ORNL-TM-3102.txt

3% .

 

:‘\'4__,\; -

   

" QASTER

OAK RIDGE NATIONAL LABORATORY

operated by
UNION CARBIDE CORPORATION  NUCLEAR DIVISION
for the

U.S. ATOMIC ENERGY COMMISSION
ORNL- TM- 3102

MSBR CONTROL STUDIES: ANALOG SIMULATION PROGRAM

W. H. Sides, Jr.

NOTICE This document contains information of a preliminary nature
and was prepared primarily for internal use at the Qak Ridge National
Laboratory. 1t is subject to revision or correction and therefore does

not represent a final report.

UISTRIBUTION OF THIS DOCUMENT IS UNLIMITER;
 

 

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, completaeness or
usefulness of any information, apparatus, product or process disclosed, or
represents that its use would not infringe privately owned rights,

 

 
ORNL-TM-3102

Contract No. W-7405-eng-26

INSTRUMENTATION AND CONTROLS DIVISION

MSBR CONTROL STUDIES: ANALOG SIMULATION PROGRAM

W. H. Sides, Jr.

 

This report was prepared as an account of work
sponsored by the United States Government, Neither
the United States nor the United Staies 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-
pieteness or usefulness of any iaformation, apparatus,
produci{ or process disclosed, or represents that its use
waould not infringe privately owned rights.

 

 

 

MAY 1971

OAK RIDGE NATIONAL LABORATORY
Oak Ridge, Tennessee
operated by
UNION CARBIDE CORPORATION
for the
U. 8. ATOMIC ENERGY COMMISSION

SISTRIBUTION OF THIS DOCUMENT IS UNIJMIT}EP
iii

CONTENTS

CIErOdUCION . . e e e e 1
. Description of the Plant and Control System . ......... ... .. . . i, 1
. Simulation of the SysStem .. .. ... e e 7
B MoOdEl .o e e e 7
3.2 System Equations and Analog Computer Program ............ ... ... .. ... L. 9
320 Reactor Core ..o i e e 9

3.2.2 Primary Heat Exchanger ... ....... ... ... ... .. . ... e 15

3.2.3 Steam Generator ..o v ittt c e ettt et e e e e e 19

324 Control SYstem . ..ottt e e e 25
MSBR CONTROL STUDIES: ANALOG SIMULATION PROGRAM

W. H. Sides, Jr.

ABSTRACT

This report describes the mathematical model and analog computer program which were used in
the preliminary study of the dynamics and control of the 1000-MW(e) single-fluid Molten-Salt Breeder
Reactor. The results and conclusions of the study were reported earlier in Control Studies of a
1000-Mwfe) MSBR, ORNL-TM-2927 (May 18, 1970), by W. H. Sides, Ir.

 

1. INTRODUCTION

A preliminary investigation was made of the dynamics and possible control schemes for the proposed
1000-MW(e) single-fluid Molten-Salt Breeder Reactor (MSBR). For this purpose an analog computer
simulation of the plant was devised. In this report the system, simulation model, and analog computer
program are described. The specific transients investigated using this simulation, the results, and the
conclusions were presented in another report.’

For the purposes of the 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 control system. The analog
simulation of the plant consisted of a lumped-parameter heat transfer model for the core, primary 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,

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 a result the requisite quantity of equipment required that the model be severely limited spatially to
minimize 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 feedwater to the steam generators was also held constant.

2. DESCRIPTION OF THE PLANT AND CONTROL SYSTEM

The proposed 1000-MW(e) MSBR steam-electric generating plant consisted of a 2250-MW(t)
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 in diameter and ~13 ft high with a primary-salt volume fraction of 0.132; and an outer zone, an
annular region ~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 2?3U and 232 Th, 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 in 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 entering the core was 1050°F and that at the core outlet was
1300°F. The liquidus temperature 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,

 

1w, H. Sides, Jr., Control Studies of a 1000-Mw(fe) MSBR, ORNL-TM-2927 (May 18, 1970).
PRIMARY

 

 

SALT PUMP
(4)
n""
REACTOR
VESSEL=a|
= | EVEL CONTROL®
9.48 X107 Ib/hr
at 1300°F
PRIMARY
GRAPHITE HEAT EXCHANGER
MODERATOR—" (4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.48 X 10" Ib/hr at 1050°F

Fig. 1. Flow Diagram of MSBR Plant,

ORNL-DVWG 70-8883

   
 
    
 
    
 

SECONDARY
SALT PUMP

(4)

1X 10" Ib/hr STEAM ai 1000°F

— i — . i ety . —— . i o o

l96X10° 1o/hr .
5X10° b/ hr

712 X10" 1b/br at 1150°F

6.16 X 10" Ib/hr at 1150°F

REHEATER
850°F STEAM GENERATOR

 

 

19 @)

REHEAT STEAM at 650°F

 

 

 

The quantities shown are totals for the entire plant.
ORNL DWG. 71-3380

+ PDEMAND

ROD T (1000°F)
DRIVE Y Mset
SERVO

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

&

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P, /D PRIMARY ., STEAM
HEAT GENERATOR j

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EXCHANGER — Bec
REACTOR % °F
- 3
Tei
l ri < I
700°F

Fig. 2. Simulation Model of Plant and Control System.

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. in diameter and were 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 a
rate of 6.30 X 10° Ib/hr. Reference 2 gives a complete description of an earlier, but quite similar, version of
the steam generator and primary heat exchanger.

The load control system used in this study maintained 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.
2. It consisted of a reactor outlet temperature controller similar to that used successfully in the MSRE® 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.

 

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

31 R, Tallackson, MSRE Design and Operations Report, Part IIA: Nuclear and Process Instrumentation, ORNL-TM-729
(February 1968).
To control the reactor outlet temperature, an external plant-load demand signal was used to obtain a
reactor outlet temperature set point. The outlet temperature set point was a linear function of load
demand, varying between 1125 and 1300°F for loads above 50% and between 1000 and 1125°F for loads
below 50%. 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 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 fora 1% error,
which was about 0.01%/sec. The maximum magnitude of reactivity that the simulation allowed was £1%.

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.
Table 1. Physical Constants

Properties of Materials

 

 

 

 

 

Cp p k
[Btulb ™! (°F)7!] (b/ft3) {Btu hr ™! (°F)~! ft 1)
Primary salt 0.324 207.8 at 1175°F
Secondary salt 0.360 117 at 1000°F
Steam
726°F 6.08 227
750°F 6.59 114
850°F 1.67 6.78
1000°F 1.11 5.03
Hastelloy N
1600°F 0.115 548 9.39
1175°F 0.129 il1.6
Graphite 042 115
Reactor Core
Central Zone Outer Zone
Diameter, ft 144 16.9
Height, ft 13 13
Salt volume fraction 0.132 0.37
Fuel 233y
Graphite-to-salt heat transfer coefficient, 1065
Btuhr7! ft72 (°F)~!
Temperature coefficients of reactivity, (°F)~!
Primary salt -1.333 X 1075
Graphite +1.056 X 1073
Thermal-neutron lifetime, sec 3.6 X107
Delayed neutron constants, g = 0.00264
i B; A; (sec™!)
1 0.00102 0.02446
2

0.00162 0.2245

 

Heat Exchangers

 

 

 

Primary
Heat Steam Generator
Exchanger

Length, ft 18.7

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)~1 Steam Qutlet  Feedwater Inlet
Tube-side fluid film 3500 3590 6400
Tube-wall conductance 3963 1224
Shell-side fluid film 2130 1316

 
Table 2. Plant Parameters (Design Point)

 

Heat flux, Btu/hr

Primary-salt flow rate, Ib/hr

Steady-state reactivity, pg

Externatl loop transit time of primary salt, sec

Heat generation, MW(t)

Salt volume fraction

Active core volume, ft3
Primary-salt volume, ft3
Graphite volume, ft3

Primary salt mass, Ib

Graphite mass, b

Number of graphite clements
Heat transfer area, ft?

Average primary-salt velocity, fps
Core transit time of primary salt, sec

Reactor Core

7.68 X 107 [2250 MW(t)]
9.48 x 107

0.00140

6.048

Zone I

1830
0.132
2117
279
1838
58,074
212,213
1466
30,077
~4.80
2.71

Primary Heat Exchanger

Total for each of four exchanges, tube region only

Secondary-salt flow rate, ib/hr
Number of tubes
Heat transfer area, ft?

Overall heat transfer coefficient, Btu hr™! ft =2 (°F)~!

Tube metal volume, ft3
Tube metal mass, 1b

Volume, ft3
Mass, ib
Velocity, fps
Transit time, sec

Primary Salt (Tube Side)

Steam Generator

1.78 x 107
6020
11,050
993

30

16,020

Zone 11

420
0.37
800
296
504
61,428
58,124
553
14,206
~1.04
12.5

 

Secondary Salt (Shell Side)

 

57
11,870
10.4
1.80

Total for each of 16 steam generators, tube region only

Steam flow rate, 1b/hr
Number of tubes

Heat transfer area, ft2
Tube metal volume, ft3
Tube metal mass, lb

Volume, ft3

Mass, 1b

Transit time, sec
Average velocity, fps

Steam (Tube Side)

7.38 X 103
434

4102

22

12,203

295
34,428
2.68
6.97

Secondary Salt (Shell Side)

 

20

235

1.15
~62.8

102
11,873
9.62
7.50

 
3. SIMULATION OF THE SYSTEM
3.1 Model

A spatially lumped parameter model used for the heat transfer system (Fig. 3) consisted of the reactor
core, one primary heat exchanger, one steam generator, the nuclear kinetics, and a control system as shown
in Fig. 2. All 4 primary heat exchangers were combined into 1 and all 16 steam generators into 1.

In the core the primary salt in the central zone was divided axially into four equal lumps, and the
graphite was divided into two. The outer 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 central-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 determined by the heat
generation rate in each zone, so that the temperature rise of 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-delayed-neutron-group approximation of the circulating-fuel nuclear kinetics equations* was
used in the model. This allowed the delayed-neutron precursor concentration term C/(t — 7, ) (see Sect.
3.2.1) to be simulated directly with two of four available transport lag devices. The delayed-neutron
fraction for 232U 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 107° 8k/k per °F, which was divided equally among the six
primary-salt lumps of the core model. The temperature coefficient for the graphite was +1.06 X 107° §k/k
per °F, which was divided equally among the three graphite lumps.

The model 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 exchanger 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 to the 0.8
power of the flow rate. The variation of the film coefficient in the reactor core and on the tube (primary
salt) side of the primary heat exchangers decreased with flow, as shown in Fig. 4. 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/ft* at the
feedwater inlet to 5 1b/ft® at the steam outlet.® The density of the steam in the lump nearest the feedwater
entrance was taken as the average density in the quarter of the steam generator represented by that lump,
or 22.7 Ib/ft?. The densities of the remaining three steam lumps were determined in a similar manner. The

 

#J. MacPhee, “The Kinetics of Circulating Fuel Reactors,” Nucl. Sci. Eng. 4, 588-97 (1958).
>Private communication from H. A. McLain, ORNL.
SPrivate communication from T. W. Pickel, ORNL.
¢ OF CORE T

Tro S— Tss
A

  

Bl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

|
---------- — - e e = —— -——)f————_— e, ——e— r— ey e | e . sttt
ZONE T T ZONE TT i T | [
i PRE SALT| | ' ! PRITSALT SECTSALT ‘ i SECTSALT
- Toa | | | PN se | ss N
| . \ ! \\ | i 1073 |\
| GRAPHITE | PRISALT| | | 4 TUBE r | N
] T '\ | Tps i i Tt M | l
| ™\ |PRi sALT | : | {PRI SALT Nsec sauf | | |sec saLt
| N Tes i | ! Tpe Ts 3 | I Tsg
! ! ' 996
GRAPHITE !
! I (i N
I - | '
i PRI SALT | i I PRI SALT sscsmi l SEC SALT
1 Tpa [ \ : ' Tpe N Ts» , ! Tst N
I PHIT ‘ | | “«| TUBE | | N
. [GRAPHITE [ PRI SALT] , \ | !
! Tg2 \\ i Tos ! | Ttz M ! |
| N PRESAT] | | | [PRISALT e saT || | [SEC sALT
I 4 TPT ' A ' { Tri T l i Tss
1 I ! ! 1 \ 850
I_ _________ — _-J [ —_ — I
| Yy “ I_T._.l Y
it} - 2
| T . W
REACTOR CORE PRIMARY HEAT EXCHANGER STEAM

Fig. 3. Lumped-Parameter Model of MSBR Plant.
ORNL DWG, 71-3378

 

 

 

 

 

 

 

 

 

7
///
L

 

 

1.0 : >
[N /
o

S 0.8 - /
2 //
L

o Vi

< £ //

=y /

w = 0,6 7

S 2 CORE /

=

S e / /" M-PRIMARY
oo / HEAT EXCHANGER
w T 04 /

L. I .

vy //

= O

=" /

'—-

'—..

=L

[T

xr

| .

o

o

'—

L

o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

Fig. 4. Variation of Film Heat Transfer Coefficient with Primary-Salt Flow Rate in the Reactor Core and Primary
Heat Exchanger.

axial temperature distribution in the steam was nonlinear also and was determined from the average
design-point temperatures in each half of the steam generator. The specific heat of each lump was
calculated from the enthalpy and temperature distributions. In the model, these resulting design-point
values of density and specific heat were assumed to remain constant during part-load steady-state
conditions and during all transients.

3.2 System Equations and Analog Computer Program

The spatially lumped parameter model used to describe the plant heat transfer system is shown in
Fig. 3.
3.2.1 Reactor Core. In the graphite the heat transfer equation was:

T

Myi Cpg dt

=hfg Agl(Tp — Tgi)+kgiPr > (1)

where
Ty; = temperature of graphite lump i,

T, = temperature of primary salt lump to which heat is being transferred,

Mgy =M, =mass of graphite lump in core zone I,

M, 3 = mass of graphite lump in core zone I,

Cpg = specific heat of graphite,
10

hfg = graphite-to-primary-salt heat transfer coefficient,

Agy = Agy = heat transfer area of lump in zone I,
Ag3 = heat transfer area of lump in zone II,
kg; = fraction of fission heat generated in graphite lump 7,

P, = reactor heat generation rate.

In the primary salt:

dT,;
Mpi Cpf'?;fl =fF1 Cp]‘{Tpi-—l — Tpt) + hfg Api(Tg — Tpl) + kpiPr s (2)
where
Tpl- = temperature of primary-salt lump i,
Mpy =My =Mpy3 = My, = mass of primary-salt lump in core zone I,

Mp5 =Mp6 = mass of primary-salt lump in core zone II,
Cp F= specific heat of primary salt,
F, =total primary-salt mass flow rate,
f = fraction of primary-salt mass flow rate in zone I,
Apy =Apy =Ap3 = Ay = heat transfer area of lump in zone I,
Aps =A,6 = heat transfer area of lump in zone II,

kp ; = fraction of fission heat generated in primary-salt lump /.

The reactor outlet temperature T, , was given by:

TFO:pr4+(1_f)Tp6‘ (3)
The heat transfer coefficient hg, varied with the primary-salt mass flow rate, as follows:

hg = hrgo Mg s

where %z, is the design-point value of the graphite-to-salt heat transfer coefficient. A diode function
generator was used to simulate the function s, (F', ), which is shown in Fig. 4 labeled “‘core.”

The fraction of the total primary-salt mass flow rate that passed through zone I (and the fraction of the
total heat generated in zone I) was given in Sect. 3.1 as 0.814. The fraction of heat generated in the primary
salt as compared with the graphite in both zones was 91.9% in the salt and 8.1% in the graphite. Thus in
zone II,

kg3 =0.186 X 0.081 =0.0151, 4)
and

kys =k, =0.186 X 0.919 X 0.5 =0.0857 . (5)
11

In zone |,
kg1 = kg2 =0.814 X 0.081 X 0.5=0.0329. (6)

The axial distribution of the reactor heat generation rate in the primary salt in core zone I was assumed to
be a chopped cosine distribution with an extrapolation distance of 8 ft. Then, in the primary salt in zone I,

0.3887 /ro.sx
kp1 =kps =0.814 X 0919(-[0.276« sin x d’x/[o.”(m smxdx) X 0.5 (7)
=0.1749,
0.5 0.5
kyy =kp3 =0.814 X 0919(-[0.38817 s1nxdx/[‘0'2761r smxdx) X 0.5 (8)
=0.1992.

The constant coefficients in the equations were calculated using Tables 1 and 2. Thus in Eq. (1),

 

hrgo g1 _ 1065 Btu X 15,039 ft* X 1b-°F X hr ©)
M1 Cpg  hrft?-°F X 1.06 X 10° 1b X 0.42 Btu X 3600 sec
=0.0998 sec ! ,
where 715, = design-point primary-salt-to-graphite heat transfer coefficient, and
kg1 P _0.0329 X °FX 7.68 X 10° BtuX hr (10)

 

My Cpy  0.4452X 10° Btu X hr X 3600 sec

=1.577°F/sec,

where P,y = design-point power level [2250 MW(t)]. The coefficients in the remaining graphite equations
(i = 2, 3) were similarly calculated.
For the primary-salt heat transfer equation (2) the constant coefficients are

fFio_ 0814X9.48X 107 Ib X hr

 

 

11
M, 0.25X 58,074 1b X hr X 3600 sec ()
=1.476sec™" |
where ', , = design point value of primary-salt mass flow rate,
hfgo Ap1  ~ 8.008 X 10° BtuX Ib-"F X hr 12)

M,y Cpy 1451916 X hr-"F X 0324 Btu X 3600 sec

=0.4729 sec”! |
12

and

kp1 Pro _0.1749 X °F X 7.68 X 10° Btu X hr

Myy Cpr 4704 Btu X hr X 3600 sec

=79.32°F/sec .

The coefficients for the remaining primary-salt equations (f =
The unscaled heat transfer equations for the core were thus

dT, L
272l _ 59998 hfg(Fl) (Tp3 — Tg1)+ 1.577—L

dt PrO
T2 = 0.0998 i (F ) (Toy - Ton)+ 157721

ar OO ) gy~ Tga) + 1. By’
T,y P

—E2= 01722 by (F) (Tys — Ty3) + 1. 3”0P— :
dT F

dlzl = 1_476F_1 (T,; ~ Tp1) + 04729 hyo(F, ) (T, —

10

dT,

Pl 476 (

ar
dT, F

d?3 = 1-476F_1 (Tpa — Tp3) + 04729 hp (F ) (T —

10

dT, F

p4 _ 1 _
b4 1.476_FT0 (T3 — Tpa) + 04729 hpy(F) ) (T
dT
71;5 = 0. 1599 ( — Tys) + 02112 g, (F)) (T3
dT

p6 —
—ps 0. 1599 ( Tpe) + 02112 hey (F ) (T3

T,q =0.814T,, +0.186T,¢

P
Tp2) + 04729 hyy(F)) (Tgy = Tpy)+90.24 57,

2—6) were similarly calculated.

P
T, )+7932 L

ro

ro

P
Tp3)+ 90.24__" |

Pro

 

         

PrO

P
7;5)+1836_1.,

Pr()

Pr
Tps)+18.36 5,
ro

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

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:

P, p—8
_____P+ +
—F = A C NGy,

(24)
13

 

—AgT
%%=§11P,-—7\,-C,-—-T-I;Ci+e CILC,.(tMrL), (25)
p=p0+Eapl~ATpl-+Eagl-ATgi+pc , (26)
1 I
where

P, = reactor heat generation rate,
C; = modified delayed-neutron precursor concentration,
B; = delayed-neutron fraction,
A; = delayed-neutron precursor decay constant,

! = neutron generation time,

T, = transit time of primary salt through core,

7, = transit time of primary salt through external loop,
p = reactivity,

po = steady-state design point reactivity (associated with flowing fuel),

ap,; = temperature coefficient of reactivity of salt lump pi,

a,; = temperature coefficient of reactivity of graphite lump g,
AT),; = variation from design-point temperature of salt lump pi,
AT,; = variation from design-point temperature of graphite lump £,
p. = 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 enable
study of transients in the primary-salt flow rate, The variation of the transit times with flow rate was given

by

T, = Teo (Fillc)—l 27
and

T, =TLo (%)—l , (28)
where

T.o = transit time of primary salt through the core at design-point flow rate,
Ty o = transit time of primary salt through the external loop at design-point flow rate,

F|[F,, = relative primary-salt flow rate.

The value of 7, was as given in Table 2, and the transit time of the primary salt through the active
core was taken to be 3.57 sec (ref. 5).
14

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.

The nuclear constants for the two-delayed-neutron-group approximation for 2?3U were as given in
Table 1. The steady-state design-point reactivity p, was given by?

 

po=6- 5 M @9)
SNt (/r) (1 —eMTLO)
which yields
po = 0.001403 . (30)

After calculation of the various coefficients, the unscaled kinetics equations for the relative reactor
power (neutron density) and relative delayed-neutron precursor concentrations are

 

 

d(P,/P P P c ¢
d Py ro Cio Ca0
d(C,/C P F
(€,/Cy0) _ 0.0630 -7 — 0.0245 S gagor ‘1
dt PFO ClO 10 ¥10
c (r 6.048 )
F 0.1479 1\"
+0.2801 [_1 exp (_ )J Fi[Fyo (32)
FlO FI/Fl() CIO
p F, C
d(Cz/C20)= 04326 —" — 0.2245 Ez_ 028011 =2
dr P, Cro 10 C20
6.048
C, [t - —=——
F 1.358 2( Fl/Flo)
+0.2801 | =L exp (- ) ’ (33)
[Fxo ( F1/F10 ] C20
6 3
p =0.001403 — L 0.2222 AT, + L 03520 AT, +p, . (34)

i=1 i=1

The functions in brackets containing the exponentials in Eqs. (32) and (33) were generated by means of
diode function generators.

Equations (14) through (23) and (31) through (34) formed the complete 'set for the thermal and
neutronic behavior of the reactor core in this model.

The system variables in these equations and in those for the primary heat exchanger, steam generator,
and control system given in the three following sections were scaled for the analog computer as follows.
15

The allowable computer voltage range from 0 to 100 V corresponded to a temperature range from 0 to
2000°F for all temperatures in the simulation. Therefore the computer variable representing temperature,
V., corresponded to system temperature, 7, as

T

VT:Z).

(35)

For all flow rates the computer voltage range of 0 to 100 V corresponded to a relative flow-rate range of O
to 1.25. Thus, the design-point flow rate (1.0) corresponded to a computer voltage ¥V of 80 V, or

F
Vp=80— .
FUF, (36)

The relative power level, P/P,, was similarly scaled. The computer variable representing power was

P
= 80— .
V=805 (37)

The computer variables, ¥, representing the relative heat transfer coefficients, 4(F), were generated using
diode function generators with the relative flow rate ¥ as the input. The computer variables were directly
proportional to the relative heat transfer coefficients such that the design-point value of A(F) corresponded
to a computer voltage V;, of 80 V.

The scaling for the relative delayed-neutron precursor concentration, C;/C,, in the nuclear kinetics
equations was similar to that for flow rate and power level. The computer variable ¥ ; was

Vi =80 C& . (38)

I
Reactivity was scaled such that the range of the computer variable ¥, of 0 to 100 V corresponded to
reactivity of 0 to 1.0%, or

V,=10°p. (39)

The resulting analog computer program for the heat transfer and nuclear kinetics of the core is shown in
Fig. 5.

3.2.2 Primary Heat Exchanger. The heat transfer model of the primary heat exchanger is shown in
Fig. 3. For the primary-salt stream:

dT,;
Mp; Cpr —d% =Fy Cop (Tpiy =Tyt hpAp Ty — Ty} - 40)

For the tube walls:

dT,;
Mti Cpt”d_tn =thp (Tpi m th)+ hsp Ap (Tsi - Tti) . (41)
F, (80.00v* DESIGN POINT)

 

Fig. 5. Analog Computer Program for the Heat Transfer and Nuclear Kinetics Equations for the Core.

ORML WG, 77-3374

91
17

For the secondary-salt stream:

aT;
M Cps 7;‘1' =F, Cps (Tsi~l — Tt hsp Ap (T;; — Tsj) ; (42)

where

T,; = temperature of secondary-salt lump 7 ,
T,; = temperature of tube wall lump i,
M7 =M,g =M, =M,; = mass of primary-salt lump,
M,; =M,, = mass of tube wall lump,
My =My =M.3 =My, = mass of secondary-salt lump,
C,¢ = specific heat of tube wall (Hastelloy N),
C

p
F, = secondary-salt mass flow rate,

¢ = specific heat of secondary salt,

h¢ = primary-salt-to-tube-wall heat transfer coefficient,
hg p= tube-wall-to-secondary-salt heat transfer coefficient,

Ap, = heat transfer area of primary heat exchanger lump.

Heat transfer coefficients in the above equations were calculated as follows. The term hyin Egs. (40)
and (41) included the film resistance inside the tube and one-half of the tube wall resistance. The other half
of the tube wall resistance and the outside-film resistance were included in the term hsp in Egs. (41) and
(42). When the flow rate of the primary salt was changed, the film coefficient varied with flow, as shown in
Fig. 4, while the tube wall conductance 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 calculation was performed on the analog computer by means of a diode function generator as

hp=hey he (F)) (43)
and
hsp = hspo hsp (F,), (44)

where Az, is the design-point primary-salt-to-tube-wall heat transfer coefficient and hspo is the design-point
tube-wall-to-secondary-salt heat transfer coefficient. For example, from Table 1:

1 05 \™*
hey = [——+ —= 45
fo (3500 3963) (42)
=2428 Btuhr ! ft7 (°F) 7! .
A diode function generator performed the following calculation:

1 0.5 }"’ 46)

= —-—+_
iFL) [1316G(F1) 3963
18

where G(F, ) is the curve for the primary heat exchanger given in Fig. 4.
The coefficients for Eqgs. (40) through (42) were calculated using Tables 1 and 2. For example, in Eq.
(40),

 

 

 

 

 

Fio 9.48 X 107 Ib X hr 47
M,; 025X 47,480 1b X hr X 3600 sec
=2218sec™!,
and
heo Ay _ 2428 Btu X 11,050 ft*> X 1b-°F X hr 48)
Mpq Cpf hr-ft*-°F X 11,870 1b X 0.324 Btu X 3600 sec
=1.938sec”! .
The unscaled heat transfer equations for the primary heat exchanger were
dT F
d!;7 = 2218F_1_ (TrO - Tp7) + 1.938 hf(Fl) (Tl‘l - Tp7) 3 (49)
10
dT, F _
dI;S = 2_213F_1 (T — Tpg) + 1.938 he (Fy)(T;) — Tpq) (50
10
dT F
—2=2218 L (Tyg ~ Tpo) + 1938 hp (Fy) (Tyy — Tpo) 1)
10
dT,; F
10
dTy 7
7 =3.608 hf' (Fl) (Tp'] — Ttl) + 2495 hSp (F2) (TS3 — Tfl) , (53)
dT,, 54
L2 =3.608 hy (F)) (Tyg — Trp )+ 2495 hyy (F3) (Tyy —Tpa), (4)
dT, F
dst‘l = 0'5737F_2 (T, — Ty)+ 04159 hsp(F?.) (T — Tgy) s (55)
20
dT, F
d;2 = 0'5737F_2 (T51 — T52) + 04159 hey (Fy) (Tyy — Tg1) s (56)
20
dT, F
df = 0.5737# (Tgy — Ty3) + 04159 hy, (F) (T — Ty3) (57)
20
dT F
_djf‘. =0.5737 ?i (T3 — Tgq) + 04159 hyp, (F) (T4 ~ Ti3) - (58)
20
19

The scaling of these equations for the analog computer is given in Sect. 3.2.1.
The analog computer program for these equations is shown in Fig. 6.
3.2.3 Steam Generator. The heat transfer model of the steam generator is shown in Fig. 3. For the

secondary-salt stream:

dT;

Mg; Cps dSI =F, Cps (Tsz'—l sz) + hssA (Tn sz) (59)

For the tube walls:

dTy;

ti Cpt—5 = tgg At Ty — Teg) + gy A (T — Ti) - (60)
For the steam:
dT,,; _ .
My priT_F3 Cowi (Typi -1 = Tyi) + Ry Ag (T — Ty 5 (61)

where

T,,; = temperature of steam (water) lump i,
M =M =M.7 = Mg = mass of secondary-salt lump,
M,,; = mass of steam lump i,
Cpwi = specific heat of steam lump 4,
F4 = steam mass flow rate,
h,, = secondary-salt-to-tube-wall transfer coefficient,
h,,1 = tube-wall-to-steam heat transfer coefficient for the water inlet half of the steam generator,
h,,3 = tube-wall-to-steam heat transfer coefficient for the steam outlet half of the steam generator,
A = heat transfer area of the secondary-salt and steam lumps,

A4, = heat transfer area of the tube lumps.

The heat transfer coefficients in these equations were calculated in the same manner as were those in
the primary heat exchanger (Sect. 3.2.2); namely, half of the tube wall resistance was included with the
secondary-salt-to-tube-wall coefficient and half with the tube-wall-to-steam coefficient. The tube wall
resistance was maintained constant under all flow and temperature conditions. The film coefficient on the
secondary-salt (shell) side varied as the 0.6 power of the secondary-salt flow rate, and that on the tube
(steam) side varied as the 0.8 power of the steam flow rate. The simulation of these coefficients was
performed with a diode function generator as

hss = hssO hss (F 2) s (62)
hywt =hy1o M1 F3) (63)

hw3 = hw30 hw3 (F3) ’ (64)
“Teo & IC. ORNL BWG. 71-3373

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

05750
05199
Tl4 D
Fig 7
o717
he T F2 Te3~Taa
Ty-Ter 05883
3.8
“T
X0
1C.
05053 “Tae
05199
Tez
o7l
“Toa he LS. T2 T hsp | Fa - Ts1~Taz
Tia~Toe 0.5207
318
“Tiz2
4510
Fy
-Ts
DFG DFG
hy(Fy) hsp{Fal
}

 

 

 

 

 

 

 

 

F, TIME | 7,
F, (80.0Ov= DESIGN POINT} @ DELAY
Tz

 

 

Fig. 6. Analog Computer Program for the Heat Transfer Equations for the Primary Heat Exchanger.

0T
21

where the “zero” subscript refers to the design-point value. For example, Ao, was calculated as follows,
using the information in Table 1:

hooo L, 053 - 6
ss0 7 V1316 1224 (65)
=855.9 Btu hr ! ft™2 (°F)™! .

A diode function generator performed the following calculations:

 

1 05 ]!
F,)= + _
hs (F3) [1316 (F,/F, )05 1224} (66)

The other heat transfer coefficients were similarly calculated.
The coefficients of Eqgs. (59) and (60) were calculated using Tables 1 and 2. For example, in Eq. (59):

 

 

F, 711X 10°IbX hr )
MsS 47,492 1b X hr X 3600 sec

=0.4159 sec”! .
hoo A, 8559 BtuX 16,408 ft> X 1b-°F X hr )

 

 

M5 C, 47,4921b X hr-ft>-"F X 0.36 Btu X 3600 sec

=0.2282sec”! .

The masses and specific heats of the steam lumps in Eq. (61) were calculated as follows. The
temperature and pressure distributions of the steam in the steam generator at design point were obtained
from ref. 6. At the midplane in the steam generator the temperature and pressure were, respectively, 750°F
and 3711 psi. From the steam tables, the enthalpy here was 1087 Btu/lb. At design point, the enthalpy of
the water was raised from its inlet value of 770.8 Btu/lb to the steam outlet value of 1421 Btu/lb, an
increase of 650.2 Btu/lb. The enthalpy rise from 770.8 to 1087 Btu/lb in the water inlet half of the steam
generator was equally divided between lumps w1 and w2, and that from 1087 to 1421 Btu/lb equally
divided between lumps w3 and w4. Thus, 48.6% of the heat was transferred in the water inlet half and
51.4% in the steam outlet half of the steam generator. The average temperature of the steam in the water
inlet half was (from ref. 6) ~726°F. The average temperature in the steam outlet half was about 850°F.
The design-point temperatures of lumps wl, w2, w3, and w4 were, therefore, 726, 750, 850, and 1000°F
respectively.

The total change in temperature of the secondary salt in the steam generator at design point was 300°F.
Since the specific heat of this salt was constant, the 48.6% of the heat transferred in the steam outlet half
of the steam generator represented a change in salt temperature of 145.9°F, or a temperature at the
midplane of the exchanger of 995.9°F, which compared well with that given by ref. 6 (997°F). This was
the design-point temperature for salt lump s6. The temperatures of lumps s5 and s7 were the average in the
two halves of the exchanger, or 1073 and 923°F respectively.

The overall temperature difference for heat transfer between salt and steam in the water inlet end of the
exchanger (between lumps s7 and w1) was 197°F. In the steam end the difference (between lumpss5 and
w3) was 223°F. The values of the average heat transfer coefficients for the steam generator were also
22

obtained from ref. 6. The average secondary-salt (shell side) film heat transfer coefficient and average tube
wall conductance over the entire exchanger were 1316 and 1224 Btu hr ™" ft ™ (°F)™' respectively. The
average film heat transfer coefficient on the steam (tube) side over the water inlet half of the steam
generator was taken to be 6400 and that for the steam outlet half was 3590 Btu hr ™! ft ™2 (°F)™'. The
average overall heat transfer coefficients in the water inlet half and the steam outlet half were about 577
and 539 Btu hr ™! ft™ (°F) 7! respectively. The heat transfer area in each half was, then, 2051 ft2. The area
of each lump was

2051 X 16
A =" "

= (69)

= 16,400 ft* .

The enthalpy and temperature of each steam lump were used to calculate the effective specific heat. For

example:

]
Cpw1 =7 (1087 — 770.8)/(726 — 700) (70)

= 6.08 Btulb™ (°F)7! .

The value of each C is given in Table 1. The value for the density of the steam for each of the four

wl
steam lumps was obfained from ref. 6 as the average density of the steam in each quarter of the steam
generator.

The steam generator was about 72 ft long. The number of 0.5-in.-OD tubes was calculated from the
heat transfer area to be 434 tubes in each steam generator. From this information and the tube wall
thickness and tube pitch given in Table 1, the mass and volume of the salt, metal, and steam were calculated
for the tube region in each steam generator. These values are given in Table 2. The coefficients of Eq. (61)
were then calculated. For example, the total flow area in the 434 tubes of each steam generator was 0.284

ft. The mass of steam lump w1 was

M, =16 X 0.284 ft* X 74—2ft X 22.7 Ib/ft? (71)
= 1860 1b.
Similarly,
M., =9341b, (72)
M,,4 =555 Ib, (73)
M4 =4121b. (74)

The design-point flow rate of the steam was 1.181 X 107 Ib/hr. Then

Fy,  1.181X 107 Ib X hr 79)
M, 18601b X hr X 3600 sec

=1.764 sec! .
23

The term h,, ;o was calculated in a manner similar to that for &, [see Eq. (65)]. Its value was 1771 Btu
hr~! ft72 (°F)™'. Then

 

 

 

 

 

 

 

hwiods _ 1771 BtuX 16,400 ft*> X 1b-"F X hr 76)
M1 Cpyy 1860 1b X hr-ft*- °F X 6.08 Btu X 3600 sec
=0.7134sec”!.
The unscaled analog computer equations for the steam generator were:
deS F2
—2 = 04159 2 (T, — Ty5)+ 02282 hy, (F))(Ty3 — Tys), (77)
20
dT F
d;f» =0.4159 =2 (Tys — Tg) + 02282 1y (F,) (Tyy = Tis) (78)
20
dT, F
51 = 0.4159 22 (Ty — Tyg) + 02282 hyg () (Ty4 — Ti) (79)
20
dT, F
__d;S =0.4159 }-;-,-?— (Tg7 ~ Tgg) + 02282 hy (F,) (Tyq — Tq7) (80)
20
dT,,
—22 206950 g (F,) (Tys — Ty3)+ 1107 kg (F3)(T,,3 - Ts3), (81)
dT 44
4= 0.6950 hes (F,) (Tyy — Tpa) + 1.570 hyyy (F3) (Tyyy — Tra) (82)
dT F
____d‘;’l = 1.764_F_i (700 — T, )+ 0.7134 hy (F3) (Ty4 — T,,1), (83)
30
dT F
T\;f% =3.513 F_3_ (Ty1 — Tyyp) ¥ 131200 F3) (Trg — Tp1) (84)
30
dT F
03 2591222 (T, = Ty3) + 7161 3 (3) (Ty3 = Tya) (85)
30
dT F
2 =7.969 =2 (Tyy3 — Typa) + 1448 hyy3 (F3) (Ty3 = Tyy3) (86)
30

Transport delays were used in the hot and cold legs of the secondary-salt loop to account for the transit
time of the secondary salt between the primary heat exchanger and the steam generator. Thus, from Fig. 3,

Toq =Tyt +71), (87)

Tog =To(t+72). (88)
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 7. Analog Computer Program for the Heat Transfer Equations for the Steam Generator.

QRNL DWG.
-T, TIME | 7, G
7 50.00
18.10
2852 2.96|
0' —_—
Tss hee <. Tia~Ty3 Nw3 F3 " T3 Tus
TiaTas 46,80
1.384
~Tia
08688
“Tus
05199 \7
= 3 DFG
s
ha(Fa)
Fs
0.2852
1. F
Ty hes 3
T Taz 2032
1.963
“Tia
0.8688
05199
F3
DFG DFG
F
LMY Ry (Fa)
F Fyl
Fp T
Fig. 8

71-337%

 

{8000y =DESIGN POINT)

¥C
25

The values used for 7, and 7, were 14.5 and 11.9 sec, respectively, at the 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 primary salt between the reactor core and the primary heat exchanger.

The scaling of the equations for the analog computer is given in Sect. 3.2.1. The analog computer
program for the steam generator is shown in Fig. 7.

3.2.4 Control System. 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
temperature caused the flow rate to change at a rate proportional to the error, that is,

dF
—7 = —a(T,,4 — 1000°F) (89)

where F, is the secondary-salt flow rate, T, 4 is the outlet steam temperature, and « 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.
Reactor Qutlet Temperature Controller. The reactor outlet temperature set point was determined by
the plant load demand (Fig. 2). The set-point equations were:

nget =350P3omang T 950 (0.5<P<1.0) (90)
and
T"Oset =250P 3. mang T 1000 (0<P<0.5), (91)

where Tyo . is the reactor outlet temperature set point and Pgpp,p 4 is the fractional plant load demand.
This set of equations was chosen so that the resulting steady-state reactor inlet temperature would decrease
linearly with load from 1050°F at full load to 1000°F at 50% load and remain constant at 1000°F for loads
below 50%.

The reactor power-level set point was proportional to the difference between the outlet temperature set
point and the measured reactor inlet temperature, that is,

P
Fse

t =A(Trose - Tri) ’ (92)

t
where P . is the reactor power level set point, T,; is the measured reactor inlet temperature, and 4 is the
proportionality constant.

The proportionality constant 4 was itself proportional to the primary-salt flow rate. The assumption of
constant specific heat of the primary salt is thus implied here. However, it is not necessary to assume
constant specific heat in an actual operating control system of this type. Additional circuitry may be
provided to compensate for this effect, as was demonstrated in the MSRE control system.>

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

€e=P, - P, . (93)
26

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

T =
) s2 +2tws + w? els)’

(94)

where G is the controller gain, w is the bandwidth, { is the damping factor, and O(s) is the Laplace
transform of the servo output, dp,/dt.

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 control-rod-drive service. The gain of the controller &
was such that, for [e] = 1% of full power, the control reactivity addition or withdrawal rate was about
0.01%j/sec; that is,

7—0.01%/36(3 s (95)

where p,. is the control reactivity.

For power level errors greater than 1% of full power, the reactivity addition or withdrawal rate was
limited to 0.01%fsec. Integration of Eq. (95) yields the value for the control reactivity in the kinetics
equations of Sect. 3.2.1.

The steam flow rate F; was obtained directly from the power demand, Pye,.04- A S-sec first-order lag
was included to obtain some simulation of the response of the steam valve:

dF, a 1
3=

dr _;Pdemand (7) _;FB ? (96)
where g is a proportionality constant and 7 is the time constant (5 sec).

The scaling of the equations for the analog computer is given in Sect. 3.2.1. The analog computer
program for the control system part of the siraisiation is shown in Fig. 8.
ORNL DWG. 71-3377

 

{ E )
Fig 6
@

Fig. 7

 

 

 

 

STEAM TEMPERATURE CONTROLLER

 

F, (80.00v = DESIGN POINT }

 

COMPARATOR
0.2188 6400

: -p,

LOAD oot

DEMAND =Q, ~
) \ P

—Ref =) 4 2 |

0.4750 \ O Tro,,,

Tri=T
LOAD 383 o o - T O 31,42
DEMAND, & n ! |
—Ref. -0 l J

0

 

+001% /SEC. |
LIMIT
31,42 1

 

 

 

 

 

 

 

 

  

 

 

 

 

 

’

 

 

:

 

 

 

 

 

1 9 CONTROL ROD DRIVE SERVO
LOAD
-Ref, .
0.4000 REACTOR OUTLET TEMPERATURE CONTROLLER

Fig. 8. Analog Computer Program for the Control System.

LT
29

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ORNL-TM-3102

=

cLain
cNeese
Wherter

gZZZ

oore
icholson
akes
arker
erry
ickel

C Robertson
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Dunlap Scott

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ggwor*r'u’fimrp
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AP ICOHIT-C T
"U'-U"U

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Central Research Library
Document Reference Section
Laboratory Records Department
Laboratory Records, ORNL R. C.

J.
R.
D.
G.
A.
J.

91. C. B. Deering, Black and Veatch Engineers, 1500 Meadowlake Parkway, Kansas City, Missouri 64114
92. Ronald Feit, Instrumentation and Control Branch, Division of Reactor Development and Technology,

U. S. Atomic Energy Commission, Washington, D.C. 20545

93. George McCright, Black and Veatch Engineers, 1500 Meadowlake Parkway, Kansas City, Missouri 64114
94-95. T. W. MclIntosh, Division of Reactor Development and Technology, U. S. Atomic Energy Commission,

Washington, D.C. 20545

96. M. Shaw, Division of Reactor Development and Technology, U. S. Atomic Energy Commission, Washington

D.C. 20545

97. 1. A. Swartout, Union Carbide Corporation, New York, N.Y.

98. Laboratory and University Division, AEC, ORO
99—-100. Division of Technical Information Extension

3

10017