Tyler Shawn Ellis BACHELOR OF SCIENCE. and. MASTER OF SCIENCE in. Nuclear Science and Engineering. at the

Transcription

1 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 Massachusetts Institute of Technology All rights reserved Signature of Author:.,, Department ofluclear Science and Engineering June 9 h, 2006 Certified by: U. Professor M jid,. Kazimi (Thesis Supervisor) TEPCO Professor ofllear Science and Engineering Dr. Pavel Hejzlar (TAesis Reader) P AWrincipal Research Scientist Accepted by: Professor Jeffrey A. Coderre Chairman, Department Committee on Graduate Students - --~I '-- MASSACHUSETTS INSTITUTE OF TECHNOLOGY OCT LIBRARIES ARCHIVES

2 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 U 238 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

3 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

4 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.

5 For Alizde

6 Table of Contents A bstract... 1 Acknowledgements... 3 Table of Contents... 5 List of Figures... 7 List of Tables... 9 List of Acronyms Introduction Societal Need for Safe and Economic Nuclear Power Review of Previous Work on Annular Fuel for Reactor Applications Objective of This W ork Organization of the Thesis Uranium Nitride Annular Fuel for PWR Applications M ethodology A nalysis Tools M C O D E CA SM O Description of Geometries Analyzed Benchm ark A nalysis MCODE/CASMO-4 Comparison CASMO-4 Pseudo-Solution for Annular Fuel Poison-free Pin Cell Correction Poisoned Pin Cell Correction Self-shielding Factor Correction Multiplication Factor Tracking with Burnup Gadolinium Tracking with Burnup Plutonium Tracking with Burnup Correction for Fully Poisoned Assembly Multiplication Factor Tracking with Burnup Plutonium Tracking with Burnup Final Uprated Design Comparison Investigation of Annular Fuel for BWR Applications M ethodology Analysis Tools: VIPRE Thermal Hydraulics Code Flow M odeling Heat Transfer Correlations CH FR Correlations CHFR/CPR Comparative Analysis Fuel A ssem bly M odels Solid Fuel 9x9 Reference Assembly Annular Fuel Assembly Design Option Space Annular 5x5 Fuel Assembly Annular 6x6 Fuel Assembly Annular 7x7 Fuel Assembly Results of Fuel Assembly Optimization Studies

7 Annular 5x5 Fuel Assembly Annular 6x6 Fuel Assembly Annular 7x7 Fuel Assembly Comparison of Optimal Designs Analysis of the Results Summary of Conclusions and Recommendations for Future Studies C onclusions Recommendations for Future Studies References Appendix A: CASMO-4 Operational Parameters for Reactivity Coefficient Calculation Appendix B: VIPRE Input Files B. 1 GE 9x9 BWR Assembly Reference B.2 Annular 5x5 BWR Assembly B.3 Annular 6x6 BWR Assembly B.4 Annular 7x7 BWR Assembly Appendix C: CASMO-4 Input Files C.1 Westinghouse 17x17 PWR Assembly Reference C.2 Annular 13x13 PWR Assembly Appendix D: MCODE/MCNP Input Files D.1 Westinghouse 17xl7 PWR Reference D.2 Annular 13x13 PWR Assembly

8 List of Figures Figure 1-1: US Electricity Consumption Projection [EIA] _--..._. _ Figure 1-2: Temperature Dependence of Thermal Conductivity for UN Figure 2-1: Flow of Calculation in MCODE-1.0 [Xu 2003] Figure 2-2: Flow of Calculations in CASMO-4 [Knott et. al. 1995] Figure 2-3: Pictorial Representation of Unit Cell Models _ Figure 2-4: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for 17x17 Solid Assembly Figure 2-5: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for 13x13 Annular A ssem bly Figure 2-6: Eigenvalue Differences between MCODE and CASMO-4._ 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 Poison- Free Pin Cell 39 Figure 2-9: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected CASMO-4 for a Poison-Free Pin Cell 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 10 Owt% GdN Poisoned Annular Fuel Pin Figure 2-12: Eigenvalue Differences between MCODE and Uncorrected/Corrected CASMO-4 for a 10wt%/o GdN Poisoned Pin Cell Figure 2-13: Total Cross Section for Gadolinium Isotopes 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 Figure 2-17: MCODE/Corrected CASMO-4 Eigenvalue versus EFPD for a Poisoned 13x13 Annular Assembly Figure 2-18: Plutonium Composition versus Burnup as Calculated by MCODE and Corrected CASMO-4 for a Full Poisoned 13x13 Annular Fuel Assembly 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 Figure 3-1: NUPEC Experimental Axial Power Peaking Profile [Kitamura 1998] Figure 3-2: NUPEC Experiment Radial Power Peaking Factors Figure 3-3: NUPEC Experiment Axial Power Peaking Factors Figure 3-4: GEl 1 Fuel Assembly Layout [Gerald 1997] Figure 3-5: Axial Power Peaking Profile for 9x9 Reference Case * Figure 3-6: Radial Power Peaking Profile for 9x9 Reference Case... _ Figure 3-7: 2-D Cross Section of the 5x5 Annular Fuel Design Concept (Not To Scale) Figure 3-8: Radial Power Peaking Profile for 5x5 Annular Case

9 Figure 3-9: 2-D Cross Section of the 6x6 Annular Fuel Design Concept (Not To Scale) Figure 3-10: Radial Power Peaking Profile for 6x6 Annular Case Figure 3-11: 2-D Cross Section of the 7x7 Annular Fuel Design Concept (Not To Scale) Figure 3-12: Radial Power Peaking Profile for 7x7 Annular Case Figure 3-13: Effect of a Reduction in Inner Diameter on the MCHFR for 5x5 Annular Fuel 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 Figure 3-15: Effect of a Reduction in Inner Diameter on the MCHFR for 6x6 Annular Fuel Figure 3-16: Effect of the Orifice Resistance Coefficient on CHFR for 6x6 Annular Fuel 91 Figure 3-17: Effect of a Reduction in Inner Diameter on the MCHFR for 7x7 Annular Fuel Figure 3-18: Effect of the Orifice Resistance Coefficient on CHFR for 7x7 Annular Fuel Figure 3-19: Effect of Spacer Grid Loss on CHFR for 7x7 Annular Fuel... 95

10 List of Tables Table 1-1: Physical and Thermal Properties of UO 2 and UN Table 2-1: Geometric Design Parameters for Investigated Fuel Assembliesm Table 2-2: BOL Reactivity Coefficients for 17x17 Solid and 13x13 Annular Table 3.1: NUPEC Experiment Operational Conditions [Kitamura 1998] 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 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 Table 3.4: EPRI-1 CPR Calculation Data 67 Table 3.5: EPRI-1 and Hench-Gillis Calculated CPR Comparison Table 3.6: Solid Fuel Reference Core Operating Parameters [Lungmen], [Nine Mile Point 2004] Table 3.7: Solid Fuel Reference Core Design Constraints Table 3.8: GEl 1 Fuel Assembly Design Parameters Table 3.9: Localized Pressure Drop Coefficients Table 3.10: Annular Design Option Space Table 3.11: Geometrical Design Parameters for 5x5 Annular Fuel Table 3.12: Geometrical Design Parameters for 6x6 Annular Fuel Table 3.13: Geometrical Design Parameters for 7x7 Annular Fuel... _ Table 3.14: Comparison of 9x9 Reference, 5x5, 6x6 and 7x7 Annular Designs Table 3.15: Mixing Contribution Comparison for 9x9 Reference and 6x6 Annular Cases Table 3-16: Effect of Radial Power Peaking on the MCHFR 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

11 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

12 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

13 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].

14 US Past, Present and Forecasted Future Electricity Consumption '^^^^ i 0.o 50000,.m 0. E r IL U/ U' , Year 30 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

15 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 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.

16 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 U 235. 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

17 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 N 1 5 was not determined to be a problem with respect to parasitic absorption in materials enriched in U 235. 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 U0 2 and UN Theoretical Density (g/cm 3 ) U0 2 UN HM Atom Density (g/cm 3 ) Specific Heat (J/Kg K) 270 (at C) 205 (at 28 0 C) Melting Point ( 0 C) Thermal Conductivity (W/m K) 7.19 (at C) 4 (at C) 3.35 (at C) 20 (at 1000 C) Linear Thermal Expansion Coefficient (10-6K-) 10.1 (at C) 9.4 (at C) Swelling Rate (normalized to U0 2 ) Fission Gas Release (normalized to UO2) 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

18 with increasing temperature. The opposite trend of the UO 2 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 TEMPERATIRE PC) Figure 1-2: Temperature Dependence of Thermal Conductivity for UN If reprocessing were to be implemented, than enrichment in the N 15 isotope would be required due to the N' 4 (n,p)c 14 reaction. The C 14 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.

19 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 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

20 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 Reddy- Fighetti) rather than the modified Hench-Gillis CPR correlation which was used previously.

21 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

22 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 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.

23 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.

24 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.

25 2.2. Analysis Tools 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.

26 L throu h all timeste s Parse MCODE input and initialize variables Initial run? NO (restart) YES Preprocess initial mcnp input and run MCNP mcn I E IE" " II I II " E II II I l "II ' J oop to p 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 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? END YES Figure 2-1: Flow of Calculation in MCODE-1.0 [Xu 20031

27 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 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

28 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.

29 Restart file Data library Data library -- Card Image file Burnup Figure 2-2: Flow of Calculations in CASMO-4 [Knott et. al 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

30 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

31 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.

32 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 was assumed in the poisoned pins. The solid U0 2 reference case used a 98% theoretical density of 10.4 g/cm 3 in the poison-free pins and g/cm 3 in the poisoned pins. The annular UN test case used a 98% theoretical density of g/cm 3 in the poisonfree pins and g/cm 3 in the 10 weight percent GdN poisoned pins. A value of 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 K. Equivalent geometrical constraints were also imposed on the 13x13 annular design such as the assembly

33 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 17x17 Solid Fuel 13x13 Annular Fuel 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) Benchmark Analysis 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 U 238 absorption in the resonance region is restricted in CASMO-4

34 to the solid cylinder. Thus, the effect of the internal surface in the annular fuel is not accounted for. Without the internal surface, the U 238 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 - MCODE EFPD Figure 2-4: MCODE/CASMO-4 Eigenvalue versus EFPD Benchmark Calculation for Assembly 17x17 Solid UO2 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

35 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 C S1.1 44,, ' -- - " CASMO-4 L MCODE Z 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.

36 Eigenvalue Differences between MCODE and CASMO-4 r U.Uo a O <K ~ ~ '~'~ ~. ~ Solid 17x7 m- Annular 13x13 0,, Y~~ 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 U 238 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 U 238 and the underestimation

37 at the EOL from the lack of appropriate Pu 239 formation. The mechanism by which the Pu 239 is formed from U 238 is shown below: U n -+ U N L- Pu 239 This formation is non-negligible since in a typical PWR the Pu 239 fissions account for roughly 40% of the energy produced in the reactor 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 U 238 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 U 238 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 U 238 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

38 appropriately mimicking the U 238 captures, doesn't accurately predict the Pu 239 formation (and hence the reactivity) at the EOL 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 U 238 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 U 238 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.

39 MCODE vs Corrected CASMO-4 for poison-free pin cells 5% Enriched UN Annular Fuel Pin 150% Power Density and 98% Theoretical Density EFPD 3000 Figure 2-7: MCODE/Corrected CASMO-4 Eigenvalue versus EFPD for a Poison-Free Annular Fuel UN Pin After a wide range of U 238 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.

40 Eigenvalue Difference for a CASMO-4 Corrected Poison-Free Pin Cell by Increasing U-238 at 150% Power Density and 98% Theoretical Density _ * i-o 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.

41 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 E+21 I l- C i C 1.00E+20 / ( -+- CASMO -- MCODE * 1.OOE+19 I 1.OOE E+17 i 1II ' EFPD 2500 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% U 238 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.

42 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 B 10 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 E E 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

43 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 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.

44 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 U 238 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 EFPD 3000 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 U 238 number density correction factors were experimented with. However it was determined that 35% increase in U238 number density gave the closest agreement

45 with the MCODE derived results. The improvement in agreement between MCODE and CASMO-4 is further shown below in Figure Eigenvalue Difference for a CASMO-4 Corrected Poisoned Pin Cell by Increasing U-238 at 150% Power Density and 98% Theoretical Density , P ki ~ ( ~- i I EFPD Figure 2-12: Eigenvalue Differences between MCODE and Corrected CASMO-4 for a 10wt% GdN Poisoned UN Pin Cell

46 I I I IIIII I I IIIIII I I I IIIId I I IIIIII I I I IIIII I I I IIIII I I IIIIII I I 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. ~ I I I I I I I 111 I I I I I i 1.1. 'Iii % ii Energy (MeV) Figure 2-13: Total Cross Section for Gadolinium Isotopes

47 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 E E+19 -A-- Corrected CASMO-4 Gd-155. Corrected CASMO-4 Gd-157 -*- MCODE Gd MCODE Gd E E 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 U 238 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.

48 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 E+21 e E+20 a 1.00E CASMO-4 - MCODE 1.00E E EFPD 2500 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% U 238 number density addition effectively tracks the Pu 239 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.

49 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 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 cm and an inner radius of cm with a cm thick Zircaloy-4 cladding and a cm gap. The pitch of the pins was taken to be

50 1.651 cm. In order to stay within the design envelope of existing PWR fuel, the assembly pitch was held constant at 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 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 -- Corrected CASMO-4 - MCODE 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

51 shows significant improvement in the ability to simulate annular fuel's reactivity over its lifetime. The plutonium production potential is plotted below in Figure 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 E E+20 -*- Corrected CASMO-4 -*-- MCODE 1.00E E E EFPD 2500 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 U 238 number density correction factors determined for the poison-free and poisoned fuel pins, 25% and 35% respectively, allow for the appropriate formation of Pu 2 39 over the lifetime of the fuel.

52 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 * 17x17 Solid Reference * 13x13 Annular 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.

53 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 17x17 UO 2 13x13 UN Reference Annular FTC (1/K) E E-5 MTC (1/K) E E-4 Boron Worth (Ap) 6.320E E-2 Void Coefficient (1/%void) E E-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 U 235 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-

54 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.

55 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.

56 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.

57 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 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:

58 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 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

59 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 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

60 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 (3.1) q"(z) 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: P CPR = crical (3.2) operating where Pctical is the critical power and Poperating is 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

61 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.

62 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 System Pressure 7.2 MPa Inlet Subcooling kj/kg Flow Rate t/hr Diameter of Heated Rod 1.12 cm Pin Pitch 1.43 cm Number of Full Length Rods 66 Axial Length of Full Length Rods m Number of Partial Length Rods 8 Axial Length of Partial Length Rods m below in Figure 3.1. The axial power peaking profile assumed for the NUPEC experiment is shown

63 1 r_ I.' S1.4 S z (cm) Figure 3-1: NUPEC Experimental Axial Power Peaking Profile [Kitamura 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 NL+fpxNp L z > Lp= 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

64 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: f:= f P(z)dz Lp a rt 0 (3.4) Thus the following axial and radial power peaking profiles, depicted in Figures 3.2 and 3.3, were determined Figure 3-2: NUPEC Experiment Radial Power Peaking Factors

65 m~ 4 0u S " 0.6 = 0.4 E 0.2 z 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.

66 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 NUPEC Hench-Gillis Hench- EPRI-1 EPRI-1 Rate Measured Calculated Gillis Calculated % (t/hr) Critical Power Critical Power % Critical Power Error (MW) (MW) Error (MW) % % % % % % % % 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 NUPEC Hench-Gillis Hench- EPRI-1 EPRI-1 Rate Measured Calculated Gillis Calculated % (t/hr) Critical Power Critical Power % Critical Power Error (MW) (MW) Error (MW) % % % % % % % % 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

67 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

68 Table 3-4: EPRI-1 CPR Calculation Data 100% Power Critical Power CHFR kw/rod Table 3-5: EPRI-1 and Hench-Gillis Calculated CPR Comparison Axial Location (m) EPRI-1 CHFR at 100% Power to 3.15 Equivalent EPRI-1 CPR to 3.15 Hench-Gillis CPR 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.

69 3.3. Fuel Assembly Models 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.

70 ooooo O 0 -OOoQQOOO.00@oo ooooo OO %1 O i ooooooo, ~---~---~ P _ I U (_ Q OQOOOOO Figure 3-4: GE11 Fuel Assembly Layout [Gerald 1997] 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:

71 Table 3-6: Solid Fuel Reference Core Operating Parameters [Lungmenl, [Nine Mile Point 2004] Parameter Value System Pressure (psia) 1035 Core Shroud Radius (in) Number of Fuel Assemblies 764 Core Mass Flow Rate (Mlbm/hr) Core Pressure Drop (psia) Core Inlet Temperature ('F) 533 Core Thermal Power (MWth) 3323 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) 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 Value Core MCHFR Average Core Exit Quality 13.34% Hot Bundle Exit Quality 24.50% Radial Power Distribution with 4 Zones 1.45, 1.30, 1.00 and 0.60 Axial Power Peaking Factor 1.51 Maximum Local Peaking Factor 1.23 H/HM Ratio 4.45 Maximum Average Fuel Temperature (oc) 1400 Maximum Center-line Fuel Temperature (TC) 2805 Maximum Cladding Surface Temperature (oc) 349 below. The GE 11 9x9 solid fuel reference assembly design parameters are listed in Table 3.8

72 Table 3-8: GE11 Fuel Assembly Design Parameters Parameters Values Fuel Assembly Pitch (in) Bundle Lattice 9x9 Fuel Pin Pitch (in) Clad Thickness (in) Gap Thickness (in) Number of Fuel Rods 74 Number of Water Rods 2 Diameter between Box Walls (in) Fuel Rod Outer Diameter (in) Water Rod Outer Diameter (in) Water Rod Inner Diameter (in) 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 Loss Coefficient Exit Plate 0.38 Grid 1.20 Entrance Plate 9.46 Orifice 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.

73 Axial Power Peaking Profile for GEl1 9x9 Reference Case 2.I 4, I $ -- -_ 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.

74 o Figure 3-6: Radial Power Peaking Profile for 9x9 Reference Case Poisoned Pin Water Rod 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 Comparative Lattice Surface Area Fuel Volume Reference 100% 100% 5x5 110% 90% 6x6 136% 90% 7x7 151% 90% 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.

75 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.

76 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 and contain a complete description of the 5x5 annular assembly as it was previously optimized without the additional grid loss in the inner annuli 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: 4A De = (3.5) PW 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.

77 Table 3-11: Geometrical Design Parameters for 5x5 Annular Fuel Reference Case Annular Case Fuel Lattice 9x9 5x5 Number of Fuel Rods Number of Water Rods 2 1 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) 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.

78 Figure 3-7: 2-D Cross Section of the 5x5 Annular Fuel Design Concept (Not To Scale) 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

79 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 Poisoned Pin Water Rod Figure 3-8: Radial Power Peaking Profile for 5x5 Annular Case 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 and contain a complete description of the 6x6 annular assembly as it was previously optimized without the additional grid loss in the inner annuli 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.

80 Table 3-12: Geometrical Design Parameters for 6x6 Annular Fuel Lattice Reference Case Annular Case 9x9 6x6 Number of Fuel Rods Number of Water Rods 2 2 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) 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.

81 Figure 3-9: 2-D Cross Section of the 6x6 Annular Fuel Design Concept (Not To Scale) 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

82 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 Poisoned Pin Water Rod Figure 3-10: Radial Power Peaking Profile for 6x6 Annular Case 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 and contain the geometric design parameters, axial and radial power peaking profiles for the 7x7 annular assembly concept.

83 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 Lattice 9x9 7x7 Number of Fuel Rods Number of Water Rods 2 3 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)

84 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

85 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 II & Poisoned Pin Water Rod Figure 3-12: Radial Power Peaking Profile for Case

86 3.4. Results of Fuel Assembly Optimization Studies 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 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 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.

87 Effect of a Reduction in Inner Diameter on the MCHFR for 5x5 Annular Fuel A -- 4 Pi., 1.2- U * Inner CHFR -*- Outer CHFR % 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.

88 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 Effect of Decreasing the Inter-Pin Gap (Via Expansion of the Overall Fuel Pin Dimensions) on the MCHFR for 5x5 Annular Fuel j i ~_...,-.-~~~ Inner CHFR Outer CHFR ---- c~h i 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% % Gap Reduction Between Annular Fuel Pins i 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 Since MCHFR for the reference case was slightly higher at this suggests that an uprate in power density is not achievable for the 5x5 annular geometry.

89 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 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 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.

90 Effect of a Reduction of Fuel Pin Inner Diameter on MCHFR for 6x6 Annular Fuel I Inner CHFR -- Outer CHFR % 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

91 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 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.

92 Effect of the Orifice Resistance Coefficient on CHFR for a 6x6 Annular Fuel Hot Assembly -- u- -~-.~ c. ---., K Inner CHFR Outer CHFR 0% 50% 100% 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: AP P ( )2 1 Vo2 2 (3.6) P 2gc

93 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 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 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.

94 Fuel Pin Dimensions Optimization 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 ~--r ~- ~.~----- ~ ~--~--~ ~~.~ *- Inner Channels Outer Channels -i~ "` ~I c% 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.

95 Inner Channel Orifice Resistance Coefficient Optimization 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----^-~ II-,--U-- - -i , Inner Channels L Outer Channels L 0 % 20% 40% 60% 80% 100% 120% % Increase of Orifice Resistance Coefficient 140% I 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

96 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 ~ t _~ ~ ~~--~ ~ I 1.2- _ Inner CHFR Outer CHFR % 5% 10% 15% 20% 25% 30% 35% % Increase of Spacer Grid Loss Coefficent 40% 45% 50% 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.

97 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 5x5 6x6 7x7 Reference Annular Annular Annular Case 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 Pin #19 Pin #2 Pin #5 Pin #7 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)

98 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: q"avg rdl + h, ril = h,, (3.7) Table 3-15: Mixing Contribution Comparison for 9x9 Reference and 6x6 Annular Cases 9x9 Solid 6x6 Reference Annular Case Case (Inner) Assembly Average CHFR Avg Assembly q" (mbtu/hr-ft2) Hot Channel Flow rate (Ibm/sec) Fuel Length (in) Diameter Ref Pin (in) Diameter Inner Annulus (in) Avg q" (btu/hr-ft2) Enthalpy Inlet (btu/lbm) Calculated Enthalpy Outlet Actual Enthalpy Outlet

99 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.

100 Table 3-16: Effect of Radial Power Peaking on the MCHFR Uprated GE 9x9 Ref 6x6 Annular Grid Loss=65 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) Avg Inner G (mlbm/hr-ft2) Avg Outer G (mlbm/hr-ft2) AP (psia) HIHM VmNf Hot Subchannel Location Ch #76 Outer-Ch #40 Outer-Ch #40 Avg Inner g" (mbtulhr-ft2) Avg Inner CHF (mbtulhr-ft2) Peak Inner q" (mbtu/hr-ft2) 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) Xexit Inner Xexit Outer G Inner (mlbm/hr-ft2) G Outer (mlbmlhr-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

101 increase the operating margins. The simulation of this 6x6 annular assembly showed that the MCHFR in the inner annuli was while the MCHFR in the outer annuli was 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

102 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

103 geometries. Prior research had conducted these thermal hydraulic simulations with the Hench- Gillis 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

104 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 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 H 2 0 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

105 present significant enough fabrication and licensing issues that the adoption of such designs would not be likely. 104

106 References Aounallah, Y. "Void Fraction and Critical Power Assessment of CORETRAN-01/NIPRE-02." Nuclear Technology. Volume (February 2004). Domenici, P. "A Brighter Tomorrow - Fulfilling the Promise of Nuclear Energy." Rowman and Littlefield Publishers. Oxford, U.K. (November 2004). Driscoll, M., Downar, T., Pilat, E. "The Linear Reactivity Model for Nuclear Fuel Management." American Nuclear Society. (February 1991). Edenius, M., Ekberg, K., Forssen, B., Knott, D. "CASMO-4, A Fuel Assembly Burnup Program, User's Manual." Studsvik/SOA-95/1. Studsvik of America, Inc. (1995). Ellis, T. "Recommendations for the Increased Utilization of Nuclear Power in the United States Energy Infrastructure." Journal of Engineering and Public Policy. Volume 8. Washington, DC. (August 2004). Energy Information Administration. "Annual Energy Outlook 2004 with Projections to 2025." DOE/EIA Department of Energy. (January 2004). Energy Policy Act of 2005 (Enrolled as Agreed to or Passed by Both House and Senate) H.R. 6.ENR. Thomas Document Management System. Library of Congress. (August 2005). Feng, D., Kazimi, M., Hejzlar, P. "Innovative Fuel Designs for High Power Density Pressurized Water Reactors." MIT-NFC-TR-075. MIT Center for Advanced Nuclear Energy Systems. (September 2005). Ferroni, P. Personal Communication. MIT Center for Advanced Nuclear Energy Systems. (May 2006). General Electric. "General Electric BWR Thermal Analysis Basis (GETAB) Data: Correlation and Design Applications." NADO (1973). Gerald D., Kvaall, Jr. "Advanced BWR MOX Fuel and Core Design Application Evaluation." Master Thesis. University of California Berkeley. (May 1997). Handwerk, C. "Preliminary Thermal Hydraulic Analysis of a Hydride Fueled Boling Water Reactor." NERIO2-189-MIT-9. (January 2005). Hejzlar, P. "Simple Argument on Why BWRs Can Achieve Much Smaller Power Uprate Than PWRs for Strategies with Increased Cooling Surface." Memo to MIT CANES Thermal Hydraulics Group. (March 10 th, 2005). 105

107 Hejzlar, P., Kazimi, M., Driscoll, M. "High Performance Annular Fuel for Pressurized Water Reactors." ANS Trans. Volume (2001). Idelchik, I. E. "Handbook of Hydraulic Resistance." U.S. Department of Commerce. Clearinghouse for Federal Scientific and Technical Information. (1966). Inoue, Y., Pilat, E., Xu, Z., Kazimi, M. "Combining Thorium with Burnable Poison for Reactivity Control of a Very Long Cycle BWR." MIT-NFC-TR-064. MIT Center for Advanced Nuclear Energy Systems. (June 2004). Kazimi, M. Personal Communication. MIT Center for Advanced Nuclear Energy Systems. (March 2006). Kitamura, M., Mitsutake, T., Takeda, T., Hayashi, H., Morooka, S., Kimura, J., Nishino, Y., Mori, K., Inoue, A. "BWR 9x9 Type Fuel Assembly Critical Power Tests at High-Pressure Conditions." 6th International Conference on Nuclear Engineering. ICONE (1998). Knott, D., Forssen, B., Umbarger, J., Edenius, M., "CASMO-4, A Fuel Assembly Burnup Program, Methodology." Studsvik/SOA-95/2. Studsvik of America, Inc. (1995). Kureta, M. "Critical Power Correlation for Axially Uniformly Heated Tight-Lattice Bundles." Nuclear Technology. Volume (July 2003). Men'shikova, T., et al. "Properties of carbide, nitride, phosphide and other fuel compositions and their behavior under irradiation." Fourth International Conference of the United Nations Organization on the Peaceful Uses of Atomic Energy. Volume 31, Number (October 1971). Metroka, R. "Fabrication of Uranium Mononitride Compacts." NASA Technical Note D Lewis Research Center. Cleveland, OH. (July 1970). Morra, P., Xu, Z., Hejzlar, P., Saha, P., Kazimi, M. "Neutronic and Thermal Hydraulic Designs for High Power Density BWRs." MIT-NFC-TR-071. MIT Center for Advanced Nuclear Energy Systems. (December 2004). Nine Mile Point Unit 2. Updated Safety Analysis Report (USAR). Rev.16. (October 2004). Nuclear Energy Institute. "Fuel Design Data." Nuclear Engineering International (September 2005). Oggianu, S., Kazimi, M. "A Review of Properties of Advanced Nuclear Fuels." MIT-NFC-TR MIT Center for Advanced Nuclear Energy Systems. (February 2000). Oggianu, S., No, H., Kazimi, M. "High Burnup Fuels for Advanced Nuclear Reactors." MIT- NFC-TR-029. MIT Center for Advanced Nuclear Energy Systems. (May 2001). 106

108 Polestar Applied Technology, Inc. "The Role of Nuclear Energy in Reducing C02 Emissions in the Northeastern United States." Boston, MA. (May 2005). Lungmen Power Station Units 1 &2 Preliminary Safety Analysis Report (PSAR). Available on internet at: Stewart, C., Cuta, J., Montgomery, S., Kelly, J., Basehore, K., George, T., and Rowe, D. "VIPRE-01 Manual." Battelle. Pacific Northwest Laboratory (August 1989). Studsvik of America, Inc. "CASMO-4 A Fuel Assembly Burnup Program User's Manual." STUDSVIK/SOA-95/1. (1995). Suzuki, Y., et al. "Recent Progress of Research on Nitride Fuel Cycle in JAERI." Japan Atomic Energy Research Institute. Tokyo, Japan. (1998). Todreas, N., Kazimi, M. "Nuclear Systems I - Thermal Hydraulic Fundamentals." Massachusetts Institute of Technology. Hemisphere Publishing Corporation. (1990). University of Chicago. "The Economic Future of Nuclear Power." (August 2004). X-5 Monte Carlo Team. "MCNP-A General Monte Carlo N-Particle Transport Code, Version 5." LA-UR Los Alamos National Laboratory (April 2003). Xu, Z., Driscoll, M., Kazimi, M. "Neutron Spectrum Effects on Burnup, Reactivity and Isotopics in UO2/H20 Lattices." Nuclear Science and Engineering. Volume (January 2002). Xu, Z., Otsuka, Y., Hejzlar, P., Driscoll, M., Kazimi, M. "Neutronic Design of PWR Cores with High Performance Annular Fuel." MIT-NFC-TR-063. MIT Center for Advanced Nuclear Energy Systems (May 2004). Xu, Z., "Design Strategies for Optimizing High Burnup Fuel in Pressurized Water Reactors." PhD Dissertation. Center for Advanced Nuclear Energy Systems, MIT (January 2003). 107

109 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 Base Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) Control Rod Position Fully Withdrawn Void Fraction 0.0 Low Fuel Temperature Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) Control Rod Position Fully Withdrawn Void Fraction 0.0 High Fuel Temperature Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) Control Rod Position Fully Withdrawn Void Fraction 0.0 Low Moderator Temperature Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) Control Rod Position Fully Withdrawn Void Fraction 0.0 High Moderator Temperature Case Fuel Temperature (K)

110 Moderator Temperature (K) Boron Concentration (ppm) Control Rod Position Fully Withdrawn Void Fraction 0.0 Low Boron Concentration Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) 0 Control Rod Position Fully Withdrawn Void Fraction 0.0 High Boron Concentration Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) Control Rod Position Fully Withdrawn Void Fraction 0.0 High Void Fraction Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) 600 Control Rod Position Fully Withdrawn Void Fraction 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) 800 Moderator Temperature (K) Boron Concentration (ppm) 600 Control Rod Position Fully Withdrawn Void Fraction 0.0 Low Fuel Temperature Case Fuel Temperature (K) Moderator Temperature (K) Boron Concentration (ppm) 600 Control Rod Position Fully Withdrawn Void Fraction

111 High Fuel Temperature Case Fuel Temperature (K) 1100 Moderator Temperature (K) Boron Concentration (ppm) 600 Control Rod Position Fully Withdrawn Void Fraction 0.0 Low Moderator Temperature Case Fuel Temperature (K) 800 Moderator Temperature (K) Boron Concentration (ppm) 600 Control Rod Position Fully Withdrawn Void Fraction 0.0 High Moderator Temperature Case Fuel Temperature (K) 800 Moderator Temperature (K) 600 Boron Concentration (ppm) 60b Control Rod Position Fully Withdrawn Void Fraction 0.0 Low Boron Concentration Case Fuel Temperature (K) 800 Moderator Temperature (K) Boron Concentration (ppm) 0 Control Rod Position Fully Withdrawn Void Fraction 0.0 High Boron Concentration Case Fuel Temperature (K) 800 Moderator Temperature (K) Boron Concentration (ppm) 1200 Control Rod Position Fully Withdrawn Void Fraction 0.0 High Void Fraction Case Fuel Temperature (K) 800 Moderator Temperature (K) Boron Concentration (ppm) 1200 Control Rod Position Fully Withdrawn Void Fraction

112 Appendix B: VIPRE Input Files B. 1 GE 9x9 BWR Assembly Reference * B * *ge9by9 BWR with 2 water rods 1,0,0, *vipre.1 Bwr solid fuel *vipre.2 geom,98,98,40,0,0,0, *normal geometry input, check last BWR normal geom input Oo *geom ,0.0,0.5, *geom.2 1,0.0754, , ,2,2,0.139,0.496,11,0.139,0.496, 2, , , ,2,3,0.139,0.562,12,0.122, , 3, , , ,2,4,0.139,0.562,13,0.122, , 4, , , ,2,5,0.139,0.562,14,0.122, , 5, , , ,2,6,0.139,0.562,15,0.122, , 6, , , ,2,7,0.139,0.562,16,0.122, , 7, , , ,2,8,0.139,0.562,17,0.122, , 8, , , ,2,9,0.139,0.562,18,0.122, , 9, , , ,2,10,0.139,0.496,19,0.122, , 10,0.0754, , ,1,20,0.139,0.496, 11, , , ,2,12,0.122, ,21,0.139,0.562, 12, ,1.3823,1.3823,2,13,0.122,0.562,22,0.122,0.562, 13, ,1.3823,1.3823,2,14,0.122,0.562,23,0.122,0.562, 14, ,1.3823,1.3823,2,15,0.122,0.562,24,0.122,0.562, 15, ,1.3823,1.3823,2,16,0.122,0.562,25,0.122,0.562, 16, ,1.3823,1.3823,2,17,0.122,0.562,26,0.122,0.562, 17, ,1.3823,1.3823,2,18,0.122,0.562,27,0.122,0.562, 18, ,1.3823,1.3823,2,19,0.122,0.562,28,0.122,0.562, 19, ,1.3823,1.3823,2,20,0.122, ,29,0.122,0.562, 20, , , ,1,30,0.139,0.562, 21, , , ,2,22,0.122, ,31,0.139,0.562, 22, ,1.3823,1.3823,2,23,0.122,0.562,32,0.122,0.562, 23, ,1.3823,1.3823,2,24,0.122,0.562,33,0.122,0.562, 24, ,1.3823,1.3823,2,25,0.122,0.562,34,0.122,0.562, 25, ,1.3823,1.3823,2,26,0.122,0.562,35,0.122,0.489, 26, ,1.3823,1.3823,2,27,0.122,0.562,36,0.122,0.600, 27, ,1.3823,1.3823,2,28,0.122,0.562,37,0.122,0.562, 28, ,1.3823,1.3823,2,29,0.122,0.562,38,0.122,0.562, 29, ,1.3823,1.3823,2,30,0.122, ,39,0.122,0.562, 30, , , ,1,40,0.139,0.562, 31, , , ,2,32,0.122, ,41,0.139,0.562, 32, ,1.3823,1.3823,2,33,0.122,0.562,42,0.122,0.562, 33, ,1.3823,1.3823,2,34,0.122,0.562,43,0.122,0.562, 34, , , ,2,35,0.0704,0.562,44,0.0704,0.562, 111

113 35, , , ,1,36,0.1308,0.562, 36, , ,1.1809,2,37,0.122,0.600,45,0.2401,0.530, 37, ,1.3823,1.3823,2,38,0.122,0.562,46,0.122,0.600, 38, ,1.3823,1.3823,2,39,0.122,0.562,47,0.122,0.562, 39, ,1.3823,1.3823,2,40,0.122, ,48,0.122,0.562, 40, , , ,1,49,0.139,0.562, 41, , , ,2,42,0.122, ,50,0.139,0.562, 42, ,1.3823,1.3823,2,43,0.122,0.562,51,0.122,0.562, 43, ,1.3823,1.3823,2,44,0.122,0.527,52,0.122,0.562, 44, , , ,1,53,0.1343,0.530, 45, ,1.2183, ,2,46,0.2401,0.530,54,0.061,0.795, 46, , ,1.1809,2,47,0.122,0.600,55,0.1308,0.530, 47, ,1.3823,1.3823,2,48,0.122,0.562,56,0.122,0.562, 48, ,1.3823,1.3823,2,49,0.122, ,57,0.122,0.562, 49, , , ,1,58,0.139,0.562, 50, , , ,2,51,0.122, ,59,0.139,0.562, 51, ,1.3823,1.3823,2,52,0.122,0.562,60,0.122,0.562, 52, ,1.3823,1.3823,2,53,0.122,0.600,61,0.122,0.562, 53, , ,1.1809,2,54,0.2401,0.530,62,0.122,0.600, 54, ,1.2183, ,1,63,0.2401,0.530, 55, , , ,2,56,0.122,0.562,65,0.0704,0.530, 56, ,1.3823,1.3823,2,57,0.122,0.562,66,0.122,0.562, 57, ,1.3823,1.3823,2,58,0.122, ,67,0.122,0.562, 58, , , ,1,68,0.139,0.562, 59, , , ,2,60,0.122, ,69,0.139,0.562, 60, ,1.3823,1.3823,2,61,0.122,0.562,70,0.122,0.562, 61, ,1.3823,1.3823,2,62,0.122,0.562,71,0.122,0.562, 62, ,1.3823,1.3823,2,63,0.122,0.600,72,0.122,0.562, 63, , ,1.1809,2,64,0.1308,0.530,73,0.122,0.600, 64, , , ,2,65,0.0704,0.562,74,0.122,0.562, 65, , , ,2,66,0.122,0.562,75,0.122,0.562, 66, ,1.3823,1.3823,2,67,0.122,0.562,76,0.122,0.562, 67, ,1.3823,1.3823,2,68,0.122, ,77,0.122,0.562, 68, , , ,1,78,0.139,0.562, 69, , , ,2,70,0.122, ,79,0.139,0.562, 70, ,1.3823,1.3823,2,71,0.122,0.562,80,0.122,0.562, 71, ,1.3823,1.3823,2,72,0.122,0.562,81,0.122,0.562, 72, ,1.3823,1.3823,2,73,0.122,0.562,82,0.122,0.562, 73, ,1.3823,1.3823,2,74,0.122,0.562,83,0.122,0.562, 74, ,1.3823,1.3823,2,75,0.122,0.562,84,0.122,0.562, 75, ,1.3823,1.3823,2,76,0.122,0.562,85,0.122,0.562, 76, ,1.3823,1.3823,2,77,0.122,0.562,86,0.122,0.562, 77, ,1.3823,1.3823,2,78,0.122, ,87,0.122,0.562, 78, , , ,1,88,0.139,0.562, 79, , , ,2,80,0.122, ,89,0.139,0.496, 80, ,1.3823,1.3823,2,81,0.122,0.562,90,0.122, , 81, ,1.3823,1.3823,2,82,0.122,0.562,91,0.122, , 82, ,1.3823,1.3823,2,83,0.122,0.562,92,0.122, , 83, ,1.3823,1.3823,2,84,0.122,0.562,93,0.122, , 84, ,1.3823,1.3823,2,85,0.122,0.562,94,0.122, , 85, ,1.3823,1.3823,2,86,0.122,0.562,95,0.122, , 112

114 86, ,1.3823,1.3823,2,87,0.122,0.562,96,0.122, , 87, ,1.3823,1.3823,2,88,0.122, ,97,0.122, , 88, , , ,1,98,0.139,0.496, 89,0.0754, , ,1,90,0.139,0.496, 90, , , ,1,91,0.139,0.562, 91, , , ,1,92,0.139,0.562, 92, , , ,1,93,0.139,0.562, 93, , , ,1,94,0.139,0.562, 94, , , ,1,95,0.139,0.562, 95, , , ,1,96,0.139,0.562, 96, , , ,1,97,0.139,0.562, 97, , , ,1,98,0.139,0.496, 98,0.0754, , , *99, , , , *water tube *"100, , , , *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 ,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,? ,0.94,? ,0.97,? ,0.96, ,0.91,? ,0.77,? ,0.59,? 113

115 136.86,0.38, ,0.12,? ,0.00, *****rods geometry input *rods.9 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, 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

116 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, ,35, ,44, ,45, ,54, ,? 36, ,53, , *Water rod (ext) *-75,2,0.0,1,99,1.0, *Water rod (int) 76,2,0.0,1,45, ,54, ,55, ,65, ,? 46, ,63, , *Water rod (ext) *-76,2,0.0,1,100,1.0, *Water rod (int) * -77,3,0.0,1,1, ,2, ,3, ,? 5, ,6, ,7, ,8, ,9, ,? 10, , *77,3,0.0,1,99,1.0, -78,3,0.0,1,10, ,20, ,30, ,? 49, ,58, ,68, ,78, ,? 98, , *78,3,0.0,1,100,1.0, -79,3,0.0,1,89, ,90, ,91, ,92, ,? 93, ,94, ,95, ,96, ,? 98, , *79,3,0.0,1,101,1.0, -80,3,0.0,1,1, ,11, ,21, ,31, ,? 41, ,50, ,59, ,69, ,79,? 115

117 ,89, , *80,3,0.0,1,102,1.0, 0 *rods.9 * *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 *74,0.562,0.139,0.44,14.43, *rods.58 * *fuel 1,nucl,0.44,0.376,12,0.0,0.028 *rods.62 0,0,0,0,0, ,0.955,0, *rods 63 *constant radial power in the pellet, no power in the clad *water tube 2,tube,0.98,0.92,1 *rods.68 3,1,0.03,1.0, *rods.69 *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 -1.0,0.0,2.0,0.005, *oper.2 *first word to be changed if you change BC 0 *oper.3 *only if first w above is not ,533.0,33.6,85.226,0.0 * *oper.5 *Rod power got from total power divided total number of rods 0, *no forcing functions *oper. 12 ********************************** *correlations corr, 1,2,0, *corr.1 epri,epri,epri,none, *corr.2 0.2, *corr.3 ditb,chen,chen,epri,cond,g5.7, *correlation for boiling curve *corr.6 epri, 1,0,0.0, *hnch, *corr.16,for epri mixx,0,0,0, 0.8,0.0048,0.0, ************************************************************* 116

118 grid,0,7, *grid , 1.104, ,21.089, , *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 *grid ,2,143.0,3 0, cont, *cont ,0,500,100,3,0, *iterative solution *cont , ,0.001,0.05,0.01,0.9,1.5,1.0, *cont.3 5,0,0,0,0,0,1,1,0,0,0,1,1,0, *cont ,0.0,0.0,0.0,0.0,0.0, *cont.7 endd * *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, *vipre.l Bwr annular fuel *vipre.2 * geom,61,61,36,0,0,0, *normal geometry input *geom. 1 * 178.5,0.0,0.5, *geom.2 1, , , ,2,2, , ,7, , , 2, , , ,2,3, , ,8, , , 3, , , ,2,4, , ,9, , , 4, , , ,2,5, , ,10, , , 5, , , ,2,6, , ,11, , , 6, , , ,1,12, , , 117

119 7, , , ,2,8, , ,13, , , 8, , , ,2,9, , ,14, , , 9, , , ,2,10, , ,15, , , 10, , , ,2,11, , ,16, , , 11, , , ,2,12, , ,17, , , 12, , , ,1,18, , , 13, , , ,2,14, , ,19, , , 14, , , ,2,15, , ,20, , , 15, , , ,2,16, , ,21, , , 16, , , ,2,17, , ,22, , , 17, , , ,2,18, , ,23, , , 18, , , ,1,24, , , 19, , , ,1,20, , ,25, , , 20, , , ,2,21, , ,26, , , 21, , , ,2,22, , ,27, , , 22, , , ,2,23, , , 23, , , ,2,24, , ,29, , , 24, , , ,1,30, , , 25, , , ,1,26, , ,31, , , 26, , , ,2,27, , ,32, , , 27, , , ,2,28, , , 28, , , ,2,29, , ,34, , , 29, , , ,2,30, , ,35, , , 30, , , ,1,36, , , 31, , , ,1,32, , , 32, , , ,1,33, , , 33, , , ,1,34, , , 34, , , ,1,35, , , 35, , , ,1,36, , , 36, , , , *Internal subchannels 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, , , , 118

120 *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 ,13.513,0,0, *rods.2 25 *Normal rod (rods.4) 0.,0.,? ,0.38,? ,0.69,? ,0.93, 24.33,1.1,? ,1.21,? ,1.3,? ,1.47, 48.66,1.51,? ,1.49,? ,1.44,? ,1.36, 72.99,1.28,? ,1.16,? ,1.06,? ,1.01,? 97.32,0.97,? ,0.94,? ,0.97,? ,0.96, ,0.91,? ,0.77,? ,0.59,? ,0.38, ,0.12, *rods3 ******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

121 -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, 25,2,0.0,1,15,0.25,16,0.25,21,0.25,22,0.25, -25,2,0.0,1,-61,1, *rc *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, ids.9 *water rod *water rod *blank line above necessary /rods.57 -HG CPR corr *25, , , , , *0 *rods.59 *rods.58, *fuel 1,tube, , ,5, * 2,1, ,0.0,? 2,2, ,0.0,? 8,3, ,1.0,? 2,4, ,0.0, 2,1, ,0.0, *inner cladding *inner gap *fuel ring *outer gap *outer cladding *rods.68 *rods.69 *rods.69 *rods.69 *rods.69 *rods.69 *water tube 2,tube, , ,1 3,1, ,0.0, * *rods.68 *rods

122 1,18,409.0,clad, *table for cladding 0.0,0.0671, ,? 25,0.0671, , 50,0.0671, ,? 65,0.0671, , 80.33,0.0671, ,? , , , , , ,? , , , , , ,? , , , , , ,? ,0.1717, , ,0.1949, ,? , , , ,0.1478, ,? ,0.112, , ,0.085, ,? ,0.085, , *rods.70 *gap 2,1,0.025,igap, *rods.70 1, , , *Cp=5195J/kg-K *gap=6000 *rods.71 *fuel 3,22, ,FU02, *rods.70 86, , ,? 176, , , 266, , ,? 356, , , 446, , ,? 536, , , 626, , ,? 716, , , 806, , ,? 896, , , 986, , ,? 1076, , , 1166, , ,? 1256, , , 1346, , ,? 1436, , , 1526, , ,? 1616, , , 1706, , ,? 1796, , , 1886, , ,? 1976, , , *rods.71 * *outer gap 4,1,0.025,ogap, *rods.70 1, , , *Cp=5195J/kg-K *gap=6000 *rods.71 *********************************** *P,T 121

123 oper, 1,1,0,1,0,1,0,0,0 *oper ,0.0,2.0,0.005, *oper.2 *first word to be changed if you change BC 0 *oper.3 *only if first w above is not ,533.0,33.30, ,0.0, *oper.5 * 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, *corr.1 epri,epri,epri,none, *corr.2 0.2, *corr.3 ditb,chen,chen,epri,cond,g5.7, *correlation for boiling curve *corr.6 epri, *corr.9 1,0,0.0, *corr. 16,for epri *mine, *corr 18, Hench-Gillis ************************ grid,0,5, *grid ,6.63,1.50,1.46,20000, *grid.2 *pressure drop is for the average rod and for the hot rod 36,10, *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, *grid.5 1.0,1,12.263,2,31.225,3,52.537,3,72.7,3,92.857,3, ,3, ,3, ,3, ,4, *grid loc. *grid.6 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, *cont ,0,750,50,3,0, *iterative solution *cont , ,0.001,0.05,0.01,0.9,1.5,1.0, *cont.3 5,0,0,0,0,0,1,1,0,0,0,1,1,0, *cont ,0.0,0.0,0.0,0.0,0.0, *cont.7 endd *end of data input 0 B.3 Annular 6x6 BWR Assembly *********************************************************************** * I assembly, 6x6 annular pins, using BWR power distribution * * Hot Assembly * 122

124 * 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, *vipre. 1 Bwr annular fuel *vipre.2 geom,85,85,36,0,0,0, *normal geometry input *geom.1 * ,0.0,0.5, *geom.2 * 1, , , ,2,2, , ,8, , , 2, , , ,2,3, , ,9, , , 3, , , ,2,4, , ,10, , , 4, , , ,2,5, , ,11, , , 5, , , ,2,6, , ,12, , , 6, , , ,2,7, , ,13, , , 7, , , ,1,14, , , 8, , , ,2,9, , ,15, , , 9, , , ,2,10, , , 10, , , ,2,11, , , , 11, , , ,2,12, , ,1, ,, , 12, , , ,2, , , , 13, , , ,2,14, , ,20, , , 14, , , ,1,21, , , 15, , , ,2,16, , ,22, , , 16, , , ,2,17, , ,23, , , 17, , , ,2,18 163, ,24, , , 18, , , ,2,19, , ,25, , , 19, , , ,2,20, , ,26, , , 20, , , ,2,21, , ,27, , , 21, , , ,1,28, , , 22, , , ,2,23, , ,29, , , 23, , , ,2,24, , ,30, , , 24, , , ,2,25, , ,31, , , 25, , , ,2,26, , ,32, , , 26, , , ,2,27, , ,33, , , 27, , , ,2,28, , ,34, , , 28, , , ,1,35, , , 29, , , ,2,30, , ,36, , , 30, , , ,2,31, , ,3, , , 31, , , ,2,32, , ,38, , , 32, , , ,2,33, , ,39, , , 33, , , ,2,34, , ,40, , , 34, , , ,2,35, , ,41, , , 35, , , ,1,42, , , 36, , , ,2,37, , ,43, , , 37, , , ,2,38, , ,44, , , 38, , , ,2,39, , ,45, , , 39, , , ,2,40, , ,46, , , 40, , , ,2, , , , 41, , , ,2,42, , , 42, , , ,1,49, , , 123