Citation

## Material Information

Title:
Static and dynamic neutronic analysis of the uranium tetra-fluoride, ultrahigh temperature, vapor core reactor system
Creator:
Kahook, Samer Dakhlallah, 1961- ( Dissertant )
Dugan, Edward T. ( Thesis advisor )
Lear, William E. ( Reviewer )
Person, Willis B. ( Reviewer )
Phillips, Winfred M. ( Degree grantor )
Lockhart, Madelyn M. ( Degree grantor )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
1991
Language:
English
Physical Description:
xx, 372 leaves : ill. ; 29 cm.

## Subjects

Subjects / Keywords:
ATMs ( jstor )
Boilers ( jstor )
Cooling ( jstor )
Coupling coefficients ( jstor )
Geometry ( jstor )
Inlets ( jstor )
Liquids ( jstor )
Neutrons ( jstor )
Reactivity ( jstor )
Vapors ( jstor )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF
Nuclear Engineering Sciences thesis Ph. D
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Abstract:
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 MW^^/m ), externally-moderated, 235 coupled core, highly-enriched U , circulating-fuel, steady-state, burst power reactor. The investigated reactor system includes two types of fissioning regions: (1) the central Ultrahigh Temperature Vapor Core region (UTVC) which contains a vapor mixture of highly-enriched uranium tetrafluoride (UF^) 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 UF^ fuel. The combination of three features differentiates the UTVR from other nuclear reactor concepts. These three features are as follows: 1. the multi-core configuration resulting in a coupled-core system by means of direct neutron transport through the media; 2. the circulating fuel and the associated neutronic and mass flow coupling between the UTVC and boiler cores; and 3. the employment of a two-phase fissioning fuel, i.e., a liquid-vapor combination. Static and dynamic neutronic analysis of this novel system indicates distinct advantages over other existing or conceptual nuclear power systems. These include a unique combination of some very effective inherent negative reactivity feedbacks such as the vapor-fuel density power coefficient of reactivity, the direct neutronic coupling among the multiple fissioning core regions, and the mass flow coupling feedback between the two types of fissioning cores. Static neutronic analysis is performed using multidimensional discrete ordi nates and Monte Carlo neutron transport codes. Parameters such as the UTVC and boiler column reactivities and reaction rates, core-to-core neutronic coupling coefficients, and neutron lifetimes as a function of vapor core density and boiler core liquid volume are obtained from the static neutronic analysis. The dynamic behavior of the UTVR is examined using a non-linear model, which incorporates circulating-fuel, coupled-core, point reactor kinetics and energetics 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 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. Thesis: Thesis (Ph. D.)--University of Florida, 1991. Bibliography: Includes bibliographical references (leaves 366-370) Additional Physical Form: Also available on World Wide Web General Note: Typescript. General Note: Vita. Statement of Responsibility: by Samer Dakhlallah Kahook. ## Record Information Source Institution: University of Florida Holding Location: University of Florida Rights Management: Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. Resource Identifier: 026382369 ( AlephBibNum ) 25138701 ( OCLC ) AJA1243 ( NOTIS ) Downloads ## This item has the following downloads: Full Text STATIC AND DYNAMIC NEUTRONIC ANALYSIS OF THE URANIUM TETRA-FLUORIDE, ULTRAHIGH TEMPERATURE, VAPOR CORE REACTOR SYSTEM By SAMER DAKHLALLAH KAHOOK A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1991 Dedicated to my parents, Mr. and Mrs. Dakhlallah Kahook, asking Allah to reward them, have mercy on them, and grant them paradise as they raised and cherished me in my childhood. ACKNOWLEDGEMENTS The author would like to express his appreciation and sincere thanks to the members of his supervisory committee, Dr. Edward T. Dugan, Dr. Nils J. Diaz, Dr. Alan M. Jacobs, Dr. Samim Anghaie, Dr. William E. Lear, Jr., and Dr. Willis B. Person for their guidance and assistance during the course of this research. Special thanks are extended to Dr. Dugan, chairman of the author's supervisory committee for his patience and enduring support. The author recognizes that much of his knowledge in reactor physics and computer programming was realized while researching under the guidance and direction of Dr. Dugan. Support for this research has been provided, in part, by the Air Force Wright Aeronautical Laboratories (AFWAL), the Frederick Hauck Fund, and the University of Florida. The AFWAL work was performed for the Innovative Science and Technology Directorate of the Strategic Defense Initiative within the Innovative Nuclear Space Power Institute (INSPI). This support is greatly appreciated. Funding for the computer analysis was provided for by the National Science Foundation at the San Diego Supercomputer Center and the University of Florida and the International Business Machines (IBM) Corporation through their Research Computing Initiative at the North East Regional Data Center. The author is grateful for these funds. iii Thanks are also due to the fellow students whose friendships, comments, and encouragements have also facilitated in this research. The author would like to express his love and respect to his parents Mr. and Mrs. Dakhlallah Kahook, to his brothers Nofal and Mohammed, and to his sisters for their love, understanding, and patience throughout the author's stay at the University of Florida. The financial support provided to the author by his family is gratefully acknowledged. Finally, the author would like to express his love and deepest appreciation to his wife, Layali, whose understanding, patience, and support provided the motivation needed to finish this research. TABLE OF CONTENTS Page ACKNOWLEDGEMENTS .... ............................................ iii LIST OF TABLES.................................................. x LIST OF FIGURES ................................................... xiv ABSTRACT........................................................ xviii CHAPTER I INTRODUCTION................................................ 1 Introduction ........................................... 1 Description of the Ultrahigh Temperature Vapor Core Reactor.... ........................................ 2 Dissertation Objectives ................................ 6 Dissertation Organization............................... 7 II PREVIOUS RESEARCH ON RELATED CONCEPTS........................ 11 Introduction .......................................... 11 Previous Research on Gas Core Reactors................... 12 Previous Research on Coupled Core Reactors............... 13 Previous Research on Circulating Fuel Reactors............ 14 Remarks............................................... 18 III DESIGN OF THE URANIUM TETRA-FLUORIDE, ULTRAHIGH TEMPERATURE VAPOR CORE REACTOR .......................... 19 Introduction.. ........................................ 19 Preliminary Design Considerations........................ 20 Choice of Materials................................... 21 The Moderator-Reflector Material...................... 21 The Fissioning Fuel Material ......................... 24 The Working Fluid Material...... .................... 29 Description of a Uranium Tetra-Fluoride, UTVR/Disk MHD-Rankine Power Cycle.............. ............... 29 Neutronic Analysis of the Ultrahigh Temperature Vapor Core Reactor......................................... 37 Static Neutronic Calculations......................... 37 Dynamic Neutronic Calculations........................ 39 IV STATIC, ONE-DIMENSIONAL, UTVR NUCLEAR CHARACTERIZATION AND CONFIGURATION OPTIMIZATION .......................... 40 Introduction ........................................... 40 Scoping Calculations.............. .. .................. 43 Geometric Variations.................................. 43 UTVC radius....................................... 43 Inner BeO moderator-reflector region thickness..... 50 Outer BeO moderator-reflector region thickness..... 55 UF4 boiler region thickness....................... 57 UF boiler core volume............................. 59 Fuel Density Variations.............................. 61 UF4 partial pressure and mole fraction (UF4:NaF) 2. in the UTVC ............................. ...... 61 U23 enrichment in UF,............................. 62 U23 as the fissile i otope....................... 62 Average density of the UF4 in the boiler region.... 66 Material Variations.......................... ...... 68 Choice of metal fluoride in UTVC................... 68 Wall cooling region..................... ......... 70 Other metal fluoride working fluids................ 70 NaF mass flow rate to the boiler region............. 73 UF /NaF inlet velocity to the boiler............... 76 Addition of Li F poison to the boiler.............. 76 BeO in the annular boiler region................... 79 Reactivity effects of liner materials.............. 81 One-Dimensional Results................................. 84 The Neutron Multiplication Factor..................... 86 Power Sharing Factor.................................. 87 Spherical "Mock-up" Comments ............................ 90 V STATIC, TWO-DIMENSIONAL, UTVR NUCLEAR CHARACTERIZATION AND CONFIGURATION OPTIMIZATION .......................... 94 Introduction .......................................... 94 Scoping Calculations in R-0 Geometry..................... 96 Geometric Variations.. .............................. 98 UTVC radius variations............................. 98 Inner BeO moderator-reflector region thickness variations .................................. 104 Variation in the area of the boiler columns........ 107 Variation in the number of boiler columns.......... 109 Fuel/Working-Fluid Density Variations................. 110 UF4 partial pressure in the UTVC................... 112 Average UF density in the boiler columns.......... 115 Varying the UF4 average density in the UTVC as a function of the radial distance from the center line ................................... 116 Scoping Calculations in R-Z Geometry .................... 121 Geometric Variations.. .............................. 124 PaRe CHAPTER V MBEO region height................................. 124 (cont.) TBEO region height................................. 129 First OBEO region height............................ 131 Boiler: subcooled and saturated liquid region height ...................................... 134 Material Variation.................................... 136 Poisoning the boiler feedline walls................ 136 Comments on Power Sharing ............................ 140 Two-Dimensional Results................................. 144 The Neutron Multiplication Factor.................... 144 The Power Sharing Factor............................. 146 Remarks.............................................. 148 VI STATIC, THREE-DIMENSIONAL NEUTRONIC ANALYSIS OF THE UTVR.... 151 Introduction .. ......................................... 151 Description of the UTVR Geometry in MCNP................. 152 Description of the Boiler Column...................... 156 Reactivity Worths of the Boiler Feedlines, UTVC Inlet Plenums, and the MHD Duct Regions..................... 158 Reducing the Uncertainty in Parameters Associated with the Boiler Columns in MCNP Calculations............... 161 Performance of Variance-Reduction Techniques.......... 165 Nuclear and Physical Characteristics of the UTVR...... 166 Energy Cutoff........... ................... ........ 168 Implicit Capture and Weight Cutoff.................... 168 Weight Windows.................................... 173 Boiler-to-UTVC Symmetry.............................. 178 Neut ~o Transport Coupling Coefficients.................. 185 Obtained Directly from MCNP...................... 187 f i Obtained Indirectly from MCNP.................... 189 Isolation of secondary coupling effets...... ..... 190 Neutron Multiplicatign Factor of the j Core, keff... 197 Reactivity of the j Core, p ... ................... 198 Prompt Neutron Generation Time, A (t)................ 198 Results of Density Variations in the UTVC and Boiler Columns............................................ 199 VII KINETIC EQUATIONS OF A FOUR-BOILER COLUMN UTVR SYSTEM....... 209 Introduction .. ......................................... 209 The Four-Boiler Column UTVR System Coupled Core Point Reactor Kinetics Equations ........................... 209 Core-to-Core Fuel-Flow Coupling....................... 211 Core-to-Core Neutron Transport Coupling............... 214 Steady-State Solution ................................ 218 The Linearized UTVR CC-PRK Equations.................. 221 Inherent Reactivity Feedbacks of the UTVR............... 229 Reactivity Feedback of the Boiler Columns, 6p (t)..... 233 Reactivity Feedback of the UTVC, Sp (t)............... 251 vii CHAPTER Page VIII DYNAMIC ANALYSIS OF THE UTVR............................... 264 Introduction .. ......................................... 264 The Unperturbed UTVR Configuration....................... 265 Results of the Dynamic Analysis ......................... 269 Boiler Column Reactivity Perturbation................. 269 UTVC Reactivity Perturbation ......................... 276 Variations in Core-to-Core Direct Neutron Transport Delay Times...................................... 283 Variations in the Coupling Coefficients............... 287 Variations in the UTVC Fuel Mass Reactivity Feedback Coefficient....................................... 291 Concluding Remark................................ ....... 296 IX SUMMARY OF RESULTS, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH... ................................ 300 Introduction .. ......................................... 300 Summary of Results...................................... 300 Results from the Static Neutronic Analysis............ 300 Results from the Dynamic Neutronic Analysis........... 302 Comments and Conclusions............................... 303 Recommendations for Further Research..................... 305 Static Neutronic Analysis ............................ 305 Dynamic Neutronic Analysis ........................... 307 APPENDICES A DESCRIPTION OF THE COMPUTER CODES .......................... 309 Introduction .. ......................................... 309 Description of Nuclear Codes ............................ 309 AMPX: A Modular Code System for Generating Coupled Multigroup Neutron-Gamma Libraries from ENDF/B..... 309 The AMPX-DRIVER module ............................... 311 The XLACS module................................... 311 The NITAWL module................................. 312 The XSDRNPM module ................................ 312 DOT-4: A One- and Two-Dimensional Neutron/Photon Transport Code....... .............................. 315 GIP................................................ 316 MCNP-A General Monte Carlo Code for Neutron and Photon Transport................................ 317 Description of the EASY5 Engineering Analysis Program.... 318 B BENCHMARK CALCULATIONS OF XSDRNPM AND DOT-4 WITH MCNP....... 320 Comparison of XSDRNPM with MCNP ......................... 320 Comparison of DOT-4 with MCNP............................ 324 Conclusion .. ........................................... 329 viii CHAPTER Paqe APPENDICES Page C DESCRIPTION OF THE ISOLATOR OF SECONDARY COUPLING EFFECTS CODE......................................... 331 Introduction .. ......................................... 331 Description of the ISCE Code............................ 331 The MAIN Module.................................. .. 331 The REED Module...................................... 332 The ERIN Module..................................... 332 The NOUT Module............................... ...... 333 The ESTM Module.................................. .. 333 The RITE Module ................................... .. 337 Input Data Format ..................................... 337 Input Data File ..................................... 337 List of Input Data Files.............................. 339 Comparison of Results Obtained from ISCE with Results Obtained Directly from MCNP .......................... 340 D CIRCULATING-FUEL, COUPLED CORE POINT REACTOR KINETICS EQUATIONS....................................... 345 Description and Definition of Symbols, Parameters, and Terms used in the Circulating-Fuel, Coupled Core Point Reactor Kinetics Equations...................... 350 Definition of Superscripts and Subscripts............. 350 Definition of Integral P rameters..................... 351 Neutron population, NJ(t).......................... 351 Reactivity, pJ(t)................................. 354 Effective delayed neutron fractio A(t)........... 354 Prompt neutron generation time, A^(t)............. 358 Effective dejlyed neutron precursor concentration for the i delayed neutron grQu, Ci(t)........ 358 Effective coupling coefficient, i (t)............ 359 Interpretation of Equations (D-1) and (D-4)........... 361 Equation (D-1) ................................... 361 Equation (D-4).................................... 365 LIST OF REFERENCES.............................................. 366 BIOGRAPHICAL SKETCH....... ... ....... ...... .............. ..... 371 LIST OF TABLES Table Page 3-1 Properties of Selected Metal Fluoride Working Materials..... 30 3-2 200 MW UF /UTVR Power Cycle Therm9dynamic Operating ChaFacteristics for NaF, KF, Li F, and RbF Working Fluids.............................................. .. 34 3-3 Energy Balance7Data for 200 MW UF,/UTVR Power Cycle with NaF, KF, Li F, and RbF Workng Fluids................... 35 3-4 PUTX/PgC as a function of the Metal Fluoride Mass Flow te- Cb the Boiler Region as Required on the Basis of Thermodynamic/Flow Considerations ....................... 36 4-1 kfA as a function of Voided UTVC Radius for the UF4/NaF efankine Cycle System.................................. 48 4-2 kefr as a function of the Liquid UF4 Core Volume for a Two Region Reactor.................................... 60 4-3 keff as a function of UTVC Radius and Metal Fluoride Type... 69 4-4 kef, as a function of NaF Entrance Velocity and Average Density in the Wall Cooling Region....................... 72 4-5 kefr as a function of Metal Fluoride Type and Wall Cooling Region Thickness................................ 74 4-6 k e and P /P as a function of NaF Diverted Flow Rate toUtlf B9CT1r Region............................... 75 4-7 k f and PUTV/Pol as a function of UF Average Density end the "ck -bp" Number of Boiler Columns in the Annular Boiler Region................................. 80 4-8 Reactivity Penalty (6k/k) as a function of UTVC Liner Material Thickness............................... ... .. 82 4-9 Reactivity Penalty (6k/k) as a function of Boiler Region Liner Material Thickness .............................. 83 4-10 Reactivity Penalty (6k/k) as a function of Both the UTVC and Boiler Region Liner Material Thickness............... 85 x Table Page 5-1 kef and P Tvr/P RO as a function of UTVC Radius for the '6F /NaFURAiki f0Cycle System in R-O Geometry for a Four-Boiler and an Eight-Boiler Column UTVR Configuration ............................................ 101 5-2 kef and P /Pn as a function of the Number of UF4 oiler Clumn Ch R-O Geometry.......................... 111 5-3 UF4 Temperature and Density Profiles in the UTVC as a function of Radial Distance for a Four-Boiler Column UTVR Configuration in the R-0 Coordinate System.......... 120 5-4 UTVR Dimensions of the Reference R-Z Cylindrical Configuration ............................................ 125 5-5 k e, P ITC/Pg p, and P P hl as a function of hGe -Mo tor-RefpYgei r lifane Separator Slab Region Height ...................................... 127 5-6 keff, P T /P C and P /nr/Ph le r versus the Top BeO Mode-ator-Reector Rh H ...................... 130 5-7 kef, P TVP/P r, and PJ as a function of ethe Frt OW r BeO MggetatoPo sector Region (OBEO#1) Height ...................................... 132 5-8 k ef, P TVC/PBnL, and P /Pho as a function of ef he Wj ht b the SubM8 ed adlturated Liquid Region of the Boiler Column............................. 135 5-9 kf P /P and P P "e as a function of kef oly Num BRckness sPP un gehe Boiler Feedlines Region............................................... 138 6-1 Description of UTVR Regions Employed in the Three- Dimensional MCNP Monte Carlo Calculations................ 155 6-2 Reactivity Worths of the Boiler Feedlines, UTVC Inlet Plenums, and MHD Duct Regions........................... 159 6-3 Selected UTVR Results from a 30-Minute MCNP Monte Carlo Analog Calculation Performed on a CRAY X-MP/48 Supercomputer ............................................ 162 6-4 UTVR Fission Rate as a function of Neutron Energy........... 169 6-5 Effect of Employing Energy Cutoff on the UTVC and Boiler Column FOM Tallies............................. ...... 169 Table Page 6-6 Effect of Employing Implicit Capture and Weight Cutoff on the UTVC and Boiler Column FOM Tallies................... 171 6-7 Effect of Employing Weight Windows on the UTVC and Boiler Column FOM Tallies.................................... 175 6-8 Effects of Employing Variance-Reduction Techniques in MCNP Monte-Carlo Calculations on Uncertainties of Selected UTVR Parameters............................... 177 6-9 Effects of Employing Variance-Reduction Techniques and utilizing Boiler-to-UTVC Symmetry in MCNP Monte-Carlo Calculations on Uncertainties of Selected UTVR Parameters ............................................... 184 6-10 Integral Kinetics Parameters as a function of the UF4 Partial Pressure in the UTVC .......................... 201 6-11 Integral Kinetics Parameters as a function of Saturated Liquid Cone Region Height for Two Different H Values.. 203 6-12 Integral Kinetics Parameters as a function of Saturated Liquid Cone Region Height at UF4 Partial Pressures of 2.5 and 7.5 atm in the UTVC ........................... 204 6-13 Integral Kinetics Parameters as a function of HSUB and HSAT in Boiler Column at a UF4 Partial Pressure of 5 atm in the UTVC.................. .......................... 206 6-14 Integral Kinetics Parameters as a function of Vapor Cone Region Density at a UF4 Partial Pressure of 5 atm in the UTVC ............................................... 208 8-1 Values of Selected UTVR Parameters at the Initial, Unperturbed Steady State Condition ...................... 267 8-2 Relevant Properties for the UF Fuel, NaF Working Fluid, and the UF4/NaF Fuel/Working Fluid Mixture............... 268 8-3 Final Equilibrium Conditions as a Result of$ 1.00 Positive
and Negative Reactivity Step Insertions Imposed on the
Boiler Columns....................................... 278

8-4 Final Equilibrium Conditions as a Result of $0.20 Positive and Negative Reactivity Step Insertions Imposed on the UTVC................................................. 282 8-5 Final Equilibrium Conditions Following a Positive Step Reactivity Insertion of$ 0.20 Imposed on the UTVC
with Normal and Reduced Coupling Coefficients............ 289

xii

Table Page

8-6 Final Equilibrium Conditions Following a Positive Step
Reactivity Insertion of $0.20 Imposed on the UTVC with Normal and Reduced UTVC Fuel Loading Coefficients of Reactivity.............................. 293 B-1 XSDRNPM and MCNP Benchmark Calculations on a Five-Region Spherical "Mock-up" of the UTVR......................... 322 B-2 DOT-4 and MCNP Benchmark Calculations on the Cylindrical "Mock-up" of the UTVR in both the R-9 and R-Z Coordinate Systems..................................... 326 C-1 Comparison of Results obtained from ISCE with Results obtained Directly using MCNP for Two Different UTVR Fuel Loadings........................................ 343 D-1 The Six Delayed Neutron Groups Energy Spectra, Decay Constants, Yied, and Fractions Data for Thermal Fission in U ......................................... 356 xiii LIST OF FIGURES Figure Page 1-1 Side View Schematic of the Ultrahigh Temperature Vapor Core Reactor...................................... 3 1-2 Top View Schematic of the Ultrahigh Temperature Vapor Core Reactor...................................... 5 3-1 UF6 and UF4 Saturation Vapor Curves......................... 25 3-2 Uranium Metal and UF4 Saturation Vapor Curves............... 27 3-3 Partial Pressures of Constituent Species of the Uranium- Fluorine System at One Atmosphere ....................... 28 3-4 Schematic of a 200 MWe UF4/KF UTVR MHD-Rankine Cycle Power System ................................................. 31 4-1 Four Region, One-Dimensional Spherical "Mock-up" of the UTVR............................................. 41 4-2 keff and PUTVC/PBCOL as a function of the UTVC Radius....... 45 4-3 kef and Fission Rates of the UTVC and the Boiler as a function of the UTVC Radius............................. 46 4-4 k and P T/P as a function of the Inner BeO Moderate r-Ref Ttor Region Thickness..................... 51 4-5 kef as a function of the Inner BeO Moderator-Reflector Region Thickness........................................ 53 4-6 kefc and PRTVr/Pr as a function of the Outer BeO Moderate r-RefT~E or Region Thickness..................... 56 4-7 ke and PUT/PRrn as a function of the UF4 Inlet Velocity t te.Boiler Region....................... 58 4-8 keff and PuTVC/Prni as a function of the UF4 Partial e Pressure 1in tf UTVC.................................... 63 4-9 k as a function of the U235 Enrichment at Different eF4 Partial Pressures in the UTVC...................... 64 xiv Figure Page 4-10 kef as a function of the Fissile Fuel (U235 and U233) Enrichment ............................................. 65 4-11 kef and PUTv /PBC as a function of the UF4 Average Density in the Biler Region.............. .............. 67 4-12 Five Region, One-Dimensional Spherical "Mock-up" of the UTVR................................................. 71 4-13 kef and P v/PR i as a function of the UF4/NaF Inlet Velocity t 0 tfl Boiler Region............................ 77 4-14 k and P /PC as a function of the Li6F Mass Flow Rate to tUf B/p r Region............................... 78 5-1 Six Region, Two-Dimensional R-B Representation of a UTVR with Six-Boiler Columns ............................ 97 5-2 kf and P TVC/PCnL as a function of the UTVC Radius for a eour- ad n Eht-Boiler Column UTVR Configuration...... 100 5-3 kf and P /P as a function of the Inner BeO eIoderatTr-Reft or Region Thickness for a Four- Boiler Column UTVR ........... .......................... 106 5-4 k f and P /PBC as a function of the UF Inlet Velocity efto the HBYer ion for a Four-Boiler CoTumn............ 108 5-5 kff and PTvr/P o as a function of the UF Partial Pressure in t ObTVC for a Four-Boiler Cotumn UTVR System............................................ 113 5-6 kff and P C/PC as a function of the UF4 Average Density iu the Biler Region for a Six-Boiler Column UTVR System............................................ 117 5-7 Thermal Neutron Flux and Vapor Fuel Temperature Profile as a function of Radial Position from the Centerline of the UTVC for a Four-Boiler Column UTVR System................ 118 5-8 Representation of the UTVR in the R-Z Coordinate System..... 122 5-9 The Horizontal Boiler Configuration of the UTVR in the R-Z Coordinate System................................. .. .. 143 6-1 Side View Schematic of the Four-Boiler Column UTVR on the y-z Plane at x=0.0................................... 153 6-2 Side View Schematic of a Boiler Column ..................... 157 Figure Page 6-3 Top View Schematic of a Four-Boiler Column UTVR System...... 180 7-1 Schematic of the Core-to-Core Circulating Fuel Coupling..... 212 7-2 Schematic of Boiler-to-UTVC Neutron Transport Coupling for a Four-Boiler Column UTVR System........................ 215 7-3 Schematic of Boiler-to-Boiler and UTVC-to-Boiler Neutron Transport Coupling for a Four-Boiler Column UTVR System.. 217 7-4 Block Diagram of the UTVC Transfer Function................. 228 7-5 Block Diagram of the Boiler Column Transfer Function........ 230 7-6 Block Diagram of the UTVR Transfer Function................. 231 7-7 Fuel/Working Fluid Density Profile in the Boiler Column due to Boiling in Space (=zero gravity).................. 234 7-8 Side View Schematic of the UTVC............................ 251 8-1 UTVC and Boiler Column Regions Power Levels as a function of Time Following a$ 1.00 Positive Reactivity Step
Insertion Imposed on the Boiler Columns at t=0 sec....... 270

Mass Flow Rates, as a function of Time Following a
$1.00 Positive Reactivity Step Insertion Imposed on the Boiler Columns at t=O sec........................... 273 8-3 Boiler Column Outlet Mass Flow Rate and U235 Loading as a function of Time Following a$ 1.00 Positive Reactivity
Step Insertion Imposed on the Boiler Columns at t=0 sec.. 274

8-4 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $1.00 Negative Reactivity Step Insertion Imposed on the Boiler Columns at t=0 sec....... 277 8-5 UTVC and Boiler Column Regions Power Levels as a function of Time Following a$ 0.20 Positive Reactivity Step
Insertion Imposed on the UTVC at t=0 sec................. 279

8-6 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $0.20 Negative Reactivity Step Insertion Imposed on the UTVC at t=0 sec................. 281 8-7 UTVC and Boiler Column Regions Power Levels as a function of Time Following a$ 0.20 Positive Reactivity Step
Inqrtion_6 posed on the UTVC at t=0 sec with
t = 10 sec .. .................................... 284

xvi

Figure Page

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

8-10 UTVC and Boiler Column Regions Power Levels as a function
of Time Following a $0.20 Positive Reactivity Step Insertion Imposed on the UTVC at t-0 sec with the UTVC Fuel Mass Reactivity Feedback Coefficient Reduced by a Factor of Five.................................. 292 8-11 UTVC and Boiler Column Regions Power Levels as a function of Time Following a$ 0.20 Positive Reactivity Step
Insertion Imposed on the UTVC at t=0 sec with the
UTVC Fuel Mass Reactivity Feedback Coefficient Increased
by a Factor of Two..................................... 295

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

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

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

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

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

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

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

xvii

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

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

By

Samer Dakhlallah Kahook

May, 1991

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

An Ultrahigh Temperature Vapor core Reactor (UTVR) system is

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

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

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

burst power reactor. The investigated reactor system includes two types

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

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

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

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

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

liquid UF4 fuel. The combination of three features differentiates the

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

follows:

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

means of direct neutron transport through the media;

xviii

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

coupling between the UTVC and boiler cores; and

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

combination.

Static and dynamic neutronic analysis of this novel system

indicates distinct advantages over other existing or conceptual nuclear

power systems. These include a unique combination of some very

effective inherent negative reactivity feedbacks such as the vapor-fuel

density power coefficient of reactivity, the direct neutronic coupling

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

feedback between the two types of fissioning cores.

Static neutronic analysis is performed using multidimensional

discrete ordinates and Monte Carlo neutron transport codes. Parameters

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

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

function of vapor core density and boiler core liquid volume are

obtained from the static neutronic analysis.

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

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

kinetics and energetic equations. These equations are solved using a

system analysis code. The dynamic analysis indicates that the unique

and strong negative reactivity feedbacks of the UTVR are capable of

stabilizing the UTVR safely and quickly even when large reactivity

insertions are imposed (6p = $1.00). The analysis also shows that the system exhibits good dynamic performance even when an inherent negative reactivity feddback is suppressed (e.g., the vapor fuel density power xix coefficient of reactivity). However, due to the strength of the UTVR's inherent negative reactivity feedbacks, it is found that external reactivity insertions alone are inadequate for bringing about power level changes during normal operations. Additional methods of reactivity control, such as variations in the mass flow rate of the fuel and/or working fluid or variations in the inlet pressure of the fuel/working fluid entering the boiler columns, are needed to achieve the desired power level control. CHAPTER I INTRODUCTION Introduction The concept of Vapor Core Reactors (VCRs) has emerged at the University of Florida (UF) as a consequence of extensive theoretical and experimental studies performed on their predecessors, the Gaseous Core Reactors (GCRs). Unlike GCRs (where the fuel is supplied to the reactor in gaseous form), the working fluid and/or fuel undergo a liquid-to- vapor phase change in VCRs. Studies performed on VCRs and GCRs indicate that gaseous-fueled (or vapor-fueled) reactor concepts have distinct advantages over other existing or proposed nuclear power systems. These advantages include high operating temperatures and efficiency, rapid startup capabilities, simple geometry, and an assortment of efficient power control methods [1-9]. The Ultrahigh Temperature Vapor Core Reactor (UTVR)/Disk Magnetohydrodynamic (MHD) Generator Power System is being studied for the Strategic Defense Initiative Organization (SDIO) as a possible source for space power. The SDI space power systems are required to operate in at least one of the three following power modes: Station-keeping mode (base load). This mode may be required to produce up to a few Megawatts electric (MWe) for a period of about 7 years. Alert mode (enhanced surveillance mode). The power requirements for this mode range from 10's of MWe up to =100 MWe. The power system must be capable of functioning for periods of a few hours to a few days. Burst power mode (defense mode). The power level for this mode ranges from =100 MWe up to =1 Gigawatt electric (GWe) for operating times of about 30 minutes; a burst power system must be capable of achieving this power level in less than 100 seconds. The UTVR/MHD Generator Power System is a burst power mode concept. At burst power levels, the UTVR can operate at very high temperatures which provides an efficient heat rejection capability and a high thermodynamic efficiency. This and other features appear to make the UTVR/MHD Generator Power System an exceptional concept for burst power operations. The UTVR/MHD Generator Power System is the concept examined in this research. Description of the Ultrahiqh Temperature Vapor Core Reactor The UTVR/Disk MHD Generator Power System is a highly enriched (>85%), BeO externally-moderated, circulating fuel reactor with uranium tetra-fluoride (UF4) as the fissioning fuel. The working fluid is in the form of a metal fluoride such as NaF, KF, RbF, and Li7F. Shown in Figure 1-1 is a side view schematic of the UTVR. The UTVR includes two types of fissioning regions: (1) the central Ultrahigh Temperature Vapor Core regions (UTVC) which contain a vapor mixture of highly-enriched UF4 and a metal fluoride working fluid at an average temperature of =3000 K and an average pressure of =50 atm, and (2) the boiler column regions (BCOL) which contain highly enriched UF4 TBEO .. ....... :y.. WallI .. ... ..-1- Cool ant 'i ^iiiiiiii~ii!!~ i\'''i.'- ...- Rejection ... .System ::: :.:.: . ...- ......... DOB E O MHD Duct V, po r *^I BEO ^ ... To Heat Region I BED p. .i.-i. i;^ Boiler S. ... ...... -.... Column . . ... .: '.. r. .." , Figure 1-1. Side View Schematic of the Ultrahigh Temperature Vapor Core Reactor fuel. This reactor has symmetry about the midplane with identical top and bottom vapor core and boiler column regions separated by a BeO slab (mid-plane BeO Region MBEO) and the MHD ducts where power is extracted. The UTVC is surrounded in the radial direction by the wall cooling region. The wall cooling region contains a subcooled liquid metal fluoride. By tangentially injecting the metal fluoride into the UTVC, the UTVC walls are maintained at the desired low temperatures (=2000 K). As the metal fluoride is injected into the UTVC, an annular buffer zone is obtained which aids in maintaining the UF4 away from the UTVC walls. This reduces the possibility of condensation of uranium or uranium compounds on the UTVC walls. Beyond this buffer zone, the metal fluoride vaporizes and mixes with the UF4 in the UTVC. The UF4 is vaporized in the boiler columns prior to its entrance to the UTVC. The boiler region, which includes a number of boiler columns, is connected to the UTVC via the UTVC inlet plenums, as shown in Figure 1-1. The UF4 liquid is supplied to the boiler columns by means of feedlines. Each boiler column consists of three distinct regions: the subcooled liquid region, the saturated liquid-vapor region, and the superheated vapor region. Shown in Figure 1-2 is a top view schematic of the UTVR. Figure 1- 2 shows three distinct BeO regions: the inner BeO region (IBEO) which separates the UTVC walls from the boiler columns in the radial direction, the annular boiler BeO region (BBEO) with a radial thickness equal to the diameter of the boiler columns, and the outer BeO region (OBEO) surrounding the boiler columns and the BBEO region. Three other BeO regions are shown in Figure 1-1. These are the mid-plane BeO region OBEO Figure 1-2. Top View Schematic of the Ultrahigh Temperature Vapor Core Reactor (MBEO) mentioned previously, the lower BeO region (LBEO) separating the boiler feedlines from the MHD duct, and the top BeO region (TBEO) above the UTVC. Use of the UF4 as the vapor fuel and metal fluorides as the working fluid in the UTVR/MHD Generator Power System allows for operation on a direct, closed Rankine type cycle and leads to space power systems with high efficiency (=20%), small radiator size (=5 m2/MWe), and high specific power (=5 kwe/kg). A description of an example UF4-Metal Fluoride UTVR/MHD Generator Rankine Cycle Power System is furnished in Chapter III. Dissertation Objectives A goal of this research is the nuclear design and analysis of the UF4-Metal Fluoride UTVR/MHD Generator Rankine Cycle Power System for space power applications. Complete characterization of this innovative system requires an integrated and thorough investigation of its neutronic, heat transfer, and mass flow behavior. Although this research focuses on the nuclear aspects of the proposed system, it incorporates results from auxiliary and supporting thermodynamic, heat transfer, and fluid flow calculations, thus, assuring a reliable and integrated nuclear analysis. The nuclear design of the UTVR incorporates results from the static and dynamic neutronic analysis performed on the UTVR. The static neutronic analysis establishes basic neutronic characteristics and obtains reference reactor configurations that are optimized for the static neutronic characteristics while also considering other important parameters like specific power (kw/kg) for the UTVR. Applicable UTVR parameters that are needed for the dynamic neutronic studies such as reactivity, neutron generation time, and core-to-core coupling coefficients are also obtained from the static analysis. The dynamic neutronic analysis focuses on characterizing the UTVR with respect to stability and dynamic response. Effects of core-to-core neutronic coupling (by means of direct neutron transport through the media and by delayed neutron emission from the decay of the delayed neutron precursors which are carried in the fuel that circulates between the UTVC and boiler columns) and effects of other important reactivity feedback phenomena such as fuel density and mass flow related feedback for the vapor and boiler cores are included in the dynamic analysis. Thus, the primary objective of this research is the development and application of the methods and the models needed for the nuclear design and analysis of this unique reactor concept. It is recognized that acoustic phenomena are inherent to the UTVR and their effects are potentially very significant. However, acoustic effects are not included in this research and are recommended for future work when the necessary tools for treating these effects are available. Recommended future work will require coupled space-time neutron field- gas density field calculations. Dissertation Organization A brief summary of previous work performed on related reactor concepts such as gas core reactors, coupled core reactors, and circulating fuel reactors is presented in Chapter II. A section addressing preliminary design considerations for the UF4 UTVR reactor system is presented in Chapter III. It includes point design conditions for the UTVR from preliminary thermodynamic, heat transfer, and fluid flow calculations. A description of an example UF4- Metal Fluoride UTVR/MHD Generator Rankine Cycle Power System is also presented in Chapter III. A section in Chapter III discusses the plan used in the nuclear design and analysis of the UTVR system. The results of the static one- and two-dimensional neutronic calculations are presented in Chapters IV and V, respectively. These calculations are performed with XSDRNPM [10], a one-dimensional discrete ordinates (Sn) neutron transport code, and with DOT-4 [11], a one- and two-dimensional Sn neutron transport code. The static analysis examines effects of variations in geometry and fuel/working fluid loadings on the neutron multiplication factor (keff) and power sharing factor (i.e., power distribution between the UTVC and the UF4 boiler columns, PUTVC/PBCOL) Basic neutronic characteristics of the UTVR such as fuel density reactivity coefficients, optimum BeO region thicknesses, optimum number of UF4 boiler columns, and a reference UTVR configuration for three-dimensional analysis are obtained from the static neutronic analysis results presented in Chapters IV and V. The results obtained from static three-dimensional neutronic calculations are presented in Chapter VI. These calculations are performed using MCNP [12], a three-dimensional Monte Carlo neutron transport code. Parameters such as UTVC and boiler core reactivities and reaction rates, core-to-core coupling coefficients, and neutron lifetimes as a function of vapor core density and boiler core liquid volume are obtained from the results of calculations performed with MCNP. The methods and models used in obtaining the core-to-core neutron transport coupling coefficients and the reactivities of the vapor and boiler cores are derived and described in Chapter VI. The circulating-fuel, coupled core, point reactor kinetics equations for a four-boiler column UTVR are derived in Chapter VII. A section in Chapter VII contains a detailed discussion of significant UTVR inherent reactivity feedbacks such as the vapor fuel density feedback of the UTVC and the liquid fuel/working fluid volume feedback of the boiler region. Energetics equations relating the power levels and the neutron population levels of the vapor and boiler cores to fuel/working fluid temperature, density, and liquid volume and flow rates are also included in Chapter VII. The dynamic neutronic analysis and performance studies are included in Chapter VIII. The dynamic analysis examines the behavior of core power levels, reactivities, fuel densities, and total system power during full power transients. Effects of the core-to-core circulating fuel and neutron transport coupling and fuel density variations in the vapor core and boiler cores are included in the dynamic analysis. The conclusions obtained from this research are included in Chapter IX. Suggestions and recommendations are made for further research which are needed before the technical feasibility of the UTVR/MHD Generator Power System can be realized. A brief description of the nuclear and system analysis computer codes used in this research is presented in Appendix A. Appendix B contains the results of benchmark calculations performed with XSDRNPM and MCNP on a reference UTVR in spherical coordinates. Results from benchmark calculations performed in R-8 and R-Z cylindrical coordinates with DOT-4 and MCNP are also included in Appendix B. A description of the Isolator of Secondary Coupling Effects (ISCE) code is presented in Appendix C. The ISCE code, a special code developed as a part of this research, incorporates the models derived in Chapter VI with results obtained from the MCNP code to obtain parameters needed for the dynamic analysis and performance studies such as core-to-core neutron transport coupling coefficients and the reactivities of the UTVC and boiler cores. Appendix D contains a description of the circulating fuel, coupled core, point reactor kinetics equations. CHAPTER II PREVIOUS RESEARCH ON RELATED CONCEPTS Introduction The UTVR can be characterized as a thermal, high power density (hundreds of MWth/m3), externally-moderated, coupled-core (vapor and boiling cores), highly-enriched, U235 circulating fuel, steady state reactor. The combination of three features differentiates the UTVR from other nuclear reactor concepts. These features are the following: 1. The multi-core configuration resulting in a coupled-core system by means of direct neutron transport through the media. 2. The circulating fuel and the associated neutronic and mass flow coupling between the UTVC and boiler cores. This feature provides additional neutronic coupling between the cores by means of delayed neutron emission from the decay of the delayed neutron precursors which are carried in the fuel/working fluid mixture. The mass flow coupling between the vapor and boiler cores is an inherently stabilizing phenomenon. For example, an increase in the power level of the boiler core increases the voiding and decreases the density of the fuel/working fluid mixture in the boiler core. This leads to a decrease in the boiler core power level. Additionally, the density of the fuel/working fluid exiting the boiler core and entering the vapor core decreases. This causes a decrease in the reactivity of the vapor core resulting in a decrease in the vapor core power level. 11 The decrease in the vapor core power level causes a decrease in the number of neutrons directly transported to the boiler cores through the media and a decrease in the delayed neutron precursor concentration decaying in the boiler cores. This causes a further decrease in the boiler core power level. 3. The employment of a two-phase fissioning fuel, i.e., a liquid-vapor combination. Studies on reactors combining all three of these key features have never been reported. However, studies and research pertaining to coupled-core reactors, circulating fuel reactors, or gaseous (vapor) core reactors have been reported. Therefore, the following sections of this chapter briefly summarize previous research on reactors that possess one of these key features or aspects of the UTVR. Previous Research on Gas Core Reactors Research on gas core reactors has been reported as early as 1955 by George Bell [13]. The reactors examined by Bell employed gaseous UF6 fuel and beryllium (Be), D20, and graphite reflectors in spherically symmetric geometries. The analysis was done using age theory to describe neutron slowing down in the moderator-reflector region and diffusion theory to describe neutron diffusion into the core and the fissions in the core. The reactor was considered to be strictly a thermal reactor. Since then, different analytical methods and models have been used in studying this and other gas core reactor concepts. This includes the Nuclear Piston Engine and Pulsed Gaseous Core Reactor Power Systems examined by E.T. Dugan [2] and the Heterogeneous Gas Core Reactor examined by K.I. Han [5]. Summaries of previous work on gas core reactors can be found in the studies reported by Dugan and Han. Previous Research on Coupled Core Reactors The initial work on the kinetics of coupled core reactors was reported in 1958 by Robert Avery [14]. Avery investigated the dynamic characteristics of coupled fast-thermal breeder reactors. The analysis incorporates the point reactor kinetics equations for each core. The equations include terms accounting for the neutronic interaction (coupling) between the cores. The coupling terms along with integral parameters used in the point reactor kinetics equations are obtained from steady state analysis of the interacting cores. Neutron kinetics studies using the coupled core treatment have been applied to nuclear reactor systems other than fast-thermal reactors. These include modular cores of large thermal power reactors, clustered reactors, and Argonaut-type reactors. Research has also been performed on coupled gas core reactors. This includes the work performed by M.M. Panicker [6] on the Coupled Multiple Chamber Gaseous Core Reactor Power System. The differences in the various approaches used in the analysis of coupled core reactor systems lie in the choice of the weighting function (neutron flux, importance function, or average fission density); the choice of suitable phase-space regions for the averaging process; and the selection of how to incorporate the coupling effects (e.g., as a source term or reactivity effect) into the pertinent dynamic neutronics equations. Detailed discussions of these differences and their applications to various reactor systems are reported by Adler et al. [15] and Panicker [6]. Previous Research on Circulating Fuel Reactors The kinetics of circulating fuel reactors is affected by the loss of a fraction of delayed neutrons due to the decay of the delayed neutron precursors outside the core. The fraction of delayed neutrons that is lost depends mainly on the time the fuel spends in the core relative to the time the fuel remains outside the core. Various methods have been used in approximating the effects of circulating fuel. The impact of various methods used for approximating the effect of circulating fuel on the kinetics of nuclear reactors has been investigated by John MacPhee [16]. In comparing the approximate methods, MacPhee employed an "exact" model ("exact" with respect to the method of treating the effect of the circulating fuel on the delayed neutrons). The "exact" model employed the following assumptions: 1. Point reactor kinetics equations are valid in the sense that the reactor kinetics effects are considered to be spatially independent. 2. Reactor power level is low enough such that the effect of neglecting reactivity feedback due to temperature and radiolytic gas formation is valid. 3. One delayed neutron group is used. 4. Perfect mixing in the core vessel occurs. 5. Fission occurs only in the core. 6. Fuel mass flow rate is constant. The reactor kinetic equations employed in the "exact" model are dN(t) p(t) N(t) + C(t) (2-1) dt A d(t) N(t) (t) + e- (2-2) dt A Tc Tc where N(t) = neutron population level in the core at time t; p(t) = core reactivity at time t; P = fraction of delayed neutrons; A = prompt neutron generation time; A average decay constant of delayed neutrons; t = delayed neutron precursor concentration; 7c time fuel remains in the core; 7T = time fuel spends in the loop outside the core. Equation (2-1) describes the time dependent behavior of the neutron population level and Equation (2-2) describes the time dependent variation of the concentration of the delayed neutron precursors. The effect of the circulating fuel is accounted for in the last two terms in Equation (2-2). MacPhee compared two approximate methods with the "exact" model. In the approximate methods, modified versions of Equation (2-2) are employed. The first method employs reduced values for # as shown by dC(t)_ f N(t) C(t) (2-3) dt A where f is the fraction of delayed neutrons lost as a result of the fuel circulating and is given by 7C f = (2-4) Tc + Tj The second method neglects the delay time associated with the delayed neutron precursors re-entering the core, i.e., C(t-T,) = C(t). With this assumption, the equation describing the delayed neutron precursors concentration is dC(t) = N(t) - C(t) (2-5) dt A aD where aD is the delayed neutron attenuation factor, obtained from steady state conditions imposed on Equation (2-2), and is given by rTc aD = -T (2-6) XTc + 1 e MacPhee analyzed the "exact" model by linearizing Equations (2-1) and (2-2), taking the Laplace transform of the linearized equations, and computing the frequency response of the linear system. The results of MacPhee's investigation and comparisons include the following conclusions: 1. The frequency response of the "exact" model predicts a peak when fast reactivity changes are introduced. The approximate methods do not predict the peaking found by the "exact" model. Thus, for fast reactivity changes the approximate methods are not valid. 2. Although the frequency response indicates peaking, circulating fuel reactors do not exhibit self-sustained oscillations as a result of the feedback produced by the delayed neutron precursors re-entering the core, i.e., the peaking is finite. The peaking is due to the coupling of the delayed neutron decay constants with the loop circulation period and occurs for small values of aD. The reason the peaking is finite is because aD is greater than zero for all practical reactor configurations. Equation (2-6) indicates that aD approaches unity as rT approaches zero for all values of T , i.e., all delayed neutrons are emitted in the core. However, as 7T approaches infinity (fuel does not re-enter core), aD approaches zero if and only if Tc approaches zero such that no delayed neutrons are emitted in the core. For such cases, the velocity of the fuel in the core is required to be infinite and an infinite amount of fuel is required to maintain the reactor critical. Since aD is always larger than zero, the peaking is therefore finite. It should be noted that an inherent assumption in MacPhee's analysis is that the employed fuel is incompressible. Thus, some of these conclusions do not pertain to the UTVR. M.A. Schultz [17] indicates that a number of smaller peaks would occur in the frequency response of circulating fuel reactors if more than one delayed neutron group is included in MacPhee's "exact" model. The fact that the mixing of the circulating fuel in the external loop of an actual reactor will smooth over the peaks and reduce any tendency toward sustained oscillations is pointed out by Schultz. The effect of fuel temperature reactivity feedback in circulating fuel reactors has been investigated by W.K. Ergen [18]. The analysis indicates damped power oscillations for circulating fuel reactors occurs with negative fuel temperature feedback. Ergen also concludes that the decrease in damping of oscillations due to the loss of delayed neutrons 18 is compensated to some extent by the damping effect caused by the circulation itself. Remarks In deriving the models needed to analyze the UTVR/MHD Generator Power System (see Chapters VI and VII and Appendix D), references to previous work are also made. Where applicable, modifications to and comparisons with previous models are indicated. CHAPTER III DESIGN OF THE URANIUM TETRA-FLUORIDE, ULTRAHIGH TEMPERATURE VAPOR CORE REACTOR Introduction In the design of nuclear power reactors, the choice of materials for fuel, moderator, coolant/working fluid, and structure and the selection of the power extraction system are based on the application and the required performance of these reactors. Once the appropriate materials and a suitable power extraction system are selected, a reference reactor configuration can be chosen. Then, a complete characterization of the reference reactor power system is required to determine its overall performance and feasibility. Although this research focuses on the nuclear aspects of the UTVR, a section in this chapter addresses preliminary design considerations that led to the reference UTVR configuration. Another section in this chapter discusses considerations involved in the materials selection for the UTVR. A detailed description of an example UF4-Metal fluoride UTVR/MHD Generator Rankine Cycle Power System is also given. This is followed by a section discussing the plan followed in this research for the neutronic analysis of the UTVR system. Preliminary Design Considerations Since the UTVR is being developed for SDI's Burst Power Mode for space power applications, the following issues need be realized: 1. The size and mass of the power system are important constraints. This is due to the following: (a) the expense and logistics involved in the deployment of the power system into space, (b) the need to constantly maneuver and relocate the defense system, and (c) the need for defense systems to be inconspicuous. 2. The required power level for this system ranges from =100 MWe up to =1 GWe for operating times of =30 minutes. Such power levels when considered with the size requirement demand a high power density system. 3. The system is required to achieve the Burst Power Mode in less than 100 seconds. Thus, the system needs to be designed to withstand thermal stresses and shocks caused by a rapid transition from the alert mode. 4. The power system is required to be able to operate during a seven year period. This requires the power system to be tested periodically; thus, the system needs to be designed to operate at full power for a total time of about three hours (assuming two-annual tests during the seven-year period lasting about ten minutes each plus the 30 consecutive minutes of operation). 5. The system needs to be operated at high temperatures to provide compact radiators for heat rejection in space and high power cycle efficiency. 21 The above issues are the primary considerations applied during the preliminary design of the UTVR. Choice of Materials The UTVR is a BeO externally-moderated, circulating fuel reactor with UF4 as the fissioning fuel and a metal-fluoride working fluid. Research is being conducted to select and develop suitable structural materials that are compatible with the fluoride fuel/working fluid mixture and the high temperature environment of the UTVR. The choice of BeO as the moderator-reflector material, UF4 as the fuel, and metal fluoride as the working fluid is based on the following considerations. The Moderator-Reflector Material For thermal reactors, moderator-reflector materials used in nuclear reactors have low mass numbers and relatively large scattering and relatively small absorption cross sections. Moderators used in nuclear reactors include ordinary water (H20), heavy water (D20), beryllium (Be) or beryllium-oxide (BeO), and graphite. The choice depends largely on the intended application of the reactor system; and on the nuclear, mechanical, physical, and chemical properties; and the cost of the moderator material. Since the size and mass of the power system are significant constraints, and since high temperatures are needed for efficient heat rejection in space, the moderator-reflector material is required to have a high melting temperature (or high boiling temperature if a liquid moderator is used) and relatively good neutronic properties (high slowing-down power and small capture cross section for neutrons). 22 For space power reactors, beryllium or BeO is superior to graphite as a moderator and reflector material from a neutronics standpoint. In the study of Highly Enriched Heterogeneous Gas Core Reactors (HGCRs), S.D. Kahook [7] has shown that the use of Be as the moderator and reflector material provides a higher reactivity (=30% Sk/k) than graphite (total size of the HGCR was fixed). This is mainly due to the higher slowing-down power (exls = average logarithmic energy loss per collision x macroscopic scattering cross section) of 16 m-I for Be versus 6.5 m-1 for graphite [19] and the (n,2n) reaction of Be. Another drawback of graphite is its larger thermal diffusion length, LT, (=54 cm versus =21 cm) and its larger slowing-down length, TT, (=192 cm versus =100 cm) compared to Be. The larger values of LT and TT require graphite-moderated reactors to have a larger size compared to beryllium- moderated reactors, an important design criterion for the space power system under investigation. Although the melting temperature of graphite is higher then that of BeO (=4000 K versus =2800 K), BeO is a better choice than graphite for the power system under investigation. The drawback of the lower melting temperature of BeO can be compensated for by the use of auxiliary coolant channels in the moderator-reflector regions to maintain BeO at safe operating temperatures (=1600 K to =2000 K). Also, due to the low heat conductivity of the vapor fuel and the fact that the fuel is the working fluid (most of the energy generated is directly deposited in and removed by the fuel/working fluid mixture), the temperature of moderator-reflector regions can be considerably cooler then the temperature of the vapor fuel. 23 E.T. Dugan [2] examined the effect of using H20, D20, Be, BeO, and graphite as moderator-reflector materials for the Nuclear Piston Engine which employed an externally-moderated UF6-fueled gas core reactor for terrestrial power generation. The study indicates that the use of H20 and graphite results in relatively low keff values. This is due to the relatively high thermal absorption cross section of H20 and high LT and TT of graphite. However, the large slowing-down power as well as the (n,2n) reaction of Be and the small thermal absorption cross section of D20, cause Be, BeO, and D20 to be excellent choices for moderator- reflector materials as proven by Dugan. The relatively large LT of D20 of =97 cm requires that the size of reactors employing D20 as the moderator to be quite large. Additionally, the high temperature environment of the UTVR, the chemical incompatibility between H20 or D20 and UF6 or UF4, the normal deterioration of D20 into H20 in time (small amounts can have large effects on neutronics), and the added complications involved with a liquid moderator versus a solid moderator in space all aid in rejecting D20 as the moderator-reflector material for the UTVR. The ceramic nature of BeO with a high melting temperature of =2800 K and its exceptional resistance to thermal shock [20] make this an especially well-suited moderator-reflector material for the high temperature environment of the power system under investigation. Although per unit mass Be is neutronically superior to BeO as a moderator, the anticipated moderator temperature range of 1600 K to 2000 K for this burst power system precludes the use of Be (melting point of Be is 1728 K). The Fissioning Fuel Material The advantages and key features of vapor-fueled reactors are more than adequate to justify the study of a fuel in the vapor state. However, uranium exists in a gaseous state in various forms such as UF4, UF6, or uranium metal vapor. Reactors employing uranium in these forms have all been investigated at the University of Florida. The choice of the fuel along with the working fluid are dictated by the type of power cycle, e.g., Brayton or Rankine cycle. It is appropriate to compare features of these cycles in order to select a suitable fuel. The Brayton cycle is simpler in design than the Rankine cycle. However, it generally has a lower thermodynamic efficiency. Due to this lower efficiency, more heat has to be rejected into space which implies that a larger radiator is needed. In addition, the heat rejection to space is done at a varying (decreasing) temperature rather than a constant temperature thereby decreasing the effective temperature of heat rejection and further increasing the required radiator size. The greater pumping power required for gas compression in the Brayton cycle demand larger and more massive compressors as compared to the pumps in a Rankine type of cycle. Since size and mass are significant constraints, and since a Brayton type of cycle requires larger radiators and more massive compressors than a Rankine type of cycle, a Rankine type of cycle appears to be the better choice, especially for high power systems. For space power Rankine cycle systems, the most desirable fuel choice is UF4. This can be seen from Figure 3-1 where the UF6 and UF4 saturation vapor curves are shown and from the uranium metal and UF4 L Il I IO o o o0 i M i0 0 (prI) afnssaJd JodPA saturation vapor curves given in Figure 3-2. For the UF6 to be in the gaseous state, at pressures required for criticality in the core, its temperature need only be in the 400 to 500 K range. This implies that the UF6 must be 400 K or less to achieve a liquid state at the exhaust pressures when a gas turbine or MHD generator is used for power conversion. This low heat rejection temperature can easily be achieved on earth, but is unrealistic in a space environment. Thus, one is restricted to a Brayton type of cycle when UF6 is the fissioning fuel fluid in a space power system. When uranium metal vapor is used as the fissioning fuel and working fluid, the difficulty is not in achieving a liquid state at the heat rejection end of the cycle as with UF6. For example, at an exhaust pressure of 1 atm one need "cool down" to only about 4000 K to achieve liquid uranium. The obstacle with uranium metal vapor is the extremely high temperatures of the vapor in the core. The fluid temperature needs to be at least 6000 K at all locations in the core to ensure the vapor state at pressures needed for criticality. This indicates that the peak gas temperature in the core will be at least 8000 K or 9000 K. The choice of UF4 as the fuel rather than UF6 or uranium metal vapor is justified by examining the saturation vapor curves, Figures 3-1 and 3-2, and the mole fraction of constituent species versus temperature curve of the uranium-fluorine system, Figure 3-3 [21]. At pressures required for criticality in the core, the temperature of UF4 need be only about 2000 K to guarantee the vapor state. On the other hand, one need cool down to only 1700 K in order to obtain liquid UF4. The extremely high uranium metal vapor temperature in the core and the 0 0 I I (iqM ) ajnssajQj jode L I- r J--08 I I - 0 0 ( 1-w S) r- S- 0 E r S- o4 0 0u 0 C-)- C o-> OS- VI ()C *O 5- 'N CO 0 II I I -0 -d 0gon extremely low UF6 heat rejection temperatures are avoided. Thus, UF4 has a saturation vapor pressure-temperature behavior that is highly desirable for a direct Rankine cycle burst power system for a space environment. Also, Figure 3-3 indicates that in the expected gas temperature operating range of 2500 K to 4000 K, UF4 is the predominant uranium-fluorine specie. The Working Fluid Material It has been shown in the previous section that a Rankine type of cycle is more appropriate for a burst mode space power system, and on this basis the fuel is selected to be UF4. Therefore, a working fluid that is compatible with the UF4 fuel and suitable for a Rankine type of cycle is needed. Preliminary chemical and material studies [22,23] indicate that a working fluid in the form of a metal fluoride should be compatible with the UF4 fuel. These working fluids include Li7F, KF, NaF, and RbF. Table 3-1 list relevant properties of these materials. Description of a Uranium Tetra-Fluoride, UTVR/Disk MHD-Rankine Power Cycle An example UF4/KF UTVR MHD-Rankine cycle power system schematic is shown in Figure 3-4. This system is capable of producing 200 MWe with a thermodynamic efficiency of z26%. The mass flow rates of UF4 and KF are 59 and 209 kg/sec, respectively. For the system illustrated in Figure 3-4, about 40 MW is required to vaporize the liquid UF4 in the UF4-boiler. The UF4 vapor is then directed to the UTVC where it is mixed with the KF. In the UTVC, 30 MW LL LL I- -J C> 0 0 LL OO 0 0 O m i ud Ci- r-. - 'CM LA; cM -4 CM CM 0 CU LL. 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of the fissioning power is deposited in the UF4 to raise its temperature

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

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

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

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

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

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

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

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

is therefore added to the KF fluid.

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

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

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

condensing radiator which allows the separation of the vapor mixture

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

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

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

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

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

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

by Hildenbrand and Lau [23].

The system described above has the potential to be extremely

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

liquid pumps.

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

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

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

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

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

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

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

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

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

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

columns based on nuclear analysis matches what is obtained from

thermodynamic and flow considerations. One method of controlling

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

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

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

4.

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

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

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

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

fluoride as compared to the UF4.

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Neutronic Analysis of the
Ultrahiqh Temperature Vapor Core Reactor

Static Neutronic Calculations

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

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

Kirtland are used in analyzing the static neutronic behavior of the

UTVR.

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

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

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

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

for the stationary system than for the corresponding circulating system.

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

detail in Appendix D.

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

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

Weighted multigroup neutron cross-sections files are generated from

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

shielding calculations are performed on the weighted multigroup neutron

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

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

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

[10].

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

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

obtained from the 1-D calculations. Basic static neutronic

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

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

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

working fluids. Reactivity penalties as a function of different liner

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

static calculations.

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

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

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

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

accurately modeled as a number of boiler columns separated by BeO

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

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

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

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

are necessary to determine the reliability of the obtained results.

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

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

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

transport code. Integral parameters for the dynamic neutronic analysis

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

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

to-core coupling coefficients, and the reactivity and neutron

multiplication factors of individual cores.

Dynamic Neutronic Calculations

The over-estimate of keff obtained from the static neutronic

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

in the UTVR kinetic model.

The dynamic analysis in the time domain is performed using

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

reactivity feedback effects such as vapor fuel density and boiler column

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

stability analysis studies are performed with the Engineering Analysis

System code, EASY5 [29].

The computer codes mentioned above are described in Appendix A.

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

Introduction

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

used to perform the preliminary nuclear characterization of the

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

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

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

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

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

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

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

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

moderator-reflector region (OBEO).

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

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

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

moderator-reflector regions. Neutronic calculations are performed using

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

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

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

XSDRNPM is described in detail in Appendix A.

Outer BeO Moderator-
Reflector Region

UF4 Boiler Region

Inner BeO Moderator-
Reflector Region -

Ultrahigh Temperature
Vapor Core

Region 1

Region 2 -- -

Region 3 -- -

Region 4

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

One-Dimensional Spherical
the UTVR

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

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

expected to be quite large due to the following:

1. Neutron leakage from the UTVR is underestimated since spherical

configurations provides the smallest surface-to-volume ratio.

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

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

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

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

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

of boiler columns separated by BeO moderator. By configuring the

boiler region as a spherical shell surrounding the UTVC, the

probability for neutrons interacting with the boiler region is

relatively large. Additionally, thermal neutron flux depression in

the boiler region is underestimated since the thickness of the boiler

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

columns.

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

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

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

represents a "clean" UTVR system.

Detailed three-dimensional neutronic analysis using MCNP [12]

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

accounted for, actual boiler configuration is modeled, and structural

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

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

analysis are "reasonable" and needed.

Scoping Calculations

To commence the nuclear characterization of the reactor system,

numerous 1-D scoping calculations are performed. These calculations

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

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

are described in this section.

Geometric Variations

As mentioned previously, size and mass are significant constraints

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

important design consideration for this system is the power sharing or

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

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

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

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

configurations are capable of meeting these constraints, the effects of

variations of the following parameters are examined:

While maintaining the inner and outer BeO region thicknesses at 20

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

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

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

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

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

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

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

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

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

decreases while PUTVC/PBCOL continues to increase.

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

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

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

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

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

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

rate versus the UTVC radius are given for both cases.

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

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

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

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

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

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

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

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

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

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

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

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

occur and a decrease in PBCOL is observed.

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

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

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

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

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

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

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

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

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

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

type of variation.

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

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

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

following section.

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

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

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

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

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

then decreases for radii beyond 70 cm. This can be explained as
follows: as the UTVC radius increases from 40 to 70 cm, the gained

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

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

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

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

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

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

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

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

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

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

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

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

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

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

UTVC and voided boiler is due to approaching infinite reactor

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

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

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

along with the IBEO thickness are the determining parameters that

influence neutronic coupling for the UTVC/boiler regions and the

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

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

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

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

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

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

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

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

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

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

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

Inner BeO moderator-reflector region thickness

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

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

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

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

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

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

The results indicate that the optimum neutronic coupling between

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

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

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

coupling phenomenon for the boiler and the decreased thickness of the

boiler at the higher IBEO thicknesses.

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

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

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

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

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

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

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

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

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

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

additional sets of calculations are needed. The first involves varying

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

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

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

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

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

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

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

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

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

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

values of 6k/k per cm of IBEO are +1.9 x 10-03 and -4.8 x 10-03 for the

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

C
U

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

and a continuous decrease in keff

However, neutronic coupling between the UTVC and the boiler cores

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

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

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

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

neutronic coupling) and PBCOL increases (due to enhanced neutronic

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The combined neutronic coupling between the UTVC and the boiler

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

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

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

15 cm is selected for IBEO.

Outer BeO moderator-reflector region thickness

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

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

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

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

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

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

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

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

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

undesirable since the system is intended for space power production.

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

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

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

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

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

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

require the use of heavier and thicker shielding.

0

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57
For all further calculations, a thickness of 40 cm is selected for

the OBEO.

UF4 boiler region thickness

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

spherical geometry is analogous to increasing the cross sectional flow

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

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

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

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

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

velocity also impacts on the boiler region friction and acceleration

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

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

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

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

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

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

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

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

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

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

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

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

causes PBCOL to decrease thus increasing PUTVC/PBCOL and decreasing

103 d/3AJLnd 'JOipej 6ULJ4qs JMOd

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U! qt

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

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

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

dimensional modeling are needed in order to select a suitable operating

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

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

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

UF4 boiler core volume

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

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

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

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

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

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

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

by 40 cm of BeO reflector or 40 cm of Be reflector. The spherical

radius of the core is varied from 4 cm to 11 cm which corresponds to an

equivalent cylindrical radius of 1.3 cm to about 6.0 cm. The boiler

contains 100% enriched U235 in completely liquid UF4. Values for keff

range from 0.491 for the spherical radius of 4 cm to 1.101 for an 11 cm

spherical radius, as shown in Table 4-2. The boiler is found to be

critical (keff = 1.0) at a spherical radius of about 9.8 cm, which

The results indicate that the UF4 boiler columns will not become

self-critical since in reality they will not contain 50 cm of liquid.

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If the reactor system has only two boiler columns at a total UF4 mass

flow rate of 62 kg/sec, then the required cross sectional flow area per

column for an entrance velocity of about 2 m/sec for the UF4 liquid will

be about 4.2 x 1003 m2. This corresponds to a cylindrical radius of
about 3.7 cm which is lower than the critical radius obtained in the 1-D

calculations; a larger number of columns would result in even smaller

boiler region radii (for an inlet velocity of 2 m/sec).

Fuel Density Variations

During reactor startup and power level changes, there will be

changes in the UF4/MF vapor pressure and temperature and, thus, in the

density. Also, the amount of liquid and the void volume fraction of the

UF4 in the boiler region will change depending on the power level. An

insight into the effect of density changes will help in predicting the

response of the reactor to power level changes and/or perturbations

introduced into the system. The effects of variations in the following

parameters are therefore studied.

UF4 partial pressure and mole fraction (UF4:NaF) in the UTVC
Preliminary calculations and analysis of the MHD generator indicate

that a mole fraction of about 10% for UF4 and 90% for NaF results in

efficient energy extraction [31]. Maintaining the UTVC radius at 60 cm,

the IBEO thickness at 20 cm, the boiler volume at 8.5 x 10-03 m3, and

the OBEO thickness at 35 cm (these calculations were performed prior to

obtaining the optimum IBEO and OBEO thicknesses of 15 and 40 cm,

respectively), the UF4 partial pressure is varied from 1 to 20 atm at

NaF partial pressures of 20, 40, and 60 atm. The result of these

variations are shown in Figure 4-8.

The results indicate that the system is essentially unaffected

neutronically by the NaF partial pressure. Thus, the UTVC can be

operated with a fuel mixture that is optimum with respect to the demands
of the MHD generator. Figure 4-8 indicates that keff saturates at UF4

partial pressures above =10 atm. This corresponds to a U235 density of

2.5 x 10-05 atoms/barn-cm. Beyond a UF4 partial pressure of 10 atm or a

U235 density of 2.5 x 10-05 atoms/barn-cm, the UTVC is becoming black to

neutrons. The results, as shown in Figure 4-8, indicate that

PUTVC/PBCOL increases as the UF4 partial pressure increases up to about
10 atm and remains at about a constant level as the UF4 partial pressure
further increases. For all further analysis, partial pressures of 5 atm
for UF4 and 45 atm for NaF are used.

U235 enrichment in UF4

The U235 enrichment is varied from 80% to 100% at UF4 partial

pressures in the UTVC of 1, 2, 3, 4, 5, 6, and 7 atm. The results, as

shown in Figure 4-9, indicate that keff increases as the enrichment

increases and as the UF4 partial pressure increases. The U235

enrichment is fixed at 100% for all further analysis.

U233 as the fissile isotope

The U235 fissile isotope in UF4 is replaced with U233. The U233

enrichment is varied from 80% to 100% at UF4 partial pressures of 3 and

5 atm. The results, as shown in Figure 4-10, indicate the same behavior

as obtained in Figure 4-9 for U235 with the exception that keff is

higher when U233 is the fissile fuel. This is due to the lower thermal

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capture cross section, ac, (48 barns versus 99 barns) and the higher

number of neutrons liberated per thermal fission, v, (2.49 versus 2.42)

in U233 versus U235; this corresponds to a higher number of fission
neutrons liberated per thermal neutron absorbed in the fuel, R, (about
2.29 for U233 and 2.07 for U235).

Average density of the UF4 in the boiler region

By varying the effective density of the UF4 in the boiler region,

the boiler column is simulated as a mixture of liquid and vapor with

some average quality. An examination of the effects of such density

changes aids in determining the reactor response due to power level

changes and UF4 inlet velocity changes. While maintaining the UTVC
radius at 60 cm, and the UF4 and NaF vapor partial pressures at 5 and 45
atm, respectively, the IBEO thickness at 20 cm, the boiler volume at 8.5

x 1003 m3, and the OBEO thickness at 35 cm, the "overall" density of

the UF4 in the boiler region is varied from 0.20 g/cm3 to 4.0 g/cm3 to

simulate the presence of both liquid and vapor UF4. A value of 0.20

g/cm3 for the density of UF4 reflects a mixture composed of about 5
volume percent liquid at 5 atm and 95 volume percent vapor, and a

density of =4 g/cm3 reflects a mixture of pure UF4 liquid.

The results, as shown in Figure 4-11, indicate an increasing

behavior for keff and a decreasing behavior for PUTVC/PBCOL as the
3
density of the UF4 increases to about 1.6 g/cm3. For densities above

1.6 g/cm3 the rate of increase of keff decreases and PUTVC/PBCOL levels
off. This indicates that above this density, the boiler starts to

become black to neutrons and begins to saturate.

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Material Variations

The types and location of structural materials needed in

constructing the UTVR are not known at this point. These structural

materials include piping, spacers, and protective coatings. Also, the

over-all cycle analysis may prove that a metal fluoride other than NaF

(e.g., KF, RbF, or Li7F) provides better over-all system performance
than the UF4/NaF does. By including some sample structural and

protective coating materials at selected surfaces or regions (e.g., the

UTVC wall) and by examining other metal fluorides, reactivity penalties

due to these materials can be estimated. The effects of variations of

the following materials are therefore studied.

Choice of metal fluoride in UTVC

At inner UTVC core radii of 40, 80, and 120 cm, while maintaining
the IBEO thickness at 20 cm, the boiler volume at 8.5 x 10-03 m3, and

the OBEO thickness at 35 cm, calculations are performed to examine the

reactivity effect of using NaF, Li7F, or KF as the working fluid in the

vapor fuel mixture. The results, as shown in Table 4-3, indicate that,

with regard to the UTVC only (the wall cooling region is not included in

these calculations), the use of Li7F as the working fluid results in the

highest value for keff, followed by NaF and then by KF. As the UTVC

radius increases, the difference in keff as a function of selected metal

fluoride working fluid becomes greater. At these larger radii, the

reactivity contribution of the boiler region to keff decreases at the

same time the reactivity contribution of the UTVC to keff increases.

This explains the behavior of the differences in keff for the different

fuel mixtures at the higher UTVC radii. Since the type of metal

E E

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fluoride has a small effect on keff, especially at a UTVC radius of 60

cm, NaF is used as the working fluid for further analysis.

Wall cooling region

Figure 4-12 shows the five region 1-D spherical "mock-up" of the

UF4/NaF UTVR system which includes the wall cooling region. To simulate

the variation of the NaF velocity in the wall cooling region, the

thickness of this region is varied from about 0.35 cm to about 3.3 cm.

This correspond to a NaF inlet velocity range of 0.5 to 5.0 m/sec.

Also, at each NaF velocity, the effective density of the NaF is varied
3 3 3
from 0.1 g/cm3 to 2.2 g/cm3. A value of 0.1 g/cm for the density of

NaF reflects a mixture composed of =4 volume percent liquid at 45 atm

and 96 volume percent vapor, and a density of 2.2 g/cm3 reflects a

mixture of pure NaF liquid. The results, shown in Table 4-4, indicate a

maximum penalty of about 10% 6k/k for a wall cooling region thickness of

3.33 cm and a NaF density of 2.2 g/cm3. However, the expected velocity

of the NaF is about 3 m/sec which corresponds to a wall cooling region

thickness of 0.58 cm. The reactivity penalty of the liquid NaF region

is then about 2.25% 6k/k for a NaF density of 2.2 g/cm3. As the inlet

velocity of the NaF increases in the wall cooling region and/or as the

effective density decreases, PUTVC/PBCOL increases.

Other metal fluoride working fluids

The NaF in the UTVC and wall cooling region is replaced by Li7F and

KF to examine the reactivity penalty or gain if other liquid metal

fluorides are used instead of NaF. The neutron multiplication factor,

keff, and the average PUTVC/PBCOL are obtained for the different metal
fluorides at wall cooling region thicknesses of 0.44, 0.87, and 3.33 cm

Outer BeO Moderator-
Reflector Region ---

UF4 Boiler Region -- '. ',

Inner BeO Moderator-
Reflector Region
Wall Cooling Region-- -

Ultrahigh Temperatuce .. ...

Region 1

Region 2 --

Region 3

Region 4

Region 5

Figure 4-12. Five Region,
"Mock-up" of

One-Dimensional 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 4-5.

The results indicate that the use of Li7F as the metal fluoride

results in the highest values for both keff and PUTVC/PBCOL' followed by
NaF and then by KF. As the thickness of the wall cooling region

increases from 0.00 to 3.33 cm, maximum reactivity penalties are about

2%, 10%, and 22% Sk/k for LiF, NaF, and KF, respectively. Comparing

these results with those in Table 4-3 where the wall cooling region is

not treated, a greater difference in keff is noticed from one type of

metal fluoride to the other. This is due to the much greater density of
the (liquid) metal fluoride in the wall cooling region which in effect

results in a higher overall parasitic absorption.

NaF mass flow rate to the boiler region

To account for the possibility that complete separation of the

UF4/NaF mixture into pure UF4 and pure NaF cannot be achieved, and to

attempt to decrease the required PUTVC/PBCOL (on the basis of

thermodynamic and flow considerations) from its present value of 21, the

NaF mass flow rate to the boiler is varied from 0 kg/sec to 158 kg/sec;

this range corresponds to diverting 0% to 100% of the NaF from the wall

cooling region to the boiler region. The results, as shown in Table 4-

6, indicate a slight increase in keff from 1.548 to 1.554 as the NaF is

diverted to the boiler.

Table 4-6 also indicates that as the NaF is diverted to the boiler

region, the thermodynamic requirement for PUTVC/PBCOL decreases while

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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 4-6, an attempt is made

to further increase UTVC/PBCOL by varying the inlet velocity of the

liquid UF4/NaF into the boiler region. The velocity is varied from 0.5
to 6.0 m/sec. The mass flow rate of the NaF is set at 94.8 kg/sec to

the boiler and 63.2 kg/sec to the wall cooling region.
Thermodynamically, this requires that PUTVC/PBCOL be 1.25. As the inlet
velocity of the mixture increases from 0.5 to 6.0 m/sec the amount of
the mixture in the boiler decreases; thus, the amount of fissile

material in the boiler decreases. This, as seen from Figure 4-13,
causes a decrease in keff from 1.577 to 1.468 and an increase in

PUTVC/PBCOL from 0.18 to 0.41.
Addition of Li6F poison to the boiler

An attempt is made to decrease the reactivity of the boiler region
by adding Li6 poison to the boiler region in order to obtain the
required PUTVC/PBCOL. Li6 is added to the boiler region in the form of
Li6F. The UF4/NaF-Li6F inlet velocity is fixed at 2 m/sec. The Li6F

mass flow rate is varied from 5.2 x 10-03 to 3.9 kg/sec. This

corresponds to an atom ratio variation from 0.1% to 75.0% (the atom

ratio being the ratio of the Li6 atoms to that of the U235). As the
mass flow rate of the Li6F increases, a decrease in keff from 1.550 to
0.957 and an increase in PUTVC/PBCOL from 0.266 to 0.574 is observed, as

shown in Figure 4-14. However, the required PUTVC/PBCOL value of 1.25

is not achieved in the 1-D configuration.

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 1-D spherical geometry is modeled as a region that contains a

homogenized mixture of liquid and vapor UF4 and BeO. The one-

dimensional boiler region annular thickness is varied from 2.0 to 4.3 cm
to simulate the actual boiler region configuration that contains from 2

to 8 boiler columns. The volume of the UF4 and the total volume of the

boiler region are conserved when converting from the true cylindrical

configuration to the 1-D spherical geometry. As the annular boiler

region thickness is varied (i.e., as the number of boiler columns is

varied), the total mass flow rate and the inlet velocity of the UF4 in
the boiler region are kept constant (i.e., the total UF4 cross sectional
flow area is fixed) but the volume of the BeO and the average UF4

density are varied. The results, keff and PUTVC/PBCOL, are given in

Table 4-7.

The results indicate that keff decreases and PUTVC/PBCOL increases

as the simulated number of boiler columns increases. This is due to the

decrease in the amount of moderator present in the boiler region; thus,

less neutron thermalization is occurring in the boiler region. This

results in a decrease in the average thermal neutron flux in the boiler

region causing keff to decrease and PUTVC/PBCOL to increase. The

results also indicate that keff increases and PUTVC/PBCOL decreases as

the UF4 density in the boiler increases. This is due to the increase in

the amount of fissile material present in the boiler region.

Full Text