ORNL-TM-2823.txt

 

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. ~ CENTRAL RESEARCH LIBRARY
DOCUMENT GOLLEGTION

 
   

 

 

[ 1 OAK RIDGE NATIONAL LABORATORY
I o operated by
(BN UNION CARBIDE CORPORATION m
| NUCLEAR DIVISION
for the
U.S. ATOMIC ENERGY COMMISSION
| ORNL- TM- 2823
" LIRART ! |
/23
3 445k 0514033 5

|
|
|
|

9
| 4

2

FREQUENCY-RESPONSE TESTING OF THE MOLTEN-SALT REACTOR EXPERIMENT
(Thesis)
R. C. Steffy, Jr.

|
|
[ % Submitted to the Graduate Council of the University of Tennessee in partial fulfillment

i for the degree of Master of Science.

 

 
ORNL-TM-2823

Contract No. W-7405-eng-26

REACTOR DIVISION

FREQUENCY-RESPONSE TESTING OF THE
MOLTEN-SALT REACTOR EXPERIMENT

R. C. Steffy, Jr.

Submitted to the Graduate Council of the University of Tennessee in
partial fulfillment for the degree of Master of Science.

MARCH 1970

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

flO(.‘IKHliEDIMAHTN ENERGY RESEARCH LIBRARIES

3 44bE 0514033 5

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TABLE

LIST OF TABLES + o &« & « & &
LIST OF FIGURES . . . . . .
ACKNOWLEDGEMENTS . . . . .

ABSTRACT . . . . . . . « . .

I.
IT.

ITT.

V.

INTRODUCTION . . . . . .
SYSTEM DESCRIPTION . . .

Physical Description.

Theoretical Predictions

EXPERIMENTAL PROCEIURE .

Test Patterns . . . .

iii

OF CONIENTS

* [} . . . » . - . a *

Pseudorandom binary sequences. . . . .
Pseudorandom ternary sequences . . . . . .
Choice of Pseudorandom sequence . . . .

Signal Generation . .
Rod-jog tests . .
Flux-demand tests.
Rod-demand tests .

Data Acquisition . .

Data Analysis Methods
Computing schemes

Comparison of data

EXPERIMENTAL RESULTS . .

235U Fuel Loading .
Rod-jog tests .
Flux-demand tests,

£33 Fuel Loading . .
Flux-demand tests,

Rod-demand tests .

LIST OF REFERENCES . . . .
APPENDIX . * . * . . . . . .

CONCLUSIONS AND RECOMMENDATIONS., o o o o o o o &

viii

ix

10
13
13
13
18
20
2l
25
26
30
32
3k
34
35
51
51
52
57
6
Qb
103
106
110
iv

LIST OF TABLES

TABLE PAGE
I. Composition of MSRE Fuel Salt . . . . . v +v v v o v o v . L
IT., DNeutronic Characteristics of MSRE with 23 and 235U Fuel
Salt at 1200°F. & v v v v v e e e e e e e e e . 6
IIT. Results of Different Analysis Techniques at 0.016L49 rad/sec
When Applied to Eight Periods of Data . . . . . . . . . Lo
IV. Results of Different Analysis Techniques at 0.4gLTh rad/sec
When Applied to Eight Periods of Data . , . . . . . . . L1
V. Results of Different Analysis Techniques at 0.989L47 rad/sec
When Applied to Eight Periods of Data ., ., . . . . . . . L2
VI. Results of Analysis at a Harmonic Frequency (0,3298 rad/sec)  kk
VII. Results of Analysis at a Non-Harmonic Fregquency (O.3h63
rad/SeC). v v v w4 e e e e e e e e e e e e e e e e e L5
VIII. Pertinent Information Related to Each Test Performed for

This Study . . o ¢ & v 0 v v i e e e e e e e e e e 111
LIST OF FIGURES

FIGURE
1. Basic MSRE Flow Diagram . . + « & o o & o o o o o o o o o o
2. Electromechanical Diagram of MSRE Contrcl Rod Drive Train .
3. MSRE Control-Rod Drive Unit Power Transmission Diagram. .
4., Theoretical Frequency Response of Z>°U-Fueled MSRE for
Several Power Levels . . 4 o o o o o o o o o o o o o o
5. Theoretical Frequency Response of £°-Fueled MSRE for
Several Power Levels . .« ¢ & ¢ ¢ o o o o & o o o o s o
6. Example of a Pseudorandom binary sequence, {a) Time Behavior,
(b) Autocorrelation Function, and (c¢) Power Spectrum. . .
T. Example of a Pseudorandom Ternary Sequence, (a) Time
Behavior, (b) Autocorrelation Function, and (c) Power
SPecTrUmM & v v ¢ ¢ ¢ o o 4 o 4 o & o o s & s s s e o s
8. Range Over Which the Power Content of a PRBS or PRIS is
Essentially Flat for Sequences of Various Length and
Bit Times . & v 4 o & o o & o o o o o o o o o o o o o o o
9. Control-Rod Position and Flux for a Typical PRBS Rod-Jog Test,
A Typical PRBS Flux-Demand Test and a Typical PRTS Flux-
Demand Test . . . ... « o e s s s s 4 s o s s s e s s e e
10. Circuitry Used for Generating the Pseudorandom Signals for
the Flux-Demand Tests . . . . + ¢« ¢ v ¢ v ¢ o o o o o« o &
11, Natural Filters for One-Period Analysis and for Eight-

Period Analys is * . . . * . . . . * * » - * o . . . . * 2

PAGE

11

12

15

19

23

27

29

37
vi

FIGURE PAGE
12, Shape of the Analysis Filter Employed by the CPSD Technique

for Various Values of the Damping Factor, ¢ . . . . . . . L8
13. [Frequency-Response Results Obtained by Analyzing a Test Case

Using the CPSD Analysis Scheme with Various Values of the

Damping Factor, £ . « v v ¢ v v v v v v 0 0 o o v o v v Lg
14, Correlation Function and Power Spectrum Results from a

Rod-Jog Test., . & v 4 4 & o v v v v 6 6 v v e o v e e e 53
15. Frequency-Response Results from Rod-Jog Tests . . . . . . . o7
16. Correlation Function and Power Spectrum Results from a Flux-

Demand Test Using a PRBS Test Pattern . . . . . . . . . . 59
17. Frequency-Response Results from a Flux-Demand Test with the

Reactor at 5 Mw with U-235 Fuel . . . . . . . . . . . . . 62
18. Frequency-Response Results from a Flux-Demand Test with the

Reactor at 2 Mw with U-235 Fuel . . . . . . .« . . . . . . 66
19. Correlation Function and Power Spectrum Results from a

Flux-Demand Test Using a PRTS Test Pattern . . . . . . . 67
20. Frequency-Response Results from a Flux-Demand Test Performed

on the £®U-Fueled Reactor .Using a PRTS Test Pattern, . . 70
21, Correlation Function and Power Spectrum Results from a Flux-

Demand Test Using a "Non-Symmetric!" PRTS Test Pattern . . 72
22, Frequency-Response Results from Flux-Demand Tests Performed

on the £2°U-Fueled Reactor Using "Non-Symmetric'" PRTS

Test Patterns . v v v v ¢ o o o o o « .

c e e e e e e 5
vii

FIGURE

23, Examples of the Uncontrolled Neutron Flux During Periods of
8 Mw Power Operation for the 23°U Fuel loading and the
233] Fuel T10adiNg o o o o o o o 0 0 . e s 4 e s 0 e e e s

ol,, Frequency-Response Results from Flux-Demand Tests Using
PRES Test Patterns Performed on the £>%-Fueled Reactor .

25, Frequency-Response Results from Flux-Demand Tests Using
PRTS Test Patterns Performed on the £°AJ-Fueled Reactor .

26. Frequency-Response Results from Rod-Demand Tests Using PRBS
Test Patterns Performed on the £>%U-Fueled Reactor. . . .

27. Frequency-Response Results from Two Periods of a Rod-Demand

Test Using a 242 x L PRTS Test Pattern. . . . . . . . . .

PAGE

78

79

86

95

100
viii

ACKNOWLEDGEMENT

The author wishes to thank Dr. T, W. Kerlin for his guidance in
the direction, for his expert instruction in the theoretical phases of
this study, and for his assistance in the data-interpretation,
Mr, S. J. Ball was responsible for the design of much of the electronic
circuitry used in the testing, was a helpful consultant for all prhases
of the testing, and was very helpful when computer-related problems
occurred. His assistance is gratefully acknowledged. The author wishes
to acknowledge Mr. J. L, Lucius for his help with computer problems.

The cooperation of the entire staff at the MSRE is appreciated,
ix
ABSTRACT

Tests to determine the neutron flux-to-reactivity frequency response
were performed on the Molten Salt Reactor Experiment with the reactor at
various power levels between zero and full power and with the reactor
fueled with a 22U fuel mixture and a 2337 fuel mixture, Test patterns
employed were pseudorandom binary sequences (PRBS) and pseudorandom ter-
nary sequences (PRTS) of various sequence lengths and minimum-pulse-
duration times. 1In some tests reactivity (control-rod position) was
forced to follow the test pattern, and in other tests the neutron flux was
forced to follow the test pattern. The experimental results were analyzed
by several different methods and the results were compared.

The frequency response of the uncontrolled reactor system was found
to be in good agreement with theoretical predictions for both the 2357 ana
233 fuel loadings. There were no indications of response characteristics
that might cause control or safety problems.

The power spectra for the various sequences were flat over the ex-
pected ranges and variations in the sequence specification changed the
power spectra in the expected manner with no anomalous changes. A diagram
is presented which makes specification of the spectral characteristics for
a particular sequence immediate.

For the 75U fuel loading, results of the flux-controlled testing
using PRBS's and PRIS's were adequate, but for the 7%y fuel loading,
additional system noise coupled with equipment limitations caused ex-
cessive scatter in the frequency-response results for both type sequences,

For the ©°2U fueled system, a closed-loop method of positioning the
control rod and use of a PRBS was necessary to obtain acceptable results.
Use of a PRTS with this method of control-rod positioning caused intro-
duction of errors in the indicated control-rod position rendering the test
results unacceptable.

Experimental data were purposely analyzed at non-harmonic frequencies
showing that careful specification of the analysis frequency is necesgary
for meaningful results, 1In data containing a large amount of noise, the
results of analysis of the same data by the different techniques were
found to contain anomalous differences, particularly at the first few har-
monic frequencies, Analysis of the data by the different methods for low-
noise tests gave results which were in excellent agreement.

Keywords: frequency-response testing, MSRE, pseudorandom binary se-

quences, pseudorandom ternary sequences, signal generation, Fourier analysis,
235y 23
’
CHAPTER T
INTRODUCTION

The dynamic response of a nuclear reactor may be characterized by
several methods.l* One of the more useful methods is the determination
of the power-to-reactivity frequency response of the uncontrolled reactor.
Mathematical models are usually formulated which predict the frequency
response before the reactor is in operation., These same models are
frequently used in application of.stability criteria, such as the
Tamiliar Nyquist stability criterion® or determination of the eigen-
values of the system matrix. 2,3  Stability criteria can seldom be
"measured" so the adequacy of the mathematical models must be determined
by some other means. Determination of the adequacy of a model is important
since it is entirely possible that analysis of a mathematical model will
show a reactor to be stable yet the mathematical model may be incapable
of accurately describing the actual response of the system.

One method by which the adequacy of a model may be determined is to
compare the theoretical frequency response with the experimentally de-
termined frequency response. Perhaps more important is that, regardless

of the agreement between the predicted and observed response, once the

 

*Superscript numbers refer to similarly numbered references in the
IList of References.
experimental frequency response is determined the dynamic response char-
acteristics of the actual system are known and this is the information
of primary interest,

The frequency response of the €357J-fueled Molten-Salt Reactor Experi-
ment (MSRE) was predicted by Ball and Kerlin® and the results of the
initial, experimental, frequency-response tests were reported by the same
authors.® The purpose of the work reported herein was to continue the
experimental tests throughout reactor operation with €357 ag the fissile
material and then to continue the testing program throughout reactor
operation with £33 as the fissile material. Variations were made in
testing signals and testing techniques and the effects of these variations

on the experimentally determined frequency response were noted.
CHAPTER IT
SYSTEM DESCRIPTION
I. PHYSTICAL DESCRIPTION

The MSRE is a liquid-fueled, graphite-moderated, thermal reactor.
The ligquid fuel is composed of the fluorides of uranium, zirconium,
lithium, and beryllium in the proportions shown in Table I. The liquid
in the secondary loop is composed entirely of LiF (70 mole percent) and
BeFo. At full power, the reactor produces about 8 Mw of power which is
dissipated to the atmosphere by an air-cooled radiator through which about
2 x 10° cfm of air is forced. Figure 1 shows the basic flow diagram for
the MSRE,

The basic differences between the dynamic behavior of the MSRE and
most other #%U-fueled reactors arise due to the circulating fuel. The
most apparent effect of the fuel circulation is the birth of delayed neu-
trons in the external loop; indeed, the fuel circulation lowered the
effective fraction of delayed neutrons born in the core from .0067 to
.00kL for the U-235 fuel loading and from .0026 to .0017 for the
U-233 fuel loading.® It requires about 17 sec for fuel leaving the core
region to reenter the core, and at higher powers the effects of fuel salt
reentering the core with a temperature which is representative of the
power level 17 sec earlier also has a pronounced effect on the dynamic
behavior of the neutron flux., Table IT lists certain important facts
about the neutronics of the MSRE, particularly those which affect the dy =

namic response of the reactor.
TABLE T

COMPOSTTION OF MSRE FUEL SALT

 

 

2357 Fuel Loading

£33] Fuel Loadingb

 

(Mole %) (Mole %)
LiF 65 6L.5
BeF o 29.1 30.2
ZrF 5 5.2
UF, 0.9 0.1k

ISOTOPIC URANTUM CONCENTRATIONS

(Atom %) (Atom %)
2337 0 8h.7
234y 0.3 6.9
235U 35 2.5
2363 0.3 0.1
2387 6L, b 5.8

 

 

a. Molten-Salt Reactor Program Semiannual Progress
Report, July 31, 1964, USAEC Report ORNL-3708, Oak Ridge
National Laboratory, p. 231, (November 1964).

b. Molten-Salt Reactor Program Semiannual Progress
Report, February 28, 1969, USAEC Report ORNL-4396, Oak Ridge
National Laboratory, p. 130, '
Il REACTOR
|| VESSEL

 

FUEL
. PUMP

0
|| o0 HEAT EXCHANGER ¢
(o =

X1 o
=\ [1100°F

OVERFLOW
TANK
FREEZE
FLANGE
|
1
F=-T\ 1175°F 1200 gpm

 

REACTOR CELL

——— — — == ===
| oraIN T 1|
'|TANK |
CELL FREEZE L I

1 VALVE |
I [ [ !
|

] |
| |
| I

SPARE FILL AND  FLUSH

FILL AND DRAIN TANK TANK

DRAIN TANK (73 cu ft)

(73 cu ft)

(73 cu tt)

FIGURE 1.

— .

I
[l

1025°F

ORNL-LR-DWG. 56870R{

850 gpm

T
5 I
=)

 

AlR

200,000 cfm

100°F

Basic MSRE flow diagram,

RADIATOR

COOLANT

 

 

 

COOLANT
PUMP

COOLANTIl
CELL

I
I
I
I
I
I
[
I
I

I
I

300°F

ORAIN TANK

(449 cu ft)
TABLE IT

NEUTRONIC CHARACTERISTICS OF MSRE
WITH 73U and 75U FUEL SALT at 1200°F

 

 

 

£33 Fuel 2357 Fuel
Minimum Critical Uranium Loadinga
. b
Concentration (g U/liter salg) 15.82 33.06d
Total Uranium Inventory (kg) 32.8 207.5
Prompt Neutron Generation Time (sec) L.o x 107% 2.4 x 107
Reactivity Coefficients®
Fuel Salt Temperature (°F)~1 -6.13 x 107° k.1 x 10°°
Graphite Temperature [(°F)~1] -3.23 x 1073 -L.0 x 10°°
Total Temperature [(°F)~1] -9.36 x 107° -8.1 x 107>
Fuel Salt Density +. 4L 0.182
Graphite Density +.54hLY 0.767
Uranium Concentration +.389 0.234
Effective Delayed Neutron Fractions
Fuel Stationary 2.64 x 10773 6.66 x 1073
Fuel Circulating 1.71 x 1072 L.k x 1073
Reactivity Change Due to
Fuel Circulation (% 3k/k) -.093 -0.222

 

 

 

“Fuel not circulating, control rods withdrawn to upper limits.

b
2357 only.

“Rased on 73.2 ft° of fuel salt at 1200°F, in circulating system

and drain tanks.

dBased on a final enrichment of 33% #7°U,

e e eas V) . .
At initial critical concentration.

Where units are shown,

coefficients for variable x are of the form &k/kdx; otherwise, coef-

ficients are of the form xak/ksx.

inghly enriched in the fissionable isotope (91.5% 23U or 93% =7°U).

Source: Haubenreich, P. N. et al,, "MSRE Design and Operations Report,
Part V-A, Safety Analysis of Operation with 237U, " USAEC Report ORNL-TM-
2111, Oak Ridge National Iaboratory, p. 41, (February 1968).
Since the reactivity perturbations for the experimental tests re-
ported herein were introduced by control rod movement, a brief description
of the control mechanism will be given, The reactor is controlled by
three control rods which are positioned in thimbles near the vertical
centerline of the core and are inserted into or withdrawn from the core
as demanded. Normal rod movement (as opposed to a rod scram) is achieved
by activating a single-phase reversible-drive motor. This, in turn,
drives a chain which is attached to a flexible cable that is threaded
with beads of the poison, gadolinium oxide. The cable maneuvers around
two 30° bends in the thimble before reaching the core centerline position.
The three control rods are essentially identical in every respect;
however, during operation, bne of the rods is positioned farther into
the core and is used as a regulating rod., It was through movement of
this rod that reactivity perturbations for the dynamics tests were
introduced,

A schematic diagram of the control-rod drive train is shown in
Figure 2, and a detailed schematic of the drive unit assembly is shown
in Figure 3. These are shown in detalil in order to give the reader a
feel for the complexity of the control rod assembly so that the problems
encountered in trying to determine the exact position of the lower end
of the control rod might be better appreciated.

A complete description of the MSRE physical plant is given in
Reference 7, and a description of the instrumentation is given in

Reference 8.
ORNL-OWG 63 -8334R
INPUT TO SIZE 18 SYNCHRQ CONTROL

TRANSFORMER, PART OF TORQUE
AMPLIFYING ROD POSITION TRANS- —
MITTER IN SHIM REGULATING ROD
LIMIT SWITCH ASSEMBLY

INPUT SIGNAL TO Q-2360 TORQUE
AMPLIFIED ROD POSITION POTEN-
TIOMETER DRIVES IN LOGGER-
COMPUTER ROOM

 

 

 

 

 

 

 

 

 

 

 

 

 

      
 

 

 

 

 

 

 

 

a— FINE
TO POSITION READOUTS SYNCRO NO.2
IN CONTROL ROOM | — cOARSE 60° PER INCH
OF ROD MOTION
POSITION
POTENTIOMETER
ROO POSITION
INPUT TO SAFETY SYSTEM b
TO SAFETY B
SYSTEM REDUCTION
GEARING
e
FAN SYNCHRO NO.1
MOTOR 5% PER INCH
OF ROD MOTION _
TACH
SERVD
MOTOR
DRIVE
ELECTROMECHANICAL SPROCKET
(m] CLUTCH ,E
REDUCTION \EOUAL RPM o SPROCKET
GEARING [ . 1-TO-¢ GEARS CHAIN
INCLUDES _f 1t
REVERSE
LOCKING

 

   

AIR FLOW

OVERRUNNIN
£ ¢ TO COOL ROD

CLUTCH

FLEXIBLE
TUBULAR ROD
SUPPORT-/

v=0.35in/sec I

 

 

T X%

POISON ELEMENTS

THIMBLE —

 

HORIZONTAL

GRAPHITE BARS — GRID PLATE

 

CORE VESSEL—™

 

FIGURE 2. Electromechanical diagram of MSRE control rcd drive train.
RATIOS:

POT. ROTATION _ 5°

ORNL-DWG 66-39154a

FINE SYNCHRO ROTATION _ 60°
ROD TRAVEL ~ in.

COARSE_SYNCHRO ROTATION __ 5° 52T, 32op

ROD TRAVEL in, ,
POTENTIOMETER
30T, 320P /c\ SINGLE TURN
ROD TRAVEL — in. 52T, 32DP (/ " 1000
7 T P @ " "
°T 320 @a COARSE" SYNCHRO
26T, 320P 02 A ‘ SIZE 31
26T, 320P &7 Ysi¥<= <57 390p
78T, 32DP “3\‘ , 32D
TS Q‘

 

SPROCKET, 64T PITCH "FINE" SYNCHRO

CIRCUMFERENCE SIZE 18
4.00 INCHES
— : ELECTROMAGNETIC
SPROCKET CHAIN
proocET , CLUTCH, 32 v dc
3~ in. /, 0.24 omp, ELECTROID CO.
26T, 320P C NO. 2EC-26CC-8-8
/ 54T, 24DP

  
 
  

54T, 24DP

OVERRUNNING CLUTCH
FORMSPRAG TYPE FS/05

WORM, 24DP, SINGLE THREAD

WORM WHEEL
52T, 24DP

    

u 54T, 24DP

41T, 24DP '
40T, 24DP

   
   
 

14T, 24DP
14T, 240P

SERVO MOTOR, 115 v,
25 2¢ — -

DIEHL cO. MoToR | S0 ¢PS» 25w, 2¢
BASIC ASSEMBLY
NO. FPF 49-91-1

 

ac TACHOMETER

 

 

BLOWER

24T, 2LDP means 24 teeth on diametral pitch of 2k.

FIGURE 3. MSRE control-rod drive unit power transmission diagram.
10
IT. THEORETICAL PREDICTIONS OF FREQUENCY RESPONSE

The mathematical model® which was used to predict the frequency
response of the 235J-fueled MSRE divided the reactor core into 18 fuel
lumps and 9 graphite lumps. The external loop (coolant system and heat
exchanger included) was also modeled using a lumped parameter model.
Results of the initial dynamics tests® were in excellent agreement with
the predictions, so the same basic model was used to predict the response
of the 23j-fueled system,->

Figures 4 and 5 show the theoretical neutron level-to-reactivity
frequency responses for the two fuels. In general, the theoretical curves
will also be shown with the experimental data and are shown here for
comparison purposes.

For the higher power levels, an outstanding feature of these plots

 

is the dip in the magnitude-ratio curves at about 0.2k rad/sec and

on
’ No-8k ’
the associated "bumps'" in the phase angle. The frequency at which these
occur corresponds to the time required for the fuel to circulate completely
around the primary loop (25 sec) and is caused by the return to the core
region of fuel which has temperature representative of the power level
25 sec earlier. With the £7°U fuel, the dips in the magnitude-ratio
curves were relatively small and were not verified in the initial testing
program,® but for the #37U fuel, the predicted dips were larger and it
was hoped that these could be verified. For a given fuel loading, the mag-
nitude of the dip is a function of the salt mixing> that occurs during the

circulation around the primary system. More mixing causes a less pronounced

dip.
11

ORNL-DWG 69-12243

ZERO POWER T g
I

104

+

 

 

 

 

 

 

30 5 Mw

 

P

AN
\

N M %
—

 

PHASE (deq)
O

\

 

 

 

-30
T

"

 

%E ";;fiLN\ |

 

-60

 

/ ZERO POWER

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-90 E
1073 1072 107! 109 101

FREQUENCY (rad /sec)

FIGURE 4, Theoretical frequency response of 275U-fueled MSRE for
several power levels.
12

4 ORNL-DWG 69-12244

ZERQO POWER

3n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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éo
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N
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g N\
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I N U
a N ™
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-30 \‘--r, P X
1T N
-60 — ZERO POWER 5
N
AT
T
-390 3 -2 - 0 {
10 2 5 10 2 5 10 2 5 10 2 5 {0

FREQUENCY (rad/sec)

FIGURE 5, Theoretical frequency response of 2337-fueled MSRE for
several power levels,.
13

CHAPTER ITI
EXPERIMENTAL PROCEDURE

In all experimental frequency-response tests which utilize a de-
terministic inputrsignal, the same general procedure must be followed:
(1) the pattern of the input signal which is to be used must be determined,
(2) the input signal must be imposed upon the system, (3) the values of
the input signal and the resulting output must be determined and recorded,
and (4) the record signals must be analyzed, While there is great variety
as to how each of these steps may be performed, they must each be per-
formed before an experimental frequency-response determination can be made,

In this section, the method by which we satisfied each of these require-

ments will be discussed.
TI. TEST PATTERNS

The basic test patterns which were used in the experimental determi-
nation of the frequency response of the MSRE were the bseudorandom binary

sequence (PRBS) and the pseudorandom ternary sequence (PRTS).

Pseudorandom Binary Seguences!©
*
Certain periodic, binary (two-level) sequences of square-wave pulses

(bits) are known to have the following important mathematical properties:

 

*
The two levels which a PRBS assumes are O and +1 during the genera-

tion stages, particularly if the shift register technique mentioned later

1s used., However, the values a PRBS assumes in practice are +1 and -1.
14

(1) The autocorrelation function of the sequence has a spike at lag
time equal zero and an identical spike at lag times of nT
(n is an integer and T is the period length). The value of the
auto correlation function is slightly less than zero between the
spikes.

(2) The power spectrum of the sequence is flat over a wide frequency
range. The particular frequency range over which the spectrum
is flat depends on the particular sequence and the pulse width,

An example of a PRBS, its autocorrelation function, and power spectrum
are shown in Figure 6. The analytical expression for the autocorrelation

function of a PRBS is:
Z + 1

 

 

Cir(t) = 1 - (57, 0=t =T/7;
Cii(7) = - 1/z, T/z<t<T- T/Z;
Cia(7) = -2+ (& ; L1, T-T/z<7<T,
where

€,:(1) = the autocorrelation function,

T = lag time,

Z = number of bits in sequence,

T = period length, and

T/z = pulse width of a single pulse (bit).

The Fourier series coefficients of the autocorrelation function define
the power spectrum of the PRBS. Since the autocorrelation function is
periodic, the power spectrum will be non-zero only at harmonic frequencies.

The amplitude of the power spectrum at these frequencies is given by:'©
15

ORNL-DWG 69-9522R2

 

0 2 4 6 8 10 12 14
TIME INCREMENT

 

 

) /\
0.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2
= 0.
3
o
s 0
2 i \ /
° (5)
-0.5
0 2 q 6 8 10 12 14
CORRELATION TIME
1.0 °
¢
@
0.5
®
(c) o
Oe o e © o °
0 2 4 6 8 10 12 14

FREQUENCY (harmonic number)

FIGURE 6, Example of a pseudorandom binary sequence, (a) time behavior,
(b) autocorrelation function, and (c) power spectrum.
16

 

A(k) = 1/2° for k = O,
sin i -
2(z + 1) 7
A(k) = oy T for O<k = 1, 2, 3, ---,
Z
where
. th .
A(k) = power in k harmonic, and
Z = number of bits in the sequence,

True random noise has a power spectrum which is flat over all fre-
quencies and the autccorrelation function of random ncise has a spike at
the origin and is zero elsewhere. The similarity between the properties
df random noise and a pseudorandom binary sequence is apparent.

Only sequences which contain certain numbers of bits (e.g., the
number of bits in one period of a PRBS must be odd) possess the possi-
bility of exhibiting the aforementioned properties. Usable sequences are
generally classed according to the number of bits in a period with the
most popular classifications being:

(1) Maximal length®®s11,%Z2 or m-sequences which have possible periods

of N = 2" -1 (n is an integer).

(2) Sequences derived from quadratic residue codes'Z; 17 which have

periods N = Uk - 1, N being a prime number and k an integer.
Other classifications include biquadratic residue, octic residue, twin
prime, and Hall sequences. A description of each of these seguences.
may be found in Reference 12,

Knowing the number of bits in the sequence is not sufficient to

ensure that it will possess the mathematical properties previously
17

mentioned. These rules merely state that it is possible to construct a
sequence of this length which will possess these properties, The actual
ordering of the bits in a sequence to get the desired mathematical
features is tedious and on-line signal generation does not appear prac-
tical except for the m-sequences, whiéh have periods o™ - 1, These may
be generated using the shift-register technique which is well sulted for
digital computers., The shift register technique is based on linear re-
cursive relationships in which the first stage is replaced, after each
shift, by adding the contents of certain other stages using Modulo-2
arithmetic. The details of shift register techniques and the stages
which must be added to obtain a particular sequence are well documented

in the literature.1%s 11

It is worthwhile to note here that if the proper
stages in the register are not used in the feedback to the first stage

a periodic sequence will be generated, but it will not have pericd

5% _ 1 and will not possess the desired mathematical features, 4 large
amount of work has been presented in the open literature on the generation
and properties of pseudorandom binary sequences ., *07 1%

From an experimental testing standpoint, the flat power spectrum of
the PRES is an important property. For by changing the reactivity in the
form of a PRBS, the power-to-reactivity frequency response may be de-
termined for a wide frequency band with one experiment; whereas, the

more conventional method of using a special control-rod oscillator re-

quires a test for each frequency cf analysis.
18

Pseudorandom Ternary Sequencesl®

A pseudorandom ternary sequence is a periodic ternary (three—level)*
sequence of square-wave pulses which possess the following important
mathematical properties:

(1) The autocorrelation function of the sequence has a positive
splke at lag time equal zero and an identical spike at lag times
of nT. There is also a negative spike of equal magnitude at
lag times of n T/2,

(2) Like the PRBS, the power spectrum of a PRTS is flat over a wide
frequency range; however, only the odd harmonics contain signal
power, Therefore, for similar tests, the PRTS would have fewer
useful harmonics than a PRBS but more signal power in the good
harmonics,

An example of a PRTS, its autocorrelation function, and power spec-

trum are shown in Figure 7. The analytical expression for the autocor-

relation function of a PRTS is

Cll('r) = l‘,'i]z""l'; OEng 3
T T
Ci:{t) = o0, g =T=5 75
C () — -Z'—:-E_...Z_ 2_:[:.< <2-
18T, = 75 T 2 7z =1=5:
C () _ -Z_ig._z E< <I+E
LN = T T T p =TSS5 T 55
T T T
Cia(t) = 0, crzsT=T->;
Z T
Cll(T) = l:_[l"T'f‘l-Z, T‘ZSTST

 

*
In generating the ternary signal the levels normally used are 0,1,2,

but in actual application the levels used are 0,1,-1. Note that the levels
0,1,2 correspond to 0,1,-1, not to =1,0,+1 as is sometimes quoted in the
literature.®® Effects of this difference are shown in Sect. 1 of Chap Iv.
19

ORNL-DWG €69-9523R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 2 4 6 8 10 12 14
TIME INCREMENT
‘ T
‘—-T/Z-_—’4
0
- 1
c
=3
-
o
= 0
o
o
(&)
|
O 2 4 6 8 10 12 14
CORRELATION TIME
1.0r—* ]
°
0.5
() *
0 2 4 © 8 10 12 14

FREQUENCY (harmonic number)

FIGURE 7. Example of a pseudorandom ternary sequence, (a) time behavior,
(b) autocorrelation function, and (c) power spectrum.
20

where the symbols have the same meaning as before. Note that the auto-
correlation function is normalized to equal 1 at 1t = Q.

The amplitudes of the power spectrum at the harmonic frequencies are

 

given by
A(k) = o for k = 0 or even
and cin _}Efll o
8(Zz + 1 Z
Alk) = _L‘j;-l' — for k = odd.
z Knt
3 Z

A PRTS has an average value of zero while the average value of a
PRBS is non-zero (but is small). For zero-power reactors or for systems
in which variable drift is a problem, the zero average value of a PRTS
may be a distinct advantage, particularly for short seguence tests in
which the deviation of the average value of the PRBS is farther from zero.

Another advantage of the PRTS is that it discriminatesZ0 against
system nonlinearities and therefore gives a better estimate of the
"linearized" system response, This should be particularly useful for
testing systems which are strongly nonlinear. The primary disadvantage
of the PRTS is the three levels. In practice it is often considerably
more difficult to achieve three levels with available system hardware than
it is two.

More information about the properties of pseudorandom ternary se-

quences may be found in References 11, 1k, 19, 20, 21, and 22.

Choice of Pseudorandom Sequence
The anticipated response of the system under investigation usually

dictates the desired frequency spectrum of the input signal. One usually
21

desires to have a spectrum with sufficient signal power over the range
where the system has a resonance peak or other interesting characteristic.
For a periodic signal, the lowest freguency containing information
is, of course, the fundamental frequency,
fo = 2£/T , (1)
where

fo

1

fundamental frequency (rad/sec), and

T

period length, sec.

For a pseudorandom binary or ternary sequence, a 'rule of thumb"” for the
highest frequency at which one should plan to obtain useful information
is the harmonic frequency at which the signal power is equal to one-half
the power in the fundamental harmonic. This is not a physical limitation,
but serves as a guide in planning tests. The actual physical high-
frequency limit for obtaining realistic results 1s based on the noise
level in the system and data-sampling rate.

Tt can be shownl® that the harmonic with about one-half the ampli-
tude of the fundamental harmonic is given approximately by the relation,
k, = 0.4z,

where

n

harmonic number of the harmonic with one-half the amplitude
of the fundamental, and

i

1

Z, number of bits in the sequence.

Tt follows that

and

H
i

0.447 2x/T (3)
22

Rearranging this expression yields

 

.88
T/Z = T (4)
but T/Z is just the duration of one bit so
. . . . 88n
basic bit duration = T/7 = T (5)

This implies that specification of = high-frequency limit also specifies
the basic bit duration. Note that the upper frequency limit is indepen-
dent of all other properties of the sequence.

With these basic relations, the graph shown in Figure 8 can be con-
structed. This graph presents all of the information one needs to deter-
mine the properties of the sequence he must use to obtain information from
a single test which will cover the frequency range of interest. The funda-
mental frequency line is a plot of the relation given in (1). The
half-power frequency lines which are parallel to the fundamental frequency
line were calculated from equation (3). The basic bit duration lines were
determined from equation (5).

Use of this graph is perhaps best illustrated using an example. Sup-
pose one had a system for which he desired to know the frequency response
in the fregquency range between 0.0l and 0.5 rad/sec. From the graph we
see that the period required to give a fundamental frequency of 0.01
rad/sec is about 630 sec. So that the signal power at the higher fre-
quencies is not less than half the signal power at the lower frequencies,

a bit time of about 5 seconds or less is necessary. The only remaining para-
meter to specify is the sequence length, A 127-bit PRBS would fit nicely
with the hypothesized conditions to give results over the required fre-

quency range. With the specified bit time, shorter sequences would
23

ORNL-DWG 69-9524R2

POSSIBLE PRBS OR

PRTS m-SEQUENCES BASIC BIT DURATION (sec)
~ & -9
PO & FY 10 5 2 1 05 0201005

  
   

 

109

HALF-POWER
FREQUENCY
LINES —~

PERIOD (sec)

102 FUNDAMENTAL —
FREQUENCY —*"

101
103 102 101 100 To} 102

FREQUENCY (rad/sec)

FIQURE 8. Range over which the power content of a PRBS or PRIS is
essentially flat for sequences of various length and bit times.
2l

increase the fundamental frequency, but shifting to longer sequences
would lower the fundamental frequency and probably be acceptable to the
experimentor,

It is apparent from this example that there is g spectrum of accept-
able sequences, bit times, and /or period lengths available for each par-
ticular application. It is this variety which emphasizes the utility of
a diagram such as that in Figure 8., The effect on the other parameters
caused by changing one item in a test specification may be directly ob-
served. This diagram was found to be very useful in planning the dynamic

tests reported herein,

IT. SIGNAL GENERATION

There are two stages in imposing the desired signal on a system.
First, the signal itself must be generated in some manner and then the
system hardware must be forced to follow the signal. Since a Bunker-Ramo-
340 digital computer was a part of the equipment at the MSRE site, it pre-
sented the opportunity for generating either a PRBS or PRTS using the
shift register technique. A machine language program was written by
S. J. Ball of the Instrumentation and Controls Division at Oak Ridge
National ILaboratory that allowed the use of a variety of different se-
quence lengths for both the PRBS and PRTS. The consequence of this pro-
gram was the opening and closing of relays in the BR-340. By applying
the appropriate voltages across these relays and summing them,a pseudo-

random signal could be generated easily,
25

There were three distinctly different methods used for getting the
generated sequence into the reactor system. The methods for implementing
these signals will be presented in this section with brief discussion of
the advantages and/or disadvantages of each, but most of the discussion

will be deferred to the results section (Chapter IV).

Rod-Jog Tests

The rod-jog method was used extensively during the early testing
program by Kerlin and Ball.® The BR-340 was used to generate the desired
sequences and integrator and comparator circuits on an Electronic Associates,
Inc., Model TR-10, analogue computer were used to determine "on" times for
the control rod drive motor. When switching from a positive to a negative
position in the sequence, the rod was required to insert for x sec., where
the time, x, was adjustable. The inverse jump in a sequence instigated a
withdraw of y sec., where y was adjustable and separate from x. Since
there was no automatic feedback from the rod position, the rod-jog tech-
nique was an open-loop procedure. Details of the rod-jog method are given
in the report by Kerlin and Ball,®

The rod-jog technigue worked when the control-rod system was new and
tight. However, as the system aged, frequent adjustments became neces-
sary on the timing circuits to keep the rods jogging at the same average
position without drifting. This method was attempted several times near
the end of operation with the ®7°U-fuel and, with one exception, produced

unacceptable rod positions.
26

Flux-Demand Tests

Since the rod-jog method was not able to provide accurate and repro-
ducible rod bositions, it was necessary to either change the testing
method or discontinue the testing program. This led to development of
the flux-demand technique,

At low powers (<1 Mw) the servo system in the MSRE compares the neu-
tron flux as indicated by the compensated ion chambers with g manually-
demanded flux and moves the control rod as necessary to meet the demand,
At powers greater than 1 Mw, the neutron flux is compared with a "computed"
flux-demand and the servo again moves the rod to meet the demand. (The
computed flux-demand is based on temperature drop across the core, neu-
tron flux, and core-outlet temperature.) Since the servo moved the con-
trol rod to match the actual flux with the demand, the flux could be
forced to simulate any reasonable test pattern by putting in a false
flux-demand at low-power levels or a false computed flux-demand at high
powers.,

This was the reverse of the normal brocedure in that the predeter-
mined signal shape was imposed on the output and the input (rod position)
became the dependent variable, Figure 9 shows control rod position and
flux plotted as a function of time for representative rod-jog and flux-
demand tests. In the rod-jog example, the rod position resembles the
shape of an ideal PRBS and the flux is determined by the system characte-
ristics; whereas, the plots of the flux-demand tes+t show that flux follows
the test pattern and the rod is the free agent. The two levels of the
PRBS flux-demand are apparent and may be compared with the three levels

of the PRTS flux-demand signal,
27

 

ORNL-DWG 68-9668

 

 

 

 

 

 

 

T o ST
ROD POSITtON
ALY ) UL e atv M v
“H\_ 7 \-' "' % _-" 5 '.“ % ; \ 4
S . Y ow ] s " s
‘\u‘ N AL A AL St NS "‘-:." s st Noazants
FLUX \/\
PRBS ROD - JOG
1 | |
I T I
- ROD POSITION
= l‘ ~\
AOA A i i A
-fv'\. N f » . \' . '.' . -
\‘“‘ : vy, s ; . -A-r-ru-._‘
« ‘ 1 ~ . ..
o - L p L
: . voA . j A .
s, * e K % o < - v’ .
v L W . Yo X
0
E
Z
>
)_
x
g FLUX [,
- o, M ™, : -
@ P .'/\'. :,\'- ;f 3 ./\', ) ;s i .
o s s * ;- .’ S : < : " S . : .
< |y s o5y v : I Doy :
WS viOA S Y\ f VoG N _
\/ N/ OV \J o —~
PRBS FLUX- DEMAND
| | |
I T [
ROD POSITION
~ ~ .
o Y %
In >N & TN ~,
:’5 “" '\_\)""3 “1. g "'9' v"f ™. Voo o
! '\ f%) . Lo s
y . . & " . -
3 N < w 7 v
@ff\gw 2 , J
;‘; "\: -
FLUX
:’\/\. : " !
\J .’ L
PRTS FLUX - DEMAND
Lo Lo 1 | ey o
0 0.5 1.0 1.5 : 2.0
TIME (min)

FIGURE 9, Control-rod position and flux for a typical PRBS rod-jog
test, a typical PRBS flux-demand test and a typical PRTS flux-
demand test,.
28

For the flux-demand technique, the pseudorandom signals were generated
with the circuits shown in Figure 10, Reference voltages from the TR-10
were fed to the BR-3L0-operated relays. The relays were off-on type so
they either fed the reference voltage or zero voltage back to the TR-10.
For the PRBS, 1f the relay were closed the up part of the sequence was
created, Opening the relay formed the down part of the sequence. For
the PRTS, two relays were operated with the following results: relay No. 1
and No.2 open created the down pulse, No, 1 open and No. 2 closed formed
the middle position, and No. 1 closed and No. 2 open caused the up part
of the sequence. Both relays closed was not allowed. Attenuator No. 9
reduced the signal to the voltage which was needed for the particular
test. At the start of a test, attenuator No. 9 was normally set at zero
and then increased slowly until the desired signal magnitude was achieved.
Normally the flux was allowed to deviate from steady state by 5 to 10%.

Attenuator No. 11 was adjusted so that the output of the second
amplifier corresponded to the steady-state flux with the pseudorandom
sequence imposed on 1t, This voltage was inserted into the servo circuits
at the indicated point in Figure 10c.

The flux-demand method offered distinct advantages over the rod-jog
technigue. During testing, adjustments of the times which the rod with-
drew and inserted were not necessary and there were no problems with sys-
tem drift since the servo automatically maintained the actual flux approxi-
mately equal to the demanded flux. The basic disadvantage of this tech-
nique was that it worked the control rods rather vigorously, especially
after the more responsive £ fuel was added to the system. While exer-

cising the control rods 1s not in itself particularly undesirable, design
29

ORNL~-DWG 69— 9525

PRBS SIGNAL GENERATOR
———— e

0 TO -10v F.5,
(a)
TO
SERVO
CIRCUITS

 

PRTS SIGNAL GENERATOR

 

 

 

 

 

|
] -5
5 | . “:\\\\47 0 TO —10y F.S.
—_
(2) | I | SERVO
| I 10 l CIRCUITS
_____ 1 -10 |
BR-340 | |
LRz _SSs.Bws _
SIMPLIF{ED SERVO CIRCUITRY SERVO
oM ‘0 100k AMPLIFIER
L A 1[\ A 92.5
aROVE ¢ W L~ W +6v OPERATES
CIRCUITRY o : v
R-237 * i R-252 RODS
FLUX
(c) CLAMPS (-0.33 T0 6v) REF. ORNL DWG
FROM 30k RC 13-12-53
ION & YW
CHAMBER R-250
y OPERATIONAL AMPLIFIER
__.l :>_ X = GAIN —MA— RESISTOR —o— SWITCH
Y= IDENTIFICATION NUMBER
——{::}a AT TENUATOR 1l gerav
Y = IDENTIFICATION NUMBER T

FIGURE 10. Circuitry used for generating the pseudorandom signals for
the flux-demand tests.
30

of the rods in the MSRE provided loose coupling between the actual and
indicated rod positions and every rod movement carried with it the in-
herent probability of an erroneous indication,

The problems encountered while using the flux-demand technigue were
primarily a result of hardware limitations in the MSRE and do not repre-
sent an inherent flaw in the technique; however, excessive noise contami-
nation in the frequency range near a resonance peak can cause erratic
results when the flux is being controlled to give a flat power spectrum.
This will be discussed in Chapter IV in relation to some of the experi-
mental results. When using this technique, the experimental testing was
less laborious for the experimentors and equipment set-up time was less
than when testing with the other methods. For zero-power reactors or for
reactors in which power drift tends to be a problem, this technique
would appear to be particularly advantageous. Since the flux is the con-
trolled parameter, it cannot drift and if the system is at steady state
initially, pseudorandom perturbations of the flux about the steady-state

value will not cause an Imbalance between power and flux,

Rod-Demand Tests

 

The disadvantages of the flux-demand tests caused a final change in
technique back to rod-controlled testing. However, instead of controlling
the rod position indirectly by adjusting the time the drive motor remained
activated, the technique was changed to directly control the rod position.
This was achieved by comparing the actual rod position with a demanded
position and keeping the drive motor activated until the desired position

was realized. Since there was feedback from the rod position, this was a
31

closed loop system, The result of this technique was to yield rod po-
sitions which were like those obtained from an ideal rod-jog test and to
circumvent the problem of excessive rod motion that was present with the
flux-demand technigue,

Since the control-rod servo 1s really a comparator circuit, it was
well suited for comparing actual rod position with demanded position, and
1t was already wired to move the control rods if the input voltages
(normally flux and flux-demand) were unbalanced. Tt was necessary to
disconnect the normal inputs to the servo system and to replace them with
actual and demanded rod positions.

The circuits for generating the pseudorandom perturbations were
basically the same as those used with the flux-demand technique (Fig. 10).
The ion-chamber connection in Figure 10c was replaced with a signal deter-
mined by the actual rod position and attenuator 11 in Figure 10a or
Figure 10b was adjusted so that the output of the servo amplifier was
approximately zero before starting a test,

One operational problem related to the rod-demand technique should
be pointed out. The rod was moved when the actual rod position was out-
side the deadband around the demanded position. When the demand shifted
at the start of a new pulse, the rod moved until the voltages were again
matched, at which time the rod would start coasting to a stop. The servo
circuits could be adjusted to start the stopping process so that the road
did not coast through the deadband and instigate an adjustment in the
opposite direction. When a PRBS test signal was being employed, the po-

sition at which the rod stopped within the deadband was not important,
32

hence the adjustments were simple., (The important point was that the rod
did stop within the deadband and at the same position each time.) However,
the three levels of a PRTS signal caused this adjustment to become more
involved. The middle position of the PRTS might occur after a pulse with
plus or minus polarity. If the rod tended to coast nearly through the
deadband before actually stopping, then the middle position of the PRTS
was satisfied by two different actual rod positions. The only adjustment
which resulted in a unique value for the middle position was a setting
which caused the rod to stop midway of the deadband. There were also
slight differences in the upper and lower positions depending on whether
the rod had started from the middle position or the extremity position.
For the MSRE, the rod-demand technique meshed with equipment limi-
tations in such a way that it was the most effective method for frequency-

response testing.

ITI. DATA ACQUISITION

For all of the tests the reactivity perturbations were initiated by
control rod movement. As described earlier, contrcl rod movement 1s con-
trolled by a drive motor, and a series of gears connects the rod drive
to the position synchros. These indicators feed a voltage to the
position indicators in the control room snd to the on-line BR-3L0
digital computer. For the dynamics tests, the signal gcing to the BR-340
was intercepted and fed into an analog computer (TR-10) where the signal
was amplified by a factor of ~ 10 and low-pass filtered using a filter

with a l-sec time constant, This amplified and filtered signal was then
33

fed back into the BR-340 where it was digitized every 0.25 sec and re-
corded on magnetic tape. This frequency of digitization made possible
the storing of useful information which had frequency components as high
as ~ 12 rad/sec; however, most of the test patterns we employed had little
signal power above 1 rad/sec, A filter with a l-sec time
constant was used to attenuate high-frequency information and prevent
aliasing effects,

The nuclear power was determined by recording the signal supplied
by a compensated ion chamber, The primary purpose of this chamber was
to feed the linear-power recorders which are located in the main control
room. This signal was also fed into the TR-10 and amplified (by ~ 10)
and filtered using a l-sec time constant. The signal was then fed to the
BR-340 where it was digitized and recorded every 0.25 sec, along with the
rod position. The rod position and flux signals were not digitized si-
multaneously. There was actually about 0.08-sec difference between the
digitizations. This causes the calculated phase angle to be in error by
0.5° at 0.1 rad/sec and 5.0° at 1,0 rad/sec. This error was not recog-
nized until after most of the results had already been obtained and since
this was not a significant error in the frequency range of interest, the
calculations were not repeated,

In order to be compatible with the analysis programs, the data were

retrieved from the magnetic tapes and stored on punched cards.,
3k
TV. DATA ANALYSIS METHODS

The purpose of the dynamics tests was the determination of
the power-to-reactivity frequency response. After the data from a par-
ticular test was reduced to a stack of IBM cards, there were three methods

for gleaning the desired information.
Computing Schemes

FOURCO. The most direct and fastest method for determining the
frequency response was to immediately Fourier transform the digitized
data and then divide the transformed output (flux) by the transformed
input (rod position) for the desired result. This was accomplished using
a computer code called FOURCO23 which uses a digital simulation of an

24  Analysis of 8 cycles of

analog method reported by Broome and Cooper.
a 127-bit PRBS with a 3-sec bit time (12,192 input and output data
points) required only 1.1 min on the IBM 360/75 for calculation of the

frequency response at 60 different frequencies.

CPSD. This analysis method utilized a digital simulation of an ana-
log filtering technique for obtaining cross-power spectral density, CPSD,
functions.®s®> This code calculated the power spectrum of the input sig-
nal and the cross-power spectrum of the input and output signals and di-
vided the cross-power spectrum by the input power spectrum toc obtain the
frequency response at each frequency of analysis, The key feature of
this ccde is an adjustable filter width about the analysis frequency.

Analysis time for 8 cycles of a 127-bit PRBS with a 3-sec bit time

on the IBM 360/75 was 2.0 min for analysis at 60 frequencies,
35

CABS.®® The third calculational procedure was more involved., The
autocorrelation functions of the input and output signals were calculated
and the cross-correlation ffinction of the signals was calculated. These
were then Fourier transformed to obtain the input, output, and cross-
power spectra. The input power spectfum was then divided into the cross-
power spectrum to obtain the frequency response. The correlation functions,
power spectra and frequency response were then machine plotted.

Calculation time using CABS for the previously mentioned case was

10 minutes,
Comparison of Data Analysis Methods

CARS and FOURCO. If an experimental test is composed of several
consecutive periods of the same sequence, there are several cholces
available for analyzing the data. One method is to evaluate a single
Fourier integral of all the data. Alternatively, the data may be split
into segments (each consisting of one or more periods of data) and a
Fourier integral for each segment can be determined, and the resulting
estimates can be averaged.

The basic difference between analyzing one period of data at a time
or several periods of data as one period is to change the effective
filter, or spectral-window, width. I a Fourier analysis is performed
at frequency «,, where ay is a harmonic frequency, the magnitude of the
harmonic will actually be composed of all the signal strength under the

filter area. The "natural filter,™ H(w,), 1s®’

H(w,) = Si%mgmi &)m%me ’

 
36

where Tm = the time duration of the data being analyzed,

n

W frequency (rad/sec), and

frequency of analysis,

Wi
This function has a maximum value when @ equals w,; and has null points
where (w; - ) Tm equals an even multiple of . Suppose Tm is equal to
one period, T, of a periodic signal then every second null point occurs
on an adjacent harmonic; however, if eight cycles of data were analyzed,
there would be 16 null points between the harmonic frequencies (see
Figure 11)., For an ideal periodic signal either filter would be suitable
since there would be spectral power at only the harmonic frequencies.
However, actual signals are not ideal and there is always random noise
contamination at every frequency; furthermore, if the harmonic frequencies
are not specified very precisely, contamination resulting from the side
lobes and the adjacent harmonics not intersecting at a null point may be
significant. Using the "eight-period" filter tends to discriminate against
noise contamination except very close to the actual harmonic frequency
but causes large errors if the frequency at which the analysis is beling
performed is not the actual harmonic frequency. ©Note that performing an
analysis at a frequency which is midway between adjacent harmonics would
not allow any of the signal strength of the periodic signal to enter into
the result since the filter would null at every harmonic frequency; hence,
analysis at these frequencies apparently provides a means of calculating
the system noise level which was present during the testing. However,
for this type analysis to be valid, 1t is necessary that the frequencies
which are midway between the true harmonics of the minimum period length

actually be harmonic frequencies also. For example, if only one period
37

ORNL— DWG 6911726

EIGHT-PERIOD FILTER

 

08 ! ‘ TYPICAL SPECTRAL
' ONE-PERIOD FILTER POWER FROM IDEAL
PERIODIC SIGNAL\

 

 

 

 

0.6 Vv

 

04

 

0.2

FILTER MAGNITUDE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.2 N N
-04
' 3n 2m _r T ar 3w
W= T W T W= T wj Wty Wty wtT

FIGURE 11. Natural filters for one-period analysis and for eight-
period analysis.
38

of data is available, analysis at mid-harmonic frequencies is not mean-
ingful; however, if two periods of data are analyzed, the frequencies mid-
way between the adjacent power-containing harmonics are harmonics of the
total period and analysis at these frequencies is allowed.

For the direct Fourier analysis method (FOURCO), application of the
preceding argument is straight-forward, but for the CABS program it is
more complex, With the CABS program, it is normal to work with at least
two cycles of data, since correlation functions are usually calculated
for lag times as long as one period. Calculation of the correlation
functions immediately reduces the data to one period length (fixing the
filter shape) which is then Fourier analyzed. Using more periods of data
in the correlation function determination improves the statistics of the
correlation function. The alternate method of using fewer periods in the
correlation function analysis yields worse statistics for the correlation
function but more power spectrum results at the same frequency, which may
then be ensemble averaged. The choice is whether to ensemble average
before or after Fourier transforming. Mathematically, at least for ideal
signals, the end result 1is the same. Since the correlation functions are
informative in themselves, the usual method is to reduce the data to
correlation functions of one-period length before Fourier analyzing.

To determine the effect of varying the periods of data which were
analyzed, eight periods of a 127-bit PRBS with a 3-sec bit time (this
will be written as 127 x 3 in the remainder of this text) were analyzed
several different ways, All eight periods were analyzed as one period —

giving a very narrow filter — then four periods were analyzed as one
39

period and the two answers averaged. This was repeated using two periods
and one period of data at a time, The results are shown in Tables III,
TV, and V for different analysis frequencies,

For the calculations in which the data were separated into smaller
segments, there is significant scattef in the data; however, the averages
agree fairly well with CABS appearing to exhibit a slight trend upward
in magnitude ratioc as the data are more finely divided, With FOURCO, the
final averaged result does not appear to be significantly affected by per-
forming the analyses on one period at a time even though the individual
results for the analysis which used one period at a time are very erratic,
particularly at the lower frequencies.

The coherence-function values listed in Tables IIT, IV, and V for
the CABS analysis are a measure of the degree to which an output of a
system is related to a certain input. Mathematically the coherence

*
function is defined®® by the relation,

2
L)
- 2
c, (1) &, (F)
where
y = the coherence function,
G. (f) = the Fourier transform of the cross-correlation function
* at frequency f,
Gx(f) = the spectral power of the input signal (rod position in
this text) at frequency f, and
Gy(f) = the spectral power of the output signal (flux) at

frequency f.

 

¥
Tn this text, only the positive root of y© is considered to have
physical meaning,
Lo

TABLE IIT

RESULTS OF DIFFERENT ANALYSIS TECHNIQUES AT 0.016L491 RAD/SEC
WHEN APPLIED TO EIGHT PERIODS OF DATA

 

 

No. of Periods

 

 

Analyzed
As One CARS FOURCO
Phase Phase
M.R."  (Deg.) cor’ M.R.”  (Deg,)
8 356 69 .95 360 70
L 373 63 .96 37k 6L
327 (L .98 322 8
Avg.© 365 67 .97 363 71
Std. Dev.d 11 6 L1h 16 10
2 430 Lg .91 361 69
435 50 1.00 393 kg
361 61 .99 395 T2
28l 67 .88 310 11
Avg. 378 60 .9l 365 69
Std. Dev. 71 6 .06 Lo 8
1 530 o9
235 99
Lol 52
333 69
336 80
451 77
312 66
319 _86
Avg. 372 7h
Std. Dev. 98 15

 

 

“Magnitude Ratio
bCoherence Function
C

Average

dStandard Deviation
RESULTS OF DIFFERENT ANALYSIS TECHNIQUES AT 0.4947L4 RAD/SEC
WHEN APPLIED TO EIGHT PERIODS OF DATA

41

TABLE IV

 

 

 

 

No. of Periods
Analyzed :
As One CABS FOURCO
g Phase o Phase
M.R. (Deg.) Coh. M.R. (Deg.)
8 671 -26 1.00 670 -26
b 69k -28 1.02 667 -27
‘ 663 -2l 1.01 672 -2k
Avg.© 679 -25 1.02 670 -26
Std, Dev. 22 5 .01 L 2
2 650 -27 1.01 Lhop -22
775 -29 1.01 ThT -31
585 -21 1.02 600 -23
120 -30 £.00 T45 -2k
Avg. 690 -27 1.01 671 -25
Std. Dev. 88 L .01 87 L
1 6hs -9
574 =37
768 ~28
729 -35
575 -20
62k ~25
748 -2
43 =27
Avg. 676 -25
Std. Dev. 80 9

 

Magnitude Ratio
bCoherence Function
CAverage

dStandard Deviation
Lo

TABLE V

RESULTS OF DIFFERENT ANALYSIS TECHNIQUES AT 0.98947 RAD/SEC
WHEN APPLIED TO EIGHT PERIODS OF DATA

 

No. of Periods

 

 

Analyzed
As One CARBS FOURCO
o Phase b a Phase
M.R. (Deg.) Coh. M.R. (Deg.)
8 509 -L6 1.02 536 -L6
L 511 -43 .99 512 -L45
51b -29 97 549 =48
Avg.© 513 -47 .98 531 -47
Std. Dev.d 2 5 .01 26 2
D 510 -46 .93 539 -h3
533 -43 1.04 L85 =47
Lo -63 .97 513 -48
52k =60 95 582 -L8
Avg. 510 -53 97 530 -Lt
Std. Dev, 27 10 .0L b1 2
] 580 -hp
500 -43
500 -48
470 -L7
L87 -Iis5
548 -51
566 -4k
603 -52
Avg. 532 -L7
Std. Dev. Lg n

 

"Magnitude Ratio

bCoherence Function
CAverage

dStandard Deviation
L3

For a causal system in which there is only one input and one ouput
and no noise contamination, the measured coherence function should be
unity. For real systems in which ideal conditions do not exist, the co-
herence function should be between 0 and 1. If two totally unrelated
signals were analyzed, the coherence ffinction would be zero. Some of
the experimentally-determined values for the coherence function shown in
Tables III, IV, and V are slightly greater than 1.0. This is theoretically
impossible and the reason for these values being greater than 1,0 is not
understood. The CPSD code, which also calculated coherence functions,
also occasionally gave results which were slightly greater than unity.
These anomalously high values did not destroy the general usefulness of
the coherence function calculations which were, in general, lower for
tests in which the results contained excessive scatter (indicating noise
contamination) than for the smoother results. Analyses at non-harmonic
frequencies yielded coherence functions which were erratic and often had
values as large as 500.

In an effort to demonstrate the effect of the analysis filter, the
same data were also analyzed by FOURCO at frequencies which were offset
from the harmonic frequencies by 10% of the difference between harmonics.
Table VI lists both the real and imaginary parts of the input and output
signals for a harmonic frequency and Table VII lists the same information
for the nearest adjacent non-harmonic frequency. The analyses were per-
formed with 1, 2, 4, and 8 periods of data as one with the appropriate
results averaged, as before. For the analysis at a harmonic frequency,

the average value of both the real and imaginary parts of the signals
Ll

TABLE VT

RESULTS OF ANALYSIS AT A HARMONIC FREQUENCY (0.3298 RAD /SEC)

 

 

Periods of

 

 

 

 

 

Data Analyzed Input Signal Output Signal
As One
Real Imaginary Resl Imaginary

8 -177 388 -193 I
L - 87 192 -107 25
- 86 198 - 84 20

Avg.D - 87 195 - 95 23

Std. Dev.b 1 L 16 3

2 - L 96 - 56 11
- 43 96 - 52 15

- kg 100 - Lk 6

- L1 100 - 4o 1L

Avg. - 43 o8 - 48 11

Std. Dev, 2 2 T L

1 - 20 L9 - 28 5
- 22 L8 - 27 6

- 20 L9 - 29 3

- 21 L - 23 13

- 27 51 - 17 1

- 21 48 - 28 Y

- 20 50 - 19 1

- 19 _20 - 21 _2

Avg - 21 Lo - 24 5

Std. Dev. 3 1 5 L

aAverage

bStandard Deviation
TABLE VII

RESULTS OF ANALYSIS AT A NON-HARMONIC FREQUENCY (0.3463 RAD/SEC)

 

 

 

 

Periods of
Data Analyzed Input Signal Qutput Signal
As One

Real Imaginary Real Imaginary

8 87 - 31 2kl 35

4 91 120 - 26 7L

3& 117 - 16 60

Aveg.? 93 119 - 21 67

Std. Dev.b 3 2 7 10

2 3 93 - L2 30

L 92 - 37 30

5 9> - 31 2l

I 92 - 29 25

Avg. 5 93 - 35 27

Std. Dev. 2 2 6 3

1 -12 L - 26 9

-1k 46 - 2l 9

-12 L7 - 27 7

-13 L6 - 20 13

~13 Lg - 1k -5

-13 L3 - 29 10

-12 L8 - 17 10

-1 b7 -1 2

Avg, -13 L7 - 21 T

Std. Dev. 1 1 7 6

aAverage

bStandard Deviation
L6

approximately doubles* each time the number of periods being analyzed as
one doubles. This indicates that most of the calculated signal energy
was resulting from a source which was unaffected by the changing filter
shape. Of course, this source was the spectral energy of the signal at
the analysis (harmonic) frequency. For the analysis at a non-harmonic
frequency, there is no apparent relation between the average values of
the signals as the number of periods being analyzed is changed. This
should be expected since the changing filter shape is weighting the sig-
nal energy in the nearby harmonic, as well as those farther away, in an

entirely different manner with each filter change.

CPSD. The advantage of the CPSD technique is that the filter shape

may be specified at the time the analysis is performed, The filter

specified by the code has the transfer functionl®

H(s) =

 

0302 -+ E;Ujos + 52

 

*
The doubling occurs because the integral being used to calculate
the signal energy is:
T

F(jo) = [ £(t) e 0% at
~0
where

H:
Eamme
ot
S

}

the time signal,

frequency (rad/sec),

= \/_l)

time, and

the total time of the recorded data.

]

H &+ £
1

The integral is not normalized by 1/T; therefore, for data sets
containing the same power at frequency w, the calculated F(jw) will be
twice as large if the number of sets analyzed is doubled.
L7

where
wo = the center frequency of the filter,
s = the Laplace transform variable, and
L = the damping factor.

Figure 12 shows H(s) for various values of t. As g takes on smaller
values, the peak in the transfer function becomes very narrow, If{ is
set too wide, the contribution from other frequencies becomes significant,
but if § is set too narrow, a slight discrepancy between the harmonic
frequency and the calculational frequency will cause a large error in the
calculation of the signal magnitude at the harmonic. The complete fre-
guency response plot for the test case (8 periods, 127 x 3 PRBS) is shown
in Figure 13 for various values of §. When { is equal to 0.5, the data
is smoothed to the extent that it does not portray the actual frequency-
response shape in the regions of sharp curvature. Damping factors of
0.05 and 0.001 give essentially the same shape; however, there is more
scatter in the data with the 0.001 damping factor.

Comparison of the CPSD method with a damping factor of 0.05 with the
CABS and FOURCO results revealed that the results were usually within 5% of
each other with occasional deviations of 10%. There were a few tests in
which there was large discrepancy between the analysis techniques at a
few frequencies., Since these appear to be a function of the testing
technique, they will be discussed in the appropriate section (Chapter 1v,
Section II),

Unless otherwise specified the data reported herein used the fol-

lowing analysis criteria:
L8

> ORNL-DWG 69-11727

FILTER MAGNITUDE

 

 

 

 

 

90 ———]EHEL <ty £ = 0.001
N~ \\Q C)O5
60 A
0 NN
\T/////ffl
O K_
AN\
\\\ N
& Rain

0

 

 

//

 

 

 

 

 

 

/!

 

| i
W
O O

]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1072 10~ 10 10°

w/wo

FIGURE 12, ©Shape of the analysis filter employed by the CPSD technigue
for various values of the damping factor, [.
k9

 

 

 

 

 

 

 

 

 

 

10° : J ] T ?RNL—DWG ?9{11;2:?

i s 1"0..'h 1 bl

s| - " T

e L
I 2 —— ] L '{II
|

10? | L] V’J

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L |
=
60
3
30 . ® 4
-
o
3 EF‘-.,.'
‘uj o R b.%
< “Ro ot
= i ‘gu‘“ob
e [=05 1&2.
_30 o {=005 M
a [=0.001 'Q%%
|
)
WL L L
10 2 5 10 2 5 10°

FREQUENCY (rad/sec)

FIGURE 13. Frequency-response results obtained by analyzing a test
case using the CPSD analysis scheme with various values of the
damping factor, §.
50

(1) When more than one period of data was analyzec using FOURCO, it
was analyzed as one period., If the periods of data were ana-
lyzed separately and the results averaged, the results are
labeled "FOURCO ENSEMBLE, "

(2) When using CABS, the data was reduced to correlation functions
of one period length and then Fourier analyzed.

(3) A damping factor of 0.05 was used with the CPSD code.

In some cases the data were analyzed using all three methods; how-
ever, the results were, in general, so nearly the same that this was not
actually necessarily so in other cases only two methods were used. In
cases where the analysis schemes gave the same results only one set of

results was usually plotted.
51

CHAPTER IV
EXPERIMENTAL RESULTS

In this chapter typical results obtained during the testing program
will be presented and discussed. In some cases preliminary results such
as correlation functions will be shown together with the frequency-
response results and in other cases only the frequency-response results
will be presented., Tests were performed which will not be discussed at
all. A listing of all the tests performed and pertinent informafion

about each test is given in the Appendix.
I. ©°°U FUEL LOADING

The initial dynamics-testing program.c'9 made extensive use of the
rod-jog technigue. But by the end of that testing program, the experi-
ments were becoming difficult to perform. There was apparently some
stiffening of the flexible~hose part of the control-rod assembly, or at
least some extra fricticn, which was causing reproducible rod positioning
to be difficult.

Near the end of operation with the £7°U fuel loading, more dynamics
tests were performed. These were two-fold in purpose. First, the tests
would indicate whether the dynamic characteristics of the MSRE had
changed after more than 72,000 Mwhrs of power operation. Second, the
groundwork was to be laid for using the flux-demand technique during the

£33 fuel loading. The plan was to do more rod-jog tests followed by
52

flux-demand tests so that comparisons between the techniques would be
straight forward. Tests with both the PRBS and PRTS test signals were
also planned., The "coarse" position indicator was used to supply the

control-rod positicn indication.

1. Rod-Jog Tests

The first rod-jog test attempted was performed without flaw, This
led to hope that the suspicions about inadequacy of the technique were
permature and that a change in technique was not warranted. However, all
subsequent attempts at rod-jogging were failures., During these tests,
almost continuous adjustment of the motor-timers was necessary, and there
were several times when a one-bit segment of the test pattern was skipped
resulting in two consecutive rod movements in the same directions, an
impossible occurrence for a true PRBS. The first problem was most likely
an extension of the previcusly-encountered problems related to friction
in the control rod assembly. The bit-skipping Suggests failure of the
sequence-generating equipment. The equipment was 'bench-tested"”, but no
equipment defects were found. So at least part of the reasons for the
failure of the rod-jog technique are not understood.

The autocorrelation function and power spectrum of the rod position
for the good rod-jog test are shown in Figure lha., These closely follow
the theoretical curves for an ideal PRBS and indicate that the test pat-
tern was well represented by the control rod. Four periods of the se-
quence were analyzed., The autocorrelation function and the power spectrum
of the flux are shown in Figure 14b and the cross-correlation function

of rod position and flux with the assoclated power spectrum are shown 1in
>3

ORNL —NWG 69— 12248

 

0.060

 

 

 

 

2 s nam

0.046 1

 

 

 

 

 

 

’
s

0.032 F

 

 

0.018 # .

 

 

 

 

 

 

0.004

AUTOCORRELATION FUNCTION (arbitrary units)

 

 

 

 

 

 

 

 

 

 

 

 

|
; |
-0.010 b
0 140 280 420 560 700
' CORRELATION TIME {sec)

 

 

POWER SPECTRUM (arbitrary units)

 

FREQUENCY (rad /sec)

(a) Autocorrelation function and power spectrum of the control-rod
position.

Periods of data analyzed — L
Type sequence — 127 x 5 PRBS

FIGURE 14 Correlation function and power spectrum results from a
rod-jog test,
54

ORNL-DWG 69-12054

 

 

 

 

 

 

 

 

 

 

 

 

2.0
1.4

+— —4 i — —
0.8 - + : —

 

 

 

e

- e

0.2 \ ‘ _ | L 1

 

 

 

 

 

 

 

 

 

 

 

 

AUTOCORRELATION FUNCTION ( arbitrary units)

 

 

 

 

 

 

 

 

 

s | |
04 L
1 | | _
_10 —— e ok —— A ;
0 140 280 420 560 700

CORRELATION TIME (sec)

FPOWER SPECTRUM (arbitrary units)

 

1072 2 5 10™ 2 5 10°
FREQUENCY {rad/sec)

(b) Autocorrelation function and power spectrum of the neutron flux.

Periods of data analyzed — 4
Type sequence — 127 x 5 PRBS

FICURE 14. (continued)
55

ORNL-DWG €9—12053

 

0.30

 

 

0.22

T

 

 

 

 

 

044 [- e =

 

 

 

 

 

0.06

-0.02 \

e,

 

 

 

 

 

CROSS~- CORRELATION FUNCTION (arbitrary units)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 140 280 420 560 700
CORRELATION TIME (sec)

CROSS—-POWER SPECTRUM (arbitrary units)

 

2 5 1072 2 5 10~
FREQUENLCY (rad/sec)

(c) Cross-correlation function and cross-power spectrum of the control-
rod position and neutron flux.

Periods of data analyzed — L
Type Sequence = 127 x 5 PRBS

FIGURE 1L, (continued)
56

Figure lhkc. Since the reactivity input was a PRBS (flat power spectrum),
the envelope of the points in the first part of the cross-correlation
function approximately defines the impulse response of the system,®®

The results of primary interest, magnitude ratio and phase, are shown in
Figure 15. Over most of the frequency range there is 1little scatter in
the data and the experimentally determined points follow the theoretical
curves very well., The scatter in the magnitude ratic at frequencies
greater than 0.6 rad/sec is due to the low power content of the input
signal in this frequency range (Figure lha). The low magnitude of the
power in the input signal causes a low signal to noise ratio and a large
amount of scatter in the results. In addition, the timing method used
with the rod-jog technique did not produce the exact period lengths which
were desired. This made specification of the fundamental frequency tedious,
and for a four-cycle test an average period length was used, This inac-
curacy may decrease the signal to noilse ratio even more because the fre-
guencies at which the analyses are performed may not be the exact harmonic
frequencies,

Also shown in Figure 15 are results of a similar test which was per-
formed during the initial testing program of the MSRE. There 1is very
little difference between the results which leads to the conclusion that
the dynamic characteristics of the MSRE were not changed by about 9000

equivalent-full-power hours of nuclear operation,
2. Flux-Demand Tests

Ten dynamics tests utilizing the flux-demand technique were per-

formed with the #7°U fuel loading., Two of these ten yielded completely
27

ORNL-DOWG 69-12256

103

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b ]
< 0
®lo
*
POWER LEVEL-8Mw
2 o TEST PERFORMED DURING EARLY
POWER OPERATION, CPSD ANALYSIS,
DATA FROM REFERENCE {6
e TEST PERFORMED NEAR END OF
OPERATION WITH U-235 FUEL,
CABS ANALYSIS
102
100
60
1 |
o] |
N |
4 ! . !
< <0 J' Y T P [ l
3 | ; |
s S =
E -20 “ s \ L/_.._\ l
- i 1 9 . n\j 1 * 4
! j I -0‘3."&19-.‘&---."'- ll Jo
> ‘ ; LT iy B Poomio ol
o |
B O s
o | L
- — f
e N
-100 | il .
10~2 2 5 Tom 2 5 10

FREQUENCY (rad/sec)

Periods of data analyzed — L
Type sequences — 127 x 5 PRBS

FIGURE 15. Frequency-response results from rod-jog tests,.
58

unusable results due to a faulty magnetic-tape unit which was supposedly
recording the data. In fact, the computer was malfunctioning throughout
this entire phase of the testing program and there were numerous bad data
points dispersed randomly throughout the data. In general, these bad
points were easy to distinguish in that they read either very large or
very small in comparison with the bulk of the data, A computer program
was written which scanned the data and discarded these points which were
obviously in error and replaced the bad points with points derived from
a linear interpolation between the two nearest good points.

Three test patterns were employed during this phase of the testing
program. These were the PRBS, PRTS, and the "non-symmetric" PRTS. The
difference between the PRTS signals will be discussed in the appropriate
section.

In this section, we will find that the flux-demand tests were un-
suitable for the required measurements, Nevertheless, the experience
with these tests is described to illustrate the problems and to show the
considerations which led to the third (and successful) technique described

in Section 3 of this chapter.

PRBS Test Patterns

 

Figures 16 and 17 are plots of a set of results from a 127 x 5 PRBS
test performed with the reactor at 5§ Mw. DNote that the flat power spec-
trum is associated with the autocorrelation of the flux signal rather
than the rod-position signal. The cross-correlation (Figure 16¢) is not
indicative of the impulse response of the system since the autocorrelation

of the input (Figure 16a) does not have a flat power spectrum. The
59

ORNL-OWG 89-12249

 

0.30

 

 

0.22

 

 

o
>

 

 

o
&

 

 

 

M' P A o AP ns 'vM
-0.02 |5 :

 

AUTOCORRELATION FUNCTION (arbitrary units)

 

LTEY]
Skt g

 

 

 

 

 

 

 

 

 

 

 

 

o 140 280 420 560 700
CORRELATION TIME {(sec)

POWER SPECTRUM (orbitrary units)
o
N

w»

 

03 2 5 1072 2 5 0! 2 5 1P
FREQUENCY (rad /sec)

(a) Autocorrelation function and power spectrum of the control-rod
position,
Pericds of data analyzed — 5
Type sequence — 127 x 5 PRBS

FIGURE 16, Correlation function and power spectrum results from a flux-
demand test using a PRBS test pattern.,
60

ORNL- DWG 69 -12250

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8
» o
te
=
5
_-'E b
o
—— 4 -
=
o
—
Q
=z
o
[V
> 2
o
%
-
T
& f
8 o VA— - v —'v“
3 [ \
= i
2 4
<I ;_-
* ]
-2
0 140 280 420 560 700
CORRELATION TIME (sec)
2
10

POWER SPECTRUM ({arbitrary units)

 

0

10
1073 2 5 1072 2 5 107! 2 5 10°
FREQUENCY (rad/sec)

(b) Autocorrelation function and power spectrum of the neutron flux.

Periods of data analyzed — 5
Type sequence — 127 x 5 PRBS

FIGURE 16, (continued)
61

ORNL -DWG 69 -12254

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.0
o
g
~ 14
5
.E
o 4
2 -
© o8
—
Q
2
5
[V
5
= 02
3 ; - —~—
W Ef‘-‘* - \—— hainas - — o
s [0 |
o
o
o ~0.4 +
0 ]
3 ]
o
O

-4.0

0 140 280 420 560 700

CORRELATION TIME (sec)

CROSS-POWER SPECTRUM (arbitrary units)

 

1073 2 5 10”2 2 5 10! 2 5 10
FREQUENCY (rad/sec)

(¢c) Cross-correlation function and cross-power spectrum of the control-
rod position and neutron flux.

Pericds of data analyzed — §5
Type sequence — 127 x 5 PRES

FIGURE 16. (continued)
62

ORNL-DWG 69-12252
10?

POWER LEVEL-5Mw
ANALYSIS METHOD

® CABS
2 — THEORY

 

 

 

 

 

 

20 \

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

>
@
= \
N

w
4 TN
I N
o 20 4 N

- 4

1 9 \_/
W
. " \H- .”a-
-60
—-100
t0~3 2 5 10°2 2 5 10~ 2 5 100

FREQUENCY (rad/sec)

Periods of data analyzed — 5
Type sequence — 127 x 5 PRBS

FIGURE 17. Frequency-response results from a flux-demand test with the
reactor at 5 Mw,
63

magnitude-ratio and phase plots are shown in Figure 17. There is more
scatter in the data near the peak in the magnitude ratio than was evident
in the rod-jog test. This is probably a result of the testing technique.
Since the output power spectrum is flat (Figure l6b), there must be a
minimum in the input power spectrum (Figure 162) in order to achieve a
peak in the magnitude-ratio plot. For a system with a relatively-white
noise input, this implies that the signal-to-noise ratio of the input
signal 1s worse at the minimum than at any other point; hence, the sta-
tistical confidence one should place in the values at the peak in the
magnitude ratio plots is the lowest of any region on the plot.

The autocorrelation functions of the test patterns as implemented
by the different techniques are shown in Figures 1llha and 16b. While they
are 1in general agreement, there are two noticeable differences. The
small negative spike which occurs at both ends adjacent to the large
positive spike in the autocorrelation function in Figure 16b is caused
by a deadband in the servo system. With the rod-jog technique, the rod
was moved and then held stationary until time for a pulse of different
polarity, With the flux-demand technique, the rod would move the flux
until the flux-demand was satisfied and then stop. The flux would con-
tinue to change and would move on through the "satisfied" state and would
have to be brought back by rod movement in the other direction. A dead-
band in the flux signal may be observed by careful inspection of Figure 9,
page 27. The width of this deadband was found to determine the magnitude

of the negative spike. Some tests were performed in which the deadband

was very narrow and the spikes were all but eliminated.
6l

The small positive spikes which occur at lag time equal to 278* sec
in the autocorrelation function in Figure 16b are thought to be a result
of the shape of the flux signal when going from a low to high value not
being the inverse of the flux signal when going from a high to low value,
Similar spikes were noted at both 35 sec and 278 sec on most other
127 x 5 PRBS flux-demand tests., Only spikes at lag times of 35 sec were
reported in similar tests with the rod-jog testing technique. One
127 x 5 rod-demand test had a small spike at ~ 33 sec with no other
anomalous spikes. The occurrence of a spike at 35 sec is predictable
(References 13, 30, 31) and is a function of the time between the longest
run of consecutive positive bits and negative bits for the particular
sequence being used. The additional spikes at 278 sec which appeared
with the flux-demand technique are thought to be caused by the same type
of phenomenon that caused spikes at 35 sec, but this has not been proven.
The spike at 33 sec with the rod-demand technique was small and should
not be considered as strong disagreement with the predicted time of 35 sec.
Spikes were also observed in PRBS tests of other length and in PRTS tests.
No theoretical work could be found which related the position of the
spikes to the properties of the PRTS, but it is likely that they are

caused by the same type phenomenon.

 

*The autocorrelation functions are very nearly symmetric about the
half-period time. There were corresponding spikes in the second half of
the autocorrelation functions at the appropriate times, but only the
spikes during the first half are mentioned in the text, for clarity of
presentation.
65

The magnitude-ratio and phase-angle plots for a 127 x 5 PRBS with
the reactor at 2 Mw is shown in Figure 18, The theoretical and experi-

mental data are in adequate agreement at this lower power,

PRTS Test Patterns

 

The faulty magnetic tape unit malfunctioned on two out of three tests
which employed PRTS test patterns. The results of the successful PRTS
test (242 x T7.25 at 8 Mw) are shown in Figures 19 and 20. The auto-
correlation function of a PRTS waveform is obvious in Figure 19b and the
assoclated power spectrum is relatively flat over nearly twe decades in
frequency.

The curvature in the autocorrelation of the rod position (Figure 19a)
is unusual compared to those previously shown. The plot indicates that
the rod position was not a true periodic signal since it was not symmetric
about the half-period time. These tests were performed in February and
March when changes in atmospheric conditions were rapid. Ambient air
temperature and/or wind velocity changes affect the heat-removal rate at
the radiator which ultimately forces a reactivity change in the core.
Since the flux was being controlled during these tests, the outside dis-
turbances were shown by changes in control rod position which were, in
turn, reflected in the correlation function calculations,

While temperature effects account for the non-symmetrical shape of
the autocorrelation function in Figure 19a, the general "bowed'" shape
must be explained by other means. The period of this test (2Lk2 x 7.25)

was long compared to most other tests performed, hence the fundamental
66

ORNL-DWG 69-12055

POWER LEVEL-2 Mw
ANALYS!S METHOD

¢ CABS
~— THEORY

3
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FREQUENCY (rad /sec)

Periods of data analyzed — 5
Type sequence = 127 x 5 PRBS

FIGURE 18. Frequency-response results from a flux-demand test with the
reactor at 2 Mw.
67

ORNL —DWG 69-—12253

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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POWER SPECTRUM (arbitrary units)

 

2 5 1072 2 5 107!

FREQUENCY (rad/sec )

(a) Autocorrelation function and power spectrum of the control-rod
position.

Periods of data analyzed — 2
Type sequence — 242 x T7.25 PRIS

FIGURE 19. Correlation function and power spectrum results from a flux-
demand test using a PRTS test pattern.
68

ORNL—DWG 69-12254

 

2.0

 

 

1.2

 

 

0.4

 

 

%""J"’""*"’JF-‘“ Mty fl-—%—w

 

 

 

AUTOCCRRELATION FUNCTION (arbitrory units)

 

 

 

 

 

 

 

 

 

 

 

 

 

~-0.4
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0 400 800 1200 1600 2000
CORRELATION TIME (sec)
102

POWER SPECTRUM (arbitrary units)

C)l
N

   
  

1 0

z 2 5 10~
FREQUENCY (rad/sec)

10”3 2 5 1o 2 5 10

(b) Autocorrelation function and power spectrum of the neutron flux.

Periods of data analyzed — 2
Type sequence — 242 x 7.25 PRTS

FIGURE 19. (continued)
69

ORNL-DWG 69-12255

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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CORRELATICN TIME (sec)

CROSS-POWER SPECTRUM ({arbitrary units)

 

10°3 2 5 107 2 5 10~ 2 5 10°
FREQUENCY (rod /sec)

(c) Cross=-correlation function and cross-power spectrum of the control-
rod position and neutron flux.

Periods of data analyzed — 2
Type sequence — 242 x 7.25 PRTS

FIGURE 19. (continued)
70

ORNL-DWG 69-42257

POWER LEVEL-8Mw

ANALYSIS METHOD
* CABS
— THEQRY

 

 

300

 

 

220

 

 

>
o

 

 

 

 

PHASE (deg)

 

N
Q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1072 2 5 1072 2 5 o 2 5 10
FREQUENCY (rud/sec)

Periods of data analyzed — 2
Type sequence — 242 x 7.25 PRTS

FIGURE 20. Frequency-response results from a flux-demand test performed
on the £7°U-fueled reactor using a PRTS test pattern.
71

frequency was exceptionally low. The reactor was at full power so the
amplitude of the frequency response was expected to be low at the low
frequency., Since the spectral power of the flux was flat, the power in
the rod-position signal at the fundamental frequency must be relatively
high to give the low value in the amplitude of the frequency response.
Note that the power content of the lowest harmonic in Figure 19a is a
factor of about 20 higher than most of the other harmonics. The relative
high power content in the fundamental frequency necessarily yields a

function similar to one period of a sine wave,

"Non-Symmetric" PRTS Test Patterns

 

One property of a PRTS is that its autocorrelation function has a
negative spike at lag time equal to T/2 which is equal in magnitude to
the positive spikes at lag times equal to zero and T (see Section I of
Chapter II). This is possible only if the second half of the sequence is
the negative of the first half, For example, if the first two bits in a
PRTS are positive, the first two bits of the second half of the sequence
will be negative.

The results of the first attempts at using a PRTS are shown in
Figures 21 and 22. These were surprising in that the autocorrelation
function of the flux signal (Figure 21b) did not assume the expected
shape of a PRTS. The reason for the unexpected correlation function was
found to be the manner in which we assigned voltage to the PRTS signal
which was generated by the on-line computer (BR-340). Instead of using
a signal which had the same number (n) of plus and minus pulses with (n-l)

intervals at zero level, as is the case for a true PRTS, we were actually
70

ORNL— DWG 69—12258

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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POWER SPECTRUM (arbitrary units)

 

73 2 5 1072 2 5 T 2 5 10

FREQUENCY (rad /sec)

(a) Autocorrelation function and power spectrum of the control-rod
position.

Periods of data analyzed — L
Type sequence — 80 x 10 "non-symmetric' PRTS

FIGURE 21. Correlation function and power spectrum results from a flux-
demand test using a "non-symmetric" PRTS test pattern.
T3

ORNL—-DWG 69—12259

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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0 160 320 480 640 800

CORRELATION TIME {(sec)

POWER SPECTRUM (arbitrary units)

 

i

2 2 5 10"

FREQUENCY (rad/sec)

2 5 10

(b) Autocorrelation function and power spectrum of the neutron flux.

Periods of data analyzed — k
Type sequence — 80 x 10 '"non-symmetric' PRTS,

FIGURE 21, (continued)
Th

ORNL-DOWG 69 -42260

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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6—-

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CROSS-POWER SPECTRUM ({arbitrary units)
61

 

192
1073 2 5 1072 2 5 107! 2 5 10°

FREQUENCY (rad/sec)

(c) Cross-correlation function and cross-power spectrum of the control-
rod position and neutron flux,

Periods of data analyzed — L
Type sequence = 80 x 10 '"non-symmetric' PRTS

FIGURE 21. (continued)
5

ORNL~DWG 69-12261

POWER LEVEL ~2 Mw

& BC x 10 PRTS, CABS ANALYSIS
o 242 x 7.25 PRTS, CABS ANALYSIS
—— THEORETICAL

a&n
Ny - Bk

 

 

 

 

140

 

 

 

 

PHASE (deg)

 

20
A
N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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-100 .
1073 2 5 1072 2 5 107" 2 5 10

FREQUENCY (rad/sec)

FIGURE 22, Frequency-response results from flux-demand tests performed
on the £7°U-fueled reactor using "non-symmetric' PRTS test patterns.
76

using a signal with the same number (n) of plus and zero pulses with (n-1)
minus pulses, which resulted in the autocorrelation function not being sym-
metric about the half-period time. Calculation of the power spectra for
this type of signal showed that 3/” of the signal power was concentrated
in the even harmonics with the remainder in the odd harmonics., This is
still a valid signal for frequency-response determination, but it defeats
one of the purposes of using the PRTS — the concentration of all the
signal power in the odd harmonics. The magnitude-ratio and phase-angle
plots for two tests which utilized this type signal are shown in Figure 22,
Most of the scatter in the data is due to including the values obtained by
analyzing the data at all harmonic frequencies instead of just on the even

harmonics which contain most of the signal power.
II. =°% FUEL LOADING

While the results of tests which utilized the flux-demand technique
during the 75U testing were less than ideal, they were adequate and
certainly better than no results. Hence, the plans for the 237U testing
program were to perform the dynamics tests using the flux-demand tech-
nigue. Both the PRBS and PRTS test signals were to be utilized with a
general shift to shorter bit times so that the signals would have more
signal power at higher frequencies., This was desired due to the shift in
the freguency response of the reactor with the fuel change (see Figures L
and 5 for a comparison of frequency responses).

While compensation for the changes in the frequency response of the
reactor was not difficult, there were other changes in the ”pefsonality”

of the reactor which did present problems, First, the control rods were
T

worth more® (about 30%) which meant that it would require less movement to
obtain the same change in reactivity. Since the control rod was suspected
of having caused problems in the U testing program, it was anticipated
that the effect of moving the rod less (0.3 in. instead of 0.5 in.) would
tend to magnify any inherent discrepancies which existed between indicated
and actual control-rod position. Second, with the £35U fuel the reactor
had been an exceptionally noise-free system, but shortly after operation
began with the 37U fuel, the void fraction increased from sbout 0.05%
to about 0.6%. This caused a large change in the background neutron noise.
An example of the uncon?rolled neutron level for both the €PU fuel
loading and the 2% fuel loading is shown in Figure 23.

Typical correlation functions for the various types of signals em-
ployed in the testing were shown in Section I of Chapter IV and these

will not be repeated for each test,.
1. Plux-Demand Tests

PRBS Test Patterns

The first tests on the 77U fuel loading were performed while the
reactor was at zero* power, The results of this test are shown in
Figure 2La. While these results do not disprove the theoretical pre-
diction, the scatter is such that they do not verify it either. Not only

is there considerable scatter in these results, but at low frequencies

 

* .
Zero power implies a neutron level which is low enough so that no

significant temperature changes occur but which is high enough not to be
significantly affected by the neutron sources other than fission.
78

 

K/\ ORNL-DWG 69-12230

 

 

— «— 1.5 Mw

 

hg———

 

 

— 5 min

TIME —

 

 

 

233 FUEL

 

 

 

 

235, FUEL

 

 

 

 

 

 

 

 

 

ot e A WYL i Pty VM A A A AAUAA M P et T e A i/

 

 

 

 

 

 

 

o)

30 40 50 60 70 30 40 50 60 70
POWER LEVEL (percent of 15 Mw)

FIGCURE 23, Examples of the uncontrolled neutron flux during periods of
8 Mw power operation for the 225U fuel loading and the 27U fuel
loading.
79

ORNL-DWG 69-12043

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

104
5
2
s A3
«:é?1()
5 POWER LEVEL-ZERO
ANALYSIS METHODS
a FOURCO ENSEMBLE
> o FOURCO
® CABS
o2 — THEORY
0
o
Q
Z -30
L
w
<
I
o
~60
-90 |
1073 2 5 4072 2 5 407! 2 5 100

FREQUENCY (rad/sec)

(a) Results from four periods of a 127 x 5 PRBS with the reactor at
zZero power,

FIGURE 24, Frequency-response results from flux-demand tests using
PRBS test patterns performed on the €2 -fueled reactor.
80

ORNL-DWG 69-12052

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_x
Q00
K .o
3 POWER LEVEL-ZERO
ANALYSIS METHODS
o FOURCO ENSEMB
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— THEORY
=
Q
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<{
I
a
-90
[»]
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o I
10 2 5 4072 2 5 40t 2 5 40°

FREQUENCY (rad/sec)

(b) Results from three periods of a 127 x 5 PRBS with the reactor at
Zero power,

FIGURE 24, (continued)
81

ORNL-DWG 69-12051

POWER LEVEL-1Mw
ANALYSIS METHODS

© FOURCO
e CABS
= THEORY

 

 

 

 

SO e
| ?

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-90 -
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FREQUENCY (rad/sec)

(c) Results from four periods of a 127 x 5 PRBS with the reactor at
1 Mw,

FIGURE 24, (continued)
82

ORNL -DWG 69-12050

FUEL STATIONARY
POWER LEVEL - ZERO

3n
Ny 84

ANALYSIS METHODS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

« CPSD
s FOURCO ENSEMBLE
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I -60 o
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-90
103 2 5 402 2 5 10! 2 5 40°

FREQUENCY (rad/sec)

(d) Results from four periods of a 127 x 5 PRBS with the reactor at
zero power and the fuel not circulating.

FIGURE 24, (continued)
83

the different analysis schemes often yielded results which were radically
different. Analysis at higher freguencies tended to decrease the scatter
in the data as well as in the differences between analysis method.
Typically, after about eight harmonics for a 127 x 5 test the differences
between the analysis methods were negligible,

An example of the strong disagreement between analysis schemes is
evident in the magnitude ratio results shown in Figure 2ha. At the first
harmonic (.00989 rad/sec) the CABS analysis resulted in a value of 230,
FOURCO using a fine filter gave 2850, and the ensemble average of results
from the four periods cof data analyzed separately (broad filter) by FOURCO
was 5200, The CPSD analysis (not shown) was 894, The coherence function
was 0.17 as calculated by CABS and was 0.65 according to the CPSD analysis.
The CABS result is obviously a low-confidence number and the CPSD coherence
of .65 does not indicate strong relationship between the measured input
and output signals.

Why the analysis techniques yielded different results when analyzing
the same data i1s not completely resolved; however, there are clues which
indicate that it is related to system noise, First, this problem was not
pronounced except when testing with the flux-demand technique, and, as
will be discussed later, the flux-demand technique caused an amplification
of errors in the control-rod position indication., Second, 1in each case
where there was a large discrepancy between analysis techniques, the CABS
calculation of the power spectrum of the input signal was found to have
a large phase angle (-89° for the point being discussed), Since only the
cross-power spectra can contain phase information, the input power spec-

tra calculations are obviously in error. The input power spectrum is
8L

actually calculated by Fourier transforming the autocorrelation function
of the input signal, and noise will make the autocorrelation function
slightly non-symmetric about the half-period time since it prevents the
signal from being exactly periodic., It is thought that this non-
periodicity of the autocorrelation function was the cause of the erroneocus
CABS results. At least, when the result was in error, the coherence
function signaled a warning to beware of placing confidence in the calcu-
lation. |

Results of another zero-power test (3 cycles of a 127 x 5) are shown
in Figure 24b. The differences between the results of different analysis
schemes are not as pronounced; however, the general scatter in the re-
sults is greater. This is probably due to using only 2 periods of data
in the analysis,

One curious feature of these results is the consistent roll-off of
the experimentally determined phase angle at frequencies above about 0.4
rad/sec, even though the theoretical calculations predict an increase.
This feature was apparent in all of the results and was not dependent on
the type signal nor the testing technique. The implication is that
either the theoretical predictions were inadequate in this aspect, or
that there was an inherent phase lag between the actual and indicated rod
position at the higher frequencies. Since the indicator was nearer the
drive motor than the lower end of the rod and was separated from the
lower end of the rod by several feet of flexible hose, it seems reasonable
to expect a phase lag in the actual position at the higher frequencies.

The results from 4 cycles of a 127 x 5 PRBS which was performed with

the reactor at 1 Mw are shown in Figure 24c. The typical scatter at all
85

frequencies and the discrepancies between analysis techniques at the low
frequencies is apparent. The low phase-angle values at the higher fre-
quencies are also present.

With the fuel not circulating, the dynamic characteristics of the
MSRE approach those of solid-fuel reactors. The results of a frequency-
response test which was performed with the fuel not circulating are shown
in Figure 2ld, page 82. The scatter in these results is much less than the
scatter in the results for the circulating-fuel tests. The magnitude-ratio
results are in general agreement with the theoretical prediction, but the

bPhase angle is below the theoretical at the higher frequencies,

PRIS Test Patterns

If some type of system noise were the cause of the éxcessive scatter
in the results of tests which utilized a PRES test signal, it does not
seem logical that going to a three-level signal would improve the results,
This logical deduction was verified by the results of tests at zero power
and at 5 Mw,

The results of three different tests at zero power are shown in
Flgures 25a, 25b, and 25c. Two of the tests are 80 x 3 sequences and the
third is a 242 x 5 sequence. There are not any significant differences
between the results of these tests, and each is characterized by the same
type scatter which was apparent in the PRBS flux-demand tests, While
there is some variation between results obtained from the different
analysis methods, the differences are not as pronounced as they were in
the results obtained in séme of the PRBS tests. However, since all of

the PRBS tests did not exhibit large differences in results for the
86

ORNL —DWG 69—142049

POWER LEVEL - ZERO

ANALYSIS METHODS
e CABS
4 FOURCO ENSEMBLE

THEQORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
e
4
. =30
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°
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° o2 4
%
-90

102 2 5 10°" 2 5 10

FREQUENCY (rad /sec)

(2) Results from four periods of an 80 x 3 PRIS with the reactor at
zero power.

FIGURE 25, Frequency-response results from flux-demand tests using
PRTS test patterns performed on the £°3-fueled reactor.
87

4 ORNL—-DWG 69— 1412048

POWER LEVEL -ZERO

ANALYSIS METHOD
o FOURCO
THEORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O
O
’;’ -30 U5 o T
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~ o '_,.p""_—_—_-'"\-f
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|
0% 2 5 (0% 2 5 10" 2 5 10°

FREQUENCY (rad/sec)

(b) Results from two periods of a 242 x 5 PRTS with the reactor at
Zero power. -

FIGURE 25. (continued)
88

ORNL-DWG 69--12047

POWER LEVEL — ZERO

ANALYSIS METHOD
4 FOURCO ENSEMBLE

THEORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

— / A a4 AJ
g N
3 1
w A O
w
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T —90
o
—120
A
100" 2 5 107" 2 5 10°

FREQUENCY (rad/sec)

(c) Results from three periods of an 80 x 3 PRTS with the reactor at
Zero power,

FIGURE 25. (continued)
89

ORNL-DWG 69-12046
104

POWER LEVEL~ 5Mw
S ANALYSIS METHODS

o CARBS, FOURCO, CPSD
{ALL GAVE SAME RESULTS)
~— THEORY

102
60

 

 

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Q
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-90
1072 2 5 10~ 2 5 10°

FREQUENCY (rad/sec)

(d) Results from twelve periods of an 80 x 3 PRIS with the reactor
at 5 Mw,

FIGURE 25. (continued)
90
ORNL-DWG 695-12045

FUEL STATIONARY
POWER LEVEL-ZERO

ANALYSIS METHOD
4 FOURCO ENSEMBLE
=——THEORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
//’
A ]
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L /’/A & &1 P
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=90
1072 2 5 o~ 2 5 10°

FREQUENCY (rad/sec)

(e) Results from four periods of an 80 x 3 PRTS with the reactor at
zero power and the fuel not circulating.

FIGURE 25, (continued)
91

different analysis methods, it is not certain that the PRTS signal dis-
criminates against this anomalous behavior, but there does appear to be
a tendency in that direction.

The significant features of the overall results of the zero-power
tests shown in Figures 25a, 25b, and 25c are almost identical to those of
the PRBS tests. The results are in general agreement with the theoretical
predictions, but the magnitude-ratio results tend to drop below the theo-
retical results at the higher frequencies, The phase angle also drops
below the theoretical predictions above 0.k rad/sec.

In an effort to improve on the statistical precision of the results,
an 80 x 3 sequence was used in a test at 5 Mw and was continually re-
peated until 12 periods of usable data were collected. The results of
this test (Figure 25d) were almost identical for each of the analysis
schemes, and the scatter in the results is lowered but is not eliminated.
The experimental magnitude-ratio results obtained for frequencies higher
than about 0.4 rad/sec are lower than the theory and the phase angle con-
tinues to be low at the higher frequencies (about 35° at 1 rad/sec). The
possible 5° error introduced by the digitization lag in the data recording
would obviously be insufficient to correct for this deviation,

An 80 x 3 PRTS was performed with the fuel stationary and yielded
the frequency-response determination shown in Figure 25e. The magnitude-
ratio results are not conéistent with the theory in magnitude but the
general shape is the same, The phase angle results are exceptionally
poor in that they do not conform to the shape of the theoretical curve at
any frequency. The poor results of this test were surprising since the

results of the PRBS test on the non-circulating fuel were so good.
92

Discussion

In sumary, the results of flux-demand tests applied to the -
fueled MSRE wefe disappointing. The results contained such excegsive
scatter that they were of little value in describing the frequency re-
sponse of the MSRE, Neither type test signal appeared to give better
results than the other and there were anomalous discrepancies between
analysis techniques when applied to the same data,

The failure of the flux-demand technique to provide adequate results
with the £ fuel is attributed to a combination of poor coupling be-
tween the indicated and actual rod position and system noise. As de-
scribed in Chapter II, the rod-drive assembly actually drives a chain
onto which the upper end of a flexible hose is attached. This hose
maneuvers around two 30° bends in the tube in which it is enclosed and
then drops vertically into a region near the center of the core. As the
control rod moves, it encounters considerable friction as is evidenced
by the normal average control-rod acceleration of only & to 15 ft/sec2
during a scram (Reference 6, pages 26, 27). This may be enough friction
to allow the rod to actually move in short jerks rather than a continuous
smooth fashion, Other possible sources of difference between the actual
rod movement and the indicated movement include stiff linkage in the
drive chain which would not allow the chain to conform to the curvature
of the sprocket, and the possibility that the rod was stiff, bowed, or
twisted in a region which was traversing the bends. This would cause the
lower region of the rod not to move in an exactly vertical direction.

In addition, there are several gears between the actual rod drive linkage

and the position indicators (the "fine" and "coarse" synchros). There is
93

likely some amount of freedom between these gears which results in errors
in the indicated rod position. Since the rod is typically moved a maxi-
mum of about 0.5 in, during a flux-demand test, a discrepancy between the
indicated position and the actual end of the control rod of only 0,05 in.
on both ends of the travel could produce an error of 20% in the indicated
reactivity change. Hence, any of the above mentioned possible error
sources are capable of significantly contributing to the total error.

The "coarse'" synchro was used to indicate rod position in all of the
tests performed on the 2357 fuel loading. After the results of the first
flux-demand tests with 22U fuel were received, the testing procedure was
changed so that a completely different rod assembly (including synchro)
was used, This did not help to reduce the scatter in the results so a
system was devised whereby the "fine" synchro could be used. This did
not appear to improve the results, but in the remainder of the testing
program the fine synchro was used.

The additional neutron noise which accompanied the 3 fuel loading
contributed to the scatter in the results in two ways. First, additional
noise on a signal tends to lower the statistical precision of compu-
tations performed with that signal. Second, the flux was required to
remain within the deadband as prescribed by the servo circuits. With the
additional noise, the control rod needed to move almost continuously in
order to keep the flux within the deadband limits, Since it 1s known
that there are errors in the indicated rod position, these additional rod

movements certainly introduced errors in the measured frequency response.
9l
2. Rod-Demand Tests

PRBS Test Patterns

The fallure of the flux-demand testing required that a change be
made in the testing technique. The results from the good rod-jog test
as described in Section I of this chapter, were very encouraging so a
change back to rod-controlled testing was desired, TInstead of attempting
to force the rod-jog method to work, it was decided to try a new approach,
the rod-demand technique. As previously described for the rod-demand
technique, the control-rod servo was changed so that it forced the indi-
cated control-rod position to match an input demand.

With the reactor at zero power, a 127 x 5 PRBS was implemented in
the reactor using this method. The results of this test are shown in
Figure 26a and, except for the phase angle results at higher frequencies,
are in excellent agreement with the theoretical predictions. The magni-
tude ratio results were normalized by multiplying by 1.75. Normalization
was usually necessary when a PRBS was used with the rod-demand technique,
The reason for this normalization will be discussed more fully later in
this section.

With the reactor at 5 Mw, a 127 x 5 PRBS was repeated until two hours
of data were collected. FEleven consecutive periods of the seguence were
obtained from this test and analysis of this data gave the excellent re-
sults shown in Figure 26b which have not been normalized. There is little
scatter in the results and they are in good agreement with the theoretical
predictions. The experimental results dip at about .24 rad/sec as theoreti-

cally predicted although the dip in the experimental results is not as
95

ORNL-DWG 69- 12044

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

« »
° 9 POWER LEVEL -ZERO
ANALYSIS METHODS
o FOURCO
« CPSD
— THEORY
o
g 30 - G ‘_ 0 e
; 0 -fi -+ | <':_6 ;?'EGEQEB/BO 0
2d | m ° ST
< ../ir TP % o°'e$
T -60 1 <
7
.
¢
-90
02 2 5 {072 2 5 10" 2 5 10°

FREQUENCY (rad /sec)

(a) Results from three periods of a 127 x 5 PRBS with the reactor at
zero power. Magnitude ratio normalized by multiplying by 1.75.

FIGURE 26. Freguency-response results from rod-demand tests using
PRBS test patterns performed on the 233J-fyeled reactor.
96

ORNL—-DWG 69-12245

10

POWER LEVEL — 5Mw
ANALYSIS METHODS
v FOURCO, CABS
(EACH GAVE SAME RESULTS)
-~ THEORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 30

S vfi

L

¢ N

o L
/\“‘---
5&7?%& TN
A\

-30 V‘Qn 7

1
~60 3 —2 —{ L0
{0 10 10 10

FREQUENCY (rad/sec)

(b) Results from eleven periods of a 127 x 5 PRBS with the reactor
at 5 Mw,

FIGURE 26. (continued)
91

ORNL -DWG 69-12246

POWER LEVEL =8Mw
ANALYSIS METHODS

o FOURCO, CABS, CPSD
(EACH GAVE SAME RESULTS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

— THEORY
. |
|
mao
A
N
60 N
N
S N\
S 30 \
a \ /‘
: A
%éflc@#& N
a ?‘L& "N
;
-30 [fi

 

1073 2 5 {1072 2 5 10! 2 5 40°
FREQUENCY (rad/sec)

(c) Results from eight periods of a 127 x 3 PRBS with the reactor at
8 Mw, Magnitude ratio normalized by multiplying by 1,30.

FIGURE 26. (continued)
98

104 ORNL -DWG 69-12247

POWER LEVEL-8 Mw
ANALYSIS METHODS

0 FOURCO, CABS, CPSD
(EACH GAVE SAME RESULTS)

THEORY

sn
N, - 8K

 

 

 

 

PHASE (deg)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-60
1072 10~ 10
FREQUENCY (rad/sec)

(d) Normalized results from five periods of a 127 x 5 PRBS with the
reactor at 8 Mw. Magnitude ratio normalized by multiplying by 1.36.

FIGURE 26. ({continued)
99

pronounced as in the predictions. The magnitude ratio and phase angle
fall below the theory at higher frequencies.

The results of two tesfs performed with the reactor at full power
are shown in Figures 26c and 26d. The results in Figure 26c are from
analysis of five periods of a 127 x 5 PRBS, and those in Figure 26d are
from analysis of eight cycles of a 127 x 3 PRBS. The magnitude ratio re-
sults were normalized to agree with the theoretical curve at 0.4 rad/sec.
Normalization factors were 1.30 and 1.36 respectively. There is little
scatter in the results and they tend to be in good agreement with the
shape of the theoretical curve except for the regular depression at the
higher frequencies, The dip in the experimental results at 0.24 rad/sec
is evident but, as before,'is not as pronounced as the theory predicted.

In general the coherence functions calculated for the rod-demand
tests were above 0.98 and below 1.0 with occasional values slightly higher
than 1.0. The value of the coherence function was usually relatively low
(about .95) for the lowest harmonic freguency but came within the quoted
range after a few harmonics and remained in the band until the power in the
input signal began the characteristic rapid decrease at the higher fre-

guencies,

PRTS Test Patterns

Results of a test in which a PRTS test pattern was implemented using
the rod-demand technique is shown in Fig, 27. The scatter in the results
resembles the scatter which was evident in the results of the flux-demand

tests, and these results do little to aid in the specification of the
100

ORNL-DWG 69- 12242

{0

POWER LEVEL - 8Mw

ANALYSIS METHOD
* CABS
= THEORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4
90 157
\\ .
®
60 \\
el I\
\| «
R N
> 30
= b
w ¢ \-
w 1‘\
T o0 \
a ¢
N
.‘ 9
®
-30
®
-60
103 2 5 102 2 5 0! 2 5 10°

FREQUENCY (rad/sec)

FIGURE 27. Frequency-response results from two periods of a rod-demand
test using a 242 x 5 PRTS test pattern.
101

frequency response of the MSRE, The results do tend to be scattered around
the theoretical curve and normalization of the results was not necessary.

The coherence functions calculated from these data generally scat-
tered in a band between about .94 and 1.08 over the frequency range at which
the signal power was relatively constant. The coherence functions at the
fundamental frequency were considerably below this scatter band (0.65 for
the results shown in Figure 27), but after a few harmonics, the values

were within the normal scatter.

Discussion

When a PRBS test pattern was used, the results from the rod-demand
technique were very encouraging. Normalization factors were often neces-
sary to get the experimental results to agree with the theoretical pre-
dictions, but the shapes of the two were in accord. When a FRTS test
pattern was employed with the rod-demand technique, there was excessive
scatter in the results. Since there is considerable interest in the PRTS
test pattern, it is unfortunate that these results were of poor quality;
however, the failure of these tests did provide another clue toward bet-
ter understanding of the MSRE.

The postulated reasons for failure of the flux-demand technigue to
provide adequate results was the behavior of the control-rod assembly,
and the results of the rod-demand tests tend to verify the postulate.
When the rod was moved in a manner which simulated a PRBES waveform, it
would be inserted, held stationary for a few seconds, withdrawn, held
stationary, and then inserted again. This pattern was repeated with the

only variation being in the length of time it remained stationary. An
102

insertion was always followed by a withdrawal and vice versa, If the
bottom end of the rod did not actually move the distance the gear train
indicated, as might be the case if any of the several possible high-
friction conditions mentioned on pages 92 and 93 actually existed, then the
waveform would still be well represented, but the indicated magnitude of
the perturbations would be in error. This certainly fits with the results
of the PRBS tests when used with the rod-demand technique and explains the
necessity of use of a normalization factor. With the PRTS wave form, each
movement of the control rod is not necessarily the opposite of the previous
movement. An insertion may follow an insertion, and a withdrawal may
follow a withdrawal., If, after a single insertion, the rod had moved to

a high-friction position which was slightly hindering its motion, another
insertion would force it on through this spot‘and it might or might not
end near a similar spot after the second insertion. The effect of sub-
sequent withdrawals and insertions is unclear since the insertions may
originate from two different positions and those from the middle position
may be following an insertion or withdrawal. If the rod-position indi-
cator was not able to provide accurate information during at least part of
these movements, then the test results would be expected to contain
scatter. This fits the results of the PRTS tests when the rod-demand
technique was used. Tt is important to note that these explanations for
the results of the different type teste have not been proven but are

offered as reasonable explanations which fit the experimental observations.
103

CHAPTER V
CONCIUSIONS AND RECOMMENDATIONS

The purpose of this work was to experimentally measure the freguency
response of the MSRE and to determine the effects of varying the testing
technigque and test signal specification. The experimental results veri-
fied the predictions and were adequate to provide a recommendation for
improving the theoretical model. The dip in the magnitude ratio which was
predicted at about 0.24 rad/sec is present in the experimental results,
but it is not as pronounced as expected, Since the magnitude of the dip
has been shown> to be a strong function of the salt mixing as it circulates
around the primary system, I conclude that the theoretical models need to
allow for more mixing of the fuel salt.

Tn the course of the testing program, three different testing tech-
niques were used, The rod-jog technique, an open-loop method of rod con-
trol, worked well when the rods were free-moving. OSince there was no
feedback, any imbalance between the withdrawal and insertion times re-
sulted in drift of the average position. The flux-demand technique im-
posed the test pattern on the flux rather than rod position. The results
from this type test contained more scatter than rod-controlled testing
but for the U fuel loading gave adequate results. The faster response
of the £3J-fueled reactor, coupled with the increased noise level and
more aging of the control rod assemblies, gave results which contained

such scatter that they were of little value in determining the frequency
104

response of the MSRE., For a system in which the rod position is well de-
fined, this technique should work well and has advantages which might make
it preferred over rod-controlled testing for certain applications.

The rod-demand technigue, a closed-loop method of rod control, when
used with a PRBS, meshed with the physical limitations of the MSRE to
give the best results of the testing program, Normalization of the re-
sults was sometimes necessary but the shapes were in good agreement with
the theory.

Various PRBS and PRTS sequences were used, The PRBS was found to
give better results with the rod-controlled testing and neither type sig-
nal was adequate when the flux-demand technique was used with the £33
fuel loading. The failure of the PRTS signal when used with the rod-
demand technique is thought to be an extension of the problems associated
with the control-rod position indication. Sequence lengths varied between
80 and 242 bits and the basic bit duration varied between 3 and 10 seconds.
The expected distributions of signal power as a function of frequency were
found and there were no anomalous effects noted for the different sequence
specifiications, As one would expect, it was found that better statistical
precision was obtained for sequences which were repeated several times.

Analysis techniques gave consistent results when applied to data
which contained a relatively low noise level but differed radically at the
low frequencies, typically the first five‘to ten harmonics, when the data
contained high noise content, such as during the flux-demand tests. No
systematic study was made to determine the reasons for these differences

which leaves this as an area in need of additional work.
105

The experience gained in this work emphasizes the need to plan the

testing of a system to match the test procedure to the characteristics

of that system. In particular, the difficulty in obtaining accurate

indications of rod position changes dictated that all unnecessary rod

movement be eliminated. In the £3J-fueled system with a high noise level

in the flux signal, the rod-demand method proved to be the best testing

procedure,

Some areas in which more work is needed are:

ln

Determination of the cause of the difference between
analysis schemes at the low frequencies when a large amount
of noise is present,.

Investigation into the meaning of the coherence function
when applied to periodic sequences and explanation for the
experimentally determined coherence functions which were
greater than 1.0.

Complete verification of the hypothesis that proper analysis
at frequencies midway between adjacent harmonic frequencies
of the minimum periocd length will provide a measure of the

system noise level that was present during the testing.
LIST OF REFERENCES
10.

11,

107

LIST OF REFERENCES

Buckner, Melvin R,, "A Study of the Application of System Identifi-
cation Techniques in the Analysis of Nuclear Reactor Dynamics, "
Unpublished Masters Thesis, Nuclear Engineering Department,
University of Tennessee, Knoxville, Tennessee (December 1968).

Ball, 5. J. and Kerlin, T, W,, "Stability Analysis of the Molten-Salt
Reactor Experiment," USAEC Report ORNL-TM-10T70, Oak Ridge
National Laboratory, (December 1965),

Steffy, Jr., R. C. and Wood, P. J., "Theoretical Dynamic Analysis of
the MSRE with U-233 Fuel," USAEC Report ORNL-TM-2571, Oak Ridge
National Laboratory (July 1969).

Haubenreich, P. N. et al., "MSRE Design and Operations Report,
Part V-A, Safety Analysis of Operation with £33, " USAEC Report
ORNL-TM-2111, Oak Ridge National Laboratory, p. 41, (February
1968).

Molten-Salt Reactor Program Semiannual Progress Report, July 31, 1964
USAEC Report ORNL-3708, Oak Ridge National Laboratory, p. 231,
(November 1964),

2

Molten-Salt Reactor Program Semiannual Progress Report, February 28,
1969, USAEC Report ORNL-4396, Oak Ridge National Iaboratory,
p. 130, (August 1969).

Robertson, R. C., "MSRE Design and Operations Report, Part 1,
Description of Reactor Design,' USAEC Report ORNL-TM-728, Cak
Ridge National Laboratory, (January 1965).

Tallackson, J. R., '"MSRE Design and Operations Report, Part II-A,
Nuclear and Process Instrumentation," USAEC Report ORNL-TM-729,
Part II-A, Oak Ridge National Laboratory, (February 1968).

Kerlin, T. W. and Ball, S, J., "Experimental Dynamic Analysis of the
Molten-Salt Reactor Experiment," USAEC Report ORNL-TM-16L47,
Oak Ridge National Laboratory, (October 1966).

Kerlin, T. W. '"The Pseudo-Random Binary Signal for Frequency Response
Testing," USAEC Report ORNL-TM-1662, Oak Ridge National
Iaboratory, (1966).

Elspas, Bernard, 'The Theory of Autonomous Linear Sequential Net-
works, " Transactions of the I.R.E. on Circuit Theory, CT-6:

L5-60 (1959).
12,

13.

1k,

15,

16.

170

18.

19.

20.

2l.

22,

23.

108

Everett, D., "Periodic Digital Sequences with Pseudonoise Properties,"
General Electric Company (Limited of England) Journal of Science

and Technology, 33(3): 115-126 (1966).

Godfrey, K. R. and Murgatroyd, W., "Input-Transducer Errors in Binary
Cross-correlation Experiments,' Proceedings of the Institute of
Electrical Fngineers, 112(3): (March 1965).

 

Briggs, P. A. N., Godfrey, K. R., Hammond, P, H., "Estimation of
Process Dynamic Characteristics by Correlation Methcods using
Pseudo Random Signals,” TFAC Symposium on Identification in
Automatic Control Systems, 12-17 June, 1967, Prague, Czecho-
slovakia, Part II, pp. 1 - 12, Academia-Prague (June 1967).

Zierler, Neal, "Linear Recurring Sequences," Journal of the Society
of Industrial Applied Mathematics, 7(1): (March 1960).

Simpson, H., C., "Statistical Properties of a Class of Pseudorandom
Sequences, " Proceedings of the Tnstitute of Electrical Engineers,
113(12): 2075, (December 1966).

Turin, G. L., "An Introduction to Matched Filters,'" Institute of Radio
Engineers Transactions on Information Theory, IT-6: p. 311 (1960).

 

Roberts, P, D. and Davis, R. H., "Statistical Properties of Smoothed
Maximal-Length ILinear Binary Sequences," Proceedings of the
Institute of Electrical Engineers, 113(1): 190 (January 1966).

 

Kerlin, T. W., "Frequency-Response Testing," Nuclear Safety, 8(L).
339-345, (Summer, 1967).

Hooper, R. J. and Gyftopoulos, E., P,, "On the Measurement of
Characteristic Kernels of a Class of Nonlinear Systems," Neutron
Noise, Waves, and Pulse Propagation, Proceedings of Symposium at
University of Florida, February 14 - 16, 1966, R. E. Uhrig,
Editor, AEC-Symposium Seriles No, 9, USAEC-DTIE, Oak Ridge
National Laboratory, (1967).

Godfrey, K. R., "Three-Level m-Sequences," Electronic Letter, 2.

U1 (1966).

 

Briggs, P. A. N, and Godfrey, K., R., "Pseudorandom Signals for the
Dynamic Analysis of Multivariable Systems,'" Proceedings of the
Institute of Electrical Engineers, 113(7): (July 1966).

 

Ball, S, J., "A Digital Filtering Technique for Efficient Fourier
Transform Calculations," USAEC Report ORNL-TM-1662, Oak Ridge
National Laboratory (July 1967).
24,

25.

26,

27,

28.

29.

30.

31.

109

Broome, P. G. and Cooper, G. C., "Fourier Spectrum Analysis by Analog
Methods, " Instrumentation and Control Systems, 35(5): 155-60
(May 1962).

Ball, S. J., Instrumentation and Control Systems Division Annual
Progress Report, September 1, 1965, USAEC Report ORNL-3875,
pp. 126 - 127, Oak Ridge National Laboratory (September 1965),

Kerlin, T. W. and Lusius, J. L., "CABS — A Fortran Computer Program
for Calculating Correlation Functions, Power Spectra, and the
Frequency Response from Experimental Data," USAEC Report ORNIL-
TM-1663 (September 1966).

Thie, J. A,, Reactor Noise, Rowan and Littlefield, Inc.,, New York
(1963).

Bendat, J. S. and Piersol, A. G., Measurement and Analysis of Random
Data, John Wiley and Sons, Inc., New York (1966).

Balcomb, J. Douglas, Demuth, H. B,, and Gyflopoulis, E.P., "A Cross-
correlation Method for Measuring the Impulse Response of Reactor
Systems," Nuclear Science and Engineering, 11: 159-166 (1961).

Godfrey, K. R., Everett, D., and Bryant, P. R., "Input-Transducer
Errors in Binary Crosscorrelation Experiments - 2," Proceedings
of the Tnstitute of Electrical Engineers, 113(1): 185-189
(January 1966).

Godfrey, K. R., "Input-Transducer Errors in Binary Crosscorrelation
Experiments — 3," Proceedings of the Institute of Electrical
Engineers, 113(6): 1095 - 1102 (June 1966).
APPENDIX
TABLE VIIT

PERTINENT INFORMATION RELATED TO EACH TEST PERFORMED FOR THIS STUDY

 

 

Power Number Results
Tape Level Test Test of in “Analysis
Number™ Fuel  (Mw) Method Signal Periods Text Methods
27333 U-235 8 Mw rod-jog 127 x 5 PRBS L Fig. 1k,15 CABS
(a) Regular analysis at har-
monic frequencies
(b) Analysis at harmonic and
mid-harmonic frequencies
FOURCO
27328 U-235 8 Mw flux-demand 242 x 7.25 PRTS 2 Fig. 19,20 CABS
FOURCO
27324 U-235 8 Mw  flux-demand 127 x 5 PRES 3 No CABS
FOURCO
27327b U-235 8 Mw  flux-demand 80 x 10 PRTS No None
27337 U-235 5 Mw  flux-demand 80 x 10 non- L No CABS
sym.2 PRTS
27336° U-235 5 Mw  flux-demand 2L2 x 5 PRTS 3 No CABS

(a) All data

(b) Two periods of data

(c) Two periods after at-
tempting to correct bad
data

FOURCO
(a) All data
(v) Two periods of data

 

TTT
TABIE VIITI (continued)

 

 

 

Power Number Results
Tape Level Test Test of in Analysis
Number ™ Fuel (Mw) Method Signal Periods Text Methods
27338  U-235 5 Mw flux-demand 127 x 5 PRBS 5 Fig. 16,17 CABS
FOURCO
27325b U-235 2 Mw flux-demand 242 x 7.25 PRIS 2 No CABS
FOURCO
07332 U-235 2 Mw flux-demand 242 x T7.25 non- 2 Fig. 22 CABS
sym. PRTS FOURCO
27340 U-235 2 Mw flux-demand 80 x 10 non-sym L Fig. 21,22 CABS
PRTS FOURCO
27343 U-235 2 Mw flux-demand 127 x 5 PRBS 5 Fig. 18 CABS
FOURCO
o732L  U-233 8 Mw flux-demand 127 x 5 PRBS 7 No CABS
+27330 CPSD
FOURCO
(2) Using 5 periods of data
(b) Using 7 periods of data
27325  U-233 5 Mw flux-demand 80 x 3 PRIS 12 Fig. 25(d) CABS

(a) At harmonic and mid--
harmonic frequencies
FOURCO
(a) Regular
(b) Ensemble
CPsD

 

cTT
TABLE VIII (continued)

 

 

 

Power Number Results
Tape Level Test Test of in Analysis
Number Fuel  (Mw) Method Signal Periods Text Methods
27339 U-233 1 Mw flux-demand 127 x 5 PRBS L Fig. 2k(c) CABS
FOURCO
27340  U-233 1 Mw flux-demand 242 x L4 PRTS 3 No CABS
2T3h3f U-233 1 Mw flux-demand 80 x 3 PRTS -—-- No -———
27326  U-233 Zero flux-demand 127 x 5 PRBES L Fig. 2L(a) cABS
(1oow) (a) Regular
(b) Analyzed first two and
last two periods of data .
and averaged results &
FOURCO
(a) Regular
(b) Ensemble
CPSD
27334  U-233 Zero flux-demand 80 x 3 PRTS L Fig. 25(a) CABS
(50w) FOURCO
(a) Ensemble
27334 .U-233 Zero flux-demand 127 x 5 PRES 3 Fig. 24(b) CABS
(50w) FOURCO
(a) Ensemble
273355 U-233 Zero flux-demand 127 x 5 PRES b Fig. 2L(d) CABS
(50w) CPSD
FOURCO

(a) Ensemble

 
TABLE VITI (continued)

 

 

 

Power Number Results
Tape Level Test Test of in Analysis
Number Fuel (Mw) Method Signal Periods Text Methods
o7342% U-233 Zero  flux-demand 80 x 3 PRTS I Fig. 25(e) CABS
(50w) FOURCO
(2) Ensemble
27336  U-233 Zero  flux-demand 242 x 5 PRTS 2 Fig. 25(c) CABS
(50w) FOURCO
(a) Ensemble
27336 U-233 Zero  flux-demand 80 x 3 PRTS 3 Fig. 25(b) CABS
(50w) FOURCO
(a) Regular
(b) Ensemble
27329 U-233 8 Mw  rod-demand 127 x 5 PRBS 5 Fig. 26(d) CABS
FOURCO
CPSD
27330 U-233 8 Mw  rod-demand 242 x 5 PRTS O Fig. 27 CABS
FOURCO
27343 U-233 8 Mw  rod-demand 242 x L PRTS 3 No FOURCO
27337 U-233 8 Mw  rod-demand 127 x 3 PRBS 3 No CABS
o734l U-233 8 Mw  rod-demand 127 x 3 PRBS 8 Fig. 13 CABS
and 26(c) (a) Two periods analyzed

then averaged results

 

HTT
TABLE VIII (continued)

 

 

Power Number Results
Tape g Level Test Test of in Analysis
Number Fuel (Mw) Method Signal Periods Text Methods
27341
(continued) Tables ITI, (b) Four periods analyzed,
v,v,VvI, then averaged results
VIT (c) Regular
CPSD
(a) £ = 0.001
(b) £ =0.05
(c) ¢ =0.5
FOURCO
(a) Regular
(b) Two periods analyzed
then averaged results
(c) Four periods analyzed
then averaged results
(d) Same as a,b,c except
analysis at non-harmonic
frequencies
27327 U-233 5 Mw rod-demand 127 x 5 PRES 11 Fig. 26(b) POURCO
+27331 (a) Using only 5 periods of
data
(b) All data
CABS
(a) Analysis at harmonic
freguencies

(b) At harmonic and mid-
harmonic frequencies

 

qTT
TABLE VIIT (continued)

 

 

 

 

 

 

 

Power Number Results
Tape Level Test Test of in Analysis
Number Fuel (Mw) Method Signal Periods Text Methods
X-8205 U-233 Zero rod-demand 127 x 5 PRBS 3 Fig 26(a) CABS
(10kw) FOURCO
CPSD
a. Recorded here to aid in future reference to the data.
b. Computer malfunctioned during data-recording making results meaningless.
c. The raw data for this test was destroyed and was not available for further analysis.
d. Non-symmetric.
e. The results from this test were very peculiar and did not resemble the expected frequency

response at all, The reason for this bad test has not been explained, but it was noted that there
was excessive drift in the fuel-salt temperature during the test, Attempts to correct for this drift
were unsuccessful.

fo

g.

Amplifiers saturated during test.

Fuel not circulating for this test.

9TT
1. N. J. Ackermann
2. R. G. Affel

3. J. L. Anderson
4L, C. F. Baes

5. S. J. Ball

6. H. F, Bauman
7. 5. E. Beall

8. E. S. Bettis
9. R. Blumberg
10. E. G. Bohlmann
11, C. J. Borkowski
l12. G. E. Boyd

13. R. B, Briggs
14, R. A. Buhl
15. 0. W. Burke
16. F. H. Clark
17. W. B. Cottrell
18, C. W. Craven
19, J. L. Crowvley
20. F. L, Culler
21, S. J. Ditto
22, W. P, Eatherly
23. J. R, Engel
2L, D. E, Ferguson
25. L. M. Ferris
26. A, P. Fraas
27. D. N. Fry
28. W. K. Furlong
29. C. H. Gabbard
30. R. B. Gallaher
31. W. R, Grimes
32. A. G. Grindell
33. R. H. Guymon
3k, P. N. Haubenreich
35. A. Houtzeel
36. T. L. Hudson
37. P. R. Kasten

38-42. T. W, Kerlin

43. R. J. Kedl

Ly, H. T. Kerr
103-10kL,

105-106.

107-109.

110.

111, ORNL Patent

117

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L6,

L7
L8
49
50
51

Office

ORNL-TM-2823

S. S, Kirslis

A, I, Krakoviak

T, S. Kress

Kermit Laughon, AEC-0SR

Ry Qu@mertHtEHY Pt D DO DO =24

g >

-

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G

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.

P EdEaoarraE=EsoHOEHOGZE HE

n

QEIOED QNG m—

D

Tucius
Iundin

. Lyon

MacPherson
MacPherson
Martin
McCoy

. McCurdy

McIntosh, AEC-Washington
McNeese

Miller

Moore

Nicholson

Oakes

Perry

Piper

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Redford

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Roth, AEC-ORO
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piewak

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Sundberg

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Trauger

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Whatley
White
Whitman

Gale Young
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113,

11k,

115.

116,

117,
118.

119.

120,

121-135.

136.

118
ORNIL-TM-2823

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E. Uhrig, University of Florida, Gainesville, Fla., 32601

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