STATIC AND DYNAMIC NEUTRONIC ANALYSIS
OF THE URANIUM TETRAFLUORIDE, 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 TETRAFLUORIDE, ULTRAHIGH
TEMPERATURE VAPOR CORE REACTOR .......................... 19
Introduction.. ........................................ 19
Preliminary Design Considerations........................ 20
Choice of Materials................................... 21
The ModeratorReflector Material...................... 21
The Fissioning Fuel Material ......................... 24
The Working Fluid Material...... .................... 29
Description of a Uranium TetraFluoride, UTVR/Disk
MHDRankine Power Cycle.............. ............... 29
Neutronic Analysis of the Ultrahigh Temperature Vapor
Core Reactor......................................... 37
Static Neutronic Calculations......................... 37
Dynamic Neutronic Calculations........................ 39
IV STATIC, ONEDIMENSIONAL, UTVR NUCLEAR CHARACTERIZATION
AND CONFIGURATION OPTIMIZATION .......................... 40
Introduction ........................................... 40
Scoping Calculations.............. .. .................. 43
Geometric Variations.................................. 43
UTVC radius....................................... 43
Inner BeO moderatorreflector region thickness..... 50
Outer BeO moderatorreflector 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
OneDimensional Results................................. 84
The Neutron Multiplication Factor..................... 86
Power Sharing Factor.................................. 87
Spherical "Mockup" Comments ............................ 90
V STATIC, TWODIMENSIONAL, UTVR NUCLEAR CHARACTERIZATION
AND CONFIGURATION OPTIMIZATION .......................... 94
Introduction .......................................... 94
Scoping Calculations in R0 Geometry..................... 96
Geometric Variations.. .............................. 98
UTVC radius variations............................. 98
Inner BeO moderatorreflector region thickness
variations .................................. 104
Variation in the area of the boiler columns........ 107
Variation in the number of boiler columns.......... 109
Fuel/WorkingFluid 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 RZ 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
TwoDimensional Results................................. 144
The Neutron Multiplication Factor.................... 144
The Power Sharing Factor............................. 146
Remarks.............................................. 148
VI STATIC, THREEDIMENSIONAL 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 VarianceReduction Techniques.......... 165
Nuclear and Physical Characteristics of the UTVR...... 166
Energy Cutoff........... ................... ........ 168
Implicit Capture and Weight Cutoff.................... 168
Weight Windows.................................... 173
BoilertoUTVC 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 FOURBOILER COLUMN UTVR SYSTEM....... 209
Introduction .. ......................................... 209
The FourBoiler Column UTVR System Coupled Core Point
Reactor Kinetics Equations ........................... 209
CoretoCore FuelFlow Coupling....................... 211
CoretoCore Neutron Transport Coupling............... 214
SteadyState Solution ................................ 218
The Linearized UTVR CCPRK 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 CoretoCore 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 NeutronGamma Libraries from ENDF/B..... 309
The AMPXDRIVER module ............................... 311
The XLACS module................................... 311
The NITAWL module................................. 312
The XSDRNPM module ................................ 312
DOT4: A One and TwoDimensional Neutron/Photon
Transport Code....... .............................. 315
GIP................................................ 316
MCNPA General Monte Carlo Code for Neutron and
Photon Transport................................ 317
Description of the EASY5 Engineering Analysis Program.... 318
B BENCHMARK CALCULATIONS OF XSDRNPM AND DOT4 WITH MCNP....... 320
Comparison of XSDRNPM with MCNP ......................... 320
Comparison of DOT4 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 CIRCULATINGFUEL, COUPLED CORE POINT REACTOR
KINETICS EQUATIONS....................................... 345
Description and Definition of Symbols, Parameters, and
Terms used in the CirculatingFuel, 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 (D1) and (D4)........... 361
Equation (D1) ................................... 361
Equation (D4).................................... 365
LIST OF REFERENCES.............................................. 366
BIOGRAPHICAL SKETCH....... ... ....... ...... .............. ..... 371
LIST OF TABLES
Table Page
31 Properties of Selected Metal Fluoride Working Materials..... 30
32 200 MW UF /UTVR Power Cycle Therm9dynamic Operating
ChaFacteristics for NaF, KF, Li F, and RbF Working
Fluids.............................................. .. 34
33 Energy Balance7Data for 200 MW UF,/UTVR Power Cycle with
NaF, KF, Li F, and RbF Workng Fluids................... 35
34 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
41 kfA as a function of Voided UTVC Radius for the UF4/NaF
efankine Cycle System.................................. 48
42 kefr as a function of the Liquid UF4 Core Volume for a
Two Region Reactor.................................... 60
43 keff as a function of UTVC Radius and Metal Fluoride Type... 69
44 kef, as a function of NaF Entrance Velocity and Average
Density in the Wall Cooling Region....................... 72
45 kefr as a function of Metal Fluoride Type and Wall
Cooling Region Thickness................................ 74
46 k e and P /P as a function of NaF Diverted Flow
Rate toUtlf B9CT1r Region............................... 75
47 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
48 Reactivity Penalty (6k/k) as a function of UTVC Liner
Material Thickness............................... ... .. 82
49 Reactivity Penalty (6k/k) as a function of Boiler Region
Liner Material Thickness .............................. 83
410 Reactivity Penalty (6k/k) as a function of Both the UTVC
and Boiler Region Liner Material Thickness............... 85
x
Table Page
51 kef and P Tvr/P RO as a function of UTVC Radius for the
'6F /NaFURAiki f0Cycle System in RO Geometry for a
FourBoiler and an EightBoiler Column UTVR
Configuration ............................................ 101
52 kef and P /Pn as a function of the Number of UF4
oiler Clumn Ch RO Geometry.......................... 111
53 UF4 Temperature and Density Profiles in the UTVC as a
function of Radial Distance for a FourBoiler Column
UTVR Configuration in the R0 Coordinate System.......... 120
54 UTVR Dimensions of the Reference RZ Cylindrical
Configuration ............................................ 125
55 k e, P ITC/Pg p, and P P hl as a function of
hGe Mo torRefpYgei r lifane Separator Slab
Region Height ...................................... 127
56 keff, P T /P C and P /nr/Ph le r versus the Top BeO
ModeatorReector Rh H ...................... 130
57 kef, P TVP/P r, and PJ as a function of
ethe Frt OW r BeO MggetatoPo sector Region
(OBEO#1) Height ...................................... 132
58 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
59 kf P /P and P P "e as a function of
kef oly Num BRckness sPP un gehe Boiler Feedlines
Region............................................... 138
61 Description of UTVR Regions Employed in the Three
Dimensional MCNP Monte Carlo Calculations................ 155
62 Reactivity Worths of the Boiler Feedlines, UTVC Inlet
Plenums, and MHD Duct Regions........................... 159
63 Selected UTVR Results from a 30Minute MCNP Monte Carlo
Analog Calculation Performed on a CRAY XMP/48
Supercomputer ............................................ 162
64 UTVR Fission Rate as a function of Neutron Energy........... 169
65 Effect of Employing Energy Cutoff on the UTVC and Boiler
Column FOM Tallies............................. ...... 169
Table Page
66 Effect of Employing Implicit Capture and Weight Cutoff on
the UTVC and Boiler Column FOM Tallies................... 171
67 Effect of Employing Weight Windows on the UTVC and Boiler
Column FOM Tallies.................................... 175
68 Effects of Employing VarianceReduction Techniques in
MCNP MonteCarlo Calculations on Uncertainties of
Selected UTVR Parameters............................... 177
69 Effects of Employing VarianceReduction Techniques and
utilizing BoilertoUTVC Symmetry in MCNP MonteCarlo
Calculations on Uncertainties of Selected UTVR
Parameters ............................................... 184
610 Integral Kinetics Parameters as a function of the UF4
Partial Pressure in the UTVC .......................... 201
611 Integral Kinetics Parameters as a function of Saturated
Liquid Cone Region Height for Two Different H Values.. 203
612 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
613 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
614 Integral Kinetics Parameters as a function of Vapor Cone
Region Density at a UF4 Partial Pressure of 5 atm in
the UTVC ............................................... 208
81 Values of Selected UTVR Parameters at the Initial,
Unperturbed Steady State Condition ...................... 267
82 Relevant Properties for the UF Fuel, NaF Working Fluid,
and the UF4/NaF Fuel/Working Fluid Mixture............... 268
83 Final Equilibrium Conditions as a Result of $ 1.00 Positive
and Negative Reactivity Step Insertions Imposed on the
Boiler Columns....................................... 278
84 Final Equilibrium Conditions as a Result of $ 0.20 Positive
and Negative Reactivity Step Insertions Imposed on the
UTVC................................................. 282
85 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
86 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
B1 XSDRNPM and MCNP Benchmark Calculations on a FiveRegion
Spherical "Mockup" of the UTVR......................... 322
B2 DOT4 and MCNP Benchmark Calculations on the Cylindrical
"Mockup" of the UTVR in both the R9 and RZ
Coordinate Systems..................................... 326
C1 Comparison of Results obtained from ISCE with Results
obtained Directly using MCNP for Two Different UTVR
Fuel Loadings........................................ 343
D1 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
11 Side View Schematic of the Ultrahigh Temperature
Vapor Core Reactor...................................... 3
12 Top View Schematic of the Ultrahigh Temperature
Vapor Core Reactor...................................... 5
31 UF6 and UF4 Saturation Vapor Curves......................... 25
32 Uranium Metal and UF4 Saturation Vapor Curves............... 27
33 Partial Pressures of Constituent Species of the Uranium
Fluorine System at One Atmosphere ....................... 28
34 Schematic of a 200 MWe UF4/KF UTVR MHDRankine Cycle Power
System ................................................. 31
41 Four Region, OneDimensional Spherical "Mockup" of
the UTVR............................................. 41
42 keff and PUTVC/PBCOL as a function of the UTVC Radius....... 45
43 kef and Fission Rates of the UTVC and the Boiler as a
function of the UTVC Radius............................. 46
44 k and P T/P as a function of the Inner BeO
Moderate rRef Ttor Region Thickness..................... 51
45 kef as a function of the Inner BeO ModeratorReflector
Region Thickness........................................ 53
46 kefc and PRTVr/Pr as a function of the Outer BeO
Moderate rRefT~E or Region Thickness..................... 56
47 ke and PUT/PRrn as a function of the UF4 Inlet
Velocity t te.Boiler Region....................... 58
48 keff and PuTVC/Prni as a function of the UF4 Partial
e Pressure 1in tf UTVC.................................... 63
49 k as a function of the U235 Enrichment at Different
eF4 Partial Pressures in the UTVC...................... 64
xiv
Figure Page
410 kef as a function of the Fissile Fuel (U235 and U233)
Enrichment ............................................. 65
411 kef and PUTv /PBC as a function of the UF4 Average
Density in the Biler Region.............. .............. 67
412 Five Region, OneDimensional Spherical "Mockup" of the
UTVR................................................. 71
413 kef and P v/PR i as a function of the UF4/NaF Inlet
Velocity t 0 tfl Boiler Region............................ 77
414 k and P /PC as a function of the Li6F Mass Flow
Rate to tUf B/p r Region............................... 78
51 Six Region, TwoDimensional RB Representation of a
UTVR with SixBoiler Columns ............................ 97
52 kf and P TVC/PCnL as a function of the UTVC Radius for a
eour ad n EhtBoiler Column UTVR Configuration...... 100
53 kf and P /P as a function of the Inner BeO
eIoderatTrReft or Region Thickness for a Four
Boiler Column UTVR ........... .......................... 106
54 k f and P /PBC as a function of the UF Inlet Velocity
efto the HBYer ion for a FourBoiler CoTumn............ 108
55 kff and PTvr/P o as a function of the UF Partial
Pressure in t ObTVC for a FourBoiler Cotumn
UTVR System............................................ 113
56 kff and P C/PC as a function of the UF4 Average
Density iu the Biler Region for a SixBoiler Column
UTVR System............................................ 117
57 Thermal Neutron Flux and Vapor Fuel Temperature Profile as a
function of Radial Position from the Centerline of the
UTVC for a FourBoiler Column UTVR System................ 118
58 Representation of the UTVR in the RZ Coordinate System..... 122
59 The Horizontal Boiler Configuration of the UTVR in the RZ
Coordinate System................................. .. .. 143
61 Side View Schematic of the FourBoiler Column UTVR on the
yz Plane at x=0.0................................... 153
62 Side View Schematic of a Boiler Column ..................... 157
Figure Page
63 Top View Schematic of a FourBoiler Column UTVR System...... 180
71 Schematic of the CoretoCore Circulating Fuel Coupling..... 212
72 Schematic of BoilertoUTVC Neutron Transport Coupling for
a FourBoiler Column UTVR System........................ 215
73 Schematic of BoilertoBoiler and UTVCtoBoiler Neutron
Transport Coupling for a FourBoiler Column UTVR System.. 217
74 Block Diagram of the UTVC Transfer Function................. 228
75 Block Diagram of the Boiler Column Transfer Function........ 230
76 Block Diagram of the UTVR Transfer Function................. 231
77 Fuel/Working Fluid Density Profile in the Boiler Column
due to Boiling in Space (=zero gravity).................. 234
78 Side View Schematic of the UTVC............................ 251
81 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
82 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
83 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
84 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
85 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
86 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
87 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
88 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
89 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
810 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 t0 sec with the
UTVC Fuel Mass Reactivity Feedback Coefficient Reduced
by a Factor of Five.................................. 292
811 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
AI Schematic of the Flow between the AMPX System Code Modules.. 314
C1 Example of the ISCE Code Input Data File.................... 339
C2 Input Data Files List Format............................... 340
C3 Output File as obtained from ISCE.......................... 341
D1 Schematic of Neutrons and Neutron Interactions in the UTVR.. 348
02 Top View Schematic of the Plasma Core Assembly (PCA)........ 357
D3 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 TETRAFLUORIDE, 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 ), externallymoderated,
coupled core, highlyenriched U235, circulatingfuel, steadystate,
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 highlyenriched 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 multicore configuration resulting in a coupledcore 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 twophase fissioning fuel, i.e., a liquidvapor
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 vaporfuel
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,
coretocore 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 nonlinear
model, which incorporates circulatingfuel, coupledcore, 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 liquidto
vapor phase change in VCRs. Studies performed on VCRs and GCRs indicate
that gaseousfueled (or vaporfueled) 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 [19].
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:
Stationkeeping 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 externallymoderated, circulating fuel reactor with uranium
tetrafluoride (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 11 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 highlyenriched 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 11. 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
(midplane 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
11. 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 liquidvapor region, and the
superheated vapor region.
Shown in Figure 12 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 11. These are the midplane BeO region
OBEO
Figure 12. 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 UF4Metal
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
UF4Metal 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 coretocore 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 coretocore
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 spacetime 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 twodimensional neutronic
calculations are presented in Chapters IV and V, respectively. These
calculations are performed with XSDRNPM [10], a onedimensional discrete
ordinates (Sn) neutron transport code, and with DOT4 [11], a one and
twodimensional 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
threedimensional analysis are obtained from the static neutronic
analysis results presented in Chapters IV and V.
The results obtained from static threedimensional neutronic
calculations are presented in Chapter VI. These calculations are
performed using MCNP [12], a threedimensional Monte Carlo neutron
transport code. Parameters such as UTVC and boiler core reactivities
and reaction rates, coretocore 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 coretocore neutron
transport coupling coefficients and the reactivities of the vapor and
boiler cores are derived and described in Chapter VI.
The circulatingfuel, coupled core, point reactor kinetics
equations for a fourboiler 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 coretocore 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 R8 and RZ cylindrical coordinates
with DOT4 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 coretocore 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), externallymoderated, coupledcore (vapor and
boiling cores), highlyenriched, 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 multicore configuration resulting in a coupledcore 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 twophase fissioning fuel, i.e., a liquidvapor
combination.
Studies on reactors combining all three of these key features have
never been reported. However, studies and research pertaining to
coupledcore 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 moderatorreflector 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 fastthermal 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 fastthermal reactors.
These include modular cores of large thermal power reactors, clustered
reactors, and Argonauttype 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 phasespace 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) (21)
dt A
d(t) N(t) (t) + e (22)
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 (21) describes the time dependent behavior of the neutron
population level and Equation (22) 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 (22).
MacPhee compared two approximate methods with the "exact" model.
In the approximate methods, modified versions of Equation (22) are
employed. The first method employs reduced values for # as shown by
dC(t)_ f N(t) C(t) (23)
dt A
where f is the fraction of delayed neutrons lost as a result of the fuel
circulating and is given by
7C
f = (24)
Tc + Tj
The second method neglects the delay time associated with the
delayed neutron precursors reentering the core, i.e., C(tT,) = C(t).
With this assumption, the equation describing the delayed neutron
precursors concentration is
dC(t) = N(t)  C(t) (25)
dt A aD
where aD is the delayed neutron attenuation factor, obtained from steady
state conditions imposed on Equation (22), and is given by
rTc
aD = T (26)
XTc + 1 e
MacPhee analyzed the "exact" model by linearizing Equations (21)
and (22), 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 selfsustained oscillations as a result of
the feedback produced by the delayed neutron precursors reentering
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 (26) 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 reenter 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 TETRAFLUORIDE,
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 UF4Metal 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 twoannual
tests during the sevenyear 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 externallymoderated, circulating fuel reactor
with UF4 as the fissioning fuel and a metalfluoride 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 moderatorreflector material, UF4 as the fuel, and metal
fluoride as the working fluid is based on the following considerations.
The ModeratorReflector Material
For thermal reactors, moderatorreflector 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 berylliumoxide (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 moderatorreflector 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 slowingdown 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 slowingdown power (exls = average logarithmic energy loss per
collision x macroscopic scattering cross section) of 16 mI for Be
versus 6.5 m1 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 slowingdown length, TT, (=192 cm versus
=100 cm) compared to Be. The larger values of LT and TT require
graphitemoderated 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 moderatorreflector
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 moderatorreflector 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 moderatorreflector materials for the Nuclear Piston Engine
which employed an externallymoderated UF6fueled 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 slowingdown 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 moderatorreflector 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
wellsuited moderatorreflector 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 vaporfueled 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 31 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 32. 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 31
and 32, and the mole fraction of constituent species versus temperature
curve of the uraniumfluorine system, Figure 33 [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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extremely low UF6 heat rejection temperatures are avoided. Thus, UF4
has a saturation vapor pressuretemperature behavior that is highly
desirable for a direct Rankine cycle burst power system for a space
environment. Also, Figure 33 indicates that in the expected gas
temperature operating range of 2500 K to 4000 K, UF4 is the predominant
uraniumfluorine 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 31 list relevant properties of these materials.
Description of a Uranium TetraFluoride,
UTVR/Disk MHDRankine Power Cycle
An example UF4/KF UTVR MHDRankine cycle power system schematic is
shown in Figure 34. 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 34, about 40 MW is required
to vaporize the liquid UF4 in the UF4boiler. 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 32 lists 200 MWe UF4/UTVR power cycle operating
characteristics for KF, NaF, Li7F, and RbF working fluids. Table 33
presents the energy balance data for a 200 MWe UF4/UTVR power cycle with
KF, NaF, Li7F, or RbF as the working fluids. Table 32 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 34 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 overestimates 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 crosssections 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 123neutron group library is then
collapsed first to 27 and then to fourneutron groups using XSDRNPM
[10].
Fourneutron group, 1D, 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 1D calculations. Basic static neutronic
characteristics of the UTVR are obtained from the 1D 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 1D neutronic
static calculations.
Twodimensional Sn cylindrical geometry calculations in the RO and
the RZ coordinate systems are performed using DOT4 [11]. The four
neutron group crosssection library produced by XSDRNPM is converted to
DOT4 format using GIP [28]. In R9 geometry, the boiler region can be
accurately modeled as a number of boiler columns separated by BeO
moderator. The nozzle, diskMHD generator, and diffuser regions can all
be modeled in the RZ geometry. Results obtained from the 1D spherical
"mockup" of UTVR are compared with results obtained from calculations
performed in the R9 and the RZ coordinate systems. These comparisons
are necessary to determine the reliability of the obtained results.
The reference UTVR configuration for the 3D analysis is obtained
from 1 and 2D static neutronic calculation results. The 3D
calculations are performed using MCNP [12], a 3D 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
tocore coupling coefficients, and the reactivity and neutron
multiplication factors of individual cores.
Dynamic Neutronic Calculations
The overestimate 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
circulatingfuel, coupledcore, 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, ONEDIMENSIONAL, UTVR NUCLEAR
CHARACTERIZATION AND CONFIGURATION OPTIMIZATION
Introduction
The initial onedimensional (1D) spherical "mockup" configuration
used to perform the preliminary nuclear characterization of the
Ultrahigh Temperature Vapor Core Reactor (UTVR) is shown in Figure 41.
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) moderatorreflector
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
moderatorreflector region (OBEO).
The actual cylindrical reactor system is converted to the 1D
spherical geometry by conserving the volumes of the UTVC and the boiler
cores and by conserving the thicknesses of the inner and outer BeO
moderatorreflector 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 41. Four Region,
"Mockup" of
OneDimensional Spherical
the UTVR
Modeling the UTVR in the 1D 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 surfacetovolume ratio.
2. Neutron streaming from the MHD duct is not accounted for since the
MHD duct regions is not included in the 1D spherical "mockup."
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 1D 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 1D spherical "mockup"
represents a "clean" UTVR system.
Detailed threedimensional 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 1D 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 1003
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 42 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 43, 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 decoupling 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 1D spherical "mockup" 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 42) is due to the
increase in PUTVC and the decrease of PBCOL as shown in Figure 43.
Although not shown in Figure 43, 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 41 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 43). 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 decoupling 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 decoupling 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 43, the gain in 6k/k for
the loaded UTVC is about 0.28 (or 9.3 x 1003 6k/k per cm of IBEO) and
the loss in 6k/k for the loaded boiler is only 0.08 (2.7 x 1004 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 1003 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 1003 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 43 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 moderatorreflector 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 1003
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 44 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 44 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 1003
m3). The results are shown in Figure 45.
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 45, as IBEO increases from 10 to 45 cm, the
values of 6k/k per cm of IBEO are +1.9 x 1003 and 4.8 x 1003 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
affected by the variation in IBEO are those listed in items 1 and 2
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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 45, and due to an increase in boilertoUTVC
neutronic coupling) and PBCOL increases (due to enhanced neutronic
coupling of the boiler region, as shown in Figure 45). 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 45
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 boilertoUTVC 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 45, for the IBEO thickness
range from 45 to 60 cm, the values of 6k/k per cm of IBEO are about 5.1
x 1003 and +3.0 x 1004 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 boilertoUTVC, UTVCtoboiler, 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 moderatorreflector region thickness
Maintaining the UTVC radius at 60 cm, the IBEO thickness at 15 cm,
and the boiler volume at 8.5 x 1003 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 46 where keff and
PUTVC/PBCOL are plotted as a function of OBEO thickness.
Figure 46 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 "mockedup"
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 47.
Figure 47 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 1D calculations is not
reasonable since the boiling and nonboiling 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 1003 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/metalfluoride
nuclear power system is the unwanted possibility of selfcriticality 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 selfcritical even under extreme
conditions. For this study, a two region core, in 1D 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 42. 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
selfcritical 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 1D
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 1003 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 48.
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 48 indicates that keff saturates at UF4
partial pressures above =10 atm. This corresponds to a U235 density of
2.5 x 1005 atoms/barncm. Beyond a UF4 partial pressure of 10 atm or a
U235 density of 2.5 x 1005 atoms/barncm, the UTVC is becoming black to
neutrons. The results, as shown in Figure 48, 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 49, 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 410, indicate the same behavior
as obtained in Figure 49 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 411, 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
overall cycle analysis may prove that a metal fluoride other than NaF
(e.g., KF, RbF, or Li7F) provides better overall 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 1003 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 43, 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 412 shows the five region 1D spherical "mockup" 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 44, 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
Region 2 
Region 3
Region 4
Region 5
Figure 412. Five Region,
"Mockup" of
OneDimensional Spherical
the UTVR
72
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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 45.
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 43 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 46 also indicates that as the NaF is diverted to the boiler
region, the thermodynamic requirement for PUTVC/PBCOL decreases while
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76
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 46, 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 413,
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/NaFLi6F inlet velocity is fixed at 2 m/sec. The Li6F
mass flow rate is varied from 5.2 x 1003 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 414. However, the required PUTVC/PBCOL value of 1.25
is not achieved in the 1D configuration.
77
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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 1D 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 1D 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 47.
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.