Advanced Design Concepts for PWR and BWR
High-Performance Annular Fuel Assemblies
by
Tyler Shawn Ellis
Submitted to the Department of Nuclear Science and Engineering
in partial fulfillment of the requirements for the degrees of
BACHELOR OF SCIENCE
and
MASTER OF SCIENCE
in
Nuclear Science and Engineering
at the
Massachusetts Institute of Technology
June 2006
©2006 Massachusetts Institute of Technology
All rights reserved
Signature of Author:
. ,,
Department ofLuclear Science and Engineering
June 9h,2006
Certified by:
U.
Professor M jid, . Kazimi (Thesis Supervisor)
TEPCO Professor ofllear Science and Engineering
Dr. Pavel Hejzlar (TAesis Reader)
AWrincipal
P
Research Scientist
Accepted by:
Professor Jeffrey A. Coderre
Chairman, Department Committee on Graduate Students
--~I '-MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
OCT 12 2007
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Advanced Design Concepts for PWR and BWR
High-Performance Annular Fuel Assemblies
by
Tyler Shawn Ellis
Submitted to the Department of Nuclear Science and Engineering
on June
9 th,
2006, in partial fulfillment of
the requirements for the degrees of
Bachelor of Science
and
Master of Science
Abstract
Sobering electricity supply and demand projections, coupled with the current volatility of
energy prices, have underscored the seriousness of the challenges which lay ahead for the utility
industry. This research addresses the impending global need for electricity through the
development of advanced annular fuel designs with both internal and external cooling which can
achieve higher power densities and hence, higher electricity output from the same basic reactor
vessel and containment. Therefore the objectives of this project are to determine the optimal
geometrical design parameters of an annular fuel assembly for both PWRs and BWRs for the
purpose of achieving maximum power density. It is theorized that utility companies can utilize
this design through either retrofitting of their existing reactor facilities or incorporation of the
fuel design into new plant concepts.
For the case of annular fuel for PWRs, a high performance uranium nitride fuel assembly
concept capable of achieving a 50% higher power density was successfully developed. It is
shown that a 5%enriched UN annular-fuel assembly can operate at 150% power density for
about 50 effective-full-power-days more than that of the nominal 17xl7 solid-fuel-pin assembly
operating at 100% power density. Furthermore, neutronic simulation times of this assembly was
reduced from approximately 2 days per simulation for a Monte Carlo based analysis to
approximately 2 minutes for a deterministic based simulation via the development of an
appropriate correction factor for the CASMO-4 neutron transport code. It was shown that a 25%
increase in U238 number density for the un-poisoned pins and a 35% increase for the 10 weight
percent gadolinium nitride poisoned pins produced the optimal plutonium tracking and infinite
multiplication factor simulation. Finally, the 13x13 annular fuel assembly was shown to have a
smaller reactivity swing over the fuel lifetime. Thus it was concluded that an annular uranium
nitride assembly at 150% power density can be designed for PWRs so as not to require
enrichments above 5%in order to reach the desirable cycle length of 18 months.
For the case of annular fuel for BWRs, thermal hydraulic simulations were carried out for
a 9x9 solid fuel reference assembly and three different annular assemblies with 5x5, 6x6 and 7x7
fuel pin geometries. Prior research had utilized the Hench-Gillis CPR correlation for all thermal
hydraulic simulations and determined that as much as an 11% uprate for 5x5 annular geometries
and an 18% uprate for 6x6 annular geometries might be achievable. However, since Hench-Gillis
uses bundle average conditions for its calculations, it was theorized that this treatment was not
appropriate for annular fuel. A benchmarking analysis against experimental critical power data
for a 9x9 assembly confirmed this is a more appropriate heat balance correlation, the EPRI-1
Reddy Fighetti, which was adopted in our simulation of the critical power using the subchannel
analysis code VIPRE. Several different strategies were pursued in order to improve the minimum
critical heat flux ratio of the three different annular fuel assemblies including optimization of the
fuel pin dimensions, fuel pin gap, and orifice loss coefficients. However it was concluded that
annular fuel is not a promising strategy for increasing the power density. This can be due to the
fact that the CHFR margin gained from the increase in heat transfer surface area is being lost due
to the need for increased flow velocity, which retards the CHF for BWR conditions. This is
exacerbated by the inability for the coolant in the inner channels to mix with the surrounding
subchannels.
Thesis Supervisor:
Mujid S. Kazimi
TEPCO Professor of Nuclear Science and Engineering
Director, Center for Advanced Nuclear Energy Systems
Acknowledgements
First and foremost I'd like to thank those most directly responsible for my ability to
complete this thesis, Professor Mujid Kazimi and Dr. Pavel Hejzlar. Their constant guidance and
inspiration throughout the years have been invaluable for my educational upbringing.
I also truly appreciate the untiring support from Dr. Zhiwen Xu, Chris Handwerk and
Mike Pope. Their aid on codes, computing and the finer points of being a graduate student has
made my tenure here infinitely easier.
Last, but certainly not least, I'd like to express my gratitude for the endless love and
support from my family back home in South Dakota. Randy, Carol, Laura-Bean, Chance and
Riley, I'm not sure I could have finished this 5 year roller coater ride without you all.
Financial support for this work was provided for by the MIT Center for Advanced
Nuclear Energy Systems and the Tokyo Electric Power Company.
For Alizde
Table of Contents
Abstract ...........................................................................................................................................
1
Acknowledgements.....................................
3
Table of Contents ..................................................
5
List of Figures ..................................................
7
List of Tables ..........................................................................................................................
9
List of Acronyms ...................................................
10
1. Introduction........................................
12
1.1.
Societal Need for Safe and Economic Nuclear Power................................ ..... 12
1.2.
Review of Previous Work on Annular Fuel for Reactor Applications ...................... 15
1.3.
Objective of This W ork ............................................................... ........................... 20
1.4. Organization of the Thesis ............................................................................................ 21
2. Uranium Nitride Annular Fuel for PWR Applications .......................................... ...... 23
2.1.
M ethodology ................................................................................................................. 23
2.2. Analysis Tools .............................................................................................................. 24
2.2.1.
M CO D E ................................................................................................................ 24
2.2.2.
CA SM O-4 .................................................. ..................................................... 26
2.3. Description of Geometries Analyzed.............................
......
................. 31
2.4. Benchm ark A nalysis .................................................................. ............................. 32
2.4.1.
MCODE/CASMO-4 Comparison........................................... 32
2.4.2.
CASMO-4 Pseudo-Solution for Annular Fuel...................................
...... 36
2.5. Poison-free Pin Cell Correction .....................................................
37
2.6. Poisoned Pin Cell Correction.................................................................................. 41
2.6.1.
Self-shielding Factor Correction...........................
.......
................. 42
........43
2.6.2.
Multiplication Factor Tracking with Burnup.................................
2.6.3.
Gadolinium Tracking with Burnup .....................................
........... 45
Plutonium Tracking with Burnup ..........................................
............ 47
2.6.4.
2.7. Correction for Fully Poisoned Assembly.............................
.....
.............. 48
2.7.1.
Multiplication Factor Tracking with Burnup....................................... 49
2.7.2.
Plutonium Tracking with Burnup .................................... .....
............ 50
2.8. Final Uprated Design Comparison....................................................................
51
3. Investigation of Annular Fuel for BWR Applications ...................................... ...... 54
3.1.
M ethodology ................................................................................................................. 54
3.2. Analysis Tools: VIPRE Thermal Hydraulics Code ........................................
... . 55
3.2.1.
Flow M odeling...................................................................................................... 56
3.2.2.
Heat Transfer Correlations..............................................
57
3.2.3.
CHFR Correlations ............................................................... .......................... 58
3.2.4.
CHFR/CPR Comparative Analysis...........................................
61
3.3.
Fuel A ssem bly M odels ................................................................................................. 68
3.3.1.
Solid Fuel 9x9 Reference Assembly..........................................
68
3.3.2.
Annular Fuel Assembly Design Option Space .........................................
73
3.3.3.
Annular 5x5 Fuel Assembly ....................................................
75
3.3.4.
Annular 6x6 Fuel Assembly ....................................................
78
3.3.5.
Annular 7x7 Fuel Assembly ...................................................
81
3.4. Results of Fuel Assembly Optimization Studies ......................................
...... 85
85
Annular 5x5 Fuel Assembly .....................................................................
3.4.1.
Annular 6x6 Fuel Assembly .............................................................................. 88
3.4.2.
92
Annular 7x7 Fuel Assembly ....................................................
3.4.3.
Comparison of Optimal Designs................................................................. 96
3.4.4.
3.4.5.
Analysis of the Results........................................ ............................................ 97
4. Summary of Conclusions and Recommendations for Future Studies ............................. 101
4.1.
C onclusions ................................................................................................................. 101
103
4.2. Recommendations for Future Studies .....................................
105
References.........................................
Appendix A: CASMO-4 Operational Parameters for Reactivity Coefficient Calculation ......... 108
Appendix B: VIPRE Input Files ................................................................................................. 111
B. 1 GE 9x9 BWR Assembly Reference .................................................... .......................... 111
117
B.2 Annular 5x5 BWR Assembly.................................
122
B.3 Annular 6x6 BWR Assembly.................................
129
B.4 Annular 7x7 BWR Assembly.................................
137
Appendix C: CASMO-4 Input Files ......................................
137
C.1 Westinghouse 17x17 PWR Assembly Reference .....................................
138
C.2 Annular 13x13 PWR Assembly .....................................
140
Appendix D: MCODE/MCNP Input Files ..................................
140
D.1 Westinghouse 17xl7 PWR Reference .....................................
162
D.2 Annular 13x13 PWR Assembly ................................
List of Figures
Figure 1-1: US Electricity Consumption Projection [EIA] _--..._
. _--------------------------13
Figure 1-2: Temperature Dependence of Thermal Conductivity for UN-. .............---------------------17
Figure 2-1: Flow of Calculation in MCODE-1.0 [Xu 2003] .......................................................... 25
Figure 2-2: Flow of Calculations in CASMO-4 [Knott et. al. 1995] .............
.... .............. 28
Figure 2-3: Pictorial Representation of Unit Cell Models ...--.......................----_.--- --......... . 31
Figure 2-4: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for 17x17
Solid Assembly
---------------------------------------------33
Figure 2-5: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for 13x13
Annular A ssembly .............................................................................................................
34
Figure 2-6: Eigenvalue Differences between MCODE and CASMO-4 ._...............----------------.-35
Figure 2-7: MCODE/Corrected CASMO-4 Eigenvalue versus EFPD for a Poison-Free Annular
Fuel Pin
38
Figure 2-8: Eigenvalue Differences between MCODE and Corrected CASMO-4 for a PoisonFree Pin Cell
39
Figure 2-9: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected
CASMO-4 for a Poison-Free Pin Cell ...--------------------------40
Figure 2-10: Cross sections of various nuclides in the Thermal Energy Range [Driscoll 19911].41
Figure 2-11: MCODE and Corrected CASMO-4 Eigenvalue versus EFPD for a 10Owt% GdN
Poisoned Annular Fuel Pin------------------------------------ 43
Figure 2-12: Eigenvalue Differences between MCODE and Uncorrected/Corrected CASMO-4
for a 10wt%/o GdN Poisoned Pin Cell------------------------44
Figure 2-13: Total Cross Section for Gadolinium Isotopes .
............................................... 45
Figure 2-14: Gadolinium Composition versus Burnup as Calculated by MCODE and Corrected
CASMO-4 for a 10wt% GdN Poisoned Pin Cell
46
Figure 2-15: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected
CASMO-4 for a 10wt% GdN Poisoned Pin Cell
47
Figure 2-16: Fully Poisoned 13x13 Annular PWR Fuel Assembly ............................................. 48
Figure 2-17: MCODE/Corrected CASMO-4 Eigenvalue versus EFPD for a Poisoned 13x13
Annular Assembly
-------------------------------------------................................................................
49
Figure 2-18: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected
CASMO-4 for a Full Poisoned 13x13 Annular Fuel Assembly ----------......-----------50
Figure 2-19: Multiplication Factor versus EFPD for a 17x17 Solid Reference U02 Fuel
Assembly at 100% Power Density and a 13x13 Annular UN Fuel Assembly at 150%
Power Density
----------------------------------------------51
Figure 3-1: NUPEC Experimental Axial Power Peaking Profile [Kitamura 1998] ....................... 62
Figure 3-2: NUPEC Experiment Radial Power Peaking Factors .
..................
..........
63
Figure 3-3: NUPEC Experiment Axial Power Peaking Factors........................--------------------64
Figure 3-4: GEl 1 Fuel Assembly Layout [Gerald 1997] .-----------------------------69
Figure 3-5: Axial Power Peaking Profile for 9x9 Reference Case*.... -------------------72
Figure 3-6: Radial Power Peaking Profile for 9x9 Reference Case .....................
_..........
73
Figure 3-7: 2-D Cross Section of the 5x5 Annular Fuel Design Concept (Not To Scale) ............ 77
Figure 3-8: Radial Power Peaking Profile for 5x5 Annular Case
--------------------.........................
78
Figure
Figure
Figure
Figure
Figure
Figure
3-9: 2-D Cross Section of the 6x6 Annular Fuel Design Concept (Not To Scale) ............. 80
3-10: Radial Power Peaking Profile for 6x6 Annular Case ................................................ 81
3-11: 2-D Cross Section of the 7x7 Annular Fuel Design Concept (Not To Scale)-------83
3-12: Radial Power Peaking Profile for 7x7 Annular Case ----------------------------------84
3-13: Effect of a Reduction in Inner Diameter on the MCHFR for 5x5 Annular Fuel ...... 86
3-14: Effect of Decreasing the Inter-Pin Gap (Via Expansion of the Overall Fuel Pin
Dimensions) on the MCHFR for 5x5 Annular Fuel ..........................................................
87
Figure 3-15: Effect of a Reduction in Inner Diameter on the MCHFR for 6x6 Annular Fuel ...... 89
91
Figure 3-16: Effect of the Orifice Resistance Coefficient on CHFR for 6x6 Annular Fuel
Figure 3-17: Effect of a Reduction in Inner Diameter on the MCHFR for 7x7 Annular Fuel ...... 93
Figure 3-18: Effect of the Orifice Resistance Coefficient on CHFR for 7x7 Annular Fuel .......... 94
Figure 3-19: Effect of Spacer Grid Loss on CHFR for 7x7 Annular Fuel .................................... 95
List of Tables
Table 1-1: Physical and Thermal Properties of UO 2 and UN -------------------------------------16
Table 2-1: Geometric Design Parameters for Investigated Fuel Assembliesm
------------------------ -32
Table 2-2: BOL Reactivity Coefficients for 17x17 Solid and 13x13 Annular .............................. 52
Table 3.1: NUPEC Experiment Operational Conditions [Kitamura 1998] .................................... 61
Table 3.2: Comparison of the Critical Powers Predicted by the Hench-Gillis and EPRI-1
Correlations to the Experimentally Measured NUPEC Data at 25 kJ/kg Inlet
Subcooling
------------------------------------------------65
Table 3.3: Comparison of the Critical Powers Predicted by the Hench-Gillis and EPRI-1
Correlations to the Experimentally Measured NUPEC Data at 126 kJ/kg Inlet
Subcooling
------------------------------------------------ 65
Table 3.4: EPRI-1 CPR Calculation Data
67
Table 3.5: EPRI-1 and Hench-Gillis Calculated CPR Comparison ...- .
--------------------.67
Table 3.6: Solid Fuel Reference Core Operating Parameters [Lungmen], [Nine Mile Point
2004] ----------------------------------------------------70
Table 3.7: Solid Fuel Reference Core Design Constraints ...........................
70
Table 3.8: GEl 1 Fuel Assembly Design Parameters..
---------------------------71
Table 3.9: Localized Pressure Drop Coefficients...............................-----------------------------71
Table 3.10: Annular Design Option Space.....................................................................................
73
Table 3.11: Geometrical Design Parameters for 5x5 Annular Fuel............................................... 76
Table 3.12: Geometrical Design Parameters for 6x6 Annular Fuel ...............................
. 79
Table 3.13: Geometrical Design Parameters for 7x7 Annular Fuel ...............
_................
82
Table 3.14: Comparison of 9x9 Reference, 5x5, 6x6 and 7x7 Annular Designs .........--------------96
Table 3.15: Mixing Contribution Comparison for 9x9 Reference and 6x6 Annular Cases ........... 97
Table 3-16: Effect of Radial Power Peaking on the MCHFR.---------....
...----.............-............. -100
Table A-i: CASMO-4 Operational Parameters for the 17x17 Reference Case Reactivity
Coefficient Determination
108
Table A-2: CASMO-4 Operational Parameters for the 13x13 Annular Case Reactivity
Coefficient Determination
109
List of Acronyms
BOL - Beginning Of Life
BWR - Boiling Water Reactor
CHF - Critical Heat Flux
CHFR - Critical Heat Flux Ratio
CMS - Core Management System
COL - Construction and Operating License
CPR - Critical Power Ratio
DC - Design Certification
AP - Pressure Drop
DNB - Departure from Nucleate Boiling
DOE - Department of Energy
EIA - Energy Information Administration
ENDF - Evaluated Nuclear Data File
EOL - End Of Life
EPRI - Electric Power Research Institute
ESP - Early Site Permit
FTC - Fuel Temperature Coefficient
GE - General Electric
HEM - Homogeneous Equilibrium Model
HM - Heavy Metal
IFBA - Integrated Fuel Burnable Absorber
JAERI - Japan Atomic Energy Research Institute
JEF - Joint Electronic Folder
LWR - Light Water Reactor
MCHFR - Minimum Critical Heat Flux Ratio
MCPR - Minimum Critical Power Ratio
MTC - Moderator Temperature Coefficient
MWe - MegaWatts electric
NEA - Nuclear Energy Agency (France)
NRC - Nuclear Regulatory Commission
NUPEC - NUclear Power Engineering Corporation (Japan)
OECD - Organization for Economic Co-operation and Development (France)
PPM - Parts Per Million
PSAR - Preliminary Safety Analysis Report
PWR - Pressurized Water Reactor
TD - Theoretical Density
USAR - Updated Safety Analysis Report
VIPRE - Versatile Internals and component Program for Reactors; EPRI
1. Introduction
1.1. Societal Need for Safe and Economic Nuclear Power
Sobering electricity supply and demand projections, coupled with the current volatility of
energy prices, have underscored the seriousness of the challenges which lay ahead for the utility
industry. According to the Energy Information Administration (EIA), the statistical arm of the
U.S. Department of Energy (DOE), worldwide energy consumption is likely to increase 57% by
2025, with consumption of nuclear generated capacity rising from 2560 billion kilowatt-hours to
over 3300 billion kilowatt-hours. The U.S. alone is expected to require at least 355,000
megawatts of new and replacement electrical generation within the next two decades, assuming
electricity demand grows at a modest rate of 1.5% per year, [EIA 2004].
US Past, Present and Forecasted Future Electricity Consumption
'^^^^
50000
i
.o
0
50000
,.m
40000
0.
E
30000-
r
120000
16
0
190
190
190
200
200
200
2
.U/
IL
10000
---
U'-
50
0
19 +
19,
1960
20
30
Year
Figure 1-1: US Electricity Consumption Projection [EIA]
In order to satisfy this incredible increase in electricity demand shown in Figure 1-1, the
nuclear industry has two available means with which to address this need. The first option,
construction of new nuclear power reactors, has been aggressively moving forward thanks to the
recent passage of the 2005 Energy Bill which implemented incentives recommended by [Ellis] in
August of 2004 and again by [Dominici] in November of that same year. This favorable
economic and political environment has allowed numerous utility companies, many of whom
had already applied for early site permit (ESP) licenses, to announce their intent to apply for
combined construction and operating licenses (COL) with recently certified reactor designs
(DC).
The second option available to address the impending need for additional electricity is to
increase the electricity output of existing reactor facilities. Since the industry has achieved an
average plant capacity factor of over 90% U.S. wide, efforts to improve the outage management
strategy of existing nuclear plants would likely only be able to achieve minimal increases in
electricity production. Investigation of existing plant component operating limits is also not
likely to uncover any significant abilities for higher electricity production capacity within the
same core design since this initiative has been continually pursued by the utility companies ever
since the NRC granted the first uprate license of 5.5% (140 MWt) to the Calvert Cliffs plant in
September of 1977. Almost 5 MWe in added capacity have been allowed over the years.
Therefore, the most promising remaining avenue with which to pursue higher electricity output
from existing nuclear plants is to develop improved core designs and components capable of
producing more electricity.
The improved core can increase electricity production by one or both of the following
strategies; increasing the number of fuel bundles per core (which implies a redesign of the
reactor vessel) and/or increasing the amount of power produced per bundle. Redesigning large
components like the reactor vessel is possible; however it could face manufacturing limits.
Advanced fuel designs, on the other hand, can be utilized with far less limitations. This thesis
pursues the development of advanced fuel designs, i.e. the development of high-performance
annular geometries which can achieve higher power densities and hence, higher electricity
output. It is theorized that utilities would be able to utilize this design through either retrofitting
of their existing reactor facilities or via incorporation of the advanced fuel design into new plant
orders.
1.2. Review of Previous Work on Annular Fuel for Reactor
Applications
Previous studies [Hejzlar et. al. 2001], [Xu et. al. 2004] and [Feng et. al. 2005] have
shown that 50% increases in power density for PWRs can be achieved with internally and
externally cooled annular fuel. This ability to uprate is primarily due to the significantly higher
fuel surface to volume ratio of the individual pellets. It was observed that the hot zero power to
hot full power reactivity loss was smaller for the annular fuel due to the lower fuel operating
temperature. It was also noted that the peak-to-average power ratio inside the pellet was smaller
and that there are two distinct rim regions, where plutonium build up will be higher than the
average; one rim region at each surface facing the moderator.
The core modeling simulations conducted in this study showed that the annular fuel cores
at 150% power density had lower fuel temperatures but equivalent moderator temperatures due
to the fixing of the power to flow ratio. However if U0 2 is used for the same cycle length, the
assembly will have to be enriched higher (-8%) than the current legal limit of 5 weight percent
U235 . This higher enrichment, due to increased total energy demand from a reduced fuel volume,
significantly affected several important core parameters. Most notably, the reactivity worth of the
assembly control rods decreased from hardening of the neutron spectrum. Therefore the annular
pins had to be loaded with increased amounts of burnable poison due to the study constraint of a
maximum core boron concentration of 1750 ppm (parts per million). Finally, it was observed that
even though the reactivity feedback effects were similar to that of the reference Westinghouse
17x17 solid fuel assembly, the shutdown margin was reduced. It was theorized that the ability to
stay at or below 5 weight percent enrichment would alleviate several of these concerns
associated with shutdown margin. Therefore, in part one this paper proposes swapping out the
UO 2 with higher density UN in order to stay below this 5% enrichment limit.
Stella Oggianu concluded in her CANES report [Oggianu 2001] that 95% smear density
uranium nitride seems to be the best practical option for once-through advanced nuclear fuel
cycles. Also, the relatively high absorption cross section of N1 5 was not determined to be a
problem with respect to parasitic absorption in materials enriched in U235 . The principal physical
and thermal attributes of both uranium dioxide and uranium nitride are summarized in the table
below.
Table 1-1: Physical and Thermal Pro•erties of U02 and UN
U0
(g/cm 3)
Theoretical Density
HM Atom Density (g/cm3)
Specific Heat (J/Kg K)
Melting Point (0C)
Thermal Conductivity (W/m K)
Linear Thermal Expansion Coefficient (10-6K-)
Swelling Rate (normalized to U0 2)
Fission Gas Release (normalized to UO2)
2
10.96
9.67
270 (at 2000 C)
UN
14.32
13.52
205 (at 280 C)
-2800
-2700
7.19 (at 2000C)
3.35 (at 1000 0C)
10.1 (at 9400 C)
1.00
1.00
4 (at 2000C)
20 (at 1000°C)
9.4 (at 1000 0C)
0.80
0.45
As shown above in Table 1-1, UN has several beneficial attributes over U0 2. The higher
theoretical and HM atom density allow the designer to pack in approximately 40% more uranium
atoms in an equivalent volume. This attribute has tremendous implications for the development
of advanced fuel designs since the integration of UN gives the enhanced ability to run the fuel
assemblies hotter and longer than current U0 2 designs. UN also has a smaller linear expansion
coefficient and swelling rate which helps with long term performance of the fuel. Furthermore,
the fission gas release is also believed to be markedly less than that of UO2. Finally, one of the
more unique attributes of UN is that the thermal conductivity of the material actually increases
with increasing temperature. The opposite trend of the UO2 gives the UN fuel tremendous
advantage in this respect. Figure 1-2 below shows a graph of precisely how the thermal
conductivity of UN depends upon temperature.
--
U
-I
-a
I-j
0
400
400
1200
TEMPERATIRE
1500
2000
PC)
Figure 1-2: Temperature Dependence of Thermal Conductivity for UN
If reprocessing were to be implemented, than enrichment in the N15 isotope would be
required due to the N' 4(n,p)C 14 reaction. The C14 product would have a significant impact upon
the environment if a radioactivity release were to occur and it is doubtful that a naturally
enriched nitride fuel would be accepted since it was the only material for which the dose
commitment in the gastrointestinal track was above current legal limits. Since it is obviously
desirable to enrich in the N 15 isotope questions regarding the economics arose. Presently, this
enrichment cost has been estimated at roughly $1000 per gram. Future development work may
help to decrease this cost to more economically acceptable levels. She concluded that the
principal concern facing the use of UN in LWRs today is its oxidation reaction with water.
Unfortunately as stated before, the materials database for uranium nitride (and
consequently gadolinium nitride) is quite small. Previously uranium nitride fuels were also
investigated for space applications in nuclear electric propulsion systems however recent
consultation with US national laboratories has indicated that no studies are currently being
performed. Presently only the research groups at the Japan Atomic Energy Research Institute
(JAERI) appear to be working with nitride fuels. They have started to assemble a materials
database and are currently developing economical fabrication and reprocessing technologies in
order to support their advanced fast reactors and transmutation of long-lived minor actinides
program [Suzuki 1998].
Internally and externally cooled annular fuel has also been investigated for BWR
applications as well. Annular arrays of 5x5 and 6x6 were previously investigated for their
potential to increase power density and it was determined that as much as a 18% uprate may be
achievable with a 6x6 annular geometry [Morra 2004]. The uprated 6x6 annular assembly was
also determined to have a 60% higher pressure drop across the core which has the possibility of
complicating the assembly hold down and vibrations of the fuel against spacer grids. It was
indicated that a vibration analysis should be conducted since this parameter might impose a limit
upon the ability of the annular assembly to uprate. This larger AP also means that significantly
larger recirculation pumps, able to handle the increased needed pumping power, would have to
be installed.
The neutronic differences between the solid 8x8 reference case and the annular 6x6 test
assembly were determined to be smaller than those of the previous PWR annular study
completed by Zhiwen Xu in 2004. Even though the annular fuel has a larger fuel surface to
volume ratio than the solid reference fuel, the effect of the significantly larger void fraction of
the coolant in the inner channels gives rise to a smaller adverse fuel surface effect than in PWRs.
The local peaking factors were comparable to that of the reference case and the neutronic penalty
of annular fuel was determined to be less for BWRs than for PWRs. Finally, under nominal
operating conditions the annular fuel assembly for the BWR exhibited a smaller fuel temperature
gain versus PWRs. This was mainly due to the fact that the annular fuel assemblies for BWRs
have a lower power density level than PWRs.
The study completed by Morra used the Hench-Gillis critical power correlation for all
analyses. This decision is problematic because Hench-Gillis is a bundle average correlation and
its use for an annular geometry, particularly for the inner annuli, is questionable. Thus, more
vigorous analysis is needed to more aptly model the annular geometry. Additionally, this study
also indicated some problems of obtaining VIPRE convergence for some of the annular designs.
In Appendix A the study documented an effect of the number of axial nodes on the calculated
CPR (critical power ratio). Therefore, in part two, this paper proposed the investigation of
annular fuel for BWRs with a more accurate heat balance CHFR correlation (EPRI-1 ReddyFighetti) rather than the modified Hench-Gillis CPR correlation which was used previously.
1.3. Objective of This Work
The primary objective of this thesis is to characterize and develop advanced highperformance annular fuel designs for both PWRs and BWRs. In particular for PWRs uranium
nitride fuel, instead of uranium dioxide fuel, was assessed in a 13x13 internally and externally
cooled annular fuel pin geometry. This objective was accomplished through three principal tasks.
First, determination if an equivalent fuel cycle length could be achieved with uranium nitride
fuel at an uprated power density as the nominal uranium dioxide fuel at 100% power density
without exceeding the current 5 weight percent licensing limit for fuel enrichment. Second,
determination of what corrections can be made to the CASMO neutronics code input deck in
order to accurately model the uranium nitride annular fuel at both 100% power density as well as
the uprated power density. Finally, the third task was a determination of what the relative
difference in reactivity swing was between an uprated 13x13 annular uranium nitride and the
17x17 solid reference uranium dioxide fuel assemblies. This task included a comparison of the
reactivity coefficients so that a comparison could be made between the annular geometry UN and
the solid pin geometry U0 2.
For boiling water reactors, it was desired to compare the best achievable designs for 5x5,
6x6 and 7x7 annular fuel pin geometries in order to determine from a thermal hydraulic
viewpoint how large of an uprate could be attained for an annular fuel geometry with uranium
dioxide fuel. This objective will be accomplished by first comparing different applicable critical
heat flux correlations in order to determine if a more accurate treatment of the annular geometry
than that of previous research efforts can be utilized. Secondly, the difference in the
thermodynamic properties of the flow between the inner and outer subchannels in the annular
assembly was characterized in order to understand how the CHFR was affected by these
parameters. Finally, the effects of varied grid coefficients on the inner and outer channels were
investigated for their ability to influence flow distribution so as to increase the minimum CHFR.
1.4. Organization of the Thesis
This thesis is organized into four main chapters. Chapter 1.0 (the current chapter) starts
by looking at the societal need for additional nuclear generated electricity at economic costs and
with enhanced safety margins. This is followed by a brief review of the previously completed
work on annular fuel for high power density reactor applications. Finally, the study objectives
and organization of the thesis round out this first chapter.
Chapter 2.0 focuses upon the utilization of uranium nitride fuel in an annular geometry
for high power density PWR fuel assembly designs. This chapter starts with the methodology for
how the study was conducted followed by a short overview of the analysis tools employed which
include MCODE and CASMO-4. These two parts are followed by a third which is comprised of
a short description of the geometries and other pertinent operating parameters for both the 17x17
reference and 13x13 annular test cases. The benchmark analysis of both the solid reference fuel
and the annular test fuel delineates the need for a correction factor for the CASMO-4 input deck.
This total assembly-wide correction factor is established by determining an appropriate
correction factor for each of the annular fuel assemblies constitutive parts (namely the poisonfree pin and the poisoned pin) and then combining them together into a full poisoned annular
assembly.
Chapter 3.0 focuses upon the utilization of uranium dioxide fuel in three different annular
geometries for high power density BWR fuel assembly designs. First the methodology for how
the study was conducted is introduced, followed by the second section which provides a short
overview of the VIPRE thermal hydraulics analysis code along with a discussion of the reasons
for the selection of each correlation used. This is followed by a short description of the
geometries and other pertinent operating parameters for both the reference and annular test cases.
Finally, the trial calculations and comparisons of all reference and test fuel assemblies along with
some brief observations of the results are presented at the end of this chapter.
Chapter 4.0 delineates summary of conclusions and recommendations for future work
from the completed analyses contained within Chapter 2.0 and Chapter 3.0 of this thesis.
2. Uranium Nitride Annular Fuel for PWR Applications
2.1. Methodology
The methodology for this chapter of the thesis is relatively straightforward. Both the solid
reference fuel and annular test fuel were benchmarked in CASMO-4 against MCODE results
where a discrepancy was found for the annular fuel. This discrepancy can be best explained by
the lack of appropriate treatment for the resonance absorption in UO 2 at the interior channel of
the annular fuel. Since Studsvik of America considers the CASMO-4 source code to be
proprietary, a correction factor was needed to be applied directly to the input file. In order to
establish this correction factor, the annular assembly was broken down into its constituent pieces
(poison-free fuel pins and poisoned fuel pins) so that an appropriate correction factor could be
determined for each piece. These constituent pieces were then brought back together into a
13x13 array so that the correct assembly level correction factor could be determined for the
CASMO-4 input deck.
2.2. Analysis Tools
2.2.1. MCODE
MCODE or MCNP-ORIGEN DEpletion program was developed at MIT in 2003 by
Zhiwen Xu [Xu 2003]. This code couples the continuous energy Monte Carlo code MCNP-4C
with the one-group point depletion code ORIGEN-2.1 in order to perform burnup simulations.
Figure 2.1 shown below delineates the flow of calculations for the MCODE-1.0 program. As can
be seen from the figure MCODE alternately executes MCNP-4C and ORIGEN to simulate
burnup using a standard predictor-corrector algorithm. Initially the MCNP simulation is run to
calculate the neutron flux and effective one-group cross sections for the burnup regions of
interest. This information is then fed into an automatically generated ORIGEN input deck which,
in turn, carries out multi-nuclide depletion simulations for each burnup region of interest. This
information output from ORIGEN is then used to generate updated material compositions in a
new MCNP input deck which is rerun. To use MCODE only two input files are needed, a MCNP
input file which appropriately defines the geometry and material composition of the problem and
a MCODE input file which defines how and what, within the MCNP input, is to be depleted. An
equilibrium MCNP source file may also be used in order to speed up calculation time.
Parse MCODE input and initialize variables
NO (restart)
Initial run?
YES
Preprocess initial mcnp input and run MCNP
mcn
oop
to
I EIE"
" I II" E II II • I l
II
L
throu
h
all
timeste
p
"II
'J
s
Extract beginning-of-timestep cross-sections and flux values
Run ORIGEN depletions for all active cells
Update MCNP input based on ORIGEN output material
composition (predictor), and run MCNP
Predictor-Corrector?
NO
NO
YES
Extract end-of-timestep cross-sections and flux values
Re-run ORIGEN depletions for all active cells
Average the predictor and corrector material, update
MCNP input, and re-run MCNP
NO
Finish all timesteps?
YES
END
Figure 2-1: Flow of Calculation in MCODE-1.0 [Xu 20031
The MCODE burnup simulation program considers two main groups of nuclides in its
calculations: actinides and fission products. Both groups represent important contributions to the
fuels properties during the burnup lifetime. The actinides as defined in this program are heavy
metal nuclides with atomic numbers equal to 90 or higher plus their associated daughter decay
products. These actinides provide a non-negligible number of fission source neutrons and
subsequent source of fission neutrons. MCNP corrects for the following reaction rates of the
actinides; capture, fission, (n,2n) and (n,3n). Since the fission products only represent a nonnegligible source of absorption, only the neutron capture cross section is corrected for by MCNP.
MCODE only incorporates those nuclides which significantly contribute to the fission source
neutron population and neutron interaction cross sections. So, in order to conduct a rigorous
burnup simulation the contributions from those nuclides defined as non-significant would be
taken into account.
2.2.2. CASMO-4
CASMO-4 is part of the Studsvik Core Management System (CMS) code package
developed by Studsvik Scandpower Inc. which also includes TABLES-3 and SIMULATE-3. It is
a multi-group two-dimensional deterministic transport theory code written in Fortran 77 which is
used to model the burnup behavior of LWR fuel. This code is capable of modeling cylindrical
geometries of arbitrary compositions in either a square or hexagonal lattice. Unless explicitly
specified, the code assumes several parameter values typical of existing LWRs. For instance if
the moderator temperature is higher than 523 K then the default core pressure of a PWR is set to
15.5 MPa [Edenius et. al. 1995]. Providing that the fuel to be modeled is relatively similar to that
of existing LWR fuel, even a fairly complex poisoned assembly can be formulated in
approximately 30 lines of code. Figure 2.2 below shows the flow of calculations for the
CASMO-4 program.
Restart file
---------Data library
Data library
--
Card Image file
Burnup
Figure 2-2: Flow of Calculations in CASMO-4 [Knott et. al. 19951
As shown in the flow diagram CASMO-4 starts by calculating the effective resonance
energy region cross sections for the resonance absorbers of interest by utilizing an equivalence
28
theorem which identifies a homogenous problem which closely relates to the heterogeneous
problem at hand. The homogenous resonance integrals are recorded in the neutron data library as
functions of potential temperature and cross section. The effective absorption and fission cross
sections are calculated by the effective resonance integrals which were determined by
interpolating from the homogeneous resonance integrals from a square root dependence of
potential temperature and cross section. Dancoff factors, which are calculated by CASMO,
account for the shielding effect between different pins within the problem.
Following the resonance calculations, the data for the microscopic group cross section is
created for each specific condition and spatial region. A micro group calculation is then
performed for each individual pin type in the problem using the macroscopic group cross
sections in order to determine the detailed neutron energy spectra which are subsequently
condensed into macro groups. The two-dimensional macro group calculation is then carried out
utilizing an approximate fast response matrix method. The neutron spectra for the energy
condensation of cross sections data obtained from this calculation is then input into the twodimensional transport calculation to obtain the eigenvalue and flux distribution in the problem. In
the case where the problem consists of only one fuel assembly, the fundamental buckling mode
is used to include the leakage effect by modifying the infinite lattice results.
An isotopic depletion calculation is performed in each fuel pin and burnable absorber
region. These burnup calculations in CASMO-4 also incorporate a predictor-corrector approach.
This approach means that the depletion is calculated twice for each burnup step, initially
predicting by using the spectra at the start of the step and finally correcting by using the newly
calculated spectrum at the end of the step. Then the average number densities from these two
steps are used as the starting values for the subsequent burnup step. This algorithm represents a
widely accepted method for carrying out these sorts of calculations since sizable burnup steps
can be used without compromising any accuracy. The version of CASMO-4 used at MIT does
not utilize any pseudo fission products because it traces fission products explicitly by using
extended heavy nuclide chains and fission products from the neutron data library J2/E6. This
library was created from the data from both ENDF/B-6 from Brookhaven National Nuclear Data
Center and JEF-2.2 from OECD/NEA data bank which contains 70-group microscopic cross
sections, decay constants and fission yields for 305 different isotopes.
2.3. Description of Geometries Analyzed
Figure 2.3 depicts a unit cell model of both solid pin from the 17x17 reference assembly
and an annular pin from the 13x13 test assembly.
Figure 2-3: Pictorial Representation of Unit Cell Models
In all of the benchmark calculations the uranium was enriched to 5 weight percent and 10
weight percent Gd 20 3 was assumed in the poisoned pins. The solid U0 2 reference case used a
98% theoretical density of 10.4 g/cm3 in the poison-free pins and 10.0374 g/cm 3 in the poisoned
pins. The annular UN test case used a 98% theoretical density of 14.0336 g/cm3 in the poisonfree pins and 13.4045 g/cm3 in the 10 weight percent GdN poisoned pins. A value of 104.5 kW
per liter-core was used to specify the 100% reference core power density level. The temperature
of the fuel was assumed to be 900 K for the solid reference fuel and 600 K for the annular test
fuel. The temperature of the moderator was the same for both cases at 583.1 K. Equivalent
geometrical constraints were also imposed on the 13x13 annular design such as the assembly
height, width and length. The following table displays the key cold dimension design parameters
for both the 17x17 solid reference case as well as the 13x13 annular test case.
Table 2-1: Geometric Design Parameters for Investi ated Fuel Assemblies
Pin Outer Radius (cm)
Outer Clad Inner Radius (cm)
Fuel Outer Radius (cm)
Fuel Inner Radius (cm)
Inner Clad Outer Radius (cm)
Pin Inner Radius (cm)
Pin Pitch (cm)
17x17 Solid Fuel
0.4761
0.4191
0.4122
1.2626
13x13 Annular Fuel
0.7684
0.7112
0.7050
0.4950
0.4888
0.4317
1.6510
2.4. Benchmark Analysis
2.4.1. MCODE/CASMO-4 Comparison
MCODE is based upon the stochastic Monte Carlo method, thus given sufficient
computing power and time, an exact solution can be found for the neutron transport equation.
However, this capability comes with an expensive (from both a time and money perspective)
price; each assembly depletion simulation takes roughly 2 days to calculate utilizing 4 nodes on a
supercomputing 20 node Beowulf cluster. Faster means of obtaining the desired solution were
needed. The deterministic CASMO-4 transport code is capable of solving the equivalent problem
in less than 2 minutes. However before the switch can be made, the results must be benchmarked
against the existing Monte Carlo standard to ensure that the problem is appropriately simulated.
In particular, the treatment of U238 absorption in the resonance region is restricted in CASMO-4
to the solid cylinder. Thus, the effect of the internal surface in the annular fuel is not accounted
for. Without the internal surface, the U238 absorption will be underpredicted in CASMO-4.
The reactivity limited burnup versus EFPD (effective full power days) as calculated by
both MCODE and CASMO-4 for the 17x17 solid UO 2 reference fuel model is shown below in
Figure 2.4.
MCODE/CASMO-4 Calculated Elgenvalues versus EFPD
for Solid 17x17 Reference Case Full Poisoned Assembly
* CASMO
-
0
200
400
600
800
1000
1200
1400
1600
1800
MCODE
2000
EFPD
Figure 2-4: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for 17x17 Solid UO2
Assembly
As can be seen from Figure 2.4, the calculated infinite multiplication factor for the solid
17xl 7 reference assembly demonstrates satisfactory agreement. This result is expected since
CASMO-4 has been tailored to provide accurate results for solid rod PWR fuel assemblies. This
calculational procedure was then repeated for the annular 13x13 UN test assembly and plotted
below in Figure 2.5.
MCODE/CASMO-4 Calculated Elgenvalues versus EFPD
for Annular 13x13 Test Case Full Poisoned Assembly
1.3
-1
1.2
44,,
C
- CASMO-4
L MCODE
S1.1
' -- -
----.
"
......
• .•--22Z
...•.
0.9
0
200
400
600
800
1000
1200
1400
1600
1800
2000
EFPD
Figure 2-5: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for 13x13 UN Annular
Assembly
Unlike the solid 17xl 7 reference case, the infinite multiplication factor calculated by
CASMO-4 is not in satisfactory agreement with the MCODE result. In order to better illustrate
this variation between the solid and annular fuel, the differences in the eigenvalue determined by
CASMO-4 and MCODE are plotted below in Figure 2.6 for both assemblies.
Eigenvalue Differences between MCODE and CASMO-4
__r
U.Uo
0.04
0.03
a
O
0.02
<K--
----
~ ~
'~'~-----·-.~.
~
----------
-.- Solid 17x7
m- Annular 13x13
0.01
,,-
0
-0.01
0-0
Y~~
0
200
400
600
800
1000
1200
1400
1600
1800
2000
EFPD
Figure 2-6: Eigenvalue Differences between MCODE and CASMO-4 for a 17x17 Solid U0 2 Assembly and a
13x13 UN Annular Assembly
The solid fuel eigenvalue difference (represented by the blue line) shows excellent
agreement between the two codes. On average over the fuel lifetime, CASMO-4 overestimates
the eigenvalue by less than 0.4%. For the annular case however (represented by the pink line)
CASMO-4 dramatically overestimates the reactivity at the BOL (beginning of life) and
underestimates the reactivity at the EOL (end of life). The principal cause of this significant
variation is due to the fact that CASMO-4 is optimized for solid pin geometry; hence it
underestimates the amount of U238 captures by applying self shielding within the solid pellet and
not taking into account the additional captures which occur near the fuel surface in the inner
annulus. This inability to account for the additional captures explains both the overestimation at
the BOL from the excess neutrons which were not absorbed in the U238 and the underestimation
at the EOL from the lack of appropriate Pu239 formation. The mechanism by which the Pu239 is
formed from U238 is shown below:
U 238 +.n-+ U 239
-
N
2 39
8L-
Pu 239
This formation is non-negligible since in a typical PWR the Pu2 39 fissions account for roughly
40% of the energy produced in the reactor.
2.4.2. CASMO-4 Pseudo-Solution for Annular Fuel
In order to be able to utilize CASMO-4 to simulate the annular fuel assembly some sort
of an adjustment needed to be applied to the code in order to correct for the underestimation of
the U238 resonance captures. Since Studsvik of America considers the CASMO-4 source code to
be proprietary, making a direct change to the code itself was impossible. Instead a correction
factor was needed to be applied to the input deck directly. Previous work [Xu et. al. 2004] has
investigated a wide variety of correction factors which were applied to CASMO-4 as input
including a reduction in the coolant density, an increase in the U238 number density and the
addition of hafnium. It turned out that an artificial increase of the U238 number density in the
input deck achieved the closest agreement with the MCODE results. This is because the
correction most appropriately accounts for the discrepancy over the fuel's life since the excess
U238 atoms absorb the appropriate number of neutrons near the BOL and produce a suitable
amount of plutonium near the EOL. A reduction in the coolant density introduces error in several
other areas by significantly hardening the neutron spectrum and the addition of hafnium, while
appropriately mimicking the U2 38 captures, doesn't accurately predict the Pu 2 39 formation (and
hence the reactivity) at the EOL.
2.5. Poison-free Pin Cell Correction
It is important to point out that this correction factor is optimized for the particular
enrichment, assembly pin layout, selection and weight percent of burnable poison in this specific
problem. The exact value of the U238 correction factor will change with variance of any of the
aforementioned parameters for new annular problems. Also this correction factor does have
implications for the determination of some of the reactivity coefficients. Therefore, this
correction factor should only be used when the solution for the average core with average fuel
enrichment is sufficient. In order to obtain the closest approximate answer for the U238 correction
factor, the input adjustment deck will first be created for a poison-free pin cell, then for a 10
weight percent GdN poisoned pin cell and finally for an entire 13x13 poisoned annular test
assembly.
This pseudo-solution has been previously investigated for UO 2 and it was shown that an
artificial increase of 20% was needed in the poison-free pin. Figure 2.7 below shows the infinite
multiplication number versus effective full power days for the 50% uprated UN poison-free pin
cell in both MCODE as well as in the corrected CASMO-4.
MCODE vs Corrected CASMO-4 for poison-free pin cells
5% Enriched UN Annular Fuel Pin
150% Power Density and 98% Theoretical Density
0
500
1000
1500
2000
2500
3000
EFPD
Figure 2-7: MCODE/Corrected CASMO-4 Eigenvalue versus EFPD for a Poison-Free Annular Fuel UN Pin
After a wide range of U238 number density additions were experimented with it turned out
that a 25% addition of U 238 number density provided for excellent agreement between the two
codes. Figure 2.8 shows how the differences in eigenvalue, as calculated by the corrected
CASMO and MCODE inputs, change with burnup.
Eigenvalue Difference for a CASMO-4 Corrected
Poison-Free Pin Cell by Increasing U-238
at 150% Power Density and 98% Theoretical Density
0.05
0.04
0.03
0.02
0.01
-260
0
*
-
.200
400
600
800
1000
1200
1400
120_
400
600
800
1000
1200
1400.
i-O0
-.......
800 .......
-0.01
-0.02
EFPD
Figure 2-8: Eigenvalue Differences between MCODE and Corrected CASMO-4 for a Poison-Free UN Pin
Cell
Comparison of the 0.2% average eigenvalue difference achieved in Figure 2.8 with the
larger swing exhibited in Figure 2.6 verifies that the selection of a 25% increase in number
density was accurate. Since the intent of this project is to accurately simulate the annular fuel
assembly over its entire lifetime, more than just a suppression of the reactivity at BOL is needed.
The plutonium production potential of the annular assembly, which becomes increasingly
important at high burnup, was also tracked as a function of burnup in order to ensure accurate
simulation of this assembly near the EOL.
Plutonium Composition versus Burnup as
Calculated by MCODE and Corrected CASMO-4
for a Poison-Free Pin Cell at
150% Power Density and 98% Theoretical Density
1.00E+22
1.00E+21 I
C
i
·
---- ------
-----
------
---
-
l-
/-------(
1.00E+20
C
* 1.OOE+19
-----
-+- CASMO
•-- MCODE
I
1.OOE+18
1.00E+17
i
1II__
1000
1500
2000
'
2500
EFPD
Figure 2-9: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected CASMO-4 for a
UN Poison-Free Pin Cell
Figure 2.9 demonstrates that the 25% U238 number density addition effectively tracks the
Pu 239 formation over the fuel lifetime. This handling of the Pu 239 formation allows for an
adequate treatment of the annular assemblies reactivity, especially near the EOL.
2.6. Poisoned Pin Cell Correction
Normal Westinghouse PWRs utilize an IFBA (thin layer of B'l coated onto the fuel pellet
surface) for their burnable poison. Other options for burnable poison include either Erbia or
Gadolinia mixed homogenously with the fuel. As shown below in Figure 2.10, the Gadolinia has
an absorption cross section two orders of magnitude larger than B10 at thermal energies. Also,
due to the significantly higher expense of Erbium and questions regarding whether or not the
IFBA coating could be applied to the inner annulus, Gd was selected for the annular assemblies'
burnable poison.
4 tlE+F
1.OE+DS
I 1.0E+03
1.0E+02
1.0E+00
0.001
0.01
0.1
1
Energy (eV)
Figure 2-10: Cross sections of various nuclides in the Thermal Energy Range [Driscoll 1991]
As previously mentioned in Section 1.2, the materials database for gadolinium nitride is
quite small. Presently the only research group working to establish a materials database and
address fabrication issues associated with nitride fuels is at JAERI [Suzuki 1998]. Although
these fabrication and material database issues are outside of the scope of this current research
effort, they will need to be addressed in the future before integration into advanced fuel designs
can take place.
2.6.1. Self-shielding Factor Correction
For the poisoned pin cell simulation the GdN was assumed to be uniformly mixed with
the UN fuel in the pin. However because Gadolinium is known as a "black" absorber, it burns
out in layers. This trait caused a slight difficulty initially with MCODE because the burnup
region was being re-homogenized between each depletion time step. This problem was
circumvented by separately defining 10 equi-volume cylinders within each poisoned fuel pin so
that each "layer" could be treated independently. This significantly increased computation time
however it was necessary in order to accurately capture the effect of the burnable poison.
2.6.2. Multiplication Factor Tracking with Burnup
As pointed out in the beginning of Section 2.5 the introduction of Gadolinium into the
fuel pin necessitated a revalidation of the U238 number density correction factor for the poisoned
pins. Figure 2.11 below shows the infinite multiplication number versus effective full power
days for the 50% uprated UN GdN poisoned pin cell in MCODE and corrected CASMO-4.
MCODE vs Corrected CASMO-4 for a 10wt% GdN poisoned pin cell
5% Enriched UN Annular Fuel Pin
150% Power Density and 98% Theoretical Density
500
1000
1500
2000
2500
3000
EFPD
Figure 2-11: MCODE and Corrected CASMO-4 Eigenvalue versus EFPD for a 10wt% GdN Poisoned UN
Annular Fuel Pin
Again a wide range of U238 number density correction factors were experimented with.
However it was determined that 35% increase in U238 number density gave the closest agreement
with the MCODE derived results. The improvement in agreement between MCODE and
CASMO-4 is further shown below in Figure 2.12.
Eigenvalue Difference for a CASMO-4 Corrected
Poisoned Pin Cell by Increasing U-238
at 150% Power Density and 98% Theoretical Density
0.05
0.04
0.03
0.02
-
.--
,
0.01
0
P
-0.01
-0.02
---
200
200
----
400 . ......
800
600
400
·
-
.-.
-
600
-
---
800
1000
1000
------
1200
1200
--
1400
1400
1800
1600
~160
.....
80
____----------·-·--.__________ __.___.._
___-------------·~-
-
2 kI0
2(
i
-0.03
I
-0.04
-0.05
EFPD
Figure 2-12: Eigenvalue Differences between MCODE and Corrected CASMO-4 for a 10wt% GdN Poisoned
UN Pin Cell
2.6.3. Gadolinium Tracking with Burnup
Figure 2.13 below shows the total cross section for Gadolinium isotopes 152, 154, 155,
156, 157, 158 and 160 which were represented by the red, green, blue, purple, light green, brown
and light red colored lines respectively. Although the Gadolinium utilized in the poison was at
natural enrichment, only Gd-155 (blue) and Gd-157 (light green) were tracked due to the
relatively insignificant absorption cross sections of the other isotopes.
~
11111111 I I I I 111
111111 I 11111111 I 11111111 I
I
11111111 I
1111111 I
1111111 I
11111111 I
1111111
185
184
1.1.
i
'Iii
3
0
1%
11
0
0
18
0
5
-12
I
ii 59
I
I
IIIII
1
I
8
I
IIIIII
I
7
16
I
I
IIIId
10
I
6
I
IIIIII
I
16
5
I
I
IIIII
15
I
I
I
IIIII
4
1
I
3
I
IIIIII
I
162
I
11
Energy (MeV)
Figure 2-13: Total Cross Section for Gadolinium Isotopes
11
16
Gadolinium Composition versus Burnup
as Calculated by MCODE and Corrected CASMO-4
for a 10wt% GdN Poisoned Pin Cell
at 150% Power Density and 98% Theoretical Density
1.0E+21
1.00E+20
0
-A--Corrected CASMO-4 Gd-155
. Corrected CASMO-4 Gd-157
1.00E+19
-*-
MCODE Gd-155
---
MCODE Gd-157
1.00E+18
1.00E+17
0
500
1000
1500
2000
2500
3000
EFPD
Figure 2-14: Gadolinium Composition versus Burnup as Calculated by MCODE and Corrected CASMO-4
for a 10wt% GdN Poisoned UN Pin Cell
The Gadolinium composition was also tracked in order to ensure that adequate treatment
of the burnable absorber was being observed. As shown in Figure 2.14 the introduction of the
U238 correction factors allowed for an appropriate tracking of the two important isotopes of
Gadolinium. The computationally intensive nature of MCODE allowed for the completion of a
certain number of points, although additional data points, particularly around dynamic features of
the graph such as between 1100 and 1600 EFPD for the Gd' 55 , would likely show increased
agreement between the two codes.
2.6.4. Plutonium Tracking with Burnup
Plutonium Composition versus Burnup as
Calculated by MCODE and Corrected CASMO-4
for a 10wt% GdN Poisoned Pin Cell at
150% Power Density and 98% Theoretical Density
1.00E+22
1.00E+21
e9 1.00E+20
--
a
CASMO-4
- MCODE
1.00E+19
1.00E+18
1.00E+17
500
1000
1500
2000
2500
EFPD
Figure 2-15: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected CASMO-4 for
a 10wt% GdN Poisoned UN Pin Cell
Figure 2.15 demonstrates that the 35% U238 number density addition effectively tracks
the Pu239 formation over the fuel lifetime. Now that an adequate correction factor has been
determined for the poisoned fuel pins, the correction factors can be combined together to form a
full 13x13 poisoned annular fuel assembly.
2.7. Correction for Fully Poisoned Assembly
The fully poisoned 13x13 annular UN assembly has 9 guide tubes and 160 fuel pins total;
16 of which are poisoned with 10% GdN by weight. The pin distribution is given below in
Figure 2-16.
0
Pisen-Free Pin
O
Pienedm lPh
0
Guide Tube
Figure 2-16: Fully Poisoned 13x13 Annular PWR Fuel Assembly
Each fuel pin has an outer radius of 0.7685 cm and an inner radius of 0.4315 cm with a
0.0575 cm thick Zircaloy-4 cladding and a 0.006 cm gap. The pitch of the pins was taken to be
1.651 cm. In order to stay within the design envelope of existing PWR fuel, the assembly pitch
was held constant at 21.50 cm and the overall fueled length was kept at 3.66 m. The moderator
temperature assumed to be 583 K while the fuel outer surface temperature was set at 600 K.
2.7.1. Multiplication Factor Tracking with Burnup
MCODE vs Corrected CASMO-4 for a Full Poisoned Assembly
5% Enriched UN Annular Fuel Pin
150% Power Density and 98% Theoretical Density
--
--
0
200
400
600
800
1000
1200
1400
1600
Corrected CASMO-4
MCODE
0
1800
200 0
EFPD
Figure 2-17: MCODE/Corrected CASMO-4 Eigenvalue versus EFPD for a Poisoned 13x13 UN Annular
Assembly
Figure 2.17 shows a plot of the MCODE and corrected CASMO-4 simulations of a full
poisoned 13x13 annular fuel assembly. A quick comparison of Figure 2.5 with Figure 2.17
shows significant improvement in the ability to simulate annular fuel's reactivity over its
lifetime. The plutonium production potential is plotted below in Figure 2.18.
2.7.2. Plutonium Tracking with Burnup
Plutonium Composition versus Burnup
as Calculated by MCODE and Corrected CASMO-4
for a Full Poisoned 13x13 Annular Assembly
at 150% Power Density and 98% Theoretical Density
1.00E+22
1.00E+21
1.00E+20
-*- Corrected CASMO-4
-*-MCODE
1.00E+19
____
1.00E+18
1.00E+17
0
500
1500
1000
2000
2500
EFPD
Figure 2-18: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected CASMO-4 for
a Full Poisoned 13x13 Annular UN Fuel Assembly
As expected from the previous sections, Figure 2.18 confirms that the U238 number
density correction factors determined for the poison-free and poisoned fuel pins, 25% and 35%
respectively, allow for the appropriate formation of Pu2 39 over the lifetime of the fuel.
2.8. Final Uprated Design Comparison
K-inf versus EFPD for both a
17x17 Solid Reference UO2 Fuel Assembly at 100% Power Density
and a 13x13 Annular UN Fuel Assembly at 150% Power Density
1.3
1.25
1.2
1.15
.--. ....
1.15
__
* 17x17 Solid Reference
* 13x13 Annular
1.05 -
0.95
-
0.85
0.8
0
200
400
600
800
1000
1200
1400
1600
1800
2000
EFPD
Figure 2-19: Multiplication Factor versus EFPD for a 17x17 Solid Reference U02 Fuel Assembly at 100%
Power Density and a 13x13 Annular UN Fuel Assembly at 150% Power Density
Assuming 3%loss to leakage (depicted as the black line in the above figure), the
multiplication factor versus EFPD is plotted for both the 17x17 solid reference case with U0 2
fuel enriched to 5%at 100% power density and for the 13x13 annular case with UN fuel
enriched to 5%at 150% power density.
The reactivity coefficients at BOL for both the 17x17 solid U0 2 fuel reference assembly
at 100% power density and the 13x13 annular UN fuel assembly at 150% power density are
summarized in Table 2-2 below. For a summary describing the operational ranges utilized in
CASMO-4 to determine these reactivity coefficients, please refer to Appendix A.
Table 2-2: BOL Reactivity Coefficients for 17x17 Solid and 13x13 Annular
FTC (1/K)
MTC (1/K)
Boron Worth (Ap)
Void Coefficient (1/%void)
17x17 UO 2
13x13 UN
Reference
Annular
-2.505E-5
-2.382E-4
6.320E-2
-7.249E-4
-2.436E-5
-3.573E-4
4.358E-2
-1.084E-3
Even though the Doppler coefficient depends mostly upon the temperature (i.e. power
level) and composition (i.e. depletion) of the fuel, the fuel temperature coefficients for both the
17x17 reference and the 13x13 annular are found to be quite similar. This demonstrates that the
10% reduction in fuel volume coupled with the change from UO 2 to UN did not have a large
impact upon the feedback coefficient. Also, since the soluble boron has a positive effect on the
MTC, the critical boron concentration is a limiting factor in PWR design. Thus, it is favorable to
have a relatively comparable MTC to that of existing PWR assemblies. The approximately 30%
higher MTC for the annular fuel is consistent with the 25% higher MTC observed in previous
studies with this fuel type [Xu et. al. 2003]. The higher U235 content also gives rise to a harder
spectrum which in turn leads to a smaller boron worth and degradation of the shutdown margin.
This degraded shutdown margin could be overcome by increasing the number of control rods
and/or increasing the effectiveness of the control rod absorber materials.
As shown above in Figure 2.19, the 5% enriched UN annular-fuel assembly operating at
150% power density reaches the minimum multiplication factor of 1.03 in about 50 effective-
full-power-days after the nominal 17x17 solid-fuel-pin assembly that operates at 100% power
density. Additionally, the 13x13 annular fuel assembly is easier to control due to the smaller
reactivity swing over the fuel lifetime. Thus, it is concluded that an annular uranium nitride
assembly at 150% power density can be designed so as not to require enrichments above 5%in
order to reach the desirable cycle length of 18 months.
3. Investigation of Annular Fuel for BWR Applications
3.1. Methodology
The methodology for this section also follows a logical progression. First, a comparative
analysis of the available correlations for critical heat flux versus a critical power correlation will
be conducted in order to decide on the best approach to conduct the study. Second, a description
of the solid rod reference assembly and annular fuel possible assemblies will follow. This design
description will be augmented with a discussion of the limitations on the annular rod design
space which provides compelling arguments for why the annular geometries were limited to the
5x5, 6x6 and 7x7 designs. The subsequent section (broken down by individual design) displays
the results of the conducted fuel assembly optimization studies. Finally, a brief summary section
discusses the relative capabilities of each annular fuel assembly design with respect to the solid
reference case.
An additional noteworthy point is that for all of these analyses, only the hot assembly was
simulated. Technically for a comprehensive thermal hydraulic analysis of the fuel design, a full
core model should be constructed and run in order to ensure the accuracy of the calculations.
However due to the fact that the design is limited by the hottest assembly, it was decided that the
additional computational time spent simulating the other "cooler" assemblies was not justified in
this preliminary scoping study. Furthermore, BWR fuel assemblies have an exterior shroud
around the pin bundle and effects from neighboring assemblies are negligible except for at the
inlet and outlet where common plena are shared.
3.2. Analysis Tools: VIPRE Thermal Hydraulics Code
The VIPRE thermal hydraulics analysis code was selected for this research study because
of several factors. Since this study investigated new and innovative fuel geometries, it was
important to utilize a tool which has been extensively used and revalidated by practicing
engineers in the nuclear field. Implied in the definition of wide acceptance by the nuclear field, is
that the code is numerically stable with a robust thermal hydraulics model which includes the
most recent CPR/CHFR correlations. Furthermore, the ability to simulate the required thermal
hydraulic parameters for an internally and externally cooled annular geometry directed the
selection of the VIPREOlmod02 code.
VIPRE, or Versatile Internals and component Program for Reactors; EPRI, computes the
3-D velocity, pressure and thermal energy fields as well as the fuel rod temperatures for singleand two-phase flow in both BWRs and PWRs. It accomplishes this by solving the finitedifference equations for mass, energy and momentum conservation in an interconnected array of
subchannels while operating under the assumption of incompressible thermally expandable
homogeneous flow. This homogeneous equilibrium model or HEM utilizes a set of void-drift
correlations which allow for more accurate simulation of two phase flow phenomena. The code
incorporates the following primary assumptions [Stewart 1989]:
1. The low velocity of the coolant dictates that the kinetic and potential energies are
negligible when compared to the thermal internal energy of the system.
2. The work imparted on the system by either body forces or shear stresses is negligible
when compared to the convective energy transport and the surface heat transfer
contributions in the energy equation.
3. The heat conduction through the fluid surface is negligible when compared to the
convective energy transport and the heat transfer from solid surfaces.
4. With the exception of subcooled boiling, all phases are assumed to be in thermal
equilibrium.
5. In the momentum conservation equation the only significant body force is that of gravity.
6. The viscous shear stresses between fluid elements are negligible when compared to the
drag force on solid surfaces.
7. The density and transport properties vary only with local temperature due to the adoption
of the incompressible thermally expandable homogeneous flow model.
3.2.1.
Flow Modeling
Under the assumptions of homogeneous two phase flow model (HEM), the
thermodynamic properties for each phase are homogenized as a mixture in which both the liquid
and vapor phases travel with the same velocity. This assumption proves accurate for situations
involving high pressure and mass velocities; however the assumption breaks down for problems
with low pressures and mass velocities. In order to correct the HEM the following modifications
were made:
Subcooled Void Correlation - As suggested by the VIPRE manual, the EPRI correlation for the
subcooled void fraction was employed. This correlation uses heat transfer from a hot wall to
model the non-equilibrium transition from a single phase liquid to a two-phase boiling flow.
More specifically, the two-phase mixture actual flowing quality and bulk temperature for the
liquid (which can still be subcooled) is calculated in this correlation.
Bulk Void/Quality Correlation - As suggested by the VIPRE manual, the EPRI correlation for
the bulk Void/Quality was employed. This correlation predicts the subcooled void fraction from
the local quality.
Two-phase Friction Multiplier Correlation - As suggested by the VIPRE manual, the EPRI
correlation for the two-phase friction multiplier was employed. This correlation modifies the
momentum conservation equation by taking into account the influence of the non-homogeneities
in the two-phase flow field on the pressure drop.
3.2.2.
Heat Transfer Correlations
In VIPRE, the heat transfer correlations are utilized to calculate the rate of heat transfer
for one location to the adjacent one. Since each correlation is only accurate for a specified range
of operational conditions, appropriate heat transfer correlations were selected for each of the four
main sections of the boiling curve; single-phase forced convection, subcooled and saturated
nucleate boiling, transition boiling and film boiling. The correlation selection was mainly
influenced by its prior validation over the operational range of interest. The selected correlations
are:
Single-Phase Forced Convection Correlation - The Dittus-Boelter correlation
Subcooled Nucleate Boiling Correlation - The Chen correlation
Saturated Nucleate Boiling Correlation - The Chen correlation
Critical Heat Flux Correlation - The EPRI correlation
Transition Boiling Correlation - The Condie-Bengtson correlation
Film Boiling Correlation - The Groeneveld 5.7 correlation
3.2.3.
CHFR Correlations
The critical heat flux can be defined as the conditions at which the heat-transfer
coefficient of the two-phase flow substantially deteriorates [Todreas and Kazimi 1990]. In
systems with a constant heat flux, the onset of CHF causes a rapid rise in the temperature of the
wall. In systems where the temperature of the wall is constant, the onset of CHF leads to a rapid
decrease in the heat flux at the surface.
This CHF phenomenon can occur via two different mechanisms depending upon the flow
quality of the two-phase mixture. When CHF occurs at low quality (where most of the two-phase
mixture is in liquid form) the bubble formation is rapid enough to cause a continuous vapor film
to form at the heated surface. Historically this has been referred to as DNB or departure from
nucleate boiling. When CHF occurs at high quality (where most of the two-phase mixture is in
gaseous form) the shear action of the vapor and the local vaporization rate leads to a stripping of
the thin liquid film from the heated wall surface via entrainment and evaporation. This
occurrence where the thin liquid film at the heated surface in annular flow completely depletes
has traditionally been referred to as dryout. The latter of the two CHF mechanisms is the
predominant concern in BWRs and was the main focus of this analysis.
Safety limits on CHF for operating reactors is set by the minimum value of the CHFR,
which is defined as:
CHFR = qcritica
q"(z)
(3.1)
where q"g•i~a is the critical heat flux and q"(z) is the local heat flux at the axial position of
interest along the length of the fuel bundle. Today BWR safety analysis is dominated by the use
of the CPR which is defined as:
CPR =
P
crical
(3.2)
operating
where Pcticalis the critical power and Poperatingis the operating power of the fuel assembly. This
approach was established by General Electric [GE 1973] as a way to eliminate the objectionable
attributes inherent in the local CHF hypothesis, mostly the wrong location for the critical heat
flux. In VIPRE two different critical power correlations (Hench-Levy and Hench-Gillis) are
available with which to determine the minimum CPR. The Hench-Levy correlation uses an older
approach of calculating the minimum CPR by determining the CHF with the conditions of the
average bundle. The Hench-Gillis correlation, however, represents a more updated approach in
that it uses a bundle enthalpy rise iteration which determines the critical power of the fuel
bundle. In this correlation the average enthalpy at an axial location and average flow of the
bundle are used to calculate the critical quality throughout the range of the boiling length in the
assembly. The correlation is equipped to reflect the power peaking conditions in the rods This
calculated critical quality is then compared to the average quality of the bundle for each axial
location in order to determine the relative thermal margin. Iteration on the average enthalpy is
then performed until the relative thermal margin is unity.
Previous research efforts [Morra 2004] have utilized a modified Hench-Gillis critical
power correlation for analysis of internally and externally cooled annular fuel. This modification
involved an adjustment of the non-dimensional boiling length (which was defined as the ratio of
the bundle heat-transfer surface area to the bundle flow area) where the additional contribution to
the heat transfer area from the inner annulus was included. Although this modification
appropriately corrected for the increased heat-transfer area due to the inner surface of the annular
fuel, there is no way to validate this with experimental data. In the recommendations for future
work section Morra recommended that the most important approximation that should be relaxed
is related to the CPR correlation. The Hench-Gillis correlation was developed for solid fuel and
theoretically is not applicable for annular fuel [Morra 2004]. However before a switch could be
made to another correlation, a benchmark calculation against actual experimental BWR bundle
data was needed. The next section contains this benchmarking analysis which compares the
experimentally observed limiting CHF to the simulated CHF as calculated by two different
correlations.
3.2.4.
CHFRICPR Comparative Analysis
In order to compare the relative accuracy of the best available correlations in the VIPRE
code, these correlations were benchmarked against experimental data obtained from critical
power experiments performed by NUPEC (Nuclear Power Engineering Corporation) in Japan
[Kitamura 1998]. The two correlations benchmarked were the Hench-Gillis CPR correlation and
the EPRI-1 Reddy Fighetti CHF correlation.
The critical power experiments performed by NUPEC were conducted on an electrically
heated 9x9 fuel assembly for BWRs with the following operational conditions.
Table 3-1: NUPEC Experiment Operational Conditions [Kitamura 19981
7.2 MPa
System Pressure
25-126 kJ/kg
Inlet Subcooling
Flow Rate
30-60 t/hr
1.12 cm
Diameter of Heated Rod
Pin Pitch
1.43 cm
Number of Full Length Rods
66
3.5875 m
Axial Length of Full Length Rods
8
Number of Partial Length Rods
Axial Length of Partial Length Rods 2.242 m
The axial power peaking profile assumed for the NUPEC experiment is shown
below in Figure 3.1.
1I.' r_
S1.4
S1.2
1
. 0.8
0.6
0.4
0 0.2
0
0
50
100
150
200
250
300
350
400
z (cm)
Figure 3-1: NUPEC Experimental Axial Power Peaking Profile [Kitamura 19981
As described in the preceding section the Hench-Gillis CPR correlation uses bundle
average mass flux, power profile and quality distribution to calculate the critical power. In order
to account for local non-uniformities within the assembly in the calculation of the critical power,
the correlation utilizes correction factors called Jl factors. Due to the fact that the 9x9 assembly
analyzed incorporated partial length fuel rods, the power profile needed to be modified. This was
accomplished according to the following formula:
NL +N P
Q P(z) forz<Lpa
NL + fp x Np L
(33)
N P(z) for z > Lp=
NL+fpxNp L
where Q'(z) is the new power profile as a function of axial position z, NL is the number of full
length fuel rods, Np is the number of partial length fuel rods,
Q is the bundle power, P(z) is the
initial axial power profile depicted in Figure 3.1, L is the total length of the fuel rods, Lpan is the
fueled length of the part length rods and fp is the integral of the initial axial power distribution
over the partially fueled length defined as:
Lp a rt
f:= f P(z)dz
(3.4)
0
Thus the following axial and radial power peaking profiles, depicted in Figures 3.2 and
3.3, were determined.
1.20
1.20
1.20
1.38
1.38
1.38
1.20
1.20
1.20
1.20
1.20
1.38
1.38
1.38
1.20
1.20
1.20
0.77
1.05
0.49
0.77
1.20
0.49
0.77
1.20
1.05
0.49
1.05
0.49
1.20
1.05
0.49
1.20
0.49
1.05
1.05
0
0
0.49
1.05
1.20
0.77
0.49
0
0
0
1.20
0.77
1.20
1.20
1.20
0
0
1.20
0.49
1.05
1.20
0.49
1.05
0.49
1.20
0.49
1.05
0.49
1.20
0.77
0.49
1.05
0.77
1.05
0.49
0.77
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
Figure 3-2: NUPEC Experiment Radial Power Peaking Factors
m~
4
0u
S1.4
. 1.2
. 0.8
" 0.6
= 0.4
E 0.2
z
0
- -- --
0
50
100
150
200
250
300
350
400
z (cm)
Figure 3-3: NUPEC Experiment Axial Power Peaking Factors
While the Hench-Gillis correlation uses bundle average conditions, the EPRI-1 Reddy
Fighetti heat balance correlation directly accounts for local effects by conducting a full
subchannel analysis. Thus, instead of having to approximate for partial length rods, the design
parameters for each rod can be directly entered in and used in the determination of the critical
power. Furthermore, this correlation also accounts for the cold wall correction factor and grid
loss coefficient of the assembly.
The following tables show how the experimentally measured critical power compares to
the critical powers predicted by the two different correlations.
Table 3-2: Comparison of the Critical Powers Predicted by the Hench-Gillis and EPRI-1 Correlations to the
Experimentally Measured NUPEC Data at 25 kJ/kg Inlet Subcoolin
Flow
Rate
(t/hr)
NUPEC
Hench-Gillis HenchMeasured
Calculated
Gillis
Critical Power Critical Power
%
EPRI-1
Calculated
Critical Power
EPRI-1
%
Error
(MW)
(MW)
Error
(MW)
30
6.40
4.98
-22%
5.42
-15%
40
7.30
5.56
-24%
6.45
-12%
50
8.20
5.94
-28%
7.23
-12%
60
8.70
6.18
-29%
7.84
-10%
Table 3-3: Comparison of the Critical Powers Predicted by the Hench-Gillis and EPRI-1 Correlations to the
Experimentally Measured NUPEC Data at 126 kJ/kg Inlet Subcoolin
Flow
Rate
(t/hr)
NUPEC
Hench-Gillis
Measured
Calculated
Critical Power Critical Power
Hench-
EPRI-1
EPRI-1
Gillis
%
Calculated
Critical Power
%
Error
(MW)
(MW)
Error
(MW)
30
7.20
5.58
-23%
6.05
-16%
40
8.00
6.32
-21%
7.23
-10%
50
8.70
6.85
-21%
8.21
-6%
60
9.30
7.20
-23%
8.97
-4%
As shown from Table 3.2 and 3.3, the Hench-Gillis critical power correlation consistently
under predicts the critical power of the assembly on average by 24%. The EPRI-1 Reddy Fighetti
on the other hand only under predicts the critical power on average by 11%. This is not
surprising since the Hench-Gillis correlation was developed for 6x6 and 5x5 solid fuel
assemblies which did not incorporate partial length fuel rods. These partial length fuel rods were
initially adopted for the 9x9 solid fuel design and now have also been included in the design for
the 10xl0 solid fuel assembly [Ferroni 2006]. In the original paper by Hench and Gillis, they
state that the validity of the correlation for 8x8 bundles was not proven since the 8x8 bundles
were not among those used to develop the correlation. However, they claim that since the 8x8 is
not so different from the 7x7, the simulated results from the correlation can be assumed to be
accurate. In fact, the size of the lattice doesn't significantly come into play for the Hench-Gillis
correlation as long as the appropriate J1 factors and bundle averaged mass fluxes are used. For
the case of full length fuel rods, both the radial power peaking factors and mass flux do not
depend on the axial location. However with partial length fuel rods, the mass flux has to increase
due to the "disappearance" of some fuel rods at a specified axial location, which changes the J
factors. Now it is possible in VIPRE to specify this disappearance of fuel rods at a specified axial
location but just not with the Hench-Gillis correlation. This is because the correlation uses the
mass flux calculated at the bottom of the bundle to compute the Ji factors. Technically it is
possible to try and modify the VIPRE source code in order to make VIPRE aware of the axial
variation in that subroutine. However given the immediate availability of the EPRI-1 correlation
it was determined that making a significant change to the VIPRE source code was not
worthwhile. Therefore due to the relative inappropriateness and excessive conservatism of the
Hench-Gillis CPR correlation, the EPRI-1 Reddy Fighetti heat balance correlation was adopted
for all critical power determinations in this analysis.
Finally, because the EPRI-1 Reddy Fighetti heat balance correlation provides the
minimum CHFR and not the minimum CPR, it was desirable to ascertain the relative difference
between the two values in order to possibly simplify the number of steps in the analysis. The
procedure of determining the CPR from the CHFR was conducted as follows. The reference case
(which is defined in Section 3.3.1) was run at normal 100% power using the EPRI- 1 heat balance
correlation to obtain the CHFR. The total assembly power was then increased until the critical
point was reached (i.e. CHFR = 1). This power level was then divided by the nominal 100%
reference power in order to obtain the CPR as defined by the formula given in Section 3.2.3.
Table 3-4: EPRI-1 CPR Calculation Data
CHFR
kW/rod
100% Power
Critical Power
1.266
85.2506
1.00
107.25
Table 3-5: EPRI-1 and Hench-Gillis Calculated CPR Comparison
Axial
Location (m)
EPRI-1 CHFR at 100% Power
Equivalent EPRI-1 CPR
Hench-Gillis CPR
1.266
1.258
1.141
3.06 to 3.15
3.06 to 3.15
3.55
As we can see from Table 3.4 and 3.5, the values for the CHFR and CPR as determined
by the EPRI-1 correlation are very close. This 0.6% difference between the two calculated values
allows for either to be used for CHF analyses. Due to the fact that calculating the CPR with the
EPRI- 1 correlation requires additional computation time, the CHFR was utilized in all of the
trade studies conducted in this analysis.
3.3. Fuel Assembly Models
3.3.1.
Solid Fuel 9x9 Reference Assembly
Performance improvements of advanced designs are always defined with respect to the
performance of a standard reference design. Therefore, in order to study the operational
attributes of an internally and externally cooled annular geometry, a reference case was needed.
The solid fuel reference case used in this study was adapted from the General Electric BWR5 of
Nine-Mile-Point Unit 2 [Nine Mile Point 2004] which uses a GEl 1 fuel assembly design [Gerald
1997]. This study utilized several plant level attributes from the Nine-Mile-Point design
including assembly power, flow rate of the coolant, number of bundles per core and total system
pressure in the simulation of all assemblies. The specific fuel assembly design parameters,
however, were predominantly adapted from the available literature on the GEl 1 type 9x9 solid
fuel assembly which is depicted in Figure 3.4 below.
- P1.
O
ooooo
0000ooooo
.00@oo
0-OOoQQOOO
00000000200
0000
0000
O
00 OO•%1
0000
0000
000000000
000000000
oOOOOOO, ~---~---~------
000i
00000
00000
000000000
I 00
_
0000
U000000000
OOOO
(_
Q OQOO
Figure 3-4: GE11 Fuel Assembly Layout [Gerald 1997]
3.3.1.1
Geometric Design Parameters
The design parameters for the assembly were collected from three different sources; the
USAR for Nine Mile Point Unit 2 [Nine Mile Point 2004], Chris Handwerk's hydride fueled
BWR thermal hydraulic analysis [Handwerk 2005] and a PSAR for the Lungmen Power Station
[Lungmen]. These parameters are summarized in Table 3.6 below:
Table 3-6: Solid Fuel Reference Core Operating Parameters [Lungmenl, [Nine Mile Point 2004]
Parameter
System Pressure (psia)
Core Shroud Radius (in)
Number of Fuel Assemblies
Core Mass Flow Rate (Mlbm/hr)
Core Pressure Drop (psia)
Core Inlet Temperature ('F)
Core Thermal Power (MWth)
Fuel Assembly Axial Length (in)
Fuel Assembly Heated Axial Length (in)
Hot Assembly Power (kWth)
Hot Assembly Mass Flow Rate (Mlbm/hr)
Hot Assembly Linear-Power-Generation-Rate (kW/ft)
Value
1035
102.56
764
108.5
24.74
533
3323
164.567
145.98
6304.5
0.1379
75.39
The remaining limiting parameters for the reference core design are summarized below in
Table 3.7, which reflects VIPRE calculations for the solid fuel reference case.
Table 3-7: Solid Fuel Reference Core Design Constraints
Parameter
Core MCHFR
Average Core Exit Quality
Hot Bundle Exit Quality
Radial Power Distribution with 4 Zones
Axial Power Peaking Factor
Maximum Local Peaking Factor
H/HM Ratio
Maximum Average Fuel Temperature (oC)
Maximum Center-line Fuel Temperature (TC)
Maximum Cladding Surface Temperature (oC)
Value
1.266
13.34%
24.50%
1.45, 1.30, 1.00 and 0.60
1.51
1.23
4.45
1400
2805
349
The GE 11 9x9 solid fuel reference assembly design parameters are listed in Table 3.8
below.
Table 3-8: GE11 Fuel Assembly Design Parameters
Parameters
Fuel Assembly Pitch (in)
Bundle Lattice
Fuel Pin Pitch (in)
Clad Thickness (in)
Gap Thickness (in)
Number of Fuel Rods
Number of Water Rods
Diameter between Box Walls (in)
Fuel Rod Outer Diameter (in)
Water Rod Outer Diameter (in)
Water Rod Inner Diameter (in)
Values
6.000
9x9
0.562
0.028
0.004
74
2
5.215
0.440
0.980
0.920
The local pressure drop coefficients were adopted from the PSAR for the Lungmen
Power Station [Lungmen]. These coefficients are listed below in Table 3.9.
Table 3-9: Localized Pressure Drop Coefficients
Structure
Exit Plate
Grid
Entrance Plate
Orifice
3.3.1.2
Loss Coefficient
0.38
1.20
9.46
21.09
Power Peaking Parameters
The BOL radial and axial power distributions given in the USAR of the Nine Mile Point
Unit 2 were used for all reference assembly simulations. A plot of this axial power peaking
factor versus position is shown below in Figure 3.5.
Axial Power Peaking Profile for GEl1 9x9 Reference Case
2
-
---
__________________---I
4,
.I
$
--
_
---
_-_--__
2
--
0
0
20
40
60
80
100
120
140
160
Axial Length (in)
Figure 3-5: Axial Power Peaking Profile for 9x9 Reference Case
Similarly for the radial power distribution, Figure 3.6 below shows how the radial power
peaking factor varies as a function of position within the fuel assembly. The lime colored cells,
which have a depressed radial power peaking factor, are the gadolinium poisoned pins and the
gray colored cells in the center of the assembly, which have a radial power peaking factor of
zero, are the water rods.
1.110 1.220 1.210 1.180 1.170 1.180 1.210 1.220 1.120
1.220 0.940 0.980 0.430 0.730 .0.430 0.980 0.950 1.220
1.220 0.980 0.410 0.840 0.970 0.890 0.420 0.990 1.220
1.180 0.430 0.840 1.100 o0
0.0
0.900 0.440 1.180
1.170 0.730 0.970 0.000
0
0.960 0.730 1.160
Poisoned Pin
Water Rod
000 1.080 0.820 0.430 1.170
1.190 0.440 0.910 10.00
1.230 0.980 04.420 0.900 0.970 0.840 0.420 0.970 1.200
1.210 0.950 0.980 0.430 0.740 0.430 0.970 0.940 1.220
1.100 1.210 1.21011.190 1.170 1.180 1.210 1.200 1.110
Figure 3-6: Radial Power Peaking Profile for 9x9 Reference Case
3.3.2.
Annular Fuel Assembly Design Option Space
Previous efforts to design BWR annular fuel [Morra 2004] held that the only possible
designs, while maintaining the same physical dimensions as current fuel assembly, are the 5x5
and the 6x6 annular arrays. A brief scoping study (shown below in Table 3.10) was conducted on
the relative surface areas and fuel volume loadings of annular fuel relative to the 9x9 reference
case. All values in Table 3.10 are normalized to the reference case.
Table 3-10: Annular Design Option Space
Comparative
Surface Area
100%
110%
Comparative
Fuel Volume
100%
90%
6x6
136%
90%
7x7
151%
90%
Lattice
Reference
5x5
It is true that a 5x5 annular assembly is the largest annular pin geometry possible. This is
primarily due to the fact that a 4x4 annular assembly has roughly equivalent surface area as the
reference assembly; hence, any possible benefit from additional heat transfer surface area is lost.
However, the 6x6 annular assembly is not the smallest allowable geometry. Estimation showed
that a 7x7 annular assembly, which has approximately 50% higher heat-transfer surface area and
less than 10% reduction in the fuel loading, could reasonably achieve a power density uprate.
Smaller annular pin geometries such as an 8x8 were determined to be not reasonable because of
the 25% reduction of the fuel loading volume, which would be too large of a penalty for the fuel
cycle length and the inner channel diameter would be too small.
The annular pin pitch within the shroud was determined by preserving the area ratios of
'corner channel to center channel' and 'edge channel to center channel' from the solid fuel
reference design. Additionally for all of the following analyses, the core exit quality and inlet
conditions were preserved at the same value as the reference design. Or in other words, an
arbitrary increase in power density implies a proportional increase in coolant mass flow rate.
Now that an appropriate upper and lower bound was found for the possible annular geometries,
an in-depth characterization of each designs' ability to increase power density was conducted.
The next section describes a brief summary of each annular design parameters and attributes.
3.3.3.
Annular 5x5 Fuel Assembly
The 5x5 annular fuel assembly concept has previously been investigated and optimized
by Morra [Morra 2004]. However due to a recently discovered inclusion of grid pressure loss
within the inner annuli which was applied in the input files and due to more rigorous CHFR
analysis using the EPRI correlation, revalidation and further study of the previously completed
work was needed. The following subsections 3.3.3.1 and 3.3.3.2 contain a complete description
of the 5x5 annular assembly as it was previously optimized without the additional grid loss in the
inner annuli.
3.3.3.1
Geometric Design Parameters
Table 3.11 below shows the geometrical design parameters for the 5x5 annular fuel
assembly. The equivalent geometrical design parameters for the solid fuel 9x9 reference case
fuel assembly were included for comparative purposes and the hydraulic diameter was defined
as:
De =4A
PW
(3.5)
where De is the hydraulic diameter, A is the flow area and Pw is the wetted perimeter (or surface
per unit length) of the channel.
Table 3-11: Geometrical Design Parameters for 5x5 Annular Fuel
Fuel Lattice
Number of Fuel Rods
Number of Water Rods
Box Wall Inner Diameter (in)
Pin Outer Diameter (in)
Outer Clad Thickness (in)
Outer Gap Thickness (in)
Fuel Outer Diameter (in)
Reference Case
Annular Case
9x9
74
2
5.215
0.440
0.028
0.004
0.376
5x5
24
1
5.215
0.942
0.033
0.004
0.867
-
0.602
0.004
0.033
0.980
0.920
0.474
0.527
0.942
0.875
0.535
0.527
0.418
0.353
Fuel Inner Diameter (in)
Inner Gap Thickness (in)
Inner Clad Thickness (in)
Pin Inner Diameter (in)
Water Rod Outer Diameter (in)
Water Rod Inner Diameter (in)
Hydraulic Diameter Exterior (in)
Hydraulic Diameter Interior (in)Hydraulic Diameter Edge (in
Hydraulic Diameter Corner (in)
0.401
0.320
Figure 3.7 below shows a two-dimensional cross section of the 5x5 annular fuel assembly
design concept. The lime colored annuli represents gadolinium poisoned pins and the thin gray
colored annuli represent the water rods. The numbers represent the individual subchannel
designations for the VIPRE thermal hydraulic analysis.
Figure 3-7: 2-D Cross Section of the 5x5 Annular Fuel Design Concept (Not To Scale)
3.3.3.2
Power Peaking Profiles
The BOL axial power distribution (shown in Figure 3.5) from the USAR of the Nine Mile
Point Unit 2 was used for all 5x5 annular assembly simulations. For the radial power
distribution, Figure 3.8 below shows how the radial power peaking factor varies as a function of
position within the fuel assembly. It was attained by scaling up the radial power profile
previously determined by [Morra 2004] to the maximum radial power peaking factor of 1.22
from the solid fuel reference case. The lime colored cells, which have a depressed radial power
peaking factor, are the gadolinium poisoned pins and the gray colored cell in the center of the
assembly, which has a radial power peaking factor of zero, is a water rod.
1.039 1.220 1.102 1.119 1.099
1.220 0.371 1.001 1.085 1.109
1.102 1.001 0.000 0.367 1.069
Poisoned Pin
Water Rod
1.119 1.085 0.367 1.002 1.083
1.099 1.109 1.069 1.083 1.081
Figure 3-8: Radial Power Peaking Profile for 5x5 Annular Case
3.3.4.
Annular 6x6 Fuel Assembly
The 6x6 annular fuel assembly design has previously been investigated and optimized by
Morra [Morra 2004]. However due to the presence of the grid loss factors within the inner annuli
as in the 5x5 input files and the new correlation, revalidation and further study of the previously
completed work on the 6x6 design was needed. The following subsections 3.3.4.1 and 3.3.4.2
contain a complete description of the 6x6 annular assembly as it was previously optimized
without the additional grid loss in the inner annuli.
3.3.4.1
Geometric Design Parameters
Table 3.12 below shows the geometrical design parameters for the 6x6 annular fuel
assembly. The equivalent geometrical design parameters for the solid fuel 9x9 reference case
fuel assembly were included for comparative purposes.
Table 3-12: Geometrical Design Parameters for 6x6 Annular Fuel
Lattice
Number of Fuel Rods
Number of Water Rods
Box Wall Inner Diameter (in)
Pin Outer Diameter (in)
Outer Clad Thickness (in)
Outer Gap Thickness (in)
Fuel Outer Diameter (in)
Fuel Inner Diameter (in)
Inner Gap Thickness (in)
Inner Clad Thickness (in)
Pin Inner Diameter (in)
Water Rod Outer Diameter (in)
Water Rod Inner Diameter (in)
Hydraulic Diameter Exterior (in)
Hydraulic Diameter Interior (in)
Hydraulic Diameter Edge (in)
Hydraulic Diameter Corner (in)
Reference Case
9x9
74
2
5.215
0.440
0.028
0.004
0.376
0.980
0.920
0.474
0.401
0.320
Annular Case
6x6
34
2
5.215
0.830
0.033
0.004
0.755
0.543
0.004
0.033
0.468
0.830
0.759
0.335
0.468
0.239
0.193
Figure 3.9 below shows a two-dimensional cross section of the 6x6 annular fuel assembly
design concept. The lime colored annuli represents gadolinium poisoned pins and the thin gray
colored annuli represent the water rods. The numbers represent the individual subchannel
designations for the VIPRE thermal hydraulic analysis.
Figure 3-9: 2-D Cross Section of the 6x6 Annular Fuel Design Concept (Not To Scale)
3.3.4.2
Power Peaking Profiles
The BOL axial power distribution (shown in Figure 3.5) from the USAR of the Nine Mile
Point Unit 2 was used for all 6x6 annular assembly simulations.
For the radial power distribution, Figure 3.10 below shows how the radial power peaking factor
varies as a function of position within the fuel assembly. It was attained by scaling up the radial
power profile previously determined by [Morra 2004] to the maximum radial power peaking
factor of 1.22 from the solid fuel reference case. The lime colored cells, which have a depressed
radial power peaking factor, are the gadolinium poisoned pins and the gray colored cells in the
center of the assembly, which have a radial power peaking factor of zero, are the water rods.
1.012
1.015
1.032
1.068
1.106
1.063
1.015
0.368
0.979
1.078
1.101
1.081
1.032
0.979
1.210
0.000
0.364
1.002
1.068
1.078
0.006
1.220
0.994
1.055
1.106
1.101
0.364
0.994
0.954
1.132
1.063
1.081
1.002
1.055
1.132
1.092
Poisoned Pin
Water Rod
Figure 3-10: Radial Power Peaking Profile for 6x6 Annular Case
3.3.5.
Annular 7x7 Fuel Assembly
A 7x7 annular fuel assembly design was also developed for this investigation. However,
since this is a brand new design, a few additional optimization and validation studies were
conducted in order to verify that the 7x7 lattice was in fact optimally designed. The following
subsections 3.3.5.1 and 3.3.5.2 contain the geometric design parameters, axial and radial power
peaking profiles for the 7x7 annular assembly concept.
3.3.5.1
Geometric Design Parameters
The pin pitch within the envelope of the assembly shroud was determined by equating the
subchannel area ratios. This was accomplished by initially calculating the 'corner to interior' and
'edge to interior' subchannel area ratios for the 9x9 solid reference design. The pin pitch of the
7x7 annular design concept was modified until the subchannel area ratios equaled that of the 9x9
solid reference design.
Table 3.13 below shows the geometrical design parameters for the 7x7 annular fuel
assembly. The equivalent geometrical design parameters for the solid fuel 9x9 reference case
fuel assembly were included for comparative purposes.
Table 3-13: Geometrical Design Parameters for 7x7 Annular Fuel
Reference Case
Annular Case
9x9
74
2
5.215
0.440
0.028
0.004
0.376
0.980
0.920
0.474
7x7
46
3
5.215
0.697
0.033
0.004
0.622
0.425
0.004
0.033
0.350
0.697
0.626
0.284
Hydraulic Diameter Interior (in)
-
0.350
Hydraulic Diameter Edge (in)
Hydraulic Diameter Corner (in)
0.401
0.320
0.238
0.211
Lattice
Number of Fuel Rods
Number of Water Rods
Box Wall Inner Diameter (in)
Pin Outer Diameter (in)
Outer Clad Thickness (in)
Outer Gap Thickness (in)
Fuel Outer Diameter (in)
Fuel Inner Diameter (in)
Inner Gap Thickness (in)
Inner Clad Thickness (in)
Pin Inner Diameter (in)
Water Rod Outer Diameter (in)
Water Rod Inner Diameter (in)
Hydraulic Diameter Exterior (in)
Figure 3.11 below shows a two-dimensional cross section of the 7x7 annular fuel
assembly design concept. The lime colored annuli represents gadolinium poisoned pins and the
thin gray colored annuli represent the water rods. The numbers represent the individual
subchannel designations for the VIPRE thermal hydraulic analysis.
Figure 3-11: 2-D Cross Section of the 7x7 Annular Fuel Design Concept
3.3.5.2
Power Peaking Profiles
The BOL axial power distribution (shown in Figure 3.5) from the USAR of the Nine Mile
Point Unit 2 was used for all 7x7 annular assembly simulations. For the radial power
distribution, Figure 3.12 below shows how the radial power peaking factor varies as a function of
position within the fuel assembly. A reasonable radial power peaking profile was attained in
consultation with [Kazimi 2006] so as to maintain the maximum radial power peaking factor of
1.22 from the solid fuel reference case. The lime colored cells, which have a depressed radial
power peaking factor, are the gadolinium poisoned pins and the gray colored cells in the center
of the assembly, which have a radial power peaking factor of zero, are the water rods.
1.11
1.21
1.17
1.18
1.21
1.22
1.18
0.42
0.85
0.85
0.85
0.42
1.17
0.85
0.90
1.00
0.00
0.85
1.18
0.85
1.00
0.00
1.00
0.85
1.21
0.85
0.00
1.00
0.90
0.85
1.20
0.42
0.85
0.85
0.85
0.42
1.12
1.20
1.21
1.18
1.16
1.21
1.11
1.21
1.21
1.18
1.17
1.21
1.11
Figure
3-12:
Radial
Power
Peaking
Profile
for
Poisoned Pin
Water Rod
II &
Case
3.4. Results of Fuel Assembly Optimization Studies
3.4.1.
Annular 5x5 Fuel Assembly
As was stated earlier in section 3.3.3, the 5x5 annular fuel assembly concept has
previously been investigated by Morra [Morra 2004]. However upon close inspection of the
input file from that study there was an additional grid loss parameter for the inner annuli which
when included in the design allowed for the power density uprate of 11% with respect to the GE
8x8 assembly (or approximately a 6% uprate for the current 9x9 reference case). Removal of this
additional interior grid loss parameter decreased the limiting CHFR to 1.006. This reduction was
determined to be primarily due to a significantly larger mass flux flowing through the inner
annuli. Therefore strategies of reducing this significantly higher inner annuli mass flux were
investigated in order to increase the CHFR of the 5x5 design and allow for a power density
uprate.
3.4.1.1
Fuel Pin Dimensions Optimization
Initially it was thought that a reduction in the diameter of the inner annuli could force
more mass flux to the outer channels and hence increase the minimum CHFR in the inner annuli.
Figure 3.13 below shows the effect of the inner annuli diameter reduction on the minimum
CHFR of the assembly.
Effect of a Reduction in Inner Diameter on the MCHFR for 5x5 Annular Fuel
1.0
1.5 -
1.4--
1.3
.-..... .. .. .
.. ......
.--
-
-
- -
-
4
-A
Pi.
,
1.2U
* Inner CHFR
-*- Outer CHFR
1.1
.......... .
.. .. ...
1-
-----
-.
0.9
0.8
0%
2%
4%
6%
8%
10%
12%
%Inner Diameter Reduction
Figure 3-13: Effect of a Reduction in Inner Diameter on the MCHFR for 5x5 Annular Fuel
While a reduction in diameter of the inner annuli is helpful for the MCHFR in the outer
subchannels, it actually worsens the MCHFR of the inner subchannels. It was thought that a
reduction in diameter of the inner annuli would help push additional flow to the outside channels
and increase the MCHFR in the inner annuli. However it appears that this effect is forcing more
mass flux through the inner annuli, which increases heat flux to the inner annuli, and hence the
MCHFR decreases. Since further reduction in diameter of the inner annuli is clearly nonbeneficial, the only other option was to open up the inner subchannels by expanding the overall
dimensions of the annular pin.
3.4.1.2
Inter-Fuel Pin Gap Study
The effect on the MCHFR of opening up the inner subchannels by expanding the overall
dimensions of the annular pin is shown below in Figure 3.14.
Effect of Decreasing the Inter-Pin Gap (Via Expansion of the Overall Fuel Pin
Dimensions) on the MCHFR for 5x5 Annular Fuel
j
1
~_...,-.-~~~
----
4i
----
Outer CHFR
c~H
i
0%
Inner CHFR
i
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
% Gap Reduction Between Annular Fuel Pins
Figure 3-14: Effect of Decreasing the Inter-Pin Gap (Via Expansion of the Overall Fuel Pin Dimensions) on
the MCHFR for 5x5 Annular Fuel
As evident from Figure 3.14 above, an opening up of the annular fuel pin is not beneficial
for the MCHFR. Furthermore, the graph predicts that the minimum critical heat flux ratios for
the inner and outer subchannels equilibrate at approximately 1.15. Since MCHFR for the
reference case was slightly higher at 1.266 this suggests that an uprate in power density is not
achievable for the 5x5 annular geometry.
3.4.2.
Annular 6x6 Fuel Assembly
As was stated earlier in section 3.3.4, the 6x6 annular fuel assembly concept has
previously been investigated by Morra [Morra 2004]. These input files also contained an
additional grid loss parameter for the inner annuli (just as in the 5x5 assembly) which when
included in the design allowed for the power density uprate of 23% with respect to the GE 8x8
assembly (or approximately a 18% uprate for the current 9x9 reference case). Removal of this
additional interior grid loss parameter decreased the limiting CHFR to 0.849. Therefore several
strategies of reducing this significantly higher inner annuli mass flux were investigated in order
to increase the MCHFR of the 6x6 design and allow for a power density uprate.
3.4.2.1
Fuel Pin Dimensions Optimization
As with the 5x5 annular assembly, it was initially thought that a reduction in the diameter
of the inner annuli could force more mass flux to the outer channels and hence increase the
minimum CHFR outside the annular pin. Figure 3.15 below shows the effect of the inner annuli
diameter reduction on the minimum CHFR of the assembly.
Effect of a Reduction of Fuel Pin Inner Diameter on MCHFR
for 6x6 Annular Fuel
1.6
1.5
1.4
1.3
I
-- Inner CHFR
1.2
--
Outer CHFR
1.1
0.9
0.8
0%
5%
10%
15%
20%
25%
30%
% Reduction of Inner Diameter
Figure 3-15: Effect of a Reduction in Inner Diameter on the MCHFR for 6x6 Annular Fuel
Again, while a reduction in diameter of the inner annuli is helpful for the MCHFR in the
outer subchannels, it decreases the MCHFR for the inner subchannels. However unlike the 5x5
annular case, the MCHFR occurring in the outer annulus is initially much smaller than the
MCHFR occurring in the inner annulus. This imbalance between the MCHFRs in the inner and
outer annuli for the base case seems to equalize at a 20% reduction in inner diameter.
Unfortunately the MCHFR at this equalization point still occurs below that of the reference case.
Thus further optimization was needed.
Unlike the 5x5 annular case, it wasn't possible to increase the size of the annular fuel pin
due to the fact that the pins in the 6x6 assembly were already at the minimum achievable pin to
pin gap of 0.048in. Due to vibrational and fabrication concerns, it was not desirable to tighten up
the pin lattice further beyond the current manufacturing limits adopted by GE. Since the strategy
of modifying the annular pin geometry did not appear promising, other means of directing
additional mass flux outside the inner annuli were investigated.
3.4.2.2
Inner Channel Orifice Resistance Coefficient Optimization
The next avenue pursued was to incorporate a large orifice (i.e. resistance to flow) at the
entrance to the inner annuli in order to push more flow to the outside channels. This strategy was
selected because the original design always had the limiting CHFR located in the outer channels.
Figure 3.16 below shows the effect of an increase in the orifice resistance coefficient on the
MCHFR for 6x6 annular fuel. Unfortunately, as shown in Figure 3.16, even a large increase in
the orifice resistance coefficient isn't sufficient to allow for the power density uprate of 6x6
annular fuel.
Effect of the Orifice Resistance Coefficient on CHFR
for a 6x6 Annular Fuel Hot Assembly
____·
K
-- u-
-~-.~...
---c.
0%
50%
100%
---.
Inner CHFR
Outer CHFR
,
150%
200%
250 %
%Increase of Orifice Resistance Coefficient
Figure 3-16: Effect of the Orifice Resistance Coefficient on CHFR for 6x6 Annular Fuel
In order to achieve the resistance coefficient of 69 (which allowed for equalization of the
inner and outer channel CHFRs) a rough design estimate was needed in order to determine if
such a plug could be reasonably designed. The "Handbook of Hydraulic Resistance" by Idelchik
[Idelchik 1966] offered the following conversion formula to transform this pressure loss
coefficient into a thin orifice plate design:
APP
Vo2
P 2 gc
(1.707-
)2 1
2
(3.6)
where 4 is the resistance coefficient, AP is the pressure drop, p is the density, vo is the velocity
through the opening, g, is the acceleration of gravity and J is the area ratio. After the VIPRE
determined optimal resistance coefficient (along with the other pertinent data) was entered into
the formula, the resultant area ratio was determined to be -0.20. Since the design had a nominal
inner annulus diameter of 0.468in, the new orifice plate area was determined to be 0.345in in
diameter. This represented about 36% reduction in diameter to the inner channel opening.
Even though it is possible to manufacture a thin orifice plate to these specifications at the
entrance of the inner annuli, the new annular assembly would still only have a MCHFR
equivalent to that of the solid fuel assembly. An equivalent MCHFR means there is no ability to
uprate and hence no incentive to switch to the 6x6 annular geometry from the current 9x9 solid
geometry.
3.4.3.
Annular 7x7 Fuel Assembly
Since no additional CHFR margin was available with the 5x5 and 6x6 annular designs, a
7x7 annular fuel assembly concept was developed. It was theorized that the additional surface
area and lower average heat flux of the 7x7 annular design would allow for a higher MCHFR
and hence an ability to uprate. Since this design was adapted from the 12x12 annular fuel pin
design for PWRs, optimization studies on pin dimensions, grid loss coefficients and radial power
peaking factors were performed to ensure that the 7x7 annular design concept was in an
advantageous configuration.
Fuel Pin Dimensions Optimization
3.4.3.1
As with the 5x5 and 6x6 annular designs, the 7x7 geometry also had higher mass flux in
the inner annuli. Therefore the inner diameter of the annular fuel pin was reduced in order to
push more mass flux outside of the inner annuli. Figure 3.17 below shows the effect of an inner
diameter reduction on the MCHFR.
Effect of Inner Diameter Reduction on CHFR for 7x7 Annular Fuel
1.5
1.4
-------------------
---
--
-----
~-
___~--r
__~__.~-----
1.3
---
__
________~~__
__.~--------
~--------·------~--~--~
1.2
1.1
__
____
|
____
___
-i~
___
__·___
0.9
0.8
-*- Inner Channels
Outer Channels
-----
-
"`
~I-
0.7
0.6
0c%
4%
6%
8%
10%
12%
14%
16%
18%
20%
%Reduction of Inner Diameter
Figure 3-17: Effect of a Reduction in Inner Diameter on the MCHFR for 7x7 Annular Fuel
As shown in Figure 3-17, a reduction in diameter of the inner annuli is not beneficial.
According to the trends of the graph it would be advantageous to enlarge the inner annuli by
increasing the size of the pin. However since the 7x7 design is already at the minimum
achievable pin to pin gap, other strategies must be employed in order to achieve an uprate.
Inner Channel Orifice Resistance Coefficient Optimization
3.4.3.2
Similarly with the 6x6 design, a large orifice resistance was incorporated at the entrance
to the inner annuli in order to push more flow to the outside channels. Figure 3.18 below shows
the effect of an increase in the orifice resistance coefficient on the MCHFR for 7x7 annular fuel.
Effect of Orifice Loss at Inner Channel Inlet on CHFR for 7x7 Annular Fuel
I
-----
·-----------
1-~~
~--~1----^-~----11--------II-
-i
-
,--U--
1.2
--
--------------------------------------------------
-- Inner Channels
L Outer Channels
1.1 • ,-•--•
......
....
. ..
..... . . .
.€ . . .
..............
0.9 -+--
0.8 L
0%
--- ·----------
I
20%
40%
60%
80%
100%
120%
140%
% Increase of Orifice Resistance Coefficient
Figure 3-18: Effect of the Orifice Resistance Coefficient on CHFR for 7x7 Annular Fuel
For the 7x7 annular case, an increase in the orifice resistance coefficient actually
decreases the MCHFR in the inner channels. Also, since the largest achievable CHFR occurs
with existing orifice plate designs, there was no need to calculate new orifice plate dimensions.
94
3.4.3.3
Spacer Grid Loss Optimization
The final strategy pursued to uprate the 7x7 annular design concept was to optimize the
loss from the spacer grids by increasing the aggressiveness of the mixing teeth. Figure 3.19
below displays the results from this optimization.
Effect of Spacer Grid Loss on CHFR
for 7x7 Annular Fuel
1.4
1.35
1.3
~-- ----..
----
------t--·----
1.25
----
_~ ~---
----
-------- ------~~--~-- ------ ------------
___
1.2-
_ _
_
_
_
_
_
_
_
I
- -~------------
-1
--
1.15
£
Inner CHFR
Outer CHFR
1.1
1.05
1-
__
_
___
_____-
__
0.95
0.9
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
%Increase of Spacer Grid Loss Coefficent
Figure 3-19: Effect of Spacer Grid Loss on CHFR for 7x7 Annular Fuel
The intersection point in the preceding figure for the inner and outer CHFRs occurs at a
140% increase in the spacer grid loss coefficient. Since a 140% higher spacer grid loss is not
practically achievable, Figure 3.19 above indicated that no uprate was achievable for the 7x7
annular fuel concept.
3.4.4.
Comparison of Optimal Designs
Table 3.14 below summarizes the important parameters on both a hot subchannel and
assembly wide scale. The best designs from the 5x5, 6x6 and 7x7 annular optimization studies
are featured along side the solid fuel 9x9 reference case.
Table 3-14: Comparison of 9x9 Reference, 5x5, 6x6 and 7x7 Annular Designs
9x9 Solid
Reference
Case
5x5
6x6
7x7
Annular Annular Annular
Case
Case
Case
Assembly Average
CHFR
Avg Assembly q" (mbtu/hr-ft2)
Avg Inner q" (mbtu/hr-ft2)
Avg Outer q"(mbtulhr-ft2)
Avg Xexit
Avg Inner Xexit
Avg Outer Xexit
Avg G (mlbmlhr-ft2)
Avg Inner G (mlbm/hr-ft2)
Avg Outer G (mlbmlhr-ft2)
AP (psia)
Flow rate (Ibm/sec)
HIHM
Vm/Vf
Hot Subchannel
Location
Avg Inner q" (mbtu/hr-ft2)
Avg Inner CHF (mbtu/hr-ft2)
Peak Inner q"(mbtulhr-ft2)
CHF at Peak Inner q"(mbtu/hr-ft2)
Avg Outer q" (mbtulhr-ft2)
Avg Outer CHF (mbtu/hr-ft2)
Peak Outer q" (mbtulhr-ft2)
CHF at Peak Outer q" (mbtu/hr-ft2)
Xexit Inner
Xexit Outer
G Inner (mlbmlhr-ft2)
G Outer (mlbmlhr-ft2)
1.266
1.155
1.204
1.064
0.2023
0.245
1.2127
23.0065
33.60
4.3055
2.8525
0.1501
0.1770
0.1349
0.245
0.1904
0.34508
1.0186
1.8115
0.6731
12.4687
33.30
4.5613
3.1202
0.1382
0.1787
0.1154
0.245
0.2376
0.2713
1.1724
1.3054
1.1350
30.1134
34.20
4.5246
3.0161
0.13949
0.1729
0.1227
0.245
0.2379
0.2851
1.2798
1.6844
1.1042
28.3493
34.20
4.3509
2.88548
Pin #19
0.2488
0.5359
0.3766
0.7445
0.27625
1.14175
Pin #2
0.2162
0.4374
0.3975
0.7442
0.1644
0.3891
0.3036
0.7239
0.2728
0.3695
1.4783
0.6521
Pin #5
0.1854
0.3963
0.3325
0.6680
0.1406
0.3232
0.2520
0.5579
0.3050
0.34025
1.2682
1.0055
Pin #7
0.1893
0.4114
0.2927
0.6094
0.1317
0.3006
0.2082
0.4901
0.2781
0.4686
1.6232
0.5058
3.4.5.
Analysis of the Results
The primary question which remained from the preceding table was, "why was there no
margin for uprating when the assembly average heat flux was lower for all three annular designs
when compared to the 9x9 solid fuel reference?" The answer in part, was thought to be that the
margin gained from the increase in heat transfer surface area, was being lost on the inability for
the coolant in the inner channels to mix with the surrounding subchannels. Table 3.15 below
summarizes the contribution that mixing with nearby channels provides by comparing the hottest
inner subchannel for the 6x6 annular case with the hottest external subchannel for the 9x9 solid
fuel reference case. The calculated enthalpy was derived from the basic heat balance formula
shown below:
rDL
DL + h,=
h,,
ril
q"avg
(3.7)
Table 3-15: Mixing Contribution Comparison for 9x9 Reference and 6x6 Annular Cases
9x9 Solid
Reference
6x6
Annular
Case
Case (Inner)
1.266
0.2023
1.204
0.1382
Assembly Average
CHFR
Avg Assembly q"(mbtu/hr-ft2)
Hot Channel
Flow rate (Ibm/sec)
0.35
0.41
Fuel Length (in)
145.98
145.98
Diameter Ref Pin (in)
Diameter Inner Annulus (in)
Avg q"(btu/hr-ft2)
Enthalpy Inlet (btu/lbm)
0.44
0.2281
528.3
0.47
0.2197
528.3
Calculated Enthalpy Outlet
779.8
748.6
Actual Enthalpy Outlet
744.4
748.6
Table 3.15 illustrates that the heat balance formula calculates the outlet enthalpy for the
inner annulus for the 6x6 quite accurately. The over-estimation of the outlet enthalpy by roughly
5%for the 9x9 reference case shows the role that inter-subchannel mixing plays in determination
of the outlet enthalpy.
In order to further understand the role of mixing, an additional study (summarized in
Table 3-16 below) was conducted where the radial power profile was homogenized. For this
study, the radial peaking factors for both the 6x6 annular and the 9x9 reference were set to unity
in order to determine how the CHFR depended upon this parameter. This reestablishment of the
radial power peaking factors showed that an uprate is possible with the 6x6 as evident from the
CHFR in the central column. Given this fact, the 6x6 assembly was uprated (by increasing the
power to flow ratio proportionally) by 21% as compared to the GE 9x9 reference assembly. It is
interesting to note that the approximately 20% power density uprate in the absence of power
peaking agrees well with Hejzlar [Hejzlar 2005].
This confirms that the absence of mixing in the inner channels, which needs to be
compensated by higher mass flux, hinders the power density uprate of annular fuel in BWRs.
This differs significantly from PWRs, where power density uprates of up to 50% were possible.
This is due to two main factors. First, the negative impact of higher mass flux associated with
power density uprate on dryout conditions in BWRs versus the positive effect of higher mass
flux on departure from nuclear boiling conditions in PWRs. Secondly, BWR assemblies have
larger power peaking factors than PWR assemblies, hence the impact of lack of mixing on the
CHFR is more pronounced in BWR annular assemblies.
Table 3-16: Effect of Radial Power Peaking on the MCHFR
6x6 Annular
GE 9x9 Ref Grid Loss=65
Uprated
6x6 Annular
Grid Loss=69
Assembly Average
Power/Rod (kW)
Rods/Assembly
Total Assembly Power (kW)
Flow rate (Ibmlsec)
PowerlFlow Ratio
CHFR
Assembly Avg q"(mbtulhr-ft2)
Avg Inner g" (mbtulhr-ft2)
Avg Outer q"(mbtulhr-ft2)
Avg Xexit
Avg Inner Xexit
Avg Outer Xexit
Avg G (mlbmlhr-ft2)
85.2
74
6306
33.60
187.7
1.288
0.2023
0.245
185.5
34
6306
34.20
184.4
1.395
0.1498
0.1798
0.1368
0.245
224.4
34
7630
41.38
184.4
1.288
0.1812
0.2178
0.1653
0.245
-
0.2420
0.2531
0.2489
0.2417
1.2127
1.2271
1.4798
Avg Inner G (mlbm/hr-ft2)
-
1.2789
1.5124
Avg Outer G (mlbm/hr-ft2)
AP (psia)
HIHM
VmNf
22.99
4.3055
2.8525
1.1752
27.81
4.5246
3.0161
1.4472
39.24
4.5246
3.0161
Ch #76
-
Outer-Ch #40
0.1798
0.4621
Outer-Ch #40
0.2178
0.4723
Hot Subchannel
Location
Avg Inner g"(mbtulhr-ft2)
Avg Inner CHF (mbtulhr-ft2)
Peak Inner q"(mbtu/hr-ft2)
-
0.2724
0.3301
0.1986
0.4552
0.3062
0.6771
0.6854
0.1319
0.3461
0.2069
0.5496
0.6983
0.1617
0.3870
0.2500
0.5715
Xexit Inner
-
0.2419
0.2486
Xexit Outer
0.301
0.2776
0.2731
G Inner (mlbm/hr-ft2)
-
1.2789
1.5124
G Outer (mlbmlhr-ft2)
1.1260
1.2333
1.5140
CHF at Peak Inner q"(mbtulhr-ft2)
Avg Outer q"(mbtu/hr-ft2)
Avg Outer CHF (mbtulhr-ft2)
Peak Outer q"(mbtulhr-ft2)
CHF at Peak Outer q"(mbtulhr-ft2)
Finally the previously designed 6x6 annular assembly with the distributed grid losses in
the inner annuli was run with the new EPRI-1 correlation in order to assess the potential for
uprating with this assembly. Although the ability to incorporate grids inside of the inner annuli is
currently beyond the economic manufacturability to existing fuel fabricators, it is reasonable to
assume that in the future this ability may be developed provided that this technique helps to
increase the operating margins. The simulation of this 6x6 annular assembly showed that the
MCHFR in the inner annuli was 1.325 while the MCHFR in the outer annuli was 1.117. As per
section 3.2.4, this result shows that the application of the Hench-Gillis correlation could
incorrectly conclude a potential for uprating the annular geometry in BWRs.
100
4. Summary of Conclusions and Recommendations for
Future Studies
4.1. Conclusions
For the case of annular fuel for PWRs, the reactivity-limited discharge burnup was
plotted for both the 17x17 solid reference assembly with UO2 fuel enriched to 5% at 100%
power density and for the 13x13 annular assembly with UN fuel enriched to 5% at 150% power
density, where 3% loss to leakage was assumed. As shown previously in Figure 2.17, the 5%
enriched UN annular-fuel assembly operated at 150% power density reached the minimum
multiplication factor of 1.03 about 50 effective-full-power-days after that of the nominal 17x17
solid-fuel-pin assembly operated at 100% power density.
Furthermore, an appropriate correction factor for uranium nitride loaded annular fuel was
determined for the CASMO-4 neutron transport code. It was shown that a 25% increase in U238
number density for the un-poisoned pins and a 35% increase for the 10 weight percent
gadolinium nitride poisoned pins produced the optimal plutonium tracking and infinite
multiplication factor simulation.
Additionally the 13x13 annular fuel assembly is significantly more controllable due to the
smaller reactivity swing over the fuel lifetime. Thus it was concluded that an annular uranium
nitride assembly at 150% power density can be designed so as not to require enrichments above
5% in order to reach the desirable cycle length of 18 months.
For the case of annular fuel for BWRs, thermal hydraulic simulations were carried out for
a 9x9 solid fuel reference and three different annular assemblies with 5x5, 6x6 and 7x7 fuel pin
101
geometries. Prior research had conducted these thermal hydraulic simulations with the HenchGillis CPR correlation however a benchmarking analysis against NUPEC critical power data has
shown that this correlation was overly conservative. The Hench-Gillis CPR correlation
consistently underpredicted the critical power of the assembly on average of 24% while the
EPRI- 1 Reddy Fighetti underpredicted the critical power on average of only 11%. Therefore due
to the excessive conservatism of the Hench-Gillis CPR correlation, it was concluded that the
EPRI-1 Reddy Fighetti heat balance correlation should be adopted for the simulation of annular
fuel. More importantly, the EPRI-1 correlation treats each subchannel separately and thus can
better predict CHFR in isolated inner channels than the bundle-average Hench-Gillis correlation.
Previous studies of annular fuel for BWRs incorporated internal grid losses for the inner
annuli which was beneficial for limiting critical heat flux conditions. However due to the high
difficulty of fabricating such an assembly, these internal grid losses were removed. The removal
of these grid losses significantly reduced the limiting critical heat flux conditions to below that of
the 9x9 solid reference fuel assembly. These studies also went on to indicate that as much as a
16% uprate (-11% today) for 5x5 annular geometries and a 23% uprate (-18% today) for 6x6
annular geometries might be achievable according to the Hench-Gillis correlation. However as
shown in this thesis, the previous utilization of the Hench-Gillis correlation was not appropriate
and hence the determined uprate was concluded not to be realistic.
Several different strategies were pursued in order to improve the minimum critical heat
flux ratio of the three different annular fuel assemblies including optimization of the fuel pin
dimensions, fuel pin gap, and orifice loss coefficients. However it was concluded that annular
fuel geometries are not a promising strategy for the uprating of BWR fuel assemblies. This
observation was attributed to the fact that the CHFR margin gained from the increase in heat
102
transfer surface area, was being lost on the inability for the coolant in the inner channels to mix
with the surrounding subchannels. More exotic design strategies could be employed in order to
mix the coolant from the inner and outer subchannels however due to the difficulty in fabrication
and licensing, these designs would not likely be adopted.
4.2. Recommendations for Future Studies
The most obvious next step for the PWR annular fuel would be to conduct an equilibrium
core design, reactivity feedback and control characterization with the 5%enriched uranium
nitride annular fuel assembly. Eventually a comprehensive transient and safety analysis for the
design would also need to be completed.
Besides the cost, the primary aspect holding back the deployment of uranium nitride fuel
assemblies is the lack of a materials database on the compound. Without a solid database
covering the materials performance in a reactor environment (for example UN and H20 reaction
kinetics) and issues associated with fabrication, assemblies utilizing this fuel cannot be deployed.
However, given the utility companies trend towards higher discharge burnup of their fuel, fuel
fabrication vendors such as Areva or Westinghouse might wish to pursue R&D into this area
because of the possibly large fiscal benefits.
For BWR annular fuel the next step would be to incorporate more exotic design strategies
which have the capability of mixing the coolant from the inner and outer subchannels. This could
be accomplished with design changes such as the incorporation of holes through the annular fuel
pin or a cutting of the assembly into two or more pieces axially. However these design strategies
103
present significant enough fabrication and licensing issues that the adoption of such designs
would not be likely.
104
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107
Appendix A: CASMO-4 Operational Parameters for Reactivity
Coefficient Calculation
The operational parameters utilized to determine the reactivity coefficients for the 17x1 7
solid reference fuel assembly at 100% power density and BOL are summarized in Table A-i
below.
Table A-1: CASMO-4 Operational Parameters for the 17x17 Reference Case Reactivity Coefficient
Determination
Parameters
Base Value
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
Low Fuel Temperature Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
High Fuel Temperature Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
Low Moderator Temperature Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
900.0
583.1
600.0
Fully Withdrawn
0.0
Base Case
565.8
583.1
600.0
Fully Withdrawn
0.0
1200.0
583.1
600.0
Fully Withdrawn
0.0
900.0
565.8
600.0
Fully Withdrawn
0.0
High Moderator Temperature Case
Fuel Temperature (K)
900.0
108
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
600.0
600.0
Fully Withdrawn
0.0
Low Boron Concentration Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
900.0
583.1
0
Fully Withdrawn
0.0
High Boron Concentration Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
High Void Fraction Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
900.0
583.1
1200.0
Fully Withdrawn
0.0
900.0
583.1
600
Fully Withdrawn
10.0
The operational parameters utilized to determine the reactivity coefficients for the 13x13
annular fuel assembly at 150% power density and BOL are summarized in Table A-2 below.
Table A-2: CASMO-4 Operational Parameters for the 13x13 Annular Case Reactivity Coefficient
Determination
Parameters
Base Value
Base Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
800
583.1
600
Fully Withdrawn
0.0
Low Fuel Temperature Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
565.8
583.1
600
Fully Withdrawn
0.0
109
High Fuel Temperature Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
Temperature Case
Moderator
Low
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
High Moderator Temperature Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
Low Boron Concentration Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
High Boron Concentration Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
High Void Fraction Case
Fuel Temperature (K)
Moderator Temperature (K)
Boron Concentration (ppm)
Control Rod Position
Void Fraction
1100
583.1
600
Fully Withdrawn
0.0
800
565.8
600
Fully Withdrawn
0.0
800
600
60b
Fully Withdrawn
0.0
800
583.1
0
Fully Withdrawn
0.0
800
583.1
1200
Fully Withdrawn
0.0
800
583.1
1200
Fully Withdrawn
10.0
110
Appendix B: VIPRE Input Files
B. 1 GE 9x9 BWR Assembly Reference
*
B
*
*ge9by9 BWR with 2 water rods
1,0,0,
Bwr solid fuel
*vipre.1
*vipre.2
geom,98,98,40,0,0,0,
145.98,0.0,0.5,
*normal geometry input , check last 0---- BWR normal geom input Oo *geom. 1
*geom.2
1,0.0754,0.94248,0.34558,2,2,0.139,0.496,11,0.139,0.496,
2,0.12573,1.25315,0.69115,2,3,0.139,0.562,12,0.122,0.51527,
3,0.12573,1.25315,0.69115,2,4,0.139,0.562,13,0.122,0.51527,
4,0.12573,1.25315,0.69115,2,5,0.139,0.562,14,0.122,0.51527,
5,0.12573,1.25315,0.69115,2,6,0.139,0.562,15,0.122,0.51527,
6,0.12573,1.25315,0.69115,2,7,0.139,0.562,16,0.122,0.51527,
7,0.12573,1.25315,0.69115,2,8,0.139,0.562,17,0.122,0.51527,
8,0.12573,1.25315,0.69115,2,9,0.139,0.562,18,0.122,0.51527,
9,0.12573,1.25315,0.69115,2,10,0.139,0.496,19,0.122,0.51527,
10,0.0754,0.94248,0.34558,1,20,0.139,0.496,
11,0.12573,1.25315,0.69115,2,12,0.122,0.51527,21,0.139,0.562,
12,0.16379,1.3823,1.3823,2,13,0.122,0.562,22,0.122,0.562,
13,0.16379,1.3823,1.3823,2,14,0.122,0.562,23,0.122,0.562,
14,0.16379,1.3823,1.3823,2,15,0.122,0.562,24,0.122,0.562,
15,0.16379,1.3823,1.3823,2,16,0.122,0.562,25,0.122,0.562,
16,0.16379,1.3823,1.3823,2,17,0.122,0.562,26,0.122,0.562,
17,0.16379,1.3823,1.3823,2,18,0.122,0.562,27,0.122,0.562,
18,0.16379,1.3823,1.3823,2,19,0.122,0.562,28,0.122,0.562,
19,0.16379,1.3823,1.3823,2,20,0.122,0.51527,29,0.122,0.562,
20,0.12573,1.25315,0.69115,1,30,0.139,0.562,
21,0.12573,1.25315,0.69115,2,22,0.122,0.51527,31,0.139,0.562,
22,0.16379,1.3823,1.3823,2,23,0.122,0.562,32,0.122,0.562,
23,0.16379,1.3823,1.3823,2,24,0.122,0.562,33,0.122,0.562,
24,0.16379,1.3823,1.3823,2,25,0.122,0.562,34,0.122,0.562,
25,0.16379,1.3823,1.3823,2,26,0.122,0.562,35,0.122,0.489,
26,0.16379,1.3823,1.3823,2,27,0.122,0.562,36,0.122,0.600,
27,0.16379,1.3823,1.3823,2,28,0.122,0.562,37,0.122,0.562,
28,0.16379,1.3823,1.3823,2,29,0.122,0.562,38,0.122,0.562,
29,0.16379,1.3823,1.3823,2,30,0.122,0.51527,39,0.122,0.562,
30,0.12573,1.25315,0.69115,1,40,0.139,0.562,
31,0.12573,1.25315,0.69115,2,32,0.122,0.51527,41,0.139,0.562,
32,0.16379,1.3823,1.3823,2,33,0.122,0.562,42,0.122,0.562,
33,0.16379,1.3823,1.3823,2,34,0.122,0.562,43,0.122,0.562,
34,0.17036,1.67088,1.14731,2,35,0.0704,0.562,44,0.0704,0.562,
111
35,0.06890,0.88126,0.53619,1,36,0.1308,0.562,
36,0.23436,1.62784,1.1809,2,37,0.122,0.600,45,0.2401,0.530,
37,0.16379,1.3823,1.3823,2,38,0.122,0.562,46,0.122,0.600,
38,0.16379,1.3823,1.3823,2,39,0.122,0.562,47,0.122,0.562,
39,0.16379,1.3823,1.3823,2,40,0.122,0.51527,48,0.122,0.562,
40,0.12573,1.25315,0.69115,1,49,0.139,0.562,
41,0.12573,1.25315,0.69115,2,42,0.122,0.51527,50,0.139,0.562,
42,0.16379,1.3823,1.3823,2,43,0.122,0.562,51,0.122,0.562,
43,0.16379,1.3823,1.3823,2,44,0.122,0.527,52,0.122,0.562,
44,0.06890,0.88126,0.53619,1,53,0.1343,0.530,
45,0.14739,1.2183,0.24591,2,46,0.2401,0.530,54,0.061,0.795,
46,0.23436,1.62784,1.1809,2,47,0.122,0.600,55,0.1308,0.530,
47,0.16379,1.3823,1.3823,2,48,0.122,0.562,56,0.122,0.562,
48,0.16379,1.3823,1.3823,2,49,0.122,0.51527,57,0.122,0.562,
49,0.12573,1.25315,0.69115,1,58,0.139,0.562,
50,0.12573,1.25315,0.69115,2,51,0.122,0.51527,59,0.139,0.562,
51,0.16379,1.3823,1.3823,2,52,0.122,0.562,60,0.122,0.562,
52,0.16379,1.3823,1.3823,2,53,0.122,0.600,61,0.122,0.562,
53,0.23436,1.62784,1.1809,2,54,0.2401,0.530,62,0.122,0.600,
54,0.14739,1.2183,0.24591,1,63,0.2401,0.530,
55,0.06890,0.88126,0.53619,2,56,0.122,0.562,65,0.0704,0.530,
56,0.16379,1.3823,1.3823,2,57,0.122,0.562,66,0.122,0.562,
57,0.16379,1.3823,1.3823,2,58,0.122,0.51527,67,0.122,0.562,
58,0.12573,1.25315,0.69115,1,68,0.139,0.562,
59,0.12573,1.25315,0.69115,2,60,0.122,0.51527,69,0.139,0.562,
60,0.16379,1.3823,1.3823,2,61,0.122,0.562,70,0.122,0.562,
61,0.16379,1.3823,1.3823,2,62,0.122,0.562,71,0.122,0.562,
62,0.16379,1.3823,1.3823,2,63,0.122,0.600,72,0.122,0.562,
63,0.23436,1.62784,1.1809,2,64,0.1308,0.530,73,0.122,0.600,
64,0.06890,0.88126,0.53619,2,65,0.0704,0.562,74,0.122,0.562,
65,0.17036,1.67088,1.14731,2,66,0.122,0.562,75,0.122,0.562,
66,0.16379,1.3823,1.3823,2,67,0.122,0.562,76,0.122,0.562,
67,0.16379,1.3823,1.3823,2,68,0.122,0.51527,77,0.122,0.562,
68,0.12573,1.25315,0.69115,1,78,0.139,0.562,
69,0.12573,1.25315,0.69115,2,70,0.122,0.51527,79,0.139,0.562,
70,0.16379,1.3823,1.3823,2,71,0.122,0.562,80,0.122,0.562,
71,0.16379,1.3823,1.3823,2,72,0.122,0.562,81,0.122,0.562,
72,0.16379,1.3823,1.3823,2,73,0.122,0.562,82,0.122,0.562,
73,0.16379,1.3823,1.3823,2,74,0.122,0.562,83,0.122,0.562,
74,0.16379,1.3823,1.3823,2,75,0.122,0.562,84,0.122,0.562,
75,0.16379,1.3823,1.3823,2,76,0.122,0.562,85,0.122,0.562,
76,0.16379,1.3823,1.3823,2,77,0.122,0.562,86,0.122,0.562,
77,0.16379,1.3823,1.3823,2,78,0.122,0.51527,87,0.122,0.562,
78,0.12573,1.25315,0.69115,1,88,0.139,0.562,
79,0.12573,1.25315,0.69115,2,80,0.122,0.51527,89,0.139,0.496,
80,0.16379,1.3823,1.3823,2,81,0.122,0.562,90,0.122,0.51527,
81,0.16379,1.3823,1.3823,2,82,0.122,0.562,91,0.122,0.51527,
82,0.16379,1.3823,1.3823,2,83,0.122,0.562,92,0.122,0.51527,
83,0.16379,1.3823,1.3823,2,84,0.122,0.562,93,0.122,0.51527,
84,0.16379,1.3823,1.3823,2,85,0.122,0.562,94,0.122,0.51527,
85,0.16379,1.3823,1.3823,2,86,0.122,0.562,95,0.122,0.51527,
112
86,0.16379,1.3823,1.3823,2,87,0.122,0.562,96,0.122,0.51527,
87,0.16379,1.3823,1.3823,2,88,0.122,0.51527,97,0.122,0.51527,
88,0.12573,1.25315,0.69115,1,98,0.139,0.496,
89,0.0754,0.94248,0.34558,1,90,0.139,0.496,
90,0.12573,1.25315,0.69115,1,91,0.139,0.562,
91,0.12573,1.25315,0.69115,1,92,0.139,0.562,
92,0.12573,1.25315,0.69115,1,93,0.139,0.562,
93,0.12573,1.25315,0.69115,1,94,0.139,0.562,
94,0.12573,1.25315,0.69115,1,95,0.139,0.562,
95,0.12573,1.25315,0.69115,1,96,0.139,0.562,
96,0.12573,1.25315,0.69115,1,97,0.139,0.562,
97,0.12573,1.25315,0.69115,1,98,0.139,0.496,
98,0.0754,0.94248,0.34558,
*99,0.66476,2.890265,2.890265, *water tube
*"100,0.66476,2.890265,2.890265, *water tube
*99,1.6694,5.415,5.415,
*100,1.6694,5.415,5.415,
*101,0.8655,10.32,10.32,
*102,0.8655,10.32,10.32,
*geom.4
prop,0,1,2,1 *internal EPRI functions *prop. 1
rods,1,80,1,3,1,0,0,0,0,0,0 *three material types,one type of geo. *rods. 1
145.98,0.0,0,0
*rods.2
26
*One axial profile only (rods.4)
0.00,0.00,?
3.04,0.38,?
9.12,0.69,?
15.21,0.93,
21.29,1.10,?
27.37,1.21,?
33.45,1.30,?
39.54,1.47,
45.62,1.51,?
51.70,1.49,?
57.78,1.44,?
63.87,1.36,
69.95,1.28,?
76.03,1.16,?
82.11,1.06,?
88.20,1.01,
94.28,0.97,?
100.36,0.94,?
106.44,0.97,?
112.53,0.96,
118.61,0.91,?
124.69,0.77,?
130.77,0.59,?
*rods3
113
136.86,0.38,
142.94,0.12,?
145.98,0.00,
*****rods geometry input
1,1,1.10,1,1,0.25,2,0.25,11,0.25,12,0.25,
2,1,1.21,1,2,0.25,3,0.25,12,0.25,13,0.25,
3,1,1.21,1,3,0.25,4,0.25,13,0.25,14,0.25,
4,1,1.19,1,4,0.25,5,0.25,14,0.25,15,0.25,
5,1,1.17,1,5,0.25,6,0.25,15,0.25,16,0.25,
6,1,1.18,1,6,0.25,7,0.25,16,0.25,17,0.25,
7,1,1.21,1,7,0.25,8,0.25,17,0.25,18,0.25,
8,1,1.20,1,8,0.25,9,0.25,18,0.25,19,0.25,
9,1,1.11,1,9,0.25,10,0.25,19,0.25,20,0.25,
*rods.9
10,1,1.21,1,11,0.25,12,0.25,21,0.25,22,0.25,
11,1,0.95,1,12,0.25,13,0.25,22,0.25,23,0.25,
12,1,0.98,1,13,0.25,14,0.25,23,0.25,24,0.25,
13,1,1.03,1,14,0.25,15,0.25,24,0.25,25,0.25,
14,1,0.74,1,15,0.25,16,0.25,25,0.25,26,0.25,
15,1,1.03,1,16,0.25,17,0.25,26,0.25,27,0.25,
16,1,0.97,1,17,0.25,18,0.25,27,0.25,28,0.25,
17,1,0.94,1,18,0.25,19,0.25,28,0.25,29,0.25,
18,1,1.22,1,19,0.25,20,0.25,29,0.25,30,0.25,
19,1,1.23,1,21,0.25,22,0.25,31,0.25,32,0.25,
20,1,0.98,1,22,0.25,23,0.25,32,0.25,33,0.25,
21,1,0.42,1,23,0.25,24,0.25,33,0.25,34,0.25,
22,1,0.90,1,24,0.25,25,0.25,34,0.290,35,0.210,
23,1,0.97,1,25,0.25,26,0.25,35,0.1779,36,0.3221,
24,1,0.84,1,26,0.25,27,0.25,36,0.25,37,0.25,
25,1,0.42,1,27,0.25,28,0.25,37,0.25,38,0.25,
26,1,0.97,1,28,0.25,29,0.25,38,0.25,39,0.25,
27,1,1.20,1,29,0.25,30,0.25,39,0.25,40,0.25,
28,1,1.19,1,31,0.25,32,0.25,41,0.25,42,0.25,
29,1,0.79,1,32,0.25,33,0.25,42,0.25,43,0.25,
30,1,0.91,1,33,0.25,34,0.290,43,0.25,44,0.210,
31,1,1.08,1,36,0.2822,37,0.25,45,0.1856,46,0.2822,
32,1,0.82,1,37,0.25,38,0.25,46,0.25,47,0.25,
33,1,0.43,1,38,0.25,39,0.25,47,0.25,48,0.25,
34,1,1.17,1,39,0.25,40,0.25,48,0.25,49,0.25,
35,1,1.17,1,41,0.25,42,0.25,50,0.25,51,0.25,
36,1,0.73,1,42,0.25,43,0.25,51,0.25,52,0.25,
37,1,0.97,1,43,0.25,44,0.1779,52,0.25,53,0.3221,
38,1,0.96,1,46,0.3221,47,0.25,55,0.1779,56,0.25,
39,1,0.73,1,47,0.25,48,0.25,56,0.25,57,0.25,
40,1,1.16,1,48,0.25,49,0.25,57,0.25,58,0.25,
41,1,1.18,1,50,0.25,51,0.25,59,0.25,60,0.25,
42,1,1.03,1,51,0.25,52,0.25,60,0.25,61,0.25,
43,1,0.84,1,52,0.25,53,0.25,61,0.25,62,0.25,
44,1,1.10,1,53,0.2822,54,0.1856,62,0.25,63,0.2822,
114
45,1,0.90,1,55,0.210,56,0.25,65,0.290,66,0.25,
46,1,0.44,1,56,0.25,57,0.25,66,0.25,67,0.25,
47,1,1.18,1,57,0.25,58,0.25,67,0.25,68,0.25,
48,1,1.22,1,59,0.25,60,0.25,69,0.25,70,0.25,
49,1,0.98,1,60,0.25,61,0.25,70,0.25,71,0.25,
50,1,0.41,1,61,0.25,62,0.25,71,0.25,72,0.25,
51,1,.84,1,62,0.25,63,0.25,72,0.25,73,0.25,
52,1,.97,1,63,0.3221,64,0.1779,73,0.25,74,0.25,
53, 1,.89,1,64,0.210,65,0.290,74,0.25,75,0.25,
54,1,.42,1,65,0.25,66,0.25,75,0.25,76,0.25,
55,1,.99,1,66,0.25,67,0.25,76,0.25,77,0.25,
56,1,1.22,1,67,0.25,68,0.25,77,0.25,78,0.25,
57,1,1.22,1,69,0.25,70,0.25,79,0.25,80,0.25,
58,1,0.94,1,70,0.25,71,0.25,80,0.25,81,0.25,
59,1,0.98,1,71,0.25,72,0.25,81,0.25,82,0.25,
60,1,1.03,1,72,0.25,73,0.25,82,0.25,83,0.25,
61,1,0.73,1,73,0.25,74,0.25,83,0.25,84,0.25,
62,1,1.03,1,74,0.25,75,0.25,84,0.25,85,0.25,
63,1,0.98,1,75,0.25,76,0.25,85,0.25,86,0.25,
64,1,0.95,1,76,0.25,77,0.25,86,0.25,87,0.25,
65,1,1.22,1,77,0.25,78,0.25,87,0.25,88,0.25,
66,1,1.11,1,79,0.25,80,0.25,89,0.25,90,0.25,
67,1,1.22,1,80,0.25,81,0.25,90,0.25,91,0.25,
68,1,1.21,1,81,0.25,82,0.25,91,0.25,92,0.25,
69,1,1.18,1,82,0.25,83,0.25,92,0.25,93,0.25,
70,1,1.17,1,83,0.25,84,0.25,93,0.25,94,0.25,
71,1,1.18,1,84,0.25,85,0.25,94,0.25,95,0.25,
72,1,1.21,1,85,0.25,86,0.25,95,0.25,96,0.25,
73,1,1.22,1,86,0.25,87,0.25,96,0.25,97,0.25,
74,1,1.12,1,87,0.25,88,0.25,97,0.25,98,0.25,
75,2,0.0,1,34,0.17006,35,0.11208,44,0.11208,45,0.15792,54,0.15792,?
36,0.14517,53,0.14517,
*Water rod (ext)
*-75,2,0.0,1,99,1.0,
*Water rod (int)
76,2,0.0,1,45,0.15792,54,0.15792,55,0.11208,65,0.17006,?
46,0.14517,63,0.14517,
*Water rod (ext)
*-76,2,0.0,1,100,1.0,
*Water rod (int)
*
-77,3,0.0,1,1,0.07105,2,0.10723,3,0.10723,?
5,0.10723,6,0.10723,7,0.10723,8,0.10723,9,0.10723,?
10,0.07105,
*77,3,0.0,1,99,1.0,
-78,3,0.0,1,10,0.07105,20,0.10723,30,0.10723,?
49,0.10723,58,0.10723,68,0.10723,78,0.10723,?
98,0.07105,
*78,3,0.0,1,100,1.0,
-79,3,0.0,1,89,0.07105,90,0.10723,91,0.10723,92,0.10723,?
93,0.10723,94,0.10723,95,0.10723,96,0.10723,?
98,0.07105,
*79,3,0.0,1,101,1.0,
-80,3,0.0,1,1,0.07105,11,0.10723,21,0.10723,31,0.10723,?
41,0.10723,50,0.10723,59,0.10723,69,0.10723,79,?
115
0.10723,89,0.07105,
*80,3,0.0,1,102,1.0,
*rods.9
0
*
*1,2,3,4,5,6,7,8,9,
*rods.57
*10,11,12,13,14,15,16,17,18,
*19,20,21,22,23,24,25,26,27,
*28,29,30,31,32,33,34,
*35,36,37,38,39,40,
*41,42,43,44,45,46,47,
*48,49,50,51,52,53,54,55,56,
*57,58,59,60,61,62,63,64,65,
*66,67,68,69,70,71,72,73,74,
*blank line above necessary /rods.57 -HG CPR corr
*rods.58
*74,0.562,0.139,0.44,14.43,
*
*fuel
*rods.62
1,nucl,0.44,0.376,12,0.0,0.028
*rods 63
0,0,0,0,0,1056.66,0.955,0,
*constant radial power in the pellet, no power in the clad
*water tube
*rods.68
*rods.69
2,tube,0.98,0.92,1
3,1,0.03,1.0,
*wall
3,wall,5.415,0.0,1
3,1,0.1,1.0,
1,1,409.7,clad,
662,0.076,10.05,
*P,T
oper,1,1,0,1,0,1,0,0,0,
*oper.1 /flow is specified
*oper.2 *first word to be changed if you change BC
*oper.3 *only if first w above is not 0.0
-1.0,0.0,2.0,0.005,
0
*oper.5
1035.0,533.0,33.6,85.226,0.0
*
*Rod power got from total power divided total number of rods
0,
*no forcing functions
*oper. 12
**********************************
*correlations
corr, 1,2,0,
epri,epri,epri,none,
0.2,
ditb,chen,chen,epri,cond,g5.7,
epri,
1,0,0.0,
*hnch,
*corr.1
*corr.2
*corr.3
*correlation for boiling curve *corr.6
*corr.16,for epri
mixx,0,0,0,
0.8,0.0048,0.0,
*************************************************************
116
*grid.1
grid,0,7,
9.4609, 1.104, 0.3751,21.089,182.049,300.000 *grid2
98,10,
*grid.4
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
*grid.5
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,
*grid.5
*
0.000,4, 7.3,1, 19.5,2, 39.0,2, 58.5,2, 78.0,2, 97.5,2,117.0,2 *grid6
136.5,2,143.0,3
0,
cont,
0.0,0,500,100,3,0, *iterative solution
0.10,0.00001,0.001,0.05,0.01,0.9,1.5,1.0,
*cont. 1
*cont.2
*cont.3
5,0,0,0,0,0,1,1,0,0,0,1,1,0,
*cont.6
100.,0.0,0.0,0.0,0.0,0.0,
endd
*cont.7
*
*end of data input
0
B.2 Annular 5x5 BWR Assembly
* 1 assembly, 5x5 annular pins, using BWR power distribution
*
Hot Assembly
*
*
*
*
*
*
one axial profile and approximate radial profile
parDi: 0.84
parfuel: 0.90
Superpower: 1.00
*
*
*
*
*
EPRI-1 Reddy Fighetti correlation for CHFR
*
*This input is under construction
1,0,0,
Bwr annular fuel
*
geom,61,61,36,0,0,0,
*
178.5,0.0,0.5,
*vipre.l
*vipre.2
*normal geometry input
*geom. 1
*geom.2
1,0.165838,1.879372,0.74592,2,2,0.117212,0.80398,7,0.117212,0.80398,
2,0.258605,2.476104,1.49184,2,3,0.117212,1.02984,8,0.108015,0.80398,
3,0.258605,2.4761044,1.49184,2,4,0.117212,1.02984,9,0.108015,0.80398,
4,0.258605,2.476104,1.49184,2,5,0.117212,1.02984,10,0.108015,0.80398,
5,0.258605,2.476104,1.49184,2,6,0.117212,0.80398,11,0.108015,0.80398,
6,0.165838,1.879372,0.74592,1,12,0.117212,0.80398,
117
7,0.258605,2.476104,1.49184,2,8,0.108015,0.80398,13,0.117212,1.02984,
8,0.38704,2.892537,2.892537,2,9,0.108015,1.02984,14,0.108015,1.02984,
9,0.38704,2.892537,2.892537,2,10,0.108015,1.02984,15,0.108015,1.02984,
10,0.38704,2.892537,2.892537,2,11,0.108015,1.02984,16,0.108015,1.02984,
11,0.38704,2.892537,2.892537,2,12,0.108015,0.80398,17,0.108015,1.02984,
12,0.258605,2.476104,1.49184,1,18,0.117212,1.02984,
13,0.258605,2.476104,1.49184,2,14,0.108015,0.80398,19,0.117212,1.02984,
14,0.38704,2.892537,2.892537,2,15,0.108015,1.02984,20,0.108015,1.02984,
15,0.38704,2.892537,2.169405,2,16,0.108015,1.02984,21,0.108015,1.02984,
16,0.38704,2.892537,2.169405,2,17,0.108015,1.02984,22,0.108015,1.02984,
17,0.38704,2.892537,2.892537,2,18,0.108015,0.80398,23,0.108015,1.02984,
18,0.258605,2.476104,1.49184,1,24,0.117212,1.02984,
19,0.258605,2.476104,1.49184,1,20,0.108015,0.80398,25,0.117212,1.02984,
20,0.38704,2.892537,2.892537,2,21,0.108015,1.02984,26,0.108015,1.02984,
21,0.38704,2.892537,2.169405,2,22,0.108015,1.02984,27,0.108015,1.02984,
22,0.38704,2.892537,2.169405,2,23,0.108015,1.02984,
23,0.38704,2.892537,2.892537,2,24,0.108015,0.80398,29,0.108015,1.02984,
24,0.258605,2.476104,1.49184,1,30,0.117212,1.02984,
25,0.258605,2.476104,1.49184,1,26,0.108015,0.80398,31,0.117212,0.80398,
26,0.38704,2.892537,2.892537,2,27,0.108015,1.02984,32,0.108015,0.80398,
27,0.38704,2.892537,2.892537,2,28,0.108015,0.80398,
28,0.38704,2.892537,2.892537,2,29,0.108015,1.02984,34,0.108015,0.80398,
29,0.38704,2.892537,2.892537,2,30,0.108015,0.80398,35,0.108015,0.80398,
30,0.258605,2.476104,1.49184,1,36,0.117212,0.80398,
31,0.165838,1.879372,0.74592,1,32,0.117212,0.80398,
32,0.258605,2.476104,1.49184,1,33,0.117212,1.02984,
33,0.258605,2.476104,1.49184,1,34,0.117212,1.02984,
34,0.258605,2.476104,1.49184,1,35,0.117212,1.02984,
35,0.258605,2.476104,1.49184,1,36,0.117212,0.80398,
36,0.165838,1.879372,0.74592,
*Internal subchannels
37,0.224628,1.680083,1.680083,
38,0.224628,1.680083,1.680083,
39,0.224628,1.680083,1.680083,
40,0.224628,1.680083,1.680083,
41,0.224628,1.680083,1.680083,
42,0.224628,1.680083,1.680083,
43,0.224628,1.680083,1.680083,
44,0.224628,1.680083,1.680083,
45,0.224628,1.680083,1.680083,
46,0.224628,1.680083,1.680083,
47,0.224628,1.680083,1.680083,
48,0.224628,1.680083,1.680083,
49,0.224628,1.680083,1.680083,
50,0.224628,1.680083,1.680083,
51,0.224628,1.680083,1.680083,
52,0.224628,1.680083,1.680083,
53,0.224628,1.680083,1.680083,
54,0.224628,1.680083,1.680083,
55,0.224628,1.680083,1.680083,
56,0.224628,1.680083,1.680083,
57,0.224628,1.680083,1.680083,
58,0.224628,1.680083,1.680083,
59,0.224628,1.680083,1.680083,
60,0.224628,1.680083,1.680083,
61,0.56337,2.66074,2.66074,
118
*geom.4
prop,0,1,2,1
*internal EPRI functions *prop.1
rods,1,50,1,2,4,0,0,0,0,0,0, *three material types,one type of geo. *rods. 1
*rods.2
144.0,13.513,0,0,
25
*rods3
*Normal rod (rods.4)
0.,0.,?
6.0825,0.38,?
12.165,0.69,?
18.2475,0.93,
24.33,1.1,?
30.4125,1.21,?
36.495,1.3,?
42.5775,1.47,
48.66,1.51,?
54.7425,1.49,?
60.825,1.44,?
66.9075,1.36,
72.99,1.28,?
79.0725,1.16,?
85.155,1.06,?
91.2375,1.01,?
97.32,0.97,?
103.4025,0.94,?
109.485,0.97,?
115.675,0.96,
121.65,0.91,?
127.7325,0.77,?
133.815,0.59,?
139.8975,0.38,
145.98,0.12,
******rods geomatry input
*rods.9
1,1,1.039,1,1,0.25,2,0.25,7,0.25,8,0.25,
-1,1,1.039,1,37,1,
2,1,1.220,1,2,0.25,3,0.25,8,0.25,9,0.25,
-2,1,1.220,1,38,1,
3,1,1.102,1,3,0.25,4,0.25,9,0.25,10,0.25,
-3,1,1.102,1,39,1,
4,1,1.119,1,4,0.25,5,0.25,10,0.25,11,0.25,
-4,1,1.119,1,40,1,
5,1,1.099,1,5,0.25,6,0.25,11,0.25,12,0.25,
-5,1,1.099,1,41,1,
6,1,1.220,1,7,0.25,8,0.25,13,0.25,14,0.25,
-6,1,1.220,1,42,1,
7,1,0.371,1,8,0.25,9,0.25,14,0.25,15,0.25,
-7,1,0.371,1,43,1,
8,1,1.001,1,9,0.25,10,0.25,15,0.25,16,0.25,
-8,1,1.001,1,44,1,
9,1,1.085,1,10,0.25,11,0.25,16,0.25,17,0.25,
-9,1,1.085,1,45,1,
10,1,1.109,1,11,0.25,12,0.25,17,0.25,18,0.25,
119
-10,1,1.109,1,46,1,
11,1,1.102,1,13,0.25,14,0.25,19,0.25,20,0.25,
-11,1,1.102,1,47,1,
12,1,1.001,1,14,0.25,15,0.25,20,0.25,21,0.25,
-12,1,1.001,1,48,1,
13,1,0.367,1,16,0.25,17,0.25,22,0.25,23,0.25,
-13,1,0.367,1,49,1,
14,1,1.069,1,17,0.25,18,0.25,23,0.25,24,0.25,
-14,1,1.069,1,50,1,
15,1,1.119,1,19,0.25,20,0.25,25,0.25,26,0.25,
-15,1,1.119,1,51,1,
16,1,1.085,1,20,0.25,21,0.25,26,0.25,27,0.25,
-16,1,1.085,1,52,1,
17,1,0.367,1,21,0.25,22,0.25,27,0.25,28,0.25,
-17,1,0.367,1,53,1,
18,1,1.002,1,22,0.25,23,0.25,28,0.25,29,0.25,
-18,1,1.002,1,54,1,
19,1,1.083,1,23,0.25,24,0.25,29,0.25,30,0.25,
-19,1,1.083,1,55,1,
20,1,1.099,1,25,0.25,26,0.25,31,0.25,32,0.25,
-20,1,1.099,1,56,1,
21,1,1.109,1,26,0.25,27,0.25,32,0.25,33,0.25,
-21,1,1.109,1,57,1,
22,1,1.069,1,27,0.25,28,0.25,33,0.25,34,0.25,
-22,1,1.069,1,58,1,
23,1,1.083,1,28,0.25,29,0.25,34,0.25,35,0.25,
-23,1,1.083,1,59,1,
24,1,1.081,1,29,0.25,30,0.25,35,0.25,36,0.25,
-24,1,1.081,1,60,1,
*water rod
25,2,0.0,1,15,0.25,16,0.25,21,0.25,22,0.25,
*water rod
-25,2,0.0,1,-61,1,
*rcids.9
*1,2,3,4,5,
*6,7,8,9,10,
*11,12,25,13,14,
"15,16,17,18,19,
*20,21,22,23,24,
*blank line above necessary /rods.57 -HG CPR corr
*rods.58,
*25,1.029839,0.119215,0.917805,16.038201,
*0
*rods.59
*fuel
1,tube,0.949763,0.534803,5,
*rods.68
*
2,1,0.033465,0.0,? *inner cladding
2,2,0.003937,0.0,? *inner gap
8,3,0.132677,1.0,? *fuel ring
*outer gap
2,4,0.003937,0.0,
*outer cladding
2,1,0.033465,0.0,
*water tube
2,tube,0.917805,0.846939,1
3,1,0.035433,0.0,
*rods.69
*rods.69
*rods.69
*rods.69
*rods.69
*rods.68
*rods.69
*
120
1,18,409.0,clad,
*table for cladding
0.0,0.0671,7.3304509,?
25,0.0671,7.3304509,
50,0.0671,7.33045093,?
65,0.0671,7.33045093,
80.33,0.0671,7.33045093,?
260.33,0.07212,8.11585329,
692.33,0.07904,9.80167423,?
1502.33,0.08955,13.2923,
1507.73,0.11988,13.3211893,?
1543.73,0.14089,13.51665,
1579.73,0.14686,13.717249,?
1615.73,0.1717,13.923198,
1651.73,0.1949,14.1347101,?
1687.73,0.18388,14.351998,
1723.73,0.1478,14.5752746,?
1759.73,0.112,14.804753,
1786.73,0.085,14.9810589,?
2240.33,0.085,18.5665964,
*gap
2,1,0.025,igap,
1,1.240834,0.346679,
*rods.70
*Cp=5195J/kg-K *gap=6000
*fuel
3,22,650.617,FU02,
86,0.05677357,4.73275874,?
176,0.06078589,4.2991726,
266,0.06366347,3.93877428,?
356,0.06581210,3.6345405,
446,0.06747631,3.37435643,?
536,0.06880819,3.1493668,
626,0.06990545,2.95294976,?
716,0.07083283,2.78005572,
806,0.07163441,2.62676801,?
896,0.07234099,2.49000319,
986,0.07297458,2.36730189,?
1076,0.07355124,2.25667975,
1166,0.07408294,2.1565193,?
1256,0.07457886,2.06549023,
1346,0.07504628,1.98248979,?
1436,0.07549123,1.90659753,
1526,0.0759191,1.83704065,?
1616,0.07633503,1.77316713,
1706,0.0767443,1.7144247,?
1796,0.07715268,1.66034425,
1886,0.07756663,1.61052668,?
1976,0.07799351,1.5646323,
*
*outer gap
4,1,0.025,ogap,
1,1.240834,0.34667666,
*rods.70
*rods.71
*rods.70
*rods.71
*rods.70
*Cp=5195J/kg-K *gap=6000
*rods.71
***********************************
*P,T
121
oper, 1,1,0,1,0,1,0,0,0
*oper. 1
*oper.2 *first word to be changed if you change BC
-1.0,0.0,2.0,0.005,
*oper.3 *only if first w above is not 0.0
0
*oper.5
1035.0,533.0,33.30,251.426000,0.0,
* 13400 kg/s ,5*Rod power got from total power divided total number of rods
*oper. 12
*no forcing functions
0,
************************************
*correlations
corr, 1,2,0,
*corr.1
*corr.2
epri,epri,epri,none,
*corr.3
0.2,
ditb,chen,chen,epri,cond,g5.7, *correlation for boiling curve *corr.6
*corr.9
epri,
*corr. 16,for epri
1,0,0.0,
*corr 18, Hench-Gillis
*mine,
************************
*grid.1
grid,0,5,
*grid.2
24.280,6.63,1.50,1.46,20000,
*pressure drop is 24.28 for the average rod and 23.37 for the hot rod
*grid.4
36,10,
*grid.5
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
*grid.5
33,34,35,36,
1.0,1,12.263,2,31.225,3,52.537,3,72.7,3,92.857,3,112.857,3,133.033,3,
*grid loc. *grid.6
153.203,3,175.445,4,
24,3
37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,
1.0,1,
1,1,
61,
1.0,5,
0,
cont,
0.0,0,750,50,3,0, *iterative solution
0.10,0.00001,0.001,0.05,0.01,0.9,1.5,1.0,
5,0,0,0,0,0,1,1,0,0,0,1,1,0,
5000.,0.0,0.0,0.0,0.0,0.0,
endd
*cont. 1
*cont.2
*cont.3
*cont.6
*cont.7
*end of data input
0
B.3 Annular 6x6 BWR Assembly
***********************************************************************
* I assembly, 6x6 annular pins, using BWR power distribution
*
Hot Assembly
*
*
122
*
*
*
*
*
*
one axial profile and approximate radial profile
*
parDi: 0.80
*
parfuel: 0.90
*
Superpower: 1.00
EPRI-1 correlation for CHFR
*
ITERATIVE solution
*
*
***********************************************************************
1,0,0,
Bwr annular fuel
geom,85,85,36,0,0,0,
*vipre. 1
*vipre.2
*normal geometry input
*geom.1
*
173.006,0.0,0.5,
*geom.2
*
1,0.07566,1.57013,0.65173,2,2,0.04430,0.66532,8,0.04430,0.66532,
2,0.12976,2.17490,1.30346,2,3,0.04430,0.87144,9,0.04163,0.66532,
3,0.12976,2.17490,1.30346,2,4,0.04430,0.87144,10,0.04163,0.66532,
4,0.12976,2.17490,1.30346,2,5,0.04430,0.87144,11,0.04163,0.66532,
5,0.12976,2.17490,1.30346,2,6,0.04430,0.87144,12,0.04163,0.66532,
6,0.12976,2.17490,1.30346,2,7,0.04430,0.66532,13,0.04163,0.66532,
7,0.07566,1.57013,0.65173,1,14,0.04430,0.66532,
8,0.12976,2.17490,1.30346,2,9,0.04163,0.66532,15,0.04430,0.87144,
9,0.21859,2.60692,2.60692,2,10,0.04163,0.87144,
10,0.21859,2.60692,2.60692,2,11,
0.87144,170.04163,0.87144,
11,0.21859,2.60692,2.60692,2,12,0.04163,0.87144,1,0.04163,,0.87144,
12,0.21859,2.60692,2.60692,2,1300163087119,0.04163,0.87144,
13,0.21859,2.60692,2.60692,2,14,0.04163,0.66532,20,0.04163,0.87144,
14,0.12976,2.17490,1.30346,1,21,0.04430,0.87144,
15,0.12976,2.17490,1.30346,2,16,0.04163,0.66532,22,0.04430,0.87144,
16,0.21859,2.60692,2.60692,2,17,0.04163,0.87144,23,0.04163,0.87144,
17,0.21859,2.60692,2.60692,2,18
163,0.87144,24,0.04163,0.87144,
18,0.21859,2.60692,1.95519,2,19,0.04163,0.87144,25,0.04163,0.87144,
19,0.21859,2.60692,1.95519,2,20,0.04163,0.87144,26,0.04163,0.87144,
20,0.21859,2.60692,2.60692,2,21,0.04163,0.66532,27,0.04163,0.87144,
21,0.12976,2.17490,1.30346,1,28,0.04430,0.87144,
22,0.12976,2.17490,1.30346,2,23,0.04163,0.66532,29,0.04430,0.87144,
23,0.21859,2.60692,2.60692,2,24,0.04163,0.87144,30,0.04163,0.87 144,
24,0.21859,2.60692,1.95519,2,25,0.04163,0.87144,31,0.04163,0.87144,
25,0.21859,2.60692,1.95519,2,26,0.04163,0.87144,32,0.04163,0.87144,
26,0.21859,2.60692,1.95519,2,27,0.04163,0.87144,33,0.04163,0.87144,
27,0.21859,2.60692,2.60692,2,28,0.04163,0.66532,34,0.04163,0.87144,
28,0.12976,2.17490,1.30346,1,35,0.04430,0.87144,
29,0.12976,2.17490,1.30346,2,30,0.04163,0.66532,36,0.04430,0.87144,
30,0.21859,2.60692,2.60692,2,31,0.04163,0.87144,3,0.04163,0.87144,
31,0.21859,2.60692,1.95519,2,32,0.04163,0.87144,38,0.04163,0.87144,
32,0.21859,2.60692,1.95519,2,33,0.04163,0.87144,39,0.04163,0.87144,
33,0.21859,2.60692,2.60692,2,34,0.04163,0.87144,40,0.04163,0.87144,
34,0.21859,2.60692,2.60692,2,35,0.04163,0.66532,41,0.04163,0.87144,
35,0.12976,2.17490,1.30346,1,42,0.04430,0.87144,
36,0.12976,2.17490,1.30346,2,37,0.04163,0.66532,43,0.04430,0.66532,
37,0.21859,2.60692,2.60692,2,38,0.04163,0.87144,44,0.04163,0.66532,
38,0.21859,2.60
692,2.60692,2,39,0.04163,0.87144,45,0.04163,0.66532,
39,0.21859,2.60692,2.60692,2,40,0.04163,0.87144,46,0.04163,0.66532,
40,0.21859,2.60692,2.60692,2,410041308714447,0.04163,
0.66532,
41,0.21859,2.60692,2.60692,2,42
,0.04163,0.66532,
42,0.12976,2.17490,1.30346,1,49,0.04430,0.66532,
123
43,0.07566,1.57013,0.65173,1,32,0.04430,0.66532,
44,0.12976,2.17490,1.30346,1,33,0.04430,0.87144,
45,0.12976,2.17490,1.30346,1,34,0.04430,0.87144,
46,0.12976,2.17490,1.30346,1,35,0.04430,0.87144,
47,0.12976,2.17490,1.30346,1,36,0.04430,0.87144,
48,0.12976,2.17490,1.30346,1,36,0.04430,0.66532,
49,0.07566,1.57013,0.65173,
*Internal subchannels
50,0.110205,1.17681,1.17681,
51,0.110205,1.17681,1.17681,
52,0.110205,1.17681,1.17681,
53,0.110205,1.17681,1.17681,
54,0.110205,1.17681,1.17681,
55,0.110205,1.17681,1.17681,
56,0.110205,1.17681,1.17681,
57,0.110205,1.17681,1.17681,
58,0.110205,1.17681,1.17681,
59,0.110205,1.17681,1.17681,
60,0.110205,1.17681,1.17681,
61,0.110205,1.17681,1.17681,
62,0.110205,1.17681,1.17681,
63,0.110205,1.17681,1.17681,
64,0.110205,1.17681,1.17681,
65,0.110205,1.17681,1.17681,
66,0.110205,1.17681,1.17681,
67,0.110205,1.17681,1.17681,
68,0.110205,1.17681,1.17681,
69,0.110205,1.17681,1.17681,
70,0.110205,1.17681,1.17681,
71,0.110205,1.17681,1.17681,
72,0.110205,1.17681,1.17681,
73,0.110205,1.17681,1.17681,
74,0.110205,1.17681,1.17681,
75,0.110205,1.17681,1.17681,
76,0.110205,1.17681,1.17681,
77,0.110205,1.17681,1.17681,
78,0.110205,1.17681,1.17681,
79,0.110205,1.17681,1.17681,
80,0.110205,1.17681,1.17681,
81,0.110205,1.17681,1.17681,
82,0.110205,1.17681,1.17681,
83,0.110205,1.17681,1.17681,
84,0.45239,2.38429,2.38429,
85,0.45239,2.38429,2.38429,
*geom.4
prop,0,1,2,1 *internal EPRI functions *prop.
*
rods,1,72,1,2,4,0,0,0,0,0,0, *three material types,one type of geo. *rods.1
145.98,13.513,0,0,
*rods.2
26
*rods3
*One axial profile only (rods.4)
0.00,0.00,?
3.04,0.38,?
9.12,0.69,?
15.21,0.93,
21.29,1.10,?
124
27.37,1.21,?
33.45,1.30,?
39.54,1.47,
45.62,1.5 1,?
51.70,1.49,?
57.78,1.44,?
63.87,1.36,
69.95,1.28,?
76.03,1.16,?
82.11,1.06,?
88.20,1.01,
94.28,0.97,?
100.36,0.94,?
106.44,0.97,?
112.53,0.96,
118.61,0.91,?
124.69,0.77,?
130.77,0.59,?
136.86,0.38,
142.94,0.12,?
145.98,0.00,
******rods geomatry input
*rods.9
1,1,1.012,1,1,0.25,2,0.25,8,0.25,9,0.25,
-,1,1,1.012,1,50,1,
2,1,1.015,1,2,0.25,3,0.25,9,0.25,10,0.25,
-2,1,1.015,1,51,1,
3,1,1.032,1,3,0.25,4,0.25,10,0.25,11,0.25,
-3,1,1.032,1,52,1,
4,1,1.068,1,4,0.25,5,0.25,11,0.25,12,0.25,
-4,1,1.068,1,53,1,
5,1,1.106,1,5,0.25,6,0.25,12,0.25,13,0.25,
-5,1,1.106,1,54,1,
6,1,1.063,1,6,0.25,7,0.25,13,0.25,14,0.25,
-6,1,1.063,1,55,1,
7,1,1.015,1,8,0.25,9,0.25,15,0.25,16,0.25,
-7,1,1.015,1,56,1,
8,1,0.368,1,9,0.25,10,0.25,16,0.25,17,0.25,
-8,1,0.368,1,57,1,
9,1,0.979,1,10,0.25,11,0.25,17,0.25,18,0.25,
-9,1,0.979,1,58,1,
10,1,1.078,1,11,0.25,12,0.25,18,0.25,19,0.25,
-10,1,1.078,1,59,1,
11,1,1.101,1,12,0.25,13,0.25,19,0.25,20,0.25,
-11,1,1.101,1,60,1,
12,1,1.081,1,13,0.25,14,0.25,20,0.25,21,0.25,
-12,1,1.081,1,61,1,
13,1,1.032,1,15,0.25,16,0.25,22,0.25,23,0.25,
-13,1,1.032,1,62,1,
14,1,0.979,1,16,0.25,17,0.25,23,0.25,24,0.25,
-14,1,0.979,1,63,1,
15,1,1.21,1,17,0.25,18,0.25,24,0.25,25,0.25,
-15,1,1.21,1,64,1,
16,1,0.364,1,19,0.25,20,0.25,26,0.25,27,0.25,
-16,1,0.364,1,65,1,
125
17,1,1.002,1,20,0.25,21,0.25,27,0.25,28,0.25,
-17,1,1.002,1,66,1,
18,1,1.068,1,22,0.25,23,0.25,29,0.25,30,0.25,
-18,1,1.068,1,67,1,
19,1,1.078,1,23,0.25,24,0.25,30,0.25,31,0.25,
-19,1,1.078,1,68,1,
20,1,1.220,1,25,0.25,26,0.25,32,0.25,33,0.25,
-20,1,1.220,1,69,1,
21,1,0.994,1,26,0.25,27,0.25,33,0.25,34,0.25,
-21,1,0.994,1,70,1,
22,1,1.055,1,27,0.25,28,0.25,34,0.25,35,0.25,
-22,1,1.055,1,71,1,
23,1,1.106,1,29,0.25,30,0.25,36,0.25,37,0.25,
-23,1,1.106,1,72,1,
24,1,1.101,1,30,0.25,31,0.25,37,0.25,38,0.25,
-24,1,1.101,1,73,1,
25,1,0.364,1,31,0.25,32,0.25,38,0.25,39,0.25,
-25,1,0.364,1,74,1,
26,1,0.994,1,32,0.25,33,0.25,39,0.25,40,0.25,
-26,1,0.994,1,75,1,
27,1,0.954,1,33,0.25,34,0.25,40,0.25,41,0.25,
-27,1,0.954,1,76,1,
28,1,1.132,1,34,0.25,35,0.25,41,0.25,42,0.25,
-28,1,1.132,1,77,1,
29,1,1.063,1,36,0.25,37,0.25,43,0.25,44,0.25,
-29,1,1.063,1,78,1,
30,1,1.081,1,37,0.25,38,0.25,44,0.25,45,0.25,
-30,1,1.081,1,79,1,
31,1,1.002,1,38,0.25,39,0.25,45,0.25,46,0.25,
-31,1,1.002,1,80,1,
32,1,1.055,1,39,0.25,40,0.25,46,0.25,47,0.25,
-32,1,1.055,1,81,1,
33,1,1.132,1,40,0.25,41,0.25,47,0.25,48,0.25,
-33,1,1.132,1,82,1,
34,1,1.092,1,41,0.25,42,0.25,48,0.25,49,0.25,
-34,1,1.092,1,83,1,
*water rod
35,2,0.0,1,18,0.25,19,0.25,25,0.25,26,0.25,
*water rod
-35,2,0.0,1,-84,1,
*water rod
36,2,0.0,1,24,0.25,25,0.25,31,0.25,32,0.25,
*water
rod
-36,2,0.0,1,-85,1,
*rods.9
"1,2,3,4,5,6,
*7,8,9,10,11,12,
*13,14,15,35,16,17,
*18,19,36,20,21,22,
*23,24,25,26,27,28,
*29,30,31,32,33,34,
*blank line above necessary /rods.57 -HG CPR corr
*rods.58,
*36,0.871438,0.044296,0.829810,15.122049,
*0
*rods.59
*fuel
1,tube,0.829810,0.374590,5,
*rods.68
*
126
2,1,0.033465,0.0,? *inner cladding
2,2,0.003937,0.0,? *inner gap
8,3,0.152829,1.0,? *fuel ring
2,4,0.003937,0.0,
*outer gap
2,1,0.033465,0.0,
*outer cladding
*water tube
2,tube,0.829810,0.758944,1
3,1,0.035433,0.0,
*
1,18,409.0,clad,
*table for cladding
0.0,0.0671,7.3304509,?
25,0.0671,7.3304509,
50,0.0671,7.33045093,?
65,0.0671,7.33045093,
80.33,0.0671,7.33045093,?
260.33,0.07212,8.11585329,
692.33,0.07904,9.80167423,?
1502.33,0.08955,13.2923,
1507.73,0.11988,13.3211893,?
1543.73,0.14089,13.51665,
1579.73,0.14686,13.717249,?
1615.73,0.1717,13.923198,
1651.73,0.1949,14.1347101,?
1687.73,0.18388,14.351998,
1723.73,0.1478,14.5752746,?
1759.73,0.112,14.804753,
1786.73,0.085,14.9810589,?
2240.33,0.085,18.5665964,
*gap
2,1,0.025,igap,
1,1.240834,0.346679,
*
*rods.69
*rods.69
*rods.69
*rods.69
*rods.69
*rods.68
*rods.69
*rods.70
*rods.70
*Cp=5195J/kg-K *gap=6000
*fuel
3,22,650.617,FUO2,
86,0.05677357,4.73275874,?
176,0.06078589,4.2991726,
266,0.06366347,3.93877428,?
356,0.06581210,3.6345405,
446,0.06747631,3.37435643,?
536,0.06880819,3.1493668,
626,0.06990545,2.95294976,?
716,0.07083283,2.78005572,
806,0.07163441,2.62676801,?
896,0.07234099,2.49000319,
986,0.07297458,2.36730189,?
1076,0.07355124,2.25667975,
1166,0.07408294,2.1565193,?
1256,0.07457886,2.06549023,
1346,0.07504628,1.98248979,?
1436,0.07549123,1.90659753,
1526,0.0759191,1.83704065,?
1616,0.07633503,1.77316713,
1706,0.0767443,1.7144247,?
*rods.71
*rods.70
127
1796,0.07715268,1.66034425,
1886,0.07756663,1.61052668,?
*rods.71
1976,0.07799351,1.5646323,
*
*outer gap
4,1,0.025,ogap,
1,1.240834,0.34667666,
*****
*rods.70
*Cp=5195J/kg-K *gap=6000
*rods.71
******* **********************
*P,T
oper, 1,1,0,1,0,1,0,0,0
*oper. 1
-1.0,0.0,2.0,0.005,
*oper.2 *first word to be changed if you change BC
*oper.3 *only if first w above is not 0.0
0
*oper.5
1035.0,533.0,34.70,185.472000,0.0,
*13400 kg/s ,5*Rod power got from total power divided total number of rods
*oper. 12
*no forcing functions
0,
**********************************
*correlations
corr, ,2,0,
epri,epri,epri,none,
0.2,
ditb,chen,chen,epri,cond,g5.7,
epri,
1,0,0.0,
*mine,
*corr.1
*corr.2
*corr.3
*correlation for boiling curve *corr.6
*corr. 16,for epri
*corr 18 , Hench-Gillis
************************
grid,0,5,
*grid.1
*grid.2
24.280,6.63,1.50,1.46,20000,
*pressure drop is 24.28 for the average rod and 23.37 for the hot rod
*grid.4
49,10,
*grid.5
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
*grid.5
49,
1.0,1,12.263,2,31.225,3,52.537,3,72.7,3,92.857,3,112.857,3,133.033,3,
*grid loc. *grid.6
153.203,3,175.445,4,
34,3,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,
1.0,1,
2,1,
84,85,
1.0,5,
0,
cont,
0.0,0,250,50,3,0,
0.10,0.00001,0.001,0.05,0.01,0.9,1.5,1.0,
5,0,0,0,0,0,1,1,0,0,0,1,1,0,
5000.,0.0,0.0,0.0,0.0,0.0,
endd
*cont.1
*cont.2
*cont.3
*cont.6
*cont.7
*end of data input
0
128
B.4 Annular 7x7 BWR Assembly
***********************************************************************
* 1 assembly, 7x7 annular pins, using BWR power distribution
*
Hot Assembly
*
one axial profile and approximate radial profile
*
*
*
parDi: 0.80
*
*
parfuel: 0.90
*
*
Superpower: 1.00
*
*
EPRI-1 CHFR Analysis
*
*
ITERATIVE solution
*
1,0,0,
Bwr annular fuel
geom,113,113,36,0,0,0,
*
145.98,0.0,0.5,
*
*vipre. 1
*vipre.2
*normal geometry input
*geom. I1
*geom.2
1,0.07186,1.36551,0.54751,2,2,0.06044,0.57092,9,0.06044,0.57092,
2,0.10889,1.82784,1.09501,2,3,0.06044,0.73283,10,0.03571,0.57092,
3,0.10889,1.82784,1.09501,2,4,0.06044,0.73283,11,0.03571,0.57092,
4,0.10889,1.82784,1.09501,2,5,0.06044,0.73283,12,0.03571,0.57092,
5,0.10889,1.82784,1.09501,2,6,0.06044,0.73283,13,0.03571,0.57092,
6,0.10889,1.82784,1.09501,2,7,0.06044,0.73283,14,0.03571,0.57092,
7,0.10889,1.82784,1.09501,2,8,0.06044,0.57092,15,0.03571,0.57092,
8,0.07186,1.36551,0.54751,1,16,0.06044,0.57092,
9,0.10889,1.82784,1.09501,2,10,0.03571,0.57092,17,0.06044,0.73283,
10,0.15536,2.19002,2.19002,2,11,0.03571,0.73283,18,0.03571,0.73283,
11,0.15536,2.19002,2.19002,2,12,0.03571,0.73283,19,0.03571,0.73283,
12,0.15536,2.19002,2.19002,2,13,0.03571,0.73283,20,0.03571,0.73283,
13,0.15536,2.19002,2.19002,2,14,0.03571,0.73283,21,0.03571,0.73283,
14,0.15536,2.19002,2.19002,2,15,0.03571,0.73283,22,0.03571,0.73283,
15,0.15536,2.19002,2.19002,2,16,0.03571,0.57092,23,0.03571,0.73283,
16,0.10889,1.82784,1.09501,1,24,0.06044,0.73283,
17,0.10889,1.82784,1.09501,2,18,0.03571,0.57092,25,0.06044,0.73283,
18,0.15536,2.19002,2.19002,2,19,0.03571,0.73283,26,0.03571,0.73283,
19,0.15536,2.19002,2.19002,2,20,0.03571,0.73283,27,0.03571,0.73283,
20,0.15536,2.19002,2.19002,2,21,0.03571,0.73283,28,0.03571,0.73283,
21,0.15536,2.19002,1.64252,2,22,0.03571,0.73283,29,0.03571,0.73283,
22,0.15536,2.19002,1.64252,2,23,0.03571,0.73283,30,0.03571,0.73283,
23,0.15536,2.19002,2.19002,2,24,0.03571,0.57092,31,0.03571,0.73283,
24,0.10889,1.82784,1.09501,1,32,0.06044,0.73283,
25,0.10889,1.82784,1.09501,2,26,0.03571,0.57092,33,0.06044,0.73283,
26,0.15536,2.19002,2.19002,2,27,0.03571,0.73283,34,0.03571,0.73283,
27,0.15536,2.19002,2.19002,2,28,0.03571,0.73283,35,0.03571,0.73283,
28,0.15536,2.19002,1.64252,2,29,0.03571,0.73283,36,0.03571,0.73283,
29,0.15536,2.19002,1.09501,2,30,0.03571,0.73283,37,0.03571,0.73283,
30,0.15536,2.19002,1.64252,2,31,0.03571,0.73283,38,0.03571,0.73283,
31,0.15536,2.19002,2.19002,2,32,0.03571,0.57092,39,0.03571,0.73283,
129
32,0.10889,1.82784,1.09501,1,40,0.06044,0.73283,
33,0.10889,1.82784,1.09501,2,30,0.03571,0.57092,36,0.06044,0.73283,
34,0.15536,2.19002,2.19002,2,31,0.03571,0.73283,37,0.03571,0.73283,
35,0.15536,2.19002,1.64252,2,32,0.03571,0.73283,38,0.03571,0.73283,
36,0.15536,2.19002,1.09501,2,33,0.03571,0.73283,39,0.03571,0.73283,
37,0.15536,2.19002,1.64252,2,34,0.03571,0.73283,40,0.03571,0.73283,
38,0.15536,2.19002,2.19002,2,35,0.03571,0.73283,41,0.03571,0.73283,
39,0.15536,2.19002,2.19002,2,35,0.03571,0.57092,41,0.03571,0.73283,
40,0.10889,1.82784,1.09501,1,42,0.06044,0.73283,
41,0.10889,1.82784,1.09501,2,42,0.03571,0.57092,49,0.06044,0.73283,
42,0.15536,2.19002,2.19002,2,43,0.03571,0.73283,50,0.03571,0.73283,
43,0.15536,2.19002,1.64252,2,44,0.03571,0.73283,51,0.03571,0.73283,
44,0.15536,2.19002,1.64252,2,45,0.03571,0.73283,52,0.03571,0.73283,
45,0.15536,2.19002,2.19002,2,46,0.03571,0.73283,53,0.03571,0.73283,
46,0.15536,2.19002,2.19002,2,47,0.03571,0.73283,54,0.03571,0.73283,
47,0.15536,2.19002,2.19002,2,48,0.03571,0.57092,55,0.03571,0.73283,
48,0.10889,1.82784,1.09501,1,56,0.06044,0.73283,
49,0.10889,1.82784,1.09501,2,50,0.03571,0.57092,57,0.06044,0.57092,
50,0.15536,2.19002,2.19002,2,51,0.03571,0.73283,58,0.03571,0.57092,
51,0.15536,2.19002,2.19002,2,52,0.03571,0.73283,59,0.03571,0.57092,
52,0.15536,2.19002,2.19002,2,53,0.03571,0.73283,60,0.03571,0.57092,
53,0.15536,2.19002,2.19002,2,54,0.03571,0.73283,61,0.03571,0.57092,
54,0.15536,2.19002,2.19002,2,55,0.03571,0.73283,62,0.03571,0.57092,
55,0.15536,2.19002,2.19002,2,56,0.03571,0.57092,63,0.03571,0.57092,
56,0.10889,1.82784,1.09501,1,64,0.06044,0.57092,
57,0.07186,1.36551,0.54751,2,58,0.06044,0.57092,
58,0.10889,1.82784,1.09501,2,59,0.06044,0.73283,
59,0.10889,1.82784,1.09501,2,60,0.06044,0.73283,
60,0.10889,1.82784,1.09501,2,61,0.06044,0.73283,
61,0.10889,1.82784,1.09501,2,62,0.06044,0.73283,
62,0.10889,1.82784,1.09501,2,63,0.06044,0.73283,
63,0.10889,1.82784,1.09501,2,64,0.06044,0.57092,
64,0.07186,1.36551,0.54751,
*Internal subchannels
65,0.09643,1.10076,1.10076,
66,0.09643,1.10076,1.10076,
67,0.09643,1.10076,1.10076,
68,0.09643,1.10076,1.10076,
69,0.09643,1.10076,1.10076,
70,0.09643,1.10076,1.10076,
71,0.09643,1.10076,1.10076,
72,0.09643,1.10076,1.10076,
73,0.09643,1.10076,1.10076,
74,0.09643,1.10076,1.10076,
75,0.09643,1.10076,1.10076,
76,0.09643,1.10076,1.10076,
77,0.09643,1.10076,1.10076,
78,0.09643,1.10076,1.10076,
79,0.09643,1.10076,1.10076,
80,0.09643,1.10076,1.10076,
81,0.09643,1.10076,1.10076,
82,0.09643,1.10076,1.10076,
83,0.09643,1.10076,1.10076,
84,0.09643,1.10076,1.10076,
85,0.09643,1.10076,1.10076,
86,0.09643,1.10076,1.10076,
130
87,0.09643,1.10076,1.10076,
88,0.09643,1.10076,1.10076,
89,0.09643,1.10076,1.10076,
90,0.09643,1.10076,1.10076,
91,0.09643,1.10076,1.10076,
92,0.09643,1.10076,1.10076,
93,0.09643,1.10076,1.10076,
94,0.09643,1.10076,1.10076,
95,0.09643,1.10076,1.10076,
96,0.09643,1.10076,1.10076,
97,0.09643,1.10076,1.10076,
98,0.09643,1.10076,1.10076,
99,0.09643,1.10076,1.10076,
100,0.09643,1.10076,1.10076,
101,0.09643,1.10076,1.10076,
102,0.09643,1.10076,1.10076,
103,0.09643,1.10076,1.10076,
104,0.09643,1.10076,1.10076,
105,0.09643,1.10076,1.10076,
106,0.09643,1.10076,1.10076,
107,0.09643,1.10076,1.10076,
108,0.09643,1.10076,1.10076,
109,0.09643,1.10076,1.10076,
110,0.09643,1.10076,1.10076,
111,0.30803,1.96740,1.96740,
112,0.30803,1.96740,1.96740,
113,0.30803,1.96740,1.96740,
*geom.4
prop,0,1,2,1 *internal EPRI functions *prop. 1
*
rods,1,98,1,2,4,0,0,0,0,0,0, *three material types,one type of geo. *rods. 1
145.98,0.0,0,0,
*rods.2
26
*rods3
*One axial profile only (rods.4)
0.00,0.00,?
3.04,0.38,?
9.12,0.69,?
15.21,0.93,
21.29,1.10,?
27.37,1.21,?
33.45,1.30,?
39.54,1.47,
45.62,1.51,?
51.70,1.49,?
57.78,1.44,?
63.87,1.36,
69.95,1.28,?
76.03,1.16,?
82.11,1.06,?
88.20,1.01,
94.28,0.97,?
100.36,0.94,?
106.44,0.97,?
112.53,0.96,
118.61,0.91,?
124.69,0.77,?
131
130.77,0.59,?
136.86,0.38,
142.94,0.12,?
145.98,0.00,
******rods geometry input
*rods.9
11,,1.11,1,1,0.25,2,0.25,9,0.25,10,0.25,
-1,1,1.11,1,65,1,
2,1,1.18,1,2,0.25,3,0.25,10,0.25,11,0.25,
-2,1,1.18,1,66,1,
3,1,1.17,1,3,0.25,4,0.25,11,0.25,12,0.25,
-3,1,1.17,1,67,1,
4,1,1.18,1,4,0.25,5,0.25,12,0.25,13,0.25,
-4,1,1.18,1,68,1,
5,1,1.21,1,5,0.25,6,0.25,13,0.25,14,0.25,
-5,1,1.21,1,69,1,
6,1,1.20,1,6,0.25,7,0.25,14,0.25,15,0.25,
-6,1,1.20,1,70,1,
71,,1.12,1,7,0.25,0.25,8,0.25,1,0.25,16,0
-7,1,1.12,1,71,1,
8,1,1.21,1,9,0.25,10,0.25,17,0.25,18,0.25,
-8,1,1.21,1,72,1,
9,1,0.42,1,10,0.25,11,0.25,18,0.25,19,0.25,
-9,1,0.42,1,73,1,
10,1,0.85,1,11,0.25,12,0.25,19,0.25,20,0.25,
-10,1,0.85,1,74,1,
11,1,0.85,1,12,0.25,13,0.25,20,0.25,21,0.25,
-11,1,0.85,1,75,1,
12,1,0.85,1,13,0.25,14,0.25,21,0.25,22,0.25,
-12,1,0.85,1,76,1,
13,1,0.42,1,14,0.25,15,0.25,22,0.25,23,0.25,
-13,1,0.42,1,77,1,
14,1,1.20,15,0.25,16,0.25,23,0.25,24,0.25,
-14,1,1.20,1,78,1,
15,1,1.17,1,17,0.25,18,0.25,25,0.25,26,0.25,
-15,1,1.17,1,79,1,
16,1,0.85,1,18,0.25,19,0.25,26,0.25,27,0.25,
-16,1,0.85,1,80,1,
17,1,0.90,19,0.25,20,0.25,27,0.25,28,0.25,
-17,1,0.90,1,8 ,1,
18,1,1.00,1,20,0.25,21,0.25,28,0.25,29,0.25,
-18,1,1.00,1,82,1,
19,1,0.85,1,22,0.25,23,0.25,30,0.25,31,0.25,
-19,1,0.85,1,83,1,
20,1,1.21,1,23,0.25,24,0.25,31,0.25,32,0.25,
-20,1,1.21,1,84,1,
21,1,1.18,1,25,0.25,26,0.25,33,0.25,34,0.25,
-21,1,1.18,1,85,1,
22,1,0.85,1,26,0.25,27,0.25,34,0.25,35,0.25,
-22,1,0.85,1,86,1,
23,1,1.00,1,27,0.25,28,0.25,35,0.25,36,0.25,
-23,1,1.00,1,87,1,
24,1,1.00,1,29,0.25,30,0.25,37,0.25,38,0.25,
-24,1,1.00,1,88,1,
25,1,0.85,1,30,0.25,31,0.25,38,0.25,39,0.25,
132
-25,1,0.85,1,89,1,
26,1,1.18,1,31,0.25,32,0.25,39,0.25,40,0.25,
-26,1,1.18,1,90,1,
27,1,1.21,1,33,0.25,34,0.25,41,0.25,42,0.25,
-27,1,1.21,1,91,1,
28,1,0.85,1,34,0.25,35,0.25,42,0.25,43,0.25,
-28,1,0.85,1,92,1,
29,1,1.00,1,36,0.25,37,0.25,44,0.25,45,0.25,
-29,1,1.00,1,93,1,
30,1,0.90,1,37,0.25,38,0.25,45,0.25,46,0.25,
-30,1,0.90,1,94,1,
31,1,0.85,1,38,0.25,39,0.25,46,0.25,47,0.25,
-31,1,0.85,1,95,1,
32,1,1.16,1,39,0.25,40,0.25,47,0.25,48,0.25,
-32,1,1.16,1,96,1,
33,1,1.22,1,41,0.25,42,0.25,49,0.25,50,0.25,
-33,1,1.22,1,97,1,
34,1,0.42,1,42,0.25,43,0.25,50,0.25,51,0.25,
-34,1,0.42,1,98,1,
35,1,0.85,1,43,0.25,44,0.25,51,0.25,52,0.25,
-35,1,0.85,1,99,1,
36,1,0.85,1,44,0.25,45,0.25,52,0.25,53,0.25,
-36,1,0.85,1,100,1,
37,1,0.85,1,45,0.25,46,0.25,53,0.25,54,0.25,
-37,1,0.85,1,101,1,
38,1,0.42,1,46,0.25,47,0.25,54,0.25,55,0.25,
-38,1,0.42,1,102,1,
39,1,1.21,1,47,0.25,48,0.25,55,0.25,56,0.25,
-39,1,1.21,1,103,1,
40,1,1.11,1,49,0.25,50,0.25,57,0.25,58,0.25,
-40,1,1.11,1,104,1,
41,1,1.21,1,50,0.25,51,0.25,58,0.25,59,0.25,
-41,1,1.21,1,105,1,
42,1,1.21,1,51,0.25,52,0.25,59,0.25,60,0.25,
-42,1,1.21,1,106,1,
43,1,1.18,1,52,0.25,53,0.25,60,0.25,61,0.25,
-43,1,1.18,1,107,1,
44,1,1.17,1,53,0.25,54,0.25,61,0.25,62,0.25,
-44,1,1.17,1,108,1,
45,1,1.21,1,54,0.25,55,0.25,62,0.25,63,0.25,
-45,1,1.21,1,109,1,
46,1,1.11,1,55,0.25,56,0.25,63,0.25,64,0.25,
-46,1,1.11,1,110,1,
47,2,0.0,1,21,0.25,22,0.25,29,0.25,30,0.25,
-47,2,0.0,1,-111,1,
48,2,0.0,1,28,0.25,29,0.25,36,0.25,37,0.25,
-48,2,0.0,1,-112,1,
49,2,0.0,1,35,0.25,36,0.25,43,0.25,44,0.25,
-49,2,0.0,1,-113,1,
*rods.9
*water rod
*water rod
*water rod
*water rod
*water rod
*water rod
*1,2,3,4,5,6,
*7,8,9,10,11,12,
*13,14,15,35,16,17,
*18,19,36,20,21,22,
*23,24,25,26,27,28,
133
*29,30,31,32,33,34,
*blank line above necessary /rods.57 -HG CPR corr
*rods.58,
*36,0.871438,0.044296,0.829810,15.122049,
*0
*rods.59
*
*fuel
1,tube,0.697126,0.350394,5,
*rods.68
*
2,1,0.033465,0.0,? *inner cladding
2,2,0.003937,0.0,? *inner gap
8,3,0.098563,1.0,? *fuel ring
*outer gap
2,4,0.003937,0.0,
*outer cladding
2,1,0.033465,0.0,
*water tube
2,tube,0.697126,0.626260,1
3,1,0.035433,0.0,
1,18,409.0,clad,
*table for cladding
0.0,0.0671,7.3304509,?
25,0.0671,7.3304509,
50,0.0671,7.33045093,?
65,0.0671,7.33045093,
80.33,0.0671,7.33045093,?
260.33,0.07212,8.11585329,
692.33,0.07904,9.80167423,?
1502.33,0.08955,13.2923,
1507.73,0.11988,13.3211893,?
1543.73,0.14089,13.51665,
1579.73,0.14686,13.717249,?
1615.73,0.1717,13.923198,
1651.73,0.1949,14.1347101,?
1687.73,0.18388,14.351998,
1723.73,0.1478,14.5752746,?
1759.73,0.112,14.804753,
1786.73,0.085,14.9810589,?
2240.33,0.085,18.5665964,
*rods.69
*rods.69
*rods.69
*rods.69
*rods.69
*rods.68
*rods.69
*rods.70
*
*gap
2,1,0.025,igap,
1,1.240834,0.346679,
*rods.70
*Cp=5195J/kg-K *gap=6000
*rods.71
*
*fuel
3,22,650.617,FUO2,
86,0.05677357,4.73275874,?
176,0.06078589,4.2991726,
266,0.06366347,3.93877428,?
356,0.06581210,3.6345405,
446,0.06747631,3.37435643,?
536,0.06880819,3.1493668,
626,0.06990545,2.95294976,?
716,0.07083283,2.78005572,
806,0.07163441,2.62676801,?
896,0.07234099,2.49000319,
*rods.70
134
986,0.07297458,2.36730189,?
1076,0.07355124,2.25667975,
1166,0.07408294,2.1565193,?
1256,0.07457886,2.06549023,
1346,0.07504628,1.98248979,?
1436,0.07549123,1.90659753,
1526,0.0759191,1.83704065,?
1616,0.07633503,1.77316713,
1706,0.0767443,1.7144247,?
1796,0.07715268,1.66034425,
1886,0.07756663,1.61052668,?
1976,0.07799351,1.5646323,
*rods.71
*
*outer gap
4,1,0.025,ogap,
1,1.240834,0.34667666,
**
*********
******
*rods.70
*Cp=5195J/kg-K *gap=6000
***********
*****
*P,T
oper,1,1,0,11,0,,0,0,0
-1.0,0.0,2.0,0.005,
*rods.71
*oper. 1
*oper.2 *first word to be changed if you change BC
0
*oper.3 *only if first w above is not 0.0
1035.0,533.0,34.20,137.103000,0.0,
*oper.5
* 13400 kg/s ,5*Rod power got from total power divided total number of rods
0,
*no forcing functions
*oper.12
***************
*******************
*correlations
corr, 1,2,0,
epri,epri,epri,none,
0.2,
ditb,chen,chen,epri,cond,g5.7,
epri,
*corr. 16,for epri
*corr 18, Hench-Gillis
1,0,0.0,
*mine,
* *****
*corr.1
*corr.2
*corr.3
*correlation for boiling curve *corr.6
****************
mixx,0,0,0,
0.8,0.0048,0.0,
* ************************
grid,0,5,
*grid.1
24.280,6.63,1.50,1.46,20000,
*grid.2
*pressure drop is 24.28 for the average rod and 23.37 for the hot rod
64,10,
*grid.4
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
*grid.5
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
*grid.5
1.0,1,12.263,2,31.225,3,52.537,3,72.7,3,92.857,3,112.857,3,133.033,3,
153.203,3,175.445,4,
*grid loc. *grid.6
46,1,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,
1.0,1,
3,1,
111,112,113,
1.0,5,
135
0,
**********************************************************
cont,
0.0,0,250,50,3,0,
0.10,0.00001,0.001,0.05,0.01,0.9,1.5,1.0,
*cont.1
*cont.2
*cont.3
5,0,0,0,0,0,1,1,0,0,0,1,1,0,
*cont.6
5000.,0.0,0.0,0.0,0.0,0.0,
endd
*cont.7
*end of data input
0
136
Appendix C: CASMO-4 Input Files
C. 1 Westinghouse 17x1 7 PWR Assembly Reference
* 345678901234567890123456789012345678901234567890123456789012345678901234567890
*
1
2
3
4
5
6
7
8
*
* FUEL SEGMENT: WS450
*
TTL * STANDARD WESTINGHOUSE PWR ASSEMBLY, 17X17 LATTICE,
***** STATE POINT PARAMETERS *****
TFU=900.0 TMO=583.1 BOR=600 VOI=0.0
SIM 'WS450' * ITYPE
***** OPERATING PARAMETERS *****
PRE 155.1296 * CORE PRESSURE, bars
PDE 104.5 'KWL' * POWER DENSITY, kW/liter
***** MATERIAL COMPOSITIONS *****
FUE 1 10.4/5.0
FUE 2 10.0374/5.0 64016=10
SPA 10.81934 0.1800E-4,,8.154/718=84.59 347=15.41
***** GEOMETRY SPECIFICATION *****
PWR 17 1.26 21.5
PIN 1 0.4096 0.4178 0.4750/'1' 'AIR' 'CAN'
PIN 2 0.4096 0.4178 0.4750/'2' 'AIR' 'CAN'
PIN 5 0.5690 0.6147/COO' 'BOX' * GUIDE TUBE
PIN 9 0.5690 0.6147/COO' 'BOX'
PIN 9 0.4331 0.4369 0.4839 0.5690 0.6147/AIC' 'AIR' 'CRS' 'COO' 'BOX'
//1 'RCC' 'ROD'
LPI 5
11
211
9119
11112
111119
9129111
11111111
111111111
***** BASE CASE WITH INSTANTANEOUS BRANCHES *****
DEP -70
STA
END
137
C.2 Annular 13x13 PWR Assembly
* 345678901234567890123456789012345678901234567890123456789012345678901234567890
7
8
5
6
3
4
* 1
2
* Fuel Assembly from IXAF Design PQN02 13x13 Lattice With 5.0 w/o UN Fuel
* + 25% Additional U-238 in the Normal Fuel Pins
* + 35% Additional U-238 in the 10% wt% GdN Poisoned Fuel Pins
* FUEL SEGMENT: XF49512G10
* with 150% Power Density
*
TTL * IXAF ASSEMBLY DESIGN, PQN-02, 13X13 LATTICE
***** STATE POINT PARAMETERS *****
TFU=800 TMO=583.1 BOR=600 VOI=0.0
SIM 'XF49512G10' 5.0 10 12 12 * ITYPE, ENR, WBA, IBAP, IBAO
***** OPERATING PARAMETERS *****
PRE 155.1296 * CORE PRESSURE, bars
PDE 156.75 'KWL' * POWER DENSITY, kW/liter
***** MISCELLANEOUS OPTIONS *****
THE 0 * NO THERMAL EXPANSION
***** MATERIAL COMPOSITIONS *****
(+25% U-238)
* FUE 1 5.0 w/o ENR
* 2 5.0 w/o ENR, 10 wt% Gd203 (+35% U-238)
FUE 1 /1.67653E21 92234=1.34123E19 92238=3.98009E22 8000=3.35307E22
FUE 2 /1.48893E21 64154=7.25117E19 64155=4.94595E20 64156=6.83114E20
64157=5.1961E20 64158=8.19435E20 64152=7.08927E18 64160=7.12374E20
92234=1.19114E19 92238=3.81749E22 8000=3.308729E22
SPA 10.81934 0.1800E-4,,8.154/718=84.59 347=15.41
***** GEOMETRY SPECIFICATION *****
PWR 13 1.651 21.5
PIN 1 0.4315 0.4890 0.4950 0.7050 0.7110 0.7685/
'COO' 'CAN' 'AIR' '1' 'AIR' 'CAN'
PIN 2 0.4315 0.4890 0.4950 0.7050 0.7110 0.7685/
'COO' 'CAN' 'AIR' '2' 'AIR' 'CAN'
PIN 5 0.7110 0.7685/'COO"BOX' * GUIDE TUBE
PIN 9 0.7110 0.7685/'COO' 'BOX'
PIN 9 0.5751 0.5789 0.6259 0.7110 0.7685/'AIC' 'AIR' 'CRS' 'COO' 'BOX'
//1 'RCC' 'ROD'
LPI 5
12
111
1112
11911
211111
1111111
***** BASE CASE WITH INSTANTANEOUS BRANCHES *****
DEP 3 11.60874 29*14.51092 26*72.55462/'DD'
STA
138
END
139
Appendix D: MCODE/MCNP Input Files
D.1 Westinghouse 17x17 PWR Reference
MCODE
$ TITLE line
TTL ICA-l7Xl7Base Unpoisoned Assembly
$ CTRL command initial-inp
MCD 0 /home/tyler9/mcnp.exe 17WT.inp
decay-lib gamma-lib
ORIGEN-LIBRARY-PATH
ORIGEN-COMMAND
$
ORG /home/xzw/bin/ORIGEN2/origen22 /home/xzw/bin/ORIGEN2/LIBS/ DECAY.LIB GXUO2BRM.LIB
$ total# CELL-ID TYPE IHM(g) VOL(cm3) ORG-XS-LIB
CEL 11
1 1 27528.10 2646.93 PWRUE.LIB
210 1 171.408 17.077 PWRUE.LIB
211
1 171.408 17.077 PWRUE.LIB
212 1 171.408 17.077 PWRUE.LIB
213 1 171.408 17.077 PWRUE.LIB
214 1 171.408 17.077 PWRUE.LIB
215 1 171.408 17.077 PWRUE.LIB
216 1 171.408 17.077 PWRUE.LIB
217 1 171.408 17.077 PWRUE.LIB
218 1 171.408 17.077 PWRUE.LIB
219 1 171.408 17.077 PWRUE.LIB
$ TOTAL VOLUME (cm3)
VOL 9343.3
$ NORMALIZATION option, I=FLUX, 2=POWER
NOR 2
$ Predictor-Corrector option, l=ON, 0=OFF
COR 1
$ power density, opt: WGU=W/gIHM, KWL=kW/(liter core)
PDE 104.5 KWL
$ opt E=MWd/kg, D=EFPD
12
11
9
10
8
6
7
5
3 4
$points 0 1 2
DEP D 0 3.7 36.7 110.2 183.7 367.48 551.2 735.0 1102.5 1469.9 1837.4 2204.9 2572.4
NMD
3 20 20 20 20 20 20 20 20 20 20 20
STA 0 $ Starting Point
END 12 $ Ending Point
MCNP
FA model of PWR - hot cell with hot dimensions from CASMO4
c
c the following are the input data to create this mcnp input deck
thcd
thfg
rfh
Icore pitch
c
c
20.0000 1.2626 0.4121 0.006945 0.057000
c
enrich enrichbl
rCRD rblan
140
c
c
0.0500 xxxxxx 0.5400 0.4121
hcrd
-1.0000
rhocol rhocolh rhocolc rhozr
0.6950 0.6950 1.0050 6.5100
tempf tempc tempg tempcd
608.0000 314.0000 350.0000 314.0000
icoolnt itemp
2
1
burnup fcomp
0
0
the above are the input data to create this mcnp input deck
some calculated parameters for check
ffuel fclad fgap
0.3348 0.1006 0.0114
c
c
c
c
fmod fcheck
0.5533 1.0000
fgpc
fvm
0.1119 0.6050
cell specification
c
mt density
geomtry
1 1 6.81885E-02 -1
u=2 imp:n=l vol=2646.9300 $ fuell
2 5 3.76622E-05 1-2
u=2 imp:n=1 $ gap
3 3 4.31672E-02 2 -3
u=2 imp:n=l $ clad
9 4 6.97171E-02 3
u=2 vol=4375.12 imp:n=l $ coolant
210 70 6.70920E-02
-40
u=3 imp:n=1 vol=17.07700 $ fuel2
211 71 6.70920E-02 40 -41
u=3 imp:n=l vol=17.07700 $ fuel2
212 72 6.70920E-02 41 -42
u=3 imp:n=l vol=17.07700 $ fuel2
213 73 6.70920E-02 42 -43
u=3 imp:n=l vol=17.07700 $ fuel2
214 74 6.70920E-02 43 -44
u=3 imp:n=1 vol=17.07700 $ fuel2
215 75 6.70920E-02 44 -45
u=3 imp:n=l vol=17.07700 $ fuel2
216 76 6.70920E-02 45 -46
u=3 imp:n=1 vol=17.07700 $ fuel2
217 77 6.70920E-02 46 -47
u=3 imp:n=l vol=17.07700 $ fuel2
218 78 6.70920E-02 47 -48
u=3 imp:n=l vol=17.07700 $ fuel2
219 79 6.70920E-02 48 -49
u=3 imp:n=1 vol=17.07700 $ fuel2
22 5 3.76622E-05 49 -5
u=3 imp:n=1 $ gap
23 3 4.31672E-02 5 -6
u=3 imp:n=1 $ clad
29 4 6.97171E-02 6
u=3 vol=282.266 imp:n=l $ coolant
47 4 6.97171E-02 -8
u=4 imp:n=1 $ gap
48 3 4.31672E-02 8 -9
u=4 imp:n=l $ Guide tube
49 4 6.97171E-02 9
u=4 vol=693.33 imp:n=1 $ coolant
101 0
-21 22 -23 24 imp:n=l u=1 lat=1 fill=-8:8 -8:8 0:0
22222222222222222
22222222222222222
22222432423422222
22242222222224222
22223222222232222
22422422422422422
22322222322222322
22222222222222222
22422432423422422
22222222222222222
22322222322222322
22422422422422422
22223222222232222
141
22242222222224222
22222432423422222
22222222222222222
22222222222222222
-25 26-27 28 u=12 fill=l imp:n=l $ core
110 0
111 4 6.97171E-02 25: -26 :27: -28 u=12 imp:n=l $ interassembly coolant
120 4 6.97171E-02 -51 52 -53 54 u=16 lat-1 imp:n=1 fill=12
130 0
-501 502 -503 504 402 -408 fill=16 imp:n=1 $ FA
1000 0
+501:-502:+503:-504:-402:408 imp:n=0 $ outside
c end of cell specification
c
c surface specification
c
trn card constants for equations
1 cz
0.41215
$ Fuell 1
2 cz
0.41909
$ Fuell 2
3 cz
0.47609
$ Fuell 3
40 cz
0.130335
$ fuel2 40
41 cz
0.184322
$ fuel2 41
42 cz
0.225747
$ fuel2 42
43 cz
0.260670
$ fuel2 43
44 cz
0.291438
$ fuel2 44
45 cz
0.319255
$ fuel2 45
46 cz
0.344835
$ fuel2 46
47 cz
0.368644
$ fuel2 47
48 cz
0.391006
$ fuel2 48
49 cz
0.41215
$ fuel2 49
5 cz
0.41909
$ fuel2 5
6 cz
0.47609
$ fuel2 6
8 cz
0.549629
$ CRD 8
9 cz
0.606746
$ CRD 9
21 px
$ pitch
0.63130
22 px
-0.63130
$ pitch
$ pitch
23 py
0.63130
24 py
-0.63130
$ pitch
$ FA pitch
25 px
10.73205
$ FA pitch
26 px
-10.73205
$
FA pitch
10.73205
27 py
$ FA pitch
-10.73205
28 py
$ FA pitch
51 px
10.80700
$ FA pitch
-10.80700
52 px
$ FA pitch
10.80700
53 py
$ FA pitch
-10.80700
54 py
$ symmetry 1
c'*61 p 83.865056 -83.865056 0.00000 0.00000
$ symmetry
0.0
c *62 py
$ core-bot
0.000
*402 pz
$ core-top
*408 pz
20.000
$ boundary
10.80699
*501 px
-10.80699
*502 px
10.80699
*503 py
-10.80699
*504 py
c end of surface specification
c data specification
142
c problem type
mode n
c
c cell and surface parameters
c
c source specification
c 9. kcode criticality source card
c nsrck rkk ikz kct msrk knrm
kcode 3000 1.0 5 150
c
c
prdmp 150 150 150
c 10. ksrc source point for kcode calculation
c
xl
yl
zi... location for initial source point
ksrc 2.525200 1.262600 0.20 2.525200 1.262600 5.20
2.525200 1.262600 10.20 2.525200 1.262600 15.20
2.525200 1.262600 19.80
c tally specification
c pin power
c f4:n (1<101[1 0 0]<110<120<130) (1<101[2 0 0]<110<120<130)
c
(1<101[4 0 0]<110<120<130) (1<101[5 0 0]<110<120<130)
c
(1<101[1 1 0]<110<120<130) (1<101[2 1 0]<110<120<130)
c
(1<101[3 1 0]<110<120<130) (1<101[4 1 0]<110<120<130)
c
(1<101[5 1 0]<110<120<130)
c
(1<101[2 2 0]<110<120<130) (1<101[3 2 0]<110<120<130)
c
(1<101[42 0]<110<120<130) (1<101[5 2 0]<110<120<130)
c
(1<101[4 3 0]<110<120<130) (1<101[5 3 0]<110<120<130)
c
(1<101[4 4 0]<110<120<130) (1<101[5 4 0]<110<120<130)
c fc4 pin-averaged fission rates for seed fuel
c frn4 6.76417E-02 1 (-6) (-6 -7)
c pin power other
c f24:n (21<101[7 0 0]<110<120<130) (21<101[8 0 0]<110<120<130)
c
(21<101[6 1 0]<110<120<130) (21<101[7 1 0]<110 <120<130)
c
(21<101[8 1 0]<110<120<130) (21<101[6 2 0]<110 <120<130)
c
(21<101[7 2 0]<110<120<130) (21<101[8 2 0]<110 <120<130)
c
(21<101[7 3 0]<110<120<130) (21<101[8 3 0]<110 <120<130)
c
(21<101[6 4 0]<110<120<130) (21<101[7 4 0]<110 <120<130)
c
(21<101[8 4 0]<110<120<130) (21<101[6 5 0]<110 <120<130)
c
(21<101[7 5 0]<110<120<130) (21<101[8 5 0]<110 <120<130)
c
(21<101[6 6 0]<110<120<130) (21<101[7 6 0]<110 <120<130)
c
(21<101[8 6 0]<110<120<130)
c
(21<101[7 7 0]<110<120<130) (21<101[8 7 0]<110 <120<130)
c
(21<101[8 8 0]<110<120<130)
c fc24 assembly-averaged fission rates for blanket fuel
c fin24 6.76417E-02 7 (-6) (-6 -7)
c
c 1. fna tally card
c
c material specification
c
c 1. mm material card
c fuel meat U02( 6.76417E-02) 3.54wt0 /o Enriched
ml 8016.54c 4.545900-2
$ fuel 02
143
36083.50c
40090.86c
40091.86c
40092.86c
40093.86c
40094.86c
40096.86c
42095.50c
42097.60c
42098.50c
42100.50c
43099.60c
44101.50c
44102.60c
44103.50c
44104.96c
45103.50c
45105.50c
46104.96c
46105.50c
46107.96c
46108.50c
47109.60c
48113.86c
53127.60c
53129.60c
54131.86c
54133.86c
54135.86c
55133.60c
55134.60c
55135.60c
57139.60c
59141.50c
60143.50c
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ begin mcode_FP
$ fuel cladding zr2
$ ORIGENID 611481
144
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
9.09180E-6
1.13648E-3
1.0000e-24
2.15839E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ end mcode FP
$ begin_mcode_ACT
$ fuel u-235
$ fuel u-238
$ ORIGEN ID 952421
$ end mcode ACT
c
m3 40000.60c
1.0
$ clad zirc
m4 1001.53c 0.0464692
$ moderator-h
8016.53c 0.0232479
$ moderator-o
mt4 lwtr.04t
$ h2o-moderator
m5 8016.54c
1.0
$ gap-O
m70 8016.54c 4.54494e-2
$ fuel 02
poisoned pins 10wt% Gd203
36083.50c 1.0000e-24
$ begin_mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
4
4102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
145
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGENID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
64155.60c 3.23517e-4
64156.60c 4.46829e-4
64157.60c 3.39880e-4
64158.60c 5.35997e-4
64160.60c 4.65968e-4 $ end mcode FP
90232.78c 1.0000e-24 $ begin mcode_ACT
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92232.60c 1.0000e-24
92233.78c 1.0000e-24
$ fuel u-234
92234.86c 7.01220E-6
$ fuel u-235
9.73916E-4
92235.54c
92236.78c 1.0000e-24
$ fuel u-238
92238.54c 1.84974E-2
93237.81c 1.0000e-24
93238.35c 1.0000e-24
93239.60c 1.0000e-24
94238.78c 1.0000e-24
94239.78c 1.0000e-24
94240.78c 1.0000e-24
146
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 952421
$ end mcode ACT
m71 8016.54c 4.54494e-2
$ fuel 02
poisoned pins 10wt% Gd203
36083.50c 1.0000e-24
$ begin mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
147
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24 $ ORIGENID 611481
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
4.63714e-6
4.74303e-5
3.23517e-4
4.46829e-4
3.39880e-4
5.35997e-4
4.65968e-4 $ end mcode FP
1.0000e-24 $ begin mcode_ACT
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.01220E-6
$ fuel u-234
9.73916E-4
$ fuel u-235
1.0000e-24
1.84974E-2
$ fuel u-238
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 952421
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ end mcode ACT
c
m72 8016.54c 4.54494e-2
poisoned pins 10wt% Gd203
$ fuel 02
36083.50c 1.0000e-24
$ begin mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
148
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
64155.60c 3.23517e-4
64156.60c 4.46829e-4
64157.60c 3.39880e-4
64158.60c 5.35997e-4
64160.60c 4.65968e-4 $ end mcode FP
90232.78c 1.0000e-24 $ begin_mcodeACT
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92232.60c 1.0000e-24
92233.78c 1.0000e-24
149
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
7.01220E-6
9.73916E-4
1.0000e-24
1.84974E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ fuel u-234
$ fuel u-235
$ fuel u-238
$ ORIGENID 952421
$ endmcodeACT
m73 8016.54c 4.54494e-2
$ fuel 02
poisoned pins 10wt% Gd203
36083.50c 1.0000e-24
$ begin mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
150
55135.60c
57139.60c
59141.50c
60143.50c
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
4.63714e-6
4.74303e-5
3.23517e-4
4.46829e-4
3.39880e-4
5.35997e-4
4.65968e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.01220E-6
9.73916E-4
1.0000e-24
1.84974E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ begin_mcode_ACT
$ fuel u-234
$ fuel u-235
$ fuel u-238
$ ORIGEN ID 952421
$ end mcode ACT
151
c
$ fuel 02
poi soned pins 10wt% Gd203
m74 8016.54c 4.54494e-2
$ begin_mcode_FP
36083.50c 1.0000e-24
$ fuel cladding zr2
40090.86c 1.0000e-24
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
152
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
--
3.23517e-4
4.46829e-4
3.39880e-4
5.35997e-4
4.65968e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.01220E-6
9.73916E-4
1.0000e-24
1.84974E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ end mcode FP
$ begin_mcode_ACT
$ fuel u-234
$ fuel u-235
$ fuel u-238
$ ORIGEN ID 952421
$ end mcode ACT
-~
m75 8016.54c 4.54494e36083.50c 1.0000e-24
40090.86c 1.0000e-24
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
$ fuel 02
poiisoned pins 10wt% Gd203
$ begin_mcode_FP
$ fuel cladding zr2
153
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
64155.60c 3.23517e-4
64156.60c 4.46829e-4
64157.60c 3.39880e-4
64158.60c 5.35997e-4
64160.60c 4.65968e-4 $ end mcode FP
90232.78c 1.0000e-24 $ begin mcode_ACT
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92232.60c 1.0000e-24
92233.78c 1.0000e-24
$ fuel u-234
92234.86c 7.01220E-6
$ fuel u-235
92235.54c 9.73916E-4
92236.78c 1.0000e-24
$ fuel u-238
92238.54c 1.84974E-2
93237.81c 1.0000e-24
93238.35c 1.0000e-24
93239.60c 1.0000e-24
94238.78c 1.0000e-24
94239.78c 1.0000e-24
94240.78c 1.0000e-24
94241.78c 1.0000e-24
94242.78c 1.0000e-24
94243.78c 1.0000e-24
154
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGENID 952421
$ end mcode ACT
m76 8016.54c 4.54494e-2
$ fuel 02
poisoned pins 10wt% Gd203
36083.50c 1.0000e-24
$ begin_mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
155
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
64155.60c 3.23517e-4
64156.60c 4.46829e-4
64157.60c 3.39880e-4
64158.60c 5.35997e-4
64160.60c 4.65968e-4
90232.78c 1.0000e-24
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92232.60c 1.0000e-24
92233.78c 1.0000e-24
92234.86c 7.01220E-6
92235.54c 9.73916E-4
92236.78c 1.0000e-24
92238.54c 1.84974E-2
93237.81c 1.0000e-24
93238.35c 1.0000e-24
93239.60c 1.0000e-24
94238.78c 1.0000e-24
94239.78c 1.0000e-24
94240.78c 1.0000e-24
94241.78c 1.0000e-24
94242.78c 1.0000e-24
94243.78c 1.0000e-24
95241.97c 1.0000e-24
95242.98c 1.0000e-24
95242.97c 1.0000e-24
95244.97c 1.0000e-24
96242.97c 1.0000e-24
96243.97c 1.0000e-24
96244.97c 1.0000e-24
96245.97c 1.0000e-24
96246.97c 1.0000e-24
96247.97c 1.0000e-24
$ end mcode FP
$ begin mcode_ACT
$ fuel u-234
$ fuel u-235
$ fuel u-238
$ ORIGEN ID 952421
$ end mcodeACT
poisoned pins 10wt% Gd203
m77 8016.54c 4.54494e-2
$ fuel 02
36083.50c 1.0000e-24
$ begin mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
156
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
64155.60c 3.23517e-4
64156.60c 4.46829e-4
64157.60c 3.39880e-4
64158.60c 5.35997e-4
64160.60c 4.65968e-4 $ end mcode FP
90232.78c 1.0000e-24 $ begin mcodeACT
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92 232.60c 1.0000e-24
92233.78c 1.0000e-24
92 234.86c 7.01220E-6
$ fuel u-234
92235.54c 9.73916E-4
$ fuel u-235
92 236.78c 1.0000e-24
157
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.84974E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ fuel u-238
$ ORIGENID 952421
$ endmcode ACT
m78 8016.54c 4.54494e-2
poisoned pins 10wt% Gd203
$ fuel 02
36083.50c 1.0000e-24
$ begin mcode_FP
40090.86c 1.0000e-24
$ fuel cladding zr2
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
158
60143.50c
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
4.63714e-6
4.74303e-5
3.23517e-4
4.46829e-4
3.39880e-4
5.35997e-4
4.65968e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.01220E-6
9.73916E-4
1.0000e-24
1.84974E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ beginmcode_ACT
$ fuel u-234
$ fuel u-235
$ fuel u-238
$ ORIGEN ID 952421
$ end mcode ACT
m79 8016.54c 4.54494e-2
$ fuel 02
36083.50c 1.0000e-24
$ begin mcodeFP
poisoned pins 10wt% Gd203
159
$ fuel cladding zr2
40090.86c 1.0000e-24
40091.86c 1.0000e-24
40092.86c 1.0000e-24
40093.86c 1.0000e-24
40094.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 4.63714e-6
64154.60c 4.74303e-5
64155.60c 3.23517e-4
64156.60c 4.46829e-4
64157.60c 3.39880e-4
160
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.86c
92235.54c
92236.78c
92238.54c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
5.35997e-4
4.65968e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.01220E-6
9.73916E-4
1.0000e-24
1.84974E-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ end mcode FP
$ begin mcode_ACT
$ fuel u-234
$ fuel u-235
$ fuel u-238
$ ORIGENID 952421
$ endmcodeACT
c
c 7. void material void card
c void
c energy and thermal treatment specification
c
c 1. phys energy physics cutoff cards
c
emax emcnf
phys:n 20 0.0
c
3. tmp free-gas thermal temperature card
tln t2n...n=index of time.tln-temi, for cell 1 at time n
tmpl
#
1 7.59287E-08
2 5.36968E-08
3 5.05947E-08
9 5.05947E-08
•
210
211
212
213
214
215
216
217
218
J.
-
_
__
7.59287E-08
7.59287E-08
7.59287E-08
7.59287E-08
7.59287E-08
7.59287E-08
7.59287E-08
7.59287E-08
7.59287E-08
161
219 7.59287E-08
22 5.36968E-08
23 5.05947E-08
29 5.05947E-08
47 5.05947E-08
48 5.05947E-08
49 5.05947E-08
101 5.05947E-08
110 5.05947E-08
111 5.05947E-08
120 5.05947E-08
130 5.05947E-08
1000 2.53000e-08
c
c 4. thtme thermal times cards
thtme 0
c problem cutoff cards
c
c user data array
c
c periferal cards
c
print
D.2 Annular 13x13 PWR Assembly
MCODE
$ TITLE line
TTL 5.0 w/o UN fuel, hot condition, 10 wt% Gd poison, full assembly, 150% Power Density
$ + 10 equal volume cylinders of Gd poisoned pins to account for Gd's self shielding factor
$
$ CTRL command initial-inp
MCD 0 mcnp.exe UN98.inp
decay-lib gamma-lib
ORIGEN-LIBRARY-PATH
ORIGEN-COMMAND
$
ORG /home/xzw/bin/ORIGEN2/origen22 /home/xzw/bin/ORIGEN2/LIBS DECAY.LIB GXUO2BRM.LIB
$ total# CELL-ID TYPE IHM(g) VOL(cm3) ORG-XS-LIB
10 1 32886.0 2343.37 PWRUE.LIB
CEL 11
131 1 254.692 19.0004 PWRUE.LIB
132 1 254.692 19.0004 PWRUE.LIB
133 1 254.692 19.0004 PWRUE.LIB
134 1 254.692 19.0004 PWRUE.LIB
135 1 254.692 19.0004 PWRUE.LIB
136 1 254.692 19.0004 PWRUE.LIB
137 1 254.692 19.0004 PWRUE.LIB
138 1 254.692 19.0004 PWRUE.LIB
139 1 254.692 19.0004 PWRUE.LIB
140 1 254.692 19.0004 PWRUE.LIB
$ TOTAL VOLUME (cm3)
VOL 9213.21
$ NORMALIZATION option, I=FLUX, 2=POWER
162
NOR 2
$ Predictor-Corrector option, 1=ON, 0=OFF
COR 1
$ power density, opt: WGU=W/glHM, KWL=kW/(liter core)
PDE 156.75 KWL
$ opt E=MWd/kg, D=EFPD
11
12
8
9
10
6 7
$points 0 1 2 3 4 5
DEP D 0 3.7 36.7 110.2 183.7 367.48 551.2 735.0 1102.5 1469.9 1837.4 2204.9 2572.4
NMD
3 20 20 20 20 20 20 20 20 20 20 20
STA 0
END 12
MCNP
Full Assembly model of PWR annular fuel for burnup, with 10 wt% Gd rods
c 13x13 Lattice with 5.0 w/o UN Fuel and 150% Power Density
c + 10 equal volume cylinders in the poisoned pins to account for Gd self-sheilding
c
c cell specification
c
c mt density
geometry
7.06685e-02 - 1
$ internal coolant 583.1K
4
u=2 imp:n=l
4.34384e-02 1-2
$ internal clad 621.1K
6
u=2 imp:n=l
$ internal gap
3.76497e-05 2 -3 u=2 imp:n=1
8
10
6.70610e-02 3-4 u=-2 imp:n=l1vol=2343.37 $ fuel pellet 650K
$ external gap
12 2 3.76497e-05 4-5 u=2 imp:n=l
$ external clad 621.1K
u=2 imp:n=l
13 3 4.34384e-02 5 -6
14 4 7.06685e-02 6
$ extenal coolant 583.1K
u=2 imp:n=l
$ internal coolant 583.1K
24 4 7.06685e-02 -1
u=6 imp:n=1
$ internal clad 621.1K
26 3 4.34384e-02 1-2
u=6 imp:n=l
$ internal gap
28 2 3.76497e-05 2 -3 u=6 imp:n=1
131 6 6.61746e-02 3 -10( u=6 imp:n= 1 vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #1)
132 7 6.61746e-02 100 -101 u=6 imp:n =l1 vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #2)
133 8 6.61746e-02 101-102 u=6 imp:n =1 vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #3)
134 29 6.61746e-02 102 -103 u=6 imp:n =1 vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #4)
135 34 0 6.61746e-02 103 -104 u=6 imp:n=l vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #5)
136 4 1 6.61746e-02 104-105 u=6 imp:n=1 vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #6)
137 4 2 6.61746e-02 105 -106 u=6 imp:n=l vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #7)
64
138 3 6.61746e-02 106 -107 u=6 imp:n=-1 vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #8)
73
139 844 6.61746e-02 107 -108 u=6 imp:n=l vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #9)
140 5 6.61746e-02 108-4 u=6 imp:n=l vol=19.0004 $ fuel pellet w/ Gd203 650K (cyl #10)
32
3.76497e-05 4-5
-6 imp:n=l1
$ external gap
33 3 4.34384e-02 5 -6
=6 imp:n=l1
$ external clad 621.1K
34
7.06685e-02 6
6 imp:n=1
$ extenal coolant 583.1K
47
U='4 imp:n=l
7.06685e-02 -8
$ coolant in guide tube 583.1K
48
4.34384e-02 8 -9
4 imp:n=l
$ guide tube 583.1K
49 4 7.06685e-02 9
4 imp:n=1
$ coolant out of guide tube 583.1K
101 0
-2122 -23 24 imp:n=l u=l lat=1 fill=-6:6 -6:6 0:0
2222222222222
2222622262222
2222422242222
2222222222222
163
2642226222462
2222222222222
2222624262222
2222222222222
2642226222462
2222222222222
2222422242222
2222622262222
2222222222222
-25 26 -27 28
110 0
u=12
111 4 7.06685e-02 25:-26: 27: -28
120 4 7.06685e-02 -51 52 -53 54
61 62 -501 402 -408
130 0
-61:-62: 501:-402: 408
1000 0
c end of cell specification
fill= l imp:n=1 $ core
imp:n=l $ interassembly coolant
u=12
u=16 lat=l fill=12 imp:n=l
fill=16 imp:n=1 $ FA
imp:n=0 $ outside
c
c surface specification
c
trn card constants for equations
$ Inner surface of inner clad
1 cz 0.43165
$ Outer surface of inner clad
2 cz 0.48878
3 cz 0.49500
$ Inner fuel surface (cylinder #1)
$ Outer surface of Cylinder #1
100 cz 0.519832
$ Outer surface of cylinder #2
101 cz 0.543530
102 cz 0.566238
$ Outer surface of cylinder #3
103 cz 0.588069
$ Outer surface of cylinder #4
104 cz 0.609118
$ Outer surface of cylinder #5
$ Outer surface of cylinder #6
105 cz 0.629464
$ Outer surface of cylinder #7
106 cz 0.649173
$ Outer surface of cylinder #8
107 cz 0.668300
108 cz 0.686895
$ Outer surface of cylinder #9
4 cz 0.70500
$ Outer fuel surface (cylinder #10)
$ Inner surface of outer clad
5 cz 0.71122
$ Outer surface of outer clad
6 cz 0.76835
$ Inner surface of guide tube
8 cz 0.71000
$ Outer surface of guide tube
9 cz 0.76837
21 px 0.8255
$ pin pitch
$ pin pitch
22 px -0.8255
$ pin pitch
23 py 0.8255
$ pin pitch
24 py -0.8255
$ FA width
25 px 10.73150
$ FA width
26 px -10.73150
$ FA width
27 py 10.73150
28 py -10.73150
51 px 10.75000
52 px -10.75000
53 py 10.75000
54 py -10.75000
*61 p 1 -1 0 0
*62 py 0.0
*402 pz 0.000
*408 pz 20.000
$ FA width
$ FA pitch
$ FA pitch
$ FA pitch
$ FA pitch
$ symmetry 1
$ symmetry
$ core-bottom
$ core-top
*501 px 10.750001
$ boundary
c end of surface specification
164
c data specification
c
c
phys:n 20 0.0
c
c
c 3. tmp free-gas thermal temperature card
c tln t2n...n=index of time,tln--temp for cell 1 at time n
tmpl
#
4 5.0246e-08
$583.1K
6 5.3520e-08
$621.1K
8 2.5300e-08
10 5.6011e-08
$650K
12 2.5300e-08
13 5.3520e-08
14 5.0246e-08
$621.1K
$583.1K
24 5.0246e-08
$583.1K
26 5.3520e-08
$621.1K
28
131
132
133
2.5300e-08
5.6011e-08
5.6011e-08
5.6011e-08
$650K
$650K
$650K
134 5.6011e-08
$650K
135 5.601le-08
$650K
136 5.6011e-08
$650K
137 5.6011e-08
$650K
138 5.6011e-08
$650K
139 5.6011e-08
$650K
140 5.6011e-08
$650K
32 2.5300e-08
33 5.3520e-08
$621.1K
34 5.0246e-08
$583.1K
47 5.0246e-08
$583.1K
48 5.0246e-08
$583.1K
49 5.0246e-08
$583.1K
101 5.0246e-08
$650K
110 5.0246e-08
$650K
111 5.0246e-08
$583.1K
120 5.0246e-08
$583.1K
130 5.0246e-08
$650K
1000 2.5300e-08
c
c material specification
c
awtab 34079 78.240500 38089 88.143700 38090 89.135400
44106 104.998000 46107 105.987000
47111 109.953000 48115 113.919000
50126 124.826000 51124 122.842000 51125 123.832000
52127
54133
58141
59142
62153
63157
125.815000
131.764008
139.697998
140.691000
151.608002
155.577000
52129
56140
58143
59143
63156
65160
127.800000
138.709000
141.684998
141.682999
154.585007
157.562000
53131
57140
58144
61151
129.781998
138.707993
142.677000
149.625000
c
165
c 5.0 wt% U-235 (14.0336g/cc, 6.70610e-02)
ml
7015.60c 3.35307e-2
36083.50c 1.0000e-24
$ begin_mcode_ FP
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24 $ ORIGENID 6 11481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64154.60c 1.0000e-24
64155.60c 1.0000e-24
64156.60c 1.0000e-24
64157.60c 1.0000e-24
64158.60c 1.0000e-24 $ end mcode F]P
_
_
166
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.34123e-5
1.67653e-3
1.0000e-24
3.18407e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ begin mcode_ACT
$ ORIGENID 952421
$ end mcode ACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #1)
m6
7015.60c 3.30873e-2
36083.50c 1.0000e-24
$ beginmcode_FP
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
167
54135.86c
55133.60c
55134.60c
55135.60c
57139.60c
59141.50c
60143.50c
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.08927e-6
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ begin_mcode_ACT
$ ORIGENID 952421
168
96245.97c 1.0000e-24
96246.97c 1.0000e-24
96247.97c 1.0000e-24
$ end mcode ACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #2)
m7
7015.60c 3.30873e-2
36083.50c 1.0000e-24
$ begin_mcode_FP
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24
$ ORIGEN ID 611481
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 7.08927e-6
169
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ endmcodeFP
$ begin mcode_ACT
$ ORIGEN ID 952421
$ endmcode ACT
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #3)
m8
7015.60c 3.30873e-2
$ begin_mcode_FP
36083.50c 1.0000e-24
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
170
47109.60c
48113.86c
53127.60c
53129.60c
54131.86c
54133.86c
54135.86c
55133.60c
55134.60c
55135.60c
57139.60c
59141.50c
60143.50c
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.08927e-6
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ begin_mcode_ACT
171
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGENID 952421
$ endmcodeACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #4)
m9
7015.60c 3.30873e-2
36083.50c 1.0000e-24 $ begin mcode_FP
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
$ ORIGEN ID 611481
61148.96c 1.0000e-24
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
172
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.08927e-6
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ end mcode FP
$ begin_mcode_ACT
$ ORIGEN ID 952421
$ end mcode ACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #5)
ml0
7015.60c 3.30873e-2
36083.50c 1.0000e-24
$ begin_mcode_FP
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
173
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 7.08927e-6
64154.60c 7.25117e-5
64155.60c 4.94595e-4
64156.60c 6.83114e-4
64157.60c 5.19610e-4
64158.60c 8.19435e-4
64160.60c 7.12374e-4
90232.78c 1.0000e-24
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92232.60c 1.0000e-24
92233.78c 1.0000e-24
92234.78c 1.19114e-5
92235.53c 1.48893e-3
92236.78c 1.0000e-24
92238.53c 2.82777e-2
93237.81c 1.0000e-24
93238.35c 1.0000e-24
93239.60c 1.0000e-24
94238.78c 1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ begin mcode_ACT
174
94239.78c 1.0000e-24
94240.78c 1.0000e-24
94241.78c 1.0000e-24
94242.78c 1.0000e-24
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 952421
96245.97c 1.0000e-24
96246.97c 1.0000e-24
96247.97c 1.0000e-24
$ endmcodeACT
c
c
ml1
5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #6)
7015.60c 3.30873e-2
36083.50c
40091.86c
40093.86c
40096.86c
42095.50c
42097.60c
42098.50c
42100.50c
43099.60c
44101.50c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ begin mcode_FP
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c
46108.50c
47109.60c
48113.86c
53127.60c
53129.60c
54131.86c
54133.86c
54135.86c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
55133.60c
55134.60c
55135.60c
57139.60c
59141.50c
60143.50c
60144.96c
60145.50c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
175
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.08927e-6
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ begin mcode_ACT
$ ORIGEN ID 952421
$ endmcodeACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #7)
m12
7015.60c 3.30873e-2
$ begin mcode_FP
36083.50c 1.0000e-24
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
176
42100.50c
43099.60c
44101.50c
44102.60c
44103.50c
44104.96c
45103.50c
45105.50c
46104.96c
46105.50c
46107.96c
46108.50c
47109.60c
48113.86c
53127.60c
53129.60c
54131.86c
54133.86c
54135.86c
55133.60c
55134.60c
55135.60c
57139.60c
59141.50c
60143.50c
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.08927e-6
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
$ ORIGEN ID 611481
$ end mcode FP
$ begin_mcode_ACT
177
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGENID 952421
$ end mcode ACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #8)
m13
7015.60c 3.30873e-2
$ begin_mcode_FP
36083.50c 1.0000e-24
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
178
60144.96c
60145.50c
60147.50c
60148.50c
61147.50c
61148.50c
61148.96c
62147.50c
62148.96c
62149.50c
62150.50c
62151.50c
62152.50c
63153.60c
63154.50c
63155.50c
63156.60c
64152.60c
64154.60c
64155.60c
64156.60c
64157.60c
64158.60c
64160.60c
90232.78c
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
7.08927e-6
7.25117e-5
4.94595e-4
6.83114e-4
5.19610e-4
8.19435e-4
7.12374e-4
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ beginmcode_ACT
$ ORIGEN ID 952421
$ end mcode ACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #9)
m14
7015.60c 3.30873e-2
36083.50c 1.0000e-24
$ begin_mcode_FP
179
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 7.08927e-6
64154.60c 7.25117e-5
64155.60c 4.94595e-4
64156.60c 6.83114e-4
64157.60c 5.19610e-4
64158.60c 8.19435e-4
64160.60c 7.12374e-4
90232.78c 1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ begin_mcode_ACT
180
91231.60c
91233.50c
92232.60c
92233.78c
92234.78c
92235.53c
92236.78c
92238.53c
93237.81c
93238.35c
93239.60c
94238.78c
94239.78c
94240.78c
94241.78c
94242.78c
94243.78c
95241.97c
95242.98c
95242.97c
95244.97c
96242.97c
96243.97c
96244.97c
96245.97c
96246.97c
96247.97c
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.19114e-5
1.48893e-3
1.0000e-24
2.82777e-2
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
1.0000e-24
$ ORIGENID 952421
$ end mcode ACT
c
c 5.0 wt% U-235 10 wt% Gd Poisoned (13.404538g/cc, 6.61746e-02) (Cylinder #10)
ml5
7015.60c 3.30873e-2
36083.50c 1.0000e-24
$ begin_mcode_FP
40091.86c 1.0000e-24
40093.86c 1.0000e-24
40096.86c 1.0000e-24
42095.50c 1.0000e-24
42097.60c 1.0000e-24
42098.50c 1.0000e-24
42100.50c 1.0000e-24
43099.60c 1.0000e-24
44101.50c 1.0000e-24
44102.60c 1.0000e-24
44103.50c 1.0000e-24
44104.96c 1.0000e-24
45103.50c 1.0000e-24
45105.50c 1.0000e-24
46104.96c 1.0000e-24
46105.50c 1.0000e-24
46107.96c 1.0000e-24
46108.50c 1.0000e-24
47109.60c 1.0000e-24
48113.86c 1.0000e-24
53127.60c 1.0000e-24
53129.60c 1.0000e-24
54131.86c 1.0000e-24
54133.86c 1.0000e-24
54135.86c 1.0000e-24
181
55133.60c 1.0000e-24
55134.60c 1.0000e-24
55135.60c 1.0000e-24
57139.60c 1.0000e-24
59141.50c 1.0000e-24
60143.50c 1.0000e-24
60144.96c 1.0000e-24
60145.50c 1.0000e-24
60147.50c 1.0000e-24
60148.50c 1.0000e-24
61147.50c 1.0000e-24
61148.50c 1.0000e-24
61148.96c 1.0000e-24
62147.50c 1.0000e-24
62148.96c 1.0000e-24
62149.50c 1.0000e-24
62150.50c 1.0000e-24
62151.50c 1.0000e-24
62152.50c 1.0000e-24
63153.60c 1.0000e-24
63154.50c 1.0000e-24
63155.50c 1.0000e-24
63156.60c 1.0000e-24
64152.60c 7.08927e-6
64154.60c 7.25117e-5
64155.60c 4.94595e-4
64156.60c 6.83114e-4
64157.60c 5.19610e-4
64158.60c 8.19435e-4
64160.60c 7.12374e-4
90232.78c 1.0000e-24
91231.60c 1.0000e-24
91233.50c 1.0000e-24
92232.60c 1.0000e-24
92233.78c 1.0000e-24
92234.78c 1.19114e-5
92235.53c 1.48893e-3
92236.78c 1.0000e-24
92238.53c 2.82777e-2
93237.81c 1.0000e-24
93238.35c 1.0000e-24
93239.60c 1.0000e-24
94238.78c 1.0000e-24
94239.78c 1.0000e-24
94240.78c 1.0000e-24
94241.78c 1.0000e-24
94242.78c 1.0000e-24
94243.78c 1.0000e-24
95241.97c 1.0000e-24
95242.98c 1.0000e-24
95242.97c 1.0000e-24
95244.97c 1.0000e-24
96242.97c 1.0000e-24
96243.97c 1.0000e-24
96244.97c 1.0000e-24
96245.97c 1.0000e-24
$ ORIGEN ID 611481
$ end mcode FP
$ beginmcode_ACT
$ ORIGEN ID 952421
182
96246.97c 1.0000e-24
96247.97c 1.0000e-24
$ end mcode ACT
c
c AIR (gap)
m2 8016.60c 3.76497E-05
c
c Zircaloy-4 (6.550g/cc)
m3
8016.60c 3.08257e-4
24000.50c 7.58604e-5
26000.55c 1.48326e-4
40000.60c 4.24242e-2
50000.35c 4.81797e-4
c
c H20 (15.5MPa at 583.1K) (0.705g/cc)
m4
8016.60c 2.35652e-2
1001.60c 4.71033e-2
mt4 lwtr.04t
c
c
ksrc
1.0 0.2 0.0
1.0 0.2 5.0
1.0 0.2 10.0
1.0 0.2 15.0
c
c
mode n
kcode 3000 1.0 5 150
prdmp 150 150 150
print
183