ORNL-4397.txt

OCKHEED MARTIN ENERGY RESEARCH LIBRARIES

' i

3 Y445k 0515563 0

 

 
ORNL-4397
Contract No. W-7405-eng-26

INSTRUMENTATION AND CONTROLS DIVISION

ANALYSES OF TRANSIENTS IN THE MSRE SYSTEM WITH 23 FUEL

O. W. Burke F.H.S. Clark

JUNE 1969

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

LOCKHEED MARTIN ENERGY RESEARCH LIBRARIES

RN

 

 

 

 

 

 

 

 

 

 

 

 

 

3 Y45k 05155L3 0

 

 
CONTENTS

ABSTRACT . v v v & v v v v o e v e v e e e
INTRODUCTION . . . . . . . . e

ANALOG COMPUTER MODELS

Reactor Core Heat Generation and Hecf Trcnsfer Model
External Heat Rejection .

Safety System Simulation. . . . . . .

Reactor Control System Simulation. . .

N DN NN
n b kN —

PROCEDURES AND RESULTS . . .

3.1 Reactor Control System Performance . .
3.2 Startup Accident . . . . . . .. ..
3.3 The ®32U Resuspension Accident . .

CONCLUSIONS . . v v v v v v v v v e e e v e e

ACKNOWLEDGMENTS . . . . .

APPENDIX . . . .« v v v v v v v e e e e e .

REFERENCES . . . . . . . . . . e e e e e e e e

Nuclear Kinetics Models . . . . . . C e

5.1 Neutron Kinetics in a Circulating Fuel Reactor

5.2 The Temperature Equations . . . . . . . . . .

5.3 External Heat Rejection . . . . . . . « . . . « . .
5.4 Sofety Systems . . . . . . . . . e e e e e e e e
5.5 Control System . . . . . . . . . .. .
5.6 Control System Lag Meosuremenfs Made af fhe MSRE ..

------

25

25

. 26

26

. 31

34

. .35
. 38

. 42

. 46

 
ANALYSES OF TRANSIENTS IN THE MSRE SYSTEM WITH *33U FUEL

O. W. Burke F.H.S. Clark

ABSTRACT

The 23U fueled MSRE system was simulated on the ORNL analog
computer. The simulated system was used to evaluate the existing MSRE
control and safety systems when used on the 23U fueled system. The
pertinent results and conclusions were as follows:

 

1. The safety system will limit the “startup accident" so that the
peak power will be 100 kw.

2. A quantity of 33U sufficient to cause a reactivity change of
approximately -1% 8K/K when precipitated out of the fuel
at some point in the system external to the core could be swept
back into the core in a concentrated form without causing
excessive core damage.

3. The existing controller will control the #3°U fueled system in
a stable manner; however, an increased velocity feedback
gain will be required.

 

1. INTRODUCTION

While plans were being made to fuel the MSRE with *33U, there was some
uncertainty pertaining to the adequacy of the existing MSRE safety and control sys-

tems. To dispel this uncertainty, the following bits of information were needed:

i | 1. The degree of stability of the 33U loaded MSRE system while under auto-

matic control of the power level.

 

 
2. The response of the safety system to a "startup accident."

3. The maximum mass of **?U that can be tolerated in a "33 resuspension
accident."

The startup accident is defined as the continuous uncontrolled withdrawal of all shim

rods at maximum rod velocity.

An analog computer simulation of the “2°U fueled MSRE was used to obtain

the desired information.

2. ANALOG COMPUTER MODELS
Analog computer models of the subsystems of the MSRE developed earlier®™*
were used in various combinations as required by the nature of the transient to be

simulated, the range of the variables of interest, and the power level of concern.

2.1 Nuclear Kinetics Models

Two point-reactor nuclear kinetics models were used with six delayed neutron
groups. The output of one model was nuclear power, P; the output of the other was
the logarithm of nuclear power, log,, P . The log P model was used for startup and
low-power operation of the reactor where the range of P was very large and the heat
generation was negligible. The regular kinetics model was used when the heat genera-

tion effects could not be ignored.

2.1.1 Regular Nuclear Kinetics Model

 

The mathematical equations describing the regular nuclear kinetics model

(Fig. 1) are as follows:

dn -
—ng = (p_f\"—@n(f) + i)\ici(r) ’ (])
i=]

 

 
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2 [ SAFETY SYSTEM 293 f ;
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- SAFETY ROD REACTIVITY GENERATOR CIMITER V6. 27 \ 9 L 1Q470_fl_4oov |
0—(~+90) \ ? MIK |
‘ LATCH !

Fig. 1. Schematic Diagrams of the Analog Computer Models of the MSRE
Control and Safety Systems and of the MSRE Reactor Kinetics.

 

 
 

 

and
AT
dCi(f) Bi Ci(f - 'TL)e L Ci(f)
g T A -G - T T @)
c c
where
n = number of neutrons in the reactor,
0 = reactivity, 5K /K ,
A = prompt neutron generation time,
B = the fractional yield of all delayed neutron precursors as a result of
fission,
N ]/Ti , where T, is the mean life of the ith group of delayed neutron
precursors,
Bi = fractional yield of the ith group of delayed neutron precursors as a result
of fission, T B. = B,
1. T core residence time of fuel,
T residence time of fuel in the loop external to the core.

The third and fourth terms on the right-hand side of Eq. (2) are not found in
the nuclear kinetics equations of stationary fuel reactors. The fourth term specifies
the rate at which delayed neutron precursors of the ith group are removed from the
core by fuel circulation. The third term specifies the rate at which the delayed neu-
tron precursors of the ith group re-enter the core after they have traversed the external
loop .

A consistent set of units must be used in these equations. In the computer
model, P (expressed in megawatts) replaced n in the equations. The computer voltage
scaling of P was different for the different transients; therefore, the machine-scaled
equations will not be shown.

The development of Egs. (1) and (2) is discussed in detail in the Appendix,
Sect. 5.1.

 
2.1.2 The Log P Nuclear Kinetics Model

 

The Log P model (Fig. 2) equations are as follows:

 

&
. dg(t) p -8
i ;kihi(f) ' )

dh.(t)

 

 

 

. dg(t) _ i 1
RS =T Dyt
-x. 7, (1)
] P L
I h.[r = 700 e : 4)
dh. (1) B.
| dg(t) _ "i 1
e T 20 h(n], (5)

and

 

‘ t _ !
h [t -5 0] :_J e - TC* h (Bt ] (6)

where
glt) = |ogel\|(’r) ,

h.(t) = Ci(f)/N(f) .

The detailed derivation of Eqs. (3), (4), (5), and (6) is shown in the Appendix,
Sect. 5. 1.

 

 
2.2 Reactor Core Heat Generation and Heat Transfer Model

The core was divided into four concentric regions in the radial direction with
respect to the direction of fuel flow. In the axial direction (direction of flow) the
regions were further subdivided into from one to three axial regions, or lumps. The .
regional layout of the core is shown in the upper right-hand corner of Fig. 3.
The mathematical equations describing each of these lumps are identical ex-
cept for the physical constants. The equations for a typical lump, which consists of

one section of graphite and two sections of fuel, are

 

 

 

 

 

 

 

iT_G: 9 __p_ - hA, (’T' __> 7)
dt MGCG T MGCG G f
dTy b hA, L -
i ke fr T mclTe T ) T m T T ) @)
ff ff f
and -
dT hA W
fo _ C z (= _ = fls _
¥ M C T M (TG TF)+M (TF TFo)’ (¥)
fo™f fof fo
where
TG = average temperature of graphite,
MG = mass of graphite section,
CG = heat capacity of graphite section,
a = fraction of total heat produced in the graphite section,
PT = total rate of heat production,
h = heat transfer coefficient between graphite and fuel,
A = heat transfer area between graphite and fuel, ]
T = average temperature of fuel in a lump,

—+

 

 
ORNL-DWG 69-2214

 

       
         

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Fig. 2. Schematic Diagrams of the Analog Computer Models of the MSRE Pericd
Safety System and the MSRE Log P Model.

 
 

 

 

 

   

 

  

   
   

   

 

  

 
 

 

 

 

   

 

  

 

    

 

 

  
 

 

 

 

 

 

    

 

    

 

 

  

 

 

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Fig. 3.

Schematic Diagram of the Analog Computer Mode!| of MSRE Heat
Generation and Heat Transfer.

 

 
MF = mass of fuel in the first section,

C]c = heat capacity of fuel,

b = fraction of total heat produced in the first fuel section,
TFi = fuel temperature entering the first section,

TFo = fuel temperature at the exit of the second fuel section,
Mfo = mass of fuel in second fuel section,

C = fraction of total heat produced in the second fuel section.

The computer schematic for nine lumps is shown in Fig. 3. The voltages repre-
senting temperatures in Fig. 3 are T’ = [T(°F) - 1100°F] /2 .

A detailed derivation of Egs. (7), (8), and (9) is shown in the Appendix,
Sect. 5.2.

2.3 External Heat Rejection

Because of a shortage of analog computer equipment, an abbreviated model
(Fig. 3) of the heat rejection system was used. The development of this model is
discussed in the Appendix, Sect. 5.3.

The voltages representing temperatures in Fig. 3 are T'(v) = [T(°F) - 1100°F1/2 .

2.4 Safety System Simulation

The MSRE has two safety-system trip signals: a power-level trip signal and
a reactor=period trip signal. Safety action is initiated if the power level exceeds
11.25 Mw or if the reactor period becomes shorter than 1 sec.

For the low-power cases (essentially no sensible heat is produced) where the
log P model was used, only the period-trip signal was used. Constant safety-rod
acceleration and constant reactivity-change per inch of travel were used in this model.

For the high-power model, both level-trip and period-trip signals were used.
The reactivity change due to safety rod motion was more accurately simulated (Sect.
3.3). Only two of the three safety rods were assumed to drop when a scram occurred.

For a more detailed discussion of the safety system see the Appendix, Sect.

5.4,

 
10

2.5 Reactor Control System Simulation

The MSRE has two modes of control: for operation at power levels less than
1 Mw, the flux (or power level) is the controlled variable; for operation at power
levels of T Mw or higher, the fuel salt temperature at the reactor core outlet is the
controlled variable. The computer circuit used to simulate the control system is dis-
cussed in the Appendix, Sect. 5.5.

Since we believed that the most uncertain part of the centrol system simula-
tion would be the time response of the control-rod-drive system to error signals that
call for rod motion, the time response of the control-rod-drive system was measured

experimentally at the MSRE. This measurement is discussed in the Appendix, Sect. 5.6.
3. PROCEDURES AND RESULTS

3.1 Reactor Control System Performance

The performance of the reactor control system under the temperature mode of
control at power levels of 1 Mw and above (Figs. 4 and 5) and the neutron flux mode
of control at power levels below 1 Mw (Figs. 6 and 7) was demonstrated.

In the run illustrated by Fig. 4, the reactor was initially operating at steady-
state full power (7.5 Mw); and at the time marked "start" in Fig. 4, the temperature
set point on the controller (TSO) was decreased at a constant rate of 5°F/min for a
total time of 2.5 min (12.5°F total). The subsequent reactor performance, that is,
that the requested change in the fuel temperature at the reactor core outlet was ac-
complished and that the error signal did not cross the dead band, indicates a stable
system. System stability is again exhibited in Fig. 5, when in the run illustrated by
this figure the heat load, or heat rejection rate, was suddenly reduced from 7.5 to
~5 Mw.

In the runs illustrated by Figs. 6 and 7, the controller was in the flux mode
of control, and the reactor was operating at a steady-state power level of 10 kw.

A perturbation was induced in the control system by suddenly reducing the flux set

point on the controller from 10 to 8 kw. Figure 6 shows that with the control system
11

START 10'set.
—-. '*| }k . ORNL DWG. 49-4518

 

 

ERROR
SIGNAL Low
DEAD [ |
8D | 7
HIGH
FULL
CONTROL ROD  wpr  —
VELOCITY
FULL [
INSERT ~
1212.5—1

FUEL TEMP AT
REACTOR CORE

 

 

OUTLET, °F i
(CONTROL SET f
POINT)
1200 ——
CHANGE IN
CONTROL ROD
POSITION INSERT—
(10 LINES/in) ; )
WDR. —
10-
POWER, Mw
1212.
FUEL TEMP AT
REACTOR CORE
QUTLET, °F
1192
175
FUEL TEMP AT
REACTOR CORE
INLET, °F
1155—i

Fig. 4. Response of the Controlled MSRE to a ~5°F/min Ramp Change in the
Temperature Set Point with Temperature Mode of Control.

 

 
12

START 10 sec
ORMNL DWG. £69-4519

 

 

ERROR ~fd-
SIGNAL Lo
DEAD
BAND 0-
HIGH
FULL
CONTROL ROD WDR. ~
VELOCITY
0
FULL
INSERT
1242.5 =

FUEL TEMP AT
REACTOR CORE

OUTLET, °F
(CONTROL SET
POINT)
1200 -
CHANGE IN
CONTROL ROD INSERT
POSITION
(10 LINES/in ) 0
WOR.
0 =
POWER, Mw
n_
1212.5
FUEL TEMP AT
REACTOR CORE
QUTLET, °F
1192.5-
FUEL TEMP AT ' 19° ~
REACTOR CORE
INLET, °F
1IE. =

 

Fig. 5. Response of the Controlled MSRE to a Sudden Reduction in Heat Load
from 7.5 Mw to ~5 Mw with Temperature Mode of Control.

 
13

10 sec

ORNMNL DWG. 69-4520

 

 

  
 

ERROR
SIGNAL DEAD :
BAND 0-;
—_—
CONTROL FULL
ROD WOR.
VELOCITY
FULL
INSERT
CONTROL ROD
POSITION WOR.
(10 LINES/in.) +
INSERT |
POWER, kw

0=

Fig. 6. Response of the Controlled MSRE to a Step Change in the Power Set
Point from 10 to 8 kw with Flux Mode of Control and with the Feedback Gain the
Same as That Used in the “°U System.
10 sec

ORML DWG. 69-4521

ERROR
SIGNAL
DEAD
BAND
FULL
CONTROL WDR.
ROD
VELOCITY
0
FULL
INSERT
CONTROL ROD WOR.
POSITION

(10 LINES /in)
INSERT

   

20~

POWER, kw

0-

Fig. 7. Response of the Controlled MSRE to a Step Change in the Power Set
Point from 10 to 8 kw with Flux Mode of Control and with the Velocity Feedback
Gain 3.3 Times That Used in the **°U System.
15

the same as that for the *3°U fueled reactor there was some instability in the run.
The error signal repeatedly traversed the width of the dead band and initiated alter-
nate rod insertions and withdrawals. Figure 7 shows that with the rod-velocity feed-
back gain in the control system at 3.3 times its value for the °U system the system

is much more stable.

3.2 Startup Accident

The startup accident was of interest because it afforded a convenient check
on how the safety system would perform in.response to a reactor period trip signal.

The log P model was used for these runs (the thermal system model was not used since
the power peaks were predicted to be very low). The rods were continuously with-
drawn in such a way that the reactivity increased at a steady rate of 0.0935% 5K/K -
sec. Various initial reactor criticality conditions, initial power levels, and initial
background-gamma=-activity levels were used in the computer runs. The resulting
power peak, even with ten times the estimated background gamma activity, was only
630 kw (Fig. 10). The strip-chart recorder charts for three of the runs are shown as
Figs. 8-10.

Figure 8 shows the recorder outputs for a startup accident with no safety rod
action. Although the period safety scram signal exceeded the scram level, there was
no scram, because the signal was disconnected from the safety system. The run was
terminated by the operator after 4.5 sec. The reactor was initially critical at a power
level of 1 w. The gamma activity level produced the same chamber current output
that a 10-kw neutron flux would produce. This was considered to be the normal gamma
activity level.

The conditions for the two runs recorded in Figs. 8 and 9 were the same except
that the safety system was connected in the run recorded in Fig. 9. The shortest re-
actor period was approximately 0.18 sec, and the peak power was approximately 42
kw (Fig. 9).

The initial conditions for the run recorded in Fig. 10 were that the reactor

was 0.04 8K/K subcritical at a power level of 0.01 w and the gamma activity level

 
16

was equivalent to a neutron flux of 100 kw. For this case, the shortest reactor period

was approximately 0.15 sec, and the peak power was approximately 630 kw.

3.3 The 23 Resuspension Accident

The °°U resuspension accident is only a postulated accident, and whether or
not a mechanism for its happening exists is debatable. If a mechanism should exist,
the events leading to the accident might be as follows:

1. During operation of the reactor, a fraction of the ***U would precipitate
from the fuel solution and collect in the primary loop external to the re-
actor core. The control rod would withdraw to compensate for the resulting
loss in reactivity. This process could take place at such a low rate as to
be imperceptible to the reactor operator. The loss in reactivity associated
with a loss of a given mass of fuel will be designated as 6KO .

2. After a substantial mass of ®22U has collected in the primary loop outside
the reactor core, it could be swept back through the core by the flowing
fuel solution.

3. As the highly concentrated *3*U mass traversed the reactor core, the re-
activity would increase, causing a power excursion.

In this accident the fuel is presumed to precipitate uniformly from the entire
fuel region, a region much greater than the core volume. The control rods need com-
pensate only for that fraction which corresponds to the fraction that the core is of the
whole volume. On resuspension the entire amount of fuel is presumed to move as one
piece through the system. The piece, when it enters the core, is several times the
entire amount which was precipitated from the core. Moreover, as the piece traverses
the system, it will af some time enter the highest importance region of the core. As
an example, while the maximum integrated amount of reactivity removed from the core
in this process may have been about 1%5K/K , the maximum postulated reactivity in-

crease on resuspension may approximate 5% 5K/K .

 
 

17

ORNL DWG. 69-4522

START fi ~’ I——fl sec
10-. ==k - —=

[LOGso P (t) ~LOG1o P (0] ==F . ===
P)=1w =

 

INVERSE REACTOR
PERIOD, SEC™!

0
+0.05

REACTIVITY DUE TO
ROD WITHDRAWAL, 8K/K

-0.05

PERIOD SAFETY 62

SCRAM SIGNAL, v

SCRAM LEVEL

Fig. 8. Startup Accident with No Safety Action.

 
18

ORNL DWG., 69-4523

 

1 sec

START —_‘

[LOGyo P(+) -LOGy P (0)] 10—
P(o) = 1w

INVERSE REACTOR
PERIOD, SEC ™!

+0.05
REACTIVITY DUE

TO ROD WITHDRAWAL,
8K/ K

PERIOD SAFETY
SCRAM SIGNAL, v

TRIP LEVEL

Fig. 9. Startup Accident with Normal Gamma Background and with the Safety
System in Operation.

 
19

START 5

CRHL DWG. 69-4524

{
[LOGyo P (£) —LOGioP ©]]
P) = 0.01w

10
INVERSE REACTOR
PERIOD, SEC ™!

+0.05
REACTIVITY DUE
TO ROD
WITHDRAWAL, &K /K

    

-0.05 1

+25
PERIOD SAFETY

SCRAM SIGNAL, v

; 0
SCRAM LEVEL £

Fig. 10. Startup Accident, Starting 0.045K/K Subcritical and with Gamma
Background Ten Times Normal.
20

The relative reactivity of the mass of resuspended “*“U as a function of time
is shown in Fig. 11, in which the mass of resuspended “““U enters the reactor core at
time zero. The curve shown in Fig. 11 was set up on a diode function generator. The
output of the function generator (relative reactivity) was multiplied by the reactivity
equivalent of the mass of “?*U deposited outside the core (’EKO) , and the result was
the reactivity as a function of time.

Computer runs were made with various values for rSKO and the power level at
the time of the accident. Examination of the run results shows that the initial power
level had very little to do with the severity of the excursion.

Both the flux and reactor-period safety signals were connected. Conservatively,
credit was taken for only two of the three rods that responded to a safety trip signal.
The reactivity due to safety rod motion (two rods) as a function of time after the rods

were released is shown in Fig. 12. The total reactivity change was -4% 5K/K .

For all cases, safety action was initiated prior to any significant increase in
system temperatures. The safety action caused the reactor to go subcritical. This
was the end of the incident for the cases where the instantaneous reactivity due to
the resuspended *°U did not exceed +4% 5K/K (the corresponding SKO is approxi-
mately +0.82% sK/K). If SKO would exceed +0.82% 3K/K , the resulting positive
reactivity would more than compensate for the -4% &5K/K due to safety rod motion,
and the reactor would go critical again. These power excursions would cause the
system temperatures to rise. The core could be damaged by excessive temperature
increases (core melting) or from excessive rates of temperature increase (pressure
surges) .

The strip chart recordings of three runs in which the only parameter varied
was 6KO are shown in Figs. 13-15. The initial power level for each of these runs
was 7.5 Mw. With a value of +0.75% 8K/K for 6KO (Fig. 13), the safety rod
motion drove the reactor subcritical, and it remained subcritical with essentially no
temperature increases. With %KO equal to +1% &K/K (Fig. 14) the system tempera-
tures did increase significantly. More damage is evident in Fig. 15 with 6KO for

the run equal to +1.2% *K/K .
2]

ORNL DWG. 69-4525

 

I

wa

RELATIVE REACTIVITY (8K/Kg)

 

 

| ] | !
0 2 4 B 8 i0 12
TIME (sec)

 

Fig. 11. Relative Reactivity of the Resuspended >3 as a Function of Time
After it Re-enters the Reactor Core. |

ORNL DWG. 69-4526

 

REACTIVITY (%% 6K/K)

 

 

I I
0 0.2 0.4 0.6 0.8 1.0
TIME (sec)

 

Fig. 12. Reactivity Change Resulting from Safety Rod Motion as a Function
of Time After Scram.

 
22

ORML DWG. 69-4527

1 sec

POWER, Mw

REACTIVITY ADDED
BY FUEL RESUSPENSION,
To 8K /K

PERIOD SAFETY
SIGNAL, v

SCRAM LEVEL

REACTIVITY DUE
TO SAFETY ROD
MOTION, % &K/K

 

2100~

FUEL TEMP AT
REACTOR CORE
QUTLET, °F
(HOTTEST REGION)

10
160
MIXED MEAN
FUEL TEMP AT
REACTOR CORE
QUTLET, °F

210

FUEL TEMP AT
REACTOR CORE
OUTLET, °F
(CENTRAL REGION)

 

"

Fig. 13. “°U Resuspension Accident with an Initial Power Level of 7.5 Mw
and with EaKo = +0.75%5K/K .

 
23

ORML DWG, 69-4528

START
1000~
POWER, Mw

+
REACTIVITY ADDED

BY FUEL

RESUSPENSION,

T 6K /K

PERIOD SAFETY e

SIGNAL, v
SCRAM LEVEL—

  

-25.-

_4....
REACTIVITY DUE
TO SAFETY ROD
MOTION, o 8K/K

2100
FUEL TEMP AT
REACTOR CORE
OUTLET, °F
(HOTTEST REGION)

1100

MIXED MEAN
FUEL TEMP AT
REACTOR CORE
OUTLET, °F

11
21
FUEL TEMP AT
REACTOR CORE
OUTLET, °F
(CENTRAL REGION)

 

1"

Fig. 14. 23 Resuspension Accident with an Initial Power Level of 7.5 Mw
and with &K_ = +1%3K/K .

 

 
 

24

ORNL DWG, 69-4529

2500

POWER, Mw

+10
REACTIVITY ADDED
BY FUEL
RESUSPENSION, %= BK/K

   

PERIOD SAFETY
SIGNAL, v

SCRAM LEVEL

REACTIVITY DUE
TO SAFETY ROD
MOTION, 7 6K/K

2100

FUEL TEMP AT
REACTOR CORE
OQUTLET, °F
(HOTTEST REGION)

1100

1600
MIXED MEAN
FUEL TEMP AT
REACTOR CORE
QUTLET, °F

1100

2100
FUEL TEMP AT

REACTOR CORE
OUTLET, °F
(CENTRAL REGION)

 

"

Fig. 15. #7°U Resuspension Accident with an Initial Power Level of 7.5 Mw
and with tK_ = +1.2%5K/K .
25
4. CONCLUSIONS

The existing controller will control the *33U fueled system in a stable manner;
however, an increased velocity feedback gain will be required.

The safety system limited the startup accident so that the peak power was only
100 kw (10 times normal gamma background).

A quantity of “3°U sufficient to cause a reactivity change of approximately
-1% *K/K when precipitated out of the fuel solution at some point in the system ex-
ternal to the core could be swept back into the core in a concentrated form without
causing excessive core damage. The maximum allowable fuel temperature increase
at the hot channel would be 340°F. The fuel outlet temperature of the hottest region
increased ~210°F for 6Ko equal to 1% 8K/K (Fig. 14). The temperature increase
for 6Ko = 1.2% 5K/K was 390°F (Fig. 15). The case where 6KO = 1% 3K/K was

conservatively chosen as the limiting case.
ACKNOWLEDGMENTS

We are grateful to J. W. Lawson for his constant assistance in keeping the
analog equipment operational and for his further assistance in performing the measure-
ment on the MSRE. J. L. Redford and R. C. Steffy were of very great help in making
arrangements for the MSRE measurements and contributed greatly to the planning of
the measurement. R. C. Steffy further assisted us at all stages with information about
the system. S. J. Ball made valuable suggestions as to the handling of the external
heat dump and conceived the simple procedure for the MSRE measurement. S. J. Ditto
offered invaluable insight into the workings of the safety trip. G. S. Sadowski has
made this manuscript more readable and has done all the things which must be done

to have it reproduced.

 
 

26

5. APPENDIX

5.1 Neutron Kinetics in a Circulating Fuel Reactor

Circulation of fuel alters the relative contributions of the various delay groups
to the neutron economy. A simple but usable model of this effect can be derived from
the following arguments.

Neglect variations in effects in directions lateral to fuel flow. Define x as
a variable in the direction of fuel flow, with x = o at the core entrance. With the
flow length in the core taken as A and outside the core as B, the system is evi-
dently periodic in x (with period A +B). Assume that the flow in the system occurs
without mixing. Further, assume that the neutron kinetic equations are separable in
time and space (although this will certainly not be true for some parts of a transient)

and, accordingly, write those equations with the space point as an explicit variable:

 

T = = Ban < ) cian (10)
and

dC.0t) B,

T = Tn(X,f) - )\Ici(x’f) r (1])

n(x,t) = neutron flux density at x,t,

subscript i = index denotingith delay group,

Ci(x,'r) = atomic density of precursor toith delay group at x,t,
0 = reactivity = (k - 1)/k,

k = multiplication rate,

Bi = number of precursors of ith group produced per fission,
Y = reciprocal time constant of ith group,

-

A system neutron generation time,

p = 1B, .

 
27

The variables ¢ and A are functions of the whole system, not of x; and

Bi ;, B, and A, are physical constants, also independent of x .

In a system with flow, the total time derivatives can be interpreted with

partial derivatives as follows:

dn(x ,t) an(x ,t) dx_ 3n(x ,t)
n n n n

_— = +
dt Dt dt BX ! (12)

 

dCi(xi,f) aCi(xi,’r) dx. 3C.(x.,t)

|
—_— = +
dt St dt dx, ! (13)

 

X is the x coordinate of n, and X, is the x coordinate of Ci . If the fixed

laboratory frame is chosen as the frame of reference, then

and

= v(t) = fuel flow velocity. (15)

Now, if Eqs. (12-15) are inserted into Egs. (10) and (11), and if Eqs. (10) and (11)

are integrated over x fromOto A, then

an(t) _ (9—[}3) n(t) + inci(f) , (16)

 

ot

and

 

P e Yt re(an - .00 17)
= =0l - A.C.) - 5L {C (A - C.ONT . (

 

 
28

Define

= core transit time,

I

external loop transit time.

With the assumption of no mixing, the following relation holds:

—K.TL(’r)
C.(0,1) = C.IAt = 7 (D)]e ! (18)

Consistent with the assumption of time-space separability, the end point value Ci(A,f)

will bear some fixed relation to the mean value C.(t), i.e.,
i

CE(A,’r) = fC.(t) . (19)

With Egs. (18) and (19) incorporated into Eq. (17), there results

ACi(f) : ¢ —x.'rL(f)

_ f |
s - - [M * W}Ci(f) ¥ :—CWC;U - 7 (e . (0

 

Equations (16) and (20) comprise the basic neutron kinetic equations for the
model of the flowing system. (In the simulation we chose the parameter f = 1 .)

In Eq. (20) for each of the six delay groups there is an equation involving
the term Ci[f - TL(’r)] . Lagging a function, as indicated by the argument t - T
involves memory. The available analog equipment contained only two such memory
lag devices. The system lags t and T are of the order of a few seconds and are,

therefore, roughly comparable to the lags of two of the delay groups. Hence, the

available lag equipment was assigned to the representation of those two groups.
-XETL(f)
For the two short-lived delay groups the factor e is a very small

quantity, 107° or less. Hence, for those two groups, the lag term can be neglected

and the following equation can be written:

 
29

 

»C.(H B, ;
57 = Tn(f) = |}\i + W}C'(f) . (20a)

| In the two longest-lived delay groups, the time constants are considerably

larger than the system T's . Therefore the term Ci(t - 7.) can be reasonably ap-

L
proximated by

 

t T
‘ C.lt - 1) = f e © C.(t)dt" . (21)

Equation (21) is the so-called first-order lag, easily achievable with analog
equipment. Hence, the lag term is handled by incorporating Eq. (21) in Eq. (20)
for the two longest-time delay groups, by using Eq. (20a) for the two shortest-time
delay groups, and by implementing Eq. (20) with the available lag devices for the
two intermediate-time delay groups.

The limit to the precision with which components are made places limits on
the accuracy of the analog computer. The precision of the analog computer used in
this study limits to the range of 107* to 1072, Such accuracies are, of course, quite
adequate for most problems. Startup is an exception, since power levels and related
quantities change by many decades.

To deal with this problem, a model is constructed which computes logarithmic-

like quantities. Define

g = logn , (22)
Ci
hi = — . (23)

When Egs. (22) and (23) are inserted in Egs. (16) and (20), the following equations

resu lt:

 

 
 

29 - p =B, Zx.h.(f) , (24)

 

 

 

The factor n[t - TL(f)]/n(f) in Eq. (25) can be troublesome to deal with.
In steady state its value is 1. When the power is rising, its value lies between zero
and 1, and when the power is falling, its value is above 1. Since interest in the
startup problem is confined to times when the system is in steady state (before startup)
or when the system is increasing the power level until a safety trip occurs, and, fur-
ther, since during times of increasing power h;(f - TL) will be less than, possibly
much less than, hi(f) , the factor n(t - TL)/n(f) is replaced with 1. Then, the

lagged terms are treated in a manner analogous to their treatment in the untransformed

model, and the final result is

 

 

 

 

 

ah.(t) B.
afl + ha(h) ag’ff) _ fl\_i _ [X; . ch(f)]hi(f)
f ')\iTL(I‘)
+ T M h.[t -7 (H)]e ' (26)
oh.(t) B
M' i hi(f)—z%(f—) = /\_I - {)\i +T:(f)}hi(f) , (26q)

 

 
31

Equation (26) is used with the analog lag devices for the two intermediate -
time delay groups; Eq. (26a) is used for the two short-time delay groups; and Eq. (27)

is used for the two long-time delay groups. Equation (24) completes the system.

5.2 The Temperature Equations

An equation for the temperature, sufficiently general for most of our purposes,

can be written as follows:

 

 

J B(HA)i
af—[ocpé] = SV (cli -0) +k, (28)
i
0 = material density,
Cp = specific heat of the material at constant pressure,
g = temperature of the material,
a. = temperature of an adjacent material,
A(HA),
=V = rate of change in the heat transfer from the ith material with an
increment in V ,
k = amount of heat deposited per unit volume per second,
AV = differential volume = Sax ,
S = cross-sectional area of the system (assumed constant).

If the material is flowing with velocity v(t) we have, as in the case of the

neutron delay group precursors,

d A 3
a_,r—[oc:pe] = a—,r-[ocpe] + v(r)a—;[one] : (29)

 

 
32

In the above discussion we assumed only one degree of spatial freedom and,
in effect, incompressibility of the flowing material. Equation (28) is integrated over
a volume between two points in x which are characterized by n -1 and n and

produces the following:

W
—_—
x
>
i
X
>
1
I_J
e
<]
—
0
@
O
D
3
L
[l
——
I
&
>
————
Q
':.
>
!
@D
3
———

or

 

:\—é’—n_(aim . gn) ’ oCL - T]('f) (@n i en-l) ' (30)

In flowing systems, those with v(t) # O, some purely mathematical instabili-
ties can arise from the way mean values are related to endpoint values. To avoid such

problems Eq. (30) is often replaced with the pair

 

 

 

30 (HA).
_ i, n k _ 2 = _

T MC "o TTm %h T % (31a)

i P n
and
X (HA).
n _ i,n [— I k 2 =

Y M C (ai,n 8n) ¥ oC T (t) (Gn 6n) : (31b)

i np P n

Past studies of the MSRE with *®°U loading have shown that to have a faithful
representation of effects at low power ’® it is necessary to make a multinode repre-
sentation of the core for heat transfer calculations. Nine such temperature nodes have
been found to produce satisfactory results. At each of the nine nodes an equation of

the form of Eq. (30) is used to determine the graphite temperature, and two equations

of the form of Eqs. (31a) and (31b) are used to determine the fuel temperatures.

 

 
33

With the subscript G denoting graphite, and f denoting fuel, and with the

substitutions

 

8 - TG ,
o - Tf ;
k - rGP ,
we get
AT (HA) r. P
Bf’n - M - (Tfn"TG n)+oGC’n (32)
Gn pG'\ f ! G pG
P = total power,
‘G on = fraction of total power deposited in unit volume of graphite at the
E’rh node.

Similarly, from Egs. (31a) and (31b) we obtain the fuel temperature equations

AT . (HA)n _ r. P 9

 

 

 

 

f,n _ ( = ) f,n (—- )
- T -7 )+l T -T, |, (33)
X M Tl Gon ™ n] TS T T B e T T
T (HA) r. P
f,n _ n (= = f,n 2 =
5t M, C (TG,n Tf,n) foE - wl Tf,n) ' (33b)
f,n pf fpf n

In the external piping where h and k are zero we adapt Eq. (31a) and write

=2 _
< W(Ti_l Ti). (34)

 

 
34

5.3 External Heat Rejection

There was not sufficient analog equipment available to simulate all aspects

of the system simultaneously . Since the detailed response of the external heat sink

was not important to any part of the study, we decided to make an abbreviated descrip-

tion of it, abstracting and representing those features which would comprise its essen-
tials. The entire system is represented by a few gains and lags appropriately jointed
together, as follows:

. The temperature signal sent to the control system as the core outlet temperature
is the core outlet temperature aofter it has passed through a gain of one lag cir-
cuit. The lag represents transport from the core outlet to the sensing element
plus thermal lag in the sensing element.

2, The temperature sent to the control system as the core inlet temperature is, in
fact, a lead value of the core inlet temperature. It is sent through a gain of one
lag circuit to the control system, the lag representing the thermal lag of the sens-
ing element. It is also sent through a gain of one lag to the core inlet, the lag
representing transport delay from sensing element to core inlet.

3. The effect of the heat exchanger is multiply represented. There is a lag repre-
senting time from the core to the center of the heat exchanger, and another lag
from the center of the heat exchanger to the inlet temperature sensing location.
There is a gain constant that represents the heat exchanger effect, and there is
an overall gain that is power dependent. Changes in the overall gain have an-
other lag associated with them. The heat exchanger gains and lags are represented

as follows:

(35)

—
I
=
|
@
1
—
~
4
o
—
N
©
-—
o)
=
~
+
———
!
Z
—
>>L_1
0.
—
-

_—l
V)
——

—
——

hi

-—
—

-
—

+

-—l
o
—

—
St
~

(36)

 

 
35

T, = fuel temperature at the heat exchanger outlet,

T. = fuel temperature at the heat exchanger inlet,
y TH = coolant salt temperature at the heat exchanger inlet,
i TA = ambient air temperature,

G = heat exchanger gain (constant),

K = system gain (power dependent),

The power dependent K is defined by

Touf - CP - TA

 

where P is the power level and C is a unit conversion constant.
The above scheme is summarized in Fig. 16. T, and T are the temperatures

delivered to the control system as the core outlet and inlet temperatures, respectively.

T, is the transport and thermal lag to outlet sensor. T is the transport lag to the

heat exchanger. 7. is the lag in the change of gain of the system with a change in

power. T, is the transport lag from the heat exchanger to the inlet temperature sensor.
- T. is the temperature at the inlet temperature sensor. T4 is the thermal lag in the

inlet temperature sensor. T is the transport lag from the sensor to the core inlet.

T. and TO , are core inlet and outlet temperatures, respectively.
in u

5.4 Sdafety Systems

5.4.1 Trips

Two kinds of safety trip were simulated for the study: a period trip and a
power level trip. The safety trip simulation brings out one of the most powerful fea-
tures of analog analysis. The simulation is hardly a simulation at all but rather a

- nearly identical copy of the components which were used to make the safety trip

system on the reactor itself.

 

 
36

Period Trip.--The reactor period is defined as

_ {13\ _ (3 log n\~* .
Ty (;gr) (af ) : (38)

 

where TR is the period and n is the neutron flux density. TR is a function of time
unless the neutron flux density is exponential. Since it is necessary in the course of
the simulation to deal with both n and log n, some switching must be provided to
avoid saturation of equipment. We define the effective flux density seen by the ion

chamber as n* = n+ G, G = gamma-ray contribution.

The MSRE safety trip circuitry is actuated when
3 -1
~— log n*) > P_r = period frip. (39)

When the neutron flux density n is on a purely exponential period 7, the

apparent period of n* is

 

T* = T . (40)
n

Evidently, the period trip is of little use until n is not much less than G . We can

reasonably simulate the trip system over different ranges of n, as follows:

n*= G, if n< 0.05G
*=n+ G, ifO.0O5G < n < 100G
*=n, if 100G < n (41)

3
|

3
|

In the first range n < 0.05 G , nosignal is sent to the trip circuit. When
n enters the second range, the log n is converted to log (n + G) and differentiated,
and the output is sent appropriately to the trip. When n enters the third range, log n
is differentiated and the output is sent to the safety trip. It is necessary to provide .
two parallel differentiating circuits and to switch them at their output end rather than

to provide a single differentiation circuit with a switch on the input. This is because

 

 
 

37

 

 

 

 

 

 

 

 

ORNL DWG. 69-4530

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T _
CORE o [caIN-1 [T, CONTROL
LAG-T, SYSTEM
A Y
T
- GAIN-1 | T2 -
GAIN-1 LAG-T, >
LAG-Ts
? (K-G)Tp
T4 GAIN-1 T -
LAG-T, ‘3—< GAIN-1 I
Y 4 -
-G Ty LAG-T, (I-K)TA( )“_
GAIN-1 CONTROL
LAG-T; SYSTEM
Fig. 16. Schematic Diagram of External Heat Sink.

 

 
38

a switched input would contain a discontinuity which, when differentiated, would
lead to spurious trips. This scheme is shown in Fig. 2. (In Fig. 1 the period trip is
simulated in the section marked "Reactor Period Safety System Actuator." This simula-
tion corresponds almost exactly to the actual wiring diagram in the MSRE system. The

n signal is fed into a log diode and from there to a differentiated circuit.)

Level Trip.--The power level trip plays the major safety monitoring role when
the system is at power. If the neutron flux detector signal exceeds a preset level, a
trip signal is sent to the safety system. The simulation of the level trip is shown in

Fig. 1.

5.4.2 Safety Rod Drive Simulation

 

In both the log n simulation (Fig. 2) and the n simulation the safety drive is
simulated in two sections. The first section is a time lag that represents the inertial
lag of the drive. This is represented by integrator 51 in Fig. 2, the log n model;
and by the section entitled "Safety System Time Lag Generator" in Fig. 1, the n model.

This latter section can be actuated by either a period or a level trip signal. There is -
no provision for level trip in the log n model.

In Fig. 2, amplifiers 70 and 71 simulate safety rod motion. A constant rod
acceleration of 10 ft/sec” was assumed. A constant reactivity—-change per inch of rod
travel was also assumed, and this was set on potentiometer Q71.

In Fig. 1, the output of amplifier 70 is a voltage proportional to time. This
voltage drives a function generator whose output is a function of time. The function
generator output as a function of time is shown in Fig. 12. This output is the change

in reactivity due to safety rod movement in units of (p/4) .

5.5 Control System
5.5.1 Control Signal

The control system signal is sketched in Fig. 3 as Temperature Controller ¢

Generator. The following discussion will concern the five amplifiers 21, 31,, 32,

30,, and 36, and their associated circuitry. This circuitry is abstracted with very

 

 
39

little adaptation from the actual MSRE control circuitry (ORNL Instrumentation and
Controls Division drawing RC-13-12-53 R4). One can most easily understand it by
considering the output of each amplifier in turn.

The feedback circuitry of 21, introduces a gain of 10 and a first-order lag of
100 sec. Lagged quantities are designated by a superscript L . Each amplifier, of

course, multiplies by =1 in addition to any gain factor.

The inputs to 21, are +0.2T’ , -0.27" . , and -0.5P,
c,out c,In
= core outlet temperature, °F,
¢, out
T . = core inlet temperature, °‘F,
c,in
P = reactor power in Mw,

T'(v) = [T(°F) - 1100°F)/2 .
The output of 21, is then

Lo o021t Co.sph). (42)

c,out c,In

—10(0.2T

The input to 31, is the output of 21, - 2T; - +112.5 . The quantity 112.5 is simply
two times the desired scaled voltage value of the core outlet temperature, or two times

the core outlet set point, Ts/o . The output of 31 is then

c,in c,In

lO{l/S(T(':LOU,r - TS’O) - 1/5<T'L - T ” - 5PL . (43)

Amplifier 32, simply inverts the signal so that its output is the same as the above but
multiplied by -1. The input of 30, is the output of 32, minus 5P . We consider the

output of 30, to be kinetic error signal 8K , with

g = 2<TIL - T’) ~ 2<TIL. - T . > + 5<P - PL> . (44)
K c,out 5O c,in c,in

We desire that each of the three terms above which go to make up € be zero.

K

 

 
40

However, the system "sees" an error only when the sum ¢ K is not zero. It appears
on first sight, therefore, that there might be off-design cases (i.e., wrong TC .
,in
or T or P) which would yield no error signal. The second and third terms on ’

c,out
the right-hand side of Eq. (44) are, in effect, time derivatives averaged over 100

sec. Hence, if €  is at some instant zero when the three terms are not, it would

K
necessarily be at a time when the system variables were changing. The only persistent
condition for 8K = 0, therefore, appears to be the one when all three terms vanish.

Before the error signal goes to the controller, it is fed through amplifier 34,

where another part is added to it to produce the system error signal ¢ :

e =X -V (45)

The term designated v is a signal, appropriately signed, that is proportional to the
rod velocity. It is a negative feedback signal so that, whenever there is rod motion,

the magnitude of ¢ is less than the magnitude of 2 (with a few insignificant ex~

K
ceptions due to relay time lags).
The velocity feedback promotes stability by minimizing "hunting." The error -
signal is fed into a deadband comparison circuit. When the error is sufficiently great
to depart from the deadband on either side, it causes the control rods to move in such
a manner as to tend to make the error signal move back into the deadband. There are
lags in the system, however and in most cases the correction will be an over correction
which drives the error signal all the way across the deadband and out the other side.
The velocity feedback is intended to combat this effect.
The MSRE control rods are designed to operate at constant velocity when in
motion (except when they are accelerating to that velocity or to zero). The velocity
feedback signal is proportional to velocity and, hence, bounded. Gains are so chosen
that this feedback is comparable to the signal produced by a small fluctuation in tem-
perature, say of the order of 1°. If a large change in set point Tso were made, the -
velocity feedback would be negligible by comparison with EK until the system ap-

proached its new steady-state configuration. Then, and during normal steady ~state

control, the velocity feedback would be significant so that only small error signals

 

 
4]

would be sent. The system is gently "tapped" a number of times by such small signals,
always from the same side of the deadband because they are never large enough to
cause it to cross. In this manner the system is brought to or kept at steady state with-
out being pushed back and forth across the deadband by over-correcting signals.

The power-level control circuit, which is used at power levels below 1 Mw
where temperature control is neither practical nor desirable, is much simpler. The
connection between 32, and 30, is broken, and amplifiers 21,, 31_, and 32, are simply
not used. In their place a positive voltage (whose value is chosen by the operator) is
fed into 30, . This is the power setpoint PSO . Hence, the input to 30; is S(Pso -P) .

We then have at the output of 30;:

€y = 5P - PSO) : (46)

The velocity feedback and subsequent signal tracing are the same as with
temperature control.

The system is manually switched into temperature or power-level control.

5.5.2 Control Drive

The error signal ¢ of Sect. 5.5.1 is sent to some comparison circuitry (dead-
band) shown as "Controller Actuation Circuit" on Fig. 1. The two comparators MO
and M1 in this circuit are actuated by voltages which correspond to the deadband
boundaries. When either is actuated, it initiates a pure transport lag as the first part
of the control rod action. This lag is generated by the "Pure Time Lag Insert" or "Pure
Time Lag Withdraw" sections. The pure time lag corresponds to the relay lag. At the
end of the pure time lag, one of the comparators M5 or M7 is actuated. The "Con-
troller Logic and Control Rod Drives" section is the circuitry activated by M5 or M7.
These comparators cause a switch to close which sends a constant voltage into the
drive circuitry. The voltage is put through a first-order lag circuit (the lag correspond-
ing to the inertial lag of the control rods), and the output is proportional to rod ve-
locity. The integral of this output, proportionally modified by passage through

potentiometers and resistors (constant reactivity change per inch of rod motion), is

the control-rod reactivity signal applied to the integrator that generates neutron flux.

 
42

The relay lag and the control-rod inertial lag were measured in an experiment

described in the Appendix, Sect. 5.6.

5.6 Control System Lag Measurements Made at the MSRE

There were no good estimates of the relay and control-rod inertial lags men-
tioned in Sect. 5.5. The range of estimates that we obtained varied from 0.05 to 1
sec (outside possibilities). Further, exploratory simulation runs indicated that the
response of the control system was unsatisfactory over much of that range. On the
other hand, the entire lower part of the range (0.05 - 0.20 sec) appeared to permit
satisfactory control. Hence, while a measurement was needed, the accuracy demanded
of it would not be great over much of the range of possible outcomes.

The measurement was performed with the MSRE in the automatic control mode.
In this mode the control system responded to a feedback signal from the Servo Ampli-
fier. (See Instrumentation and Controls System Division drawing RC-13-12-53 R4.)
This amplifier corresponds to 36, in Fig. 3. The signal then went to some relays whose
bias determined the deadband width. The relays started or stopped the control-rod
drive motor.

In the measurement the Servo Amplifier was replaced with a circuit that sent
a controlled signal to the refays. Signals describing the subsequent motion of the
control rods were produced, and their time behavior was compared with that of the
controlled signals. From these comparisons a pure transport lag, which is associated
with the relays, and an inertial lag (the time required for the control rods to move
from their initial velocity to within 62% of their final velocity) were determined.

A TR-10 portable analog computer (Fig. 17) provided all the facilities neces-
sary to produce the excitation signal and to analyze the response voltages. Data were
taken on an 8-channel Sanborn recorder. As shown in Fig. 17, the Time Pulse Gen-
erator section caused the comparator relay to close for a time period fixed by potenti-
ometer 17. The Relay Actuator section caused a constant voltage, above the relay
bias, to be sent to the relays for the duration of the time pulse. (This voltage corre-

sponds to an error signal outside the deadband.) The control-rod drive responded to

 
500K 100K

 

VELOCITY BUFFERING CIRCUIT

 

 

10K ORNL DWG., 69-4531

 

 

 

 

 

 

 

 

 

RECORDER |
CHANNEL 2

 

 

 

 

 

 

 

10K

+HO0v o—y 10K
26 TP
FS1 & B;l vy

 

 

 

 

 

 

 

 

 

AV
10K
10K
/\}S/FQ/\ RECORDER
100K CHANNEL 8
RECORDER
M- CHANNEL 6 DIFFERENTIATOR CIRCUIT
VELOCITY INTEGRATOR
@ RECORDER
™ CHANNEL 1
0 - 10v GAIN OF 24

VWA

10K

 

 

100K§ H
100K
YW

 

TIME PULSE GENERATOR

 

WOR

T10v op—o—y o 500 40K I "ON" TIME
ON NS TP 0

_1OVIN5ERT FS2 Mt T

 

~ | RECORDER
(A)—o— CHANNEL 7

RELAY ACTUATOR

 

 

 

 

+10v

ROD POSITION BUFFERING CIRCUIT

LEGEND:
@ CONNECTOR TO ROD DRIVE RELAY

 

CONNECTOR TO ROD VELOCITY OUTPUT SIGNAL

{C) CONNECTOR TO ROD POSITION OUTPUT SIGNAL

Fig. 17. TR-10 Computer Circuit Used in the MSRE Rod Drive Response

Experiment,

 

 
44

this voltage. The output of the synchro-demodulator (Instrumentation and Controls
Division drawing RC-13-12-53 R4) was proportional to the control-rod velocity.
(There was a time lag of no more than 0.02 sec between this signal and the rod ve-
locity. An error in time of this magnitude can be ignored.) This velocity signal was
fed to the Sanborn recorder and the TR-10 computer where it was differentiated (see
Differentiator circuit) and integrated (see Velocity Integrator). The derivative and
integral were also recorded on the Sanborn recorder. The time signal sent to the re-
lays and a rod position indicator signal available in the MSRE circuitry were recorded
on the Sanborn recorder.

The rod position signal and the integral of the rod velocity should be propor-
tional to each other. They were recorded only as an overall check on the system.
The derivative of the velocity should be the rod acceleration, which, along with the
relay actuating signal, should provide a complete description of the system. To avoid
infinite derivatives, which are the derivatives of stray pulses or noise, an analog
signal must be smoothed over some time period before differentiation. In the circuit
used, the smoothing process intraduced too much distortion to permit credible use of
the derivative as an acceleration. The derivative did, however, provide a very clear
mark of the time when the control rod began its acceleration or deceleration (except
for those very short time pulses when deceleration began before rated velocity was
reached). Therefore, the velocity trace itself was also analyzed.

During the generated time pulse, a constant voltage was sent to the relays.
This voltage was a square pulse of magnitude £10 v and had a width the duration of
the pulse. The leading edge of the pulse signaled the relays to close, initiating the
signal for the control rod to begin moving. The trailing edge signaled the relays to
open, initiating fthe signal for the control rod to stop moving. The derivative showed
a sharp change when the control rod began to accelerate or decelerate (except for
very short width time pulses). The time displacement between the leading edge and
the derivative acceleration pulse and the displacement between the trailing edge
and the derivative deceleration pulse gave measures of the pure time lags associated
with the relays. The shape of the velocity curve from the beginning of acceleration

(or deceleration) to the final velocity value was fitted with an exponential. The

exponential time characteristic was associated with the rod inertial lag.

 

 
45

For all four of the cases determined by rod startup, stop, insert, or withdraw,
the relay lag could be taken as 0.05 sec + 0.01 sec and the rod inertial lag 0.04 sec +
0.02 sec. The uncertainties are acceptable. The recorder traces for the 0.5-sec time
pulse case are shown in Fig. 18. For comparison purposes, recorder traces for the same

case obtained from the simulated control-rod drive system are shown in Fig. 19.

-1 ‘Fn.os sec ORNL DWG. 49-4532

   

FULL WDR,

  

CONTROL ROD
VELOCITY

|
T

   
  
 
  
 

FULL INSERT
CONTROL ROD
DRIVE RELAY
ACTUATING WDR.
VOLTAGE

INSERT |5
|
DERIVATIVE ===
" OF CONTROL =

ROD VELOCITY

Fig. 18. Response of the MSRE Control Rod Drive (as Measured).

ORNL DWG, 69-4533
- 0.05 sec

—12.5-
ROD DRIVE RELAY _
ACTUATING WOR. —— L
VOLTAGE +
0=
INSERT
$12.5=
FULL
" WOR.
CONTROL ROD
VELOCITY
0
-
FULL INSERT

Fig. 19. Response of the Computer Simulated MSRE Control Rod Drive.

 

 
REFERENCES

O. W. Burke, MSRE-Preliminary Analog Computer Study: Flow Accident in

 

Primary System, ORNL unpublished internal document (June 1960).
O. W. Burke, MSRE-Analog Computer Simulation of a Loss of Flow Accident

 

in the Secondary System and a Simulation of a Controller Used to Hold the

 

Reactor Power Constant at Low Power Levels, ORNL unpublished internal docu-

ment (November 1960).

 

O. W. Burke, MSRE-Analog Computer Simulation of the System with a Servo-

 

Controller, ORNL unpublished internal report (December 1961).
S. J. Ball and T. W. Kerlin, Stability Analysis of the Molten Salt Reactor Ex-
periment, ORNL-TM-1070 (December 1965).

 
ORNL-4397
UC-80 — Reactor Technology

INTERNAL DISTRIBUTION

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