Table Of ContentANALYSIS OF THE MAGNETOHYDRODYNAMIC FLOW
OF A FISSIONING GAS IN A
DISK MHD GENERATOR
By
GERARD EDWARD WELCH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS OF THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1992
UNIVERSITYOFFLOHIDALIBRARIES
iiiiiili
31262085524535
Copyright 1992
by
Gerard E. Welch
"Myeyes are ever toward the Lord,
for he will free my feet from the snare."
(Psalm 25:15)
To myparents,
in the name ofourLordJesusChrist.
ACKNOWLEDGEMENTS
The author wishes to extend his sincere appreciation and thanks to the
members ofhis supervisory committee, Dr. Edward T. Dugan, Dr. William E.
Lear, Jr.,Dr. William G. Vemetson, Dr. Alan M. Jacobs, Dr. Calvin C. Oliver,
and Dr. Robert J. Hanrahan, for their assistance and direction throughout the
course ofthis work. The author considers it a privilege to have worked under
these outstanding academicians.
Special thanks isextended to Dr. Dugan for the hours devoted to reviewing
this dissertation, and for his guidance, patience, example, and friendly support
over the many years ofthe author's graduate career. The author thanks Dr. Lear
for the many enjoyable hours ofdiscussion on MHD and gas dynamics. Thanks is
also extended to Dr. Oliver for his detailed insights into all facets ofthermal fluid
flow,and for hours ofenjoyable and educational conversation.
The author willalways be thankful for the support and constant
encouragement provided by Dr. Vernetson throughout his graduate career.
Thanks isalso extended to Dr. T. I-P. Shih ofCarnegie-Mellon University
for his time spent in answering detailed questions on computational fluid
mechanics, and to Dr. J.G. Appelbaum for the interesting discussions and help on
the plasma physics modeling.
Support for the author's graduate work has been provided in part by the
University ofFlorida. The early phase ofthis dissertation work was supported by
the Air force Wright Aeronautical Laboratories for work performed within the
Innovative Nuclear Space Power Institute ofthe University ofFlorida. The
author's masters work was supported byInstitute ofNuclear Power Operations.
All this support isgreatly appreciated.
The author thanks his friends and family in Gainesville for their moral
support throughout this work. A special thanks isextended Jean Roach for her
true friendship through some ofthe roughest periods ofthe author's graduate
career and for the many prayers made on the author's behalf by her, and the
members ofher intercessory prayer group.
Finally, the author thanks his parents, Gerard J. Welch and Mary G.
Welch, for their patience and love, for the hope they communicated to the author
during these past years, for their many sacrifices in devoting time and financial
support during the author's graduate career, and especially for their faithful
presence and prayers to the Lord who has sustained the author.
1
TABLE OF CONTENTS
Eage
ACKNOWLEDGMENTS
iv
LIST OF TABLES viii
LIST OF FIGURES x
ABSTRACT xviii
CHAPTERS
INTRODUCTION
1 1
LO Overview 1
1.1 Outflow Disk MHD Generator Power Generation 3
1.2 Background 13
1.3 Problem Statement 17
1.4 Organization ofDissertation 18
2 THEORETICAL MODELING 19
2.0 Introduction 19
2. Overview ofAssumptions 19
2.2 Fluid Mechanics 26
2.3 Electromagnetics 68
2.4 Plasma Physics Modeling and Transport Properties .... 83
2.5 Overall MHD Solution 96
3 ANALYSIS 98
3.0 Introduction 98
3.1 Solution Method Modifications for MHD Calculations .. 99
3.2 Duct Geometry Selection 127
33..34 CUonmipfaorrimsoPnlsasmwiathPrQoupaesrit-yOnMe-HDDimeSnosliuotnioanls Flow Solver . 114544
3.5 Nonuniform Plasma Transport Properties 180
1
CHAPTERS Bags
3 ANALYSIS (cont.)
3.6 Nonuniform Fission-Model Plasma Property MHD
Solutions 202
3.7 Comparison ofTwo-Dimensional and Quasi-One-
Dimensional Predictions for Reference Equilibrium/
Fission-Model Generator 242
4 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 253
4. Summary ofResults 253
4.2 Conclusions 262
4.3 Recommendations for Future Study 265
APPENDICES
A QUASI-ONE-DIMENSIONAL DISK MHD FLOW SOLVER 271
B GRID GENERATION 279
C SHOCK CAPTURING 292
LIST OF REFERENCES 300
BIOGRAPHICAL SKETCH 307
LIST OF TABLES
Table Cage
LI Disk MHD Generator Current Density Component 11
2.1 Governing Equations ofMagnetohydrodynamics 20
2.2 Governing Equations ofMagnetohydrodynamics with Fission
Density Terms in Cylindrical Coordinates with Tangential-
Symmetry 30
2.3 Transformed Governing Equations ofMHD with Thin-Layer
Approximation in Boundary-Fitted Curvilinear Coordinate
System (I.tj) 35
2.4 Pure UF4 and He Gas Properties and UF4-(94%)He Working
Fluid Mixture Properties 44
2.5 Explicit Method ofMacCormack with Generalized Finite-
Differencing Sequence 66
2.6 Transformed MHD Electromagnetics Equations in Boundary-
Fitted Curvilinear Coordinate System (1,77) 73
2.7 Constants ofPlasma PhysicsTransport Property Models 92
3.1 Uniform Plasma Property MHD Generator Parameters 156
3.2 Fluid Property Data for a UF4-(85%)He Working Fluid Mixture
for Example Fissioning Plasma Transport Property Calculations .... 186
3.3 Wall-to-Free Stream Plasma Property Ratios for Hot and Cold
Generator Walls with Example Generator Free Stream Flow
Conditions 199
3.4 Working Fluid Properties for Equilibrium Electron Temperature/
Fissioning Plasma (Sff > SjahJ MHD Generator Calculations 203
Table page
3.5 MHD Generator Inlet Conditions and Specified Global Parameters
for Nonuniform Fission-Model Plasma Property MHD Generator
Calculations 206
3.6 Comparison ofTwo-Dimensional MHD Solver and Quasi-One-
Dimensional Euler Solver Predictions for Reference Fissioning
Plasma Generator 245
