AN ABSTRACT OF THE THESIS OF
Anh T. Mai for the degree of Master of Science in Nuclear Engineering presented on
December 9, 2011
Title: Thermal Hydraulic and Fuel Performance Analysis for Innovative Small Light
Water Reactor Using VIPRE-01 and FRAPCON-3
Abstract approved:
Brian G. Woods
The Multi-Application Small Light Water Reactor (MASLWR) is a small natural
circulation pressurized light water reactor design that was developed by Oregon State
University (OSU) and Idaho National Engineering and Environmental Laboratory
(INEEL) under the Nuclear Energy Research Initiative (NERI) program to address the
growing demand for energy and electricity. The MASLWR design is geared toward
providing electricity to small communities in remote locations in developing countries
where constructions of large nuclear power plants are not economical. The MASLWR
reactor is designed to operate for five years without refueling and with fuel enrichment up
to 8 %. In 2003, an experimental thermal hydraulic research facility also known as the
OSU MASLWR Test Facility was constructed at Oregon State University to examined
the performance of new reactor design and natural circulation reactor design concepts.
This thesis is focused on the thermal hydraulics analysis and fuel performance analysis of
the MASLWR prototypical cores with fuel enrichment of 4.25 % and 8 %. The goals of
the thermal hydraulic analyses were to calculate the departure nucleate boiling ratio
(DNBR) values, coolant temperature, cladding temperature and fuel temperature profiles
in the hot channel of the reactor cores. The thermal hydraulic analysis was performed for
steady state operation of the MASLWR prototypical cores. VIPRE Version 01 is the code
used for all the computational modeling of the prototypical cores during thermal
hydraulic analysis. The hot channel and hot rod results are compared with thermal design
limits to determine the feasibility of the prototypical cores.
The second level of analysis was performed with a fuel performance code FRAPCON for
the limiting MASLWR fuel rods identified by the neutronic and thermal hydraulic
analyses. The goals of the fuel performance analyses were to calculate the oxide
thickness on the cladding and fission gas release (FGR). The oxide thickness results are
compared with the acceptable design limits for standard fuel rods.
The results in this research can be helpful for future core designs of small light water
reactors with natural circulation.
©Copyright by Anh T. Mai
December 9, 2011
All Rights Reserved
Thermal Hydraulic and Fuel Performance Analysis for Innovative Small Light Water
Reactor Using VIPRE-01 and FRAPCON-3
by
Anh T. Mai
A THESIS
Submitted to
Oregon State University
in partial fulfillment of
the requirement for the
degree of
Master of Science
Presented: December 9, 2011
Commencement June 2012
Master of Science thesis of Anh T. Mai presented on December 9, 2011.
APPROVED:
Major Professor, representing Nuclear Engineering
Head of the Department of Nuclear Engineering and Radiation Health Physics
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon State
University libraries. My signature below authorizes release of my thesis to any reader
upon request.
Anh T. Mai, Author
ACKNOWLEDGEMENTS
I would like to take this opportunity to thank Dr. Brian G. Woods for all his support,
guidance and patience to help me through this process. I am very grateful for all his help
and support of my thesis project. I am a better student and a better person today because
of all the encouragement and advice that Dr. Woods has given me.
I would like to thank Dr. Alexey Soldatov for all his help and support to make this
research project possible. Dr. Soldatov has given me great ideas and advices throughout
this research.
I would like to thank all the faculty members in the Nuclear Engineering Department at
OSU. I am grateful for Dr. Qiao Wu for all his guidance, patience and advice that he has
given me through my time at Oregon State. I am very glad to have the chance to work
with Dr. Wu on the MASLWR Test Facility.
I would like to thank Dr. Leah Minc and Dr. Jamie Kruzic for agreeing to be on my
master defense committee. They have gave me valuable inputs.
I would like to thank everyone at Anatech Corporation in San Diego, and particularly
Michael Kennard, Robert Montgomery, Bill Lyon and Tony for all their support during
my time at Anatech. I would have struggle a great deal in trying to extract the power
history from SIMULATE-3 for this research without their help. I would also like to
thank Garry Gose from CSA Inc for providing technical support with VIPRE.
Finally I would like to acknowledge my family (my dad, Yen Mai and my mom, Oanh
Vu) and friends at Oregon State University and in California for all their support and
motivation. I am very grateful for all my brothers and sisters (Victor, Thu, Hoa, Nga,
Minh, Vincente, and Sally Mai) for all their sacrifice, support and encouragement during
my time here at OSU. This thesis work is dedicated to them.
TABLE OF CONTENTS
Page
1
2
INTRODUCTION ....................................................................................................... 1
1.1
Research Objective ............................................................................................... 2
1.2
Assumptions ......................................................................................................... 5
1.3
Limitations ........................................................................................................... 6
1.4
Importance ............................................................................................................ 7
1.5
Overview of the Following Chapters ................................................................... 7
SURVEY OF LITERATURE ..................................................................................... 9
2.1
Overview of Small LWR Reactor Designs in Development................................ 9
2.2
MASLWR Concept and Design Overview ........................................................ 10
2.3
MASLWR Test Facility ..................................................................................... 13
2.4
Natural Circulation and Passive Safety System Overview ................................ 14
2.5
CHF Correlations for Thermal Hydraulic Analysis ........................................... 15
2.6
Previous RELAP5 Thermal Hydraulic Analyses for the MASLWR Design..... 17
2.7
Previous TRIGA Studies Relevant to the MASLWR Thermal Hydraulic
Analysis ......................................................................................................................... 19
3
4
MASLWR PROTOTYPICAL CORES DESCRIPTION .......................................... 20
3.1
Prototypical cores Overview .............................................................................. 20
3.2
Prototypical Cores with Burnable Absorber ...................................................... 22
3.3
Data from SIMULATE Output .......................................................................... 23
3.3.1
Overview of Prototypical Core M_4-25A .................................................. 24
3.3.2
Overview of Prototypical Core M_4-25B................................................... 27
3.3.3
Overview of Prototypical Core M_8A ........................................................ 29
3.3.4
Overview of Prototypical Core M_8B ........................................................ 32
3.3.5
Overview of Prototypical Core M_8C ........................................................ 34
METHODOLOGY .................................................................................................... 38
4.1
Research Goal .................................................................................................... 38
4.2
VIPRE-01 Overview .......................................................................................... 38
4.3
FRAPCON-3 Overview ..................................................................................... 40
4.4
Codes Interaction................................................................................................ 42
4.5
Initial Data-- Prototypical Cores Geometry and Operating Parameters ............. 44
4.6
Description of the VIPRE Models ..................................................................... 47
TABLE OF CONTENTS (Continued)
Page
4.6.1
One-eighth Prototypical Core A411, A412, A413, and A512 VIPRE
Models ..................................................................................................................... 48
5
4.7
Physical Models and Correlations Input ............................................................ 59
4.8
Convergence Criteria.......................................................................................... 62
4.9
Descriptions of the FRAPCON Model .............................................................. 63
4.10
DNB Analysis Method ....................................................................................... 64
4.11
Subchannel Analysis and Hot Channel Determination ...................................... 64
4.12
LWR Fuel Behavior and Modeling .................................................................... 66
4.12.1
Fission Gas Release in Fuel Rod ................................................................ 67
4.12.2
Clad Oxidation and Water Chemistry ......................................................... 68
4.13
Fuel Failure in Normal Operation Overview ..................................................... 68
4.14
Fuel Design Criteria and Limits ......................................................................... 69
4.15
NRC Licensing Process ...................................................................................... 71
RESULTS AND DISCUSSION ................................................................................ 72
5.1
VIPRE Model Results ........................................................................................ 72
5.1.1
5.2
Steady State BOC, MOC, EOC Results Comparison ................................. 74
VIPRE Independent and Sensitivity Studies ...................................................... 82
5.2.1
Critical Heat Flux Correlations Study......................................................... 82
5.2.2
Mixing Coefficient Sensitivity Studies ....................................................... 84
5.2.3
Gap Conductance Sensitivity Studies ......................................................... 85
5.2.4
Spacer Grids Sensitivity Study ................................................................... 85
5.2.5
Two Phase Flow Correlations Study........................................................... 86
5.2.6
Heat Transfer Correlations Study ............................................................... 88
5.2.7
Number of Axial Nodes Study.................................................................... 90
5.3
VIPRE Results for Using Single-Phase Heat Transfer Coefficient Correlation
Only 91
5.4
Limiting Rod Determination .............................................................................. 95
5.5
FRAPCON Results Comparisons....................................................................... 98
5.5.1
FRAPCON Results for Single-Phase Heat Transfer Correlation Only .... 100
5.5.2
Flow Rate Sensitivity Studies ................................................................... 102
5.6
Uncertainties..................................................................................................... 105
TABLE OF CONTENTS (Continued)
Page
6
5.6.1
Uncertainties in the Analysis Method ....................................................... 105
5.6.2
Uncertainties in Operating Conditions...................................................... 106
5.6.3
Uncertainties in Physical Characteristics of the Core ............................... 106
CONCLUSION ....................................................................................................... 107
6.1
Steady State ...................................................................................................... 107
6.2
Recommendations for Future Works ............................................................... 108
BIBLIOGRAPHY ........................................................................................................... 109
APPENDICES ................................................................................................................ 114
A APPENDIX (4.25 % Enriched Fuel, No BP Core Results) ....................................... 115
B APPENDIX (4.25 % Enriched Fuel, Standard BP Core Results) ............................. 122
C APPENDIX (8 % Enriched Fuel, No BP Core Results) ........................................... 129
D APPENDIX (8 % Enriched Fuel, Standard BP Core Results) .................................. 136
E APPENDIX (8 % Enriched Fuel, Advanced BP Core Results) ................................ 143
F APPENDIX (FRAPCON Comparison Results) ........................................................ 150
LIST OF FIGURES
Figure
Page
Figure 2.1 Cross Section view of the MASLWR core...................................................... 11
Figure 2.2 MASLWR conceptual designed. .................................................................... 13
Figure 2.3 OSU MASLWR Test Facility ........................................................................ 14
Figure 2.4 RELAP5 model .............................................................................................. 17
Figure 3.1 Schematic of the MASLWR prototypical cores. ............................................ 21
Figure 3.2 Standard burnable poison map ........................................................................ 23
Figure 3.3 Axial power factors for prototypical core M_4-25A. ..................................... 25
Figure 3.4 Beginning of cycle (BOC) assembly average peaking factor. ........................ 25
Figure 3.5 Middle of cycle (MOC) assembly average peaking factor. ............................. 25
Figure 3.6 End of cycle (EOC) assembly average peaking factor. .................................. 25
Figure 3.7 Assembly A411 beginning of cycle (BOC) rod average power factor. ......... 26
Figure 3.8 Assembly A411 middle of cycle (MOC) rod average power factor. .............. 26
Figure 3.9 Assembly A411 End of cycle (EOC) rod average power factor. .................... 27
Figure 3.10 Axial power factors for prototypical core M_4-25B. .................................... 27
Figure 3.11 Beginning of Cycle (BOC) assembly average peaking factor. ...................... 28
Figure 3.12 Middle of Cycle (MOC) assembly average peaking factor. .......................... 28
Figure 3.13 End of Cycle (EOC) assembly average peaking factor. ................................ 28
Figure 3.14 Assembly A411 beginning of cycle (BOC) rod average power factor. ........ 28
Figure 3.15 Assembly A411 middle of cycle (MOC) rod average power factor. ............ 29
Figure 3.16 Assembly A411 end of cycle (EOC) rod average power factor. ................... 29
Figure 3.17 Axial power factors for prototypical core M_8A. ......................................... 30
Figure 3.18 Beginning of cycle (BOC) assembly average peaking factor. ..................... 30
Figure 3.19 Middle of cycle (MOC) assembly average peaking factor. ........................... 30
Figure 3.20 End of cycle (EOC) assembly average peaking factor. ................................ 30
Figure 3.21 Assembly A411 beginning of cycle (BOC) rod average power factor. ....... 31
Figure 3.22 Assembly A411 middle of cycle (MOC) rod average power factor. ........... 31
Figure 3.23 Assembly A411 end of cycle (EOC) rod average power factor. .................. 32
Figure 3.24 Axial power factors for prototypical core M_8B. ........................................ 32
LIST OF FIGURES (Continued)
Figure
Page
Figure 3.25 Beginning of cycle (BOC) assembly average peaking factor. ..................... 33
Figure 3.26 Middle of cycle (MOC) assembly average peaking factor. .......................... 33
Figure 3.27 End of cycle (EOC) assembly average peaking factor. ................................. 33
Figure 3.28 Assembly A411 beginning of cycle (BOC) rod average power factor. ....... 33
Figure 3.29 Assembly A411 middle of cycle (MOC) rod average power factor. ........... 34
Figure 3.30 Assembly A411 end of cycle (EOC) rod average power factor. .................. 34
Figure 3.31 Axial power factors for prototypical core M_8C. ........................................ 35
Figure 3.32 Beginning of cycle (BOC) assembly average peaking factor. ..................... 35
Figure 3.33 Middle of cycle (MOC) assembly average peaking factor. .......................... 35
Figure 3.34 End of cycle (EOC) assembly average peaking factor. ................................ 36
Figure 3.35 Assembly A411 beginning of cycle (BOC) rod average power factor. ....... 36
Figure 3.36 Assembly A411 middle of cycle (MOC) rod average power factor. ........... 36
Figure 3.37 Assembly A411 end of cycle (EOC) rod average power factor. .................. 37
Figure 4.1 Simplified FRAPCON-3 Flow Chart ............................................................. 42
Figure 4.2 Codes interaction diagram. .............................................................................. 43
Figure 4.3 Axial zone locations. ...................................................................................... 46
Figure 4.4 Assemblies being modeled by VIPRE. .......................................................... 48
Figure 4.5 Channels and rods layout for the half fuel assembly models. ........................ 49
Figure 4.6 Channels and rods layout for the full fuel assembly models. .......................... 49
Figure 4.7 Channels and rods layout for A411 VIPRE model. ....................................... 50
Figure 4.8 Axial channels layout for A411 VIPRE model. .............................................. 51
Figure 4.9 Channels and rods layout for A512 VIPRE model. ....................................... 51
Figure 4.10 Axial channels layout for A512 VIPRE model. ........................................... 52
Figure 4.11 Channels and rods layout for A412 VIPRE model. ..................................... 53
Figure 4.12 Axial channels layout for A412 VIPRE model. ........................................... 53
Figure 4.13 Channels and rods layout for A413 VIPRE model. ..................................... 54
Figure 4.14 Axial channels layout for A413 VIPRE model. ........................................... 54
Figure 4.15 Boiling curve schematic ............................................................................... 61
LIST OF FIGURES (Continued)
Figure
Page
Figure 4.16 Flow channel of a rectangular and triangular array. ..................................... 65
Figure 4.17 Fuel safety criteria list. ................................................................................. 70
Figure 4.18 Relationship between the three categories of fuel safety criteria. ................ 70
Figure 5.1 Beginning of cycle DNBR axial profile comparisons. ................................... 74
Figure 5.2 Middle of cycle DNBR axial profile comparisons. ........................................ 74
Figure 5.3 End of cycle DNBR axial profile comparisons. ............................................. 75
Figure 5.4 BOC clad average temperature comparisons. ................................................ 76
Figure 5.5 BOC outer cladding surface temperature comparisons. ................................. 76
Figure 5.6 MOC outer cladding surface temperature comparisons. ................................ 77
Figure 5.7 EOC outer cladding surface temperature comparisons. ................................. 77
Figure 5.8 BOC fuel centerline temperature profiles comparison. .................................. 78
Figure 5.9 MOC fuel centerline temperature profiles comparisons. ............................... 79
Figure 5.10 EOC fuel centerline temperature profiles comparisons................................ 79
Figure 5.11 BOC bulk coolant temperature profiles comparison. ................................... 80
Figure 5.12 MOC bulk coolant temperature profiles comparison. .................................. 81
Figure 5.13 EOC bulk coolant temperature profiles comparison. ................................... 81
Figure 5.14 BOC heat transfer coefficients comparison .................................................. 82
Figure 5.15 Critical Heat Flux correlation comparisons (BOC). ..................................... 83
Figure 5.16 Axial DNBR distributions for different CHF correlations (BOC). .............. 83
Figure 5.17 BOC fuel centerline temperatures comparison at different gap conductance.
........................................................................................................................................... 85
Figure 5.18 BOC DNBR profiles comparison. ................................................................ 90
Figure 5.19 BOC outer cladding surface temperature comparisons. ............................... 91
Figure 5.20 MOC outer cladding surface temperature comparisons. .............................. 92
Figure 5.21 EOC outer cladding surface temperature comparisons. ............................... 92
Figure 5.22 BOC fuel centerline temperature comparisons............................................. 93
Figure 5.23 MOC fuel centerline temperature comparisons. ........................................... 94
Figure 5.24 EOC fuel centerline temperature comparisons. ............................................ 94
LIST OF FIGURES (Continued)
Figure
Page
Figure 5.25 Limiting rods boundary conditions. ............................................................. 96
Figure 5.26 Rod average LHGR. ..................................................................................... 97
Figure 5.27 Maximum nodal LHGR. ............................................................................... 97
Figure 5.28 Maximum nodal oxide thickness. ................................................................. 99
Figure 5.29 Limiting rods boundary conditions (single-phase heat transfers correlation
only). ............................................................................................................................... 100
Figure 5.30 Maximum nodal oxide thickness. ................................................................ 101
Figure 5.31 Oxide thickness at various flow rates for 4.25 % fuel enrichment ............. 102
Figure 5.32 Oxide thickness at various flow rates for 8 % fuel enrichment with standard
burnable poison. .............................................................................................................. 103
Figure 5.33 BOC boundary conditions inputs for FRAPCON ...................................... 103
Figure 5.34 MOC boundary conditions inputs for FRAPCON. ..................................... 104
Figure 5.35 EOC boundary conditions inputs for FRAPCON. ..................................... 104
Figure A.1 Axial DNBR profiles………………………………………………………115
Figure A.2 Axial critical heat flux (CHF) profiles…………………………………….115
Figure A.3 Bundle average axial pressure drop profiles………………………………116
Figure A.4 BOC axial temperature profiles……………………………………………116
Figure A.5 MOC axial temperature profiles…………………………………………...117
Figure A.6 EOC axial temperature profiles....................................................................117
Figure A.7 Axial velocity profiles……………………………………………………..118
Figure A.8 Axial void fraction profiles………………………………………………..118
Figure A.9 Axial true quality profiles………………………………………………….119
Figure A.10 Axial equilibrium quality profiles………………………………………..119
Figure A.11 Axial mass flux profiles……………….………………………………….120
Figure A.12 Axial heat transfer coefficient profiles…………………………………...120
Figure A.13 Axial heat flux profiles…………………………………………………...121
Figure A.14 Axial cross-flow profile between two channels………………………….121
LIST OF FIGURES (Continued)
Figure
Page
Figure B.1 Axial DNBR profiles………………………………………………………122
Figure B.2 Axial critical heat flux (CHF) profiles…………………………………….122
Figure B.3 Bundle average axial pressure drop profiles……………………………….123
Figure B.4 BOC axial temperature profiles……………………………………………123
Figure B.5 MOC axial temperature profiles…………………………………………...124
Figure B.6 EOC axial temperature profiles... …………………………………………124
Figure B.7 Axial velocity profiles……………………………………………………..125
Figure B.8 Axial void fraction profiles………………………………………………...125
Figure B.9 Axial true quality profiles………………………………………………….126
Figure B.10 Axial equilibrium quality profiles………………………………………...126
Figure B.11 Axial mass flux profiles…………………………………………………..127
Figure B.12 Axial heat transfer coefficient profiles…………………………………...127
Figure B.13 Axial heat flux profiles…………………………………………………...128
Figure B.14 Axial cross-flow profile between two channels…………………………..128
Figure C.1 Axial DNBR profiles………………………………………………………129
Figure C.2 Axial critical heat flux (CHF) profiles……………………………………..129
Figure C.3 Bundle average axial pressure drop profiles……………………………….130
Figure C.4 BOC axial temperature profiles……………………………………………130
Figure C.5 MOC axial temperature profiles…………………………………………...131
Figure C.6 EOC axial temperature profiles……………………………………………131
Figure C.7 Axial velocity profiles……………………………………………………..132
Figure C.8 Axial void fraction profiles………………………………………………...132
Figure C.9 Axial true quality profiles………………………………………………….133
Figure C.10 Axial equilibrium quality profiles………………………………………...133
Figure C.11 Axial mass flux profiles…………………………………………………..134
Figure C.12 Axial heat transfer coefficient profiles…………………………………...134
Figure C.13 Axial heat flux profiles…………………………………………………...135
Figure C.14 Axial cross-flow profile between two channels…………………………..135
LIST OF FIGURES (Continued)
Figure
Page
Figure D.1 Axial DNBR profiles………………………………………………………136
Figure D.2 Axial critical heat flux (CHF) profiles…………………………………….136
Figure D.3 Bundle average axial pressure drop profiles……………………………….137
Figure D.4 BOC axial temperature profiles……………………………………………137
Figure D.5 MOC axial temperature profiles…………………………………………...138
Figure D.6 EOC axial temperature profiles……………………………………………138
Figure D.7 Axial velocity profiles……………………………………………………..139
Figure D.8 Axial void fraction profiles………………………………………………...139
Figure D.9 Axial true quality profiles………………………………………………….140
Figure D.10 Axial equilibrium quality profiles………………………………………..140
Figure D.11 Axial mass flux profiles…………………………………………………..141
Figure D.12 Axial heat transfer coefficient profiles…………………………………...141
Figure D.13 Axial heat flux profiles…………………………………………………...142
Figure D.14 Axial cross-flow profile between two channels………………………….142
Figure E.1 Axial DNBR profiles………………………………………………………143
Figure E.2 Axial critical heat flux (CHF) profiles……………………………………..143
Figure E.3 Bundle average axial pressure drop profiles……………………………….144
Figure E.4 BOC axial temperature profiles……………………………………………144
Figure E.5 MOC axial temperature profiles…………………………………………...145
Figure E.6 EOC axial temperature profiles…………………………………………….145
Figure E.7 Axial velocity profiles……………………………………………………...146
Figure E.8 Axial void fraction profiles………………………………………………...146
Figure E.9 Axial true quality profiles………………………………………………….147
Figure E.10 Axial equilibrium quality profiles………………………………………...147
Figure E.11 Axial mass flux profiles…………………………………………………..148
Figure E.12 Axial heat transfer coefficient profiles……………………………………148
Figure E.13 Axial heat flux profiles…………………………………………………...149
Figure E.14 Axial cross-flow profile between two channels…………………………..149
LIST OF FIGURES (Continued)
Figure
Page
Figure F.1 Fission gas release comparisons.…………………………………………...150
Figure F.2 Rod average burnup…………………..……………………………………150
Figure F.3 Maximum fuel centerline temperature…...………………………………...151
Figure F.4 Rod internal pressure......……………………….…………………………..151
LIST OF TABLES
Table
Page
Table 2.1 Small Light Water Reactor (LWR) designs currently in development. ............ 9
Table 2.2 MASLWR design concepts. ............................................................................. 11
Table 2.3 Critical heat flux (CHF) correlations data ranges. ........................................... 16
Table 2.4 Comparison of MASLWR conditions to different CHF Correlations. ............ 16
Table 2.5 Steady-state operating conditions. ................................................................... 18
Table 2.6 Transient cases summary and results. .............................................................. 19
Table 3.1 MASLWR reactor main parameters. ................................................................ 20
Table 3.2 Prototypical cores descriptions. ....................................................................... 22
Table 3.3 Time of operation at full power. ....................................................................... 24
Table 4.1 Geometry input for VIPRE-01. ......................................................................... 44
Table 4.2 Fuel rod geometry input for VIPRE-01. ........................................................... 44
Table 4.3 Total axial length and number of axial nodes model in VIPRE. ..................... 46
Table 4.4 Operating conditions for VIPRE-01 input ....................................................... 47
Table 4.5 Channel geometry calculations. ....................................................................... 55
Table 4.6 Channel geometry calculations for gap width. ................................................ 55
Table 4.7 BOC axial power profiles. ............................................................................... 57
Table 4.8 MOC axial power profiles. .............................................................................. 57
Table 4.9 EOC axial power profiles. ............................................................................... 58
Table 4.10 Rod layout summary for A411 VIPRE model. .............................................. 59
Table 4.11 Two-phase flow and heat transfer correlations. .............................................. 61
Table 4.12 Data ranges of surface heat transfer coefficient correlations. ........................ 62
Table 4.13 Convergence Criteria for all VIPRE models .................................................. 63
Table 4.14 Initial geometry and materials for FRAPCON models. ................................. 64
Table 5.1 Hot channel and hot rod location at beginning of cycle (BOC). ..................... 73
Table 5.2 Hot channel and hot rod location at middle of cycle (MOC). ......................... 73
Table 5.3 Hot channel and hot rod location at end of cycle (EOC). ................................ 73
Table 5.4 Hot channel and hot rod for each CHF correlations. ....................................... 83
Table 5.5 MDNBR values for various mixing coefficients (BOC). ................................ 84
LIST OF TABLES (Continued)
Table
Page
Table 5.6 Spacer grid designs. ......................................................................................... 86
Table 5.7 MDNBR values for various spacer grid type (Beginning of cycle). ............... 86
Table 5.8 Two-phase flow correlation combinations. ..................................................... 87
Table 5.9 Two-phase flow correlation combinations. ..................................................... 87
Table 5.10 Heat transfer correlation combinations. ......................................................... 88
Table 5.11 Outer cladding temperatures comparison for different nucleate boiling
correlations. ....................................................................................................................... 89
Table 5.12 BOC A411 VIPRE model axial nodes comparison. ...................................... 90
Table 5.13 Prototypical cores limiting rods. .................................................................... 95
Table 5.14 Axial stations locations. ................................................................................. 98
LIST OF ACRONYMS
BOC
BWR
CHF
DCD
DNB
EOC
EFPD
FGR
IAEA
INEEL
LWR
MASLWR
MDNBR
MOC
NERI
NRC
ORNL
OSU
PWR
PZR
SMR
TRIGA
VIPRE
Beginning of Cycle
Boiling Water Reactor
Critical Heat Flux
Design Control Document
Departure Nucleate Boiling
End of Cycle
Effective Full Power Day
Fission Gas Release
International Atomic Energy Agency
Idaho National Engineering and Environmental Laboratory
Light Water Reactor
Multi-Application Small Light Water Reactor
Minimum Departure Nucleate Boiling Ratio
Middle of Cycle
Nuclear Energy Research Initiative
Nuclear Regulatory Commission
Oak Ridge National Laboratory
Oregon State University
Pressurized Water Reactor
Pressurizer Heaters
Small Modular Reactor
Training, Research, Isotopes, General Atomics
Versatile Internals and Component Program for Reactors; EPRI
Thermal Hydraulic and Fuel Performance Analysis for Innovative Small Light
Water Reactor Using VIPRE-01 and FRAPCON-3
1
INTRODUCTION
Smaller nuclear reactors have generated a lot of interest in the past few years for their
lower capital cost, shorter construction time and ability to service small electricity grids
compared to today‟s large reactors. According to the International Atomic Energy
Agency (IAEA) „small‟ reactors are defined as less than 300 MWe, but an upper limit to
„small‟ is consider to be 500 MWe. While there are many small reactors currently in
development in the United States (US) and other countries, small light water reactors
(LWRs) appear to be the most feasible to be deployed in the near future due to the
experiences with light water reactors technology in the nuclear industry and the navy.
Generally, small light water reactor concepts are expected to have simpler designs that
may include the use of passive safety system. These reactors may be built independently
or as modules that allow for more units to be added as needed. They can also be built in
large number quickly due to their simpler designs. In 2009, the IAEA projected up to 96
small modular reactors (SMRs) to be in operation around the world by 2030. Small
communities and remote regions that have small electricity grids can greatly benefit from
these smaller units. The future development directions for small reactor concepts include
improvement and simplification in systems designs, reductions in construction time,
easier maintenance, optimization of core design, and reduction in operation, fuel,
construction and maintenance cost [43]. It‟s critical that these reactors can operate
reliably and efficiently to be competitive. Recent Fukushima nuclear accidents in Japan
due to magnitude 9.0 earthquakes and tsunami have raised many questions about the
safety of larger and older nuclear power plants. Many of these plants were not designed
with passive safety systems and rely on pumps for cooling and normal operations. The
Fukushima accidents have brought renewed interest in smaller reactor designs and those
that incorporate the use of passive safety system which are considered to be safer.
2
As demand for energy and electricity continue to increase, Oregon State University
proposed the Multi-Application Small Light Water Reactor (MASLWR) design in 2002
to address the energy needs and the growing concern for the environment. The
MASLWR reactor is a small natural circulation light water reactor that includes the use
of passive safety systems, and off-site refueling. It‟s designed to use standard equipment
that would minimize development and deployment time, and have a core lifetime of
about 5 years [4]. The MASLWR reactor is designed to operate under natural circulation
and at much lower temperatures and pressures than those of traditional PWRs.
According to Modro et al [4], the design is considered to be a safe and reliable source of
energy for small communities and industry. A more detailed description of the
MASLWR reactor design is discussed in the next chapter.
The core design and fuel design of a reactor with MASLWR operating condition has
many challenges despite the use of standard fuel design and equipments. In designing
new reactor cores, safety analyses play a very important role. The reactor characteristics
must be analyzed under normal conditions, transients as well as accident scenarios.
Therefore, safety analyses are conducted in this research for five proposed prototypical
small LWR cores to better understand their characteristics and determine their feasibility.
The NRC requires complete neutronic, thermal hydraulic and fuel performance analyses
under normal operations, transients and accident scenarios as part of its new reactor
design licensing process. The neutronic analyses for the proposed prototypical small
LWR cores with the MASLWR geometry and operating conditions have been done by
Soldatov [1] in 2009. With regards to the thermal hydraulic and fuel performance
analysis, key characteristics identified below are meant to provide a better understanding
of small light water reactor designs.
1.1 Research Objective
The objective of this research is to determine the feasibility of the MASLWR
prototypical cores and whether the use of standard fuel technology, geometry and
materials can work for “non-standard” conditions of lower pressures, flow rates and
temperatures. The simulations from this research generated data for new ranges of fuel
3
enrichment, temperature, pressure and flow rates for a new fuel design. The MASLWR
prototypical cores were designed by Soldatov [1] and contain increased enrichment fuel,
deeper burn up rates, and burnable poison. A thermal hydraulic and fuel performance
investigation was conducted for these prototypical cores. The results from this
investigation help determine the feasibility of the MASLWR prototypical cores and
support small LWR core designs. The goal is to use state of the art thermal hydraulic and
fuel performance tools to model the characteristics of the prototypical small LWR cores
during normal operations based on MASLWR operating conditions and geometry. Since
the prototypical cores are symmetric, only 1/8th of the reactor core was needed to be
model by the thermal hydraulic code.
The primary focused of this research work was to determine and analyze the hot channel
and limiting rod from each of the prototypical cores. The neutronic analyses of the
prototypical cores with MASLWR design features and requirements were done
previously by Soldatov [1]. The SIMULATE-3 outputs from the neutronic analysis for
each the five prototypical cores were provided by Soldatov [1] for this investigation.
Thermal hydraulic analysis is part of the safety analysis methodology. The first level of
analysis was performed with a thermal hydraulic code VIPRE-01 for the prototypical
cores. This analysis allowed for the determination of the hydraulic characteristics of hot
channels and hot rods that might be considered to be limiting in the reactor. Thermal
hydraulic calculations are performed to obtain a specific set of limits called thermal
margin limits, which are intended to prevent fuel damage due to the occurrence of
departure from nucleate boiling (DNB) at anytime in the core [12]. The thermal
hydraulics characteristics are driven by the core power, core geometry, and coolant inlet
temperatures. The core power is obtained from SIMULATE-3 output. The goals of the
thermal hydraulics analyses are to:

Calculate coolant temperatures, fuel temperatures, and channel velocities of a
natural circulation system as a function of the core power for the prototypical
cores.
4

Calculate the hot channel temperature profiles, pressure drops, DNBR, and peak
values of the fuel and cladding surface temperatures during steady state operation
for the prototypical cores.

Provide the boundary conditions (clad surface temperatures and/or heat transfer
coefficients) of the limiting rods to be used in the fuel performance code.
The important thermal hydraulic characteristics for the prototypical cores with MASLWR
fuel are the fuel, clad, coolant temperatures profiles and DNBR value of the hot channel
and hot rod. The limiting rods are determined from the neutronic and thermal hydraulic
analyses based on the power history (highest peaking factor) and the cladding surface
temperatures.
The second level of analysis was performed with a fuel performance code FRAPCON for
the limiting MASLWR fuel rods identified by the neutronic and thermal hydraulic
analyses. The characteristics from the limiting MASLWR fuel rods were compared with
the limits from conventional PWR fuel rods. The fuel performance characteristics are
driven by the core power history, operating conditions, fuel geometry, and boundary
conditions obtained from the simulations of thermal hydraulic code. The goals of the fuel
performance analyses are to:

Calculate the integral fuel rod performances which include oxide thickness, fuel
temperatures and fission gas release (FGR) for the limiting rods from the
proposed prototypical cores.
The important integral fuel performance characteristic for this study is the oxide
thickness (corrosion) of the limiting rods. Therefore, the primary focused of this second
level analysis will be on the oxide thickness (corrosion) of the MASLWR fuel.
The safety analysis methodology from this investigation is important for the core designs
of small light water (LWR) reactors. It provides a better understanding of the thermal
hydraulics and fuel performance characteristics for small LWR designs with natural
5
circulation. The results for the hot channel and limiting rod for each of the MASLWR
prototypical cores are provided in chapter five.
1.2 Assumptions
There are several assumptions made in this research. These assumptions are presented
below.

The MASLWR prototypical cores designed by Soldatov [1] using Studsvik tools
were assumed to be acceptable for this investigation.

The neutronic results and analysis used in this investigation were assumed to be
valid.
VIPRE Version 01 (Versatile Internals and Component Program for Reactors; EPRI) is
the code used for all the modeling of the MASLWR prototypical cores during thermal
hydraulic analysis. The basic computational philosophy of VIPRE is the use of the
subchannel analysis concept where channels communicate laterally by diversion
crossflow and turbulent mixing. The flow field is assumed to be incompressible and
homogeneous. Conservation of mass, energy and momentum are solved in VIPRE for
interconnected array of channels. A brief description of the assumptions for the VIPRE
models in this research is presented below:

The thermal hydraulic hot channel is assumed to be the channel with the
minimum DNBR value. This assumption would give the most conservative
results.

The hot rod is assumed to be the rod with the highest cladding surface
temperature. The limiting rod is assumed to be rod with the highest power history
and peak cladding surface temperature.

The MASLWR fuel assembly is assumed to contain five spacer grids in this
research. The spacer grids location is illustrated in Chapter 4. It‟s assumed that
five spacer grids are appropriate since the MASLWR fuel length is much shorter
than those in current PWR reactor.
FRAPCON Version 3.4 is the computer code used for all the modeling of the fuel rods in
the MASLWR prototypical cores during fuel performance analysis. It‟s assumed that
6
FRAPCON can sufficiently model the fuel performance characteristics of the limiting
fuel rods found in the MASLWR prototypical cores. A brief description of the
assumptions for the FRAPCON model in this research is presented below:

A five day startup to full power is assumed in the FRAPCON model. The startup
time of five days to get to full power is assumed to be valid for a natural
circulation type reactor.

The MASLWR fuel design is assumed to have the same or similar attributes and
characteristics as standard PWR fuel for this research.
1.3
Limitations
This study is limited to the thermal hydraulics and fuel performance correlations within
the VIPRE and FRAPCON computer codes. In VIPRE, there are only a few heat transfer
coefficient correlations available for single phase regime and subcooled nucleate boiling
regime. The default Dittus-Boelter [10] Correlation was selected to calculate the heat
transfer coefficient in the single phase regime. For the subcooled nucleate boiling
regime, the Thomp [10] plus single phase Correlation was selected. This correlation is
also default in VIPRE and is considered suitable for the MASLWR operating conditions.
The other subcooled nucleate boiling regime correlations include Chen [10] Correlation
and Schrock-Grossman [10] Correlation. These two correlations were not used in this
study since the Thomp plus single phase Correlation was considered to be acceptable and
the result between these correlations did not show a big difference. The results for this
study assumed only the single-phase regime at first for the calculation of the heat transfer
coefficient. The single-phase and subcooled nucleate boiling regime was considered later
to determine if there‟s boiling in the core. If there‟s nucleate boiling or saturated boiling
in the core, then only the heat transfer coefficients and fuel rod temperatures results are
affected when compare to single-phase regime results. However, saturated boiling is
unwanted in nuclear reactor core designs.
When referring to the fission gas release model in FRAPCON-3, only the ANS-5.4 [14,
15] Model and the MASSIH/Forsberg [14,15] Model options are available to select from.
Both FGR models compare well with steady state data. The MASSIH/Forsberg [14]
7
Model was selected as the FGR model for this study. When referring to the cladding
waterside corrosion model, FRAPCON-3 uses the 1987 EPRI/ESCORE oxidation model
for PWRs and BWRs.
The results of the thermal hydraulic analysis and fuel performance analysis conducted for
this study is limited to MASLWR reactor. There is much data generated from VIPRE and
FRAPCON, it‟s not reasonable to analyze all the data. This is a numerical analysis study
only. No experimental data were generated from this research. This research is also
limited to steady-state condition only. No transient analysis was done. The results are
very limited to a very specific operational profile. The operational profiles are those of
the MASLWR reactor. The MASLWR reactor is currently only in its conceptual design
stage.
1.4 Importance
The results of this work will help identify core design issues for small reactors with
4.25% and 8% fuel enrichment and low core flow.
1.5 Overview of the Following Chapters
Chapter two provide a general understanding of the OSU MASLWR Test Facility and
past MASLWR reactor design. A discussion of the different CHF correlations, fuel
behaviors and fuel design criteria is also presented in this chapter.
In chapter three, a comprehensive description of the MASLWR prototypical cores design
by Soldatov[1] with different fuel enrichment and burnable poison is presented. This
study The VIPRE models were created using the power factor from this chapter as input.
In chapter four, the development of the VIPRE models and FRAPCON models for this
study is presented. The capabilities and limitations of the thermal hydraulic code VIPRE
and fuel performance code FRAPCON are also presented.
8
Chapter five presents the steady state thermal hydraulic results for the hot channel and
hot rod from the VIPRE models. The results include comparison of the DNBR values
and outer clad surface temperature profile for the prototypical cores. The FRAPCON
results for the limiting rod in each of the prototypical cores are also presented in this
chapter. The conclusion and future work is presented in chapter six.
9
2
SURVEY OF LITERATURE
2.1 Overview of Small LWR Reactor Designs in Development
Currently, there are many small light water reactor (LWR) designs under development in
the United States and various other countries around the world to meet the market needs.
Small LWR reactors are great for remote sites and small communities in developing
countries that have small electricity grids. These communities generally do not have
enough capital to build a large nuclear reactor. A list of some of the new small LWR
reactor designs currently in development is shown below in Table 2.1. There are many
technical reports [26, 27, 28, 29, 33, 34, 36] from the International Atomic Energy
Agency (IAEA) regarding the status of innovative small and medium sized reactors
designs and safety features. The design and safety features of the IRIS reactor currently
in development by Westinghouse can be found in [23].
Name
Capacity
Type
Developer
KLT-40S
35 MWe
PWR
OKBM, Russia
VK-300
300 MWe
PWR
Atomenergoproekt, Russia
CAREM
27 MWe
PWR
CNEA & INVAP, Argentina
IRIS
100-335 MWe
PWR
Westinghouse-led, International
mPower
125 MWe
PWR
Babcock & Wilcox, USA
SMART
100 MWe
PWR
KAERI, South Korea
NuScale
45 MWe
PWR
NuScale Power, USA
MASLWR
35 MWe
PWR
Oregon State University, USA
SMART
90 MWe
PWR
KAERI, South Korea
Table 2.1 Small Light Water Reactor (LWR) designs currently in development.
There are many advantages to building smaller nuclear reactors. Small LWR reactors
require much lower capital cost and can be built faster compared to today‟s large
reactors. They can be manufactured in large scale at a factory and transported to the
reactor sites. They can also be built as modules to generate revenues and add more units
10
as needed to meet the demand. These designs typically are smaller than 300 MWe and
could be used to replace older fossil power plants of similar size that may no longer be
economical to operate due to carbon emission constrained. Many of the infrastructures
and facilities already exist at these sites which would further reduce the cost.
Recent nuclear accident at the Fukushima Daiichi Nuclear Power Plants has brought back
a lot attention into the safety of older nuclear power plants. Smaller reactors have
simpler design and can incorporate new safety systems that would make nuclear reactors
much safer. The reduced power levels in small reactors allow for greater used of passive
safety systems and plant simplification such natural circulation of the primary coolant
[1]. Descriptions of natural circulation and passive safety system in water cooled nuclear
power plants are presented in the IAEA reports [25, 30].
This research is primarily focused on the small LWR prototypical cores designed at
Oregon State University. The goal is to understand the thermal hydraulics and fuel
characteristics of the prototypical cores designed by Soldatov [1] with MASLWR
operational parameter and geometry found in the MASLWR final report [4]. An
overview of the various small LWR designs and competitors to the MASLWR reactor
was previously discussed by Soldatov [1].
2.2 MASLWR Concept and Design Overview
The Multi-Application Small Light Water Reactor (MASLWR) is a small natural
circulation pressurized light water reactor design that was developed by Oregon State
University and Idaho National Engineering and Environmental Laboratory (INEEL)
under the Nuclear Energy Research Initiative (NERI) program to address the growing
demand for energy and electricity. The MASLWR design is gear toward providing
electricity to small communities in remote locations in developing countries where
constructions of large nuclear power plants are not economical. This is a small
pressurized water reactor that is designed to have a net output of 35 MWe for each
module. The design concept of the MASLWR reactor is presented in Table 2.2 below.
11
The MASLWR reactor core consists of 24 assemblies of standard 17x17 fuel design. A
cross-section view of the core is illustrated in Figure 2.1 below.
Thermal Power
150 MWt
Net Electrical Output
35 MWe
Steam Generator Type
Vertical, helical tubes
Fuel
, 8 % enriched
Refueling Intervals
5 years
Life-Cycle
60 years
Coolant Mass Flow Rate
424 kg/s
Cold Leg/Hot Leg Temperature
489.6 K/560.2 K
Number of Assemblies
24
Fuel Design
17x17
Average Power Density
100 kW/L
Cladding
Zircaloy-4
Table 2.2 MASLWR design concepts [4].
Figure 2.1 Cross Section view of the MASLWR core [4].
12
The MASLWR design operates at a much lower flow rate, temperature and pressure than
traditional PWR. The performance and safety studies for the MASLWR design have been
performed previously by thermal-hydraulic system codes called RELAP5-3D. The
purpose of the studies was to demonstrate the passive safety features and evaluate the
steady state and transient performance characteristics. The assumptions and results for
this safety studies is presented in the MASLWR final report [4, 7].
The MASLWR module would be fabricated at a factory and transported to its site. The
strategic goals and key features of the MASLWR design discussed by Modro et al [4] and
Soldatov[1] are listed below:
MASLWR design goals and key features:

Passive safety systems

Natural circulation reactor cooling

Long core lifetime (five year turbine and core replacement)

Transportable reactor module

Utilize existing institutional licensing and safety experience

Phased construction with new reactor modules added as needed

Utilize existing components, fuel, and off the shelf hardware

Minimize deployment time to three years or less for the first plant

Minimize capital, and operational costs

Enhanced safety due to simpler design

Defense in depth philosophy

Standard fuel assembly design

Lower temperature and pressure parameters compare to large PWR
The MASLWR design consists of an integral reactor and steam generator contained in a
single vessel that is located within a steel cylindrical containment filled with water [2, 4].
The containment is submerged under a pool of water to act as a heat sink. This
MASLWR design concept is illustrated in a schematic in Figure 2.2 below. The core flow
of the MASLWR is driven by natural convection. The MASLWR‟s nuclear steam supply
13
system is contained within the reactor vessel with the steam generators located in the
upper region of the vessel [2]. The entire module can be pull and replace for refueling
and maintenance every five years. The MASLWR is designed to have passive safety
systems and rely on natural circulation during steady state and transient operation.
Figure 2.2 MASLWR conceptual designed [2].
2.3 MASLWR Test Facility
In 2003, an experimental thermal hydraulic research facility also known as the OSU
MASLWR Test Facility was constructed at Oregon State University (OSU) to examined
the performance of new reactor design and natural circulation reactor design concepts.
This is currently the only small light water reactor (LWR) test facility in the world. The
original purpose of the of the OSU MASLWR test facility is to assess the operation of the
MASLWR under normal full pressure and full temperature conditions and to assess the
passive safety systems under transient conditions [2]. This purpose was expanded to
include other reactor designs that rely on natural circulation. The test facility is scaled at
1:3 in length, 1:254.7 in volume and 1:1 in time [2]. Its major internal components inside
the reactor pressure vessel include the core heaters, hot leg riser, steam generators helical
14
coil, and pressurizer (PZR) heaters. The hot fluid flow upwards through the core and hot
leg riser and the cooler fluid flows back down around the outside of the hot leg riser into
the lower plenum. The data generated from the OSU MASLWR Test Facility can be used
to assess computer code calculations for natural circulation system design and analyses.
The data from this test facility is critical in the development and design of natural
circulation reactors. A picture of the OSU MASLWR Test Facility is illustrated below in
Figure 2.3. A more detailed descriptions of the OSU MASLWR Test Facility and
performance and safety studies can be found in the following literatures [2,3,4,5,6,7,8].
Figure 2.3 OSU MASLWR Test Facility [2].
2.4 Natural Circulation and Passive Safety System Overview
In a natural circulation type reactor, no pumps are used to circulate the primary coolant.
The coolant flow in the core is driven completely by natural convection. One issue of a
natural circulation type reactor is there may be significance cross-flow in the coolant
15
between fuel assemblies. The core flow rate is depended on the secondary circuit
parameters and geometry of the reactor internals [1]. Experimental data from the OSU
MASLWR Test Facility and other test facilities can be used to improve the system model
for natural circulation phenomena. The IAEA issued technical documents [25, 30] in
2005 and in 2009 that describes the use of natural circulation and passive safety system in
advanced nuclear reactor designs for water cooled power plants. The goal was to give
insights into the design, operation and reliability of these types of reactor designs.
2.5 CHF Correlations for Thermal Hydraulic Analysis
The thermal hydraulic analysis requires the use of a critical heat flux (CHF) correlation
which is derived from experimental CHF data. The purpose of the CHF correlation is to
determine the operation or parametric limits that will assure departure from nucleate
boiling (DNB) will not occur and that the heat flux is below the predicted critical heat
flux. A detailed discussion of the different CHF correlations for the thermal hydraulic
code VIPRE can be found in Appendix D of the VIPRE Manual [9]. The data ranges of
the critical heat flux correlations are presented in Table 2.3 below. The EPRI-1, W-3
(uniform), and Bowring correlations from Table 2.3 were identified as the possible CHF
correlation to be used in the VIPRE models. The CHF correlation that gave the most
conservative departure from nucleate boiling (DNB) values would be selected as the
correlation to be used for this research. Table 2.4 compared the MASLWR operating
conditions to the data ranges of the CHF correlations. The comparisons show the
MASLWR conditions are within the data ranges of EPRI-1 and Bowring Correlations.
VIPRE contains a large database of CHF correlations for heated rods. However, many of
these correlations are inappropriate in their prediction of CHF for low flow conditions.
The reason is the CHF data were developed under high flow conditions. The CHF
phenomenon at low flow conditions is more complicated to predict than forced
convection due to the effects of buoyancy and flow instabilities [48]. It‟s assumed for this
investigation that the chosen CHF correlation in VIPRE is adequate to model the
prototypical cores with MASLWR parameters.
16
For the natural circulation reactor, the core flow rate, pressure and temperature are much
lower than those of traditional PWR. There are very limited CHF data correlations
available for low flow and low pressure. It‟s critical to have more CHF data for low flow
and low pressure to obtain more accurate DNBR prediction for natural convection. An
experimental study of low pressure, natural convection CHF was previously done for
typical TRIGA reactor. The results of this experimental study can be found in [13]. The
study of the effects of mass velocity and cold-wall on critical heat flux in advanced light
water reactor can be found in [47]. The experimental study observed that a CHF increases
rapidly at low velocities, and it increases at am much slower rate at higher velocities [47].
Table 2.3 Critical heat flux (CHF) correlations data ranges [10].
MASLWR
EPRI-1
Bowring
W-3s
Pressure (psia)
1247
200 - 2450
99 - 2250
1000 - 2000
Mass velocity
0.53
0.2 – 4.5
0.04 – 3.0
1.0 – 5.0
Hydraulic Diameter (in)
0.47
Not Reported
0.03 – 14.0
0.2 – 0.7
Heated Length (ft)
5.25 ft
2.5 – 15 ft
5.0 – 15.0
0.8 - 12
(Mlbm/hr-ft2)
Table 2.4 Comparison of MASLWR conditions to different CHF Correlations.
17
2.6 Previous RELAP5 Thermal Hydraulic Analyses for the MASLWR
Design
Previous performance and safety studies for the MASLWR design have been performed
by RELAP5. RELAP5 is a thermal-hydraulic systems code. These studies are discussed
in chapter 4 of the MASLWR final report [4]. The MASLWR design normal and
transient performance characteristics and the passive safety features were evaluated in
these studies [4]. The RELAP5 model is shown in Figure 2.4. A description of this model
is provided in chapter 4 of the MASLWR final report [4] and Fisher et al [7].
Figure 2.4 RELAP5 model [4].
18
A variety of accident scenarios were considered for these performance and safety analysis
studies. The studies include only events from normal, full-power operation, at the
beginning of life core condition [4]. The steady state operating conditions used for these
studies are given in Table 2.5 below. They are different from the MASLWR operating
conditions found earlier in the MASLWR final report [4]. This research used the
MASLWR operating conditions given in [1, 4].
Table 2.5 Steady-state operating conditions [4].
For normal operation, the parameters used for the axial core power peaking factor is 1.36,
hot assembly factor is 1.1, and hot fuel pin factor is 1.4. In this research, the axial core
peaking factor, hot assembly factor, and hot fuel pin factor from the neutronic results are
much higher for the MASLWR prototypical cores. These factors are given in Chapter 3.
According to the Fisher et al [7], the reactor core was found to operate in subcooled
nucleate boiling regime during steady-state operation. The results from the studies show
no significant transient cladding temperature excursions and containment pressure remain
within design limits for all the cases analyzed [4]. The reactor core received adequate
cooling source to remove decay heat and the vessel liquid collapsed is stable. A summary
of the transient cases performed and the results is provided in Table 2.6 below.
19
Table 2.6 Transient cases summary and results [4].
2.7 Previous TRIGA Studies Relevant to the MASLWR Thermal Hydraulic
Analysis
There are many thermal hydraulic analyses performed previously on TRIGA reactors.
TRIGA reactors are primarily used for training and research purpose. Similar to the
MASLWR design, the primary cooling of TRIGA reactors is provided by natural
convection. Another similarity between TRIGA reactors and the MASLWR design is
that they operate at low pressure and low flow when compare to commercial nuclear
reactors. A thermal hydraulics analyses conducted on the Oregon State TRIGA reactors
using RELAP5-3D can be found in [49]. A recent study conducted on TRIGA reactors
includes characterizing subcooled flow instability can be found in [50]. Under normal
operations, subcooled nucleate boiling occurs in TRIGA reactors [13].
20
3
3.1
MASLWR PROTOTYPICAL CORES DESCRIPTION
Prototypical cores Overview
In 2009, preliminary prototypical cores with MASLWR operating conditions and
parameters were designed by Soldatov [1] using Studsvik tools for neutronic analyses.
The prototypical cores were designed to meet the MASLWR key features and goals
discussed by Soldatov [1] and Modro et al [4]. The MASLWR reactor main parameters
used in the design of the prototypical cores are presented in Table 3.1 below.
Table 3.1 MASLWR reactor main parameters [1].
The prototypical cores were designed to have 24 assemblies of standard half length
Westinghouse 17x17 fuel. Each fuel rod contains 160.0 cm of fuel and is 197.104 cm
long [1]. A schematic of the prototypical core with the identification of each fuel
assembly is presented in Figure 3.1 below. Since the prototypical cores are symmetric,
this research will focus only on assembly A411, A412, A413 and A512. Only half of
assembly A411 and A512 are considered in this research since they are symmetric. These
four assemblies make up 1/8th of the core. Fuel enrichment of 4 to 4.95% and 8% with
and without burnable absorbers were considered in the prototypical core designs for a
five effective full power years. Burnable absorbers are used in nuclear reactors to absorb
neutrons and lower the reactivity of fresh fuel load. The use of burnable absorbers in
core designs and management have economic benefits that include: longer fuel cycle
21
length and higher fuel utilization and burnup. The burnable absorbers study for the
prototypical cores were discussed in greater detailed by Soldatov [1].
A101
A111
A202
A201
A211
A212
A303
A302
A301
A311
A312
A313
A403
A402
A401
A411
A412
A413
A502
A501
A511
A512
A601
A611
Figure 3.1 Schematic of the MASLWR prototypical cores.
According to Soldatov [1], prototypical cores with enrichment of 4 to 4.95% does not
meet the design goals for the MASLWR transportable core with a five effective full
power years of operation. The results from the core studies done by Soldatov [1]
concluded that it‟s possible to design a core for five effective years of operation and
within a burnup of 60 MWD/kgHM fuel assembly average. The studies show that 8%
enriched fuel with advanced burnable absorber final core design satisfied a five effective
years of operation and a burnup within 60 MWD/kgHM fuel assembly average
requirements. This research will focus on the feasibility of five prototypical cores
presented in Table 3.2 below. A name is given to each of the five MASLWR prototypical
cores to make it easier to identify and refer to in later chapters. These prototypical cores
were designed by Soldatov [1] with fuel enrichment of 4.25% and 8%. The prototypical
cores were designed with either no burnable absorbers, standard burnable absorbers or
advanced burnable absorbers. Prototypical cores with fuel enrichment of 4.25 % are used
22
as comparisons to prototypical cores with fuel enrichment of 8 %. They are not expected
to be feasible for a five year operation without refueling in this research.
Prototypical Core Name
Enrichment
Descriptions
M_4-25A
4.25 %
No Burnable Absorbers
M_4-25B
4.25 %
Standard Burnable Absorbers
M_8A
8%
No Burnable Absorbers
M_8B
8%
Standard Burnable Absorbers
M_8C
8%
Advanced Burnable Absorbers
Table 3.2 Prototypical cores descriptions.
According to Soldatov [1], the current power density of the prototypical cores being
analyzed is significantly higher than other competing small LWR designs. There may be
a need to reduce the power density, modify the core geometry and operational parameters
to avoid subcooled boiling in this reactor. This research will determined whether
subcooled boiling occurred in the prototypical cores. It will also determine whether the
amount of oxide thickness present an issue in the fuel rod.
3.2 Prototypical Cores with Burnable Absorber
Standard burnable absorber for the fuel with enrichment of 4.25% and 8% were analyzed
in this research. Figure 3.2 below present the standard burnable absorber map for the
prototypical cores with fuel enrichment of 4.25% and 8%. According to Soldatov [1], the
fuel assembly with burnable poisons contains 12 fuel pins with 4%
pins with 8%
fuel pins with 8%
. The 12 fuel pins with 4%
and 16 fuel
have a purple marker and the 16
have a red marker. The fuel pins with green marker are standard
fuel pins that contain no gadolinium. The layout of the standard burnable poison is based
the information mentioned in the ORNL report [38]. The layout is similar to M1
modification of 17x17 fuel assembly mentioned in this report.
23
Figure 3.2 Standard burnable poison map [1].
It was concluded by Soldatov[1] that the standard burnable absorber layout was not
sufficient for compensation of the initial excess reactivity for the fuel with enrichment of
8%. A new burnable absorber layout was designed Soldatov[1] to address the excess
reactivity compensation for fuel enrichment of 8%. This type of burnable absorber design
is being referred to as advanced burnable absorber in this research. A more detailed
descriptions and analyses of the standard and advanced burnable absorbers studies for the
prototypical cores can be found in the Soldatov dissertation [1].
3.3 Data from SIMULATE Output
For each of the five prototypical cores, data was extracted from SIMULATE output to be
used as inputs for the thermal hydraulic and fuel performance code. The data was
extracted for the beginning of life, middle of life and end of life of the core. The
beginning of life, middle of life, and end of life of the core will be refer to as beginning
of cycle (BOC), middle of cycle (MOC), and end of cycle (EOC) in this research. The
24
effective full power day (EFPD) chosen for the BOC, MOC and EOC in this research is
illustrated in Table 3.3 below.
Prototypical
Core Name
Effective Full Power Days (EFPD)
BOC (0 GWd/MT) MOC (25 GWd/MT)
EOC (50 GWd/MT)
M_4-25A
0
806.1
1612.3
M_4-25B
0
803.8
1607.6
M_8A
0
806.1
1612.2
M_8B
0
803.7
1607.5
M_8C
0
791.1
1612.3
Table 3.3 Time of operation at full power.
3.3.1
Overview of Prototypical Core M_4-25A
Figure 3.3 present the beginning of cycle (BOC), middle of cycle (MOC), and end of
cycle (EOC) axial power factor for the prototypical core with no burnable poison and fuel
enrichment of 4.25%. The assembly average relative power fraction for BOC, MOC, and
EOC is presented in Figure 3.4 to Figure 3.6. The assembly with the highest average
relative power fraction for BOC, MOC, and EOC is found to be assembly A411. This
main focus of this research will be on assembly A411 since the hot rod and hot channel is
most likely to be in this assembly. Assembly A411 rod average relative power fraction
for BOC, MOC, and EOC is presented in Figure 3.7 to Figure 3.9 below. Highlights in
yellow are the average pin power factors used in this research. The rod with the highest
average power factor is highlight in red.
25
1.60
BOC
Axial Power Factor
1.40
MOC
EOC
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.0
20.0
40.0
60.0
80.0
Axial Location (in.)
Figure 3.3 Axial power factors for prototypical core M_4-25A.
0.534
0.534
1.246
1.246
0.74
0.534
1.7
1.7
1.246
0.534
0.534
1.7
1.7
1.246
0.534
1.246
1.246
0.74
0.534
0.534
Figure 3.4 Beginning of cycle (BOC) assembly average peaking factor.
0.74
1.246
1.246
0.74
0.733
0.733
0.844
1.186
1.186
0.844
0.733
1.186
1.316
1.316
1.186
0.733
0.733
1.186
1.316
1.316
1.186
0.733
0.844
1.186
1.186
0.844
0.733
0.733
Figure 3.5 Middle of cycle (MOC) assembly average peaking factor.
0.811
0.811
1.141
1.141
0.871
0.811
1.225
1.225
1.141
0.811
0.811
1.225
1.225
1.141
0.811
1.141
1.141
0.871
0.811
0.811
Figure 3.6 End of cycle (EOC) assembly average peaking factor.
0.871
1.141
1.141
0.871
26
1.686
1.693
1.709
1.726
1.744
1.755
1.739
1.732
1.735
1.708
1.688
1.675
1.638
1.593
1.552
1.511
1.482
1.693
1.708
1.731
1.771
1.802
1.862
1.804
1.783
1.822
1.76
1.751
1.778
1.692
1.635
1.572
1.524
1.487
1.709
1.731
1.798
1.89
1.931
0
1.891
1.876
0
1.851
1.836
0
1.813
1.745
1.632
1.545
1.5
1.726
1.771
1.89
0
1.964
1.94
1.845
1.826
1.877
1.801
1.791
1.852
1.844
0
1.715
1.58
1.514
1.744
1.802
1.931
1.964
1.916
1.927
1.849
1.831
1.873
1.806
1.794
1.84
1.798
1.812
1.751
1.606
1.529
1.755
1.862
0
1.94
1.927
0
1.904
1.882
0
1.857
1.847
0
1.808
1.788
0
1.658
1.536
1.739
1.804
1.891
1.845
1.849
1.904
1.826
1.812
1.862
1.787
1.771
1.815
1.733
1.699
1.711
1.605
1.521
1.732
1.783
1.876
1.826
1.831
1.882
1.812
1.803
1.844
1.777
1.757
1.794
1.715
1.68
1.696
1.584
1.512
1.735
1.822
0
1.877
1.873
0
1.862
1.844
0
1.818
1.805
0
1.753
1.726
0
1.617
1.513
1.708
1.76
1.851
1.801
1.806
1.857
1.787
1.777
1.818
1.752
1.732
1.768
1.689
1.654
1.67
1.559
1.488
1.688
1.751
1.836
1.791
1.794
1.847
1.771
1.757
1.805
1.732
1.716
1.757
1.676
1.643
1.654
1.549
1.467
1.675
1.778
0
1.852
1.84
0
1.815
1.794
0
1.768
1.757
0
1.717
1.697
0
1.57
1.452
1.638
1.692
1.813
1.844
1.798
1.808
1.733
1.715
1.753
1.689
1.676
1.717
1.676
1.687
1.627
1.49
1.415
1.593
1.635
1.745
0
1.812
1.788
1.699
1.68
1.726
1.654
1.643
1.697
1.687
0
1.562
1.436
1.373
1.552
1.572
1.632
1.715
1.751
0
1.711
1.696
0
1.67
1.654
0
1.627
1.562
1.458
1.376
1.333
1.511
1.524
1.545
1.58
1.606
1.658
1.604
1.584
1.617
1.559
1.549
1.57
1.49
1.436
1.376
1.33
1.293
1.482
1.487
1.5
1.514
1.529
1.536
1.521
1.512
1.513
1.488
1.467
1.452
1.415
1.373
1.333
1.293
1.264
Figure 3.7 Assembly A411 beginning of cycle (BOC) rod average power factor.
1.279
1.279
1.287
1.295
1.305
1.312
1.312
1.313
1.316
1.307
1.301
1.297
1.287
1.274
1.261
1.249
1.245
1.279
1.285
1.296
1.31
1.331
1.351
1.335
1.335
1.345
1.328
1.325
1.337
1.313
1.289
1.271
1.256
1.245
1.287
1.296
1.324
1.357
1.375
0
1.362
1.36
0
1.353
1.352
0
1.358
1.336
1.299
1.267
1.252
1.295
1.31
1.357
0
1.385
1.374
1.355
1.351
1.361
1.343
1.344
1.361
1.368
0
1.332
1.281
1.26
1.305
1.331
1.375
1.385
1.377
1.376
1.357
1.352
1.364
1.344
1.347
1.363
1.359
1.364
1.349
1.3
1.269
1.312
1.351
0
1.374
1.376
0
1.371
1.367
0
1.361
1.361
0
1.358
1.352
0
1.319
1.274
1.312
1.335
1.362
1.355
1.357
1.371
1.357
1.353
1.364
1.346
1.346
1.357
1.338
1.331
1.334
1.301
1.272
1.313
1.335
1.36
1.351
1.352
1.367
1.353
1.351
1.365
1.345
1.342
1.352
1.331
1.325
1.33
1.298
1.269
1.316
1.345
0
1.361
1.364
0
1.364
1.365
0
1.36
1.352
0
1.342
1.334
0
1.307
1.27
1.307
1.328
1.353
1.343
1.344
1.361
1.346
1.345
1.36
1.337
1.333
1.343
1.321
1.315
1.32
1.288
1.26
1.301
1.325
1.352
1.344
1.347
1.361
1.346
1.342
1.352
1.333
1.332
1.342
1.323
1.314
1.317
1.283
1.253
1.297
1.337
0
1.361
1.363
0
1.357
1.352
0
1.343
1.342
0
1.338
1.33
0
1.293
1.246
1.287
1.313
1.358
1.368
1.359
1.358
1.338
1.331
1.342
1.321
1.323
1.338
1.332
1.335
1.317
1.266
1.232
1.274
1.289
1.336
0
1.364
1.352
1.331
1.325
1.334
1.315
1.314
1.33
1.335
0
1.293
1.238
1.215
1.261
1.271
1.299
1.332
1.349
0
1.334
1.33
0
1.32
1.317
0
1.317
1.293
1.252
1.216
1.197
1.249
1.256
1.267
1.281
1.3
1.319
1.301
1.298
1.307
1.288
1.283
1.293
1.266
1.238
1.216
1.196
1.18
1.245
1.245
1.252
1.26
1.269
1.274
1.272
1.269
1.27
1.26
1.253
1.246
1.232
1.215
1.197
1.18
1.169
Figure 3.8 Assembly A411 middle of cycle (MOC) rod average power factor.
1.221
1.217
1.218
1.219
1.224
1.226
1.228
1.23
1.233
1.224
1.219
1.216
1.213
1.208
1.205
1.204
1.207
1.217
1.217
1.219
1.222
1.236
1.247
1.238
1.239
1.242
1.231
1.229
1.237
1.225
1.211
1.206
1.203
1.202
1.218
1.219
1.233
1.25
1.263
0
1.252
1.25
0
1.241
1.242
0
1.251
1.237
1.22
1.205
1.203
1.219
1.222
1.25
0
1.267
1.255
1.243
1.241
1.243
1.232
1.234
1.244
1.254
0
1.236
1.208
1.204
1.224
1.236
1.263
1.267
1.259
1.256
1.244
1.24
1.243
1.232
1.234
1.245
1.247
1.253
1.248
1.221
1.207
1.226
1.247
0
1.255
1.256
0
1.252
1.249
0
1.241
1.242
0
1.243
1.241
0
1.231
1.209
1.228
1.238
1.252
1.243
1.244
1.252
1.243
1.24
1.245
1.232
1.233
1.241
1.231
1.229
1.235
1.22
1.209
1.23
1.239
1.25
1.241
1.24
1.249
1.24
1.242
1.25
1.235
1.23
1.238
1.227
1.226
1.232
1.22
1.209
1.233
1.242
0
1.243
1.243
0
1.245
1.25
0
1.241
1.234
0
1.228
1.226
0
1.222
1.211
1.224
1.231
1.241
1.232
1.232
1.241
1.232
1.235
1.241
1.223
1.218
1.225
1.215
1.214
1.222
1.21
1.202
27
1.219
1.229
1.242
1.234
1.234
1.242
1.233
1.23
1.234
1.218
1.219
1.226
1.217
1.215
1.221
1.207
1.216
1.237
0
1.244
1.245
0
1.241
1.238
0
1.225
1.226
0
1.226
1.223
0
1.212
1.196
1.19
1.213
1.225
1.251
1.254
1.247
1.243
1.231
1.227
1.228
1.215
1.217
1.226
1.227
1.232
1.226
1.199
1.183
1.208
1.211
1.237
0
1.253
1.241
1.229
1.226
1.226
1.214
1.215
1.223
1.232
0
1.21
1.182
1.174
1.205
1.206
1.22
1.236
1.248
0
1.235
1.232
0
1.222
1.221
0
1.226
1.21
1.191
1.173
1.167
1.204
1.203
1.205
1.208
1.221
1.231
1.22
1.22
1.222
1.21
1.207
1.212
1.199
1.182
1.173
1.166
1.161
1.207
1.202
1.203
1.204
1.207
1.209
1.209
1.209
1.211
1.202
1.196
1.19
1.183
1.174
1.167
1.161
1.158
Figure 3.9 Assembly A411 End of cycle (EOC) rod average power factor.
3.3.2
Overview of Prototypical Core M_4-25B
Prototypical core M_4-25B contained 4.25 % fuel enrichment with standard burnable
absorber design describes above. The axial power factor at BOC, MOC, and EOC is
illustrated in Figure 3.10 below. The peaking factor at BOC is very high as shown in
Figure 3.10. The assembly average relative power fraction for BOC, MOC, and EOC is
presented in Figure 3.11 to Figure 3.13. The assembly with the highest average relative
power fraction for BOC, MOC, and EOC is found to be assembly A411. Assembly A411
rod average relative power fraction for BOC, MOC, and EOC is presented in Figure 3.14
to Figure 3.16 below.
2.00
Axial Power Factor
BOC
1.80
MOC
1.60
EOC
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.0
20.0
40.0
60.0
80.0
Axial Location (in.)
Figure 3.10 Axial power factors for prototypical core M_4-25B.
28
0.754
0.754
0.738
1.182
1.182
0.738
0.754
1.183
1.388
1.388
1.183
0.754
0.754
1.183
1.388
1.388
1.183
0.754
0.738
1.182
1.182
0.738
0.754
0.754
Figure 3.11 Beginning of Cycle (BOC) assembly average peaking factor.
0.719
0.719
0.851
1.191
1.191
0.851
0.719
1.191
1.329
1.329
1.191
0.719
0.719
1.191
1.329
1.329
1.191
0.719
0.851
1.191
1.191
0.851
0.719
0.719
Figure 3.12 Middle of Cycle (MOC) assembly average peaking factor.
0.806
0.806
0.878
1.143
1.143
0.878
0.806
1.143
1.224
1.224
1.143
0.806
0.806
1.143
1.224
1.224
1.143
0.806
0.878
1.143
1.143
0.878
0.806
0.806
Figure 3.13 End of Cycle (EOC) assembly average peaking factor.
1.512
1.501
1.494
1.496
1.476
1.432
1.478
1.518
1.536
1.509
1.458
1.4
1.432
1.44
1.426
1.422
1.423
1.501
1.475
1.44
1.498
1.484
0.908
1.488
1.54
1.589
1.531
1.467
0.883
1.438
1.44
1.374
1.397
1.413
1.494
1.44
0.821
1.559
1.623
0
1.573
1.565
0
1.555
1.55
0
1.573
1.498
0.775
1.363
1.406
1.496
1.498
1.559
0
1.673
1.617
1.477
1.434
0.835
1.424
1.455
1.58
1.621
0
1.485
1.416
1.406
1.476
1.484
1.623
1.673
1.618
1.564
0.826
1.418
1.455
1.408
0.809
1.526
1.565
1.606
1.544
1.4
1.385
1.432
0.908
0
1.617
1.564
0
1.511
1.504
0
1.493
1.487
0
1.511
1.55
0
0.847
1.34
1.478
1.488
1.573
1.477
0.826
1.511
1.485
1.437
0.894
1.426
1.461
1.472
0.792
1.413
1.492
1.4
1.381
1.518
1.54
1.565
1.434
1.418
1.504
1.437
1.454
1.472
1.443
1.413
1.464
1.367
1.369
1.482
1.446
1.415
1.536
1.589
0
0.835
1.455
0
0.894
1.472
0
1.461
0.875
0
1.401
0.79
0
1.489
1.427
1.509
1.531
1.555
1.424
1.408
1.493
1.426
1.443
1.461
1.432
1.401
1.451
1.354
1.355
1.466
1.431
1.399
1.458
1.467
1.55
1.455
0.809
1.487
1.461
1.413
0.875
1.401
1.433
1.443
0.771
1.382
1.458
1.365
1.347
1.4
0.883
0
1.58
1.526
0
1.472
1.464
0
1.451
1.443
0
1.463
1.497
0
0.811
1.287
1.432
1.438
1.573
1.621
1.565
1.511
0.792
1.367
1.401
1.354
0.771
1.463
1.497
1.532
1.469
1.329
1.311
1.44
1.44
1.498
0
1.606
1.55
1.413
1.369
0.79
1.355
1.382
1.497
1.532
0
1.394
1.325
1.311
1.426
1.374
0.775
1.485
1.544
0
1.492
1.482
0
1.466
1.458
0
1.469
1.394
0.711
1.257
1.292
1.422
1.397
1.363
1.416
1.4
0.847
1.4
1.446
1.489
1.431
1.365
0.811
1.329
1.325
1.257
1.272
1.28
1.423
1.413
1.406
1.406
1.385
1.34
1.381
1.415
1.427
1.399
1.347
1.287
1.311
1.311
1.292
1.28
1.272
Figure 3.14 Assembly A411 beginning of cycle (BOC) rod average power factor.
29
1.284
1.286
1.295
1.305
1.315
1.326
1.323
1.321
1.324
1.315
1.312
1.312
1.297
1.283
1.269
1.254
1.245
1.286
1.295
1.312
1.324
1.344
1.35
1.349
1.345
1.356
1.338
1.338
1.336
1.325
1.302
1.286
1.265
1.251
1.295
1.312
1.309
1.373
1.387
0
1.377
1.375
0
1.368
1.367
0
1.369
1.351
1.284
1.282
1.261
1.305
1.324
1.373
0
1.397
1.39
1.376
1.375
1.351
1.367
1.365
1.376
1.379
0
1.347
1.294
1.271
1.315
1.344
1.387
1.397
1.391
1.398
1.347
1.379
1.389
1.371
1.336
1.384
1.372
1.375
1.36
1.312
1.28
1.326
1.35
0
1.39
1.398
0
1.394
1.388
0
1.381
1.384
0
1.379
1.367
0
1.317
1.288
1.323
1.349
1.377
1.376
1.347
1.394
1.373
1.37
1.367
1.363
1.361
1.379
1.328
1.352
1.348
1.314
1.282
1.321
1.345
1.375
1.375
1.379
1.388
1.37
1.367
1.382
1.362
1.359
1.373
1.359
1.35
1.344
1.307
1.274
1.324
1.356
0
1.351
1.389
0
1.367
1.382
0
1.379
1.358
0
1.369
1.327
0
1.314
1.271
1.315
1.338
1.368
1.367
1.371
1.381
1.363
1.362
1.379
1.354
1.349
1.364
1.348
1.339
1.334
1.296
1.265
1.312
1.338
1.367
1.365
1.336
1.384
1.361
1.359
1.358
1.349
1.347
1.365
1.313
1.335
1.331
1.295
1.263
1.312
1.336
0
1.376
1.384
0
1.379
1.373
0
1.364
1.365
0
1.358
1.345
0
1.292
1.261
1.297
1.325
1.369
1.379
1.372
1.379
1.328
1.359
1.369
1.348
1.313
1.358
1.344
1.346
1.329
1.278
1.243
1.283
1.302
1.351
0
1.375
1.367
1.352
1.35
1.327
1.339
1.335
1.345
1.346
0
1.307
1.251
1.225
1.269
1.286
1.284
1.347
1.36
0
1.348
1.344
0
1.334
1.331
0
1.329
1.307
1.239
1.231
1.206
1.254
1.265
1.282
1.294
1.312
1.317
1.314
1.307
1.314
1.296
1.295
1.292
1.278
1.251
1.231
1.205
1.186
1.245
1.251
1.261
1.271
1.28
1.288
1.282
1.274
1.271
1.265
1.263
1.261
1.243
1.225
1.206
1.186
1.169
Figure 3.15 Assembly A411 middle of cycle (MOC) rod average power factor.
1.219
1.215
1.217
1.219
1.224
1.227
1.228
1.229
1.232
1.222
1.221
1.219
1.216
1.21
1.207
1.202
1.202
1.215
1.217
1.221
1.223
1.238
1.227
1.239
1.239
1.242
1.23
1.229
1.217
1.228
1.213
1.211
1.206
1.203
1.217
1.221
1.193
1.25
1.263
0
1.252
1.25
0
1.241
1.242
0
1.251
1.239
1.183
1.211
1.207
1.219
1.223
1.25
0
1.267
1.255
1.246
1.244
1.201
1.235
1.236
1.244
1.255
0
1.239
1.213
1.21
1.224
1.238
1.263
1.267
1.259
1.258
1.204
1.245
1.248
1.236
1.194
1.246
1.247
1.254
1.25
1.226
1.214
1.227
1.227
0
1.255
1.258
0
1.255
1.253
0
1.243
1.245
0
1.246
1.243
0
1.215
1.215
1.228
1.239
1.252
1.246
1.204
1.255
1.245
1.243
1.226
1.235
1.235
1.244
1.193
1.234
1.239
1.225
1.213
1.229
1.239
1.25
1.244
1.245
1.253
1.243
1.244
1.252
1.237
1.234
1.242
1.234
1.232
1.236
1.222
1.209
1.232
1.242
0
1.201
1.248
0
1.226
1.252
0
1.244
1.217
0
1.237
1.19
0
1.222
1.206
1.222
1.23
1.241
1.235
1.236
1.243
1.235
1.237
1.244
1.225
1.221
1.229
1.222
1.221
1.225
1.212
1.2
1.221
1.229
1.242
1.236
1.194
1.245
1.235
1.234
1.217
1.221
1.221
1.229
1.18
1.219
1.224
1.21
1.2
1.219
1.217
0
1.244
1.246
0
1.244
1.242
0
1.229
1.229
0
1.229
1.225
0
1.197
1.198
1.216
1.228
1.251
1.255
1.247
1.246
1.193
1.234
1.237
1.222
1.18
1.229
1.228
1.234
1.228
1.205
1.191
1.21
1.213
1.239
0
1.254
1.243
1.234
1.232
1.19
1.221
1.219
1.225
1.234
0
1.215
1.188
1.183
1.207
1.211
1.183
1.239
1.25
0
1.239
1.236
0
1.225
1.224
0
1.228
1.215
1.159
1.183
1.175
1.202
1.206
1.211
1.213
1.226
1.215
1.225
1.222
1.222
1.212
1.21
1.197
1.205
1.188
1.183
1.173
1.165
1.202
1.203
1.207
1.21
1.214
1.215
1.213
1.209
1.206
1.2
1.2
1.198
1.191
1.183
1.175
1.165
1.158
Figure 3.16 Assembly A411 end of cycle (EOC) rod average power factor.
3.3.3
Overview of Prototypical Core M_8A
Prototypical core M_8A contained 8 % fuel enrichment with no burnable poison. The
axial power factor at BOC, MOC, and EOC is illustrated in Figure 3.17 below. The
assembly average relative power fraction for BOC, MOC, and EOC is presented in
Figure 3.18 to Figure 3.20. The assembly with the highest average relative power fraction
for BOC, MOC, and EOC is found to be assembly A411. Assembly A411 rod average
30
relative power fraction for BOC, MOC, and EOC is presented in Figure 3.21 to Figure
3.23 below.
1.60
BOC
MOC
1.40
Axial Power Factor
EOC
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.0
20.0
40.0
60.0
80.0
Axial Location (in.)
Figure 3.17 Axial power factors for prototypical core M_8A.
0.685
0.685
1.172
1.172
0.848
0.685
1.438
1.438
1.172
0.685
0.685
1.438
1.438
1.172
0.685
1.172
1.172
0.848
0.685
0.685
Figure 3.18 Beginning of cycle (BOC) assembly average peaking factor.
0.848
1.172
1.172
0.848
0.805
0.805
0.898
1.13
1.13
0.898
0.805
1.13
1.233
1.233
1.13
0.805
0.805
1.13
1.233
1.233
1.13
0.805
0.898
1.13
1.13
0.898
0.805
0.805
Figure 3.19 Middle of cycle (MOC) assembly average peaking factor.
0.881
0.881
1.094
1.094
0.928
0.881
1.122
1.122
1.094
0.881
0.881
1.122
1.122
1.094
0.881
1.094
1.094
0.928
0.881
0.881
Figure 3.20 End of cycle (EOC) assembly average peaking factor.
0.928
1.094
1.094
0.928
31
1.372
1.378
1.391
1.405
1.425
1.434
1.422
1.419
1.424
1.406
1.394
1.39
1.365
1.331
1.303
1.276
1.257
1.378
1.39
1.409
1.448
1.483
1.549
1.488
1.475
1.524
1.462
1.459
1.502
1.421
1.371
1.32
1.287
1.262
1.391
1.409
1.479
1.571
1.618
0
1.576
1.567
0
1.554
1.545
0
1.551
1.489
1.385
1.305
1.274
1.405
1.448
1.571
0
1.647
1.617
1.525
1.51
1.572
1.497
1.495
1.568
1.578
0
1.471
1.34
1.286
1.425
1.483
1.618
1.647
1.592
1.609
1.528
1.517
1.571
1.503
1.497
1.559
1.525
1.56
1.514
1.372
1.303
1.434
1.549
0
1.617
1.609
0
1.59
1.576
0
1.562
1.558
0
1.541
1.531
0
1.432
1.311
1.422
1.488
1.576
1.525
1.528
1.59
1.514
1.504
1.566
1.49
1.483
1.54
1.462
1.442
1.474
1.375
1.3
1.419
1.475
1.567
1.51
1.517
1.576
1.504
1.501
1.551
1.487
1.474
1.526
1.451
1.428
1.465
1.362
1.296
1.424
1.524
0
1.572
1.571
0
1.566
1.551
0
1.537
1.534
0
1.503
1.486
0
1.406
1.299
1.406
1.462
1.554
1.497
1.503
1.562
1.49
1.487
1.537
1.473
1.46
1.512
1.437
1.414
1.45
1.348
1.282
1.394
1.459
1.545
1.495
1.497
1.558
1.483
1.474
1.534
1.46
1.453
1.508
1.431
1.411
1.441
1.343
1.27
1.39
1.502
0
1.568
1.559
0
1.54
1.526
0
1.512
1.508
0
1.49
1.479
0
1.382
1.264
1.365
1.421
1.551
1.578
1.525
1.541
1.462
1.451
1.503
1.437
1.431
1.49
1.456
1.488
1.443
1.306
1.24
1.331
1.371
1.489
0
1.56
1.531
1.442
1.428
1.486
1.414
1.411
1.479
1.488
0
1.384
1.258
1.207
1.303
1.32
1.385
1.471
1.514
0
1.474
1.465
0
1.45
1.441
0
1.443
1.384
1.285
1.209
1.179
1.276
1.287
1.305
1.34
1.372
1.432
1.375
1.362
1.406
1.348
1.343
1.382
1.306
1.258
1.209
1.177
1.153
1.257
1.262
1.274
1.286
1.303
1.311
1.3
1.296
1.299
1.282
1.27
1.264
1.24
1.207
1.179
1.153
1.134
Figure 3.21 Assembly A411 beginning of cycle (BOC) rod average power factor.
1.156
1.16
1.171
1.183
1.199
1.207
1.203
1.202
1.206
1.197
1.194
1.193
1.181
1.161
1.145
1.13
1.121
1.16
1.169
1.186
1.212
1.238
1.276
1.246
1.24
1.267
1.235
1.236
1.262
1.22
1.19
1.159
1.138
1.125
1.171
1.186
1.231
1.289
1.317
0
1.297
1.294
0
1.289
1.288
0
1.299
1.266
1.204
1.155
1.135
1.183
1.212
1.289
0
1.337
1.321
1.275
1.268
1.301
1.263
1.266
1.307
1.318
0
1.26
1.18
1.147
1.199
1.238
1.317
1.337
1.314
1.321
1.278
1.273
1.302
1.267
1.268
1.306
1.295
1.312
1.288
1.205
1.162
1.207
1.276
0
1.321
1.321
0
1.311
1.306
0
1.301
1.302
0
1.301
1.297
0
1.242
1.168
1.203
1.246
1.297
1.275
1.278
1.311
1.275
1.271
1.303
1.265
1.264
1.296
1.258
1.25
1.267
1.21
1.164
1.202
1.24
1.294
1.268
1.273
1.306
1.271
1.269
1.298
1.264
1.261
1.291
1.252
1.242
1.263
1.204
1.161
1.206
1.267
0
1.301
1.302
0
1.303
1.298
0
1.294
1.292
0
1.281
1.274
0
1.229
1.164
1.197
1.235
1.289
1.263
1.267
1.301
1.265
1.264
1.294
1.258
1.254
1.284
1.245
1.235
1.256
1.197
1.154
1.194
1.236
1.288
1.266
1.268
1.302
1.264
1.261
1.292
1.254
1.253
1.285
1.246
1.237
1.254
1.197
1.15
1.193
1.262
0
1.307
1.306
0
1.296
1.291
0
1.284
1.285
0
1.283
1.278
0
1.221
1.147
1.181
1.22
1.299
1.318
1.295
1.301
1.258
1.252
1.281
1.245
1.246
1.283
1.27
1.287
1.262
1.178
1.134
1.161
1.19
1.266
0
1.312
1.297
1.25
1.242
1.274
1.235
1.237
1.278
1.287
0
1.227
1.146
1.112
1.145
1.159
1.204
1.26
1.288
0
1.267
1.263
0
1.256
1.254
0
1.262
1.227
1.164
1.114
1.093
1.13
1.138
1.155
1.18
1.205
1.242
1.21
1.204
1.229
1.197
1.197
1.221
1.178
1.146
1.114
1.092
1.076
1.121
1.125
1.135
1.147
1.162
1.168
1.164
1.161
1.164
1.154
1.15
1.147
1.134
1.112
1.093
1.076
1.066
Figure 3.22 Assembly A411 middle of cycle (MOC) rod average power factor.
1.062
1.065
1.073
1.083
1.093
1.1
1.101
1.101
1.104
1.099
1.098
1.098
1.092
1.081
1.072
1.064
1.06
1.065
1.072
1.083
1.098
1.115
1.131
1.121
1.121
1.13
1.119
1.119
1.13
1.114
1.097
1.083
1.071
1.064
1.073
1.083
1.108
1.135
1.15
0
1.144
1.143
0
1.141
1.142
0
1.15
1.135
1.108
1.083
1.072
1.083
1.098
1.135
0
1.159
1.153
1.141
1.139
1.147
1.136
1.139
1.152
1.159
0
1.136
1.098
1.082
1.093
1.115
1.15
1.159
1.156
1.157
1.145
1.142
1.151
1.139
1.142
1.156
1.155
1.16
1.15
1.115
1.092
1.1
1.131
0
1.153
1.157
0
1.154
1.153
0
1.151
1.152
0
1.156
1.153
0
1.131
1.098
1.101
1.121
1.144
1.141
1.145
1.154
1.146
1.144
1.152
1.142
1.143
1.152
1.143
1.14
1.143
1.119
1.097
1.101
1.121
1.143
1.139
1.142
1.153
1.144
1.144
1.154
1.142
1.142
1.151
1.14
1.137
1.141
1.118
1.095
1.104
1.13
0
1.147
1.151
0
1.152
1.154
0
1.153
1.15
0
1.149
1.144
0
1.126
1.097
32
1.099
1.119
1.141
1.136
1.139
1.151
1.142
1.142
1.153
1.139
1.138
1.147
1.135
1.132
1.138
1.114
1.098
1.119
1.142
1.139
1.142
1.152
1.143
1.142
1.15
1.138
1.138
1.148
1.138
1.134
1.138
1.113
1.092
1.09
1.098
1.13
0
1.152
1.156
0
1.152
1.151
0
1.147
1.148
0
1.151
1.148
0
1.124
1.089
1.092
1.114
1.15
1.159
1.155
1.156
1.143
1.14
1.149
1.135
1.138
1.151
1.15
1.154
1.143
1.106
1.081
1.081
1.097
1.135
0
1.16
1.153
1.14
1.137
1.144
1.132
1.134
1.148
1.154
0
1.127
1.087
1.068
1.072
1.083
1.108
1.136
1.15
0
1.143
1.141
0
1.138
1.138
0
1.143
1.127
1.097
1.07
1.057
1.064
1.071
1.083
1.098
1.115
1.131
1.119
1.118
1.126
1.114
1.113
1.124
1.106
1.087
1.07
1.055
1.045
1.06
1.064
1.072
1.082
1.092
1.098
1.097
1.095
1.097
1.092
1.09
1.089
1.081
1.068
1.057
1.045
1.037
Figure 3.23 Assembly A411 end of cycle (EOC) rod average power factor.
3.3.4
Overview of Prototypical Core M_8B
Prototypical core M_8B contained 8 % fuel enrichment with standard burnable poison.
The axial power factor at BOC, MOC, and EOC is illustrated in Figure 3.24 below. The
assembly average relative power fraction for BOC, MOC, and EOC is presented in
Figure 3.25 to Figure 3.27. The assembly with the highest average relative power fraction
for BOC, MOC, and EOC is found to be assembly A411. Assembly A411 rod average
relative power fraction for BOC, MOC, and EOC is presented in Figure 3.28 to Figure
3.30 below.
1.60
BOC
MOC
1.40
Axial Power Factor
EOC
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.0
20.0
40.0
60.0
80.0
Axial Location (in.)
Figure 3.24 Axial power factors for prototypical core M_8B.
33
0.878
0.878
0.837
1.108
1.108
0.837
0.878
1.108
1.191
1.191
1.108
0.878
0.878
1.108
1.191
1.191
1.108
0.878
0.837
1.108
1.108
0.837
0.878
0.878
Figure 3.25 Beginning of cycle (BOC) assembly average peaking factor.
0.787
0.787
0.895
1.133
1.133
0.895
0.787
1.133
1.264
1.264
1.133
0.787
0.787
1.133
1.264
1.264
1.133
0.787
0.895
1.133
1.133
0.895
0.787
0.787
Figure 3.26 Middle of cycle (MOC) assembly average peaking factor.
0.867
0.867
1.098
1.098
0.931
0.867
1.138
1.138
1.098
0.867
0.867
1.138
1.138
1.098
0.867
1.098
1.098
0.931
0.867
0.867
Figure 3.27 End of cycle (EOC) assembly average peaking factor.
0.931
1.098
1.098
0.931
1.217
1.215
1.216
1.221
1.216
1.189
1.219
1.245
1.258
1.241
1.211
1.177
1.2
1.2
1.191
1.186
1.185
1.215
1.2
1.184
1.235
1.24
0.797
1.247
1.28
1.331
1.276
1.239
0.787
1.223
1.213
1.159
1.171
1.182
1.216
1.184
0.716
1.317
1.377
0
1.333
1.328
0
1.324
1.325
0
1.357
1.294
0.697
1.155
1.183
1.221
1.235
1.317
0
1.417
1.369
1.251
1.219
0.734
1.216
1.242
1.354
1.397
0
1.288
1.204
1.187
1.216
1.24
1.377
1.417
1.363
1.332
0.721
1.215
1.263
1.211
0.715
1.317
1.342
1.39
1.345
1.207
1.181
1.189
0.797
0
1.369
1.332
0
1.302
1.298
0
1.294
1.292
0
1.311
1.342
0
0.771
1.153
1.219
1.247
1.333
1.251
0.721
1.302
1.268
1.233
0.794
1.229
1.258
1.286
0.707
1.224
1.3
1.211
1.18
1.245
1.28
1.328
1.219
1.215
1.298
1.233
1.247
1.278
1.242
1.223
1.281
1.193
1.192
1.293
1.242
1.204
1.258
1.331
0
0.734
1.263
0
0.794
1.278
0
1.273
0.785
0
1.24
0.714
0
1.29
1.215
1.241
1.276
1.324
1.216
1.211
1.294
1.229
1.242
1.273
1.237
1.218
1.276
1.187
1.186
1.286
1.235
1.197
1.211
1.239
1.325
1.242
0.715
1.292
1.258
1.223
0.785
1.218
1.246
1.273
0.697
1.21
1.284
1.195
1.164
1.177
0.787
0
1.354
1.317
0
1.286
1.281
0
1.276
1.273
0
1.289
1.318
0
0.753
1.127
1.2
1.223
1.357
1.397
1.342
1.311
0.707
1.193
1.24
1.187
0.697
1.289
1.312
1.356
1.31
1.173
1.145
1.2
1.213
1.294
0
1.39
1.342
1.224
1.192
0.714
1.186
1.21
1.318
1.356
0
1.245
1.161
1.142
1.191
1.159
0.697
1.288
1.345
0
1.3
1.293
0
1.286
1.284
0
1.31
1.245
0.665
1.105
1.129
1.186
1.171
1.155
1.204
1.207
0.771
1.211
1.242
1.29
1.235
1.195
0.753
1.173
1.161
1.105
1.113
1.119
1.185
1.182
1.183
1.187
1.181
1.153
1.18
1.204
1.215
1.197
1.164
1.127
1.145
1.142
1.129
1.119
1.114
Figure 3.28 Assembly A411 beginning of cycle (BOC) rod average power factor.
34
1.19
1.194
1.205
1.218
1.235
1.245
1.237
1.234
1.238
1.228
1.225
1.226
1.21
1.187
1.169
1.151
1.141
1.194
1.204
1.223
1.248
1.277
1.321
1.283
1.275
1.303
1.269
1.27
1.302
1.252
1.217
1.186
1.162
1.146
1.205
1.223
1.262
1.331
1.357
0
1.338
1.333
0
1.327
1.325
0
1.331
1.299
1.221
1.18
1.157
1.218
1.248
1.331
0
1.377
1.361
1.316
1.31
1.341
1.303
1.302
1.342
1.351
0
1.291
1.204
1.169
1.235
1.277
1.357
1.377
1.352
1.364
1.317
1.315
1.345
1.308
1.302
1.344
1.325
1.344
1.317
1.232
1.184
1.245
1.321
0
1.361
1.364
0
1.354
1.347
0
1.34
1.34
0
1.337
1.327
0
1.274
1.193
1.237
1.283
1.338
1.316
1.317
1.354
1.31
1.308
1.346
1.301
1.296
1.333
1.288
1.281
1.296
1.235
1.185
1.234
1.275
1.333
1.31
1.315
1.347
1.308
1.304
1.336
1.298
1.294
1.326
1.287
1.275
1.291
1.227
1.18
1.238
1.303
0
1.341
1.345
0
1.346
1.336
0
1.33
1.333
0
1.317
1.304
0
1.253
1.182
1.228
1.269
1.327
1.303
1.308
1.34
1.301
1.298
1.33
1.291
1.287
1.318
1.279
1.267
1.283
1.219
1.172
1.225
1.27
1.325
1.302
1.302
1.34
1.296
1.294
1.333
1.287
1.282
1.318
1.27
1.265
1.281
1.219
1.169
1.226
1.302
0
1.342
1.344
0
1.333
1.326
0
1.318
1.318
0
1.314
1.304
0
1.25
1.169
1.21
1.252
1.331
1.351
1.325
1.337
1.288
1.287
1.317
1.279
1.27
1.314
1.294
1.312
1.284
1.199
1.152
1.187
1.217
1.299
0
1.344
1.327
1.281
1.275
1.304
1.267
1.265
1.304
1.312
0
1.25
1.163
1.128
1.169
1.186
1.221
1.291
1.317
0
1.296
1.291
0
1.283
1.281
0
1.284
1.25
1.171
1.132
1.108
1.151
1.162
1.18
1.204
1.232
1.274
1.235
1.227
1.253
1.219
1.219
1.25
1.199
1.163
1.132
1.107
1.089
1.141
1.146
1.157
1.169
1.184
1.193
1.185
1.18
1.182
1.172
1.169
1.169
1.152
1.128
1.108
1.089
1.077
Figure 3.29 Assembly A411 middle of cycle (MOC) rod average power factor.
1.076
1.079
1.089
1.099
1.108
1.119
1.116
1.116
1.117
1.113
1.113
1.115
1.105
1.095
1.084
1.073
1.068
1.079
1.087
1.104
1.115
1.134
1.152
1.139
1.138
1.146
1.135
1.135
1.089
1.104
1.128
1.158
1.169
0
1.163
1.163
0
1.16
1.16
1.149
1.13
1.111
1.099
1.082
1.072
0
1.166
1.154
1.124
1.099
1.099
1.115
1.158
0
1.178
1.173
1.165
1.164
1.171
1.16
1.083
1.161
1.17
1.175
0
1.154
1.111
1.108
1.134
1.169
1.178
1.176
1.181
1.168
1.167
1.177
1.093
1.164
1.164
1.178
1.172
1.175
1.165
1.129
1.119
1.152
0
1.173
1.181
0
1.178
1.176
1.102
0
1.173
1.175
0
1.178
1.17
0
1.147
1.116
1.139
1.163
1.165
1.168
1.178
1.165
1.112
1.164
1.174
1.161
1.161
1.175
1.164
1.16
1.158
1.133
1.116
1.138
1.163
1.164
1.167
1.176
1.108
1.164
1.162
1.174
1.16
1.16
1.172
1.163
1.158
1.158
1.13
1.117
1.146
0
1.171
1.177
1.104
0
1.174
1.174
0
1.173
1.172
0
1.173
1.166
0
1.137
1.113
1.135
1.16
1.16
1.103
1.164
1.173
1.161
1.16
1.173
1.156
1.156
1.168
1.158
1.154
1.154
1.125
1.113
1.135
1.16
1.1
1.161
1.164
1.175
1.161
1.16
1.172
1.156
1.155
1.169
1.158
1.153
1.152
1.126
1.101
1.115
1.149
0
1.17
1.178
0
1.175
1.172
0
1.168
1.169
0
1.171
1.163
0
1.138
1.102
1.105
1.095
1.13
1.166
1.175
1.172
1.178
1.164
1.163
1.173
1.158
1.158
1.171
1.165
1.167
1.156
1.118
1.09
1.111
1.154
0
1.175
1.17
1.16
1.158
1.166
1.154
1.153
1.163
1.167
0
1.143
1.097
1.078
1.084
1.073
1.099
1.124
1.154
1.165
0
1.158
1.158
0
1.154
1.152
0
1.156
1.143
1.111
1.083
1.065
1.082
1.099
1.111
1.129
1.147
1.133
1.13
1.137
1.125
1.126
1.138
1.118
1.097
1.083
1.064
1.068
1.051
1.072
1.083
1.093
1.102
1.112
1.108
1.104
1.103
1.1
1.101
1.102
1.09
1.078
1.065
1.051
1.041
Figure 3.30 Assembly A411 end of cycle (EOC) rod average power factor.
3.3.5
Overview of Prototypical Core M_8C
Figure 3.31 present the beginning of cycle (BOC), middle of cycle (MOC), and end of
cycle (EOC) axial power factor for the prototypical core with advanced burnable poison
design and fuel enrichment of 8%. The assembly average relative power fraction for
BOC, MOC, and EOC is presented in Figure 3.32 to Figure 3.34. The assembly with the
highest average relative power fraction for BOC and EOC is found to be assembly A411.
35
The assembly with the highest average relative power fraction for MOC is found to be
assembly A412. Assembly A411 rod average relative power fraction for BOC, MOC,
and EOC is presented in Figure 3.35 to Figure 3.37 below. From Figure 3.35 to Figure
3.37, it was observed that the fuel rod average power factors in this final core are not as
uniform when compare to other prototypical cores. This is due to the way the burnable
absorbers are design in this core.
1.60
BOC
MOC
Axial Power Factor
1.40
EOC
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.0
20.0
40.0
60.0
80.0
Axial Location (in.)
Figure 3.31 Axial power factors for prototypical core M_8C.
0.925
0.925
1.097
1.097
0.834
0.925
1.12
1.12
1.097
0.925
0.925
1.12
1.12
1.097
0.925
1.097
1.097
0.834
0.925
0.925
Figure 3.32 Beginning of cycle (BOC) assembly average peaking factor.
0.834
1.097
1.097
0.834
0.919
0.919
0.865
1.1
1.1
0.865
0.919
1.1
1.097
1.097
1.1
0.919
0.919
1.1
1.097
1.097
1.1
0.919
0.865
1.1
1.1
0.865
0.919
0.919
Figure 3.33 Middle of cycle (MOC) assembly average peaking factor.
36
0.806
0.806
1.109
1.109
0.935
0.806
1.237
1.237
1.109
0.806
0.806
1.237
1.237
1.109
0.806
1.109
1.109
0.935
0.806
0.806
Figure 3.34 End of cycle (EOC) assembly average peaking factor.
0.935
1.109
1.109
0.935
0.781
0.461
0.461
0.472
0.493
0.528
1.162
1.317
1.367
1.315
1.16
0.527
0.493
0.473
0.462
0.464
0.793
0.461
0.459
0.45
0.484
0.51
0.559
1.262
1.381
1.491
1.379
1.26
0.558
0.51
0.484
0.451
0.462
0.468
0.461
0.45
0.486
0.521
0.558
0
1.439
1.538
0
1.536
1.437
0
0.558
0.521
0.487
0.453
0.468
0.472
0.484
0.521
0
1.334
1.459
1.48
1.53
1.619
1.529
1.478
1.456
1.332
0
0.522
0.486
0.478
0.493
0.51
0.558
1.334
1.453
1.571
1.55
1.583
1.664
1.582
1.548
1.568
1.45
1.332
0.558
0.511
0.498
0.528
0.559
0
1.459
1.571
0
1.644
1.687
0
1.686
1.642
0
1.568
1.455
0
0.559
0.531
1.162
1.262
1.439
1.48
1.55
1.644
1.616
1.619
1.717
1.619
1.615
1.641
1.546
1.475
1.434
1.258
1.162
1.317
1.381
1.538
1.53
1.583
1.687
1.619
1.653
1.73
1.653
1.619
1.685
1.579
1.524
1.529
1.372
1.31
1.367
1.491
0
1.619
1.664
0
1.717
1.73
0
1.732
1.719
0
1.661
1.612
0
1.476
1.35
1.315
1.379
1.536
1.529
1.582
1.686
1.619
1.653
1.732
1.654
1.618
1.682
1.576
1.519
1.523
1.365
1.302
1.16
1.26
1.437
1.478
1.548
1.642
1.615
1.619
1.719
1.618
1.611
1.635
1.538
1.465
1.421
1.245
1.149
0.527
0.558
0
1.456
1.568
0
1.641
1.685
0
1.682
1.635
0
1.554
1.44
0
0.55
0.522
0.493
0.51
0.558
1.332
1.45
1.568
1.546
1.579
1.661
1.576
1.538
1.554
1.433
1.313
0.549
0.501
0.487
0.473
0.484
0.521
0
1.332
1.455
1.475
1.524
1.612
1.519
1.465
1.44
1.313
0
0.511
0.475
0.465
0.462
0.451
0.487
0.522
0.558
0
1.434
1.529
0
1.523
1.421
0
0.549
0.511
0.476
0.441
0.454
0.464
0.462
0.453
0.486
0.511
0.559
1.258
1.372
1.476
1.365
1.245
0.55
0.501
0.475
0.441
0.45
0.454
0.793
0.468
0.468
0.478
0.498
0.531
1.162
1.31
1.35
1.302
1.149
0.522
0.487
0.465
0.454
0.454
0.774
Figure 3.35 Assembly A411 beginning of cycle (BOC) rod average power factor.
0.902
0.688
0.679
0.703
0.762
0.873
1.121
1.162
1.177
1.16
1.123
0.882
0.771
0.714
0.693
0.707
0.935
0.688
0.682
0.7
0.754
0.853
1.036
1.181
1.209
1.247
1.207
1.183
1.046
0.864
0.767
0.715
0.701
0.714
0.679
0.7
0.784
0.935
1.081
0
1.259
1.276
0
1.273
1.259
0
1.095
0.951
0.801
0.719
0.704
0.703
0.754
0.935
0
1.261
1.277
1.252
1.26
1.298
1.257
1.252
1.281
1.27
0
0.954
0.774
0.727
0.762
0.853
1.081
1.261
1.268
1.298
1.269
1.276
1.31
1.273
1.269
1.301
1.275
1.273
1.101
0.873
0.786
0.873
1.036
0
1.277
1.298
0
1.306
1.318
0
1.315
1.306
0
1.304
1.287
0
1.058
0.898
1.121
1.181
1.259
1.252
1.269
1.306
1.284
1.279
1.322
1.277
1.285
1.309
1.274
1.26
1.27
1.196
1.142
1.162
1.209
1.276
1.26
1.276
1.318
1.279
1.292
1.325
1.291
1.28
1.322
1.281
1.266
1.283
1.219
1.175
1.177
1.247
0
1.298
1.31
0
1.322
1.325
0
1.328
1.328
0
1.318
1.306
0
1.253
1.181
1.16
1.207
1.273
1.257
1.273
1.315
1.277
1.291
1.328
1.294
1.281
1.321
1.279
1.263
1.279
1.213
1.168
1.123
1.183
1.259
1.252
1.269
1.306
1.285
1.28
1.328
1.281
1.286
1.308
1.271
1.254
1.262
1.186
1.131
0.882
1.046
0
1.281
1.301
0
1.309
1.322
0
1.321
1.308
0
1.299
1.279
0
1.045
0.885
0.771
0.864
1.095
1.27
1.275
1.304
1.274
1.281
1.318
1.279
1.271
1.299
1.269
1.263
1.087
0.86
0.772
0.714
0.767
0.951
0
1.273
1.287
1.26
1.266
1.306
1.263
1.254
1.279
1.263
0
0.941
0.761
0.712
0.693
0.715
0.801
0.954
1.101
0
1.27
1.283
0
1.279
1.262
0
1.087
0.941
0.79
0.706
0.688
0.707
0.701
0.719
0.774
0.873
1.058
1.196
1.219
1.253
1.213
1.186
1.045
0.86
0.761
0.706
0.689
0.699
0.935
0.714
0.704
0.727
0.786
0.898
1.142
1.175
1.181
1.168
1.131
0.885
0.772
0.712
0.688
0.699
0.918
Figure 3.36 Assembly A411 middle of cycle (MOC) rod average power factor.
37
1.23
1.242
1.265
1.284
1.295
1.278
1.237
1.215
1.211
1.209
1.225
1.257
1.266
1.247
1.22
1.189
1.17
1.242
1.26
1.284
1.308
1.32
1.308
1.257
1.236
1.237
1.231
1.245
1.287
1.29
1.27
1.239
1.206
1.181
1.265
1.284
1.32
1.346
1.339
0
1.271
1.253
0
1.248
1.259
0
1.31
1.307
1.273
1.23
1.203
1.284
1.308
1.346
0
1.316
1.285
1.256
1.245
1.248
1.24
1.245
1.265
1.287
0
1.297
1.252
1.221
1.295
1.32
1.339
1.316
1.285
1.271
1.251
1.242
1.246
1.238
1.24
1.252
1.258
1.278
1.291
1.263
1.231
1.278
1.308
0
1.285
1.271
0
1.254
1.247
0
1.242
1.244
0
1.244
1.248
0
1.251
1.213
1.237
1.257
1.271
1.256
1.251
1.254
1.241
1.234
1.239
1.23
1.231
1.237
1.225
1.221
1.226
1.203
1.175
1.215
1.236
1.253
1.245
1.242
1.247
1.234
1.231
1.236
1.228
1.225
1.23
1.217
1.21
1.209
1.183
1.152
1.211
1.237
0
1.248
1.246
0
1.239
1.236
0
1.232
1.23
0
1.221
1.214
0
1.184
1.147
1.209
1.231
1.248
1.24
1.238
1.242
1.23
1.228
1.232
1.221
1.218
1.224
1.212
1.206
1.206
1.179
1.148
1.225
1.245
1.259
1.245
1.24
1.244
1.231
1.225
1.23
1.218
1.218
1.225
1.214
1.211
1.217
1.194
1.165
1.257
1.287
0
1.265
1.252
0
1.237
1.23
0
1.224
1.225
0
1.226
1.231
0
1.236
1.197
1.266
1.29
1.31
1.287
1.258
1.244
1.225
1.217
1.221
1.212
1.214
1.226
1.232
1.253
1.267
1.239
1.207
1.247
1.27
1.307
0
1.278
1.248
1.221
1.21
1.214
1.206
1.211
1.231
1.253
0
1.265
1.22
1.189
1.22
1.239
1.273
1.297
1.291
0
1.226
1.209
0
1.206
1.217
0
1.267
1.265
1.231
1.189
1.163
1.189
1.206
1.23
1.252
1.263
1.251
1.203
1.183
1.184
1.179
1.194
1.236
1.239
1.22
1.189
1.158
1.135
1.17
1.181
1.203
1.221
1.231
1.213
1.175
1.152
1.147
1.148
1.165
1.197
1.207
1.189
1.163
1.135
1.117
Figure 3.37 Assembly A411 end of cycle (EOC) rod average power factor.
38
4
METHODOLOGY
4.1 Research Goal
The primary goal of this research was to perform safety analyses on the MASLWR
prototypical cores for small light water reactor designs. The prototypical cores were
designed with a 5 year refueling cycle and have fuel enrichment of 4.25% and 8%. The
method used to model the subchannel from the four fuel assemblies in the 1/8th core and
the limiting fuel rods is outline in this chapter. Another goal of this research was to
demonstrate how the neutronic, thermal hydraulic and fuel performance codes interact
with one another as part of the safety analysis methodology.
The thermal hydraulic code chosen for the current research to calculate the subchannel
hydraulic conditions is VIPRE-01. The fuel performance chosen for the current research
to calculate the fuel rod thermal and mechanical performance is FRAPCON-3.
FRAPCON is a steady state fuel performance code used to calculate the integral rod
performance.
4.2 VIPRE-01 Overview
VIPRE Version 01 (Versatile Internals and Component Program for Reactors; EPRI) is
the code used for all the computational modeling of the prototypical cores during thermal
hydraulic analysis. VIPRE is designed to help evaluate safety limits of nuclear reactor
core in steady state, transients and assumed accident conditions [9]. These safety limits
include minimum departure from nucleate boiling ratio (MDNBR), fuel and clad
temperature, and coolant state. It can predict the three-dimensional velocity, pressure,
fuel rod temperatures for single and two-phase flow in PWR and BWR cores [12]. The
efficient and accurate used of VIPRE can be valuable in determining safety system set
points and in preparing licensing submittals. It‟s assumed that VIPRE can sufficiently
model the thermal hydraulics characteristics found in the MASLWR core.
39
The general capabilities and key features of VIPRE-01 are [9]:

Ability to run multiple cases with varying operating conditions for steady
state analyses.

Capable of iterating operate condition and radial power factor to a given
MDNBR.

Ability to model geometries other than reactor core.

Has expanded choice of correlations for Critical Heat Flux and two phase
flow and heat transfer.

Input options for one-pass hot channel analysis.

Ability to vary the inlet flow, enthalpy, system pressure, average power,
local pin power, and axial and radial shape of the power profiles during
transients.

Ability to apply nonuniform inlet flow and enthalpy transient forcing
functions.

Generalized rod conduction model for nuclear fuel rod, electric heater
rods, hollow tubes, and wall.

Flow reversal and recirculation computing capability.

Ability to model a few subchannels in the fuel bundle up to an entire
reactor core.
While VIPRE has a wide range of applicability, there are certain limitations to the code
due to its mathematical formulation and empirical models. In VIPRE, the conservation
equations assumed homogeneous equilibrium incompressible flow [12].
The limitations of VIPRE include [12]:

Homogeneous equilibrium formulation is not sufficient for cases with
large relative phase velocities, countercurrent flow, or condition where the
flow regime changes radically.

Not sufficient for conditions such as low-flow boil off, annular flow, and
phase separation involving sharp liquid/vapor interface.
40

In subchannel modeling method, the cross flow is assumed to exist only in
the gap connections that defines its flow path.

Correlations may have a narrow range of applicability.

Correlations are generally based on steady state data and are not verified
for transients.

Most correlations are derived from water data only.

The internal water properties functions are useful only in the enthalpy
range from 200 to 1500 Btu/lbm.

Cannot consider reflood or hot wall rewet problems.
To meet the safety requirement defined by 10CFR50 (Appendix A), the plant FSAR, and
core design analysis, an analyses must be performed to determine the limiting set points
and limiting conditions for operations [12]. The methodology of these analyses is applied
to the initial core designs. A thermal hydraulic code such as VIPRE is one of many
specialized analyses tool used in the methodology.
Like most other thermal hydraulic codes, the numerical solution for VIPRE-01 requires
solving finite-difference equations for mass, energy and momentum conservation for
interconnected array of channels assuming incompressible thermally expandable
homogeneous flow [10]. VIPRE was developed base on COBRA-IIIC to model
subchannel. According to the VIPRE manual Volume 1 [9], VIPRE uses an implicit
boundary value solution that repeatedly sweep the computation mesh, rather than a
marching solution that solves the flow field a step at a time solely on the basis of
upstream information. An improvement to VIPRE was made by adding the COBRA-WC
“RECIRC” scheme to allow reverse and recirculating flows.
4.3 FRAPCON-3 Overview
FRAPCON Version 3 is the computer code use to calculate steady state response of a
single fuel rod in light water reactor during long-term burnup. This is a NRC sponsor
code that was developed to accurately calculate the fuel rods performance of LWR up to
41
burnup of 65 GWD/MTU. A single channel coolant enthalpy rise model is use in this
code. The code iteratively calculates the interrelated effects of fuel and cladding
temperature, rod internal gas pressure, fuel and cladding deformation, release of fission
product gases, fuel swelling and densification, cladding thermal expansion and
irradiation-induced growth, cladding corrosion, and crud deposition as functions of fuel
rod specific power and coolant boundary conditions with time dependent [15]. Some of
the model updates including mixed oxide fuel properties can be found in FRAPCON
Volume 4 manual [17].
The general capabilities and features of FRAPCON Version 3 are [15]:

Generate initial conditions for FRAPTRAN for transient analysis.

Calculates steady-state fuel behavior of a single fuel rod at high burnup (up to 65
GWD/MTU).

Calculates all significant fuel rod variables, including fuel and cladding
temperatures, cladding hoop strain, cladding oxidation, fuel irradiation swelling,
fuel densification, fission gas release, and rod internal pressure as a function with
time.
The limitations of FRAPCON are [15]:

Steady state calculations only. Not capable of calculating fast transients (< 1
minutes).

No axial variation of fuel pellet dimensions.

Only cladding deformation of <5 % strains are meaningful.

The code‟s ability to predict cladding strains resulting from pellet-cladding
mechanical interaction is not expected to be accurate.

Limited assessment of mixed oxide fuel and fuel rods that contain gadolinia.

Cladding types are Zr-2 and Zr-4 only.

In reactor operating conditions only.

Burnup up to 65 GWD/MTU.
Aside from the limitations discussed above, it‟s assumed for this investigation that the
fuel performance code FRAPCON can adequately model the MASLWR limiting fuel
42
rods with fuel enrichment of 4.25 % and 8 %. A simplified flowchart of FRAPCON-3
solution scheme is illustrated in Figure 4.1. FRAPCON is linked to the MATPRO
material properties package and FRACAS-I mechanic model. The solution for each time
step consists of: calculating the fuel and cladding temperature, calculating the fuel and
cladding deformation, and calculating the fission product generation and internal gas
pressure [15].
Figure 4.1 Simplified FRAPCON-3 Flow Chart [15].
4.4 Codes Interaction
One of the goals of this research is to develop a safety analysis methodology to
demonstrate how the neutronic, thermal hydraulic, and fuel performance codes interact
with one another to support new core designs. A diagram of how the codes interact with
one another is illustrated in Figure 4.2 below. The power factor/power histories
calculated from the neutronic codes are used as input for both the thermal hydraulic and
fuel performance codes. The VIPRE thermal hydraulic code output the local hydraulic
conditions which include boundary conditions that can be used as input in the FRAPCON
43
fuel performance code. The fuel performance code output the thermal and mechanical
behavior of the fuel rod.
Power Factor/Power
Histories Data
(From neutronic codes,
CASMO-SIMULATE-3)
Fuel Rod Geometry/
Compositions
VIPRE-01
(Thermal Hydraulic Codes)
DNBR/CHFR
Heat Transfer Coefficient,
Coolant Temperatures
and/or Cladding Surface
Temperatures Profiles
Fuel Temperature
Profiles
Pressure Drop, Velocity,
Void Fraction, Heat Flux
FRAPCON-3/FRAPTRAN
(Fuel Performance Codes)
Cladding Oxidation
and Ballooning
Dimensional Change
and Deformation in
Cladding/Fuel
Fission Gas
Release
Fuel/Cladding
Temperatures
Fuel
Swelling/Densification
Figure 4.2 Codes interaction diagram.
44
4.5 Initial Data-- Prototypical Cores Geometry and Operating Parameters
The geometry of the problem for this research taken from [1, 4, 10] is given in Table 4.1
and Table 4.2. While many of the MASLWR design characteristics are not fixed, the
current research uses the design parameters and operational conditions given in Table 4.1,
Table 4.2, and Table 4.4 below. The core contains 24 assemblies of standard PWR
17x17 designs. Each fuel assembly contains 264 fuel rods and 25 guide tubes. The fuel
rod is 197.104 cm long and contains an active fuel length of 160 cm. The length of the
fuel rod for this research is about one half of the length of those in current typical PWR
reactors. The fuel rod geometry is given in Table 4.2 [1, 10].
Core Geometry
Number of Fuel Assemblies (17x17 array)
Number of Fuel Rods per Assembly
Number of Control Rod Thimbles per
Assembly
Active Fuel Length
Spacer Grid Loss Coefficient
Number of Spacer Grids (Assumptions)
Spacer Grid Locations (Assumptions)
Input for VIPRE01
24
264
25
62.99 in (160 cm)
0.86
5 (Bot(1), Mid(3), Top(1))
3.15 in, 18.90 in, 34.65 in, 50.39 in,
66.14 in
Grid spacing (Assumptions)
15.75 in
Table 4.1 Geometry input for VIPRE-01.
Fuel Rod Geometry
Input for VIPRE01
Fuel Rod Diameter
0.950 cm
0.374 in
Fuel Pellet Diameter
0.819 cm
0.322 in
Pin Pitch
1.260 cm
0.496 in
Clad Thickness
0.057 cm
0.0224 in
Control Rod Thimble Diameter
1.224 cm
0.482 in
Assembly Pitch (nominal)
21.504 cm
8.466 in
Uniform Gap Conductance
5.678 kW/ -⁰C
1000 Btu/hrTable 4.2 Fuel rod geometry input for VIPRE-01.
⁰F
It‟s assumed for this research that there are five spacer grids to model the hydraulic loss
associated with the spacer grids. The spacer grids are used to hold the fuel rods together
in the fuel assembly. The spacer grids can be used to model the irrecoverable axial
45
pressure loss that occurs in a channel. The types of loss include flow through the grids
and orifices. The local pressure loss is given by [10]:
Where G is the upstream mass flux and
is the loss coefficient.
The total axial length and number of axial nodes for the VIPRE model is illustrated in
Table 4.3 below. The axial length is divided into the number of axial zones. The location
of the spacer grids selected and the axial zone numbers for the fuel rod is illustrated in
Figure 4.3 below. A total of 22 axial zones were selected for the VIPRE model in this
research. Zones 1 and 22 modeled the top and bottom reflector. Zones 2 to 21 modeled
the active fuel length of 160 cm. Each zone is 8 cm long. The grids are space 15.75 in (40
cm) from each other with three in the middle and one at the top and bottom of the fuel
assembly. Current typical PWR fuel assembly contains 8 spacer grids with a grid spacing
of 16.6 inches and a spacer grid loss coefficient of 0.86. It‟s assumed that five spacer
grids are sufficient for this research since the fuel rods design are significantly shorter
(about one-half in length) than current typical PWR fuel rods. The spacer grid loss
coefficient used for this research is a constant 0.86, same as those used to model typical
PWR core. A sensitivity study of the effect of the spacer grid locations was performed
and discussed in the next chapter.
46
Axial Node Z (cm) Level Z (in) Level
Numbers
23
176
69.291
Reflector
22
168
66.142
21
160
62.992
20
152
59.843
19
144
56.693
18
136
53.543
17
128
50.394
16
120
47.244
15
112
44.094
14
104
40.945
Active Fuel
13
96
37.795
Length
12
88
34.646
11
80
31.496
10
72
28.346
9
64
25.197
8
56
22.047
7
48
18.898
6
40
15.748
5
32
12.598
4
24
9.449
3
16
6.299
2
8
3.150
1
0
0.000
Reflector
Table 4.3 Total axial length and number of axial nodes model in VIPRE.
Figure 4.3 Axial zone locations.
47
The operating conditions for the prototypical cores are given in Table 4.4 below. The
core is modeled to have a uniform inlet temperature of 491.8 K and uniform core flow of
424 kg/s. The system exit pressure for the core is 1247.3 psia. The average core power
input expressed in MBtu/hrexpressed in Mlbm/hr-
is calculated to be 0.15717. The average mass flux input
is calculated to be 0.52976.
Operating Conditions
Input for VIPRE01
Inlet Temperature
491.8 K
425.57 ⁰F
Exit Pressure
8.6 MPa
1247.3 psia
Average Mass Flux
718.47 kg/sec0.52976 Mlbm/hrAverage Heat Flux
495.79 kW/
0.15717 MBtu/hrCore Power
150 MWt
Core Flow
424 kg/s
Table 4.4 Operating conditions for VIPRE-01 input [1,4].
4.6 Description of the VIPRE Models
Since all the prototypical cores in this research are symmetric, only one-eighth section of
the prototypical core is modeled. Since all the prototypical cores contained 24 fuel
assemblies, the one-eighth section of the core contained two half fuel assemblies and two
full fuel assemblies. Figure 4.4 below illustrated the 1/8th section of the core and the
assemblies being modeled by VIPRE. The name of the fuel assemblies being modeled are
A411, A412, A413, and A512. A VIPRE model was developed separately for each of the
assemblies in the one-eighth section of the prototypical core to determine the hot channel
and hot rod. Two of the fuel assemblies are being modeled as half assemblies (A411 and
A512) and the other two are modeled as full assemblies (A412 and A413). A VIPRE
input deck was created for each of these assemblies. The VIPRE model for each of the
assemblies is discussed in the sections below.
48
A101
A111
A202
A201
A211
A212
A303
A302
A301
A311
A312
A313
A403
A402
A401
A411
A412
A413
A502
A501
A511
A512
A601
A611
Figure 4.4 Assemblies being modeled by VIPRE.
4.6.1
One-eighth Prototypical Core A411, A412, A413, and A512 VIPRE Models
In this research, assembly A411 and A512 are modeled by VIPRE as half fuel assembly
and assembly A412 and A413 are modeled by VIPRE as full fuel assembly in the 1/8th
core. All the channels and rods in the half and full fuel assembly are modeled. The
channels and rods layout and numbering scheme selected for the half fuel assembly is
illustrated in Figure 4.5 below. The channels and rods layout and numbering scheme
selected for the full fuel assembly is illustrated in Figure 4.6 below. The flow areas,
wetted perimeters, heated perimeters, and width of gap connections for the channels are
shown in Table 4.5 below. The geometry data used to calculate the flow areas, wetted
perimeters, heated perimeters and width of gap connections is given in Table 4.2 above.
In a half fuel assembly, a total of 171 channels and 153 rods are modeled as illustrated in
Figure 4.5. In a full fuel assembly, a total of 324 channels and 289 rods are modeled as
illustrated in Figure 4.6. Figure 4.5 and Figure 4.6 also give information on the
connection between channels. The areas of the channels are not all the same. The channel
area is simply a cross-sectional area of a given region. The flow area between fuel rods in
a rectangular or triangular array is defined as a subchannel as shown in Figure 4.16.
49
Figure 4.5 Channels and rods layout for the half fuel assembly models.
19
1
1
2
3
19
21
3
4
22
6
7
23
25
7
8
9
10
28
11
46
27
10
29
11
12
31
13
13
14
32
15
33
51
33
16
35
17
36
67
71
51
54
72
105
124
107
118
125
102
108
135
126
151
136
144
194
230
212
298
281
249
300
283
266
318
284
267
251
319
301
285
268
284
317
283
282
265
248
299
266
250
316
282
265
263
234
315
281
280
264
247
217
297
264
248
233
229
200
152
185
168
178
160
161
143
119
211
183
279
262
246
216
314
280
302
320
184
286
150
167
201
218
235
252
269
177
213
159
231
249
303 321
195
267
285
134
142
193
166
228
199
296
247
232
313
279
263
261
245
215
210
278
231
227
295
262
246
230
214
198
182
245
260
244
226
209
192
176
158
133
141
117
101
85
90
123
106
89
140
116
100
84
68
122
149
213
197
181
165
175
157
132
115
99
83
88
70
53
34
104
87
139
121
208
191
174
311
278
261
277
229
243
225
196
180
164
148
131
310
276
293
275
259
242
212
207
190
173
259
244
227
228
224
195
179
163
147
156
138
114
98
82
66
50
103
86
69
120
97
81
65
49
52
34
17
48
32
85
64
68
50
31
15
16
47
102
155
130
113
309
275
292
274
242
257
241
211
194
206
189
172
210
223
178
162
146
129
137
96
80
154
136
112
119
101
84
63
67
49
30
14
66
118
95
79
62
46
29
100
291
258
256
225
308
274
273
241
239
193
205
188
171
145
128
221
177
161
153
135
111
203
208
257
255
224
238
220
191
176
160
144
237
207
290
272
240
209
260
277
226
243
175
192
204
276
222
240
258
294 312
186
187
170
152
127
117
94
78
83
65
45
48
30
82
134
110
202
254
223
219
190
174
159
169
143
126
116
93
77
61
109
99
81
64
47
76
60
44
28
12
63
43
26
80
59
151
133
92
168
236
206
201
185
158
142
125
218
189
173
184
167
150
132
108
183
157
141
124
115
98
149
131
114
97
75
58
42
45
27
79
62
44
25
9
61
140
200
172
156
166
123
107
91
74
165
148
130
90
96
78
57
41
24
73
155
139
122
106
113
95
77
60
112
182
138
147
129
105
89
164
146
121
111
94
72
56
40
43
26
8
18
42
24
6
59
39
22
76
128
104
88
71
55
110
87
93
75
58
38
41
23
70
54
163
181
199
235
127
145
217
253
289
307
271
103
120
137
154
205
222
239
273
171
188
256
109
86
92
74
57
40
69
53
37
21
5
56
39
91
73
52
36
20
4
5
35
38
20
2
55
37
18
196
169
179
202
186
197
203
215
219
232
214
220
233
253
236
250
268
269
287
304
271
254
237
251
270
286
287
322
288
305
323
153
221
238
255
289
170
187
204
272
162
198
180
216
234
252
270
288
306 324
Figure 4.6 Channels and rods layout for the full fuel assembly models.
50
When all the channels and rods in the A411 or A512 half assembly of the 1/8th section
core are being modeled, they will be referred to as the A411 VIPRE model or A512
VIPRE model in this research. The channels and rods layout and numbering scheme for
the A411 VIPRE model and A512 VIPRE model is illustrated in Figure 4.7 and Figure
4.9 below. The axial channels layout is illustrated in Figure 4.8 and Figure 4.10
respectively. The channel and rod layout selected for the A411 VIPRE model and A512
VIPRE model contain 174 channels and 156 rods. The channels can range in size from
single subchannels to several bundles. The layout for channel 1-171 and rod 1-153 is
given in Figure 4.5 above. The last three channels (channel number 172, 173, and 174)
are modeled as either a half or full bundle (one assembly). The subchannels in an
assembly are lumped together to form a full bundle. For the A411 VIPRE model, channel
172 and channel 174 modeled a full bundle and channel 173 modeled a half bundle as
shown in Figure 4.7. For the A512 VIPRE model, channel 173 and channel 174 modeled
a full bundle and channel 172 modeled a half bundle as shown in Figure 4.9. The
geometry input for all 174 channels in the A411 VIPRE model and A512 VIPRE model
can be found in Table 4.5 and Table 4.6 below.
Figure 4.7 Channels and rods layout for A411 VIPRE model.
51
Channel
1-171
Channel
172
Channel
173
Channel
174
0.500 in
Figure 4.8 Axial channels layout for A411 VIPRE model.
Figure 4.9 Channels and rods layout for A512 VIPRE model.
52
Channel
172
Channel
173
Channel
1-171
Channel
174
0.500 in
Figure 4.10 Axial channels layout for A512 VIPRE model.
When all the channels and rods in the A412 or A413 full assembly of the 1/8th section
core are being modeled, they will be referred to as the A412 VIPRE model or A413
VIPRE model in this research. The channels and rods layout and numbering scheme for
the A412 VIPRE model and A413 VIPRE model is illustrated in Figure 4.11 and Figure
4.13 below. The axial channels layout is illustrated in Figure 4.12 and Figure 4.14
respectively. The channel and rod layout selected for the A412 VIPRE model and A413
VIPRE model contain 327 channels and 292 rods. The layout for channel 1-324 and rod
1-289 is illustrated in Figure 4.6 above. The last three channels (channel number 325,
326, and 327) are modeled as either a half or full bundle (one assembly). For the A412
VIPRE model, channel 325 and channel 326 modeled a half bundle and channel 327
modeled a full bundle as shown in Figure 4.11. For the A413 VIPRE model, channel 325
and channel 327 modeled a half bundle and channel 326 modeled a full bundle as shown
in Figure 4.13. The geometry input for the 327 channels in the A412 VIPRE model and
A413 VIPRE model can be found in Table 4.5 and Table 4.6 below.
53
Figure 4.11 Channels and rods layout for A412 VIPRE model.
Channel
325
Channel
1-324
Channel
326
Channel
327
0.500 in
Figure 4.12 Axial channels layout for A412 VIPRE model.
54
Figure 4.13 Channels and rods layout for A413 VIPRE model.
Channel
325
Channel
326
Channel
327
Channel
1-324
0.500 in
Figure 4.14 Axial channels layout for A413 VIPRE model.
55
A flow channel that can communicate laterally through gaps by diversion flow is
uniquely identified by number, cross-sectional area, wetted perimeter and heated
perimeter [12]. Table 4.5 listed the different size channels cross-sectional areas, wetted
perimeters, and heated perimeters and Table 4.6 list the width of gap connections to be
used as channel geometry input for the VIPRE models. The sum of the perimeters of all
solid heated surfaces facing the channel is also known as the heated perimeter. The sum
of the perimeters of all solid heated and unheated surfaces facing the channel is also
known as wetted perimeter.
Subchannel Descriptions
Standard full (1) subchannel
Thimble full (1) subchannel
Standard half (1/2) subchannel
Thimble half (1/2) subchannel
Standard half (1/2) side
subchannel
Standard quarter (1/4) corner
subchannel
Standard octant (1/8) corner
subchannel
Full (1) bundle lumped channel
Half (1/2) bundle lumped
channel
Cross-Sectional
Area ( )
0.1362
0.1181
0.0681
0.0590
0.0763
Wetted
Perimeter (in)
1.1750
1.2597
0.5875
0.6299
0.5875
Heated
Perimeter (in)
0.1221
0.0681
0.5875
0.4406
0.5875
0.0425
0.2937
0.2937
0.0213
0.1469
0.1469
38.113
19.0567
348.0358
174.0179
310.1883
155.0942
Table 4.5 Channel geometry calculations.
Descriptions
Gap Width (in)
Rod to rod
0.1221
Rod to control rod (thimble)
0.0681
Rod to side
0.07757
Bundle to bundle
2.1081
Table 4.6 Channel geometry calculations for gap width.
56
The rods in this research are modeled as either nuclear fuel rods or dumy rods. Heat
conduction in nuclear fuel rods is simulated in VIPRE. The thimbles (guide tubes) are
modeled as dumy rods and do not use the conduction model. For the A411 VIPRE model,
rods 1-153 are modeled as either half or full fuel pin as shown on the layout in Figure 4.5.
Rods 154 and 156 each model a full fuel bundle contained in channels 172 and 174. Rod
155 models half of a fuel bundle contained in channel 173. For the A512 VIPRE model,
rods 1-153 are also modeled as either half or full fuel pin as shown on the layout in
Figure 4.5. Rods 155 and 156 each model a full fuel bundle contained in channels 173
and 174. Rod 154 models half of a fuel bundle contained in channel 172. For the A412
VIPRE model, rods 1-289 are modeled as full fuel pin as shown on the layout in Figure
4.6. Rods 290 and 291 each model half of a fuel bundle contained in channels 325 and
326. Rod 292 models a full fuel bundle contained in channel 327. For the A413 VIPRE
model, rods 1-289 are also modeled as full fuel pin as shown on the layout in Figure 4.6.
Rods 290 and 292 each model half of a fuel bundle contained in channels 325 and 327.
Rod 291 models a full fuel bundle contained in channel 326. Each rod is given a radial
power factor. The radial power factor given is an average of the radial power factors of
the fuel pins it represents. The average radial power factors for the fuel pins and fuel
assemblies for each of the prototypical cores in this research can be found in Chapter 3.
The input requirements for the VIPRE model for the fuel rod consist of axial power
profiles, rod to channel heat transfer connection, and rod geometry type data. The axial
power profiles for BOC, MOC and EOC for the prototypical cores are given in Table 4.7,
Table 4.8 and Table 4.9 below. A quick example of the rod to channel heat transfer
connection for A411 VIPRE model is illustrated in Table 4.10 below. A more detailed
discussion how this was done can be found in Volume 2 [10] of the VIPRE manual. The
rod geometry type data is given in Table 4.2 above.
Zone Number
1 (bottom)
2
3
4
5
M_4-25A
0
0.4862
0.78663
1.01562
1.19226
BOC (P/Po)
M_4-25B M_8A
0
0
1.34466 0.50431
1.89207 0.77092
1.84779 0.98057
1.61374 1.14584
M_8B
0
0.87751
1.23356
1.32583
1.30537
M_8C
0
0.67314
0.93389
1.01507
1.02066
57
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22 (top)
1.31775
1.44988 1.26758 1.29662
1.39559
1.30652 1.34851 1.27672
1.43125
1.17824 1.39256 1.24612
1.43103
1.06499 1.40438 1.20723
1.40153
0.96631 1.38866 1.16209
1.34892
0.88141 1.34991 1.11242
1.27881
0.80941 1.29222 1.05964
1.19683
0.74949 1.21907 1.00487
1.1074
0.70095 1.13337 0.94897
1.01074
0.66317 1.0375 0.89257
0.90737
0.63572 0.93381 0.83607
0.79635
0.61831 0.82272 0.77977
0.67762
0.61271 0.70379 0.72502
0.55017
0.63646 0.57661 0.68517
0.41322
0.6076 0.44056 0.60349
0.25472
0.42057 0.28711 0.42098
0
0
0
0
Table 4.7 BOC axial power profiles.
Zone Number
MOC (P/Po)
M_4-25A M_4-25B M_8A
M_8B
0
0
0
0
0.62728
0.54765 0.61419 0.53986
0.87212
0.76679 0.85585 0.75662
0.9843
0.88428 0.99031 0.89107
1.03323
0.9529 1.06388 0.98146
1.05115
0.99189 1.1006 1.04147
1.05576
1.01598 1.11654 1.08218
1.05649
1.03416 1.12179 1.11141
1.05799
1.05151 1.12233 1.13408
1.06225
1.07066 1.1214 1.15277
1.06976
1.0925 1.12046 1.16826
1.0802
1.11667 1.11964 1.17984
1.09245
1.1416 1.11812 1.18559
1.10471
1.16448 1.1141 1.18262
1.11411
1.18106 1.10469 1.16724
1.11625
1.1852 1.08557 1.13526
1.10421
1.16853 1.05067 1.08239
1.06759
1.12001 0.99164
1.005
0.99136
1.02586 0.89757 0.90271
0.85396
0.87256 0.75471 0.76013
0.60482
0.61571 0.53595 0.54003
0
0
0
0
Table 4.8 MOC axial power profiles.
1 (bottom)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22 (top)
1.03737
1.05004
1.05439
1.05533
1.05348
1.05061
1.04883
1.04727
1.04962
1.05226
1.05242
1.0555
1.0416
1.03943
0.95952
0.70956
0
M_8C
0
0.65052
0.84055
0.91927
0.94505
0.9802
1.01096
1.03193
1.0469
1.0586
1.06974
1.08427
1.0948
1.1049
1.114
1.12301
1.15025
1.11574
1.05316
0.9238
0.68236
0
58
Zone Number
1 (bottom)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22 (top)
Rod Index
EOC (P/Po)
M_4-25A M_4-25B M_8A
M_8B
0
0
0
0
0.71638
0.70895 0.71539 0.69181
0.90949
0.90192 0.92886 0.90046
0.98095
0.97836 1.0122 0.99009
1.00627
1.00859 1.03819 1.02558
1.01435
1.01873 1.03958 1.0341
1.01746
1.02152 1.03276 1.03173
1.02036
1.02299 1.02555 1.02719
1.02456
1.02546 1.02132 1.02473
1.03025
1.02975 1.02127 1.02626
1.03727
1.03606 1.02564 1.03243
1.04549
1.04446 1.03415 1.04314
1.05489
1.05489 1.04624 1.05772
1.06531
1.06701 1.06093 1.07479
1.07616
1.07977 1.07647
1.092
1.08587
1.09102 1.08964 1.10534
1.09083
1.09623 1.09467 1.10819
1.08328
1.08663 1.08154 1.08982
1.04795
1.04669 1.0335 1.0337
0.95506
0.94891 0.92331 0.91766
0.73782
0.73205 0.6988 0.69325
0
0
0
0
Table 4.9 EOC axial power profiles.
1
Number of
rods modeled
by rod N
0.5
2
1.0
3
0.5
4
1.0
Channel(s)
seen by rod
N
1
2
3
2
3
4
5
3
5
6
4
5
7
8
M_8C
0
0.74616
0.97848
1.09233
1.15445
1.18218
1.19135
1.18872
1.17901
1.16417
1.14448
1.11967
1.09068
1.05643
1.01603
0.96838
0.91231
0.85246
0.7788
0.67642
0.50749
0
Fraction of rod N
seen by channel I
0.125
0.250
0.125
0.250
0.250
0.250
0.250
0.125
0.250
0.125
0.250
0.250
0.250
0.250
59
.
.
.
153
.
.
.
0.5
.
.
.
.
.
.
153
0.125
170
0.250
171
0.125
154
264.0
172
264.0
155
132.0
173
132.0
156
264.0
174
264.0
Table 4.10 Rod layout summary for A411 VIPRE model.
The power generation in the coolant is 1.95% (FCOOL=1.95). This value is reasonable
for PWR core. A constant gap conductance of 1000 Btu/hr-
⁰F was selected for nuclear
fuel rod geometries for this research. The gap conductance value is considered to be
appropriate for this study. The gap conductance selection only affects the fuel rod
temperatures. A gap conductance sensitivity study was performed and discussed in the
next chapter. The calculated gap conductance as a function of cold diametral gap in a
typical LWR fuel rod can found in Figure 8-22 of Todreas et al [24].
4.7 Physical Models and Correlations Input
The different parameters and correlations used in VIPRE to model two-phase flow effects
and the heat exchange between the rod walls and the coolant are given in Table 4.11. The
effects of two-phase flow on friction pressure losses, subcooled boiling, and the
relationship between the flowing quality and the void fraction is being model by these
correlations in flow solution. There are many combinations of correlations available for
modeling two-phase effects and heat transfer. The validation work for these correlations
is documented in Volume 4 [11] of the VIPRE manual. A detailed discussion of the two
phase flow correlations is available in Volume 1 [9] of the VIPRE manual.
There are three major categories for the two-phase flow correlations. These categories
are: two-phase friction multipliers, subcooled void correlations, and bulk void relations.
The two-phase friction multipliers are used to model the effect of two-phase flow on the
friction pressure drop. The subcooled void correlations are used model the
60
nonequilibrium transition from single-phase to boiling flow with heat transfer from a hot
wall [10]. The bulk void correlations are used to predict the subcooled void. In VIPRE,
the default model for the two-phase friction multipliers is the EPRI correlation. The EPRI
void model is the default model for subcooled void fractions and bulk void fractions.
After looking through the VIPRE validation work reported in Volume 4 [11] and the
detailed discussion of the two-phase correlations reported in Volume 1 [9], the VIPRE
defaults for two-phase flow was determined to be suitable correlation selection for this
research. Therefore, the default EPRI models were selected as the two-phase flow
correlations for this particular investigation as shown in Table 4.11 below. The hot wall
friction correction is optional in VIPRE and is neglected for this investigation.
For the heat transfer coefficient correlations, the VIPRE default correlations were
selected for single phase convection regime and nucleate boiling regime. The conditions
are not expected to exceed the CHF point for the current research so the code can be
restrict to only consider single phase convection regime and nucleate boiling regime for
heat transfer calculations. The default Dittus-Boelter correlation was selected as the heat
transfer coefficient correlation for single-phase convection regime. There are several
correlations available in the nucleate boiling regime. The default correlation selected for
both the subcooled and saturated region was the Thom plus single-phase (THSP)
correlation. Using the Thom plus single-phase correlation for both subcooled and
saturated region allow it to avoid the discontinuous transition that can occurred between
separate subcooled nucleate boiling and saturated nucleate boiling. A schematic of the
boiling curve is given in Figure 4.15 below. The ranges of the data for surface heat
transfer coefficient correlations are given in Table 4.12 below. The mass velocity ranges
in the THOM correlation is higher than the mass velocity of the MASLWR reactor. The
MASLWR operating pressure falls within the range of only the THOM and the JensLottes correlations.
The correlation selected to determine the peak of the boiling curve is the EPRI-1 CHF
correlation. This correlation was selected because it has a wide range of PWR operating
61
conditions and has been shown to be reasonably accurate. The EPRI-1 correlation is the
default correlation in VIPRE.
There are many critical heat flux correlations available for DNB analysis. The correlation
selected for calculating the critical heat flux (CHF) is the EPRI-1 correlation. The EPRI-1
CHF correlation was found to give the minimum DNBR value when compare with other
CHF correlations and therefore was selected for this research. This was discussed in the
next chapter. The data ranges of critical heat flux correlations can be found in Table 2.3
in Chapter 2 of this research. A comparison of the data ranges with the MASLWR
operating condition is given in Table 2.4.
Parameter/ Correlation
Subcooled Void Fraction
Bulk Void/Quality Fraction
Two-Phase Friction Multiplier
Hot Wall Friction Correction
Single Phase Forced Convection Correlation
Subcooled Nucleate Boiling Correlation
Saturated Nucleate Boiling Correlation
Input for VIPRE01
EPRI void model
EPRI (for Zuber-Findlay drift flux
equation with coefficients developed
for EPRI void model)
EPRI (for Columbia/EPRI correlation)
NONE (no hot wall correction)
EPRI (for Dittus-Boelter correlation)
THSP (for Thom plus the single-phase
correlation)
THSP (for Thom plus the single-phase
correlation)
EPRI-1 Correlation
CHF Correlation to Define Peak of Boiling
Curve
CHF Correlation for DNB Analysis
EPRI-1 Correlation
Table 4.11 Two-phase flow and heat transfer correlations.
Figure 4.15 Boiling curve schematic [10].
62
Correlation
Pressure
(psia)
Mass Velocity
(Mlbm/hrft^2)
Heat Flux
(MBtu/hfft^2)
Quality
Subcooled Boiling:
Thom
750 – 2000
0.77 – 2.80
Up to 0.500
Not Reported
Jens-Lottes
100 – 2500
0.008 – 7.74
Up to 0.400
Not Reported
Saturated Boiling:
Schrock42 – 505
0.176 – 3.20
0.06 – 1.45
0.0 – 0.57
Grossman
Wright
15.8 – 68.2
0.396 – 2.52
0.014 – 0.088
0.0 – 0.19
Chen
8 – 505
0.044 – 3.28
0.002 – 0.76
0.0 – 0.7
Table 4.12 Data ranges of surface heat transfer coefficient correlations [10].
The turbulent mixing group is optional in VIPRE and was not selected to be used in this
investigation. A sensitivity study of the effect of turbulent mixing is discussed in the next
chapter. Turbulent mixing is model as a fluctuating crossflow computed as a fraction of
the axial flow [11]. The turbulent mixing describes the exchange of energy and
momentum between adjacent channels. It is an attempt to account empirically for the
effect of turbulent mixing [10]. The contribution of turbulent mixing can be neglected in
many cases.
4.8 Convergence Criteria
The convergence criteria used for the problem modeled in VIPRE is given below in Table
4.13. The convergence limits used are the same as the default values in VIPRE. There are
three choices for solution scheme in VIPRE. The three choices are: iterative solution,
direct solution, and RECIRC solution. The three solution methods have different
numerical methods but solve the same energy, momentum and continuity equations. The
direct and iterative solutions are used to solve problems with positive flow only and
cannot calculate flow reversals. The RECIRC solution was designed to solve problems
with low velocity buoyancy-dominanted flow conditions. A detailed discussion of the
three solution methods is reported in Volume 1 [9] of the VIPRE manual. Both the direct
and iterative solutions have great difficulties solving these types of problems. The direct
solution and the iterative solution methods did not yield convergence for many of the
VIPRE models. Therefore, the RECIRC solution method was used in the calculations for
63
the A411, A412, A413, and A512 VIPRE models. It‟s assumed that the convergence
limits for the problem in this research gives acceptable results.
Convergence Criteria
Input for VIPRE01
Maximum no. of External Iterations
200
Maximum no. of Internal Iterations
NA
Crossflow convergence limit (External)
0.1
Axial flow convergence limit
0.001
rod temperature convergence limit
0.05
heat transfer convergence limit
0.01
damping factor, sp term
0.9
damping factor, axial flow
0.9
Rod temperature convergence limit
0.05
Heat transfer convergence limit
0.01
Numerical solution method
RECIRC
Table 4.13 Convergence Criteria for all VIPRE models
4.9 Descriptions of the FRAPCON Model
A FRAPCON model was developed for the limiting rod identified from the neutronic and
thermal hydraulic analyses for each of the five prototypical cores. The limiting rods were
identified by their power history and boundary conditions. The cladding type selected for
the FRAPCON model in this research is Zircaloy-4. Many current PWR fuel rods used
Zircaloy-4 as the cladding type. The fuel rod geometry, materials and models used for
the FRAPCON model are given in Table 4.2 and Table 4.14. Many of these values are
default in FRAPCON and are considered to be appropriate for this research. One of the
primary goals of this research is to investigate the feasibility MASLWR core and the
MASLWR fuel for a five years operation without refueling and with maximum fuel
enrichment of 8 %. The fill gas pressure of 345 psi is considered appropriate for this
research. This value and other fuel rod fabrication information were selected from an
example input deck in Volume 2 [15] of the FRAPCON manual. A more detailed
MASLWR fuel design would provide better results and reduce some of the uncertainties
in this research.
64
Initial Data
Input for FRAPCON
Fuel pellet type
Cladding type
Zircaloy-4
Type of plant
PWR
Cladding cold work
0.2
Cladding texture factor
0.05
Fuel pellet density
96 % of theoretical density (10.97 g/cc)
Plenum length
6.8 in
Active Fuel Length
62.99 in
Open porosity
5%
Fuel U-235 Enrichment
4.25 % or 8 %
Oxygen to Metal (O/M) ratio
2.0
Fill gas
Helium
Fill gas pressure
345 psi
fission gas atoms per 100 fissions
31.0
Pellet sintering temperature
2911 ⁰F
Fuel rod pitch
0.496 in
Crud model
Constant thickness
Fission gas release model
Massih/Folsberg Correlation
Cladding waterside corrosion model Modified-1987 EPRI/ESCORE oxidation model
Table 4.14 Initial geometry and materials for FRAPCON models.
4.10 DNB Analysis Method
In DNB analysis, the predicted critical heat flux is compared with the specific local heat
flux to determine if the flow solution is departed from reality [10]. In evaluating the
thermal margin and operating limits in thermal hydraulic analysis of a PWR core, the
DNB ratio has become a major parameter. The MDNBR in the hot channel must not fall
below a certain value (usually on the order of 1.2 to 1.3) under normal operation [12].
The Departure from Nucleate Boiling Ratio (DNBR) is calculated by the equation below.
4.11 Subchannel Analysis and Hot Channel Determination
The flow area between fuel rods in a rectangular or triangular array is known as a
subchannel. Subchannel modeling is a powerful tool for predicting the detailed flow
65
configuration in very complex geometries [12]. The hydraulic character of each
subchannel for various models and correlations is determined primarily by the hydraulic
diameter and the flow area. The flow channel of a rectangular array is shown below in
Figure 4.16.
Figure 4.16 Flow channel of a rectangular and triangular array [12].
One of the objectives of this research is to model the hot subchannel in detail. This
required the determination of where the hot assembly and hot subchannel are located at.
The hot channel in PWR can be defined as the subchannel with the most limiting DNBR
on one of its surrounding rods [12]. It depends on the most adverse combination of rod
heat flux, flow, and subchannel enthalpy rise [12]. There are four factors that are of
primary importance in determining the hot assembly and hot subchannel based on the
information available from the neutronics codes.
These four factors are [12]:
 Assembly radial power
 Peak one-pin radial power factor
 Subchannel radial factor
 Assembly inlet flow
66
The hot assembly is considered to be the one with the highest power factor and minimum
flow. The hot subchannel is likely to be in the same assembly. This research modeled the
hydraulic characteristics for all the channels of the 1/8th core to determine the hot
subchannels and the limiting rods.
4.12 LWR Fuel Behavior and Modeling
The fuel behavior modeling plays a very important role in licensing new reactor. Fuel
rod behavior is determined by complex thermal, mechanical, physical and chemical
processes depending on design and operational parameters, material selection, loading
conditions, burnup etc [20]. Reliable predictions of fuel behavior in computer codes are
important in achieving improve fuel design and economics of the nuclear fuel cycle.
Fuel performance code such as FRAPCON used the correlations from the material
properties (MATPRO) library [45] to model the fuel behavior. MATPRO is a
compilation of fuel and cladding material property correlations. It has been used
extensively in many fuel performance and severe accident code. The integral assessment
of the steady state fuel behavior code FRAPCON-3 is discussed in [16]. The properties
and model updated for high burnup in FRAPCON can be found in [15].
This research modeled the limiting fuel rods in the five prototypical cores with
MASLWR operating conditions to understand the effect of low and high enrichment fuel
behavior with and without burnable poison cores. Fission gas release and corrosion play a
crucial role in the behavior and integrity of nuclear fuel rod. Any fuel rod that operates at
a high enough power and fuel temperature will release fission gas into the gap between
the fuel and cladding. The gas release into the gap increases the fuel rod internal
pressure. In helium filled rods, the gap conductance is reduced considerably due to
fission gas. This would cause an increased fuel temperature and affects the corrosion rate
on the clad. Water corrosion and hydrizing impair the thermal conductivity and
mechanical properties of the zircaloy based cladding. The issue of water chemistry is of
particular importance in protecting the cladding from corrosion and extended its lifetime.
67
An overview of fission gas release and clad oxidation and water chemistry are presented
below.
4.12.1 Fission Gas Release in Fuel Rod
During reactor operation, fission gas is generated within the fuel. The amount of fission
gas release is dependent on the burnup. The dominant parameter that controlled fission
gas release is temperature. The concern of fission gas release is the pressure within the
fuel rod. High quantity of fission gas release can cause high pressure in the fuel rod that
can threaten the integrity of the clad. At high burnup, there is evidence of a higher fission
gas release rates within the fuel pellet. The FGR has a significant impact on the gap
conductance prediction which affects fuel temperatures. The calculation of the rod
internal pressure from the prediction of FGR is also very important because there‟s a
limit to the EOL rod pressure. The linear heat generation rate (LHGR) limits is
determined based on the rod pressure toward the EOL.
Fission gas release is the main problem that prevents many utilities from operating at
increase burnup today. A description of the fission gas release model used in the fuel
performance code FRAPCON can be found in the MATPRO library [45]. There are two
fission gas release model options in FRAPCON-3.4. One is the ANS-5.4 model and the
other is Massih/Forsberg model. The ANS-5.4 model is considered an industry standard
for its good steady state, high temperature FGR prediction at both low and high burnup.
The fission gas release mechanism for ANS-5.4 model only includes gas diffusion from
the grain. The Massih/Forsberg model analyzed the accumulation of gas at the surface. A
saturation criterion for the gas release was imposed from the grain boundary to the rod
void volume. The grain boundary gas is released when the concentration reaches the
saturation value. A more detailed description of the ANS-5.4 and Massih/Forsberg model
for FGR is provided in FRAPCON Volume 1 [13] and Volume 3 [16]. The integral
assessment of steady state fission gas release prediction can be found in Volume 3 [16] of
the FRAPCON manual. Several technical reports and papers that discussed about fission
gas release in nuclear fuel can be found in [18, 19 , 20, 22, 42, 44, 46]. There are
68
continuous efforts to better understand fission gas behaviour from new experimental data
that can be used to improve the fission gas release model.
4.12.2 Clad Oxidation and Water Chemistry
Clad oxidation occurs in nuclear fuel cladding during operation. There is a limit to the
amount of oxide formed on the fuel cladding. Generally, a limit of 100 microns is
applied. Below this limit, the oxide acts as a protective layer for the clad from further
corrosion. Above this limit, the protective oxide layer breaks down and can cause the clad
to weaken or failed. In PWR with standard Zircaloy-4 cladding, the oxide limit is reached
at an average burnup of around 45 GWd/tU. However, the introduction of new cladding
alloys or clad improvement that are more oxidation resistant can allowed the fuel to
operate at a higher burnup. However, the introduction of new cladding material is slow
and can be very expensive due to the necessary experimental testing that must be done to
be used in commercial nuclear power plants. The integral assessment of the cladding
corrosion can be found in Volume 3 [16] of the FRAPCON manual. A description of the
cladding corrosion model is discussed in the MATPRO library [45].
Water chemistry plays a very important role in the integrity of the fuel cladding. Changes
in the water chemistry can influence fuel oxidation rates and the migration of corrosion
products that can deposit as crud. Using fuel with higher enrichment can cause power
distribution to be less uniform and create local hotspot. The deposition of crud at local
hotspot can cause fuel failure through enhanced oxidation.
4.13 Fuel Failure in Normal Operation Overview
Fuel failure occurs when there is a breach in the cladding that allow fission product to
escape from the fuel rod. Failed fuel can cause higher exposure to the operator and is
expensive to repair and clean. There are several fuel failure mechanisms that have been
identified. These mechanisms include manufacturing defects, grid-rod fretting, and debris
ingress to the coolant circuit. Grid-rod fretting is caused by the grid springs rubbing
against the fuel rods and wearing through the cladding. There is a huge economic
69
incentive to reduce or achieve zero fuel failures in normal operations. Improvement in the
fuel performance, design, operations and reliability can reduce the number of failures.
The burnup level for LWR fuel have now reach near 60 GWd/tU and are likely to
increase with more advanced cladding alloys and improvement in calculational tools to
predict fuel performance. More on fuel failures and fuel safety criteria can be found in
[20, 21, 32, 37, 44]. The structural behavior of fuel assembly for water cooled reactors
and the accident analysis methodology can be found in [31, 35].
4.14 Fuel Design Criteria and Limits
Fuel integrity must be maintained during steady state and transient operations. This
requires the fuel rods to maintain specified acceptable design limits even in the event of
an off-normal condition. The fuel design limits are set by the Nuclear Regulatory
Commission (NRC) for fuel cladding temperatures, heat fluxes, cladding oxidation and
hydrogen generation from chemical reaction between water/steam with cladding. Under
severe reactor operating conditions and transients conditions, cladding integrity must be
ensured. According to Argonne National Laboratory, the outer cladding temperature
limit for zircaloy cladding of LWR fuel is 2200 ⁰F (1204 ⁰C). The outer cladding limit is
related to the instability of water and two-phase boiling that can lead to runaway heating
of the cladding. The heat flux limit is a major design limit in preventing the outer
cladding temperature from going above the saturated temperature. It‟s important to
maintain temperature and heat flux limits to assure fuel integrity and prevent radioactive
materials from leaking from the fuel rod. A report of the fuel safety criteria in Nuclear
Energy Agency (NEA) member countries can be found in [37]. The report presents the
safety criteria, operational/licensing criteria and design criteria as the three categories for
all fuel safety criteria. Figure 4.17 lists all the fuel safety criteria discussed in this report.
This report also provided the fuel safety limit values from various NEA member
countries.
70
Figure 4.17 Fuel safety criteria list [37].
The first category contained safety criteria that is imposed by regulator and must be met
at all times. The second category is operational criteria which are provided by the fuel
vendor for licensing basis. The third category is the fuel design criteria and limits that are
aim to meet the first or second category and approved by regulator. The relationship
between the three categories is illustrated in Figure 4.18 below.
Figure 4.18 Relationship between the three categories of fuel safety criteria [37].
71
In most commercial nuclear reactors in the US, the fuel used is in the form of uranium
dioxide
pellet. The typical
fuel is enriched to about of 3-5% percent and has a
melting point of over 2,800 ⁰C. However, the operating peak centerline temperature is
less than 1400 ⁰C to provide enough margins to prevent fuel melting. The pre-specified
design criteria and limits must be maintained in fuel design to ensured fuel integrity.
4.15 NRC Licensing Process
One of the biggest challenges to build SMRs in the United States is to get through the
NRC licensing process. In 2009, the NRC set up an office to handle licensing process for
Small Modular Reactors (SMR) based on the experience obtained over the past 40 years
in licensing light water reactors. The NRC‟s current licensing requirement for certifying a
design, construction and operating license is contained in 10 CFR Part 50 and 10 CFR
Part 52. Since some of the design features and technical issues in SMRs are distinct from
those of large nuclear reactors, there‟s a big push by the NRC to recognize this and
improve its licensing process for SMRs. The licensing process is costly and can take
anywhere between 2 to 10 years. The NRC is currently in open communication with
many SMR vendors to develop usable and acceptable licensing process for SMRs. Many
of the SMRs that are based on light water technology are well understood by the NRC
and thus have the advantage of moving ahead first. New reactor designs must follow the
standard review guidelines known as NUREG-0800 established by the NRC. The thermal
hydraulics analysis must meet the criteria in Chapter 4.4 of NUREG-0800 [41]. The fuel
performance characteristics must satisfy the requirement and acceptance criteria in
Chapter 4.2 of NUREG-0800 [40]. The NRC licenses fuel to the most limiting fuel rod in
the core. To deployed new SMRs overseas, the international nuclear community must
develop codes and standard that is acceptable.
72
5
RESULTS AND DISCUSSION
5.1 VIPRE Model Results
The VIPRE results in this section assumed single-phase forced convection and nucleate
boiling only to calculate the heat transfer coefficients. The conditions are not expected to
exceed the CHF point for the current research. The boiling curve will be used only to the
CHF point for this case. The Dittus-Boelter correlation was selected as the heat transfer
coefficient correlation for single-phase convection regime. The Thom plus single-phase
(THSP) correlation default correlation was selected for both subcooled and saturated
region. The VIPRE results that assumed single-phase convection only to calculate the
heat transfer coefficients is discussed in Section 5.3.
For each of the five prototypical cores, the hot channel and hot rod in the core were
identified for BOC, MOC, and EOC. The hot channel was determined by the MDNBR
value and the hot rod was determined by the outer cladding temperature and the pin
peaking factor. VIPRE automatically output the hot channel and hot rod index number in
a separate output file once the model was run. The BOC, MOC, and EOC hot channel
and hot rod along with the assembly name in which they were found in are listed in Table
5.1 to Table 5.3 below. The goal was to determine the most limiting rod for each of the
five prototypical cores for fuel performance analysis. The hot channel and hot rod do
vary at the BOC, MOC and EOC. However, the most limiting rod in the core can be
found by locating the rod with the highest power history. The thermal hydraulic results in
this chapter will mainly be focus on the BOC, MOC, and EOC comparison for the five
MASLWR prototypical cores. The BOC core was found to be the most limiting for all
five cores since it was loaded with fresh fuel. The core axial peaking factor is highest at
the BOC core. The hot fuel assembly was found to be assembly A411. Assembly A411
contains the highest power factor at BOC, MOC and EOC. The thermal hydraulic results
for each of the prototypical cores can be found in Appendix A to Appendix E.
73
BOC
Prototypical
MDNBR
Cores
Hot
Hot Chan
Hot
Max Hot Rod Outer
Hot Rod
Chan
Assembly
rod
Clad Temp. (F)
Assembly
M_4-25A
1.565
20
A411
14
588.5
A411
M_4-25B
1.874
20
A411
14
586.9
A411
M_8A
1.852
20
A411
14
586.3
A411
M_8B
2.171
20
A411
14
582.9
A411
M_8C
1.633
53
A411
44
585.8
A411
Table 5.1 Hot channel and hot rod location at beginning of cycle (BOC).
MOC
Prototypical
MDNBR
Cores
Hot
Hot Chan
Hot
Max Hot Rod Outer
Hot Rod
Chan
Assembly
rod
Clad Temp. (F)
Assembly
M_4-25A
2.018
20
A411
14
584.3
A411
M_4-25B
1.982
20
A411
20
584.8
A411
M_8A
2.127
20
A411
14
583.7
A411
M_8B
2.067
20
A411
14
584.2
A411
M_8C
2.068
65
A411
54
584.2
A411
Table 5.2 Hot channel and hot rod location at middle of cycle (MOC).
EOC
Prototypical
MDNBR
Cores
Hot
Hot Chan
Hot
Max Hot Rod Outer
Hot Rod
Chan
Assembly
rod
Clad Temp. (F)
Assembly
M_4-25A
2.155
20
A411
14
583.5
A411
M_4-25B
2.158
20
A411
14
583.5
A411
M_8A
2.349
20
A411
14
582.4
A411
M_8B
2.310
20
A411
20
582.8
A411
M_8C
2.184
9
A411
9
583.1
A411
Table 5.3 Hot channel and hot rod location at end of cycle (EOC).
74
5.1.1
Steady State BOC, MOC, EOC Results Comparison
The following thermal hydraulic results are produced for the BOC, MOC, and EOC
prototypical cores. A comparison of the thermal hydraulic characteristics for the hot
channel and hot rod from the five MASLWR prototypical cores are presented below. The
DNBR axial profiles of the hot channel in the prototypical cores are illustrated in Figure
DNBR (BOC)
5.1 to Figure 5.3 below.
M_4-25A_A411_chan_20
M_4-25B_A411_chan_20
M_8A_A411_chan_20
M_8B_A411_chan_20
M_8C_A411_chan_53
10
9
8
7
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
Axial Location (in)
50.0
60.0
70.0
Figure 5.1 Beginning of cycle DNBR axial profile comparisons.
DNBR (MOC)
M_4-25A_A411_chan_20
M_4-25B_A411_chan_20
M_8A_A411_chan_20
M_8B_A411_chan_20
M_8C_A411_chan_65
10
9
8
7
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
Axial Location (in)
50.0
60.0
70.0
Figure 5.2 Middle of cycle DNBR axial profile comparisons.
75
DNBR (EOC)
M_4-25A_A411_chan_20
M_4-25B_A411_chan_20
M_8A_A411_chan_20
M_8B_A411_chan_20
M_8C_A411_chan_9
10
9
8
7
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Axial Location (in)
Figure 5.3 End of cycle DNBR axial profile comparisons.
The 4.25 % enrichment fuel with no burnable poison core contained the lowest MDNBR
value of 1.565 for the BOC normal core. The MDNBR typical thermal design limits for
PWR is ≥ 1.3 during transient behavior at 112% power [24]. The DNB safety limits
found in [37] ranges from 1.10 to 1.33 and operating limits range from 1.3 to 1.5
depending on the countries. According to NUREG-0800 chapter 4.4, there should be a
95-percent probability at the 95-percent confidence level that a hot fuel rod in the reactor
core does not experience a DNB or boiling transition condition during normal operation
or anticipated operational occurrences [41]. The steady-state BOC, MOC, and EOC
MDNBR value for all five prototypical cores appear to be very close but within the
thermal design safety limits for PWR. This limit is set to prevent critical conditions that
would result in a sudden reduction of heat transfer capability of two-phase coolant. The
reduction in heat transfer capability would cause the clad temperature to rise. There‟s a
design limits for clad average temperature to prevent extensive metal-water reaction. The
current design criteria for Zircaloy peak cladding temperature is below 2200 ⁰F (1204.4
⁰C) for PWR [24, 37, 40]. The BOC clad average temperature for the hot fuel rods are
presented in Figure 5.4 below. The BOC clad average temperature for the hot fuel rods
were found to be well below the peak cladding temperature design limits.
Clad Average Temperature (F)
76
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
650
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.4 BOC clad average temperature comparisons.
The hot rods outer cladding temperatures for BOC, MOC and EOC are presented in
Figure 5.5 to Figure 5.7 below. Most of these outer cladding temperatures are used as
BOC Outer Cladding Temperature (F)
boundary conditions for the fuel performance analysis.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.5 BOC outer cladding surface temperature comparisons.
MOC Outer Cladding Temperature (F)
77
M_4-25A_A411_rod_14
M_4-25B_A411_rod_20
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_54
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
EOC Outer Cladding Temperature (F)
Figure 5.6 MOC outer cladding surface temperature comparisons.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_20
M_8C_A411_rod_9
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.7 EOC outer cladding surface temperature comparisons.
78
The outer clad surface temperature results for the hot rods show only a small difference
in temperatures around axial locations of 10 inches and after for BOC, MOC and EOC
cores. This is due to the occurrence of subcooled and saturated nucleate boiling. The
VIPRE results show that the subcooled and saturated nucleate boiling correlations were
used at these locations for the calculation of the heat transfer coefficients. Based on
looking at the heat transfer mode, the subcooled nucleate boiling was found to occur very
early on at the bottom of the hot fuel rods. At BOC, the hot rod that show lowest outer
cladding temperature axial profile came from the core with 8 % enrichment fuel and
standard burnable absorber design. The different temperature in the hot rod temperature
profiles showed the effects of burnable absorber and higher fuel enrichment in the reactor
core.
The fuel centerline temperature profiles for BOC, MOC and EOC are illustrated in Figure
5.8 to Figure 5.10 below. For PWR, the operating peak temperature for fuel centerline is
2552⁰F (1400⁰C). The melting temperature for
is 5072⁰F (2800⁰C) [24]. Fuel
centerline melting is not permitted for normal operation and anticipated operational
occurrences (AOOs) [40].
Fuel Centerline Temperature (F)
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
4000
3500
3000
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.8 BOC fuel centerline temperature profiles comparison.
79
Fuel Centerline Temperature (F)
M_4-25A_A411_rod_14
M_4-25B_A411_rod_20
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_54
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.9 MOC fuel centerline temperature profiles comparisons.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_20
M_8C_A411_rod_9
Fuel Centerline Temperature (F)
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.10 EOC fuel centerline temperature profiles comparisons.
80
At BOC, only the 8% enrichment fuel with standard and new burnable poison cores
contained fuel centerline temperature profiles below the peak operating temperature limit.
The 4.25% enrichment fuel with no burnable poison and standard burnable poison
contained a much higher centerline temperatures than the peak operating temperature
limit at BOC.
The BOC, MOC, and EOC bulk coolant temperatures are illustrated in Figure 5.11 to
Figure 5.13 below. For all five MASLWR prototypical cores, the hot rod coolant
temperature reaches saturation of around 572.07 ⁰F at axial locations between 35 inches
and 55 inches for the BOC core. The hot rod channels were found to operate in subcooled
and saturated nucleate boiling regime. Saturated nucleate boiling is not desirable in
PWR. The results in this section assumed only single-phase convection and nucleate
boiling heat transfer correlations. The BOC heat transfer coefficients result for the hot
rods is given in Figure 5.14 below. Heat transfer is enhanced in the subcooled and
saturated boiling regime.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
Bulk Coolant Temperature (F)
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.11 BOC bulk coolant temperature profiles comparison.
81
M_4-25A_A411_rod_14
M_4-25B_A411_rod_20
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_54
Bulk Coolant Temperature (F)
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.12 MOC bulk coolant temperature profiles comparison.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_20
M_8C_A411_rod_9
Bulk Coolant Temperature (F)
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.13 EOC bulk coolant temperature profiles comparison.
Heat Transfer Coefficients (Btu/sec-ft^2-F)
82
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
30000
25000
20000
15000
10000
5000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.14 BOC heat transfer coefficients comparison
5.2 VIPRE Independent and Sensitivity Studies
5.2.1
Critical Heat Flux Correlations Study
Three different critical heat flux correlations were considered for the VIPRE model early
on in this research. The three CHF correlations are EPRI, W-3s, and Bowring. These
correlations were briefly compared and discussed in Chapter 2. To compare the
relationship between these correlations, the beginning of cycle A411 VIPRE model from
the prototypical core with 4.25 % enrichment fuel and no burnable poison (M_4-25A)
core was chosen for analysis. The critical heat flux and DNBR was taken from the hot
channel for each CHF correlations. Table 5.4 below list the hot channels, hot rods and
MDNBR values for each of the CHF correlations from the A411 VIPRE model. The
channel and rod numbering scheme for assembly A411 can be found in Figure 4.5.
83
A411 VIPRE Model
CHF Correlations
EPRI-1
W-3s
Beginning of Cycle (BOC)
MDNBR
Hot Chan
Hot Rod
1.565
20
14
2.074
20
14
Bowring
1.562
20
14
Table 5.4 Hot channel and hot rod for each CHF correlations.
W-3s
EPRI-1
BOWR
Critical Heat Flux (BOC)
2
1
0
0.0
10.0
20.0
30.0
40.0
Axial Location (in)
50.0
60.0
70.0
Figure 5.15 Critical Heat Flux correlation comparisons (BOC).
W-3s
EPRI-1
BOWR
DNBR (BOC)
10
9
8
7
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
Axial Location (in)
50.0
60.0
70.0
Figure 5.16 Axial DNBR distributions for different CHF correlations (BOC).
84
As presented in Figure 5.15 and Figure 5.16, the EPRI-1 correlation produces the most
conservative critical heat flux and DNBR values, follow by Bowring, and W-3s
correlations. The MDNBR values between the EPRI-1 and Bowring was found to be
close to each other as shown in Table 5.4. Based on the results presented in Figure 5.15
and Figure 5.16, the EPRI-1 correlation was selected as the CHF correlation in the
VIPRE model for the MASLWR prototypical cores. The EPRI-1 correlation was chosen
because it produces the most limiting DNBR profiles over other correlations considered
for this study. Also, the EPRI-1 correlation has a wider applicable data ranges than other
correlations. The operating pressure of the MASLWR prototypical core is within the data
ranges of the EPRI-1 correlation.
5.2.2
Mixing Coefficient Sensitivity Studies
Since the mixing coefficient (ABETA value) was not known for the VIPRE model, the
mixing coefficients group was not used in this research. A sensitivity study of the mixing
coefficients in the VIPRE model is provided below. The beginning of cycle A411 model
from the prototypical core with 4.25 % enrichment fuel and no burnable poison (M_425A) core was chosen to help determine the effects of the mixing coefficients on the
DNBR values. The relationship between the DNBR values for various mixing
coefficients is illustrated in Table 5.5 below. The mixing coefficient (ABETA value)
value of 0.0 gave the lowest DNBR values. Not using the mixing coefficients group in
the VIPRE model would give the same results as using the mixing coefficient ABETA
value of 0.0. The MDNBR values are higher with higher ABETA values.
ABETA Value
MDNBR
Axial Level (in)
Hot Channel
0.0
1.565
53.5
20
0.001
1.570
53.5
20
0.005
1.587
53.5
20
0.01
1.600
53.5
20
0.05
1.638
53.5
20
0.1
1.655
50.4
20
Table 5.5 MDNBR values for various mixing coefficients (BOC).
85
5.2.3
Gap Conductance Sensitivity Studies
In this research, a constant gap conductance of 1000 Btu/hr-
was used. A sensitivity
study on the effects of gap conductance on the fuel rod temperatures is provided below. A
constant gap conductance values between 1000 to 2200 Btu/hr200 Btu/hr-
were used at every
. The beginning of cycle A411 model from the prototypical core with 4.25
% enrichment fuel and no burnable poison (M_4-25A) core was chosen for this analysis.
Figure 5.17 show the fuel centerline temperature profiles of the hot rods for each gap
conductance value. The bulk coolant temperatures and the cladding temperatures do not
change. Higher gap conductance result in lower fuel centerline temperatures.
4000
1000 Btu/hr-ft^2
1200 Btu/hr-ft^2
1400 Btu/hr-ft^2
1600 Btu/hr-ft^2
1800 Btu/hr-ft^2
2000 Btu/hr-ft^2
2200 Btu/hr-ft^2
Fuel Centerline Temperature (F)
3500
3000
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.17 BOC fuel centerline temperatures comparison at different gap conductance.
5.2.4
Spacer Grids Sensitivity Study
The effects of the spacer grid locations on the MDNBR results are provided in this
section. Four types of spacer grid locations were designed for this study. The location for
the spacer grids for each type of spacer grid design is given in Table 5.6 below. Type 1
contains the same spacer grid locations used in this research. The spacer grid loss
86
coefficient used is 0.86. The beginning of cycle A411 model from the prototypical core
with 4.25 % enrichment fuel and no burnable poison (M_4-25A) core was chosen for this
analysis. Table 5.7 show the MDNBR results for each type of spacer grid designs. The
number of spacer grids used and the locations does affect the DNBR results.
Spacer
Number of
Spacer Grid Locations (The heated length begin
Grid
at 3.15 in)
Spacing
Grid Type Spacer Grids
Type 1
5
3.15 in, 18.90 in, 34.65 in, 50.39 in, 66.14 in
15.75 in
Type 2
5
9.45 in, 22.05 in, 34.65 in, 47.24 in, 59.84 in
12.60 in
Type 3
4
6.30 in, 25.20 in, 44.09 in, 62.99 in
18.90 in
Type 4
6
3.15 in, 15.75 in, 28.35 in, 40.94 in, 53.54 in,
12.60 in
66.14 in
Table 5.6 Spacer grid designs.
Spacer
MDNBR
Grid Type
Axial Level
(in)
Type 1
1.565
53.5
Type 2
1.565
53.5
Type 3
1.549
53.5
Type 4
1.556
50.4
Table 5.7 MDNBR values for various spacer grid type (Beginning of cycle).
5.2.5
Two Phase Flow Correlations Study
There are many combinations of two phase flow correlations available in VIPRE-01. This
section modeled 8 different combinations of two phase flow correlations. The list of
combinations for two phase flow correlations is given in Table 5.8 below. Combination
number 1 is default in VIPRE and was selected to be used in this research for two phase
flow. The beginning of cycle A411 model from the prototypical core with 4.25 %
enrichment fuel and no burnable poison (M_4-25A) core was chosen for this analysis.
The MDNBR result for the hot channels is given in Table 5.9 below. The results showed
87
a small difference in MDNBR value. Using the default two phase flow correlations give a
slightly higher MDNBR value than using other combinations of two phase flow
correlations.
Correlation
Combination
number
1
2
3
4
5
6
7
8
Subcooled Void
Correlation
Bulk
void/quality
Correlation
EPRI
ARMA
ARMA
Friction
multiplier
Correlation
EPRI
HOMO
ARMA
EPRI
LEVY
NONE (for
homogeneous
model)
NONE (for
HOMO
HOMO
homogeneous
model)
NONE (for
HOMO
BEAT
homogeneous
model)
LEVY
ARMA
ARMA
LEVY
HOMO
HOMO
LEVY
ZUBR
HOMO
Table 5.8 Two-phase flow correlation combinations.
Correlation
MDNBR
Axial Level
Combinations
(in)
number
1
1.565
53.5
2
1.550
53.5
3
1.552
53.5
4
1.555
56.7
5
1.547
56.7
6
1.548
53.5
7
1.540
53.5
8
1.550
53.5
Table 5.9 Two-phase flow correlation combinations.
Hot Wall
Friction
Correction
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
88
5.2.6
Heat Transfer Correlations Study
There are several correlations available in VIPRE for the nucleate boiling regimes. The
default correlation for both subcooled and saturated region is the Thom plus single-phase
(THSP) correlation. This correlation was selected in this research for nucleate boiling
regimes. The Dittus-Boelter correlation was used for single-phase regime. To compare
the relationship between the different nucleate boiling regime correlations, the beginning
of cycle A411 model from the prototypical core with 4.25% enrichment fuel and no
burnable poison (M_4-25A) core was chosen for analysis. The different combination of
nucleate boiling correlations is given in Table 5.10 below. A comparison of the hot fuel
rods outer cladding surface temperature profiles for the different nucleate boiling regime
correlations is shown below in Table 5.11. The heat transfer mode in Table 5.11 shows
the range where subcooled and saturated nucleate boiling correlations were used. The
results below in Table 5.11 show a higher outer cladding surface temperatures profile
when using a different saturated nucleate boiling correlation than Thom plus single-phase
(THSP) correlation. The subcooled nucleate boiling heat transfer mode was activated at
an axial range of 6.3- 9.4 inches (toward the bottom of the fuel rod). The saturated
nucleate boiling heat transfer mode was activated toward the middle of the hot fuel rods.
Correlation
Combinations
number
1
2
3
4
Single Phase
Subcooled
Saturated Nucleate
Convection
Nucleate Boiling
Boiling Correlation
Correlation
Correlation
EPRI (for DittusTHSP
THSP
Boelter correlation)
EPRI (for DittusTHSP
CHEN
Boelter correlation)
EPRI (for DittusCHEN
CHEN
Boelter correlation)
EPRI (for DittusJENS
CHEN
Boelter correlation)
Table 5.10 Heat transfer correlation combinations.
89
Axial
Range
(in)
66.169.3
63.066.1
59.863.0
56.759.8
53.556.7
50.453.5
47.250.4
44.147.2
40.944.1
37.840.9
34.637.8
31.534.6
28.331.5
25.228.3
22.025.2
18.922.0
15.718.9
12.615.7
9.412.6
6.39.4
3.16.3
0.03.1
Combination 1
Outer
Heat
Clad
Transfer
Temp.
Mode
(F)
572.0
epri
Combination 2
Outer
Heat
Clad
Transfer
Temp.
Mode
(F)
572.0
epri
Combination 3
Outer
Heat
Clad
Transfer
Temp.
Mode
(F)
572.0
epri
Combination 4
Outer
Heat
Clad
Transfer
Temp.
Mode
(F)
572.0
epri
579.1
thsp
584.5
chen
584.5
chen
584.5
chen
581.1
thsp
589.3
chen
589.3
chen
589.3
chen
582.6
thsp
592.8
chen
592.8
chen
592.8
chen
583.8
thsp
595.5
chen
595.5
chen
595.5
chen
584.8
thsp
597.7
chen
597.7
chen
597.7
chen
585.7
thsp
599.4
chen
599.4
chen
599.4
chen
586.5
thsp
600.6
chen
600.6
chen
600.6
chen
587.1
thsp
601.4
chen
601.4
chen
601.4
chen
587.7
thsp
601.8
chen
601.8
chen
601.8
chen
588.3
thsp
602.0
chen
602.0
chen
602.0
chen
588.5
thsp
590.3
chen
601.0
chen
584.9
chen
588.4
thsp
588.4
thsp
600.2
chen
584.2
jens
588.0
thsp
588.0
thsp
599.2
chen
584.3
jens
587.4
thsp
587.4
thsp
597.8
chen
584.3
jens
586.5
thsp
586.5
thsp
596.0
chen
584.2
jens
585.2
thsp
585.2
thsp
593.7
chen
584.1
jens
583.5
thsp
583.5
thsp
590.5
chen
583.8
jens
580.9
thsp
580.9
thsp
586.1
chen
583.3
jens
576.4
thsp
576.4
thsp
578.7
chen
582.6
jens
525.3
epri
525.3
epri
525.3
epri
525.3
epri
425.6
epri
425.6
epri
425.6
epri
425.6
epri
Table 5.11 Outer cladding temperatures comparison for different nucleate boiling
correlations.
90
5.2.7
Number of Axial Nodes Study
A comparison between running the VIPRE model for 22 axial nodes versus 42 axial
nodes is provided below. The beginning of cycle A411 model from the prototypical core
with 4.25 % enrichment fuel and no burnable poison (M_4-25A) core was chosen for this
analysis. The MDNBR value for the 42 axial nodes run is 0.046 lower than the 22 axial
nodes run. A comparison of the DNBR profile is shown in Figure 5.18 below. The results
showed only a small difference in MDNBR value. For the purpose of this research, using
22 axial nodes is sufficient.
M_4-25A Core
Number of
BOC
MDNBR
Axial Nodes
Hot
Hot rod Axial Level
Channel
Max Hot Rod Outer
(in)
Clad Temp. (F)
22
1.565
20
14
53.5
588.5
42
1.519
20
14
56.1
588.6
Table 5.12 BOC A411 VIPRE model axial nodes comparison.
M_4-25A_A411_chan_20_22axialnodes
M_4-25A_A411_chan_20_42axialnodes
10
9
DNBR (BOC)
8
7
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
Axial Location (in)
Figure 5.18 BOC DNBR profiles comparison.
60.0
70.0
91
5.3 VIPRE Results for Using Single-Phase Heat Transfer Coefficient
Correlation Only
The VIPRE results below assumed single-phase forced convection Dittus-Boelter
correlation only to calculate the heat transfer coefficients. Single-phase forced convection
is more desirable in PWR. The boiling curve will not be used. Only the fuel rod
temperatures are affected by this assumption. Assuming single phase heat transfer
coefficients correlation only provide a more conservative results in the outer cladding
surface temperatures. The outer cladding temperatures for BOC, MOC and EOC are
presented in Figure 5.19 to Figure 5.21 below.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
Outer Cladding Temperature (F)
850
800
750
700
650
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.19 BOC outer cladding surface temperature comparisons.
MOC Outer Cladding Temperature (F)
92
M_4-25A_A411_rod_14
M_4-25B_A411_rod_20
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_54
750
700
650
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
EOC Outer Cladding Temperature (F)
Figure 5.20 MOC outer cladding surface temperature comparisons.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_20
M_8C_A411_rod_9
700
650
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.21 EOC outer cladding surface temperature comparisons.
93
At BOC, the hot rod with the lowest outer cladding temperature axial profile came from
the core with 8 % enrichment fuel and standard burnable absorber design. The effects of
burnable absorbers and higher fuel enrichment on the hot rod and the reactor can be
observed much better in this section. The fuel centerline temperature profiles for BOC,
MOC and EOC are illustrated in Figure 5.22 to Figure 5.24 below.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_14
M_8C_A411_rod_44
Fuel Centerline Temperature (F)
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure 5.22 BOC fuel centerline temperature comparisons.
70.00
94
M_4-25A_A411_rod_14
M_4-25B_A411_rod_20
M_8A_A411_rod_14
Fuel Centerline Temperature (F)
M_8B_A411_rod_14
M_8C_A411_rod_54
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Fuel Centerline Temperature (F)
Figure 5.23 MOC fuel centerline temperature comparisons.
M_4-25A_A411_rod_14
M_4-25B_A411_rod_14
M_8A_A411_rod_14
M_8B_A411_rod_20
M_8C_A411_rod_9
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure 5.24 EOC fuel centerline temperature comparisons.
70.00
95
This section assumed only single-phase convection heat transfer correlations and
neglecting nucleate boiling or saturated boiling occurring in the core. The results show
much higher cladding surface temperatures than previously observed in the VIPRE run
that include both single-phase and nucleate boiling heat transfer correlations. This is due
to the heat transfer coefficients being lower in the single-phase regime. The fuel
centerline temperature is slightly higher when compare to the previous VIPRE run that
include both single-phase and nucleate boiling heat transfer correlations. The results in
this section again do not take into account the nucleate boiling heat transfer correlations.
5.4 Limiting Rod Determination
Based on the results above and the fuel rod power history, the limiting fuel rod for each
of the prototypical cores was determined to be the same as the hot rod at BOC listed in
Table 5.1 above except for the M_8C core. Rod index number 54 was found to be the
limiting rod for the M_8C core. Table 5.13 listed the limiting rod for each of the
MASLWR prototypical cores. These limiting rods contained the peak power in the
reactor core. The outer cladding surface temperature profiles for each of these limiting
rods were extracted from the A411 VIPRE models for BOC, MOC and EOC to be input
as boundary conditions for the fuel performance model. The BOC, MOC, and EOC
boundary conditions for most the limiting rods can be found in Figure 5.5 to Figure 5.7
above. The boundary conditions for the limiting rods that can‟t be found in Figure 5.5 to
Figure 5.7 are shown below in Figure 5.25.
Prototypical Cores
Limiting Assembly
Limiting Rod
M_4-25A
A411
14
M_4-25B
A411
14
M_8A
A411
14
M_8B
A411
14
M_8C
A411
54
Table 5.13 Prototypical cores limiting rods.
96
M_4-25B_MOC_A411_rod_14
M_8B_EOC_A411_rod_14
M_8C_BOC_A411_rod_54
M_8C_EOC_A411_rod_54
Outer Cladding Temperature (F)
600
580
560
540
520
500
480
460
440
420
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.25 Limiting rods boundary conditions.
The limiting rod average and maximum linear heat generation rate (LGHR) extracted
from the neutronic results (SIMULATE) in each reactor core are presented in Figure 5.26
and Figure 5.27 below. The rod average linear heat generation rates along with its axial
shapes extracted from SIMULATE are input as power history for the fuel performance
analysis. A fuel performance model was created for each of these limiting rods.
Rod Average LHGR, Kw/ft
97
M_4-25A_A411_rod14
M_4-25B_A411_rod14
M_8A_A411_rod14
M_8B_A411_rod14
M_8C_A411_rod54
10
9
8
7
6
5
4
3
2
1
0
0
200
400
600
800
1000
1200
1400
1600
1800
Elapsed Times from BOC, Days
Figure 5.26 Rod average LHGR.
M_4-25A_A411_rod14
M_4-25B_A411_rod14
M_8A_A411_rod14
M_8B_A411_rod14
Maximum Nodal LHGR, Kw/ft
M_8C_A411_rod54
18
16
14
12
10
8
6
4
2
0
0
200
400
600
800
1000
1200
1400
Elapsed Times from BOC, Days
Figure 5.27 Maximum nodal LHGR.
1600
1800
98
5.5 FRAPCON Results Comparisons
The steady state FRAPCON results in this section provide the fuel behavior for the
limiting rod identify for each of the prototypical cores. The main fuel behavior of interest
in this section is the cladding oxidation. Other fuel behavior s of interest such as fuel
centerline temperature, and rod internal pressure (gap gas pressure) are presented in
Appendix F. The FRAPCON results in this section can provide significant insight and
help identify some of the core design issues facing small LWR reactors. A comparison of
the fuel performance results for the limiting rod in each of the prototypical cores is
provided below. The axial stations location from the fuel performance results is given in
Table 5.14 below. Figure 5.28 below illustrate the oxide thickness of the limiting rods
from beginning to end of cycle. A five days startup to full power was assumed for the rod
power history. The Nuclear Regulatory Commission (NRC) fuel design acceptance
criteria can be found in chapter 4.2 of the NUREG-0800 document [40]. The current
criteria require that the peak cladding oxidation remains below 17 percent of the
equivalent cladding reacted [40]. From the literature [37], the acceptable oxide thickness
limit ranges from 60 microns to 100 microns for Zircaloy cladding.
Axial Station
Axial Station
Axial Station
Number
Locations (ft)
Locations (in)
1
0.1458
1.7496
2
0.4374
5.2488
3
0.7291
8.7492
4
1.0207
12.2484
5
1.3123
15.7476
6
1.6039
19.2468
7
1.8955
22.7460
8
2.1872
26.2464
9
2.4788
29.7456
10
2.7704
33.2448
11
3.0620
36.7440
12
3.3536
40.2432
13
3.6453
43.7436
14
3.9369
47.2428
15
4.2285
50.7420
16
4.5201
54.2412
17
4.8117
57.7404
18
5.1034
61.2408
Table 5.14 Axial stations locations.
Zircaloy-4 Oxide Thickness (µm)
99
M_4-25A_A411_rod14_axialstation_13
M_4-25B_A411_rod14_axialstation_15
M_8A_A411_rod14_axialstation_14
M_8B_A411_rod14_axialstation_14
M_8C_A411_rod54_axialstation_13
16
14
12
10
8
6
4
2
0
0
200
400
600
800
1000
1200
1400
1600
1800
Times (Days)
Figure 5.28 Maximum nodal oxide thickness.
The oxide thickness results in Figure 5.28 are well below the acceptable oxide thickness
limit of 60 to 100 microns for Zircaloy cladding. A transition at 2 microns was observed
for the oxidation rate. This oxidation rate transitions was observed in out-of-pile test
data. The thermal and mechanical properties of oxidized zircaloy are very different than
unoxidized properties. At high enough temperature, oxidized zircaloy can proceed very
rapidly and can have significance influence on temperatures [45]. The corrosion model
used in FRAPCON-3 was assessed against in-reactor experimental data. For Zircaloy-4
under PWR conditions, a cubic rate law for corrosion-layer thickness as a function of
time is applied until 2.0 microns is attained, then a flux-dependent linear rate law is
applied with the rate constant being an Arrhenius function of oxide-metal interface
temperature [15]. A more detailed descriptions of the equations used to calculate the
oxide thickness can be found in the FRAPCON manual [15, 45]. The oxide thickness rate
is strongly dependent on the boundary conditions input into the fuel performance models.
At low temperature, (temperature range from 573 to 673 K), the rate of oxidation of
zirconium alloys by water is in part controlled by the migration of oxygen vacancies [45].
After the transition at 2 microns, the oxide layer does not affect the rate of oxidation. The
rate of oxidation is in part controlled by the migration and lifetime of the oxygen
100
vacancies. A more detail explanations of the cladding oxidation rate for pretransition and
posttransition modes can be found in the MATPRO library [45]. The boundary
conditions (outer cladding surface temperature) inputs to calculate the oxide thickness
above are taken from the VIPRE models that used both single-phase and nucleate boiling
heat transfer correlations.
5.5.1
FRAPCON Results for Single-Phase Heat Transfer Correlation Only
The following FRAPCON results used the boundary conditions from the VIPRE models
that assumed only single-phase convection heat transfer correlations. The boundary
condition inputs are the outer cladding surface temperatures at BOC, MOC and EOC.
The boundary conditions for the limiting rods can be found in Figure 5.19 to Figure 5.21
above and Figure 5.29 below. The power histories for the limiting rods remain the same.
The oxide thickness result is shown in Figure 5.30 below.
M_4-25B_MOC_A411_rod_14
M_8B_EOC_A411_rod_14
M_8C_BOC_A411_rod_54
M_8C_EOC_A411_rod_54
Outer Cladding Temperature (F)
750
700
650
600
550
500
450
400
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure 5.29 Limiting rods boundary conditions (single-phase heat transfers correlation
only).
Zircaloy-4 Oxide Thickness (µm)
101
M_4-25A_A411_rod14_axialstation_9
M_4-25B_A411_rod14_axialstation_3
M_8A_A411_rod14_axialstation_10
M_8B_A411_rod14_axialstation_12
M_8C_A411_rod54_axialstation_15
160
140
120
100
80
60
40
20
0
0
200
400
600
800
1000
1200
1400
1600
1800
Times (Days)
Figure 5.30 Maximum nodal oxide thickness.
Using the new boundary conditions, the results showed the oxide thickness for the
limiting rods far exceed the acceptable design limits of 60 to 100 microns for fuel rods.
The FRAPCON run for the limiting rods with fuel enrichment of 4.25 % stop running
after a few time steps due to the oxide thickness being too great to continue. The code
limit for oxide thickness was reached for all five limiting rods due to the boundary
conditions and power history being too high. The limiting rod for fuel enrichment of 8 %
with standard burnable poison core performed better than the other limiting rods. The
outer cladding surface temperatures (boundary conditions) input for this model was much
higher than the previous FRAPCON run. The results show a significant corrosion issues
in the current prototypical core designs. The outer cladding surface temperatures are too
high which cause significant corrosion on the cladding.
One of the goals of this research was to determine whether the prototypical cores with
fuel enrichment of 8 % can operate five years without refueling. It is not feasible to
expect the prototypical cores with fuel enrichment of 4.25 % to operate five years without
102
refueling in this research given the power density. Current PWR plants with fuel
enrichment below 5 % operate between 18 to 24 months before refueling.
5.5.2
Flow Rate Sensitivity Studies
A flow sensitivity studies was performed to determine the core flow rate that would give
acceptable oxide thickness. The sensitivity studies were performed for the core with
4.25% enrichment with no burnable poison and the core with 8 % enrichment with
standard burnable poisons. The results for the flow rate sensitivity studies are illustrated
in Figure 5.31 and Figure 5.32 below. The power history for the limiting rods remained
the same. New boundary conditions taken from the VIPRE output for each flow rates
were used in the FRAPCON run to calculate the Zircaloy oxide thickness. The input
boundary conditions (outer cladding surface temperature) are shown in Figure 5.33 to
Figure 5.35 below. The results below assumed only single-phase convection heat transfer
correlation to calculate the boundary conditions.
M_4-25A_424kg/s_axialstation_9
M_4-25A_600kg/s_axialstation_10
M_4-25A_650kg/s_axialstation_12
M_4-25A_700kg/s_axialstation_12
Zircaloy-4 Oxide Thickness (µm)
160
140
120
100
80
60
40
20
0
0
200
400
600
800
1000
1200
1400
1600
1800
Times (Days)
Figure 5.31 Oxide thickness at various flow rates for 4.25 % fuel enrichment.
103
Zircaloy-4 Oxide Thickness (µm)
M_8B_424kg/s_axialregion_12
M_8B_500kg/s_axialregion_14
M_8B_550kg/s_axialregion_14
M_8B_600kg/s_axialregion_14
160
140
120
100
80
60
40
20
0
0
200
400
600
800
1000
1200
1400
1600
1800
Times (Days)
BOC Outer Cladding Temperature (F)
Figure 5.32 Oxide thickness at various flow rates for 8 % fuel enrichment with standard
burnable poison.
M_4-25A_A411_rod14_424kg/s
M_4-25A_A411_rod14_600kg/s
M_4-25A_A411_rod14_650kg/s
M_4-25A_A411_rod14_700kg/s
M_8B_A411_rod14_424kg/s
M_8B_A411_rod14_500kg/s
M_8B_A411_rod14_550kg/s
M_8B_A411_rod14_600kg/s
850
800
750
700
650
600
550
500
450
400
0
10
20
30
40
Axial Location (in)
50
60
Figure 5.33 BOC boundary conditions inputs for FRAPCON.
70
MOC Outer Cladding Temperature (F)
104
M_4-25A_A411_rod14_424kg/s
M_4-25A_A411_rod14_600kg/s
M_4-25A_A411_rod14_650kg/s
M_4-25A_A411_rod14_700kg/s
M_8B_A411_rod14_424kg/s
M_8B_A411_rod14_500kg/s
M_8B_A411_rod14_550kg/s
M_8B_A411_rod14_600kg/s
750
700
650
600
550
500
450
400
0
10
20
30
40
Axial Location (in)
50
60
70
EOC Outer Cladding Temperature (F)
Figure 5.34 MOC boundary conditions inputs for FRAPCON.
M_4-25A_A411_rod14_424kg/s
M_4-25A_A411_rod14_600kg/s
M_4-25A_A411_rod14_650kg/s
M_4-25A_A411_rod14_700kg/s
M_8B_A411_rod14_424kg/s
M_8B_A411_rod14_500kg/s
M_8B_A411_rod14_550kg/s
700
650
600
550
500
450
400
0
10
20
30
40
Axial Location (in)
50
60
Figure 5.35 EOC boundary conditions inputs for FRAPCON.
70
105
The oxide thickness results for the fuel enrichment of 4.25 % with no burnable poisons
are shown in Figure 5.31. The results show that the flow rate need to be increase from
424 kg/s to 700 kg/s in order to get the oxide thickness to be within the acceptable design
criteria for five years of operation. However, it‟s not feasible to operate this reactor core
for five years without refueling since there might not be enough fuel to burn. Another
core design issues is to determine how the flow rate can be increase in a natural
circulation type reactor to lower the outer cladding surface temperature. For the flow rate
of 700 kg/s, the peak outer cladding surface temperature input is 673.2 °F at BOC.
The oxide thickness results for the fuel enrichment of 8 % with standard burnable poisons
are shown in Figure 5.32. The results show that the flow rate need to be increase from
424 kg/s to 550 kg/s in order to get the oxide thickness to be within the acceptable design
criteria for five years of operation. For the flow rate of 550 kg/s, the peak outer cladding
surface temperature input is 628.5 °F at BOC.
5.6 Uncertainties
Uncertainties that affect the results of analysis must be conservatively taken into account
in the safety analysis methodology. There are three broad categories of uncertainties in
the thermal hydraulic analyses. These categories include uncertainties in the analysis
method, uncertainties in operating conditions, and uncertainties in the physical
characteristics of the core [12].
5.6.1
Uncertainties in the Analysis Method
The uncertainties in the analysis method consist of uncertainties in the computer code and
uncertainties in the CHF correlation used to calculate the MDNBR [12]. The code
uncertainties consist of the convergence criteria selected, approximations of the
conservation equations, and the discretization of the radial and axial mesh. It‟s extremely
difficult to quantify the magnitudes of these uncertainties [12]. Comparisons to
experimental data and sensitivity studies can be used to lower the uncertainties. The CHF
correlation used to calculate the MDNBR has uncertainties or biases that are embedded in
106
the correlation in which it was derived. Since the CHF correlations are derived from
experimental data, the uncertainties in the correlations are easier to characterize than the
code limitations [12]. These uncertainties are applicable and were taken into account in
this research.
5.6.2
Uncertainties in Operating Conditions
The uncertainties in the operating conditions of the core consist of the method in which
the operating conditions are used. The uncertainties are associated with the selection of
the operating conditions to be examined. The “most adverse” operating conditions can be
used to characterize the uncertainties [12].
5.6.3
Uncertainties in Physical Characteristics of the Core
The physical characteristics of the core consist of uncertainties in the local power,
uncertainties in the core geometry, and uncertainties in the boundary conditions [12].
Uncertainties in the radial power are due to the uncertainties in the neutronics code used
to calculate three-dimensional power distribution [12]. The uncertainties in the boundary
conditions are due to measurement uncertainties and limitations on the possible
instrumentation in the core [12].
The safety analysis methodoloty in this research take into account the uncertainties
discussed above. Sensitivity studies were performed to characterize some of these
uncertainties. There are uncertainties associated with the neutronics code used to
calculate the power factor used in this research. Many of the uncertainties associated with
the thermal hydraulics code can be found for the fuel performance code. One use of fuel
performance code is to perform bound design calculations. This require the fuel rod
design inputs to be biased up or down based on their uncertainty levels [15]. The
limitations on the number of axial power shape that can be input into FRAPCON
contribute to the uncertainties in the fuel performance code.
107
6
CONCLUSION
6.1 Steady State
The current research was performed for steady state operating conditions as part of the
safety analysis methodology for MASLWR prototypical cores. The results demonstrate
that the MASLWR prototypical cores design in this research are not feasible for five
years of operation without refueling due high fuel and clad temperatures and large
corrosions. The fuel centerline temperature for the MASLWR prototypical cores was
found to be too high at the BOC. During steady state operation, the MDNBR values
obtained from the hot subchannel demonstrate that the core operates very close to the
thermal margin design limits at BOC. The results of this research also found that all the
MASLWR prototypical cores considered in this research operates in the subcooled and
saturated nucleate boiling regime. Operating in the saturated nucleate boiling regime is
not desirable for PWR because boiling can potentially damage the fuel and cause fuel
failures.
The power density was found to be too high for the current MASLWR core designs. The
flow rate is too low for such high power density. Reducing the power density and
reconsidering the core geometry and operating conditions would help avoid nucleate
boiling in the reactor core. In order to generate the same amount of thermal power at
lower power density, either longer fuel rods are needed or a new core design with more
fuel assemblies.
The 8 % enrichment fuel core with standard burnable absorber was found to operate
slightly better than the other MASLWR prototypical cores. The fuel centerline and outer
cladding surface temperature of the hot rod for the 8 % enrichment fuel core with
standard burnable absorber was found to be lower than the other prototypical cores.
The following conclusions that can be drawn from the fuel performance study presented
in Chapter 5:
108

The fuel performance results showed that the outer cladding surface
temperature input as boundary conditions would be too high if there were
no nucleate boiling occurring in the reactor core.

If there were no nucleate boiling occurring, the corrosion driven by the
power history and boundary conditions is well above the acceptable design
limits for the current flow rate in MASLWR designs. Too much corrosion
can cause fuel failures.
While this research identified several core design issues in the current prototypical cores
provided by Soldatov [1], one of the objectives was achieved. The objective achieved in
this research was to demonstrate the interaction between the neutronic, thermal hydraulic
and fuel performance codes to performed safety analysis on the prototypical cores.
6.2
Recommendations for Future Works
The results in this research support the feasibility of small reactor designs. Based on the
results, the following recommendations are made for future works:

To better support the MASLWR design and small reactor designs with
natural circulation, a more detail thermal hydraulics analysis and fuel
performance studies at lower power density should be undertaken.

Investigate various transients, operational events, and minor accidents that
are critical to the safety analysis methodology to determine whether the
core operates within the thermal margin design limits at all time.

Investigate new small reactor cores with more fuel assemblies and longer
fuel rods at lower power density and different operating conditions.
109
BIBLIOGRAPHY
MASLWR
1. Alexey I. Soldatov, Design and Analysis of a Nuclear Reactor Core for
Innovative Small Light Water Reactors, Dissertation, Oregon State University,
March 9, 2009.
2. Jose N. Reyes, Qiao Wu, John Groome, Brian G. Woods, Eric Young, Kent Abel,
You Yao, Yeon Jong Yoo, Testing of the Multi-Application Small Light Water
Reactor (MASLWR) Passive Safety Systems, Oregon State University, Journal of
Nuclear Engineering and Design, 2007.
3. Brian G. Woods, Jose N. Reyes, Qiao Wu, Flow Stability Testing Under Natural
Circulation Conditions in Integral Type Reactors, Oregon State University,
Corvallis, OR.
4. S.M. Modro, J.E. Fisher, K.D. Weaver, J.N. Reyes Jr, J.T. Groome, P. Babka,
T.M. Carlson, Multi-Application Small Light Water Reactor Final Report, Idaho
National Engineering and Environmental Laboratory, 2003.
5. F. Mascari, B.G Woods, M. Adorni, Analysis of the OSU-MASLWR Natural
Circulation Phenomena Using TRACE Code, Oregon State University, Corvallis,
OR.
6. F. Mascari, G. Vella, B.G. Woods, K. Welter, J. Pottorf, E. Young, M. Adorni, F.
D‟auria, Sensitivity analysis of the MASLWR helical coil steam generator using
TRACE,
Nuclear Engineering and Design, 2010.
7. James E. Fisher, S. Michael Modro, Kevan D. Weaver, Performance and Safety
Studies for Multi-Application, Small, Light Water Reactor (MASLWR), INEEL.
8. Glen Roth, Using RELAP5-3D to Design a Small, Factory-Built Reactor, Idaho
National Engineering and Environmental Laboratory.
Other
9. VIPRE-01 Team, Volume 1: Mathematical Modeling, Electric Power Research
Institute, Palo Alto, California, 2001.
10. VIPRE-01 Team, Volume 2: Users Manual, Electric Power Research Institute,
Palo Alto, California, (2001).
110
11. VIPRE-01 Team, Volume 4: Applications, Electric Power Research Institute, Palo
Alto, California, (2001).
12. VIPRE-01 Team, Volume 5: Guidelines, Electric Power Research Institute, Palo
Alto, California, (2001).
13. Micahel Avery, Jun Yang, Mark Anderson, Michael Corradini, Critical Heat Flux
in TRIGA-Fueled Reactors Cooled by Natural Convection, University of
Wisconsin-Madison, Madison, WI
14. FRAPCON-3 Team, Volume 1: Modifications to Fuel Rod Material Properties
and Performance Models for High Burnup Application, Pacific Northwest
National Laboratory, Richland, Washington, 1997.
15. FRAPCON-3 Team, Volume 2: A Computer Code for the Calculation for SteadyState, Thermal Mechanical Behavior of Oxide Fuel Rods for High Burnup, Pacific
Northwest National Laboratory, Richland, Washington, 1997.
16. FRAPCON-3 Team, Volume 3: Integral Assessment, Pacific Northwest National
Laboratory, Richland, Washington, 1997.
17. FRAPCON-3 Team, Volume 4: Updates, Including Mixed-Oxide Fuel Properties,
Pacific Northwest National Laboratory, Richland, Washington, 1997.
18. James Anthony Turnbull, Review of Nuclear Fuel Experimental Data, Nuclear
Energy Agency, OECD Documents, January 1995.
19. Miroslav Hrehor, Enrico Sartori, Nuclear Fuel Behavior Activities, OECD/NEA,
April 2001.
20. NEA Nuclear Science Committee Task Force, Scientific Issues in Fuel Behaviour,
OECD/NEA, January 1995.
21. CEA Cadarache/DEN/DEC, International Seminar on Pellet-Clad Interactions
with Water Reactors Fuels, OECD/NEA, IAEA, EDF, FRAMATOME ANP,
COGEMA, March 2004.
22. NEA/CSNI/R, Seminar on Fission Gas Behaviour in Water Reactor Fuels
Executive Summary, Nuclear Energy Agency, OECD, (2000)
23. Mario D. Carelli, L.E Conway, L. Oriani, The Design and Safety Features of the
IRIS Reactor, Nuclear Engineering and Design 230 (2004).
24. Neil E. Todreas, Mujid S. Kaimi, Nuclear Systems I: Thermal Hydraulic
Fundamentals, Taylor & Francis Group, New York, NY, 1990.
111
25. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1624,
Description of Natural Circulation and Passive Safety Systems in Water Cooled
Nuclear Power Plants, IAEA, Vienna, Austria, 2009.
26. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1193,
Staffing Requirements for Future Small and Medium Reactors (SMRs) Based on
Operating Experience and Projections, IAEA, Vienna, January 2001.
27. INTERNATIONAL ATOMIC ENERGY AGENCY, NP-T-2.2, Design Features
to Achieve Defense in Depth in Small and Medium Sized Reactors, IAEA, Vienna,
2009.
28. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1536,
Status of Small Reactors Design Without On-Site Refueling, IAEA, Vienna,
January 2007.
29. INTERNATIONAL ATOMIC ENERGY AGENCY, Progress in Design and
Technology Development for Innovative Small and Medium Sized Reactors,
ANNEX IV, Nuclear Technology Review 2007, Vienna (2007).
30. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1474,
Natural Circulation in Water Cooled Nuclear Power Plants, IAEA, Vienna,
November 2005.
31. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1351,
Incorporation of Advanced Accident Analysis Methodology into Safety Analysis
Reports, IAEA, Vienna, May 2003.
32. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1381,
Analysis of Differences in Fuel Safety Criteria for WWER and Western PWR
Nuclear Power Plants, IAEA, Vienna, November 2003.
33. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1391,
Status of Advanced Light Water Reactor Designs 2004, IAEA, Vienna, May 2004.
34. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1451,
Innovative Small and Medium Sized Reactors: Design Features, Safety
Approaches and R&D trends, IAEA, Vienna, June 2004.
35. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1454,
Structural Behaviour of Fuel Assemblies for Water Cooled Reactors, IAEA,
Vienna, July 2005.
36. INTERNATIONAL ATOMIC ENERGY AGENCY, IAEA-TECHDOC-1485,
Status of Advanced Light Water Reactor Designs 2005, IAEA, Vienna, March
2005.
112
37. NEA/CSNI/R, Fuel Safety Criteria in NEA Member Countries, Organization for
Economic Co-operation and Development, July 2003.
38. C.E. Sanders, J.C. Wagner, Study of the Effect of Integral Burnable Absorbers for
PWR Burnup Credit, NUREG/CR-6760, ORNL/TM-2000/321, U.S Nuclear
Regulatory Commission, Washington, DC, March 2002.
39. Charlotta E. Sanders, John C. Wagner, Impact of Integral Burnable Absorbers on
PWR Burnup Credit Criticality Safety Analyses, Oak Ridge National Laboratory,
Oak Ridge.
40. NUREG-0800, U.S. Nuclear Regulatory Commission Standard Review Plan,
Chapter 4.2 Fuel System Design,March 2007.
41. NUREG-0800, U.S. Nuclear Regulatory Commission Standard Review Plan,
Chapter 4.4 Thermal and Hydraulic Design, March 2007.
42. Paul Van Uffelen, Contribution to the Modeling of Fission Gas Release in Light
Water Reactor Fuel, Universite de Liege, January 2002.
43. P. J. Meyer, W. Gruner, Improvement in Current Light-Water Technology, IAEA
Bulletin, 3/1989.
44. Donald R. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements,
Technical Information Center, Office of Public Affairs, 1976.
45. W.G. Luscher and K.J. Geelhood, PNNL-19417, Material Property
Correlations: Comparisons between FRAPCON-3.4, FRAPTRAN 1.4, MATPRO,
PNNL, March 2011.
46. J A Turnbull, P Menut, E Satori, A Review of Fission Gas Release Data Within
The NEA/IAEA IFPE Database,
47. Dae-Hyun Hwang, Se-Young Chun, Keung-Koo Kim, Chung-Chan Lee, Mass
velocity and cold –wall effects on critical heat flux in an advanced light water
reactor, Korea Atomic Energy Research Institute, Journal of Nuclear Engineering
and Design, 2007, 237: p. 369-376.
48. Moon, S., et al., An experimental study on the critical heat flux for low flow of
water in a non-uniformly heated vertical rod bundle over a wide range of
pressure conditions, Nuclear Engineering and Design, 2005, page 2295-2309.
49. Wade R. Marcum, Thermal Hydraulic Analysis of the Oregon State TRIGA®
Reactor Using RELAP5-3D, Dissertation, Oregon State University, January 23,
2008.
113
50. Hainoun, A. and A. Schaffrath, Simulation of Subcooled Flow Instability for High
Flux Research Reactors Using the Extended Code ATHLET, Nuclear Engineering
and Design, 2000.
114
APPENDICES
115
A APPENDIX (4.25 % Enriched Fuel, No BP Core Results)
The hot channel and hot rod results for the 4.25 % enriched fuel with no burnable
absorber core are provided below in this appendix. The VIPRE results below used both
the single-phase and nucleate boiling heat transfer correlations.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
10
9
8
7
DNBR
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Axial Location (in)
Critical Heat Flux (Mbtu/hr-ft^2)
Figure A.1 Axial DNBR profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Axial Location (in)
Figure A.2 Axial critical heat flux (CHF) profiles.
70.0
116
BOC_A411
Bundle Average Pressure Drop (psi)
MOC_A411
EOC_A411
2.5
2
1.5
1
0.5
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure A.3 Bundle average axial pressure drop profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
BOC Temperature (F)
4000
3500
3000
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure A.4 BOC axial temperature profiles.
70.00
117
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
2000
MOC Temperature (F)
1750
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure A.5 MOC axial temperature profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
2000
EOC Temperature (F)
1750
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
Axial Location (in)
Figure A.6 EOC axial temperature profiles.
60.00
70.00
118
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
12
Velocity (ft/sec)
10
8
6
4
2
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure A.7 Axial velocity profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.8
0.7
Void Fraction
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Axial Location (in)
Figure A.8 Axial void fraction profiles.
60
70
119
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.25
True Quality
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
60
70
Axial Location (in)
Figure A.9 Axial true quality profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.3
Equilibrium Quality
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure A.10 Axial equilibrium quality profiles.
70.00
120
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.7
Mass Flux (Mlbm/hr-ft2)
0.6
0.5
0.4
0.3
0.2
0.1
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Heat Transfer Coefficients (Btu/sec-ft2-F)
Figure A.11 Axial mass flux profiles.
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_14
30000
25000
20000
15000
10000
5000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure A.12 Axial heat transfer coefficient profiles.
70.00
121
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_14
500000
450000
Heat Flux (Btu/hr-ft2)
400000
350000
300000
250000
200000
150000
100000
50000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure A.13 Axial heat flux profiles.
BOC, w(15,20)
MOC, w(15,20)
EOC, w(15,20)
0.003
Crossflow (lbm/sec)
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure A.14 Axial cross-flow profile between two channels.
70.00
122
B APPENDIX (4.25 % Enriched Fuel, Standard BP Core Results)
The hot channel and hot rod results for the 4.25 % enriched fuel with standard burnable
absorber core are provided below in this appendix. The VIPRE results below used both
the single-phase and nucleate boiling heat transfer correlations.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
10
9
8
7
DNBR
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Axial Location (in)
Critical Heat Flux (Mbtu/hr-ft^2)
Figure B.1 Axial DNBR profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Axial Location (in)
Figure B.2 Axial critical heat flux (CHF) profiles.
70.0
123
Bundle Average Pressure Drop (psi)
BOC_A411
MOC_A411
EOC_A411
2.5
2
1.5
1
0.5
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure B.3 Bundle average axial pressure drop profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
BOC Temperature (F)
4000
3500
3000
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure B.4 BOC axial temperature profiles.
70.00
124
Bulk Coolant (A411, Rod20)
Outer Cladding (A411, Rod20)
Fuel Centerline (A411, Rod20)
MOC Temperature (F)
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure B.5 MOC axial temperature profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
2000
EOC Temperature (F)
1750
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
Axial Location (in)
Figure B.6 EOC axial temperature profiles.
60.00
70.00
125
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
8
7
Velocity (ft/sec)
6
5
4
3
2
1
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure B.7 Axial velocity profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.6
Void Fraction
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Axial Location (in)
Figure B.8 Axial void fraction profiles.
60
70
126
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.12
True Quality
0.1
0.08
0.06
0.04
0.02
0
0
10
20
30
40
50
60
70
Axial Location (in)
Figure B.9 Axial true quality profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.15
0.1
Equilibrium Quality
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure B.10 Axial equilibrium quality profiles.
70.00
127
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
Mass Flux (Mlbm/hr-ft2)
0.65
0.6
0.55
0.5
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Heat Transfer Coefficients (Btu/sec-ft2-F)
Figure B.11 Axial mass flux profiles.
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_14
25000
20000
15000
10000
5000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure B.12 Axial heat transfer coefficient profiles.
70.00
128
BOC_A411_rod_14
MOC_A411_rod_20
EOC_A411_rod_14
600000
Heat Flux (Btu/hr-ft2)
500000
400000
300000
200000
100000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure B.13 Axial heat flux profiles.
BOC, w(15,20)
MOC, w(15,20)
EOC, w(15,20)
0.004
Crossflow (lbm/sec)
0.003
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure B.14 Axial cross-flow profile between two channels.
70.00
129
C APPENDIX (8 % Enriched Fuel, No BP Core Results)
The hot channel and hot rod results for the 8 % enriched fuel with no burnable absorber
core are provided below in this appendix. The VIPRE results below used both the singlephase and nucleate boiling heat transfer correlations.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
10
9
8
7
DNBR
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Axial Location (in)
Critical Heat Flux (Mbtu/hr-ft^2)
Figure C.1 Axial DNBR profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Axial Location (in)
Figure C.2 Axial critical heat flux (CHF) profiles.
70.0
130
Bundle Average Pressure Drop (psi)
BOC_A411
MOC_A411
EOC_A411
2.5
2
1.5
1
0.5
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure C.3 Bundle average axial pressure drop profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
BOC Temperature (F)
3000
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure C.4 BOC axial temperature profiles.
70.00
131
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
2000
MOC Temperature (F)
1750
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure C.5 MOC axial temperature profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
1750
EOC Temperature (F)
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure C.6 EOC axial temperature profiles.
70.00
132
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
9
8
Velocity (ft/sec)
7
6
5
4
3
2
1
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure C.7 Axial velocity profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.7
0.6
Void Fraction
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Axial Location (in)
Figure C.8 Axial void fraction profiles.
60
70
133
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.14
0.12
True Quality
0.1
0.08
0.06
0.04
0.02
0
0
10
20
30
40
50
60
70
Axial Location (in)
Figure C.9 Axial true quality profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.2
0.15
Equilibrium Quality
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure C.10 Axial equilibrium quality profiles.
70.00
134
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
Mass Flux (Mlbm/hr-ft2)
0.6
0.55
0.5
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Heat Transfer Coefficients (Btu/sec-ft2F)
Figure C.11 Axial mass flux profiles.
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_14
25000
20000
15000
10000
5000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure C.12 Axial heat transfer coefficient profiles.
70.00
135
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_14
400000
350000
Heat Flux (Btu/hr-ft2)
300000
250000
200000
150000
100000
50000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure C.13 Axial heat flux profiles.
BOC, w(15,20)
MOC, w(15,20)
EOC, w(15,20)
0.002
Crossflow (lbm/sec)
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure C.14 Axial cross-flow profile between two channels.
70.00
136
D APPENDIX (8 % Enriched Fuel, Standard BP Core Results)
The hot channel and hot rod results for the 8 % enriched fuel with standard burnable
absorber core are provided below in this appendix. The VIPRE results below used both
the single-phase and nucleate boiling heat transfer correlations.
BOC_A411_chan_20
MOC_A411_chan_20
DNBR
EOC_A411_chan_20
10
9
8
7
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Axial Location (in)
Critical Heat Flux (Mbtu/hr-ft^2)
Figure D.1 Axial DNBR profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Axial Location (in)
Figure D.2 Axial critical heat flux (CHF) profiles.
70.0
137
Bundle Average Pressure Drop (psi)
BOC_A411
MOC_A411
EOC_A411
2.5
2
1.5
1
0.5
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure D.3 Bundle average axial pressure drop profiles.
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
BOC Temperature (F)
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure D.4 BOC axial temperature profiles.
70.00
138
Bulk Coolant (A411, Rod14)
Outer Cladding (A411, Rod14)
Fuel Centerline (A411, Rod14)
MOC Temperature (F)
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure D.5 MOC axial temperature profiles.
Bulk Coolant (A411, Rod20)
Outer Cladding (A411, Rod20)
Fuel Centerline (A411, Rod20)
1750
EOC Temperature (F)
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure D.6 EOC axial temperature profiles.
70.00
139
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
7
Velocity (ft/sec)
6
5
4
3
2
1
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure D.7 Axial velocity profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.5
Void Fraction
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Axial Location (in)
Figure D.8 Axial void fraction profiles.
60
70
140
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.07
0.06
True Quality
0.05
0.04
0.03
0.02
0.01
0
0
10
20
30
40
50
60
70
Axial Location (in)
Figure D.9 Axial true quality profiles.
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
0.1
Equilibrium Quality
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure D.10 Axial equilibrium quality profiles.
70.00
141
BOC_A411_chan_20
MOC_A411_chan_20
EOC_A411_chan_20
Mass Flux (Mlbm/hr-ft2)
0.65
0.6
0.55
0.5
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Heat Transfer Coefficients (Btu/sec-ft2-F)
Figure D.11 Axial mass flux profiles.
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_20
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure D.12 Axial heat transfer coefficient profiles.
70.00
142
BOC_A411_rod_14
MOC_A411_rod_14
EOC_A411_rod_20
350000
Heat Flux (Btu/hr-ft2)
300000
250000
200000
150000
100000
50000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure D.13 Axial heat flux profiles.
BOC, w(15,20)
MOC, w(15,20)
EOC, w(15,20)
0.0005
0
Crossflow (lbm/sec)
-0.0005
-0.001
-0.0015
-0.002
-0.0025
-0.003
-0.0035
-0.004
-0.0045
-0.005
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure D.14 Axial cross-flow profile between two channels.
70.00
143
E APPENDIX (8 % Enriched Fuel, Advanced BP Core Results)
The hot channel and hot rod results for the 8 % enriched fuel with advanced burnable
absorber core are provided below in this appendix. The VIPRE results below used both
the single-phase and nucleate boiling heat transfer correlations.
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
10
9
8
7
DNBR
6
5
4
3
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Axial Location (in)
Critical Heat Flux (Mbtu/hr-ft^2)
Figure E.1 Axial DNBR profiles.
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
2
1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Axial Location (in)
Figure E.2 Axial critical heat flux (CHF) profiles.
70.0
144
Bundle Average Pressure Drop (psi)
BOC_A411
MOC_A411
EOC_A411
2.5
2
1.5
1
0.5
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure E.3 Bundle average axial pressure drop profiles.
Bulk Coolant (A411, Rod44)
Outer Cladding (A411, Rod44)
Fuel Centerline (A411, Rod44)
BOC Temperature (F)
2500
2000
1500
1000
500
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure E.4 BOC axial temperature profiles.
70.00
145
Bulk Coolant (A411, Rod54)
Outer Cladding (A411, Rod54)
Fuel Centerline (A411, Rod54)
2000
MOC Temperature (F)
1750
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure E.5 MOC axial temperature profiles.
Bulk Coolant (A411, Rod9)
Outer Cladding (A411, Rod9)
Fuel Centerline (A411, Rod9)
2000
EOC Temperature (F)
1750
1500
1250
1000
750
500
250
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure E.6 EOC axial temperature profiles.
70.00
146
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
9
8
Velocity (ft/sec)
7
6
5
4
3
2
1
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure E.7 Axial velocity profiles.
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
0.7
0.6
Void Fraction
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Axial Location (in)
Figure E.8 Axial void fraction profiles.
60
70
147
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
0.16
0.14
True Quality
0.12
0.1
0.08
0.06
0.04
0.02
0
0
10
20
30
40
50
60
70
Axial Location (in)
Figure E.9 Axial true quality profiles.
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
0.2
0.15
Equilibrium Quality
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure E.10 Axial equilibrium quality profiles.
70.00
148
BOC_A411_chan_53
MOC_A411_chan_65
EOC_A411_chan_9
Mass Flux (Mlbm/hr-ft2)
0.6
0.55
0.5
0.45
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Heat Transfer Coefficients (Btu/sec-ft2F)
Figure E.11 Axial mass flux profiles.
BOC_A411_rod_44
MOC_A411_rod_54
EOC_A411_rod_9
25000
20000
15000
10000
5000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure E.12 Axial heat transfer coefficient profiles.
70.00
149
BOC_A411_rod_44
MOC_A411_rod_54
EOC_A411_rod_9
350000
Heat Flux (Btu/hr-ft2)
300000
250000
200000
150000
100000
50000
0
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Axial Location (in)
Figure E.13 Axial heat flux profiles.
BOC, w(44,53)
MOC, w(55,65)
EOC, w(6,9)
0.012
0.01
Crossflow (lbm/sec)
0.008
0.006
0.004
0.002
0
-0.002
-0.004
-0.006
-0.008
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Axial Location (in)
Figure E.14 Axial cross-flow profile between two channels.
70.00
150
F APPENDIX (FRAPCON Comparison Results)
This appendix provides the FRAPCON comparison results for the limiting fuel rods. The
FRAPCON results below used the boundary conditions from VIPRE run that use both the
single phase and nucleate boiling heat transfer correlations.
M_4-25A_A411_rod14
M_4-25B_A411_rod14
M_8A_A411_rod14
M_8B_A411_rod14
M_8C_A411_rod54
Fission Gas Release (%)
6
5
4
3
2
1
0
0
200
400
600
800
1000
1200
1400
1600
1800
Times (Days)
Rod Average Burnup (MWd/kgU)
Figure F.1 Fission gas release comparisons.
M_4-25A_A411_rod14
M_4-25B_A411_rod14
M_8A_A411_rod14
M_8B_A411_rod14
M_8C_A411_rod54
80
70
60
50
40
30
20
10
0
0
200
400
600
800
1000
Times (Days)
1200
Figure F.2 Rod average burnup.
1400
1600
1800
Max Fuel Centerline Temperature (F)
151
M_4-25A_A411_rod14
M_4-25B_A411_rod14
M_8A_A411_rod14
M_8B_A411_rod14
4000
3500
3000
2500
2000
1500
1000
500
0
0
200
400
600
800
1000 1200 1400 1600 1800
Times (Days)
Figure F.3 Maximum fuel centerline temperature.
M_4-25A_A411_rod14
M_4-25B_A411_rod14
M_8A_A411_rod14
M_8B_A411_rod14
M_8C_A411_rod54
Gap Gas Pressure (psia)
1400
1200
1000
800
600
400
200
0
0
200
400
600
800
1000 1200 1400 1600 1800
Times (Days)
Figure F.4 Rod internal pressure.