• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Preface
 Table of Contents
 List of Tables
 List of Figures
 List of symbols
 Abstract
 The university of florida spert...
 Introduction
 Design of the facility
 Operational safety
 The data acquisition system
 Nuclear calibration of the UFSA...
 Space-time reactor kinetics studies...
 Introduction
 Theoretical notes
 Description of the measurement...
 Experimental and theoretical results...
 Experimental and theoretical results...
 Spatial dependence of pulsed-neutron...
 Conclusions
 Appendix
 Reference
 Biographical sketch
 Copyright














Title: Space-time reactor kinetics studies with the University of Florida, SPERT Assembly.
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Title: Space-time reactor kinetics studies with the University of Florida, SPERT Assembly.
Series Title: Space-time reactor kinetics studies with the University of Florida, SPERT Assembly.
Physical Description: Book
Creator: Diaz, Nils Juan,
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Bibliographic ID: UF00090226
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Table of Contents
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
        Page iv
    Preface
        Page v
    Table of Contents
        Page vi
        Page vii
        Page viii
        Page ix
        Page x
    List of Tables
        Page xi
        Page xii
    List of Figures
        Page xiii
        Page xiv
        Page xv
        Page xvi
        Page xvii
    List of symbols
        Page xviii
    Abstract
        Page xix
        Page xx
        Page xxi
    The university of florida spert assembly - design and calibration
        Page 1
    Introduction
        Page 2
        Page 3
        Page 4
    Design of the facility
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
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        Page 31
    Operational safety
        Page 32
        Page 33
        Page 34
        Page 35
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        Page 38
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    The data acquisition system
        Page 45
        Page 46
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    Nuclear calibration of the UFSA subcritical
        Page 64
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    Space-time reactor kinetics studies with the University of Florida spert assembly
        Page 79
    Introduction
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
    Theoretical notes
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
    Description of the measurements
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
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    Experimental and theoretical results in the time domain
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
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    Experimental and theoretical results in the frequency domain
        Page 156
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    Spatial dependence of pulsed-neutron reactivity measurements
        Page 174
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    Conclusions
        Page 185
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    Appendix
        Page 187
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        Page 257
    Reference
        Page 258
        Page 259
        Page 260
        Page 261
    Biographical sketch
        Page 262
        Page 263
    Copyright
        Copyright
Full Text











SPACE-TIME REACTOR KINETICS STUDIES WITH THE

UNIVERSITY OF FLORIDA SPERT ASSEMBLY














By

NILS J. DIAZ














A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA
1969







































TO

ZENA















ACKNOWLEDGMENTS


The author wishes to express his sincere appreciation to his

graduate committee for their guidance. Special recognition is due

Dr. M. J. Ohanian, whose encouragement, dedication and detailed

scientific knowledge made this work possible.

The support of the Nuclear Engineering Sciences Department of

the University of Florida throughout the author's graduate work is

greatly appreciated. In particular Dr. R. E. Uhrig's support and

friendship is gratefully recognized.

The author feels fortunate and proud in having studied and worked

with a remarkable scientist and gentleman, Dr. R. B. Perez, now at

Oak Ridge National Laboratory. The author's years of association with

Dr. T. F. Parkinson, now at the University of Missouri, formed the

necessary background for this work.

The continuous assistance of Mr. G. W. Fogle throughout the ex-

perimental program is sincerely appreciated. Mr. L. B. Myers designed

and built the control instrumentation. Mr. R. E. Schoessow was respon-

sible for the design and construction of the assembly. Mr. E. Dugan

and Mr. H. Leydolt aided in the data processing. The cooperation of

the staff of the Nuclear Engineering Sciences Department during the

construction of the facility is acknowledged.

Most of this work was financed under subcontract No. C281 and

C635 with Atomic Energy Division of the Phillips Petroleum Company,








I
under a prime contract with the United States Atomic Energy Commission.

The technical aid of the University of Florida Computing Center in the

development of the computer programs and their financial assistance is

gratefully acknowledged.

Special mention is due Messrs. S. 0. Johnson, R. W. Garner,

G. A. Mortensen and Mrs. M. E. Radd of the Nuclear Safety Research

Branch, Atomic Energy Division, Phillips Petroleum Company for their

continuous assistance and invaluable suggestions throughout the

research program.

To my sister, Miss Lydia Gonzalez, my sincere appreciation for

typing an elegant manuscript from my unintelligible characters.

To the fellow students, who struggled with me to reach the un-

reachable star, my space and time independent friendship.















PREFACE


The text of this dissertation is divided into two related but

essentially independent parts:

Part 1. The University of Florida SPERT Assembly
Design and Calibration -

Part 2. Space-Time Reactor Kinetics Studies with the
University of Florida SPERT Assembly

In Part 1, the design, operational safety and nuclear calibration

of the large-in-one-space dimension, highly multiplicative University

of Florida SPERT Assembly (UFSA) are described. The presentation of

this material is pertinent for a complete understanding of the physical

characteristics of the system to be studied in Part 2 and also because

the system in itself is interesting from the nuclear engineering point

of view. The data acquisition system used for the experimentation is

presented in Chapter IV of this section.

In Part 2, the linear reactor kinetics studies performed with the

UFSA are presented. The space-time dependent distribution of the

neutrons in the assembly, following the introduction of a burst of

neutrons at one end of the core, are studied in the time and in the

frequency domain.

The study of the spatially dependent time profile of the neutron

flux required a large number of figures containing the calculational

and experimental results at different positions in the core. Some

typical figures are included in the main text but most of the recorded

(and calculated) time profiles are included as appendices to the main text.
















TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS ..................... ................ ......... iii

PREFACE ............... ............................... ......... v

LIST OF TABLES ................................................. xi

LIST OF FIGURES ................................................ xiii

LIST OF SYMBOLS ................................................ xviii

ABSTRACT .. ........ ....... ..... ........... ..... ............... xix



PART 1
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
DESIGN AND CALIBRATION ................. 1

CHAPTER I INTRODUCTION ........................................ 2

CHAPTER II DESCRIPTION OF THE FACILITY ........................ 5

General Features ........................................... 5

Fuel Characteristics ...................................... 9

Mechanical Design .......................................... 10

Moderator Flow Control System .............................. 15

Instrumentation and Interlock System ....................... 22

Fuel Storage ............................................... 27

Neutron Sources .......................................... 30

CHAPTER III OPERATIONAL SAFETY ................................ 32

Introduction ............................................... 32

Initial Loading ............................................ 33















TABLE OF CONTENTS (cont'd)


Page

Operating Limits .......................................... 35

Design Basis Accident Analysis ............................. 39

CHAPTER IV THE DATA ACQUISITION SYSTEM ........................ 45

Introduction ................................................ 45

The Neutron Detector ....................................... 47

The Electronic Instrumentation ............................. 50

The Resolution Time Correction ............................. 54

The Normalization Technique ................................ 61

Comments ....................................... ......... ... 62

CHAPTER V NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL ......... 64

Introduction ............ ................................... 64

Theoretical Notes .......................................... 64

Inverse Multiplication Measurements ........................ 68

Absolute Determination of kf ............................. 73
eff
Conclusions ....................................... ...... .. 75.



PART 2
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY ......... 79

CHAPTER I INTRODUCTION ........................................ 80

Statement of the Problem ................................... 80

Description of the Study ................................... 81
















TABLE OF CONTENTS (cont'd)


Page

Nomenclature Used in the Description of
Pulse Propagation Phenomena ............................... 83

CHAPTER II THEORETICAL NOTES .................................. 85

Introduction ................................................ 85

Review of the Literature .................................. 85

The WIGLE Calculational Scheme ............................. 87

Neutron Wave Analysis ................................. .... 89

CHAPTER III DESCRIPTION OF THE MEASUREMENTS ................... 91

Introduction .................................... ........... 91

The Epicadmium Subtraction Method .......................... 92

The Geometrical Arrangement .............................. 94

Synopsis of the Measurements ............................... 97

CHAPTER IV EXPERIMENTAL AND THEORETICAL RESULTS IN THE
TIME DOMAIN ....................................... 100

The Analytical Model ....................................... 100

Flux Traverses ...................................*...... 109

Clean Core Pulse Propagation Measurements ................... 118

Propagation of a Narrow Pulse ............................ 147

Propagation of a Wide Pulse ................................. 148

Pulse Shape vs. Input Pulse Width .......................... 150

Effect of Room Return at Peripheral Detector Positions ..... 152


viii















TABLE OF CONTENTS (cont'd)


Page

CHAPTER V EXPERIMENTAL AND THEORETICAL RESULTS IN
THE FREQUENCY DOMAIN .................................. 156

Introduction ................................................ 156

Method of Analysis ........................................... 157

Comparison of the Theoretical and the Measured
Results of the Neutron Wave Analysis ......................... 159

CHAPTER VI SPATIAL DEPENDENCE OF PULSED-NEUTRON
REACTIVITY MEASUREMENTS .............................. 174

Introduction ................................................. 174

The Decay Constant ........................................... 175

The Ratio ksB/ ................. ........... ........ .. ....... 176

The Measured Reactivity and keff Values ...................... 179

CHAPTER VII CONCLUSIONS ........................................ 185

APPENDICES

A CALCULATIONAL PROCEDURES USED IN THE DETERMINATION
OF THE NUCLEAR PARAMETERS AND THE k VALUES ............. 187
eff

B DESCRIPTION OF THE COMPUTER PROGRAMS ...................... 191

C UFSA Rl CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT NINETEEN CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC ............ 196

D UFSA Rl CLEAN CORE
TIME PROFILES OF FAST NEUTRON FLUX AT SEVERAL CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC ............ 235

E UFSA Rl CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT FOUR POSITIONS
IN THE CORE FOR A 0.1 MSEC INPUT PULSE .................... 248
















TABLE OF CONTENTS (cont'd)


Page

F UFSA Rl CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A WIDE (10 MSEC) INPUT PULSE ... 253

G UFSA Rl CLEAN CORE
SHAPE OF THE PROPAGATING PULSE AS A FUNCTION OF INPUT
PULSE WIDTH .............................................. 255

LIST OF REFERENCES .............................................. 258

BIOGRAPHICAL SKETCH ............................................. 262
















LIST OF TABLES


TABLE Page

I k vs. MODERATOR LEVEL OF UFSA REFLECTED
eff
CORES ....... ............... .... .......... ............. 7

II UFSA INSTRUMENTATION AND CONTROL .......................... 25

III SUMMARY OF 1/M AND PULSED MEASUREMENTS .................... 74

IV INPUT PARAMETERS FOR THE WIGLE CALCULATIONAL
SCHEME ......................................... ............. 104

V TIME STEPS USED FOR THE WIGLE CALCULATIONS ................ 106

VI DELAY TIMES MEASURED ACROSS THE WIDTH OF
THE CORE
0.5 MSEC INPUT PULSE .......................... 119

VII CLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
0.5 MSEC INPUT PULSE WIDTH ................. 127

VIII CLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
1.0 MSEC INPUT PULSE WIDTH ................... 128

IX ASYMPTOTIC PROPAGATION VELOCITY v ........................ 133
p
X DYNAMIC INVERSE RELAXATION LENGTH Kd ...................... 134

XI CHANGES IN THE NUCLEAR PARAMETERS DUE TO
CHANGES IN THE TRANSVERSE BUCKLING ........................ 138

XII THE CALCULATED ASYMPTOTIC VELOCITY OF
PROPAGATION AND DYNAMIC INVERSE RELAXATION
LENGTH vs. CORE HEIGHT
0.5 MSEC INPUT PULSE WIDTH ........................ 146

XIII DELAY TIMES AND FWHM FOR A NARROW INPUT PULSE ............. 148

XIV DELAY TIMES AND FWHM FOR A WIDE INPUT PULSE ............... 149

XV PULSE SHAPES vs. INPUT PULSE WIDTH ........................ 151
















LIST OF TABLES (cont'd)


TABLE Page

XVI THE REAL AND THE IMAGINARY COMPONENTS
OF THE COMPLEX INVERSE RELAXATION LENGTH
0.5 MSEC INPUT PULSE ........................ 164

XVII THE REAL AND THE IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION LENGTH
1.0 MSEC INPUT PULSE ........................ 165

XVIII THE DECAY CONSTANT AND kB/ VALUES MEASURED
AS A FUNCTION OF INPUT PULSE WIDTH ........................ 180

XIX REGION-WISE DEPENDENCE OF THE REACTIVITY
MEASUREMENTS ............................................. 183














LIST OF FIGURES


FIGURE Page

1 OVERALL VIEW OF THE FACILITY ............................... 6

2A BOTTOM FUEL ROD SPACING SYSTEM ............................. 12

2B BOTTOM FUEL ROD SPACING SYSTEM ............................. 13

3 TOP FUEL ROD SPACING SYSTEM ............................... 14

4 REACTIVITY-CONTROL FLOW SYSTEM ............................ 16

5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE
WEIR APEX ............................................ 18

6 WEIR "BOX" ................................................ 19

7 AIR SYSTEM SCHEMATIC ....................................... 21

8 UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM ...................... 23

9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT ............... 44

10 PHYSICAL CHARACTERISTICS OF THE He3 NEUTRON COUNTERS ....... 49

11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM .................. 51

12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM ............. 52

13 TIME PROFILES OF NEUTRON BURST RECORDED BY
CONVENTIONAL ELECTRONIC INSTRUMENTATION AND BY THE
TIME-PICKOFF SYSTEM ....................................... 58

14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME
CORRECTION AS A FUNCTION OF COUNT RATE ..................... 60

15 DETECTOR POSITIONING SCHEME ................... ......... 69

16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL ................. 71

16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT .......... 72


xiii
















LIST OF FIGURES (cont'd)


FIGURE Page

17A DECAY CONSTANT vs. MODERATOR LEVEL ........................ 76

17B kB/k AND k vs. MODERATOR LEVEL ............................ 77

18 THE TOTAL, EPICADMIUM AND THERMAL FLUX 117.44 CM
FROM THE SOURCE ........................................... 95

19 UFSA SOURCE-SUBCRITICAL ASSEMBLY GEOMETRICAL
ARRANGEMENT PLAN VIEW ................................ 96

20 PLAN AND FRONT VIEW OF THE CORE REGION ENCLOSING THE
NEUTRON SOURCE ............................................ 102

21 ONE-DIMENSIONAL ARRANGEMENT OF THE UFSA CORE USED IN THE
WIGLE CALCULATIONAL SCHEME ............................... 103

22 SPATIAL DISTRIBUTION OF SOURCE NEUTRONS INCORPORATED
INTO THE WIGLE SCHEME ..................................... 107

23A PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE ............................. 110

23B PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE ............................. 111

23C PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA Rl CORE ............................. 112

24A THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE .................. 113

24B THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE .................. 114

25 THE ASYMPTOTIC STEADY-STATE VERTICAL FLUX ................. 116

26 THE ASYMPTOTIC STEADY-STATE HORIZONTAL FLUX ............... 117

27A EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE ....................................... 122


xiv















LIST OF FIGURES (cont'd)


FIGURE Page

27B EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA Rl CORE ......................................... 123

27C EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA Rl CORE ...................................... 124

28A EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PUSLE ........... 125

28B EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE ........... 126

29 CALCULATED AND EXPERIMENTAL DELAY TIMES
1.5 MSEC INPUT PULSE .......................... 129

30 CALCULATED AND EXPERIMENTAL DELAY TIMES
1.0 MSEC INPUT PULSE ......................... 130

31 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
0.5 MSEC INPUT PULSE .......................... 131

32 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
1.0 MSEC INPUT PULSE .......................... 132

33 DELAY TIMES OF THE THERMAL FLUX CALCULATED BY THE
WIGLE CALCULATIONAL SCHEME FOR DIFFERENT CORE HEIGHTS ..... 139

34 AMPLITUDE ATTENUATION OF THE THERMAL FLUX CALCULATED
BY THE WIGLE CALCULATIONAL SCHEME FOR DIFFERENT
CORE HEIGHTS .............................................. 140

35A THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING ....................................... 141

35B THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING ....................................... 142















LIST OF FIGURES (cont'd)


FIGURE Page

35C THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING ........................................ 143

36 EXPERIMENTAL PULSE SHAPES AS A FUNCTION OF CORE
HEIGHT .................... ........... ......................... 144

37A EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS .................................................. 153

37B EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS ............................ ...................... 154

38 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
0.5 MSEC INPUT PULSE .................... 160

39 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
1.0 MSEC INPUT PULSE .................... 161

40 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
0.5 MSEC INPUT PULSE ......................... 162

41 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
1.0 MSEC INPUT PULSE ....................... 163

42 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED DAMPING COEFFICIENT a ............................. 166

43 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED PHASE SHIFT PER UNIT LENGTH ..................... 167

44 THE UFSA Rl CORE p DISPERSION LAW .......................... 169

45 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED (a2 2) ................................... .... 171


xvi
















LIST OF FIGURES (cont'd)


FIGURE Page

46 COMPARISON OF THE THEORETICALLY PREDICTED
AND THE MEASURED 2 a .................................... 172

47 THE UFSA Rl CORE p DISPERSION LAW ..................... 173

48 DECAY CONSTANT vs. AXIAL POSITION ...................... 177

49 kB/2 vs. AXIAL POSITION ................................ 178

50 REACTIVITY (-$) keff vs. AXIAL POSITION ................ 182
eff
Cl Through C19 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE
CORE FOR A 0.5 MSEC INPUT PULSE ....................... 195-213

C20 Through C38 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE CORE
FOR A 1.0 MSEC INPUT PULSE ............................ 214-232

Dl Through D6 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 0.5
MSEC INPUT PULSE ...................................... .. 234-239

D7 Through D12 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 1.0
MSEC INPUT PULSE ........................................ 240-245

El Through E4 TIME PROFILES OF THERMAL NEUTRON
FLUX AT FOUR POSITIONS IN THE CORE FOR A 0.1
MSEC INPUT PULSE ...................................... 247-250

Fl TIME PROFILES OF THERMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A 10.0 MSEC INPUT PULSE ...... 252

G1 Through G2 SHAPE OF THE PROPAGATING PULSE AS A
FUNCTION OF PULSE WIDTH ............................... 254-255


xvii



























Di .........


eff
.........


z .........

a .........
a


p .........

z .........


.........
P





4,


LIST OF SYMBOLS



TRANSVERSE BUCKLING

DELAYED NEUTRON PRECURSOR CONCENTRATION OF THE
ith GROUP

DIFFUSION COEFFICIENT OF THE ith GROUP

FREQUENCY (cps)

EFFECTIVE MULTIPLICATION CONSTANT

NEUTRON LIFETIME

NEUTRON MULTIPLICATION

VELOCITY OF THE ith GROUP

AXIAL COORDINATE

DECAY CONSTANT (IN THE TIME DOMAIN)

DAMPING COEFFICIENT (IN THE FREQUENCY DOMAIN)

EFFECTIVE DELAYED NEUTRON FRACTION

PHASE SHIFT PER UNIT LENGTH

REACTIVITY

COMPLEX INVERSE RELAXATION LENGTH

MACROSCOPIC CROSS SECTION

NEUTRON FLUX


xviii













Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy



SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY


By


Nils J. Diaz


March 1969


Chairman: Dr. M. J. Ohanian
Major Department: Nuclear Engineering Sciences

A large-in-one-space dimension, side reflected, highly multiplica-

tive (keff ~ 0.99) subcritical assembly was designed and calibrated.

The sole purpose of the facility is the experimental investigation of

the dynamic behavior of large reactor cores and to provide a test for

space-time kinetics models presently in use. With this facility the

linear aspects of neutron physics phenomena can be investigated in the

absence of inherent feedback effects. This work was conducted under a

subcontract with the Nuclear Safety Research Branch, Atomic Energy

Division, Phillips Petroleum Company, under a prime contract with the

United States Atomic Energy Commission.

The University of Florida SPERT Assembly (UFSA) is a light-water

moderated subcritical facility fueled by 4.81% enriched U02 pellets

encased in stainless steel tubes of 0.465 inch outside diameter (SPERT

F-l Fuel). The fuel arrays are contained in a rectangular tank, 8 feet


xix










long, 39 inches high, and of variable width. In this study, the core

was 6.5 inches wide and 30 inches high. The effective multiplication

constant of the assembly was determined to be 0.990+.003. The assembly

is equipped with nuclear instrumentation capable of automatic scram

action.

For the kinetics studies, a fast data acquisition system was

developed to handle accurately the very high, time-changing count rate

encountered in the measurements. It essentially consists of a trans-

former-coupled pulse amplifier to produce a fast logic signal at the

input of a multichannel analyzer from the input signal originating in

a long, thin He3 counter. The instrumentation adequately handled count

rates up to 3 x 10 counts/sec at the peak of the pulses. A high degree

of reproducibility and fidelity in following the pulse profiles was

obtained with this instrumentation.

The space-time kinetics studies were performed by analyzing the

propagation of a fast neutron burst introduced at one end of the assem-

bly, in the absence of inherent feedback effects. The experimental

results are compared with the results obtained from the two-group,

space-time dependent, one-dimensional diffusion theory scheme known as

the WIGLE program. A stringent test of the model is provided by a

combined analysis in the time and the frequency domain.

The WIGLE calculational scheme accurately predicts the delay times

and the attenuation of the pulses when a first-flight spatial distribu-

tion is assumed for the fast source. At large distances from the source

WIGLE underpredicts (- 8% in the FWHW) the spreading of the pulse. A

marked sensitivity to small changes in the transverse buckling was

-found for the model, as well as the experiment.

xx










A one-to-one comparison of the predicted and measured values in

the frequency domain was provided by performing identical numerical

Fourier transformations of the WIGLE time profiles and the measured

pulse shapes. The analysis in the frequency domain confirmed the

results obtained in the time domain, although discrepancies past 100
2
cps are found in the ultrasensitive p plane. The agreement in the p

plane, the system's dispersion law, is good up to 200 cps and reasonable

up to 800 cps. Both theory and experiment showed a smooth behavior
2
throughout the frequency range investigated, in both the p and the p

plane.

Spatial effects in large cores are clearly demonstrated in this

work. The determination of the range of applicability of the one-

dimensional scheme requires extending the study to cases in which two-

dimensional effects will be noticeable and the important feedback

effects can be considered.


xxi




































PART 1

THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
DESIGN AND CALIBRATION -















CHAPTER I


INTRODUCTION


The development and construction of large power reactors focused

the attention of industry and of the United States Atomic Energy Com-

mission on the necessity of having reliable reactor dynamics analysis

methods to accurately describe the spatial and temporal behavior of the

neutron flux in these systems. The point-model reactor kinetics calcu-

lations seem to have been adequate for the gross evaluation of the time-

dependent neutron flux during the occurrence of a transient but the

model can be in large error when the physical size of the system and the

magnitude of the perturbation necessitates that spatial effects in the

redistribution of the neutron flux be considered. Preliminary calcula-

tions done by Johnson and Garner using a one-dimensional space-time

kinetics model [1] showed that the space-time dependent scheme predicts

a "destructive zone" much larger than that predicted by point-model

kinetics.

The necessity of experimentally determining the validity of the

various space-time kinetic analysis methods was brought out by Johnson

and Garner [1], and recognized by the USAEC in establishing the Large

Core Dynamics Experimental Program. The primary responsibility for this

program has been vested in the Nuclear Safety Research Branch, Atomic

Energy Division, Phillips Petroleum Company as major contractor for

USAEC.









The Large Core Dynamics Experimental Program is to be performed

in three phases:

Phase I. Pulsed Source Experiments in Subcritical, Multiplying Media,
Large in One-Dimension

The first phase of the experimental program is to be conducted in

a close-to-critical subcritical assembly, 8 feet long, 3 feet deep and

with widths changing from 6.5 inches to 16 inches according to the core

configuration and whether bare or side reflected cores are studied.

The experimental information obtained from studying the pulse

propagation phenomena in this assembly is to be used to test the valid-

ity of current space-time kinetic models in the absence of inherent

feedback effects.

Phase II. Kinetic Behavior for Control-Rod-Induced Power Excursions in
Large, One-Dimensional Cores

A reactor large in one-dimension, 16 feet long, three feet deep

and with varying widths to accommodate different metal/water ratios will

be used to investigate the one-dimensional kinetic behavior of large cores

subjected to a large perturbation. Both non-feedback (low power exper-

iments) and self-shutdown measurements will be conducted.

Phase III. Kinetic Behavior for Control-Rod-Induced Power Excursions
in Large, Two-Dimensional Cores

The same type of measurements performed for the one-dimensional

core will be conducted in a two-dimensional core.

The measurements should provide the necessary information to

establish the validity ranges for one-dimensional models, the basis for

the development of a two-dimensional scheme and as a bridge to the

complex, three-dimensional problem.

Phase II and Phase III of the research program will be performed









at the SPERT IV facility at the National Reactor Testing Site, Idaho.

The appropriate existing experimental equipment, as well as the

extensive kinetics studies conducted by the Nuclear Engineering Sciences

Department at the University of Florida, was conducive to the granting

of a subcontract by the Phillips Petroleum Company so that the basic,

linear kinetics studies of Phase I could be performed at the University

of Florida.

The research to be performed as Phase I of the Large Core Dynamics

Experimental Program can be succinctly defined as the experimental and

analytical determination of the dynamic behavior of the neutron flux in

slightly subcritical water moderated assemblies of SPERT F-l fuel rods.

The facility in which the required measurements for Phase I, Large

Core Dynamics Experimental Program, are to be conducted necessitated a

thorough design and safety analysis. The assemblies are to be close to

critical and the core has a large U235 inventory. The nuclear capabil-

ities of such systems were the object of a detailed study to determine

their operational characteristics under normal and accident conditions.

The flexible mechanical design, the safety instrumentation, the

nuclear evaluation, as well as the experimental calibration of the

first configuration under study constitutes Part 1 of this dissertation.

The reactor kinetics studies performed in the first of the con-

figurations to be studied are dealt with in Part 2 of this manuscript.















CHAPTER II


DESCRIPTION OF THE FACILITY


General Features


The University of Florida Spert Assembly is a light water-

moderated subcritical facility fueled by 4.81% enriched U02 pellets

encased in stainless steel tubes of 0.4655" outside diameter. The fuel

arrays are contained in a rectangular tank, 8 feet long, 39 inches high,

and of variable widths. The system is designed so that both bare and

reflected cores can be studied. Only one reflected core will be dealt

with in Part 2 of this manuscript; information on three reflected cores

is included in this chapter. The .assembly width and fuel spacing may be

varied in order to:

a) have a keff not to exceed 0.99 in all cases to be

considered.

b) accommodate non-moderator/moderator ratios of

0.5, 1.0, and 1.5, respectively.

Shown in Table I are the k eff's as a function of the moderator
eff
height, the fuel spacings, core widths, and total number of fuel ele-

ments for the different reflected cases to be considered. The calcu-

lational procedures used in the determination of the nuclear parameters

and the keff values for the three reflected configurations of the

assembly are described in Appendix A. Only the sides of the assembly

will be reflected. Fig. 1 shows an overall view of the facility.

5




















































DUMP
VALVES


FIG. 1 OVERALL VIEW OF THE FACILITY











TABLE I


keff vs. MODERATOR LEVEL OF UFSA REFLECTED CORES


Calculated Using the AIM6 Code
Core Length = 243.8 cm (96")
Reflector Width = 30.48 cm (12")
Active Fuel Height = 91.4 cm (36")

Metal to Water Ratio = 0.5
Lattice Pitch (in) = 0.7152
Core Width (cm) = 16.35
No. of Fuel Rods = 1206


1.0
0.584
19.28
2132


Moderator Level


Moderator Level
(cm)

20

25

30

35

40

45

50

55

60

65

70

75

80

85

91.4


Effective Multiplication Constant


.7695

.8288

.8715

.9022

.9249

.9420

.9551

.9655

.9738

.9805

.9870

.9906

.9944

.9977

1.0012


.7397

.8028

.8471

.8793

.9032

.9213

.9353

.9465

.9554

.9626

.9686

.9736

.9777

.9813

.9851


.7276

.7941

.8416

.8761

.9020

.9218

.9372

.9494

.9592

.9672

.9738

.9793

.9840

.9880

.9922


1.5
0.5332
25.73
3420









The assemblies are highly multiplicative; this is important for

the extrapolation of the results of the study to critical systems. The

system's subcriticality is attractive because of the inherent safety

of such systems and of the absence of inherent feedback effects.

In order to provide as "clean" a core as possible, a unique control

system which has been successfully used on the UFAPA [2] will be em-

ployed. In this system the reactivity is controlled by adjustment of

the water height in the assembly. The water height is controlled by

the position of two "V"-notched weirs located in a water "box" hydrau-

lically coupled with the assembly through flexible lines. The quantity
5/2
of water discharging through a "V"-notched weir varies as H5/2 (H is the

distance between the apex of the weir and the water level) thus pro-

viding precise control of the moderator height. The hydraulic coupling

assures that under normal operating conditions (with continuous flow)

there will be the same water level in the core and the reflector tanks.

The UFSA subcritical assembly is located in an isolated and

shielded room in the Nuclear Research Field Building, approximately

three miles from the University campus.

The Nuclear Research Field Building consists of four bays, two of

them having shielded rooms for experiments with subcritical and moder-

ating assemblies. The shielded walls consist of stacked concrete block

eight feet high and thirty-eight inches wide covered with plywood to

assure that the blocks remain in place. The ceiling of this single-floor

building is approximately 15 feet above the floor and consists of excel-

sior-filled cement bonded board. Neutron reflection from this ceiling.

over the walls does not constitute a hazard to personnel operating the

accelerator-type neutron source. The access door from the control room









is interlocked with the neutron generator and the subcritical assembly

scram system, as is the door on the only other entrance to the shielded

room from the fuel storage area. Across the front face of the assembly,

a screened wire cage with a lockable door controls access to the core.

While not in use in the assembly the fuel is stored in a room

adjacent to the facility, built entirely for this purpose.

A more complete description of the facility and its characteristics

can be found in the Design and Hazards of the UFSA and its addenda

[3, 4, 5].

The system has been licensed under Atomic Energy Commission SPECIAL

NUCLEAR MATERIAL LICENSE SNM 1050, March 1968. The license allows for

the possession of 5400 fuel rods with a total U235 inventory of 190 kgs.


Fuel Characteristics

The UFSA is fueled with Spert F-l type fuel elements provided by

the Phillips Petroleum Company.

The fuel characteristics are:

Fuel Composition: UO2 in pellet form

U enrichment: 4.81 + .15%
235
Active Fuel Length: 36" + .062"

Active Fuel Diameter: .42" + .0005"

Fuel Tube Material: stainless steel

Fuel Tube Length: 41.625"

Fuel Tube o. d.: .4655" + .0025"









Mechanical Design

The entire assembly can be divided into three components: the

supporting platform and dump tank; the basic core tank and fuel rod

support structure; and the combination core side walls and side

reflector tanks.

The supporting platform is composed of 5 inch steel I-beams, raised

5 feet from the floor level by six steel columns 3 1/2 inches in diam-

eter. The column footings rest within a 6x8x2 foot steel rank which

serves as a reservoir for the continuous water flow system and as a dump

tank. Under normal operating conditions, this represents a minimum

distance of about 4 feet between the bottom of the assembly and the

water surface in the reservoir. This distance is sufficiently large so

that the bottom of the assembly is considered to be unreflected under

all conditions.

All the core and reflector hardware is made of type 5456-H321

aluminum. The bottom of the basic tank is made of a 24x96x3/4 inch plate

bolted to the steel I-bean platform. The underside of the plate is

covered with a .030 inch thick Cadmium sheet. The lower fuel rod sup-

port assembly rests on the plate. The end walls of the basic tank are

made of a 24 x 39 3/4 inch plate and are supported by two 2 1/2 x 2 1/2

x 1/4 inch steel angle braces welded to the I-beam platform. Two four-

inch aluminum channels span the eight foot dimension of the tank, con-

fining the upper fuel rod support system and detector mounts.

The side walls of the basic tank serve also as reflector tanks when

the reflected cores are under study. These tanks have dimensions of

12 x 96 x 37 inches. The arrangement allows one to vary the width of the

core with a sole structural support.









The end walls are permanently covered with Cadmium on the outside

surface while the side walls have movable Cadmium covers to define the

boundaries for the bare and reflected cases. To optimize the number of

neutrons inserted into the assembly by the neutron generator, the accel-

erator target penetrates about 4 inches into the core. A water-tight

port is provided for this purpose. The port can be removed and a blind

flange inserted in its place. Several fuel rods must be taken out, the

number depending on how deep the target goes into the assembly and on the

lattice pitch.

The core section of the assembly consists of an interchangeable

fuel rod spacing system made of 3/4 x 1/2 x 1/8 inch channels, 5/8 x 1/4

inch bars and aluminum shims mounted on the base plate of the tank. The

bars have milled slots to accommodate the .25 inch end tip of the fuel

rod and to set the pitch along the core width. The shims are placed

between the channel bar units to set the pitch along the core length

(96 inches) (see Fig. 2). The top fuel rod spacing system consists of

an aluminum grating. The mesh is determined by the lattice pitch under

study. The grating is made of aluminum bars and spacers, as shown in

Fig. 3. Thus, fuel rod removal along the length of the core is pos-

sible to locate the detector for the experimental measurements.

The one-half inch long rod tip is fully surrounded by aluminum,

with practically no reflecting characteristic, but there is a 7/8 inch

length of rod between the end of the active fuel and the tip which is

surrounded by water. This bottom reflector is unavoidable and will be

considered in the calculations.
























FUEL ROD





c WIDTH
SPACE




WIDTH SPACE
CHANNEL


LENGTH
SPACER
SHIM


FIG. 2A BOTTOM FUEL ROD SPACING SYSTEM





































7~- J


WIDTH SPACER




-WIDTH
CHANNEL
I__ SPACERS


BASE PLATE



CADMIUM


FIG. 2B BOTTOM FUEL ROD SPACING SYSTEM


_ L ___ _~ __


w






S14


ALUMINUM SUPPORT
FRAME


FUEL ROD


CORE WIDTH
FUEL ROD
SPACING
GRATE


CORE LENGTH
/ FUEL ROD
/ SPACING
GRATE


FIG. 3 TOP FUEL ROD SPACING SYSTEM


SPACER







TIE ROD









Moderator Flow Control System

The moderator flow control system of the UFSA can be better des-

cribed by'the water flow schematic shown in Fig. 4. Besides the normal

fill and drain functions for the moderator, it serves as an accurate

reactivity control using adjustable moderator height by continuous flow.

The characteristic components of this system are described below.

A. Storage Tank: A 6 x 8 x 2 foot steel tank located directly

below the assembly will serve as the reservoir for the circulating

light-water moderator and as a dump tank. Normal water heights while

operating will be between 6 and 12 inches. The tank also serves as a

footing for the assembly supports. This arrangement makes a very con-

venient and compact facility.

B. Core and Reflector Tanks: As seen from the flow diagram, water

is pumped from the reservoir to the core and reflector tanks through a

manifold at one end of the assembly and flows from the other end of the

core and reflectors tanks to the weir "box". From the weir "box", water

flows over the weirs back to the storage tank through a flexible line.

The core section is equipped with two normally open solenoid

activated dump valves, 3 inches in diameter, located at each end of the

core. These valves provide the reactor with a fast shutdown safety

system. The reflector tanks have their own 1 1/2 inch normally open

solenoid valves actuated by the same safety system.

Since the quantity of water discharging through a V-notched weir

varies as H5/2 where H is the height of the water level above the apex

of the V-notch, the water level and hence, the reactivity, can be con-

trolled in a precise manner simply by varying the height of the weirs

and the rate of flow of water into the tank. This is accomplished by







WEIRR DRAIN
--- DISTRIBUTION MANIFOLD


ION EXCHANGE BED


m\









PU MPt
CONTROL ORIFICE
VALVE


FIG. 4 REACTIVITY-CONTROL FLOW SYSTEM









an automatically operated pneumatic control valve. A plot of the flow

rate versus the height of the water level above the apex of the weirs

is shown in Fig. 5.

The weir plate is rigidly mounted on a "box" or small tank (see

Fig. 6). The weir "box" is connected to a drive mechanism composed

of the following: guide post, slide block, and drive screw. The guide

post is a 2 inch diameter pipe attached to the support column of the

crane which is used for removal of the reflector tanks. The "box" is

mounted on the guide block which slides along the vertical post and

provides a rigid support for the system and is driven up and down by

means of the drive screw which is fixed at the top of the guide post

support and passes through the guide block. The upper limit of the

position of the weir"box"is controlled by mechanical stops whose posi-

tion is determined as part of the initial start-up procedure for each

configuration to be considered.

The final adjustment of the position of the weir"box"is such that

when the water reaches the moderator level in the assembly corresponding

to k < .99 for a given configuration it will be flowing about 2.0
eff -
inches above the apex of the V-notch weirs. At this design level the

flow rate is 7 gallons per minute with the keff values as given in

Table I for the full fuel loading. After the operating height of the

weir box has been determined for k ff 0.99 in the initial start-up,

stops are inserted to prevent raising the weirs above this height (if

the height is less than the active fuel height). It should also be

pointed out that the orifice in the line limits the pump capacity to a

flow rate which is just sufficient to bring the weirs to full flow. A

further increase in flow rate would cause discharge over the entire

















S 2.8-


j 2.4
1,4

> 2.0

0
< 1.6
r-i

4 1.2 o0
4

S 0.8


0.4


0 I I -_1 1 _I
0 2 4 6 8 10 12

Flow Rate (gpm)


FIG. 5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE WEIR APEX












4



3.5"

._


i.5" O.D. x 1/8 WALL (3)


2" O.D. x 1/8 WALL


FIG. 6 WEIR "BOX"









perimeter of the weir "box" into the drain line effectively preventing

any further increase of the moderator level in the assembly.

The measurement of the water height in the core is accomplished by

fixing a reference mark on the slide block at the same level as the

bottom of the weir within the "box". An accurate scale is provided to

read off the distance between the bottom of the core and the apex of the

weirs. Continuous indication of the moderator level in the core is

provided on the console by means of a recorder calibrated between the

bottom of the active fuel and the maximum moderator height and by a

manometer, connected directly to the core, for precise measurement of

the water level. These two measuring systems insure reproducibility of

the moderator height for the experiments.

The water is pumped out of the storage tank by a constant speed

centrifugal pump which has a "no load" capacity of 20 gal/min. The

control valve is designed to restrict the flow to the maximum design

value of 12 gal/min. A deionization system is provided to keep the

water as pure as possible at all times. The pneumatic flow control

system consists of two differential pressure cells, transmitters, control

valve, and recorder-controller. The strip type chart recorder-con-

troller records both flow rate and moderator level in the core. The

control valve is of the air-to-open type which will close in the case of

air supply loss, stopping the flow into the assembly. The flow diagram

for the air system is shown in Fig. 7. A pressure differential from the

pressure transmitters applied to the recorder-controller allows both

manual and automatic control of the flow rate through the valve operated

by the controller.








SOLENOID
TO INTERLOCK


L WEIR


I I
I I


DIFFERENTIAL
PRESSURE
TRANSMITTER


FROM PUMP


I I


-----. ORIFICE ----. TO CORE


-- WATER

AIR


FLOW
VALVE


FIG. 7 AIR SYSTEM SCHEMATIC


CORE


DUMP
VALVE









Instrumentation and Interlock System

The instrumentation and interlock system of the UFSA has been

discussed extensively in the reports submitted to the Atomic Energy

Commission [3, 4, 5] in conjunction with the license application. More

recently, Mr. L. B. Myers submitted a detail technical report on the

subject [6]. A brief descriptive explanation is given below.

A block diagram of the safety system logic flow in use at the UFSA

subcritical assembly for routine monitoring is shown in Fig. 8. There

are five principal channels of instrumentation:

a. Start-up channel using a He proportional counter, scaler, and

rate meter. The counter is located at the bottom of the core, close to

the geometrical center of the assembly.

b. Log power and period instrument No. 1 channel using a compen-

sated ion chamber (operated uncompensated) as a signal to a Log N

amplifier. The chamber is located along the longitudinal axis of the

assembly, on the bottom of the core some two feet from the neutron

generator end.

c. Period instrument No. 2 channel using a compensated ion chamber

(operated uncompensated) as a signal to a log N amplifier. The chamber

is located along the longitudinal axis of the assembly, on the bottom

of the core, some six feet from the neutron generator end.

d. Linear neutron flux No. 1 channel using an uncompensated ion

chamber as a signal to a micromicroammeter. The chamber is mounted on

the top core support frame, close to the geometrical center of the core.

e. Linear neutron flux No. 2 channel using a compensated ion

chamber (operated uncompensated) to feed a signal to a micromicroammeter.

The chamber is mounted on the top core support frame on the opposite































And Manual 1 And
CKT. SCRAM CKT.

And1 And
CKT. C Y, CKT.

And And
CKT. CKT.


mp CAnd Core Dump And
WidthT. Valve # 2 CKT

Refl. Dump v Pump
Valves


FIG. 8 UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM









side from the linear channel No. 1.

Items a. through d. are part of the safety amplifier while item f.

is used to display the neutron flux on a console front panel meter.

The safety amplifier monitors the seven continuously varying input

signals and provides a trip signal if any of the input signals fall

outside of acceptable limits. The safety amplifier provides means of

adjusting these limits over a wide range.

The duality of the scram action (see Fig. 8) is a prominent feature

of the safety system. It can be said that no single failure will

invalidate both automatic scram channels. Furthermore, it.has been

determined that no single failure can invalidate both the manual and

automatic scrams. The method of measurement and the function of each

instrumentation and safety channelare shown in Table II (parts A and B).

A series of safety interlocks prevent water from flowing into or

remaining in the assembly unless a proper sequence of events are fol-

lowed and certain conditions are satisfied. The conditions are:

a. The moderator temperature must be > 60F. This is established

by the desire to obtain the experimental data near room temperature con-

ditions. The insertion of water at 32*F will introduce a maximum k of

.00342 (based on the calculated negative temperature coefficient of

reactivity) above the design keff value with no hazards created.

b. The four instrumentation channels must have their high voltage

on.

c. The core width must be smaller than 26 cm.

d. The door to the assembly room must be locked.

e. The start-up channel must count more than 2 counts/sec.

f. The neutron flux, subcritical assembly power level and period










TABLE II


Measured Parameter

a. Low level neutron flux



b. Linear neutron flux


c. Log neutron fluxb


d. Linear neutron flux


e. Reactor period 1


f. Gamma flux



g. Detector power supply
voltage


h. Reactor period 2


UFSA INSTRUMENTATION AND CONTROL
A. NUCLEAR


Method of Measurement

He3 detector pulse discriminatory;
at neutron generator end of core


CICa ammeter; on side of core


CICa log N and period amp; under
core near center line

UIC ammeter; on side of core


CICa log N and period amp


Ion chamber area monitor; on front
of reactor cage


Unijunction transistor oscillator
and relay. Monitor detector
voltage for b, c, d and e

CICa log N and period amp; under
core near center line


Application

Insure source is present before
adding reactivity. Scram on low
count rate

Indicate power level scram on
power

Indicate power level scram on
high power; log N recorder

Indicate reactor power; linear N
recorder

Indicate reactor period; scram on
short period

Criticality monitor for storage
room. Area monitor for reactor
room. Activate evacuation alarm

Scram reactor on low detector
voltage


Indicate reactor period; scram on
short period


To be operated in the uncompensated mode
Common detector and instrument










TABLE II (Continued)


B. NON-NUCLEAR


Measured Parameter

a. Reactor water temper-
ature

b. Reactor water level



c. Reactor door and per-
sonnel



d. Reactor core width




e. Reactor water level


f. Reflector tank water
level (low)

g. Flow control valve
shut


h. Reactor flow


Method of Measurement

Fenwall temperature switch in
inlet line

Barksdale pressure switch mounted
on weir"box"with sensing line
connected to core

Limit switches on doors and push
buttons inside reactor room



Limit switches on reflector tanks




Barnstead pressure switch senses
level in weir box

Float switches in reflector tanks


Limit switch on valve


Differential pressure cell and
pneumatic control

D/P cell and pneumatic system


Application

Scram reactor on low reactor
inlet water temp. (600F)

Scram reactor if water level in
core exceeds top of weir height


Scram system and shut down neutron
gun if reactor doors are opened
or interior switches are acti-
vated

Prohibit filling reflector tanks
when distance between tanks
exceeds widest reflected core
width

Stops pump when water reaches llcm
below weir apex

Indicates water is filling reflec-
tor tanks

Requires closing valve before
starting pump


Control flow rate.
record flow rate


Indicate and


Indicate and record water level


i. Reactor water level









must be as specified under Operating Limits in this report.

g. After a normal start-up, the water height in the core must be

within 0.5" of the level set by the position of the weirs.


Fuel Storage

The large amount of fuel needed for the experimental program

required a detailed criticality analysis of the fuel storage area.

Criticality considerations of the fuel storage arrangements follow the

Atomic Energy Commission regulations regarding the subject. Three dif-

ferent criteria were used to calculate the effective multiplication of

the fuel storage area to assure that the array will remain subcritical

under the worst circumstances. The methods and the corresponding con-

ditions are outlined below.

The fuel storage array consists of three slabs of air-spaced fuel

pins, separated by a minimum distance of 54 inch face to center. The

fuel is stored in steel baskets containing 308 pins per basket. Two

sets of 1/4 inch thick plastic plates, located at the bottom and top of

each basket, drilled to properly position the fuel rods. The charac-

teristics of the fuel slab are:

Slab Width = 3.73 in = 9.46 cm (corresponds to 7 fuel pins in

transverse direction)

Slab length = 14 ft

Height = 3 ft (active fuel height)

a. Multiregion-multigroup calculation

The effective multiplication factor of the fuel storage array con-

sisting of three slabs (3.73 inch wide, 14 ft long and 3 ft wide) which

are 54 inch apart (face to face) was computed for the case of flooding









the storage area to the level of the active fuel height. A 2-foot

reflector on both sides was used to represent an infinite reflector.

No reflector was considered on the ends, but the contribution of this

to the system would be small. The calculation was done using four

groups and seven regions and followed the method outlined in Appendix

A of this thesis. The following configuration, which is symmetric about

the indicated center line, was assumed:


3.73"


Water


24"


Fuel Water


Under these water-moderated and reflected conditions, a keff =

0.79 was obtained

b. Solid angle criterion for slabs

To determine the interaction between the fuel storage slabs in the

proposed 3-slab array, the solid angle criterion established in 10 CFR,

Part 70, 70.52, paragraph (b) was used. This establishes the maximum









total solid angle subtended by any unit in the array to be 6 steradians

if the effective multiplication factor for the individual slabs is less

than 0.3, as is the cese here.

From 10 CFR 70.52 (d) (2) (i) the minimum required separation dis-

tance, i.e., center of one slab to face of adjacent slab, is obtained

from:
S cross sectional area
3 steradians =
(separation distance)2

1/2
This gives, separation distance = ( x 3 ) = 3.74 ft.

We propose to establish a minimum distance between faces of adja-

cent slabs of 4.5 ft. This gives a total solid angle for the center

slab of 3.88 steradian, which is well below the established criteria.

c. Comparison with Clark's criteria

For 5% enriched, 0.4 inch diameter uranium oxide rods with a 190.13

gm/liter U-235 concentration (compared to 4.81% enriched, 0.42 inch

diameter uranium oxide rods with a 200 gm/liter U-235 concentration in

our case) the following data is obtained from pp. 39 and 59, respectively,

of DP-1014:
-2
Width of Slab (cm) Buckling (cm2)
Critical Safe Critical Safe
11.2 10.4 0.014945 0.015912

It should be noted that the slab widths quoted on page 39 of DP-1014

are for an infinite water-moderated and reflected slab. From the buck-

ling values given, the critical width of the infinite water-moderated

unreflected slab is 25.7 cm; the corresponding safe width is 24.9 cm.

When twice the reflector savings for the latter case as given on page

59 of DP-1014 is subtracted, a safe width for the infinite, water-










moderated reflected slab of 10.44 cm is obtained consistent with the

10.4 cm value.

Thus the slab width of 9.46 cm proposed by us compares favorably

from the safety viewpoint with the safe width for an infinite, water-

moderated and reflected slab and is considerably narrower than the safe

width for an infinite, water-moderated and unreflected slab. Within the

present context it should also be pointed out that as indicated on page

54 of the Design and Hazards Report [3], no flooding of the storage area

seems possible from natural causes.


Neutron Sources

Two types of neutron sources were used throughout this work.

1) Two Pu-Be sources mounted in an aluminum cylinder which can be

driven remotely through a plastic pipe from a shielded box located in

one corner of the facility room to underneath the center of the core.

Neon lights provide indication at the console of the position of the

sources. These sources, which have a combined yield of ~ 3.2 x 106

n/sec are used for start-ups and for the inverse multiplication meas-

urements.

2) A Texas Nuclear Neutron Generator which is used in continuous

mode for static measurements and in the pulsing mode for the pulse

propagation measurements. The generator is of the Cockcroft-Walton

type, TNC Model 150-1H with continuously variable high voltage from

0-150 kv and has been modified to obtain larger currents by removing

the einzel lenses and installing a new 22 electrode accelerator tube and

gap lense. Pre- and post-acceleration beam deflection produces sharp,

low-residual pulses.






31


The accelerator was used with a 4-5 curie tritium target.

The position of the target can be changed to keep the source

centered on the target-end of the assembly for any given moderator

level.















CHAPTER III


OPERATIONAL SAFETY


Introduction


The University of Florida SPERT Assembly, due to its large size,

enriched uranium-oxide fuel and nuclear potentialities required a

thorough study of its capabilities, operational characteristics, initial

loading procedures and of the behavior of the assembly under accident

conditions. The study was part of the requirements established by the

Division of Material Licensing of the USAEC prior to the granting of an

operating license.

Legally, a subcritical assembly has to comply with regulations

under 10 CFR Part 70 "Licensing of Special Nuclear Materials" since no

self-sustaining nuclear reaction is envisioned. In the case of the

UFSA, however, the Commission felt-that certain technical sections of

10 CFR Part 50, which deals with nuclear reactor licensing, should apply

and serve as a guide for the design and the safety analysis.

The basic philosophies employed in the design of the system were:

a) The UFSA facility has been designed to remain subcritical under

normal operating conditions.

b) The safety instrumentation (see Part 1, Chapter I) has been

designed such that a single failure will not invalidate both the manual

and automatic scram and will not cause subsequent failures.

c) The design basis accidents were postulated on a single failure
32









criterion.

d) Operating limits have been set to delineate the normal oper-

ating ranges of the assembly.

e) Initial loading procedures have been established to determine

the safe operating multiplication factor of each configuration.

A series of administrative controls are necessarily applied to all

segments of the experimental program and strictly enforced.


Initial Loading

A series of calculations were done to determine which of the two

following schemes should be employed for the initial loading of UFSA:

I) Step loading of the fuel from the center out, accompanied by

step increases in water level with the usual inverse multiplication

determination.

II) Loading all the fuel into the dry tank and proceeding with a

careful evaluation of the multiplication as a function of water level.

Since the UFSA core is very loosely coupled as far as the lumped

reactivity parameter is concerned, the second method was selected due to

the fact that a better determination of the multiplication was possible

from a basic moderator height-zero loading inverse counts determination.

The slope of the keff vs. water height curve has a slope substantially

smoother than the keff vs. per cent fuel loading (full water height)

curve.

The moderator level control system in operation at the facility

provides a extremely reliable and safe mode of adjusting the water level

without safety compromises.

The following regulations were followed for the initial fuel









loading, and will be followed for subsequent cores:

1) After the fuel has been loaded, prior to each new incremental

change in the water level, the water is drained completely and the weir

(and water level scram) adjusted to prevent a level increase beyond the

desired value.

2) The first three measurements of the inverse multiplication are

obtained at water heights of approximately 20 cm, 25 cm, and 30 cm above

the bottom of the active fuel. As shown in Table I, the maximum kff

calculated for a water height of 30 cm is 0.87. Subsequent filling

increments are not to exceed the least of the following:

a. An increase in water height of 10 cm.

b. An increase in water height which, by extrapolation of the

inverse multiplication curve, would increase the keff by one-half of the

amount required to make the assembly delayed critical.

c. An increase in water height which would, by extrapolation of

the inverse multiplication curve, result in a k of 0.990. For values
eff
of keff above 0.95, the keff of the assembly are also determined by

pulsed source techniques.

3) At each filling step, the measured k effof the assembly is

compared with the calculated value. If significant deviations of the

experimental values from the calculated keff vs. water height curves

occur, the experiments are to be discontinued, and a detailed analysis

of the results obtained performed. If it is determined that the dimen-

sions of the assembly should be changed in order to achieve the desired

keff at maximum water height, the University of Florida will apply for

and obtain written approval from the Atomic.Energy Division of the

Phillips Petroleum Company before such changes are made.










Operating Limits

A description of the operating limits of the subcritical assembly,

including the basis for such limits ate listed below.

Effective Multiplication Factor

Specification: the maximum allowable keff will be 0.985+.005.

The absolute value of keff as well as the slope of the keff vs. water
eff eff
height will be carefully measured so as not to exceed the limiting value.

Basis: the upper limit of kf = 0.985+.005 is established by:
eff
the accuracy with which keff can be measured, the reported [7] differ-

ences between calculations and experiments in similar cores and the value

of the multiplication factor required to make a meaningful study of the

dynamic properties of large cores. Comparison [7] between 29 calcula-

tions and the corresponding critical experiments (on cores similar to

the UFSA) established that an overestimate of keff is generally made; the

standard deviation for these cases was + 0.00175 and the maximum under-

stimate of the multiplication was for a case yielding keff = 0.9966, a

0.34% deviation.

The absolute value of keff will be determined for water levels
eff
yielding a keff >.95 by pulsed techniques independently of the inverse

multiplication measurements. The method to be used is the Garelis-

Russell[8] method which, when appropriate corrections are made for the

reflector, has been shown to give good results. In this method both
1-keff(l-8) keffB
a = and -- are determined; then keff may be. obtained by

independently obtaining $ or A. Since of the two parameters 8 changes

the most slowly with keff, it is valid to use a value based on theoret-

ical calculations.









Reactivity Addition Rate

Specification: the reactivity addition rate is controlled by the

water flow rate into the subcritical assembly. The maximum flow is fixed

to be 12 gpm. At this maximum flow rate, the rates of addition of water,

and consequently or reactivity, computed between water heights of 30 and

45 cm. are:


0.5332"


Lattice Pitch

0.584"


0.7152"


Rate of increase of
water level 0.0435 0.0439 0.0431

Ak/cm 0.0093 0.00865 0.008

Ak/sec 0.0004 0.0038 0.000344

$/sec 0.057 0.054 0.049

It should be noted that these reactivity addition rates are a large

overstimate compared to the calculated rates at keff- .98.

Basis: the maximum rate of addition of reactivity was established

by the calculated values of keff vs. water height and the maximum flow

rate. The values specified above constitute an upper limit in the

region of interest and are considered to be safe under circumstances.

The flow rate is a function of the capacity of the pump, the ori-

fice and the pneumatic control valve and cannot exceed 12 gpm.

Reactivity Removal Rate

Specification: a conservative value for the reactivity removal

rate is taken from the slope of the keff vs. water height curves near

the maximum designed k -, values. Since no difference is detected for
err
the scram times of the three configurations, only one rate of removal

will be specified, corresponding to the smallest slope.










Drain rate, including the system

reaction time ................... 2.65 cm/sec

Rate of removal of reactivity ....... 0.00037 Ak/cm

....... 0.00098 Ak/sec

....... 0.140 $/sec

it should be noted that the value of Ak/cm used to specify the reac-

tivity removal rate is 20 times smaller than the corresponding value

specified for the reactivity insertion rate.

Basis: the rate of drainage from the assembly established the

reactivity removal rate. Consistent with the approach taken when

specifying the reactivity, the time to drain 45 cm of water from the

assembly was measured to establish a lower limit on the rate of de-

crease of water height. Even under these extreme assumptions, i.e.,

using the maximum slope of the keff vs. water height curve for the

insertion rate, the small calculated slope around k ef=.99 for the

removal rate and the reduced pressure head, the reactivity removal rate

is three times larger than the insertion rate.

Subcritical Assembly Power Level and Power Level Scram

Specification:

Power Level ........................ 0.5 watt

Power Level Scram ................... 1.0 watt

Basis: with the maximum source strength available and with k -e
eff
0.985 the maximum average power was calculated to be .130 watts by

taking into account the spatial dependence of the flux and a steady

source at one end.

Assuming that a reactivity accident occurs, based on the maximum

reactivity addition rate specified above, the design basis accident









predicts that from a keff of 0.993 it would take approximately 15

seconds to double the power level. Even if the power level indicator

were not to scram the system until the power level reached 10 kw,

assuming a one second delay time to actuate the scram, the power would

increase to only 69 kw by the time the scram actually begins. Based on

the reactivity removal rate described above, the power level would then

decrease rapidly to a very low value.

Period Scram

Specification:

Period scram ........................ 15 sec

Basis: A positive period will be obtained in the subcritical assem-

bly for any addition of reactivity beyond a given steady state condition.

If the maximum reactivity insertion rate of 0.05 $/sec is considered,

the initial positive period is about 50 sec and decreases monotonically

with time. The period channel has been determined to respond reliably

to periods = 50 sec. Originally, the period scram was set at 50 sec but

repeated scrams caused by the start-up of the neutron generator forced

the reduction of the scram period to 15 sec for operational reasons.

Average Neutron Flux and Neutron Flux Scram

Specification:

Ave neutron flux for

most reactive core .................. 1.5 x 105 n/cm2 sec
C 2
Neutron flux scram .................. 3.0 x 105 n/cm sec

Basis: the above are based on the average power calculated for the

assembly. Doubling of the flux will occur when 0.75 $ worth of reac-

tivity is added to the system from any design subcriticality level.

Under these conditions, even at the maximum keff status, the facility
ef f










will still be subcritical and the instrumentation will have sufficient

time to scram the system before accidental criticality occurs.


Design Basis Accident Analysis

Two types of accidents have been postulated to occur in conjunction

with the UFSA experimental program. The design basis accident analysis

will deal with the following two cases: a) a dropped fuel rod accident

in which a fuel rod is broken releasing the fission products accumulated

during previous operation of the assembly; b) an accidental criticality

resulting in a power excursion. It will be shown below that the poten-

tial consequences of either accident are well within the radiation dose

limits specified by Title 10 CFR Part 20.

Dropped Fuel Rod Accident

For the purposes of this analysis, it is assumed that a dropped

fuel rod results in a broken pin releasing the accumulated fission pro-

ducts. The following bases have been established to calculate the

radiation dose from such an accident:

a. It is stipulated that the assembly has been operated continu-

ously for 200 hr at an average power level of 0.065 watt. It should be

noted that this is a conservative value since the assembly will not be

operated on a continuous basis; the 200 hours of operating time for each

configuration is essentially spread over a period of several weeks.

b. The assembly contains 1200 rods. Since the actual loadings for

the three reflected cases are 1206, 2132 and 3430 rods respectively, this

will result in conservative results.

c. The peak to space-averaged flux ratio during operation is a

maximum of 120, with the rod at peak flux contributing 1/10 of the









total power of the assembly.

d. The fuel rod subjected to the specified highest specific power

is broken open and the fuel is completely fragmented, releasing 100% of

the gaseous fission products.

e. The iodine (in elementary form) diffuses uniformly throughout

the 18' x 32' x 15' room to calculate the on-site internal dose. The

off-site dose was calculated using the very conservative Pasqual's

principle of atmospheric diffusion.

The fission products inventory was calculated by means of the RSAC

code [9]. The results indicated that the iodine isotopes were the only

significant contributor to the inhalation dose. Using the active worker
-4 3
breathing rate of 3.47 x 10 m /sec specified in 10 CFR 20, a person

remaining in the room would accumulate a thyroid dose of 0.023 mr for

each minute he remains in the room, after the hottest rod breaks open.

The total dose to a person that inhales all of the iodine contained in

the rod would be 0.2 r. The established radiation safeguards at the

University of Florida require the personnel to abandon the area imme-

diately and notify the Radiation Safety Officer. The maximum time

required to evacuate the assembly and the fuel storage area is 10 sec

with 30 sec needed to evacuate the entire building; these times have

been measured during practice evacuation of the building.

The off-site total inhalation dose, calculated assuming the iodine

is released in one puff with zero wind velocity, cloud inverted con-

dition, were typically:









Distance'from site (m) Total dose (mrem)

200 4.5 x 104

500 2 x 104
1000 7 x 10-6

The direct radiation dose from all the fission products of the

irradiated fuel elements is calculated to be 1.3 mr/hr.

Accidental Criticality and Subsequent Power Excursion

Accidental criticality and a subsequent power excursion could occur

only by the uncontrolled addition of water to the assembly and gross

error in the calculations and/or procedures. The occurrence of such an

accident is highly improbably and would require:

a. Setting a core width corresponding to the 1.5 metal/water ratio

and proceed to install the fuel spacer system for the 0.5 metal/water

ratio, load the fuel under these conditions and disregard small water

height increments and 1/M measurements. To do this, several administra-

tive rules would have to be wilfully ignored.

and/or

b. Improper setting of the following: the weir height, the water

height scram system for any configuration and a gross error in the

calculations causing criticality at about half the design core height

(91.44 cm). It should be noted that the calculational method used to

predict that keff values has been tested successfully against the

results of 29 different critical assemblies [7].

and/or

c. An obstructed 2 inch line from the core to the weir drain

system and a simultaneous failure of the water height scram together

with the referred to error in the calculations.









d. Violation by the facility operator of the administrative

procedures requiring a visual check of the assembly before start-up and

continuous attention to the control console instrumentation to determine

the status of the assembly at all times.

The consequences of such an accident were determined by assuming

the following:

1. The assembly is initially at a steady state power level of 10

watts (normal average power is .065 watt).

2. Water flows into the system at the maximum rate of 12 gpm.

3. The reactivity addition rate is 0.05 $/sec. This rate is

larger than the calculated rate (.04 $/sec) for the case discussed

above and more than that calculated to occur near critical for properly

loaded assembly.

4. The power scram is set, through calibration or other error, at

10 kw. Corresponding error settings occur for the neutron flux and

period scram.

5. A scram occurs 1 sec after a power level of 10 kw is reached.

This time has been determined as the elapsed time from the initiation

of a scram signal to the opening of the dump valves.

6. No feedback effects are considered. This is a good approxima-

tion to our case due to the low power levels involved and again is a

conservative assumption.

The calculations were made using the IREKIN code, described in

reference [10]. IREKIN numerically solves the point model kinetics

equations.

Starting with the assembly one dollar subcritical (ke = .993),
and proceeding with the described excursion, the accident would yield
and proceeding with the described excursion, the accident would yield










a peak power of 69 kw, the total energy release is 0.5 Mwsec. The

power vs. time behavior of the assembly for the postulated power excur-

sion is shown in Fig. 9.

The combined neutron and gamma dose to the operator is 1.5 rem

assuming that: the energy release is instantaneous, all neutrons have

an energy of 1 MeV and there is no attenuation in the assembly. The

proper RBE factors were taken into consideration.

It is concluded that, even if such an improbable accident would

occur, the hazards to personnel and the general population are not

significant.







7x104


3 -At t=0: k eff=0.993, Power=0
Ramp Insertion of .05$/sec
2 Scram 1 sec after 10 kw
Scram Rate = .14$/sec
Total Energy Release=0.5Mwse


Time secss)


FIG. 9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT















CHAPTER IV


THE DATA ACQUISITION SYSTEM


Introduction


In the delicate and laborious task of performing nuclear experi-

ments the most common source of difficulties and errors lies in the

acquisition of the data. Modern nuclear instrumentation with its excel-

lent time-energy resolution has enhanced detection sensitivity to the

extent that deviations previously masked by the poorer resolution of the

equipment are easily distinguishable. The major problem now lies in the

degree of reproducibility of the results. Although in general the in-

strumentation is very reliable the enhanced sensitivity demands contin-

ual standardization for the sake of reproducibility.

The "brain" of the data acquisition system for pulsed neutron

measurements is the multichannel analyzer (MCA) which is now available

with a large number of data channels and narrower channel widths for

increased time resolution. In general, the mode of data acquisition

for a pulsing experiment differs from that of many other types of

nuclear experiments. In particular, neutron interactions with a suitable

detector are fed into the analyzer while it is time-sweeping. Ideally

every neutron interaction should be counted regardless of the ampli-

tude of the collected pulse. This implies that the linear signal

originated at the neutron detector should be converted to a logic .signal

so that its probability of being recorded is independent of its amplitude.

45









Logic signals have fixed amplitude-shape characteristic and convey

information by their presence, absence of time relationship with

respect to a reference signal. Only gamma and noise discrimination

are necessary; this process will inherently eliminate the counting of

weak neutron interactions.

The process of registering events whose density per unit time

varies considerably requires an electronic system with extremely high

time resolution and a broad frequency response. Typically the counting

rates at the peak of the neutron burst in pulsed neutron measurements

vary from 10 to > 10 event/sec. This high, time-varying count rate

caused drastic losses in conventional instrumentation due to pulse

pile-up and circuit induced distortion when the dynamic range of the

circuit is exceeded causing a net amplitude shift in excess of that

tolerable by the system. The alternative modus operandi is to use low

count rates so that resolution losses are minimized; this, however,

increases the probability of systematic errors due to much longer run-

ning times.

The count rates encountered during the initial experiments with a

He counter close to the neutron generator target in the SPERT assembly

exceeded 10 event/sec at the peak. Saturation effects were observed

in modular instrumentation incorporating the latest F.E.T. preamplifier

and double-delay line pulse shaping amplifier at about 105 event/sec.

The fast pulse train caused a drop in the base voltage of the Field

Effect Transistor which prevented further counting until a significant

reduction in the count rate allowed the voltage to recover. Changing

to a fast scintillation prototype preamplifier improved the situation

somewhat. However, if the potential count rate in the UFSA assembly









were efficiently handled with few losses the actual running time of a

particular experiment could be reduced to a few minutes. This possi-

bility forced the development of the ultra-fast instrumentation chan-

nels used in this work.

The electronic counting system used throughout the experimentation

used a transformer-coupled pulse amplifier to produce a fast logic sig-

nal to the input of the MCA from a slower input signal originating in a

He counter. The system has superior counting and stability character-

istics. The resolution time of the system is practically nil compared

to that of the MCA. In general, data acquisition times were reduced

to a few minutes; in that time it was possible to obtain, at most of

the detector locations, the following counting statistics:

Peak Channel Counts: 217

Counting Time: 2 10 minutes

No. of data channels: 1024

Channel Width: 20 micro sec

Pulse repetition rate: 30 hz

Noise Level: 40 event/min

Background Level: 140 event/min


The Neutron Detector

The neutron detectors used throughout the experimental program were
3
proportional counters filled with He The counters are of the Texlium

variety made by Texas Nuclear Corporation and were specially built to

conform to the UFSA core grid. Detectors of this type have been



1. The assistance of Mr. Joel B. Ayers of ORTEC, Inc.,who suggested
this electronic instrumentation is gratefully acknowledged.









preferred over the BF3 variety at the University of Florida because of

the larger neutron absorption cross section and operational reliability.
3
He undergoes the following reaction

He3 + n H3 + p + 0.764 Mev.

The cross section for this reaction is 5327 + 10 barn at v = 2200
-- o
10 3
m/sec compared to 3840 + 11 barn for B He follows a 1/v law in the

energy range from 0 to 200 kev. The pulse heights yielded by a He3

filled counter are proportional to the energy of the neutrons plus 764

kev. The reaction has been used for neutron spectroscopy from the 100

kev to 2 Mev energy range. Gamma discrimination can be easily accom-

plished by the use of a biased integral discriminator.

The detectors were long and thin and each took the place of a fuel

element in the core. The active length of the counter is slightly less

than the active length of the fuel. Two one atmosphere (predominantly

thermal detection) and one ten atmosphere (more responsive to higher

energy neutrons) detectors were used in the experimental program. A

sketch of the physical characteristics of the counters is shown in

Fig. 10. The thin, long cylindrical shape enhances the time character-

istics'of the counter. Although normally a 1 atmosphere He detector

operates with a bias voltage of 1000 volt, the minimum input pulse

voltage requirement of the pulse transformer was such that the operating

voltage of the counters had to be raised to 1200 volt. At this

voltage the slope of the counts vs. high voltage curve was about 8% per

100 volt; therefore very stable, low ripple high voltage supplies were

used to insure reproducibility of the detector response.













HV BNC Connector


.- 5.1 25"-4


ive Volume Stoinless Casing







*: . * *
.247"




4- 33" 2.375"


40.5" 0.5" ---


FIG. 10 PHYSICAL CHARACTERISTICS OF THE He NEUTRON COUNTERS










The Electronic Instrumentation

A block diagram of the instrumentation used in the pulse propaga-

tion experiments is shown in Figs. 11 and 12. Two independent data

acquisition systems with a common start-stop clock are necessary to

carry out the measurements: (1) a system connected to a movable detec-

tor that obtains the time profile of the propagating pulse at a given

position and (2) the all important normalizing detector, fixed at one

position. Two 1 atmosphere He3 detectors with the characteristics de-

scribed above were used for these purposes. The system is essentially

composed of signal transmitting devices and data registering and

handling units.

The movable detector data acquisition system (MDDAS) consists of:

1. Detector High Voltage Power Supply

The high voltage power supply was an ultrastable FLUKE 405 B with

superior stability and negligible ripple. Manufacturer's specifications

state the stability at .005% per hour and the ripple at less than 1 my

RMS.

2. ORTEC Model 260 Time-Pickoff unit, with 3000 volt isolation

The time-pickoff units are normally used to detect the time of

arrival of a detected particle, usually with subnanosecond precision..

The use of this characteristic and the electronic arrangement shown in

Figs. 11 and 12 permitted the counting of neutron events with excellent

time resolution. To our knowledge this is the first time that the time-

pickoff units have been used for this application.

Briefly, the system operates as follows: the primary of a toroidal

transformer, having a bandpass for very high frequencies only, is

inserted between the detector and the bias power supply. Fast














4-RTC I
LORTEC 260 TIME-PICKOFFj


FIG. 11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM













4I 2_ I

ORTEC 260 TIME-PICKOFFJ


FIG. 12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM









components of the detector signal will actuate a wide band transistor

amplifier and tunnel diode discriminator from the secondary of the

transformer. A line driver buffer is also provided. The power and

control bias are provided by the ORTEC 403 Time Pickoff Control.

3. Modified ORTEC 403 Time Pickoff-Control

The 403 Time-Pickoff Control provides control and fan-out buf-

fering for time derivation units such as the 260 Time Pickoff Unit.

The fan-out buffer accepts the fast negative logic signal from the 260

unit and provides either fast negative or slower positive logic output

signals.

The 403 Time-Pickoff Control had to be modified to make its out-

put signal compatible with the input requirements of the 212 Pulsed

Neutron Logic Unit used with the MCA. The 212 plug-in unit requires

pulses with rise times longer than 50 nsec while the positive output

from the 403 control unit has a rise time ~ 10 nsec. Furthermore, the

positive logic signal from the 403 control has a 0.5 microsec pulse

width which is too wide for the time resolution required. Therefore

two modifications were made: a capacitor2 (C12) was changed from 270

pf to 68 pf reducing the pulse width to 0.12 microsec and an inductor

coil (Ll) was removed from the system changing the rise time to 50

nsec.

The modifications made the system compatible with the input

requirements of the MCA and avoided overdriving the analyzer.





2. Refer to ORTEC, Inc. "Instruction Manual for 403 Time-Pickoff
Control."









4. Technical Measurement Corp. 1024 Multichannel Analyzer

(MCA) and Data Handling Units

The time analysis of the pulse and the corresponding data output

are obtained from the following coupled instrumentation:

Pulsed Neutron Logic Unit, TMC Model 212

Digital Computer Unit, TMC Model CN1024

Data Output Unit, TMC Model 220C

Digital Recorder, Hewlett-Packard Model 561B

Binary Tape Perforator, Tally Model 420

A trigger from an external pulse generator starts the sweep of the

analyzer as controlled by the pulsed neutron logic unit and initiates

the burst at the accelerator. The 212 has variable channel widths from

10 to 2560 microsec. The full 1024 channels were used in all the meas-

urements. The storage capacity of the CN1024 is 217 counts. Both

printed paper tape and perforated binary tape were obtained as output.

5. ORTEC 430 Scaler

For some of the flux traverses and the 1/M measurements, the

integral counts were recorded in a 10 Mhz scaler.

The normalizing detector data acquisition system (NDDAS) consists

of the same components as the movable detection system except that a

256 multichannel analyzer, TMC Model CN110 was used for data handling

and the integral counts were accumulated in an ORTEC 429 Scaler, modi-

fied for 7 Mhz counting rate.


The Resolution Time Correction

The resolution time of the pulsed neutron data acquisition system

was the parameter under consideration while searching for a well-matched









and fast electronic instrumentation set-up. Some of the findings were

surprising and may explain some of the discrepancies found in previous

pulse propagation and neutron wave experiments which used an acceler-

ator type neutron source. In these experiments it has been customary

to increase the neutron yield of the genetator as the movable detector

is positioned farther away from the source to keep running times within

tolerable limits. The count rate at the movable detector is then

maintained at a level which has been determined to be acceptable; how-

ever the normalizing detector usually fixed in a position close to

the source (normally at the "thermalizing tank" if one is used) may

then be exposed to count rates beyond the capabilities of the detector

and the associated instrumentation. Since the movable detector signal

was always fed into an analyzer, saturation effects could be easily

detected; the signal from the normalizing counter, however, was always

being fed into a scaler where saturation effects may go unnoticed since

a time profile is not available.

During most of the present work, two MCA's were available and the

phenomenon described above was observed and count rates throughout the

experimental program limited to those permissible by the time charac-

teristics of the counting system.

The experimental program being carried out with the UFSA subcrit-

ical calls for the one to one comparison between theoretically calcu-

lated and experimentally determined time profiles of the neutron flux

as a function of space. The shape of the pulse, rather than conven-

tional integral parameters extracted from it, is therefore the signif-

icant and required information. For this reason the influence of the

resolution time correction on the shape of the pulse came under close









scrutiny.

The resolution time of several, submicrosecond preamplifier-linear

amplifier combinations was shown to be a function of the mode of opera-

tion and of the count rate. For this type of instrumentation, there is

a significant difference between the resolution time as determined by a

steady-state technique (two source method) and a dynamic method (maximum

count rate method [11]), the latter method yielding a much larger reso-

lution time.

For the instrumentation finally chosen to carry out the pulsed

experiments in this work no significant difference was found between

the results of the two methods. Furthermore the pulse transformer-

amplifier combination behaves like an ideal non-paralyzing system. The

resolution time of the overall data acquisition system was found to be

primarily determined by the multichannel analyzer.

As a matter of illustration, when the system depicted below was

used the resolution time changed from -0.24 microsec as determined

under low count rate steady-state conditions to -8 microsec as deter-

mined under high count rate, pulsing mode conditions.









Shown in Fig. 13 are two time profiles obtained at the same posi-

tion in the UFSA core for the same count rate. The conventional

preamplifier-linear aLaplifier system shown above was used to obtain one

of the profiles and the instrumentation selected for this work was used

to obtain the other. Both were corrected for resolution time losses

with the best available value for the resolution time. The distortion

observed in the pulse shape obtained with the conventional preamplifier-

linear amplifier system is non-linear due to the count-rate dependent

resolution time. It should be noted that the count rate near the peak

of the pulse was less than 105 count sec. The conventional system

response "flattens out" when it reaches complete saturation in this

case above 105 count sec. Saturation effects are not observed in the

pulse transformer system until the count rate exceeds 3.3 x 10 count

sec. An erroneous resolution time correction, or one which used a

resolution time that does not characterize the system throughout the

range of count rates will change the shape of the neutron pulse and

consequently affect any analysis done on the pulse shape obtained.

As pointed out by Bierman, Garlid and Clark [11], in a pulsing

experiment it is necessary to determine whether the counting system

has the characteristics of a purely non-paralyzing system or those

of a mixture of paralyzing and non-paralyzing systems. Using the

method described by Bierman and co-workers, it was established that

the data acquisition system being used in the present work is, as

close as can be determined, non-paralyzing. The resolving time of the

system is essentially determined by the width of the input pulse to the

analyzer and the MCA characteristics.

It should be noted that for a wide range of count rates, depending





58



40












30


Conventional








Time-Pickoff
20












10






30 microsec between channels




SI I I I I I I I l I !
0 4 12 16 24 32 40 48 56

Channel Number


FIG. 13 TIME PROFILES OF NEUTRON BURST RECORDED BY CONVENTIONAL
ELECTRONIC INSTRUMENTATION AND BY THE TIME-PICKOFF SYSTEM










on the magnitude of the resolving time, it is not necessary to prop-

erly identify the counting system since no significant difference in

the corrected counts are observed when using the paralyzing or non-

paralyzing correction. This is shown in Fig. 14.

The resolution time correction for the UFSA data acquisition

system is then given by:

No
N = o
T Noxtr
1-
CWxTrs

where

NT = true number of events in a given channel

N = observed number of events in a given channel

tr = resolution time of the system

CW = channel width

Trs = number of sweeps of the analyzer

and, for a non-paralyzing system

tr = reciprocal of the maximum observable count rate

Using this method the following resolution or resolving time fac-

tors were determined:

A) MDDAS including 1024 Multichannel Analyzer

tr = 0.31 + .015 microsec

B) MDDAS excluding Multichannel Analyzer

tr 0.20 + .01 microsec

C) NDDAS including 256 Multichannel Analyzer

tr = 0.56 + .02 microsec

D) NDDAS excluding Multichannel Analyzer

tr 0.20 + .01 microsec




I-w


700




600




- 500



0
z 400

S-- Non-paralizable


o 300 Paralizable
u /

") 0 80% non-paralizable
S20% paralizable

- i 200




100





0 100 200 300 400 500 600 700 800 900 1000

True Count Rate NT (x 103)


FIG. 14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME CORRECTION AS A FUNCTION
OF COUNT RATE









The Normalization Technique

The analysis of a pulse propagation experiment will yield informa-

tion on the velocity of propagation, the attenuation and pulse shape as

a function of position of a propagating disturbance. To determine the

attenuation or relative amplitude of the pulse at different positions

in an assembly, the data must be normalized to a fixed reference so

that variations in the source strength, data acquisition time, etc.,

can be properly accounted for. The usual technique requires accumulating

integral counts in a scaler for each measurement and reducing all meas-

urements to the fixed reference afterwards. As was mentioned previously,

the resolution time correction can have a significant effect on the nor-

malizing factor since widely differing count rates are employed. It is

extremely hard, if not impossible, to obtain a proper resolution time

correction based on integral counts determined from a time-varying count

rate.

Two methods of normalization and their relative merits are discussed

below.

The Integral Count Method is the normally employed method of nor-

malization. The total counts accumulated with the NDDAS for all runs

is referred to a predetermined one, with the normalizing detector in a

fixed position while the movable detector changes position.

The Analyzer Method, which is essentially the same as the above

except that the counts arising from the normalizing detector are stored

as a function of time in a multichannel analyzer. The average of a

series of ratios obtained by dividing the corrected channel counts by

the corresponding channel counts of a predetermined measurement gives

the normalizing factor.









The Analyzer Method is intrinsically more accurate than the

Integral Count Method because it permits an "exact" correction for

resolution time losses by the use of the expression previously given

applied to the recorded time profile. The correction for the integral

counts is, on the other hand, inaccurate since the count rate is con-

tinuously changing and no base exists for a resolution time correction.

It was found, however, that as long as the count rate near the

peak of the pulse is kept well within the capabilities of the NDDAS no

significant difference is observed in the results of the two methods.

This is due to the fact that ratios are being taken in both cases; this

tends to minimize whatever differences there might be. Thus, it is

concluded that with proper care the Integral Method is adequate whenever

an analyzer is not available for normalization purposes.

It should be noted that an "effective" resolution time can be used

to improve the results of the Integral Method. This "effective" reso-

lution time can be found by forcing the normalizing ratio obtained from

two runs by the Integral Method to match the normalizing ratio obtained

from the Analyzer Method for the same two runs by adjusting the reso-

lution time correction applied to the integral counts.


Comments

Certain inconsistencies in the results of the first few experi-

ments prompted a careful inspection of the multichannel analyzer modus

operandi. For the sake of completeness the significant findings are

listed below.

A) Operation with the 10 microsec channel width (selected by the

settings of the 212 plug-in-unit) proves to be unreliable due to insta-

bilities in the clock and gating circuits. Channel widths of 20









microsec or longer are stable.

B) The address current setting of the CN1024 is extremely criti-

cal, markedly so for high count rates.

C) An optimum pulse into the analyzer should have a rise time of

50 nanosec, a total width of .1 microsec and an amplitude of 3-5

volt.

D) Above noise level, the discriminator setting of the 212 logic

unit becomes irrelevant when a constant pulse height is used as input.

E) Reproducibility tests were performed on the analyzer with the

neutron generator in continuous mode.

The statistical analysis of the channel counts gave:

72% were less than 1 from the mean

25% were between 1 and 2 from the mean

3% were between 2 and 3 from the mean

The system is statistically well-behaved.















CHAPTER V


NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL


Introduction


The nuclear calibration of the University of Florida SPERT Assem-

bly was performed prior to the space-time kinetics studies. The cali-

bration involved conventional inverse multiplication measurements,

absolute keff determination by pulsing techniques and comparison with

multigroup-multiregion diffusion theory calculations. The Garelis-

Russell technique was employed to determine ka/I and this result used to

calculate keff by coupling it with the experimentally determined decay

constant and the theoretically calculated effective delayed neutron

fraction. During this phase of the experimentation, "spatial effects"

were noted in both a and k8/t. These effects and other interesting

kinetic phenomena involving these basic reactor parameters were con-

sidered worthy of further study and were investigated during the main

part of the research. They are discussed in Part 2, Chapter V. In

this section the results pertinent to the necessary calibration of the

system are given.


Theoretical Notes

The Inverse Multiplication Method

Under ideal conditions, usually met only in small-fast assemblies,

the reactivity can be represented by
64










1 k 1
~ M or 1 k /M
k M 1

where M is the net neutron multiplication in the assembly with a

centrally located source. In practice, the multiplication is obtained

from the ratio of multiplied to unmultiplied counts with a centrally

located source. The unmultiplied counts are obtained with the fissile

material removed and all other conditions undisturbed. In water-

moderated cores it is difficult to match neutron spectra for multiplied

and unmultiplied counts and deviations from the ideal M are to be ex-

pected. If possible, a search for detector locations should be con-

ducted so as to obtain curves that follow the expected behavior of l/M.

Even if k can not be directly inferred from the 1/M determination, the

curve of reciprocal count rate vs. the parameter that controls reac-

tivity (fuel loading or moderator height or % control rod withdrawal)

is a useful guide for safely approaching criticality if a well-behaved

curve can be obtained.

The inverse multiplication curve can be obtained as a function of

moderator height by first obtaining a series of unmultiplied counts at

various water levels and the multiplied counts as the water level is

raised with the assembly originally air-spaced. Sensitivity to geo-

metrical configuration (source-detector-water level) requires an empir-

ical determination of "well-behaved" detector positions.

Reactivity Measurements by the Pulsing Technique

The pulsed-neutron technique has been used successfully for several

years to measure reactivity. The transient neutron density following a

burst of neutrons is used to determine the reactivity of the system by

either the Simmons and King method [12], Sjostrand's area ratio method









[13], Gozani's extrapolated area-ratio analysis [14] or the Garelis-

Russel technique [8]. In all these techniques it is essential that a

fundamental spatial distribution of the neutrons be established for a

correct determination of the decay constant and, therefore, the reac-

tivity of the system.

The Sirmons and King method established that a value for the

reactivity can be obtained directly if a prompt fundamental decay con-

stant can be measured at delayed critical. The value of a at delayed

critical determines B/k and if these parameters are assumed constant

over the reactivity range of interest a value of a can be obtained. The

technique has given good results up to ~ $20 subcritical in small mul-

tiplicative systems. The method strongly depends on being able to

establish the prompt fundamental decay mode; it suffers from the incon-

venient necessity of a delayed critical measurement and the assumed

constancy of B/k throughout the ranges of reactivity.

The Sjostrand method improves the Simmons and King method in that

the delayed critical measurement is no longer necessary but the results

are shadowed by the strong influence of higher spatial harmonics. The

method is based on the premise that the impulse response curve of the

system is dominated by the prompt fundamental mode.

Gozani's treatment is a significant improvement over Sjostrand's

method. Gozani proposed the extraction of the fundamental mode of

prompt neutron decay from the impulse response curve and the extrapola-

tion of this curve to zero time. The reactivity in dollars can be found

by integrating under this curve; the method is independent of the pres-

ence of higher prompt spatial modes.

The Garelis-Russelltechnique, similar to Gozani's extrapolated










area-ratio method, is of practical value because of its intrinsic

elimination of the effect of prompt higher harmonics. This method,

which was used in the present work, was postulated originally for a

repetitively pulsed (with a delta function source in time), bare,

monoenergetic reactor but has proven to be of broader application.

Garelis and Russellpostulate, that for the conditions specified above:

1/R 1/R
fNp exp((k3B/)t)dt = fNpdt + Nd/R

where

Np = prompt contribution to the neutron density

Nd = delayed contribution to the neutron density

R = pulsing rate

The following conditions should be satisfied for the correct ap-

plication of the method.

a) R>>X, where A is the decay constant of the shortest lived

precursor group.

b) R >> a, where a is the prompt fundamental decay constant.

c) The system must be pulsed a sufficient number of times so that

exp (masn/R) << exp (-as /R), where m + 1 is the total number of pulses

and the a are the roots of the inhour equation.
sn
d) The prompt root dominates the decay.

The Garelis-Russelltreatment permits the determination of p ($)

when all the above conditions are satisfied, by the relation:


P ($) = k -

An absolute value of p is obtained by the use of a calculated effective

delayed neutron fraction. Garelis has discussed the use of the method

in reflected systems; the technique seems to be of practical value in









these systems [15].

Becker and Quisenberry were able to compute a correction [16] for

the observed spatial dependence of the reactivity in two-region systems

by recognizing the differences in the spatial distributions of prompt

and delayed neutrons. Their excellent comparative study of the above

techniques emphasized the need for their recommended spatial correction

unless the neutron detector is properly positioned to minimize this

correction.

The study of Garlid and Bierman [17] correctly points out that in

very large systems "an asymptotic spatial distribution cannot be estab-

lished before the pulse has decayed away, since the asymptotic mode is

one that is uniform everywhere in space." They proceed to apply a

combination of first flight, age, and time-dependent diffusion theory

to the study of pulsed measurements in large aqueous media; their con-

clusion is that their measured apparent decay constant is a good ap-

proximation to the asymptotic value and that pulsed measurements in very

large multiplying systems may also give good results.


Inverse Multiplication Measurements

The safe approach to the design value of k <.99 was undertaken
eff -
with the conventional 1/M measurements until k 0.95 and then by both

the 1/M and the pulsing technique.

To establish detector positions free from geometrical effects

(source-detector-water level), six different locations were used until

a water level of 60 cm (k .98) was reached and four locations afterwards.

Two of the detector locations, the closest to the neutron source, failed

to describe the multiplication of the system. Shown in Fig. 15 are the




SI VV I,














GRID POSITION

134 101 84 1 59 42

----- B 0-- '-b - *- i--
0 c- TNC
- -- DO- ,- 4' 5
WEIRS F 2 4 5, GENERATOR
Ho- I i S
HI ------, I HG ,
1 0_-_,l 6
ro


- 241.61
DISTANCE IN CM.


FIG. 15 DETECTOR POSITIONING SCHEME









locations employed for these measurements and for the absolute keff

determination by pulsing. Two 1 cu, centrally located Pu-Be sources

were used for these measurements.

The measurements were performed in the following sequence:

a) Unmultiplied counts vs. water level were obtained from a water

level of 20 cm to 91.4 cm above the bottom of the active fuel in steps

of 5 cm.

b) The fuel was loaded in the assembly in the presence of two

centrally located Pu-Be sources, with proper monitoring.

c) Multiplied counts vs. water level were obtained from a water

level of 20 cm in 5 cm steps until an effective multiplication factor

<.99 was reached. This procedure follows the criteria established for

Initial Loading of the assembly, Part 2, Chapter III of this work; the

5 cm steps were more conservative increments than those specified for

the Initial Loading of the assembly.

The results of these measurements are shown in Figs. 16 (A, B).

All the curves were well behaved in the sense that none "nose-dived."

Position 2 and 4 failed to properly describe the multiplication of the

assemblies because of their nearness to the source. Position 1 seems

to overestimate the multiplication, mainly because the unmultiplied

count rate was extremely low at this position thus an apparently high

ratio of multiplied/unmultiplied counts was obtained. A detector more

sensitive to high energy neutrons was used in locations 1 and 6.

It should be noted that when the inverse multiplication is plotted

vs. 1/H2 the predictions become quite linear much earlier than when

plotted versus H. Better predictions are therefore made with the 1/H2

curves but the approach can become less conservative by underestimating




w w







.6


.5 \ R Core
.5
o Position No 1
\ No2
A No 3
.4 \ No 4
SNo 5
.r-
A\ No 6
U\ \ \ o

S3 \\ \
*.3













0
( .2\\ \ < e








--4-
20 30 40 50 60 70 80

Moderator Level (cm)


FIG. 16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL




w


V I


w


Moderator Level (cm)


30.5


4 8 12 16

(1/Moderator Level)2 x 10-4 (cm-2)


FIG. 16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT










the multiplication.

Shown in Table III are the values estimated for keff for the four
eff
locations that seemed to represent the system best. Position 3 gives

a lower limit and Position 1 an upper bound. No attempt was made to

establish the error associated with measured keff but it is believed

that the 0.99 value obtained at the last water level is within +.005

of the true value.


Absolute Determination of keff

After an estimated value of keff >.95 was obtained from the 1/M
eff -
measurements, an independent determination of k was required by the

operating license at every new increment in the moderator level (as

determined by the criteria established in Part 1, Chapter 3). The

technique chosen for this determination was the Garelis-Russellmethod

of measuring kB/W and a simultaneous determination of the prompt funda-

mental decay constant.

Different detector locations were used to determine the influence

of the source and of higher order harmonics contamination. Strong

"spatial effects" were observed in both a and kS/P. This phenomena will

be discussed in detail in Part 2, Chapter V because of its importance.

A seemingly true fundamental decay constant and "spaced-converged"

kB/ were obtained at large distances from the source and were used to

determine the reactivity of the system.

A Fortran IV, IBM 360 computer program named UNIPUL was coded to

perform a unified analysis of the pulsed neutron data (see Appendix B).

The program calculates the decay constant using Peierl's statistical

analysis [18] and kB/k using the Garelis-Russellapproach after the data













TABLE III


SUMMARY OF 1/M AND PULSED MEASUREMENTS


UFSA RI Core
0.5 M/W Ratio
16.35 cm wide reflected core

INVERSE MULTIPLICATION
Moderatora keff
eff


Height (cm) Pos. 1 Pos. 3


PULSED EXP
keffb


Pos. 5 Pos. 6


20 .415 .481 .425

25 .744 .629 .705

30 .867 .737 .824

35 .914 .794 .881

40 .944 .84 .908

45 .9612 .873 .934

50 .973 .895 .950

55 .98 .918 .962

60 .985 .936 .973

65 .9891 .95 .980

70 .9925 .96 .9853

75 .9949 .971 .989

80

85

91.4

Above bottom of active fuel
Averaged from 3 detector positions


.581

.771

.865

.900

.927

.946

.961

.969

.971

.979

.986

.990


.948+.01

.965+.007

.972+.006

.9796+.005

.9855+.004

.990+.003


PREDICTED
keff


.7675

.8287

.871

.9022

.925

.9419

.955

.9655

.974

.980

.986

.9906

.9944

.9976

1.00117









has been resolution time corrected and background subtracted. A "pure"

delayed neutron background is statistically calculated and used to

determine kB/t. The data can be normalized to a reference detector

position for the analysis of the pulse propagation measurements in the

time and in the frequency domain. A Fourier analysis of the pulse can

also be performed if required.

Shown in Fig. 17 (A, B) are the experimentally determined a, kBg/

and k as a function of moderator height obtained by averaging results

from three chosen detector locations in the "asymptotic" region. The

results are summarized, together with the 1/M measurements and theoreti-

cally calculated values in Table III. The excellent agreement between

the experimental and theoretical results should be considered somewhat

fortuitous. The calculations were done following the method outlined

in Appendix A. Some later calculations [19] done by the Phillips

Petroleum Co.,showed more disagreement, especially at low water levels.

The last calculations tried to account for the fact that there is a

fissionable reflector above each experimental moderator height. This

fact was disregarded in the calculational results shown in this work.

The agreement at the 75 cm water level is good for all calculational

methods.


Conclusions

The University of Florida SPERT Assembly has been operated for

several months with very few operational problems. The system has

proven to be extremely reliable and the instrumentation has performed

adequately. The calibration of the system has established that mean-

ingful values for the reactivity can be obtained when applying the













N


R1 Core


N.


N
N


-0


I S I I


i i i I I


0 60 70 r


Moderator Level (cm)


FIG. 17A DECAY CONSTANT vs. MODERATOR LEVEL


w


w


1200


1000 C


800


400 k


200 -


05
5


* g t




w


210 -


I I I


' "I


I I I I I


Moderator Level (cm)


FIG. 17B k8/W AND k vs. MODERATOR LEVEL


w


R1 Core


1.00




0.99




0.98




0.97 ;




0.96




0.95


200 1


190 L


0 o


.J


4=-


/


170 1-


160 1-


~1
d/


150


d


I I









Garelis-Russelltechnique to a reflected slab assembly when proper care

is taken. Agreement between calculated and experimentally determined

values of the reactivity is termed excellent but since only one case

has been studied judgement on the overall applicability of the technique

to this type of reactor configurations should be reserved until the

other assemblies to be studied in the UFSA facility are duly analyzed.

It should be pointed out that multiple detector positions are necessary

to establish when an asymptotic decay constant is obtained, and that the

value of k/ is affected by the input pulse width. As mentioned previ-

ously, a more detailed analysis of the pulsed neutron reactivity meas-

urements is conducted later in this thesis.




































PART 2

SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY




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