ORNL-TM-2489.txt

 

."”(

OAK RIDGE NATIONAL LABORATORY
operated by
UNION CARBIDE CORPORATION
NUCLEAR DIVISION
for the
U.S. ATOMIC ENERGY COMMISSION

ORNL- TM-2489
€5

COPY NO. -

 

DATE - June 2, 1969

Instrumentation and Controls Division

MSBR CONTROL STUDIES

W. H. Sides, Jr.
ABSTRACT

A preliminary study was made of the dynamics and control of a 1000 Mw(e),
single-fluid MSBR by an analog computer simulation. An abbreviated, lumped-
parameter model was used. The control system included a steam temperature con-
troller and a simplified version of the MSRE reactor temperature control system. The
results of the study indicate a need for a variable speed, secondary=salt pump for
close control of the steam temperature. During severe transients, considerable care
must be taken in designing the control system if freezing or overheating of the salts
is to be avoided.

NOTICE This document contains information of a preliminary nature
and was prepared primorily for internal use ot the Quk Ridge National
L.aboratory. It is subject to revision or correction and therefore does
not represent. a final report.

FSTRIBUTION Qb LHts OQCUMENE # UNLIMITER,
 

- - - - LEGAL NOTICE -~ - = =-eme

This report was prepared as an account of Government sponsored work. Neither the United States,

nor the Commission, nor any person acting on behalf of the Commission:

A. Makes any warranty or representation, expressed or implied, with respect to the accuracy,
completeness, or usefulness of the information contained in this report, or that the use of
any information, apparotus, method, or process disclosed in this report may not infringe
privately owned rights; or

B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of
any information, apparatus, method, or process disclosed in this report.

As used in the above, *'person acting on behalf of the Commission'” includes any employee or

contractor of the Commission, or employee of such contractor, to the extent that such employee

or contractor of the Commission, or employee of such contracter prepares, disseminates, or
provides access to, any information pursuant to his employment or contract with the Commission,

or his emplaoyment with such contractor.
CONTENTS

. |
1. Infroduction « « « ¢ ¢ « 4 o v o v o o v v 4 e 0 o s

e e ... 5
lation of the Control System . s

> FO""‘2U 10 |Invesflgclfion of Plant Conditions for Less than Full-Load 5
Oeraflon...........................

2.2 Trznsienf Behavior of Control Method with Constant .

Secondary-Salt Flow Rate. . . . . . Ce e

2.3 Study of Steam Temperature Control with Variable .

Secondary-Salt Flow Rate. . . . . . . . .. .. oo

| ... 14

3. Resu|ts e

3.1 Decrease in Load Demand. . . . . . . .. . .. .. e
oFReachit............:.......

gg g’r,’:;n%isunges of Reué/tivi'ry with Controller Dis.connect:add. Coe gg

3.4 Ramp Changes of Reactivity with Controller Disconnected . . -

3.5 Step Loss of One Secondary-Salt Cool-an‘r loop. . v+ v .. s
3.6 Measurement of System Transfer Function. . . . . .. . ..

- 4
4, Concluding Remarks . « . « « ¢« v o v v v v oo

LEGAL NOTICE
This report was prepared as an a
States, nor the Commission,
* A. Makes any warranty

ccount of Government spansored work. Neither the United
ROr any person acting on behalf of the Commission:
or representation,

B. Assumes any liabilities wi
use of any information, apparatus,
As used in the above, *¢
pleyee or contractor of the C

ih respect to the use of, or for damages resulting from the
method, or process disclosed in this report.
person acting on behalf of the Commiasion?’

includes any em-
ommission,

or employee of such coniractor, to the extent that

 
1. INTRODUCTION

By means of an analog computer simulation, a preliminary investigation was
made of the dynamics and possibilities for control of the proposed 1000~-Mw(e) single-
fluid Molten-Salt Breeder Reactor (MSBR). For the purposes of this analysis the MSBR
plant consisted of a graphite-moderated, circulating-fuel (primary salt) reactor, a
shell-and-tube heat exchanger for transferring the generated heat to a coolant (sec-
ondary) salt, and a shell-and-tube supercritical steam generator. The analog simula~
tion of the plant consisted of a lumped-~parameter heat transfer model for the core,
primary heat exchanger, and steam generator; a six-group model of the circulating-
fuel nuclear kinetics with temperature reactivity feedbacks; and an external control
system. This investigation was concerned with the formulation of this control system
and the integrated plant response; it was not concerned with a safety analysis of the
system, although some of the transients introduced would be of an abnormal nature
(e.g., step changes in the load demand on the plant). It was an initial probe into
the response of the system initiated by such perturbations as changes in load demand,
reactivity changes, and sudden loss of a secondary-salt coolant loop.

The simulation was carried out on the ORNL Reactor Controls Department an-
alog computer. So that the model would have the maximum dynamic range, the system
differential equations were not linearized, and, as aresult, the requisite quantity of
nonlinear equipment required the model to be severely limited spatially to minimize
the number of equations. In addition, the pressure in the water side of the steam gen-
erator, as well as in the rest of the plant, and the physical properties of the salts and
water were taken to be time invariant. The flow rate of the primary salt and the tem-
perature of the feedwater to the steam generators were also held constant.

In this report, the path taken to arrive at the conceptual control system is out-
lined along with the equations and values of the system parameters used in the simula-
tion. The results are given as summary curves and graphs of the variations encountered
in the system variables (femperatures, flows, etc.).
2. FORMULATION OF THE CONTROL SYSTEM

2.1 investigation of Plant Conditions for Less than Full-Load Operation

The primary objective of this study was to formulate a control system that would
maintain the temperature of the steam delivered to the turbines at a design value of
1000°F during all steady-state conditions and to within a narrow band around this value
during plant transients. To accomplish this objective, the first step was to investigate
the plant conditions (temperature profile, flows, etc.) for less than full-load operation.
(The full-load temperature profile is shown in Fig. 1. The steady-state heat transfer
equations and the method used in calculating off-design conditions are given in the
Appendix, Sect. 5.1.) Three basic methods of plant operation at less than full foad
were investigated:

1. The average reactor temperature was held at its 100% power level value, and a
secondary-salt bypass line was included in parallel with the steam generators.
The salt flow in the bypass line was given by

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P
Fa = on(] " ‘P‘“) (M)

0

where Foo is the secondary-salt flow rate at the 100% power level PO.

ORNL DWG. 69-6633

1300 °F T2 Te yisoor Ty

> ———————— —— 1000°F

|
: f2 ) (F:a
7 <)
|
|
PRIMARY g
CORE HEAT ngggiron
EXCHANGER :
|
l
|
|
-
1050 °F T 850°F Ty Ts 850°F Te  700°F

Fig. 1. Model for Calculating Off-Design Steady-State System Temperature
Profiles. Temperature Values are for 100% Power Level.
2. The average reactor temperature was held fixed ot its 100% power-level value, and
there was no secondary-salt bypass.

3. The secondary-salt flow rate was held fixed at its 100% power-level value, and
there was no secondary-salt bypass.

With the first two methods of plant operation the temperature of the secondary
salt approached its freezing point of 725°F at power levels = 50% of full power. With
the third method, however, the secondary-salt temperatures remained well above the
freezing point. With the second method, the AT from primary to secondary salt in the
primary heat exchanger increased from 150 to 335°F at the primary-salt exit end of
the exchanger at 50% power, and the AT increased at the steam outlet end of the steam
generator as well. The increases in these AT's were reduced for the first method where
a valved bypass line had been placed around the steam generator, but this also was
more complex because a flow control valve and a variable speed pump were required.
The simpler arrangement of the third method showed that the AT's from primary to sec-
ondary salt and from secondary salt to steam decreased with decreasing power level
except at the feedwater inlet end of the steam generator where it increased only 65°F
at 30% power (Fig. 2). This AT increase occurred in the coolest part of the system,
however. Therefore, the third method of plant control, in which the secondary-salt
flow rate was held constant, appeared to be the most promising from the viewpoint of
simplicity and thermal stresses on the heat exchangers.

2.2 Transient Behavior of Control Method with Constant Secondary=Salt Flow Rate

A steam-temperature controller was devised to vary the plant temperature pro-
file as shown in Fig. 2. The transient behavior of such a control scheme was investi-
gated by use of the analog computer simulation model shown in Fig. 3. Each heat
exchanger was divided into five lumps: two for each of the two fluids and one for the
tube walls. The reactor heat transfer system was approximated by two lumps for the
circulating primary salt and one for the graphite moderator. A two-group approxi~
mation of the circulating-fuel nuclear kinetics equations was used, and temperature
reactivity feedbacks were included. (The system equations that describe the model
are given in the Appendix, Sect. 5.2. The values of the physical constants and system
parameters used as "given" information are shown in Table 1. The values for various
system volumes, masses, etc., were calculated from these constants and are listed in

Sect. 5.2.)

The steady-state partial-load calculations showed that a reasonable system-
temperature profile could be obtained for off-design conditions by maintaining a con-
stant secondary=-salt flow rate and by allowing the reactor and secondary-salt temper-
atures to vary. The transient behavior of such a system was investigated, using at first
only that part of the simulation model that included the primary heat exchanger and
the steam generator. The secondary=-salt flow rate was held constant, and the steam
 

ORNL DWG. 69-6634

  
  
 
   

 

 

  

 

 

 

 

REACTOR OUTLET (T3) ————100% POWER LEVEL PROFILE
1300~ ———=-30% POWER LEVEL PROFILE
12004—
AVERAGE PRIMARY /—SECONDARY SALT HOT LEG (T,)
SALT TEMPERATURE _

1100
o
-
x
>
-
-
& 1000
O
: —————
et
'—-

00— SECONDARY SALT \

COLD LEG (T3) N
-} N
N
N
800 N\
\ FEEDWATER (Tg)
N
oo PRIMARY PRIMARY S ECONDARY STEAM STEAM
-~ CORE SALT LOOP —»le——HEAT EXCHANGER SALT LOOP'—_"_ GENERATOR —-I—_AND_.I
TUBE WALL TUBE WALL FEEDWAT ER

Levels.

 

Fig. 2. Steady-State System Temperature Profiles for 100 and 30% Power
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FLOW RATE AT

ORNL DWG. 69-6635

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

REACTOR REACTOR OUTLET —
POWER TEMP SETPOINT OOSGETOC&?:‘AER?I ;i‘fiL
RROR SETPOINT (Toser) - FLOW RATE _ STEAM
ROD (€] = (Prger) ERROR (F2) ERROR
= — stavo - X f = - i At r— ©m = SeTeomT
: + — 2 7 +
| CONTROLLER 1| | Y (1000 °F)
REACTOR POWER l | REACTOR INLET 7 - l T,
e . TEMP 4 = | -
[ o [ - Tq ' STEAM
CONTROL Ts
ROD | Tz | /FJ“"
| |
|
L PRIMARY A PRIMARY SECONDARY SECONDARY STEAM
SALT [ 120N SALT SALT Fa SALT
Fy V] \ N\ T,
T2 T \ T Tss I\ g LOAD
l ‘ DEMAND
T | TUBE TUBE
GRATZH! N\ | TuBe Lt
LY 12
\\ I <
\ | PRIMARY PRIMARY \ SECONDARY SECONDARY STEAM
SALT | SALT W sALT SALT T
Tr | Ty TSP Ts
- S
n T T, Ts  FEEDWATER
PRIMARY (700°F)
REACTOR CORE HEAT EXCHANGER STEAM GENERATOR
Fig. 3. Lumped Model of MSBR for Plant Simulation.
Table 1. Physical Constants

 

Primary Secondary
Parameter _Solt Salt Steam Hostelloy N Graphite
Ce B b o™ 0.324 0.36 2.17 0.126 0.409
o, |b/fr3 207.8 ot 1175°F 117 at 1000°F 19.7, 7.01 548 17
k, Bty helop T _— _— _— 11.0 4]
Primary Heat Steam
Parameter Exchanger Generator
Length, f 19 63.8
Triangulor tube pitch, in. 0.625 0.875
Tube OD, in. 0.375 0.5
Wall thickness, in. 0.035 0.077
Heat transfer coefficients, Btu hr_]ft_2°F—]:
tube side fluid to tube wall 2786 4000
tube wall conductance 3770 1715
shell side fluid to tube wall 1624 3745
Reactor Core
Octagon: 13 ft across flats.
Height: 13 ft.
Fuel: 233U.
Primary-salt volume fraction: 0.16,
Graphite to primary-salt heat tramfer coefficient: 1700 Btu hr—IH_2°F—] ]
Temperature coefficient of reactivity
primary salt 1,333 x 107>/°F.
grephite 1.056 x 10_5/°F.
Thermal neutron lifetime: 3.6 x 10-4sec.
Deloyed neutron constants for 233U:
; Bi x 104 \, sec-]
1 2.3 0.0126
2 7.9 0.0337
3 6.7 0.139
4 7.3 0.325
5 1.3 1.13
é 0.9 2.50

 

 
10

temperature was controlled by altering the temperature of the primary salt entering the
primary heat exchanger. The rate of change of this primary-salt temperature was pro-
portional to the steam temperature error, or

dT2

ar - GP} T 70} @)

where a is the controller gain, and T7 is the design value of the steam temperature T7.

0
A brief parameter study of a showed that with a gain of about 1°F/sec change
in To per 10°F error in T the steam temperature returned to its design value of 1000°F
and remained stable. At higher gains the system became unstable. For a typical trans-
ient initiated by a 10% step decrease in load demand from 100 to 90% of full load
(Fig.4), 100 sec was required for the steam temperature to return to within 1°F of its
design value. One method of reducing the time required for the steam temperature to
return to its design value would be to vary the secondary-salt flow rate during a trans-
ient. This would enable close control of the amount of heat delivered to the steam
generator, resulting in more restrictive temperature control.

ORNL DWG. 69-6636

150

 

o
B~
0
1050
L 1000

  

 

950~ 50 100 150 200

SECONDS

Fig. 4. Transient for 10% Step Decrease in Load Demand with Constant
Secondary-Salt Flow Model.
11

2.3 Study of Steam Temperature Control with Variable Secondary-Salt Flow Rate

Restrictive temperature control was accomplished by the control system shown in
Fig. 3. The steam-temperature error was allowed to control the rate of change of the
secondary-salt flow rate by

dF

— -a(T7 ~ 170). (3)

Then, after the steam temperature transient, the flow rate was slowly adjusted to its
original full-power value by allowing the flow rate error to change the temperature of

the primary salt entering the primary heat exchanger by a second controller having a
gain of fB:

dT F

- - Bl - =), )
20
where F20 is the initial full-power value of the secondary-salt flow rate Fy

A brief parameter study of a and B indicated that a reasonable steam-temperature
response was obtained when a 1°F steam-temperature error produced a secondary=-salt
flow rate change of 10%/min and a 1% error in flow rate produced a primary-salt tem~-
perature change of 1°F/min.

With this control system, a 10% step decrease in power demand from 100 to
90% of full load produced the transient shown in Fig. 5. The steam temperature re-
turned to within 1°F of the design value in about 30 sec, as compared with 100 sec
described previously. The maximum change in the secondary-salt flow rate was about
20%, i.e., from 100 to 80% of the design value; the maximum rate of change was
about 50%/min. The flow rate returned to within 3% of its design value in approx-
imately 250 sec (4.2 min).

With the addition of the reactor heat transfer and nuclear kinetics equations
to the model, the temperature of the primary salt entering the primary heat exchanger
(reactor outlet temperature) was controlled by inserting or withdrawing control rods to
change the reactor power according to the error in the secondary=-salt flow rate. Steam
temperature control by means of the secondary=-salt flow rate remained the same. The
rate of change of the set point for the reactor outlet temperature Ty op WOS obtained
from the error in the secondary=~salt flow rate, as follows: 2 set

 

- Bl - =), (5)
12

which is similar to Eq (4). This controller slowly adjusted the reactor outlet temperature
set point in the proper direction until the secondary-salt flow rate returned to its 100%
power value.

The values for the controller gains a and B were adjusted for the transient runs
such that a 3°F error in steam temperature yielded a 10% per min rate of change of the
secondary-salt flow rate and a 1% error in the secondary-salt flow rate yielded a 1.7°F
per min rate of change of the reactor outlet temperature set point. These values were
obtained after a brief parameter study in which a 10% step decrease was initiated in
the plant load demand and the gains were adjusted to yield the minimum steam temper=
ature deviation.

The required set point for the reactor power level Pr sef is obtained from the
reactor outlet temperature set point by
= - 6
lDr set A 12 set T] ! ©)

where A is the proportionality constant between reactor power and reactor AT. Thus,
as the reactor outlet temperature set point is altered by the secondary-salt flow rate,
the reactor power level set point will be altered as well. The error in the reactor
power level is given by

& =P -P (7)

r r set’

This error signal is the input to a proportional servo rod controller which is described
by the second-order transfer function

2
T6) = 28 ®)

2
s t 20ws tw

where G is the controller gain, w is the bandwith, and ( is the damping factor. In
this simulation w equaled 31.42 radians/sec (5 Hz) and  equaled 0.5. These values
are typical of the kind and size of servo which may be used in this control-rod-drive
service. The gain of the controller was such that for €. 2 1% of full reactor power
the control reactivity addition or withdrawl rate was

doc
—d'i_— = O.TA:/sec. (9)
13

For errors less than 1%, the rate of change of reactivity was proportional to
the error. For errors greater than 1%, the reactivity rate was maintained constant at
the 0.1%/sec valve. Integration of Eq. (9) yields the term p _ in the reactivity equa-
tion (see Sect. 5.2). This method of con’rrollin% the reactor outlet temperature is
similar to that used in the MSRE control system.

To obtain more realistic transient results from the simulation, limits were im-
posed on several of the system variables, as follows:

1. The secondary-salt flow rate was limited to a range from 40 to 110% of the full-
power flow rate.

2. The maximum steam flow rate was limited to 110% of the full-power flow rate.

3. The reactor outlet temperature set point was constrained to a range from 1000 to
1400°F (100°F over and 300°F under its full-power value of 1300°F).

4, A 5-sec first-order lag was introduced between the steam flow rate demand F
in Eq. (43) in Sect. 5.2 and the steam flow rate in the system F, in Egs. (363 -
(40), in order to better simulate the response of a turbine throttle valve.

ORNL DWG. 69-6637

150

 

0 30 100 150 200 250 300
SECONDS

Fig. 5. Transient for 10% Step Decrease in Load Demand with Variable
Secondary-Salt Flow Model.
14
3. RESULTS

Calculations of the temperature profiles with the system under partial load at
steady state were made using the steady-state form of the analog simulation equations
in Sect. 5.2. The variation of salt temperatures with various steady-state power
levels is shown in Fig. 6. Figure 6 also shows the variation of the same salt temper-
atures obtained by use of another method of calculation described in Sect. 5.1.
Divergence of the two sets of curves begins at about the 50% power level. Thus, if
it is assumed that the calculation method of Sect. 5.1 is more reliable for predicting
system temperature profiles at steady state, the present analog simulation model is
valid only at power levels greater than approximately 50%.

Several transient cases were run which included (1) decreases in load demand
P from 100% by steps of 10, 30, 50, and 60%; (2) ramp changes of 30 and 70% each
of 5 and 10%/min; (3) changes in reactivity of steps of +0.05, +0.1, and -0.5%; and
(4), with the reactivity controller disconnected, (a) reactivity steps of £0.05, +0.01,
and -0.1% and (b) ramp changes in reactivity of +0.05 and =0.1% at 0.1%/min. Also,
the step loss of one secondary-salt coolant loop was simulated. The system transfer
function Pe(s)/p(s) was also measured.

ORNL DWG. 69-6638

*300p— /

12501— e LOG MEAN AT CALC { APPENDIX, SECT. 3.
————— STEADY-STATF FORM OF ANALOG SWULATIO}/
EQUATIONS (APPENDIX, SECT. 5.2) Z

12001—
REACTOR QUTLET, T2

# 50— / /
1100+— // :
e
s SECONDARY SALT HOT LEG, T,
s
: 7
7
e
/

 

 

o 1050 — /-
- S—e ¢
2 1000 :‘,’7'_' - o REACTOR INLET, Ty
a —— = i
3 7/ >
—_ X // //
50— ~ -
/ . -—
- >
L7~
po
Q00— \
——— T, SECONDARY SALT COLD LEG, T2
e
850|— T T —
800 +—
750}—
200 | ] | ] 1 1 | ] J
0.1 0.2 0.3 0.4 05 6.6 0.7 0.8 0.9 1.0
P!/p!l

Fig. 6. Variation of Steady-State Salt Temperatures with Power Level.
15

3.1 Decrease in Load Demand

The action of the system during a typical load demand transient was as follows.
When the load demand P, was decreased, the steam flow rate decreased, transferring
less heat out of the steam generators and decreasing the heat transfer coefficient be-
tween the steam generator tubes and the steam. This caused the steam femperature to
begin to rise. The steam temperature controller sensed the steam temperature error
and began to decrease the secondary-salt flow rate at a rate proportional to the tem-
perature error in order to transfer less heat into the steam generator and to decrease
the heat transfer coefficient between the secondary salt and the steam-generator tubes.
The transfer of heat from the secondary salt at the reduced flow necessary for steam
temperature control caused the temperature of the secondary salt leaving the steam
generator to decrease. The reduction in flow rate also decreased the amount of heat
transferred out of the primary heat exchanger as well as the heat transfer coefficient
between the primary-heat-exchanger tubes and the secondary salt. The primary salt
was, thus, returned to the reactor at a higher temperature, producing the reactor
power error signal . As this error was sensed by the reactivity servo controller, the
control rods were withdrawn (inserting negative reactivity) to reduce the reactor power
commensurate with the decrease in load demand. The secondary=~salt flow rate con-
troller sensed the decrease in the flow rate and began to decrease the reactor outlet
temperature set point at a rate proportional to the secondary-salt flow rate error. A
new steady-state operation was achieved when the steam temperature reached its
design value of 1000°F and the secondary-salt flow rate its full-power value.

The results of a 30% decrease in load demand from 100% as o step and af rates
of 10 and 5%/min are shown in Figs. 7-9. The reduction of the temperature of the
secondary-salt leaving the steam generator after a change in load demand is shown in
these figures. For large, rapid changes in load demand, the temperafure of the sec-
ondary-salt may approach its freezing point (725°F). This possibility exists also when
the load demand on the plant is increased. Under such conditions the steam temper-
ature initially tends to decrease, causing the steam temperature controller to accel-
erate the flow of secondary salt, which will transfer more heat into the steam gen-
erator. Since this flow may increase only to 110% of full flow, a sufficiently rapid
load increase will cause the temperature of the secondary salt leaving the steam gen-
erator to decrease and, perhaps, approach the freezing point. However, increases
in plant load will usually occur in a more orderly and controlled fashion than decreases
since, under accident conditions, decreases will be more probable. Increases in load
must be accomplished in a carefully controlled manner.

The data from Figs. 7-9 and the results of other runs made with changes in load
demand are summarized in Table 2 which also lists the maximum steam temperature de-
viations from 1000°F, the maximum required rates of change of the secondary=-salt flow
rate and of the control reactivity, and the maximum magnitude of the control reactivity
requited. The highest reactivity rate was well below the 0.1%/sec maximum allowed
by the controller.
16

ORNL DWG. 69-6639

+

150>§Y,, ¢ o e -t Pt 1

  

&
0 -
150
e°
0
150
.

 

 

0 160 200 300 400 500 600 700 800 900

1000

 

 

 

o

     

i

0 100 200 300 400 500 6§00
SECONDS

700 800 900

Fig. 7. Transient for 30% Step Decrease in Load Demand.
17

ORNL DWG. 69-6640

150 oo T
' +

md e e e e e

 

 

 

 

 

 

 

 

 

 

 

 

bt b b b b e e e s e
P . , ! : ; oLl gt bagly i i i ;
P ; | | 1 7T 1 LOAD DEMAND,Pg * ° |
I e oot rereem s et TR ey
Lo b * Poboce b e e
s? L 4 ‘ v I oo 1 doopoep o deg d g b S P e
~ P ! ! ! = =
_ -4 B i t T * i } ¥ : , C 4 ? 4 -4 . ’ : : |r 4
—— i : o
i"{'i ! Pyl o P i ! b P i o
i P i t ' ! : 3 . | ; : .
P b e
0 bRy vl i be e i 4 Ledo w3000 008 4 d i
150 t A

  

To

150

Do

150

o

 

0 100 200 300 400 500 600 700 800 900
1050

& 1000

 

950 .
950 |

- 850

4

    

0o 100 200 300 400 500 600 700 800 900
SECONDS

Fig. 8. Transient for 30% Ramp Decrease in Load Demand at 10%/min.
18

ORNL DWG. 69-6641
150 = Prorrr s et - 3 : : L P i
T e SR LT

-

 

 

 

 

 

   

 

5
0
150
&
0
150
53
0
150
&
0
1050
L 1000
Yl %;,fl;;
950 . B
950 <~ e - o
'; STEAM GENERATOR SALT OUTLET
TEWP, T,
& B850 —— . o -
- |
o
150 ‘
0 100 200 300 400 500 600 700 800 900 1000

Fig. 9. Transient for 30% Ramp Decrease in Load Demand at 5%/min.
19

Table 2. Results of Load Demand Perturbations

A. For Step Losses of Load Demand (from 100%)

 

Magnitude of Step (%)

 

 

10 30 50

Final steady-state temperatures, °F

T] — 1009 976

T2 — 1183 1098

T — 867 875

Ty — 1077 1025
Max steam temperature error, °F 13 44 147
Max rate of change of secondary-

salt flow rate, %/sec -0.74 -2.3 -4.3
Max rate of change of reactivity,

%/sec 3.5x10 21.06x 107 -3.0x 107
Max value of o, % -0.014 -0.045 -0.075

 

B. For 30% Ramp Loss of Load Demand from 100 to 70%

 

Ramp Rate (%/min)
10 5

 

Max steam temperature error, °F 9 5
Max rate of change of secondary-
salt flow rate, %/sec -0.41 ~0.26
Max rate of change of reactivity,
%/sec 1.75% 107 1.5x 107
Max value of control reactivity

required, % -0.045 -0.045

 
20

A plot was made of the maximum steam temperature variation from 1000°F as
a function of change in load demand (Fig. 10). The plot shows, for example, that a
step change of 30% in load demand from 100 to 70% of full power produced a max-
imum steam temperature deviation of about +42°F at some point in the transient. The
break upwards in the three curves for load changes greater than 30% was caused by the
40% lower limit imposed on the secondary=-salt flow rate. Changes in load of more than
30% required a change of greater than 60% in the secondary-salt flow rate to maintain
control of the steam temperature. When this lower [imit was reached, control of the
steam temperature was considerably reduced and higher deviations allowed to occur.

3.2 Changes of Reactivity

The results of reactivity steps of 0.1 and -0.5% are shown in Figs. 11 and
12. A +0.1% step yielded a peak reactor power of about 155% as a puise with a
fwhm (full-width, half maximum) of about 0.75 sec. This is an excess energy input
of approximately 930 Mw~sec. The reactor outlet temperature peak deviation from
1300°F was about 25°F. The reactor inlet temperature and steam temperatures varied
only a few degrees. The control reactivity changed at its maximum allowable speed
in a direction te counter the reactivity step. A negative reactivity insertion of -0.5%
decreased the reactor power sharply to about 18% before the control reactivity re-
turned it to its 100% level ofter a 35% overshoot (Fig. 12). The reactor outlet tem-
perature peak change was about =100°F, and the peak steam temperafure variation
was about -15°F.

ORNL DWG. 69-6642

250

STEP(WITH 40 % LOWER LIMIT ON SECONDARY
SALT FLOW)

50

   
  
  

STEP (WITHOUT 409, LOWER LIMIT ON SECONDARY
(- SALT FLOW)

MAX STEAM TEMP CRROR, ATy (°F)

30— WITH 40 % LOWER LIMIT ON SECONDARY

RAMP AT 1090 / MIN
SALT FLOW

RAMP AT 5% /MIN

B_~WITHOUT 40% LOWER LIMIT ON
SECONDARY SALT FLOW
‘ 1 | _
¢ 10 20 30 40 50 60 70 80 90 100
CHANGE IN LOAD DEMAND (%)

 

Fig. 10. Maximum Steam Temperature Error for Changes in Load Demand

from 100%.
21

ORNL DWG. 69-6643

Ty T T OF rot =

   

150~

 

 

 

e

 

 

 

0125

 

1275

10 t5 0 5 10" 15 20 O 5 10 150 5 10 15 20
SECONDS

Fig. 11. Transient for Steps in Reactivity of £0.1% with Reactivity

Controller Active.
22

CRNLDWG 69-6644
! lpi - 1

0 R, P
T }L - : L ]
| :_ .) ._-; -4 - . E 4. 4 ) ._E, <I 4 b 4 1|
E-I “ ' g " Lo ; [ , o q - ._

.25 — "

 

 

150{ 1

 

 

 

 

 

 

Ts
—
“
e L

 

 

 

 

 

 

 

 

 

 

0 _r;" |

_fif;
o
|
|

 

s
_—_—

|
! Py ;_._,_._ . [ » -'I'A;-

-1.25 b : 5 ' 7 ! t
1025
Y- 1000

$75
1550

w 1300

1050
1100

w1050

 

1000

0 5 10 45 20 25 30 35 40 45 50 55 60
SECONDS

Fig. 12. Transient for Step in Reactivity of =0.5% with Reactivity
Controller Active.
23

3.3 Step Changes of Reactivity with Controller Disconnected

With the reactivity controller disconnected so that a reactor power-level
error proditced no response from the reactivity servo (i.e., no control-rod motion),
step changes of +0.05 and -0.1% were studied (Figs. 13 and 14). The +0.05%
step change produced a peak reactor power of about 147%, and the reactor tem-
peratures increased to a value commensurate with the negative temperature coef-
ficient of reactivity. The secondary-salt flow rate decreased to its 40% lower
[imit, after which steam temperature control was lost. The final steam temperature
deviation was +75°F. The decrease in secondary-salt flow rate caused a decrease
in the temperature of the secondary-salt leaving the steam generator. This temper-
ature decreased to as low as 690°F during the transient, returning to a steady-state
value of approximately 735°F. (The secondary-salt freezing point is 725°F.) Sim-
ilar reactivity transients in runs made without limiting the secondary-salt flow rate
to a minimum of 40% of full flow caused this temperature to decrease to well below
its freezing point. Without the reactivity controller, control of the reactor outlet
temperature set point was lost; the outlet temperature reached 1485°F as its steady -
state value (Fig. 12). The steady-state temperature of the secondary-salt leaving
the primary heat exchanger was 1470°F.

The negative reactivity step of -0.1% (Fig. 14) required a decrease to 50%
in the steady-state reactor power level to produce the compensating reactivity by
means of the negative temperature coefficient. The primary-salt temperature at the
reactor inlet decreased to approximately 865°F--well below its freezing point of
930°F. The secondary-salt flow rate quickly increased to its 110% limit, after
which steam temperature control was lost. The final steam temperature was 840°F.
At this low temperature, the steam flow rate increased in an attempt to meet the
100% load demand on the plant, but it was also limited to 110% of full flow rate.
These conditions correspond to a plant output of 51% of full power, which matches
the observed steady-state reactor power.

3.4 Ramp Changes of Reactivity with Controller Disconnected

With the reactivity controller still disconnected, ramp changes in reactivity
of +0.05 and -0.1% at 0.1%/min were inserted. The positive-ramp insertion pro-
duced a peak power of about 130%. Again, the secondary-salt flow rate decreased
to its 40% lower limit, and steam temperature control was lost. Both of these ramp
reactivity perturbations produced much the some response as the step insertions of
the same amount except that the reactor power changed more slowly.
ORNL DWG. 69-6645

  

150 1550

1

 

w 1300
& . :
o-_— 1050
150 1300 -
° . 1050
& .
0 800
150 1650
& w 1150
0 650
1100 1100
1000 w 850

°F

  

600
0 100 200 300 400 500 ¢ 100 200 300 400 500

SECONDS SECONDS

Fig. 13. Transient for Step in Reactivity of +0.05% with Reactivity Controller Inactive.

ve
25

ORNL DWG. 69-6646
t50

T

150

o

150

T

uw 1000

150
1800

o 1300

800
1300

< 1050

 

800

0 100 200 300 400 500 600
SECONDS '

Fig. 14. Transient for Step in Reactivity of -0.1% with Reactivity Controller
Inactive.
26

3.5 Step Loss of One Secondary~-Salt Coolant Loop

A simulation of the loss of one secondary-salt coolant loop was attempted as
follows (see Fig. 3). In a four~loop system the temperature of the primary-salt enter-
ing the reactor core is the average of the temperatures of the primary-salt leaving the
four primary heat exchangers. We call the reactor core inlet temperature T]T, and the
primary~salt outlet temperatures from the four primary heat exchangers Ty 127 T]3,
and TM} then, with perfect mixing

To= Ty # T, + T

]
- 1
] 4} 11 12 (10)

13 7 Tl

We now assume that if one of the primary heat exchangers, e.g., number 4, suddenly
were to cease to remove heat from the primary salt, the reduction in heat removal
would appear as a step increase in the primary-salt outlet temperature T4 from 1050
to 1300°F. If the other heat exchangers were to remain unchanged, the reactor core
inlet temperature would become

-

1 T..+tT,.,+T

- +

2T T T2 T g T Ty (n
Thus, the reactor core inlet temperature would be changed as a step at t = 0 from T
to T,.

1
Similarly, the steam temperature to the turbine is the average of the steam

temperatures from the sixteen steam generators, four of which are supplied heat by
each secondary-salt coolant loop. If we call the steam temperature at the turbine T,
and the steam generator steam temperatures T7., then

o

L
7518 ]T7. (12)
|

i

If one secondary=-salt loop were to be lost suddenly, four steam generators would be
supplied heat no longer, say generators 13, 14, 15, and 16. We assume that this re-
duci'ion would appear as a step decrease in the steam generator outlet temperatures

B T7, 14~ T7’ 15 and T7’ 16 from 1000 to 700°F. The turbine steam temperature
would becdme

12
. 1
o +
T, ]6(;5i 4T6). (13)
£

Thus, the turbine steam temperature would be changed as a step at t = 0 from T

to T7. 7
27

The results of such a run are shown in Fig. 15. The turbine steam temperature
dropped as a step to 925°F, and the reactor inlet temperature rose to 1113°F. This
increase in reactor inlet temperature was accompanied by a sudden decrease in the
reactor power sef point, producing an error signal that indicated high reactor power.
The control rods were withdrawn (inserting negative reactivity) and, with the aid of
the negative primary=-salt reactivity temperature coefficient, the reactor power dropped
sharply to 70%. The steam flow rate increased to its 110% limit in an attempt to meet
the 100% load demand at the reduced steam temperature. The secondary-salt flow rate
increased to its 110% limit in an attempt to maintain the steam temperature at 1000°F.
With the loss of 25% of the heat transfer capability in the secondary [oop, the reactor
temperatures began to rise to meet the 100% load demand. However, when the reactor
outlet temperature reached its 1400°F limit, the reactor power had increased to only
92% of full load, and the steam temperature had increased to 956°F. Therefore, under
this accident condition and with the temperature and flow limits placed on the system,
the plant could not deliver 100% of full load with one secondary=salt loop inoperable.
Figure 15 also shows the result of decreasing the load demand to 75% at a rate of
10%)/min beginning 325 sec after the step loss of heat transfer capacity. The plant
could meet this demand at design steam conditions.

3.6 Measurement of System Transfer Function

The full power system transfer function Pr(s)/o(s) was measured with and with-
out the reactivity servo controller (Fig. 16). The curve for the case with no controller
is similar to previous data for the two—fluid MSBR,2 although the magnitude of the
peak gain at about 3 radians/sec (~0.5 Hz) was greater by a factor of about & for the
single-fluid case. Adding the servo controller greatly decreased the low~frequency
gain, as expected; above the upper cutoff frequency of 5 Hz ¢30 radians/sec) for the
servo it had no effect.

4. CONCLUDING REMARKS

We have described a preliminary investigation of the control problems asso-
ciated with the 1000-Mw(e) single-fluid MSBR. The control system was formulated
in four basic steps: the first was an estimation of the system temperature profiles for
partial load conditions, assuming various possible modes of plant control. Based on
these results the most promising mode of plant control was investigated for its dynamic
response, using only the primary heat exchanger and steam generator. The results
indicated that a variable secondary=salt flow rate would give better steam temper-
ature control during o transient, and this was investigated using the same model.

The reactor was then added to the simulation, and the response of the entire plant
to various perturbing conditions was studied.
28

ORNL DWG. 69-6647
“50 i T - r - - - rer et e

 

e
0
150
.
0
150 1
O
0
159
s
0
+0425 —
s 0
-0425 -

1100

*F

1000

900
1550

1300

°f

1050
1309

1050

o

 

800" - : ‘
100 200 300 400 500 600 700 800 900 1000
SECONDS

Fig. 15. Transient for Step Loss of One Secondary=-Salt Cooling Loop
Followed by a 25% Reduction in Load Demand.
29

The results indicate that careful control will be required to maintain the
temperatures of the two salts within the rather narrow allowable limits. Such plant
maneuvers as increasing and decreasing the load demand on the plant and certain
reactivity excursions might allow these temperatures to decrease below freezing
points. However, since the models used in these simulations and calculations were
abbreviated, the results are regarded only as indicative of possible trends that might
be elucidated in more detailed investigations. Such investigations were not possible
with the analog equipment available to the author without either linearizing the
simulation equations (reducing the dynamic range) or simulating only a part of the
plant ot a time, or both. Even then, the modeling of such a unit as a supercritical
steam generator would be a difficult task on the analog computer.3 A more detailed
simulation than was tried here should be attempted by employing more powerful sim-
ulation techniques, e.g., hybrid computation.

ORNL DWG. 69-6648

   
 

 

 

107 g
WITHOUT REACTIVITY CONTROLLER
= 10"}~
<
%
z
=
=
(|
=
S
/
10— 4
/&
/{ WITH REACTIVITY CONTROLLER
7/
/
&
,Od | i i
0.01 0.1 1.0 10 100 1000

FREQUENCY jradiemn/sesd

Fig. 16. System Full-Power Transfer Function Pr(s)/p(s).
30

5. APPENDIX

5.1 Calculation of Steady-State System Temperature Profiles

The model used in this calculation appears in Figure 1. The two basic
equations used were

ATa - ATb |
Q = UA{ NG J (14)
ln(m
AV FCPAT (15)
where
] Ar ] -l
UZ[K+T+F_] (16)
i o
and

Q = heat power (Btu/hr), 1 22 o
U = overall heat transfer coefficient (Btu hr ft "°F '),
A = heat transfer area (ft2),
T = temperature,
a,b = ends of heat exchanger,
F = mass flow rate (Ib/hr)1
C, = specific heat (Btu Ib~ °F“]), 12
hi = heat transfer coefficient inside tubes (Btu hr ~ ft — °F ),
k = tube thermal conductivity (Btu he™l =2 op=1/ft),

Ar = tube wall thickness (ft),

hg = heat transfer coefficient outside tubes (Btu hr_] fi'_z °F_]).

The heat transfer coefficient inside the tubes h; was taken to be proportional
to the 0.8 power of the flow rate through the tubes 7 the coefficient on the shell-

side of the tubes was taken to be proportional to the 0.6 power of the shell-side flow
rate, i.e,,

_, 0.8
h. =k Fy o8, (17)
31

and
(18)

where k is a proportionality constant.

The following equations were written based on given full-load plant con-
ditions. [The subscript "o" denotes the full-load (100% power) value of all vari-
ables.]

In the primary heat exchanger:

(_g’_. , TZ_'_‘__., (19)
0 20 ~ N0
Q Up[m]““ (20)

QO UPO[MQ Im’

Q F4 * F2 T3 - T4 21)

Q  Fao T Fao Ta0 ™ T4o

 

For the steam generator:

Q2 475 22
Q  FaoTao ™ Tso
Q Us [AT] Im (23)
Q0 UsO AT0 |

m
Q _ '3 77 24)
Qy  Fap T70 ™ Teo
32
In Egs. (20) and (23)

ATG - AT
Im AL] (25)

The 100% plant-load temperature profile, used as given information in these
calculations is shown in Fig. 1. In all calculations that follow, the temperature T
of the water entering the steam generator and the steam temperature T, were held
fixed at their 100% plant load values of 700 and 1000°F, respectively. The values
of the tube-side and shell-side heat transfer coefficients for the primary heat ex-
changer at 100% power were respectively

h. = 2786 Bty he ! g2 opT !

and

h = 1624 Btu hr | ft 2 oF .
00

For the steam generator the tube-side and shell-side heat transfer coefficients were

h. = 4000 Btu he ! g2 op!

and

h = 37458t he | ft 2 oF
o0

The values of k/Ar in E?. (16) were 3770 Btu hr—] fl"z °F-] for the primary
heat exchanger and 1715 Btu hr™ ft=2 °F~1 for the steam generator .

The overall heat transfer coefficient for the primary heat exchanger was
calculated from Eq. (16):

-1
0.6

F, +F
U:1+1+1(4o 20) , 26)

 

 

o~ |2786 T 370 T T2\ F, +F,

The overall heat transfer coefficient for the steam generator was

0.6 0.

F F
o1 [P 1 1 {F30 ”7
Ys = |37z (‘F’é‘) * 1715 * 7000 (‘F‘g) ' (27)

 
33

Equations (19) through (23) form a set of five equations in eight unknowns.
The unknowns are Q/Qq, (Fy *+ F2)/(F40 + Foqg), Fo/Fpg, and Ty, To, T3, Ty, and
T5. Several variables must be specified in order to solve the set of equations. The
variable Q/QO, the relative power level, was used as a parameter. The remaining
two variables were specified in three ways, forming the three case studies reported
here.

Case 1: Average reactor temperature fixed at its 100% power level value
and the bypass flow given by

_ Q
T ]

Case 2: Average reactor temperature fixed at its 100% power level value
and no bypass line around the steam generator, i.e.,

Tl Tio ™ Ty

2 2

and

Case 3: Constant flow rate of the secondary=-salt and no bypass line, i.e.,

F4 =0
and
F2 _
o 1.
20

5.2 Description of the Analog Simulator Model

The following equations describe the analog simulation model used in this
study and shown in Fig. 3. The heat transfer driving force across the heat exchanger
tubes and from the graphite to the primary salt is shown by the dotted lines in the
figure. The mass of the primary salt and the primary-salt-to-tube-wall heat transfer
area in the primary heat exchanger were equally divided between the two primary-salt
lumps. Similar statements can be made about each of the remaining pairs of lumps
except in the case of the two steam lumps.
34

For the two steam lumps wy and wp, the density of the steam varies by a
factor of 7 in passing through the steam generator.® The mass of the steam in lump 1
was determined by the average density of the steam in the half of the steam generator
at the steam exit end. The mass was determined in a similar manner for lump 2. The
steam pressure was assumed constant at all times.

For the reactor core (see Fig. 3):

dT
G
— = - + 28
McCoc T = Piofra (T =~ Tgl * kaPer (<8)
T
L - + 0. - 14, 29
M Corar = FiCpe(l = T * kP T 05 A (T~ T (29)
T2 T (30)
_ - + - .
Mg prar = FiCe(Te = To) * koP T 0-9his A (Te ~ Ty
For the primary heat exchanger:
dT, 3
—_— = - - - ]
MCof g = FipdT2 = Te) ~ eAy(Te ~ Th), 1)
T, )
= - - h A T = T
MCor T = FSelTe = ) " AT T Ty (
T
o - -2h AT, -TJ, 33
MaCor = = 2T~ TH) PPt ™ T (33)
T, .
Mspcps dt F2Cps(TsI - T4) - hspAp(Ts] - TH)' (34)
dT

]
Mspcps—_dsf_ - F2Cps(T3 - Ts]) - hspAp(Ts] - TH) ‘ (35)
35

For the steam generator:

de3

Mssts & FZCps(T5 - Ts3) - hssAs(Ts3 - TfZ),
M C — = F2Cps(T53 ~ T8) - hssAs(TSS - sz),
MTZCpf dar 2hssAs(Ts3 - T1'2) - 2ths(T1‘2 - Tw)'

Mwlcpsf ar F3Cps’r(Tw - T7) - ths(Tw - T’rZ}'

dT

w

szcpst at F3Cpsi{T6 - Tw) - ths(Tw . Ti'Z,'
T ) = Ts"r + Tll'
Tgt) = T4 ‘t + Tz)'

Pe = F3Cot{T7 = Te)r

As in the steady-state off-design calculations in Sect. 5.1
0.6

"o f?__)

hspo F20

0.6
s [z
hsso FZO

 

 

(39)

(40)

(41)

(42)

(43)
36

 

0.8
h
W F3
h T 7
WO F30
where
T = temperature of lump,
P = reactor power,
PE = load demand (power to turbines),
M¢ = mass of primary=salt lump,
MG = mass of graphite in core,
M; = mass of tube-wall lump,
M, = mass of secondary-salt lump,
M,, = mass of steam (water) lump,
Cp = specific heat of lump,
kg = fraction of power generated in graphite,
kr,2 = fraction of power generated in primary-salt lumps,
A = heat transfer area of lump,
F = salt or steam flow rate,
hg = primary -salt-to-tube heat transfer coefficient,
th = graphite-to-primary-salt heat transfer coefficient,
hsp = tube-to-secondary-salt heat transfer coefficient in primary
heat exchanger,
hgs = secondary-salt-to-tube heat transfer coefficient in steam
generator,
h,, = tube-to-steam heat transfer coefficient,
T = transit time of secondary salt between the primary heat ex-
changer and the steam generator (assumed to be 10 sec).
The reactor kinatics equations used in the simulation were
dPr 5 - g
@ T NG ()
dc, s, ] ST
—_— = - - — + - T
7 = TP NG TG T G ‘L), (43)
c c
also

P =gy T GAT Fa AT+ o (46)
37

where

B = delayed neutron fraction,
| = neutron generation time,
N ith delayed group decay constant,
T, = transit time of primary salt through the core,
T| = transit time of primary salt through external loop,
0g = positive, net steady-state reactivity associated with the cir-
culating fuel,
ag = temperature coefficient of reactivity for the primary salt,
dc = temperature coefficient of reactivity for the graphite,
= control rod reactivity.

i

Oc

The simulation of C.{t - TL] requires a transport lag device of which only
two were available in the Reactor Controls Department analog computer. Both were
employed in the simulation of Eqs. (41) and (42), the transport lag between heat ex-
changers. Therefore, the term Ci(’r - TL) was approximated by

 

 

dCi(f)
Ci (t ~ TL’ A Ci('r) " T (47)
With this approximation Eq. (45) became
dc, B, M
_ ' __tp - 48
dt ~ Ib. Pr a.b. C?' (48)
i i
where
AT
g = i c
ATt 1 —exp(-kT)
and
T
38

The coefficients for these equations were calculated using the physical con-
stants listed in Table 1. The resulting calculated values for the various system volumes,
masses, etc., were as follows:

1. For the reactor core (active region only)
Initial heat flux, 7.68 x 107 Btu/br 12250 Mw (th)]
Primary-salt flow rate, 9.48 x 107 lb/hr
Active core volume, 1820 f53 (primary salt plus graphite)
Primary -salt volume, 291 ft
Graphite volume, 1529 ft°
Primary-salt mass, 60,512 lb
Graphite mass, 178,873 Ib
Number of graphite elemen'rs,2 1223
Heat transfer area, 22,121 ft
Primary-salt velocity, 5.66 ft/sec
Core transit time of primary salt, 2.30 sec
External loop transit time of primary salt, 6.5 sec
Steady-state reactivity 0q 0.00161.

2. For the primary heat exchanger (total for 5our exchangers, tube region only)
Secondary-salt flow rate, 7.11 x 107 Ib/hr 1 1
Overall heat transfer coefficient, 806 Bi'uzhr ft ~ °F

Primary -salt heat transfer area, 55,000 ft

Number of tubes, 29,400 3

Tube metal volume, 145 ft

Primary-salt volume, 283 ft 3

Secondary-salt volume, 883 ft

Volume of four primary heat exchangers, 1311 ft

Primary -salt mass, 58,800 Ib

Tube mass, 79,400 lb

Secondary-salt mass, 103,300 b

Transit time of primary salt, 2.23 sec

Transit time of secondary salt, 5.23 sec

Primary-salt velocity, 8.5 ft/sec

Secondary-salt velocity, 3.6 ft/sec.

3. For the steam generator (total for 16 steam generators, tube region only)
Steam flow rate, 1.18 x 107 Ib/hr 1 -2 o
Overall heat transfer coefficifnf, 909 Btu hr ~ ft ~ °F
Heat transfer area, 56,300 ft
Number of tubes, 6740
Tube metal volume, 306 ft
Secondary-salt volume, 1394 ft
Steam volume, 281 3 3
Volume of 16 steam generators, 1980 ft

3
3
39

Secondary-salt mass, 163,000 lb

Tube mass, 168,000 Ib

Steam mass, 3750 Ib

Secondary-salt transit time, 8.26 sec

Steam transit time, 1.15 sec

Secondary-salt velocity, 7.72 ft/sec

Average steam velocity in lump wy, 212 ft/sec
Average steam velocity in lump wo, 76 ft/sec

The simulation equations coefficients were calculated from these values.

REFERENCES
1J. R. Tallackson, MSRE Design and Operations Report, Part IIA: Nuclear
and Process Instrumentation, ORNL-TM-729 (February 1968).
Private communication from T. W. Kerlin, ORNL.

3
F. H. Clark and O. W. Burke, Dynamic Analysis of a Salt Supercritical
Water Heat Exchanger and Throttle Used with MSBR, ORNL-TM-2405 (January 1969).

 

 

4
C. O. Bennett and J. E. Myers, Momentum, Heat, and Mass Transfer, pp.
333-50, McGraw-Hill, New York, 1962.

 

Private communication from C. E. Bettis, ORNL.

6Ge:nerc:l Engineering Division Design Analysis Section, Design Study of a
Heat-Exchange System for One MSBR Concept, ORNL-TM-1545 (September 1967).

7J. MacPhee, "The Kinetics of Circulating Fuel Reactors, " Nucl. Sci. Eng.
4, 588-97 (1958). -
4]

ACKNOWLEDGMENTS

The author acknowledges the suggestions of S. J. Ditto and J. L. Anderson
for the control system design and for improvement of the system and the model.
ORNL-TM-2489

INTERNAL DISTRIBUTION

W. Kerlin 85-99.

J. L. Anderson 30.
C. F. Baes 31.
S. J. Ball 32.
H. F. Bauman 33.
S. E. Beall 34.
M. Bender 35.
E. S. Bettis 36.
E. G. Bohlmann 37-61.
C. J. Borkowski 62.
R. B. Briggs 63.
F. H. Clark 64-65.
C. W. Collins 66.
F. L. Culler 67 -68.
S. J. Ditto 69.
W. P. Eatherly 70.
J. R. Engel 71,
D. E. Ferguson 72.
L. M. Ferris 73.
W. K. Furlong 74.
W. R. Grimes - G. M. Watson 75.
A. G. Grindell 76.
R. H. Guymon 77-78.
P. M. Haubenreich 79.
R. E. Helms 80-82.
P. P. Holz 83.
P. R. Kasten 84,
T.

R

. B. Korsmeyer 100.

M. 1. Lundin

R. E. MacPherson
H. A. Mclain
H. E. McCoy

. R. McWherter
. L. Moore

. L. Nicholson
. C. Odkes

R. W. Peele

A. M. Perry

M. M. Rosenthal
Dunlap Scott

W. H. Sides

O. L. Smith

J. R. Tallackson

R. E. Thoma

J. R. Weir

M. E. Whatley

J. C. White - A. S. Meyer

L. V. Wilson

Gayle Young

Central Research Library

Document Reference Section

Laboratory Records Department

Laboratory Records, ORNLR. C.

ORNL Patent Office

Division of Technical Information Extension
Laboratory and University Division, ORO

~— m 3o

EXTERNAL DISTRIBUTION

101. C. B. Deering, AEC, Washington, D. C.
102. A. Giambusso, AEC, Washington, D. C.
103. George McCright, Black and Veatch Engineers,
1500 Meadowlake Parkway, Kansas City, Mo. 64114