• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Previous research on related...
 Design of the uranium tetra-fluoride,...
 Static, one-dimensional, UTVR nuclear...
 Static, two-dimensional, UTVR nuclear...
 Static, three-dimensional neutronic...
 Kinetic equations of a four-boiler...
 Dynamic analysis of a four-boiler...
 Summary of results, conclusions,...
 Appendix A: Description of the...
 Appendix B: Benchmark calculations...
 Appendix C: Description of the...
 Appendix D: Circulating-fuel, coupled...
 References
 Biographical sketch














Title: Static and dynamic neutronic analysis of the uranium tetra-fluoride, ultrahigh temperature, vapor core reactor system /
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Permanent Link: http://ufdc.ufl.edu/UF00097389/00001
 Material Information
Title: Static and dynamic neutronic analysis of the uranium tetra-fluoride, ultrahigh temperature, vapor core reactor system /
Physical Description: xx, 372 leaves : ill. ; 29 cm.
Language: English
Creator: Kahook, Samer Dakhlallah, 1961-
Publication Date: 1991
Copyright Date: 1991
 Subjects
Subject: Nuclear Engineering Sciences thesis Ph. D
Dissertations, Academic -- Nuclear Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1991.
Bibliography: Includes bibliographical references (leaves 366-370)
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Samer Dakhlallah Kahook.
 Record Information
Bibliographic ID: UF00097389
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001689207
oclc - 25138701
notis - AJA1243

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Table of Contents
    Title Page
        Page i
        Page i-a
    Dedication
        Page ii
    Acknowledgement
        Page iii
        Page iv
    Table of Contents
        Page v
        Page vi
        Page vii
        Page viii
        Page ix
    List of Tables
        Page x
        Page xi
        Page xii
        Page xiii
    List of Figures
        Page xiv
        Page xv
        Page xvi
        Page xvii
    Abstract
        Page xviii
        Page xix
        Page xx
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Previous research on related concepts
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
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    Design of the uranium tetra-fluoride, ultrahigh temperature vapor core reactor
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    Static, one-dimensional, UTVR nuclear characterization and configuration optimization
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    Static, two-dimensional, UTVR nuclear characterization and configuration optimization
        Page 94
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    Static, three-dimensional neutronic analysis of the UTVR
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    Kinetic equations of a four-boiler column UTVR system
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    Dynamic analysis of a four-boiler column UTVR
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    Summary of results, conclusions, and recommendations for further research
        Page 300
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    Appendix A: Description of the computer codes
        Page 309
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    Appendix B: Benchmark calculations of XSDRNPM and dot-4 with MCNP
        Page 320
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    Appendix C: Description of the isolator of secondary coupling effects code
        Page 331
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    Appendix D: Circulating-fuel, coupled core point reactor kinetics equation
        Page 345
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    References
        Page 366
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    Biographical sketch
        Page 371
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Full Text









STATIC AND DYNAMIC NEUTRONIC ANALYSIS
OF THE URANIUM TETRA-FLUORIDE, ULTRAHIGH
TEMPERATURE, VAPOR CORE REACTOR SYSTEM















By

SAMER DAKHLALLAH KAHOOK


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

UNIVERSITY OF FLORIDA


1991
























Dedicated to

my parents,

Mr. and Mrs.

Dakhlallah Kahook,

asking Allah

to reward them,

have mercy on them,

and grant them paradise

as they raised and cherished me in my childhood.













ACKNOWLEDGEMENTS


The author would like to express his appreciation and sincere

thanks to the members of his supervisory committee, Dr. Edward T. Dugan,

Dr. Nils J. Diaz, Dr. Alan M. Jacobs, Dr. Samim Anghaie, Dr. William E.

Lear, Jr., and Dr. Willis B. Person for their guidance and assistance

during the course of this research.

Special thanks are extended to Dr. Dugan, chairman of the author's

supervisory committee for his patience and enduring support. The author

recognizes that much of his knowledge in reactor physics and computer

programming was realized while researching under the guidance and

direction of Dr. Dugan.

Support for this research has been provided, in part, by the Air

Force Wright Aeronautical Laboratories (AFWAL), the Frederick Hauck

Fund, and the University of Florida. The AFWAL work was performed for

the Innovative Science and Technology Directorate of the Strategic

Defense Initiative within the Innovative Nuclear Space Power Institute

(INSPI). This support is greatly appreciated.

Funding for the computer analysis was provided for by the National

Science Foundation at the San Diego Supercomputer Center and the

University of Florida and the International Business Machines (IBM)

Corporation through their Research Computing Initiative at the North

East Regional Data Center. The author is grateful for these funds.


iii







Thanks are also due to the fellow students whose friendships,

comments, and encouragements have also facilitated in this research.

The author would like to express his love and respect to his

parents Mr. and Mrs. Dakhlallah Kahook, to his brothers Nofal and

Mohammed, and to his sisters for their love, understanding, and patience

throughout the author's stay at the University of Florida. The

financial support provided to the author by his family is gratefully

acknowledged.

Finally, the author would like to express his love and deepest

appreciation to his wife, Layali, whose understanding, patience, and

support provided the motivation needed to finish this research.













TABLE OF CONTENTS
Page

ACKNOWLEDGEMENTS .... ............................................ iii

LIST OF TABLES.................................................. x

LIST OF FIGURES ................................................... xiv

ABSTRACT........................................................ xviii

CHAPTER

I INTRODUCTION................................................ 1

Introduction ........................................... 1
Description of the Ultrahigh Temperature Vapor Core
Reactor.... ........................................ 2
Dissertation Objectives ................................ 6
Dissertation Organization............................... 7

II PREVIOUS RESEARCH ON RELATED CONCEPTS........................ 11

Introduction .......................................... 11
Previous Research on Gas Core Reactors................... 12
Previous Research on Coupled Core Reactors............... 13
Previous Research on Circulating Fuel Reactors............ 14
Remarks............................................... 18

III DESIGN OF THE URANIUM TETRA-FLUORIDE, ULTRAHIGH
TEMPERATURE VAPOR CORE REACTOR .......................... 19

Introduction.. ........................................ 19
Preliminary Design Considerations........................ 20
Choice of Materials................................... 21
The Moderator-Reflector Material...................... 21
The Fissioning Fuel Material ......................... 24
The Working Fluid Material...... .................... 29
Description of a Uranium Tetra-Fluoride, UTVR/Disk
MHD-Rankine Power Cycle.............. ............... 29
Neutronic Analysis of the Ultrahigh Temperature Vapor
Core Reactor......................................... 37
Static Neutronic Calculations......................... 37
Dynamic Neutronic Calculations........................ 39









IV STATIC, ONE-DIMENSIONAL, UTVR NUCLEAR CHARACTERIZATION
AND CONFIGURATION OPTIMIZATION .......................... 40

Introduction ........................................... 40
Scoping Calculations.............. .. .................. 43
Geometric Variations.................................. 43
UTVC radius....................................... 43
Inner BeO moderator-reflector region thickness..... 50
Outer BeO moderator-reflector region thickness..... 55
UF4 boiler region thickness....................... 57
UF boiler core volume............................. 59
Fuel Density Variations.............................. 61
UF4 partial pressure and mole fraction (UF4:NaF)
2. in the UTVC ............................. ...... 61
U23 enrichment in UF,............................. 62
U23 as the fissile i otope....................... 62
Average density of the UF4 in the boiler region.... 66
Material Variations.......................... ...... 68
Choice of metal fluoride in UTVC................... 68
Wall cooling region..................... ......... 70
Other metal fluoride working fluids................ 70
NaF mass flow rate to the boiler region............. 73
UF /NaF inlet velocity to the boiler............... 76
Addition of Li F poison to the boiler.............. 76
BeO in the annular boiler region................... 79
Reactivity effects of liner materials.............. 81
One-Dimensional Results................................. 84
The Neutron Multiplication Factor..................... 86
Power Sharing Factor.................................. 87
Spherical "Mock-up" Comments ............................ 90

V STATIC, TWO-DIMENSIONAL, UTVR NUCLEAR CHARACTERIZATION
AND CONFIGURATION OPTIMIZATION .......................... 94

Introduction .......................................... 94
Scoping Calculations in R-0 Geometry..................... 96
Geometric Variations.. .............................. 98
UTVC radius variations............................. 98
Inner BeO moderator-reflector region thickness
variations .................................. 104
Variation in the area of the boiler columns........ 107
Variation in the number of boiler columns.......... 109
Fuel/Working-Fluid Density Variations................. 110
UF4 partial pressure in the UTVC................... 112
Average UF density in the boiler columns.......... 115
Varying the UF4 average density in the UTVC as a
function of the radial distance from the
center line ................................... 116
Scoping Calculations in R-Z Geometry .................... 121
Geometric Variations.. .............................. 124


PaRe


CHAPTER









V MBEO region height................................. 124
(cont.) TBEO region height................................. 129
First OBEO region height............................ 131
Boiler: subcooled and saturated liquid region
height ...................................... 134
Material Variation.................................... 136
Poisoning the boiler feedline walls................ 136
Comments on Power Sharing ............................ 140
Two-Dimensional Results................................. 144
The Neutron Multiplication Factor.................... 144
The Power Sharing Factor............................. 146
Remarks.............................................. 148

VI STATIC, THREE-DIMENSIONAL NEUTRONIC ANALYSIS OF THE UTVR.... 151

Introduction .. ......................................... 151
Description of the UTVR Geometry in MCNP................. 152
Description of the Boiler Column...................... 156
Reactivity Worths of the Boiler Feedlines, UTVC Inlet
Plenums, and the MHD Duct Regions..................... 158
Reducing the Uncertainty in Parameters Associated with
the Boiler Columns in MCNP Calculations............... 161
Performance of Variance-Reduction Techniques.......... 165
Nuclear and Physical Characteristics of the UTVR...... 166
Energy Cutoff........... ................... ........ 168
Implicit Capture and Weight Cutoff.................... 168
Weight Windows.................................... 173
Boiler-to-UTVC Symmetry.............................. 178
Neut ~o Transport Coupling Coefficients.................. 185
Obtained Directly from MCNP...................... 187
f i Obtained Indirectly from MCNP.................... 189
Isolation of secondary coupling effets...... ..... 190
Neutron Multiplicatign Factor of the j Core, keff... 197
Reactivity of the j Core, p ... ................... 198
Prompt Neutron Generation Time, A (t)................ 198
Results of Density Variations in the UTVC and Boiler
Columns............................................ 199

VII KINETIC EQUATIONS OF A FOUR-BOILER COLUMN UTVR SYSTEM....... 209

Introduction .. ......................................... 209
The Four-Boiler Column UTVR System Coupled Core Point
Reactor Kinetics Equations ........................... 209
Core-to-Core Fuel-Flow Coupling....................... 211
Core-to-Core Neutron Transport Coupling............... 214
Steady-State Solution ................................ 218
The Linearized UTVR CC-PRK Equations.................. 221
Inherent Reactivity Feedbacks of the UTVR............... 229
Reactivity Feedback of the Boiler Columns, 6p (t)..... 233
Reactivity Feedback of the UTVC, Sp (t)............... 251


vii


CHAPTER


Page









VIII DYNAMIC ANALYSIS OF THE UTVR............................... 264

Introduction .. ......................................... 264
The Unperturbed UTVR Configuration....................... 265
Results of the Dynamic Analysis ......................... 269
Boiler Column Reactivity Perturbation................. 269
UTVC Reactivity Perturbation ......................... 276
Variations in Core-to-Core Direct Neutron Transport
Delay Times...................................... 283
Variations in the Coupling Coefficients............... 287
Variations in the UTVC Fuel Mass Reactivity Feedback
Coefficient....................................... 291
Concluding Remark................................ ....... 296

IX SUMMARY OF RESULTS, CONCLUSIONS, AND RECOMMENDATIONS
FOR FURTHER RESEARCH... ................................ 300

Introduction .. ......................................... 300
Summary of Results...................................... 300
Results from the Static Neutronic Analysis............ 300
Results from the Dynamic Neutronic Analysis........... 302
Comments and Conclusions............................... 303
Recommendations for Further Research..................... 305
Static Neutronic Analysis ............................ 305
Dynamic Neutronic Analysis ........................... 307

APPENDICES

A DESCRIPTION OF THE COMPUTER CODES .......................... 309

Introduction .. ......................................... 309
Description of Nuclear Codes ............................ 309
AMPX: A Modular Code System for Generating Coupled
Multigroup Neutron-Gamma Libraries from ENDF/B..... 309
The AMPX-DRIVER module ............................... 311
The XLACS module................................... 311
The NITAWL module................................. 312
The XSDRNPM module ................................ 312
DOT-4: A One- and Two-Dimensional Neutron/Photon
Transport Code....... .............................. 315
GIP................................................ 316
MCNP-A General Monte Carlo Code for Neutron and
Photon Transport................................ 317
Description of the EASY5 Engineering Analysis Program.... 318

B BENCHMARK CALCULATIONS OF XSDRNPM AND DOT-4 WITH MCNP....... 320

Comparison of XSDRNPM with MCNP ......................... 320
Comparison of DOT-4 with MCNP............................ 324
Conclusion .. ........................................... 329


viii


CHAPTER


Paqe







APPENDICES Page

C DESCRIPTION OF THE ISOLATOR OF SECONDARY COUPLING
EFFECTS CODE......................................... 331

Introduction .. ......................................... 331
Description of the ISCE Code............................ 331
The MAIN Module.................................. .. 331
The REED Module...................................... 332
The ERIN Module..................................... 332
The NOUT Module............................... ...... 333
The ESTM Module.................................. .. 333
The RITE Module ................................... .. 337
Input Data Format ..................................... 337
Input Data File ..................................... 337
List of Input Data Files.............................. 339
Comparison of Results Obtained from ISCE with Results
Obtained Directly from MCNP .......................... 340

D CIRCULATING-FUEL, COUPLED CORE POINT REACTOR
KINETICS EQUATIONS....................................... 345

Description and Definition of Symbols, Parameters, and
Terms used in the Circulating-Fuel, Coupled Core
Point Reactor Kinetics Equations...................... 350
Definition of Superscripts and Subscripts............. 350
Definition of Integral P rameters..................... 351
Neutron population, NJ(t).......................... 351
Reactivity, pJ(t)................................. 354
Effective delayed neutron fractio A(t)........... 354
Prompt neutron generation time, A^(t)............. 358
Effective dejlyed neutron precursor concentration
for the i delayed neutron grQu, Ci(t)........ 358
Effective coupling coefficient, i (t)............ 359
Interpretation of Equations (D-1) and (D-4)........... 361
Equation (D-1) ................................... 361
Equation (D-4).................................... 365

LIST OF REFERENCES.............................................. 366

BIOGRAPHICAL SKETCH....... ... ....... ...... .............. ..... 371













LIST OF TABLES


Table Page

3-1 Properties of Selected Metal Fluoride Working Materials..... 30

3-2 200 MW UF /UTVR Power Cycle Therm9dynamic Operating
ChaFacteristics for NaF, KF, Li F, and RbF Working
Fluids.............................................. .. 34

3-3 Energy Balance7Data for 200 MW UF,/UTVR Power Cycle with
NaF, KF, Li F, and RbF Workng Fluids................... 35

3-4 PUTX/PgC as a function of the Metal Fluoride Mass Flow
te- Cb the Boiler Region as Required on the Basis of
Thermodynamic/Flow Considerations ....................... 36

4-1 kfA as a function of Voided UTVC Radius for the UF4/NaF
efankine Cycle System.................................. 48

4-2 kefr as a function of the Liquid UF4 Core Volume for a
Two Region Reactor.................................... 60

4-3 keff as a function of UTVC Radius and Metal Fluoride Type... 69

4-4 kef, as a function of NaF Entrance Velocity and Average
Density in the Wall Cooling Region....................... 72

4-5 kefr as a function of Metal Fluoride Type and Wall
Cooling Region Thickness................................ 74

4-6 k e and P /P as a function of NaF Diverted Flow
Rate toUtlf B9CT1r Region............................... 75

4-7 k f and PUTV/Pol as a function of UF Average Density
end the "ck -bp" Number of Boiler Columns in the
Annular Boiler Region................................. 80

4-8 Reactivity Penalty (6k/k) as a function of UTVC Liner
Material Thickness............................... ... .. 82

4-9 Reactivity Penalty (6k/k) as a function of Boiler Region
Liner Material Thickness .............................. 83

4-10 Reactivity Penalty (6k/k) as a function of Both the UTVC
and Boiler Region Liner Material Thickness............... 85

x







Table Page
5-1 kef and P Tvr/P RO as a function of UTVC Radius for the
'6F /NaFURAiki f0Cycle System in R-O Geometry for a
Four-Boiler and an Eight-Boiler Column UTVR
Configuration ............................................ 101
5-2 kef and P /Pn as a function of the Number of UF4
oiler Clumn Ch R-O Geometry.......................... 111
5-3 UF4 Temperature and Density Profiles in the UTVC as a
function of Radial Distance for a Four-Boiler Column
UTVR Configuration in the R-0 Coordinate System.......... 120
5-4 UTVR Dimensions of the Reference R-Z Cylindrical
Configuration ............................................ 125
5-5 k e, P ITC/Pg p, and P P hl as a function of
hGe -Mo tor-RefpYgei r lifane Separator Slab
Region Height ...................................... 127
5-6 keff, P T /P C and P /nr/Ph le r versus the Top BeO
Mode-ator-Reector Rh H ...................... 130
5-7 kef, P TVP/P r, and PJ as a function of
ethe Frt OW r BeO MggetatoPo sector Region
(OBEO#1) Height ...................................... 132
5-8 k ef, P TVC/PBnL, and P /Pho as a function of
ef he Wj ht b the SubM8 ed adlturated Liquid
Region of the Boiler Column............................. 135
5-9 kf P /P and P P "e as a function of
kef oly Num BRckness sPP un gehe Boiler Feedlines
Region............................................... 138
6-1 Description of UTVR Regions Employed in the Three-
Dimensional MCNP Monte Carlo Calculations................ 155
6-2 Reactivity Worths of the Boiler Feedlines, UTVC Inlet
Plenums, and MHD Duct Regions........................... 159
6-3 Selected UTVR Results from a 30-Minute MCNP Monte Carlo
Analog Calculation Performed on a CRAY X-MP/48
Supercomputer ............................................ 162
6-4 UTVR Fission Rate as a function of Neutron Energy........... 169
6-5 Effect of Employing Energy Cutoff on the UTVC and Boiler
Column FOM Tallies............................. ...... 169







Table Page

6-6 Effect of Employing Implicit Capture and Weight Cutoff on
the UTVC and Boiler Column FOM Tallies................... 171

6-7 Effect of Employing Weight Windows on the UTVC and Boiler
Column FOM Tallies.................................... 175

6-8 Effects of Employing Variance-Reduction Techniques in
MCNP Monte-Carlo Calculations on Uncertainties of
Selected UTVR Parameters............................... 177

6-9 Effects of Employing Variance-Reduction Techniques and
utilizing Boiler-to-UTVC Symmetry in MCNP Monte-Carlo
Calculations on Uncertainties of Selected UTVR
Parameters ............................................... 184

6-10 Integral Kinetics Parameters as a function of the UF4
Partial Pressure in the UTVC .......................... 201

6-11 Integral Kinetics Parameters as a function of Saturated
Liquid Cone Region Height for Two Different H Values.. 203

6-12 Integral Kinetics Parameters as a function of Saturated
Liquid Cone Region Height at UF4 Partial Pressures of
2.5 and 7.5 atm in the UTVC ........................... 204

6-13 Integral Kinetics Parameters as a function of HSUB and HSAT
in Boiler Column at a UF4 Partial Pressure of 5 atm in
the UTVC.................. .......................... 206

6-14 Integral Kinetics Parameters as a function of Vapor Cone
Region Density at a UF4 Partial Pressure of 5 atm in
the UTVC ............................................... 208

8-1 Values of Selected UTVR Parameters at the Initial,
Unperturbed Steady State Condition ...................... 267

8-2 Relevant Properties for the UF Fuel, NaF Working Fluid,
and the UF4/NaF Fuel/Working Fluid Mixture............... 268

8-3 Final Equilibrium Conditions as a Result of $ 1.00 Positive
and Negative Reactivity Step Insertions Imposed on the
Boiler Columns....................................... 278

8-4 Final Equilibrium Conditions as a Result of $ 0.20 Positive
and Negative Reactivity Step Insertions Imposed on the
UTVC................................................. 282

8-5 Final Equilibrium Conditions Following a Positive Step
Reactivity Insertion of $ 0.20 Imposed on the UTVC
with Normal and Reduced Coupling Coefficients............ 289

xii







Table Page

8-6 Final Equilibrium Conditions Following a Positive Step
Reactivity Insertion of $ 0.20 Imposed on the UTVC
with Normal and Reduced UTVC Fuel Loading
Coefficients of Reactivity.............................. 293

B-1 XSDRNPM and MCNP Benchmark Calculations on a Five-Region
Spherical "Mock-up" of the UTVR......................... 322

B-2 DOT-4 and MCNP Benchmark Calculations on the Cylindrical
"Mock-up" of the UTVR in both the R-9 and R-Z
Coordinate Systems..................................... 326

C-1 Comparison of Results obtained from ISCE with Results
obtained Directly using MCNP for Two Different UTVR
Fuel Loadings........................................ 343

D-1 The Six Delayed Neutron Groups Energy Spectra, Decay
Constants, Yied, and Fractions Data for Thermal
Fission in U ......................................... 356


xiii













LIST OF FIGURES


Figure Page

1-1 Side View Schematic of the Ultrahigh Temperature
Vapor Core Reactor...................................... 3

1-2 Top View Schematic of the Ultrahigh Temperature
Vapor Core Reactor...................................... 5

3-1 UF6 and UF4 Saturation Vapor Curves......................... 25

3-2 Uranium Metal and UF4 Saturation Vapor Curves............... 27

3-3 Partial Pressures of Constituent Species of the Uranium-
Fluorine System at One Atmosphere ....................... 28

3-4 Schematic of a 200 MWe UF4/KF UTVR MHD-Rankine Cycle Power
System ................................................. 31

4-1 Four Region, One-Dimensional Spherical "Mock-up" of
the UTVR............................................. 41

4-2 keff and PUTVC/PBCOL as a function of the UTVC Radius....... 45

4-3 kef and Fission Rates of the UTVC and the Boiler as a
function of the UTVC Radius............................. 46

4-4 k and P T/P as a function of the Inner BeO
Moderate r-Ref Ttor Region Thickness..................... 51

4-5 kef as a function of the Inner BeO Moderator-Reflector
Region Thickness........................................ 53
4-6 kefc and PRTVr/Pr as a function of the Outer BeO
Moderate r-RefT~E or Region Thickness..................... 56

4-7 ke and PUT/PRrn as a function of the UF4 Inlet
Velocity t te.Boiler Region....................... 58

4-8 keff and PuTVC/Prni as a function of the UF4 Partial
e Pressure 1in tf UTVC.................................... 63

4-9 k as a function of the U235 Enrichment at Different
eF4 Partial Pressures in the UTVC...................... 64

xiv







Figure Page

4-10 kef as a function of the Fissile Fuel (U235 and U233)
Enrichment ............................................. 65

4-11 kef and PUTv /PBC as a function of the UF4 Average
Density in the Biler Region.............. .............. 67

4-12 Five Region, One-Dimensional Spherical "Mock-up" of the
UTVR................................................. 71

4-13 kef and P v/PR i as a function of the UF4/NaF Inlet
Velocity t 0 tfl Boiler Region............................ 77

4-14 k and P /PC as a function of the Li6F Mass Flow
Rate to tUf B/p r Region............................... 78

5-1 Six Region, Two-Dimensional R-B Representation of a
UTVR with Six-Boiler Columns ............................ 97

5-2 kf and P TVC/PCnL as a function of the UTVC Radius for a
eour- ad n Eht-Boiler Column UTVR Configuration...... 100

5-3 kf and P /P as a function of the Inner BeO
eIoderatTr-Reft or Region Thickness for a Four-
Boiler Column UTVR ........... .......................... 106

5-4 k f and P /PBC as a function of the UF Inlet Velocity
efto the HBYer ion for a Four-Boiler CoTumn............ 108

5-5 kff and PTvr/P o as a function of the UF Partial
Pressure in t ObTVC for a Four-Boiler Cotumn
UTVR System............................................ 113

5-6 kff and P C/PC as a function of the UF4 Average
Density iu the Biler Region for a Six-Boiler Column
UTVR System............................................ 117

5-7 Thermal Neutron Flux and Vapor Fuel Temperature Profile as a
function of Radial Position from the Centerline of the
UTVC for a Four-Boiler Column UTVR System................ 118

5-8 Representation of the UTVR in the R-Z Coordinate System..... 122

5-9 The Horizontal Boiler Configuration of the UTVR in the R-Z
Coordinate System................................. .. .. 143

6-1 Side View Schematic of the Four-Boiler Column UTVR on the
y-z Plane at x=0.0................................... 153

6-2 Side View Schematic of a Boiler Column ..................... 157







Figure Page

6-3 Top View Schematic of a Four-Boiler Column UTVR System...... 180

7-1 Schematic of the Core-to-Core Circulating Fuel Coupling..... 212

7-2 Schematic of Boiler-to-UTVC Neutron Transport Coupling for
a Four-Boiler Column UTVR System........................ 215

7-3 Schematic of Boiler-to-Boiler and UTVC-to-Boiler Neutron
Transport Coupling for a Four-Boiler Column UTVR System.. 217

7-4 Block Diagram of the UTVC Transfer Function................. 228

7-5 Block Diagram of the Boiler Column Transfer Function........ 230

7-6 Block Diagram of the UTVR Transfer Function................. 231

7-7 Fuel/Working Fluid Density Profile in the Boiler Column
due to Boiling in Space (=zero gravity).................. 234

7-8 Side View Schematic of the UTVC............................ 251

8-1 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 1.00 Positive Reactivity Step
Insertion Imposed on the Boiler Columns at t=0 sec....... 270

8-2 UTVC Pressure, U235 Loading, and UF /NaF Inlet and Outlet
Mass Flow Rates, as a function of Time Following a
$ 1.00 Positive Reactivity Step Insertion Imposed on
the Boiler Columns at t=O sec........................... 273

8-3 Boiler Column Outlet Mass Flow Rate and U235 Loading as a
function of Time Following a $ 1.00 Positive Reactivity
Step Insertion Imposed on the Boiler Columns at t=0 sec.. 274

8-4 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 1.00 Negative Reactivity Step
Insertion Imposed on the Boiler Columns at t=0 sec....... 277

8-5 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Positive Reactivity Step
Insertion Imposed on the UTVC at t=0 sec................. 279

8-6 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Negative Reactivity Step
Insertion Imposed on the UTVC at t=0 sec................. 281

8-7 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Positive Reactivity Step
Inqrtion_6 posed on the UTVC at t=0 sec with
t = 10 sec .. .................................... 284

xvi







Figure Page

8-8 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Positive Reactivity Step
Insertion _posed on the UTVC at t=O sec with
7T = 10 sec.................. .................. .. 285
t
8-9 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Positive Reactivity Step
Insertion Imposed on the UTVC at t=O sec with the
Coupling Coefficients Reduced by One Order in Magnitude.. 288

8-10 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Positive Reactivity Step
Insertion Imposed on the UTVC at t-0 sec with the
UTVC Fuel Mass Reactivity Feedback Coefficient Reduced
by a Factor of Five.................................. 292

8-11 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $ 0.20 Positive Reactivity Step
Insertion Imposed on the UTVC at t=0 sec with the
UTVC Fuel Mass Reactivity Feedback Coefficient Increased
by a Factor of Two..................................... 295

A-I Schematic of the Flow between the AMPX System Code Modules.. 314

C-1 Example of the ISCE Code Input Data File.................... 339

C-2 Input Data Files List Format............................... 340

C-3 Output File as obtained from ISCE.......................... 341

D-1 Schematic of Neutrons and Neutron Interactions in the UTVR.. 348

0-2 Top View Schematic of the Plasma Core Assembly (PCA)........ 357

D-3 Probability Distribution function of Delay Times for the
Transport of Neutrons from Core k to Core j.............. 364


xvii













Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

STATIC AND DYNAMIC NEUTRONIC ANALYSIS
OF THE URANIUM TETRA-FLUORIDE, ULTRAHIGH
TEMPERATURE, VAPOR CORE REACTOR SYSTEM

By

Samer Dakhlallah Kahook

May, 1991

Chairman: Dr. Edward T. Dugan
Major Department: Nuclear Engineering Sciences

An Ultrahigh Temperature Vapor core Reactor (UTVR) system is

investigated in this research. The UTVR can be characterized as a

thermal, high power density (hundreds of MWth/m ), externally-moderated,

coupled core, highly-enriched U235, circulating-fuel, steady-state,

burst power reactor. The investigated reactor system includes two types

of fissioning regions: (1) the central Ultrahigh Temperature Vapor Core

region (UTVC) which contains a vapor mixture of highly-enriched uranium

tetrafluoride (UF4) fuel and a metal fluoride working fluid at an

average temperature of =3000 K and an average pressure of =50 atm; and

(2) the Boiler COLumn region (BCOL) which contains highly enriched

liquid UF4 fuel. The combination of three features differentiates the

UTVR from other nuclear reactor concepts. These three features are as

follows:

1. the multi-core configuration resulting in a coupled-core system by

means of direct neutron transport through the media;

xviii







2. the circulating fuel and the associated neutronic and mass flow

coupling between the UTVC and boiler cores; and

3. the employment of a two-phase fissioning fuel, i.e., a liquid-vapor

combination.

Static and dynamic neutronic analysis of this novel system

indicates distinct advantages over other existing or conceptual nuclear

power systems. These include a unique combination of some very

effective inherent negative reactivity feedbacks such as the vapor-fuel

density power coefficient of reactivity, the direct neutronic coupling

among the multiple fissioning core regions, and the mass flow coupling

feedback between the two types of fissioning cores.

Static neutronic analysis is performed using multidimensional

discrete ordinates and Monte Carlo neutron transport codes. Parameters

such as the UTVC and boiler column reactivities and reaction rates,

core-to-core neutronic coupling coefficients, and neutron lifetimes as a

function of vapor core density and boiler core liquid volume are

obtained from the static neutronic analysis.

The dynamic behavior of the UTVR is examined using a non-linear

model, which incorporates circulating-fuel, coupled-core, point reactor

kinetics and energetic equations. These equations are solved using a

system analysis code. The dynamic analysis indicates that the unique

and strong negative reactivity feedbacks of the UTVR are capable of

stabilizing the UTVR safely and quickly even when large reactivity

insertions are imposed (6p = $ 1.00). The analysis also shows that the

system exhibits good dynamic performance even when an inherent negative

reactivity feddback is suppressed (e.g., the vapor fuel density power


xix







coefficient of reactivity). However, due to the strength of the UTVR's

inherent negative reactivity feedbacks, it is found that external

reactivity insertions alone are inadequate for bringing about power

level changes during normal operations. Additional methods of

reactivity control, such as variations in the mass flow rate of the fuel

and/or working fluid or variations in the inlet pressure of the

fuel/working fluid entering the boiler columns, are needed to achieve

the desired power level control.












CHAPTER I
INTRODUCTION

Introduction


The concept of Vapor Core Reactors (VCRs) has emerged at the

University of Florida (UF) as a consequence of extensive theoretical and

experimental studies performed on their predecessors, the Gaseous Core

Reactors (GCRs). Unlike GCRs (where the fuel is supplied to the reactor

in gaseous form), the working fluid and/or fuel undergo a liquid-to-

vapor phase change in VCRs. Studies performed on VCRs and GCRs indicate

that gaseous-fueled (or vapor-fueled) reactor concepts have distinct

advantages over other existing or proposed nuclear power systems. These

advantages include high operating temperatures and efficiency, rapid

startup capabilities, simple geometry, and an assortment of efficient

power control methods [1-9].

The Ultrahigh Temperature Vapor Core Reactor (UTVR)/Disk

Magnetohydrodynamic (MHD) Generator Power System is being studied for

the Strategic Defense Initiative Organization (SDIO) as a possible

source for space power. The SDI space power systems are required to

operate in at least one of the three following power modes:

Station-keeping mode (base load). This mode may be required to

produce up to a few Megawatts electric (MWe) for a period of about 7

years.









Alert mode (enhanced surveillance mode). The power requirements

for this mode range from 10's of MWe up to =100 MWe. The power system
must be capable of functioning for periods of a few hours to a few days.

Burst power mode (defense mode). The power level for this mode

ranges from =100 MWe up to =1 Gigawatt electric (GWe) for operating

times of about 30 minutes; a burst power system must be capable of

achieving this power level in less than 100 seconds.

The UTVR/MHD Generator Power System is a burst power mode concept.

At burst power levels, the UTVR can operate at very high temperatures

which provides an efficient heat rejection capability and a high

thermodynamic efficiency. This and other features appear to make the

UTVR/MHD Generator Power System an exceptional concept for burst power

operations. The UTVR/MHD Generator Power System is the concept examined

in this research.

Description of the Ultrahiqh
Temperature Vapor Core Reactor

The UTVR/Disk MHD Generator Power System is a highly enriched

(>85%), BeO externally-moderated, circulating fuel reactor with uranium

tetra-fluoride (UF4) as the fissioning fuel. The working fluid is in

the form of a metal fluoride such as NaF, KF, RbF, and Li7F. Shown in

Figure 1-1 is a side view schematic of the UTVR.

The UTVR includes two types of fissioning regions: (1) the central

Ultrahigh Temperature Vapor Core regions (UTVC) which contain a vapor
mixture of highly-enriched UF4 and a metal fluoride working fluid at an

average temperature of =3000 K and an average pressure of =50 atm, and

(2) the boiler column regions (BCOL) which contain highly enriched UF4









TBEO


.. ....... :y.. WallI
.. ... ..-1- Cool ant
'i ^iiiiiiii~ii!!~ i\'''i.'-







...- Rejection
... .System
::: :.:.: . ...- ......... DOB E O







MHD Duct
V, po r *^I BEO ^ ... To Heat

Region
I BED



p. .i.-i. i;^ Boiler
S. ... ...... -.... Column
. . ... .: '.. r. .." ,






Figure 1-1. Side View Schematic of the Ultrahigh Temperature
Vapor Core Reactor









fuel. This reactor has symmetry about the midplane with identical top

and bottom vapor core and boiler column regions separated by a BeO slab

(mid-plane BeO Region MBEO) and the MHD ducts where power is extracted.

The UTVC is surrounded in the radial direction by the wall cooling

region. The wall cooling region contains a subcooled liquid metal

fluoride. By tangentially injecting the metal fluoride into the UTVC,

the UTVC walls are maintained at the desired low temperatures (=2000 K).

As the metal fluoride is injected into the UTVC, an annular buffer zone

is obtained which aids in maintaining the UF4 away from the UTVC walls.

This reduces the possibility of condensation of uranium or uranium

compounds on the UTVC walls. Beyond this buffer zone, the metal

fluoride vaporizes and mixes with the UF4 in the UTVC.

The UF4 is vaporized in the boiler columns prior to its entrance to

the UTVC. The boiler region, which includes a number of boiler columns,

is connected to the UTVC via the UTVC inlet plenums, as shown in Figure

1-1. The UF4 liquid is supplied to the boiler columns by means of

feedlines. Each boiler column consists of three distinct regions: the

subcooled liquid region, the saturated liquid-vapor region, and the

superheated vapor region.

Shown in Figure 1-2 is a top view schematic of the UTVR. Figure 1-

2 shows three distinct BeO regions: the inner BeO region (IBEO) which

separates the UTVC walls from the boiler columns in the radial

direction, the annular boiler BeO region (BBEO) with a radial thickness

equal to the diameter of the boiler columns, and the outer BeO region

(OBEO) surrounding the boiler columns and the BBEO region. Three other

BeO regions are shown in Figure 1-1. These are the mid-plane BeO region









OBEO


Figure 1-2. Top View Schematic of the Ultrahigh Temperature
Vapor Core Reactor









(MBEO) mentioned previously, the lower BeO region (LBEO) separating the
boiler feedlines from the MHD duct, and the top BeO region (TBEO) above

the UTVC.

Use of the UF4 as the vapor fuel and metal fluorides as the working

fluid in the UTVR/MHD Generator Power System allows for operation on a

direct, closed Rankine type cycle and leads to space power systems with

high efficiency (=20%), small radiator size (=5 m2/MWe), and high

specific power (=5 kwe/kg). A description of an example UF4-Metal

Fluoride UTVR/MHD Generator Rankine Cycle Power System is furnished in

Chapter III.

Dissertation Objectives

A goal of this research is the nuclear design and analysis of the

UF4-Metal Fluoride UTVR/MHD Generator Rankine Cycle Power System for
space power applications. Complete characterization of this innovative

system requires an integrated and thorough investigation of its

neutronic, heat transfer, and mass flow behavior. Although this

research focuses on the nuclear aspects of the proposed system, it

incorporates results from auxiliary and supporting thermodynamic, heat

transfer, and fluid flow calculations, thus, assuring a reliable and

integrated nuclear analysis.

The nuclear design of the UTVR incorporates results from the static
and dynamic neutronic analysis performed on the UTVR. The static

neutronic analysis establishes basic neutronic characteristics and

obtains reference reactor configurations that are optimized for the

static neutronic characteristics while also considering other important









parameters like specific power (kw/kg) for the UTVR. Applicable UTVR

parameters that are needed for the dynamic neutronic studies such as

reactivity, neutron generation time, and core-to-core coupling

coefficients are also obtained from the static analysis.

The dynamic neutronic analysis focuses on characterizing the UTVR

with respect to stability and dynamic response. Effects of core-to-core

neutronic coupling (by means of direct neutron transport through the

media and by delayed neutron emission from the decay of the delayed

neutron precursors which are carried in the fuel that circulates between

the UTVC and boiler columns) and effects of other important reactivity

feedback phenomena such as fuel density and mass flow related feedback

for the vapor and boiler cores are included in the dynamic analysis.

Thus, the primary objective of this research is the development and

application of the methods and the models needed for the nuclear design

and analysis of this unique reactor concept.

It is recognized that acoustic phenomena are inherent to the UTVR

and their effects are potentially very significant. However, acoustic

effects are not included in this research and are recommended for future

work when the necessary tools for treating these effects are available.

Recommended future work will require coupled space-time neutron field-

gas density field calculations.

Dissertation Organization


A brief summary of previous work performed on related reactor

concepts such as gas core reactors, coupled core reactors, and

circulating fuel reactors is presented in Chapter II.









A section addressing preliminary design considerations for the UF4

UTVR reactor system is presented in Chapter III. It includes point

design conditions for the UTVR from preliminary thermodynamic, heat

transfer, and fluid flow calculations. A description of an example UF4-

Metal Fluoride UTVR/MHD Generator Rankine Cycle Power System is also

presented in Chapter III. A section in Chapter III discusses the plan

used in the nuclear design and analysis of the UTVR system.

The results of the static one- and two-dimensional neutronic

calculations are presented in Chapters IV and V, respectively. These

calculations are performed with XSDRNPM [10], a one-dimensional discrete

ordinates (Sn) neutron transport code, and with DOT-4 [11], a one- and
two-dimensional Sn neutron transport code. The static analysis examines

effects of variations in geometry and fuel/working fluid loadings on the

neutron multiplication factor (keff) and power sharing factor (i.e.,

power distribution between the UTVC and the UF4 boiler columns,

PUTVC/PBCOL) Basic neutronic characteristics of the UTVR such as fuel
density reactivity coefficients, optimum BeO region thicknesses, optimum
number of UF4 boiler columns, and a reference UTVR configuration for

three-dimensional analysis are obtained from the static neutronic

analysis results presented in Chapters IV and V.

The results obtained from static three-dimensional neutronic

calculations are presented in Chapter VI. These calculations are

performed using MCNP [12], a three-dimensional Monte Carlo neutron

transport code. Parameters such as UTVC and boiler core reactivities

and reaction rates, core-to-core coupling coefficients, and neutron

lifetimes as a function of vapor core density and boiler core liquid









volume are obtained from the results of calculations performed with

MCNP. The methods and models used in obtaining the core-to-core neutron

transport coupling coefficients and the reactivities of the vapor and

boiler cores are derived and described in Chapter VI.

The circulating-fuel, coupled core, point reactor kinetics

equations for a four-boiler column UTVR are derived in Chapter VII. A

section in Chapter VII contains a detailed discussion of significant

UTVR inherent reactivity feedbacks such as the vapor fuel density

feedback of the UTVC and the liquid fuel/working fluid volume feedback

of the boiler region. Energetics equations relating the power levels

and the neutron population levels of the vapor and boiler cores to

fuel/working fluid temperature, density, and liquid volume and flow

rates are also included in Chapter VII.

The dynamic neutronic analysis and performance studies are included

in Chapter VIII. The dynamic analysis examines the behavior of core

power levels, reactivities, fuel densities, and total system power

during full power transients. Effects of the core-to-core circulating

fuel and neutron transport coupling and fuel density variations in the

vapor core and boiler cores are included in the dynamic analysis.

The conclusions obtained from this research are included in Chapter

IX. Suggestions and recommendations are made for further research which

are needed before the technical feasibility of the UTVR/MHD Generator

Power System can be realized.

A brief description of the nuclear and system analysis computer

codes used in this research is presented in Appendix A. Appendix B

contains the results of benchmark calculations performed with XSDRNPM









and MCNP on a reference UTVR in spherical coordinates. Results from

benchmark calculations performed in R-8 and R-Z cylindrical coordinates

with DOT-4 and MCNP are also included in Appendix B. A description of

the Isolator of Secondary Coupling Effects (ISCE) code is presented in

Appendix C. The ISCE code, a special code developed as a part of this

research, incorporates the models derived in Chapter VI with results

obtained from the MCNP code to obtain parameters needed for the dynamic

analysis and performance studies such as core-to-core neutron transport

coupling coefficients and the reactivities of the UTVC and boiler cores.

Appendix D contains a description of the circulating fuel, coupled core,

point reactor kinetics equations.












CHAPTER II
PREVIOUS RESEARCH ON RELATED CONCEPTS

Introduction

The UTVR can be characterized as a thermal, high power density

(hundreds of MWth/m3), externally-moderated, coupled-core (vapor and

boiling cores), highly-enriched, U235 circulating fuel, steady state

reactor. The combination of three features differentiates the UTVR from

other nuclear reactor concepts. These features are the following:

1. The multi-core configuration resulting in a coupled-core system by

means of direct neutron transport through the media.

2. The circulating fuel and the associated neutronic and mass flow

coupling between the UTVC and boiler cores. This feature provides

additional neutronic coupling between the cores by means of delayed

neutron emission from the decay of the delayed neutron precursors

which are carried in the fuel/working fluid mixture. The mass flow

coupling between the vapor and boiler cores is an inherently

stabilizing phenomenon. For example, an increase in the power level

of the boiler core increases the voiding and decreases the density of

the fuel/working fluid mixture in the boiler core. This leads to a

decrease in the boiler core power level. Additionally, the density

of the fuel/working fluid exiting the boiler core and entering the

vapor core decreases. This causes a decrease in the reactivity of

the vapor core resulting in a decrease in the vapor core power level.

11









The decrease in the vapor core power level causes a decrease in the

number of neutrons directly transported to the boiler cores through

the media and a decrease in the delayed neutron precursor

concentration decaying in the boiler cores. This causes a further

decrease in the boiler core power level.

3. The employment of a two-phase fissioning fuel, i.e., a liquid-vapor

combination.

Studies on reactors combining all three of these key features have

never been reported. However, studies and research pertaining to

coupled-core reactors, circulating fuel reactors, or gaseous (vapor)

core reactors have been reported. Therefore, the following sections of

this chapter briefly summarize previous research on reactors that

possess one of these key features or aspects of the UTVR.

Previous Research on Gas Core Reactors


Research on gas core reactors has been reported as early as 1955 by

George Bell [13]. The reactors examined by Bell employed gaseous UF6

fuel and beryllium (Be), D20, and graphite reflectors in spherically

symmetric geometries. The analysis was done using age theory to

describe neutron slowing down in the moderator-reflector region and

diffusion theory to describe neutron diffusion into the core and the

fissions in the core. The reactor was considered to be strictly a

thermal reactor.

Since then, different analytical methods and models have been used

in studying this and other gas core reactor concepts. This includes the

Nuclear Piston Engine and Pulsed Gaseous Core Reactor Power Systems









examined by E.T. Dugan [2] and the Heterogeneous Gas Core Reactor

examined by K.I. Han [5]. Summaries of previous work on gas core

reactors can be found in the studies reported by Dugan and Han.

Previous Research on Coupled Core Reactors

The initial work on the kinetics of coupled core reactors was

reported in 1958 by Robert Avery [14]. Avery investigated the dynamic

characteristics of coupled fast-thermal breeder reactors. The analysis

incorporates the point reactor kinetics equations for each core. The

equations include terms accounting for the neutronic interaction

(coupling) between the cores. The coupling terms along with integral

parameters used in the point reactor kinetics equations are obtained

from steady state analysis of the interacting cores.

Neutron kinetics studies using the coupled core treatment have been

applied to nuclear reactor systems other than fast-thermal reactors.

These include modular cores of large thermal power reactors, clustered

reactors, and Argonaut-type reactors. Research has also been performed

on coupled gas core reactors. This includes the work performed by M.M.

Panicker [6] on the Coupled Multiple Chamber Gaseous Core Reactor Power

System.

The differences in the various approaches used in the analysis of

coupled core reactor systems lie in the choice of the weighting function

(neutron flux, importance function, or average fission density); the

choice of suitable phase-space regions for the averaging process; and

the selection of how to incorporate the coupling effects (e.g., as a

source term or reactivity effect) into the pertinent dynamic neutronics









equations. Detailed discussions of these differences and their

applications to various reactor systems are reported by Adler et al.

[15] and Panicker [6].

Previous Research on Circulating Fuel Reactors


The kinetics of circulating fuel reactors is affected by the loss

of a fraction of delayed neutrons due to the decay of the delayed

neutron precursors outside the core. The fraction of delayed neutrons

that is lost depends mainly on the time the fuel spends in the core

relative to the time the fuel remains outside the core. Various methods

have been used in approximating the effects of circulating fuel.

The impact of various methods used for approximating the effect of

circulating fuel on the kinetics of nuclear reactors has been

investigated by John MacPhee [16]. In comparing the approximate

methods, MacPhee employed an "exact" model ("exact" with respect to the

method of treating the effect of the circulating fuel on the delayed

neutrons). The "exact" model employed the following assumptions:

1. Point reactor kinetics equations are valid in the sense that the

reactor kinetics effects are considered to be spatially independent.

2. Reactor power level is low enough such that the effect of neglecting

reactivity feedback due to temperature and radiolytic gas formation

is valid.

3. One delayed neutron group is used.

4. Perfect mixing in the core vessel occurs.

5. Fission occurs only in the core.

6. Fuel mass flow rate is constant.









The reactor kinetic equations employed in the "exact" model are

dN(t) p(t) N(t) + C(t) (2-1)
dt A

d(t) N(t) (t) + e- (2-2)
dt A Tc Tc
where

N(t) = neutron population level in the core at time t;

p(t) = core reactivity at time t;
P = fraction of delayed neutrons;

A = prompt neutron generation time;
A average decay constant of delayed neutrons;
t = delayed neutron precursor concentration;

7c time fuel remains in the core;

7T = time fuel spends in the loop outside the core.

Equation (2-1) describes the time dependent behavior of the neutron

population level and Equation (2-2) describes the time dependent

variation of the concentration of the delayed neutron precursors. The

effect of the circulating fuel is accounted for in the last two terms in

Equation (2-2).

MacPhee compared two approximate methods with the "exact" model.

In the approximate methods, modified versions of Equation (2-2) are

employed. The first method employs reduced values for # as shown by

dC(t)_ f N(t) C(t) (2-3)
dt A

where f is the fraction of delayed neutrons lost as a result of the fuel

circulating and is given by









7C
f = (2-4)
Tc + Tj


The second method neglects the delay time associated with the

delayed neutron precursors re-entering the core, i.e., C(t-T,) = C(t).

With this assumption, the equation describing the delayed neutron

precursors concentration is

dC(t) = N(t) - C(t) (2-5)
dt A aD

where aD is the delayed neutron attenuation factor, obtained from steady

state conditions imposed on Equation (2-2), and is given by

rTc
aD = -T (2-6)
XTc + 1 e

MacPhee analyzed the "exact" model by linearizing Equations (2-1)

and (2-2), taking the Laplace transform of the linearized equations, and

computing the frequency response of the linear system. The results of

MacPhee's investigation and comparisons include the following

conclusions:

1. The frequency response of the "exact" model predicts a peak when fast

reactivity changes are introduced. The approximate methods do not

predict the peaking found by the "exact" model. Thus, for fast

reactivity changes the approximate methods are not valid.

2. Although the frequency response indicates peaking, circulating fuel

reactors do not exhibit self-sustained oscillations as a result of

the feedback produced by the delayed neutron precursors re-entering

the core, i.e., the peaking is finite.









The peaking is due to the coupling of the delayed neutron decay

constants with the loop circulation period and occurs for small values

of aD. The reason the peaking is finite is because aD is greater than

zero for all practical reactor configurations. Equation (2-6) indicates

that aD approaches unity as rT approaches zero for all values of T ,

i.e., all delayed neutrons are emitted in the core. However, as 7T

approaches infinity (fuel does not re-enter core), aD approaches zero if

and only if Tc approaches zero such that no delayed neutrons are emitted

in the core. For such cases, the velocity of the fuel in the core is

required to be infinite and an infinite amount of fuel is required to

maintain the reactor critical. Since aD is always larger than zero, the

peaking is therefore finite.

It should be noted that an inherent assumption in MacPhee's

analysis is that the employed fuel is incompressible. Thus, some of

these conclusions do not pertain to the UTVR.

M.A. Schultz [17] indicates that a number of smaller peaks would

occur in the frequency response of circulating fuel reactors if more

than one delayed neutron group is included in MacPhee's "exact" model.

The fact that the mixing of the circulating fuel in the external loop of

an actual reactor will smooth over the peaks and reduce any tendency

toward sustained oscillations is pointed out by Schultz.

The effect of fuel temperature reactivity feedback in circulating

fuel reactors has been investigated by W.K. Ergen [18]. The analysis

indicates damped power oscillations for circulating fuel reactors occurs

with negative fuel temperature feedback. Ergen also concludes that the

decrease in damping of oscillations due to the loss of delayed neutrons








18

is compensated to some extent by the damping effect caused by the

circulation itself.

Remarks


In deriving the models needed to analyze the UTVR/MHD Generator

Power System (see Chapters VI and VII and Appendix D), references to

previous work are also made. Where applicable, modifications to and

comparisons with previous models are indicated.












CHAPTER III
DESIGN OF THE URANIUM TETRA-FLUORIDE,
ULTRAHIGH TEMPERATURE VAPOR CORE REACTOR

Introduction

In the design of nuclear power reactors, the choice of materials

for fuel, moderator, coolant/working fluid, and structure and the

selection of the power extraction system are based on the application

and the required performance of these reactors. Once the appropriate

materials and a suitable power extraction system are selected, a

reference reactor configuration can be chosen. Then, a complete

characterization of the reference reactor power system is required to

determine its overall performance and feasibility.

Although this research focuses on the nuclear aspects of the UTVR,

a section in this chapter addresses preliminary design considerations

that led to the reference UTVR configuration. Another section in this

chapter discusses considerations involved in the materials selection for

the UTVR. A detailed description of an example UF4-Metal fluoride

UTVR/MHD Generator Rankine Cycle Power System is also given. This is

followed by a section discussing the plan followed in this research for

the neutronic analysis of the UTVR system.









Preliminary Design Considerations

Since the UTVR is being developed for SDI's Burst Power Mode for

space power applications, the following issues need be realized:

1. The size and mass of the power system are important constraints.

This is due to the following: (a) the expense and logistics involved

in the deployment of the power system into space, (b) the need to

constantly maneuver and relocate the defense system, and (c) the need

for defense systems to be inconspicuous.

2. The required power level for this system ranges from =100 MWe up to

=1 GWe for operating times of =30 minutes. Such power levels when

considered with the size requirement demand a high power density

system.

3. The system is required to achieve the Burst Power Mode in less than

100 seconds. Thus, the system needs to be designed to withstand

thermal stresses and shocks caused by a rapid transition from the

alert mode.

4. The power system is required to be able to operate during a seven

year period. This requires the power system to be tested

periodically; thus, the system needs to be designed to operate at

full power for a total time of about three hours (assuming two-annual

tests during the seven-year period lasting about ten minutes each

plus the 30 consecutive minutes of operation).

5. The system needs to be operated at high temperatures to provide

compact radiators for heat rejection in space and high power cycle

efficiency.







21

The above issues are the primary considerations applied during the

preliminary design of the UTVR.

Choice of Materials

The UTVR is a BeO externally-moderated, circulating fuel reactor

with UF4 as the fissioning fuel and a metal-fluoride working fluid.

Research is being conducted to select and develop suitable structural

materials that are compatible with the fluoride fuel/working fluid

mixture and the high temperature environment of the UTVR. The choice of

BeO as the moderator-reflector material, UF4 as the fuel, and metal

fluoride as the working fluid is based on the following considerations.

The Moderator-Reflector Material

For thermal reactors, moderator-reflector materials used in nuclear

reactors have low mass numbers and relatively large scattering and

relatively small absorption cross sections. Moderators used in nuclear

reactors include ordinary water (H20), heavy water (D20), beryllium (Be)

or beryllium-oxide (BeO), and graphite. The choice depends largely on

the intended application of the reactor system; and on the nuclear,

mechanical, physical, and chemical properties; and the cost of the

moderator material. Since the size and mass of the power system are

significant constraints, and since high temperatures are needed for

efficient heat rejection in space, the moderator-reflector material is

required to have a high melting temperature (or high boiling temperature

if a liquid moderator is used) and relatively good neutronic properties

(high slowing-down power and small capture cross section for neutrons).







22

For space power reactors, beryllium or BeO is superior to graphite

as a moderator and reflector material from a neutronics standpoint. In

the study of Highly Enriched Heterogeneous Gas Core Reactors (HGCRs),

S.D. Kahook [7] has shown that the use of Be as the moderator and

reflector material provides a higher reactivity (=30% Sk/k) than

graphite (total size of the HGCR was fixed). This is mainly due to the

higher slowing-down power (exls = average logarithmic energy loss per

collision x macroscopic scattering cross section) of 16 m-I for Be

versus 6.5 m-1 for graphite [19] and the (n,2n) reaction of Be. Another

drawback of graphite is its larger thermal diffusion length, LT, (=54 cm
versus =21 cm) and its larger slowing-down length, TT, (=192 cm versus

=100 cm) compared to Be. The larger values of LT and TT require

graphite-moderated reactors to have a larger size compared to beryllium-

moderated reactors, an important design criterion for the space power

system under investigation. Although the melting temperature of

graphite is higher then that of BeO (=4000 K versus =2800 K), BeO is a

better choice than graphite for the power system under investigation.

The drawback of the lower melting temperature of BeO can be compensated

for by the use of auxiliary coolant channels in the moderator-reflector

regions to maintain BeO at safe operating temperatures (=1600 K to =2000

K). Also, due to the low heat conductivity of the vapor fuel and the

fact that the fuel is the working fluid (most of the energy generated is

directly deposited in and removed by the fuel/working fluid mixture),

the temperature of moderator-reflector regions can be considerably

cooler then the temperature of the vapor fuel.







23

E.T. Dugan [2] examined the effect of using H20, D20, Be, BeO, and

graphite as moderator-reflector materials for the Nuclear Piston Engine

which employed an externally-moderated UF6-fueled gas core reactor for

terrestrial power generation. The study indicates that the use of H20

and graphite results in relatively low keff values. This is due to the

relatively high thermal absorption cross section of H20 and high LT and

TT of graphite. However, the large slowing-down power as well as the
(n,2n) reaction of Be and the small thermal absorption cross section of

D20, cause Be, BeO, and D20 to be excellent choices for moderator-

reflector materials as proven by Dugan.

The relatively large LT of D20 of =97 cm requires that the size of

reactors employing D20 as the moderator to be quite large.

Additionally, the high temperature environment of the UTVR, the chemical

incompatibility between H20 or D20 and UF6 or UF4, the normal

deterioration of D20 into H20 in time (small amounts can have large

effects on neutronics), and the added complications involved with a

liquid moderator versus a solid moderator in space all aid in rejecting

D20 as the moderator-reflector material for the UTVR. The ceramic

nature of BeO with a high melting temperature of =2800 K and its

exceptional resistance to thermal shock [20] make this an especially

well-suited moderator-reflector material for the high temperature

environment of the power system under investigation. Although per unit

mass Be is neutronically superior to BeO as a moderator, the anticipated

moderator temperature range of 1600 K to 2000 K for this burst power

system precludes the use of Be (melting point of Be is 1728 K).









The Fissioning Fuel Material

The advantages and key features of vapor-fueled reactors are more

than adequate to justify the study of a fuel in the vapor state.

However, uranium exists in a gaseous state in various forms such as UF4,

UF6, or uranium metal vapor. Reactors employing uranium in these forms

have all been investigated at the University of Florida. The choice of

the fuel along with the working fluid are dictated by the type of power

cycle, e.g., Brayton or Rankine cycle. It is appropriate to compare

features of these cycles in order to select a suitable fuel.

The Brayton cycle is simpler in design than the Rankine cycle.

However, it generally has a lower thermodynamic efficiency. Due to this

lower efficiency, more heat has to be rejected into space which implies

that a larger radiator is needed. In addition, the heat rejection to

space is done at a varying (decreasing) temperature rather than a

constant temperature thereby decreasing the effective temperature of

heat rejection and further increasing the required radiator size. The

greater pumping power required for gas compression in the Brayton cycle

demand larger and more massive compressors as compared to the pumps in a

Rankine type of cycle. Since size and mass are significant constraints,

and since a Brayton type of cycle requires larger radiators and more

massive compressors than a Rankine type of cycle, a Rankine type of

cycle appears to be the better choice, especially for high power

systems.

For space power Rankine cycle systems, the most desirable fuel

choice is UF4. This can be seen from Figure 3-1 where the UF6 and UF4

saturation vapor curves are shown and from the uranium metal and UF4




































































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saturation vapor curves given in Figure 3-2. For the UF6 to be in the

gaseous state, at pressures required for criticality in the core, its

temperature need only be in the 400 to 500 K range. This implies that

the UF6 must be 400 K or less to achieve a liquid state at the exhaust

pressures when a gas turbine or MHD generator is used for power

conversion. This low heat rejection temperature can easily be achieved

on earth, but is unrealistic in a space environment. Thus, one is

restricted to a Brayton type of cycle when UF6 is the fissioning fuel

fluid in a space power system.

When uranium metal vapor is used as the fissioning fuel and working

fluid, the difficulty is not in achieving a liquid state at the heat

rejection end of the cycle as with UF6. For example, at an exhaust

pressure of 1 atm one need "cool down" to only about 4000 K to achieve

liquid uranium. The obstacle with uranium metal vapor is the extremely

high temperatures of the vapor in the core. The fluid temperature needs

to be at least 6000 K at all locations in the core to ensure the vapor

state at pressures needed for criticality. This indicates that the peak

gas temperature in the core will be at least 8000 K or 9000 K.

The choice of UF4 as the fuel rather than UF6 or uranium metal

vapor is justified by examining the saturation vapor curves, Figures 3-1

and 3-2, and the mole fraction of constituent species versus temperature

curve of the uranium-fluorine system, Figure 3-3 [21]. At pressures

required for criticality in the core, the temperature of UF4 need be

only about 2000 K to guarantee the vapor state. On the other hand, one

need cool down to only 1700 K in order to obtain liquid UF4. The

extremely high uranium metal vapor temperature in the core and the




































































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has a saturation vapor pressure-temperature behavior that is highly

desirable for a direct Rankine cycle burst power system for a space

environment. Also, Figure 3-3 indicates that in the expected gas

temperature operating range of 2500 K to 4000 K, UF4 is the predominant

uranium-fluorine specie.

The Working Fluid Material

It has been shown in the previous section that a Rankine type of

cycle is more appropriate for a burst mode space power system, and on

this basis the fuel is selected to be UF4. Therefore, a working fluid

that is compatible with the UF4 fuel and suitable for a Rankine type of

cycle is needed.

Preliminary chemical and material studies [22,23] indicate that a

working fluid in the form of a metal fluoride should be compatible with

the UF4 fuel. These working fluids include Li7F, KF, NaF, and RbF.

Table 3-1 list relevant properties of these materials.

Description of a Uranium Tetra-Fluoride,
UTVR/Disk MHD-Rankine Power Cycle


An example UF4/KF UTVR MHD-Rankine cycle power system schematic is

shown in Figure 3-4. This system is capable of producing 200 MWe with a

thermodynamic efficiency of z26%. The mass flow rates of UF4 and KF are

59 and 209 kg/sec, respectively.

For the system illustrated in Figure 3-4, about 40 MW is required

to vaporize the liquid UF4 in the UF4-boiler. The UF4 vapor is then

directed to the UTVC where it is mixed with the KF. In the UTVC, 30 MW























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of the fissioning power is deposited in the UF4 to raise its temperature

from 2350 K to 4000 K. The KF flows around the UTVC cooling the vapor

core wall region where about 35 MW is added to it in the form of

sensible heat to raise its temperature from 1920 K to 2300 K. Then the

KF is injected into the vapor core where it is mixed with the UF4. In

the UTVC, 115 MW is added to the KF to raise its temperature from 2300 K

to 2665 K and 367 MW is added in the form of latent heat to vaporize it

at 2665 K. Another 180 MW of heat is then required to raise the KF

temperature from 2700 K to 4000 K. A total of 697 MW of thermal power

is therefore added to the KF fluid.

The UF4/KF mixture is then passed through the nozzle, the MHD

generator, and the diffuser. In the MHD generator, about 10 MW of
energy is produced by fission and 200 MWe is extracted. Waste heat in

the amount of 526 MW is rejected to space via a 720 m2 primary

condensing radiator which allows the separation of the vapor mixture

into UF4 vapor and KF liquid. The UF4 vapor is then passed through a 56

m2 secondary condensing radiator in which 31 MW is rejected to space.

Both the UF4 and the KF are then compressed via separate pumps.

For the purpose of generating this cycle, it is assumed that UF4

and KF are completely separable; this may not be the case. In a real

system many species, including KxU Fz species, may be present as shown

by Hildenbrand and Lau [23].

The system described above has the potential to be extremely

reliable since the only components with moving parts are the UF4 and KF

liquid pumps.









Table 3-2 lists 200 MWe UF4/UTVR power cycle operating

characteristics for KF, NaF, Li7F, and RbF working fluids. Table 3-3

presents the energy balance data for a 200 MWe UF4/UTVR power cycle with

KF, NaF, Li7F, or RbF as the working fluids. Table 3-2 indicates that
if none of the metal fluoride is vaporized in the boiler columns, then

the required power sharing (or power ratio) of the UTVC to the boiler

core (PUTVC/PBCOL) based on thermodynamic/flow considerations is =20.

It also indicates that =90% of the total fission power produced is

deposited in the metal fluoride. The power sharing ratio, PUTVC/PBCOL'

places another restriction on the power system. That is, the UTVR needs

to be configured so that the power sharing between the UTVC and boiler

columns based on nuclear analysis matches what is obtained from

thermodynamic and flow considerations. One method of controlling

PUTVC/PBCOL is to divert part of the metal fluoride from the UTVC wall
cooling region to the boiler region. The power sharing as a function of

metal fluoride mass flow rate to the boiler region as determined on the

basis of thermodynamic and mass flow requirements is listed in Table 3-

4.

Table 3-4 indicates that the required power sharing ratio decreases

by a factor of =3 for NaF, KF, and Li7F and by a factor =2 for RbF when

only 10% of the metal fluoride is diverted to the boiler region. This

is due to the large amount of power needed to vaporize the metal

fluoride as compared to the UF4.


















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Neutronic Analysis of the
Ultrahiqh Temperature Vapor Core Reactor


Static Neutronic Calculations

A number of computer codes existing at the University of Florida,

San Diego SuperComputer Center, and the Air Force SuperComputer Center-

Kirtland are used in analyzing the static neutronic behavior of the

UTVR.

In the static neutronic analysis, the fuel is assumed to be

stationary. Thus, the effect of the loss of delayed neutrons outside

the cores is ignored. This assumption over-estimates the contribution

of the delayed neutrons inside the cores, i.e., keff is somewhat larger

for the stationary system than for the corresponding circulating system.

This effect is corrected for in the dynamic model and is discussed in

detail in Appendix D.

One of the computer packages used at University of Florida is the

AMPX [24] modular code system which is described in Appendix A.

Weighted multigroup neutron cross-sections files are generated from

ENDF/B [25] data using the XLACS [26] code, an AMPX module. Self-

shielding calculations are performed on the weighted multigroup neutron

library created by XLACS using NITAWL [27]. NITAWL produces a 123-

neutron group AMPX library. This 123-neutron group library is then

collapsed first to 27- and then to four-neutron groups using XSDRNPM

[10].

Four-neutron group, 1-D, spherical geometry, discrete ordinates

(Sn) calculations are performed using XSDRNPM. Group dependent neutron
flux distributions in space, region reactions rates, and eigenvalues are









obtained from the 1-D calculations. Basic static neutronic

characteristics of the UTVR are obtained from the 1-D calculations.

These include keff and PUTVC/PBCOL behavior as a function of moderator-

reflector regions thickness, fuel density and enrichment, and types of

working fluids. Reactivity penalties as a function of different liner

materials and their thicknesses are also obtained from the 1-D neutronic

static calculations.

Two-dimensional Sn cylindrical geometry calculations in the R-O and

the R-Z coordinate systems are performed using DOT-4 [11]. The four-

neutron group cross-section library produced by XSDRNPM is converted to

DOT-4 format using GIP [28]. In R-9 geometry, the boiler region can be

accurately modeled as a number of boiler columns separated by BeO

moderator. The nozzle, disk-MHD generator, and diffuser regions can all

be modeled in the R-Z geometry. Results obtained from the 1-D spherical

"mock-up" of UTVR are compared with results obtained from calculations

performed in the R-9 and the R-Z coordinate systems. These comparisons

are necessary to determine the reliability of the obtained results.

The reference UTVR configuration for the 3-D analysis is obtained

from 1- and 2-D static neutronic calculation results. The 3-D

calculations are performed using MCNP [12], a 3-D Monte Carlo neutron

transport code. Integral parameters for the dynamic neutronic analysis

are calculated from MCNP results by using ISCE, a special code developed

as a part of this research. Parameters obtained from ISCE include core-

to-core coupling coefficients, and the reactivity and neutron

multiplication factors of individual cores.









Dynamic Neutronic Calculations

The over-estimate of keff obtained from the static neutronic

calculations due to the assumption of a stationary fuel is corrected for

in the UTVR kinetic model.

The dynamic analysis in the time domain is performed using

circulating-fuel, coupled-core, point reactor kinetics models. Inherent

reactivity feedback effects such as vapor fuel density and boiler column

liquid volume changes are included in the dynamic model. Dynamic and

stability analysis studies are performed with the Engineering Analysis

System code, EASY5 [29].

The computer codes mentioned above are described in Appendix A.













CHAPTER IV
STATIC, ONE-DIMENSIONAL, UTVR NUCLEAR
CHARACTERIZATION AND CONFIGURATION OPTIMIZATION

Introduction

The initial one-dimensional (1-D) spherical "mock-up" configuration

used to perform the preliminary nuclear characterization of the

Ultrahigh Temperature Vapor Core Reactor (UTVR) is shown in Figure 4-1.

It consists of four regions (the wall cooling region is neglected in the

initial calculations). The first is the Ultra High Temperature Vapor

Core (UTVC) region which contains the fuel mixture that consists of

highly enriched UF4 vapor and a metal fluoride vapor at 3000 K and 50

atm. The second is the inner beryllium oxide (BeO) moderator-reflector

region (IBEO) which contains only BeO. The third is the boiler column

(BCOL) region where the UF4 is vaporized. The fourth is the outer BeO

moderator-reflector region (OBEO).

The actual cylindrical reactor system is converted to the 1-D

spherical geometry by conserving the volumes of the UTVC and the boiler

cores and by conserving the thicknesses of the inner and outer BeO

moderator-reflector regions. Neutronic calculations are performed using

XSDRNPM [10]. XSDRNPM is capable of computing the system's neutron

multiplication factor (keff), region average and local neutron fluxes

and currents, and the fission rate in each region (power produced).

XSDRNPM is described in detail in Appendix A.


















Outer BeO Moderator-
Reflector Region

UF4 Boiler Region

Inner BeO Moderator-
Reflector Region -




Ultrahigh Temperature
Vapor Core

Region 1




Region 2 -- -


Region 3 -- -



Region 4


Figure 4-1. Four Region,
"Mock-up" of


One-Dimensional Spherical
the UTVR









Modeling the UTVR in the 1-D spherical geometry is expected to

result in excessively high values for keff. The keff values are

expected to be quite large due to the following:

1. Neutron leakage from the UTVR is underestimated since spherical

configurations provides the smallest surface-to-volume ratio.

2. Neutron streaming from the MHD duct is not accounted for since the

MHD duct regions is not included in the 1-D spherical "mock-up."

3. Reactivity worth of the boiler column is overestimated since the

boiler column is treated as a spherical shell surrounding the UTVC.

The boiler column in the actual reactor system consists of a number

of boiler columns separated by BeO moderator. By configuring the

boiler region as a spherical shell surrounding the UTVC, the

probability for neutrons interacting with the boiler region is

relatively large. Additionally, thermal neutron flux depression in

the boiler region is underestimated since the thickness of the boiler

region in 1-D is small compared to the thickness of the actual boiler

columns.

4. Core protective materials (liners and cladding), structural support

members, and piping are not included in the analysis in order to

simplify the scoping analyses. That is, the 1-D spherical "mock-up"

represents a "clean" UTVR system.

Detailed three-dimensional neutronic analysis using MCNP [12]

(Chapter VI) indicate that, when neutron leakage and streaming are

accounted for, actual boiler configuration is modeled, and structural

and liner materials are employed, keff values of =1.05 is obtained.









Therefore, the high keff values obtained in this preliminary stage of

analysis are "reasonable" and needed.

Scoping Calculations

To commence the nuclear characterization of the reactor system,

numerous 1-D scoping calculations are performed. These calculations

examine the effect of variations in geometry, fuel density, fuel

enrichment, mole fraction, and materials. The results of these studies

are described in this section.

Geometric Variations

As mentioned previously, size and mass are significant constraints

on space power systems. In addition to the total power requirement, an

important design consideration for this system is the power sharing or

the amount of power generated in each fissioning region (UTVC regions

and the boiler regions). Of these constraints (power sharing, total

power production, and size and mass of the reactor system), the power

sharing is expected to be the most restrictive. To determine which

configurations are capable of meeting these constraints, the effects of

variations of the following parameters are examined:

UTVC radius

While maintaining the inner and outer BeO region thicknesses at 20

cm and 35 cm, respectively, and the boiler region volume at 8.5 x 10-03

m3 (the boiler region contains an equal mixture by volume of liquid and

vapor UF4 with an inlet velocity of 2 m/sec at a mass flow rate of 68

kg/sec), the radius of the vapor core (UTVC) is varied from 40 to 150









cm. The fuel mixture in the UTVC region is maintained at 3000 K with

the partial pressures of the UF4 and the NaF fixed at 5 and 45 atm,

respectively. The results, keff and PUTVC/PBCOL' are given in Figure 4-
2 as a function of UTVC radius.

Figure 4-2 indicates that keff increases from 1.462 to 1.479 and

PUTVC/PBCOL increases from 0.23 to 0.53 as the UTVC radius increases
from 40 cm to about 70 cm. However, for UTVC radii above 70 cm keff

decreases while PUTVC/PBCOL continues to increase.

The interpretation of the behavior of keff and PUTVC/PBCOL as a

function of the UTVC radius requires two further sets of calculations.

The first consists of varying the UTVC radius from 40 to 150 cm while

the boiler region is voided. The second consists of varying the UTVC

radius over the same range but with a voided UTVC and a loaded boiler.

The results are given in Figure 4-3, where values of keff and fission

rate versus the UTVC radius are given for both cases.

The fission power produced in a region is a function of the thermal

neutron flux, the macroscopic fission cross section, and the volume of

the fissioning region. When the boiler is voided and the UTVC radius is

varied from 40 to 150 cm, the most significant change is an increase in

the UTVC volume. This increase in the UTVC volume results in an

increase in PUTVC. On the other hand, when the UTVC is voided and the

UTVC radius is varied from 40 to 150 cm, two phenomena occur: (1)

neutronic de-coupling of the annular boiler region, and (2) reduced

number of mean free paths that a neutron encounters when passing through

the boiler. That is, as the UTVC radius increases and the boiler volume

is fixed, the boiler region in the 1-D spherical "mock-up" becomes






















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thinner and more separated in space from itself. Thus, fewer fissions

occur and a decrease in PBCOL is observed.

Thus, the observed increase in PUTVC/PBCOL as the UTVC radius

increases, when both cores are loaded (Figure 4-2) is due to the

increase in PUTVC and the decrease of PBCOL as shown in Figure 4-3.

Although not shown in Figure 4-3, when the vapor core is voided an

optimum value for keff is obtained at a UTVC radius between 0 and 40 cm

for an inner BeO thickness (IBEO) of 20 cm. This optimum UTVC radius is

due to optimum neutronic coupling from one segment of the boiler region

to the other. Calculations for the voided UTVC configuration have been

performed as its radius is varied from 0 to 80 cm at IBEO thickness of

0, 5, 10, 15, and 20 cm. The results are given in Table 4-1 for this

type of variation.

For the case where the IBEO is 20 cm, keff peaks at a voided UTVC

radius of about 30 cm. At this radius, the strongest neutronic coupling

for the boiler region exists. However, for smaller IBEO thicknesses of

15, 10, 5, and 0 cm, a larger voided UTVC radius (beyond 40 cm) is

needed to show the peak in keff. This indicates that as the IBEO

thickness decreases, the voided UTVC region radius required for optimum

boiler coupling increases. However, when the UTVC is loaded, the radius

required for optimum boiler coupling is different as is shown in the

following section.

As mentioned previously, for an IBEO of 20 cm and UTVC radii

greater than 40 cm, keff increases as the loaded UTVC radius increases

when the boiler is voided and keff decreases as the unloaded UTVC radius

increases when the boiler is loaded (as shown in Figure 4-3). However,













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the overall or net effect for the reactor system when both cores are

loaded is an increase in keff until the UTVC radius is about 70 cm; keff
then decreases for radii beyond 70 cm. This can be explained as
follows: as the UTVC radius increases from 40 to 70 cm, the gained

reactivity from the "larger" UTVC core overrides the lost reactivity due

to the de-coupling of the boiler region. For vapor core radii beyond 70

cm, there is a diminishing gain in reactivity due to the larger UTVC and

the boiler region de-coupling effects dominate. A justification for

this assertion is as follows: in the range of 40 to 70 cm for the UTVC

radius, from the data used to generate Figure 4-3, the gain in 6k/k for

the loaded UTVC is about 0.28 (or 9.3 x 10-03 6k/k per cm of IBEO) and

the loss in 6k/k for the loaded boiler is only 0.08 (2.7 x 10-04 6k/k
per cm of vapor core radius); thus, a net increase in keff is obtained.

However, when the UTVC radius increases from 70 to 150 cm, the gain in

6k/k for the loaded UTVC is only about 0.18 (or 2.3 x 10-03 6k/k per cm

of vapor core radius) and the loss in 6k/k for the loaded boiler is

about 0.37 (or 4.6 x 10-03 6k/k per cm of IBEO); thus, a net decrease in

keff is obtained. The observed decrease in the rate of increase of keff

as the UTVC radius increases beyond 70 cm for the case of the loaded

UTVC and voided boiler is due to approaching infinite reactor

configuration; this is seen in Figure 4-3 where the vapor core keff

clearly begins to saturate as the UTVC radius increases beyond =100 cm.

It is concluded from the above discussions, that the UTVC radius

along with the IBEO thickness are the determining parameters that

influence neutronic coupling for the UTVC/boiler regions and the

neutronic coupling from one segment of the boiler to the other. That









is, varying the UTVC radius for a fixed IBEO thickness, or varying the

IBEO thickness for a fixed UTVC radius, will lead to an optimum

configuration with respect to neutronic coupling. Thus, for a given

UTVC radius, an IBEO thickness can be selected to yield optimum overall

neutronic coupling between the boiler and the UTVC. A value of 60 cm is

selected for the UTVC region radius for further analysis. This value is

based on the fact that the UTVC is in reality a cylinder and is expected

to be 100 cm in height with a radius of about 55 cm. These dimensions

appear to be in a range that is acceptable with respect to thermo-

hydraulics and acoustic calculations performed on the system [30].

Inner BeO moderator-reflector region thickness

With the UTVC radius fixed at 60 cm, the vapor fuel temperature set

at 3000 K, the UF4 partial pressure set at 5 atm, the NaF partial

pressure set at 45 atm, the boiler region volume fixed at 8.5 x 10-03

m3, and the OBEO region thickness held at 35 cm, the IBEO thickness is

varied from 5 to 50 cm. The results are given in Figure 4-4 where keff

and PUTVC/PBCOL are plotted as a function of IBEO.

The results indicate that the optimum neutronic coupling between

the vapor core and the boiler region occurs at an IBEO thickness of

about 16 cm where keff is greatest with a value of about 1.507. Beyond

a BeO thickness of 16 cm, keff decreases. This is due to the de-

coupling phenomenon for the boiler and the decreased thickness of the

boiler at the higher IBEO thicknesses.

Figure 4-4 also indicates that PUTVC/PBCOL initially increases as

the IBEO thickness increases from 5 cm to about 16 cm and remains at a

constant level of 0.39 as the IBEO thickness increases from about 16 to




















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45 cm. This ratio then undergoes a further increase as IBEO increases

beyond 45 cm. Three relevant phenomena occur as the IBEO thickness is

increased, they are: (1) a decrease in the number of mean free paths

that a neutron encounters when passing through the boiler due to the

decrease in the boiler thickness as IBEO increases; (2) neutronic de-

coupling of the annular boiler region; and (3) an increase and then a

decrease in the neutronic coupling between the UTVC and boiler cores.
In order to explain the observed behavior of k ff and PUTVC/PBCOL two

additional sets of calculations are needed. The first involves varying

the IBEO thickness from 5 to 60 cm for a fully loaded UTVC with a radius

of 60 cm and with the boiler voided. The second set involves varying

the IBEO thickness over the same range for a voided vapor core with a

radius of 60 cm and with a loaded boiler (volume fixed at 8.5 x 10-03

m3). The results are shown in Figure 4-5.
The results indicate that for a 60 cm radius voided UTVC, optimum

neutronic coupling of the boiler column occurs at an IBEO thickness of

=12 cm. As the IBEO increases beyond 12 cm a decrease in keff occurs.

This decrease in keff of the boiler region translates to a decrease in

PBCOL* However, for the case where the boiler is voided and the UTVC is
loaded, keff continues to increase as IBEO increases. From the data

used to generate Figure 4-5, as IBEO increases from 10 to 45 cm, the

values of 6k/k per cm of IBEO are +1.9 x 10-03 and -4.8 x 10-03 for the
loaded UTVC and for the loaded boiler cases, respectively. These values

reflect the change in reactivity expected if the only phenomena that are

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above, and the net result should be a continuous increase in PUTVC/PBCOL

and a continuous decrease in keff

However, neutronic coupling between the UTVC and the boiler cores

is also affected by variations in the IBEO thickness. As the IBEO

thickness increases from 5 to =12 cm, PUTVC increases (due to increase

in the UTVC neutron reflection rate, which can be inferred from the keff

curve shown in Figure 4-5, and due to an increase in boiler-to-UTVC

neutronic coupling) and PBCOL increases (due to enhanced neutronic

coupling of the boiler region, as shown in Figure 4-5). However, the

increase in PUTVC is larger than the increase in PBCOL" This causes

PUTVC/PBCOL to increase. As the IBEO region increases from 12 to =16
cm, PUTVC continues to increase while PBCOL begins to decrease, thus a

further increase in PUTVC/PBCOL is obtained. Although Figure 4-5

indicates that an increase in PUTVC should occur in the IBEO thickness

range of 16 to 45 cm for the case the vapor core is loaded and the

boiler region is voided, the actual result when both cores are loaded is

a decrease in PUTVC* For IBEO thicknesses above 16 cm, a decrease in

the boiler-to-UTVC neutronic coupling occurs which causes PUTVC to

decrease. In this IBEO thickness range, PUTVC is decreasing at about

the same rate PBCOL is decreasing. The net result is a constant

PUTVC/PBCOL behavior over an IBEO range from about 16 to 45 cm.
From the data used to generate Figure 4-5, for the IBEO thickness

range from 45 to 60 cm, the values of 6k/k per cm of IBEO are about -5.1
x 10-03 and +3.0 x 10-04 for the loaded boiler cases and the loaded

UTVC, respectively. Above an IBEO thickness of 45 cm, the rate of









decrease in PBCOL is greater than the rate of decrease of PUTVC* This

leads to an increase in PUTVC/PBCOL and a further decrease in keff'

The combined neutronic coupling between the UTVC and the boiler

region (i.e., the combined boiler-to-UTVC, UTVC-to-boiler, and annular

boiler region neutronic coupling) is an optimum at an IBEO thickness of

=16 cm for this configuration. For future calculations, a thickness of

15 cm is selected for IBEO.

Outer BeO moderator-reflector region thickness

Maintaining the UTVC radius at 60 cm, the IBEO thickness at 15 cm,

and the boiler volume at 8.5 x 10-03 m3 (0.12 cm thick), the OBEO region

thickness is varied from 10 to 100 cm in order to obtain the optimum

outer BeO thickness. The results are shown in Figure 4-6 where keff and

PUTVC/PBCOL are plotted as a function of OBEO thickness.
Figure 4-6 clearly indicates that keff saturates at an OBEO

thickness of about 40 cm. At this thickness and beyond, keff is around

1.52 and PUTVC/PBCOL is 0.36. Increasing the OBEO thickness beyond 40

cm does not enhance the system neutronically, i.e., the value of keff*

It only increases the size and the mass of the system. This is very

undesirable since the system is intended for space power production.

The results also indicate that as the OBEO thickness decreases below 40

cm, PUTVC/PBCOL increases since PBCOL decreases. This is anticipated

since the OBEO has a direct effect on the boiler region and less of an

effect on the UTVC. Thus, a method to increase PUTVC/PBCL is to reduce

the thickness of the OBEO. However, this will cause a greater number

of- and more energetic neutrons to leak out of the reactor which will

require the use of heavier and thicker shielding.























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For all further calculations, a thickness of 40 cm is selected for

the OBEO.

UF4 boiler region thickness

Increasing the UF4 boiler region thickness in the "mocked-up"

spherical geometry is analogous to increasing the cross sectional flow

area of the actual boiler column configuration. This in turn results in
a decrease in the inlet velocity of the UF4 liquid to the boiler

(assuming a fixed mass flow rate is required). The inlet velocity of

the UF4 liquid to the boiler dictates the amount of liquid UF4 present

in that region at a given power level. Thus, the reactivity worth of

the boiler is strongly influenced by the inlet UF4 velocity. This

velocity also impacts on the boiler region friction and acceleration

pressure losses. The lower the inlet velocity the lower the pressure

losses, but if the velocity is too low, then the size (area) of the

boiler region will be great. Knowledge of the neutronic behavior of the

system as a function of the inlet velocity of the UF4 liquid to the

boiler is obviously essential. The velocity of the UF4 liquid is varied

from 0.5 m/sec to 6.0 m/sec which corresponds to annular boiler region

thicknesses from about 0.48 cm to about 0.04 cm. The keff and

PUTVC/PBCOL results as a function of UF4 inlet velocity are plotted in
Figure 4-7.

Figure 4-7 indicates that as the inlet velocity of the UF4 liquid

increases, keff decreases and PUTVC/PBCOL increases. Both behaviors are

due to the decrease of the boiler area (volume) as the velocity

increases. A decrease in the amount of fissile material in the boiler

causes PBCOL to decrease thus increasing PUTVC/PBCOL and decreasing























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keff, respectively. It should be noted that selecting an inlet UF4

velocity based only on results from these 1-D calculations is not
reasonable since the boiling and non-boiling regions (amount of vapor

versus liquid UF4) cannot be accurately modeled. Two- and three-

dimensional modeling are needed in order to select a suitable operating

velocity. For these preliminary studies, a flow rate of 2 m/sec is

chosen. This flow rate, 2 m/sec, corresponds to a boiler volume of 8.5

x 10-03 m3 (100 cm in height) at a mass flow rate of 68 kg/sec.

UF4 boiler core volume

A safety consideration in the design of the UF4/metal-fluoride

nuclear power system is the unwanted possibility of self-criticality in

a UF4 boiler region. That is, the size of the boiler columns and the

amount of the liquid UF4 present in the boiler region should be chosen

so that the region cannot become self-critical even under extreme

conditions. For this study, a two region core, in 1-D spherical

geometry, is used to mockup a 50 cm in height UF4 boiler core surrounded

by 40 cm of BeO reflector or 40 cm of Be reflector. The spherical

radius of the core is varied from 4 cm to 11 cm which corresponds to an

equivalent cylindrical radius of 1.3 cm to about 6.0 cm. The boiler

contains 100% enriched U235 in completely liquid UF4. Values for keff

range from 0.491 for the spherical radius of 4 cm to 1.101 for an 11 cm

spherical radius, as shown in Table 4-2. The boiler is found to be

critical (keff = 1.0) at a spherical radius of about 9.8 cm, which

corresponds to a cylinder with a radius of about 5 cm.

The results indicate that the UF4 boiler columns will not become

self-critical since in reality they will not contain 50 cm of liquid.



























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If the reactor system has only two boiler columns at a total UF4 mass

flow rate of 62 kg/sec, then the required cross sectional flow area per

column for an entrance velocity of about 2 m/sec for the UF4 liquid will

be about 4.2 x 1003 m2. This corresponds to a cylindrical radius of
about 3.7 cm which is lower than the critical radius obtained in the 1-D

calculations; a larger number of columns would result in even smaller

boiler region radii (for an inlet velocity of 2 m/sec).

Fuel Density Variations

During reactor startup and power level changes, there will be

changes in the UF4/MF vapor pressure and temperature and, thus, in the

density. Also, the amount of liquid and the void volume fraction of the

UF4 in the boiler region will change depending on the power level. An

insight into the effect of density changes will help in predicting the

response of the reactor to power level changes and/or perturbations

introduced into the system. The effects of variations in the following

parameters are therefore studied.

UF4 partial pressure and mole fraction (UF4:NaF) in the UTVC
Preliminary calculations and analysis of the MHD generator indicate

that a mole fraction of about 10% for UF4 and 90% for NaF results in

efficient energy extraction [31]. Maintaining the UTVC radius at 60 cm,

the IBEO thickness at 20 cm, the boiler volume at 8.5 x 10-03 m3, and

the OBEO thickness at 35 cm (these calculations were performed prior to

obtaining the optimum IBEO and OBEO thicknesses of 15 and 40 cm,

respectively), the UF4 partial pressure is varied from 1 to 20 atm at









NaF partial pressures of 20, 40, and 60 atm. The result of these

variations are shown in Figure 4-8.

The results indicate that the system is essentially unaffected

neutronically by the NaF partial pressure. Thus, the UTVC can be

operated with a fuel mixture that is optimum with respect to the demands
of the MHD generator. Figure 4-8 indicates that keff saturates at UF4

partial pressures above =10 atm. This corresponds to a U235 density of

2.5 x 10-05 atoms/barn-cm. Beyond a UF4 partial pressure of 10 atm or a

U235 density of 2.5 x 10-05 atoms/barn-cm, the UTVC is becoming black to

neutrons. The results, as shown in Figure 4-8, indicate that

PUTVC/PBCOL increases as the UF4 partial pressure increases up to about
10 atm and remains at about a constant level as the UF4 partial pressure
further increases. For all further analysis, partial pressures of 5 atm
for UF4 and 45 atm for NaF are used.

U235 enrichment in UF4

The U235 enrichment is varied from 80% to 100% at UF4 partial

pressures in the UTVC of 1, 2, 3, 4, 5, 6, and 7 atm. The results, as

shown in Figure 4-9, indicate that keff increases as the enrichment

increases and as the UF4 partial pressure increases. The U235

enrichment is fixed at 100% for all further analysis.

U233 as the fissile isotope

The U235 fissile isotope in UF4 is replaced with U233. The U233

enrichment is varied from 80% to 100% at UF4 partial pressures of 3 and

5 atm. The results, as shown in Figure 4-10, indicate the same behavior

as obtained in Figure 4-9 for U235 with the exception that keff is

higher when U233 is the fissile fuel. This is due to the lower thermal



























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capture cross section, ac, (48 barns versus 99 barns) and the higher

number of neutrons liberated per thermal fission, v, (2.49 versus 2.42)

in U233 versus U235; this corresponds to a higher number of fission
neutrons liberated per thermal neutron absorbed in the fuel, R, (about
2.29 for U233 and 2.07 for U235).

Average density of the UF4 in the boiler region

By varying the effective density of the UF4 in the boiler region,

the boiler column is simulated as a mixture of liquid and vapor with

some average quality. An examination of the effects of such density

changes aids in determining the reactor response due to power level

changes and UF4 inlet velocity changes. While maintaining the UTVC
radius at 60 cm, and the UF4 and NaF vapor partial pressures at 5 and 45
atm, respectively, the IBEO thickness at 20 cm, the boiler volume at 8.5

x 1003 m3, and the OBEO thickness at 35 cm, the "overall" density of

the UF4 in the boiler region is varied from 0.20 g/cm3 to 4.0 g/cm3 to

simulate the presence of both liquid and vapor UF4. A value of 0.20

g/cm3 for the density of UF4 reflects a mixture composed of about 5
volume percent liquid at 5 atm and 95 volume percent vapor, and a

density of =4 g/cm3 reflects a mixture of pure UF4 liquid.

The results, as shown in Figure 4-11, indicate an increasing

behavior for keff and a decreasing behavior for PUTVC/PBCOL as the
3
density of the UF4 increases to about 1.6 g/cm3. For densities above

1.6 g/cm3 the rate of increase of keff decreases and PUTVC/PBCOL levels
off. This indicates that above this density, the boiler starts to

become black to neutrons and begins to saturate.
























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Material Variations

The types and location of structural materials needed in

constructing the UTVR are not known at this point. These structural

materials include piping, spacers, and protective coatings. Also, the

over-all cycle analysis may prove that a metal fluoride other than NaF

(e.g., KF, RbF, or Li7F) provides better over-all system performance
than the UF4/NaF does. By including some sample structural and

protective coating materials at selected surfaces or regions (e.g., the

UTVC wall) and by examining other metal fluorides, reactivity penalties

due to these materials can be estimated. The effects of variations of

the following materials are therefore studied.

Choice of metal fluoride in UTVC

At inner UTVC core radii of 40, 80, and 120 cm, while maintaining
the IBEO thickness at 20 cm, the boiler volume at 8.5 x 10-03 m3, and

the OBEO thickness at 35 cm, calculations are performed to examine the

reactivity effect of using NaF, Li7F, or KF as the working fluid in the

vapor fuel mixture. The results, as shown in Table 4-3, indicate that,

with regard to the UTVC only (the wall cooling region is not included in

these calculations), the use of Li7F as the working fluid results in the

highest value for keff, followed by NaF and then by KF. As the UTVC

radius increases, the difference in keff as a function of selected metal

fluoride working fluid becomes greater. At these larger radii, the

reactivity contribution of the boiler region to keff decreases at the

same time the reactivity contribution of the UTVC to keff increases.

This explains the behavior of the differences in keff for the different

fuel mixtures at the higher UTVC radii. Since the type of metal













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fluoride has a small effect on keff, especially at a UTVC radius of 60

cm, NaF is used as the working fluid for further analysis.

Wall cooling region

Figure 4-12 shows the five region 1-D spherical "mock-up" of the

UF4/NaF UTVR system which includes the wall cooling region. To simulate

the variation of the NaF velocity in the wall cooling region, the

thickness of this region is varied from about 0.35 cm to about 3.3 cm.

This correspond to a NaF inlet velocity range of 0.5 to 5.0 m/sec.

Also, at each NaF velocity, the effective density of the NaF is varied
3 3 3
from 0.1 g/cm3 to 2.2 g/cm3. A value of 0.1 g/cm for the density of

NaF reflects a mixture composed of =4 volume percent liquid at 45 atm

and 96 volume percent vapor, and a density of 2.2 g/cm3 reflects a

mixture of pure NaF liquid. The results, shown in Table 4-4, indicate a

maximum penalty of about 10% 6k/k for a wall cooling region thickness of

3.33 cm and a NaF density of 2.2 g/cm3. However, the expected velocity

of the NaF is about 3 m/sec which corresponds to a wall cooling region

thickness of 0.58 cm. The reactivity penalty of the liquid NaF region

is then about 2.25% 6k/k for a NaF density of 2.2 g/cm3. As the inlet

velocity of the NaF increases in the wall cooling region and/or as the

effective density decreases, PUTVC/PBCOL increases.

Other metal fluoride working fluids

The NaF in the UTVC and wall cooling region is replaced by Li7F and

KF to examine the reactivity penalty or gain if other liquid metal

fluorides are used instead of NaF. The neutron multiplication factor,

keff, and the average PUTVC/PBCOL are obtained for the different metal
fluorides at wall cooling region thicknesses of 0.44, 0.87, and 3.33 cm

















Outer BeO Moderator-
Reflector Region ---


UF4 Boiler Region -- '. ',

Inner BeO Moderator-
Reflector Region
Wall Cooling Region-- -




Ultrahigh Temperatuce .. ...

Region 1


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One-Dimensional Spherical
the UTVR












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which reflect metal fluoride inlet velocities of 4.0, 2.0, and 0.5

m/sec, respectively. The average density of the metal fluoride is also

varied and results are presented for two different cases, as shown in

Table 4-5.

The results indicate that the use of Li7F as the metal fluoride

results in the highest values for both keff and PUTVC/PBCOL' followed by
NaF and then by KF. As the thickness of the wall cooling region

increases from 0.00 to 3.33 cm, maximum reactivity penalties are about

2%, 10%, and 22% Sk/k for LiF, NaF, and KF, respectively. Comparing

these results with those in Table 4-3 where the wall cooling region is

not treated, a greater difference in keff is noticed from one type of

metal fluoride to the other. This is due to the much greater density of
the (liquid) metal fluoride in the wall cooling region which in effect

results in a higher overall parasitic absorption.

NaF mass flow rate to the boiler region

To account for the possibility that complete separation of the

UF4/NaF mixture into pure UF4 and pure NaF cannot be achieved, and to

attempt to decrease the required PUTVC/PBCOL (on the basis of

thermodynamic and flow considerations) from its present value of 21, the

NaF mass flow rate to the boiler is varied from 0 kg/sec to 158 kg/sec;

this range corresponds to diverting 0% to 100% of the NaF from the wall

cooling region to the boiler region. The results, as shown in Table 4-

6, indicate a slight increase in keff from 1.548 to 1.554 as the NaF is

diverted to the boiler.

Table 4-6 also indicates that as the NaF is diverted to the boiler

region, the thermodynamic requirement for PUTVC/PBCOL decreases while













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the value of PUTVC/PBCOL obtained from the neutronic calculations shows
a slight increase.
UF4/NaF inlet velocity to the boiler
Building on the results obtained in Table 4-6, an attempt is made

to further increase UTVC/PBCOL by varying the inlet velocity of the

liquid UF4/NaF into the boiler region. The velocity is varied from 0.5
to 6.0 m/sec. The mass flow rate of the NaF is set at 94.8 kg/sec to

the boiler and 63.2 kg/sec to the wall cooling region.
Thermodynamically, this requires that PUTVC/PBCOL be 1.25. As the inlet
velocity of the mixture increases from 0.5 to 6.0 m/sec the amount of
the mixture in the boiler decreases; thus, the amount of fissile

material in the boiler decreases. This, as seen from Figure 4-13,
causes a decrease in keff from 1.577 to 1.468 and an increase in

PUTVC/PBCOL from 0.18 to 0.41.
Addition of Li6F poison to the boiler

An attempt is made to decrease the reactivity of the boiler region
by adding Li6 poison to the boiler region in order to obtain the
required PUTVC/PBCOL. Li6 is added to the boiler region in the form of
Li6F. The UF4/NaF-Li6F inlet velocity is fixed at 2 m/sec. The Li6F

mass flow rate is varied from 5.2 x 10-03 to 3.9 kg/sec. This

corresponds to an atom ratio variation from 0.1% to 75.0% (the atom

ratio being the ratio of the Li6 atoms to that of the U235). As the
mass flow rate of the Li6F increases, a decrease in keff from 1.550 to
0.957 and an increase in PUTVC/PBCOL from 0.266 to 0.574 is observed, as

shown in Figure 4-14. However, the required PUTVC/PBCOL value of 1.25

is not achieved in the 1-D configuration.










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BeO in the annular boiler region

The boiler region in the actual reactor system is made of a number

of cylindrical boiler columns separated by BeO moderator. To account

for this, i.e., the presence of BeO in the boiler region, the boiler

region in 1-D spherical geometry is modeled as a region that contains a

homogenized mixture of liquid and vapor UF4 and BeO. The one-

dimensional boiler region annular thickness is varied from 2.0 to 4.3 cm
to simulate the actual boiler region configuration that contains from 2

to 8 boiler columns. The volume of the UF4 and the total volume of the

boiler region are conserved when converting from the true cylindrical

configuration to the 1-D spherical geometry. As the annular boiler

region thickness is varied (i.e., as the number of boiler columns is

varied), the total mass flow rate and the inlet velocity of the UF4 in
the boiler region are kept constant (i.e., the total UF4 cross sectional
flow area is fixed) but the volume of the BeO and the average UF4

density are varied. The results, keff and PUTVC/PBCOL, are given in

Table 4-7.

The results indicate that keff decreases and PUTVC/PBCOL increases

as the simulated number of boiler columns increases. This is due to the

decrease in the amount of moderator present in the boiler region; thus,

less neutron thermalization is occurring in the boiler region. This

results in a decrease in the average thermal neutron flux in the boiler

region causing keff to decrease and PUTVC/PBCOL to increase. The

results also indicate that keff increases and PUTVC/PBCOL decreases as

the UF4 density in the boiler increases. This is due to the increase in

the amount of fissile material present in the boiler region.




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