is
necessary to remove the dc component from the signal. To suppress the dc
component in the signal the sensor was compensated by a series of four
thermo-couples attached to the wall of the tube. These "slow" couples only
follow the mean temperature of the salt. Thus the differences between the
sensor and these compensating couples represented the fluctuations of the
FLiNaK temperature. A diagram of the electronic equipment is given in
figure 2.4-8. After the first amplifier the signal is filtered by means of
a low pass filter (cut-off frequency 10 c/s) to remove high frequency noise
which might overload the subsequent equipment. A high pass filter (cut-off
frequency 0.7 c/s) is provided to suppress long-term drift which could
shift the signals beyond the useful dynamic range of the amplifier. After
the second amplifier the signal is either recorded on tape or on a line
recorder, or directly connected to the correlator. The correlator used is a
so called polarity coincidence correlator. Rather than computing the
correlation function proper given in equation (2.4.1) this equipment only
determines whether the signals have the same polarity or not. Mathemati-
cally this is given by:
) g ¢ B
plt) = ——— [ sgign (v2(t)) . sign (vl(t—T))dt (2.4-4)

t_ -t t
£ S S

VELTMAN [ 2.4-11 ] shows in detail that determination of the delay time from
the pcc-correlation function yields the same result as from the correlation
function proper, provided the frequency distribution function fulfills
certain conditions. The accuracy of the correlation function thus obtained
is somewhat lower, as the standard deviation of the pcc covariance function
is a factor Vm greater than that of the covariance function proper. This is
further discussed in subsection 2.4.4. The pcc-correlator is obviously much
simpler and less expensive than a real correlator, which is an advantage
for practical application of this method.

Figures 2.4-3, 2.4-4 and 2.4-9 show examples of pcc-correlation functions
as recorded on an x-y recorder. The delay time is directly measured from
this diagram.

Signals:

Tests have been carried out with three different types of signals:

- natural temperature noise
- artificial random signals
- thermal shocks

As mentioned above the tests with natural temperature noise failed as
expected. Correlation could only be found over short distances and even for
that case the response of the thermo-couples proved too slow for sufficient
accuracy (cf. figure 2.4-9). 4

The introduction of artificial noise by diverting a small part of the flow
through an air-cooled bypass somewhat sharpened the top of the correlation
function, but did not lead to a significant improvement. The thermal shock
type of signal was realized by stepwise increase of the heat supplied to
the system in the main heater. This caused a temperature profile along the
loop as shown in figure 2.4-10. It will be clear that with this single
disturbance of the temperature the correlation technique could not be
applied and the transit time had to be computed from the delay in response
and the known distance between the sensors. An example of the line recor-
dings of the two sensor signals is given in figure 2.4-11. While this
method proved successful, it was recognized that the need for a sizeable
stepwise power change severely limits its practical applicability. Moreover
the averaging effect of the correlation technique is lacking in this case.
Therefore a different way of introducing artificial noise was subsequently
tested. A square wave generator was connected to the controller of the main
heater and adjusted to generate fluctuations with an amplitude of 20% of
full power. The frequency of the wave was varied at random, resulting in
random fluctuations of the mean temperature of = 0.1 Oc in a cross section.
Correlation of these signals proved to be successful. The results will be
discussed in section 2.6.

Note: The results of the measurements utilizing temperature fluctuations
induced by thermal shocks show systematic deviations from the results
obtained from the measurements utilizing artificial random temperature
variations, the values obtained by the first method being consistently
higher than those obtained by the second method.

These deviations can be explained by considering the mechanism of the
turbulent mixing process present in the flow. This mixing does not
affect the delay time obtained from the correlation of the two signals,
corresponding to the mean velocity of the fluid in the cross-section.
In the case of the thermal shock method, however, the velocity is
derived from the delay of the first effect of a disturbance.

As there are always fluid particles, however few, which remain in the
area of maximum velocity, especially in turbulent flow with its flat
velocity profile, the first effect of a temperature disturbance is
transported with a velocity very near the maximum velocity in the
cross section. The mass flow rate derived from this delay time must
therefore be corrected for this effect.

The correction factor, i.e. the mean velocity/maximum velocity ratio
is given by HINZE [ 2.4-10 ] as:

2
(n+1) (n+2)

Gy = (2.4-5)

where n is a function of Re.

- 2.15 -

In the range of measurements Re varies from = 10% - 10°.

. . 1 : ; i
The corresponding range for n is from glg-to 5 yielding a correction
of .805 - .817. The effect of this correction will be discussed in
section 2.6.

v 5% 9 Accuracy.

The possible sources of error in the correlation flow measurement can best
be traced by following the path of the signal:

a. the first source of inaccuracy could lie in the process itself.
If next to the delay time other mechanisms (e.g. turbulent mixing,
wall effects) were to play a significant role, the top of the
correlation function would shift away from T = Tq-

b. a second source of inaccuracy lies in the equipment for signal pick-up
and processing. The theory deals with the signal as present in the
fluid. In fact, however, the correlated signals have been influenced
by the sensor and the subsequent filtering and amplification.

c. a third source of inaccuracy lies in the application of the correla-
tion technique itself (finite observation time) and more in particular
in the application of the polarity coincidence correlation technique
{pee) «

In the following each of these sources of error will be discussed in
some detail.

ad a.:

The presence of other mechanisms than the delay time proper would
follow from the shape of the cross covariance function, viz. any
process shifting the top away from 1 = Td causes an asymmetric shape
of the cross covariance function.

This can be understood by assuming an arbitrary transfer function,
solely characterized by the fact that the cross covariance function
ny(T) of the input signal x and the output signal y is symmetrical

with respect to 17 =71 Assume a random input signal with arbitrary

a
spectral density Sxx(v). Random signal theory shows that for this

signal the covariance function ny can be computed from:

e32flvT

R (1) = { s (v dv (2.4-6)
Xy - Xy

where the cross spectral density is:

S (v) = H(v) S (V) (2.4-7)
Xy x

*
Introduction of a new independent variable T = T - T and
rearrangement of this equation yields:

- 2.16 -

R Sxx{Re(H(v)). cos(2nv1m) + Im(H(v)). sin(2nvrm)} >

+
% cos(2mvt )dv

400
I

-00

S {Im(H(v))cos(2mvTt ) + Re(H(V))sin(2mvT )} =
XX m m

-
% sin(2mvt )dv (2.4-8)

The first integral in the right hand side of this equation is

*
symmetrical with respect to T = 0 and therefore with respect to
T = Tm. The second integral, however, is not.

To fulfill the assumed condition of symmetry it is therefore necessary

*
that the second integral vanishes for any value of T .
This means:

{Im(H(v)cos(2wVTm) + Re(H(v))sin(ZflVTm)} = (

which shows that the initial assumption of a symmetric cross-
covariance function can only be valid if the transfer function
satisfies the condition:
-j2mvT
H(v) = A(v) e J2 m
where A(v) is a real function. In words: the transfer function must

consists of a combination of a frequency dependent attenuation (or

amplification) and a delay time of 17_ = 1 .
d m

As the cross-correlation functions of the measured signals have only a
very slight asymmetry (cf. subsection 2.6) the delay times found are
considered infinitely accurate as far as this aspect is concerned.

ad b.:

Although the dynamic behaviour of a thermocouple is more complicated
Than that of a simple first order system, the time constant - defined
as the time needed for a 63% response to an imposed temperature

step - is a good measure for the rise time of the sensor in this
application. For the 1 mm sheathed thermocouples utilized here the
aforementioned time constant is 0.3 second * 10% for a temperature
step caused by dipping the couple in water.Although the non-linearity
of the sensors does distort the signals, it does not affect the
resulting delay time if the sensors are identical. Differences between
the two sensors, however, cause an error in the delay time measured.
As a first approximation this error can be defined by an additional
positive or negative delay between the two sensors, equal to the
difference in time constant of the two sensors.

The maximum error of 0.03 second in the sensor time constant causes a
maximum additional delay time of 0.04 second (Gaussian error law). The
maximum relative error occurs at the maximum velocity of approximately
5 m/s.

The maximum distance between two sensors in our experiments is 3.20 m
corresponding to a delay time of 0.64 seconds at the maximum velocity.

- 2.17 -

Hence the maximum error due to differences between the two sensors
will be 4%.

The subsequent electronic equipment does not cause additional delays;
the absence of additional delays has been checked by interchanging the
equipment used for the processing of both signals.

As the pcc-correlation only detects the polarity of the signals the
accuracy of the amplification is of no account.

ad c.:

For a signal with e.g. a Gaussian distribution function it can be
proven that the position of the top of the curve and thereby the
established delay time is the same for the two types of functions
VELTMAN [ 2.4-11]. It is very difficult, however, to derive the
relationship between the correlation function proper and the polarity
coincidence correlation function (pcc) for a signal with an arbitrary
distribution function.

There is, however, a way around this problem. If each of the signals
of the sensors is mixed with an artificial signal having a uniform
distribution function, the resulting pcc function is an attenuated
copy of the cross-covariance function of the two original signals,
independent of the distribution function of these signals [ 2.4-11 ].
This technique was applied to some of the measurements in order to
check the validity of the method applied.

As no difference in delay time could be detected between the signals
processed with and without extra signals, it was concluded that the nature
of signals proper obviated the need for these extra signals.

The effect of finite observation time is again difficult to evaluate
theoretically. Therefore a number of measurements were processed for ten
times the standard observation time (160 seconds). As this did not result
in a noticeable shift of the derived delay time the standard observation
time was considered adequate. The delay time is derived from the pcc-curve
as shown in figure 2.4-3.

The error caused by the inaccuracy of this method of determination is
estimated at 5%. '

Combined with the error found under b) this yields a total error of 7% for
the present case.

2.5. Test program for flow measurements.

The purpose of the test program was to gain practical experience with the
different methods proposed and to verify the predicted accuracies. In the
abcense of a reference the latter aim could only be fulfilled in a relative
way by mutual comparison of the results of the different measurements.

Two series of measurements were performed:

series A: comparing the results of the venturi measurement to those
of the thermal flow meter

series B: comparing the results of the venturi measurement to those of
the transit time measurements.

The venturi used during these tests was of the compact type utilizing the
two-electrode dP-converter (the final design with three electrodes in the
dP-converter did not bhecome available until much later).

During each test the flow was varied from ~ 2 to 9 kg/s (the maximum range
that could be obtained with the FliNaK pump because of its limited control-
lability) at three temperature levels to detect possible temperature

- 2.18 =

2.6,

effects.
Each test of series A was repeated after an interval of one week to check
the occurrence of time dependent drift in the thermocouples.

Experimental results.

Figure 2.6.1 presents the results of the series A measurements. The result
of the second part of this series (675, 625, 575 0C) showed less scatter
than the results of the first three runs. This may well be due to the
experience obtained in performing these experiments and operating the loop
in general. All thermal flow measurements are within a band of 0 - 20%
above the corresponding venturi measurements. This deviation is larger than
the 15% predicted in section 2.3.4. In the author's opinion this should be
ascribed to the fact that the annular correction of the heat transfer
correlation is still somewhat optimistic. This latter problem grows worse
for smaller diameter ratio's, such as would occur for practical applica-
tions of this type of flow meter (tube diameters up to 500 mm).

The results of the series B measurements are presented in figures 2.6-2
through 2.6-5.

The first four of these figures show the results of the "thermal shock"
measurements.

For each measurement two values are plotted: the mass flow computed
directly from the delay time found, and a value corrected for the mean
velocity/max. velocity ratio (cf. subsection 2.4.3). ,

The latter are in better agreement with the venturi measurements,
supporting the validity of the assumption that the temperature disturbances
were transported more or less at the maximum velocity.

These corrected values lie within 10% of the venturi measurements.

The agreement is even better for the correlation flow measurements applying
artificial random signals, vix. within 5% of the venturi results.

Figure 2.6-6 shows the results of this type of measurements performed at
two different temperature levels (625 Oc and 675 Oc).

All results confirm that both types of transit time flow measurement are
independent of the fluid temperature and thus of the physical properties of
the fluid.

Conclusions.

All three methods for flow measurement discussed above have their
advantages and disadvantages.

The venturi was found to be the most practical instrument for measuring
stationary flows. It was also the one with the highest accuracy, although
the value of 4% seems rather disappointing by normal industrial standards.
This, however, is mainly due to the limited accuracy (5%) of the FLiNakK
density wvalue rather than to inaccuracies inherent to the method. Further-
more it is the method easiest to adapt for larger diameters.

Its main disadvantage is its slow response to transients.

The thermal flow meter has proven a reliable instrument but its charac-
teristics have to be determined by calibration due to uncertainties in the
applied heat transfer correlation and the physical properties of the fluid
for its evaluation.

This calibration presents a difficult problem for large diameters and mass
flows.

- 2.19 -

The correlation flow measuring technique looks promising for application in
molten fluorides except for its 7% margin of inaccuracy. This inaccuracy is
mainly caused by the "blunt" top of the cross correlation function. This
top might be "sharpened" absolutely by applying faster temperature sensors
or relatively by increasing the distance between the sensors.

However, even granting such improved accuracy, the method may prove diffi-
cult to develop for every day use, as up till now it requires application
of artificial temperature fluctuations.

In the author's opinion it is most suited, because of the simplicity and
small dimensions of the sensors, for special applications under circum-
stances preventing or rendering difficult the installation of other types
of flow meter.

- 2.20 -

- TURBULENT HEAT AND MOMENTUM TRANSFER

3.1. Introduction.

The availability of accurate heat transfer and pressure drop correlations
is an essential prerequisite for the adequate design of heat exchanging
equipment. Acquisition of this information for FLiNaK formed the main
objective.of the original Delft Molten Salt Project experimental program
formulated in 1965 (cf. LATZKO [ 3.1-1]).

3.2. Heat transfer.

3.2.1. Introductory remarks.

Upon completion of a series of preliminary tests in simplified molten salt
loops a special salt-to-salt heat exchanger was designed and built during
1968 and 1969. Due to its complex geometry (cf. figure 3.2-2) and the
severe operating conditions combining elevated temperatures and a highly
corrosive medium, instrumentation of this test module with thermocouples
unfortunately proved to be beyond our technological capability at that
stage. To a large extent this was due to the decision to determine the
heat flux by measuring the temperature drop across the channel wall. In
order to obtain a temperature drop of sufficient magnitude for accurate
results, the heat resistence of the metal tube wall had to be significantly
augmented. The only practical solution for this problem seemed the
application of a double metal wall separated by a stagnant liquid, as the
difference in thermal expansion practically excluded the application of a
solid insulating layer. The temperature drop across the liquid layer - in
this case a molten salt - was measured by means of thermocouples embedded
in the two metal walls.

Unfortunately these measurements failed for two reasons:

- failure of the major part of the thermocouples during the first day of
operation, due to an inadequate technique for fabricating thermocouple
penetrations

- from the evaluation of the experimental data obtained with the remaining
thermocouples it became clear that the shape of the salt-filled gap was
not only not exactly annular, but also changed unpredictably with time
due to thermal expansion and relaxation of post-weld residual stresses
in the material.

As immediate replacement of the heat exchanger was impossible the experi-
mental program proceeded with frictional pressure drop measurements and
flow meter tests, later followed by extensive tests of the steam generator
discussed in Chapter 4. In the course of all these experiments enough
experience had been gained to start in 1976 the design of a second heat
exchanger for the heat transfer measurements discussed in the remainder of
this section.

3.2.2. Description of the test module.

A simple salt-to-air heat exchanger was chosen as test module for the
second series of heat transfer experiments to simplify instrumentation as
much as possible. Figure 3.2-3 shows its basic geometry. The heat exchanger
consists of two concentric tubes. The inner tube forms the salt channel,
while the air flows upward through the annular gap between the two tubes in
counterflow with the molten salt.

-3l -

3.2.3. Description of the loop.

The test module was built into the same molten salt loop as used for the
flow meter experiments.

The air inlet was situated at the bottom of the heat exchanger, while the
hot air was blown off to atmosphere at the top (cf. figure 3.2-4). To
obtain a sufficiently high heat transfer coefficient between wall and

air, the air pressure in the heat exchanger was raised by throttling the
air outlet by means of a manually controlled valve. The process conditions
are listed in the table shown in figure 3.2-5.

3.2.4. Outline of the method.

The heat transfer coefficient a is defined as:

—d (3.2~1)
9, -9 )

b w

Contrary to the temperatures appearing in this equation, the heat flux g
cannot be measured directly and has to be derived either from the tempera-
ture drop across the channel wall or from the heat balance of one or both
of the media. In view of the experience from the earlier experiments the
former method was rejected in favour of the second one. Experience with the
preceding steam generator experiments had taught us that determination of
the transferred heat from the small ( < 5 9C) temperature drop of the salt
would not yield a satisfactory degree of accuracy.

Therefore a series of thermocouples were provided in the air gap to measure
the rise in air temperature ( > 400 O¢).

3.2.5. Instrumentation.

Three pairs of salt and wall thermocouples were placed equidistantly along
the circumference of the inner tube at five different levels, as shown in
figure 3.2-6. In addition, three thermocouples equidistantly spaced along
the circumference were provided in the air gap at 10 levels. The wall
penetrations for the thermocouples measuring the bulk temperature of the
salt (cf. figure 3.2-7) were brazed under vacuum using a nickel-braze
similar in composition to that of INCONEL-600, to provide the required
corrosion resistance. To minimize the number of penetrations, the couples
for measuring the wall temperatures were placed in grooves machined into
the outside of the tube wall. These slots were closed by brazed-in wedges
of INCONEL-600 (figure 3.2-8). For this purpose a normal type of silver-
braze could be used as there was no contact with the salt.

In addition to the aforementioned local temperatures the following
variables were measured (cf. figure 3.2-4):

salt inlet temperature (Pt resistance thermometer)

salt outlet temperature (Pt resistance thermometer)

salt mass flow (venturi flow meter)

air inlet temperature (Pt resistance thermometer)

air outlet temperature (Pt resistance thermometer)

air inlet pressure (Bourdon pressure transmitter)

air outlet pressure (Bourdon pressure transmitter)

air mass flow (floating body flow meter = rota meter)
- 3.2 -

Wall temperature correction.

Measurement of the true surface temperature is impossible due to the finite
dimensions of the measuring element. The temperatures measured by the
thermocouples, - embedded in the wall - therefore have to be corrected for
the resulting finite temperature differences between wall and thermocouple
tip. Additional uncertainties are introduced by imperfections of the
thermocouples (eccentricity of the hot junction (cf. figure 3.2-9) and of
the brazing (cf. figure 3.2-10).

To reduce these uncertainties the special calibrating equipment shown in
figure 3.2-11 was built and operated. The central part of this equipment
was formed by a heat exchanger into which the different instrumented
sections of FLiNaK tube were fitted in turn after completion of the
measurements (cf. figure 3.2-12).

The inside of the tube was heated by steam at atmospheric pressure, while
at the outside the wall was cooled by water boiling under reduced pressure.
In view of the very high heat transfer coefficients associated with both
condensation and boiling, the inner and outer wall surfaces were assumed to
be at the saturation temperatures corresponding to the respective local
pressures.

Under the assumption of a linear temperature gradient through the wall, the
location of the embedded thermocouples could be determined from the
readings of the three thermocouples, as shown in figure 3.2-13. The
temperature differences between tube wall and salt thermocouples, obtained
during the actual heat transfer tests, could then be corrected by subtrac-
ting the temperature drop between tube wall surface and equivalent
thermocouple location, expressed as:

8
= AO _ — -
trve 3 meas q A (3.2-2)

3.2.6. Data reduction and processing.

Data reduction.

For each measurement including the calibration runs all signals were
scanned ten times to reduce the influence of random errors. These values
were recorded on paper tape for further processing on an IBM 370/158
computer.

Data reduction was performed by a special program, MEANTAB, available from
the laboratory program library. This program averages the values obtained
from a number of scans and checks for excessive deviations. The computed
average signals are tabulated with their standard deviations and trans-
ferred to disk.

Data processing.

The data set thus obtained was processed by a special purpose program
consisting of three consecutive stages:

a. determination of the calibration constants for the various thermo-
couples (cf. also subsection 3.2.7).

b. determination of the heat transfer coefficient o from the data by a
procedure called FLILU.

c. fitting of all measured a-values by a standard correlation in proce-
dure APPROX.

“'Jed =

ad:b. s

A part of the second stage requiring some elaboration is the increased
accuracy obtained for the heat flux g by means of a least squares
curve fitting technique applied to the air temperature measurements.

ep(z)

For this curve the approximation aair = was chosen,

where p(z) is a polynomial in z, i.e. the axial coordinate of the heat
exchanger.

The local heat flux is determined from the steady state energy balance
for the air:

oY

air
TTDiq a ¢mcp 0z

(3.2-3)

by substituting the z-derivative of the obtained approximation of the
air temperature distribution. A correction of less than one percent is
applied to g to take into account expansion work in the air due to the
small axial pressure drop.

ad.c.:

The experimental data is approximated by a correlation of the general
form:

Nu = C Reb Prb (3.2-4)

The coefficient C and the exponents m and n have to be determined so
as to fit the experimental results as closely as possible.

To make this problem amenable to linear regression analysis the
natural logarithm of equation (3.2-4) was taken, yielding:

*
In Nu=C + m 1ln Reb + n 1ln Prb (3.2-5)

*
(C = 1n C)

It should be noted that this approach minimizes the sum of the squares
of the relative errors instead of that of the absolute errors.

3.2.7. Calibration.

® platinum resistance thermometers

The platinum resistance thermometers were calibrated by the manufac-
turer to a guaranteed accuracy within 0.25 Oc.

® Jlocal thermocouples

- temperature differences
As in the thermal flow meter (cf. subsection 2.3) the temperature
differences were measured directly by connecting the wall and bulk
thermocouple in such a way that the resulting e.m.f. is the diffe-
rence between the two separate e.m.f's.
As explained in subsection 2.3.4 this connection results in an
accuracy of 1%, obtained by calibration during isothermal operation.

- 3.4 -

absolute air temperatures

These thermocouples are calibrated against the FLiNaK Pt-resistance
thermometers during isothermal operation of the loop (no air

flow). In this way an accuracy of better than 1 Oc is obtained.
FLiNaK venturi flow meter

For the calibration of the venturi flow meter the reader is referred
to subsection 2.2.3, where an accuracy of 4% is mentioned for this
instrument.

pressure transducers

The pressure transducers are calibrated against a special high accu-
racy manometer to an overall accuracy of 2%.

air flow meter

The air flow meter of the float-type was calibrated by the manufac-
turer to a guaranteed accuracy within 2%.

3.2.8. Accuracy.

The heat transfer coefficient o is computed from:

& =q/ (Aameas a qd/)\in

=
o,
air

where q = ¢m . ! Ny

/(m Di) + correction for expansion
work (< 1%) (3.2-7)

The accuracy of the different variables will now be discussed in the order
of their appearance in equations (3.2-7) and (3.2-6) respectively:

accurate to within 2%

the specific heat of the air depends on temperature and pressure
thus on the measured values of these two variables:

the limits of inaccuracy of the absolute air temperature
and the air pressure have been established in the previous
section at 1 OCc and 2% respectively. Using the temperature
dependence of ¢ tabulated in [ 3.2-3 ], this amounts
air
to a relative error in c of < 0.5%
air

air
0z

The accuracy of the axial derivative of the air temperature is the
most difficult to establish due to the complex method applied for its
determination. 89

An upper bound can be estimated by assuming —— to be simply determined
from two adjacent air gap thermocouples as:

ov 1 u (3.2-8)

The average temperature difference (¥, - 6u) amounts to some 50 OC,

1
while the maximum absolute error in this difference is vV 2 times the

absolute error in the separate temperatures, i.e. v 2 x 1 = 1.4 Oc.
For a maximum relative error in Az of 0.5% the total relative error

9
in %;—is less than 3%. %)

- D.
2

Measurement of the inner diameter Di of the test module is accurate
within 0.25%. *)
The relative inaccuracy of g resulting from these inaccuracies is:

€, = /22 4+ 0.52 + 32 + 0.252 = 4%

- AY

The actual measured temperature difference between bulk and wall
thermocouples is accurate within 1% (cf. subsection 2.3.4).

- A,
inc

The thermal conductivity is accurate within 5% (cf. [3.2-11]).
- 0

The equivalent embedding depth is determined from the temperatures
measured in the special calibration heat exchanger shown in figure

3.2—13' as:
U, - 0m
1
§ = 5 5 S
1 O

Typical values for 01, 6m and 30 are 40 %c, 75 Oc and 100 Oc respec-

tively. The accuracy of the thermocouple measurements in this range
was 1 0c., Evaluation of the inaccuracy of § yields:

Noting from equation 3.2-6 that for the maximum FLiNaK flow, the wall
correction term g G/Ainc is about 40% of the measured temperature

difference A6, the maximum total relative error in the locally

*) ineluding thermal expansion effects.

- 3.6 -

measured heat transfer coefficient amounts to:

_ 10 2 ) 2 % 2 4 2 g
ea_/(6 1) +(6.4) +(6.6) +(6.5) + 4 = 9%

The final value for the heat transfer coefficient is determined as an
average of 9 measured values - the top and lowest of the five diffe-
rent measuring levels having been omitted because of reduced thermo-
couple quality - thus reducing the error to:

The Reynolds number is given by:

) D, 4 ¢
R e S o kR (3.2-9)
fl v /4 Diov T D, oV :

The FLiNaK mass flow is measured by means of the venturi flow meter
discussed in section 2.2 with an accuracy of 4%.

As stated at the end of subsection 2.2.3 the main cause of this inaccuracy
is the inaccuracy of the density value of FLiNaK. For this purpose the mass
flow meter can be represented by:

Vil 0, 5 A
¢m Cve (Ap p) (3.2-10)
where e is accurate within 1.2% (cf. subsection 2.2.3).

Substitution of this relation into equation (3.2-9) yields:

b
Re = %— ¥l Y w (3.2-11)

This representation shows that the direct influence of the density on the
accuracy of the Reynolds number and that via the FLiNaK mass flow measure-
ment cancel out to some extent. The margin of uncertainty for Refl

resulting from the combined inaccuracies of ¢ , D - cf. above - p and v
; ve
amount to 6% (cf. figure 2.2-13).

the maximum relative error in Pr based on the inaccuracies of the physical
constant as given in the table shown in figure 2.2-13 amounts to:

Pr=/(52+52+22+102)=13%

- 3.7 -

d. accuracy of the computed heat transfer coefficients.

It would appear from the above that the accuracy of a-values computed from
the proposed Dittus-Boelter type correlation, i.e. based on the computed
Reynolds and Prandtl values, will be poor. However, a closer look at the
Dittus-Boelter type correlation indicates that errors in the Reynolds and
Prandtl numbers caused by the same inaccurate physical properties tend to
cancel out:

A—-Re()'8 prl.% = 2 (¢m -

_ 0.8 FCr0 1
a . > S /2D ) (p X )
- 7 DDU.B 0.8 0.1 % 204
0.k 0.8
™ ve

The total relative error thus amounts to:

/ (0.8x1.2)2 + (0.6x10)2 + (0.4x2)2 + (0.4x5)2 + (1.8x0.25)2= 6%
and is dominated by the error margin of the FLiNaK thermal conductivity.

3.2.9. Test program.

Four series of heat transfer measurements were carried out
tively increasing air mass flow. The increase in secondary
resulted in augmented heat transfer rates and consequently
overall accuracy. The test conditions of the last and most
are shown in figure 3.2-14 giving the Reynolds and Prandtl

with consecu-
mass flow

in an improved
accurate series
numbers for

FLiNaK of each measurement based on the properties given in figure 2.2-13.
The Reynolds number ranged from 1.3 x 10* to 9.3 x 10%, while the Prandtl
number was varied from 4.0 to 6.8 corresponding to a temperature range of

575 - 675 Oc.

3.2.10. Experimental results.

The table given in figure 3.2-15 shows the results of the measurements

performed at maximum air mass flow.

The same table shows the results of the correlating procedure described

in subsection 3.2,6. The resulting correlation:

Nu = 0.0137 Re0.83 pr0.tl (3.2-13)
fits 90% of the measurements to within 2.5%.
The table given in figure 3.2-16 shows a comparison of the measurements

with values computed according to a corrected version of the Dittus-

Boelter correlation:
Nu = 0.020 Rel+8 pyO.th

3.2.11. Discussion of results.

(3.2-14)

Of the three differences between the correlation given in equation (3.2-13)

and the Dittus-Boelter correlation:

0.023 ReP.8 py0.h

- 3.8 -

(3.2-15)

- which is seen to overestimate the actual heat transfer coefficient by
approaximately 17% - the slight difference in exponent of the Prandtl
number is of little consequence, as the corresponding change in value of
the coefficient amounts to 3% only. The increased value of the exponent of
the Re-number, however, has a significant effect on the value of coefficient
C (25%), partly explaining the lower value of the coefficient appearing in
equation (3.2-13). Higher values than 0.8 for the exponent of the Re-number
occur in several other heat transfer correlations (cf. e.g. BISHOP
(equation 4.2-21) and GROENEVELD [ 3.2-2 ] mentioning exponents of 0.886 and
0.853.

However, even retaining coefficients of 0.8 and 0.4 (cf. equation (3.2-14)
the best fit of the experimental data requires a decreased coefficient:

C = 0.20 instead of 0.23.

The overestimation of the heat transfer coefficient by the original Dittus-
Boelter correlation may well be due to inaccuracy of the FLiNaK thermal
conductivity (cf. APPENDIX 2A) - as compared to A = 1.3 W/m Oc used here -.
A value of A = 1.03 W/ (m Oc) would yield a very close fit of the measured
heat transfer data by the Dittus-Boelter correlation.

In view of the wish to conform as much as possible to the Dittus-Boelter
correlation and the very limited loss of accuracy, equation (3.2-14) was
preferred over equation (3.2-13) for the computations for the thermal flow
meter discussed in section 2.3.

3.3. Momentum transfer.

3.3.1. Introductory remarks.

As stated in section 1 the heat transport capability, defined as the ratio
of thermal power removed to pumping power required, determines to a large

extent the effectiveness of a fluid as a heat transfer agent.

As the heat transport capability is directly proportional to the friction

factor £ of the fluid determination of this factor for FLiNaK was included
in the aims of the original DMSP program.

3.3.2. Description of the method.

The friction losses in a straight tube are usually obtained from the
formula:

L o v2 (3.3-1)

where f is the so-called friction factor, solely depending on the
Re-number and the roughness of the tube wall.

The purpose of this study was to determine the friction factor f as a
function of Re in the turbulent flow regime and to verify whether this
relationship may be represented by one of the usual formulae or graphs,
such as the Blasius formula [3.3-1 ]:

el
f = 0.3164 Re (3.3-2)

or the Moody chart (cf. figure 3.4-1).

The friction factor was obtained from pressure drop measurements across a
calibrated straight tube in the DMSP primary loop.

The fluid velocity has not been measured directly but was calculated from
the venturi mass flow measurements described in section 2.2 by evaluating:

- 3.9 -

¢ ¢ Ya&p__p _c Ap

. In - ve ve - ve ve =
VT o w/aDpZ T b n/ap? /4 D2 ' » (3.3-3)

where Apve stands for the pressure drop measured across the venturi.

To validitate the above formula the loop was operated isothermally during
these measurements, viz. with a uniform density. Combining equations
(3.3-1) and (3.3-3) yields:

2 (n/4)2 p DPsg
L 2 Ap

C ve
ve

£ =

(3.3-4)

where the specific mass p of the fluid has been eliminated.
The Re-number is obtained from equation (3.2-11).

3.3.3. Description of equipment.

3.3.3.1. Test tube.

The test tube consists of a length of tube mounted in the DMSP loop between
the main heater and the heat exchanger, at a downward angle of 69 with the
horizontal in the flow direction for drainability (cf. figure 3.3-2).

The dimensions of the test tube are shown in figure 3.3-3. In accordance
with [ 3.3.2 ] straight sections of 30 D upstream and 10 D downstream were
provided to ensure the necessary undisturbed fully developed flow. The
pressures were measured through single bore pressure taps, flush at the
inside tube wall. For this type of taps it is essential:

- that they are at a right angle with the centerline of the tube
- that the tube has a perfectly cylindrical shape in the vicinity of the
holes.

To fulfill these requirements two solid studs were welded into the tube at
the specified locations and subsequently drilled at right angles with the
center line, so as to avoid errors caused by post-welding distortion.

The main tube was then internally ground over the full upstream and
downstream lenghts to obtain a perfectly cylindrical bore.

Subsequent to this machining the tube bore was measured at a number of
cross sections. The results of these measurements are given in figure
3.3-4. Another important property of the test tube bore is its surface
roughness. The mean height § of the rogghness was 15 ru, corresponding

to a relative roughness of /D = 1.10°
According to [ 3.3-1 ] a tube with this relative roughness may be considered
completely smooth.

3.3.2.2. Differential pressure measurement.

The differential pressure measurement device used for the friction pressure
drop measurements is essentially the same as that of the earlier version of
the venturi (two-electrode type) described in subsection 2.2.2.2 and shown
in figure 3.3-5. To reduce the error caused by friction losses the connec-
ting tubes (cf. subsection 2.2.3) the control gas release rate was further
reduced to about 2 cc/min. The gas pressure difference was transformed into
an electrical signal by a combination of a differential pressure cell and
an amplifier. This signal was recorded on a line recorder.

- 3.10 -

3.3.4. Test program.

As the tube may be considered completely smooth the only remaining quantity
influencing the friction factor is the Reynolds number. For the given
diameter Re could only be changed by varying the mass flow and the FLiNakK
temperature. Tests were performed at three temperature levels; approximately
575 C, 625 C and 675 C. At each temperature level the mass flow was varied
over the range 2 - 9 kg/s (cf. figure 3.3-6).

3.3.5. Experimental results.

The table in figure 3.3-7 gives the results of the various measurements.

In addition to the two differential pressures and the temperature of the
FLiNaK measured during each experiment this table compares the measured
friction factor to the one computed from the Blasius formula by listing both
their absolute and relative difference.

By applying the least squares procedure APPROX a best fit of the measured
friction factors is obtained, reading:

_0.,2058
f = 0.265 x Re (3.3-5)

(cf. figure 3.3-8).

Figure 3.3-9 shows a graphical comparison between the test results (drawn
line) and the Blasius formula (dotted line).

3% 358, Accuracy.

The friction factor f is calculated from equation (3.3.4):

2(m/4)2 D5 Ap g
= o (3.3-6)
ve ve

il

The values and the maximum errors of the various quantities appearing in
this formula are given in the table in figure 3.3-10.

These inaccuracies amount to a total of 3% of the maximum value f = 0.03
(cf. Appendix 3A). max

The accuracy of the Reynolds number is better than 7% (cf. subsection
3.4:.8)3

3.3.7. Discussion of results.

As evident from figure 3.3-10 the shape of the experimental curve closely
resembles that of the Blasius correlation, but the absolute values of the
fraction factor show a consistent "overshoot" of approx. 20%.

No scientifically convincing explanation could be found for this phenomenon.
The author is inclined to attribute at least a significant part of the
discrepancy to the fact evidenced in figure 3.3-4, viz. that, despite the
accurate machining, small diameter variations with a relatively large wave
length are present along the tube length. Although these variations cannot
be considered as roughness proper the experimental results indicate that
they may have induced an additional pressure drop.

For reasons of expediency repetition of the experiments with a different
tube bore proved impossible.

=-3.11 -

4, BAYONET TUBE STEAM GENERATOR

4.1. Introduction.

4.1.1. General background.

All concepts for molten salt breeder reactor power plants published so far
incorporate an intermediate coolant for heat transport from the intensely
radioactive circulating fuel primary circuit to the steam cycle. Compati-
bility and high temperature stability requirements limit the choice of this
secondary coolant to fluoride salt mixtures, thereby entailing some
specific design problems for the steam generator.

These problems result from two properties of the salt mixture (cf. figure
2.2-13). The first of these concerns the high heat capacity, causing a
small temperature drop of the heating fluid and hence a very large
difference between the salt outlet and feedwater inlet temperatures and
correspondingly large thermal stresses in the tube wall separating the two
fluids. '

For those familar with the design of other high temperature steam genera-
tors such as those heated by sodium, this problem by itself will hardly
appear specific to the use of molten fluorides.

It must be borne in mind, however, that in addition to the aforementioned
much smaller temperature drop of the hot fluid, its inlet temperature will
be some 100 Oc higher in the case of the salt, increasing the steady state
temperature difference at the cold end of the steam generator by a factor
of about 3 as compared to sodium heating (for the same feedwater inlet
temperature) .

The second property of the salt causing problems is the high melting point,
because it raises the danger of salt freezing on the outer tube walls in
the economiser section.

As briefly mentioned in the introduction to this thesis, the presence of
the DMSP molten fluoride system in the author's laboratory offered an
attractive possibility for contributing to the solution of these problems
because of the availability of:

- the molten salt loop described earlier, containing a 250 kW electrical
heater

- the necessary special instruments

Apart from these, there was the knowledge and experience in designing and
operating a molten salt system.

Prior to the definition of an experimental program, a choice had to be made
between the two basic alternatives for avoiding the aforementioned problems,
viz. raising the feedwater inlet conditions to some 350 Oc through the
adoption of supercritical operating conditions or interposing an additional
thermal barrier between the primary and secondary fluids.

The former alternative, selected in the MSBR design reported by ROSENTHAL
[4.1-1 ] was rejected for the present study on the following grounds:

® in Europe there is considerably less experience with supercritical steam
plants than in the U.S.A.

® at the time of taking the decision no such plant was operating in the
Netherlands at all *)

® it was deemed desirable to make the present tests as relevant as possible
for the (subcritical) sodium-heated steam generator development being
carried out in the Netherlands.

* . ’ : ; o
) at the time of completion of this thesis two 600 MW _ units had started

operating at supercritical steam conditions in the ~ Netherlands.

- 4.1 -

A number of possible design solutions for the subcritical alternative
chosen here were evaluated by FRAAS [4.1-2 ], viz.:

® double walls, separated by a heat barrier
® re-entry or bayonet tube boiler

On a number of grounds not reproduced here for brevity's sake he arrived at
the conclusion, shared by the present author, that the bayonet tube boiler
is the most promising design for overcoming the aforementioned problems.

4.1.2. The bayonet tube steam generator.

4.1.2.1. Design characteristics.

The bayonet concept schematically shown in figure 4.1-1 combines the
evaporator and the superheater in one system. The tube bundle with the
molten salt flowing around it consists of a great number of so-called
bayonet tube sets, each made up of two concentric tubes (cf. figure
4.1-2). The outer tube, closed at the top, is the pressure tube which
separates the salt and water regions, while the inner tube contains the
economiser and evaporator sections.

Feedwater enters this inner tube at the bottom, is preheated, evaporated
and slightly superheated before it reaches the top. There the steam flow is
reversed and the steam is superheated while flowing downward through the
annular gap to the steam outlet at the bottom of the steam generator.

The steam layer in the superheater gap acts as an effective thermal
barrier between salt and water. In order to prevent excessive heat loss
from the superheated steam to the incoming feedwater the lower part of

the evaporator tube is covered by an insulating layer of sprayed-on Z Oj.
As to the thermal stresses, both the evaporator tube and the pressure tube
can expand freely without causing stresses, while the thermal stresses
resulting from the radial temperature gradient across the tube walls are
limited due to the insulating steam layer.

Another advantage of this concept lies in the fact that the cyclic thermal
stresses resulting from the fluctuating dry-out location occur in the
evaporator tube which has no load-bearing function, rather than in the
mechanically highly loaded pressure tube.

The single tube steam generator model forming the test module for the
investigations to be described in this chapter was designed according to
the principle just explained.

The feedwater and steam conditions were chosen in accordance with modern
subcritical power plant practice, viz.:

steam pressure = 18 MN/m?
feedwater temperature = 280 Oc
steam temperature = 540 Oc

The primary inlet temperature was fixed at 625 OC to ensure a reasonable
margin with respect to the primary circuit operating limit, while at the
same time maintaining similarity with MSBR design studies (cf. [4.1-11]).
The one remaining process variable, the primary mass flow rate, should be
optimized to yield the highest value for k.AGL still giving an accep-
table primary pressure drop.
A preliminary optimization (IPENBURG [ 4.1-3 ]) indicated mass flow ratios
of about 9 for subcritical steam cycles, resulting in a primary temperature
drop of the order of 125 Oc. For given process conditions the design of any
steam generator should be optimized for minimum capital costs. To do so
would however require intimate knowledge of not only material and semi-
finished products prices for all the constituent parts, but also of the

MTD

- 4,2 -

unit costs and standard times of all the manufacturing steps concerned.
Such a task was considered beyond the scope of the present thesis.
Therefore optimization was limited in the sense of: minimum heating surface.
The three principal dimensions to be determined are: diameter of the
evaporator tube, width of the superheater gap, and length of the bayonet
tube. Simple considerations of enthalpy rise and estimated heat transfer
coefficients indicate that the length of the evaporator tube, needed for
preheating and complete evaporation of the feedwater, far exceeds the
length of the steam gap required for superheating.

Hence the length of the bayonet is determined by the length of the
evaporator.

The average heat transfer coefficient in the steam generator can be
increased by raising the feedwater mass flow rate. However, as most of the
local heat transfer coefficients are proportional to the mass flow rate to
the power 0.8, while nucleate boiling heat transfer and heat conduction
through the wall are even flow independent, the increase will be less than
proportional. As on the other hand the required heat is proportional to the
flow rate, this means that a longer evaporator tube is required for
obtaining the same outlet conditions at the top of the evaporator.

The length of the evaporator wil be limited by building height requirements.
Once this limit is reached further increase in flow rate is still possible
by reducing the inner diameter of the evaporator tube and thus improving
the ratio of heated perimeter and cross-sectional area. Although there is a
small decrease of the heat transfer coefficient associated with a reduction
of the diameter the net effect of mass flow rate increase and diameter
reduction on the average heat transfer coefficient remains possitive. Once
the economical and/or technical limit for reduction of the evaporator tube
diameter is reached the last possibility to increase the overall heat
transfer coefficient lies in reduction of the superheater gap width.

The effect of this reduction on the heat transfer coefficient to the two
adjacent walls can be derived from the relevant superheated steam heat
transfer correlation. In our case the correlation of BISHOP [4.1-4 ]:

D
Nu = 0.0073 Re0+886 pr0.6 (1 4+ 2.76 E§° (4.1-1)

has been applied for reasons discussed in subsection 4.2.3.
Transformation of this correlation shows the total effect of the gap
width w on the heat transfer coefficient:

2w

A . év
( ) 0886 pr0.6 (1 4+ 2,76 . =5 (4.1-2)

a = 0.0073 v s

L

i.e. one of approximately inverse proportionality (for constant mean gap
diameter D).

In summary an optimum design is obtained by combining the following
measures:

® maximum bayonet tube length

® minimum evaporator tube diameter

® ninimum superheater gap width

® maximum flow rate (under the condition that evaporation is completed
in the central tube)

The following practical limits to these measures were observed in the
optimization:

® 15 m for the evaporator tube length, corresponding to a total length of
20 m for the entire steam generator. This total length of 20 m is
about equal to that of the contemporary straight tube sodium heated
steam generators

® 3/8" (17.2 mm O0.D.) for the evaporator tube because of the steeply
increasing cost per unit of heat transfer surface below this diameter
and structural requirements concerning the slenderness of the bayonet
tube

® 2 mm for the minimum gap width compatible with spacing and assembly
requirements.

N.B. Superheater pressure drop restrictions may increase this minimum
even further.

4.1.2.2. Potential interest.

While the above characteristics explain the potential interest of the
bayonet tube design for MSBR steam generators, it should be noted that a
similar design has also been proposed for application in LMFBR's.

To the author's knowledge KINYON [ 4.1-5 ] was the first to do so. His
proposal has been followed by several other authors: BARRATT [4.1-6 ],
PETREK [ 4.1-7 ], HUNSBEDT [ 4.1-8 ], of which Hunsbedt reported actual
performance tests on a seven tube experimental steam generator. These
designs, however, although featuring a bayonet tube, differ essentially
from the design proposed by Fraas and discussed here in that they do not
combine the superheater and the evaporator in the same bayonet tube. They
are provided with a separate superheater, sometimes contained in a separate
pressure vessel. The bayonet tube serving as evaporator only is reversed in
position (closed end down with the feedwater flowing downward through the
inner tube and evaporation taking place during upward flow in the annulus).
While this type of evaporator does not solve the aforementioned special
problems posed by the high melting point and high average operating tempe-
rature of the heating salt, its application to LMFBR's holds two important
advantages:

® problems caused by different thermal dilatation of tube bundle and shell
are avoided, thus eliminating the need for differential expansion devices
such as bellows

® the tube-to-tubesheet connections are not in touch with the sodium, which
decreases corrosion and thermal stress problems.

Application of the Fraas type bayonet tube steam generator to the LMFBR
would add the advantage of reducing the sodium-water reaction through
decreased mass flow into the surrounding sodium because of the substitution
of superheated steam for two-phase mixture or even water. It would, however,
require a substantial raise of the primary temperatures.

4.1.3. Aims and scope of the present investigations.

The general aim of the present investigations is a first assessment of the
suitability of the once-through bayonet tube concept for high pressure
steam generation. To the author's knowledge this is the first use of a
bayonet tube steam generator operating in the once-through mode with steam
conditions representative for modern power station practice.

The present study is restricted to the thermal-hydraulic performance of
such a steam generator.

- 4.4 -

The thermo-hydraulic design of a steam generator has to cover three aspects:

® steady-state behaviour
® dynamic behaviour under large transients
® flow stability

4.1.3.1. Steady state behaviour.

An essential prerequisite for the design of a steam generator is the
availability of information needed for a realistic assessment of the
necessary heat transfer area, preferably in the form of a computer code.
The second step in steady state performance analysis is the prediction of
fluid outlet conditions, internal temperature distribution and total
pressure drop at partial loads.

In the case of the present investigation this information was also required
as input for the dynamic stability simulation program discussed in section
4.6.

The accuracy of the above thermo-hydraulic performance predictions is
directly dependent upon the accuracy of the heat transfer and pressure drop
correlations applied.

An extensive survey and evaluation of the available information was
presented by TEN WOLDE [ 4.1-9 ] in 1972. The additional information
published since (e.g. by CAMPOLUNGHI [ 4.1-10 ]) does not in the author's
opinion warrant modifications in the set of correlations recommended by Ten
Wolde (cf. subsection 4.2.3.2).

Recognizing that the best available correlations were only of limited
accuracy, two courses of action were open at the initiation of this project:

® experimental investigations of heat transfer and pressure drop
correlations under conditions valid for the bayonet tube steam genera-
tor, followed by computer simulation of the steady state performance
using these experimentally determined correlations

® development of a computer code utilizing the available correlations,
and subsequent verification of the results of this code in an experi-
mental bayonet tube steam generator so as to define the causes of,
and qualitatively explain, possible discrepancies.

The former course would be more appropriate for a laboratory specializing
in heat transfer than for one mainly aiming at equipment development.

It would also be beyond or at best in the margin of the present scope of
investigations. It was therefore decided to follow the second course.

The question may arise whether both types of investigation could not have
been combined in one experimental program. The present author's answer to
this question is an emphatic no. The complex geometry of the experimental
bayonet tube steam generator permitted only a very limited amount of
internal instrumentation. Any attempt to instrument the test module to the
extent required for establishing or verifying individual heat transfer
correlations would have invited the kind of problems typical for multi-
purpose applications of highly complex test equipment, as exemplified by
the salt-to-salt heat exchanger experience discussed in subsection 3.2.1.
This experience convinced the author that such experimental apparatus
should serve one single purpose only, so as to permit the simplest and most
reliable design possible.

To check the overall performance and to locate and qualitatively explain
possible discrepancies between experiment and simulation a limited amount

- 4.5 -

of instrumentation was sufficient.
The selection of this instrumentation is discussed in subsection 4.3.3.2.

4.1.3.2. Dynamic behaviour.

4.1.3.2.1. Large transients.

A thorough knowledge of the dynamic behaviour of steam generators under
large transients is essential for the safety assessment of any nuclear
plant. It is also highly desirable for the design of control systems for
new or extrapolated steam supply systems if one is to avoid surprises at
the commissioning stage. Such knowledge should preferably be at the
designer's disposal in the form of a computer code, suitable for accurate
simulation of the highly non-linear processes in the steam generator.

A further aim of the DMSP-program concerned development of such a program
for the complex geometry of a once-through bayonet tube steam generator and
subsequent verification of the results of this program by comparison with
experimental data obtained in the test facility mentioned above (cf.
section 4.5).

4.1.3.2.2. Stability.

Secondary side flow instabilities in steam generators are well known as a
cause for tube failures: by thermal fatigue through oscillations in the
location of the dry-out point; by mechanical fatigue through sustained
forced vibrations; by local overheating due to temporary flow starvation or
by combination of the aforementioned effects.

The absence of such instabilities within the normal range of operating
conditions (including start up and shut down) is therefore essential for
sound steam generator design.

A number of different types of oscillatory flow have been identified in the
literature. The following summary classification follows the excellent
review by BOURE [4.1-11 ].

The first distinction to be made is between static and dynamic instability.
The static or Ledinegg instability, characterized by incidental random
oscillations between metastable steady state conditions, occurs if the
slope of the channel pressure drop-versus-flow rate curve is algebraically
smaller than the slope of that curve for the remainder of the loop (cf.
figure 4.1-3). This may result in severe flow excursions, as in this case a
change in flow is reinforced rather than opposed by the resulting change in
pressure drop. This mechanism, though aperiodic by nature, may under
certain conditions cause an apparent oscillation (cf. STENNING [4.1-12 ],
but this notwithstanding it is essentially the steady state that is un-
stable.

The so-called dynamic instabilities can be divided into two classes.

The first class is characterized by the propagation of pressure waves
through the steam generator, while the second class is characterized by the
occurrence of density waves. These two types can easily be distinguished by
their frequencies. In the case of the density wave oscillations these are
related to the fluid velocity, while the frequency of the pressure wave
oscillations depends on the velocity of sound in the fluid, resulting in
much higher values (e.g. 10 versus 0.1 - 1.0 c¢/s). This study is restricted
to the former type of oscillation as being the more potentially damaging
one to steam generators, because the temperature variations of much higher
frequency caused by pressure wave oscillations are of smaller amplitude and
effectively damped by the heat capacity of the wall.

= Gl -

The original aim of developing a computer code suitable for the assessment
of the stability of once-through bayonet tube steam generators, followed by
experimental verification, was extended as the project progressed.

From a literature survey (discussed in detail in subsection 4.6.1.1) it
became clear that even for simpler geometries the accuracy of predictions
leaves much to be desired. To a large extent this appears to be due to the
absence of sufficiently accurate empirical relations, in particular for
subcooled boiling and two-phase frictional pressure drop.

During the development of a special purpose program, restricted to stabi-
lity simulations for once-through bayonet tube steam generators (cf. sub-
section 4.6.1.2) it became more and more apparent that a need existed for a
very flexible program, suitable for different geometries and process con-
ditions, while facilitating eventual replacement of all empirical relations
by newer, more accurate ones.

The last period of the project was devoted to the development of such a
program, viz. the CURSSE program discussed in subsection 4.6.1.4.

4.2. Basis for analysis.

4.2.1. General assumptions.

The thermo-hydraulic processes in a steam generator consisting of a great
number of parallel tubes between a common inlet header and a common outlet
header are very complex. It is impossible to simulate these processes in
all detail. The commonly accepted procedure is to select a subsection of
the steam generator whose behaviour under load is considered characteristic
for the entire component. The usual choice for this characteristic section
is one single, so-called "characteristic", tube representing the average
behaviour of all tubes in the steam generator. This approach is obvious for
the stationary and transient simulations. It is also customary for the
simulation of hydro-dynamic stability. This application will be discussed
in detail in subsection 4.6.1.2.

While limitation of the simulation to a single tube represents a considera-
ble simplification, the momentum and heat transfer processes occurring in a
single tube are still highly complex.

A brief introductory and qualitative description of these processes there-
fore appears in order with special reference to the bayonet tube design
discussed in the preceding section.

Subcooled water entering the evaporator at the bottom is heated by single-
phase forced convection until the temperature of the tube wall inner
surface exceeds the saturation temperature by a sufficient margin to allow
bubble formation (subcocled boiling).

In this transition region a significant and sharp increase of the effective
heat transfer coefficient to the water occurs due to bubble detachment and
transport and the resulting partial destruction of the laminar boundary
layer. This augmented heat transfer is maintained as the water reaches
saturation temperature and the bubbles leaving the tube wall no longer
condense, but become dispersed in the water. As vapour generation continues
and the void fraction increases, the flow pattern changes from bubble - via
slug - to annular flow, where the vapour forms the continuous phase in the
core of the tube, with the liquid either flowing in the form of an annulus
along the tube wall or dispersed as droplets.

Continuing evaporation reduces the thickness of the liquid film until the
void fraction reaches the critical value, where the annular ring of liquid
disappears resulting in a dry tube wall and a sharply decreased heat trans-
fer coefficient: dry-out.

- 4.7 =

The remainder of the water is evaporated in the mist flow region where the
flow consists of steam with entrained droplets and thermal non-equilibrium
- i.e. vapour superheating at qualities x < 1 - may exist. Finally, at

X = 1 the true superheat region is entered, where all the heat supplied is
used to superheat the steam.

The processes described above, governed by the well-known conservation laws
for mass, momentum and energy, are essentially two-dimensional. Velocity,
temperature and pressure variations are present in two different directions
and on two different scales: local variations over the cross section, i.e.
in the radial direction, and the axial distribution of the mean values along
the length of the channel. The cross-sectional variations, determining the
local heat transfer and the friction pressure drop, are of too complex a
nature to be analysed in detail. To avoid these problems it has become
common engineering practice to assume uniform distributions based on the
mean values and to define the heat and momentum exchange between the fluid
and its boundary by heat transfer and pressure drop correlations defined
with respect to these values.

This one-dimensional approach, elaborated in a number of textbooks (e.q.
WALLIS [ 4.2-1 ]), essentially consists of the replacement of the mean value
of a product by the product of the mean values of its constituent factors.
Although this is known to cause only marginal errors in single phase turbu-
lent flow, it may cause significant errors in two-phase flow, notably in
studies concerning momentum transfer. This fact is mainly due to the non-
uniform radial void distribution.

Two possible solutions have been proposed for this problem. In the first,
adopted by HANCOX and NICOLL [ 4.2-2 ], the product of mean values is multi-
plied by a correction factor based on assumed radial distribution functions
of the properties concerned.

The value of this factor will of course tend towards unity as the system
pressure increases towards the critical pressure. Values based on experi-
mental data for steam/water flow at pressures up to 11 MN/m? are presented
in [4.2-2].

In the second method a separate mean velocity is introduced for each of the
two phases. The ratio of the average gas and liquid velocities is called
slip. This latter approach, underlying i.a. the well known slip correla-
tion proposed by BANKOFF [ 4.2-3 ], was adopted for the two-phase flow
region in the present thesis because of easier application.

Having thus eliminated the radial dimension, one is left with the one-
dimensional problem of determining the distribution of the average values
along the length of the channel by solving the system of one-dimensional
mass, momentum and energy balance equations completed with the empirical
heat transfer and pressure drop correlations.

4.2.2. Balance equations.

In addition to the energy balance for the tube wall, balance equations for
the fluid are required for the following regimes:

® single-phase flow (pre- and superheating)

® two-phase flow
- thermal equilibrium (saturated boiling and post-dryout mist flow)
- thermal non-equilibrium (subcooled boiling)

In adopting the above subdivision no account is taken of non-equilibrium
effects in the post-dryout mist flow region. For a justification of this
approach at the pressure level of interest for this thesis (= 17 MN/m?)
the reader is referred to GROENEVELD [ 4.2-4 ]. An extensive review of the

pertinent balance equations with their derivations was given by TEN WOLDE
[4.1-9 1.

The remainder of the present section is therefore limited to a listing of
these equations with additional comments for the case of thermal
non-equilibrium.

4.2.2.1. Single phase flow.

The mass balance equation reads:

R , (4.2-1)
ot 0z

The momentum balance reads:

oV v op TO ;
s e . ¥ Sies 5§ sin B195Y
5 ot 0z J 0z A kg " ( )

while the energy balance equation reads:

2R o 0y R SR -
p{at+v~é;}—at+vaz+A (4.2-3)

For the three applications given in sections 4.4 through 4.6 additional
assumptions have been made which will be discussed in the pertinent
sections. '

4.2.2.2. Two-phase flow.

AN

An exact description of two-phase flow would require the explicit inclusion
of the equations for the two separate components in the simulation, result-
ing in twice the number of basic equations as for single-phase flow. In
addition the boundary conditions are more complex, involving interaction
forces and heat transfer between the two-phases.

However, knowledge of these interaction processes is still too limited for
practical application of such a detailed mathematical description. Hence

the usual engineering approcach of applying mixture balances has been chosen
for this study.

1.2.2.2.1. Thermal equilibrium.

This refers to the saturated boiling regime and the post-dryout mist flow
region.

mass balance:

9p '~ 96 _

T T (4.2-4)
where mixture density p = (1~ a)_pl + apg (4.2-5)
and mass velocity G= (1 - a) plvl + ocpgvg (4.2-6)

- 4.9 -

momentum balance:

3G . 9 _ 2 2 1 o
5t T 3z ¢ (1 - @) pyvy + oo ve )
4.2-7
=SB o D T o | )
0z A P9

The above momentum balance equation of the mixture is obtained by addition
of the two balance equations for the separate phases, thus eliminating the
interaction forces between the two phases. Consequently their effect, viz.
the slip, has to be accounted for by an empirical correlation of the
general form:

v -
J=-s=f (p,h,0G)
Vl S

For further discussion of the slip correlation actually applied the
reader is referred to subsection 4.2.3.4.

energy balance:

This balance will be written in the internal energy u in accordance with
TEN WOLDE [ 4.1-9 ]:

9
( u a)+ — ( u o v )
F pg g g

3t g g 0z
+ é—-( u, (1 - a) + §""( u, (1 -a) v.)
3t P11 W 3z ‘P1 M1 1
e 3 (o v + (1 -a) v.) + ° (4.2-8)
P 3z g 4 a4 :

where u = h -

4.2.2.2.2. Thermal non-equilibrium.

The principal consequences of the absence of thermal equilibrium for the
balance equations are threefold:

- the thermo-hydraulic state of the mixture is no longer uniquely
determined by three variables (e.g. p, h, G for fully developed boiling)
but requires a fourth variable (e.g. x)

- the ratio of the amounts of heat transferred to each of the two phases
depends on the rate of heat transfer between the two phases

- the physical properties of the subcooled liquid are a function of both
pressure and temperature of the bulk.

While the mass and momentum balances for subcooled boiling are identical to
those for fully developed, i.e. saturated boiling ~ be it that the physical
properties depend on bulk pressure and temperature - the above mentioned
consequences of thermal non-equilibrium indicate the need for two separate
energy balances and thereby raise the problem of quantifying energy
transfer between the phases, i.e. the very problem avoided so far by the
use of mixture balances.

- 4.10 -

BOWRING | 4.2-5 ] formulated these two separate energy balances by dividing
the total heat supplied into the parts kg used for evaporation and (1-k)g
serving to heat the remaining water. The two energy equations are derived
in Appendix 4A.

The constant k is determined from a semi-empirical relation of general
appearance:

k=¢f.(h, P, G, %, Gw) (4.2-9)

The exact relation applied in this study will be discussed in subsection
Q20305

For a channel of constant cross-sectional area - postulated throughout this
section - the two energy equations read:

® for evaporation:

au ou
o pg SE—-+ o pg vg gzg-+
+{p (== + (a - ) o
g : 5
- B EEE.+ 5 o EEE;'= kq 2 ' (4.2-10)
0 ot g 9z A :

where ¢lg = the amount of evaporated water per unit of volume and time:

ap o °
¢lg = SEE-+ 5;°(vgpga) » (4.2-11)

® for preheating of the water:

ou au
A3 -8By g il Py S
ap 9p
g X1 _ MNE 3 A ks 2 * o .
5 ((1 a) ys + (1 o) Vi 32 ) (1 k) g A (4.2-12)

1

4.2.2.3. Energy balance of the wall.

From an extensive study of the subject TEN WOLDE [ 4.1-9 ] concluded that a
"zero layer" aproximation is sufficiently accurate for simulating steam
generator transient dynamics.

This model only considers the heat resistance of the tube wall, as defined
by the equation:

( g referring to the outer surface) (4.2-13)

and hence neglects storage effects.

- 4.11 -

This model has been applied in the transient analysis. In the stability
simulation program, however, a "multi layer" model has been implemented
for reasons discussed in subsection 4.6.1.4.1.

4.2.3. Empirical relations.

Following the flow path of the f£fluid the subdivision of the steam generat-
ing process described in subsection 4.2.1. results in the following five
consecutive regions: (cf. figure 4.2-1)

1. preheat region

2. subcooled region

3. saturated boiling *) recgion
4. mist flow region

5. superheat region

The empirical relations required for a mathematical model of the steam
generator can be divided into the following categories:

- transition criteria defining the boundaries between the above regions
- heat transfer correlations

- pressure drop correlations

- slip correlations

- inter-phase exchange correlations

4.2.3.1. Transition criteria.

4,2.3.1.1, Preheat - subcooled.

Bubble growth starts, where the wall temperature slightly exceeds satura-
tion temperature. For high pressure systems this wall superheat amounts to
only a few degrees (cf. JENS and LOTTES [ 4.2-6 ]) and has therefore been
neglected in this study: i.a.v. transition from the preheat to the sub-
cooled region is considered to occur where the wall reaches saturation
temperature.

4.2.3.1.2. Subcooled - saturated boiling.

This transition occurs where the bulk of the fluid reaches saturation
temperature and the mixture resumes a state of thermo-dynamic equilibrium.
The transition equation reads:

h =nh ' (4.2-14)

4.2.3.1.3. Saturated boiling - mist flow.

This transition, defined as "dry-out" in subsection 4.2.1, has been the
subject of extensive studies. Numerous dry-out correlations can be found
in literature, each with its own ranges of validity with respect to
pressure, heat flux, mass flux, channel diameter, etc.

The dry-out correlation selected after TEN WOLDE [ 4.1-9 | was first
proposed by LEE [ 4.2-7 ]:

778 0.201

DO h -nh 0.575 ¢ (4.2-15)
s W G

(h in kJ/kg °C and q in kJ/m?s).

* . P
) Sometimes called nucleate boiling.

- 4.12 -

This correlation is valid for:

13.8 < P < 18.5 MN/m?
2000 et 4400 kg/m?
0.009 < D < 0.020 m
0.2 <Xy < 0.4

4.2.3.1.4. Mist flow - superheat.

The transition from mist flow to superheating occurs theoretically where
the steam quality reaches unity (x = 1.0). In reality however this
transition is less abrupt, the steam being already superheated before the
last droplets have been evaporated. For high pressures, however, the
theoretical schematization can be adopted without loss of accuracy (cf.
GROENEVELD [ 4.2-4 ] ).

Hence the transition equation reads:

h =n (4.2-16)

4.2.3.2. Heat transfer correlations.

The heat transfer correlations as selected by TEN WOLDE [ 4.1-9 ] for the
various regions defined above are given here without further comments.

1. (convective preheat region)

Dittus-Boelter

Nu = 0.023 Reg-8 Prg-‘+ (4.2-17)

limits of application:

104 < Re < 6.10°
0.6 < Pr < 120

2 and 3. (subcooled and saturated boiling)

Rohsenow

- 8 -9 3 2 -
q C, C, ( . Sat) [ kJ/m?s ] (4.2-18)
where:

5

= 3 i 0.5 40,5 ’ -
c, Cpl ny (py og) g Py / (hy © 077)
C, # 1 103 for water/steel (4.2-19)

The correlation given above épplies to clean surfaces. Although
fouling affects its accuracy, such deviations are of little importance
for the bayonet tube case, where the overall heat resistance across
the evaporator tube wall is dominated by the superheated steam film
coefficient.

Therefore no special attention has been paid to this aspect.

- 4.13 -

4. (mist flow region)
Bishop - Sandberg - Tong
— 0.8 l1.23 ~y0,68 0.068 4.2-20
Nu. = 0.0193 Re Pr (pg/o) (pg/ol) ( )
limits for application
10.0 < P < 20.0 MN/m?
1100 < G < 5000 kg/(m?s)
0.0 < X500 < 0.4
S. (superheat region)

Bishop - Krambeck - Sandberg

Nu_ = 0.0073 Refo'886 Prf0°61 (4.2-21)

limits for application

16.5 < p < 21.5 MN/m?
0.236 10° < g < 2.5 10°% J/(m?s)
660 < G < 3280 kg/ (m?s)
0.0025 < D < 0.005
1.1 10° < Re < 6 10°
0.93 < Pr_ < 610

4.2.3.3. Frictional pressure drop correlation.

1. Single phase flow.

In the single phase flow regions the well known Blasius correlation for the
friction factor f is applied:

3p _ _ 0.316 1 _

o v (4.2-22)

3
92Zs.  Rel.25 Py 2

2. Two-phase flow.

In contrast with single phase flow no simple and accurate correlations are
available for the determination of two-phase frictional pressure drop due
to the complexity of the physical processes involved. A large number of
semi-empirical correlations has been proposed in literature, but all show
considerable deviations in comparison with experimental data. WISMAN e.q.
[4.2-8 ] compared the well known correlation of MARTINELLI - NELSON
[4.2-9 ] and a correlation proposed by DUKLER [ 4.2-10 ] with one of himself.
The latter correlation proved to be by far the most accurate of the three,
yet shows a mean deviation of 28% in comparison with experimental data.

In the simulations to be discussed later a further development of the
original Wisman correlation has been used, thought to be more accurate at
that time.

- 4.14 -

The correlation reads:

o AR . 2 2 ol
(az)fr 5 DH ( (1-a) p v{ + a pg vg ) (4.2-23)
where:
o 9;21%___ (4.2-24)
.25
Retf
Re, . = ( (1-a) p

v, + 0 og Vg) / ( (1-a) n

1 V1 + o ng) (4.2-25)

tf 1
However, subsequent comparison with the experimental data used in [ 4.2-8 ]
yielded a mean deviation of 40%. Hence the original correlation of Wisman
is recommended as the most accurate two-phase flow friction correlation
available as yet. It will be clear, however, that for accurate simulations,
especially those concerned with hydrodynamic stability, improved accuracy
in predicting two-phase frictional pressure drop is required.

4.2.3.4. Slip correlation.

As discussed above a slip correlation is required not only to account for
the actual difference in gas and liquid velocities but also to correct for
non-uniform distributions of the separate phases. The derivation of the
well-known Bankoff slip correlation was even solely based on the latter
effect as the local gas and liquid velocities were assumed to be egqual. The
numerical value of the Bankoff constant KB' however, was obtained by

fitting actual slip data, thus incorporating physical slip as well (cf.
BANKOFF [ 4.2-3 ]).

Formulation of a universal physically well-founded slip correlation being
hampered by the complexity of the physical processes involved, a great
number of semi-empirical relationships have been proposed in literature,
each with its own ranges of validity.

A very widely applied correlation is the so called Bankoff - Jones slip
correlation (cf. JONES [ 4.2-11 ]). In our case a slightly adapted vension
of this correlation is proposed. The reasons for this adaptation are
discussed in detail in Appendix 4B.

The adapted version reads:

(148 - a) - (4.2-26)
(K+6) + (1-K ) o -
where:
Ky = 0.71 + 0.29 B (4.2-27)
o
2
> e 1.3 0.8)7 B ¢ 40T B (4.2-28)
pCI’ Cr
§ = 0.04 (4.2-29)

- 4,15 -

4.2.3.5. Heat distribution paramater.

For reasons explained in the foregoing the only coefficient needed in this
category is the k factor suggested by Bowring (cf. subsection 4.2.2.2.2.1).
After comparing a number of different correlations with the experimental
evidence available for this constant VAN VONDEREN [ 4.2-12 ] recommended the
following correlation:

o el (4.2-30)

where 0b is the local bulk temperature and 0r is the bulk temperature at

the initial point of net vapour generation.

4.3. Test facility.

4.3.1. Test module.

While this unit was meant to resemble as closely as possible one module of
a possible future full-size steam generator, this tendency was limited by
several constraints imposed by practical considerations. The acceptance of
such constraints and of the resulting non-optimized thermo-hydraulic design
of the test module appeared justified in view of the explorative nature of
the study.

In order to put the resulting compromise into proper perspective, these
constraints will be discussed under the following headings:

® heating fluid

® flow pattern

® process conditions
® dimensions

4.3.1.1. Heating fluid.

Contrary to later MSBR design studies (cf. ROSENTHAL [4.1-1 ]) proposing

a mixture of sodium fluoride and sodium fluoroborate for intermediate heat
carrier, mainly because of its lower melting point (385 Oc), FLiNaK was
retained because of its availability in our laboratory from the earlier

experiments and because of the experience accumulated with this salt
mixture.

4.3.1.2. Flow pattern.

In any large size steam generator the shell-side salt flow would be baffled
for effective heat transfer, resulting in partial crossflow.

In our test module the shell consists of a third concentric tube of
slightly larger diameter than the pressure tube, forming an annular space
through which the salt flows downward in pure parallel flow.

While it is obvious that the resulting straight counterflow will not be
representative of the complex shell-side flow in a baffled exchanger, this

was considered to be of minor importance in view of the aims of the present
investigation.

- 4.16 -

4.3.1.3. Process conditions.

The conditions given in section 4.1 were slightly modified for the
experimental single tube steam generator. While the water/steam side
temperatures and the salt inlet temperature proposed for the full size
steam generator could be maintained, the salt outlet temperature had to be
raised significantly above the value of 460 O¢c proposed in [4.1-1 ] in
order to avoid salt flow rates too small for the operating range of the
pump (3-10 kg/s for the primary circuit under consideration).

An additional reason for raising the salt outlet temperature was given by
the melting point of the salt. For the proposed MSBR coolant the margin
between its melting point of 385 Oc and the proposed outlet temperature of
460 % would be quite adequate; however, for FLiNaK with its melting point
at 453 Oc this margin is far too small.

As a result of these considerations the primary temperature drop during the
experiments ranged from 0 - 12 OC, the latter value corresponding to a
rated mass flow rate of 6.8 kg/s. As the main aim of the experiments was to
verify the performance predictions obtained from analysis this deviation
from the proposed condition was not considered of vital importance.

For fixed in- and outlet conditions the secondary mass flow would normally
be determined by the primary heat source, i.e. the 250 kW electrical
heater. However, for reasons resulting from the design and therefore to be
discussed in a subsequent section, the maximum amount of heat to be trans-
ferred in the steam generator is limited to about 130 kW, corresponding to
a secondary mass flow rate of 0.065 kg/s.

The nominal process conditions discussed above are summarized in the table
given in figure 4.3-1 and indicate that - for the reasons mentioned above -
the optimal primary secondary mass flow ratio of 9 proposed in 4.1.1 had to
be raised to about 105.

4.-3.1.4. Dimensions,

The dimensions of the test module are listed in the table given in figure
4,3-2. These dimensions correspond to the results of the optimization
discussed in subsection 4.1.2.1 with the exception of the evaporator length
and hence the dimensions of the ceramic insulation layer.

As the design of the test module was completed before the optimization, the
importance of the evaporator length was not yet fully appreciated at that
time. The length was restricted to 9.1 m in view of the maximum building
height in our laboratory.

Again considering the aim of these investigations this is not considered of
vital importance.

4.3.2. Water/steam loop.

4.3.2.1. General.

Figure 4.3-3 gives a flowsheet of the DMSP bayonet tube steam generator
test facility. The left part of the figure shows the molten salt loop. This
loop is identical to the loop used for the FLiNaK heat transfer measure-
ments described in section 3.2. The right part of the flowsheet shows the
water/steam loop comprising the feedwater supply system and the heat sink.
Both loops are thermally connected by the test module, i.e. the single-tube
experimental steam generator.

- 48.17 -

4.3.2.2. Feedwater supply system.

At rated conditions feedwater should enter the steam generator at a tempe-
rature of 280 %C and a pressure sufficient to provide for a steam exit
pressure of 18 MN/m? .

Demineralized and deaerated watexr is obtained from a central make-up tank
serving several test facilities in the laboratory. The water stored in this
tank is kept at a pH close to 7 and a conductivity below 20 uS.

The feedwater is pressurized by a duplex piston pump of variable capacity
and subsequently preheated in a counterflow oil-heated preheater. The
heated o0il is obtained from a separate oil-fired heater. The heating oil
temperature can be adjusted to provide the kind of variation of feedwater
temperature with secondary mass flow typical for a steam turbine plant.

A small pressurizer filled with nitrogen is provided to damp the fluctua-
tions due to the piston pump.

During pre-operational testing of the facility the steam generator showed a
certain tendency to develop flow oscillations at start-up. Therefore an
adjustable restriction in the form of a pneumatically adjustable valve was
provided downstream of the pressurizer. The pressure ahead of this control
valve was maintened at a constant value of some 1.5 MN/m? above system
pressure so as to provide an additional stabilizing single phase pressure
drop in the system.

4.3.2.3. Heat sink.

The superheated steam leaving the steam generator at about 18 MN/m? and
540 Oc is first throttled to atmospheric pressure by a pneumatic control
valve and subsequently cooled by a desugerheating spray obtained from the
same make-up tank to approximately 150 YC. This low pressure, low tempe-
rature steam is led into a condenser, whence the condensate is returned to
the make-up tank, thus closing the water/steam loop.

4.3.3. Instrumentation and control.

Distinction can be made between loop operational instrumentation with
control panel display and experimental instrumentation pertaining to the
experiments proper and connected to a data acquisition system with punched
tape output. A number of instruments, such as those for flowrate, pressure,
and some of the temperatures are used for both purposes.

4.3.3.1. Loop instrumentation and control.

Figure 4.3-4 shows an operational instrumentation diagram. The controlled
variables of the system are:

® salt inlet temperature

feedwater flow

feedwater inlet temperature

feedwater (pressurizer) pressure

outlet steam pressure

waste steam temperature after pressure reduction

The salt inlet temperature is controlled as described in subsection 3.2.2,
i.e. by adjusting the electrical power supplied to the main heater to the
amount of heat transferred in the steam generator (load following).

The feedwater flow is measured by an orifice with integrated pneumatic
differential pressure transmitter. The signal of this transmitter is
converted to an electrical input signal for an electronic PI controller
with manual setpoint adjustment.

- 4,18 -

The controller output signal is reconverted into a pneumatic signal
actuating a control valve in the bypass across the feedwater pump *). The
feedwater inlet temperature is controlled indirectly in order to avoid
stability problems resulting from the large distance (some 60 m) between
the oil heater and the preheater.

The fact that the preheater proved to be of ample capacity, resulting in a
very small temperature difference between the oil inlet and feedwater
outlet temperatures, offered the possibility to avoid this problem by
remote manual adjustment of the oil heater control setpoint. In this simple
way a nearly constant feedwater temperature could be obtained, as only
small adjustments of the oil heater control setpoint were required to
restore the feedwater temperature to its original value even for large
changes in power.

The feedwater (pressurizer) pressure was controlled by a pneumatic PI
controller positioning the inlet throttle valve so as to adapt the amount
of throttling to the load.

For controlling the outlet steam pressure a pressure signal is picked up at
the outlet of the steam generator and transmitted to a pneumatic PI
controller governing the throttling valve downstream of the steam generator.
For controlling the waste steam temperature a temperature signal is picked
up downstream of the spray cooler and transmitted to a pneumatic PI
controller governing the spray water supply valve.

4.3.3.2. Test instrumentation.

4.3.3.2.1. Instrumentation for steady state and transient experiments.

As mentioned before the aim of these experiments is to provide information
on the temperature distribution in the steam generator for comparison with
the results of the computer programs discussed in sections 4.4, 4.5 and
4.6.

This means that local pressures and temperatures should be determined in
addition to the overall conditions of the steam generator.

The overall conditions measured and the instruments used for this purpose
are:

at the primary side of the steam generator:

- FLiNaK mass flow (venturi flow meter: cf. section 2.2)
- FLiNaK inlet and outlet temperatures (Pt-thermometers)

at the secondary side:

- feedwater mass flow (integrated-orifice flowmeter)

- feedwater temperature (Pt-thermometer)

- feedwater pressure

- outlet steam pressure

- pressure drop across
the steam generator (diaphragm pressure-differential transmitter)

- outlet steam temperature (Pt-thermometer)

(Bourdon pressure transmitters)

Unfortunately only a limited amount of internal instrumentation for local
measurements was possible due to the following reasons:

- extrgme conditions: a highly corrosive salt at a temperature of about
B25:"C

ok This double conversion was imposed by the availability of equipment in
the author's laboratory.

- 4,19 -

- complex geometry of the bayonet tube
- the necessity to avoid disturbances in the evaporator flow that could
prematurely start and thus unduly affect the boiling process.

The geometry of the bayonet made it impossible to tap secondary pressures
at more points than at the in- and outlet of the water/steam channel, as
the salt channel completely surrounds the bayonet.

As regards the temperature distributions, thermocouples were installed at
eighteen levels in the outer (salt) gap for measuring the primary tempe-
rature profile. The necessity to avoid flow disturbances in the evaporator
tube prohibited the installation of thermocouples in the central tube.
Therefore the only temperature profile to be measured at the secondary
side was the temperature distribution in the superheater gap, where a
total of 25 thermocouples was installed. The location of the various
thermocouples in the steam generator is shown in figure 4.3-5.

While this may seem rather poor, a method will be discussed in subsection
4.4.3.2 by which the enthalpy profile in the evaporator can be estimated
fairly accurately from the measured salt and steam temperatures, permitting
a detailed comparison of experimental results and computer simulations.

4.3.3.2.2. Instrumentation for the stability experiments.

As will be discussed in subsection 4.5.1 verification of the analytical
simulations of the bayonet tube hydro-dynamic stability behaviour required
measurements of the response of the total secondary side pressure drop to
harmonic perturbations in the feedwater mass flow rate.

The only instrumentation needed for these measurements proper consisted of
a fast flow meter for the secondary inlet mass flow rate and a differential
pressure meter for measuring the secondary side pressure drop variations.
The latter instrument was the same as used in the other experiments,
described in subsection 4.3.3.2.1.

The fast flow meter, installed in order to avoid uncertainties due to
dynamic effects in orifice-type mass flow measurement, was a turbine flow
meter with excellent dynamic properties (time constant v = 0.05 s).

4.3.3.2.3. Calibration..

The calibration of the different instruments will be discussed in the
order of their appearance in subsection 4.3.3.2.1.

According to the analysis of section 2.2 the accuracy of the venturi flow
meter amounts to 4% of full scale. The only part of the venturi prone to
drift, viz. the differential pressure meter, was repeatedly calibrated
against a dead weight tester (a special instrument for calibration of
pressure transmitters). This instrument was applied for the calibration of
all pressure meters in the system.

The platinum resistance thermometers had been calibrated by the manufac-
turer and calibration sheets were included in the delivery. To avoid
sealing problems these thermometers were inserted in the loop in thermo-
wells welded in the wall of the tubing. The additional heat resistance
between the thermometer and the thermowell is taken into account by adding
0.15 0c to the measured values after applying the inaccuracy correction of
0.1 O¢ given by the manufacturer for the thermometers proper. A check
after the measurements showed no noticeable drift from the data given in
the calibration sheets.

The flowmeters for the feedwater mass flow rate were calibrated by the
"bucket and weight" method (the time for a certain amount of water,
determined by weighing, to flow into a vessel is measured). In this way
the total chain of instruments between flow and reading of the electrical

- 4,20 -

instrument is calibrated at once, thus avoiding accumulation of errors,
possible if all links are calibrated separately.

The thermocouples for local temperature measurement were calibrated against
the pt-resistance thermometers in the salt channel during isothermal
operation of the loop, as discussed in section 3.2.

4.3.4., Operational procedures.

It seems useful to mention some operating experiences gained during the
experiments on this special type of steam generator.

In the first place the start-up is completely different from the customary
procedure. In normal steam generators the procedure starts with the
circulation of the feedwater at a low pressure. Then ignition of the
burner follows and generation of steam commences (in sodium heated steam
generators the temperature of the primary fluid is raised). The desired
conditions are reached by simultaneous raising of the outlet steam tempe-
rature and the pressure. ,

For the salt-heated bayonet tube this scheme fails because of the high
melting point of the salt. It is not possible to start the heat transfer
gradually as the system must be filled at a temperature a sufficiently

far above the melting point. Failure to observe this margin would not

only give rise to the danger of plugging the channels by frozen salt,

but also cause intolerable thermal stresses.

Therefore the primary fluid must be in circulation before water enters the
steam generator. Now the stress problem is reversed, as it is equally
disastrous to inject feedwater into the steam generator that has attained
a uniform temperature of about 600 Oc. To solve these problems a start-up
boiler was applied, capable of delivering a small mass flow (10% of the
maximum capacity) of steam at a lower pressure (7 MN/m?) . This steam,
superheated to 280 Oc, was fed into the steam generator to cool down the
central tube. The much smaller heat transfer coefficient of steam compared
to feedwater ensured a slow and smooth cooling of the interior of the
bayonet. When the temperatures were stabilized to some degree, the
pressure of the steam was gradually raised, causing first saturated and
then increasingly wet steam to enter the steam generator, until at last
zero quality (water) was obtained at the entrance. Careful execution of
this procedure ensured a trouble free start-up.

During the first steam generator tests it became clear that an additional
restriction in the feedwater line would be required to avoid the occurence
of spontaneous oscillations. After installation of this restriction stable
operation of the steam generator proved possible over the entire range of
interesting conditions.

The cause and significance of this so-called loop-instability will be
discussed in subsection 4.6.2.2.

Shutdown proved a more delicate operation than start-up. The procedure
followed was the reverse of the start-up procedure. Nevertheless sometimes
oscillations occurred, during which the top temperature (exit of the
central tube) fluctuated severely, in some cases over 100 Oc (cf. figure
4.3-6) , indicating that saturated water reached the thermocouples located
at the exit of the evaporator tube.

This example of loop instability (cf. figure 4.6.2.2) was probably

triggered off by flow-pattern transitions in the two-phase region (cf.
BOURE [4.1-11 ]).

- 4,21 -

l

4.4. Steady state.

4.4.1. Analysis.

4.4.1.1. Additional assumptions.

The balance equations in subsection 4.2.2. contain a minimum of simplifying
assumptions. However not all the simulations reported here require these
complete equations. Furthermore the development of the different simulation
programs took place over a period of several years, in the course of which
increased insight and experience in simulation techniques sometimes led to
a different approach.

The following additional assumptions were made for the steady state
analysis:

a) equal mean velocities of gas and liquid i.e. homogeneous flow (s = 1)
b) neglection of the pressure terms in the energy equation

c) a value of k = 0 for the Bowrind constant, i.e. no net wvapour
production in the subcooled boiling region.

ad.a) Experimental evidence shows that the slip s decreases rapidly with
increasing pressure. This effect is often explained by the decrease
in buoyancy of the bubbles, due to the decreasing difference in
density between the liquid and the gas phase. This explanation,
however, appears incomplete for the following reasons: the buoyancy is
proportional to the difference in density between liquid and gas. This
difference decreases far less rapidly with pressure than the slip
values given by JONES [ 4.2-12 ] (the former by a factor of 0.75, the
latter by a factor of 0.25 between 8 and 18 MN/m?). To the author's
opinion part of the rapid decrease in slip, is due to the rapid
decrease in surface tension with increasing pressure.
It is this surface tension which mainly determines the bubble size
(c£. WISMAN [ 4.4-1 ]). The resulting much smaller bubbles at higher
pressures have a greater specific flow resistance, i.e. do not rise as
fast as larger bubbles, and are more uniformly distributed by the
turbulence in the fluid, thereby decreasing the effects of non-uniform
radial void distribution. These two effects might offer a more
complete explanation for the lower slip values observed at higher
pressures.

ad.b) TEN WOLDE [ 4.1-9 ] shows that in high pressure steam generators the
pressure terms in the energy balance amount to only 0.1% of the total
and may therefore safely be neglected.

ad.c) The assumption made in subsection 4.2.3.2 that the Rohsenow heat
transfer correlation, developed for saturated boiling, will also be

valid for the subcooled region implies that taking k . = 0 for
Bowring

the entire subcooled region will only have a limited local effect. The
fact that the void fraction and the velocities thus obtained for this
region differ from the true values will not affect the amount of heat
transferred to the mixture, nor the enthalpy distribution.
Consequently the conditions in the downstream regions will be
predicted correctly.

- 4,22 -

4.4.1.2. Modified equations.

With these additional assumptions the two-phase balance equations for
steady state simplify to (cf. TEN WOLDE [ 4.1-9 ]):

- mass balance:

"G = constant (4.4-1)

- momentum balance:

The pressure distribution was considered of little interest because of
its negligible effect on mass flow rate in a once-through steam
generator. Therefore the momentum balance is omitted from the steady
state analysis.

- energy balance:

)

For the primary fluid, where the specific heat is taken constant, the
enthalpy can be written as:

h=c? ; (4.4-3)

Substitution of this equation yields:

G c (4.4-4)

3% _
dz q

>0

Set of equations.

The total set of equations to be solved in the steady state is formed by
the energy balances for the three different channels (cf. figure 4.1-1):

- primary channel:

¥p %
e (4.4-5)
P
- superheater gap:
G TsH _ B q Jsu (4.4-6)
8 8z 9p>SH Ay, SHOEV " A
~ evaporator channel:
Tev_ . e —
325,  SHOEV A__

note: all axial coordinates are positive in the respective flow direction.

- 4,23 -

The heat fluxes are given by:

Usu =~ ¥posu Pp ~ Ps (4.4-8)

and:

Ispory ~ Ksporv Vs T Ymv S B2

In keeping with common engineering practice the overall heat transfer
coefficients refer to the outer tube surfaces.

4.4.1.3. Solutional procedure.

This set of first order differential equations is solved by direct inte-
gration. More or less for historical reasons the author has selected this
procedure despite its infrequent use in heat exchanger analysis, caused by
its inherent numerical stability problems in pure counterflow applications.
Stability analysis of the present case, however, proved that, provided the
following condition:

+
kp—SH % . *su-ev Osn & kE:SH O, su-Ev Osn

A . A G
o %o o Pev Cmv mv Bsu ®su Csm

> g

is fulfilled, only a very weakly instable component, not posing problems,
remains in the solution. For integration from top to bottom (cf. figure

4.1-1, Gp and GEV negative, GSH positive) the stability criterion mentioned

above will always be fulfilled, due to the weak thermal flux of the super-
heater steam. Against this advantage of direct integration stands the
disadvantage that the boundary conditions for both primary and secondary
sides are prescribed at the bottom of the steam generator. This
necessitates an iterative procedure following an initial guess of the
conditions at the top of the steam generator. In spite of this iterative
approach downward integration has proved to be an efficient method,
requiring only five iteration steps to converge as compared to ten
iterations for the CSDT method applied by TEN WOLDE [ 4.1-9 ] for a pure
counterflow once-through steam generator.

The integration algorithm actually applied is the HEUN predictor corrector
method (cf. e.g. LEE [4.4-2 ]). This algorithm reduces the accumulation of
rounding-off errors while allowing application of relatively large inte-
gration steps. Figure 4.4-2 shows a simplified flow sheet of the program.
For a detailed description the reader is referred to IPENBURG [ 4.4-3 ].
Figures 4.4-3 and 4.4-4 show typical results of the program: a print-out
and a plot respectively. In view of the direction of integration the origin
of the axial coordinate has been located at the top of the steam generator.
For reasons of consistency this choice, though somewhat illogical from the
point of view of geometry, has been maintained throughout this thesis.

4.4.2. Experiments.

4.4.2.1. Data acquisition.

To reduce the effect of random errors all measuring points were scanned ten
times for each steady state measurement by means of a H.P. data logger and
the output was transferred to punched tape. These tapes were read into the
computer (IBM 370/158) off line and processed by means of a special data
reduction program (MEANTAB), yielding the average millivolt value for each

- 4.24 -

measuring point.

Excessive deviations (> 1.5 o) were automatically deleted and signaled in
the output.

The obtained average values for all measuring points were transferred to a
special purpose data processing program (SMEBT) for:

® transformation of millivolt values into the associated physical values

® deriving evaporator data from the salt and superheated steam measure-
ments

® tabulation and plotting of data as shown in figures 4.4-4 and 4.4-5
respectively.

The second point requires some elaboration.

The original idea was to obtain evaporator temperatures or qualities from
energy balances for small sections of the steam generator. Assuming perfect
insulation such a balance states that the heat transferred to the evapora-
tor equals the heat removed from the salt decreased by the heat retained in
the steam: :

Q (4.4-10)

ev - % ~ 9sm
The two right hand side terms were to be determined from the measured
temperature distribution in the primary and superheater channels by

applying steady state energy balances to small sections of the steam

generator. The amounts of heat released by the salt and retained by the
steam in an element of length A% (cf. figure 4.4-6) are given by:

Q =G _A_c_ (9 S OF e (4.4-11)
P p P P out pin
p = S5 By (hgy - bgy ) (4.4-12)
out in
respectively.

The amount of heat absorbed in the evaporator is given by:

Sy G A (h - ) (4.4-13)

As motivated in subsection 4.4.1.1 expansion work has been neglected.

The boundaries of the sections have been chosen at the locations of the
thermocouples (0.5 m apart) with the exeption of the lowest section that
has its lower boundary at the resistance thermometer in the feedwater inlet
(cf. figure 4.3-5). ,

Combination of equations (4.4-10), (4.4-11), (4.4-12) and (4.4-13) yields
the final expression for the evaporator enthalpy at the top of a section:

G AC (0 = 9%.. ) =GA_(h - h )
h = h + PPP pout pin B SHout SHin
EV EV,
out in G A
s EV

(4.4-14)

Starting at the feedwater inlet repeated application of this formula to the
successive sections should have yielded the complete enthalpy distribution

in the evaporator and hence - in combination with the local pressure - the

temperature or quality distribution in this channel.

- 4,25 -

Unfortunately this scheme failed due to insufficient accuracy of the
FLiNaK temperature measurements. Application of equation (4.4-11) yielded
errors in Qp of up to 50%. Therefore the alternative described below

had to be applied.
The total amount of heat transferred from the salt to the water/steam side
could be determined very accurately from:

P _=¢__ (h -h ) (4.4-15)

thanks to the large difference in enthalpy and the accuracy of the Pt
thermometers located at the feedwater inlet and steam outlet.
The problem was to determine the distribution of this heat along the length
of the steam generator. The overall heat transfer coefficient from salt
channel to superheater gap could be assumed fairly constant along the
length of the steam generator, its only significant varying component being
the film coefficient in the superheater gap. This film coefficient varied
with steam temperature and mass flow. Thus the overall heat transfer
coefficient may be written as:
k sg = : (4.4-16)
B a+b £(¢) g(d)

The functions f and g were determined from the heat transfer correlation of
BISHOP (cf.subsection 4.2.3.2):

D

g, e %.0,0073 Re0+886 pr0.6 (1 + 2.76 =) (4.4-17)
From this equation it follows that:
0,886
f (¢m) = (¢m) (4.4-18)
while g(¢#) turns out to be proportional to:
0.6
¥ (4.4-19)
,0.886

For steam of 18 MN/m2 this term can be approximated to within 1% by a

polynomial:
g(®) = Ry % By d + 8 92 4+ P, 93 (¢ in Y¢) (4.4-20)
where PO = 12.44
_2
P1 = - 6.47 10
_L
P2 = 1.17 10
_b
P, = - 0.
3 0.07 10

for a temperature range from 350 Oc to 700 %c. The total amount of heat
transferred from the salt to the water/steam side can now be found by
integrating:

- 4,26 -

= o = d_ - 9 L
Ytot =~ fms. o P b Xosgn T D5l Sifgl.g
out in 0
B fL (g - 9) as (4.4-21)
° 4 a+b f(¢m) g (%)

The only unknowns in this equation are a and b. These two unknowns were
determined from a number of steady state measurements by minimizing:

2

- P ) (4.4-22)
meas, calc,
i

As this is a non-linear regression problem a special optimization routine

had to be applied. This optimization yielded the following values:

3.42
0.308

a

As apparent from the table in figure 4.4-7 substitution of these values
into equation (4.4-21) yields very accurate results for most of the
measurements. Introducing a correction factor fc for each measurement to

adapt the total power determined from the latter equation to the power
actually transferred according to equation (4.4-15), the local heat flux
between salt and superheater channel may be determined from:

Ysgn = Te Xorem (O = d5p) (4.4-23)

Substitution of this heat flux and of equations (4.4-12) and (4.4-13) into
equation (4.4-14) vyields:

g =9 L -
nDO fC kp+SH ( . SH) A GS As(hSH _h . )
hEV = hEV + out in
L+A0L '3 Gs A

o (4.4-24)

Application of this equation for the successive sections starting at the
feedwater inlet yields the enthalpy distribution in the evaporator. The
temperature or quality distribution can be derived from this distribution
provided the pressure distribution is also known. As in the present case
only the pressure at the feedwater inlet and steam outlet could actually be
measured, an approximate pressure distribution had to be derived. A rough
analysis showed that 80% of the pressure drop was concentrated in the
superheater gap due to the high velocities occurring there. The remaining
part was assumed to be uniformly distributed along the length of the
evaporator.

In view of the small total pressure drop values (< 3 bar at the maximum
secondary flow rate) the effect of this approximation was very small.

4.4.2.2. Test program.

The conditions for the reported experiments are summarized in figure 4.4-8.

- 4,27 -

4.4.2.3. Experimental results.

The results of these experiments are given in subsection 4.4.3, where they
are compared with computed temperature and quality distributions (cf.
figures 4.4-9a through 4.4-9k).

4.4.3. Evaluation of results.

Comparison of the analytical and experimental results for higher feedwater
flow rates (¢m > 0.035 kg/s =~ 50% load) shows excellent agreement. For

lower feedwater mass flow rates analysis and experiment tend to differ.
Examination of figures 4.4-9k and 4.4~9j indicates that these differences
are the result of underestimation of the heat transfer coefficient in the
superheater gap. The values of the local mass fluxes occurring under those
conditions (G < 325 kg/m?s vs G = 605 kg/mzs at full load) are well below
the range of validity of the heat transfer correlation applied (equation
(4.2-21); range: 660 < G < 3280 kg/m?s).

Extrapolation below G = 325 kg/mzs is clearly not justified and hence more
accurate predictions would require new heat transfer correlations valid for
this lower range of mass fluxes. The preliminary optimization discussed in
IPENBURG [ 4.1-3 ], however, yields a mass flux in the superheater gap of
1019 kg/m?s at full load and correspondingly higher values at part load,
thus obviating the need for new correlations except for very low loads

(< 25%).

For loads ranging from 25% to full load the applied set of correlations is
found to be adequate and thus the BASTA program proves a suitable tool for
optimization purposes and part load prediction.

A remarkable property of the bayonet tube concept is evidenced by the
figures of the various part loads: the steam outlet temperature is almost
completely independent of load. This is easily understood, by visualizing
this temperature as result of "equilibrium" between the salt and feedwater
inlet temperatures. This property is completely at variance with the
operating characteristics of other steam generator designs, where the
steam outlet temperature normally exhibits a strong inverse relation with
load. In the present case the steam temperature will follow the salt inlet
temperature, a dependence that could well be used for controlling the
steam outlet temperature, thus obviating or reducing desuperheating usually
applied for this purpose.

4.5, Transients.

4

.5.1. Introduction.

A significant number of mathematical models for simulation of the transient
behaviour of once-through steam generators had been published in the open
literature prior to the steam generator test program described in the
present thesis. Some of these were (multiple) lumped models, e.g. SANATHANAN
[4.5-1 ], others distributed paraheter models, e.g. TEN WOLDE [4.1-9 ].

It appears worth while here to point out that the difference between these
two groups is gradual rather than one of principle, as the inevitable
discretization of the partial differential equations occurring in the
solution procedure of the distributed parameter models results in finite
difference equations that are in fact overall balances for lumps the size
of which is determined by the spacing. Except for some earlier models, e.qg.
HOLD [ 4.5-2 ], all models found in literature solve the original, non-
linear equations, linearization being inadequate for predicting large

-~ 4,28 =

transients. For a review of the various approaches, with particular
emphasis on distributed parameter models, the reader is referred to BRUENS
[4.5-3].

None of the models available in literature was found readily adaptable to
the complex geometry of the bayonet tube steam generator and a new model
had to be developed for this purpose. Previous steam generator transient
simulations at the author's laboratory had all been performed on hybrid
computers. At that time, however, the rapid development of digital computing
hardware heralded a shift from hybrid to purely digital simulation and

it was therefore decided to follow the latter route. However, in order to
take full advantage of the experience gained in hybrid modeling it was
decided to adopt basically the same solutional technique by applying a
special language: Continuous System Modeling Program (CSMP), developed for
using the analog approach on a purely digital computer (cf. [4.5-3 ]). Due
to causes discussed later this CSMP program, called DYBRU, yielded an
undesirably high ratio of computing to process time. In an attempt to
improve this ratio a new transient model was developed from a program
originally generated for simulating the bayonet tube steam generator's
hydro-dynamic stability behaviour in the time domain (cf. subsection
4.6.2.3). This model utilizes the Lagrangian description of fluid dynamics,
i.e. it describes the behaviour of fluid particle travelling from inlet to
outlet. In this respect it differs from the models mentioned earlier in
this introduction which are based on the Eulerian description, where the
conservation equations are formulated for a stationary control volume (lump
or grid step). :

In the remainder of this section both approaches will be described and
their results compared to measurements. In order to explain the limited
effort spent on the development, verification and improvement of these
models their limitation to the bayonet tube geometry should be emphasized
and contrasted with the aim of general applicability for part of the work
on stability reported in subsection 4.6.3.

WP 5 Analzsis.

4,.5.2.1. Modified equations.

For the transient models the same simplifying assumptions have been made as
for the steady state model (listed in subsection 4.4.1.1). The basic con-
servation equations given in subsection 4.2.2 hence simplify to (cf. TEN
WOLDE [ 4.1-9 ]:

mass balance:

Ty + Ly =0 ; (4.5-1)

= b "
p{_v+v.?_x}=_§_a_£§_¢pg (4.5-2)

( - for upward flow, + for downward flow)

* 4
) In case op two-phase flow the upper bar denotes mixture values as

defined in subsection 4.2.2.2.1.

- 4,29 -

energy balance:

o { .} + v R0 (4.5-3)

4.5.2.2. Solution in Eulerian codrdinates (DYBRU).

The equations underlying this approach differ from the set of equations
given in the previous subsection because of an additional assumption: the
mass storage effect is neglected for both single and two-phase flow,
reducing the mass balance (4.5-1) to:

@
I

G(t) (4.5-4)
where:
G = 5 v

~

0 a0, | ;
This assumption, implying that not only 5%-but also 3¢ 1S zero, introduced

as part of the overall effort to reduce computing times but evidently
unrealistic for the two-phase mixtures under consideration, was dropped
from subsequent dynamic models for the secondary flow.

The basic solution technique applied here is identical to the one applied
by TEN WOLDE [ 4.1-9 ] on a hybrid computer, viz. CSDT (Continuous Space
Discrete Time).

The set of partial differential equations in z and t is transformed into a
set of ordinary differential equations in z by replacing the differentials

Ty by finite differences. The analog part of a hybrid computer is perfectly

suited for integrating these ordinary differential equations along the
length of the steam generator. The problem of avoiding numerically unstable
integration is solved by consistently integrating the channels in the
direction of flow, while assuming the conditions in adjacent counterflow
channels to remain constant (cf. figure 4.5-1). Iteration starts by
assuming arbitrary conditions in the superheater gap and integrating the
evaporator and salt channel from inlet to top. Then the process is reversed,
with the superheater being integrated in the flow direction starting from
the top, while conditions in the evaporator and salt channels are assumed
constant. This process is repeated until the temperature at the top remains
constant within a certain limit.

This approach was implemented in CSMP (Continuous System Modeling Program) .
CSMP was developed by IBM to provide a sophlstlcated digital method for
simulating analog systems with the objective to combine the advantages of
both methods.

To make its application as simple as that of an analog computer a
significant number of actions are performed automatically by the system,
e.g.

- integrating step size is selected dynamically so as to obtain the
specified accuracy

- in a system with a number of integrators, an iterative module is
assembled automatically. This module is repeatedly executed for each
time step so as to approximate simultaneous integration as closely
as possible, be it at the expense of an increased number of operations.

- 4,30 -

For our application, these automatic system actions proved disadvantageous;
though simplifying operation, they give the system a certain degree of
rigidity hampering adjustment to special requirements.

For example in the CSDT method, where integration is performed with respect
to the axial codrdinate instead of time, free selection of integration

step size is not possible as the boundaries of the different flow regions
have to coincide with the end of a step. Special measures required to
prevent free selection of step size in the neighbourhood of region
boundaries, not only increased computing time but also severely complicated
programming.

Hence the expected advantages of easy and clear programming proved to a
large degree absent, whereas the drawback of increased computing time
proved much worse than anticipated (computing time = 100 & 120 times

real time), leading to the abandonment of this approach. For further
details the reader is referred to BRUENS [ 4.5-4 ].

4.5.2.3. Solution in Lagrangian codérdinates (DSTS).

For a solution in Lagrangian codrdinates the equations (4.5-1) through
(4.5-3) have to be transformed to take account of the fact that in a
Lagrangian description a moving codrdinate system is assigned to each
fluid particle, with the origin located in its center.

The following relationship holds between a time derivative in the
Lagrangian and one in the Eulerian system:

9, _ (90 9p, 9z _ 9p. 90
G = Gele Y GPe e - Gele VS (4.5-5)

where v is the velocity of the particle under consideration.
Combination of this expression with the mass balance of equation (4.5-1)
yields:

(2es), = = 0 (1) (4.5-6)

Applying a similar process to the energy balance of equation (4.5-3)
yields:

3h _goO
(at)L - (4.5-7)

If pressure effects on the density are neglected as assumed, the
following relationship holds between variations of p and h:

§ p==—4¢0p (4.5-8)

Combination of equations (4.5-6), (4.5-8) and (4.5-7) yields:

(), 90 (BhE Top g e

BE'L " 0h ot'L T ShoA . P o SRS
or after rearranging:

v __1 390

93z p2 9 A (4.5-10)

-4.31 -~

For two-phase flow, where as derived in Appendix 4C:

0 et L (4.5-11)
oh pgpl r

equation (4.5-10) yields:

- P

P
o % (4.5-12)

l g
0z ¥

0]
gpl a

An interesting aspect of equations (4.5-10) and (4.5-12) is that, though
valid under dynamic conditions, they do not contain time derivatives.

The dynamic behaviour of the bayonet tube steam generator is determined by
observing the behaviour of a number of particles distributed along the
length of the channels on their way from inlet to outlet.

By integrating equation (4.5-12) along the length of the channels, starting
with the prescribed velocity at the inlet, the velocity distribution in the
steam generator can be determined. Then the velocity of all observed
particles is known. It is now assumed that during a small time step these
velocities remain constant, thus enabling determination of the approximate
location of the particles at the end of the time step. During this time
step heat has been transferred to these particles. The increase in enthalpy
of each particle is determined by application of equation (4.5-7), where g
is the average heat flux along the distance a particular particle has
travelled during the time step. The location and enthalpy of each particle
is registered in a special table. The heat flux distributions along the
length of the channels based on these new conditions are derived and the
process can be restarted for the next time step. At each time step a new
particle is assumed to enter at the inlet of a channel to replace particles
leaving the channel at the end. Figure 4.5-2 shows the displacement of
particles during a time step.

The initial steady state conditions may be derived by application of
approximately the same algorithm, as can be understood by keeping in mind
that a steady state may be considered the response to a zero disturbance.
As the conditions at the inlet are known it is possible to derive enthalpy
and location at the end of a time step of the particle just entering the
channel at the start of that time step (cf. figure 4.5-3). Now the con-
ditions of a particle somewhat downstream of the inlet are known and based
on these conditions its displacement and enthalpy rise during the next time
step can be derived. At the start of this time step a new particle enters
the channel and, due to the steady state conditions, copies the behaviour
of his predecessor. This process is repeated until the first particle
leaves the evaporator. Now the conditions are known for a complete set of
particles and the simulation of dynamics as described above may start. The
problem of interaction between the channels, ignored so far is solved in
the same way as discussed in subsection 4.5.2.3, i.e. by iteration.

During the first iteration the heat fluxes are based on assumed temperature
distributions which are improved during further iterations in the fashion
shown in figure 4.5-1.

For engineers the method of following particles holds the attraction of
transparency. However, some inherent problems were encountered in the
implementation of this method:

- 4,32 -

- an inherently uneven distribution of particles along the length of the
secondary channel, due to the change in fluid velocity caused by
evaporation and thermal expansion. This effect, already a disadvantage
at the high pressure of interest here, (for p = 18 MW/m2 there is a
ratio of approx. 6 between particle distances at inlet and outlet of
the secondary channel) would cause a prohibitive rise in computing
time with decreasing pressure. This rise results from the enormous
number of particles required in the preheat and early two-phase
region for obtaining an adequate particle distance in the superheat
region

- the addition of special routines to the program to account for
particles crossing boundaries of flow or heat transfer regions during
the time step.

For further information the reader is referred to PRINS [ 4.5-5 ].
In view of the above mentioned problems this approach was found less
favourable than originally expected and hence was also abandoned.

4.5.3. Critique of the methods employed.

In retrospect the approach of developing special purpose programs for
describing bayonet tube steam generator dynamics was far from optimal.
Apart from the high computing times characterizing the final versions of
both programs the essential objection seen by the author is the unfavour-
able ratio between the numbers of test runs and production runs. This
unfavourable ratio is likely to be inherent to a research laboratory
studying one-of-a kind objects, but was aggravated in our case by the
complex formulation of the governing equations and the interconnection
between their formulation and solution.

Rather than following such an ad-hoc approach one should, from the very
beginning of an investigation such as the present one, look for a uniform
mathematical description applicable to a wide variety of dynamical problems.
In the author's opinion such a description is presented by the state-space
approach, e.g. discussed by ZADEH [ 4.5-6 ] . In this approach any dynamic
problem is transformed to a set of first order ordinary differential
equations:

== if (x) + g-(u) (4.5-13)

where X is the so-called state vector and u the vector of boundary condi-
tions.
A linearized version of this equation reads:

— = |a| x + |B| u (4.5-14)

In recent years subroutines have been and are being developed for the
solution of such sets of equations (cf. e.g. HOFER [ 4.5-7 ]).

The general applicability of these subroutines justified a considerable
effort for their development by teams containing skilled mathematicians,
thus yielding high quality and reliability.

In summary it is the author's present opinion that dynamic problems - such
as that of the bayonet tube steam generator - should be described in state
variables, yielding a set of first order ordinary differential equations in

- 4.33 -

time. The resulting simulation programs should contain separate modules
for the ad-hoc formulation of these equations and for their solution, the
latter consisting of standard routines.

In this way the investigator, rather than devoting a significant effort to
the design and testing of computer programs, may concentrate on his
specific analytical and experimental problems.

4.5.4. Experiments.

4.5.4.1. Data acquisition.

During the transients all (32) measuring points were continuously scanned
in succession (0.45 chan/s). To obtain a number of profiles (all values

at specific intervals in time) these data had to be processed by a special
computer program (MASCARA) developed in the course of an earlier project
(cf. GOEMANS [ 4.5-8 ]). The transformation of these data to physical
values was performed in roughly the same way as for the steady state
experiments. Determination of the temperature and quality distributions in
the evaporator from these data, however, posed additional problems con-
nected to storage effects in the evaporator. Due to the varying void
fraction and the resulting variation in specific mass of the mixture, the
two-phase region has a certain mass storage capacity *).

Following a drop in inlet mass flow rate it will take some time to
displace the excess mass present in the evaporator tube and consequently
to reduce the outlet mass flow rate to the reduced inlet mass flow rate.
This dynamic behaviour complicates the formulation equivalent to equation
4.4-24 for the evaporator.

The heat released from the salt was determined in the same way as for the
steady state experiments from equation 4.4-23, be it that the value of the
correction factor fc was determined in a different way to be discussed

later. To determine the amount of heat accumulated in the steam *%),
equation 4.4-12 had to be extended with a dynamic term to:

5h

QSH = Gs ASH (hSH - hSH, ) + AR ASH 0 32- (4.5-15)
out in

or, in terms of figure 4.5-4:

Qu., = A 2 {p + p + p +p }

3 {(h + h ) (h + h )} /4t

2 SH SH -

£, t,8-1 SHe 1,8 SHeoq,g-1
+ L A (G + G._){(n + h )
4 SH SH SH
£-1 g e  SBeg.y
- (h + h ) }/4s (4.5-16)

. 5
) Mass storage effects due to compressibility of water and steam have
been neglected as justified by TEN WOLDE [ 4.1-9 ].

**) Heat storage effects due to the heat capacity of the wall have been
neglected as justified by TEN WOLDE [4.1-9 1.

~ 4,34 -

Under the assumption - justified in section 4.2.4.1.1 - that slip in the
two-phase region may be neglected the local energy balances for the
evaporator are similar to equation (4.5-16):

0w At

EV gv 4 Pe-1,0-1 T

Pe1,2

1

2

L LR e S +h Mt

BS

1
8 Prv (Gt-1,2-1

(4.5-17)

The dynamic mass flux G(z) appearing in both equations (4.5-16) and
(4.5-17) could not be measured and therefore had to be derived from the
available data.

The decision to omit a steam outlet mass flow meter, made in view of the
well-known problems of accurately measuring steam flows at high pressures
and temperatures, was much regretted in later stages of the experimental
program. The experiences gathered during both transient and stability
experiments have convinced the present author that such a measurement
would have been very valuable for verifying the steam generator dynamic
simulations. Therefore such a device should be incorporated in any steam
generator test rig.

Assuming no slip, equation (4.5-12) may be used to determine the dynamic
axial velocity distribution by simple integration with respect to z.

An expression for heat flux g is obtained by combination of equations
(4.4-10), (4.5-16) and (4.4-23).

The latter equation, though derived for steady state conditions, is consi-
dered to retain its validity for the dynamic case because of the nearly

constant value of kp+SH' The second equation contains the superheater mass

flux G = P which is the result of the integration of equation

sH = "sE 'sB
4,5-12, This mutual dependence requires solution by an interative scheme.
In this scheme it is first assumed that the mass flux distribution at
time t was identical to the known distribution at time t-At. Based on this
assumption the heat flux distribution and - by application of equation
(4.5-7) - the enthalpy and thus the specific volume distribution at time t
are computed. Integration of the spatial derivative of the velocity v
combined with the local specific density yields a first approximation of
the mass flux distribution at time t. This procedure is repeated until it
converges and the final distribution is obtained, after which the next
step can be started.
As equation 4.4-21 is not wvalid during a transient and consequently can
not be used to determine the heat flux correction factor fC appearing in

equation 4.4-23, this correction factor was varied until the process
outlined above would yield a steam temperature at the top of the evaporator
channel matching the measured value.

Figure 4.5-5 shows a typical result.

w35 -

The values of the correction factor fC for the various time steps, also

given in this figure, show that the heat flux has to be adapted less than
10%. It may therefore be concluded that the axial distribution in the
evaporator thus obtained will be fairly accurate.

4.5.4.2. Test program.

Two different types of transient were investigated in the experiments,
viz. positive and negative stepwise variations of:

- feedwater mass flow (steam outlet pressure constant) *)
- steam outlet pressure (feedwater flow constant)

Limitations in the test equipment precluded fast variations in inlet
temperature and primary mass flow rate.

The table shown in figure 4.5-6 lists the conditions of the experiments
reported in detail by VAN LEEUWEN [ 4.5-9 ].

The first 10 experiments are stepwise feedwater mass flow variations, the
remaining 8 are stepwise variations in steam outlet pressure.

4.5.4.3. Experimental results.

Figures 4.5-7b through 4.5-7g (exp. no. 10 of figure 4.5-6) show the
effects of an (approximately) stepwise negative variation in feedwater
mass flow shown in figure 4.5-7a.

Figure 4.5-7b shows the resulting steam outlet temperature during this
transient. It confirms the remarkable flow independence of the steam
outlet temperature observed earlier for different steady state loads.
Within the steam generator itself, however, temperatures do vary, as
witnessed by figures 4.5-7c and d showing the variations in temperature at
various locations within the steam generator gap. The temperatures are
numbered 01 through 18. The table figure 4.5-8 relates these numbers to
the corresponding thermocouple numbers given in figure 4.3-5. It is clear
from these figures that superheater temperature variations increase with
distance from the steam outlet.

The behaviour of secondary inlet and outlet pressures shown in figure
4.5-7e clearly demonstrates the inadequate steam outlet pressure control
action mentioned above. Finally FLiNaK temperatures at four locations are
shown for the sake of completeness in figure 4.5-7f. Thermal inertia in
the primary system's heat supply, not designed to cope with such steep
transients, caused the FLiNaK temperatures to increase for a considerable
time after the stepwise feedwater flow increase, explaining the continuing
increase of superheater temperatures.

The responses given so far are the results of direct measurements. The
responses of evaporator conditions, derived in the way discussed in
subsection 4.5.3.1, are given in figure 4.5-7qg.

Similar results of a "stepwise" increase in steam outlet pressure from
16.2 to 18.3 MN/mZ, shown in figures 4.5-7h through 4.5-7m, indicate the

*) Control of the steam outlet pressure proved very difficult due to the
large pressure drop - down to atmospheric — across the control valve
(ef. figure 4.3-3).

In the author's opinion a high pressure condenser of ample capacity,
mounted directly behind the steam generator outlet and connected to
1t through a large duct, would have been required for adequately
maintaining a constant outlet pressure. The absence of this equipment
was due to fimancial reasons.

- 4.36 -

weak effects of such pressure variations. The increase in saturation
temperature propagates into the superheat region of the evaporator tube
and slowly decreases in the superheater gap. At the steam outlet hardly
any effect is noticed. For similar results of the other experiments
reference is made to VAN LEEUWEN [ 4.5-9 ].

4.5.5. Evaluation of results.

4.5.5.1. Introductory remarks.

Due to the problems discussed in subsection 4.5.2.4, encountered in
simulating the bayonet tube's transient behaviour, only a limited effort
has been made to simulate the experiments.

4.5.5.2. Comparison of DYBRU with an experiment.

To assess the accuracy of DYBRU e.g. experiment nr. 10 of figure nr 4.5-6
has been simulated. Figure 4.5-9 shows the result of this simulation.
Inspection of this figure yields two differences between the responses of
the top temperatures in experiment and simulation, viz.:

- in the simulation the reaction is faster
- in the simulation the final increase in top temperature is smaller

The faster reaction of the simulated top temperature can be explained by
the fact that the storage capacity of the two-phase region has been
neglected in the simulation. As a result of this assumption the transit
time through the evaporator changes abruptly following the change in
feedwater flow, whereas in reality the original velocities are maintained
for some time as a result of the storage capacity, causing a delayed
increase in enthalpy and thus in temperature.

The difference in final top temperature is caused by the limited validity
of the applied empirical relations, pointed out earlier in subsection
4.4.3 on partial load simulation.

4.5.5.3. Comparison of DSTS with an experiment.

In addition to the simulation of a stepwise change by DYBRU figure 4.5-9
also shows a similar result obtained by DSTS (Lagrangian approach). The
hysteresis immediately following the steps is simulated better by this
program, because of the fully implemented mass balance. The total response
however is much too fast compared to the experimental results. The
development of this program was discontinued for reasons explained above
before the cause of this deviation could be established.

4.6. Stability.

4.6.1. Analysis.

4.6.1.1. Introductory remarks.

As already stated in subsection 4.1.3.3 this study is restricted to the
so-called density wave or void flow instability *) of evaporators. The
physical cause of this type of instability is illustrated in figure 4.6-1

B
) In our case a system is considered stable if it 18 asymptotically

stable which means that following some small disturbance, the system
returns to its original steady state conditions.

- 4.37

showing the effect of a stepwise increase in the feedwater mass flow rate
for a heated evaporatcr tube with uniform and constant heat supply. An
increase in feedwater mass flow rate leads to an opposite variation in
mixture density: the same amount of steam (constant heat supply) is, as it
were, mixed with a larger amount of water. This density variation
propagates through the evaporator at approximately the speed of the
mixture. The dynamic storage of water, caused by the decrease in average
void fraction, delays the response of the velocities and hence of the
pressure drops further down-stream in the evaporator. As the frictional
pressure drop is concentrated near the end of the evaporator tube *)

where velocities are highest, the pressure drop response of the entire
tube will be delayed. Under unfavourable conditions this time delay
between disturbance (feedwater flow variation) and reaction (opposing
pressure drop variation) may result in a positive feedback causing a
diverging oscillation. As the propagation velocity of the density waves
approximates that of the mixture the frequency of this type of oscillation
is strongly dependent on the residence time of the water in the evaporator.
From the above it will be clear that density wave oscillations are more
likely to occur as the pressure drop is more markedly concentrated near
the end of the steam generator, i.e. at high exit qualities and/or lower
system pressures.

The purpose op the present chapter, namely to predict the onset of void-
flow stability for steam generators, may be achieved by either one of two
distinct approaches:

a application of an empirical relation obtained by curve-fitting of a
great number of experimental data

b simulation of the steam generator's dynamic behaviour by applying a
mathematical model

Both approaches have their advantages and disadvantages.

ad.a) The main advantage of this approach, taken e.g. by SHOTKIN [ 4.6-1 ]
and UNAL [ 4.6-2 ], lies in the potentially high accuracy.
Unal has developed a relation correlating the outlet quality of the
" steam generator at the stability limit with: the system pressure, the
L/d ratio of the heated channel part and the amount of subcooling Ah.
This empirical correlation predicts the stability limits within 6%
for 95% out of some hundred experimental data obtained on single tube
once-through steam generator models. The approach however also has
some significant disadvantages:

- it requires experimental evidence obtained on actual steam generators
or large scale models under operating conditions (mass flow rate,
pressure, temperature, etc.) matching those of the steam generator
design under investigation.

- due to their empirical origin - curve-fitting techniques applied to
experimental data - the correlations hardly contribute to the
physical understanding of the void-flow mechanism.

- it follows from the above that the availability of experimental data
is doubtful. Any general relation defining the limits of density wave
instability would have to include all dimensionless numbers that can

* . . L . d »
) Frictional pressure drop will increase with mass flow . because of

2
1ts proportionality with —%—-and will predominate over the concurrent

inerease in hydrostatic head.

- 4.38 -

be constructed from the geometrical- and process constants governing
the phenomenon in question.

For identifying the effects of changes in the various dimensionless
numbers (and possibly concluding that some of them may be neglected)
the experimental data should consist of separate sets, for each of
which only one particular dimensionless number varies over a
sufficiently wide range. This implies so large a volume of
experimental data as to be almost prohibitive in engineering
practice. A further complication is that some effects, notably those
due to spatial distribution like that of the heat flux variation
along the length of the channel, can hardly be accounted for in the
correlation. Different correlations for different types of heating
may prove to be required. A case in point is the aforementioned
empirical stability limit derived by Unal. His set of experimental
data in UNAL [ 4.6-2 ] contained one group of experiments on a tube
with uniform electrical heating and extreme L/d ratio (= 9000),
whereas the remainder concerned channels of lower L/d ratio (< 4000)
heated non-uniformly by sodium. Unal fitted these experiments solely
by adjusting the L/d ratio dependence of his correlation, though it
is quite probable that the difference in heat transfer distribution
also has a significant effect on the stability limits. This assumption
is corroborated by the experimental results of DIJKMAN [4.6-3 ], who
found that the change from a uniform heat flux to a sine-shaped heat
flux significantly improved the stability of his evaporator. It is
the present author's opinion that, unless additional data is provided
to make up for this deficiency in experimental basis, the accuracy of
extrapolations to sodium heated steam generators with high L/d
ratio's (> 6000) may well be less than the 6% stated in UNAL [ 4.6-3 ].

ad.b) The mathematical modeling underlying this approach is based on
physical insight in the mechanism combined with empirical knowledge
of (single- and two-phase) pressure drop, heat transfer and void
fraction vs gquality relations. Although largely analytical in nature
this method is inevitably based on a number of these empirical
relations of limited accuracy.
Simulations reported in literature suggest that these inaccuracies
and those caused by deficiencies in the mathematical model tend to
accumulate. Hence an accuracy of 10%, obtained in some cases, is
already considered an excellent result, which compares unfavourably
with the abovementioned value of 6%. Though significant improvement
of this accuracy may prove difficult, it is the author's opinion that
it is possible to at least maintain it over wide ranges of conditions
and geometries by applying a sufficiently flexible computer program.
Furthermore this approach will extend the understanding of the
physical process, e.g. by allowing a designer to study the sensitivity
of his design to variations in the various geometrical and process
constants. The need for experimental evidence, if existing at all to
support new designs, is thus greatly reduced through the reduction in
the number of variables to be studied. Thus applied, simulation can
in combina-tion with the former method improve the accuracy and
reliability of stability threshold predictions.

Two different classes of simulation models can be distinguished:

1 time domain models

b
b 2 frequency domain models

- 4,39 -

ad.bl) Here the dynamic response of an evaporator tube to a given

perturtubation is computed as a function of time for the boundary
conditions relevant to parallel channel instability, i.e. constant
inlet and outlet pressure and constant inlet enthalpy (cf. section
8.6612:3) s

Stability behaviour is derived from the inlet mass flow response. In
a stable system this mass flow will return to its original value
following perturbations. In unstable systems the inlet mass flow will
start to oscillate either with a limited or with a diverging amplitude.
Models operating in the time domain may or may not be linearized,
depending upon the desired accuracy for simulating the steam
generator's actual physical behaviour. Non-linearized models
reproduce - within the accuracy of the model - the exact response of
the real system. Examples of this approach are given by SPIGT

[4.6-4 ], DIJKMAN [ 4.6-3 ] and VAN VONDEREN [ 4.6-5 ] . The application
of their programs is limited to the case of prescribed heat flux,
viz. electrically heated tubes, as opposed to the case of a prescribed
primary mass flow and inlet temperature typical for actual steam
generators. Even for this simplified case the increase in accuracy
has to be bought by considerable increases in computing time over
that needed for linearized models. By contrast the accuracy of the
latter group of models is limited.

In stability studies this loss in accuracy of the physical modeling
due to linearization is most evident with respect to limit cycle
behaviour. This behaviour is characterized by constant amplitude
oscillations, occurring under unstable conditions when stabilizing
and unstabilizing forces balance as a result of a difference in
amplitude dependence between driving forces and damping forces due to
the strong non-linearity of the latter (cf. figure 4.6-2). The
amplitude of a limit-cycle depends on how far operating conditions
are pushed beyond the stability limit, as illustrated e.g. by figure
4.6-3 taken from VAN VONDEREN [ 4.6-5 ] . This figure confirms the
author's own experience that a relatively small excess of the
stability limits causes large flow excursions. Where non-linearity is
the cause of 1limit cycle behaviour it will not be predicted by linear
models. This inability is sometimes singled out as an argument
against the use of linearized models by those who consider the
prediction of limit cycles to be important for the purpose of
assessing structural damage incurred during temporary flow
oscillations e.g. during startup or shutdown. With reference to this
argument it is the author's opinion that as a result of unpredictable
deviations from prescribed operating conditions, combined with the
observed strong dependence of oscillation amplitudes on variations in
operating conditions, such predictions of structural damage will fail
to yield sufficiently accurate results to be of any practical value.
Thus linearized models, predicting solely the stability limit, should
suffice for engineering purposes.

ad.b2) Frequency domain models consider the evaporator as a feedback

- 4.40 -

system, the loop gain of which is investigated. As transformation
from time domain to frequency domain is only possible for linearized
systems, this class of models is incapable of simulating limit cycles.
An advantage of models in this class is the insight in the physical
mechanism,to be gained from amplitude and phase relations between the
various process conditions in the steam generator. Furthermore this
information allows of a detailed experimental verification by
frequency analysis of the systems (cf. POTTER [4.6-6 ]).

Over the years a great number of these models have been built. One of
the first, mainly intended for demonstrating the void-flow mechanism
very clearly, was given by DAVIES [4.6-7 ]. As for clarity's sake the
solutional procedure was largely analytical, the results were not very
accurate. A more accurate description is applied in the program of
JONES [4.6-8 ]. In an evaluation of several models NEAL [ 4.6-9 ]
reports that this model predicts stability limits within 20% for 70%
of the experimental data available. The STABLE program of [ 4.6-8 ]
contains no provisions for DNB and mist flow simulations, hence its
use is restricted to steam generators with low outlet quality.
EFFERDING [ 4.6-10 ] extended the Jones program to once-through steam
generator simulation by including these provisions. Other examples of
this approach are given by HALOZAN [ 4.6-11 ] and SHITTKE [ 4.6-12 ].
The accuracy of their models is hard to judge as comparisons with
experiments are omitted in their reports. The same applies to two
Japanese models by TAKAHASHI [ 4.6-13 ] and SUZUOKI [4.6-14 ]. The
former has made some restricting assumptions such as: no wall
dynamics, void fraction linearly dependent on the space codrdinate
throughout the entire two-phase region and no slip between the two
phases. Suzuoki also assumes homogeneous flow. The nature of
additional assumptions is very difficult to derive from his report. As
regards experimental verification, Suzuoki reports comparison of the
computed and measured frequencies only, which agree very well. Neither
reports on comparisons of stability limits. Both Japanese models
differ in solutional procedure from the models mentioned earlier by
computing the eigenvalues of the oscillations rather than a transfer
function of the system. This approach will be elaborated in subsection
4.6.1.3 in connection with the CURSSE program which also has this
option.

A program, remarkably free of limiting assumptions is reported by
DEAM [4.6-15 ]. In this respect his basic equations are equivalent to
the set given in subsection 4.2.2. Although the dynamic variation of
the location of transitions is omitted in the model the comparisons
given in the report indicate a high degree of accuracy. A comparison
with other models in this respect is difficult as he computes the
inlet throttling required to obtain stable operation, whereas the
others compare computed and measured maximum power transferred.

This program, which is not available, appears to share with, all the
others a lack of the geometrical flexibility required to simulate a
bayonet tube steam generator.

In conclusion it may therefore be stated that, of the models reviewed
so far, those in the time domain were found inadequate for actual
steam generators due to the imposed boundary condition, viz. heat
flux rather than primary mass flow, whereas none of the various
models in the frequency domain was suited to the particular geometry
of the bayonet tube steam generator. For these reasons it was decided
to develop new models suitable for the bayonet tube configuration and
to do so both in the time and frequency domains.

As work progressed it became gradually more evident that a time
domain model of sufficient accuracy for the bayonet tube would have
an unacceptably low process time/simulating time ratio. Hence most of
the effort was shifted towards the frequency domain model, the more
so as it was found that this approach could more easily be extended
to cover a broad range of geometries and conditions.

- 4.41 -

4.6.1.2. Identification of characteristic sections.

4.6.1.2.1. Linearized analysis of the total system.

The task of avoiding void flow instabilities by proper design is complica-
ted by the fact that actual steam generators consist of a large number of
parallel tubes, connected at the bottom and the top by feedwater and steam
headers, respectively.

While these tubes are generally geometrically identical, their thermal
loadings may differ according to their location in the total bundle, thus
causing non-uniform behaviour. Further complexity is introduced by possible
effects of feedwater and steam line characteristics (cf. figure 4.6-4) on
hydrodynamic stability of the entire system.

Any stability analysis aimed at verifying that a given steam generator
design will behave in a stable manner for all operating conditions foreseen
(including start-up and shut-down periods) will have to take into account
the aforementioned complexities. It does not, however, seem practicable to
simulate the behaviour of the entire system because - apart from the high
computing costs - it would require a larger computer than presently
available.

The approach generally adopted in simulations is to limit the extent of
the study by identifying a characteristic section whose behaviour will be
identical to that of the entire steam generator if subjected to the same
conditions.

Most investigators choose a single tube as characteristic section of the
steam generator. The resulting problem of defining the boundary conditions,
i.e. the pressure at the inlet and outlet of the single tube, is usually
solved by keeping these pressures constant.

This choice of boundary conditions is based on the somewhat vague reasoning
that in an evaporator consisting of a large number of parallel tubes the
various tubes will oscillate with random mutual phase shifts, thus leaving
the total mass flow and consequently the in- and outlet pressures
unaffected.

This assumption was experimentally verified for two and three parallel
tubes by CROWLEY [ 4.6-16 ], D'ARCY [4.6-17 ] and VAN VONDEREN [ 4.6-5 ].

In a number of these experiments the latter has however observed yet
another mode of instability, where the total mass flows and consequently
the in- and outlet pressures did vary. While no further discussion of this
mode is included in [ 4.6-5 ], its very occurrence contradicts the general
validity of the afore mentioned assumption. Hence, in the following a
mathematical description is presented of the entire system, i.e. the steam
generator proper - consisting of headers, interconnected by parallel
channels - as well as the associated feedwater supply and steam utilization
subsystems.

In this way the various possible modes of oscillation and their associated
characteristic sections and boundary conditions are derived from the set
of governing equations and thus given a mathematical basis.

This analysis is performed in the frequency domain for convenience and to
obtain results that can be directly compared with the results of the
stability experiments on the DSMP-bayonet tube to be discussed in
subsection 4.6.2.

The stability criteria for the various modes are expressed in the transfer
functions of the different subsystems. As these transfer functions can be
measured in a single tube test facility this approach, in addition to
avoiding the limitations discussed above, offers the advantage of
requiring only one type of experiment, i.e. frequency response analysis,

- 4.42 -

for both control studies and stability analysis.

As the title of this subsection indicates, all mathematical descriptions
in this analysis are linearized.

The state space description given in section 4.5:

X=AX+Bu (4.6-1)

Q:io.-
t

<
Il

& §_+ D u

is less suitable for the present purpose, hence it will be transformed
into a description in the frequency domain.

Replacing the time derivative by the Laplace operator s and rearranging
results in:

1
y=1{C.[s.E-A] .B+D}u=H(s).u (4.6-2)

giving the direct relation between input vector u and output vector y
through transfer function matrix H(s). Each element of this matrix is the
transfer function between one input and one output variable and is a
function of the complex Laplace operator s =)\ + i w.

Note: Positive, zero, or negative values of A indicate that the amplitudes
of the signals in the system diverge, remain constant or damp out

respectively:
g,
X =xe t sin w t (4.6-3)

4.6.1.2.2, Linearized description of subsystems.

Single evaporator channel.

In the case of a single evaporator channel two input and two output signals
may be distinguished: variations in inlet mass flow and outlet pressure are
considered to be inlet signals whereas variations in outlet mass flow and
inlet pressure are seen as outlet signals (cf. figure 4.6-5).

Equation (4.6-2) reads for this case:

§ 1< H (s) H  (s) § p

S ¢out H¢p(s) H¢¢(s) $ ¢in (4.6-4)

This equation shows that the evaporator's behaviour is fully described by
four transfer functions:

(s), H, (s), H  (8)

H ’
p(s) -

H
P p¢

The second of these transfer functions, Ho¢' which plays a central part in
this analysis, is usually referred to as the input impedance.

Figure 4.6-6 shows an idealized shape of the inlet impedance curve of an
evaporator, measured by applying test signals of constant amplitude. The
shape of this curve can be understood by recollecting the physical
mechanism. The increase in phase shift with rising frequency between
pressure drop and inlet flow oscillation is caused by the time delay
present in the system as explained in subsection 4.6.1.1.

& d.43 ~

Feedwater system.

The feedwater supply system consists of the pump, the main feedwater line
and the inlet header. Velocities and hence pressure differences in the
header are so small that uniform pressure can be assumed throughout the
entire header.

For constant pump speed the pressure at the inlet header is solely
dependent on the total mass flow into the evaporator. Therefore a system
with one inlet and one outlet suffices:

S p.. ==2, (s). § ¢, (4.6-5)
where transfer function Zin is called the impedance of the feedwater
system.

Outlet system.

A similar description holds for the outlet system, consisting of outlet
header, main steam line, turbine and condenser.

Excluding external disturbances the pressure at the outlet of the tubes is
given by:

S p =2 (s). 6§ ¢ (4.6-6)

Total system.

The foregoing component descriptions shall now be combined to form one
mathematical description of the entire system (cf. figure 4.6-7).

To define the governing equations of the system the mass balances of the
headers are first derived.

n
Feedwater header: S ¢, = I 6 ¢, (4.6-7)

n
Steam header: LI 6 ¢ =4 ¢ (4.6-8)

i
where n is the number of tubes in the bundle.

Suitable transformations, given in detail in APPENDIX 4E, yield a number
of n linear equations with the n different inlet mass flows ¢ ¢, for
the separate steam generating channels as unknowns. Ty

The general form of these equations is:

n Zout H¢¢j
H S + I - -
p¢i q>1ni =1 {(Zln pri n . ¢1n,} 0
? (1 +2,, I H) ]
k=1 *Px (4.6-9)
By introducing two new functions defined as:
A.(s) =H_  (s) - and y -
i p¢i (4.6-10)

- 4.44 -

B,.(s) =2, + H (4.6-11)
ij

n
A, § ¢, » LB, G b, =0 (4.6-12)

B 0
A e . 0 By ni=-1 1,n ¢1nj
: 0
B0 Mt Beon s - g | s o0 ¢1n2
X t—3
Bn -1,1 Bn - 1,2 Bn - 1,3 An—1+Bn—1,n—1 Bn - 1,n ¢inn _ U
- +
Bn,l Bn,2 Bn,3 Bn,n 1 An Bn,n ¢in 0
n- 2
(4.6-13)

4.6.1.2.3. Stability criteria.

After a disturbance the total system described in the previous subsection
will start to oscillate.

This oscillation, that may be damped, have a constant amplitude or
diverge, is described by the solution of the system of homogeneous linear
equations (4.6-12).

The complex frequency s = A + iw characterizing the oscillation is the
root of the equation D = 0 where D is the determinant of the coefficient
matrix of equations (4.6-13), as a non-zero solution can only exist if
this determinant vanishes (cf. e.g. PIPES [4.6-18 ].

The real part of this root determines whether the oscillation diverges and
thus whether the system is stable (A < 0). marginally stable (A = 0) or
unstable (A > 0).

Hence our stability criterion reads:

a system is stable if the real parts of all s, are < 0, where sy

i

represents the roots of equation D(s) = 0.

Expansion of this determinant for a general case yields a very complex
condition.

However, if the tube bank can be subdivided into sets of identical
channels we can factorize the determinant. This may be illustrated for the
simple case of a tube bank consisting of three tubes, of which tubes

1 and 2 are identical.

- 4.45 -

In this case matrix (4.6-13) reads:

By ¥ By Bi1 By3
D(s) = Byy Ay + By Bis
Bay et T B = (4.6-14)

The determinant can be rearranged by subtracting the second row from the
first and separating the common factor A

1:
By By By B3
D(s) = &, (s) . -1 +1 0 (4.6-15)
B3y Byy A3 1 Bsj

In the general case this process can be applied to each set of identical
tubes present in the bundle in succession, yielding:

| (4.6-16)

consisting of a product of the powers of the coefficient Ai' representative

for each set of identical channels, and a residue of the original matrix.
The exponents are the numbers of identical channels in each particular set
minus one.

The above shows that there are two different types of factors in the
expansion of D.

is Ai(s) =0 (4.6-17)

. ] lmres(s)l = 0 (4.6-18)

each yielding a different stability criterion.
ad.l) If the real part of a root of equation:

A,(s) =H ,(s) =0 (4.6-19)
1 p

is positive or zero, the system is unstable.
The mode of oscillation connected with this instability can be found
by substituting Ai = 0 into the set of equations (4.6-13).

After this substitution the columns with identical coefficients can
be added. Thus a new set of equations is formed with a smaller number
of unknowns.

For equations (4.6-14) this process yields:

By (9 #9050 + B3 ¢5]=10
B11 (¢1 - ¢2) + B13 -x¢3 =10 (4.6-20)
Byy (&) + ¢5) + By + Bysl1é,|=(0

- 4.46 -

The two unknowns in this set of equations are ¢ = ¢1 + ¢2 and ¢3.

As the upper two equations are identical one of them can be omitted,
yielding a set of two homogeneous eguations with two unknowns. As it
is very unlikely that the determinant of the coefficient matrix of
this set of equations vanishes for the value of s, for which
Hp = Ai = 0, only the zero solution holds. w

i
For the above case this means that ¢, + ¢, =0 and ¢, =0, i.e. the

total mass flow through the set of two identical tubes is constant
(the mass flows through the individual tubes may oscillate in
counterphase), whereas the mass flow through the third tube is also
constant.

As in this case the oscillation is restricted to a number of parallel
itubes, DAVIES [ 4.6-7 ] called this type of instability: parallel
channel instability.

Generalization of this result for a steam generator consisting of a

number of sets of two or more identical channels and possibly a number

of channels different of all others, yields that each set of identical

channels may be unstable. The stability of a particular set can be

checked by determining the real parts of the roots of equation

Ai = Hp¢' = 0, where Ai is representative for the channels of this set.
i

A positive real part indicates unstability. The total mass flow through

each unstable set of identical channels will be constant. As the

mass flow through each tube not forming part of such a set is also

constant, it follows that the total mass flow through the steam

generator is constant too, and hence so are inlet and outlet

pressures.

The results agree with the experimental data gained to date. For

example VAN VONDEREN [ 4.6-5 ] observed the following three different

modes of instability in his experimental evaporator, consisting of

one set of three identical parallel channels (cf. figure 4.6-8):

1. all three tubes oscillating with the same amplitude, each with a
phase shift of 120° with respect to the others

2. two tubes oscillating in phase and with the same amplitude, with
the third one oscillating in counterphase at twice this
amplitude

3. one tube remaining stable while the other two oscillated with
the same amplitude but in counterphase.

All three modes agree with the above mentioned condition. The first
mode was the most common one; if the system started to oscillate in
one of the other modes it always changed to the first mode after some
time. A possible explanation for this phenomenon is given in APPENDIX
4F.

For very unstable conditions VAN VONDEREN [ 4.6-5 ] observed yet
another mode of instability, mixed with one of the modes mentioned
above, viz. oscillation of the total mass flow at a frequency
slightly below the frequency of the other mode. To explain this type
of instability we shall need the second criterion.

ad.2) A second type of instability occurs if the root of equation (4.6-18):

|l M___(s) I‘ = 0 (4.6-21)

- 4.47 -

has a positive or zero real part (A =2 0).
Expansion of this determinant again yields a very complex stability

criterion.

The mode of oscillation associated with this criterion involves all

channels as well as

the inlet and outlet systems.

DAVIES [ 4.6-7 ] called this type of instability loop instability.
Combination of equations (4.6-18) and (4.6-15) yields the following
set of equations for the system represented by equation (4.6-14):

From the second row

identical tubes are
analogously for the
behaves as a single
be replaced by such

The results of the above

B11 B3 % ¢
1 0 , 6, | = |o| (a.6-22)
Bya Byt Bg 45 O

it follows that ¢1 = ¢2: the mass flows through

the same. It will be clear that this result holds
general case: each set of n identical channels
one of n-fold capacity. In an analysis they can

a channel, thus reducing the size of the problem.

analysis may be summarized as follows:

steam generators consisting of parallel steam raising channels, with their
associated feedwater supply and steam discharge systems, may exhibit two
different types of void flow instability:

1. parallel channel instability

2. loop instability

ad 1. parallel channel instability should better be called identical
parallel channel instability as it can only occur in a group of
identical parallel channels within a steam generator bundle. During
parallel channel instability the total mass flow through this group
of channels and consequently the pressures at the in- and outlets

remain constant.

To determine the stability of the design of a steam generator at
certain operating conditions all sets of identical parallel channels

have to be examined

to find the one that is most susceptible to

parallel channel instability.

The stability behaviour of a set of identical parallel channels is

the same as that of

a single tube provided that the inlet and outlet

pressures of that tube are kept constant. These are the characteristic
section and boundary conditions normally chosen in stability analyses.

ad 2. During loop instability all tubes within a set of identical tubes
behave in an identical manner and may therefore be assumed to be
replaced by a single tube of n-fold capacity where n is the number cf
tubes present in the set. Thus a steam generator consisting of a
large number of tubes that can be divided into a small number of sets
of identical channels may, as far as loop instability is concerned, be
replaced by a limited number of larger tubes with the same total

capacity.

The question whether the
reached before those for

- 4.48 -

limits for parallel channel instability are
loop instability has no general answer.

A case where loop instability occurs before parallel channel instability
can be found in KAKAC [4.6-19 ]. In experiments on four parellel tubes the
density wave oscillations in all four tubes are in phase for all observed
cases of instability.

The criteria developed for parallel channel and loop instability may be
applied in analyses in the form given above. They can however be trans-
formed so as to become applicable both for analytical and for experimental
determination of stability limits. In APPENDIX 4G a relation is derived
between the criteria and the behaviour of transfer functions for signals
of constant amplitude. These transfer functions can be obtained either by
simulation or by experiments.

As regards parallel channel instability the derivation of APPENDIX 4G
shows that the number of roots of the inlet impedance H ,(s) with positive

ol

real parts equals the net number of clockwise encirclements of the origin
by the complete inlet impedance curve (anti-clockwise encirclements are
counted negative). If the contour does not encircle the origin the system
is stable. Although in principle the impedance curve has to be determined
for all frequencies from zero to infinity, in practical measurements it
often becomes apparent from the results that above a certain frequency no
further encirclements will occur. The range of frequencies measured can be
restricted accordingly.

In the case of loop instability a similar relationship holds (cf.
APPENDIX 4G).

4.6.1.3. Analysis in the time domain.

4.6.1.3.1. Introductory remarks.

Figure 4.6-9 schematically compares the principles of the two methods for
stability analysis in the time domain to be discussed. Whereas for the
second method it suffices to determine the pressure drop response for a
prescribed inlet mass flow variation, the first method additionally
requires a feedback loop to fulfill the prescribed boundary condition of
constant inlet and outlet pressures.

In the following subsections the digital simulation program and its two
underlying methods will be discussed. The two alternative applications of
this program formed our first attempts to predict the hydro-dynamic
stability of the bayonet tube steam generator. They contain simplifying
assumptions subsequently omitted from the frequency domain program.
Furthermore no attempt was made to extend their applicability to other
geometries. Hence they are less accurate and less complete than the
frequency domain program to be discussed in subsection 4.6.1.4.

4.6.1.3.2. Additional assumptions.

- subcooled boiling is treated in much the same way as in the steady state,
model BASTA, viz. by taking into account the resulting increase in heat
flux, but assuming no vapour generation before the average enthalpy h

reaches the saturation value hz

- as the present model was developed exclusively for the bayonet tube steam
generator and hence for a system pressure of approximately 18 MN/m?,

homogeneous flow (s = 1) was assumed in view of the slip data presented in
APPENDIX 4B.

in view of the very small relative pressure variations, occurring during

onset of instability, the physical properties were assumed independent of
pressure

.49 -

- as this model constituted our first attempt to simulate bayonet tube
stability behaviour, it was further simplified by taking the inter-channel
heat fluxes constant in time.

For the primary channel this assumption results in a constant temperature
distribution, eliminating it from further consideration.

- even for constant heat fluxes, the temperature in the superheater gap
would vary due to the varying mass flow rate. However, measurements during
the stability experiments discussed in subsection 4.6.2 showed that only
in a minor part (near the top) these variations were significant. Hence it
was assumed as a first approximation that the temperature in the super-
heater also remains constant.

4.6.1.3.3. Modified equations.

The assumption of homogeneous flow (s = 1) greatly simplifies the two-
phase balance equations presented in subsection 4.2.2.2.1.

These equations reduce to those given earlier by equations (4.5.1),
(4.5.2) and (4.5.3).

The equations actually applied in this model are obtained by combining
these basic equations. Combination of the mass and energy balance
equations yields:

o
(1—53)

oV _ % q0

3z p (h -h) A kil Gr200)
g g 2

An interesting feature of this equations is the absence of dynamic terms.
Combining this equation and the mass balance for steam yields:

oQ qo 1 pg o0
oa { & [f-m{] = A} = == (4.6-27)
0 A h -nh ot

= L
\

4.6.1.3.4. Solutional procedure.

The constant input values of the heat fluxes are obtained from the steady
state program BASTA (cf. section 4.4).

The assumption of constant heat fluxes implies thermal decoupling of the
channels, permitting each channel to be treated separately.

The assumption of pressure independent physical constants decouples the
momentum balance equation from the mass and energy balances. As a result
it is possible to start by solving the combination of mass and energy
balance and subsequently to ccmpute the total pressure drop.

Evaporator channel.

In this program three different regions are distinguished in the central
tube; viz.:

- preheat region (up to h = hQ)
- two-phase flow region (h2 < h < hg)
- superheat region (h > hl)

- 4.50 -

Preheat region.

For determination of the preheat length the same Lagrangian description
was adopted as used in the DSTB transient simulation program discussed in
subsection 4.5.2.3. In fact, as the earlest version of this stability
simulation program was developed before this transient program it was our
first application of this approach. For details reference is therefore
made to the aforementioned subsection.

Two-phase region.

As shown in equation (4.6-26), the spatial derivative of velocity v
depends solely on the prescribed heat flux g, hence the velocity
distribution can be obtained by direct integration starting from the end
of the preheat length. Subsequently the void fraction distribution is
derived by integrating equation (4.6-27). For this purpose the latter
equation is transformed by substituting: :

o, = a
) t-At
it At (4.6-28)
which yields an ordinary differential equation:
s, R qo g % 7 Y-t
—_—= {1-a@1--—21}- 1  (4.6-29)
0z vt Apg (hg - hQ) o2 At

The suffixes t and t-At denote the current and previous time levels,
respectively. Integration is continued until void fraction o becomes
unity, indicating that the end of the two-phase region is reached.

Superheat region.

In the superheat region of the central tube the temperature is assumed
constant in time and equal to the steady state values obtained by BASTA.

Superheater channel.

Assuming a constant temperature distribution and thus neglecting the
effect of varying density on pressure drop, the superheater gap may be
replaced by a single restriction at the outlet of the evaporator tube.

Total pressure drop.

Having determined the enthalpy (void fraction) distribution throughout the
evaporator the total pressure drop acorss the secondary channel can be
computed by direct integration of the momentum balance equation (4.6-23).
The frictional pressure loss is accounted for by substitution of the
relevant fricticnal pressure drop correlation from the set given in
subsection 4.2.3.3.

Repeated application of the above procedure for subsequent time steps

yields the total pressure drop response p, (t) - p t(t) to a variation
of the inlet velocity vo(t). A =

- 4,51 -

Method 2.

By application of the above procedure for a harmonic variation of the mass
flow rate the harmonic response of the total pressure drop is computed.
From these input and output signals, computed for a range of frequencies,
the inlet impedance curve may be constructed and hence by application of
the criterion given in subsection 4.6.2 the stability behaviour of the
bayonet tube derived.

Figure 4.6-10 shows a typical result for the bayonet steam generator.

Method 1.

In this method the boundary conditions of constant inlet and outlet
pressures are prescibed.

For application of this method determination of the pressure drop response
following an initial perturbation, as discussed above, must be extended
with an iterative procedure. This iteration starts by assuming a small
increase of the feedwater inlet velocity and computing the resultant
variation of the inlet pressure for a constant outlet pressure. If this
variation is negative the next step of the iteration is started with a
further increased feedwater velocity and vice versa. The iteration
procedure is continued until the inlet pressure remains constant. Then the
program progresses with the next time step, etc. In this way the response
of the system following an initial disturbance is computed.

Under unstable conditions the system will start a diverging oscillation,
whereas under stable condition the initial disturbance will damp out.
Figures 4.6-11 through 4.6-15 show plots of the results of this method
applied to a uniformly heated tube for increasing degrees of inlet
throttling. The stabilizing effect of throttling is clear from these
figures (c5 is the inlet gag pressure loss coefficient).

4.6.1.4. Analysis in the frequency domain.

4.6.1.4.1. Extensions in the model.

As mentioned in subsection 4.1.3.2.2 a new frequency domain program was
developed aiming at highest flexibility and general applicability. The
acronym CURSSE for: Computer program for UniveRsal Simulation of Stability
Experiments-proved a very appropriate name in view of the programming and
testing efforts involved. .

One way to provide the required geometrical flexibility mentioned in the
introductory remarks of subsection 4.6.1.1 would have been the incorpora-
tion in the program of a number of standard geometries. This system was
rejected as not sufficiently flexible in favour of a "building block"
approach defining the geometry by three basic parts:

- channels
- headers (and connecting nozzles)
- heat exchanging walls

By applicaticn of these "building blocks" it is possible to construct a
great number of different geometries. It is for example possible to include
feedwater and steam systems for simulating loop instability or to study
the behaviour of a number of non-identical parallel tubes.

channels:

a channel is characterized by the vertical location of its inlet and
outlet header and its length. For an inclined channel (e.g. a helically
coiled tube) this length exceeds the difference in height between the two
headers

headers:

a header is characterized by the location and number of its channel
cennections and its volume.

If present, flow restrictions are assumed to be located in the nozzles
connecting the system with the surroundings and the in- and/or outlets of
the individual channels.

Separate modeling of the headers yields a set of equations additional to
the equations given in subsections 4.2.2 and 4.2.3.

Figure 4.6-16 shows the general form of a header consisting of a vessel
provided with inlet and outlet nozzles. These may be either proper nozzles
or channel out- or inlets respectively.

Before deriving the conservation equations for such a header a number of
simplifying assumptions should be made:

- the pressure is uniform throughout the entire header vessel. The
pressure drops are supposed to be concentrated in the nozzles (this
assumption appears justified by the low velocities in the header
vessel). _

- perfect mixing takes place, i.e. all outlet conditions immediately
ahead of the outlet restrictions are identical to the bulk conditions
in the header.

- the pressure drop across a nozzle restriction can be described by the
general equation:

162

Ap = ¢ . 5 (4.6-30)

Y

for both single and two-phase flow, if the specific mass o for the
latter case is defined by:

The validity of equation (4.6-30) for single phase flow is generally
accepted. The application of this equation to two phase flow is supported
by experimental results published by TREMBLAY [ 4.6-22 ].

With these assumptions the conservation equations for a header can be
formulated as follows:

® mass:

n m 3
A G, - I A G, =y £B. (4.6-31)

® momentum:

the following momentum balance can be formulated for each inlet nozzle:

2

G
G e
H % -
& pin.
i

=

40 g
P, (4.6-32)

- 4,53 -

where C, represents the loss coefficient for inlet nozzle nr. i anc Py is
i

the uniform pressure inside the header.
The corresponding equation for an outlet nozzle reads:

2
Ci Gouti
PH - pouti - 5 C (4.6-33)
pout.
:
® energy:
this equation reads:
n m B(MH uH)
E: B G h - L A G h = e— (4.6-34)
in in in. out. out. out, ot
J=1 j J j j=1 j J J
Expansion of the right hand side yields:
ou oM
) H H
—— = —_— e .0
ot (MH uH) MH Y Uy 3% (4.6-35)
Substitution of:
P
- -_— 4-_
u, hH - (4.6-36)

and of equation (4.6-35) into equation (4.6-34) yields for the energy
balance of the header:

n m
Z - |
. Aln Gin. hln .Z Aout Gout. hout
i=1 j : | j  j=1 J J j
oh ap op
H H H
Ve Pr 3t Y Ve Pwsr T Vet (4.6-37)

As the throttling process in the nozzle restrictions leaves the enthalpy
constant the energy balances of the nozzles yields:

h = h (4.6-38)

for outlet nozzle nr. i

The above extensive description of the header behaviour may appear overdone
for most headers occurring in practice.

Unfortunately the possible simplifications differ from case to case,
requiring a number of simplified models for the different types of headers
(compare e.g. a main steam header to the top of the bayonet tube connecting
the evaporator and superheater parts).

Therefore the analysis of the header behaviour given above was considered
the best approach to retain the desired universality.

- 4.54 -

heat exchanging walls:

a heat exchanging wall, always in the shape of a tube, separates two
channels in the structure.

As the CURSSE program was meant to serve as a reference program, it was
deemed desirable to implement a two capacity wall-model instead of the
zero-capacity model discussed in subsection 4.2.2.4, in order to verify
the general validity of the conclusion by TEN WOLDE [ 4.1-9 ] that the
latter model is sufficiently accurate for simulating steam generator
dynamics. Originally the wall model given by DE GREEF [ 4.6-23 ] was
implemented in the CURSSE program. In this model the total capacity of the
wall is divided amongst two capacities located at the inner and outer
surfaces of the wall, respectively. During test runs it became clear that
this model has distinct disadvantages. If the boundary layer heat
resistance 1/a is very low, as is the case with boiling heat transfer, the
heat capacity is more or less "short circuited" to the adjacent medium.
Changes in bulk temperature result in very high heat fluxes between medium
and capacity. It will be clear that this is at variance with the actual
behaviour of the wall. Tc remedy this deficiency the locations of the
capacities were changed to those shown in figure 4.6-17, i.e. some
distance below the surface of the tube wall. In our model the two capa-
cities are arbitrarily located at such radii r; and r,, that the corres-
ponding circles divide the cross-sectional area of the tube wall into: one
quarter outside r;, one half between r; and rp and the remaining quarter
inside rj. Optimization of the values for r; and r; should improve the
accuracy of this mathematical model. '

In this way there always remains a heat resistance between the bulk of the
medium and the adjacent capacity, even if the boundary layer resistance
tends to vanish. The energy balance equation for the outer capacity (per
unit tube length) reads:

5 ad, ('9b - 397) (8, = ¥7)
o ).-pC o - + = (4.6-39)
o m

1 2
2 " (ro

The heat resistance RO between the bulk of the outer medium and the outer

capacity, located at r; is composed of the boundary layer resistance and
the tube wall located between r, and ry:

o
ln —
1 rs
R, = 2 T r o 3T (4.6-40)

The resistance between the two capacities is:

r
ln}—-
2
Rm = - P : (4.6-41)

The equation for the inner capacity is analogous.
In connection with the structure of the program the temperatures ¥; and 9,
were expressed in the basic variables 00 and fii and the bulk temperature as:

- 8,55 -

r o 1ln —
O O .
= 1 = - 9
01 9O+ % (190 b)

ro

r. o, ln —

i i ri
3, = & g -9 4,6-42
2 v 5 (O b) (4.6 )

O

Figure 4.6-18 shows the aforementioned schematization for the bayonet tube
applying the building blocks discussed above.

A second set of additional equations stems from the transitions in the
evaporating process as mentioned in subsection 4.2.1.

Such a transition occurs where the local values of the basic variables
(p, h, G, (%), Sw) fulfill the transition equation given in subsection

4.2.3.1. In general:

= ( -
(hZ’ GZI pzl (xz)l ez) 0 (4.6-43)

During oscillations in the inlet mass flow rate the location of these
transitions will oscillate as well. In a time-domain program this does not
pose a problem, as the locations of the transitions can be recalculated for
each time step. In a frequency domain program such as the CURSSE program,
however, this is not possible. The method by which this problem has been
solved requires introduction of a number of additional equations. To
illustrate the problem let us consider the dynamic behaviour of basic

variable v. Figure 4.6-19 shows
the spatial coordinate z in two
two elements has been chosen to
the transition. At the location

a possible behaviour of v as a function of
adjacent elements. The boundary between the
coincide with the steady state location of
of the transition the gradient of the v-

function shows a discontinuity. Under dynamic conditions (e.g. increased
mass flow rate, heat supply, etc.) the transition will shift from its
steady state position, to for example the one indicated by the dotted line
in figure 4.6-19. The region of the pre-transition processes is extended,
that of the post-transition processes is reduced.

However, in a frequency domain model those regions remain constant due to
the fixed location of the transitions.

As only one set of correlations can be applied in a single element this
results in a distribution in the downstream element according to the
straight line F-H, rather than to the discontinuity in gradient as E-K-H.
The requirement of continuity would result in the faulty distribution
along G-E-I. This problem can be solved by introducing a double value for

v at the boundary coinciding with the steady state transitions: vF and VE'
- vE can be derived from the up- and downstream

conditions and the transition shift 8z, as follows:

The discontinuity Av = vF

(4.6-44)

- 4,56 -

Replacing the dynamic value of v by the sum of its steady state value and
a variation such as e.g.:

= 4,6-45
Vs v, + GVA ( )

yields, after neglecting second order terms:

SVF - GVE = 8z ( o - AZD ) = 62 (tgaU B tgaL) (4.6-46)

Thus the discontinuity in an arbitrary basic variable is expressed in its
steady state distribution and the value of the dynamic shift §z. The
latter is determined from the transition equation mentioned above (cf.
equation (4.6-43)). The local values of the basic variables appearing in
this equation can be expressed in the steady state values of these
variables at the boundaries of the upstream element and their variations
as exemplified by the following egquation (cf. figure 4.6-20):

v, = Vg + GVE + tgaL Sz (4.6-47)

Substitution of similar equations for all appearing basic variables in
equation (4.6-43) yields a relation between the variations of the upstream
variables GVE and the transition shift 6z:

g(GVE, §z) =0 (4.6-48)

from which the shift can be determined. This equation is combined with
equations (4.6-46), each providing an additional relation for the
corresponding additionally introduced double value of the variations at
the transition, to form the so-called coupling equations.

4.6.1.4.2. Modified equations.

The basic set of equations, given in subsections 4.2.2 and 4.2.3, extended
with the additional equations consists of:

- partial differential equations in z and t
- ordinary differential equations in t
- algebraic equations.

The set is modified in two steps:

1. the solutional procedure starts with the spatial discretization of
the partial differential equations. For this purpose the steam
generator is axially subdivided into elements. Replacement of the
spatial derivatives by finite differences results in a set consisting
of ordinary differential equations and algebraic equations. Figure
(4.6-21) shows the location of the basic model variables for a
channel and a wall element. A channel element requires nodal variables
at the upper and lower boundaries because of the appearance of spatial
derivatives in the pertinent conservation equations, whereas the
definition of nodal temperatures solely at the center of the element
suffices for a wall element.

- 4.57 -

2. the next step is linearization of the equations. All equations are
expanded in Taylor series and truncated after the first order terms,
thus neglecting second and higher order effects:

§ £(%X, Vs Zye..) = = 0x + =— Oy +-%§— 0 # smas (4.6-49)
"o

After discretization and linearization around the steady state conditions
the set consists of:

- linear ordinary differential equations in t
- linear algebraic equations.

4.6.1.4.3. Solutional procedure.

The bulk of the variables contained in these equations can be eliminated by
substituting all algebraic equations into the differential equations,
retaining only the following variables:

- for the channels h, G, p
- for the walls 31 and 90
- for the headers hH' Py (hN, Py GN)

(and nozzles)

These are called basic variables.
Discretization, linearization and substitution yield a set of equations
expressed in variations of the basic variables and their time derivatives:

oV

== = R(t) (4.6-50)

|a[ v + |B]
where R(t) represents the forcing functions at the boundaries. APPENDIX 4H
illustrates these processes by application to the single phase mass balance
equation.
Though elimination of the dependent variables by combination of the
linearized equations is relatively simple in certain cases such as the
example shown in APPENDIX 4H, it proved very complex, time-consuming and
error-prone in cases such as the two-phase balance equations, involving up
to 88 equations. ,
Therefore a special purpose program SLINQ, written in PL1, was developed
for the automatic substitution of linear equations. APPENDIX 4J shows an
example of applicaEion of this program. A gbecial and in our view
indispensable feature of SLINQ is the incorporation of a check that is
completely independent of the substitution process. All independent
variables and constants are given arbitrary values. Evaluation of both the
original set of equations and the result of the substitution process
yields two numerical values. Comparison of these two values yields a
reliable check on the correct performance of the substitution. During
application of SLINQ this check has proven very valuable for detection of
input errors.

There are two ways in which this set of equations (4.6-50) may be utilized

for stability studies, each corresponding to a different formulation of
the boundary conditions.

- 4,58 -

These are:

a. the actual boundary conditions for parallel channel instability: i.e.
constant inlet and outlet pressures. Thus the r.h.s. of the equations
(R(t)) becomes zero.

Laplace transformation of equation (4.6-50) transforms the problem into a
generalized eigenvalue problem:

|al v+ s |B| v=0 (4.6-51)

This is the straightforward approach to stability analysis.

As derived is subsectiocn 4.6.1.2 parallel channel instability may also be
determined from the shape of the transfer function Hp¢, leading to:

b. frequency response analysis by sinusoidal variation of the inlet
pressure, i.e. retaining the R(t) term at the r.h.s. of the equations.
This indirect approach obviates the need for constant inlet pressure.

For reasons described in subsection 4.6.2 the experimental facilities did
not permit to maintain a constant inlet pressure, imposing the use of
approach b for a proper comparison of analysis and experiments. However,
in view of the aim of general applicability set for the CURSSE program,
both approaches are retained as options in this program and will hence be
described in some detail.

ad.a. The A and B matrices of the generalized eigenvalue problem, defined
by equation (4.6-51), are non-symmetric. In this case two different
classes of eigenvalues and associated eigenvectors are possible.

- real eigenvalues s = A combined with real eigenvectors V.
They describe non-oscillatory transients of the steam generator from
one state to an other:

e B (4.6-52)

iy

- conjugated pairs of complex eigenvalues s = A * i w and associated
eigenvectors V and V, representing damped or diverging oscillatory
behaviour of the system:

v=ave’ ®sin(wt) (4.6-53)

Inspection of equations (4.6-52 and 4.6-53) shows that the system is
stable if all A values are less than zero.

The size of the matrices can become considerable for the steam
generator problem under consideration due to the large number of
small elements required for obtaining sufficient accuracy. (up to 500
%x.500) .

The resulting problem of core memory storage capacity was overcome by
concentrating the non-zero elements of the relatively sparse matrices
in a narrow band *) around the principal diagonal and only storing
the elements of the bhand.

* L . . L4
) possible because the conservation equations for a particular element

involve only the variables defined at the boundaries of that element.

- 4,59 -

This, however, imposed the choice of the so-called power-method for
solving the eigenvalue problem, as a literature survey by PAULUSMA

[ 4.6-24 | showed that only this method permitted full use of the band
structure storage mode.

The power methcd outlined in APPENDIX 4K is an iterative procedure
requiring the repeated solution of a set of linear equations with
varying right hand side vectors, but unchanged coefficient matrix and
yielding the largest absolute eigenvalue of the system and its
associated eigenvector (cf. WILKINSON [ 4.6-25 1). Two methods exist
to extend its use for the determination of additional eigenvalues,
viz. matrix deflation and vector deflation.

The former could not be applied in our case as it destroys the band
structure of the original matrices. The second method, i.e. vector
deflation, is based on careful selection of the "arbitrary" starting
vector of the power method. Both power method and vector deflation,
described in detail by WILKINSON [ 4.6-25 ], had to be adapted in our
case in order to be applicable to the generalized eigenvalue problem.
For these adaptations the reader is referred to APPENDIX 4K, except
for the following point. As explained in said Appendix application of
the power method to our generalized eigenvalue yields the smallest
instead of the largest absolute eigenvalue. This suits our aims
perfectly as our interest is focussed on the fundamental oscillation
and possibly a few of the higher harmonics, due to the fact that
higher order harmonics are more stable than lower order ones.

ad.b. The frequency response analysis, as described e.g. in OLDENBURGER
[4.6-26 ], is initiated by imposing a harmonic perturbation on one of
the boundary variables of the system. For this situation the vector
R(t) changes into:

B(t) = R sin (w t) (4.6-54)

where R is a vector of zero elements except in the case of the
perturbed boundary variable and w represents the angular velocity of
the perturbation. Combination of equations (4.6-51) and (4.6-54)
yields:

QU Q@
ot 1<
|

Av+B = R sin (w t) (4.6-55)

A solution of this set of equations is obtained by substituting the
trial solution:

v=asinwt+bcoswt
into the set of equations (4.6-55).

This substitution,; followed by some rearrangements, yields a system of
linear equations:

1o

RN REYINEY
= ’ (4.6-56)
ol 1al | el ol

~ 4,60 -

By solving this set of equations for perturbed inlet mass flow and
constant inlet enthalpy and outlet pressure, one point of the transfer
function H is determined.

P
Repeated application of this process for a range of frequencies yields
the complete curve of this transfer function. By applying the
criterion derived in APPENDIX 4G the stability of the steam generator
under consideration can be determined from the shape of this curve.

4.6.1.4.4. Program structure.

Around the time of initiation ( = 1975) a vast amount of publications - cf.
r.g. SPAAS [ 4.6-37 ], BRUKX [4.6-28 ], STEVENS [4.6-29 ] and [4.6-30 ] -
appeared on improved programming techniques, aiming at more transparent
programs. The latter quality in particular appears of overriding importance
in actual use.

In our view a clear distinction should be made between two essentially
different parts of the simulation program: the analytical part consisting
of the conservation equations for mass, momentum and energy and the
empirical or semi-empirical correlations for friction, heat transfer and
slip.

The analytical part may be considered the framework of the program; hence
subsequent changes would involve adjustments throughout the entire program
and should therefore be avoided. For this reason as much detail as
practically possible was incorporated in this part of the program right
from the start. In view of the excellent results on stability analysis
reported by VAN VONDEREN [ 4.6-5 ] his formulation of the balance equations
for the channels, followed essentially in subsection 4.2.2, was considered
to embody sufficient detail to be used as a starting point. As regards the
second, (semi-)empirical part, the pursuit of maximum accuracy implies the
use of empirical relations with limited ranges of validity. In view of the
considerable number of well-documented correlations available to date and
the continuing addition of new and possibly more accurate ones the goal of
general applicability of the program required easy exchange of these
correlations. This led to their incorporation as separate subroutines, in
accordance with the modular approach. A further requirement for flexibility
concerns the data transfer between the various subroutines. In order to
avoid compatibility problems in case of replacement of a correlation the
data transferred has to be general and complete. In view of the above the
values of all basic variables were transferred in all cases involving
empirical relations. The structure of the CURSSE-program, based on these
principles, in shown in the hierarchy table given in figure 4.6-22. This
table shows the highly modular structure of the program (106 subroutines).
The following five basic sections can be distinguished, each controlled by
the main program and calling a number of lower level subroutines:

1. INPUT

purpose:

- input and preliminary processing of all data (including steady
state conditions)

2. SYSEQ

purpose:

- determination of all coefficients of the total set of linear
equations

- 4.61 -

K

4.

5y

ad 1)

ad 2)

ad 3)

- 4.62 -

PRELUD

purpose:

- composition of the band structured coefficient matrices
EIGVEC

purpose:
- determination of a prescribed number of eigenvalues and associated
eigenvectors

TRANSF

purpose:

- determination of the solution vectors of the frequency analysis
problem (cf. equation (4.6-5) for a prescribed number of different
frequencies.

In addition to the actual input of data the INPUT routine takes care
of the generation of keys, identifying each of the "nodal points" in
the system.

This identification system is needed to facilitate future operations,
e.g. computation of the coefficients of the equations.

Each key is an eight digit number (2 digits for each item) consisting
of (cf. figure 4.6-23):

the type number of the part
(channel, wall, header, nozzle: primary or secondary)

the serial number of that particular part (e.g. 2nd wall)

the level number. The total geometry is divided into sections by a
number of levels indicating the presence of either a header or a
transition in one of the channels

the element number. Between each two consecutive levels the geometry

is divided into as many elements as required to obtain the desired
accuracy.

As in a keyed system the sequence of operations on the various
elements of the system can be based on logic rather than on the
particular geometry of the case at hand, such a description of the
topology has proven a powerful aid for obtaining programming
flexibility and yields a transparency otherwise impossible to achieve.

In the SYSEQ part of the program the coefficients of all equations of
the total system are determined and stored as two rows of numbers (A
and B matrices). Simultaneously their location in the matrices is
recorded by storing their row and column numbers.

In this way the amount of storage required in this stage is reduced
to only those elements of the matrix that contain actual coefficients.

The first action performed in PRELUD is generation of the band
matrices proper. This action has to await the determination of the
location of the last coefficients in SYSEQ, prior to which determina-
tion of the actual band width is impossible. Where determination of

eigenvalues is required PRELUD subsequently performs scaling of the
matrices and L U decomposition. The purpose of the scaling operations
is to improve the numerical conditioning of the system of equations.
By means of iterative multiplication of rows and columns by scaling
factors it is tried to keep the largest absolute values of the
elements in each row and column within a specified range.

ad 4)

EIGVEC is explained in some detail in Appendix 4K and in
OP DEN BROUW [ 4.6-31 ].

ad 5)

The algorithm of TRANSF is explained above in subsection 4.6.1.4.3,
whereas programming aspects of this subroutine are discussed in
[4.6-31].

The results of the program are given both as tables (cf. figure 4.6-24)
and in graphical form (cf. figure 4.6-25).

In the latter both the amplitudes and the phase shifts of the various
basic variables are displayed, but in addition a sort of three-dimensional
plot is given to illustrate the total effect. Figure 4.6-25 shows p, H and
G in the evaporating channel of the DMSP-bayonet tube test module during a
frequency response test.

4.6.2. Stability experiments.

4.6.2.1. Introductory remarks.

Over the last two decades a considerable number of publications have dealt
with experimental investigations of hydro-dynamic instability in particular
density wave oscillations in parallel evaporator channels. The bulk of
these experiments are based on the following approach. Evaporator tubes -
either single or in sets of up to four identical or non-identical parallel
tubes -~ are operated over a wide range of process conditions, under the
boundary conditions of constant in- and outlet pressure.

In practice these boundary conditions are fulfilled by keeping both the
outlet pressure and the pressure drop across the test section constant. For
the outlet pressure this is achieved either by a downstream control valve
or by installing a high-pressure condenser immediately downstream of the
test section. The latter method, though more complicated, appears prefer-
able, as has been discussed in subsection 4.4.3.

Maintaining a constant pressure drop across a single tube is achieved by
installing a non-heated bypass of sufficiently large capacity. As shown in
subsection 4.6.1.2 this condition is automatically fulfilled in the case of
a number of identical parallel tubes.

The stability boundaries are determined by changing the steady state
conditions until spontaneous oscillations occur. This "proof of the
pudding" method is very direct, reliable and accurate, provided the
boundary conditions are satisfied with sufficient accuracy. However, this
method contributes but little to the understanding of the physical
phenomena involved. Moreover the results of experiments with non-identical
parallel channels are only valid for that particular tube arrangement and
its inlet and outlet systems and hence yield no information for the design
of other tube banks, as has been shown in subsection 4.6.1.2.3.

- 4.63 -

By contrast, application of the frequency response analysis widely used in
control studies, holds the following advantages over the purely empirical
approach mentioned above:

- by not implying the assumption of constant in- and outlet pressures i £
avoids the need for a bypass in the test rig and makes the experimental
results more directly applicable to actual steam generators

- through its systematic determination of the transfer functions between
the different evaporator process variables it provides an insight into
the physical phenomena and allows detailed comparisons between experi-
mental evidence and analytical predictions.

However, the method has so far found only limited application in the
determination of hydrodynamic stability limits.

To the author's knowledge the only publications on its use for this purpose
are those of GOODYKOONTZ [ 4.6-32 ], STEVENS [4.6-33 ], KREJSA [4.6-34 ] and
DORSCH [ 4.6-35 ], who studied boiler-feed system coupled instability in a
mono-tube boiler. They did not, however, consider either the effects of
parallel tubes or those of an outlet system.

Frequency response measurements were also performed by SPIGT [ 4.6-4 ] and
DIJKMAN [ 4.6-3 ] in a steam generator consisting of three parallel tubes
and by PAUL and RIEDLE [ 4.6-36 | on a single tube evaporator using

FREON-11 as evaporating fluid. None of these authors did however utilize
the experimentally obtained transfer functions for the purpose of deriving
stability limits.

4.6.2.2. Experimental procedure and data acquisition.

Limitations of our experimental facility, concerning secondary mass flow
and heat generating capacity, excluded the application of a large bypass
and of parallel tubes. Hence it was decided to apply frequency response
analysis for the investigation of the stability behaviour of the bayonet
tube steam generator in the way suggested in subsection 4.6.1.2.3, i.e. by
measuring the inlet-impedance of a single tube.

Bij superimposing a signal to that from the controller to the control valve
(cf. figure 4.3.4) a variation of the feedwater mass flow rate was obtained.
During the stability experiments both this mass flow variation and the
resulting variation of the total pressure drop across the test tube were
recorded. The outlet pressure was kept (more or less) constant by means of
the steam pressure control valve also shown in figure 4.3-4. Correlation

of the two recorded signals yields the amplification and phase shift of the
inlet impedance Hp¢ as a function of frequency.

In our experiments two different types of signal have been applied:

- binary noise
- harmonic oscillation

As a binary noise signal contains a range of frequencies, applicaticn of
this type of signal has the advantage that all information needed for a
complete Bode diagram can be obtained in a single test. Figure 4.6-26 shows
a typical result of this approach cbtained by processing the recorded
signals on a PDP-8 digital computer.

As it proved difficult to maintain the steady state conditions over the
long recording periods required for obtaining the desired accuracy over the
frequency range of interest (0.01 - 0.6 c¢/s), this method was rejected in
favour of harmonic analysis. Moreover the latter method facilitated the
investigation of amplitude dependency of the results, required for the

- 4,64 -

assessment of non-linear effects. In this method a single harmonic -
oscillation is super-imposed on the feedwater mass flow to the test
section. From a simultaneous recording of both this flow rate and the
variation of the total pressure drop on a multi-line recorder the
amplification and phase-shift of the inlet impedance can be derived for the
particular frequency of the test signal. Figure 4.6-27 shows a typical
example of such a recording. Repeated performance of this test for a number
of different frequencies yields the information required for constructing a
complete Bode diagram. Although less sophisticated than the binary noise
approach this method proved sufficiently accurate and very reliable. Figure
4.6-28 shows a typical Bode diagram of the DMSP bayonet tube obtained by
this type of impedance measurement.

4.6.2.3. Test program.

Stability tests on the DMSP bayonet tube test module were performed at two
FLiNaK inlet temperatures, two steam outlet pressures, three feedwater
inlet temperatures and three feedwater mass flow rates.

The combinations of these variables which were actually tested are listed
in figure 4.6-29.

4.6.3. Evaluation of analytical and experimental results.

4.6.3.1. Introductory remarks.

In contrast to the other simulation programs under discussion, which were
specially developed for the bayonet tube steam generator geometry, the much
wider applicability of the CURSSE-program made it desirable to extend the
verification of this latter program to other geometries. For this purpose
CURSSE simulations of experiments performed elsewhere on two sodium heated
steam generator geometries, straight tube and helically coiled tube
respectively, will also be discussed below.

4.6.3.2. Preliminary program verification in the frequency domain.

Prior to the development of the universal CURSSE program the solutional
methods underlying it and described in subsection 4.6.2.4 were tested by
applying them to a simplified problem, viz. a single uniformly electrically
heated evaporator tube fed by saturated water and producing steam of 95%
quality at a pressure of 18.0 MN/m?.

Further particulars are given in figure 4.6-30.

4.6.3.2.1. Eigenvalue analysis.

Eigenvalue analysis by application of the power method vector deflation
yielded the values given in- figure 4.6-31.

These values were found to be in exact agreement with those obtained
applying the so-called QR-method (cf. WILKINSON [ 4.6-25 ]), whose
applicability is restricted to relatively small problems.

4.6.3.2.2. Frequency analysis.

Determination of the inlet impedance for this simple case yields the curve
shown in figure 4.6-32.

The point designated by A represents the frequency corresponding to that of
the first eigenvalue of figure 4.6-31.

- 4.65 -

Bl 33y 1 thh steam generator experiments.

4.6.3.3.1. Outline cf experiments.

Experiments reported by SANO [ 4.6-37 ] have been performed on a 1 MW
sodium heated test module consisting of two parallel helically
cociled evaporator channels (cf. figure 4.6-33). Heat was transferred in
counterflow from the downward flowing sodium to the upward flowing water/
steam mixture.

Four experiments reported in [ 4.6-37 ] were simulated using CURSSE. The
required input data concerning steady state conditions were derived from
computer output kindly made available by the experimenter.

The four experiments may be characterized as follows:

th

M1 full load R = - I8 stable
M2 part load 62% R= 11 stable
M3 part load 62% R= 12 unstable
M4 part load 62% R= 13 unstable

where R is the sodium/water mass flow ratio.
During the experiments steam outlet pressure was kept constant at
approximately 14.5 MN/m? .

4.6.3.3.2. Eigenvalue analysis.

Contrary to our expectation that only a very limited number of real
eigenvalues would have low absolute values, a considerable number of such
eigenvalues were found in this case (cf. figure 4.6-34).

As will be clear from APPENDIX 4K the power method will fail under such
conditions as the vector deflation method is restricted to a limited number
of eigenvalues.

Due to this unforseen complication the eigenvalue option failed in the
present case. This failure indicates the need for a different method for
determinating eigenvalues. Time did not, however, permit the implementation
and verification of such an alternative method.

4.6.3.3.3. Frequency analysis.

Applying the frequency analysis option of the CURSSE-program the inlet
impedance curves for the four experiments mentioned in subsection 4.6.3.3.1
have been determined.

These curves are shown in figures 4.6-35a through 4.6-35d.

The full load case (experiment 1) is evidently stable. The curves for the
remaining three experiments enclose the origin and thus should be unstable.
Comparison with the above table shows these findings to agree with the
experiments, except for experiment nr. 2. Examination of the impedance
curve (figure 4.6-35b) shows, however, that the curve passes just to the
left of the origin, whereas passage to the right would have implied an
anti-clockwise encirclement and hence stability.

As a general point of interest it should be noted that comparatively small
differences resulting from changes in R for a given load are reflected in
the CURSSE results for experiments M2 through M4, whereas such effects are
completely neglected in some of the other approaches published (cf., UNAL
[4.6-2 ]).

-.4.66 -

4.6.3.4. SWISH experiments

4.6.3.4.1. Outline of experiments.

These experiments were performed by TNO in their sodium heated steam
generator test facility operated at Apeldoorn, Holland. In this single tube
test facility (cf. figure 4.6-36) the pressure drop is maintained constant
by applying a non-heated by-pass.

The conditions of the five straight tube experiments simulated are
summarized below.

G P P Tond. xuit results results
o MN/m? KW 0 of exp. of anal.
M1 1500 14.41 183.78 31.0 0.43 stable unstable
M2 1393 11.91 180.48 64.5 0.50 unstable | unstable
M3 1391 11.97 180.15 64.9 0.50 unstable | unstable
M4 1797 12.05 196.69 63.5 0.38 stable stable
M5 1324 12.04 175.91 65.6 0.52 unstable | unstable

4.6.3.4.2. Frequency analysis.

The computed inlet impedance curves for these experiments are shown in
figures 4.6-37a through 4.6-37e.

Except for the first one the simulations agree with the experiments.
During the experiments it was found that very small variations in
conditions could change the system from stable into highly unstable. This
probably explains the faulty prediction for experiment nr. 1 found by
JANSSEN [ 4.6-38 ] to be closest to the stability boundary.

For further details on these tests and verifications the reader is
referred to JANSSEN [ 4.6-38 ].

4.6.3.5. Bayonet tube experiments.

4.6.3.5.1. Time domain analysis.

Figures 4.6-38a through 4.6-38f show the results of inlet impedance
measurements on the bayonet tube test module for two different loads
(30% and 60% load) and of time domain simulations as discussed in
subsection 4.6.1.3; simulation by the time domain program of the 90% load
experiment proved impossible, due to certain restrictions in the
mathematical description.

The results are presented also in the form of Bode-diagrams, showing
separate amplification and phase shift responses, as this form of
presentation was selected earlier for the results of the experiments.
These figures show, that although phase shifts are approximated fairly
accurate amplification is strongly underestimated. This must probably be
attributed to progressive disintegraticn of the zirconia thermal

- 4,67 -

insulation layer discussed in subsection 4.1.2 *).

This effect was revealed during steam generator disassembly following
termination of the experiments.

While this progressive failure had no noticable effect on the overall
thermal behaviour, the resulting obstruction in the superheater gap caused
a slowly progressing but ultimately substantial increase in total pressure
drop. Though pressure drop recordings over the entire test period indicate
that cracking of the insulation was a slowly increasing process, the
destabilizing effect of this downstream restriction must have made itself
felt fairly early in the series of experiments. It explains in all
probability why the system, after showing stable behaviour during the first
start-up without any restriction in the feedwater flow,to our surprise
subsequently required the installation of a feedwater throttling valve

(cf. subsection 4.3.3.1) as a prerequisite to stable operation.

Due to the unknown history of the cracking process, comparison of the
inlet impedance amplification obtained by experiment and simulation becomes
doubtful. By contrast the phase shifts are hardly affected by this increase
in down stream pressure drop and hence detailed comparison remains possible
for that part of the results (figures 4.6-38b and 4.6-38c).

4.6.3.5.2. Frequency domain analysis.

In addition to the experimental results figures 4.6-38a through 4.6-38i
also show the results of the CURSSE simulations. Frequency domain
simulation of the 90% load case proved possible due to the increased
flexibility of CURSSE.

4.6.3.5.3. Additional remarks.

Although the phase shifts computed by CURSSE approximate the experimental
results somewhat closer than those computed by the time domain program both
types of simulations yield to a large degree identical results. With
increasing frequency the phase shifts obtained by simulation follow the
experimental results rather closely up to a point where a sudden jump to
higher phase shifts for the former occurs while the experimentally obtained
phase shifts vary more gradually. As the frequencies increase further the
three lines tend to coincide again.

The sudden jump in the simulated curves is better understood if the results
are shown in a polar plot. The simulated curves pass much closer to the
origin than the experimental one, which explains the jump (cf. figure
4.6-38¢c). :

The discrepancies may be caused by imperfections in either the models or
the experiments. First considering the mathematical models, it is remark-
able that the two different models developed independently, yield
approximately the same results. In the authors opinion this eliminates the
possibility of programming errors in the simulation programs.

*) .. . . .
This fatlure of the insulation layer in the DMSP test module should

not be comstidered proof of that spraying of 720, is not a viable
solution for the present application.

A layer sprayed on a smooth tube was tested for 300 hours in 400 °¢
steam,.with cooldown to ambient temperature and subsequent rapid
reheating occuring every 30 hours and found to remain intact without
a trace of cracking. It seems likely that the failure in the test
module was due to severe weakening of the layer by the presence of
thermo-couple wires embedded in the tube wall. .

-4.68 -

TECHNISCHE HOGESCHOOL DELFT
Bibliotheek

Postbus 98, 2600 MG Delft Nederland

Tel. 015-78 5679

Telexnr. 38070

IFLA -telecode

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Boeknr. (/p/@j()m(]

Wij verzoeken u het hierboven vermelde werk waarvan de vitleen-
termijn is verstreken, binnen 2 dagen te retourneren.

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Indien u aan dit verzoek niet voldoet, zijn wij genoodzaakt u
een rekening te presenteren voor de vervangingswaarde van het
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Verzoeke bij beantwoording onze referentie aan te halen
792771

As regards the experimental conditions, it is assumed in the simulations
that the outlet pressure is kept constant. As mentioned in subsection 4.5.4
this proved impossible in the test facility. On the contrary, substantial
steam outlet pressure variations up to 0.7 MN/m2 occurred during the
frequency response tests. These pressure drop variations could not be
simulated. It is probably this effect which causes the differences between
experimentally and analytically obtained phase shifts.

- 4,69 -

CONCLUSIONS AND RECOMMENDATIONS

The first objective of this study, viz. assessment of the potential of
FLiNaK as a high temperature heat transfer agent, has led to the following
conclusions:

® regarding equipment performance: prolonged trouble-free operation is
attainable with equipment made of INCONEL-600 provided the (TIG)
welding is performed by qualified welders and 100% X-rayed

® regarding heat and momentum transfer: the validity of the correlations
in general use for single-phase turbulent heat and momentum transfer
of fluids with Prandtl numbers not too far different from unity was
unequivocally confirmed

® redarding flow measurements: the venturi type flow meter was the only
one yielding adequate accuracy and releability under prolonged
operation.

The second objective of this study, viz. assessment of the beyonet tube
design for molten salt heated steam generators, has led to a positive
overall conclusion regarding its expected performance. A notable operating
advantage is the almost uniform steam outlet temperature obtained over a
wide range of loads (from 100 down to about 30% of rated power).

Although some preliminary design work on large (about 625 MWth) bajonet
tube units was undertaken within the DMSP framework KNAAP [ 5-1 ] and

VAN DER KROCHT [ 5-2 ] the results were not reported in this thesis because
they were neither followed by an in depth evaluation comparing this design
to the single tube super-critical alternative proposed by ROSENTHAL [ 5-3 ]
nor by a serious search for design improvements.

If further development of this design were to be considered for either
salt- or sodium-heated applications the following points would require
additional study:

® long term integrety of the evaporator tube's thermal insulation layer

® amount of inlet throttling required for hydro-dynamic stability of the
optimized geometry with its much higher superheater pressure drops

® means for preventing reducing instability during shutdown.

The following conclusions appear in order concerning the third objective of
the study, viz. computer modeling of steam generator thermo-hydraulics:

- the steady state program BASTA has proven to be an adequate tool for
the design of bayonet tube steam generators

- no satisfactory solution was found for the computer time consuming
problem of non-linear transient analysis.

Both the reasons for these negative findings and suggestions for
improvement are given in subsection 4.5. 3.

- the CURSSE program was found to be a very flexible and universally
applicable tool for establishing the stability limits of geometri-
cally complex steam generators. The very complete form of the basic
balance equations incorporated in CURSSE enables the user to perform
detailed sensitivety analyses. The simple way in which improved
empirical relations can be implemented forms an additional advantage.

- use of the eigenvalue option incorporated in CURSSE did not produce an
adequate number of eigenvalues. Improvement would require replacing
the power method by a different solution scheme

“. D¢l =

- 5.2 -

- use of the frequency analysis option in combination with properly
defined stability criteria resulted in generally correct predictions
for the "parallel channel" stability behaviour of three different
steam generator designs

- the same approach opens the possibility for predicting the "loop"
stability behaviour of complex systems consisting of non-identical
parallel tubes or tube banks

- further application of CURSSE preferably for the stability analysis
of operating multi-tube steam generators appears desirable.

ACKNOWLEDGEMENTS

The work reported in this thesis was performed in the Laboratory for
Thermal Power Engineering of the Delft University of Technology and
stretches over a good number of years.

It would be impossible to name everyone who has contributes to it, some
however have to be mentioned.

The author feels indebted to Neratoom B.V. and TNO which contributed to
the systems design and programming of the CURSSE program, and to the
Oak Ridge National Laboratory for providing equipment as well as know-how
on molten salt technology.

Though the author gratefully acknowledges the contributions of all the
staff of the Laboratory, special thanks are due to Messrs Hoppesteyn,
Maissan and Vincenten who in addition to all their valuable work in
designing and building the loops, under difficult circumstances cleared
away the mess caused by a mayor salt spill, which resulted from leak in
the loop.

Thanks also go to the students, who in the course of their graduate
studies actively participated in the investigations.

The author whishes to thank Mr Op de Brouw, whose contributions gave a
professional touch to teh CURSSE program and to Mr Middelkoop who
supervised the design erection and testing of the loops.

Messrs Wessling and Brouwer and Mrs Van Kampen translated the authors
hieroglyphs into drawings, graphs and carefully typewritten pages
respectively. ;

Last but not least the author thanks his wife and children for enduring
his ugly mocds during the last period of this work.

- 6.1 -

REFERENCES CHAPTER 2

il

v . R 8

TURNER, G.E.
Liquid metal flow measurement: state-of-the-art study.
LMEC - Memo 68-9, June (1968).

BRIGGS, R.B.

Molten salt reactor program: semi annual progress report for period
ending August 31, 1965.

ORNL - 3872 (1965).

V.D.I. Durchfluszmeszregeln.
DIN-1952, Nov. (1948).

VERBEEK, P.R.H.
IJking verturi tuiten (in Dutch).
Report Waterloopkundig laboratorium Delft, March (1973).

BEVINGTON, P.R.
Data reduction and error analysis for the physical sciences.
Mc.Graw-Hill (1968).

COHEN, S.I.
A physical property summary for ANP Fluoride mixtures.
ORNK-2150, Oak Ridge National Laboratory (1956).

OYE, H.A.
University of Trondheim, Instutt for uorganisk kjemi.
Private Communication (1977).

BENSON, J.M.
Survey of thermal devices for measuring flow.
Symposium on flow, Pittsburg, Pa. May 10 - 14 (1971).

MOELLER, R und TSCHOEKE, H.
Theoretische Untersuchungen zur Wandtemperaturmessung an simulierten

Brennstédben fiir thermodynamische Experimente in Natrium.
KFK 1555, Apr. (1972).

LEUNG, E.Y,.

Heat transfer in concentric and eccentric annuli with constant and
variable heat flux.

AHT-4, Stanford University (1962).

CROOKSTON, R.B.
Turbulent heat transfer in annuli.
Int. J. of Mass and Heat Transfer, Vol. 11, pp. 415-426 (1968).

JUDD, R.L. and WADE, J.T.
Forced convection heat transfer in eccentric annular passages.
Stanford University Press, pp. 272-288 (1963).

PRESSER, K.H.

Warmelbergang und Druckverlust an innenbeheizten Ringspalten bei
Hochdruck-Gaskhlung.

Chemie-Ing. Tech. no. 38, pp. 180-181 (1966).

- 7.1 -

24341

2 iy

y 8

2+4%.9

2.4.10.

- Tod >~

QUARMBY, A.

Some measurements of turbulent heat transfer in the thermal entrance
region of concentric annuli.

Int. J. of Heat and Mass Transfer, Vol. 10, pp. 267-276 (1967).

LEE, Y and BARROW, H.
Turbulent flow and heat transfer in concentric and eccentric annuli.
I. Mech. E. Convention, Cambridge (1964).

Kays, W.M. and LEUNG, E.Y.
Heat transfer in annular passages. Hydro-dynamically developed flow
with arbitrarily prescribed heat flux.

ALBERS, H.J.

Correlatie-snelheidsmetingen aan een hoge druk stoomketel (in Dutch).
A-6. Lab. Meet- en Regeltechniek University of Technology, Delft
(Neth.) (1964).

BENTLEY, P.G.

Fluid flow measurements by transit time analysis of temperature
fluctuations.

Trans. of the Soc. of Instrument Technology, Sept. (1966).

RANDALL, R.L.

Transit time flow meter employing Noise Analysis Techniques
Part 1. Water loop tests.

AI-AEC-12802, March (1969).

RANDALL, R.L. .

Transit time flow measurement employing Noise Analysis Techniques.
Part 2. 2" sodium loop tests.

AI-AEC-12941 (1971).

MURI, R.J. de

Transit time flow meter: six-inch-diameter water and sodium testing
summary.

LMEC-72-4, Aug. (1972).

GORDOV, A.N. .
An experimental investigation of the inertia of micro-thermocouples.
High Temperature Vol. 3, (1965) pp. 268-273.

TAYLOR, C.
The dispersion of matter in turbulent flow through a pipe.
Proc. Roy. Soc. A-223 (1954).

TAYLOR, C.
Diffusion by continuous movements.
Proc. London Math. Soc. (2), (1922).

SCHMIDTL, H.
Die Dynamik der axialen WarmelUbertragung bei turbulenter Rohrstrdmung.
Int. J. of Heat and Mass Transfer, Vol. 16, pp. 12-13 (1973).

HINZE, J.O.
Turbulence.
McGraw-Hill (1975).

2.4.11. VELTMAN, B.P.Th und KWAKERNAAK, H.
Theorie und Technik derPilaritatskorrelation flr dynamische Analyse
niederfrequenter Signale und Systeme.
Regelungstechnik, Vol. 9 (1961), pp. 357-364.

REFERENCES CHAPTER 3

3.1-1 LATZKO, D.G.H.
Delft Molten Salt Project: Design Summary Report.
DMSP-G-8, Laboratory for Thermal Power Engineering.
Delft University of Technology, aug. (1966).

3.2-1 Engineering properties of INCONEL alloy 600.
Technical bulletin T-7, Huntington.
Alloy products Division.

3.2-2 GROENEVELD, D.C.
Post-dryout heat transfer: physical mechanisms and a survey of
prediction methods.
Nuclear Engineering and Design, Vol. 32 (1975), pp. 283-294.

3.2-3 BAEHR, H.D.
Gleichungen und Tafeln der Thermodynamische Funktionen .von Luft und
einem Model-Verbrennungs Gas zur Berechnung von Gasturbinen Prozessen.
Fortschritt Berichte Reihe 6, nr. 13, V.D.I. Verlag Diusseldorf.

K P L | V.D.I.-Warme-atlas, Berechnungsbldtter fir den Warmeubergang.
V.D.I.-Verlag, Disseldorf (1963).

3.3-2 V.D.I., Durchfluszmeszregeln,

REFERENCES CHAPTER 4

4. 1'1. ROSENTHAL' M.W.
The developemnt status of molton salt breeder reactors.
ORNL-4812, Oak Ridge National Laboratory, Aug (1972).

4.1-2. FRAAS, A.P.
A new approach to the design of steam generators for molton salt
reactor power plants.
ORNL-TM-2953, Oak Ridge National Laboratory, June (1971)

4.1-3. IPENBURG, P,
Optimalisatie bajonetpijp stoomgenerator.
KR-434, Laboratory for thermal power engineering,
Delft University of Technology, Dec. (1975).

4.1-4. BISHOP, A.A., KRAMBECK, F.J.K. and SANDBERG, R.O.
Forced convection heat transfer to superheated steam at high
pressure and high Prandtl numbers.
ASME, 65-WA/MT (1965).

- 7.3 =

4.1-10.

4.1-11.

4.1-12.

4.2-1.

- 7.4 -

KINYON, B.W., ROMANOS, N.D. and RITLEDGE, G.A.

Steam generator utilizing steam boundary to transfer heat from
sodium to evaporating water.

ASME 69-WA/NE-20, Nov. (1969).

BARRATT, R.

Selection of the steam generator for the proposed 350-MW(e)
demonstration plant.

ASME 71-NE-5, March (1971).

PETREK, J.P.
Bayonet sodium-in-tube steam generator.
ASME 73-Pwr-13 (1973).

HUNSBEDT, A.
Thermal-hydraulic performance of a 2 MWt sodium-heated, forced
recirculation steam generator model.

TEN WOLDE, D.G.
Transient behaviour of nuclear steam generators.
Thesis, Delft University of Technology, Apr. (1972).

CAMPOLUNGHI, F., CUMO, M,, FERRARI, G., LEO, R. and VACARRO, G.
An experimental study on heat transfer in long, sub-critical
once-through steam generator.

Proc. of International Meeting on Reactor Heat Transfer,
Karksruhe, Oct. 9-11 (1973).

BOURE, J.A., BERGLES, A.E. and TONG, L.S.
Review of two-phase flow instability.
ASME 71-HT-42 (1971).

STENNING, A.H., VEZIROGLU, T.N. and CALLAHAN, G.M.

Pressure drop oscillations in forced convection flow with boiling.
Proc. of symposium on two-phase flow dynamics,

Eindhoven, The Netherlands, Sept. 4-9 (1967).

WALLIS, G.B.
One-dimensional two-phase flow.
McGraw-Hill, Inc., New York (1961).

HANCOX, W.T. and NICOLL, W.B.

A general technique for the prediction of void distributions in
non-steady two-phase forced convection.

J. of Heat Mass Transfer, vol. 14 (1971), pp. 1377-1394.

BANKOFF, S.G.

A variable density single-fluid model for two-phase flow with
particular reference to steam-water flow.

J. of Heat Transfer, ASME, Series C, Vol. 82 (1960).

GROENEVELD, D.C. and DELORME, G.G.J.
Prediction of thermal non-equilibrium in the post-dryout regime.
Nuclear Engineering and Design, Vol. 36 (1976), pp. 17-26.

4.2-6.

4.2+7.

4.2+-9.

4.2-10.

4.2-11,

4.2-12.

BOWRING, R.W.

Physical model, based on bubble detachment, and calculation of
steam-voidage in the subcocled region of a heated channel.
OECD Halden Reactor Project, HPR 10 (1962).

JENS, W.M. and LOTTES, P.A.

Analysis of heat transfer, burn-out, pressure drop and density
data for high pressure water.

ANL-4627 (1951).

LEE, D.H. |

Studies of heat transfer and pressure drop relevant to subcritical
once-through evaporators.

IAEA-SM-130/56 (1970).

WISMAN, R.

Analytical pressure drop correlation of addiabatic vertical
two-phase flow.

Applied Scientific Research, Vol. 30, March (1975), pp. 367-380.

MARTINELLI, R.C. and NELSON, D.B.

Prediction of pressure drop during forced-circulation boiling of
water.

Transactions of ASME, Aug. (1948).

DUKLER, A.E., WICKS, M. and CLEVELAND, R.G.

A comparison of existing correlations for pressure loss and holdup,
an approach through similarity analysis.

A.I.Ch.E. Journal, Vol. 10 (1964).

JONES, A.B.
Hydrodynamic stability of a boiling channel.
KAPL-2170 (1961).

VAN VONDEREN, A.C.M.

On the hydrodynamic behaviour of parallel boiling water channels.
Thesis, Laboratory for Heat Transfer and Reactor Engineering,
Eindhoven University of Technology, March (1971).

WISMAN, R.

Fundamental investigations on interaction forces in bubble swarms
and its application to the design of centrifugal separators.
Thesis, Delft University of Technology, to be published shortly.

LEE, J.A.N.
Numerical analysis for computers.
Reinhold, New York (1966).

IPENBURG, P.
Stationaire stoomgenerator proeven DMSP. (in dutch)

KR-418, Delft University of Technology, Laboratory for Power
Engineering Nov. (1975).

SANATHANAN, C.K.

Dynamic modeling of a large once-through steam generator.
Nuclear Engineering and Design, Vol. 23 (1972), pp. 321-330.

- 7.5 -

4.5-3.

4.5-7.

4.6-1.

4.6-2.

- 7.6 -

HOla, A.

Linear analytical one-dimensional model describing the frequency
response behaviour of shell-and-tube type counterflow heat exchangers
with respect to primary and secondary inlet temperature and mass flow
perturbations.

Nuclear Engineering and Design, Vol. 26 (1974), pp. 231-241.

BRUENS, N.W.S.

Modeling of nuclear steam generators.

Proc. of the Second Power Plant Dynamics, Control and Testing.
Symposium, Tennessee, Sept. 3-5 (1975).

BRUENS, N.W.S.

Digitaal computerprogramma voor de simulatie van het dynamische
gedrag van de DMSP-bajonetpijp stoomgenerator.

KR-357, Delft University of Technology, Laboratory for Power
Engineering, Aug. (1973).

PRINS, R.T.G.

DSTB, digitaal computerprogramma voor de simulatie van het
dynamisch gedrag van de DMSP-bajonetpijp stoomgenerator,

met een N.L.-model.

EV-1014, Laboratory for Thermal Power Engineering,

Delft University of Technology, The Netherlands, June (1978).

ZADEH, L.A. and DESOUR, C.A.
Linear system theory.
McGraw-Hill Book Company, New York.

HOFER, E.

A partially implicit method for large stiff systems of ode's
with only few equations introducing small time-constants.
Siam J. Numer. Anal., Vol. 13, no. 5, Oct. (1976).

GOEMANS, T., VAN MAREN, D. and TEN WOLDE, D.G.

MASCARA: a multi-variable data-prosessing code for quasi- and
non-stationary measurements.

Delft University of Technology,

Dept. of Mechanical Engineering, WTHD-18, Feb. (1970).

LEEUWEN, H.N.,

Metingen van het dynamisch gedrag van de DMSP-bajonetpiijp
stoomgenerator.

KR-419, Delft University of Technology,

Laboratory for Power Engineering, Aug. (1975).

SHOTKIN, L.M.
Stability considerations in two-phase flow.
Nuclear Science and Engineering, Vol. 28 (1967), pp. 317-324.

UNAL, H.C. and VAN GASSELT, M.L.G.

Dynamic instabilities in tubes of a large capacity, straight-tube,
once-through sodium heated steam generator.

Int. J. Heat Mass Transfer, Vol. 20 (1977), pp. 1389-1399, and
private communications.

4.6-5.

4.6-10.

4.6-11.

4.6-12.

4.6-13.

4.6-14.

DIJKMAN, F.J.M.
Some hydro-dynamic aspects of a boiling channel.
Thesis, University cf Technology, Eindhoven, The Netherlands (1969).

SPIGCT, C.L.

On the hydraulic characteristics of a boiling water channel with
natural circulation.

Thesis, University of Technology, Eindhoven, The Netherlands (1966).

VAN VONDEREN, A.C.M.
On the behaviour cf parallel boiling water channels.
Thesis, University of Technology, Eindhoven, The Netherlands (1971).

POTTER, R.

A review of two-phase flow instability aspects of boiler dynamics.
Proc. of Symposium on Power Plant Dynamics, Control and Testing,
Knoxville, Tennessee, Oct. 8-10 (1973).

DAVIES, A.L. and POTTER, R.

Hydraulic stability: an analysis of the causes of unstable flow in
parallel channels.

Proc. of Symposium on two-phase flow dynamics,

Eindhoven, The Netherlands, Sept. 4-9 (1967).

JONES, A.B.
Hydro-dynamic stability of a boiling channel.
KAPL-3070, Aug. (1964).

NEAL, L.G. and ZIVI, S.M.

Hydro-dynamic stability of natural circulation boiling systems.
A comparative study of analytical models and experimental data.
TWR-Systems, STL 372-14 (1), (1965).

EFFERDING, L.E.

DYNAM: A digital computer program for study of the dynamic stability
of once-through boiling flow with steam superheat.

GAMD-8656 (1958).

HALOZAN, H.
Statische und dynamische Instabilitat der Zweiphasenstrdémung. (german)
Thesis, Technological University of Graz, Mai (1973).

SEITTKE, H.J,
Berlucksichtigung von Druck und Zweiphasen-Impulsaustausch bei der

Dynamik eines konvectiv beheizten Zwangdurchlaufdampferzeugers.
Zwischenbericht nr. 5.

Institut flir Verfahrenstechnik und Dampfkesselwesen, Dec. (1975).

TAKAHASHI, R. and FUTAMI, T.

Theoretical study of flow instability of a sodium heated steam
generator.

Nuclear Engineering and Design, Vol. 41 (1977), pp. 103-204.
SUZUOKI, A. and YAMAKAWA, M,

Studies of thermal-hydrodynamic flow instability.
Bulletin of the JSME, Vol. 19, No. 132, June (1976), pp. 619-626.

- 7.7 -

4.6~15,

4.6-16.

4.6-17.

4.6-18.

4.6-19,

4.6-20.

4.6-21.

4.6-22.

406-230

4.6-24.

4.0-25.

- 7.8 -

DEAM, R. and MURRAY, J.

The prediction of dynamic stability limits in once-through boilers
using DYMEL.

Paper: European Two-Phase Flow Group Meeting, Erlangen, May (1976).

CROWLEY, J.D., DEANE, C. and GOUSE, S.W.

Two-phase flow oscillations in vertical, parallel, heated channels.
Proc. of Symposium on two-phase flow dynamics,

Eindhoven, The Netherlands, Sept. 4-9 (1967).

D'ARCY, D.F.

An experimental investigation of boiling channel flow instability.
Proc. of Symposium on two-phase flow dynamics,

Eindhoven, The Netherlands, Sept. 4-9 (1967).

PIPES, A.L.
Matrix methods for Engineering.
Prentice-Hall (1963).

KAKAC, S., VEZIROGLU, T.N., LEE, S.S. and OZBOYA, N.
Transient boiling flow instability in a multi-channel upflow system.
Warme 'und Stoffibertragung, Vol. 10 (1977), pp. 175-188.

JANSEN, J.B.

Simulatie hydro-dynamische stabiliteitsgedrag van de DMSP-bajonetpijp
stoomgenerator in het tijdsdomein. (in dutch).

EV-1035, Delft University of Technology,

Laboratory for Power Engineering, Jan. (1978).

BLOEM, J.R.

Digitale simulatie in het tijdsdomein der hydro-dynamische
instabiliteit in de DMSP-bajonetpijp stoomgenerator. (in dutch).
KR-421, Delft University of Technology,

Laboratory for Power Engineering, Aug. (1975).

TREMBLAY, P.E.

Thermo~hydrodynamic instabilities in a boiling channel in parallel
with a finite by-pass.

Thesis, University of Toronto, Oct. (1972).

DE GREEF, J.F.

Cylindrical thermal equations for the analog computer.
Annales de 1l"Association Internationale pour le Calcul
Analogique, Vol. 9, Oct. (1967), pp. 195-197.

PAULUSMA, J.C.P.

Een methode voor het oplossen van een gegeneraliseerd eigenwaarden
probleem met niet-symmetrische bandmatrices van grote orde t.b.v.
een stabiliteits rekenprogramma voor stoomgeneratoren.

EV-1041, Laboratory for Thermal Power Engineering,

Delft University of Technology, June (1976).

WILKINSON, J.H.
The algebraic eigenvalue problem.
Academic Press, New York (1966).

4.6-26.

4.6-27.

4.6-28.

4.6-29,

4.6~-30.

4.6-31.

4.6-32.

4.6-33.

4.6-34.

4.6-35.

4.6-36.

4.6-37.

OLDENBURG, R. (editor)
Frequency response.
McMillan, New York (1956).

SPAAS, H.A.C.M.

Some contributions to the structural design and analysis of pressure
vessel and piping components.

Thesis, Delft University of Technology, March (1977).

BRUKX, J.F.L.M. and BUIS, J.P.

Hybrid simulation of LMFBR heat transfer system dynamics.

AICA Symposium on Hybrid computation in dynamic systems design,
Rome, Nov. 11-14 (1974).

STEVENS, W.P., MYERS, G.J. and CONSTANTINE, L.L.
Structured design.

I.B.M. Systems Journal, Vol. 13 (1974), pp. 115-118.

HIPO - A design aid and documentation technique.
IBM, publ. no. GC20-1851-1.

OP DEN BROUW, H.

Programmers Manual to CURSSE.

Delft University of Technology, EV-1066.
Laboratory for Power Engineering, June (1978).

GOODYKOONTZ, J.H.
Frequency response of forced-flow single-tube boiler with inserts.
NASA TN D-4189, Oct. (1967).

STEVENS, G.H.

Frequency response of a forced-flow single-tube boiler with inserts
and exit restriction.

NASA TN D-5023, Feb. (1969).

KREJSA, E.A.
Frequency response of a forced-flow single-tube boiler.
NASA TN D-4039, June (1967).

DORSCH, R.G.

Frequency response of a forced-flow single-tube boiler.
Proc. of Symposium on two-phase flow dynamics,
Eindhoven, The Netherlands, Sept. 4-9 (1967).

PAUL, F.W. and RIEDLE, K.J.

Experimental frequency response characteristics for diabatic
two-phase flow in a vertical mono tube vapor generator.
Journal of Heat Transfer, Vol. 96, Nov. (1974), pp. 504-510.

SANO, A.
1 MWt steam generator operating experience.

ASME, 73-HT-53 (1973).

- 7.9 -

JANSSEN, J.B.

Simulatie hydrodynamisch stabiliteitsgedrag van diverse stoom-
generatorgeometrieén m.b.v. het CURSSE-programma. (in Dutch).
EV-1049 Delft University of Technology.

Laboratory for Power Engineering, March (1978).

REFERENCES CHAPTER 5

Dsda

- 7.10 -

KNAAP, M.H.

Enige constructive aspecten van doorpomp-bajonetpijpen in een
door gesmolten zouten verhitte 680 MW h stoomgenerator.
KR-248 Laboratory for thermal power engineering,

Delft University of Technology, Apr. (1970).

VAN DER KROCHT, C.A.J.

Keramische isolatie van een deel van de verdamperpijp en
afstoppen van beschadigde pijpen van een door gesmolten
zouten verhitte 680 MWth stoomgenerator met doorpomp-bajonetpijpen.
(in dutch)

KR-254, Laboratory for thermal power engineering,
Delft University of Technology, June (1970).

ROSENTHAL, M.W.
The development status of molten salt reactor power plants.
ORNL-TM-2953, Oak Ridge National Laboratory, June (1971).

SAMENVATTING

Dit proefschrift bestaat uit twee delen.

In het eerste deel worden de mogelijkheden besprcken, die een mengsel van
gesmolten zouten biedt voor toepassing als warmteoverdrachts medium bij
temperaturen boven 500 Oc.

De behoefte aan een dergelijke warmtedrager kan ontstaan uit nieuwe
chemische processen, waarvoor meer gebruikelijke lage druk warmteover-
drachts media niet toepasbaar zijn. Het hier besproken zoutmengsel - het
ternaire entecticum van natrium-, kalium- en lithium fluoride bekend onder
de naam FLiNaK - is zeer korrosief.

In hoofdstuk 2 wordt de bruikbaarheid van drie verschillende methoden voor
het meten van de massastroom van een dergelijke korrosieve vloeistof bij
hoge temperatuur, respektievelijk gebaseerd op het principe van de venturi,
de "hete vinger" en de meting van looptijden, besproken. De metingen werden
uitgevoerd in een gesmolten zout kringloop op semi-technische schaal.

In dezelfde kringloop werden empirische warmteoverdrachts- en drukverlies
korrelaties bepaald. Deze experimenten aan een zout-op-lucht warmte-
wisselaar en een speciaal gekalibreerd leidinggedeelte worden, tezamen met
de gevonden korrelaties, besproken in hoofdstuk 3.

In het tweede deel van dit proefschrift wordt het thermo-hydraulisch gedrag
van bajonetpijp stoomgeneratoren besproken. De relatie met het eerste deel
bestaat hierin, dat dit ontwerp de enige mogelijkheid biedt voor opwekking
van stoom bij subkritische kondities in een met FLiNaK of een ander
fluoride-mengsel verhitte stoomgenerator, in verband met het hoge smeltpunt
van deze vloeistoffen. De behoefte aan een dergelijke stoomgenerator
ontstaat bij verdere ontwikkeling van thermische kweekreaktoren met
gesmolten zouten als koelmiddel.

Voor ieder van de drie aspekten van het thermo-hydraulisch ontwerp,
besproken in hoofdstuk 4, n.l.:

- stationair gedrag (vollast en deellast)
- gedrag bij grote verstoringen
- hydro-dynamische stabiliteit

zijn één of meer komputerprogramma's ontwikkeld en geverifieerd door
vergelijking met resultaten van experimenten aan een éénpijps testmodel
waarin stoom werd opgewekt van 18 MPa/540 Oc.

Tijdens de ontwikkeling van de programmatuur voor het laatste onderdeel
werd het duidelijk dat er behoefte bestond aan een simulatieprogramma
waarmee de stabiliteitsgrenzen van doorpomp stoomgeneratoren van verschil-
lende geometrieén zouden kunnen wordt bepaald, zowel voor "parallel
channel" als voor "loop" instabiliteit. Voor dat doel werd een modulair
opgebouwd, programma (CURSSE) ontwikkeld en geverifieerd door vergelijking
met resultaten van experimenten aan de bovengenoemde éénpijps bajonetpiijp
stoomgenerator en twee verschillende, elders geteste stoomgeneratoren.

De konklusies voor beide delen van dit proefschrift, geformuleerd in
hoofdstuk 5, kunnen als volgt worden samengevat:

® FLiNaK lijkt zeer geschikt als warmteoverdrachts medium bij
temperaturen tussen de 500 en 700 Oc

® het bajonetpijp ontwerp biedt een theoretisch veelbelovende, maar
mogelijk ekonomisch minder aantrekkelijk alternatief voor de
produktie van stoom in een met gesmolten zouten gekoeld kweekreaktor
systeem

® het CURSSE programma is een flexibel en betrouwbaar hulpmiddel
gebleken voor het voorspellen van de stabiliteitsgrenzen van doorpomp
stoomgeneratoren van verschillende geometrieén.

- 8.1 -

APPENDIX 2A

Thermal conductivity of FLiNak.

The values found in literature for the thermal conductivity of FLiNakK
range from 0.6 - 5.4 W/ (m C).
COHEN [ 2A-1 ] reports a value of 2.6 W/ (m Co).

EWING [ 2A-2 ], using a longitudinal heat flow apparatus, mentions values
of:

A = 2.40 - 5.38 W/ (m 9%c) for 500 - 850 Oc

In a subsequent publication [ 2A-3 ] he concluded after reviewing his
previous data that thermal radiation was the major transport mechanism
relevant to the conductivity of FLiNaK:

A = 0.6 W/ (m %) for 490 - 850 Oc

COOKE [2A-4 ] and [ 2A-5 ] in his studies with molten salts found radiation
to be significant but made no measurements with FLiNaK. However, he
estimates A = 1.2 W/(m 9C) for FLiNaK at the melting temperature (454 Og).
His estimates show good agreement with measured values for several other
salts.

A survey by DEBOIS-BLANC [ 2A-6 ] in 1973 recommends the following value
attributed by him to J.P. Sanders of Oak Ridge National Laboratory:

A =1.3 W/ (m %)

For consistency this latter value was uniformly used throughout this thesis.
Except for being the most recent value its selection was rather arbitrary
(Ref. [ 2A-6 ]) quotes no accuracy for this value.

- 2.1 -

APPENDIX 3A

Error analysis of the friction pressure drop measurement.

The pressure drop across the test tube is measured by means of the
following chain of four instruments:

- de dP-transducer consisting of the two vessels with single electrode
control systems

- the pressure difference transmitter

- the amplifier

- the recorder.

Figure 3A-1 shows a typical recording of the signal.

The wave line appearing on the recorder instead of the straight line
expected, is explained by the control action of the single electrode
control system (cf. subsection 2.2.2.2). The actual pressure drop is
determined by smoothing the signal. The total error of the dP-transducer
including the error caused by this smoothing is estimated at less than 2%
of the maximum pressure drop (0.008 MN/m? # 400 mm salt head) measured.
(The error due to the dead band of = 2.5 mm is 0.6%. The ripple on the
recording is estimated at = 1.5%).

As the remainder of the chain consisting of dP-transducer, amplifier and
recorder was calibrated in line, only the repeatability of these instru-
ments needs to the considered for the error analysis. The repeatability of
these instruments is 0.1%, 0.5% and 0.25% respectively. These inaccuracies
amount to a total inaccuracy of less than 3% of the maximum value measured.

- 3R.1 -~

APPENDIX 4A

Energy balances for the subcooled region.

As stated in subsection 4.2.2.2.2 the engineering approach towards the
complex heat transfer processes in the subcooled region is to define a
fraction of the total transferred heat: k used for vapour generation. The
remainder of the heat serves for heating of the subcooled bulk. The above
indicates the need for two separate energy balances. To derive these
balances we start with the energy balance for the mixture as given by
equation (4.2-8):

3 3

e — +——— —_—

5% (pg ug o + p2 u2 (1-a)) e (pg ug o vg + pz u2 (1-a) vz)

+ E-—-(oc v. + (1-a) v,) = 2 (4A-1)
P 3z g 92

The two terms of these equation on the first line represent storage and
convective transport of internal energy of the mixture respectively whereas
the first term on the second line represents the expansion work performed
by the mixture.

Differentiation of the products in the first two terms of equation (4A-1)
yields:

R e
Qo pg (at + Vg g ) '+ u (SE%a pg) + 5—%a p_Vv.))
ou ou 5
+ (1-a) Py (SE—'+ v, 5;—0 + uy (SE((I—G) Py )
3 3 3 _ 0 N
+ 5;1(1-0) pg Vz) + p { gzia Vg) % 5;1(1—&) Vg) } = qA (4A 2)

The rate of evaporation per unit is derived by TEN WOLDE [ 4A-1 ] as:

(4a-3)

©-
b
]
)
Q
+
)
<
Q

or:

- —g-—t-mg (1-0)) - 2= (p, v, (1-a)) (4n-4)

9)

Substitution of equation (4A-3) and (4A-4) in equation (4A-2) yields:

au au

- ¢2g (ug - uQ) II
ou Buz
+ (1-a) QQ(S-E—+ VQ, g‘z—) 0 3 o
8 a - 2
+p { 5;{& vg) + 5;%(1—&) Vz) } = =y IV (4A-5)

- 4A.1 -

The physical meaning of the first three terms of equation (4A-5) should
be kept in mind, viz.:

I the increase in internal energy of the steam present in the mixture.
" o o the increase in internal energy of the evaporating water.
ITII the increase in internal energy of the remaining water.

Term IV of equation (4A-5) requires some discussion. Differentiation of
the righthand terms of equation (4A-3) and (4A-4) vyields:

803 Bpg o 3 .
¢xg = Q Yy + o vg 2 + pg (SE-+ Sz{u v )) (42-0)
9 Py 30 8
T g T Umed g+ (1m0) vy aem ey (Bogp ¥ g ((lme) V) (4A-T)

Combination of equations (4A-6) and (4A-7) with term IV of equation (4A-5)

yields:
term IV =
1 1
PSSR Fa e \Y
p ¢2g (p p2)
ap ap
-B (a3 +a J VI
P pt g 0z
g
op op
_P (1) X _ L .
p2((1 o) oy + (1-0) VR s VII (4A-8)

Thus term IV is divided into three parts with the following physical
meaning:

Y, expansion work due to evaporating.
pff * expansion work of the gas.
VII expansion of the water.

Having established the physical meaning of the various parts of mixture
energy equation (4A-1) formulation of the two subcoocled energy equations
becomes straight forward.

The first energy equation, comprising all terms connected with the gas
phase and the evaporating proper, reads:

I +II +V + VI =

Bug Bug
= ——— + (1 - +
- pg ot - pg Vg 0Z ¢2g ‘dg uQ)
ap ap
1 1 p . g g k goO
+ —_—— ) = = + = 47-9
P ¢Rg (OO QQ) pg(a ot = Vg 9z ) A (42=9)

whereas the second one, comprising the terms connected with the water
phase, reads:

- 4A.2 -

¥ i il £ R SRR T I 6

APPENDIX 4B

An adapted version of the Bankoff - Jones slip correlation.

The Bankoff - Jones slip correlation was derived from the correlation
originally formulated by BANKOFF [ 4B-1 ]:

S = - (4B-1)

where:

k. = 0,71 ¥ 0.29 (4B-2)
P pcr

The general shape of the s versus a curve shown in figure 4B-1 indicates
that this correlation can only be valid for values smaller than the value
of the constant KB.

The need for a correlation valid over the full range of possible o values
promted JONES [ 4B-2 ] to adapt the Bankoff correlation by substituting KJ
for KB in equation (4B-1):

(4B-3)

where KJ reads:

X

KJ = KB + (l—KB) o (4B-4)

rm 3,33 % 0,507 Bews 4§70 (Kbt ? (4B-5)
il g ko

Introduction of KJ prevents the denominator of equation (4B-2) from

vanishing or becoming negative. Jones determined his r(a) function by
fitting slip data for lower values of a (< ®# 0.8). Inspection of a typical
Bankoff - Jones slip correlation curve (cf. figure 4B-1) shows that slip
ratio s increases monotonously with o, reaching its highest value for

o = 1. This appears physically improbable as for higher o values the
mixture consists of a bulk of steam containing very small droplets of
water (mist flow) with a relatively high resistance against motion with
respect to the surrounding steam. It hence appears probable that with
increasing o values the relative velocity of the water is reduced rather
than enhanced, thus decreasing the slip ratio. The Bankoff - Jones slip
correlation, although succesfully avoiding numerical problems, will
therefore not (nor claims to) predict accurate slip ratios for higher

o values.

It follows from the above that for o values approaching unity the steam
and water velocities tend to become equal. In that case the limit for the
slip ratio solely depends on the cross-sectional void and velocity distri-
butions. An upper limit for this ratio is given by the Vmax/v ratio

- 4B.1 -

(assuming all droplets to be concentrated in the region with the highest
velocity). This ratio depends weakly on the Re-number but a typical value
is 1.2. (cf. HINZE [ 4B-3 ]). However, it is more likely that due to turbu-
lence effects the crosssectional void distributions will be approximately
uniform, yielding a limit for s equal to unity when a > 1.
Seeking to correct the Bankoff - Jones correlation by a simple extension
the present author investigated the following adapted version:
§ + 1-u
S = S—:T?;;:E (4B-6)

obtained simply by adding a small quantity 6 to both numerator and
denominator of equation (4B-3). Figure 4B-1 shows the result of this
approach: the slip ratio s increases for lower o values closely approxi-
mating the original Bankoff - Jones correlation, but decreases for higher

o values until reaching unity for a = 1. Determination of the best values
for §, chosen here rather arbitrarily as 0.04, requires fitting to reliable
slip data for higher o values. It should be stressed that no physical
significance is claimed for this approach.

However, in the continuing absence of accurate and physically well-based
slip correlations for high o values the proposed correlation may serve as a
simple formula better fitting the true relation between slip ratio and void
fraction than the Bankoff - Jones correlation it is based on.

- 4B.2 -

APPENDIX 4C

The derivative of the specific mass of two-phase mixtures with respect to

the mixture enthalpy.

The two-phase mixture density is defined by equation (4.2-5) as:

0 = oy © +p, (1-0) (4C-1)

whereas the two-phase enthalpy is defined as:

h=h x+h (1-x) (4C-2)
g 2

Neglecting pressure effects the derivative of o with respect to h can be
written as:

el veglh el (4C-3)
ah da dx dh
From equations (4C-1) and (4C-2) follows respectively:
dp: | '
e (p OQ) (4Cc-4)
and:
R (4c-5)

Assuming no slip (s 1.0) the relationship between o and x is given by:

g
X = (4C-6)
(1—a)p2 - apg

Differentiating with respect to a yields:

DQ P

ax _ % g (4Cc-7)
dOL 52

After combination of equations (4C-4), (4C-5) and (4C-7) follows:

apradtnigly . ok
5h %

- 4C.1 -

APPENDIX 4E

Derivation of the equations describing the total system.

¢ p,_ = Hp¢ (w) 6 ¢in. * pr

J

. ¢outi - H¢¢ S ¢in. &
§ ., =-2 (w) § ¢.
in n lntot
S p = 2 (w) 6 ¢
out out outtot
n
S ¢, = I 6 ¢,
ot =1 0y
n
S ¢ = I § ¢
outtot j=1 outj

Combination of equations (4.6-4b), (4.6-6) and (4.6-8) yields:

¢p

Pl pout

(w) © p-out

n
¢ Pout = Zout ,Z (H¢¢_ in, i Zout
I=1 J J
or after transformation:
n H¢¢j : Zout
: Pout = 'El n S ¢
=1+ 3z 5 )

H
OUL smi-. TP

Substitution of equations (4E-2) and (4.6-7) in (4.6-4a) yields:

n
A. 8
RS TR T e T
i J=1 J
where:
A, =H
i~ Ppg,

for all j

p)) . pout

(4.6-4a)

(4.6-4Db)

(4.6-5)

(4.6-6)

(4.6-7)

(4.6-8)

(4E-1)

(4E-2)

(4E-3)

(4E-4)

(4E-5)

- 4E.1 -

pp. ¢¢, out (4E-6)

(1 + Z L H. )
out k=1 ¢pk

In order to provide a better insight into the physical meaning of these
equations let us divide the system into two parts: upstream and downstream
of the inlet header (cf. figure 4.6-7).

A according to equation (4.6-4a) the inlet pressure of a channel is
affected by the inlet mass flow and the outlet pressure. Now let us assume
that the mass flow into channel j increases. This will affect the inlet
pressure in two ways, viz: first directly through:

and indirectly through the outlet pressure. The latter would increase by:

. pout - Zout H¢¢j i ¢j

if the total outlet mass flow were to increase by exactly the same amount
as the mass flow through channel j . However, there is an attenuating
effect. The increasing outlet pressure tends to reduce the outlet mass flow
of all channels (cf. equation (4.6-4b)) and thus reduces the increase of
the total outlet mass flow. This is why the outlet pressure increases only
by:

Zout H¢¢j . ¢j

n
(1 + 2 I H,_ )

- out k=1 ¢pk
The increase in outlet pressure raises the inlet pressure of an arbitrary
channel i by:

It will be clear now that the total change in inlet pressure due to down-
stream effects is:

Z H
out ¢¢,
el

S 4E-8
¢j) ( )

j
(1 + 2 T H )
out - ¢pk

- 4E.2 -

According to equation (4.6-5) the inlet pressure change caused by upstream
effects is:

n
Sp.. = L -2, § ¢, (4E-9)

2s there is only one inlet pressure the two variations given by equations
(4E-8) and (4E-9) must of necessity be equal which explains equation
(4E-7) .

- 4E.3 -

APPENDIX 4F

Explanation for the existence of predominant modes of parallel channel
instability.

The linear analysis presented so far can not explain the existence of
Predominant modes of parallel channel oscillation as observed by

VAN VONDEREN [ 4.6-5 ].

For that purpose one has to consider the effects of non-linearities.

The most notable effect of these non-linearities is the change in shape of
flow cscillations with increasing amplitude.

The examinations of a line recording of a measured oscillation shown in
figure (4F-1) shows that with increasing amplitude the tops become flatter
whereas the bottom parts become sharper.

In addition to the original pure sine the signal now contains harmonics.
Figure (4F-2) shows a signal resulting from the addition of a sine and its
second order harmonic having a third of the first order amplitude, which
closely resembles the line recording. Returning to parallel channel insta-
bility we remind the reader of the main characteristic of this type of
oscillation: the constant total mass flow.

In the linear analysis this condition merely yields for a set of identical
channels that the sum of the oscillations in the individual channels is
constant.

This condition can be met by an infinite number of combinations of sines.
However, it will be clear that the possibilities to meet this condition
with oscillations as shown in figure (4F-2) are less numerous.

The variation of the second order signal of figure (4F-2) can be repre-
sented by the complex formula:

§ $ = u+ cu? (u and c are complex numbers) (4F-1)

The first term on the right hand side represents the basic sine whereas the
second term represents the second order component.

c represents the degree of non-linearity.

Now let us consider the case of VAN VONDEREN [ 4.6-5 ] : three parallel
identical channels.

The flows through these channels can according to equation (4F-2) be given
by:

:

S 9y u; + ¢ ug
§ ¢p = up + c uy? (4F-2)
S ¢3 = ug + c u32

The condition to be met for parallel channel instability is:

S ¢1 + 8 ¢o + S 93 =0 _ (4F-3)

To chieve this all times the sum of the first order harmonics and the sum
of the second order harmonics have to vanish:

u; + up + uz =0
(4F-4)

c (u;? + up? + uz?) =0

- 4F.1 -

Solution of these equations yields:

u, = (- 1—+ %—i V3) u)

N

(4F-5)

1
—;-i/iul

N e

This is the predominant mode observed by VAN VONDEREN [ 4.6-5 ]: all three
tubes oscillating with the same amplitude and a mutual phase shift of 1200
(cf. figure 4F-3). This result is physically easy to understand: this mode
is the only combination of "non-linear" signals satisfying the above
condition, viz. that both the sum of the first order harmonics and that of
the second order harmonics be zero (cf. figure 4F-4). In none of the other
modes mentioned in subsection 4.6.1.2.3 the sum of the second order
harmonics vanishes. It is hence to be expected that this predominant mode
will generally prevail whenever the oscillation amplitude becomes large
enough for the second order harmonics to assume sufficient importance.

- 4F.2 -

APPENDIX 4G

Zero's of H , and EM
pol]

The problem to be discussed in this appendix concerns the determination of

the number of zero's with a positive real part of the functions H ,(s) and

p¢

Mres(s) (if any) form the polar plots obtained by frequency analysis.

In presenting the approach leading to the solution of this problem the
author assumes the readers familiarity with the principles of linear system
stability as described in ROUTH [ 4G-1 ], PORTER [ 4G-2 ].

Consider an arbitrary complex function F(s). For each complex value of s,
this function has a value: F(s) that can be plotted in the complex plane
(cf. figure 4G-1).

If s goes once clockwise around a closed contour E in the s-plane the
function value describes its own contour I' known as the map of E by F(s).
The function F(s) is assumed to have z zero's (s-values for which F(s)
vanishes) and p poles (s-values for which F(s) becomes infinite) within
contour E.

A theory known as "the argument principle" (cf. CHURCHILL [ 4.6-3 ]) gives
a relationship between the number of zero's z, the number of poles p and
the shape of the map I'.

This theory states that map I' encircles the origin z - p net times in
clockwise direction (anti-clockwise encirclements are counted negative).

res'”’

As the aim is to determine the number of zero's with a positive real part;
that is: located in the right half of the complex plane the contour E has
to be chosen accordingly. Such a contour enclosing the entire right half of
the complex plane consists of the imaginary axis and an infinite semi-
circle (cf. figure 4G-2). This curve is known as the Nyquist path.
Application of the argument principle on the map of the Nyquist path by a
transfer function yields the difference between the number of zero's and
the number of pole's with a positive real part of this transfer function.
As it can be shown that, neither of the two transfer functions under
consideration possesses such a pole, the net number of encirclements equals
the number of zero's. The existence of a pole in the right half of the
complex plane for H would imply, that, even if the inlet mass flow and

p¢
the outlet pressure were kept constant, a diverging pressure would occur at
the inlet. This is physically inconsistent with the density wave mechanism
as presented.

For the second criterion a similar relation exists.

The determinant IMresl is the sum of a number of products of Ai's and
B .8,
1]
Therefore |Mreslcan only become infinite if one of these factors becomes

infinite. That Ai = H does not posses a pole with a possitive real part

ol

has been shown above. That the same applies to the Bij's can be understood

by examining their physical meaning (cf. APPENDIX 4E).
Bij is the ratio of the variation of the inlet pressure of channel number

i due to effects of a variation of the inlet mass flow in channel number j.
it Bij would posses a pole with a positive real part a diverging pressure

oscillation would occur at the inlet of the tubes even if the inlet mass
flows of all channels, and the pressure at their outlets were kept constant.

As this is also inconsistent with the density wave mechanism, IM (s)l
possesses no such poles.

Consequently for both transfer functions is valid, that the net number of
encirclements of the origin by the map of the Nyquist path equals the
number of zero's with a positive real part. Due to the symmetry of transfer
functions zero's always occur in complex adjugated pairs (s = A * iw)
constituting one mode of instability.

Now however arises the problem how to obtain the map of the Nyquist path as
it can only be measured for a limited range of positive frequencies w

(s = iw) and thus for a part of the positive half of the imaginary axis. To
solve this problem some additional properties of the transfer functions
have to be considered. The first one, valid for all transfer functions is
the symmetry with respect to w mentioned above.

res

The remaining part of the Nyquist path to be mapped is formed by the
infinite semi-circle enclosing the right half plane.

To derive the shape of the map of this part of the Nyquist path by each of
the two transfer functions, we have to consider their limit behaviour for
very high frequencies:

H .
po

An harmonic variation of the inlet mass flow of an evaporator tube causes
three typres of pressure loss variations, viz. of the:

1. hydro-static pressure losses
2. friction pressure losses
3. acceleration pressure losses

The magnitude of the first two depends on the amplitude rather than on the
frequency of the variations in the conditions within the steam generator
and consequently do not increase with frequency. Acceleration forces
however are proportional to the frequency for an harmonic oscillation of
the inlet velocity:

%§-= -0 %%— y gz = -ps §v = —p iw &v (4G-1)

Due to its observed proportionality with frequency the acceleration
pressure variation outgrows all other pressure losses for increasing
frequency. Equation (4G-1) shows that for higher frequencies the inlet
impedance tends to behave as a pure differentiator:

This differentiator maps the infinite semi-circle of the Nyquist path into
an identical one in the Hp¢—plane (cf. figure 4G-3).

Bij (cf. equation (4.6-11).

At higher frequencies the damping effect of the compressibility of the
steam present in the evaporator, causes H - the ratio of an outlet mass

il

flow disturbance and its causing inlet mass flow variation - to vanish.

- 4G.2 -

For the behaviour of Zin - the remaining part of Bifi -, a similar analysis

as given above for H yields an identical result:

po’

w > ®

Inspection of IMres' shows that it is a sum of products of A's and B's:

aP B? yhere m = p + g is equal for all products. m is the total number of
sets of identical tubes (a tube different of all others is counted in this
respect as a set of one).

As both A and B tend to s for higher frequencies, the limit of these
products is:

| M

- ~ereg

|

Such a function maps the semi-circle into m semi-circles in the |M

plane (cf. figure 4G-4 where m = 2). res

APPENDIX 4H

Details of the discretization, linearization and substitution steps in the
solutional procedure.

The procedure will be illustrated by applying it to the single phase mass
balance:

ap oG
—_— — =
ot 0z .
| . A, R e R
In the first step the spatial derivative 5;-15 replaced by 5;'= T
(cf. figure 4.6-21) and the other properties are evaluated as the average
P4 * P
of the two boundary values: p = ;e yielding:
ap ap
1 1 1 2 3 1
i g N vl T il el S

The relevant algebraic equation in this case is the relation for the
specific mass as a function of pressure p and enthalpy h:

p = p(p, h) (4H-2)

The second step is linearization. In this case the first equation is
already linear. Linearization of the second one yields:

_ 30 3
iy P 5l as. PP i ey o

1,2

The third step i.e. substitution yields:

1 30y 3_ 1 3p, 3_ 1 %0, 3_ 1 dpy 3_
7 Gp'1 3 %P1 3 Gl 3e M Y3 GRla e P 3 Gl by Y
A e - G Sl e

Thus the partial differential equation has been transformed in a linear
ordinary differential equation in the basic variables. The, in this case,
simple process can involve in some cases over eighty algebraic equations.

- 4H.1 -

APPENDIX 4J

Example of an application of the SLINQ program for substitution of linear
eaquations.

To derive the two-phase energy equations expressed in the basic nodal

variables of a channel element &h, o 6G1 5 and 6p1 - (the indices 1,2
-y ! ’

designate upper and lower boundary of the element respectively) 88 linear
equations have to be combined (cf. figure 4J-1). The general cocefficients
given in the resulting equation represent quite complex expressione in the
coefficients of the combined equations.

The purpose of a special developed computer program SLINQ is:

- to derive these expressions automatically

- to reduce computing time consumption by identifying common factors
that can be evaluated before hand

- to punch these common factors and expressions as FORTRAN statements
automatically, to avoid human errors during copying

- to verify by means of a separate test the correct performance cf the
combination process.

Figure 4J0-2 shows the result of SLINQ as they are punched.

As mentioned above the substitution process is checked for correctness by
evaluation of the original set of equations and the set resulting from the
substitutions. For this evaluation the unknown coefficients and basic
variations have been designated arbitrary values. Figure 4J-3 shows the
results of the two evaluations indicating that the substitutions have been
performed correctly.

APPENDIX 4K

Power method and vector deflation as applied for determining eigenvalues
in the CURSSE PROGRAM.

Although described fully in WILKINSON [ 4K-1 ] the power method and vector
deflation are outlined here to be able to discuss the adaptations requires
for solving the generalized eigenvalue problem of equation (4.6-5).

The eigenvalue problem proper is defined by:

|Cl V=58V | (4K-1)

By applying the power method, both the largest absolute eigenvalue and its
associated eigenvector are determined from the vectors obtained by succes-
sive iterations.

Each subsequent iteration vector x is determined by a multiplication of

n+1
matrix lCl and its predecesser X starting with an arbitrary vector p:

- PO |c| o (4K-2)

Znet T lcl %n e

The starting vector p may be expressed in the eigenvectors Yi of matrix |C|
as follows:

n
p = z o Y, (4K-4)

%

|
Qa

©

I
a

B
Q
<

b L0 G (4K-5)

th
It will be clear that repeated multiplication by |C| yields for the m

iteration:

n
= J- 0, 8, V, (4K-6)

to be the largest absolute eigenvalue and o, # 0, equation

Assuming s 1

1
(4K-6) may be written as:

X = o + Ig o va
R T R A -t %%
i=2
n n sim
- e 4K -7
S, { o, v, ¥ 'Ez oy (Sl) v, } ( )

- 4K.1 -

For large values of m the iteration vector X is seen to approximate the

eigenvector v,, whereas the eigenvalue s, is approximated by the ratio of

1
two successive iteration vectors:

1

n s. m+l
1 + I ai (—)
X+l i=2 1 _
X = By n s.m -1 (4K-8)
1+ I a. (—3%
i=2 T %1

For the determination of additional eigenvalues vector deflation was
applied. As shown above application of the power method yields the largest
absolute eigenvalue Sy provided its coefficient in the expansion of

equation (4K-4) is non-zero. If however this coefficient is zero, i.e. the
starting vector p does not possess a component in the direction of the
eigenvector associated with the largest absolute eigenvalue, it will be
clear that the next largest eigenvalue will be obtained provided again its
coefficient in equation (4K-4) is non-zero. Hence it is possible to deter-
mine additional eigenvalues by cleaning the starting vector p of components
associated with the previous determined eigenvalues:

J
p =p~- % a, V. (4K-9)

The process of removing these components from an arbitrary starting vector
is called vector deflation. Determination if the ai values is based on a

property of the eigenvectors of the original eigenvalue problem, defined by
equation (4K-1) and those of the so-called transposed problem:

IClT W=5SW (4K-10)

X i
Matrix ICI and its transpose |C| have the same eigenvalues S, - Correspon-
T :
ding to each S there are eigenvectors v, of |C| and w, of ICI and in
general these are different. However, Yi and Yi are biorthogonal, which

means that, their inner product vanishes for different values of i and j:
w, v, =20 (i # 3) (4K-11)
Multiplication of the transpose of the eigenvector wj with an arbitrary

starting vector p yields after substitution of equation (4K-4) :

n
% P =W Lo, v, = L Q, W, V, (4K-12)
- - " i=-j-i

Due to the biorthogonality of w and v all elements but one vanish in the
sum: '

P =0, W, V, (4K-13)

- 4K.2 -

Some transformation yields:

a, = Zj—i}— (4K-14)
-

After determination of all required aj values, a cleaned starting vector

can be determined as given in equation (4K-9).

The more complicated case for conjugated complex eigenvalue, discussed in
detail in WILKINSON [ 4K-1 ], is based on the same principles.

The above theory on vector deflation has been resumed mainly to show that
vector deflation requires determination of eigenvectors of both the
original and the transposed problem.

The generalized eigenvalue problem of interest here (cf. subsection
4.6.1.3.3) and defined by:

|al v+ s |[B| v=0 (4K-15)
may be transformed to the basic form:

lc] v=s"v (4K-16)

by definition of two new variables:

B| (4K-17)
and

By SRS, S (4K-18)
S

It will be clear from the definition of s**that, where the power method
determines the largest absolute value of s , in accordance with our
objective now the smallest s is found.

For the generalized problem the iterative equation similar to equation
(4K-3) reads:

-1
ter = 17N 18] 5, (ax-19)

or after some transformation:

|a] 8] x

= - ) (4K-20
Zn+1 En' 3 )
The latter equation shows clearly that each next iteration results from the
solution of a system of linear equations where the right hand side r
varies but the coefficient matrix |A| remains the same.
Due to the different structure of the transposed problem, defined by:
*
|ClT Ww=s w (4K-21)

it requires its own iterative scheme.

- 4K.3 -

Ccmbination of equations (4K-14) and (4K-18) yields:

L] Tw=s"w (4K-22)

which after some transformation reads:

IB]T { |A|_1 1T w = s* W (4K-23)

The iterative equation for this case reads:

A {ial "1y (4K-24)

Solution of this equation can be separated into two stages by introduction
of a new variable defined as:

z= (a7 )Ty (4K-25)

Rearrangement of this equations yields:

z=y_ (4K-26)

The new iterate is subsequently computed from:

Yooy ™ |B|" z (4K-27)

Again the solutional procedure is centered around the repeated solution of
a set of linear equations with different r.h.s. vectors but unchanged

coefficient matrix, viz. |A|T.

This requirement for repeated solution called for the reduction of the
amount of operations required for each subsequent solution through
appropriate matrix manipulation to obtain reduction of CPU-time. Matrix
inversion while reducing solution of the set of equations to a simple
multiplication of this inverse and the right hand side vectors, was
unsuitable in our case, as the process of inversion loses the band struc-
ture and hence the aforementioned economic storage mode. A literature
survey yielded a method, the so-called LU-decomposition. Largely possessing
the advantages of preliminary matrix preparation while retaining the
advantages of the band structure storage mode.

By LU-decomposition a system of linear equations given by:

el x =« (4K-28)
is transformed to:

|L| [Ul x = X (4K-29)
where lLi and IUI are two triangular matrices having only zero elements

above and below the main diagonal respectively, the product of which is
identical to matrix iC . By introducing a new vector y defined by:

= |u| x (4K-30)

L

- 4K.4 -

solution of the original set of equations can be replaced by the subsequent
solution of two sets, viz.:

L] y =« (4K-31)

and:

a
X
I

y (4K-32)

Due to the very simple structure of the \LI and IU\ matrices, the combined
solution of equations (4K-28) and (4K-29) requires considerably less CPU-
time than direct solution of equation (4K-25). As the CPU-time reduction
obtained during repeated solution (up to 60 times) of equations (4K-28) and
(4K-29), amply exceeds the CPU-time required for the previous LU-decompo-
sition, application of this method is particularly advantageous in our
case. Unfortunately it was found that (cf. IBM-SSP [ 4K-2 ], NAG [ 4K-3 ],
IMSL [ K-4 ]and EISPACK [ 4K-5 ]) none of the existing routines was suited
for our purpose as all had been designed for application in structural
analysis and as such for symmetrical band matrices. Therefore a new routine
based on the LU-decomposition (cf. WILKINSON [ 4K-1 ]) and adapted for non-
symmetrical band matrices, called LUDEC, was developed.

By application of LUDEC the v, and W, eigenvectors associated with the

largest eigenvalue s, are determined. After cleaning of the starting

1
vector p from components of v and w and their congugated counterparts the

proces can start again to find v and w, and so on. The process described

above is performed by calling subroutine EIGVEC.

- 4K.5 -

REFERENCES PERTAINING TO APPENDICES

REFERENCES APPENDIX 2A

2A_1 COHEN, S.Io’ e.a.

A physical Property summary for ANP Fluoride mixtures.
ORNL 2150 (1958).

2A—2 EWING’ C.T., S.a.

Radiant Transfer of Heat and the Thermal Conductivity of FLiNakK
(Salt Aa).

US Naval Research Laboratory Report - NRL-5568, Washington D.C.
(1960) .

2A-3 EWING, C.T. e.a.

Radiant Transfer of Heat in Molten Inorganic Compounds at High
Temperatures.

Journal of Chem. & Eng. Data: 7, 246-250 (1962).

2A-4 COOKE, J.W.
Estimation of the Thermal Conductivity of Molten Salt Mixtures.
ORNL Program Report MSR-68-28 (1968).

2A-5 COOKE, J.W. .

Improved Method for Calculating the Ionic Number for Estimating the
Thermal Conductivity of Molten Salts.
ORNL Program Report MSR-68-43 (1968).

2A-6 DEBOIS-BLANC, D.R.

Ebasco Services, Inc., New York, USA.
Private comminication.

REFERENCES APPENDIX 4B

4B-1. BANKOFF, S.G.

Avariable density single fluid model for two-phase flow with
particular reference to steam-water flow.
Journal of Heat Transfer, November (1960).

4B-2. JONES, A.B.
Hydrodynamic stability of a boiling channel.
KAPL-2170, October (1961).

4B-3. HINZE, I.O.
Turbulence.
McGraw-Hill (1975).

- 9.1 -

REFERENCES APPENDIX 4G

4G-1.

4G-2.

ROUTH, E.J.
Stabilization of Motion.
Taylor & Francis Ltd. London (1975).

PORTER, B.
Stability Criteria for linear dynamical systems.
Oliver & Boyd, Edinburgh/London (1967).

REFERENCES APPENDIX 4K

4K-1.

4K-2.

4K-3.

4K-4 .

4K-5.

- 9.2 -

WILKINSON, J.H.
The algebraic eigenvalue problem.
Academic Press, New York (1966).

System/360 Scientific Subroutine Package.
Programmers Manual, IBM GH 20-02.

NAG. Library Manual, Mark 5.
Numerical Algorithms Group, Oxford, U.K. (1976).

IMSL Library, Edition 6.
International Mathematical Statistical Libraries,
Inc. Houston, U.S.A. (1977).

SMITH, B.T., BOYLE, J.M. and GARBOW, B.S.
Matrix Eigensystem Routines.
Springer, Berlin (1974).

STELLINGEN

1.

10,

11.

Door de toename van specialistische kennis bij de industrie, zal de nadruk
bij de inbreng door ingenieursbureau's in de toekomst minder op kennis en
meer op projektorganisatie en -beheer komen te liggen.

Ten onrechte veronderstelt Van Vonderen, dat de oorzaak van density-wave
instabiliteit ligt in een lokale terugkoppeling tussen dampgehalte en
massastroom en dat een fase-verschuiving van 1800 tussen deze grootheden
voorwaarde is voor het ontstaan van oscillaties.

A.C.M. van Vonderen,

On the behaviour of parallel boiling water channels,

proefschrift TH-Eindhoven, 1971.

In verhouding tot het grote belang van warmteopslag voor het dynamisch op
elkaar afstemmen van warmte- en krachtvraag bij gekombineerde opwekking
worden de technische mogelijkheden hiertoe nog onvoldoende onderzocht.

Bij wetenschappelijk onderzoek aan universitaire instituten ontbreekt het
veelal aan een systematische projektbegeleiding.

Er dienen op korte termijn dwingende voorschriften te komen voor adequate
geluidsisolatie van woningen, teneinde verdere schade aan de volksgezond-
heid te voorkomen.

De moeilijkheid van wetenschappelijk onderzoek ligt niet zo zeer in het
vinden van een verklaring voor waargenomen verschijnselen, als in het
verwerpen van deze verklaring wanneer latere experimentele resultaten
daarmee in tegenspraak zijn.

Het zou van te waarderen aandacht voor het geboren kind getuigen, wanneer
politieke partijen zouden bevorderen, dat ook het dragen van veiligheids-
gordels achterin auto's verplicht gesteld wordt.

De misvatting, dat een voltooide akademische studie een voldoende voor-
waarde zou zijn voor het goed ontwerpen en programmeren van komputer-
programma's geeft blijk van ernstige onderschatting van de hiervoor
vereiste vakbekwaamheid en ervaring. Dit resulteert in verspilling van
programmeer- en komputertijd en in een groot aantal weinig efficiente
programma's.

De vervanging van handberekeningen door komputerprogramma's bij het
ontwerpen van komponenten en installaties blijkt veelal gepaard te gaan
aan een verlegging van de verantwoordelijkheid voor het resultaat naar
medewerkers met een lager opleidingsniveau. Deze ontwikkeling leidt tot
vergroting van het risico van onjuiste of onjuist geinterpreteerde
resultaten.

Het meer en meer negeren van verkeerslichten zou sterk worden tegengegaan,
door uitschakeling ervan bij gering verkeersaanbod.

Wanneer niet op korte termijn maatregelen worden genomen om aan de
stijgende energiebehoefte te voldoen, kdn de soep in de toekomst niet eens
meer heet worden gegeten.

ASPECTS OF MOLTEN FLUORIDES AS HEAT
TRANSFER AGENTS FOR POWER GENERATION

FIGURES AND TABLES

B. VRIESEMA

ASPECTS OF MOLTEN FLUORIDES AS HEAT
TRANSFER AGENTS FOR POWER GENERATION

FIGURES AND TABLES

B. VRIESEMA

Na K

Y AL LT A WL S

force beam of differential
pressure transducer

L
%

; AR

FIGURE 2.2-1.

NaK filled dp-transmitter.

cover gas supply

Sl o LN

F TS A S P

electrodes

J*I 77

differential
pressure
meter

e

FIGURE 2.2-2.

Principle of the FLiNaK venturi measurement.

@ 40.9

98
61 B
]
\\M—p

NN

Z
/ | /—3 holes @ 3mm
o Z {B__ re I
R=10.1 % P —Rr=101
Jo R=61 ] &
P " o _"I - \

@50 __J

|

FIGURE 2.2-3.

The venturi as applied in the experiments.

//%k I I I | l | | l l

700//
10414 104 \3 104 '
Vg

"

i’

& 600

i A i S R e 0

0 5 10

FIGURE 2. 2-4.

The Re-number in the venturi as a function of mass
flow rate and temperature (in the non—shaded area

the accuracy of equation (2.1-1) is better than
1.2%).

T to vent

flow control

| ,r_ fi, alarm electrode
|
Vit phii -—:——\Y/'I/"/ control electrodes
I g
o (f Vil
| [
| : I ' dead band of control system
: v : LA high pressure vessel
| E
| L E ===
: |
| |
Y _J
A
/\
Tgos supply
FIGURE 2.2-5.

Diagram of the two-electrode control system.

£ ol
"5 i« e T TEIPIRPPRRL
-

FIGURE 2.2-6.

Photograph of the two venturi vessels showing
the eceramic insulators for the electrodes.

salt level |max.column height = 25 mm

max. column height Lless than
‘'with a cilindrical electrode

FIGURE 2.2-7.

Salt column under an electrode dipped in the
fluid and raised subsequently.

———= venturi millivolt signal

60

50

40

30

20

10

20

15 10 5

time [min] -

FIGURE 2.2-8.

Dynamic response of the venturi reading to a stepwise change
in FLiNaK flow rate (two electrode control system).

to vent.

flow control

| alarm electrode

S S "'T“'?'Zi control electrode
~)

high pressure vessel

\

Tgas supply

"IGURE 2. 2-9.

Diagram of single electrode control sustem.

(
———d
————== output d/P transmitter

15 10 5 0
————— — tiMie [min]

FIGURE 2.2-10.
Reading of the venturi flow meter with single electrode control system.

g

D1 &ji‘
C #— R1 R2 8
—{____1 {:::}——t::

y 5
TATEY s T2

RL1
T1
R3 c2
D # [JRS Ré E'{u

+

FIGURE 2.2-11.

Delayed action relais applied to avoid rattling of the magnetic valves.

e

A

[

Il

FIGURE 2.2-12.

Instrumentation of the venturi flow meter.

H.P.
datalogger
2012 D
1
voltage
foxboro
d/p cell
613 D.M.
gas d/p
d/p
transformer
liquid d/p

—_—— venturi . -

/_\

output
punched tape

composition mol % NaF 11.5 aces ref.
KF 42.0
LiF 46.5
composition weight % NafrF 11.70
KF 59.09
LiF 29.21 2.2=5
melting point Oc 454
Liquid state
density kg/m3 2530 - 0.73 T 10%
(T = temp. in Oc)
specific heat kJ/kg Yc 1.89 5%
thermal conductivity w/m Oc 1.30 7 APP. 2A
_6
kinematic viscosity m? /s at 500 Oc 3.90 10
_b
at 600 Oc  2.63 10 2% 2.2-6
_6
at 700 %¢ 1.95 10
_b
at 800 %¢ 1.23 10

FIGURE 2.2-13.

Physical properties of FLiNaK.

eeeeeeeeeee

_ \ eeeeeeeeeee } ooooooooooooo

Principle of the second type of thermal flow meters

mm
o J— 5'
wn venturli rea Ing
E’ 6 /—' ‘
- Y ? X (‘r
=
2 5 C e
3 +
P
O
=
s 3
-
£
- 2
T :
. 575 600 625 650 675

—— FliNak temperature [°C]

FIGURE 2. 3-3.

Temperature dependence of thermal flow meter output (obtained
at a corresponding venturi reading of 6 kg/s).

THERMO COUPLE PENETRATIONS

FLOW DIRECTION

ELECTRICAL HEATING ELEMENT

t
----
A5

FLUID THERMO COUPLE

WALL THERMO COUPLE

PROCES - TUBE

FLOW DIRECTION

FIGURE 2.3-4. THERMAL FLOWMEASUREMENT

Thermal flow meter.

aaaaaaaaaaaa

%

&
I

hhhhhhh

eeeeeeeeeeee

Location of thermo-couples in the probe wall

470[oc]
| ! 490
Tm Tm
530
1550

\;—?/ 570

Average surface heat flux 300 Watt /cm?

Ni-braze thermal conductivity A equal to that of Incoloy 800
BN electrical insulation AN =0240/(m.K.s)

BN t/c insulation AN =024 J/(m.K.s)

t/c contact heat transfer (AklpN = 20*10* (m2.K.s)
contact heat transfer between

electrical

insulation and electrode or sheath (Ak)BN :25‘101'(m2AK.s)

minimum clearance of t/c in slot 0,0Tmm

FIGURE 2.3-6.

Temperature field using Ni-braze for surface embedded thermocouples.
[2.3=2. ]

SV ref

o~ -
e 4
(o}
. | l .
S - g 10V2 10 kyy
100 k 2 | 5 , " c
o x| l0-3v 100k 1
E }, yeed
- >/ —{)- / 9 [0 33 J Lk
A 100k 71 [To-2v 100 o %
1000 x o 6 instellen
o~
3 4 8 op 37.5Q 100 mV
- 100k C | N O ¢ Mo
B 1509 _(
VOEDINGSSPANNING  +15V MEETGEDEELTE THERMISCHE FLOWMETER TI
—~15V
UITGANGSSPA NNING 010V
WEERSTANDEN s%, W
PO TMETERS 20/,

FIGURE 2.3-7.

Design of an electronic device for linearization
of the reading of the thermal flow-meter.

0.5

pooopo00QO0O00QO00JO00

vt [ 233
A—— }, Yy

0.4 [2.3-5]
Sesro e [2.3“6]
++++++ [2.3-7]
[ —
00000000 [13-8]
A 0.3
seares |4 e by s —
e
~\.~
0.2 \fi'** A o I
" gy
\-
\n.\
B ¢
0.1
0 .
0 0.5 1.0
~s= Di/Do
FIGURE 2.3-8.

Literature survey of values of the exponent n of the annular
flow correction on the Dittus-Boelter heat transfer correlation.

1 :
Q\O’:OBW oz%
Bl e T ~_0=0613 _s
Sl : €E=—
Z|z \ D-d
0.8 D—
A d
1%
0.6 :
0 0.2 0.4 0.6 08 Ll
i €
FIGURE 2.3-9.

Effect of the eccentricity of an annular channel on the
average Nusselt number according to LEE and BARROW [ 2.3-8 ].

Property Value Errorx
I
A_ 0.967 10 [m? ] 5%
) 1
¢w ~ 3,0 103 [T s ] 2%
X
A 0.0235 [m? ] 0.5%
ok gl
A J
0 [T m c ]
_1
Wy [m2 s ] 10%
cf. figure 2.213 _3
k 5%
on [kg m ] |
Co [J kg~ Oc™ ] 10%
_3
Di 21.0 10 [ mm ] 0.5%
_3
DO 40.9 10 [ mm ] 0.25%
A6 10 - 25 [ Oc ] 2%
m
_1
Cq [m? %cw ] 10%

FIGURE 2.3-10.

List of properties appearing in equation (2.3-5) and their inaccuracies.

L

sensors

I | / \

— flOw

—JI— - _—l_

FIGURE 2.4-1.

Prineiple of correlation flow measurement.

Tm=delaytime
penei -

— (1)

FIGURE 2.4.2.

Example of correlation function to two signals,
one of which is delayed by . seconds.

Tm=delaytime

FIGURE 2.4-3.

Example of a correlation function of two sensors
at a distance of 3200 mm.

o
.
|

%

FIGURE 2.4-4.

Example of a correlation function of two sensors
at a distance of 200 mm.

MAIN HEATER

SEE DRAWING No-
DMSP-D-4-14

SEE DRAWING
DMSP -D-4~40

FIGURE 2.4-56.

CIRCULATION PUMP

CIRCULATING SALT
DUMP VESSEL (FLINAK)

| SEE_DRAWING NO DMSP-D-4-9

NULLNAS WD

Location of the correlation test section in the DMSP loop.

STAGNANT SALT

DUMP VESSE L

SEE DRAWING NO. DMSP-D-4-8

- 4
] :
: ™
1% O i
= |z
g i
i o é
j:53 58 &
318 !mo
) 2 - 5
1 |5 Zzzz
= |s Lu"on:
- B
: |5 =l |&
H n |3 @
=18 | =28 3
1 H K - WU
S Q15
< ~ > 1] o
s 3415 "
oot 8 N
gl x| ok 3
© z —<{| T a2
z w | w@ g
= s x®
< - P &
z x|l o w
w O N 3
@ k|0 (Up)] - a
812l |~ z X
2|2 -3 ¥
$|El2(z]F Clw
HIIHE -
DUlO
ol B
= &
%333,1-.'
P EHHEEREE
[®)
AMEEEHEE IR
o|33(3)2 4 (505/2) 3
(04 N|—=|=|RINT|~| N
g—qumohg
HEAT EXCHANGER
<
e
>
A -
)
A
g
%
NP N
Pl S
(,
e

800

1600

3200

491003 ssod-[ig

FIGURE 2.4-6.

Correlation section showing position of sensors.

FIGURE 2.4-7.

Thermo—-couple sensor and wall penetration.

i (] ¢
| T
| 6k8 68k | I 22uF 'hwwLW’
Lwall t/e ‘ | l (N E— l 1 2 ===y T
Wlow) ::>> | [se0 22pF 0.22pF | ::>>
4 liquid t/c 1 | | ; 20K 680K 1 1
s 100 x o - . ——100x s @ @
' low pass filter high pass filter —
<01 HZ >01HZ !
‘ | . . . .
| l

1 MJ"*AL :

delay
correlgtor

FIGURE 2.4-8.

Diagram of measuring equipment (per sensor).

f(t)
F

FIGURE 2.4-9.

Correlation function for natural noise signals
(sensor spacing 100 mm apart).

_z —J——
(flowdirection

FIGURE 2.4-10.

Temperature profile in the primary loop as a result of
a stepwise increase of main heater power.

1 time delay between signals B -I

‘Y"r"/' ey h) A i
I/ ,lel’/‘.f'/ Goe '_]l .
4 O

a 7 o, L L sy 4 p S = 2ON/N i v " entsPen B S,
Stragnals from the two sensors 3200 mm apart after a stepwis
v L L

inerease in main heater power.

fm thermal flowmeter [kg/sec.]

~

(=)}

18y

~

0%

X 650°C
© 600 °C
* 579°0
0 675°C
A 625°C
bat Ti hm

AN
-«

L

FIGURE 2.6-1.

4

Results of thermal flow measurements.

6
o ¢m venturi [kg/sec.]

12 —T

e B e corrected

it vaolues °
; 10
sl

5 9 ol Lo
@

E o]

3 8

o

— [ ]

- ¥ i

o [ ]

E

aad 6

- o [ ]

-

ot 3 o °

€ 4
- L

T 3 .

2 »
1

0 1 2 3 L 5 6 7 8 9 10
—= @, venturi flowmeter [kg/sec]

FIGURE 2.6-2.

Results of the thermal shock "correlation'" flow
measurement at a FLiNaK temperature of 575 0C.

12
—
e n e corrected
£ values °
o 10 o
X v
| S ]
= 9 e
° °
£ )
3 8
=
.- Ll
i 7
E g
: 8 °/'»
@
5 ° | "o
£ 4 O
T 3 ‘ .
2 L J
1
!
6

0 1 2 3 L 5 7 8 9 10

——— @, venturi flometer [kg/sec}

FIGURE 2.6-3.

Results of the thermal shock "correlation” flow
measurements at a temperature of 625 0C.

12

1
e
o e corrected °
< 10 values 5
=,

9
o
° o q
E 8 .
; o
s

7
P ) .
£ .
- 6
i, :
[ ~4
o °/ o

4
sE- °

3 [ ]

o]
2
1

0 1 2 3 (A 5 6 7 8 g 10

—— (yy venturi flowmeter [kg/sec]

FIGURE 2.6-4.

Results of the thermal shock "correlation" flow
measurements at a FLiNaK temperature of 675 0C.

12
gy 11
(8]
o
e
S 10
Lol
® 9 e
:
3 8 x°
s
- 7
o
£
- 6 x
.“7".
g 5
e
€ 4L
-
3
J FLiNak
2 a . o = 625 °C
x = 675 °C
1

0 1 2 3 s S 6 7 8 92 10

——» @ venturi flowmeter [kg/sac]

FIGURE 2.6-6.

Results of the "artificial noise'" correlation
flow measurements.

EXPANSION VESSEL ¢-302
AND
CIRCULATION PUMP_P-301

CIRCULATION PUMP_P-101

MAIN HEATER F-101

MAIN HEATEXCHANGER E-101

STAGNANT SALT
DUMP VESSEL V-101

il A LN & A
=
PREEZE wave-t '

OWS SEALED VALVES

STORAGE AND DUMPVESSEL V-301

FIGURE 3.2-1.
Flow sheet of the original Delft Molten Salt Project.

G50% yibuay 11pJ3A0

T

[} = [
'
.
i
[l —
» AN
M SO S SN SN NS SSoos
E | e —— - — — . - — _J
~ L 1 . ” __
H ! Il
— I
2 TR R R Y NN b W N . V., W, SN NS
A\
¥ L7 —V

FIGURE 3.2-2.

Cross section of the salt-to-salt heat exchanger.

salt in
i iy
air outlet

O L S

/| r\& g
. 5d . g :. .9_'] imlet

\4~.'
B g
salt out
FIGURE 3.2-3.

Basic geometry of the salt-to-air heat exchanger.

salt inlet
|

Il

air exhaust

56

/

_Jé% .\§%_—f¥’ (;:)Pf

|  —e

L‘kscllt outlet

FIGURE 3.2-4.

Flow sheet of the secondary side of the FLiNaK to air heat exchanger test rig.

3MN/m2 air supply

FLiNaK inlet temperature
FLiNaK temperature drop
FLiNaK mass flow rate
Air inlet temperature
Air outlet temperature
Air inlet pressure

Air pressure drop

Air mass flow

575 - 675 Oc

<5 0c
)
2.3 - 9.5 kg s

25 Oc

430 - 630 Oc
2

0.5 MN m

2

0.002 - 0.02 MN m_
1

0.05 - 0.16 kg s

FIGURE 3.2-o.

Process conditions of the FLiNaKk-to-air heat exchanger.

=
/

wall & bulk salt
thermocouples ' m from Pt, th, level
.62 1.2 18 2.6 3.8

air couples .62 1.02 1.42 1.82 r g 2.62 3.02 3.42 382 L.22

m from Pt,th, Llevel

AN : 7]
& >

Positions of the thermo-couples in the FLiNaK-to-air heat exchanger.

salt bulk
thermocouple
AN

W//////////////A//////////////////V///////////////////// SRR R y

-
== e rzrrzrr ]
[ ESEITIET TSI I T T LT OBEHTS \\\\\\\\\\\\\\\\\\\\\\\\\VJN.AA\\\\ \\\\\\\\\\\\\\\\\\\\N\m
\\\ N~

[ ;
V. N
\ 27 RSN \
\ 4 AN
.\ )

\\\ . // \
I \ // \
/ \\\ // \
\ // /
\

P 5 -
[ LLLLLLLL 772222 22222022 22 Rl L P22l 22222222228 2L 222 L2 Tl 7 2l 2 Pl P P L R L L L L L L L L L Ll Ll

: A1 11 i i i i i I ATEE I I i t i i i - Hfi T INNRNRRRRARRARRRRRNRRNS SN

flinak

<

wall thermocouple

air thermocouple

Details of thermocouple penetrations.

FIGURE 3.2-7.

thermocouple inconel 600 wedge silver braze

L - \ outer side

inner side

tube wall/

FIGURE 3.2-8.
Imbedding of thermo—couples in the wall of the FLiNaK channel.

// hot junction
“d (actual measuring point)

thermocouple wires

,eccentricity

3 electrical insulation

FIGURE 3.2-9.

Non-symmetrical position of the hot junction im a sheated thermo-couple.

inconel wedge

{:\\\\\‘:§\

o S b
SRR,

braze

thermocouple

gap in brazing due
to insufficient fluxing of
the braze

inconel tube wall

FIGURE 3.2-10.
Example of imperfect brazing of thermocouple in tube wall.

vacuum ejector water supply

——

cooling water
drain

- CO0lLing water
supply

bulk thermocouple

I wall thermocouple

—
1 o |

\

— T condensate

* drain

steam supply

FIGURE 3.2-11.

Stmplified flow sheet of test facility for measuring equivalent thermo-—couple location.

|

U RN RENHR N B oY

\\\;5\33&

water film
spoiler ring

\\\\)Q\Xfi\l‘\\

wall thermocouple

\\\\\\&\\XLX\;1L
\\‘L\\\\\ESLY\

e

bulk thermocouple

3) section of the inner tube of the
) Nlinqk-to-air heat exchanger

s 1

ol

SN NGRCAE NI IR

FIGURE 3.2-12.

Special heat exchanger for calibrating purpose.

outside of the wall inside of the wall

NN
\ 9i boiling temp. atmospheric
\ — \pressure (100°C)

A&

temperature meagsured

Kby thg_rmocoupl.ewfi

equivalent embedding
depth of hot junction

|

saturation temp. for 8,

boiling at reduced
pressure

wn

FIGURE 3.2-13.
Method for deriving the equivalent embedding depth of thermo-couples.

10
x H x x|» x k x x xx(i575°C)
o 5 x| x k x|x w| x x x xx (¥625°C)__
a.
(£675°C)
0

0 5 10

i R 10

FIGURE 3.2-14.

Test conditions of FLiNaK heat transfer measurements.

Ve4l06

VeB311

PR

*

NUSS = 0.,0137 # Rt

ALPHA

PRANDTL

(computed)

'(measured)

REL DEV

ABS DEV

NUSS

NUSSELT

REYNOLDS

" N CDOEMOMMtO DO MO O st Dt Ot NSO P OMND
6§59‘1§626“9.61‘7‘62‘2981‘02

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MEAN RELATIVE ERRUR=

FIGURE 3.2-15.

& Ren Prn.

Table of experimental heat transfer data and best fit of general form Nu

(VIR SVEVEY)

UeRBUOU

¢ PR

UaVl95 # RE

NUSS

ALPHA

(measurcd)

(computed)

REL DEV

NUSSELT NUSS ABS DEV

PrRanDIL

REYNOLDS

MIFIMO~RANNVNDVN~FO~OONDSONDVI~FTDRDTINM
MO D CRHRON OONMFTNFNDNO~NOMNN O O~ONO

T EEREEEEEE NN I SRR NN I SR RN S W
ODOFTD~NIM~ODNOPIPNR~NDI~DVOET~MOOMNN I~ O
SNNMO ROV OM~=NIOIOOMET~ODRO FiF MO O FTO~N
O M=~~~ ORDF—~MASFTRAFIOMINIIN~-FONNMNDTIOR
MINOSSDRARNDODNMINNO O DOM S L NON~-DTCHD

r—f =t

MANNM~=ND~N\IFN~DVIFOODMONS~SFINNOSINOMS-IN
® ®© & ® & © & ¢ S & 9 &% O O 6 0O O T O OO @ s e v e 00
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NOIMNOOITNASNDSMDO0NDV TP OO~V ONDOE =N
345677899012345566778534456,78990

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ROR R AR R R PR RR R RRR AR RMR AR R R RRRARARRPR R RR R
OO EIMO I NINIMO NP ~OIMMINOO~OD
IO MIOI-ODVDNOMN O~ 0NN~ M~A D ONNCO~NO
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103’

cRRUR=

MEAN KEL&T]VF

i

-
e

FIGURE

pPr0.4

Q
o

lable of experimental heat transfer data and best fit of general form Nu = C Rel-

m
L

ft

values of (VD) for water 60°E (velocity in xdiameter in inches)

RELATIVE ROUGHNESS &

sec
éulues of (VD) for atmospheric air at 60°E 6000 10000
01, 02 04 0.6081 2 4 6810 20 40 6080 200 400 600 1000 2000 4000 800O|
e 1 33 I e | L |
B oy foarrs. = ya g v } 800 1 6000 |10000 104000
04l -2 | & 16810 | 20| 40 | 60/100 | 200| 400 600 {000 2000 | 4000] | 8Q00] 0| 40000] /
PO R R W W A S T
0.9 A -H——HHHHHHA
asld laminar ortical transition
=\ flow —zone — zone | complete turbulence rough pipes
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: Biolot 04
0642\ T >
:Eé. 03
SE\E=
us:ngi ; 02
o~ Im C o\ Gi‘ ' 015
>l . N
I T~y ——

.c“-ic ‘\l R : ] A 008
- % 4 . 006
o o 004
= 025 == =
% 1\ 002
Y ~
3 : =2 80bs
: . 0006
&) - = 0004
@ 015 RN :

o Mo0g, >R = 0002
A \ N "n‘
40/06.s~ :! [t e I B 0001
et iy
000.05
001 . S
.009 =11 s
.008 - 009.01
103 23 3 456 8104 24 3 456 8105 25 3 456 8106 2 3 4S6 810'7\27’\~4~5Q108
(103) (104) (105) (106) (10 000,09, 000,9
REYNOLDS ‘NUMBER R.- (vinEL . pinFT, vin £1Z)
SEC. SEC.

FIGURE 3.3-1.
Moody diagram.

FIGURE 3.3=2.

The location of the pressure drop section in the test loop
18 shown in figure 2.4-5.

test tube: 11/2" sched. 40

DO= 48.3mm
Di:{LO.Qmm (standard)
4£1.25mm (after being ground internally)

material: inconel 600

pressure taps

Thorizontal

FIGURE 3. 3-8.

Test tube for frictional pressure drop measurements.

‘\‘F&——aaom. 48,30
\FF:

S 1 )
E I % "L‘A=L1.25
1 [l
w0
o ' 1
]|
l - ——8=41.23
: N
i
g | I |
.
" C=41,24
1l
e -
S E | E
= "
5 t E__-—_ozu.zs
E R
3 | ] |
N
|
ol ——€=41.26
. 1
¢ |||
| lg
-1 F=41,27
.
N
i
6l G-u28
14!
FIGURE 3.3-4. —\«fl:—TQi‘———diam. 48,32

Dimensions of the test tube.

dPt

salt Level 2 \Z
L
77 IZZ salt Level 1 /\
1
i s
L 2z,

700

o) o)
o q o & |6 ood oo

650
~ o O S 1 olo
(&

O o O @ O olo|0oD

o
@
O
600
&
p==
D
5 00 0o (@ do Och Qbog:@c%
a
E
3
i
24550

500

1 2 3 A 5 6 7 8 9 10
flinak mass flow (kg/sec)

FIGURE 3.3-6.

Summary of test conditions for frictional pressure drop measurements.

FLINAK FRICTION FACTOR MEASUREMENT

MEASUREMENT IDENTIFICATION ]-8-72

.l...............'.........Q........C..D..'OOOOQ.0.0'.0".09090600000DGQOOOQQOQQID.C...D’.D.Q.QO0.00

hd | | | | i |

® DELTA P, | DELTA P. | MASS FL. | TEMP. | ~E | FRICTION FACTOKR | DIFF. TEST=-BLAS "
b | | | | | | "
A | | | | | S i o o e 1 O e e |w—eane Sewwes cenasnssee!)
i | | | | | | | | “
w VENTURI | FRICTION | FLINAK | FLINAK | /1le®es | TEST | BLASIUS | aBs | PEL @
® | | | | | | | | ®
" BAR | BAR | KG/SEC | DEGR. C | | | | I % OF vFa, ¢
" | | | | | | | | @
Nzsz=zsss=z=z2z====s==s2==SS===-Z=SS=====23=SS=ZCC=FSI=SSSS-zZSSSSSSSSsSSSE=ISSSSTSISSIsZZZ=sssszszzsssss=zl
% 0.0030 ¥ 0.022 | 2.03 | 684 \ 2.04 { 0.0181 | 0.0265 | 0.0084 | ~47 o
" 0.0125 | 0.062 | 3.39 | 687 | .46 | 0,0271 | 0.0232 | 0.,0039 | 14 *
" 040195 | 0.090 | 4,09 | 681 ! 4.05 | 0.0291 | 0.0223 | 0.0068 | 23 »
" 0.0265 | 0.121 | 4,74 | 684 | 4475 I 0.0294 | 040214 | 0.0080 | 27 “
" 0.0360 | 0.170 | S.61 | 687 | 5.73 | 0.0284 | 040205 | 0.0080 | 28 b
" 0.0460 | 0.214 | 6.30 | 685 | 6.35 I N.0288 | ©.0199 | 0.0089 | 31 *
" 0.0550 | 0.258 | 6.92 | 684 | 6.94 0.0286 | 0.0195 | 0.,0091 | 32 i

Q.........'.‘.'...I....‘..'.Q'...Q.QOO..C.OOO’O...'0.00Q“..QQO'.'OOOO.'QQ..“Q’OD.Q'O.Q.'QQ.Q....QOOQ

MEASUREMENT IDENTIFICATION 3-8-72/1

......"..D.....'..'...'.Q".....Q....'.QQOGQ...DGQ.Q'..OOQQOOQQ...9..'00.’l.QQQQOOOQG.QQ“QOG’.O..“.

o

| |
# DELTA P. | DELTA Pe | MASS FLW | TEMP, | wE | FRICTION FACTOR DIFF. TEST=BLAS "
@ | | | | | | "
" | | | | | mememcccnvncnn- ceeven | ccce- vesscrcccen——- -
" ) | | | | | | | L
" VENTURI | FRICTION | FLINAK | FLINAK | zluses ) TEST | BLASINS ) ARS | REL -
" | | | | | | | b
" BAR | BAR | KG/SEC | DEGR., C 1| | | | : 2 OF vFeo,®
" I I I i | I | I e
“:::======::::::::::::::=======:::::=::==:=::::::::::::::::::::::::====:=::=:::5;::::::::::::::::::“
" 0,003 | 0.020 | 1.93 | 682 | 1.92 I 0.0356 | 0.0269 | 0.0087 | 24 ©
" 0.0120 | 0.047 | 2.97 | 678 | 2491 I 0.0339 | 0.0242 | 0.0097 | 29 ®
" 0.0180 | 0.080 | 3.85 | 682 | 3.84 I 0.,0302 | 0.0226 | 0.0076 | 2s “
" 0.0250 | Oelle | 4,60 | 681 | 4.56 I 0.029 | 0.0217 | 0,0078 | 26 @
" 0.0330 | 0.158 | S.42 | 680 | S5.34 I 0.0280 | 0.0208 | 0,0072 | 26 @
" 0.0490 | 0.200 | 6.10 | 681 | 6.04 I 0,0329 | 0.0202 I 0.0127 | 39 «
" 0.0535 | 0.245 | 6.75 | 681 | 6.68 | 0.0293 | 0.0197 1| 0.009¢ | 33 ©
" 0.0680 | 0.305 | 7.53 | 682 | 7.50 I 0.0299 | 0.0191 I 0.0108 | 36 @«
" 0.0770 | 0.368 | 8.27 | h82 | B.24 I 00,0281 I 0.0187 | 0.0094 | 33 ©

.l'....QQQD"...'...'I....O.’....O'..QQQQQ.D....'Q'GDQQ#DDOQCGOOOOGQOGOl.GGQGOQOQQQ.QQCGGOQGOOQODOO

MEASUREMENT IDENTIFICATION

3-8-72/2

BB R N RO R BB R P R R PR R RTRRRPR BN BRO PP O CE RO RRCRCOCORRBOBCRTE DB RLOCREROR RO RNRROCBCORORORODRERRR RN RO

. | | | I | | “°
® DELTA P, | DELTA P, | MASS FL« | TEMP. | KE | FRICTION FACTOR | DIFF, TEST-BiLAS
bl | | | I | | L
" | | | I | eessesacnaensmsseans B | S e e S o e Ll
" | | | | | | | | ®
" VENTURI | FRICTION | FLINAK | FLINAK | /lu®®s | TEST | BLASIUS | a8s | wEL ®
" | | | | | | | | »
" BAR | BAR | KG/SEC | DEGr. C | | | | I % OF MES ®
" | I | I | | | | »
P P PP T I T T I P PP P22 2T T P P P33T T T PP I 3322 P T T 2 2 333 22 PP ¥ 232322 2232 2223 P23 s 122 33 2 223 2 2 2 2 2 2 2 3 1 3 3 44
" 0.0065 | 0.022 | 2.06 | 631 | 1.58 | 0.0388 | 0.0282 | 0.010~ | 27 &
" 0.0137 | 0.052 | 3.13 | 634 | 2445 | 0,035 | 0.0253 | 0.0101 | é9 »
" 0.0200 | 0.086 | 4.03 | 632 | .12 | 0.,0312 | 0.0238 | 0.0074 | 264 @
" 040260 I 0.117 | 4.70 | 634 l 3.68 I 0.0298 | 0.0228 | 0.0070 | 23 *
" 00360 | 0.163 | 5.55 | 632 | 4.29 I 0.0296 | 0.0220 | 0.0077 | 26 #
" 0.0465 | 0.207 | 6.25 | 633 | 4.86 | 0.0301 | 040213 | 0.0088 | 9 ©
" 0.0690 | 0.315 | 7.72 | 632 | 5.96 I 0.,0294 | 0.0202 | 0.0092 | 31 #
" 0.0775 | 0.375 | 8.42 | 632 I 6.51 I 0.0277 | 0.0198 | 0.0079 | 29 @

BOAR BB RN RB P OCDORCVO PR DR PN OB PR T VOO RPORERRRUORUOORROOLRGROROUORORORCERRTRNRERCORBENROARRDERCRRDDRLDROE

FIGURE 3.3-7%.

Experimental data of frictional pressure drop measurements.

MEASUREMENT I10ENTIFICATION 10=-8-72/1
P T R D R R R L e T T T Ty
# | | | | | | "

# DELTA Po | DELTA P, | MASS FL. | TEMP . | RE | FRICTIUON FACTOR | OIFF, TEST=BLAS "
» | | | | | | 3
" | | | | | recmevrccnvmnrcccccnn | secccccccnnccancccnnal
. | | | | | | | | -
" VENTURI | FRICTION | FLINAK | FLINAR | /1lness | TEST |  BLASIUS | ABS i WEL il
" | | | | | | | | bl
" BAR | BAK | KG/SEC | DEGR., C | | | | I & OF vFA,*®
" | | | | | | | | &
P e P Y T P I P P P P Y S P S T Y P P e PP P FFE PP R PP P T T3 PP PP I 213 22 22 P 22 2P 23 P12 P A2 PP P2 2 2 P 2 2 4
" 0.0040. | 0.015 | 1.70 | 569 | 0.91 I 0,035+ | 0.0324 | 0,0034 | 10 -
v 08130 . ) 0.055 | 3.25 | 56l | 1.88 I 0.0317 | 0.0270 | 0.,0047 | 18 *
v 0.0210 | 0.090 | 4.16 | S&1 | 2.41 | 0.0313 | 0.0254 | 0.0059 | 19 *
w. 00,0278 1 0.125 | 4.90 | SH1 | 24K3 I 0.029¢ | 0.0244 | 0,0055 | 1R b
" 0.0365 | 0.167 | 5.67 | 582 | 3.30 I 040293 | 0.0235 | 0.0059 | 20 hed
" 040465 | 0.200 | 6.20 | 581 | 3.59 I 0.0312 | 0.0230 | 0.0082 | 2 hot
“  0.,0590 | 0.240 | 6.80 | 581 | 3.93 | 040330 | 0.0225 | 0.0105 | 32 ®
" 0.0710 | 0.305 | 7.66 | 581 | 4.43 | 040312 | 0,021 | 0,009« | 30 »
" 0.,0775 | 0.380 | 8.55 | 582 | 4,98 | 0.027¢ | 0.,0212 | 0.0062 | e3 o
" 0.0810 | 0.430 | 9.09 | SKZ | S5.30 I 0.0253 | 0.0209 | 0.004s 17 o
........ R AR AP AR e AR R AARARARRRAAB AR AR BABBAARBARRBDEOLSBBDOODVDBVBVVLDOVVOLVDDRNRS

MEASUREMENT IDENTIFICATION 10-8-72/2

e A e e e s s R Al sl

|
RE | FRICTION FACTOR

|

# DELYA P, | DELTA P. | MASS FL. | TEMP, " | ! DIFF, TEST-BLAS "
# | | | | I | "
" I | ' l ' .......... - —— - - .-- - - "
" [ | | I I [ [ | ®
" VENTURI | FRICTION | FLINAK | FLINAK | /loses | TEST | BLASIUS | ABS | WEL ©
" | | 1 ) | | | 1 v
" BAR | BAR | KG/SEC | DEGR. C | | | | | % OF ~Fo,.%
" | | | | | | | | i
“::::::::::::::::::::::::::::::.’:::::::::::::::::::::==:=::::::::::::====:::::::::::::::::::::::::::“
" 0.0810 | 0.430 | 9.10 | S81 | 5.26 | 0,0253 | 0.0209 | 00,0046 | 17 ®
" 0.0800 | 0.410 | 8.88 | 581 [ S5.13 I 0.,0262 | 0.0210 | 0.0052 | 20 ®
W 0.0745 | 0.350 | 8.21 \ S81 | 4,74 i 0.0286 | 0.0214 1 0,007} | 2s *
" 0.0630 | 0.2R0 | 7.34 | 581 | 4.24 | 0.0302 | 0.0220 | 0,0082 | 27 ®
5. 10,0835 .1 0.235 | 6.72 ! 581 | 3.89 I 0.0306 | 040225 | 0,0080 | 26 #
“ o 0.0640 0.185 | 5.97 \ S81 } 3.45 i 0.0319 | 0.0232 | 0,0087 | el o
" 0.0320 | 0.125 | 4490 | 581 | 2.83 | 00,0344 | 0.0244 | 0.0100 | 29 e
" 0,025 | 0,095 | 4.28 | 581 | 2.47 I 0.0360 | 040252 | 0.0108 | 30 ®
" 0.0170 04055 | 325 -} SR1 } 1.88 I 040615 | 0.0270 | 0.0145 | 35 °
" 0.0105 | 0.025 | 2.19 | S81 | 1.27 | 040564 | 0.0298 | 0.0266 | 47 o

MM MM WM e MR M e MM MR M MR N NN MMM MR R R MARARARANARRAARARAARNRAB DB DBBBBBBDVVOIVVVVVVVDRTRBRRRRRDDENRBRRRD

MEASUREMENT IDENTIFICATION 8-9-72/1

B e e A R L RS A TR SRR el dd

| | |

* DELTA P. | DELTA Po. | MASS FL. | TEMP, | RE | FRICTION FACTOR | DIFF, TEST-BLAS *
* | | | | | | -
o | | | | |= | "
i | | \ | | | | | .
" VENTURI | FRICTION | FLINAK | FLTNAK | /lu®es | TESY | BLASIVS | ABS | REL -
» | | | | | | | | .
" BAR \ BaR | KG/SEC | DEGR. € \ | \ | 3 OF nEA,®
" | | | | | | | | o
"====::::"_‘::=:::==============:=:======================================3:===::====================="
*0.0065 | 0.028 | 2.30 | 627 \ 1.73 I 0.0312 { 0.0276 | 0,0036 | i *
" 060145 | 0.059 | 3.34 | 624 | 2.48 | 040330 | 0.0252 | 0.0078 | 24 *
" 0,0215 | 0.094 | 4.22 | 626 | 3.15 | 040307 | 0.0237 |+ 0,0070 | 23 *
" 0,028 | 0,130 | 4.96 | 626 | 3.71 | 0.0294 | 0.,0228 | 0.,0066 | €3 *
" 0.06410 | 0.180 | S.84 | 626 | 4436 I 0.0306 | 0.0219 | 0.0087 | 28 L
" 0.0520 | 0.240 | 6.74 | 626 | S5.04 | 0.0291 | 0.0211 | 0.0080 | 27 -
" 0.0610 | 0.293 | T.45 | 626 | 5.57 | 040279 | 0.0206 1 10,0073 | 26 »
" 0.,0740 | 0.365 | 8.32 | 626 | 6.21 I 0.0272 | 0.0200 | 0.0072 | 26 b
" 0.0805 | 0,439 | 9.12 | 626 | 6.81 I 0.0246 | 0.0196 | 0.0050 | 20

Rl R R R R R R e e e e e R s R R e R RS RS R st s 2 dd

MEASUREMENT JIDENTIFICATION 8-9-72/2
R g T R L L L L L L L T vrpnprarpeprgprgrgugrpeegupuggn
| | e

| | |
® DELTA P. | DELTA P. | MASS FL. | TEMP, | RE | FRICTION FACTOR | DIFF. TEST-BLAS
» | | | | | l ny
Lo | | | | | menesacrecnarccsssans | g
i | | | | | | ®
" VENTURI | FRICTION | FLINAK | FLINAK | 7/luses | TEST | BLASTUS | ABS | el *
" | | | | | | | | &
i BAR | BAR | KG/SEC | DEGR. C | | | | | 3 OF “Fa,®
s | | | | | | | | »
":.‘::=::==============:===========:::::;::::::==:==:================================================“
" 0.0810 | 0.461 | 9.21 | 580 | 5.29 I 0.0247 | 0.0209 | 0.00358 | 15 L
" 0.0760 | Qs372 | 8.46 | 581 | 4.89 I 0.0274 | 0.0213 | 0.,0061 | e2 \d
" 0.0630 | 0.306 | 7.68 | 580 | 4.40 I 0.0276 | 0.0218 | 0.0058 | 21 »
" 040535 | 0,249 | 6.92 | 580 | 3.97 I 0.,0288 | 0.0224 | 0.0064 | 22 *
" 0.0380 | 0.194 | 6.11 I 581 | 3.53 | 0.0263 | 0.0231 | 0.0032 | 12 4
N 0030 " | 0.138 | 5.15 | 580 | 2+96 I 00311 | 040241 | 0.0070 | en »
e 0s0225 | 0.100 | 4,39 | 581 | 24564 | 0.0302 | 040251 1 0.0051 | 17 *
w0150 | 0.062 | 3.45 | 580 I . 198 | 0.0325 | 0.0267 | 0.,0058 | 18 o
" 0.0050 | 0.028 | 2.32 | 581 | l.36 | 0.0240 | 0.0294¢ | 0.,0054 | -23 g

i R R g R T T T T T T T YT T P T Y YT S

FIGURE 3.3-7b.

Experimental data of frictional pressure drop measurements.

ERROR

REL.

ABS ERROR

F_FR(CORL)

= 0.,2657 * RE
F_FR(MEAS)

F_FR
RE

962112b831235571359776073147071‘7974 6131754&74’6361“.
O O @00 0O F (NN G =4 00 80 QO e~ (N 4N O 0 INF O F OO VD © NID B et N O N T O OIS LN (- )

® 0 00 00 08 050 00 00 80P TP 000 00 00 0P OB e o008 59D e e 9o - o9
4211%6150406717461204523067618562281112685240233 &990
- i el fl.fl. | -8 1) eted I I ._...flél (B Ll

'

NOMNO AP0 NNINODO g O N F AP et D O=ININN $ F VN0 DR O R OORFOT T~
O =3 DO OIN Q=N O O F =i O O =il il OO F O 0~ OO0 F N N 1P IN NM D i F O MO INO OO O
00 M $ NN 0 OO NENM N O F =t PO M= M O M DN MO O M F NN Oret 00 & MILN st OO T ¢ D
MOOO et OO O OINNMANINNQ OO rird O MONO 4 rdod VNN OO O ONN QY O OO NM
meo ololelalolololelololslolelolelelolelelolelale (elelolelnlal=lololelel-Tal~lale -] o0
(=] (o]elololeloleclalalelololelalsloelaleclnle’olelalelole ololelalslololslololeloleTola) (allelel=Tels]
® D 0o 806 0 00 0 8 o0 e 8 e 0 P o s O OO0 ORI O PO PG P OD et YO OO PO 9P OO0 0O

e A L e S h s 4700 ) s s

- OMNN D O 40 OMAUI NPt NV O N NN O Dt O N DO O iiN S F O D

QO OR OO NN ~OOND DD DO O ONM N\ N1 O OO
N 0O (0 M N NN N OO (N0 O NN O 0D 00 00 00 (0N AN N O O OO 0 00 00 M 0O O @ 0O M NN NN

ololelolelololslolelolalolololeloleTololelololelololalalelelellaleJalsls]olelslolelololelole /e lola]l~lol -]

.O..0.00..00.‘..0‘0...00..0.....0..0.00.0.0.0........

(olelolnlolelolsloleleclolofolololalolvolrlololoclolololalelolol-lalelololelalnlolololololelolelelolelalal]

504114819761918095524425421%14074066“71
nmn903834586222029937185942 OO =N D fl%
O N O

30927

29940

28973
7878
129
680
4909
2051
0269

000000000000000000000000000000000000000000&0000000000
O DO Nt P el O Y 0 et (N O P D et (O T O NN N OO F =0 O ON PO MDP= O DO NI 0 F ~irdify
QOMIVOVINANF OOMONOM=M N D et F PPy OO N NN NN OMO TN~ FINONDOD
R 0BONMOPRONN 0D INNOON OO rird O\ O et N P NN O O O O 4G O 4 O~ NO O NI~ F
NN NN M 0O Y NN VNN N O NI M NN A O NN OO NN N IO M OO O $ N 0D M NI NN NI
(olelelolelofolelalelolololololelolelolalololololo slalololololololelolololololelolalelolololelololelalole]
@ 06 ® 0" 8 600 000 0 2P o b0 o0 b oe P o0 B 000D et 20000 00 OO e H B e
(elolelelolololelalololololalolelolololelolololelolelelolalololelolololalslolololnlslelolelololelolelalole)]

olelelolalelolslolelelelelalaleloleloclalelelalololelalolelelolela]slolelelololelololelolelololelolelelolx]
elelololeleloleclolelelolela]olelolalaleleololololelelololelalalclolalalelelelelclolelolalelolalslolelelele]
00,090oho.?uLbo.O.oooo‘ooQ“oocooooooooooflu-ooooooooo.MTNOoo.obfifloh
~ON DY © (N O = ettt (1) ot O° M= (N OO (N e N O @0 OO NI NN O DN =N O N e a0 a0 o

9907%60808572863451842520560 I P L\ 1= ) (Y N D = vt O ot © N O e O U ot 4 U
TN NO FINMM DO M DOIN =1 DO OO O rd D 308227953468537863“50636118
FOMNPMMOCOONMO VT NINT 4O N DOONMNON 0 F O MINONF N NrtP=NC IO F ONN e id=MONNON
fl44 & TINININ & & O ON N b eted NO NN S O N

56612345%67812334‘56 -4 Ll ) 7
- i i .

s
L

F 4
experimental da

6.43
of

Least squares approximation

MEAN RELATIVE ERROR

FIGURE 3.3-8

0.04

°
-
»
I~ ..
~ . [ ° © [ ] o
003 \\“\ = e '. *3 P °
\\\\ . . @ . . é
\\\TN\\ .. . @& R
\\\\-L ' @ T —
5 002 P ot S
o ————]
S | —_———— blasius
§ = measurements
.ZSj best fit
" 001
0 4
10 2 3 L 5 6 7 8 9 10°
Re ~number
FIGURE 3.3-9.
Experimental data of frictional pressure drop measurments,
best fit and Blasius formula.
: b relative error ——
variable vwvalue abs. error BY of max. value ]
L 1200 [ mm ] 1 0.08 % fig. 3.3-3
D 41.25 [mm ] 0.5 0.1 % fig. 3.3-3
_k
c 9.55 10 [m? ] 1.2 % ref. 2.2-3
re
P
# } cf. figure 2.2-13
AP 2% subsection
v 2.2-3
APf 3% Appendix 3A

FIGURE 3.3-10.

Aceuracies of properties appearing in equation (3.3-6).

salt outlet

pRAEAL] .
BRI & salt inlet
LR
steam out “HIH!
| 'llll.’!
il

FIGURE 4.1-1.

Cross—section of a full-size bayonet tube steam generator.

salt
outlet

\\

insulation layer

- Steam outlet

t

feedwater
inlet

FIGURE 4.1-2.

Cross—-section of the bayonet tube test module.

characteristic of
evaporator tube

Ap

stable unstable stable
f\ by /
K410racteristic of
system of

parallel tubes

JUCHSE— = Pm feedwater

FIGURE 4.1-3.
Region of static instability in parallel tubes.

;% -
i o single -phase flow t g\
o W : K]
- d=d film A8 forced convection oo
= X=1 T
@ — .
transition region
e S
> f\\ \j‘ : g
3 i’w-‘-’CmVAesqt \A,{ mist flow =
m P SBatN o8 =
| A S S [~}
BAILY 0.2¢x€0,4] dry out 3
(4, 1-5] % 8D g £
g |
§ | 3%&,% nucleate boiling g
G| BwsCicp a0y [l
5 p
g g2 ¢
e g Rl 2
T ' transition region S G| P
- albers. B
w [T T -
2 £
: dw=dpy i 48 single—phase flow ]
> @ forced convection i
e ©
= 3
= L FALd
heat transfer actual flow patterns

correlations

FIGURE 4,2-1.

Secondary side flow patterns and heat transfer correlations.

Temp. FLiNaK in

Temp. FLiNaK out 614 Oc
Mass flow FLiNakK 6.8 kg/s
Temp. feedwater in 280 Oc
Temp. steam out 540 Oc
Pressure steam out 18 MN/m?
Mass flow feedwater 0.065 kg/s

FIGURE 4.3-1.
Table of process conditions at full load.
Lenght 9.1 m
tube diameters
evaporator tube
top 6.7 m 17.2/12.6 mm
lower ‘2.4 m (insul.)| 15.2/10.6 mm B e 080
pressure tube 26.0/20.8 mm
outer tube 60.3/52.5 mm  noonel €00
insulation layer
app. thickness 1.5 mm 20, —
heat resistance 1.0 m? %c/kw

FIGURE 4.3-2.

Dimensions and materials of test module.

FIGURE 4.3-3.

Flowsheet of bayonet tube steam generator test facility.

O

OO U W=

FLiNaK pump

Main heater

Dump vessel

Steam generator test module

Rupture disc

Salt make up and storage tank

Feedwater pump (plunger type)

Feedwater mass flow control valve
Pressuriser

Adjustable restriction (for stabilization)
0Oil heated preheater

Hand valves (for start-up and close-down)
Three-way valve (for blow-off of the steam generator)
Pressure reduction valve

Spray cooler (for desuperheating the steam)
Spray cooling control valve

Condensor

Condensate pump

4
1@
——

flinak

FIGURE 4.3-4.

RS 4ato

TTVWTI Fl =
01/\g0: 80/ Iy A
M& 1 :0'. 801
AT
N e w

RS 130°C ! K805

Pl

= | ©6

Instrumentation diagram of bayonet tube test facility.

H80.5

|
tk1 \
tk2(TT703) (::> tk25
tk3 [ i
| o
i R
tk5
tk 26 @ the =I__fi{
l 8
wn
war |
‘ S
(72]
tk7 -
! 8
wn
i 5]
tk 8 \
tk 30 @tks =)
&
(T3]
@ tk31 } !
tk10 {A 3
tk32 @ tk11 '=1‘ g
@ tk33 ‘
: =
un
tk12 ~ Yy |
tk34 @ tk13 =1. g
| 2
! wn
tk35 ‘
i 8
un
tk15 ,
tk 36 tk1e =
\ g
wn
tk37 ‘
‘ 8
wn
tk 38 tk16 ={ ‘
| 2
:“:1‘; @ tk 39 l
{ =1
. l m
tk20 !
tk40 tk19 =
g
tk21 \
tk22 tk 4 :
g
tk24 !
tk42 g %
TT70.2
platinum |
resistence
thermometer

FIGURE 4.3-6.

Thermo-couple locations in the test module.

008

(Do) 9injpiadwaydo} 103DI0ADAY ~——egt———

00L 009 00s 00% (1113

0oz

(11]8

B e

I

|

075

009

time (sec)

FIGURE 4.3-6.

down instability.

Top temperature during shut

input
. geometry
«process cond.

estimate of
conditions at
the top of
the S.G.

integration
routine

correction of
conditions at the
top of the S.G.

comparison of

computed

and prescribed
values at the
inlets of S.G.

output
of results

FIGURE 4.4-1.

Structure of steady state program.

P N VP P T P P P T T P e e T T P P ST TSI TIeITITI Y

* “
* METING 2 INPUT ZATA BASTA %
* *

A A R ROR RROR R R Rk R KR R ok R kR R & R o ok R R R R ok R R R Rk K

T'J]A; L.f\uTr‘l 7 e1( M
PIPE J1laMzT. R 1 Jel0U3 M
PIPE CSLAMETL~ ¢ 0eG525 4
PIPE DIAM=T:ZR 3 Jeli25( M
PIPE DIAMETER 4 Ga 3208 A
PIPE DIAMZITZR b GelUlT2 ™
PIPc OIAMETER 6 Veullé ]
HEAT a=s5IoTANCE QF INSJULATLILN (26140 CMx»*_/nW
INSULATI v L=NGTH -e40 M
SALT In TEMP 5862 G
MASSFLOwW GALT re V7 Ko/s
STEAM PRESSUKC 1772 SAR
FEEDWNATeR TEMYP 2§5e3 G
MASSFLOW FoEJWATeR Jeubb Ko/S
STEAM_TuP =NT 2647543 KJ/KE

TR E R AR RS F AR SRR S R R A AR Kk Rk Rk ROk KRR R AR R E R R R R R

* -
* METING 2 CVvIRALL CuTPuv UATA BASTA %
* i

Aok e o g o ok AR Bk 0K o o oK o ke o o ok o ok ok A R i 8 Kok o ok o kR o RO R RO O

TRANSMITTEC POWER 1218 K
SALT IN TEMP Scoel G
SALT UJT TEMP ST4e3 c
MASSFLUW LALT de Y <L/S
FEtuaATEX TEMP 27440 64
SATUSATI_N ToMP 355,57 L
TUP Tz=MP I0le9D <
STEAM SUI TEMP 50t e c
MASSFLOW FESLUWATER Cel55 Ke/s
STEAM ¢#R:-SSULRE 177.0 1AR

FIGURE 4.4-2.
Sample output of "BASTA".

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274.CCcE

C.C3CcCCC

C.C2CCCC

CeC2CCCC

CeC2CCCC

CoC2CCCC

€ C2CCCC

CeC2CCCC

C.C2CCCC

Ce2CCCCC

Co.3CCOCC

Ce2CCCCC

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CelClCCC

«2CCCCC

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Ce GCOCCC

CecClCCOC

CeCCCCCC

GesCCOCCC

CeCCGUCL

0eUCYVVO

GeUCNO0U

——— temperature (°C)

quality

700 T T I I U I I 1 o I T T I

650 -1

FLINAK -channel

superheater

evaporator

quality X in evaporator
o S T e e MR T RRELE DA SN s e Baai kil Ll £~ o SN s mam

—————== lenght (m)

flow = 0,65 kg /s p = 176 bar P=131kw

FIGURE 4.4-3.
Sample plot output of "BASTA".

METING 2 SERIE 180 09-3-75

FLINAK FLOW = 6.94 KG/S
TEMPERATURE IN = 586 DEGREE CENTIGRADE
TEMPERATURE QUT = 577 DEGREE CENTIGRADE
SPECIFIC HEAT = 2.02KJ/KG*DEGREECENTIGRADE

WATER FLOW =.0580 KG/S
TEMPERATURE IN = 275 DEGREE CENTIGRADE
PRESSURE 1IN = 179 BAR

STEAM TEMPERATURE QUT = 501 DEGREE CENTIGRADE
PRESSURE OUT = 177 BAR

POWER DELIVERED = 120 KW

TEMPERATURE=-,  QUALITY —AND HEAT_RESISTANCE DISTRIBUTION IN STEAMGENERATOR

LENGTH T_FLINAK T_STEAM T_WATER QUALITY R FL/ST R ST/MW

(M) (C) (C) (C) (M*%2%C /KW)

0.00 576.0 362.8 362.8 1.00

025 0576 =0.140

0.50 576.5 403.7 3684 1.0C

0.75 0.625 0.155

1.00 577,0 414.4 35T.4 1.00

1.25 0.643 0.231

1.50 577.6 425.0 356.3 0.87

1.75 0.661 0.301

2.00 578.1 435 .6 356 .4 072

2425 Ceb6T7 0.383

2.50 578.7 44642 356.4 0.59

275 0699 1.612

3.00 579.2 472.4 356.4 0.55

3.25 0.719 1.150

3.50 579.7 487.1 356.4 0.49

3.75 0.728 1l.744

4.00 580.2 501.9 356.4 Q.44

4425 0.732 1.073

4.50 580.6 50542 356.4 0.36

4,75 0.732 0.839

5.00 581.1 502.6 356.4 0.26

5.25 0.731 0.794

5.50 581.6 499.9 356.4 0.15

575 0.728 0.515

6.00 582.0 487.3 355.9 0.00

625 0.720 0.444

6.50 582.2 4747 340.5 0.00

6.75 0.714 0.562

7.00 582.4 4717 322.8 0.00

T.25 0.718 1.267

T7.50 582.6 485.0 312.8 0.00

T.75 . 0.727 1.827

8.00 582.7 4983 304.5 0.00

8.25 0.731 1315

B«50 582.9 501.1 291.1 0.00

8.75 0.731 1.263

9.00 586.2 501.1 275.3 0.00

FIGURE 4.4-4.
Sample print output of "SMEBT".

temperature (°C)

temperaturedistribution in steamgenerator

I I | T I | I I I I I | I I I 1

&~ (%,)

350 - & &

quality X in bayonet tube steamgenerator P
| [ [ I | I I I I T | | I [ | I I

——— = |ength (m)

FIGURE 4.4-6.
Sample plot output of "SMEBT".

;,//&pout §\\h5hin % Mevout

Z Gp § Gs é .Gs_

1IN

N

N

Z § Z FIGURE 4.4-6.

N U fhon e S
/A.&pip N hSho_ut%/ Mevin | (4.4-14).

P-MEAS (kW) P-CAL (kW) ERROR (% of measured P)
56.00 54.45 -2.76
72.00 69.24 -3.84
120.00 119.48 -0.43
98.00 98.88 0.89
72:100 7913 0:17
80.00 77.83 -3 1 for
97.00 96.01 -1.02 = 3.42
119.00 118.40 -0.50 b = 0.308
119.00 115.76 -2s13
51.00 50.20 -1.57
54.00 53.57 -0.79
56.00 54.50 -2.68
26.00 23.16 -10.93
74.00 71,85 |
78.00 82.34 5:51
97.00 97.68 0.71
98.00 102.47 4.57
FIGURE 4.4-7.

Results of the least squares fitting of a number of

steady state measurements by equation (4.4-21).

Testnumber 1 2 3 4 5 6 7 8 9 10 11

FLiNaK Flow [ kg/s ] 6.82 6.94 6.97 6. 58 6.96 6.58 7.62 5.66 5.50 5.950 6.90
Temp. in [% ] 573 586 596 583 586 625 640 600 602 622 600
Temp. out [OC ] 564 577 588 515 578 621 635 598 594 620 592

Water Flow [ kg/s ] 0.0648]0.0580|0.0568|0.0493]0.0445| 0.039 | 0.027 | 0.013] 0.045)] 0.012] 0.052
Temp. in _[OC ] 281 275 276 257 250 271 221 248 201 249 262
Pressure in [ bar ] 178 179 179 179 178 176 192 183 103 161 138

Steam Temp. out [OC ] 493 501 508 496 498 540 525 497 516 516 D22
Pressure out [Dbar ] 176 179 179 177 176 174 192 182 161 161 137

Power supplied [ kw ] 131 120 119 106 97 90 66 28 98 26 113

FIGURE 4.4-8.

Conditions of reported steady state experiments.

(C)

TEMPERSTURE

GURLITY

ys

TEMPERGTURELISTRIBUTIAN IN STESGMGEN.
l | [ l i | | l l | | 1 | | |
| I S W | SR | SU-, W . M; S LSS, R s e & ‘f
= R VREE”. M MU SN . M- . SR - S VR .
QUALIT X IN GNNULAR TUBE STEAGMGENERGTCOR |
B |
| l 1 | i I | T | Py T | Pl T | |
[ . = 4%1_, T —
C 1 2 3 4 5 | 5 7 5 9
0703/5'FLON;.065KG/3 PRESS-176845R P::131KW ~LENGTH (M)

FIGURE 4.4-9a.

Comparison of measured
and computed temperature
and quality distributions
in the bayonet tube test
module.

(experiment no. 1).

TEMPERSTUREDISTRIBUTICN IN STERMGEN,

\ 1 ] I T ] T | i i J | = 1 I I | I
B! & 053
~ 695 |— gon -
uJ ; e
9: ¥ BK) [ \C‘
= 6LC |~ —
— i
g (B T Y T KT T T KKK KT ”—*AAT
2 osse —
-
J
e 3
5G2 » ol W= ’
— J/"
Li"_-“_ T e
P,,,er””a
Pradd
HGO —;/’}V e
300 b ~ % T —S S SH—H—&
360
GUARLITY X IN GNNULAR TUBE STEQMGENERQJ@R [
i, 5 l
e 1 | I | i Ko T R | 5 = I I |
>— :
.00 = -
_af
=
=
< 0.7Y ~| FIGURE 4.4-9b.
Comparison of measured
0.58 |- —| and computed temperature
and quality distributions
o B —| in the bayonet tube test
module.
e : C I | | L P - (experiment no. 2)
o R 3 oy 5 | 5 7 g )

70375 FLOW=.053KG/S PRESS=173E26GR P::120KNW -LENGTH (M)

1)

TEMPERSTURE

CGURLIT

TEMPERGTURELISTRIBUTION IN STEABMGEN.
10¢C 1 | T 1 T T T | | 1 I l T 1

d

QUARLITY X IN GNNULAS TUBE STEHMGENERQTFH

o l |
o l ]] T l [ | | | I | | R | l
0o s _
C.7% ~
B FIGURE 4.4-9ec.

Q.50 h _| Comparison of measured
and computed temperature
qnd quality distributions

0,28 |~ — in the bayonet tube test
module.

310 3 | | | l 2 i | & TN—_— | (experiment no. 3)

5 1 2 3 y 5 5 I3 5 g -
70375 FLOW=.057KG/S PRESS~173BGR P::110KNW - =LENGTH (M) -

(C)

TEMPEAS TURE

LGURL L

s0k 5 o 1 I I | I | l l e 1 1 T

550 | b - 043

Cgllh

50C x BOIH
g - s BN o — ¥ 5 -5 s, er o HHD K . e = :%
S50 |— KL

QUALITY X IN GNNULAR TUBE STEQMGENERfiT@R

258 ..

S l l] 1 l l 1 | | | o] 1 gD T | 1 1

o G——i L= -
.75 = | FIGURE 4.4-9d.

i _| Comparison of measured
.5¢ and computed temperature

and quality distributions

G.25 | — in the bayonet tube test

module.
. (experiment no. 4)

6. e S e L L i N éfi#fi#——éflé '
c [} 2 3 et g - | 5 7 3 9

70375 FLOW=.043KG/5 PRESS=1778GR P 1C6HANW -LENGTH (M)

-

(C)

TEMPERSTURE

R

CURL I

TEMPERGTUREQISTRIBUTIAN IN STEGMGEN,
ot [ I I 1 T l l T T } ] l I T
SLWF oAl H——5 +3- Kt t3- ¥ KK g = W
958
S RIN . S o '

QUALITY X IN SNNULAR TUBE STESGMGONERGTCR
e | | T [ A N N B | T 1
1. 00 B3 —B

™
0.7 \E\*\\E
O ’3\_ L‘
O.2% = ‘N\
o AN N TR TR A S N S B \f<§§5 R T N N N
(70375 FLOW=.C45KG/S PRESS=176R88 P37 KW ~LENGTY (M)

. 045
%« BSTS

FIGURE 4.4-9e.

Comparison of measured
and computed temperature
and quality distributions
in the bayonet tube test
module.

(experiment no. 5)

TEMPERGTUREDISTRIBUTION IN STEGMGEN.
| T | | i | [ | 1 1 | | | [

(C)
—

TEMPERSTURE

LURL I

FIGURE 4.4-9f.

Comparison of measured
and computed temperature
ard quality distributions
in the bayonet tube test
module.

b o giike 1 e _& (experiment no. 6)

7 3 9

190974 FLOA=.032KG'S FPRESS-174EGR P20 AW -LENGTH (M)

GNNULAR

STEGMGENERGTOR

12}

l ]

1. (experiment no. 7)

3

=

-LENGTH (M)

FIGURE 4.4-9g.

Comparison of measured
and computed temperature
and quality distributions

- in the bayonet tube test

module.

2

(C)

TEMPERGTURE

VTT

i 3

tURL

=
3

TEMPERGTUREDISTRIB

UT1

IN S

TEAGMGEN.

| |

o G173
—— wd
BST4H
2 = i - s - Jme & bt = .
=4 =B e s b o {3 . o
!
e ——l_Y
- N
“flg o
SNY e
AN i e 7N

GUARLITY X IN GNNULAR TUBE STEGMGENERGTCR ‘kN
| | | {
] l I I | [l ] I l I ] N I T
|
= ity = KK —

= e
FIGURE 4.4-9h.

- _| Comparison of measured
and computed temperature
and quality distributions

— — in the bayonet tube test
module.

i | 1 [ 1 || R | ! | (experiment no. 8)

o 1 2 I3 R 3

Sl 0W=0

-LENGTH (M)

(C)

TEMPESGSTURE

~ 0.75%

TEMPERGTURECISTRIBUTIAN IN STESMGEN.

10e T I T I I [ | I I | i T 1 I
LR

CST | - 0 Gd5
. ¢ G \

~ ~ 3 S =5 “':_\: : WWD B J I C'

3GC |- ~
QUALITY X IN SNNULAR TUBE STEGMGENERGTER :

eus . I 1 [ I 1 I I I I l T T [ l I

1.CC OB & —

F1GURE 4.4-97.

Comparison of measured

¢.5¢ and computed temperature
and quality distributions
0.2L — in the bayonet tube- test
, module.
o i i 1 l | N S | i (experiment no. 9)
Yo 3 4 5 7 5 3
CS50375 FLOW=. 045KG/S PRESS-1

61BGR P35 KW -LENGTH (M)

()

TEMPESSTURE

GURLI

TEMPERGTURERISTRIBUTION IN STESMGEN.

{e . I T I T /4 I T T T T Rl T N
- A
« BSTH

00 : \1&% .

QUALITY X IN GNNULAR TUBE STEGMGEINERGTCR - \
s OB PRLE T e e R W I WG VRS PR B e e
CC S oK = .{S H— 5 5 = ) =B -~

FIGUKE 4.4-9].

Comparison of measured
and computed temperature
and quality distributions

QD

20 in the bayonet tube test
module.
L 1 1 | | | o T | (experiment no. 10)

C L 2 3 4 5 & 7 g 3

503375 FLOW=.012KG/5 PRESS=161E5R P-gh iKW ~LENGTH (M)

(C)

 TURE

-

TEMPER!

C.Co

TEMPERAGTUREDISTRIBUTICON

C tLp Nt = 7 —t o5 =5 N

QURLITY X IN SNNULAR 7URE STEGMGENERGTOR mflx\\&\\fla\\fi,
T T T T T T T T T T T T T T T 7
| | | N SO N N

C 1 2 3 y o 6 ' 3 9
(70275 FLOW=.052KG/S PRESS=-13786R Pl 15KNW -LENGTH (M)

FIGURE 4.4-9k.

Comparison o] iieusured
and computec. ter: .crature
and quality diotributions
in the bayonet tube test
module.

xHL (experiment no. 11)

temp.

salt-channel(computed)

%porotor(computed)

—= direction of integration

_as computed in first step

“-

superheater(assumed)

— e
— e
— —
— —
‘-
—
e
— —
— e
— e
-—
—

computed
o
//’
B S e . Bl A i i b s e 7
”
-
_ -~ " as computed in first step
-
— direction of integration
top

bottom

- ength of S.G.

1st step

2nd step

FIGURE 4.6-1.
First two steps in the iterative procedure for determination of the

dynamic temperature profiles in the bayonet tube test module.

Location of particles in channel

2z (5)9=22(5)
zz(4)e=22(4)
zzo(S)'}
zz (4) 9=22 (4)
2z (&) o =22,(3)
Z
zz(3) =22(2)
z2z,(2) ¢
2z (1)4=z2 (1)
zz(1)¢¢ 2z (1)
220(1)1’////////////‘l
zz,(0) 22 (0) 5~2z,(0) zz(0)|=2z,(0)
t=t t=tA t=t+z At R—— 4§ i

FIGURE 4.5-2.

Dynamic displacement of particles under observation.

zz(4)

zz(3)

zz(2)

————= [ocation of particles in channel

FIGURE 4.5-3.

Displacement of particles under steady state conditions.

1,1-1
Gt-1 (~1 Gt -1, 1-1
s
(=}
o
>
QL
Q
£z
-
&
o
e
O
e |bhe-1,1 L ht,t o
Pt-1. Pt.L
Gt-1,1 Al
L At S
I 1

—_— tlm!

FIGURE 4.6-4.

A time-space representation of the conditions at the boundaries
of a channel section of the superheater or the evaporator.

temperature (C)

length from top (m)

FIGURE 4.5-5.

t(sec)
0.0

15.0
18.0
21.0
24,0
27. 0
31.0

900.

Temperature profiles in the bayonet tube steam generator

following a step in the feedwater mass flow.

fo
1.00

1.06

1.08

1.07

1.07

Exp. before transient after transient
nY. feedwater steam feedwater steam

flow pressure i flow pressure powex

kg/s MN/m? kw kg/s MN /m? kW
1 0.0312 11,74 69 0.02353 17.59 56
P 0.0251 17.68 56 0.0331 17.66 sd.
v 0.0335 17:0%9 74 0. 0555 $.79 120
4 0.0552 17.78 118 0.0458 372,70 98
< 0.0468 &1 P 100 0.0368 17.70 19
6 D.0373 17569 81 0.0378 17.61 80
7 0.0376 17.66 80 0.0443 1772 97
8 0.0447 17.83 95 0.0557 17.70 119
9 0.0467 17,65 103 0.0556 17.60 119
10 0.0553 O Py b | 121 0.0229 17.64 51
11 0.0250 16.16 56 0.0246 18.28 54
14 0.0264 18.34 59 0.0248 16.14 56
19 0.0117 16.18 26 0.0129 18.25 28
14 0.0159 18.14 35 0.0116 16.06 26
15 0.0341 16.05 76 0.0338 18.43 74
16 0.0337 18,32 75 PR35 16.11 78
17 0.0447 16.08 99 0.0437 18.21 97
18 0.0445 18.11 96 0.0446 16.09 98

FIGURE 4.95-6.

Conditions of transient experiments.

— = flow (kg/s)

——— == temp.(°C)

temp.(°c)

0.08

007

006

0.05

0.04

0.03

0.02

0.01 |-

0.00

600

550

500

450

400}

350

300

250

200

650

600 -

550

500

450

400

FIGURE 4. 5-7a.

stepwise decrease

Flow measurement during a
in feedwater flow.

steamoutlet temperature
feedwater temperature

FIGURE 4.5-7b.

Feedwater and steam outlet temperature following
a stepwise decrease in feedwater flow.

- e = - ———
————— ——— p——p—— — i ———— - - S ————————

—
-
—=4—
-4

‘ | |

-

| ] ] |

90 100 120

110

130 150 160 170

= time(s)

FIGURE 4.6=7c.

Superheater gap temperatures following a
stepwise decrease in feedwater flow.

temp.(°c)

——= flinaktemp.(°C)

I ! I I S I T | I I 1 S Ko T T I T
650 =
600 - =
450 I~ =
TS12
W teu -
FIGURE 4.5-7d.
N L |
TS 1 Superheater gap temperatures following
w7 " a stepwise decrease in feedvater flow. -
250 -
| | | i | | | | | | | | 1 | ik | l
1 [ [ T [ i} | I [ I I I T 13 [ [ I
inlet pressure
—————— outlet pressure
@
3
wn
o
(=%
E
g
@
~ o~
Bab: o
3 S
F— N
\\ —.__-‘____—————"___———\___‘___
’/’
\ E o
\ ///
\ -
Ne——” FIGURE 4.5-7e.
Secondary inlet and outlet pressure following
a stepwise decrease in feedwater flow.
L__ | | | | | 1 ] L | L | 1 | ] | | |
700 h I | T T T I l | T l T el T T T
—_—— — TF18
TF 13
————- TF 07
——————— TF 01
675 =
_— P TTIV T
A ETPT i
T T _—-—-"'".:—"
R i .———__:—: _______
rr\"“"".‘(. g /'_—::._—:"'_
.:‘.f'*" ) _/—-”’—’—
FrTTT I T T TYTY e : :’_”’
S B
6501 D el _
///’
P o e e e _'/
625 | | | | | | | l 1 | | I | | | | 1
0 10 20 30 40 50 60 70 80 S0 100 110 120 130 140 150 160 170 180

————a=— time (s)

FIGURE 4.5~7f.

FLiNaK temperatures following a stepwise
decrease in feedwater flow.

PRESSURE

183-161

BARS 026 KG/S

C)

(

TEMPERATURE

I R N S N SR R

| l | 1

1

FIGURE 4.5-7g.

Tgmpepa ture p}’(,)j'”z/' Les f() [ ZOZJZ'H;'J

3 4 5 6
. PARQMETER=SECCNDS FROM -START -

a stepwise decrease in feedwater flow.

7 8
LENGTH FROM TQP

(M)

3

0

time (8)

0.0

15,0
18,0
21,0
24,0

27.0

water pressure
—————— steam pressure

— = water /steam pressure (no scale)

| | | | ] | | | ! | | | | | L l |
0 10 20 30 40 S0 60 70 80 90 100 10 120 130 140 150 160 170 180
——— time (s)

FIGURE 4.5-7h.

Stepwise increase in outlet pressure and response of the inlet pressure.

0.08

007 |- .

——= flow (kg/s)
[=]
o
»
|

000 | 235 ! | | I 1 L 1 1 L | ! L I !
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
————— time (s)

FIGURE 4.5-71.

Feedwater flow response to a stepwise
increase in outlet pressure.

temp.(°c)

temp.(c?)

——== temp. (°C)

feedwatertemperature
—————— steam outlet temperature
550+ -
500 -
LSO =
400 - z =
FIGURE 4.5-77.

30 Feedwater and steam outlet temperature responses ]
- to a stepwise increase in steam outlet pressure.

/11| e G L e i S e —
200 rl 11 ll 11 11 Il Il |l rl + lL l1 ll |1 II ll 1|

650 - —

B TS01 ]
------- TS02
—_———— TS0 ]
|| Ee——" TS 06
—w—== 1808 FTGURE 4.5-7K.
|  ———= TS10
Superheater gap temperatures response to a
- ' stepwise increase in steam outlet pressure.
| | | | | | l | | L ! ! ! | 1 I .
I T ! ! T I T T | Ll 1 | T I I 1 I

‘| 1 1 L 1 I | 1 | | | | | 1 | | .. J
0 10 20 30 40 50 60 70 80 S0 0 10 120 130 140 150 160 170 180

— time(s)

FIGURE 4.5-71.

Superheater gap temperatures response to
stepwise increase in steam outlet pressure.

F BRI DD SSRGS D i77 BGAS

1 | l l T l I T l l | | l time (s)
= X SRR
L ] X
- -~ & ——5—8 88— —8—8—8—9% P 5. C
o

I &
& A 13. 0
G
e 35
i 4 21.C

x ch.C

4 2 1.4

l —
’r’ e g
|~ B —
, | l [ ! | | 1 | 1 1 i ' I [ 1

r i b 3 4 5 : I 9 g

2-SECCNGS FREM SIGRT - LENGTH FSOM TEP (M)

FIGURE 4.5-7m,

Temperature profiles following a stepwise increase in ateam outlet press

Property Plot symbol Thermocouple nr.
cf. figure 3.4-5

Superheater gap TS 01 Y 1

temperatures 02 5

04 4

06 8

08 10

10 12

12 14

14 16

15 18

16 19

17 22

18 23

FLiNaK channel 01 a0

temperatures 07 31

13 37

18 42

FIGURE 4.5-8.

Thermocouple numbers/symbols.

temperature (°C)

p(bar)

dmikg/s)

600

500} —
+Wt__‘i‘ifl
LOO | _'}fb( —
300 3
200 | | | |
200
160 ' . :
005
0 | | | | |
0 10 20 30 40 50 60
time(5)
exp DYBRU DSTS
salt inlet
salt outlet TS GOt . |
FORUWALEPr = Scsissdian | sasinsssasns  soessressis
top ————— —— —

steam outlet - ==

e | —— . ——— e s s ——— — — —

FIGURE 4.5-9.

Bayonet tube steam generator:

temperature responses

steam outlet pressure
simulation
experiment
feedwater mass flow
experiment
simulation

measured and calculated (DYBRU and DSTS) time-depentent
responses following a stepwise decrease in feedwater

mass flow from 85% to 35%.

——» steam/volume fraction o

= [Nlet mass flow

steady state conditions

intermediate transients

=ZXVI, e —
’/ ot

——— physical length of steam generator Z

FIGURE 4.6-1.

Dynamic response of void-fraction distribution following
a step in the inlet mass flow rate.

exponential growth

/ Limit cycle

steady state value

s, o, S, BTSSR

™
/
/
A
| .
|
.' |
T |

- time

FIGURE 4.6-2.

Growing amplitude of a diverging oscillation resulting
in a limt cycle.

. N

=— amplitude of inlet velocity aj m/s

FIGURE 4.6-8.

Oscillation amplitudes versus channel power
(taken from VAN VONDEREN [4.6-5]).

.0
Kin =14 exp. a A e =1
% o i x
13'_-',clt =200 C &sub Qinres B e j:g
: =
8 °c  197kw | !
----------- 10°C  124kW [
—_—— 20°C  143kW ||
= e R R
_.._.._{ 1°C 198 kW |
i from T.F.A. analysis /
------------- imaginary case 40 |{I Jr/
LO KW ! 1
, | arbitrary
&" r 9 /units
A b
I / :
. :F ' +'I :/l
kil i
2 f o/ r
Al £ / /
. ! l
7 )
P.. I‘ - —
0 .......... ' 00--0-000 -0
40 80 120 160 200 240
—==— total channel power Qg kW

pout.¢t°ut

- Heas
pturbz¢ turb.
P cond-Pcond
pin.¢tin Pcond.
ppump L.P feedheating
®pump system
—————
FIGURE 4.6-4.

Stmplified diagram of steam generator turbine system.

P out T lpout

T T

FIGURE 4.6-5.

Four-pole element.

imaginary axis

Apin
Aébm

Sp ]
/ / real axis
\ W
w

FIGURE 4.6-6.

Idealized shape of the inlet impedance curve
of an evaporator channel.

up stream of inlet down stream of
header - - inlet header
% in 4’1out
— 1th channel
Pout
pump + m steam lin
feedwater 2 " channel +turbine
line +condenser
¢t P 92 $2 Pt out
inlet system N : = M E = outlet system
| |
| |
nth channel
’nin ’nout

FIGURE 4.6-7.

Block diagram of a steam generator turbine system.

@2
: 1
A Y 7

b4 4

b3

FIGURE 4.6-8.
The three different modes of oscillation
observed by VAN VONDEREN [ 4.2-12 ].

Ap=0 )
P iterative dfw

procedure

H1
method 1
¢ T
fw H Ap + criterion
R 1 b
method 2

FIGURE 4.6-9.
Two simulation methods stability prediction
in the time domain.

102

. [ .
. e
]
6 ) =
5 \\ ' 3
1 |
4 \
\ \
3 v —
v\ |/ v
2 \/
| )
1 /
0 | 1/
10-2 2 3 4 56789107 2 3 456789100 2 3 4 5678910!
__.——_»
frequency f (c/s)
0.
—
T
-~
\‘~
N
9
90° &\
N
\
\
|
\
180°
\
\
1
\
\
\
270° \
\L;
\
\
\
\\
360° \
L3
\
\
\
450° :
102 2 3 & 5 6 7 89100

2 N
frequency f (e/s)

6 7 8 910!

B

FIGURE 4.6-10.

Sample result of method 2 simulation.

~—— = inlet velocity

Inlet velocity [m/Y]

L
i
i
E. 8
!
1 ,g"_ -
|
“.20— -
1 10‘7 -
1m% o]
080} 1
270 -
inlet velocity
060 s -
050 i
040 -
030 -
0.20 .
010k .
0 I I 1 1 | I I ! 1
o0 5 10 15 20 25 30 35 40 45 50
———— - time (sec.)
FIGURE 4.6-11.
Sample results of method 1 simulations.
1.50 T T T T T T T T T
1.40 —-—-=— Velo =4
130+ - AL10 -<§
o
] AL20 | E
®
w1l ——-— AL30 |}
1.00 - -~ AL
090 —os
08
0.80 L . /*\ p S
_.__.__I—A_.___\”_.--\\_._“_ e ~~ —07
0.70 -~ N \
0.60} /\-\i“’ .ZOS
e e Ty / A
050F — =T i S v \ /A i /05
ek | == s = e \-/__. ..... . P \ /
W Y ., - o
0.40— \T / —04
0.3} \-\/ —a3
BBl it e —— N g sapanar F  a c npn EAE Si P
C.10 —01
000 PO .....t.. esscans L t r 1 wes .l.--. I 1 , ..t o-c
0 5 10 15 20 25 3c 35 40 L5 50

FIGURE 4.6-12.

Sample results of method 1 simulations.

1.50— T T T T T T | % T
o
~ 140 —
£, R\, 5
5 £ -
2 1,30‘ - AL10 §
(=] -
$ 1.zolk ----- AL20 13
- { >
E 1.10 AL — AL 30 =1
1.00 - AL4LD —10
o.go[- 409
080+ —08
-
v T e e e TN . . s SR "oy P / 07
0.70[> o Rl e S
0.60} —os
e S
¥ e -\‘ / .
BEPECT vy Sep i e iy B T Sy S B Sl S N\ ,Aos
R s a3 S 4 S 4y ST & ¢ S ¢ © S ___..————_:”'_—‘\_\__/
040+ —04
030} —03
B o S e B et e oo e e S s __A02
010} —o1
0 5 10 15 20 25 30 35 40 45 50
FIGURE 4 6-13 time [s)
FIGURE 4.6-13.
Sample results of method 1 simulations.
-y.3¥
AP postamioy T Ty g puterifeay ) F e R ity
140 gl
e —— — Vel
LE__} 1.30 g
; ............. AL‘O E
5 120 e ba
2 h-)
= et * 00 < - =--ew AL 20 43
3 i s e AL 30
€ 100 1.0
—— e e e A L0
080 0.9
80 - —{0.8
0'70Ffi**r‘**"(*‘**v’*Am*“'*-'\*\‘_f’- il P
060 |- 0.6
—_—— " i
e e S L PO e, S e
g TRl TR e el A T s e Tl st
0.40 —10.4
0.30 103
R R e it =20 WS o o S AN T el By - =02
010 —0.1
000 C-.. sesebanns ..T..<.. ...1..‘.. «.‘Y.. ....‘~.‘j.._ ..-1..~ ~A1--~~ Ai..\. .4!..... “nad 0
0 5 10 15 20 25 30 35 40 45 56"
time | s
FIGURE 4.5-14 (<]
FIGURE 4.6-14.
Sample results of method 1 stmulations.

o = :
s o void fraction

o
@

l I T I T T T T T '
w140
E\ L —— e VelO
Cd
> 1.30 0 |
-4 o s o < AL 1
o |
52 1.20L -
s ——————— AL 20 1
® 110 -1
= r' —_————— AL3C f
| |
1.00
{ —— e AL 40 —]I
090 - 2
|
080
070L!~-.—-.--.—-.—""‘\-‘-—0—-.._._—fi.l"-o.-fi-&..__’-v“‘-*‘.—.“’""“-*--o-..___*""
060
L e A A s T s vui)
— o cm— —— —— @\ —— — —__ | — — — — . — — — — o _—-—1
040}
030+
0,20 [ e e e
010
0.00 bz 2o inaifioSinsnennsediimornsbusisfenhasantssasjunurysasnes irabo ke sauduia 4 e
0 5 10 15 20 25 30 35 45

FIGURE 4.6-16.

Sample results of method 1 simulations.

n hin Pout Gout hout

FIGURE 4.6-186.

O

Schematization of a header.

8p

90\
8

I I "De Greef™ model

o)

0

1
] 20 o
Jolq 8, Roe, Rma, Ri g Ni dj O
o i

IC IC present model.

FIGURE 4.6-17.

Modeling of wall dynamics.

header 3 header 6
C—7 > C
channet 2 77/ S
o
wall 2 ; h %
channe
]
wall 1 1 /% i\ channel 4
N R
header 2 \LA P wall 3
channel 1 / fi\":! header 5
ZIN
/ \\
header 1 - Q'{J :
H I) | CI& header 4
feedwater steam flinak

FIGURE 4.6-18.

Schematization of bayonet tube test module.

------ =dynamic
U =z upstream
D =downstream

= steady stcte

\ A __lav
A —1dy B 62 bve |
Ay R 2 AZp
upstream down stream
element element

FIGURE 4.6-19.

Approximation of the dynamics of a transition

—

in a frequency domain model.

upstream
element

down Sstream
element

™ TITTS '\ N
FIGURE 4.6-20.

Determination of local values of the basic variations.

hy: GyPy
e -
: \?\f'\
\
NN

8o\ N\X 8]

N

1. G1‘ p1

channel element wall element

FIGURE 4.6-21.

Location of nodal variables of channel and wall elements.

01 02 03 04

b — — — —
e — — — —

r—-———-—

Key designated to element nr. 04 of channel (type 01)
nr. 02, between level 03 and level 04.

01

Q.

.

( CURSOR )

1.01 L 3.02 3.ofl
| 1nPUT fl [consum | [ cenkey |
Bt
STATIN 5,02 | 5,03] 5.04 | 5.05 5.06 |
| statany | | statw | | starc | | rsreEck | | rsrecc |
5.07] 5,07 |
Loneor | [ znreor ]
6,01
SYSEQ 7,01 7 oa[ PR 3.67]
[ EQune ” [Eorric | [Eacw | [crseas |
|see H.T.2| Lsee H.T.3J
3,(Jl+l Spepey
| PASE | [PUTAB | | EQTR |
' | H.T.4
6,02
PRELUD 3.06 6,03 6,0k 6.05 061
[spoor | |RrEsuME | [ BANDIT | | ScaLE | [ LUDEC |
3.06] 3.08]
L GETAB }*—<::2_
16,01
SLGYEC 6.05 | 16,03 | 16,06] 16,08} )
[ctean | [wuso | [ Buxcv | [pampy |
2,04 | 16,04 16,07] 2,09 3,06
[priev | [runsor | | RvxBM | | PLoEv | | spooL |
3,04 23.05 3,04 :
| pAsE | I—NORM 1 | pase | Q
16,02
i 3.06] 3,05] 6,06] 16,03
[spoor ] [Cmorv | [ruwpec ) [ rusor |
2,04 f 7fifL 2.0
[ Priev | [ pronyq ¢ [_proev_]
3 ouk 13 05 304
l__PASE | | Noxm | pase |

B

FIGURE 4.6-23.

Hierarchy table of the CURSSE program.

Z

# THE CILUMN NUMSER

STASBILITEITS MTTIANG Re 1S
CHANNEL

3 CONTAINING L PHASE
werrros PR
«018157 =1)20838
5138157 =-13c4830
«642150C ~1 33 371
a214317C =104. 5065
«30ilB0 =113.864L
«3VUT136 =113406¢C
« 360773 -113.0CC
413578 =1llae 046
2465543 -11l6. 156
«5GT735 -122.752
eoulins =125+ 752
s 527324 -1234428
«53i%061 =1264284
«e5495693 =130.366
456147 ~13Te%11
e 294124 =157+ 396
74124 =151e 396
¢ 368595 -1655%5¢ 392
«434800 1734992
eb4lllo 109910
2455910 3342613
255710 33.26lb
le4o?76 571573
«3376175 93.1234
26226415 1216 079
293456 blebde
2493435 651 +6252

STABILIT=ITS MITINS NR. 15
Fx IMARY FLUID

CHANNEL - 4 CONTAINING
THIS CHANNEL HAS NO EXT:ZRNAL wALL
z . CNTHALPY ____
A4PLITUD P A SE
J‘ .. . v
25 34754480-7"3 58.6354
51 Te4lllC0=-03 b6le.51Cc
Ce31 T.41110L-33 61.5102
0e31 14155390-352 b4ed. 56
lelo 1.56':’)-.)’0(.' 66.60824
1e4) 1.9445CD-v2 53.7836
1le72 23261 1=-22 72.30467
Le7C 263061 70=-.2 7248347
leB4 2e469:290-02 Tle9cCc
1e98 2462504U-v2 T2.9521
2.13 2:7Ta6lD~22 14.1115
2:2T7T 24916620=0c 15.3167%
2641 3.C057140-32 Tbe626%
3.08 3.750570-.2 82.6507
3e74 44.50T7190-02 5bec 154
441 5.394.60-02 93.2532
Se08 64643260-.2 94,9940
5.C8 6464326D0-.2 94.994C
6+29 B8.635960-22 845513
Te09 34879¢10-302 137.423
8413 «1099.C 116.1l06
911 +12554C 1244 c46
Fell 12504 l24. 40
125464 2%e 2406
THERE AKE 3 PLOTS PREPARED,
e DATA PRUCESSING TudX 12300

OF THE NOZzZL=

FIGURE 4.6-24.
Example of printed output of CUR

VEREETEKDE

MASSFLO
ug

NN U N o~ e =

a w o

-

%

>
NONONOPC VWS PN GUNWE OO

o

o

WL NI 8 SLONT ST F NS

SN

MILLISECONDS

I
NCY

T e~

W
PH

=-12G.33¢

~139+33¢C

3S

24.Cy
=12929:1

-139.136
04450
=-139.164
“70:_)
-159.143
':)9. o4
-135.152
S5cebu
=~139:31 %5

VER4ETERDE ISJLATIE WAAND
NC Y ST=ZP ANKe

OF HEAOzR ¥R 1 PROPERTY 3 IS=

~ &

w
® 8 88 0 0 00
OHENFOOFAFOD O8N0

N = = = U U v @ 0o 3 0 0 v ¢

OND =\ N - Q)

® C 0 0000 e

«s CONTINUED

251323

RESSURE .o
PHASE

=1368.945

59.72
-135.120

-139.12C
61436
~139.175
o2l
-139.19C
0le26
=1394193
«68
-139.191

=139+191
62 e30

-136.191
62.97

o
—

o
-

1(.‘ .
=139.847
91e53
=140 ,064
=14C.064

«s CUNTINUED
«25133

results.

vl

EX1T

EXIT

HEADZR NR.

NOZILE

ENTRY HEADER

e 'v

ENTRY

NOZZLE

ENTRY HcADER

EXIT
EXIT

HEADER NRa

NOZZLE

STABILITEITS METING NR. IS VERJONGD, VERBETERDE ISULATIE WAND

ENTHALPY

AMPLITUDES AND PHASE SHIFTS
ALONG THE LENGTH OF

CHANNEL 1 AND 2

HIGHEST LEVEL =

LOWEST LEVEL

FREQUENCY STEP NR. 3 UMEGA < 0.2513

FIGURE 4.6-26a.
Example of plotted output of CURSSE results.

STABILITEITS METING NR. S VERJONGD, VERBETERDE ISULATIE WAND

PP P PP PPPPPP P P P P P P

P I
. 2
-
=
1 -
. b
L5
s
by
o
=
=4 .
L5
Mo
<
»
by
w [
- L1 | 1 ) I () 3 W U I | { { 1 | 1 -
r: S { PR | Ll | e S R 1 1 ) ; B | T T (=]
*s
e
._
<
L
1L.PE.P. P P PPPPPP....EP....R....EB....EB.cc.... S o o e e P
t
s
=J

AMPLITUDES AND PHASE SHIFTS
ALONG THE LENGTH OF

CHANNEL 1 AND 2

HIGHEST LEVEL
LOWEST LEVEL

3.44
0.00

Y STEP NR. 3 OMEGA

It

FIGURE 4.6-25b.
Example of plotted output of CURSSE results.

0.2513

PRESSURE =x(0

PRESSURE

STABILITEITS METING NR. 1[5

VER JONGO,

VERBETERDE 1

G

SOLATIE WAND

G

.oc

]

10.0C  20.00 4

ee

4.

PHASE
-58.CC

~
i

: 1 8e 2 4
MQSSFLUA

MY

T
.

-3C.00
i

~;30.0C

-486.0C

AMPLITUDES AND PHASE SHIFTS
ALONG THE LENGTH OF

CHANNEL 1 AND 2
HIGHEST LEVEL -=

.11
LOWEST LEVEL 0.00

i

Rk U ENCY

=

STEP NR.

3 OMEGH

FIGURE 4.6-25c.

Example of plotted output of CURSSE results.

Qi2al3

-

-------

MASSFLOW

amplification

phase shift

IGURE 4.6-26.

10

1 ':: . 382
i
0,1 g
b
0,01
~90
O
0
[~
90
180 .
P L
270
001 0.1 1. 10

@ .
L]

Example of a Bode~diagram obtained by
applying binary noise signals,
processed by a PDP-8 computer.

———= AP, Pm

time shift

_______ =approximation

= tijd

FIGURE 4.6-27.

Example of a recording of flow variation and pressure response in the
DMSP bayonet tube steam generator test module.

—
—

W U OVAao0

N

~u

1 2 3 4 5678910 2 3 45 6789102 2 3 4 56789103

N

180° \

]

240

360° ‘\

450’ \

78910 20 30 4050 70/90
1 2 3 4L 56789 50’ 80 %00

FIGURE 4.6-28.

Amplitude ratio and phase shift
of the inlet impedance of the
DMSP-steam generator test module.

feedwater feedwater steam FLiNakK

No flow temp. pressure inlet temp.
[xg/s ] Ve MN/m? Oc
5 79 222 ' 18.5 623
6 142 227 18.5 618
7 145 224 18.5 619
8 144 224 38.5 622
12 147 241 18.0 626
1 15 267 18.0 620
4 L 273 18.5 618
15 76 280 18.0 620
3 134 282 18.0 632
9 142 270 18.8 .623
10 146 270 18.7 622
11 145 271 18.4 620
2 201 287 18.0 626
14 145 gol 14.0 630
23 145 ey 14.0 630
16 142 280 18.0 630
17 146 273 14.5 670

FIGURE 4.6-29.

Conditions of frequency-response stability experiments performed
on the DMSP-bayonet tube test module.

g=constant

—

——

——

T
D=10mm $
Lo

feedwater

FIGURE 4.6-30,

outlet conditions
aout =0,95
P out =constant

note:

simplified pressure
loss correlation used:

% _f 1= 2
52 oD /2P V

inlet conditions
Qin :'Ocain ’-"asqt_ Vin=1 m/s
Pin =180 bar (constant)

f = friction factor
_C_(= void fraction
P = mean specific mass

Geometry ana process conditions of the test case.

X W
rad/s (c/s)
- 0.38 1310 (0.17)
- 1.10 £37 $0.37)
- 2.71 3s /0 (0.59)
- 6.13 4.12 (0.65)

FIGURE 4.6-31.

Data for determining eigenvalues s = A + Zw
obtained by application of the power
method/vector deflation on the test—case
shown in figure 4.6-30.

Imaginary axis

numbers represent the frequencen
of the test signal in c¢/s (Hz)

0,28 i
"025 )
)"—'— w5
‘.ng real axis
J{OJQ
(tA
.9.16
/
/
’/
o 12 /
/
/

T

FIGURE 4.6-32.

Polar plot of the inlet impedance of the test case
shown in fugyre 4.6-30 as computed by applying
the CURSSE program.

Emergency Releace System

—e X 2 75 |

Steam Outlet |

A & poedwater Inlet

Dummy Tube leader !

=—=x Argon Gas

i o Vo

l - Sodium Level
(in operation)

< Sodium Level
e (before operation)
n
o
- .
3
O
L
@

Active Tube

; Dummy Tube
{
i
|
k

d§ B9 Sodium Outlet

FIGURE 4.6-338.

1 th steam generator-schematic.

M. 2

Eigenvalues no.: 1 - 0.11709
- 0.11899
- 0.12230
0.12654
- 0.13194
- 0.13464

O U1 B W N
I

FIGURE 4.6-34.

Table of the first smallest absolute eigenvalues
computed for the 1 MW “ experiments (full load).

o

) At

' T
A

sl 1]7]
sl
i el
Wl T (Miniel gy,
o L e
I 2 2 I e o

T bl
Wi hiiieai!)

o
(T
| Iy ”,‘y

e aad OID

Moore

LT

114
444 0 s

4

"

Iy
LI

Y

b

AP

M@fiQWfi¢fi 3

11
‘ u}hui"
N

i
i
T
T

\ IS W
LAY
i

FIGURE ¢ (M3).
FIGURE 4.6-35.

Polar plot of the inlet impedance of the 1 MW

t

fit

Tibhebiatitd
" 148 4e b

+ ,

T TR

o
“+

FIGURE d (M4).

% test module.

W \
L mfi
paAMARARE (0 ”V uuy‘mu HH
1 ..I'-.r“ LTIV

caeed

it NE-50e80t tasnan TTiLIIIN

\
\\V
Al
\\
\
\
|

it i |

I
T

i i |

f 4

it Mlh.{.fl I/
i

water out

mixture vessel

sodium in

A
* ‘A bij-pass

cross —-section A-A

'y
1l
|
S.
N
w0
<
S
3

sodium out
-

water in
e -2 .

FIGURE 4.6-36.

Geometry of the SWISH test module.

Tosdai ], y o~ < |
Fhas. o4 -
e
laaassr e Maaas N = : |
L [t AT - \ 1
T 008 Shovesase: 7 {2
Hidd - 200 s \

FIGURE a (M1). FIGURE b (M2).

aasanst (N iling:
i, ™

St :

A

B Lk o8

FIGURE c (MS)_

FIGURE 4.6-37.

Polar plot of the inlet impedance of the
SWISH test module.

FIGURE e (Ms5).

~g———— phase shift

inlet impedance [bflf-’/k’].

1 2 3 4 5678910 2 3 4 56789102 2 3 4 56 789103

33
6 7
5
4L
3 Experiment
— % — % Analysis in time domain
2 ®  Analysis in freq domain
2
1
R e
PR STt
S L I
- N
! 4

A
. MR TN\

\ \g\\

] ,0
2

\ y, 3 30°/s load

(exp. no15)

10’

102 2 3 4 5678910 2 3 &4 5678900 2 3 4 5678910!

= freg (c/s)

®
N experimen

0
S0 N

180" \

270 . \

360

i

0
450

10 2 2 45678910 2 3 45678910° 2 3 4 5678910°
= freg(c/s)

FIGURE 4.6-38 a + b.

Amplitude ratio and phase shift of the inlet
impedance of the DMSP bayonet tube steam

generator test module (30% load).

| et 'expdnmem

‘/)\\_. N/ v
P : / o Fé :
4 NG/ L ....a..__,—— nnqtys&fn time  domain
NG AN i G cnol)rs:s in, frequency domom
N 2 S PEaEr At s i b h
4 e/ P : x \
/ N / - - y_‘._ s ;/ " :

FIGURE 4.6-38c.

Polar plot of the inlet impedance
of the DMSP bayonet tube steam
generator test module (30% load).

phase shift

"o 103
B 4
S 4
w
o
g
S p experiment
e = o o = e @NALY SIS in time domain
g 3 o analysis in freg domai
o
g . e, T
< '\\\‘\\ ’/"\\
E 2 N | TN \
/ ] !
5 “ l‘ V
4
" "‘ ‘,
3 ~ ..
2 L ]
® 60 % load
(exp nol16)
10! e

"2 2 3 45678910°" 2 3 4 5678910° 2 3 45678910

—————— freg (/)

e
K\ 4.
“_____.I_\, x
oxlll] x = time domain
o
g0’
N
%
\\
o
180
\
3
\
1 \
270
. \
. A
o
x ~ ‘
o X
360 .
\
\
x
450" [
10-2 y A 5578910.1 7.4 . g ¢ 56789100 CN3NG D 5789101

freg(c/s)

FIGURE 4.6-38 d + e.

Amplitude ratio and phase shift of the
inlet impedance of the DMSP-bayonet tube
steam generator test module (60% load).

: (\;_ g
N \
‘\ N
. %
" \
~ ANy
« ’ R
R &
W
«/;
~ g £

FIGURE 4.6-38f.

7
of the DMSP bayonet
generator tes

/

expariment .-\ ,
/o = === analysis in time domain

analysis in_freg, domain -

i

inlet impedance ( bar.s/kg)

phase shift

1{
€
5 =
X = experiment
] e = analysis in freq. domain
2
15'
6
. e
4L
4 [ ] ® L]
2
90 % Load
(exp no2)
1
10
—= freq(c/s)
0
[ ]
e ol -
B
90 A
L ®
\
\\
180 .
\
A\
® .
270 -
°
L ]
360
C.01 01 1.0 10

————= freq(c/s)

FIGURE 4.6-38 g + h.

Amplitude ratio and phase shift of the inlet
impedance of the DMSP bayonet tube steam
generator test module (90% load).

Nt ¥ e HEL1 5, Vi
p SN e i
% F ‘, " . . = \

'Y
i -
et R + =T X

\ / / \
/ N A ST .: f
N/ NS e fregd xiamo?n an aLys»s
7\ N Y ;oo { 4
b / 8 I ot g o .
g 7 e / ; = \ - 'x.\
. ~_ / T l" i _E‘_;__.’_ - x " \\
N S S / 0” E - "' "\
fiTT e T
/ 3 \\ i 5 I/ ! ! x \ \
. ”4 . "r' 1 " ‘
/ o ) EEM Ty

FIGURE 4.6-387.

Polar plot of the inlet impedance
of the DMSP bayonet tube steam
generator test module Load) .

dp -transmitter

out put

pr—
~S—

FIGURE 3A-1.

Output signal of the dP-meter.

3.0

0
|
|
|

Bankoff
Bankoff /Jones
present correlation

FIGURE 4B-1.

Slip values as given by Bankoff, Bankoff-Jones
and present correlation.

inlet flow

—a time

FIGURE 4F-1.
Typical shape of a developing oscillation.

first order component

Pav N om %

second order component

LF -2

FIGURE 4F-2.
Super position of a first order and a second

order component

az (=12 +V3i)

a (1)

az (-1/2-V3i)

FIGURE 4F-3.

Graphical representation of the solution of equations (4F-4).

V2 120° d
° 2
S 2 120 cuj
3
120° 120°
2
cu 2
Us
first order components second order components

FIGURE 4F-4.

First and second order components of the predominant mode of oscillation.

s-plane

FIGURE 4G-1.

Mapping of a contour by a complex function.

FIGURE 4G-2.
The Nyguist path.

FIGURE 4G-3.

Schematized inlet impedance curve. 1b<°

FIGURE 4G-4.

\.J //

measured branch o<w<o /
symmetric branch —co<w<o
2 infinite semi circles /

l Mapping of the Nyguist path by M}e .

S

ENERG =Evpztvp2+EVPltvp145vuthH20EVHltvuloEvcltvc1oevsztvcz0EDTVP2*DTVP2+EDTVPl*DTVP10EDTVHZ*DTVHZ*EDTVHL'DTVHle
Va*vQ

UIT DE VOLGENDE 38 VERGELIJKINGEN =

le ENERG =iWRGL+NRG2+NRG3+NRG4
<« NRG1 =E201+E202+E2034E204+E205
3. NRG2 =E206+E20T+E2C8+4E209+E210
4. NRG3 =E2LL+E212+E213+E214+E215
5. NRG4 =E216+E21T+E218+4E219 .
6. E213 =E2131*%DZVUL+E2132%VVL+E2133*%VAL+E2134*VRL
Ts EELE =E2161*DZVAL+E2162%VVG+E2163*VP
8. EZ215 =E2151%DZVVG+E2152*%VAL+E2153*VvP
9. E207 =E2071*%DZVVG+E2072*VAL+E2073*VUG+E2074*VRG
10. E214 =E2141%DZVRL+E2142*%VVL+EZ2143*VAL+E2144*VUL
11. E217 =E21T1*DZVVL+E21T72*VAL+E2173*VP
12. E211 =E2111*DZVVL+E2112%VAL+E2112%VUL+E2114*VRL
13.:E222 =E2121*DZVAL+E2122*%VVL+E2123*VUL+E2124*VRL
14. E208 =E2081*DZVAL+E2082*%VVG+E2083*%VUG+E2084*VRG
15. E218 =E2181%DZVAL+E2132%VVL+E2183%VP
l6. DTVRLL =DRLOPL*DTVP1
17. DTVX1 =DXDH1*DTVH1+DXDP1*DTVP1
18. DTVHGl =DHGDP1#*DTVP1
19. DTVRG1 =DRGDPL1*DTVP1
20s DTVHLL =CHLP1*DTVP1+CHLHL*DTVHL+CHLX1*DTVX1
2l. DTVRLZ2 =DRLDP2*DTVP2
22« VRL1 =DRLOPL*VP1
23. VX1 =0XDH1*VH1+DXDP1*VP1
24. VHG1 =DHGDP1*VP1
25. VRG1 =DRGDP1*VP1l
26. VRLZ2 =DRLDP2*VP2
27. VHL1 =DHLDP1*VP1+DHLDH1*VH]1 +DHLDX 1*VX1
238. DZVRL =COZ1*VRL1+CDZ2%VRL2
29. VRM1 =CRMRLLI*VRLL1+CRMAL1*VAL1+CRMRG1*VRG1

30. VX2 =DXDH2%VH2+DXDP2*VP2
31. VVML  =CVMG1*VG1+CVMRM1*VRM1

32. VRG2  =DRGDP2*VP2

33, 219  =CVQ*VQ

34, DTVX2 =DXDH2*DTVH2+DXDP2*DTVP2 FIGURE 4J-1la.

35, DTVRG2 =URGDP2*DTVP2 X .

36. DTVRG =0.5%*DTVRG1+0.5%DTVRG2 List of equations to be combined.
37. E203 =CE203*DTVRG

38. DTVAL =0.5%DTVALL1+0.5*DTVAL2 (two-phase energy balance)

39. DTVRL =0.5%*DTVRL1+0.5*DTVRL2

40. E206 =CE206*DTVRL

4l. E204 =CE204*DTVAL

42. DTVUGl =1.0*%DTVHG1+CVUG21*DTVRG1+CVUG21*DTVP1
43. DTVHG2 =DHGDP2%*DTVP2

44, DTVULL =1.0%*DTVHL1+CVULL1*DTVRL1+CVUL21*DTVP1
45, DTVHL2 =CHLP2*DTVP2+CHLH2*DTVH2+CHL X2*DTVX2
46, DTVUG2 =1.0*%DTVHG2+CVUG22*DTVRG2+CVUG21*DTVP2
47. DTVUG =0.5%*DTVUGL+0.5*DTVUG2

48. E202 =CE202*DTVUG

49. DTVUL2 =1.0%DTVHL2+CVULL2*DTVRL2#+CVUL22*DTVP2
50. DTVUL =0.5%*DTVULL+0.5*DTVUL2

51. E205 =CE205*DTVUL

D2s 'EL01 =CE201=*DTVAL

DTVALL

=CDZ1*VRG1+CDZ2*VRG2
=1.0*VHG1+CVUG11*VRG1+CVUG21%*VP1l
=1.0%*VHL1+CVYUL11*VRL1+CVYUL21%VP1
=CRMRL2*VRL2+CRMAL2*VAL2+CRMRG2*VRG2
=CVMG2*VG2+CVMRM2%VRM2
=0.5*VALL1+0.5*VAL2
=CDZ1*VAL1+4CDZ2%*VAL2

=DHGDP2*VP2

=1 0%*VHG2+CVUG12*VRG2+CVUG22*VP2
=DHLDP2*VP2+DHLDH2*VH2+DHLDX2*VX2
=]l 0%*VHL2+CVUL12*VRL2+CVUL22*VP2
=0.5*VRG1+0.,5%VRG2
=0.5*%*VVG1l40,.5*%VVG2
=0.5*VRL1+0.5*%VRL2
=CDZ1#*VVL1+CDZ2%*VvvVL2
=0.5%VVL1+0,5%VVL2
=CDZ1&VVG1+(CDZ2*VVG2

=0.5%VUGL1 +0.5*%VUG2

=0.5%*VP1+40.,5*VP2
=£2101*%DZVRG+E2102*VVG+E2103*VAL+E2104*VUG
=CDZ1*VUG1+(CDZ2*VUG2
=E2091*DZVUG+E2092*VVG+E2093*VAL+E2094*VRG
=0, S*VULI "OQS*VULZ
=CDZ1*VUL1+CDZ2*VUL2

=CVGRM2*VRM2+CVGVM2*VVM2+CVGAL2*¥ VAL2+CVGRG2*VRG2+CVGRL 2*VRL2+CVGS 2*VS2
=CVGRML*VRM1+CVGVML1*VVML1+CVGAL 1*VALL+CVGRG1*VRGL+CVGRL1*VRL1+CVGS1*VS1l

=CSH1*VH1+CSP1*VP1+CSG1*VG1
=CSH2%*VH2+CSP2*VP2+CSG2*VG2
=CSHL1*DTVHL+CSPI*DTVPL+CSG1*DTVG1
=CSH2*DTVH2+CSP2%DTVP24CSG2*DTVG2

=CALRLLI*VRL1+CALX1*VX1+CALRGLI*VRGL+CALS1*VS1
=CALRL2*VRL2+CALX2*VX2+CALRG2*VRG2+CALS2*VS2
=CVLRM2*VRM2+CVLVM2*VVN2+CVLAL2*VAL2+CVLRG2*VRG2+CVLRL2*VRL2+CVLS2*VS2
=CVLRMLI*VRMI+CVLVM1*VVML+CVLAL1*VAL1+CVLRG1*VRGL +CVLRL1*VRL1+CVLS1*VSl
=CALRL2*DTVRL2+4CALX2*DTVX2+CALRG2*DTVRG2+CALS2*DTVS2
=CALRLLI*DTVRL1+CALX1*DTVX1+CALRG1*DTVRGL+CALS1*DTVS1

FIGURE 4J-1b.

List of equations to be combined.

(two-phase energy balance)

ENRUJ1=E2082+E2092+E2102

ENROO2=E2071*CDZ2+ENROO1*0.5
ENROJ3=ENROO2*CVGRM2+ENROO2*CVGVM2*C VMRM2
ENROV4=E2072+E2093+4E2103
ENROO5=ENROO3*CRMAL2+ENROO2*CVGAL2+ENROO4*0. 5¢E2081%CDZ2
ENROO6=E2073+E2083+E2104

ENROO7=ENROO6*0.5+E2091*CD22

ENROO8=E2074+E2084+E2094

ENROU9=ENROUS*CALS2+ENRO02*CVGS2
ENROLO=E2071*CDZ1+ENROO1*0.5
ENROL1=ENROLO*CVGVM1+E2111%CDZ1*CVLVM]L
ENRO12=ENROLO*CVGRM1+ENROL1*CVMRM1+E2111*CDZ1*CVLRM1
ENRO13=ENRQO12*CRMALLI+ENROL1O*CVGAL1+ENRQOO4*0.5+E2081%CDZ1
ENROL4=ENROLO*CVGRML+ENROLO*CVGVM1*CVMRM1+E2111*CDZ1*CVLRM1
ENROL1S5=ENRO14*CRMALI+ENROL1O*CVGAL1+ENROO4*0.5+E2081%CDZ1
ENROL6=ENRO06*0.5+E2091*CDZ1
ENROL7=ENROLS5*CALS1+ENRO1O0*CVGS1 :
ENROL18=CE201+CE204

ENROL9=ENROLB8*0.5*%CALX2+CE205%0.5*CHLX2
ENRO20O=ENROL8*0.5*%CALX1+CE205*0.5*%CHLX1
ENRO21=E2122+#E2132+E2142

ENRO22=E211L*CDZ2+ENRQ21%*0.5
ENRO23=ENROO3+ENRO22*CVLRM2+ENRQ22*CVLVM2*CVMPM2
ENROZ%SENROZZ*CVLRHZ*ENROZZ*CVLVHZ*LVHRMZ
ENRO25=E2112+E2133+4E2143

ENRO26= ENROUS*ENROZ#*CRMALZ*ENROZZ‘CVLALZ*ENROZ5*0 5+E2121%CDZ2
ENRO2T=E2113+E2123+E2144

ENRO28=ENRO27*0.5+E2131%CDZ2

ENRO29=E2114+E2124+E2134

ENRO30=ENRO26*CAL X2+ENRO28*DHLDX2
ENRO31=ENRO24*CRMAL24ENRO22*CVLAL2+ENRO25%0,.5+E2121%*CDZ2
ENRO32=ENROO9+ENRO31*CALS2+ENRO22%CVLS2
ENRO33=E2111*CDZ14ENRO21*0.5

ENRO34=ENR0O21*0.5%CVLRMI +ENRO21%0.5¥CVLVMLI*CVMRML1 +E2151%CDZ1*"
& CVGRM1
ENRO35=ENROL3+ENRO33*CVLALI+ENRQ25%0.,5+E2121*CDZ1+ENRO34*CRMALL
ENRO36=ENRO27*0.5+E2131*CDZ1
ENRO37=ENRO35*CALX1+ENRO36*DHLDX1
ENRO38=ENRO33%CVLVMI*CVMRM1I+ENRO21*0.5*%CVLRM1+E2151*CDZ1*CVGRM1
ENRO39=ENRO38*CRMALL1+ENRO33*CVLAL1+ENR025%0.5+E2121*CDZ1
ENRO4O=ENROL7+ENRO39*%CALS1+ENRO33%CVLS1
ENRO41=E2151%CDZ224E2162%0.5
ENRO42=ENRO41*CVGVM2+E2171*CD22*CVLVYM2
ENRO43=ENROZ23+ENRQO4L*CVGRM2+ENRO42*CVMRM2+E21T7) *CDZ2*CVLRM2
ENRO44=ENRO41*CVGRM2+ENRO42*CVMRM2+E2171*C0Z2*CVLRM2
ENR045=E2152+E2172
ENRO46=ENRO26+ENRO44*CRMAL2+ENRO41*CVGAL2+ENRO45*%0.5+E2161*%CD22+
& E2171*CDZ2*CVLAL2

ENRO4T=ENROQ24E2151*%CDZ2+E2162%0.5

ENRO48=ENRO22+E2171*%CDZ2
ENRO49=ENRO44*CRMAL2+ENRO41*CVGAL2+ENRO45*0.5+E2161*CD22+4E2171%*
& CDZ2*CVLALZ

ENRO50=ENRO30+ENRC49*CAL X2
ENRUSL=ENRO3Z+ENRO49*CALS2+ENRO41*CVGS2+E21T1*CDZ2*CVLS2
ENRO52=E2153+E2163+4E2173

ENRO53=ENRO21*0.5+E2171*CDZ1

ENRO54=E2151%CDZ1+E2162%0.5
ENRO55=ENRO54*CVGVM1+E2171*CDZ1*CVLVMIL
ENROS6=ENRO55*%CVMRM1+E2162%0.5%CVGRML+E2171*CDZ1*CVLRM1
ENROS57=E2161+E2181

ENROSB=ENROLO+E2151*CDZ1+E2162%0.5

ENRO59=ENRQ33+4E2171*%CDZ1
ENRO6O=ENROS560*CRMAL1+ENROS54*CVGALL1+ENRO45%0,5+ENROST*CDZ1+E2171%*
& CDZ1*CVLALL

ENRO61=ENRO3T+ENRO6O*CALX]
ENRO62=ENROS6*CRMALL+ENROS4*CVGALL+ENRO45%0,5+E2161%CDZ1+E2171*
& CDZ1*CvVLALL
ENRU63=ENRO4O+ENRO62*CALS1+ENROS54*CVGS1+E2171*CDZ1*CVLS1
ENRO64=ENRO43+E2182%0,5*CVLRM2+E2182%0.5%CVLVM2*CVMRM2
ENRO65=E2182%0,5*CVLRM2+E2182%0.5%¥CVLVM2*CVMRM2
ENROG6=ENRO4O+E2181*CDZ2+ENRO65*CRMAL2+E2182%0.,5*%CVLAL2
ENROL7=ENRO4B+E2182%0.5
ENRU68=E2181*CDZ24ENRO65*CRMAL2+E2182%0.5*%CVLALZ2
ENRO69=ENROSO+ENROG6B*CALX2
ENRO7O0=ENROSL+ENROGB*CALS2+E2182*%0.5%CVLS2
ENRO71=ENRO52+EL2183

ENRO72=ENRO53+E2182%0.5

ENROT3=E2171%CDZ1+E2182%0.5

ENROT4=ENROS59+¢E2182%0,.5
ENRO75=E2182%0.5*CVLRM1+E2182%*0.5*CVLVML*CVMRML
ENROT6=ENRO75%*CRMAL1+E2182*%0.5*CVLALL
ENROT7=ENRO6L+ENRO76*CALX1
ENRO78=E2181*CDZ1+ENRO75*CRMAL1+E2182%0.5*%CVLALL
ENROT9=ENROOG3+ENROT78*CALS1+E2132%0.5*%CVLS1

FIGURE 4J-2.

List of common factors (punched automatically).

ENERG O °
ENERG 5
ENERG 10
ENERG 15
ENERG 20
ENERG 25
ENERG 30
ENERG 35
ENERG - 40
ENERG 45
ENERG 50
ENERG 55
ENERG 60
ENERG 65
ENERG T0
ENERG 75
ENERG 80
ENERG 85
ENERG 90
ENERG 95
ENERG100
ENERG105
ENERG110
ENERG115
ENERG120
ENERG125
ENERG130
ENERG135
ENERG140
ENERG145
ENERG150
ENERG155
ENERG160
ENERG165
ENERG170
ENERG175
ENERG180
ENERG185
ENERG190
ENERG195
ENERG200
ENERG205
ENERG210
ENERG215
ENERG220
ENERG225
ENERG230
ENERG235
ENERG240
ENERG245
ENERG250
ENERG255
ENERG260
ENERG265
ENERG270
ENERG275
ENERG280
ENERG285
ENERG290
ENERG295
ENERG300
ENERG305
ENERG310
ENERG315
ENERG320
ENERG325
ENERG330
ENERG335
ENERG340
ENERG345
ENERG350
ENERG355
ENERG360
ENERG365
ENERG370
ENERG375
ENERG380
ENERG385
ENERG390
ENERG395
ENERG400
ENERG405
ENERG410
ENERG415

ENERG=

EVP2=(ENROG4*CRMRL2+ENROS66*CALRL2+ENRO4T*CVGRL2+ENROGT*CVLRL 2+
& ENRO28*CVUL12+ENR0O29%0.5+E2141%CDZ2)*DRLDP2+ENRO69*DXDP2+
& (ENRO60*CALRG2+ENRO64*CRMRG2+ENRO4T*CVGRG2+ENROOT*CVUG12+ENROOS*
& 0.5+E2101%COZ2+ENRO6T*CVLRG2)*DRGDP2+ENROT0O*CSP2+ENROQ7*DHGDP2+
& ENROOT7*CVUG22+ENRO28*DHLDP2 +ENRO2B8*CVUL22+ENRQ71%*0.5
EVPL=((ENROL2+ENRO72*CVLRM1+ { ENROT2*CVLVMI+ENRQS54*CVGVM]1)*CVMRM1+

FIGURE 4J-3.

Expressions in the coefficients of the 88 combined equations.

0.548760332730C7990D
0.10833243125568500D
0.332037375088172000
0.56185135931479990D
0.50568733984969990D
0.18727571739981650D
0.32766090000000000D
0.577461000000000000
0.181iU04400000000000
0.20344800000000000D
0.105000200000000000D
0.15984000000000000D
0.79409400000000000D

4.12047665440422000D

FIGURE 4J-4.

ENERG420
ENERG425
ENERG430
ENERG435
ENERG440
ENERG445

& ENRO54%*CVGKM1)*CRMRL1+(ENRO35+(ENRO56+E2182%0,5*CVLRM]1+E2]182% ENERG#50
& 0.5¥*CVLVML*CVMRM1)*CRMALL+ENROS4*CVGALL+ENRO45%0.5+ENROST*C021+ ENERGY55
& ENRO73*CVLALL)*CALRLI+ENROS58*CVGRLL+ENROT4*CVLRL1+ENRO36*CVUL11+ ENERGA60
& ENRO29%0.5+E2141%CDZ1)*DRLDPL+ENROT7*DXDP1+((ENROL5+(ENRO38+ ENERG465
& (ENRO55+E2182*%0.5*CVLVML)*CVMRM1+E2162%0.5%CVGRM1+ENROT3* ENERG470
& CVLRML)*CRMAL1+ENROT4*CVLAL1+(ENRO254ENRO45)1*0,5¢+(E2121+ENRO5T)* ENERG4T75
& CDZ1+ENRO54*CVGAL1)*CALRG1+ (ENROL4+(ENROT4*CVLVML+ENROS4* ENERG480
& CVGVML)*CVMRML+ENROT2*CVLRM1+ENRO54*CVGRML)*CRMRG1+ENRO58%* ENERG485
& CVGRGL+ENRO16*CVUG11+ENROO8*0.5+E2101*CDZ1+ENROT4*CVLRG1)* ENERG490
& DRGDPL+ENRO79*CSPL1+ENROL6*DHGDPL+ENRO16*CVUG21+ENRO36*DHLDP 1+ ENERG495
& ENRO36%CVULZI+ENRQT1I*0.5 ENERGS500
EVH2=ENRO69*DXDH2+ENRO7O0*CSH2+ENRO28*DHLDH2 ENERG505
EVHL=ENROT77*DXDH1+(ENRO4O+{ENROGO+ENRO7T5*CRMAL1+E2182%0.5% ENERGS510
& CVLALL)*CALS1+ENROS4*CVGSI+ENRO73*CVLS1)*CSHI+ENRO36*DHLDH1 ENERG515
EVGL=ENRO79*CSG1+(ENROLLI+ENRO72*CVLVMLI+ENRO54%CVGVYM1 ) *CVMGL ENERG520
EVG2=ENRQT0*CSG2+(ENRO4T*CVGVM2+ENRO6T*CVLVM2) *CVYMG2 ENERG525
EDTVP2=(ENROLB8*0.5*%CALRL2+4CE205%0.5*CVUL12+EE206*%0.5)*DRLDP2+ ENERG530
& ENRO19*%DXDP2+({ENRO18%*0.5%CALRG2+CE202%0.5*%CVUG22+CE2023%0.5)%* ENERGS535
& DRGDP2+ENRO18*0,5*%CALS2*CSP2+4CE202%0.5*%DHGDP2+¢CE202%0.5*%CVUG21+ ENERG540
& CE205%0.5%*CHLP2+CE205%0.5%C VUL 22 ENERGS545
EOTVPL=(ENRU18B*0,5*CALRL1+CE205%0.5*%CVULL1+CE206%0.5)*%DRLDP 1+ ENERG550
& ENRO20*DXDP1+(ENRO18*0,5*CALRG1I+CE202*0.5*CVUG21+CE203%0.5)* ENERG555
& DRGOPL+ENRO18*0.5*CALS1*CSP1+CE202%0.5%*DHGOP1+CE202%0.5*%CVUG21+ ENERG560
& CE205%0.5%CHLP1+CE205%0.5*CVUL21 ) ENERG565
EDTVH2=ENROL19*DXDH2+ENRO18%*0 . 5*CALS2*CSH2+CE205%0,5*CHLH2 ENERGS570
EDTVH1=ENRO2U*DXDH1+ENRO18*0 . 5%*CALSL1*CSH1+CE205%0,.5*%CHLH1 ENERGS575
EVE=CVQ ENERG580
EDTVG1l=ENRO18%*0,5%CALS1*CSGlL ENERG585
EOTVG2=ENRO18*0,5%CALS2*CSG2 ENERG590
ENERG=EVP2¢«VP2+EVP1*VPL+EVH2*VH2+EVH1*VH1+EVG1*VG1+EVG2*VG2+ ENERG595
& EDTVP2%DTVP2+EDTVPI*DTVP1+EDTVH2*DTVHZ2+EDTVH1I*DTVHL4EVQ®VQ+ ENERG600
& EDTVGLI*DTVGL+EDTVG2*DTVG2 ENERG605

Output of the check: the two-numerical values to be compared have been
underlined. Following these a message 18 printed indicating that the
substitution has been successfull.