ORNL-TM-2927.txt

 

OAK RIDGE NATIONAL LABORATORY
operated by

 

UNION CARBIDE CORPORATION
NUCLEAR DIVISION CARBIDE
for the

U.S. ATOMIC ENERGY COMMISSION
ORNL- TM- 2927

COPY NO. - £
DATE - May 18, 1970

 

RECEIVED BY DTIE JUL 23 1970

CONTROL STUDIES OF A 1000 - Mw(e) MSBR

W. H. Sides, Jr. MASTER

ABSTRACT

Preliminary studies of the dynamics and control of a 1000-Mw(e), single-~
fluid MSBR were continued. An analog simulation of an expanded lumped-parameter
model was used. Steam temperature control was accomplished by varying the sec-

. ondary=-salt flow rate. Improved reactor temperature control was accomplished by
applying the load demand signal directly to the reactor outlet temperature controller
as well as to the steam generators. .

2

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

PISTRIBUTION OF THIS DOCUMENT IS UNLIMITED
This report was prepared as an account of Government sponsored work, Neither the United States,

nor the Commissien, nor any parson acting on behalf of the Commission:

A. Mokes any warranty or representation, expressed or implied, with respect to the occuracy,
completensss, or usefulness of the information centained in this report, or that the use of

i any informetion, apparatus, method, or process disclosed in this report may not infringe

‘ privately owned rights; or

B. Assumes any liabilities with respact to the use of, or for domages resulting from the use of
any information, apparatus, method, or process disclesed 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

i or contractor of the Commission, or employee of such contractor prepares, disseminates, or

| provides access to, any information pursuant to his employment or contract with the Commission,

; or his employment with such contractor.

e e e LEGAL NOTICE - mrm o o m —nn nn e

 
CONTENTS

Inh‘OdUCi.ion- . - . . . . . . * * * . . . . * . . . . . .

Description of the Plant and Model . . . . « v« o v 4
2.1 Plant Description « v v v v v v o o v 0 0 v 0 o v

2.2 Model of the Plant. « v v ¢ ¢ ¢ ¢ v ¢ ¢ ¢ o o o o s

Steady State, Part Load Operation . . v ¢« v v v o v o &

ConfrOl System - - . . . . e e . * » . . . . . . - . . .

ResUItSe o ¢ v o v o v o o 0 o o 8 o 0 o o aie o aue o0
5.1 Load Demand Changess + « « « « o« v ¢ v v ¢ ¢ o &
5.2 Primary Flow Transienfs « « « « ¢ ¢ 0 0 ¢ 0 v o v s
5.3 Secondary Flow Transients. . « « « o v v v o o v &
5.4 Summary of Primary and Secondary Flow Transients
5.5 Reactivity Transients. « « « « ¢ « ¢ o ¢ o 0 s o s s

Transfer FUNCHION & ¢« « ¢« ¢ ¢ o o o o « « s ¢ o o s » o o

Appendix: Analog Simulation Medel. . . o . v o v .
7.1 Heat Transfer Model. . . . . . ¢ v o0 v v o vt
7.2 Nuclear Kinetics Model. . . . . v o v v 0 o0 vt
7.3 Control System + v o v v v v v 0 v v v o0 e .

LEGAL NOTICE

This report was prepared as an account of work
sponsored by the United States Government, Neither
the United States nor the United States Atomic Energy
Commission, nor any of their employees, nor any of
their contractors, subcontractors, or their employees,
makes any warranty, express or implied, or assumes any
legal liability or responsibility for the accuracy, com-
pleteness or usefulness of any information, apparatus,
product or process disclosed, or represents that its use
would not infringe privately owned rights,

 

 

 

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1. INTRODUCTION

By means of an analog computer simulation, preliminary investigation of the
proposed 1000-Mw(e), single-fluid Molten-Salt Breeder Reactor (MSBR) was con-
tinved.' 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 (secondary salt), a shell-and-tube
supercritical steam generator, and a possible confrol system. The analog simulation
of the plant consisted of a lumped-parameter heat transfer model for the core, pri-
mary heat exchanger, and steam generator; a two-delayed-neutron-group model of
the circulating-fuel nuclear kinetics with temperature reactivity feedbacks; and
the external control system. This investigation was concerned with the integrated
plant response; it was not concerned with a safety analysis of the system, although
several of the transients infroduced would be of an abnormal nature (e.g., loss of
flow). It was an initial probe into the response of the system initiated by such per-
turbations as changes in load demand, loss of primary or secondary flow, and reac-
tivity changes.

The simulation was carried out on the ORNL Reactor Controls Department
analog 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 equipment required that the model be severely limited spatially to min-
imize the number of equations. In addition, the pressure in the water side of the
steam generator, 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 temperature of the feed-
water to the steam generators was also held constant.

2. DESCRIPTION OF THE PLANT AND MODEL

2.1 Plant Description

The proposed 1000-Mw(e) MSBR steam-eleciric generating plant consisted
of a 2250-Mw(th), graphite=moderated, molten-salt reactor, 4 shell-and-tube
primary heat exchangers, and 16 shell-and-tube supercritical steam generators
(Fig. 1). The reactor core contained two zones: a central zone, a cylinder ~14.4
ft diameter and ~13 ft high with a primary-salt volume fraction of 0.132; and an
outer zone, an annular 1egion ~1.25 ft thick and the same height as the central
zone. The salt volume fraction in this region was 0.37. The primary=salt, bearing

 

]W. H. Sides, Jr., MSBR Control Studies, ORNL-TM-2489 (June 2, 1969).

 
PRIMARY
SALT PUMP
(4)
e
REACTOR
VESSEL=™

9.48 X107 Ib
at 1300°F

 

GRAPHITE el
MODERATOR=—""

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

= LEVEL CONTROL®

/hr

  

PRIMARY
HEAT EXCHANGER
(4)

 

  
  
  
       
  
   
 
 

712 X10" Ib/hre af 1150°F

850°F

SECONDARY
SALT PUMP

(4)

FLOW
DIVIDER

6.16 X 10" 1b/hr dt 1150°F

STEAM GENERATOR

 

 

 

\E o 9.48X10" Ib/hr at 1050°F

Fig. 1. Flow Diagram of MSBR Plant.

(16)

 

  
  
 

1% 10" Ib/hr STEAM at 1000°F

—— — — . — ——— — T —— T T o— — — —

1% 10" 1b/hr FEED WATER 4t 700°F

e e — —— — D —— S — — — ——

196 X10° Ib/hr

5%10% Ib/hr
———————— -

REHEAT STEAM dt 1000°F

REHEATER
(2)

850°F

 

———————— -

 

REHEAT STEAM at 650°F

The quantities shown are totals for the entire plant.
2
33U and 232Th, flowed upward through the graphite core in a single pass and then

to the tube side of one of four vertical, single-pass, primary heat exchangers, each
~19 ft long, 5 ft diameter, and constructed of Hastelloy=N. The salt flow rate at
design point was 9.48 x 107 Ib/hr. The design-point temperature of the salt enter-
ing the core was 1050°F and that at the core ocutlet was 1300°F. The liquidus tem-
perature of this salt was approximately 930°F.

The heat generated in the primary salt in the core was transferred from the
tube side of the primary heat exchangers to a countercurrent secondary salt passing
through the shell side. This salt flowed in a closed secondary loop to one of four
horizontal supercritical steam generators. The four secondary loops, one for each
primary heat exchanger, were independent of each other, with each loop supplying
heat to four steam generators. Thus, there was a total of 16 steam generators in the
plant. The design-point flow rate of secondary salt in each loop was 1.78 x 107 Ib/hr.
At the design point the secondary-salt, cold-leg temperature was 850°F, and the
hot-leg temperature was 1150°F, The liquidus temperature of this salt was ~725°F.

The shell-and-tube supercritical steam generators were countercurrent,
single-pass, U-tube exchangers ~73 ft long and ~18 in. diameter and constructed
of Hastelloy~N. Feedwater entered the steam generators at the design point at 700°F
and a pressure of about 3750 psi. The outlet steam conditions at the design point
were 1000°F and 3600 psi. Each steam generator produced steam at the design point
at arate of 6.30 x 109 Ib/hr. Reference 2 gives a complete description of an earlier,
but quite similar, version of the steam generator and primary heat exchanger.

2.2 Model of the Plant

A spatially lumped parameter model used for the heat fransfer system (Fig. 2)
consisted of the reactor core, one primary heat exchanger, one steam generator, the
nuclear kinetics, and a confrol system as shown in Fig. 5.

In the core, the primary salt in the central zone wes divided axially into
four equal lumps, and the graphite was divided into two. The oufer zone was divided
equally into two primary-salt lumps and one graphite lump. Since the primary salt
density varied only slightly with temperature, the four cenfral-zone lumps were of
equal mass, as were the two outer-zone lumps. The two central-zone graphite lumps
were of equal mass as well.

The mass flow rate of the primary salt in the two zones of the core was de-
termined by the heat generation rate in each zone so that the temperature rise of

 

2Generc:l Engineering Division Design Analysis Section, Design Study of a
Heat Exchange System for One MSBR Concept, ORNL-TM~1545 (September 1967).

 

 
¢ OF CORE .
ro
- P & ittt
g X ! Ts:
‘‘‘‘‘‘‘‘‘ - T 1T T - Tt Tt /T,
ZONE | . ZONETI ' r | [ i
ori sar| ! ! | |PRISALT SEC SALT] i |SEC SALT STEAM |
T i | ! Tp1 X Ts, ! ‘ Tss \ Tra |
pa , | ! \ | i \ i
GRAPHITE | PRI SALT] | | Ny TUBE ' - Ny TUBE -
Tg1 \\ i TPG i i Thy \ I l Tt.} \\ |
\ ' . ,
r I
M\ PRI SALT | ' I PRI SALT NSEC SALT | | gsec SALT N STEAM | |
\1 Tps l | | | Tos Tss || | Tse Tws i
1 5 ' i
' '
|l i 2o
' | | | | — |
PRI SALT | AN i t | PRI SALT SECSALTi t ISEC SALT STEAM | ,
Tpa | \ i ! Tpo M\ Ts. ' ! i Ts \\ Twa !
' \ | AN
SRAPHITE | qprisactl ! o TUBE , ! N TUEE I
Tez N i Tos | I T M ! | Tty \\ |
\ - . . :
N {PrisaT| | | | [PRISALT — NSEC sa || | |sEc sALT N STEAM | |
N Ty ' 1 Tri Tsy i ' Tss Twe |
i s | l ' | I
b e d i____v__.-___-_ _____ N L i
A
= : T @ ¥ 7;0"0"F
Tri ¢ ’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

REACTOR CORE

 

PRIMARY HEAT EXCHANGER

Fig. 2. Lumped~Parameter Model of MSBR Plant.

 

 

 

 

 

 

STEAM GENERATOR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

1.0

 

W4
///
CORE //’/
L
/// HEA?’PE;(,(\:‘:E:JGER
04 7

0.2
7

17

0 0.2 0.4 0.6 0.8 1.0
RATIC OF REDUCED FLOW RATE TO DESIGN FLOW RATE

 

 

 

0.6

 

 

TO THAT AT DESIGN FLOW

 

 

 

RATIO OF HEAT TRANSFER COEFFICIENT AT REDUCED FLOW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 3. Variation of Film Heat Transfer Coefficient with Primary-Salt Flow
Rate in the Reactor Core and Primary Heat Exchanger.
the primary salt in the two zones was equal. Thus, 81.4% of the flow passed
through the central zone and 18.6% through the outer zone.

A two-de layed-neutron-group approximation of the circulating fuel nuclear
kinetics equationsS was used in the model. This allowed the delayed-neutron pre-
cursor conceniration term C;(t - 1) (see Appendix, Sect. 7) to be simylated directly
with two of four available transport lag devices. The delayed=-neutron fraction for
233y was 0.00264, and the prompt-neutron generation time was 0.36 msec. The
coefficient of reactivity for the primary salt was =1.33 x 1072 per °F, which was
divided equally among the six primary-salt lumps of the core model. The tem-
perature coefficient for the graphite was +1.06 x 10~ per °F, which was divided
equally among the three graphite lumps.

The mode! was designed to accommodate a variable flow rate of the primary
salt as well as the secondary salt and steam. The required variations of film heat
transfer coefficients with the various salt and steam flow rates were included.

The film coefficient for secondary salt on the shell side of the primary heat ex-
changer and steam generator was proportional to the 0.6 power of the flow rate.
The film coefficient for steam on the tube side of the steam generators was assumed
to be proportional fo the 0.8 power of the flow rate. The variation of the film co-
efficient in the reactor core and on the tube (primary salt) side of the primary heat
exchangers decreased with flow, as shown in Fig. 3. The heat conductance across
the tube wall in both exchangers was assumed to be constant.,

The primary and secondary salts in the primary heat exchanger were divided
axially into four equal lumps, with the tube wall represented by two lumps. As
did the primary-salt density, the secondary=salt density varied only slightly with
temperature, and, thus, the masses of the salt lumps were assumed to be equal and
constant. A variable transport delay was included in the hot and cold legs of the
secondary-salt loop to simulate the transport of secondary salt between the primary
heat exchanger and the steam generator.

The secondary salt in the steam generator was axially divided into four
lumps of equal mass, as in the primary heat exchanger. The steam on the tube side
was likewise divided into four equal lumps spatially, but of unequal mass. Under
design conditions the supercritical steam density varied from 34 Ib/ft3 at the feed-
water inlet to 5 Ib/ft3 at the steam outlet. The density of the steam in the lump
nearest the feedwater enirance was taken as the average density in the quarter of

 

3J. MacPhee, " The Kinetics of Circulating Fuel Reactors,” Nucl. Sci.
Eng. 4, 588-97 (1938).

 

4Priva’re communication from H. A. MclLain, ORNL.

Private communication from C. E. Bettis, ORNL.
10

the steam generator represented by that lump, or 22.7 |b/ff3. The densities of the
remaining three steam lumps were determined in a similar manner. The axial tem-
perature distribution in the steam was nonlinear also and was calculated from the
enthalpy by assuming that equal amounts of heat were fransferred into each of the
steam lumps from the secondary salt. The specific heat of each lump was then cal-
culated from the enthalpy and temperature distributions. In the model, these re-
sulting design-point values of density and specific heat were assumed to remain
constant during part-load, steady-state conditions and during all transients.

The physical constants used in this simulation are summarized in Table 1.
The various system volumes, masses, flow rates, etc., calculated from the constants
are listed in Table 2. The system equations used are given in the Appendix, Sect. 7.

3. STEADY STATE, PART LOAD OPERATION

The first step in the formulation of a control system to endble the plant to
undergo changes in load was to determine the steady-state, poart-load, temperature
and flow profiles for the plant for loads between 20 and 100%. For the series of
transients included in this report, the steady-state values of the following variables
were fixed at part load: (1) the steam temperature was 1000°F, and (2) the reactor
outlet temperature was a function of load (Fig. 4), i.e., the reactor cutlet tem-
perature was a linear function of load varying between 1125°F and 1300°F for
loads above 50% and between 1000°F and 1125°F for loads below 50%. The pri-
mary~salt flow rate and feedwater temperature remained constant at their design-
point values of 100% flow and 700°F, respectively. With the values of these
parameters fixed, the remaining temperatures and flows, viz., the secondary-salt
hot- and cold-leg temperatures, the reactor inlet temperature, and the secondary-
salt and steam flow rates,were determined from steady-state, heat balance consid-
erations. Figure 4 shows the resulting variations as a function of load. The reactor
inlet temperature varied linearly between 1000 and 1050°F for loads above 50% and
remained constant at 1000°F for loads below 50%. The secondary-salt, cold-leg
temperature varied approximately linearly between 850°F at design point and about
710°F at 20% load. Arbitrary minimum limits for the steady-state, primary- and
secondary-salt temperatures were set at 1000 and 800°F, respectively, to ensure a
margin against freezing. Figure 4 shows that while the primary salt does not violate
this minimum, the secondary-salt, cold-leg temperature decreases below its minimum
of 800°F at approximately 75% load. Steady=-state calculations for this model in-
dicated that, by decreasing the reactor outlet temperature more rapidly with de-
creasing load in the range near 100% load, the secondary=-salt, cold-leg temperature
decreased less rapidly with load and lowered the power level at which it crossed the
800°F minimum. However, since it may be undesirable to decrease the reactor outlet
temperature more rapidly with decreasing load than is shown in Fig. 4, other methods
may be required to maintain the steady-state, cold-leg temperature above its 800°F
11

Table 1. Physical Constants

A. Properties of Materials

 

 

 

Cp p k
Btu Ib~! °F"! b/t Btu hr=! °F~" ¢~
Primary Salt 0.324 207.8 at 1175°F  -——--
Secondary Salt 0.360 117 ot 1000°F  c==em
Steam
726°F 6.08 2.7 eee—
750°F 6.59 1.4 e
850°F 1.67 6.78 e
1000°F 1.1 503 0 emee-
Hastelloy-N
1000°F 0.115 548 9.39
1175°F 0.129  eee-- 11.6
Graphite 0.42 ms e
B. Reactor Core
Central Zone Quter Zone
Diameter, ft 14.4 16.9
Height, ft 13 13
Salt volume fraction 0.132 0.37
Fuel B3y
Graphite~to-salt heat transfer
coefficient, Btu hr=! ft=2 °F-] 1065
Temperature coefficients of reactivity, °F"
primary salt -1.333 x 1073
graphite +1.056 x 1073
Thermal neutron lifetime, sec 3.6 x 107
Delayed neutron constants, 8 = 0.00264
8 l;(sec-])

 

i
1 0.00102 0.02446
2 0.00162 0.2245

 

C. Heat Exchangers

 

Primary Heat

 

 

Exchanger Steam Generator
Length, ft 18.7 72
Triangular tube pitch, in. 0.75 0.875
Tube OD, in. 0.375 0.50
Wall thickness, in. 0.035 0.077
Heat transfer coefficients, Btu hr™! ft=2 °F~! Steam Qutlet Feedwater Inlet
tube=side-fluid to tube wall 3500 3080 9210
tube-wall conductance 3963 1224 1224

shell-side~fluid to tube wall 2130 1316 1316

 
12

Table 2. Plant Parameters (Design Point)

Reactor Core

Heat flux 7.68 x 10 Btu/he [2250 Mw(th)]
Primary salt flowrate 9.48 x 107 Ib/hr
Steady state reactivity, p 0.00140
External loop transit time of primary salt 6.048 sec

Zone 1 Zone 11
Heat generation 1830 Mw(th) 420 Mw(th)
Salt volume fraction 0.132 3 0.37 3
Active core volume 2117 ft 800 ft
Primary salt volume 279 i3, 296 ft
Graphite volume 1838 ft 504 £
Primary salt mass 58,074 Ib 61,428 Ib
Graphite mass 212,213 Ib a 58,124 b
Number of graphite elements 1466 553
Heat transfer area 30,077 12 14,206 2
Average primary salt velocity ~4.80 ft/sec ~1.04 ft/sec
Core transit time of primary salt 2.71 sec 12.5 sec

Primary Heat Exchanger (total for each of four exchanges, tube region only)

 

Secondary salt flow rate 1.78 x ]07 Ib/hr
Number of tubes 6020 2
Heat transfer area 11,050 ft
Overall heat transfer coefficient 993 Btu hr™! ft~2 o~
Tube metal volume 30 f
Tube metal mass 16,020 |b

Primary salt (tube side) Secondary salt (shell side)
Volume 57 §13 295 ft3
Mass 11,870 Ib 34,428 Ib
Velocity 10.4 ft/sec 2.68 ft/sec
Transit time 1.80 sec 6.97 sec

Steam Generator (total for each of 16 steam generators, tube region only)

Steam flowrate

Number of tubes

7.38 x 10° Ib/hr
434

Heat transfer area 4,102 Ff2
Tube metal volume 22 #3
Tube metal mass 12,203 Ib

Steam (tube side)

Secondary salt (shell side)

Volume 20 £3 102 ft3
Mass 235 b 11,873 Ib
Transit time 1.15 sec 9.62 sec
Average velocity ~62.8 ft/sec 7.50 ft/sec
13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1300 //
1200 /‘/REACTOR OUTLET o
ul Ve
// TEMPERATURE g
./ ~
£100 g HOT-LEG 0.8 =
o = — TEMPERATURE 2
- " %
o // :
E ey e
< -—-—-"""__74 S
5 1000 | A REACTOR INLET TEMPERATURE 4, S
o I / [ I V.0
= / -
L SECONDARY-SALT FLOW S
— ] =
— v
/ é
900 9_45
o
/ <
// o

800 0.2
o1
1 COLD-LEG TEMPERATURE
/,
——
,.....---1-"""'
700 0
0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

FRACTIONAL LOAD

Fig. 4. Steady-State Temperatures and Flows as Func

tions of Load,
14

minimum at the lower power levels. Such methods are: (1) increasing the steam
temperature above its 1000°F design point as the load decreases, with subsequent
attemperation of the steam with injected feedwater; (2) increasing the feedwater
temperature above its 700°F design point as the load decreases; and (3) reducing
the number of steam generators in use as the load decreases. If valves or bypasses
are considered for use in the salt systems, other methods may prove feasible as well.

Further investigations of steady-state, system temperatures and flows are
being carried out, including studies of off-design conditions in the steam generator.
In the present analog model, insufficient machine time was available to adjust the
model to include a variable steam or feedwater temperature with load, and insuf-
ficient equipment was available to include more than one steam generator.

4. CONTROL SYSTEM

The objective of the load control system used in this study was to maintain
the temperature of the steam delivered to the turbines at a design value of 1000°F
during all steady-state conditions and within a narrow band around this value during
plant transients. The rudimentary control system used in this simulation is shown
in Fig. 5. It consisted of a reactor outlet temperature controller similar to that used
successfully in the MSRES and a steam temperature controller.

Steam temperature control was accomplished by varying the secondary-salt
flow rate. This method was chosen because of the relatively tight coupling which
existed between steam temperature and secondary-salt flow rate. The measured
steam temperature was compared with its set point of 1000°F, and any error caused
the secondary-salt flow rate to change at a rate proportional to the error if the
error was 2°F or less. If the error was greater than 2°F, the rate of change of the
secondary-salt flow rate was limited to its rate of change for a 2°F error, which was
approximately 11%/min. The reason for imposing this limit is discussed in Sect. 5.1.

To control the reactor outlet temperature, an external, plant-load demand
signal was used to obtain a reactor outlet temperature set point. The outlet femper-
ature set point versus load demand was the same as that for the steady-state, reactor
outlet temperature versus load in Fig. 4. The measured value of the reactor inlet
temperature was subtracted from the outlet temperature set point, and, since the
primary-salt flow rate was constant, a reactor (heat)-power set point was generated
by multiplying this AT by a proportionality constant. The reactor-power set point
was a function of inlet temperature during a transient and, thus, a function of

 

6
J. R. Tallackson, MSRE Design and Operations Report, Part IIA: Nuclear
and Process Instrumentation, ORNL-TM-729 (February 1968).

 

 
 

 

 

 

 

 

 

 

 

 

 

REACTOR

 

 

 

Tri

15

 

 

 

 

PDEMAND

 

 

 

 

 

 

 

+ Tstg,y1000)

Tst

 

 

 

 

 

 

+ s
7 Tro
Tri set f
Fs -
Th
of 1]
PRIMARY Fe STEAM
HEAT GENERATOR
EXCHANGER 7
2 Pen—
i Tc

 

 

 

J

 

(Fst

 

 

 

 

 

 

 

 

T00°F

Fig. 5. Simulation Model of Plant and Control System.

 
16

dynamic load. The measured value of reactor power (from neutron flux) was compared
with the reactor-power set point, and any error was fed to the control rod servo for
appropriate reactivity adjustment. Under normal conditions, the control rod servo
added or removed reactivity at a rate proportional to the reactor-power error if the
error was 1% or less. If the error was greater than 1%, the addition or removal

rate was limited to the rate for a 1% error, which was about 0.01%/sec. This max-
imum rate was encountered only during the studies of reactivity transients. The
maximum magnitude of reactivity that the simulation allowed was +1%.

An example of the action of the conirol system during a load change is given
in Sect. 5.1. The equations for the simulation are given in the Appendix, Sect. 7.

To obtain more realistic transient results from the simulation, the following
limits were imposed on several of the system variables:

1. The secondary-salt flow rate was limited to a range from 10% to 110% of the
design-point flow rate.

2. The maximum steam flow rate was limited to 110% of the design-point flow rate.

A 5-sec first-order lag was used between the plant-load demand signal and the

steam flow rate in the steam generator.

w

5. RESULTS

5.1 Load Demand Changes

5.1.1 Load Change of 10%/min

 

Various load change transients were investigated, including a change from
100 to 50% load demand at a rate of 10%/min. After equilibrium had been estab-
lished at 50%, the load demand was increased to 100% at the same rate. The re-
sults are shown in Fig. 6.

The load demand signal reduced the steam flow rate to 50% of full flow at
very nearly the same rate as the load reduction rate.

The reduction of the steam flow rate increased the fransit time of the steam
through the steam generator, and the steam temperature rose. This rise was com=-
pared with the steam temperature set point of 1000°F, and the resulting error signal
reduced the secondary-salt flow rate. Less heat was thus transferred into the steam
generator, and the rate of the steam temperature rise was reduced. The increased
transit time of the secondary salt in the steam generator tended to cause a reduction
in the secondary-salt, cold-leg temperature. Since the steady-state, secondary-
salt flow rate and temperatures decreased with decreasing load for this control
(%) (%)

)

(%

(% 8k /k )

(°F) (°F)

{°F)

17

 

 

 

 

12= ] T -
100 jk\hk_% E 2N |
e T LOAD DEMAND | LT
| [ ] L] 1] g_ [ n
0 _ %’ i ] —+

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

125

 

12%

   
 

SALT FL
. —h .

 

1050

1000

 

950
15

  
 

1300

1050
1150

1050

   

950
sec—» 0

    

200 1 200 300
min —== ¢ 10 1

TIME AFTER START OF CHANGE

00

ugr—

Fig. 6. Load Demand Change from 100% to 50% at 10%/min.
18

scheme, the new steady-state, 50% load conditions were assumed quickly for this
transient when the demand reached steady state. The maximum steam temperature
error of ~10°F could be reduced by increasing the rate at which the secondary-salt
flow rate would be allowed to change for a given steam temperature error. This

rate was limited to about 11%/min for a steam temperature of 2°F or more. When
this limit was relaxed or eliminated and faster changes of salt flow rate were allowed
to occur, the flow rate tended to undershoot its new steady-state value, and con-
siderable time was required for the salt flow rate to allow the system to come to
equilibrium.

The load demand signal also reduced the reactor outlet temperature set point
175°F, i.e., from 1300°F at full load to 1125°F at 50% load at a rate of 35°F/min.
As shown in Fig. 6, at the time that the load demand signal reached the 50% level
the reactor inlet temperature had dropped to about 1010°F. Subtraction of this mea-
sured reactor inlet temperature from the outlet temperature set point of 1125°F yields
a AT of 115°F. Since the reactor AT at full load was 250°F, this reduced AT cor-
responded to a reactor power set point of 46%. Therefore, a slight amount of pos-
itive reactivity was added to start the reactor power upward towards 46%. The re-
actor inlet temperature momentarily increased during this transition, but then it
continued to decrease, since the system was being cooled down by the load ( the
load was at 50% and the reactor power was at 45.5%). As the reactor inlet tem-
perature approached 1000°F, the AT between the outlet temperature set point (now
constant at 1125°F) and the measured inlet temperature approached 125°F, and
thus the reactor power set point approached 50%. If the reactor inlet temperature
had dropped below T1000°F, the reactor power set point would have been greater
than 50%, and the reactor power would have been raised momentarily to supply
additional heat to the overcooled primary salt. Fig. é indicates that for this tran-
sient no undershoot in reactor inlet temperature was experienced, and the system
stabilized quickly at 50% load. A reactor inlet temperature of 1000°F at 50% load
with 100% flow of the primary salt implies a reactor outlet temperature of 1125°F,
which, of course, is the same as its set point. In fact, the measured reactor outlet
temperature in Fig. é closely followed the change in its set point.

The fransient encountered during the increase in load to 100% at 10%/min
was equally well behaved. The steam temperature was controlled to within 7°F of
its T000°F design point by the increasing secondary-salt flow rate. Previous
studies! indicate that when increases in load were begun with the secondary-salt
flow rate initially near 100%, the load could be increased only very slowly if the
steam temperature was to be closely controlled. This was due to the small increases
allowed in the secondary=salt flow rate. (The flow rate was limited to 110% of full
flow.) In the present case, however, since the secondary-salt flow rate was re-
duced at reduced loads, larger increases were allowed in this flow rate, which per-
mitted control of the steam temperature during faster load increases. For this rea-
son, when the off-design, steady-state system profiles are investigated further,
reduced secondary=-salt flow rate at reduced loads should be considered.
19

5.1.2 Load Change at 5%/min

 

A load change at a rate of 10%/min is considered a relatively severe one
for a large steam plant. Under normal operating conditions, load change rates of
less than 5%/min are more usual. Figure 7 shows the transient results for a load
demand change from 100 to 50% of full load at a rate of 5%/min, with a subsequent
increase in load demand, after equilibrium had been established, fo full load at the
same rate. The maximum steam temperature error during the load reduction was de-
creased to 2°F. During the load increase, the error was held to within 2°F until
the increasing secondary=-salt flow rate reached its 110% limit. At this point the
steam femperature began to decrease and the error reached a maximum of about 5°F.
After the load demand reached 100% and the secondary-salt temperatures continued
to rise, the steam temperature increased to 1000°F. As the steam temperature tended
to exceed 1000°F, the secondary-salt flow rate decreased from its 110% limit and
maintained the temperature at 1000°F.

For the fransients described above, the magnitudes and rates of change of
temperatures and flow rates during the transient were determined essentially by the
rate of change of the load and the steady-state, temperature and flow profiles chosen
for this simulation. This indicates that the final choice of steady-state, temperature
and flow profiles may greatly affect the rate at which the load can be changed on
the salt systems for normal operation. This should be considered in further steady-
state investigations.

The results of these and the following transients are summarized in Table 3.
Listed in the table are the values of the maximum magnitude of the deviation from
the initial steady~state of a system variable and the maximum rate of change of
that variable. The values listed are the maxima encountered at any time during
the transient; they are not necessarily initial rates of change or differences in steady-
state magnitudes. The values in most cases are taken directly from the figures and
are intended only as an aid in interpreting the analog curves and as an order~of-
magnifude estimate of the kinds of variations encountered in the transient cases in-
cluded in this report. Obviously, any change of the conditions under which these
curves were obtained would likely alter these values.

5.2 Primary Flow Transients

5.2.1 Step Loss of One Pump

 

Three cases were studied involving transient perturbations in the primary-
salt flow rate. The first was an attempt to simulate the sudden (step) loss of one of
the four primary-salt pumps. This case could not be simulated directly because the
model of the plant included only one primary heat exchanger. Therefore, the loss
of one of four pumps was approximated in the following way. The primary-salt
(%)

(%) (%)

(%dk/k)

(°F)

(°F):

(°F)

20

125 , -
100 LOADDE?AND_

125
100

125
100
SECONDA

0.125

~0.125
1050

1000

950
1550

1300

1050
1150

MPERATURE

1050 -

950 _ ’
sec— 0 200 | 400 sqo 800 | 1000 1200 0O 200 | 400 6?0.
min —e § 10 15 20 5 10

TIME AFTER START OF CHANGE

Fig. 7. Load Demand Change from 100% to 50% at 5%/min.

00

 

15

 

     

1000
Table 3. Maximum Magnitude and Rate of Change of System Temperature, Flow Rate, and Reactivity During Transients

 

LOAD DEMAND CHANGES

FLOW RATE TRANSIENTS

REACTIVITY STEPS

 

 

Primary Flow Loss of Loss of
Reduction to  Loss of Primary Loss of  Secondary Flow +0. 15% from 25%
100 to 50% 50 to 100% 100 to 50% 50 to 100% 75% as Primary Flow and Lo%d Secondary and Load +0. 15% from Power Level with
Varicble at 10%/min  at 10%/min  at 5%/min ot 5%/min Step Flow®  Reduction®r Flow® ReductiondsP -0.2% 25% Power Level No Control Reactivity

Reactor Qutlet

Temperature, °F -175 175 =175 175 12 100 -250 -30 -320 -100 100 592

Rate of Change, °F/sec -0.56 0.56 -0.27 0.27 10 13 13 4.4 17 ~36 50 X]
Reactor Inlet

Temperature, °F -50 50 =50 50 ~200 =220 210 135 =40 56 580

Rate of Change, °F/sec -0.15 0.17 -0.09 0.16 1.3 -8.3 -8.8 20 20 -5.9 14 19
Sec-Salt Hot-leg

Temperature, °F -60 60 -&0 &0 - - - - -- ~24 65 >350

Rate of Change, °F/sec  -0.22 0.17 -0.17 0.20 - - - - - -1 9.7 13
Sec=Salt Cold~Leg

Temperature, °F -80 80 -80 80 - - - - -- -4 -15 -40

Rate of Change, °F/sec  -0.36 0.28 0.18 0.18 - - - - -- 7. 0.48 0.67
Steam

Temperature, °F 10 -7 2 -5 -- - e - - -32 28 195

Rate of Change, °F/sec -1.0 0.30 D0.1 -0.09 - -- -- -- - -3.4 2,2 5.0
Sec~Salt Flow Rate

Magnitude, % -58 60 -56 63 - 10 10 =90 =90 10 =6.5 -12

Rate of Change, #/min  -11 1 -9 " - 1 " -600 -600 1 i 1
Control Reactivity

Magnitude, % sk/k ~0.06 0.06 -0.06 0.05 ~0.025 =0.21 ~0.4 -0.063 -1.0 0.22 -(.28 0

Rate of Change, $/sec  -0.0002  0.0004  -0.0001  0.0001 .01 -0.01 0.0 -0.01 -0.01 0.0 0.01 0

 

%Flow rate decreased to 10% at a rate of 10%/sec.

b

Load demand reduced to 20% at 20%/sec initiated 5 sec after initiation of flow reduction.

td
22

flow rate in the reactor core was reduced by 25% as a step while a constant, full
flow rate was maintained in the primary heat exchanger. The transit time of the
primary salt through the core in the neutron kinetics equations was increased as a
step, but the transit time of the salt through the loop external to the core was
maintained constant.

The results of such a transient are shown in Fig. 8. The load demand on
the plant was maintained at 100% and, thus, the reactor outlet temperature set
point at 1300°F. The proportionality constant between the desired reactor AT (i.e.,
the measured reactor inlet temperature subtracted from the reactor outlet tempera-
ture set point) and the reactor power set point was directly proportional to the pri-
mary-salt flow rate and, thus, was also decreased as a step by 25%. Therefore,
for the same reactor inlet temperature and ocutlet temperature set point, the reactor
power set point decreased 75% upon the step reduction of the primary-salt flow rate.
The measured value of reactor power (100%) was compared with the set point, and
the error of 25% caused the control rod servo to insert negative reactivity at the
maximum rate of 0.01%/sec. The reactor power was reduced to 75% in a few
seconds, incurring only a small transient increase in reactor outlet temperature
(12°F max). The total magnitude of control reactivity needed was 0.025% &k/k.
A very small, delayed perturbation of less than 2°F in maximum magnitude was
observed in the steam temperature. In the final steady state, the reactor temper-
atures and the steam temperature were restored to their design-point values. The
load demand was 100% and the reactor power was 75%. However, because of the
way in which the loss of one primary pump was approximated for this case, the 100%
in load demand now refers only to the three remaining, fully operating primary
pumps and associated secondary loops and steam generators. Therefore, the power
delivered to the load under these conditions was 75%.

5.2.2 Loss of All Primary Pumps

 

As a second case of interest, the simultaneous coastdown of all four primary
pumps to an aribtrary minimum flow of 10% was investigated. It was assumed that
some device such as a battery powered pony motor on the primary pumps would
maintain some minimum pumping capacity in the primary loop upon loss of power to
the main primary pump motors. The primary-salt flow rate was thus reduced in all
parts of the primary loop to 10% of full flow at a rate of 10%/sec. The results of
this transient are shown in Fig. 9. The proportionality constant between the de-
sired reactor AT and reactor power set point, described in the previous case, was
decreased with the reduced primary-salt flow rate which produced the reactor power
error signal. Negative reactivity was thus introduced at the maximum rate, and
the reactor power decreased in about 25 sec to about 12%. The maximum amount
of control reactivity required was about =0.21% sk/k. The reactor outlet temper-
ature rose at first to about 1400°F in 15 sec, then decreased to about 1340°F. The
inlet temperature fell below 1000°F in 15 sec. The loss of primary flow while full
(%)

(%)

(% sk/k)

(°F)

23

125

0.1

-0.125

1300

1250
1100

1050

 

1000

TIME AFTER START OF CHANGE (sec)

Fig. 8. Primary Flow Decrease to 75% as a Step.
(%) (%) (%)

{%8k/k)

(°F)

(°F)

24

125
100

125
100

125
100

 

0.25
: ‘ |
CONTROL ROD REACTIV

-0.25
1550

1300

MPERATURE

10504
1300

1050

 

800
0 30 60 90 120 150 180 210 240 270 300

TIME AFTER START OF CHANGE (sec)

Fig. 9. Loss of Primary Flow to 10% af 10%/sec.
25

heat extraction from the steam generators was maintained caused the secondary-salt,
hot-leg temperature to fall sharply. The cold-leg temperature also decreased. The
decreasing secondary=-salt temperatures caused a severe reduction in steam temper-
ature. The secondary-salt flow rate increased to its limit of 110% in an attempt to
maintain the steam temperature at 1000°F, but with little result.

Due to the assumptions concerning the variations in steam properties made in
formulating the model of the steam generator used in this simulation, the useful
range of the steam generator model was greatly limited (see Appendix, Sect. 7).
The model, therefore, simulated only small variations in steam temperature near
1000°F. Loss of primary or secondary flow to 10%, however, effectively decoupled
the reactor from the steam system, and large magnitude changes in the steam gen-
erator had a greatly reduced effect on the reactor system. Only the direction of
these changes was important. The reactor system transient results are therefore in-
cluded for the flow transient cases.

5.2.3 Loss of All Primary Pymps with Load Reduction

 

The third case involved the same loss of primary flow as described in the
second case (Sect. 5.2.2) but with a reduction in load demand from 100 to 20% at
a rate of 20%/sec. This rate was limited by the assumed maximum rate at which
the turbine steam interceptor valves could close. It was assumed that an auxiliary
heat rejection system would be capable of disposing of 20% of the full plant power.
The reduction of load was initiated 5 sec after the primary pump coastdown was
begun so that some delay time would be simulated for the system to sense and eval-
uate the incident. The results are shown in Fig. 10. The proportionality constant
beiween the desired reactor AT and reactor power set point was reduced with the
reduction in flow rate. The reactor power reached 12% in about 20 sec. The
reactor outlet temperature rose to about 1400°F, then decreased to about 1200°F at
60 sec, and continued to decrease at a rate of about 0.3°F/sec. The reactor inlet
temperature transient was much like that in the previous case, as were the transients
in the secondary=salt, hot- and cold-leg temperatures.

The steam temperature initially rose in this transient, since the fast load
reduction dominated the response in the steam generator when it occurred 5 sec after
the primary flow coastdown. However, this did not prevent large sudden decreases
in the secondary-salt temperatures. Some additional corrective action may be re-
quired to prevent such decreases in temperature, such as a reduction of the secondary-
salt flow rate when primary flow is lost.

The results of these primary flow transients indicate a need for further inves-
tigation of the conditions existing in the secondary-salt loops and steam generators
following a loss of primary flow transient. Attention must be paid to the resulting
26

 

®
*
®

125

1
®

0

0.5 Tl LT
= CONTROL ROD
3 ]
w .

-0.5

1550
= 1300
*

 

1050
1300

(°F)

1050

    

800 120 150 180 210 240 270 300

TIME AFTER START OF CHANGE (sec)

Fig. 10. Loss of Primary Flow fo 10% at 10%/sec Followed in 5 sec by Load
Reduction to 20% at 20%/sec.
27

magnitude and rates of change of temperature in this part of the system. The model
of the steam generator used in this simulation was not adequate for such studies
because of the approximations made.

5.3 Secondary Flow Transients

The results of the simultaneous reduction of the secondary-salt flow rate in
all four secondary loops to a level of 10% of full flow (the assumed level of auxil-
iary pumping power) at a rate of 10%/sec are shown in Figs. 11 and 12. In Fig.
11, the load demand was maintained constant at 100%, and in Fig. 12 it was de~-
creased to 20% at a rate of 20%/sec beginning 5 sec after the flow reduction. As
in the case of loss of all primary flow to 10%, the loss of secondary flow decoupled
the reactor from the steam system. For the case of constant load demand, the re-
actor inlet temperature initially rose about 200°F in about 60 sec. Since the load
demand remained at 100%, the reactor outlet temperature setpoint remained at
1300°F. The rising inlet temperature thus decreased the reactor power set point,
and negative reactivity was added to reduce the reactor power. The outlet temper-
ature control system maintained the outlet temperature at 1300°F with a maximum
variation of 30°F.

The reduction in the secondary-salt flow rate with a constant load demand
on the steam generators caused an increase in the difference between the secondary -
salt, hot- and cold-leg temperatures. The hot-leg temperature increased and the
cold-leg temperature decreased. The cold-leg temperature approached the freezing
point. Following the loss of secondary-salt flow, there was no steam temperature
control.

When the load demand was decreased rapidly (20%/sec) to 20% starting 5
sec after the start of the loss of secondary-salt flow (Fig. 12), the initial transients
in system temperatures were, of course, the same as those for constant load demand.
However, when the load demand was decreased, the reactor outlet temperature set
point was decreased to 1050°F for 20% load. Therefore, the reactor outlet temper-
ature controller began to decrease the outlet temperature to 1050°F. The initial
rise in the reactor inlet temperature caused a decrease in the reactor power set point
as before, and negative control reactivity was inserted to decrease power. The
power decreased to about 10% in 30 sec. The secondary-salt, hot-leg temperature
initially tended to rise and the cold-leg temperatures to fall as before, but now the
decreasing reactor outlet temperature decreased the hot-leg temperature after its
initial increase. The cold-leg temperature again approached its freezing point.

A greater amount of negative reactivity was inserted in the reactor during
this transient. The rapidly increasing reactor inlet temperature due to loss of sec-
ondary-salt flow and rapidly decreasing reactor outlet temperature set point due to
the large load demand reduction combined to produce a large sustained reactor
28

power error. As aresult, areactor power of only a few per cent was reached and
sustained for many seconds. The positive reactivity inserted between 160 and 250

sec during recovery caused a sudden increase in reactor power when criticality was
again achieved. The system quickly recovered, however, and the appropriate steady-
state conditions were reached.

5.4 Summary of Primary and Secondary Flow Transients

The loss of salt flow in the primary - or secondary=salt loops decoupled the
reactor system from the steam generating system. The reactor outlet temperature
control system confrolled the reactor outlet temperature following the loss of pri-
mary or secondary flow with or without a subsequent reduction in load demand. If
the load demand was not reduced, the control system maintained the reactor outlet
temperature to within 100°F of its design point of 1300°F. When a reduction in
load demand followed the loss of flow, the controller decreased the reactor outlet
temperature in accordance with the accompanying reduction in its set point (1050°F
at 20% load). The reactor inlet temperature, however, decreased well below the
freezing point of the primary salt upon loss of the primary flow because of the in-
creased transit time of the salt in the primary heat exchanger whether or not the
load demand was reduced 5 sec after loss of flow. Therefore, upon the loss of pri-
mary flow, steps must be taken to prevent areduction in the reactor inlet temper-
ature. Decreasing the secondary-salt flow through the primary heat exchangers to
transfer out less heat would probably be the most effective way to accomplish this.

The secondary-salt temperatures also decreased upon loss of primary flow.
To prevent an undesirably low temperature of the coldHeg, the load must be re-
duced sufficiently fast. Decreasing the secondary-salt flow rate to control reactor
inlet temperature as discussed above aggravates this situation, because the transit
time of the secondary salt through the steam generator is increased, which further
lowers the secondary~-salt temperatures. Upon loss of primary flow, then, the sec-
ondary-salt flow rate must be decreased to prevent a low reactor inlet temperature,
and the load must be reduced sufficiently fast to prevent low secondary-salt cold-
leg temperatures.

Upon loss of secondary=salt flow to 10% the reactor inlet temperature tended
to increase and remain above 1050°F when the load demand was not reduced (i.e.,
a constant outlet temperature set point). When the load was reduced, the inlet
temperature remained above 260°F.

Loss of secondary=salt flow rate produced undesirable decreases in the sec-
ondary-salt cold-leg temperatures. Therefore, as in the case of loss of primary flow,
the load must be reduced at a rate sufficiently fast to prevent freezing of the sec-
ondary salt when loss of secondary salt flow rate occurs. Some additional control
action may also be required to maintain the reactor inlet temperature above 1000°F.
(°F) (% &k/k) {%) (%)

(°F)

125
100

125
100

T T T T T [T T
| |1 .. .| CONTROL ROD REACTWITY| =
O 4ot — - fiz‘ } 4 ; ‘ 4 +(.fl; z ,;,,4,,1_'_
; cf L4t | b Cono
—fi;_,-:-——’-—*i‘ff’ Cog :
. | Loy

29

DARY-SALT FL
NERER

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.125

1300

1050
1300

10

800

0

RINLETT Ty

30 60 90 120 150 180 210 240 270

Fig. 11. Loss of Secondary Flow to 10% at 10%/sec.

 

   

 
30

125
100

(%)

 

       
      
      
 

125 -
R POWER
4

i
J

(%)

125
SALT FL

4 to
; :

t
i

(%)

  

wm O

 

1.2

B ; T., L I
= b
= bttt CONTROL ROD REACTIVITY, - T
« Ob—i—— ¢ ¢ - - - b s Ll b

L1 T | b i P
5 + b - i

 

 

 

 

 

 

el

 

i RIS
el et T b e T
1800 T
' ; , TEMPERATURE _
1300 |1+ f b i

 

“
800
1300
T 1050

+

1 1 210 240 270 330 360

     

800 i

TIME AFTER START OF CHANGE (sec)

Fig. 12. Loss of Secondary Flow to 10% at 10%/sec Followed in 5 sec by
Load Reduction to 20% at 20%/sec.
31

5.5 Reactivity Transients

Transients initiated by both positive and negative reactivity excursions were
investigated. The excursions included a negative step in reactivity of -0.2% 8k/k
and positive steps of 0.15% with and without the control rod servo operative. The
positive reactivity steps were investigated from an initial steady-state power level
of 25% to obtain the maximum positive power-excursion range for this simulation.
The maximum reactor power allowable was about 160% due to the scaling chosen
for the simulation. Therefore, the maximum positive power-excursion range for the
simulation was from about 25 to 160%, or a factor of 6.4 in power. Under normal
conditions, the control rod servo added or removed reactivity at a rate proportional
to the reactor power error for errors of 1% or less. Above this value, the addition
or removal rate was limited to its rate at 1% power error, which was about 0.01%/sec.
The maximum magnitude of reactivity which simulation allowed was £1%.

5.5.1 Negative Step of 0.2% sk/k

Figure 13 shows the results of a negative step in reactivity of 0.2% sk/k.
First, the reactor power decreased rapidly to about 38%. Since the load demand
signal remained at 100%, the reactor outlet temperafure set point remained at
1300°F. The reactor inlet temperature did not immediately change upon insertion
of the negative reactivity, and thus the reactor power set point remained momen-
tarily at 100%. The resulting initial power error signal of 62% caused the control
rod to add reactivity to the system at its maximum rate of about 0.01%/sec.

The sudden reduction in reactor power also caused a rapid decrease in the
reactor outlet temperature from 1300 to about 1200°F. After a few seconds delay,
this reduction in the primary-salt temperature appeared as a decrease in the reactor
inlet temperature. When the inlet temperature returned to about 1015°F, the pos-
itive reactivity added by the control rods and the negative primary-salt temperature
coefficient had returned the reactor power to about 115%. The reactor power set
point for this inlet temperature was 114%, since the outlet temperature set point
remained 1300°F during the entire fransient. Therefore, the reactor power error
had changed sign, and the control rod now began to add negative reactivity to the
system. As the reactor inlet temperature approached 1050°F, the reactor power
set point approached 100%, and the system slowly returned to design-point conditions
with a control rod reactivity of +0.2% to cancel the ~0.2% inserted.

The effect of the reduction in the primary-salt temperatures appeared as
reduction in the steam temperature of about 32°F, which was delayed about 15 sec
owing to the transit time of the secondary salt between the primary heat exchanger
and the steam generator. The steam temperature controller increased the secondary-
salt flow rate at its maximum rate of about 11%/min in an attempt to return the steam
temperature to 1000°F. This flow rate, however, had an upper limit of 110% of
32

full flow. When this limit wos reached, further increases in steam temperature were
accomplished only by increases in the secondary-salt temperatures. When the steam
temperature reached 1000°F and tended to exceed this level, the secondary-salt
flow rate began to decrease from its 110% limit, maintaining the steam te mperature
at 1000°F. The maximum system temperature deviations and maximum ratfes of
change of temperatures encountered during this transient are summarized in Table 3.

5.5.2 Positive Step of 0.15% sk/k

 

Figure 14 shows the results of a positive step in reactivity of 0.15% from an
initial power of 25%. The reactor power increased rapidly to about 144% while the
control rod added negative reactivity at its maximum rate. The sudden increase in
the reactor power caused a rapid increase in the reactor outlet temperature of 100°F
from its initial value of 1063°F. An increase in the reactor inlet temperature of
56°F from its initial value of 1000°F followed. When the inlet temperature returned
to 1040°F, the reactor power had decreased to 8.5%. Since the reactor outlet tem-
perature set point was constant during this transient at 1063°F, the reactor power
set point at this time was 9%, and, thus, the control system began to add pesitive
reactivity to the system to increase the reactor power. As the inlet temperature
approached 1000°F, the power set point approached the initial level of 25%. The
temporary increase in the reactor inlet temperature beginning at approximately 70
sec was due to the decrease in the secondary-salt flow rate which was attempting
to control the delayed response in the steam temperatfure. The increasing reactor
temperatfures produced an increase in the steam temperature, which was delayed by
about 65 sec because of the transit time of the secondary salt between the heat ex-
changers at the initial 22% flow rate. The steam temperature rose to about 1028°F
before the decreasing secondary-salt flow rate returned it to 1000°F. The relatively
long, secondary-salt loop transit time reduced the capability of the secondary-salt
flow rate to control the steam temperature, and several oscillations were allowed to
occur before the system returned to normal steady-state conditions at 25% power
level. The total excess energy added to the system by the reactor power “pulse"
from the initial power rise to the point at which the power first returned to the 25%
level was approximately 13,000 Mw~sec. The maximum system temperature devia-~
tions and maximum rates of change of temperatures encountered during this transient
are summarized in Table 3.

5.5.3 Positive Step of 0.15% &k/k with Control Rod Servo Inactive

 

A positive step in reactivity of 0.15% was also inserted with the power level
at 25% and with the confrol rod servo inactive; that is, no control reactivity was
added or subtracted from the system at any time. Only the temperature coefficients
of reactivity were allowed to control the transient. The coefficients used in the
simulation were =2.4 x 1072 per °C for the primary salt and +1.9 x 1072 per °C for
the graphite. The results of this fransient are shown in Fig. 15. The reactor power
33

125

100

ac-
el
=
o
o
o
o
- -
had

i

(%)

o

v
o

8

 

(%)

0.25

o
=
o
|
o
-t
el
o
o
=
B -
x-

 

<

(%)

=0.25

0.25

_

o
=
=
P
-
-k
hid
as
-t
=
oac
—
a
o=
(=]

 

o

%)

-0.25

1051

STEAM TEMPERATURE .|

8

N

28

had
-
| ]
-
R
E
b
o
e
il
anad
o
-
o
as
<
P
<
-
il
o=

 

8
2

[40]

g3

ad
o
=
[
-
s
(Y9
B
xE
il
—
o
i
L

REAC

[4o)

 

 

 

 

 

 

 

 

 

 

 

 

'

Co 1

"7 SECONDARY-SALT Bfilflfi-filffi TEMPERATURE |~
H
|
[

i ,’-:._...__: oo .

 

 

 

 

 

 

 

 

250

100

50

 

 

200

150

D
TIME AFTER START OF CHANGE (sec)

Fig. 13. Input Reactivity Step of -0.2%.
34

 

 

 

 

 

 

 

 

 

 

 

 

 

-
; —
i . e e et e}
N — 34 R — —_— . . + ——
bad . o]
=" - _

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mw.fl z — |
S . _.“| - .
- S N

; T
= = t-ed -]
[ 4 ol T -

 

 

 

 

i i s g
e e

1
i
;
E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

%

 

 

|

STEAM TEMPERATURE

et L LS L L

o

L

 

 

 

 

 

 

 

 

 

 

 

 

T Tl
ot Y o
T T .;._.@..._ :
[ 1o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+— s
. P e
- e P —
C e e -
—_ -

 

 

 

 

 

 

l
|
¥
i
|
{
|

 

 

 

| 'SECONDARY-SALT COLD-LEG TEMPERATURE

el

.....

 

.
.
-t .
..... — .
" .
- e
— +

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

150 200 250 300

T
TIME AFTER START OF CHANGE (sec)

 

 

(%]

[~

125

(%]

(%)

 

850 1 -

(46])

600

Fig. 14. Input Reactivity Step of 0.15% from 25% Power Level.
35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[ T iiv..l_r.x.z-l.,l,zfiyflfi [" T TH
200( | || REACTOR POWE ‘GL._*. | l |
= ot TR
= é T L |
o FEEEE dhadedir T 1
125 T T T LTI T 1 T
_ SECONDARY-SALT FLOW RATE
) PRERS L ULl
= TR L T ‘
o LI L 1“~f+r% L
. 025 1T 11 { T ] T !
=T T AT
0 1;” TINPUT REACTIVITY‘:, i
ot

 

 

 

 

 

 

 

 

 

 

 

 

T
AM TEMPERATURE

(°F]

 

o EACTOR QUTLET TEMPERATURE, .
2 INLET TEMPERATURE

6 5 100 1% 200 25 300
TIME AFTER START OF CHANGE (sec)

Fig. 15. Input Reactivity Step of 0.15% from 25% Power Level with No
Control Red.
36

reached a peak of about 169% before the negative reactivity added by the increcse
in the primary-salt temperatures was sufficient to terminate the excursion., The re-
actor autlet and inlet temperatures increased to a maximum of about 1655 and 1580°F,
respectively, at about 200 sec, which represented increases of 592 and 580°F from

their initial steady-state values. The steam temperature increased to about 1150°F
at about 115 sec in its delayed response because of the secondary-salt transit time.

When the steam temperature error occurred at about 65 sec, the secondary-salt flow
rate decreased in an attempt to reduce the steam temperature, since this part of the
control system was still operative. However, a lower limit wos placed on the sec~

ondary-salt flow rate at 10% of full flow. The steam temperature was decreased by
the decreasing flow rate until this limit was reached, after which the steam temper~
ature began to rise again to a maximum of 1195°F at 340 sec.

6. TRANSFER FUNCTION

The full-power transfer function relating small input reactivity perturbations
to reactor power with constant power removal from the system was measured on the
plant simulation and calculated by the use of a digital computer code. A sine wave
oscillator was used to introduce small reactivity perturbations in the analog com-
puter simulation, and the resulting reactor power peri’urbohons were recorded. The
magnitude of the input reactivity was about 2 x 107 3 sk/k peak-to-peak. The
magnitude of the power oscillations varied between 0.4 to 1.5% peak-to-peak in
the frequency range of 0.01 to 2.0 Hz. The measured values of transfer function
are plotted in Fig. 16.

The digital code used to calculate the transfer function from the same set of
simulation equations was SFR-3.7 The calculated resulfs are also plotted in Fig. 16
for frequencies in the range of 0.0016 fo 2.0 Hz. The phase shift versus frequency
is also plotted.

SFR-3 was also used to calculate the same transfer function but with later

~ values for the temperature coefficients of reactivity. The values used in the simu-
lation and in the calculahons described above were -2.4 x 1072 sk/k/°C for the
primary salt ond +1.9 x 1072 sk/k/°C for the graphite. The later values were
-3.52 x 1072 sk/k/°C for the primary salt and +2, 47 x 1072 sk/k/°C for the graph-
ite, or a net isothermal coefficient of -1.05 x 1072 sk/k/°C which is somewhat
greater in magnitude than before. The resulting transfer function for this case is also
shown in Fig. 16. Due to the considerably larger isothermal coefficient, the low-
frequency portion of the gain is somewhat lower. This effect fends to increase the
linear stability of the system.

 

7T. W. Kerlin and J. L. lucius, The SFR-3 Code--A Fortran Program for

Calculating the Frequency Response of a Multivariable System and Its Sensitivity to
Parameter Changes, ORNL-TM=1575 (June 30, 1965).

 

 

 
PHASE (deg)

37

 

 

 

 

 

 

 

 

 

 

 

4x103
L — ANALOG SIMULATION
B — e ——— SFR-3
. SFR-3 WITH LATER VALUES
i OF TEMPERATURE COEFFICIENTS
I /\ | OF REACTIVITY
= o
\
5 10% — '
3 [ C “&;C‘ :
== - \ '9‘3{:\\
— a / \ STl A\
z [ / \ /7
< - \_,/
o - /
_ , /
i /
- /
_ / \
I~ 1
o / \
- /
- /
10 Dol Lt Lo gl L Lt tiid
1077 10 2 10! 1 10 10¢
FREQUENCY w (radians /sec)
120
—— ©—— ANALOG SIMULATION
Loo —— — —— SFR-3
| L e SFR-3 WITH LATER VALUES OF
- T TEMPERATURE COEFFICIENTS OF
80 |- “ REACTIVITY
\
N\
60 t— \
\
40
20
0
20
40 -
60
80
b. Phase
e ettt v v b L
1073 1072 107! 1 10 102

FREQUENCY w (radians /sec)

Fig. 16. Full-Power Transfer Function.
38
7. APPENDIX: ANALOG SIMULATION MODEL

7.1 Heat Transfer Model

A spatially lumped parameter model was used to describe the plant heat
transfer system. The model is shown in Fig. 2.

7.1.1 Reactor Core
For the graphite lumps

dT

M C hAT-—T +k P . 1
gpgdf ( 9) g r M

For the primary salt lumps

dT

P _ i}
Mcfdf FCF( T)+h A(T Tp)+krPr, (2)

where

Tg = graphite temperature,

T, = primary-salt temperature,

'IE? inlet temperature to fump,
specific heat of primary salt,

Cpg = specific heat of graphite,

= mass of primary-salt lump,

mass of graphite lump,

i

0O
O
- .
1!

&F

hfg = graphite—to—primary-salt heat fransfer coefficient,

A. = heat transfer area,

P = reactor heat generation rate,

kg = fraction of fission heat generated in graphite lump,

k. = fraction of fission heat generated in primary-salt lump,
F1 = primary=salt mass flow rate in lump.

The reactor autlet temperature T, was given by

Tro = 0.814T 4 + 0.186T (3)

p6 I
since 81.4% of the primary salt flowed through zone I and 18.6% through zone II.
39

7.1.2 Primary Heat Exchanger

 

For the primqry salt

dT
£ = -T)+ -
MGCf I Flcpf(Ti Tp) hFAp(Tt Tp) . (4)
For the tube walls
dTi-
— = - + -
Mtcpf T thp(Tp Tf) hsAp(Ts Tf) ’ (5)
and for the secondery salt
dT
_> = - + -
Mscps T F2Cps(Ti Ts) hspAp(Tf Ts) , (6)
where
T = tube wall temperature,
T, = secondary=salt temperature,
Cpt = specific heat of tube wall metal,
Cps = specific heat of secondary salt,
Mt = mass of tube wall lump,
M = mass of secondary-salt lump,
hf = primary=-salt—to—tube-wall heat transfer coefficient,
hsp = tube-wall—+to—secondary-salt heat transfer coefficient,
Ap = heat transfer areq,
Fo = secondary=-salt mass flow rate.

7.1.3 Steam Generator

For the secondary salt

dT
— = -T)+ -
Mscps dt FZCpS(Ti Ts) Ifl'.«ss'fi‘s(.ri' Ts) ’ 7)

For the tube wall

dT

o _ _
Mfcpf dt hssAs(Ts Tf) ¥ I"wAs(Tw Ti') ’ (8)
40

For the steam

dT
w
_— = - + -
chpw 5 Fs C (T T ) h A(T Tw)' (9)
where
T,, = steam temperature,
Cpw = specific heat of steam,
My = mass of steam lump,
hss = secondary-salt—to—tube-wall heat transfer coefficient,

I

tube-wall~to—steam heat transfer coefficient,
heat transfer area,
steam mass flow rate.

!
I

Transport delays were used in the secondary-salt hot- and cold~legs to account
for the transit time of the secondary salt between the primary heat exchanger and the
steam generator. Thus, from Fig. 2,

T, = Tt +m), (10)
Tg = T(t+1). (11)

The values used for 1y and = were 14.5 and 11.9 sec, respectively, at design-
point flow rate of the secondary salt and were inversely proportional to that flow
rate at off-design conditions. No transport delay was included for the flow of pri-
mary salt between the reactor core and the primary heat exchanger.

Heat fransfer coefficients in the above equations were calculated as follows.
In the primary heat exchanger, the term h¢ in Eqs. (4) and (5) included the film
coefficient inside the tube and one-half of the tube~wall conductance. The other
half of the tube-wall conductance and the ocutside-film coefficient were included in
the term h,, in Egs. (5) and (6). When the flow rate of the primary salt was changed,
the film coefficient varied with flow, as shown in Fig. 3, while the tube-wall con-
ductance was maintained constant. Similarly, the film-coefficient part of the term
hg,, varied as the 0.6 power of the secondary-salt flow rate, and the tube-wall-
conductance part was constant. The heat transfer coefficients h cmd h in the
steam generator were similarly calculated. W

The heat transfer driving force AT used in the above equations is indicated
by the dashed lines in Fig. 2. In each case, the AT for a salt (or steam) lump with-
out a dashed line was that indicated by the dashed line on the immediately preceding
(upstream) lump.
4]

In the Egs. (1)-(9) the masses associated with each graphite, salt, and steam
lump were constant during all steady-state and transient conditions. So also were
the values of the specific heats of each lump. The temperatures, flow rates, and
heat transfer coefficients were allowed to vary.

The masses of the graphite and salts were equally divided among the appro-
priate lumps. For example, the total mass of the primary salt in zone [ was equally
divided among lumpsp1, p2, p3, and p4 (Fig. 2). In the case of the steam, the
mass of each lump was calculated from the design-point conditions under the assump-
tion that equal amounts of heat were transferred into each of the four lumps., The
specific heat of each lump was similarly calculated. The values of mass and specific
heat were then assumed to be constant under all steady-state and transient conditions.
This assumption greatly limited the range of the steam generator model, and any
transients involving large steam-temperature variations are subject to error,

7.2 Nuclear Kinetics Model

A two-delayed neutron group approximation of the circulating-fuel, point-
kinetics equations was used for the nuclear behavior of the core. The equations were:

dP

_r-2-8
P +2,Cy +2,C

3F 7 1 (12)

2 I

1 1 e M17L
- = —P -G -;-r-:c] + - Cilt =) (13)

 

C

 

1
- = G =G - 7)), (14)

Cc C

3~ 7 T %2

o = o, + ?aiATpi + J (15)

where

reactor power level,

modified delayed-neutron precursor concentration,
delayed-neutron fraction,

delayed=-neutron precursor decay constant,

£ = neutron generation time,

(l

> ™ () U
i
42

T. = fransit time of primary salf through core,
T = transit time of primary salt through external loop,
o = reactivity,
0, = steady-state design point reactivity (associated with flowing fuel),
a; = temperature coefficient of reactivity of core lump pi,
ATp; = variation from design-point temperature of lump pi,

oc = control rod (or other externally introduced) reactivity.

Variation of the primary-salt flow rate through the core varies the value of
the transit times 7. and 7| inversely proportional to flow rate. Provision was made
in the simulation for these variations to endble study of transients in the primary-salt
flow rate. The lag term Ci(i' = ) was also included in the simulation.

The negative temperature coefficient of reactivity for the primary salt was
divided equally among the six primary-salt lumps in the core model. Similarly, the
positive coefficient of the graphite was divided equally among the three graphite
lumps.

Due to the low value of the delayed~neutron fraction for 233U, the gains
associated with the nuclear kinetics equations were among the highest in the simu-
lation. However, a small net temperature coefficient of reactivity required only
modest amounts of reactivity for normal control.

7.3 Control System

7.3.1 Steam Temperature Controller

 

The steam temperature was controlled by varying the secondary-salt flow
rate and, thus, the heat input to the steam generator. An error in steam tempera-
ture caused the flow rate to change af a rate proportional to the error, i.e.,

dF2

- = -o(T, - 1000°F), (16)

where F,, is the secondary salt flow rate, T is the outlet steam temperature, and
a is the controller gain.

The controller gain a used in the simulation was approximately 5.5%/min
change in flow rate for each 1°F error in steam temperature for errors of 2°F or
less. For errors greater than 2°F, the rate of change of flow rate was limited to
11%/min. No optimization was carried out to obtain these values, but they
produced reasonably good system response.
43

7.3.2 Reactor Outlet Temperature Confroller

 

The reactor outlet temperature set point was determined by the plant load
demand (Fig. 5). The set point as a function of load demand is given in Fig. 4.
The equations are

= + <
Tro 350 Pdemcmd 950 (0.5<P=1.0), (17)
set
and
= + <
Tro 250 Pdemcmd 1000 0< Pz 0.5, (18)
set
where Troget is the reactor outlet temperature set point, and Pdemcnd is the fractional

plant load demand.

The reactor power-level set point was proportional to the difference between
the outlet temperature set point and the measured reactor inlet temperature, i.e.,

Pr = A(Tro - Tri) , (19)
set sef
where P"sei' is the reactor power level set point, T.: is the measured reactor inlet

temperature, and A is the proportionality constant.

The proportionality constant A was itself proportional to the primary-salt
flow rate, which was maintained constant for all cases except for the studies of loss
of primary flow. In these studies the proportionality constant varied directly with
flow rate in the simulation. The assumption of constant specific heat of the primary
salt is also implied here. If is not necessary to assume constant flow and constant
specific heat in an actual operating confrol system of this type. Additional circuitry
may be provided to compensate for these effects, as was demonsirated in the MSRE
control system (Ref. 6).

A reactor-power-level error was obtained by subtracting the set point value
from the measured value (from neutron flux), i.e.,

e =P -P . (20)

r
set

This power error ¢ was the input signal to a control rod servo described by
the second~order transfer function:

) = 2, @1)
44

where G is the controller gain, w is the bandwidth, and ¢ is the damping factor.

In this simulation the bandwidth was 5 Hz and the damping factor was 0.5.
These values are typical of the kind and size of servo which may be used in this
confrol-rod—drive service. The gain of the controller G was such that, for
le| = 1% of full power, the control reactivity addition or withdrawal rate was about

0.01%/sec, i.e.,

dp

m‘i = 0.01%/sec , (22)

where g is the control reactivity (see Sect. 7.2).
For power level errars greater than 1% of full power, the reactivity addition

or withdrawal rate was limited to 0.01%/sec. Integration of Eq.(22) yields the
value for the control reactivity in the kinetics equations of Sect. 7.2,

ACKNOWLEDGMENTS

The author acknowledges the suggestions and contributions of S. J.
Ditto and J. L. Anderson for the control system design and for improvement
of the system and the model.
45

ORNL-TM- 2927

INTERNAL DISTRIBUTION

1. J. L. Anderson 30.
2, C. F. Baes 31.
3. H. F. Bauman 32.
4, S. E. Beall 33.
5. C. E. Bettis 34,
6. E. S. Bettis 35.
7. E. G. Bohlmann 36.
8. C. J. Borkowski 37.
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14-15. D. F. Cope 62,
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27. P. G. Herndon 76.
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79-80. Ceniral Research Library

T. W. Kerlin

R. B. Korsmeyer

. Lundin
MacPherson

. McCoy

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McNeese
McWherter

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Moore
Nicholson
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APrmMAISCITIRZ
flrru?w>mwk

E. Whotley

M.
J. C. White - A. S. Meyer
L

81. Document Reference Section
82-84. Laboratory Records Depariment
85. Laboratory Records, ORNL R. C.
86. ORNL Patent Office
87-101. Division of Technical Information Extension
102. Laboratory and University Division, ORO
103.

104,

105.
106-107.

108.

46

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Kansas City, Missouri 64114

T. W. Mclntosh, Division of Reactor Development and Technology, U. S.
Atomic Energy Commission, Washington, D. C. 20545

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