DEVELOPMENT OF AN INNOVATIVE SPACER GRID MODEL UTILIZING COMPUTATIONAL FLUID DYNAMICS WITHIN A SUBCHANNEL ANALYSIS TOOL

Size: px
Start display at page:

Download "DEVELOPMENT OF AN INNOVATIVE SPACER GRID MODEL UTILIZING COMPUTATIONAL FLUID DYNAMICS WITHIN A SUBCHANNEL ANALYSIS TOOL"

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering DEVELOPMENT OF AN INNOVATIVE SPACER GRID MODEL UTILIZING COMPUTATIONAL FLUID DYNAMICS WITHIN A SUBCHANNEL ANALYSIS TOOL A Thesis in Nuclear Engineering by Maria Avramova 2007 Maria Avramova Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2007

2 The thesis of Maria Avramova was reviewed and approved * by the following: Kostadin N. Ivanov Professor of Nuclear Engineering Thesis Advisor Co-Chair of Committee Lawrence E. Hochreiter Professor of Mechanical and Nuclear Engineering Co-Chair of Committee John H. Mahaffy Associate Professor of Nuclear Engineering Cengiz Camci Professor of Aerospace Engineering Markus Glueck AREVA, AREVA NP GmbH, Germany FDEET (Thermal Hydraulics) Special Member Jack Brenizer Professor of Mechanical and Nuclear Engineering Chair of Nuclear Engineering Program * Signatures are on file in the Graduate School ii

3 ABSTRACT In the past few decades the need for improved nuclear reactor safety analyses has led to a rapid development of advanced methods for multidimensional thermal-hydraulic analyses. These methods have become progressively more complex in order to account for the many physical phenomena anticipated during steady state and transient Light Water Reactor (LWR) conditions. The advanced thermal-hydraulic subchannel code COBRA-TF (Thurgood, M. J. et al., 1983) is used worldwide for best-estimate evaluations of the nuclear reactor safety margins. In the framework of a joint research project between the Pennsylvania State University (PSU) and AREVA NP GmbH, the theoretical models and numerics of COBRA-TF have been improved. Under the name F-COBRA-TF, the code has been subjected to an extensive verification and validation program and has been applied to variety of LWR steady state and transient simulations. To enable F-COBRA-TF for industrial applications, including safety margins evaluations and design analyses, the code spacer grid models were revised and substantially improved. The state-of-the-art in the modeling of the spacer grid effects on the flow thermalhydraulic performance in rod bundles employs numerical experiments performed by computational fluid dynamics (CFD) calculations. Because of the involved computational cost, the CFD codes cannot be yet used for full bundle predictions, but their capabilities can be utilized for development of more advanced and sophisticated models for subchannel-level analyses. A subchannel code, equipped with improved physical models, can be then a powerful tool for LWR safety and design evaluations. The unique contributions of this PhD research are seen as development, implementation, iii

4 and qualification of an innovative spacer grid model by utilizing CFD results within a framework of a subchannel analysis code. Usually, the spacer grid models are mostly related to modeling of the entrainment and deposition phenomena and the heat transfer augmentation downstream of the spacers. Nowadays, the influence that spacers have on the lateral transfer of momentum, mass, and energy within fuel rod bundles are not modeled. The goal of this study is to address the missing phenomena in the current F-COBRA-TF spacer grid model and namely the turbulent mixing enhancement due to spacers and the lateral flow patterns created by specific configurations of the spacers structural elements. iv

5 TABLE OF CONTENTS LIST OF FIGURES... ix LIST OF TABLES... xii NOMENCLATURE... xiv ACKNOWLEDGEMENTS... xviii CHAPTER 1 Introduction Spacer Grid An Important Element of the Fuel Assembly Design Challenges in the Spacer Grid Modeling in the Subchannel Codes Need of an Improved F-COBRA-TF Spacer Grid Model New F-COBRA-TF Spacer Grid Model Objectives and Theoretical Aspects Thesis Outline...8 CHAPTER 2 Review of the State-of-the-Art in the Spacer Grid Modeling Recent Trends Experimental Studies on the Spacer Grid Effects Numerical Studies on the Spacer Grid Effects Subchannel-Based Modeling of the Spacer Grid Effects Concluding Remarks...18 CHAPTER 3 Advanced Thermal-Hydraulic Subchannel Code COBRA-TF - Basic Models and Development Overview of the COBRA-TF Models and Features Worldwide COBRA-TF Development and Applications COBRAG (General Electric Nuclear Energy, USA) WCOBRA/TRAC (Westinghouse Electric Company, USA) F-COBRA-TF (AREVA NP GmbH, Germany) COBRA-TF (Korean Power Energy Company, Korea) v

6 3.2.5 MARS (Korean Atomic Energy Research Institute, Korea) COBRA-TF (Japan Atomic Energy Research Institute, Japan) COBRA-TF (University Polytechnic of Madrid, Spain) COBRA-TF (Pennsylvania State University, USA) F- COBRA-TF Improvements Performed under the AREVA NP GmbH Sponsorship F-COBRA-TF Coding Improvements F-COBRA-TF Numerical Methods Improvement F-COBRA-TF Models Improvements Turbulent Mixing and Void Drift F-COBRA-TF Validation and Verification Program Concluding Remarks...51 CHAPTER 4 F-COBRA-TF Spacer Grid Model COBRA/TRAC Spacer Grid Model Pressure Losses on Spacers De-Entrainment on Spacers COBRA-TF_FLECHT SEASET Spacer Grid Model Evaluation of the Spacer Loss Coefficients Single-Phase Vapor Convective Enhancement Grid Rewet Model Droplet Breakup Model Improvements of the COBRA-TF Spacer Grid Model Performed at PSU Modeling of the Spacer Effects on Entrainment and Deposition Modeling of the Spacer Effects in Dispersed Flow Film Boiling Regime Current F-COBRA-TF 1.03 Spacer Grid Model Features and Drawbacks Concluding Remarks...74 CHAPTER 5 Modeling of Spacer Grid Effects on the Turbulent Mixing in Rod Bundles Background Turbulent Mixing Modeling in Subchannel Analysis Codes Overview Turbulent Mixing Model of THERMIT Turbulent Mixing Model of COBRA-TF vi

7 5.1.4 Turbulent Mixing Model of MATRA Turbulent Mixing Model of FIDAS Turbulent Mixing Model of VIPRE Turbulent Mixing Model of NASCA Turbulent Mixing Model of MONA F-COBRA-TF Turbulent Mixing Model F-COBRA-TF Turbulent Mixing and Void Drift Models Modifications to the F-COBRA-TF Turbulent Mixing and Void Drift Models Addressing the New Spacer Grid Modeling Modifications to F-COBRA-TF Turbulent Mixing and Void Drift Models Addressing Some Experimental Findings Evaluation of the Single-Phase Mixing Coefficient by Means of CFD Calculations Methodology CFD Model Evaluation of the Single-Phase Turbulent Mixing Coefficient Incorporation of the CFD Results into F-COBRA-TF Evaluations of the Spacer Grid Void Drift Multiplier F-COBRA-TF Modeling of the Turbulent Mixing Enhancement by the ULTRAFLOW TM Spacers Concluding Remarks CHAPTER 6 Modeling of Directed Crossflow Created by Spacer Grids Background New F-COBRA-TF Model for the Directed Crossflow by Spacer Grids F-COBRA-TF Transverse Momentum Equations Calculation of the Transverse Momentum Change by Directed Crossflow Verification of the Proposed Directed Crossflow Model Validation of the Proposed Directed Crossflow Model Concluding Remarks CHAPTER 7 Conclusions vii

8 REFERENCES APPENDIX A: CFD Results for the 2 1 Case TM APPENDIX B: CFD Results for the ULTRAFLOW Spacer APPENDIX C: CFD Data for the Mixing Coefficient Multiplier APPENDIX D: Evaluation of the Transverse Momentum Change by Means of CFD Predictions of the Velocity Curl TM APPENDIX E: CFD Results for the FOCUS Spacer APPENDIX F: CFD Data for the Lateral Convection Factor viii

9 LIST OF FIGURES Figure 1: COBRA-TF numerical solution flow-chart 43 Figure 2: F-COBRA-TF/SPARSKIT2 coupling scheme 44 Figure 3: Two-region grid quench and rewet model 59 Figure 4: Radiation heat flux network 60 Figure 5: Droplet breakup 66 Figure 6: Two-phase multiplier Θ TP as a function of quality x according to Beus (1970) 82 Figure 7: Definition of the gap size at the lateral distance in NASCA 87 Figure 8: Turbulent mixing two-phase multiplier as function of local void fraction 95 Figure 9: Void drift multiplier as function of local void fraction 95 Figure 10: Model for the evaluation of the single-phase mixing coefficient by the turbulent viscosity 96 Figure 11: Model for evaluation of the single-phase mixing coefficient by the turbulent heat flux across the gap 97 Figure 12: 2 1 CAD model for thermal-hydraulic analysis of heat transfer by turbulent diffusion 102 Figure 13: Side and top views of the mixing vanes configuration 102 Figure 14: Mesh grid of the 2 1 model 103 Figure 15: Geometrical characteristics of the mixing vanes in the 2 1 model 103 Figure 16: The non-dimensional eddy thermal diffusivity calculated by Ikeno (Ikeno,T., 2001) 107 Figure 17: Evaluation of the single-phase mixing coefficient using surface-averaged turbulent viscosity and vertical velocity dependence on the strap thickness 108 Figure 18: Evaluation of the single-phase mixing coefficient using gap-averaged turbulent viscosity and vertical velocity dependence on the strap thickness 108 Figure 19: Evaluation of the single-phase mixing coefficient using surface-averaged turbulent viscosity and vertical velocity dependence on the declination angle (strap thickness of 0.4 mm) 109 Figure 20: Evaluation of the single-phase mixing coefficient using gap-averaged turbulent viscosity and vertical velocity dependence on the declination angle (strap thickness of 0.4 mm) 109 ix

10 Figure 21: Evaluation of the single-phase mixing coefficient by local heat balance over the gap dependence on the strip thickness 110 Figure 22: Evaluation of the single-phase mixing coefficient by local heat balance over the gap dependence on the declination angle (strap thickness of 0.4 mm) 110 Figure 23: Schematic of the spacer multiplier distribution over the axial length 111 Figure 24: 3D view of the ULTRAFLOW TM spacer 114 Figure 25: Mixing vanes configuration of the ULTRAFLOW TM spacer design 115 Figure 26: Schematic of the CFD model for the ULTRAFLOW TM spacer 115 Figure 27: CFD results for the single-phase mixing coefficient for ATRIUM TM 10 XP bundle with ULTRAFLOW TM spacers 117 Figure 28: CFD results for the single-phase mixing coefficient for the ATRIUM bundle without spacers TM 10 XP TM Figure 29: CFD results for the spacer grid mixing multiplier for the ULTRAFLOW design Figure 30: Axial positions of the ULTRAFLOW TM mixing spacers along the heated length of the ATRIUM TM 10 XP bundle 121 Figure 31: Axial distribution of the spacer multiplier along the heated length of the ATRIUM TM 10 XP bundle 121 Figure 32: Layout of the F-COBRA-TF model of the ATRIUM TM 10 XP bundle 122 Figure 33: Mixing coefficient determined by the standard and the new F-COBRA-TF models 122 Figure 34: Liquid crossflow by turbulent mixing, ULTRAFLOW TM spacer 123 Figure 35: Vapor crossflow by turbulent mixing, ULTRAFLOW TM spacer 123 Figure 36: Void fraction in the hotter subchannel, ULTRAFLOW TM spacer 124 Figure 37: Void fraction in the colder subchannel, ULTRAFLOW TM spacer 124 Figure 38: Flow quality in the hotter subchannel, ULTRAFLOW TM spacer 125 Figure 39: Flow quality in the colder subchannel, ULTRAFLOW TM spacer 125 Figure 40: Enthalpy distribution in the hotter subchannel, ULTRAFLOW TM spacer 126 Figure 41: Enthalpy distribution in the colder subchannel, ULTRAFLOW TM spacer 126 Figure 42: Components of the total crossflow 127 Figure 43: Comparison of the code temporal convergence 127 Figure 44: Comparison of the code convergence on mass balance 128 Figure 45: Comparison of the code convergence on heat balance x

11 Figure 46: Schematic of the HTP TM Spacer 131 Figure 47: Schematic of the FOCUS TM Spacer 131 Figure 48: F-COBRA-TF transverse momentum mesh cell 133 Figure 49: Schematic of two intra-connected fluid volumes 139 Figure 50: Mixing vanes configuration in the 2 2 FOCUS TM model 142 Figure 51: 3D views of the FOCUS TM spacer 142 Figure 52: CFD predictions for the lateral velocity for different mixing vane angles 145 Figure 53: CFD predictions for the lateral mass flux for different mixing vane angles 145 Figure 54: Lateral convection factor for different mixing vane angles 146 Figure 55: Schematic of the spacers positions in the 5x5 bundle with FOCUS TM spacer 146 Figure 56: F-COBRA-TF predictions for the lateral velocity for different mixing vane angles 148 Figure 57: F-COBRA-TF predictions for the lateral mass flux for different mixing vane angles 148 Figure 58: Schematic of the F-COBRA-TF 5 5 model of DTS53 mixing test bundle 153 Figure 59: Mixing vanes arrangement and meandering flow patterns in the 5x5 bundle with FOCUS TM spacer 153 Figure 60: Comparison of the code temporal convergence when modeling directed crossflow 168 Figure 61: Comparison of the code convergence on mass balance when modeling directed crossflow 168 Figure 62: Comparison of the code convergence on heat balance, directed crossflow modeling 169 Figure C-1: Flow chart of the modeling of the enhanced turbulent mixing due to mixing vanes 199 Figure D-1: Schematic of the model for evaluation of the lateral momentum change by velocity curl 200 Figure E-1: Axial distribution of the lateral (UW) velocity for FOCUS TM spacer with mixing vanes of Figure E-2: Axial distribution of the lateral (UW) velocity for FOCUS TM spacer with mixing vanes of Figure E-3: Axial distribution of the lateral (UW) velocity for FOCUS TM spacer with mixing vanes of Figure E-4: Axial distribution of the lateral (UW) velocity for FOCUS TM spacer with mixing vanes of Figure F-1: Flow chart of the modeling of the directed crossflow 212 xi

12 LIST OF TABLES Table 1: Comparison of the F-COBRA-TF equations to the Reynolds-averaged Navier- Stokes equations...7 Table 2: F-COBRA-TF efficiency with different pressure matrix solvers...48 Table 3: Summary of the published correlations for single-phase mixing coefficient...82 Table 4: Single-phase mixing coefficient as calculated with different correlations...83 Table 5: Suggested values for the Θmax...83 Table 6: Description of the 2x1 channels model used in the STAR-CD calculations Table 7: Description of the 2x2 channels model used in the STAR-CD calculations Table 8: Geometrical characteristics of test section DTS Table 9: Range of conditions for test section DTS Table 10: Tests operational conditions Table 11: Geometrical characteristics of the F-COBRA-TF model Table 12: Statistical analyses for data set 1: all subchannels. Mean value and standard deviation of absolute temperature differences Table 13: Statistical analyses for data set 2: peripheral subchannels only. Mean value and standard deviation of absolute temperature differences Table 14: Statistical analyses for data set 3: internal subchannels. Mean value and standard deviation of absolute temperature differences Table 15: Statistical analyses for data set 4: central subchannels only. Mean value and standard deviation of absolute temperature differences Table 16: Statistical analyses for data set 1: all subchannels. Mean value and standard deviation of relative temperature differences Table 17: Statistical analyses for data set 1: peripheral subchannels only. Mean value and standard deviation of relative temperature differences Table 18: Statistical analyses for data set 1: internal subchannels. Mean value and standard deviation of relative temperature differences Table 19: Statistical analyses for data set 1: central subchannels only. Mean value and xii

13 standard deviation of relative temperature differences Table 20: Statistical analyses: Temperature differences for each subchannel i averaged over the calculated test points Table A-1: Temperature field distribution at different strip thickness Table A-2: Turbulent viscosity, vertical velocity, and temperature field distribution at the gap region at different strip thickness Table A-3: Vertical velocity distribution at different strip thickness Table A-4: Turbulent viscosity distribution at different strip thickness Table A-5: Temperature field distribution at different vane angles Table A-6: Turbulent viscosity distribution at different vane angles Table A-7: Pressure field distribution at different vane angles Table A-8: Turbulent Viscosity Distribution over the Subchannels Centroids Line Table B-1: Flow pattern at different altitudes (UV velocity component, m/s) Table B-2: Temperature distribution at different altitudes (in Kelvin Table B-3: Turbulent viscosity at different altitudes (in Pa-s Table C-1: Description of the format of the additional input deck with the CFD data for the mixing multiplier Table C-2: Example for the CFD data set for the 2 1 case Table C-3: Example for the CFD data set for ULTRAFLOW TM spacer Table E-1: Lateral (UW) velocities field immediately downstream of the mixing vanes Table E-2: Lateral velocity field further downstream of the spacer Table E-3: Lateral velocities field at the position of velocity inversion Table F-1: Description of the format of the additional input deck with the CFD data for the lateral convection factor Table F-2: Example for the CFD data set for the FOCUS TM spacer xiii

14 NOMENCLATURE A D dx g G G h l P q i q Flow area Channel hydraulic diameter Axial mesh node size Gravitational acceleration Mass flux Bundle average mass flux Enthalpy Mixing length Pressure Interfacial heat transfer Fluid-fluid conduction heat flux q '' t Heat flux due to mixing effects Qt Energy exchange rate due to mixing effects Q Re S ij Gap length between the adjacent channels i and j S Net rate of entrainment per unit volume U t t T T Wall heat flux Reynolds Number Velocity Time Averaging time interval Temperature Reynolds stress tensor S x W - Gap width Vertical dimension of mesh cell Fluctuating Cross-flow Absolute value xiv

15 Greek α Phasic volume fraction β Г ε Mixing coefficient Rate of mass gain by interfacial transfer or chemical reaction Eddy diffusivity µ Dynamic viscosity ν Kinematical viscosity ρ Phasic density ''' τ Shear stress ''' τ I θ θ M χ Interfacial grad Two-phase multiplier Value of the peak-to single phase mixing rate Quality Subscripts calc Calculated conv Convective e, ent Entrainment field ev, ent-vap Between entrainment and vapor exp Experimental EQ Equilibrium FD Fully developed hyd Hydrauliq g Non condensable gases i Channel index j Channel index k Phase index l, liq Liquid field lat Lateral lv, liq-vap Between liquid and vapor xv

16 max Maximum min Minimum mix Mixture mom Momentum rad Radiation sat Saturation SG Spacer grid SP Single-phase tot Total TP Two-phase turb Turbulent v, vap Vapor field vg Vapor-gas mixture w Wall wall-liq Between wall and liquid Superscripts abs Absolute CFD Computational Fluid Dynamics in Inlet out Outlet rel Relative SCH Subchannel surf Surface T Turbulent TM Turbulent Mixing TM Trademark VD Void Drift xvi

17 Acronyms BOHL Beginning of the Heated Length BWR Boiling Water Reactor CFD Computational Fluid Dynamics CHF Critical Heat Flux CMFD Computational Multi-phase Fluid Dynamics COBRA-TF Coolant Boiling in Rod Arrays Two Fluids DFFB Dispersed Flow Film Boiling DNB Departure from Nucleate Boiling DNBR Departure from Nucleate Boiling Ratio EOHL End of the Heated Length FA Fuel Assembly LWR Light Water Reactor LOCA Loss Of Coolant Accident LHS Left Hand Side MDNBR Minimum Departure from Nucleate Boiling Ratio MSLB Main Steam Line Break PWR Pressurized Water Reactor RHS Right Hand Side xvii

18 ACKNOWLEDGEMENTS I would like to thank my advisor, Prof. Kostadin Ivanov, for his continuous support and guidance throughout the course of this study. I am also very grateful to Prof. Lawrence Hochreiter for his technical help and advice, which were very important for accomplishment of the objectives of this research. I would like to express my sincere appreciation to AREVA NP GmbH (former Siemens/KWU) for funding of my research and making their resources available. Further, I would like to thank to the committee members Prof. John Mahaffy, Prof. Cengiz Camci, and Dr. Markus Glueck for reading and making additional suggestions to improve this thesis. I extend my thanks to my friends and colleagues from Reactor Dynamics and Fuel Management Group, Disparagement of Mechanical and Nuclear Engineering, Penn State University for creating of a multicultural and friendly atmosphere of cooperation and patience during my study at Penn State. I would like to thank my family for their continuous love and understanding. Finally, I would like to express my special gratitude to Rudi Reinders for his lessons to think positively and to believe in myself. xviii

19 CHAPTER 1 INTRODUCTION 1.1 Spacer Grid An Important Element of the Fuel Assembly Design Originally designed to maintain proper geometrical configurations of the fuel rod bundles, spacer grids have a significant influence on the fluid dynamics and the heat transfer in LWR fuel assemblies (FA). The spacers act as flow obstructions in the bundles and therefore increase the overall pressure losses due to form drag and skin friction. On another side, spacer grids change the flow area by contracting the flow and then expanding it downstream of each grid, thereby disrupting and re-establishing the fluid and thermal boundary layers on the fuel rod, which increases the local heat transfer within and downstream of the spacer. In BWR rod bundles they also lead to a local liquid film thickening due to droplets collection and run-off effect and local upstream dry patches due to horseshoe effect. Spacers are in a direct contact with the liquid film on the rod surfaces causing an increase of the entrainment rate. Spacer grids may have special geometrical features to promote turbulence, the effect of which may propagate further downstream. The coolant mixing within a subchannel and between the subchannels can be significantly enhanced by the mixing vanes, which work as mixing promoters and/or flow deflectors and have a very specific impact on the flow distribution. Some vane configurations may create a strong lateral flow and thus enhance the mass, heat and momentum exchange between neighboring subchannels. For example, the split vanes, which are integrally formed on the upper edges of the interlaced strips of a grid and bent over in the flow channel, deflect the upward flow to mix between neighboring subchannels or to swirl within the subchannel. The swirl vanes are intended to generate a strong swirling flow in the subchannel. They are designed to provide a fuel spacer with swirl blades each capable to generate a strong swirl. If the grid has four swirl deflectors attached at the upper ends of 1

20 the interconnections between the straps, the design will result in a small blockage area and thereby will minimize the pressure losses. The twisted vanes have a two mixing vanes at the upper ends of the interconnections between straps, which are bent in opposite directions at the top slope of the triangular base. This is a modified design of the swirl vanes, which generates a crossflow between subchannels as well as swirling flow in the subchannel by directing flow simultaneously to the fuel rod and to the gap region. In general, spacer grids have a beneficial effect on the critical heat flux/critical power in the LWR fuel assemblies. The hydrodynamic behavior of the spacers depends on their geometrical characteristics as well as on the local flow conditions as pressure, local mass velocity and quality and has to be taken into consideration in the core thermal-hydraulic calculations. 1.2 Challenges in the Spacer Grid Modeling in the Subchannel Codes When modeling the thermodynamic phenomena in a real rod bundle, one should take into account the existence of spacer grids and their mixing promoters and flow deflectors. The classical subchannel analyses codes, which are currently used for routine evaluations of the local thermalhydraulic safety margins and design studies in LWRs, are not yet capable of accurate and complete modeling of the spacer effects. Their models are primary based on empirical correlations and are usually limited to simulations of the pressure losses, the entrainment and deposition, and the downstream heat transfer augmentation. The subchannel analyses codes are capable of predicting the bulk flow re-distribution inside rod bundles, but they are not able to simulate local flows caused by mixing vanes. The lateral exchange of momentum, mass, and energy due the re-direction of flow through the rod-to-rod gap regions by the mixing vanes and the enhancement in the turbulent diffusion are partially or not modeled. 2

21 Because of the specifics in each new spacer design, it is impossible to perform accurate studies for the fuel assembly performance without involving costly thermal-hydraulic experiments; bur with its newest developments, the computational fluid dynamics (CFD) has the potential to significantly reduce the need for such expensive experiments and to expedite the improvement process. Recent development in computer technology makes us to believe that both, experiments and subchannel analyses could be replaced by CFD and computational multi-phase fluid dynamics (CMFD). But to be realistic, we have to recognize that the CFD/CMFD capabilities are not yet sufficiently advanced to simulate the complex nature of two-phase phenomena in a boiling flow. We have to recognize as well that even the newest massive parallel computers are not powerful enough to allow full bundle CFD calculations for routine applications. In this situation, the subchannel analyses remain the most practical and reasonable option. Nowadays, the experiments are still indispensable and the CFD calculations would be used as a supporting tool on behalf of subchannel analyses. 1.3 Need of an Improved F-COBRA-TF Spacer Grid Model In 1999 the Pennsylvania State University (PSU) public version of the COBRA-TF code (COBRA-TF_FLECHT SEASET by Paik, C.Y. et al., 1985) was transferred to AREVA NP GmbH (former Siemens KWU) and further improved in a framework of a joint research project between PSU and AREVA NP GmbH. Later, under the name F-COBRA-TF, the code was adopted as an inhouse AREVA NP GmbH subchannel code for reactor core thermal-hydraulic design analyses. The spacer grid model of F-COBRA-TF, code version 1.03, is identical to the COBRA- TF_FLECHT SEASET code version. The model will be described in detail in Chapter 4. Briefly, F- COBRA-TF 1.03 includes models for: 3

22 Local pressure losses in a vertical flow due to spacer grids; De-entrainment on the spacers grid; Single-phase vapor convective enhancement downstream of the spacers grids; Grid rewet under dispersed flow conditions; Droplet breakup model. F-COBRA-TF 1.03 is not equipped with adequate models for Spacers effects on the mass, heat, and momentum exchange mechanisms such as turbulent mixing and void drift; Lateral flow patterns created by specific configurations of the vanes (directed crossflow); Swirl flow created by the mixing vanes. In order to enable the F-COBRA-TF code for industrial applications including LWR safety margins evaluations and design analyses, the code modeling capabilities related to the spacer grid effects were revised and substantially improved. 1.4 New F-COBRA-TF Spacer Grid Model Objectives and Theoretical Aspects The objectives of this PhD research were formulated as development, implementation, and qualification of an innovative spacer grid model utilizing CFD results within the framework of an efficient subchannel analysis tool. The F-COBRA-TF 1.03 code was used as a test bed for implementation of the new advanced spacer grid modeling capabilities. The goal was to improve the F-COBRA-TF such that it can be a suitable tool for LWR fuel assembly design and analyses. To accomplish this objective several new and improved analytical models, which represent the missing physics in the current version of F- 4

23 COBRA-TF, needed to be developed. Thermal-hydraulic phenomena addressed in the new F-COBRA-TF spacer grid model consists of an enhancement of the turbulent mixing between the subchannels downstream of spacer and a directed crossflow due to flow deflection on the spacer. The spacer effect on the entrainment and deposition were not a part of this PhD thesis. The spacer grid enhances the lateral turbulent transport between subchannels due to increased turbulence level in the flow. Therefore, the turbulent transport needs to be increased locally within the basic code framework where the spacer grid exists. The directed crossflow is a flow pattern caused by the sweeping effects of the mixing vanes or other grid structures. The magnitude of the directed crossflow depends of the spacer geometry. Each phenomena of interest was accounted for into the code conservation equations by an additional source term. In other words, the new model is a construction kit system, separating the effects of different phenomena. Additional points of interest were the stability analysis of the explicit time discretization scheme with respect to new source terms and the possible increase of CPU time due to new model or finer spatial discretization. The new models were developed and calibrated using detailed CFD calculations performed at AREVA NP GmbH with the STAR-CD code, version Comparisons to experimental data were performed for each phenomenon. The theoretical aspects of implementing additional terms, due to spacer grid, in the F-COBRA- TF transport equations were studied and clarified. The existing F-COBRA-TF conservation equations were compared to the full Reynolds-averaged Navier-Stokes equations. The missing 5

24 physics and the phenomena directly influenced by the spacers were identified. Decision was taken which of them to be modeled in F-COBRA-TF. It can be seen from Table 1 that F-COBRA-TF, as a thermal-hydraulic code developed on a subchannel basis, does not account for: 1) the lateral exchange between subchannels due to molecular and turbulent diffusion in swirling flow in a horizontal plane; 2) the lateral exchange between subchannels due to centrifugal force in swirling flow in a horizontal plane; 3) the transverse flow between subchannels due to flow patterns created by different deflectors; 4) the lift force; 5) the turbulent dispersion force; 6) the virtual mass force; and 7) the wall lubrication force. Although all these local-scale processes are influenced by the spacers, the effect on the first three is significantly strong and cannot be considered negligible. To address the implementation and validation aspects of the new model, the different spacer grid phenomena were classified into three groups. The first group includes those models that can be accommodated within current code framework, such as pressure losses in axial and lateral flow directions and the transverse mass exchange between neighboring subchannels caused by spacer loss coefficients. The second group includes those models that require (need) new experimental data as a basis for new improved correlations within current code framework. These are the turbulent mixing downstream of spacers (particularly two-phase mixing); the spacer vanes induced swirl within a subchannel; and the spacers effect on the void drift phenomenon. The third group includes those models that can be developed using results of detailed CFD calculations. Such phenomena are the swirl within a subchannel; the directed crossflow due to specific vane design; turbulent mixing between subchannels; and the effect of spacers on the void drift. A detailed discussion of the new F-COBRA-TF spacer grid modeling capabilities is given in Chapters 5 and 6. The aspects of the incorporation of CFD results into a subchannel code are presented and the selection of the experimental data for model validation is discussed. 6

25 Table 1: Comparison of the F-COBRA-TF equations to the Reynolds-averaged Navier-Stokes equations RANS Equations F-COBRA-TF Terms Affected by the Spacers F-COBRA-TF 1. Gravity force modeled no n/a n/a 2. Transverse flow between subchannels due to lateral pressure gradients (diversion crossflow) 3. Pressure Losses frictional losses head losses interfacial drag forces 4. Lateral exchange between subchannels due to molecular and turbulent diffusion in axial flow (turbulent mixing) modeled yes not modeled modeled modeled modeled modeled yes yes 5. Void drift modeled yes modeled as head losses in axial direction due to spacers not modeled Comments Can be modeled following the current code logic for the horizontal pressure loss coefficient for a gap by adding the contribution of the spacers. The horizontal spacer loss coefficient may be determined from experimental data or CFD calculations. Needs further validation: measure data for the pressure drop with and without spacers are needed. The turbulent mixing and the void drift have to be modeled in the momentum equations as separate terms. Thus the spacers influence on both phenomena can be modeled and validated independently. An additional multiplier, accounting for the enhanced turbulent mixing due to spacers, can be applied to the turbulent mixing coefficient following the currently existing logic. Its value can be obtained with CFD calculations. 6. Lateral exchange between subchannels due to molecular and turbulent diffusion in swirl flow in a horizontal plane (turbulent mixing in the transverse momentum equation) not modeled yes not modeled Can be modeled as an additional term to the transverse momentum equation based on CFD calculations. 7. Lateral exchange between subchannels due to centrifugal forces in swirl flow in a horizontal plane not modeled yes not modeled Can be modeled as an additional term to the transverse momentum equation based on CFD calculations. 7

26 RANS Equations F-COBRA-TF Terms Affected by the Spacers F-COBRA-TF 8. Transverse flow between subchannels due to other flow patterns created by spacers/spacer vanes (directed flow) not modeled yes not modeled 9. Lift force (Magnus effect on bubbles and droplets; relative velocity and rotation not modeled yes n/a n/a in velocity field of continuous phase) 10. Turbulent dispersion force (Diffusive bubble movement due not modeled yes not modeled to turbulence in the continuous phase) 11. Virtual mass force not modeled yes n/a n/a 12. Wall lubrication force not modeled yes n/a n/a 13. Entrainment of modeled; modeled droplets in annular yes currently under flow improvement 14. Deposition of droplets in annular flow modeled yes modeled; currently under improvement Comments Can be modeled as an additional term to the transverse momentum equation based on CFD calculations. Can be modeled as an additional term to the transverse momentum equation based on CFD calculations. Current models are mostly based on experimental data. CFD calculations are also valuable if provided by advanced twophase capabilities. 1.5 Thesis Outline Chapter 2 of the thesis discusses the state-of-the-art in the modeling of spacer grid effects on the flow distribution within rod bundles. Chapter 3 presents the basic models and features of the advanced thermal-hydraulic subchannel code COBRA-TF. In addition, the worldwide COBRA-TF development and applications are summarized. Special attention is given to the F-COBRA-TF code and its numerics and models improvements performed within the framework of the cooperation between the PSU and AREVA 8

27 NP GmbH, Germany. Chapter 4 provides a comprehensive review of the current F-COBRA-TF 1.03 spacer grid model, which is based on the COBRA-TF_FLECHT SEASET spacer grid model. Chapter 5 focuses on the effects of spacer grids on the turbulent mixing phenomenon. The F- COBRA-TF models and their modifications are discussed in details. Methodologies for and results of evaluations of single-phase mixing coefficient by means of CFD calculations are given. The incorporation of the CFD results into F-COBRA-TF is presented and comparative analyses for the ATRIUM TM 10 BWR rod bundle are given. Chapter 6 described the modeling of the directed crossflow created by the mixing vanes. The validation of the model against the AREVA NP GmbH 5x5 mixing tests is presented. Chapter 7 summarizes the contribution of this PhD thesis and outlines the further improvements that need to be performed. 9

28 CHAPTER 2 REVIEW OF THE STATE-OF-THE-ART IN THE SPACER GRID MODELING 2.1 Recent Trends A comprehensive review of the open literature indicated that the efforts in understanding the spacer grid impact on the core thermal-hydraulics involves performing experimental mockup tests, numerical simulations, and developing of reliable empirical or semi-empirical models. Recently, the following approach is being adopted. First, a given CFD code is being validated against experimental data. Once validated, the features of the computational fluid dynamics are utilized for prediction of the flow thermal-hydraulic behavior for a particular spacer design. The CFD results are then used to improve the spacer grid models implemented into a subchannel code. An example is the work performed at Mitsubishi Heavy Industries, Ltd., Japan. Single-phase flow tests have been carried out in a system of two or four assemblies of 5x5 and 4x4 rod bundle with staggered grids (Ikeda, K. et al., 1998). Crossflow around the grid has been measured with laser Doppler velocimeter. The effect of different grid type has been examined grid without vanes, grid with guide vanes, grid with mixing vanes, and grid with guide tabs. CFD analytical method has been developed to model the test section area using a porous medium for the grid resistance. CFD predictions have been found to be in good agreement with measurements. Thus, in order to improve the performance of the subchannel code MIDAS (Akiyama, Y., 1995) the assembly wise analysis and computational fluid dynamics have been combined to evaluate crossflow velocity in the bundle (Hoshi, M. et al., 1998). Such methodology could be used for whole LWR core evaluations with relatively short CPU times and reasonable computer resources. 10

29 2.2 Experimental Studies on the Spacer Grid Effects There is a wide range of published experimental studies that investigate the spacer grid effects on the thermal-hydraulic performance of rod bundles. The major phenomena examined are the additional pressure drop in the axial flow; the natural mixing between adjacent subchannels resulting from lateral pressure gradients; the specific flow patterns, axial and lateral, created by mixing vanes; and the heat transfer augmentation near spacers due to enhanced turbulence. The experimental data on the flow mixing between subchannels of bare rod bundles collected by Rowe et al., (Rowe, D. S. et al., 1974), Möller (Möller, S. V., 1991), and Rehme (Rehme, K., 1992) showed that the inter-subchannel mixing, resulting from lateral pressure differences, is mostly due to periodical flow pulsations between the subchannels. However, the presence of a spacer grid equipped with mixing devices leads to a forced mixing either within a subchannel or between the subchannels. An investigation of the crossflow mixing in a rod bundle caused by a spacer grid with ripped-open blades has been performed at Xi an Jiaotong University, China (Shen, Y. F. et al., 1991). Using a laser-doppler velocimeter measurements of the flow transverse mean and the RMS velocities have been carried out in a sixteen-rod bundle with spacers grids with ripped-open blades. The mixing rate was found to be strongly dependent on the declination angle of the blades: the larger is the angle, the larger is the mixing rate and more rapidly the mixing intensity decreases. Also, at larger blade angles the mixing rate distribution inside the subchannel was characterized with a larger non-uniformity. A cylindrical vortex flow was observed as well. The vortices were rotating in the direction of the vanes. Phenomenon defined by Shen as a velocity inversion was reported. Downstream of the spacer, the velocity distributions at the gap regions were not symmetrical: at one rod surface the velocity was higher than at another; and as a 11

30 result an inversion of the lateral velocity occurred. Using particle image velocimetry, measurements of the axial development of a swirl flow have been carried out at the Clemson University 5 5 rod bundle test facility (McClusky, H. L. et al., 2002). Swirl flow has been introduced in a subchannel by attaching split vanes at the downstream edge of a support grid. Lateral flow fields and axial vorticity fields over a range of 4.2 to 25.5 hydraulic diameters downstream of the grid were examined for a Reynolds number of The axial vorticity fields showed that the swirl flow generated by the split vanes is qualitatively consistent with the definition of a classical vortex. As the flow developed in the axial direction, the swirling flow migrated away from the center of the subchannel. The lateral velocity was measured in a radial direction from the centroid of vorticity at different axial locations. Results showed that the lateral velocity increased to a maximum and then decreased. Circulation profiles were found to increase from the vorticity centroid to the edge of the region and their magnitude decayed with the axial length. The aforementioned Clemson University test facility has been used by Conner et al. (Conner, M. E. et al., 2004) to measure the lateral flow field downstream of a grid with mixing vanes for four unique subchannels. In an agreement with McClusky et al. (McClusky, H. L. et al. 2002), the experiment showed that the mixing vanes produce vortices that persist far downstream of the grid. Two vortices were observed in the subchannel central region. The direction of the swirl changed among the subchannels as driven by the vane orientation. Downstream of the grid the vortices tended to get slightly closer together and toward to one of the rod surfaces. In addition, small vane knee vortices were found near gap regions. They were local effects and did not last. Also, the presence of stagnation points (low flow due to flow moving away from rod surface), impingement points (flow directed into rod surface), and a swirl in the lateral flow indicated that the rod surface 12

31 sees significantly different flow conditions, both in axial and lateral domains and thus, the heat transfer around the rod has variability. Yao et al., (Yao, S. C. et al., 1982) have proposed an empirically derived model for a heat transfer augmentation for straight and swirling spacer grids in single-phase and post CHF dispersed flow. Experimental data for the pressure drop and rod surface temperature has been collected at the PSU rod bundle heat transfer test facility. The spacer grid is a 7 7 mixing vane grid representative of an actual PWR grid (Campbell, R. L. et al., 2005). Detailed pressure measurements over a spacer grid in low adiabatic single- and two-phase bubbly flows have been carried out in an asymmetric 24-rod sub-bundle, representing a quarter of a Westinghouse SVEA-96 fuel assembly (Caraghiaur, D. et al. 2004). The pressure distribution comparison between single- and two-phase flows for different subchannel positions and different flow conditions has been performed over a spacer. The primary purpose of this work was to support the development of a CFD code for BWR fuel bundle analysis. 2.3 Numerical Studies on the Spacer Grid Effects A numerical study with the CFD code CFX (AEA Technology, 1997) has been performed to examine the flow mixing in nuclear fuel assembly that is created by four typical mixing promoters: split vanes, twisted vanes, side-supported vanes, and swirl vanes (In, W. K. et al., 2001). The calculations demonstrated that the split and twisted vanes cause primarily a crossflow through the gap region and a weak swirling flow in the subchannel. The swirl vanes produce the strongest circular swirling flow that persists farther downstream of the spacer. The predicted axial and lateral mean flow velocities and the turbulent kinetic energy in a rod bundle with split vanes were 13

32 validated against two experiments, Karoutas, C. Y. et al., 1995 and Shen, Y. F. et al., 1991, and showed good agreement. The comparison of the pressure distribution indicated that the swirl vanes result in a smaller pressure drop. The distance for effective flow mixing was estimated to be 15 to 20 hydraulic diameters from the top of the spacer by the swirling flow and 10 hydraulic diameters by the crossflow. The turbulent kinetic energy rapidly decreased to a fully develop level in approximately 5 to 10 hydraulic diameters downstream of the upper edge of the spacer. Cui and Kim (Cui, X. Z. and Kim K. Y., 2003) have evaluated the effects of the mixing vane shape on the flow structure and the downstream heat transfer by obtaining the velocity and pressure fields, the turbulent intensity, the crossflow factors 1, the heat transfer coefficient, and the friction factor using the CFD code CFX-TASCflow (AEA Technology Engineering Software ltd., 1999). To evaluate the heat transfer enhancement, a commercialized mixing vane design was compared to mixing vane configurations with four different twist angles at a constant blockage ratio. Cui and Kim concluded that the crossflow factor and the turbulent intensity are the factors that most strongly affect the heat transfer downstream of the vane. Beyond 20 hydraulic diameters downstream, the larger crossflow factor induced a larger turbulent intensity and thus a higher heat transfer coefficient. The twist angle influenced the crossflow mixing between subchannels. The crossflow increased with increasing the twist angle. Also, it was found that swirl does not significantly affect the heat transfer, and at constant blockage ratio, both swirl and cross-flow do not noticeably affect the friction factor. The work of Cui and Kim has been extended by Kim and Seo (Kim, K-Y. and Seo J-W., 2005), 1 V 1 cross Crossflow factor is defined as FCM = dy, where s is the distance between fuel rods, Vcross is the s V V bulk crossflow velocity component, and is the axial velocity averaged over cross sectional area. bulk 14

33 where the response surface method has been employed as an optimization technique and an objective function has been defined as a combination of the heat transfer rate and the inverse of the friction loss with a weighting factor. The blend angle and the base length of the mixing vane have been selected as design variables. Numerical experiments have been performed with the CFD code CFX-5.6. It was found that the heat transfer enhances with the increase in both bend angle and base length. A close relationship between the swirl factor 1 and the hear transfer rate was indicated. The pressure loss increased with both design variables. The objective function was found to be more sensitive (by a factor of ten) to the bend angle than to the base length. Gu et al. (Gu, C-Y, et al., 1993) in their earlier work have also assumed the magnitude of swirl (via a swirl factor) to be a qualitative indicator of the spacer design impact on the departure from nucleate boiling performance of PWRs. To improve the numerical predictions of the axial and lateral phase distributions in a BWR assembly in a bubbly two-phase flow, Windecker and Anglart (Windecker, G. and Anglart, H., 2001) proposed a methodology for modeling the effect of spacers by introducing additional pressure drop and turbulence source terms in the momentum and turbulence equations of the CFD code CFX4. The local pressure loss due to spacers was modeled by modifying the body force 2. The source of the turbulent kinetic energy was estimated as the work done by the drag force on the 1 V 1 tan Swirl factor is defined as Sr = dr, where V tan is the tangential velocity component, Va the local axial R V velocity component 1 B = K sp 2 d 2 ρ U U h sp is the local pressure loss coefficient. a, r is the radial distance from the center, and R indicates the effective swirl radius., where dh sp is the characteristic length of the spacer, U is the flow velocity vector, K sp 15

34 surrounding liquid and the source of dissipation of the kinetic energy was modeled as well 1. The model predictions were compared to measurements performed at the FRIGG loop of Westinghouse, Sweden. Although the comparisons showed a good agreement, the well known problem of overprediction of the vapor content in the corner region of the fuel bundle was not fully resolved. In subchannel codes, the turbulent exchange of momentum, mass, and energy is commonly modeled in a similarity to the molecular diffusion by assuming linear dependence between the change rate of a given quantity and its gradient. That approach involves the definition of the proportionality coefficient, the so-called turbulent diffusion coefficient or turbulent mixing coefficient. Attempts were made in a numerical prediction of the single-phase mixing coefficient. Recently two approaches of CFD evaluation of the single-phase mixing coefficient were published. Ikeno (Ikeno, T., 2001) pointed out that the enthalpy exchange through the gap between rods depends on large-scale turbulent structures, which cannot be resolved by the standard k ε turbulence model. To overcome this deficiency Ikeno adopted the Kim and Park flow pulsation model (Kim, S. and Park, G.-S., 1997), but instead using an empirical correlation for the Strouhal number for a flow pulsation through gaps without a spacer grid, an analytical formula was derived. Ikeno (Ikeno, T., 2001) has performed comparative analyses which showed that when using the standard k ε turbulence model the calculated mixing coefficient 2 is one order of magnitude lower than the one calculated with the modified model. The calculated axial distributions of the mixing coefficient with and without the pulsation model were input into a subchannel code to predict measured hot channel exit coolant temperatures in a PWR 5 5 fuel assembly mock-up. Results S 1 ε Cse 3 = K ρu, Sε = ( KspρU ), where C se is the dissipation coefficient. k 2d 1 3 k sp 2d h sp h sp 2 t The mixing coefficient was calculated by turbulent viscosity ν t : β = ν yu 16

35 showed a better agreement to experimental data when the mixing coefficient obtained with the modified k ε model was used. More recently, Ikeno (Ikeno, T., 2005) proposed a computational model, based on a large eddies simulation (LES) technique, for evaluation of the turbulent mixing coefficient. The use of large eddies simulations is believed to contribute for modeling the anisotropy in the turbulent energy distribution the turbulent energy produced from the main flow was transferred predominantly into the lateral component in the gap region. The single-phase mixing coefficient can be evaluated from the heat transferred between adjacent subchannels by the turbulent mixing 1. This approach was used by Jeong et al. (Jeong, H. et al., 2004). The total heat flux between two neighboring subchannels was evaluated by a balance of the inlet and outlet heat flow rates into the two subchannel control volumes. The heat flux due to turbulent mixing was defined by subtracting the heat flux due to molecular diffusion from the transferred total heat flux. 2.4 Subchannel-Based Modeling of the Spacer Grid Effects In regard to the critical power/critical heat flux prediction, in the subchannel codes the spacer grid effects are mostly attributed to modeling of the entrainment and deposition and the heat transfer augmentation downstream of the spacers (Ninokata, H., 2004b; Nordsveen, M. et al., 2003; and Chu, K. H. and Shiralkar, B. S., 1993; Naitoh, M. et al., 2002). The droplets trajectory is governed by the turbulence generated around spacers. Droplet-spacer collisions create additional liquid film on the surface of the spacer and the liquid film run-off effect influences the deposition 1 q& turb _ mix β =, where q & turb _ mix is the heat transferred due to turbulent mixing, T is the temperature difference. c U T p 17

36 rate and its axial distribution. However, entrainment and deposition effects are not among the objectives of this PhD work and will be not addressed hereinafter. Except for the work of Ikeno (Ikeno, T., 2001), no examples of modeling the spacer grids influence on the lateral exchange of momentum, mass, and energy at a subchannel basis inside the fuel rod bundles was found in the open literature. It is well known that the new spacer grid designs with mixing promoters create significant crossflow through the gap regions due to flow deflection and turbulent mixing. No references were found on how the spacer effect on the void drift is modeled. Comprehensive modeling of the above listed phenomena is crucial for accurate prediction of the thermal-hydraulic safety margins. 2.5 Concluding Remarks The state-of-the-art in the modeling of the spacer grid effects on the thermal-hydraulic performance of the flow in LWR rod bundles employs numerical experiments performed by CFD calculations. The capabilities of the CFD codes are usually being validated against mock-up tests. Once validated, the CFD predictions can be used for improvement and development of more sophisticated models of the subchannel codes. Because of the involved computational cost, CFD codes can not be yet efficiently utilized for full bundle predictions, while subchannel codes equipped with advanced physics are a powerful tool for LWR safety and design analyses. 18

37 CHAPTER 3 ADVANCED THERMAL-HYDRAULIC SUBCHANNEL CODE COBRA-TF - BASIC MODELS AND DEVELOPMENT COBRA-TF (COolant Boiling in Rod Arrays Two Fluid) is an advanced thermal-hydraulic subchannel code applicable to both PWR and BWR analyses. The code is widely used for bestestimate evaluations of the nuclear reactors safety margins. The original version of the code was developed at the Pacific Northwest Laboratory as a part of the COBRA/TRAC thermal-hydraulic code (Thurgood, M.J., et al. 1983). 3.1 Overview of the COBRA-TF Models and Features The two-fluid formulation, generally used in thermal-hydraulic codes, separates the conservation equations of mass, energy, and momentum to each phase, vapor and liquid. COBRA- TF extends this treatment to three fields: vapor, continuous liquid and entrained liquid droplets. Dividing the liquid phase into two fields is the most convenient and physically reasonable way to handle two-phase flows. The COBRA-TF two-fluid, three-field representation of the two-phase flow results in a set of nine time-averaged conservation equations. The averaging scheme is a simple Eulerian time average over a time interval. The interval is assumed to be long enough to smooth out the random fluctuations in the multiphase flow, but short enough to preserve any gross unsteadiness in the flow. The general assumptions postulated in the COBRA-TF two-fluid phasic conservation equations are: gravity is the only body force; no volumetric heat is generated in the fluid; radiation heat 19

38 transfer is limited to rod-to-drop and rod-to-steam; pressure is the same in all phases; viscous dissipation is neglected in the enthalpy formulation of the energy equation; turbulent stresses and turbulent heat flux of the entrained liquid phase are neglected; viscous stresses are partitioned into fluid-wall shear and fluid-fluid shear; fluid-fluid shear in the entrained liquid phase is also neglected; conduction heat flux is partitioned into a fluid-wall conduction term and a fluid-fluid conduction term; and a fluid-fluid conduction term is assumed to be negligible in the entrained liquid field. Four mass conservation equations are solved, respectively for the vapor phase, continuous liquid phase, entrained liquid phase, and non-condensable gas mixture. The non-condensable gas mixture transport equation is solved explicitly at the end of each time step. The user can specify up to eight species of different non-condensable gases. The mass conservation equations in a vector form are: ''' α v ρ v + ( α v ρ vu v ) = Γ + G t T v (vapor) (3.1) α l ρ l + ( α l ρ lu t l ) = Γ ''' l S ''' + G T l (continuous liquid) (3.2) α t ''' e ρ l + α eρ lu e ) = Γe + ( S ''' (entrained liquid) (3.3) α g ρ g t + ( α ρ U g g v ) = Γ ''' g + G T g (non-condensable gas mixture) (3.4) Two energy conservation equations are solved, respectively for the vapor-gas mixture and combined liquid field. The use of a single energy equation for the continuous liquid and entrained droplets, which are assumed to be in equilibrium, implies that both fields are at the same 20

39 temperature for a given computational cell. In the regions where both liquid fields are present, this assumption can be justified in the view of the large mass transfer rate between these two fields that tends to draw both to a same temperature. This simplification in the numerical solution results in a reduced computational cost. The energy conservation equations in a vector form are: t ''' ''' '' T ( α ρ h ) + ( α ρ h U v ) = Γ h + q + Q ( α q ) v vg vg v vg vg vg iv vg v vg (vapor-gas mixture) (3.5) t ''' ''' T (( α + α ) ρ h ) + ( α ρ h U l ) = Γ h + q + Q ( α q ) l e l l l l l l f il (combined liquid field ) (3.6) For each direction, axial and transverse, a set of three momentum equations are solved, respectively for the vapor phase, continuous liquid phase, and entrained liquid phase, allowing the liquid and entrained droplets fields to flow with different velocities relative to the vapor phase. The momentum conservation equations in a vector form are: l v l t ( α vρ vgu v ) + ( α ρ U v vg v v U v ) = α P + α ρ v vg g τ ''' wv ''' τ I lv ''' τ I ev + ( Γ ''' U ) + ( α T v T vg ) ( l ρlu l ) α + ( α l ρlu lu l ) = t ''' ''' ''' α P + α ρ g τ wl τ Ilv ( Γ U ) ( S U ) + ( α T l l l ''' l (vapor) (3.7) l T l ) t ( α eρl e ) U + ( α eρlu eu e ) = α P + α ρ g τ e e l ''' we ''' ''' e τ Ive ( Γ U ) + (continuous liquid) (3.8) ( S ''' U ) (entrained liquid) (3.9) 21

40 One of the most important features of COBRA-TF is that the code was developed for use with either rectangular Cartesian or subchannel coordinates. This flexibility allows a fully threedimensional treatment in geometries amenable to description in a Cartesian coordinate system. For more complex or irregular geometries, the user may select only a subchannel formulation or a mixture of rectangular Cartesian and subchannel coordinates. In the subchannel formulation fixed transverse coordinates are not used. Instead all transverse flows are assumed to occur through gaps between the fuel rods. Only one transverse momentum equation applies to all gaps regardless of the gap orientation. A typical finite-difference mesh is used in COBRA-TF for solving the scalar continuity and energy equations (mass/energy cell). The fluid volume is partitioned into a number of computational cells. The equations are solved using a staggered difference scheme. The phase velocities are obtained at the cell faces, while the state variables - such as pressure, density, enthalpy, and void fraction - are obtained at the cell center. The momentum equations are solved on staggered cells that are centered on the scalar mesh face. COBRA-TF two-fluid three-field finite difference equations are written in a semi-implicit form using a donor cell differencing for the convective quantities. These equations must be simultaneously solved, to obtain a solution for the fields mass flow rates. The process must be completed in a reasonable amount of time and must converge to the correct solution. At the first stage of the COBRA-TF numerical solution process, using currently known values for all variables, the momentum equations are solved for each cell and estimates of the new time step fields mass flow rates are obtained. All explicit terms in the momentum equations are also computed at this stage and they are assumed to stay constant for the rest of the time step. The semiimplicit momentum equations are written in a matrix form as follows: 22

41 c1 1 d1 c2 d d 3 0 f l e 2 f v e 3 1 f e a = a a b1 P b2 P b P 3 (3.10) where a 1, a2, and a3 are constants standing for the explicit terms in the momentum equations such as momentum efflux terms and the gravitational force; b 1,, and b are the explicit portion of the b2 3 pressure gradient force term; c and c are the explicit factors that multiply the liquid flow rate in 1 2 the wall and interfacial drag terms; d 1, d 2, and d 3 are the explicit factors that multiply the vapor flow rate in the wall and interfacial drag terms; and e 2 and e 3 are the explicit factors that multiply the entrained liquid flow rate in the wall and interfacial drag terms. Eq.3.10 is solved by Gaussian elimination and the fields mass flow rates are computed. As a second stage, the tentative velocities are calculated to be used in the linearization of the mass and energy equations. If the right hand side (RHS) of each of the mass and energy equations is moved to the left hand side (LHS), and if the current values of all variables satisfy the equations, the sum of the terms on the left side should be identically equal to zero. The energy and mass equations will not generally be satisfied when the new velocities computed from the momentum equations are used to compute the convective terms in these equations. There will be some residual error in each equation as a result of the new velocities and the changes in the magnitude of some of the explicit terms in the mass and energy equations. The vapor mass equation, for example, has a residual error given by: E CV n ~ ~ [( α ) ( ) ] NA [( ) ] NB vρv v v Ac v v Uv jam j [( v v) Uv j Am j ] j α ρ α ρ * α ρ * j j KA NKK KB SL x KA j x = 1 KB= 1 j L= 1 = t [( α ρ )* V ] v v Γ S ~ j cvj vl j x j x j (3.11) In Eq.3.11 the star symbol (*) indicates donor cell quantities, the superscript n denotes quantities at 23

42 new time step, the symbol (~) over the velocities indicates that they are tentative values computed from the momentum equations, and all terms are defined using currently known values of each of the variables. The variation of each of the independent variables required to bring the residual errors to zero can be obtained using block Newton-Raphson method. This is done by linearizing the equations with respect to the independent variables α v, α v h v, (1-α v )h l, α e and the pressure of the actual cell, P j, and those in contact with it, P i, (index i is varying from 1 to the total number of cells NCON in contact with the one of interest). The flowing matrix equation (Eq. 3.12) is obtained for each cell: = = = EV EL CE NCON i i j e EV EV EV EV EV EV CG EV EL EL EL EL EL EL EL EL CE CE CE CE CE CE CE E E E P P P P E P E P E E h E h E E E E E E E E E E E E E E E E E E δ δ δ δα α α α α α M L L L 1 ) (1 = = = = = CV CL CG l v v v v NCON i j e l v v v v g NCON i j e l v v v v g NCON i j e l v v v v g C NCON CV i CV j CV e CV l v CV v v v g NCON i j e l v E E E E h h P P P h h P P P h h E P E P E P E E h E h P P P h α δ δα α α α α α α α α α α α α α α α α α L L L ) (1 ) (1 ) (1 ) (1 ) (1 (3.12) or written in an operator form: (3.13) where [R(x)] is th = g CV CV CV CL CL CL CL CL v v CL v CL g CL NCON CG i CG j CG e CG l v CG v v CG v CG g CG E E E E E E E E h E E E P E P E P E E h E h E E E δα δα α α α α α α α α 1 ) (1 ( ) [ ]{ } E (x) x R = δ e Jacobian of the system of equations evaluated for the set of independent variables (x) and composed of analytical derivatives of each equation with respect to linear variation of independent variables; δ is the solution vector containing these linear variations; and E is the errors vector. Once all derivatives are calculated, the former system (Eq.3.12) is analytically reduced using 24

43 the Gaussian elimination technique to obtain solutions for the independent variables. Void fraction related variables and pressure of the actual cell depend on the pressure of adjacent cells (Eq. 3.14). r r r r r r r r r r r r r r r r r r r r r r r r r r r L L L L L L r 1(6+ NCON ) r 2(6+ NCON ) r 3(6+ NCON ) r 4(6+ NCON ) r 5(6+ NCON ) r 6(6+ NCON ) δα g δα v a δαvhv a δ (1 α v ) hl a δαe = a δp j a δpi = 1 a M δpi = NCON (3.14) After reducing the system, an equation of the form δp j NCON = a + g iδpi i= 1 (3.15) is derived for each cell. Thus, in order to obtain the pressure variation for each cell, a system with a number of equations equal to the number of computational cells should be solved. After this step the linear variation of the other independent variables is unfolded. In regard to the system of pressure equations, the size of this system depends on the number of cells in the problem. The dimension of the matrix is a square of the number of cells. For a case with a small number of cells the equations set may be solved by direct inversion. For a case with a large number of mesh cells the Gauss-Seidel iterative technique is recommended. This technique is based on splitting the mesh cells in groups of cells that greatly influence each other. These groups of cells are called simultaneous solution groups. The equations set is split in the same way. When a given solution group is being solved, the values of δp j for the cells that do not belong to this group are set to the previously calculated values. The multiplication of the pressure matrix by the independent variables vector produces a linear system with the same number of equations as the number of cells 25

44 in the solution group. This linear system is solved by Gaussian elimination. The Gauss-Seidel iteration is carried out over the groups of cells to obtain the new pressure vector. Convergence is reached when the change in δp j for each cell fulfills a specified convergence criterion. The convergence rate, and thus the efficiency of the iteration, can be enhanced by using a process called rebalancing. The process involves obtaining an initial estimate for the pressure variation in each cell (otherwise the linear pressure variation in each cell is set to zero). During the rebalancing, the multi-dimensional mesh is reduced to a one-dimensional and then a solution for the pressure variation at each level of the one-dimensional problem is obtained by direct inversion. Then, the one-dimensional solution for the linear pressure variation at each level is used as an initial guess for the linear pressure variation in each mesh cell on that level in the multi-dimensional problem. Since the COBRA-TF finite-difference equations are written in a semi-implicit form using donor cell differencing for the convective quantities, the time step is limited by the material Courant limit. Before the solution process proceeds to the next time step, evaluations are made on the values of the new calculated variables to assure that their time variations fall within reasonable limits. If these new time variables have nonphysical values or their time variations are unreasonably large, then the solution is returned to the beginning of the time step. The variables are set to their old time values, the time step is halved and repeated. This is done in such a way that the linearized equations will be sufficiently representative of the nonlinear equations to provide an acceptable level of accuracy in the calculation. The flow regime map used in COBRA-TF can be divided into two main parts: logic used to select a physical model in an absence of unwetted hot surfaces and logic used in a presence of unwetted hot surfaces. The flow regimes described by the first set of logic are called normal flow regimes, while those described by the second set are called hot wall flow regimes. Flow regimes 26

45 are determined from fluid properties and flow conditions within each cell or in the immediate surrounding cells. Since the code was developed for vertical two-phase flow simulations, horizontal flow regimes are not considered. The normal flow regime logic considers dispersed bubbly flow, slug flow, churn-turbulent flow, film flow, and film mist flow. The hot wall flow regimes include subcooled inverted annular flow, saturated liquid chunk flow, dispersed droplets-vapor flow, falling film flow, and top deluge. Droplets deposition and entrainment is allowed in the falling film regime. An inverted annular flow regime is assumed during a bottom reflood if the continuous liquid phase is subcooled. Entrainment of liquid is allowed, permitting a transition to dispersed flow based on the physical models for the entrainment rate and droplet-vapor interfacial drag. The deposition and breakup of droplets on grid spacers are also considered. The COBRA-TF code considers the following de-entrainment mechanisms: de-entrainment in the liquid film, de-entrainment in the cross-flow, de-entrainment at area changes, and deentrainment at solid surfaces and liquid pools. In addition, the code accounts for droplet breakup at spacer grids. The heat transfer models in COBRA-TF determine the material heat release rates and the temperature response of the fuel rod and structural components of LWRs during operational and transient conditions. At the beginning of each time step, before the hydraulic solution proceeds, all the heat transfer calculations are performed. Heat transfer coefficients based on previous time step liquid conditions are used to advance the material conduction solution. The resultant heat release rates are explicitly coupled to the hydrodynamic solution as source terms in the fluid energy equations. 27

46 The COBRA-TF conduction model specifies the conductor geometry and material properties, and solves the conduction equation. The rod model is designed for nuclear fuel rods, heater rods, tubes, and walls. The model consists of options for one-dimensional (radial), two-dimensional (radial and axial), and three-dimensional (radial, axial and azimuthal) heat conduction. This flexibility allows the user to simulate most of the conduction geometries found in the reactor vessels. In addition, an unheated conductor model is provided for structural heat transfer surfaces. Moreover, using the COBRA-TF three-dimensional rod model, the fuel rod may be modeled with up to eight individual circumferential sections with each section having a connection to a different fluid channel. The quench front model is a fine mesh-rezoning method that calculates a quench front propagation due to the axial conduction and the radial heat transfer. The large axial computational mesh spacing usually used in coupled thermal-hydraulic numerical simulations of rewetting cannot adequately resolve the axial temperature profile and surface heat flux across the quench front. During the quenching the entire boiling curve can be encompassed by one hydrodynamic mesh cell. This can lead to stepwise cell-by-cell quenching, producing flow oscillations that can obscure the correct hydrodynamic solution. In the COBRA-TF fine mesh-rezoning technique, fine mesh heat transfer cells with axial and radial conduction are superimposed on coarse hydrodynamic mesh spacing, and a boiling heat transfer package is applied to each node. It should be noted that the fine mesh nodes are stationary and do not have a fixed mesh spacing. Thus, the fine mesh nodes are split to create a graduated mesh spacing that re-adjusts itself constantly to a changing axial temperature gradient. The COBRA-TF gap conductance model dynamically evaluates fuel pellet-clad conductance for a nuclear fuel rod. The model computes changes in the fuel rod structures and fill gas pressure 28

47 that affect the gap conductance and fuel temperature during a transient. The subchannel-based radiation model for rod-rod, rod-vapor, and rod-droplet radiation heat transfer was developed and implemented in COBRA-TF in order to simulate a reflood phase of loss-of-coolant accident (LOCA) transients. The COBRA-TF heat transfer package consists of a library of heat transfer coefficients and a selection logic algorithm. Together these produce a boiling curve that is used to determine the phasic heat fluxes. The maximum of the Dittus-Boelter turbulent convection correlation (Dittus, F. W. and Boelter, L. M. K., 1930), the FLECHT SEASET 161-rod steam cooling correlation (Wong, S. and Hochreiter, L. E., 1981), and a laminar flow Nusselt number is used to determine the singlephase vapor heat transfer coefficient. For single-phase convection to vapor, all vapor properties are evaluated at the liquid film temperature. Convection to single-phase liquid is computed as the larger of either Dittus-Boelter turbulent convection correlation or laminar flow with a limit Nusselt number equal to When the surface temperature is greater than the saturation temperature but less than the critical heat flux temperature and liquid is present, the Chen nucleate boiling correlation (Chen, J. C., 1963) is used. The Chen correlation applies to both saturated nucleate boiling region and two-phase forced convection evaporation region. The transition to a single-phase convection at low wall superheat and pool boiling at low flow rate is automatically performed. The Chen correlation assumes a superposition of a forced-convection correlation (Dittus-Boelter type) and a pool boiling equation (Forster-Zuber). An extension of the Chen nucleate boiling correlation into the subcooled region is used for subcooled nucleate boiling. During the subcooled boiling, a vapor generation occurs and a significant void fraction may exist despite the presence of subcooled water. The processes of interest in this regime are the forced convection to liquid, vapor generation at the wall, condensation near the wall, and bulk condensation (subcooled liquid core). 29

48 The COBRA-TF critical heat flux package consists of three regimes pool boiling, forced convection departure from nucleate boiling (DNB), and annular film dryout. Pool boiling DNB is selected when the mass flux is less than 30 g/cm 2 -sec and the flow regime is not annular film flow. The pool boiling heat flux is given by Griffith s modification (Griffith, P. et al., 1977) of the Zuber equation (Zuber, N. et al., 1961). Forced-convection DNB is considered when the mass flux is greater than 30 g/cm 2 -sec and the flow regime is not annular film flow. In this case, the critical heat flux is given by the Biasi correlation ( Biasi, L. et al., 1967). Annular film dryout is assumed if the mass flux is greater than 30 g/cm 2 -sec and annular film flow exists. In this regime, the heat flux is not limited by a correlation, but rather forced convection vaporization exists until the film dries out. The COBRA-TF code employs a simple additive scheme for heat transfer beyond the critical heat flux temperature. The transition boiling heat transfer is composed of both liquid contact (wet wall) and film boiling (dry wall). Heat transfer in the film boiling region is assumed to result either from dispersed flow film boiling or from inverted annular film boiling. 3.2 Worldwide COBRA-TF Development and Applications The previous section discussed COBRA-TF models as originally developed in early 1980s. Since then, various academic and industrial organizations adapted, developed and modified the code in many directions. The COBRA-TF 1 version owned by PSU originates from a code version modified in cooperation with the FLECHT SEASET program (Paik, C. Y. et al., 1985). The following sections will discuss the code modifications as compared to the original code version. 1 This code version will be called COBRA-TF_FLECHT SEASET from now on. 30

49 3.2.1 COBRAG (General Electric Nuclear Energy, USA) COBRAG is an improved version of COBRA-TF developed by General Electric Nuclear Energy. There are articles published in 1990s that discussed the COBRAG models improvements as well as the assessment of the code capability of predicting critical power at steady state and transient conditions (Chu, K. H. and Shiralkar, B. S., 1993; Chen, X. M. and Andersen, J. G. M, 1997a; and Chen, X. M. and Andersen, J. G. M, 1999) and the cross sectional void distribution in BWR fuel bundles (Chu, K. and Shiralkar, B. S., 1992 and Chen, X. M. and Andersen, J. G. M, 1997b). The major improvements comparing to the original COBRA-TF code are as follows. An individual film thickness model has been introduced: the liquid films on different surfaces within a subchannel have their own set of conservation equations (Shiralkar, B. S. and Chu, K. H., 1992). Since the different rod surfaces within a subchannel could have very different heat generation rates and surface characteristics, the model allows for four film segments around a fuel rod. Critical power is controll ed by the film dryout, which is modeled as a balance between evaporation, entrainment and deposition processes leading to a critical film thickness in an annular flow regime. To account for the void drift phenomenon the model by Drew and Lahey (Drew, D. A. and Lahey, R. T., 1979) has been incorporated in COBRAG. A spacer model has been developed and implemented into COBRAG to account for the spacer effects on the critical power. A semi-empirical approach has been applied to formulate the spacer model. The model analyzes the major effects of the spacer on the flow distribution by focusing on the mechanisms which influence the film flow rate on the fuel rods: upstream film thinning, downstream turbulence enhancement, and collection and run-off at the spacer. 31

50 3.2.2 WCOBRA/TRAC (Westinghouse Electric Company, USA) WCOBRA is a part of the Westinghouse Electric Company WCOBRA/TRAC-MOD7A code package licensed for best-estimate LOCA analyses. The package is an improved version of the COBRA/TRAC code. The achievements in the WCOBRA/TRAC development are in the area of code performance in large break loss LOCA transient simulations (Takeuchi, K. et al., 1998 and Bajorek, S. M. et al, 1998) F-COBRA-TF (AREVA NP GmbH, Germany) Currently COBRA-TF is being developed and qualified for reactor core thermal-hydraulic design analyses at AREVA NP GmbH (Germany). The work was started within the scope of coope ration w ith the Pennsylvania State University. The official AREVA NP GmbH version of the code is named F-COBRA-TF 1. A software package has been developed at AREVA NP GmbH to enable the code for industrial applications (Glueck, M. and Kollmann, T., 2005). The package include a preprocessor (INCA input generator for a wide variety of PWR and BWR rod bundles), a solver (F-COBRA-TF) and two postprocessors for a one-dimensional visualization (PLOCOB) and for a threedimensional visualization (CoreView3D). The major model improvements consist of a new individual film model and an improved criterion for transition between different flow regimes (Glueck, M., 2006). In the implemented individual film model, liquid films on each boundary structure of a given subchannel (rod segment or bounding wall) are balanced individually with regard to the 1 This section discusses the code modifications carried out without the PSU participation. The F-COBRA-TF development performed by the author of this PhD thesis will be summarized in Section

51 evaporation, entrainment, and deposition. In addition to the original COBRA-TF flow regime logic, two new approaches, based on the work by Taitel et al. (Taitel, Y. et al., 1980) and Mishima and Ishii (Mishima, K. and Ishii, M., 1984) have been implemented in F-COBRA-TF COBRA-TF (Korean Power Energy Company, Korea) A very interesting work on COBRA-TF extension to a system code has been performed at the Korean Power Energy Company (Park, C. E. et al., 2005). Horizontal flow channel modeling capability has been introduced for simulations of the horizontal pipes in nuclear reactor system. A point kinetics model is utilized for simulation of the core neutronic response. The code modifications have been verified against pressurized level control system (PLCS) malfunction and main steam line break (MSLB) MARS (Korean Atomic Energy Research Institute, Korea) The best-estimate system code MARS has been developed at the Korean Atomic Energy Research Institute (Lee, S. Y. et al., 1992 and Jeong, J.-J. et al., 1999). The code is a merged version of the system code RELAP5/MOD3 and the subchannel code COBRA-TF. COBRA-TF has been adapted as a three-dimensional module in MARS (Jeong, J.-J. et al., 2004). The code improvements consist of a translation to FORTRAN90 language, an implementation of an equalvolume exchange model and the Drew and Lahey s void drift model, where the void drift coefficient is calculated as function of the pressure (Jeong, J.-J. et al., 2005a). 33

52 3.2.6 COBRA-TF (Japan Atomic Energy Research Institute, Japan) An extensive program for COBRA-TF assessment and improvement for predicting dryout type CHF has be en carried out at the Japan Atomic Energy Research Institute in early 1990s (Murao, Y. et al., 1993 and Okubo, T. et al., 1994). The performed modeling modifications have focused on phenomena as the entrainment and deposition, the single- and two-phase mixing, and the critical heat flux. The new entrainment/deposition model has been based on the correlation by Wurtz s (Wurtz, J., 1978) and Sugawara s (Sugawara, S., 1990). Nevertheless that it is not officially stated, it is believed that this particular version of COBRA- TF was used as a base of the currently developed code NASCA (New Advanced Sub-Channel Analysis) (Ninokata, H. et al., 2001, Hotta, A. et al., 2004, and Shirai, H. et al., 2004). Most recently, a tremendous amount of academic efforts and financial support from industrial, private and government organizations in Japan have been put in the NASCA development (Ninokata, H. et al., 2004a). This level of efforts will most likely make the code one of the major competitors among the commercial subchannel codes COBRA-TF (University Polytechnic of Madrid, Spain) The COBRA-TF computational efficiency was improved by implementing two optimized matrix solvers, Super LU library and Krylov non-stationary iterative methods for solution of the linear system of pressure equations. The work was performed in cooperation between PSU and University Polytechnic of Madrid (UPM) (Cuervo, D. et al., 2004 and Cuervo, D. et al., 2005) COBRA-TF (Pennsylvania State University, USA) As it was mentioned above, the COBRA-TF version owned by the Pennsylvania State University originates from a code version modified in cooperation with the FLECHT SEASET 34

53 program (Paik, C. Y. et al., 1985). Besides the code utilization to teach and train students in the area of nuclear reactor thermal-hydraulic safety analyses, the code has undergone different assessment studies as well as development and improvement of the two-phase flow models. The work of Ergun (Ergun, S. et al., 2005a) contributes in introducing a smaller droplet field as an additional field in the COBRA-TF conservation equations. The work of Holowach (Holowach, M. J. et al. 2002) is important in modeling of the fluid-to-fluid shear in-between calculational cells over a wide range of flow conditions. Other examples for a high quality COBRA-TF development and applications are the works of Solís, (Solís, J. et al., 2004), and Ziabletsev (Ziabletsev, D. et al., 2004). Most recently, a three-dimensional neutron kinetics module was implemented into COBRA-TF by a serial integration coupling scheme to the PSU Nodal Expansion Method (NEM) code (Avramova, M. N. et al., 2006a, Tippaykul, C. et al., 2007). The new PSU coupled code system was named CTF/NEM. 3.3 F- COBRA-TF Improvements Performed under the AREVA NP GmbH Sponsorship The cooperation between the Pennsylvania State University and AREVA NP GmbH (former Siemens KWU) started in 1999 as a joint project for coupling COBRA-TF with the Siemens Nuclear Power system code RELAP5/PANBOX. In the coupling scheme COBRA-TF replaced COBRA 3-CP code and an initial testing of the functionality of the new coupled system and benchmarking against PANBOX/COBRA 3 CP was performed (Ziabletsev, D. and Böer, R., 2000). Further, the joint PSU-AREVA NP GmbH efforts were moved in the direction of stand-alone COBRA-TF development, qualifications, and validation for LWR analyses (Frepoli, C. et al., 35

54 2001a, 2001b; Kronenberg, J. et al., 2003; and Avramova, M.N. et al., 2002, 2003a, 2003c). Since 2003, under the name F-COBRA-TF, the COBRA-TF code is adopted as an in-house AREVA NP GmbH subchannel code for reactor core thermal-hydraulic design analyses. A special F-COBRA-TF validation/verification and models development program was established. PSU has a significant contribution to both, assessment of the current F-COBRA-TF models and development of new F-COBRA-TF models. The F-COBRA-TF validation program consists of a large set of simulation problems representative of LWR nominal operating and anticipated transient conditions. In addition, as a part of the F-COBRA-TF models development program, several improvements and modifications were performed in order to enhance code predictive capability for LWR steady state and transient analysis. To improve the F-COBRA-TF computational efficiency, the code numerical methods were revised as well F-COBRA-TF Coding Improvements Translation to FORTRAN 90/95 Language The original COBRA-TF code was written for CDC 7600 operation platform. Later the source was adapted for a PC environment by removing machine dependent features and some old nonstandard FORTRAN statements. The code was based on static allocation memory and the special header file was used to set the arrays dimensions through PARAMETER operators. However, the FORTRAN90 dynamic allocation memory option is preferable to the static allocation memory because of the optimized memory usage. Thus, in order to enhance code performance, the code was 36

55 translated to the FORTRAN 90/95 standards (Avramova, M. N., 2003b) F-COBRA-TF Dump/Restart Capability In the original stand-alone version of COBRA-TF only a simple dump/restart is possible. During the simple restart run the user is allowed to change only the time domain data, but not the power distribution and the flow conditions. To improve the code dump/restart capability it was decided to recover the dump/restart code logic by including also the so-called full restart (Avramova, M. N., 2004a). During the full restart run, the user can specify changes in the operating conditions, power distribution, boundary conditions, printout options, and the time domain data User Friendly Code Environm ent Since F-COBRA-TF is being developed for industrial applications, the code input/output procedures must be settled in such a way that the possibility of user-introduced errors is minimized as much as possible. It is common that most of the old computer codes are not user-friendly oriented. In particular, COBRA-TF code has a complicated input structure requiring a great amount of information which is, very often, not clear for an inexperience user. Along with the formatted input deck syntax and the lack of an adequate warning/error reporting, this created an environment for user-related errors. To overcome the problem, an unformatted input deck structure was adapted in the F-COBRA-TF code (Avramova, M. N., 2004a). This improvement automatically allowed the use of SI units instead of British units, traditionally used in COBRA-TF. The convergence between both units systems has been coded in the original code version, but SI units could not be used because of the 37

56 required input format. In addition, an automated input deck cross-checking procedure was introduced as well (Avramova, M. N., 2004b). While reading the input deck, the code is performing an internal checking for user-introduced errors and a warning/error message is immediately given Code Maintenance The PSU activities related to the F-COBRA-TF assessment and development are subjected to the quality assurance (QA) program established in the Reactor Dynamic and Fuel Management Group (RDFMG), Nuclear Engineering Program. The RDFMG QA program was reviewed and approved by AREVA NP GmbH (Schlee, H., 2006). Independently, an internal quality assurance is being performed in AREVA NP GmbH as well F-COBRA-TF Numerical Methods Improvement Background One of the major drawbacks of the early developed subchannel codes is their poor computational efficiency. The increased use and importance of detailed reactor core descriptions for LWR subchannel safety analysis and coupled local neutronics/thermal-hydraulics evaluations require improvements of the subchannel code numerical methods performance and efficiency in order to obtain reasonable running times for large problems. For two-fluid codes, such as COBRA- TF, due to the extended set of complex equations, the necessity of highly efficient numerical method is even more pronounced. An exhaustive analysis of the CPU times needed by the code for different stages in the solution process has revealed that the solution of the linear system of pressure equations is the most time consuming process. 38

57 There are two numerical methods originally implemented in COBRA-TF: direct inversion and Gauss-Seidel iterative technique. The first one is only recommended for cases with a small number of cells. The second one belongs to the group of stationary iterative methods. As described in Section 3.2.7, the performance of currently existing solvers was investigated in the work of Cuervo and Avramova (Cuervo, D. et al., 2004 and Cuervo, D. et al., 2005). It was found that when direct inversion is used the subroutine performing the pressure matrix solution is taking more than 70 percents of the total CPU time for large cases and less than 30 percents for small cases. The Gauss-Seidel technique shows contradictory results: it speeds up the pressure matrix solution especially for large cases but greatly slows it down for cases with non-stationary mass flow conditions. In order to improve the code efficiency two optimized matrix solvers, Super LU library (Demmel, J. W. et al., 2003) and Krylov non-stationary iterative methods (Saad, Y., 2000) were successfully implemented in the PSU/UPM version of COBRA-TF for solution of the linear system of pressure equations. The performed comparative analyses demonstrated that for large cases, the implementation of the bi-conjugate gradient stabilized method (Bi-CGSTAB) combined with the incomplete LU factorization with dual truncation strategy pre-conditioner reduced the total computational time by factors of 3 to 5. Both new solvers converge smoothly regardless of the nature of simulated cases and the mesh structures. They show better accuracy comparing to the Gauss-Seidel iterative technique for all investigated test cases. Based on this experience, Krylov non-stationary iterative methods were chosen for implementation in F-COBRA-TF code for solution of the linear system of pressure equations (Avramova, M. N., 2005a). 39

58 Implementation of Krylov Non-Stationary Iterative Methods for Solution of the F- COBRA-TF Linear System of Pressure Equations The term iterative method refers to a wide range of techniques that use successive approximations to obtain more accurate solutions to a linear system at each step. Stationary methods are older and simpler to understand and implement but usually not very effective. Nonstationary methods are a relatively recent development; their analysis is usually more difficult to understand but they can be highly efficient. The non-stationary methods are based on the idea of sequences of orthogonal vectors. An exception is the Chebyshev iteration method, which is based on orthogonal polynomials. The rate at which an iterative method converges depends greatly on the spectrum of the coefficient matrix. Hence iterative methods usually involve a second matrix that transforms the coefficient matrix into one with a more favorable spectrum. The transformation matrix is called a preconditioner. A good preconditioner improves the convergence of the iterative method sufficiently to overcome the extra cost of constructing and applying the preconditioner. Indeed without a preconditioner the iterative method may even fail to converge. The superior performance of Krylov solvers, as compared to the stationary iterative methods, has been well documented for the nuclear reactors thermal-hydraulic problems. The application of preconditioned conjugate gradient methods to the linearized pressure equation is presented in the work of Turner and Doster (Turner, J. and Doster, J., 1991). Downar and Joo (Downar, T. and Joo, H., 2001) have applied the Bi-CGSTAB method to obtain the continuity equation solution in VIPRE-02, which is a two-fluid two-field code for subchannel analysis. Allaire (Allaire, G., 1995) has utilized a preconditioned Krylov solver for the solution of the linearized three-dimensional two-phase flow equations of the subchannel code FLICA-4 developed at CEA, France. 40

59 The SPARSKIT2 library (Saad, Y., 2000) includes subroutines with most of the Krylov solvers and preconditioners. The library was created by CSRD, University of Illinois and RIACS (NASA Ames Research Center) under the sponsorship of NAS System Division and US Department of Energy. The subroutines are coded in Fortran 77. The SPARSKIT2 library is free software; it can be redistributed and/or modified under the terms of the GNU General Public License as published by the Free Software Foundation (Copyright (C) 1989, 1991 Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA). The library is available via Internet. The SPARSKIT2 library was utilized for the F-COBRA-TF pressure matrix solution by use of coupling subroutines. The original F-COBRA-TF numerical solution logic was described in Section 3.1. Here, flow-chart of the solution scheme is given in Figure 1. The F-COBRA-TF/SPARSKIT2 coupling scheme is shown in Figure 2. In the original COBRA-TF code, the selection of the numerical method for the pressure matrix solution is done by the user. If the user specifies only one simultaneous solution group, the pressure matrix will be solved with Gaussian elimination (direct inversion). In case of more than one simultaneous solution groups Gauss-Seidel iterative technique will be used. The coupling to the SPARSKTI2 library was performed by developing two additional subroutines. The first subroutine is an alternative to the original F-COBRA-TF pressure matrix solver and the second subroutine is a bridge to the SPARSKIT2 library. The first subroutine, the alternative, consists of the following steps: 1) changing the pressure matrix format to Compressed Sparse Format (CSR) as required by the library; 2) calling the preconditioner; 3) calling the Krylov solver (via the bridge subroutine); and 4) re-assigning the solution. In order to interrupt the original coding as little as possible, the alternative subroutine is called from the original F-COBRA-TF solver and thus replacing the Gauss-Seidel iterations loop. The user can select, as an input option, 41

60 between the direct inversion, the Gauss-Seidel iterative method, and the Krylov solver. From sensitivity studies, preformed among all the solvers and preconditioners available in the SPARSKIT2 library, the combination of Bi-Conjugate Gradient Stabilized (BCGSTAB) method and incomplete LU factorization with dual truncation mechanism (ILUUT) was found to be the best in the computational efficiency achievement. However, links to the rest of the solvers and preconditioners are coded as well and can be activated if desired. To investigate the efficiency of the new pressure solver for the system of pressure equations, a test matrix was established. The test matrix contains six test cases, which differ each from other by the number of computational cells and the simulated conditions (steady state or transient). The following is a short description of the cases. 42

61 IN Solution of momentum equations Linearization of mass, energy equations Block Newton- Raphson method Solution of the pressure matrix Outer iteration Y Direct? Gaussian elimination N Perform one iteration step in Gauss-Seidel Inner iteration Time step halved δp converged? N Y Unfolding of independent and dependent variables N Time step control Y Proceed to next time step Figure 1: COBRA-TF numerical solution flow-chart 43

62 Original F-COBRA-TF solver Gaussian elimination Y Direct Solution? Krylov? Link to the SPARSKIT2 library alternative solver Perform one iteration step in Gauss-Seidel SPARSKIT2 via bridge subroutine δp converged? Figure 2: F-COBRA-TF/SPARSKIT2 coupling scheme ATRIUM10 test case models the ATRIUM TM 10 XM/STS 94.1 bundle (AREVA NP GmbH trademark) on a refined cell-by-cell level. The bundle is divided radially in 117 subchannels and axially in 80 nodes, which results in total 9360 computational cells, or matrix to be solved. Since the water channel and part length rods are also modeled, the cross-sectional area of a given cell could vary. The simulations are performed at steady state conditions reached after four seconds real time simulations. PWR MSLB test case simulates a Mean Steam Line Break transient in a PWR core. This is a full core model on a course FA-by-FA level, or each fuel assembly is represented by one thermohydraulic subchannel. The model includes 157 fuel assemblies (subchannels), each divided into 40 axial nodes that result in total 6280 computational cells, or matrix to be solved. The 44

63 simulation includes the first fifty seconds after the scram event. This period of the MSLB transient is characterized with slow power increase (return-to-power), almost constant core mass flow rate, and significant system pressure reduction. TMI FA test case is a model of Three Mile Inland I fuel assembly on cell-by-cell level. The fuel assembly is divided radially in 268 subchannels and axially in 24 nodes, which results in total 6144 computational cells, or matrix to be solved. This is a steady state simulation for five seconds. Cell-by-cell test case represents a PWR core ( FA) in a 1/8 th symmetry. The hottest fuel assembly, located in the core center, is modeled on a cell-by-cell level, while the rest of the core is modeled as a subchannel per fuel assembly. The model consists of 56 subchannels each divided axially in 50 nodes, or in total of 2800 computational cells. A flow reduction transient was simulated. The core inlet mass flow rate was reduced up to 50 % of its nominal level in fifteen seconds, accomplished by a total core power decrease. For reasons discussed later, this test case was repeated at steady state conditions. FA-by-FA test case represents a PWR core ( FA) in a 1/8 th symmetry; 26 subchannels on FA-by-FA level (one subchannel per fuel assembly). Each subchannel is divided axially in 50 nodes, or in total 1300 computational cells. Steady state condition is simulated for five seconds. For reasons discussed later, this test case was also repeated for simulation of the flow reduction transient as defined in the Cell-by-cell test case. PELCO-S 4x4 test case models 4x4 rod bundle at BWR conditions. The model includes 25 subchannels, each in 36 axial nodes, or in total 900 computational cells. This is a steady state simulation for ten seconds. 45

64 All cases were calculated using as a pressure matrix solver Gaussian elimination (direct inversion), Gauss-Seidel iterative method, and Bi-Conjugate Gradient Stabilized method with incomplete LU factorization with dual truncation mechanism. The results show that when applying direct inversion for the larger cases, the outer iteration process takes between 85% (ATRIUM TM 10) to 94 % (TMI-FA) of the total CPU time. The time spent for the pressure matrix solution (inner iteration) is between 67 % (ATRIUM TM 10) to 89 % (TMI-FA) of the total CPU time. For the smaller cases, the inner iteration time decreases with the reduction of the pressure matrix size. For the PELCO-S test case, which is the smallest case, only 8% of the total time is due to the solution of the pressure equations system. The inner iteration time (as a percentage of the total CPU time) sharply decreases, when the Gauss-Seidel iterative technique is used: to 8 % for ATRIUM TM 10 case and 7 % for both TMI-FA and PWR MSLB cases. For the smaller cases this percentage varies between 2 and 4. However, this significant speed-up is observed only when stationary conditions or transients not involving mass flow rate variation (like MSLB) are simulated. For flow transients, as the cell-by-cell flow reduction test case, the Gauss-Seidel solver converges slowly, leading to tremendous increase of the CPU time. Actually, the cell-by-cell test case has an embedded mesh structure (detailed micro-cell region connected to lumped subchannels). Thus, to confirm that the lack of convergence is not due to the mesh structure but due to the hydraulic boundary conditions, the following sensitivity studies were performed. First, the cell-by-cell case was repeated at steady state conditions. The results show about 25 times speed-up in the pressure matrix solution, which results in twice reduced total CPU time comparing to the cell-by-cell flow reduction transient case. Second, the FA-by-FA test case was repeated at the same flow transient conditions. The same tendency was found but at lower magnitude probably due to the smaller matrix size of this test case. This unstable behavior at flow 46

65 rate varying conditions is clearly observed in all cases for the so-called null transient time (the first 2 seconds), which is typical for the F-COBRA-TF simulations. Like the Gauss-Seidel technique, fo r the larger cases the BCGSTAB solver greatly reduces the inner iteration time (as a percentage of the total CPU time) - between 8 % for TMI-FA case and 12 % for ATRIUM TM 10 case. For the smaller cases this percentage varies between 4 and 8. In regard to the total CPU time, BCGSTAB solver sometimes performs better than Gauss-Seidel method (PWR MSLB; cell-by-cell; FA-by-FA cases), sometimes not (ATRIUM 10; TMI-FA; PELCO-S cases). Howev er, comparing to the Gaussian elimination, BCGSTAB solver achieves 2.5 times reduction of the total CPU time for AT RIUM TM 10 case. The speed-up is even higher for the PWR MSLB case 4.5 times and for the TMI-FA case 7.5 times. Other major advantage of the BCGSTAB method is its stable convergence at transient conditions. Another important issue that must be conside red is the accuracy of an iterative solver. The CoreView3D visualization tool was used to investigate the accuracy of both Gauss-Seidel and BCGSTAB solvers. The calculated thermal-hydraulic quantities were compared to predictions obtained with the Gaussian elimination method. It was found that Krylov solver shows better accuracy comparing to the Gauss-Seidel iterative technique for all investigated test cases. In summary, the new iterative solver conver ges smoothly with excellent accuracy regardless of the simulated conditions (stationary and non-statio nary) and the mesh structure. For small cases, with pressure matrix si ze less than ( ), the Gaussian elimination method is recommended for bo th steady state and transient simulations. For larger matrices, BCGSTAB solver is recommended be cause of its competitive efficiency and better accuracy comparing to the Gauss- Seidel technique. Results are summarized in Table 2. TM 47

66 Table 2: F-COBRA-TF efficiency with different pressure matrix solvers Atrium TM 10 bundle, steady state: 9360 cells; t end = 4 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB PWR core, MSLB: 6280 cells; t end = 50 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB TMI FA, steady state: 6144 cells; t end = 5 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB Cell-by-Cell, flow reduction: 2800 cells; t end = 15 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB Cell-by-Cell, steady-state: 2800 cells; t end = 15 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB FA-by-FA, steady state: 1300 cells; t end = 5 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB FA-by-FA, flow reduction: 1300 cells; t end = 15 s Solver Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB PELCO-S 4x4: 900 cells; t Solver end = 10 s Inner iteration Outer iteration Time per Total number of Total real time, time, s time, s time step, s time steps s Direct Inversion Gauss-Seidel BCGSTAB

67 3.3.3 F-COBRA-TF Models Improvements Turbulent Mixing and Void Drift One of the most important phenomenon that must be accounted for in subchannel analyses is the crossflow between adjacent subchannels, which leads to the transfer of mass, energy and momentum. A proper crossflow modeling results in a correct prediction of the velocity, mass, and heat distribution and subsequently to the correct safety margins evaluation. Moreover, the crossflow effect is greatly influenced by the presence of obstructions inside the subchannel and thus it is directly related to the code spacer grid modeling. The COBRA-TF turbulent mixing model has been modified in-between the COBRA/TRAC version and the FLECHT SEASET code version. In the later, the single-phase turbulent mixing has been modeled by means of the traditional inter-subchannel mixing coefficient approach and a simple formulation of void drift phenomenon, typical for two-phase flow conditions, based on the work of Lahey (Lahey, R. T. and Moody, F. J., 1993) and Kelly (Kelly, J. E. and Kazimi, M. S., 1980) has been employed. In 1980s, both approaches were representing the state-of-the-art in turbulent mixing and void drift modeling. Nowadays, they are still used in the most of the subchannel codes. However, the way they have been implemented into COBRA-TF led to a distortion of the mass balance and numerical instabilities, especially at pre- and post-chf conditions. Thus, to preserve the mass balance and to improve and enhance code capability of simulation of both single and two-phase turbulent mixing and net transverse mass, energy, and momentum exchange between adjacent subchannels, the code turbulent mixing and void drift models were revised and re-implemented. In addition, the Beus model for an enhanced two-phase turbulent mixing (Beus, S.G., (1970) was implemented (Avramova, M. N., 2003b). A detailed description of the current F-COBRA-TF turbulent mixing and void drift models is given in Section 5.2, where the grid structures effect on both phenomena is discussed as well. 49

68 3.3.4 F-COBRA-TF Validation and Verification Program As a part of the F-COBRA-TF assessment for LWR analyses, an extensive validation and verification program was established. The program consists of validation against phenomenological tests (void distribution and critical power/heat flux experiments) and verification to standard (LWR nominal operation and anticipated transients) and challenging (LWR core conditions characterized by reverse flow at low inlet mass flux and strong transverse flow due to mid-span mixing grids) core applications F-COBRA-TF Validation Progra m In the framework of the F-COBRA-TF validation program PSU was involved in the F-COBRA- TF simulations of two void distribution experiments General Electric Nine-Rod Bundle Experiment (Lahey, R. T. et al., 1970 and Janssen, E., 1971) and Joint Research Center ISPRA PELCO-S Sixteen-Rod Bundle Experiment (Herkenrath, H. et al., 1979). For both experiments automatic procedures for input decks generation, tests point calculations, and results reporting were created. The work was summarized by Glueck (Glueck, M., 2005a) F-COBRA-TF Verification Program for PWR An alyses An extensive verification program for PWR stand-alone applications was defined and successfully completed (Avramova, M. N., 2006). The related activities consist of two parts: codeto-code comparative analyses and F-COBRA-TF core wide and hot subchannel predictions for steady-state and anticipated transient conditions. In the first part, a PWR core wide and hot channel analysis problem was modeled using F- COBRA-TF and compared with COBRA 3-CP code, which is used at AREVA NP GmbH as a 50

69 thermal-hydraulic subchannel analysis and core design code for PWRs. In the second part of the code validation program, F-COBRA-TF stand-alone simulations of the PWR core were performed. Two COBRA-TF PWR core models were utilized for comparisons of core-wide to hot subchannel analyses. The simulations were performed for both steady state and transient conditions. The analyzed transients were flow reduction (pump coast-down), power rise (bank withdrawal at power), and pressure reduction (anticipated activation of pressurizer spray). The code capability of predicting reverse flow situations was assessed in the performed simulation of main steam line break accident. 3.4 Concluding Remarks Due to its comprehensive modeling features, the thermal-hydraulic subchannel code COBRA- TF is widely used for LWR safety margins evaluations and design analyses. Under the name F-COBRA-TF and in the framework of a joint research project between PSU and AREVA NP GmbH the code has undergone through an extensive validation/verification and qualification program. To make the F-COBRA-TF code applicable for industrial applications, the code programming, numerics, and basic models were improved. The current version of F-COBRA-TF is considered to be a good base for implementation of new modeling capabilities. 51

70 CHAPTER 4 F-COBRA TF SPACER GR - ID MODEL The spacer grid model of F-COBRA-TF is based on the spacer grid model of the COBRA-TF FLECHT SEASET code version (Paik, C. Y. et al., 1985). D uring the FLECHT SEASET validation program, the COBRA/TRAC code (Thurgood, M.J. et al., 1983) was modified to enhance the code predictable capabilities for reflood transients. The models for inter-subchannel thermal radiation, spacer grid effects, and flow blockage heat transfer were added and validated. 4.1 COBRA/TRAC Spacer Grid Model Pressure Losses on Spacers In the COBRA/TRAC code version (Thurgood, M.J. et al., 1983), the local pressure losses in vertical flow due to spacer grids, orifice plates, and other local obstructions are modeled as velocity head losses: 2 U P = ζ ρ, (4.1) 2g c where ζ denotes the pressure loss coefficient, ρ is the density, U is the vertical flow velocity, and g c is the gravitational conversion constant. The loss coefficients along with the locations of the local losses due to spacers are user-specified values. The loss coefficients have to be defined a ssuming positive upflow in the subchannel and to be specified for the momentum (not continuity) cell that contains the spacer. 52

71 As it was discussed in Section 3.1 the code semi-implicit momentum equations have the form (in a matrix form it corresponds to Eq. (3.10): & liq = a1 + b1 P + c1m& liq + d 1 m m& vap - continuous liquid flow rate; & vap a b P c m& liq d m& vap + e2 m = m& - vapor flow rate; ent & entr a b P d m& vap + e3 m = m& - entrained liquid flow rate. ent In the above equations, the pressure losses due to local obstructions are accounted for by the coefficient for the liquid phase and the coefficient d for the vapor phase: c1 2 c 1 axial t f liq vap x = f x wall α liq ρliq axial liq x, (4.2) where axial liq vap f is the vertical interfacial drag coefficient between the vapor and the continuous liquid and axial wall liq f is the vertical liquid-wall drag coefficient: d 2 = t ( f x axial liq vap x f α vap ρ axial ent vap vap x) f axial wall vap x, (4.3) where f axial ent vap is the vertical interfacial drag coefficient between the vapor and the entrained liquid and f axial wall vap is the vertical vapor-wall drag coefficient. The vertical liquid-wall drag coefficient ( f axial wall liq ) and the vertical vapor-wall drag coefficient ( f axial wall vap ) are defined as a sum of the form pressure losses (due to spacer grids, orifice plates, etc.) and the rod frictional pressure losses: 53

72 axial i j f ( ζ (, ) i) U liq ( i, j) ζ wall liq = + rod _ friction, liq ( 4.4) 14 x ζ form, liq and f axial wall vap ζ ( i, j) ( i) = U vap ( i, j) + ζ rod _ friction, vap (4.5) 14 x ζ form, vap In Equations (4.4) and (4.5), U liq ( i, j) and ( i, j) are, respectively, the vertical liquid velocity U vap and vertical vapor velocity in the computationa l cell ( i, j) ; ζ ( i, j) is the spacer grid pressure loss coefficient as specified by the user; indices i and j stand for the subchannel and axial node numbers De-Entrainment on Spacers The COBRA/TRAC code employs a simple model for de-entrainment on the spacer grids. The model assumes that any droplets that are in the path of the spacer grid im pinge on its surface and de-entrain. Thus, the de-entrainment rate is given as m& = 0.15 α ρ U A, (4.6) DE ent liq entr where α ent is the entrained liquid volume fraction; ρ it the liquid density; is the vertical liq U ent velocity of the entrained liquid field; and A is the spacer area seen by the droplets. Once a liquid film is established on the grid, it is assumed that the same amount of liquid is reentrained: m & = m& E DE 54

73 4.2 COBRA-TF_FLECHT SEASET Spacer Grid Model Section 4.1 described the spacer grid modeling in the COBRA/TRAC code version. Later, during the code assessment against the FLECHT SEASET experiments, several modification have been introduced (Paik, C. Y. et al., 1985) including a grid heat transfer model for convective enhancement downstream of the spacers, a model for the grid rewet during bottom reflood phase of LOCA, and a model for the droplet breakup on spacers. A capability of internal code evaluation of the spacer loss coefficients based on the spacer geometry has been implemented as well Evaluation of the Spacer Loss Coefficients In this code version, rather than using input-specified values for the spacer loss coefficients, they are calculated from the grid dimensions as follows: spacer spings ( A A ) 2 ζ = min(20, 196 Re (4.7) grid f loss ) f mix loss blocked + spacer where is the pressure loss coefficient multiplier (input parameter); is the fraction of blocked channel flow area blocked by the grid (input parameter); A blocked spings A blocked is the fraction of channel flow area blocked by the grid springs (input parameter); number. Re mix is the droplets-bubbles mixture Reynolds The Reynolds number of the droplets-bubbles mixture is calculated as G D mass h Re mix = ; (4.8) µ mix where the total mass flux G mass is given as 55

74 G mass = G = A + A + A liq mom mom mom + G vap m& ( i, j) m& ( i, j) m& ( i, j) + G = ( i, j) α ( i, j) liq liq ( α ( i, j) + α ( i, j + 1) ) liq ( i, j) α vap vap ( α ( i, j) + α ( i, j + 1) ) ent vap entr ( i, j) α 2 ( i, j) 2 ( i, j) ( α ( i, j) + α ( i, j + 1) ) ent ent 2 liq vap ent (4.9) If the phase k has a negative velocity then G k = A mom m& k ( i, j) α k ( i, j + 1). ( i, j) 0.5 α ( i, j) + α ( i, j + 1) ( k k ) The dynamic viscosity of the droplets-bubbles mixture is given as the minimum of the droplets dynamic viscosity and the bubbles dynamic viscosity: where ( µ ) µ, mix min droplets µ bubbles µ bubbles =, (4.10) ( α ( i, j) + α ( i, j 1) ) 2.5( µ vap µ ) liq µ + vap µ liq vap vap + = µ liq 1 (4.11) 2 µ droplets = µ vap ( α ( i, j) + α ( i, j 1) ) 2.5( µ vap µ ) liq µ + vap µ liq vap vap + 1 (4.12) 2 If the Reynolds number of the droplets-bubbles mixture is spacer spings ( A A ) ) f mix loss blocked + 4 greater than 10 then ζ = max(6.5, 41Re (4.13) grid blocked The pressure loss coefficients due to other local blockages (obstructions) are calculated in a 56

75 similar manner: ( 20, 196 Re ) f ( A ) 2 ζ = min if blockage mix blockage blockage Re 4 mix 1 10 (4.14) and 0.16 ( 6.5, 41 Re ) f ( A ) 2 4 ζ = max if Re > 1 10 (4.15) blockage mix blockage blockage mix where f blockage is the pressure loss coefficient multiplier for blockages (input parameter); A blockage is the blockage area ratio (input parameter); and Equations (4.8) through (4.12) are used to calculate the Reynolds number and the dynamic viscosity of the droplets-bubbles mixture. In comparison to the COBRA/TRAC version (Equations (4.4) and (4.6)), the vertical liquidaxial wall drag coefficient ( f ) and the vertical vapor-wall drag coefficient ( f ), are modified wall liq axial wall vap 1 as follows : f axial wall liq ( ζ ( ig) + ζ ( ib) ) grid blockage ( i) = 0.5 U liq ( i, j) + ζ x ζ form, liq rod _ friction, liq (4.16) and ( ζ ( ig) + ζ ( ib) ) axial grid blockage f wall vap ( i) = 0.5 U vap ( i, j) + ζ rod _ friction, vap (4.17) x ζ form, vap In Equations (4.16) and (4.17), the term ζ (ig) is the grid loss coefficient as calculated by the grid code using the grid geometry input data for the grid index (ig) ; and ζ (ib) is the loss coefficient due to blockage (ib) as specified by the user. blockage 1 The COBRA/TRAC model is available in the code as an input option and the user can choose between COBRA/TRAC and COBRA-TF_FLECHT SEASET modeling of the spacer grid pressure losses. 57

76 4.2.2 Single-Phase Vapor Convective Enhancement The single-phase vapor heat transfer augmentation downstream of spacers for Reynolds number higher than 10 4 has been modeled by a correlation for the local Nusselt numbers (Yao, S. C. et al., 1982): Nu Nu x ( x / D) = ε e, (4.18) where Nu x is the local Nusselt number with presence of spacers; Nu 0 is the local Nusselt number without spacers; ε is the blockage ratio of spacers to flow channel; D is the flow channel hydraulic diameter; and x is the axial distance from the downstream end of the spacer. The correlation has been developed for egg-crate grids and blockage ratios between and The implementation has been validated against FLEACH SEASET 21-bundle tests with steam cooling (Loftus, M. J. et al., 1982) Grid Rewet Model During the dispersed flow stage of a bottom reflood the spacer grids are responsible for significant cooling of the vapor passing through them. To account for that effect, a grid rewet model has been implemented into COBRA-TF. The spacers have no internal heat generation and do not store significant amount of energy. Thus, when droplets impinge on the spacer grid, they will cool it down and form a liquid film on its surface. To determine the fraction of grid that is covered by such a liquid film, a two-region grid quench model has been implemented. The regions are separated by the quench front location. As shown in Figure 3, upstream of the grid quench front both, grid and liquid film are at saturation temperature. In the dry region, the grid temperature is close to the rod surface temperature. 58

77 During the reflood transient, the dry grid temperature is between the vapor temperature and heater rods temperature. The transient temperature response of the dry region is determined by a heat balance between radiation, convection and droplet contact heat transfer: dry '' '' '' T grid ( Pgrid Ac ) ( qrad qconv qdcht ) =, t ρ C p (4.19) dry where T is the dry grid temperature; P is the perimeter of the grid strap; Ac is a half of the grid grid grid cross-sectional area, A c δ Pg '' = ; δ is the grid half thickness; q rad is the radiation heat flux 2 from rods and vapor; '' q conv is the convective heat flux; and '' q dcht is the heat flux due to droplet contact. droplet flow liquid film T, deg quench front T DRY T SAT Figure 3: Two-region grid quench and rewet model x The radiation heat flux from the rods and vapor to the grid is calculated utilizing the radiation heat flux network shown in Figure 4: q '' rad _ dry 4 Bgrid σ Tgrig = (4.20) (1 ε ) ε grid grid 59

78 The black body radiosity of the grid spacer, B grid, is calculated as 4 Brod σ Trod 4 B grid = + ( Brod σ Tvap ) ε vap + (1 rod ) ε ε ε rod 1 ( 1 vap ) Brod (4.21) and the black body radiosity of the rod, B rod, is calculated as B rod C = 4 4 rodσ Trod + C gridσ Tgrid + C 4 C vap σ T 4 vap (4.22) VAPOR 4 σ T vap ROD 4 σ T rod B rod B grid GRID 4 σ T grid Figure 4: Radiation heat flux network In Equations (4.21) and (4.22) T is the rod surface temperature, [ºR]; T is the grid rod grid temperature in the dry region, [ºR]; T vap is the vapor temperature, [ºR]; σ is the Stefan-Boltzman constant, σ = [Btu/hr-ft 2 -ºR]; rod ε is the rod emissivity ( ε rod = 0. 9 ); ε grid is the grid emissivity ( ε grid = 0. 9 ); and ε vap is the vapor emissivity. The vapor emissivity is calculated as ε vap P L M vap = 1. 0 e A (4.23) 60

79 where A is the mean absorption coefficient for w ater vapor, [psi-ft] -1 ; P is the pressure, [psi]; and vap L is the mean beam length, [ft]: L = 0.9 channel hydraulic diameter. M M In Equation (4.23) the mean absorption coefficient for water vapor is given by vap vap A = 2.146e, where is the vapor temperature, [ºK]. vap 3 6 [ ( T ) T ] T vap The coefficients C C, and C are defined as follows rod, grid, Cvap 4 ( 1 ε rod ) C rod = A ε rod 1 ε vap C grid (1 ε = ε rod rod ) 1 (1 ε vap 1 ) ε vap 2 1 ε rod ε grid 1 C vap = + A ε rod ε vap (1 ε vap ) ε grid (1 ε vap ) C 4 (1 ε = ε rod rod ) 1 ε vap 1 (1 ε vap (1 ε ) ε rod rod ) (1 ε + ε grid grid ) 1 + (1 ε vap 1 A ) ε vap (1 ε + A ε rod rod ) where 1 1 (1 ε grid ) = + 1 A (1 ε ) ε ε vap vap grid ε vap 1 + (1 ε vap. ) The convection from the dry region of the grid spacer to the vapor is calculated using the heat transfer coefficient for convection from the rod to the vapor: q '' conv = h ( T dry grid T vap ) (4.24) where '' q conv is the heat transfer from the dry grid region, [Btu/hr-ft 2 ]; h is the heat transfer 61

80 coefficient from rod to vapor, [Btu/hr-ft 2 -ºF]; T is the temperature of the dry region, [ºF]; is the vapor temperature, [ºF]. dry grid The droplet contact heat transfer results from the deposition of droplets on the dry grid surface caused by the lateral turbulence migration of droplets: T vap q '' dcht = m& DE h fg η, (4.25) where sat m& is the lateral deposition rate; η is the fraction of droplets evaporated η = e. DE [1 ( T dry grid / T 2 ) ] The lateral deposition rate is calculated as m & k C ( 4.26) DE = D where the deposition coefficient k D is calculated as k D 1/ 2 1/ 2 µ vap f Gvap = ( 4.27) Dhσρliq 2 ρvap In Equation (4.27) G is the vapor mass flux; Re vap 0.25 f = is the friction factor; C is the droplet concentration, C = ρ G D ; and G D is the droplet mass flux. vap Gvap The wet region heat balance is calculated in a similar way. The grid quenching is promoted by the impinging droplets. That will increase the liquid film on the grid surface. All the droplets flowing within the projected area of the grid are assumed to be captured: A grid & DE = m& E, (4.28) Aflow m where m& DE is the liquid deposition rate; m& is the entrained liquid flow rate; A is the grid E grid 62

81 projected area; and Aflow is the channel flow area. The radiatio n heat flux from the rod to the wet grid region is calculated by using saturation temperate and assuming that the liquid emissivity is equivalent to the spacer grid emissivity: q '' rad _ wet B grid _ wet sat =, (4.29) grid σ T 4 (1 ε ) ε grid where B _ is the black body radiosity of the wet grid region: grid wet B grid _ wet B = (1 ε rod grid _ wet rod σ T ) ε rod 4 sat B + rod grid _ wet ε vap σ T 4 vap 1 (1 ε vap + ) B rod grid _ wet (4.30) B rod grid _ wet is the black body radiosity of the rod for the wet grid region: B rod grid _ wet 4 4 Crodσ Tsat + Cgridσ Tgrid + = C 4 C vap σ T 4 vap. (4.31) The interfacial heat transfer between the vapor and the liquid film is given as: q '' vap film = h conv ( T vap T sat ), (4.32) where the heat transfer coefficient is calculated using the fluid properties at the top of the continuity cell (center of the momentum cell). However, if the droplet deposition rate is less than the evaporation rate (due to the radiation and interfacial heat transfer) the grid quench front will not advance: m & > & DE m EVAP, where 63

82 m& EVAP is the liquid evaporation rate: '' '' (q rad _ wet + qvap film ) Pgrid f qlgrid m& EVAP = ; h fg f q is the fraction of grid quenched; Lgrid and Pgrid are, respectively, the grid length and the grid perimeter. Advancement rate is limited by the quench front velocity and the availability of water. The Yamanouchi model (Yamanouchi, A., 1968) for quenching thin plate by a liquid film is utilized in the code. Quench velocity V Q can be expressed as follows: V Q ρ = grid 1/ 2 2 1/ 2 dry C p _ grid δ Tgrid Twet hwetk grid Twet Tsat 1 ; (4.33) where ρ is the density of the grid material; is the specific heat of the grid material; is grid C p _ grid k grid dry the thermal conductivity of the grid material; Tgrid is the dry grid temperature; wet is the wet region h heat transfer coefficient; T is the rewet temperature; and δ is the grid half thickness. wet The heat flux has its maximum at the quench front location. It is physically reasonable to assume that q q '' max '' CHF. Thus, the wet region heat transfer coefficient is equal to '' '' qmax q h wet = = CHF. (4.34) T T T T wet sat wet sat The Zuber pool boiling critical heat flux correlation is used to determine q '' CHF. The rewet temperature 1968). T wet is set to 260 ºC (500 ºF) as recommended by Yamanouchi (Yamanouchi, A., 64

83 The quench front velocity is also constrained by the water remaining after evaporation by radiation and interfacial heat transfer. The flow rate of remaining water is given as m& R = m& DE m& EVAP A = A grid flow m& E '' ( qrad _ wet + q '' vap film h fg ) P grid f q L grid. (4.35) In reality, only a fraction of the remaining water can be evaporated, since some water will be blow off the grid by sputtering. Thus, the water fraction available for evaporation at the quench front is 2 dry T grid 1 T sat m & = m& e. (4.36) QF R Using the stored energy balance and having in mind that the stored energy removed at the quench front cannot exceed the product of water fraction available for evaporation, m& latent heat h, fg, the following expression is obtained QF, and the m& QF h fg dry ( ρ C p A) grid VQ ( Tgrid Tsat ). (4.37) The quench velocity is estimated as V Q m& QF h fg, (4.38) dry ( ρ C p A) grid ( Tgrid Tsat ) and the wet region heat transfer coefficient is limited by h wet 2 dry 2 δ m& QFh fg Tgrid Twet 2 1 dry ) dry T 4kgrid Pgrid δ ( Tgrid sat Tgrid Tsat. (4.39) Quench front regression occurs when the film evaporation rate exceeds the liquid deposition rate. At this point th e grid will begin to dryout. The grid dryout velocity is defined as 65

84 V dryout ( m& DE m& EVAP ) h fg = dry ( ρ C A) ( T T p grid grid sat. (4.40) ) Droplet Breakup Model The COBRA-TF droplet breakup model accounts for the breakup that can occur when droplet impinges on a spacer (Figure 5). The grid strap is relatively thinner compared to the droplet diameter. This results in a slicing of the impinging droplet in one or two large droplets and several microdroplets. These microdroplets are preferentially evaporated downstream of the grid leading to an enhanced heat transfer (vapor superheat is reduced). The shattered fraction of the incident droplet is treated by a separate small drop field. The increase of interfacial area due to the large droplet fragment is assumed negligible. The new field is characterized by the fraction of the incident droplet that is shattered into microdroplets and the initial diameter of the new distribution. grid strip microdroplets Figure 5: Droplet breakup The mass flow rate of the microdroplets is a function of the entrainment liquid flow rate and the grid blockage area: 66

85 m & DB A grid = η E m& E, (4.41) A flow where ηe is the grid efficiency factor, equal to the portion of droplet within the grid projected area that is shattered into a populat ion of microdroplets. A suggested value is η = The microdroplets are incide nt upon the next grid spacer. They are assumed to breakup with the same grid efficiency. Then, the mass flow rate of the new microdroplets becomes E A grid m & DB =η E ( m& E + m& SD ), (4.42) A flow where m& is the mass flow rate of small droplets immediately upstream of the grid. SD The ratio of shattered to incident droplet diameters is determined as D SD We 0 53 D =. (4. D I 43) and the Weber number is given by ρliqv 2 DI DI We D =, (4.44) σ where V DI is the impacting droplets velocity normal to the surface and D I is the diameter of impacting droplets. At low Weber number of the impact droplet, the shattered droplet diameter is predicted in the same order as the incident droplet diameter. Then, rather than considering these large shattered droplets in the small droplet field, they are shifted to the entrained liquid field. To accomplish this, the interfacial area created by droplet breakup, when We 150 D, is added as a source term to the interfacial area conservation equation. 67

86 For Weber number of the impact droplet greater than 250, the shattered drops are added to the small drop field in the normal manner. At intermediate values, a linear ramp as a function of We D is used for transition between the two different treatments. Thus, the mass source term for small drop field is given by m & SD = ξ m& and the mass source associated with large drop interfacial area SD source term is given by m & = ( 1 ξ ) m&, SD SD where We 150 ξ = (4.45) The mass source and the initial droplet diameter are calculated at every grid location. Droplets in the small drop field are present just upstream of the grid, in addition to the entrained liquid field. These droplets can be also broken and the two droplet populations are merged, preserving the droplet mass, interfacial area, and momentum. 4.3 Improvements of the COBRA-TF Spacer Grid Model Performed at PSU The COBRA-TF spacer grid models have been modified at PSU to improve the entrainment and deposition modeling of liquid film with applications to BWR fuel rod dryout (Ratnayake, R. K., 2003) and spacer effects on the droplets-vapor cooling typical for the dispersed flow film boiling (DFFB) regime during blowdown and reflood phases of PWR loss of coolant accidents (Ergun, S., 2005b) Modeling of the Spacer Effects on Entrainment and Deposition The PhD thesis of Ratnayake (Ratnayake, R. K., 2003) aimed to develop and implement into COBRA-TF a mechanistic spacer grid model capable of accurate evaluation of entrainment and deentrainment caused by spacer grids in BWR bundles, and thus to improve the code predictions of 68

87 the dryout phenomenon. It was discussed in Section that COBRA-TF employs a simple model for de-entrainment on the grid spacers and this is the only such related spacer grid model. The code does not feature any models for the spacer-caused entrainment or downstream deposition effects. Moreover, COBRA-TF critical power analyses (Frepoli, C. et al., 2001a) have indicated that in order to match the expe rimental data the code film entrainment rate has to be significantly increased. In other words, the current code model miss-predicts the critical power. The Ratnayake s objectives were to develop new model that satisfies the following criteria: The model should be able to calculate the individual effects of entrainment and deposition exclusively for a given spacer grid geometry; The deposition model should capture the turbulent enhancement effect of spacer grids; The model should be able to explain the qualitative behavior of entrainment at spacer grids and the downstream deposition behavior; The overall model should be able to capture the geometrical variations between different grid designs, but should not be design-dependent. Regarding entrainment phenomenon two sub-models have been developed - acceleration entrainment model and geometrical entrainment model. While the first calculates the entrainment due to vapor flow acceleration at the spacer grid location, the second calculated the amount of liquid removal from the film by mechanical interventions of the spacer grids. Both entrainment models have been developed using mechanistic approaches. In the acceleration entrainment model, to estimate the increased film entrainment in the grid 69

88 section, the normal film entrainment calculated for the non-grid section (Thurgood, M. J. et al., 1983) has been modified by recalculating the vector vapor velocity using blockage parameters: k Sτ I U V µ I 1 S u = F 144 σ P W ( grid ) non-grid section blockage, where U V = U V grid (1.0 F ) and grid is the axial grid length., blockage The geometrical entrainment is caused by a mechanism related to the wet/dry patch formation at the grid-rod contact location. Thus, the geometrical entrainment model has been based on the horseshoe vortex theory involving parameters such the bluff body width, the radius of curvature at the sides of the wet patch boundary, the distance between the leading edge of the bluff body, and the straight portion of the wet patch boundary. Both, acceleration and geometrical entrainment models have been incorporated into COBRA- on user-specified input parameters. TF depending The new deposition model has been developed from a fundamental approach of modeling the turbulence generated by spacer grids. The model is a modification of the Yao and Hochreiter correlation for the heat transfer augmentation downstream of spacer grids (Yao, S. C. et al.,1982) by embedding a blockage parameter that adequately represents the grid generation of turbulence. The blockage parameter is routed via a user interface as a two-dimensional parameter indexed for an appropriate subchannel and node numbers. The new spacer grid model has been validated against Siemens 9x9 rod bundle data. The improved code version predicts dryout reasonably well, however, the dryout locations calculated by the new code are at lower elevation comparing to the experimentally determined ones. 70

89 4.3.2 Modeling of the Spacer Effects in Dispersed Flow Film Boiling Regime In her PhD study Modeling of dispersed Flow Film Boiling and Spacer Grid Effects on Heat Transfer with Two-Flow, Five-Filed Eulerian-Eulerian Approach, Ergun has added a small drople t field to the mass conservation equations of COBRA-TF. The effect of the smaller and thus thermally more effective droplets on the heat, mass, and momentum transfer during dispersed film flow boiling has been modeled. However, at DFFB conditions spacer grids play an important role via two effects: first, the breakup of large droplets on spacer grids generates significant source of sma ll droplets and second, the wet spacer grids provide a large interfacial area for heat transfer between the superheated vapor and the liquid film deposed on its surface. As summarized by Ergun, there are several drawbacks in the COBRA-TF spacer grid models for dispersed drop film flow: In the calculation of the interfacial heat transfer area between liquid film on the grid and vapor, the amount of the vapor mass generated at saturation temperature and momentum transferred are not taken into account; The initial grid temperature is estimated as high as the rod temperature; In the grid quench modeling, the amount of liquid mass deposed on the grid surface and the mass loss from deposited liquid due to evaporation and/or entrainment are not taken into account. As a result, comparisons to experimental data (Rosal, E. R. et al., 2003) show that the code overpredicts the grid temperature and thus a higher large drop breakup is estimated because the quenched grid droplet breakup is not simulated. A smaller vapor generation from the liquid film is estimated as well. 71

90 To improve the modeling of the spacer grid effects, logic has been added for solution of mass and momentum equations for the liquid film on the spacer grid. At each time step the following equations are solved: Mass equation: SGM ( SGM ) t n = Γ grid + S DEgrid S Egrid, where Γ grid is the evaporation of the liquid film on the grid; S is the de-entrainment rate on the grid; and S is the entrainment rate from DEgrid the liquid film on the grid. Egrid Momentum equation: SGMom n n n ( SGMom) U grid ρliq Agrid K grid, liq U vapρvap AflowKi = +, t x x n n n ΓgridU grid ( S DEgridU entr S EgridU grid ) + x x vgridl, where U is the grid velocity of the liquid film on the grid; U and U are, respectively, velocities of the vapor vap entr and entrainment fields; K, is the wall grad coefficient between the liquid film and the grid grid liq surface; A grid is the grid projected area; ; A flow is the subchannel flow area; K i, vgridl is the vapor- liquid film interfacial drag coefficient. I n the a bove equations index n stands for the new time step values. The evaporation rate, entrainment, and de-entrainment calculated for the spacer grids are coupled with the code s solution scheme as source or loss terms for the mass, momentum and energy equations as long as the heat transfer regime is a hot wall flow regime. The modified code version shows better agreement with the experimental data; however, Ergun 72

91 has recommended further improvement of the heat transfer package regarding spacer grid effects. In particular, the minimum film boiling temperature for spacers and the heat transfer coefficients used to determine the quench velocity have to be revised as well as the spacer grid rewet model. 4.4 Current F-COBRA-TF 1.03 Spacer Grid Model Features and Drawbacks The theoretical basis of the current F-COBRA-TF spacer grid model is identical to the one presented in Section 4.2. The improvements described in Section 4.3 are not implemented in F- COBRA-TF code. In summary, F-COBRA-TF 1.03 includes models for: Local pressure losses in vertical flow due to spacer grids; De-entrainment on the spacers grid; Single-phase vapor convective enhancement downstream of the spacers grids; Grid rewet under dispersed flow conditions; Droplet breakup model. F-COBRA-TF 1.03 is not equipped with adequate models for Spacers effects on the mass, heat, and momentum exchange mechanisms such as turbulent mixing and void drift; Lateral flow patterns created by specific configurations of the vanes; Swirl flow created by the mixing vanes. Moreover, studies on the currently available models (Avramova, M. N., 2005b) indicated several inconsistencies between the theoretical models as described by Paik (Paik, C. Y. et al., 1985) and the actual coding. 73

92 4.5 Concluding Remarks In order to enable the F-COBRA-TF code for industrial applications including LWR safety margins evaluations and design analyses, the code modeling capabilities related to the spacer grid effects have to be revised and substantially improved. 74

93 CHAPTER 5 MODELING OF SPACER GRID EFFECTS ON THE TURBULENT MIXING IN ROD BUNDLES 5.1 Background One of the most important phenomenon that must be accounted for by the rod bundles thermalhydraulic analyses is the crossflow of mass, energy and momentum between adjacent subchannels. At an equilibrium flow conditions there are no lateral pressure differences between subchannels leading to a crossflow and the flow rates of both liquid and vapor in each subchannel do not vary in the axial direction. At non-equilibrium conditions, flow re-distributions occur along the channel axis and the flow tends to approach equilibrium. The single-phase crossflow can be attributed to two effects - turbulent mixing and diversion crossflow. At single-phase isothermal conditions, turbulent mixing is an inter-subchannel mixing due to turbulence of the fluids, which may cause momentum transfer between the subchannels but no net mass and energy transfer. Diversion crossflow is a crossflow due to lateral pressure gradients, which may be introduced by differences in the subchannel geometry. At two-phase flow conditions one additional effect, void drift, plays a role in the exchange processes. Void drift is a crossflow driven by the two-phase flow tendency to approach an equilibrium condition. The void drift results in a net transfer of liquid and vapor from one subchannel to another. Known also as vapor diffusion, the void drift has been postulated in order to describe experimental observations which could not be explained with the gradientdiffusion concept for the turbulent mixing. The presence of obstructions, such as spacer grids, in the flow channels has a significant effect 75

94 on all the three mechanisms: turbulent mixing, diversion crossflow, and void drift. In addition, specific spacer structures may create a strong net transfer between adjacent subchannels due to velocity deflection on their surfaces. This lateral transfer is known as a directed crossflow. Because of its high importance for the nuclear reactor safety performance and power efficiency, the single- and two-phase mass, energy and momentum exchange has been investigated for decades, however, with a questionable success. A lot of experiments have been performed to study the turbulent mixing in fuel rod bundles and several correlations for the mixing rate have been proposed. Examples are the work by Rowe and Angle (Rowe, D. S. and Angle, C. W., 1967); Rogers and Rosehart (Rogers, J. T. and Rosehart, R. G., 1972); Rogers and Tahir (Rogers, J. T. and Tahir, A. E. E., 1975); Gonzalez-Santalo and Griffith (Gonzalez-Santalo, J. M. and Griffith, P., 1972); Rudzinski et al. (Rudzinski, K. F. et al., 1972): Kuldip and Pierre (Kuldip, S. and Pierre, C. C. St., 1973); Beus (Beus, S. G., 1970); Yadigaroglu and Maganas (Yadigaroglu, G. and Maganas, A., 1994); and Wang and Cao (Wang, J. and Cao, L.). Except the last two, these experiments have been carried out using an air-water mixture as a working fluid. The points of interest were the dependence of the mixing rate on the fluid conditions (mass flux, quality, etc.) and on the geometry (square or triangular array, gap width, etc.). It was found that mixing rates are both flow regime and geometry dependent. Rudzinski et al. (Rudzinski, K. F., et al., 1972) reported that for an increased mass flux there is a decrease in the mixing Stanton number and the quality region over which higher mixing rates are observed. In an agreement with Rowe and Angle (Rowe, D. S. and Angle, C. W., 1967), Beus (Beus, S. G., 1970), and Kuldip and Pierre (Kuldip, S. and Pierre, C. C. St., 1973), the maximum of the mixing rate was found near slug-annular transition. Regarding geometry effects, Kuldip and Pierre (Kuldip, S. and Pierre, C. C. St., 1973) reported an increase in the mixing rate for wider gap 76

95 spacing. However, most of the above listed experimental studies have been performed in a way that the void drift contributed as well to the measured mixing rates. In the last decade, substantial efforts have been made at the Kumamoto University in Japan to separate the effects of turbulent mixing, void drift, and diversion crossflow during the measurement. There is a series of publications describing air-water experiments performed for a variety of subchannels configurations: Sato and Sadatomi (Sato, Y. and Sadatomi, M.); Kano et al. (Kano, K. et al., 2002); Sadatomi et al. (Sadatomi, M. et al., 1994); Shirai and Ninokata (Shirai, H. and Ninokata, H., 2001); Kano et al. (Kano, K. et al., 2003); Sadatomi et al. (Sadatomi, M. et al., 2003); Kawahara et al. (Kawahara, A. et al., 2004); Sadatomi (Sadatomi, M., 2004), etc. Most of these experiments have been utilizing clean rod bundles and the derived correlations do not account for the presence of spacer grids. However, Lahey and Moody (Lahey, R. T. and Moody, F. J., 1993) refer to the Rowe and Angle data (Rowe, D. S. and Angle, C. W., 1969) showing graphs for the mixing parameter dependence on the steam quality at different mass fluxes with and without spacers. It was shown that spacers change not only the amount of the turbulent mixing but also its distribution over the axial length. Lahey et al. ( Lahey et al., 1972) proposed a simple approach for modeling of the eddy diffusivity enchantment downstream of the spacers. Most currently Hotta et al. (Hotta, A. et al., 2004) have discussed a strategy for improving the crossflow models in the subchannel code NASCA including a non-isotropic diffusion coefficient model that includes localized geometrical effects. The following sections will discuss the effect of the spacer grids on the turbulent mixing in rod bundles and the modeling of turbulent mixing in the subchannel analysis codes, particularly in the F-COBRA-TF 1.03 code version. 77

96 5.1.1 Turbulent Mixing Modeling in Subchannel Analysis Codes Overview In the subchannel codes, th e exchange of momentum, energy, and mass due to turbulence, or the so-called turbulent diffusion or turbulent mixing, is commonly modeled in analogy to the molecular diffusion under the assumption of a linear dependence between the exchange rate of the given quantity and its gradient in the medium. The proportionality coefficients are called turbulent diffusion coefficients. Unlike molecular diffusion coefficients, which are material dependent, the turbulent diffusion coefficients depend only on the location in the flow domain. The turbulent kinematical viscosity and turbulent temperature diffusivity are of the same order of magnitude (turbulent Prandtl number approaches unity). This assumption allows applying the same turbulent diffusion coefficient to all momentum, mass, and energy exchanges: C t : = Dt = ν t = at. In case of gradient in y direction, the aforementioned assumption takes the form of: Turbulent mixing of mass: dc d( α k ρ k ) m& k = ρdt A = Ct A (5.1) dy dy Turbulent mixing of momentum: du d U dg I& ( α k ρ k k ) k k = ρν t A = Ct A = Ct A (5.2) dy dy dy Turbulent mixing of energy: dt d c T d h Q & ( α k ρ k p, k k ) ( α k ρ k k ) k = ρc pat A = Ct A = Ct A dy dy dy (5.3) Here the index k stands for the given field (liquid, vapor, and droplets); D is the turbulent t diffusion coefficient for mass transfer; ν t is the turbulent kinematical viscosity; a t is the turbulent 78

97 temperature conductivity; c is th e concentration; c p is the specific heat capacity; A is the area relevant for lateral exchange; α, ρ, U, and h are, respectively, the volume fraction of given field, density, vertical velocity, and enthalpy. C In the subchannel analyses, very often the ratio t dy is substituted with the ratio of the turbulent kinematical viscosity ε and the mixing length l, ε, and the mixing length is commonly l approximated as the centroid distance between the adjacent subchannels. Regarding turbulent diffusion coefficients, a dimensionless parameter can be defined C t β =, (5.4) yu where U AU i i + AjU j = is the area averaged vertical velocity of the adjacent subchannels 1. A + A i j Using the definition of the turbulent mixing coefficient, the exchange rate of mass, momentum and energy (Equations 5.1 through 5.3) can be written as: Turbulent mixing of mass: G m& k = β ( α k ρ k ) A (5.5) ρ Turbulent mixing of momentum: G I& k = β Gk A (5.6) ρ 1 If simple averaging is taken, β is reduced to the mixing Stanton number. 79

98 Turbulent mixing of energy: G Q & k = β ( α k ρ k hk ) A (5.7) ρ where G = A G i tot, i i + A j A + A j G tot, j. As concluded from Equation 5.4, the turbulent mixing coefficient is a function of the particular geometry and the flow conditions. Under single-phase flow conditions, it is usually correlated to the flow Reynolds number, subchannel hydraulic diameter, heated rod diameter, gap width, and the c entroid between the adjacent subchannels: β = f (Re, d, d, d, y). The correlations that SP hyd gap rod are more often used in the subchannel analyses are summarized in Table 3. Simple hand calculations for a case of two adjacent subchannels with equal hydraulic diameters show that these correlations differ strongly from each other (see Table 4). Nowadays, the state-of-the-art is to evaluate β SP utilizing numerical experiments in means of CFD calculations. It is experimentally observed that in a two-phase flow the turbulent mixing is much higher than in a single-phase flow. Most often, the dependence of the mixing rate on the flow regime is modeled by the Beus correlation (Beus, S. G., 1970). The two-phase turbulent velocity is assumed to b e a function of the single-phase turbulent velocity: ε l TP = Θ TP ε l SP, where the two-phase multiplier, Θ TP, depends on the quality. The approach by Faya (Faya, A. J. G., 1979) has been adopted in the subchannel analysis codes. Faya has slightly modified the Beus approach by applying the two-phase multiplier Θ TP to the single-phase mixing coefficient: 80

99 β TP = Θ β, where Θ = f ( x) (5.8) TP SP TP The mixing rate, and hence the turbulent velocity, reaches its maximum at the slug-annular regime transition point. According to the model of Wallis (Wallis, G. B., 1969), this point can be obtained by an expression for the corresponding quality: 0.4 g ρliq ( ρliq ρvap) dhyd Gtot x max = (5.9) ρliq ρ vap The function for ΘTP is assumed to increase linearly for x xmax and to decrease hyperbolically for x > x max (Figure 6). Θ x = if x x max (5.10) x TP 1 + ( Θmax 1) max Θ = 1 + Θ TP ( max 1) xmax x x x 0 0 with x0 57 x max = 0. Re if x > x max (5.11) where G tot d hyd µ mix µ mix = 1 α µ + α µ. Re = and ( vap ) liq vap vap The parameter Θ max, which is the maximum of the ratio β TP / βsp, is treated as a constant and can be estimated experimentally. Table 5 gives examples for suggested values of Θ. max 81

100 1θ TP 1θ max 1 1x 0 1x max 1x Figure 6: Two-phase multiplier Θ TP as a function of quality x according to Beus (1970) Beus (1970) Table 3: Summary of the published correlations for single-phase mixing coefficient Rogers and Rozehart (1972) Rogers and Tahir (1975) R owe and Angle (1967) β SP = Re 0.1 d d hyd gap dgap βsp = Re 2 d rod d β SP = d rod λ gap Re gap hyd β = 0. Re ; SP 0062 d d 0.1 d d hyd gap d 1 + d d hyd hyd, j hyd, i w,1 1.5 d hyd, i d rod 4( A1 + A2 ) = p + p 1/8 d hyd gap S SP Re d adatomi et al. (1996) β = * dgap Fi d rod b β SP = a Re d b hyd β SP = a Re Stewart et al. (1977) d gap b dhyd β SP = a Re y Wang and Cao d hyd 0.1 β Subcooled = Re (at sub-cooled boiling) d gap 2 α D 1 S Kim and Chung (2001) 12 β / 2 2 α z h ij Dh fr β / 2 St = Re + a Str Re 2 8 Pr δ 2 x γ S b γ 8 S d ij t ij 0.52 w,2 12 Referenced in Jeong, et. al., (2004) 82

101 Table 4: Single-phase mixing coefficient as calculated with different correlations Two adjacent subchannels with equal hydraulic diameters β = 1 β SP, RoweAngle. 77 SP, Beus βsp, RogersRosehart 66 d = β SP, RogersTahir = 0.46 rod 1. β SP, Beus dgap d gap 1.43 βsp, Beus drod GE 3 3 rod bundle Janssen (1971) SP, RogersRosehart β S P, Beus SP, RogersTahir βsp, Beus β = β = Table 5: Suggested values for the Θ max Bellil et al. (1999) air-water measurements 5 Θmax 10 Faya (1979) - by numerical studies Θ max = 5 Gonzalez-Santalo and Griffith (1972) 13 Θ max = 50 air-water measurements Kelly (1971) ) - by numerical studies 5 Θ max 10 Sagawara et al. (1991) 14 air-water measurements depending on the liquid mass flux jliq Θ 37 1 max = + 13, where j liq is the 1.0 m/s superficial velocity of liquid Sato (1992) air-water measurements Θ max = 5 2 A brief summary of the turbulent mixing modeling in the known subchannel analysis codes is 13 In stead of a sharp peak, a steep increase within the bubbly flow regime to the maximum value within the whole slug flow regime, was observed. Θ max, which lasts 14 Sagawara et al. assumed that the two-phase multiplier reaches its maximum at the transition from bubbly to slug flow. Comparing to Beus, 1970: Θ TP max, Sugawara xmax, Beus x =. 83

102 given below 15. It will be seen that, excluding NASCA code, the subchannel analysis codes do not model the spac er grids effect on the amount of turbulent mixing between adjacent subchannels Turbulent Mixing Model of THERMIT-2 THERMIT-2 is a two-fluid two-phase subchannel code developed at the Massachusetts Institute of Technology (Kelly, J. et al., 1981). The lateral exchanges of mass, energy, and momentum due to turbulent mixing are given respectively as W = ( W '' s dx ; Q = ( q'' s dx ; and k k ) ij ij k k ) ij ij F k the = (τ k ) ij sij dx. In these equations, s ij is the gap length between subchannels i and j; the dx is axial mesh node size; W '' k is the phase k mass flux due to turbulent mixing; q '' k is phase k heat fluxes due to turbulent mixing; τ is the phase k shear stress due to turbulent mixing. k ( ) G G j The turbulent shear stress term is approximated as τ ε where the turbulent velocity l i is defined as ' ε W =. l ρ s ij The single-phase turbulent velocity is calculated using the correlation by Rogers and Rosehart (Rogers, J. T. and Rosehart, R. G., 1972). The dependence of the mixing rate on the flow regime is modeled by Beus (Beus, S. G., 1970). The maximum of the two-phase multiplier is assumed equal to 5: Θ max = Turbulent Mixing Model of COBRA-TF The FLECHT_SEASET version of COBRA-TF (Paik, C.E. et al., 1985) is utilizing the same models for turbulent mixing and void drift as the THERMIT-2 code but without applying the Beus 15 In the following description, the nomenclature is as given in the corresponding References 84

103 model for the two-phase turbulent mixing Turbulen t Mixing Model of MATRA The subchannel code MATRA is an improved version of COBRA-IV-I developed at KAERI, Korea. (Yoo, Y. J. et al., 1999). In similarity to THERMIT-2, MATRA calculates the net lateral mass flux due to turbulence as W '' = β S G and uses the Beus model for the two-phase turbulent mixing. k ij Turbulent Mixing Model of FIDAS FIDAS is a three-fluid three-field code (Sagawara, S. et al., 1991). The code calculates the net T lateral mass flux due to turbulence as W ( ε + ε ) ρ = + ρ ij ij T µ µ = M M ij T ρ Sc ρ Sc, where Sc = µ ρ D c T u u is the Schmidt number. The turbulent dynamic viscosity is given as µ = ρ l + m, L z where L is the lateral length; z is the axial length; and the mixing length is calculated 2 asl m = K D 1 h, ave = K 1 D h, i + D 2 h, j. The single-phase turbulent velocity is calculated by Rogers and Rosehart (Rogers, J. T. and Rosehart, R. G., 1972). The Beus model (Beus, S. G., 1970) is modified such as jliq x max,sugawara = 0.22 xmax, Beus and Θ max = m/s Turbulent Mixing Model of VIPRE-2 VIPRE-2 is a two-fluid two-phase code developed at PNL/EPRI, USA and currently used in Westinghouse, USA for safety analyses (VIPRE-02, 1994). The turbulent crossflow occurs by an equal mass exchange between subchannels and is assumed equal to ' W = β S m G. As a second 85

104 option, an empirical formulation of the turbulence in terms of eddy diffusivity ε t is employed: W ' S = ε t ρ m l, where S is the gap width, l is the gap centroid length, G is the average mass flux in the lateral control volume, ρ m is the mixture density, ε = t 1 β m is an empirical mixing l U m coefficient, and U m is the mixture axial velocity. The turbulent energy exchange in the lateral direction for each phase is weighted by the phase mass fraction, and it is computed using the relation Q tφ = X k ε i α φ ρφ ' W hφ, where X is the axial node l ength, h φ is the enthalpy ρ m difference across the lateral control volume for phase φ, and k ε i is a summation over all gaps k connected to channel i. The turbulent mixing between channels is included as a force in the axial momentum equation. The total axial force, F m, in each phase due to turbulent momentum mixing is computed as F m = C T X k ε i α φ ρφ ' W U ρ m φ, where Uφ is the axial velocity difference for phase across the lateral control volume. The term is an empirical correction factor (the so called C T turbulent momentum factor) to account for the imperfect analogy between turbulent transport of thermal energy and momentum. If C T = 1.0, energy and momentum are mixed with equal strength. If C T = 0.0, only energy is mixed by the turbulent crossflow. Turbulent momentum exchange is not considered in lateral direction Turbulent Mixing Model of NASCA The development of the NASCA code is a joint work of several academic and industrial organizations in Japan (Ninokata, H. et al., 2001, Hotta, A. et al., 2004, and Shirai, H. et al., 2004). 86

105 Turbulent mixing is modeled as φ ε {( α ρ ) ( α ρ ) } kij TM = k k i k k l j, where the two-phase turbulent, TP, TM velocity is given as ε l TP, TM ε = l SP θ TM ρ k ρtp. NASCA assumes a dependence of the single- phase mixing velocity on the geometry. The geometry effect is modeled by applying the so-called rod shape factor * F i, which accounts for the spacer grids as well: * * 1 ε 1 1 F F j 1 S y) i yi 0 l SP = l l ki kj + ε ki ε kj = S ij + ε i ε j at the lateral distance (see Figure 7). = S ij 0 1 ( ε i dy + y j 1 dy S( y) ε j 1, where S(y) is the gap size y=y i y=0 i j S(y) Figure 7: Definition of the gap size at the lateral distance in NASCA Turbulent Mixing Model of MONA-3 MONA-3 is a three-field two-phase code developed in Westinghouse, Sweden in cooperation with Studsvik Scandpower AS and the Royal Institute of Technology, Stockholm (Nordsveen, M. et al., 2003). The effect of turbulent mixing is modeled for momentum and energy equations. A turbulent viscosity concept is used and both a Prandtlt type model and a model by Ingesson 87

106 (Inges son, L., 1969) are implemented: ν = l Tk U ( ν + + ν ), 2 2 k ki kj m lij l m d gap ij = Prandtl type gap l d + l ij ν Tk ν k Re k f 0. 2 = Υ, f = 0.18 Re, k 20 8 P Υ = 6.12 Ingesson s model D h In the above equations, l m is the mixing length; d gap is the gap width, U k is the phase velocity difference between the two subchannels; Υ is the velocity adjustment factor; and l ij is the distance between the centers of gravity of the subchannels. 5.2 F-COBRA-TF Turbulent Mixing Model In the COBRA/TRAC code version, only a single-phase mixing (single-phase liquid for void fractions below value of 0.6, single-phase vapor for void fractions above value of 0.8, and a ramp between the two) has been modeled by means of the traditional mixing coefficient approach. Later, in the FLECHT SEASET code version, a void drift model based on the work of Lahey and Moody (Lahey, R. T. and Moody, F. J., 1993) has been employed (see section 3.3.3). Void drift was only assumed to occur when the liquid is continuous phase and its modeling has been not applied to the hot wall flow regimes. However, the model implementation into the COBRA-TF conservation equations led to a distortion of the mass balance and numerical instabilities at pre- and post-chf conditions. As discussed in section 3.3.3, F-COBRA-TF modeling of turbulent mixing and void drift was revised and improved by Avramova (Avramova, M. N., 2003b). The following sections will describe the current code models for intra - and intersubchannel mass, momentum, and energy transfer. 88

107 5.2.1 F-COBRA-TF Turbulent Mixing and Void Drift Models The F-COBRA-TF turbulent mixing and void drift models assume that the net two-phase mix ing (including void drift) is proportional to the non-equilibrium void fraction gradient. At an annular film flow regim e a void drift offset is assumed and only the turbulent mixing of vapor and entrained droplets is modeled. In other words, the void drift is only modeled in bubbly, slug, and churn flow, where liquid is the continuous phase and vapor is the dispersed phase (Glueck, M., 2005b). The lateral exchange due to turbulent mixing is modeled as follows: Turbulent mixing of mass in phase k: TM G G & = β ( α ρ A = β ( α ρ α ρ ) m k k ) ρ k k, j k, j k, i k, i ρ (5.12) Turbulent mixing of momentum in phase k: G I & TM k = β Gk A ρ (5.13) Turbulent mixing of energy in phase k: TM G Q& k = β ( α k ρ k hk ) A (5.14) ρ In Equations 5.12 through 5.14 β = Θ β is the two-phase turbulent mixing coefficient. TP SP Currently the single phase mixing coefficient β may be either specified as a single input value or internally calculated choosing between two empirical correlations: Rogers and Rozehart (Rogers, J. T. and Rosehart, R. G., 1972) and Rogers and Tahir (Rogers, J. T. and Tahir, A. E. E., 1975). The SP 89

108 two-phase multiplier Θ is calculated using the Beus approach (Beus, S. G., 1970) for two-phase TP turbulent mixing as given by Equations 5.8 through The lateral exchange due to void drift is modeled as follows: Mass exchange in phase k by void drift: VD G m& k = β ( α k, j,eq ρ k, j,eq α k, i,eq ρ k, i,eq )A (5.15) ρ Momentum exchange in phase k by void drift: G I& VD k = β ( Gk, j,eq Gk, i, EQ )A (5.16) ρ Energy exchange in phase k by void drift: G Q& VD k = β ( α k, j,eq ρ k, j,eq hk, j,eq α k, i,eq ρ k, i,eq hk, i, EQ )A (5.17) ρ According to Levy (Levy, S., 1963) the equilibrium density distribution is related to the mass flux distribution. This assumption was further used by Drew and Lahey (Drew, D. A. and Lahey, R. T., 1979) for analytical derivation of a void drift model for subchannel analyses. The model is well documented and currently used in many subchannel codes. Detailed description of the implementaion of the Drew and Lahey s model in the THERMIT-2 (MIT) and the COBRA-TF (PSU) subchannel codes are published in Kelly, J. E. et al., 1981 and Avramova, M. N., 2003b. The model is used in F-COBRA-TF as well. 90

109 5.2.2 Modifications to the F-COBRA-TF Turbulent Mixing and Void Drift Models Addressing the New Spacer Grid Modeling In F-COBRA-TF only one explicit source term, which accounts for both turbulent mixing and void drift, is added to each code conservation equation (Equations 3.1 to 3.9). Moreover, the same mixing coefficient is applied to both processes: Mass equations: m& k = m& TM k + m& VD k G ( α ρ α ρ ) A + β ( α ρ α ρ ) G = β j k, j k, i k, i ρ k, j,eq k, j,eq k, i,eq k,,eq A ρ k, i turbulent mixing void drift (5.18) Momentum Equations: I& k = I& TM k + I& VD k G ( G G ) A + β ( G G ) G = β k, j k, i k, j,eq k, i,eq A (5.19) 1444 ρ ρ turbulent mixing void drift Energy equations: Q& k = Q& TM k + Q& VD k G ( α ρ h α ρ h ) A + β ( α ρ h α ρ h ) G = β k, j k, j k, j k, i k, i k, i ρ turbulent mixing k, j,eq k, j,eq k, j,eq k, i,eq k, i,eq k, i,eq A ρ void drift (5.20) In order to prepare F-COBRA-TF for implementation of the new spacer grid model, in which the spacer effects on the turbulent mixing and the void drift have to be modeled independently, 91

110 minor coding modifications were performed such that at two-phase conditions two different two- phase multipliers are applied to the turbulent mixing and to the void drift terms: the two-phase turbulent mixing multiplier TM Θ TP VD and the void drift multiplier ΘTP. Then, for example, the source to the mass conservation equation of phase k is given as: m& k = m& TM k + m& VD k VD G ( α ρ α ρ ) A + Θ β ( α ρ α ρ ) TM G = ΘTP β SP j k, j k, i k, i ρ k, TP SP k, j,eq k, j,eq k, i,eq k, i,eq A turbulent mixing ρ void drift (5.21) Moreover, instead of introducing one combined source term m & = m& m& to the right hand k TM k + VD k TM VD side (RHS) of the phase k mass equation, two independent terms m& k and m& k are evaluated and added: TM TM G m& k = ΘTP β SP ( α k, j ρ k, j α k, i ρ k, i )A (5.22) ρ and m& VD k VD G = ΘTP β SP ( α k, j,eq ρ k, j,eq α k, i,eq ρ k, i, EQ )A (5.23) ρ In similarity, sources to the phase k momentum equation are I & TM TM G k = ΘTP β SP ( Gk, j Gk, i )A ρ (5.24) I& VD VD G k = ΘTP β SP ( Gk, j,eq Gk, i, EQ )A (5.25) ρ and sources to the phase k energy equation are 92

111 G Q & TM TM = Θ β ( α ρ h α ρ h )A ρ (5.26) k TP SP k, j k, j k, j k, i k, i k, i G Q & VD VD = Θ β ( α ρ h α ρ h )A ρ (5.27) k TP SP k, j,eq k, j,eq k, j,eq k, i,eq k, i,eq k, i, EQ In the above equations, superscripts TM and VD stand for turbulent mixing and void drift, respectively. It can be seen that the major assumption of the turbulent mixing modeling is not changed: the same single-phase mixing coefficient β SP is applied to the mass, momentum, and energy exchange: C t β SP =, where Ct : = Dt = ν t = at. yu A sensitivity study confirmed that the new coding approach does not create numerical instabilities since the net amount of mass, momentum, and energy added to the RHS of the conservation equations have not changed Modifications to F-COBRA-TF Turbulent Mixing and Void Drift Models Addressing Some Experimental Findings During the Kumamoto University air-water experiments it has been found that the two-phase multiplier Θ TP, which corrects the single-phase mixing coefficient, has different dependence on the void fraction for fully-developed and for developing flows, as it is shown in Figure 8 and Figure 9. Based in this observation, the authors of NASCA code (Hotta, A., 2005) have applied two different two-phase multipliers: turbulent mixing two-phase multiplier Θ TM and void drift multiplier Θ VD. The Kumamoto University experimental observations were modeled in F-COBRA-TF. In F- 93

112 COBRA-TF, the transition to annular flow is not necessary controlled by a fix void fraction value, therefore to be in an agreement with the code flow regime logic, the void drift coefficient was disabled in annular flow. The code modification was validated against 4 4 PELCO-S experiments (Herkenrath, H. et al., 1979). Because the F-COBRA-TF comparisons showed that the implementation of the Kumamoto University model into F-COBRA-TF leads to significant misprediction of the measured distribution of the exit quality, the model was removed from the code. In addition, the equilibrium distribution weighting factor K M, was correlated to the pressure as proposed by KAERI (Jeong, J. J. et al., 2005b): [ 0. ] K = 6.2 exp 215P. M 94

113 6 iplier Turb ul ent Mi xi ng Tw o-p hase Mult Void Fraction Figure 8: Turbulent mixing two-phase multiplier as function of local void fraction Void Drift Multiplier Void Fraction Figure 9: Void drift multiplier as function of local void fraction 95

114 5.3 Evaluation of the Single-Phase Mixing Coefficient by Means of CFD Calculations Methodology Computational fluid dynamics can be utilized for an evaluation of the single-phase mixing coefficient in two ways: 1) by CFD predictions of the turbulent viscosity (Ikeno, T., 2001) or 2) by CFD predictions of the turbulent heat flux across the gap between adjacent subchannels (Jeong, H. et al., 2004). In both methods, the CFD model must be settled correctly to assure the diffusive nature of the turbulent mixing processes: no net mass flow over the gaps between subchannels must occur. Approach 1: Evaluation of the single phase mixing coefficient by the turbulent viscosity Let s assume two identical subchannels connected through a gap (Figure 10). y Figure 10: Model for the evaluation of the single-phase mixing coefficient by the turbulent viscosity According to Equation 5.4 the dimensionless turbulent mixing coefficient applying kinematical turbulent viscosity as a turbulent diffusion coefficient ( C t β can be defined by ν ): turb turb β SP = ν, ( 5.28) yu where ν turb is the surface-averaged kinematical turbulent viscosity, U is the surface-averaged 96

115 vertical velocity, and y is the centroid distance between adjacent subchannels. Both, ν turb and U can be evaluated from single-phase CFD calculations. Approach 2: Evaluation of the single phase mixing coefficient by the turbulent heat flux across the gap Let us assume two adjacent subchannels with identical geometries and equal inlet mass velocities (Figure 11). A temperature difference of 10 C between the subchannels is applied. The subchannel i (left side) is assumed to be the hot one, while the subchannel j (right side) is the cold one. Thus, the heat transfer between both subchannels is achieved only by two processes conduction and turbulent diffusion (mixing). Q out i Q out j y x hot cold S ij in Q i in Q j Figure 11: Model for evaluation of the single-phase mixing coefficient by the turbulent heat flux across the gap The heat rate due to turbulent mixing and conduction per unit length through the gap S ij (at stea dy state flow conditions) is equal to Q total = Q out i Q in i = q '' total S x. (5.29) ij The heat flux through the gap is given as: 97

116 q '' total S ij x = m& h i i out in ( T T ) flow = ρ iu i Ai c p i i m& i h i (5.30) out in ( Ti Ti ) '' '' U A c = ρ qconduction flow '' i i i p q total Sij x = qturbulence + (5.31) The heat flux through the gap due to conduction is: q '' conduction = λ out out ( T T ) j y i. (5.32) The heat flux through the gap due to turbulent mixing is: q '' turbulence = q '' total q '' conduction ρ iu i Ai = flow S c ij p out in out out ( T T ) ( T T ) i x i λ j y i. (5.33) Thus, the turbulent mixing coefficient can be defined as: s ingle- phase mixing coefficient = heat flux due to turbulence axial heat flux or (5.34) '' qturbulence β =. c p ρu( T T ) j i Since, for water the turbulent thermal conductivity is much higher than the molecular one Equation 5.34 can be written as: '' q total β = (5.35) c p ρu( T T ) j i where q q. '' total '' turbulence 98

117 In theory, when the mixing coefficient is defined using Equation 5.28 it will be representing only turbulent diffusion, but not molecular diffusion. On other hand, Equation 5.35 will calculate the mixing coefficient due to turbulent and molecular diffusion together. Here, it should be highlighted that the heat flux determined by a subchannel based heat balance out in ( T T ) will include the contribution of both convective and diffusive transfers. The real i i diff usive heat flux over the gap region can be evaluated only by a local (near gap) heat balance ( out T g ap T ). in gap In regard to F-COBRA-TF, since the code is developed for LWR applications both methodologies are applicable, but the one using heat transfer balance seems to be more appropriate for the scale of subchannel analyses. However, both approaches were examined and compared in regard to their applicability and numerical stability CFD Model For purpose of preliminary investigations of the proposed methodology for the single-phase mixing coefficient evaluation, a simple 2 1 STAR-CD (STAR-CD Version 3.26) model for thermalhydraulic analyses of the heat transfer between adjacent subchannels has been developed at AREVA NP GmbH (Kappes, Ch., 2006). The model corresponds to ones shown in Figure 10 and Figure 11 and it simulates only a heat transfer by diffusive effects. No net mass transfer is assumed to occur. The objective was to study the turbulence in the gap between the rods. Segments of six rods with outer diameters of 9.5 mm were arranged in a 2 1 subchannels configuration with a rodto-rod pitch of 12.7 mm over the axial length of 540 mm. The coupled subchannels have equal inlet velocities, but the inlet temperatures differ by 10 C. The applied boundary conditions are inlet velocity of 5 m/s and outlet pressure of 160 bars; symmetry condition is assumed at the gaps 99

118 between the rods; the walls are smooth, no-slip, and adiabatic. The inlet turbulence intensity of 5 % is modeled. The water properties are assumed to remain constant along the axial length. A simple conjugated-gradient solver with upwind discretization was used. The standard k ε high Reynolds number turbulence model was utilized. The accuracy was set to 10-4 and typical mesh size of 0.3 mm was selected. The 2 1 STAR-CD model is summarized in Table 6. In total ten sub-models were calculated. At the beginning no internal structures were included: a clean bundle was simulated. In the next four models straps with different thicknesses were inserted, respectively 0.3 mm, 0.4 mm, 0.5 mm, and 0.6 mm. In the last set of calculations, the model with strip thickness of 0.4 mm was selected and four mixing vanes were attached at the upper edge of the strip. The vane angle was varied between 10 and 50 degrees in intervals of 10 degrees. The mixing vanes were mirrored and rotated in order to produces pure circular flow inside the subchannels. The model and the mixing vanes configuration are visualized in Figure 12 and Figure 13, respectively. Figure 14 shows the mesh structure of the model. The mixing vane geometry is given in Figure 15. The distributions of the temperature field, turbulent viscosity, vertical velocity, and pressure field are given in Table A-1through Table A-8 of Appendix A. 100

119 Table 6: Description of the 2x1 channels model used in the STAR-CD calculations Thermal Hydraulic Analyses of Flow and Heat Transfer Coupled Subchannel Analyses STAR-CD Calculation coupled 2 x 1 subchannels Characterization of Run channels with equal inlet velocities inlet temperature of channels differ by 10 K study flow distribution without cross flow turbulence in the gap between the rods Objective enthalpy transfer between the subchannels by turbulent diffusion averaged temperature at inlet and outlet indicate the enthalpy exchange between the sub-channels rod diameter 9.5 mm pitch 12.7 mm length 540 mm Model Inlet velocity 5 m/s 1) clean subchannels 2) no vanes; strip thickness 0.3; 0.4; 0.5; and 0.6 mm 3) strip thickness of 0.4 mm, vane angle 10, 20, 30, 40 and 50 Boundary Conditions Outlet Gaps between rods Walls Outlet / Pressure condition symmetry condition no-slip, adiabatic, smooth Temperature at inlet 300 / 310 C Properties Method Turbulence at inlet Density Lam. Viscosity Thermal conductivity Specific heat Solver Discretization Accuracy Turbulence typical cell dimension Intensity 5%, length 2 mm kg/m³ e-5 kg/m/s 0.56 W/m²/K 4457,3333 J/kg/K Simple, CG + AMG Upwind 1.00E-04 standard k-ε, wall fucnction 0.3 mm 101

120 Figure 12: 2 1 CAD model for thermal-hydraulic analysis of heat transfer by turbulent diffusion Figure 13: Side and top views of the mixing vanes configuration 102

121 Figure 14: Mesh grid of the 2 1 model Figure 15: Geometrical characteristics of the mixing vanes in the 2 1 model 103

122 5.3.3 Evaluation of the Single-Phase Turbulent Mixing Coefficient Using the results obtained with the above described 2 1 STAR-CD model, the single-phase mixing coefficient was evaluated with both approaches discussed in section (Equations 5.32 and 5.34). For each sub-model the following data was extracted from the CFD results: 1) Axial distribution of the subchannels surface-averaged temperatures T and T ; surf i surf j 2) Axial distribution of the surface-averaged dynamic turbulent viscosity µ surf turb ; 3) Axial distribution of the subchannels gap-averaged temperatures gap i T and gap T ; j gap gap 4) Axial distribution of the subchannels gap-averaged dynamic viscosities and ; 5) Axial distribution of the subchannels gap-averaged vertical velocities U µ turb,i gap gap i and j µ turb, j U. The surface-averaging is done over each subchannel cross-sectional area at every 10 mm axial elevation and the gap-averaging is done over shells of -0.1 mm (left side subchannel i ) and 0.1 mm (right side subchannel j ) from the gap between subchannels at every 10 mm axial elevation. The data is available also in a fine axial scale of 3 mm. Because of the assumption for constant water properties, the surface-averaged axial velocity, 5 m/s over the whole length. surf U, is equal to the inlet vertical velocity of During the investigation of the single-phase mixing coefficient by a heat balance, it was found that a smother axial distribution of the heat flux across the gap is evaluated when instead of taking the heat balance over a subchannel control volume, the balance is performed with a local temperature gradient over the gap. Figure 17 through Figure 22 show the axial behavior of the evaluated single-phase mixing 104

123 coefficients for different strap thickness and vane declination angles. For the purpose of comparative analyses, the evaluations with Approach 1 were performed in two ways: 1) using surface-averaged quantities - surf turb surf β SP = ν ; and 2) using gap-averaged quantities - yu β SP = ν yu gap turb gap. It can be seen in Figure 17 and Figure 18 than for the cases with no mixing vanes both methods predict relatively close axial distributions of the mixing coefficient: there is a sharp increase downstream of the strap upper edge followed by a decrease, after which a tendency exists of stabilizing around the clean bundle value. The mixing coefficient calculated by surface-averaged quantities tends to be a little bit higher. The picture becomes more complicated and somehow difficult to explain when the mixing vanes are added - Figure 19 and Figure 20. Physically, due to the swirl flow created by the mixing vanes, the turbulence downstream of the vanes is expected to be significantly enhanced. However, this phenomenon is not captured by our evaluations of the mixing coefficient by using turbulent viscosity. In completely opposite manner, Figure 19 indicates a decrease of the mixing coefficient. This unexpected result is not due to errors during the extractions of the CFD data or during the evaluations, because it is in an agreement with the turbulent viscosity distributions over subchannel centroids line as given in Table A-8 of Appendix A. When evaluating the single-phase mixing coefficient β SP β SP by the turbulent viscosity and the vertical velocity averaged over the gap region (see Figure 20) there is an increase in the mixing rate, but upstream of the mixing vanes and a sharp decrease exists over and shortly after the mixing vanes. After that region the turbulence tends to reach the clean bundle values. Again, these predictions are following the turbulent viscosity distributions over gap between rods as given in 105

124 Table A-8 of Appendix A. Other important observation is that the magnitude of the mixing coefficients evaluated with Approach 1 is one order lower than the expected value of 10-3 for the simulated conditions. Let s recall that our CFD calculations were performed with the standard k ε turbulence model. This model neglects the large eddy structures, which exist in the gap region and have a significant contribution to the exchange processes between subchannels by their cyclic flow pulsation through the gaps. As already discussed in section 2.3 the same finding were reported by Ikeno (Ikeno,T., 2001). From analyses of the evaluated mixing coefficients by the heat transfer balance (Approach 2, see Figure 21 and Figure 22) it can be stated that this method results in more stable and physically reasonable results. Right after the straps there is an augmentation in the turbulent mixing due to flow area expansion. Thicker the strap is, stronger the mixing is. An interesting behavior is found shortly downstream of the mixing vanes (see Figure 22) - a decrease in the turbulent mixing is observed in that region. After that the turbulence quickly recovers and lasts up to the next strap. The length of the decrease depends on the declination angle larger the declination angle is, shorter the decrease is. Higher mixing coefficient corresponds to larger vane angle. It should be mentioned here that the short decrease right downstream of the vanes has been seen also in the improved model of Ikeno (Ikeno,T., 2001) (see Figure 16). As described in section 2.3, Ikeno overcame the deficiency of the standard k ε turbulence model to capture the large eddy structure at the gap region by adopting the flow pulsation model of Kim and Park (Kim, S., and Park, G.-S., 1997) with analytical formula for the Strouhal number. 106

125 Figure 16: The non-dimensional eddy thermal diffusivity calculated by Ikeno (Ikeno,T., 2001) Another important advantage that Approach 2 shows is the magnitude of the evaluated mixing coefficients they are in the expected range of The above discussed investigations of the proposed methodologies for evaluation of the singlephase mixing coefficient by means of CDF calculations led to the selection of the so-called Approach 2: Evaluation of the single-phase mixing coefficient by the turbulent heat flux across the gap for an implementation into F-COBRA-TF for modeling of the enhanced turbulent mixing by the spacer grids. The selected method was used for estimations of the spacer mixing coefficient for the ULTRAFLOW TM spacer design (trademark of AREVA NP GmbH). Comparative analyses to the original F-COBRA-TF spacer grid modeling were performed for the ATRIUM TM 10 XP BWR bundle, with is equipped with ULTRAFLOW TM spacers. The lack of suitable AREVA NP in-house measurements does not allowed a validation of the proposed method against experimental data. 107

126 Single-Phase Mixing Coefficient surface-averaged Mixing coefficient mm 0.4 mm 0.5 mm 0.6 mm clean channels strip Height, mm Figure 17: Evaluation of the single-phase mixing coefficient using surface-averaged turbulent viscosity and vertical velocity dependence on the strap thickness Single-Phase Mixing Coefficient gap-averaged Mixing coefficient strip 0.3 mm 0.4 mm 0.5 mm 0.6 mm clean channels Height, mm Figure 18: Evaluation of the single-phase mixing coefficient using gap-averaged turbulent viscosity and vertical velocity dependence on the strap thickness 108

127 Single-Phase Mixing Coefficient surface-averaged strip Mixing coefficient deg 20 deg 50 deg no vanes clean channels Height, mm Figure 19: Evaluation of the single-phase mixing coefficient using surface-averaged turbulent viscosity and vertical velocity dependence on the declination angle (strap thickness of 0.4 mm) Single-Phase Mixing Coefficient gap-averaged Mixing coefficient strip Height, mm 10 deg 20 deg 50 deg no vanes clean channels Figure 20: Evaluation of the single-phase mixing coefficient using gap-averaged turbulent viscosity and vertical v elocity dependence on the declination angle (strap thickness of 0.4 mm) 109

128 Single-Phase Mixing Coefficient Mixi ng coeffi ci ent clean channels 0.3 mm 0.4 mm 0.5 mm 0.6 mm strip Height, mm Figure 21: Evaluation of the single-phase mixing coefficient by local heat balance over the gap dependence on the strap thickness Single-Phase Mixing Coefficient Mixing coefficient strip Height, mm 10 deg 20 deg 30 deg 50 deg no vanes clean channels Figure 22: Evaluation of the single-phase mixing coefficient by local heat balance over the gap dependence on the declination angle (strap thickness of 0.4 mm) 110

129 TM Θ SG Incorporation of the CFD Results into F-COBRA-TF The effect of the spacer grids on the turbulent mixing is modeled by an additional multiplier,, which is applied to the turbulent mixing rate as their are calculated by the current F-COBRA- TF models. The multiplier is a ratio of the single-phase mixing coefficient evaluated for a bundle with mixing type spacer grid, clean bundle, no spacers βsp mixing vanes angle ϕ : spacers β SP, and the single-phase mixing coefficient evaluated for a. It is a function of the axial distance y downstream of spacer and the Θ TM SG ( y, ) β ϕ = β spacers SP no spacers SP. (5.36) It was expected that the spacer multiplier will have a peak near the upper edge of the mixing vanes and will decrease further downstream. Its magnitude will increase with the strap thickness (following the magnitude of the change in the flow area) and with the declination angle of the vanes (following the magnitude of the swirling flow). Schematically, this behavior is shown in Figure 23. TM Θ SG φ 1 > φ φ 2 φ Z SG,1 Z SG,2 Z SG,N x Figure 23: Schematic of the spacer multiplier distribution over the axial length 111

130 Thus, Equations (5.29); (5.31); and (5.33) were modified as follows: TM TM TM G m& k = Θ SG ΘTP β SP ( α k, j ρ k, j α k, i ρ k, i )A (5.37) ρ G I& TM TM TM k = Θ SG ΘTP β SP ( Gk, j Gk, i )A (5.38) ρ G Q & TM TM TM = Θ Θ β ( α ρ h α ρ h )A (5.39) k SG TP SP k, j k, j k, j k, i k, i k, i ρ If the new spacer model is being developed to use correlations for the spacer multiplier, this will require an extensive set of numerical experiments in order to cover a large envelope of operational conditions. However, in the view of the F-COBRA-TF development for industrial applications, instead of implementing such correlations it will be more efficient to develop an interface module to be applied to the code turbulent mixing model. The module will: 1) contain data base with detailed information for the spacer multiplier distribution across a given bundle for a set of different mixing vane designs (obtained by means of CFD calculations) and 2) will maintain the exchange between the CFD data base and F-COBRA-TF. For the purposes of routine safety analyses, the code could be supplied with sets of CFD data, which represent spacer designs that are currently used. The users will be able to choose which data set to be used. In case of new design studies, an experienced user will create a new data set based on recent CFD calculations. The flow chart of the enhanced turbulent mixing modeling and examples for the CFD obtained data sets of the mixing multipliers are given in Appendix C. To address the flow regime dependence of the mixing coefficient, the axial velocity used in the CFD pre-calculations (Eq. 5.35) must be calibrated to the actual axial flow velocity of the given F- COBRA-TF computational cell. 112

131 5.3.5 Evaluations of the Spacer Grid Void Drift Multiplier Here, a few words must be s aid for the spacer effect on the void drift phenomenon. The void drift is characterized by the vapor affinity for high velocity regions. On the other hand, the spacers are known to change the main velocity profile because of the flow area contraction and expansion near their locations and/or flow deflection on their surfaces. The extent of this change could be used as a criterion for an enhancement or a suppression of the local void drift. In similarity to the spacer grid turbulent mixing multiplier, a spacer grid void drift multiplier, Θ VD SG, could be defined by means of CFD predictions for the change in the main velocity profile at the spacer locations. The purpose of applying a spacer grid void drift multiplier will be to drive more vapor into the subchannel with the higher main flow velocity. Thus, Equations (5.30), (5.32), and (5.34) can be modified as follows: VD VD VD G m& k = Θ SG ΘTP β SP ( α k, j,eq ρ k, j,eq α k, i,eq ρ k, i, EQ )A (5.40) ρ G I& VD VD VD k = Θ SG Θ TP β SP ( Gk, j,eq Gk, i, EQ )A (5.41) ρ G Q & VD VD VD k = Θ SG ΘTP β SP ( α k, j,eq ρ k, j,eq hk, j,eq α k, i,eq ρ k, i,eq hk, i, EQ )A ρ (5.42) However, there is yet no clear concept how exactly the applied spacer grid void drift coefficient will be calibrated to the main velocity. 113

132 5.3.6 F-COBRA-TF Modeling of the Turbulent Mixing Enhancement for ULTRAFLOW TM Spacers ULTRAFLOW TM Spacer Design The ULTRAFLOW TM spacer design has swirl type mixing vanes intended to generate intensive intra-subchannel swirl and turbulence, but no net mass crossflow. In each pair of adjacent subchannels the swirling flows have opposite directions. A 3D view of the ULTRAFLOW TM spacer is given in Figure 24. The spacer includes four swirl deflectors attached at the upper edge of the interconnections between the straps. The swirl deflectors have an air vane structure including blades that are configured to have the same vane rotation direction. Each swirl vane has a pair of intersecting triangular base plates extending upward from the interconnecting strips. The swirl vanes are bent in the same direction from the associated side base plates. A schematic of the mixing vanes arrangem ent in a 2 2 subchannels array i s shown in Figure 25. Figure 24: 3D view of the ULTRAFLOW TM spacer 114

133 Figure 25: Mixing vanes configuration of the ULTRAFLOW TM spacer design CFD Model of ULRTAFLOW TM Spacer An existing geometrical model of ULTRAFLOW TM spacer, developed at AREVA NP GmbH for STAR-CD 3.26, was utilized for the evaluation of the mixing coefficient by heat balance across the gap between adjacent subchannels. A schematic of the model is shown in Figure 26. Surface of the control volume at altitude z ±15 mm - used for crosssectional averages Center of the control volume at altitude z - used for evaluation of the temperature differences between adjacent subchannels Figure 26: Schematic of the CFD model for the ULTRAFLOW TM spacer 115

134 An existing coordinate system from the ULTRAFLOW TM spacer model was chosen. It starts at 45.7 mm and ends at mm. For our evaluations, the region between 40 to +440 mm was selected. Then, the leading edge of the spacer is on the coordinate z = mm. The top of the vanes is at z = mm. Since the axial spacing for the evaluation is 30 mm, the first axial section, -40 to -10 mm, is completely upstream the spacer; the second axial section, -10 to +20 mm, is almost completely containing the spacer; the third axial section, +20 to +50 mm, is almost completely downstream the spacer (only the first 3mm contain a part of the top of the vanes); and the fourth and following axial sections are in the region of the undistorted geometry of the bare rod bundle. The CFD analyses were all conducted with an inlet velocity of 2.59 m/s. The coupled subchannels have equal inlet velocities, but different inlet temperatures. The water properties are assumed to remain constant. A simple conjugated-gradient solver with upwind discretization was used. The standard was set to k ε high Reynolds number turbulence model was utilized. The convergence CFD calculations were performed for two cases: 1) simulation of one span of a real ULTRAFLOW TM spacer and 2) simulation of a clean 2 1 array of the ATRIUM TM 10 XP bundle. The distributions of the velocity and temperature fields and the turbulent viscosity are given in Table B-1 through Table B-3 of Appendix B. The axial distributions of the mixing coefficients, evaluated with Equation 5.35, are given in Figure 27 and Figure 28. The calculated spacer grid multiplier is shown in Figure 29. As it is seen in the graphs, the first point, at altitude -25 mm, show s very high values. These values are taken just upstream the spacer. Here we have to take into 116

135 account, that the inlet boundary conditions have some impact on the flow situation. The flow is not yet fully developed. This causes also increased turbulent viscosities, which has an impact on the numerically evaluated heat flux across the gap. Also, the inlet temperature is set to different values for both subchannels. By this, we get a temperature step at the gap and with this a very high temperature gradient. In our CFD analysis, the temperature gradient is reduced already significantly, but still higher than the more developed flow situation downstream the spacer. Passing the spacer gives so much change to the flow, that it is not more influenced at the outlet of the spacer by the incoming temperature gradients. Thus, the suggestion is to not use the results upstream the spacer for further analyses. Under reactor conditions, we always will have much more developed flow situations than in a spacer span wise calculation. Therefore, it is more realistic to apply values taken from regions close to the outlet of the calculation, because here the flow shows an almost developed behavior. In reality, this would be anyway the inlet condition for the next spacer span. Single-Phase Mixing Coefficient from CFD ULTRAFLOW Spacer Mixing coefficient Height, mm Figure 27: CFD results for the single-phase mixing coefficient for the ATRIUM TM 10 XP bundle ULTRAFLOW TM spacers 117

136 Single-Phase Mixing Coefficient from CFD "Clean" Rod Bundle Mixi n g coef fi cient Height, mm Figure 28: CFD results for the single-phase mixing coefficient for the ATRIUM TM 10 XP bundle without spacers Spacer Grid Multiplier for Single-Phase Mixing Coefficient ltiplier Mu Height, mm Figure 29: CFD results for the spacer grid mixing multiplier for the ULTRAFLOW TM design 118

137 F-COBRA-TF Calculations of ATRIUM TM 10 XP Bundle with ULTRAFLOW TM Spacers There are seven grids with mixing vanes instrumented along the heated length of the ATRIUM TM 10 XP bundle. The axial locations of the spacers are depicted in Figure 30. Using the CFD results for the spacer grid mixing multiplier shown in Figure 29, a two-dimensional (2D) table for the axial distribution of the spacer multiplier along the heated length of the ATRIUM TM 10 XP bundle was prepared. The distribution is given in Figure 31. Two F-COBRA-TF calculations were carried out. In the first one the standard spacer grid model was used. In the second calculation, at the spacer grid locations the single-phase mixing coefficient, as defined with the correlation by Rogers and Rosehart, was enhanced with the spacer mixing multiplier obtained by the CFD pre-calculations. The enhancement can be seen in Figure 33. According to the F-COBRA-TF turbulent mixing model, the amount of the crossflow between two adjacent subchannels is proportional to the density and void fraction gradients and the turbulent mixing coefficient is a proportionality coefficient. By that reason, subchannels with equal cross- The layout of the F-COBRA-TF model is given in Figure 32. It is a full bundle model, which consists of 117 subchannels and a large water channel. There are 91 fuel rods in total and 10 of them are part-length rods. The model includes an unheated inlet part with one structural grid. The turbulent mixing model, utilized in the performed calculations, defines the single-phase mixing coefficient using the correlation by Rogers and Rosehart (Rogers, J. T. and Rosehart, A. E., 1975) and the Beus model for two-phase mixing (Beus, S. G., 1970). The pressure losses in the vertical flow are modeled with Equation 4.1 using experimentally defined subchannel loss coefficients. 119

138 sectional flow area, but different power loadings were selected for comparative analyses. The one with the lower peaking factor is called cold channel, and the other is called hot channel. The impact of the new model on the mass and energy redistribution inside the bundle is shown in Figure 34 through Figure 41. A strong increase of the lateral flow transfer by turbulent mixing is seen for both phases near and shortly downstream of the mixing vanes. However, Figure 42 shows that for this particular bundle geometry the magnitude of the crossflow by turbulent diffusion is far smaller than the diversion crossflow. Therefore, significant changes in the overall fluid thermalhydraulic performance due to the increased turbulence cannot be observed. Regarding the graphs on Figure 34 and Figure 42, it has to be clarified that the axial position of 2.8 m, where there is a change of the crossflow direction, corresponds to the end of the part-length rods. It seems that although the chosen subchannels do not contain surfaces of part-length rods, the fluid behavior in those subchannels is also affected by the flow area expansion at that elevation. Additionally, the computational performance and efficiency of the modified code version was investigated. Comparisons of the code temporal convergence are given in Figure 43. It is clearly indicated that the new model does not result in a prolonged CPU time. Performed stability analyses showed no distortions in the code convergence on mass and heat balance due to the new modeling. The shape of the graphs in Figure 44 and Figure 45 is defined by the simulated step-wise increase of the total power: the power of 100% is assumed to be reached at 1.8 second, after which the code needs about 1.2 seconds to obtain a steady state solution. 120

139 Spacer grid Mixing vanes End of the Heated Length 512 mm 512 mm 512 mm 512 mm 3708 mm 512 mm 512 mm mm 275 mm Beginning of the Heated Length Figure 30: Axial positions of the ULTRAFLOW TM mixing spacers along the heated length of the ATRIUM TM 10 XP bundle 5 Spacer Grid Multiplier for ULTRAFLOW Design ATRIUM 10 XP Bundle 4 Multiplier Heated lenght, m Figure 31: Axial distribution of the spacer multiplier along the heated length of the ATRIUM TM 10 XP bundle 121

140 Figure 32: Layout of the F-COBRA-TF model of the ATRIUM TM 10 XP bundle Spacer Grid Effect in the Mixing Coefficient standard model spacer grid model Mixing Coefficient Heated lenght, m Figure 33: Mixing coefficient determined by the standard and the new F-COBRA-TF models 122

141 Lateral Flow by Turbulent Mixing of Liquid standard model spacer grid model Flow rate, kg/s Axial position, m Figure 34: Liquid crossflow by turbulent mixing, ULTRAFLOW TM spacer Lateral Flow by Turbulent Mixing of Vapor standard model spacer grid model Flow rate, kg/s Axial position, m TM Figure 35: Vapor crossflow by turbulent mixing, ULTRAFLOW spacer 123

142 0.5 Void Fraction hot channel standard model spacer grid model 0.4 Volume fraction, Axial position, m Figure 36: Void fraction in the hotter subchannel, ULTRAFLOW TM spacer 0.5 Void Fraction cold channel standard model spacer grid model 0.4 Volume fraction, Axial position, m Figure 37: Void fraction in the colder subchannel, ULTRAFLOW TM spacer 124

143 0.05 Flow Quality hot channel standard model spacer grid model 0.04 Quality, Axial position, m Figure 38: Flow quality in the hotter subchannel, ULTRAFLOW TM spacer 0.05 Flow Quality cold channel standard model spacer grid model 0.04 Quality, Axial position, m Figure 39: Flow quality in the colder subchannel, ULTRAFLOW TM spacer 125

144 1350 Enthalpy- Mixture hot channel standard model spacer grid model Enthalpy, kj/kg Axial position, m Figure 40: Enthalpy distribution in the hotter subchannel, ULTRAFLOW TM spacer 1350 Enthalpy- Mixture cold channel standard model spacer grid model Enthalpy, kj/kg Axial position, m Figure 41: Enthalpy distribution in the colder subchannel, ULTRAFLOW TM spacer 126

145 Lateral Flow Components total turbulent mixing void drift diversion Flow rate, kg/s Axial position, m Figure 42: Components of the total crossflow CPU time per time step, s Code Convergence time step standard model spacer grid model Time step number Figure 43: Comparison of the code temporal convergence 127

146 Mass Balance 100 standard model spacer grid model De viatio n from s teady st ate, % Time, s Figure 44: Comparison of the code convergence on mass balance Heat Balance 100 standard model spacer grid model e, % D eviatio n from st ead y stat Time, s 5 Figure 45: Comparison of the code convergence on heat balance 128

147 5.4 Concluding Remarks A comprehensive review of the recent trends in the turbulent mixing modeling in subchannel codes indicates that the enhancement in the turbulent diffusion due to spacer grids in rod bundles is neglected in most of the codes. The development of new models requires either carrying out costly experiments or performing computational fluid dynamics simulations. CFD capabilities allow us to model the fluid behavior on a very refined spatial mesh and therefore to model local flow patterns such as turbulence in the flow near spacer grids which are not seen by analyses on a subchannel level. Two methodologies were proposed for evaluation of the single-phase mixing coefficient by means of CFD calculations: by evaluation of the turbulent viscosity and by heat balance across the gap between two adjacent subchannels. The performed studies indicated that the second approach gives more stable and physically reasonable results and therefore it was chosen for implementation into F-COBRA-TF. The F-COBRA-TF turbulent mixing model was modified to use pre-calculated CFD results for the enhanced turbulence due to spacer grids in rod bundles. A procedure that can be considered as an off-line coupling between a CDF and a subchannel code was developed and verified for the particular case of ATRIUM TM 10 XP bundle with ULTRAFLOW TM spacer. For now, validation of the model is not possible due to lack of suitable experimental data. 129

148 CHAPTER 6 MODELING OF DIRECTED CROSSFLOW CREATED BY SPACER GRIDS 6.1 Background The crossflow in rod bundles can be divided into three categories: turbulent mixing, void drift, and diversion crossflow. Additionally, some spacer designs create specific lateral flow patterns due to velocity deflection on their structural elements as the mixing vane blades. This kind of diversion crossflow is very often referred as directed crossflow. In other words, the directed crossflow is a flow pattern caused by the sweeping effects of the vanes or other grid structures. The magnitude of the directed crossflow depends of the spacer geometry. Examples for spacer designs creating directed crossflow are the HTP TM and FOCUS TM spacers (both are trademarks of AREVA NP GmbH). Schematics of both designs are shown in Figure 46 and Figure 47. The HTP TM design has a specific shape at the rod-to-rod gap regions that directs the flow to enter or leave the subchannel. In the FOCUS TM design the mixing vanes configuration (mirrored and rotated in 90 degree) leads to coexistence of an intra-subchannel swirling flow and a crossflow meandering in opposite directions within one subchannel. A correct modeling of the directed crossflow would require detailed geometrical information such as vanes length and orientation, declination angle, etc. The subchannel codes usually do not have advanced mechanistic models for evaluation of the lateral flow rates specified by a change of the axial velocity vector. An exception is the COBRA-IV code (Stewart, S. W. et al., 1977), which utilizes a simplified directed crossflow model. However, the work of Krulikowski (Krulikowski, T. E., 1997) has shown that the model needs further improvements and more extensive validation. 130

149 Figure 46: Schematic of the HTP TM Spacer Figure 47: Schematic of the FOCUS TM Spacer A very coarse approach is still used in the subchannel analyses: the cont ribution of the lateral convection to the crossflow is approximated by artificially increasing the single-phase mixing coefficient to calculate a crossflow with a magnitude sufficient to reproduce experimental results of the available mixing tests. In this way, the single-phase mixing coefficient combines the effects of the turbulent diffusion and the forced convection by mixing devices or other discrepancies from the bundle symmetry. Such a methodology violates the physics behind the turbulent diffusion approximation: the mixing rate is proportional to the gradients in the medium and should not depend on convective mechanisms. To overcome the above discussed modeling deficiency, the new generation subchannel codes must separate the treatment of the diffusive and the convective effects of the spacer grids. 131

150 6.2 New F-COBRA-TF Model for Directed Crossflow by Spacer Grids The current version of F-COBRA-TF (as well as the PSU versions of COBRA-TF) does not model the directed crossflow. To improve the code capabilities of simulating convective lateral flows due to spacer grids in rod bundles, a new model based on CFD calculations was developed F-COBRA-TF Transverse Momentum Equations In the variety of COBRA-TF code versions, including F-COBRA-TF, the lateral mass flow rates are defined by solving the transverse momentum equations for each field: continuous liquid, entrained liquid, and vapor. Recalling Chapter 3, the generalized phasic momentum equation has the following form: Γ d T ( α k ρku k ) + ( α k ρku ku k ) = α k ρk g α k P + ( α kτ ) + M k k + M k + M k (6.1) t where α is the average k-phase void fraction; k ρ k is the average k-phase density; U k is the average k-phase velocity vector; g is the acceleration of gravity vector; τ is the average k-phase viscous k stress tensor; M is the average supply of momentum to phase k due to mass transfer to phase k; Γ k d M k is the average drag force on phase k by the other phases; and T M k is the average supply of momentum to phase k due to turbulent mixing and void drift. The F-COBRA-TF momentum equations are solved on a staggered mesh where the momentum cell is centered on the scalar mesh cell boundary. The mesh cell for the transverse velocities is shown in Figure 48. The finite-difference transverse momentum equations are given in Equations 6.2 through 6.4. Quantities that are evaluated at the old time carry the superscript n. Donor cell quantities that have the superscript n ~ are evaluated at the old time. 132

151 In the transverse momentum equations, the pressure force term and the velocities in the wall and interfacial drag terms are new time values, while all other terms and variables are computed using old time values. The rate of momentum efflux by transverse convection is given as the sum of the momentum entering or leaving the cell through all transverse connections. Momentum convected by transverse velocities (that are in the direction of the transverse velocities being solved for) is the sum of the momentum entering or leaving through mesh cell faces connected to the face of the mesh cell for which the momentum equation is being solved. NKII is the number of mesh cells facing the upstream face of the mesh cell and NKJJ is the number facing the downstream face of the mesh cell. Momentum convected out through the sides of the mesh cell by velocities that are orthogonal to the velocity to be solved for, but lying in the same horizontal plane, is given by the sum of the momentum convected into or out of cells connected to the sides of the transverse momentum mesh cell. The number of cells connected to the mesh cell under consideration, whose velocities are orthogonal to its velocity, is given by NG. The momentum convected through the top and bottom of the mesh cell by vertical velocities is the sum of the momentum convected into (or out of) cells connected to the top and bottom of the mesh cell and depends on the number of cells connected to the top (NKA) and bottom (NKB) of the mesh cell. z NG S NKA NKII V j NKJJ x NKB Scalar Mesh Cell (II) Scalar Mesh Cell (JJ) Figure 48: F-COBRA-TF transverse momentum mesh cell 133

152 Vapor Phase n [( α vapρvapwvap ) ( α vapρvapwvap ) ] + + NKJJ NG n~ n n~ on [ S ] x [( α ρ W ) ( W ) S ] x ( α vapρvapwvap ) ( Wvap ) NKII n~ n ( α vapρvapwvap ) ( Wvap ) L= 1 NKA n~ [ Alat ] [( α vapρvapwvap ) ( U vap ) Alat ] NKB n~ ( α vapρvapwvap ) ( U vap ) IB= 1 ( α K ) vap II JJ ( i, vap _ ent) J ( P JJ z t z z j n [ 2( W W ) ( W W ) ] vap j J J II J ent IB J L P ) S x J L J S x IB J J vap J K = IA= 1 wall _ vapj ent L= 1 J vap n [ ] n ( 2W W ) K 2( W W ) ( W W ) vapj n n n [ Γ W ( 1 η) Γ V ηγ V ] C vap z vap j vap J z vapj J vap L IA E z J IA ( i, vap _ liq) J liq L J + L= 1 E ent J vap + liq J S ( mom _ vap) J z J vap J z J L liq J SL x 2 J (6.2) Continuous Liquid Phase n [( αliqρliqw liq) ( αliqρliqw liq) ] NKJJ NG n~ n n~ on [ S ] x [( α ρ W ) ( W ) S ] x ( αliqρliqw liq) ( Wliq ) NKII n~ n ( αliqρliqw liq) ( Wliq) L= 1 NKA n~ [ Alat ] [( αliqρliqw liq) ( Uliq) Alat ] NKB n~ ( αliqρliqw liq) ( Uvap) IB= 1 K S wall_ liqj ( mom_ liq) J z J t n [ ] n ( 2W W ) + K 2( W W ) ( W W ) liqj J z z J j liqj L IB SJ x J = J L IB J IA= 1 ( i, vap_ liq) J L= 1 liq liq liq J vap z z j liq J J vap L IA vap IA L J liq J + L= 1 liq II JJ ( α ) ( P P ) S x JJ z n n [( 1 η) Γ W ( 1 η) Γ V ] C j II vap J z J z J J J L SL x 2 J E liq J (6.3) Entrained Liquid Phase n [( αentρliqwent ) ( αentρliqwent ) ] + + NKII NKJJ n~ n~ n n [ ( α entρliqwent ) ( Went ) SL ] xj ( W ) ( W ) L αentρliq ent ent L= 1 IB= 1 + NKA n~ [ Alat ] [( αentρliqwent ) ( U ent ) Alat ] NKB n~ ( αentρliqwent ) ( U ent ) K S wall _ entj ( mom _ ent) J z J t z NG n~ on [ S ] x ( α entρliqwent ) ( Went ) n [ ] n ( 2W W ) + K 2( W W ) ( W W ) entj J z j J entj IB SJ xj = J IB IA= 1 ( i, vap _ ent) J L J L L J J L L= 1 L=1 2 vap z j ent J J IA vap IA ent J ( α + z z ent II JJ ) n n [ ηγ W ηγ V ] C vap j z J J ( PJJ PII ) S z J x J E ent J S xj (6.4) 134

153 The terms in the phasic transverse momentum equations can be described as follows: Rate of change of Transverse Momentum ( ) = α k ρ kwk A t Rate of Transverse Momentum Efflux by Transverse Rate of Transverse Momentum Efflux by Transverse ( ) ( ) α k ρ kwkwk Az α k ρ kwkwk Az II Side Convection JJ Side Convection z z Rate of Transverse Momentum Efflux by Orthogonal Rate of Transverse Momentum Efflux by Vertical + ( ) + ( ( ) ) o o W U A TransverseConvection α k ρ kwk Wk S α k ρ k k k z IB NG NG Convection ( below) NG z Rate of Transverse Momentum Efflux by Vertical Pr essure Gradient force ( α ( ) ) k ρ kwku k Az IA P Convection ( above) α k Az z L Transverse Wall Shear ''' ± ( τ wall _ k ) A z z Iterfacial Continuous Transverse Momentum Exchange due to + Mass Transfer between fields ΓWk + SWk Drag between Vapor and Iterfacial Drag between Vapor and Drops Liquid ± ''' ( ) ( τ ''' i, ent _ vap ) A z z τ A i, liq _ vap z z Transverse Momentum + Source Term S mom The equations are solved first using currently known values for all variables to obtain an estimate of the new time flow. All explicit terms and variables are computed at the beginning of the current time step and are assumed to remain constant during the remainder of the time step. The semi-implicit momentum equations have the form: m & = a + b P + cm& + dm& + em& (6.5) liq vap ent where & liq = a b P c m& liq d m& vap ; m & vap a b P c m& liq d m& vap e m& ent m = ; and m& ent = a3 + b3 P + d m & vap e m& ent. The constants a 1, a 2, and a 3 (in kg / s ) represent the explicit terms such as momentum efflux 135

154 terms and the gravitational force; b 1, b 2, and b 3 (in gradient force term; c 1 and c 2 (in 2 m m s ) are the explicit portion of the pressure ) are explicit factors that multiply the liquid flow rate in the 2 wall and interfacial drag terms; d 1, d2, d 3, e 2, and e 3 (in m ) are the corresponding terms that multiply the vapor and entrained liquid flow rates. The equations can be written in a matrix form as c1 1 c2 0 d 2 d d e 2 e 3 1 m& m& m& liq vap ent = a a a b1 P b2 P b P 3 (6.6) and then solved by Gaussian elimination to obtain a solution for the phasic mass flow rates as a function of the pressure gradient across the momentum cell, P : & m liq = g1 h1 P (6.7a) & P (6.7b) m va p = g 2 h2 m& g h P c) ent = 3 3 (6.7 In regard to the new spacer grid model, the rate of change of momentum by directed crossflow can be added to the coefficients a in Equation 6.5, which are calculated as a t I = y t, (6.8) where t is the time difference (time step size), y is the spatial difference (gap length), and I t is the change of momentum. Thus, the total rate of momentum change in transverse directions will be modified as follows: 136

155 Rate of change of Transverse Momentum k k k A t ( α ρ W ) = ± [ Rate of Transverse Momentum Efflux by DirectedCrossflow] Rate of Transverse Momentum Efflux by Transverse Rate of Transverse Momentum Efflux by Transverse + ( ) ( ) α k ρ kwkwk A z α k ρ kwkwk Az II Side Convection JJ Side Convection z z Rate of Transverse Momentum Efflux by Orthogonal Rate of Transverse Momentum Efflux by Vertical + ( ) + ( ( ) ) o o k kw TransverseConvection α ρ α k k z IB k ρ kwk Wk S U A NG NG Convection ( below) NG z Rate of Transverse Momentum Efflux by Vertical Pr essure Gradient force ( ( ) ) α k ρ kwku k Az IA P Convection ( above) α k Az z L Iterfacial Drag between Vapor and Transverse Wall Shear Iterfacial Drag between Vapor and Drops ''' ± Continuous Liquid ± ''' ( τ wall _ k ) A ( ) ( ) τ i ent vap A z z ''', _ z z τ i, liq _ vap A z z Transverse Momentum Exchange due to + Transverse Momentum Mass Transfer between fields + Source Term S mom ΓWk + SWk Calculation of the Transverse Momentum Change by Directed Crossflow During the development of the new methodology for CFD based subchannel modeling of the directed crossflow the goal was to establish a model that: 1) represents the convective nature of the phenomenon; 2) is simple and can be easily implemented into the subchannel momentum equations; and 3) is efficient in regard to the CPU time. Three alternative modeling approaches (the so-called candidates) were considered for preliminary investigations. While the first two candidates utilize CFD predictions for the velocity curl in a lateral plane for evaluation of the lateral momentum change, the third candidate uses CFD prediction for the lateral velocity. Based on performed comparative analyses the third candidate was selected for further development since it performs with a high accuracy and is numerically stable. 137

156 Short descriptions of candidates 1 and 2 are given in Appendix D. The description of the third method is following hereinafter. Consider two fluid volumes, geometrically fully identical, connected to each other through a gap with an area A lat = S x (see Figure 49). The fluid in both volumes is at isothermal conditions ij and is moving in axial direction x with a constant velocity U U inlet. Assume that at given elevation along the length there exits a force F that results in a non-zero fluid velocity V in the lateral direction y. Since, the model is constructed to avoid pressure and temperature gradients in a lateral plane, the force can be defined as F = m& lat V, (6.9) where m& lat is the mass flow rate in direction y equal to m& = V ρ, (6.10) lat A lat where ρ is the fluid density. Then, the force acting on the fluid in the gap region will be given as F = m& V = V ρ 2 lat A lat (6.11) and it is equal to the momentum change I lat in the lateral direction y over a time interval t : I & lat I t lat 2 = F = V ρ Alat. (6.12) Consider now a rod bundle of geometrically identical subchannels with uniform distribution of the power and the inlet flow. Let obstacles exist in each subchannel and cause a change of the 138

157 velocity vectors, which results in a non-zero lateral flow. At such conditions the crossflows existing in the bundle will be only due to velocity deflection on the obstacles. If we can predict in advance the magnitude and the direction of the resulting lateral velocities, the above described model can be used for prediction of the lateral momentum change due to specific mixing vane configurations in fuel rod bundles - the coefficients a in Equation 6.8 can be corrected to account for the additional momentum change I & lat as calculated by Equation However, the lateral velocity predicted with the CFD code will account for the transverse pressure losses due to skin friction on the rods. Therefore, action has to be taken either to correct the CFD results or to terminate the modeling of the transverse friction pressure losses in the subchannel model. x Channel i S ij Channel j y x flow Figure 49: Schematic of two intra-connected fluid volumes The subchannel analysis codes are not able to calculate such local changes in the velocity field. Fortunately, we can utilize the features of computational fluid dynamics to evaluate the lateral 139

158 velocity across the gaps between the adjacent subchannels. Under the consideration that the inlet fluid velocity, the fluid density, and the area available for lateral flow exchange in the simulated bundle correspond to ones used in the CFD calculations, the force to be added to the momentum equations of the subchannel code can be given as F = m& V V CFD CFD CFD 2 lat _ SG lat = ( ) ρ CFD A CFD lat (6.13) However, since the CFD calculations are costly in regard to the computational time, it is inefficient to perform CFD pre-calculations for each particular case to be simulated with the subchannel cod e. Moreover, the CFD calculations are performed at given axial velocity, which is assumed to remain constant over the axial length. This is not the case of the subchannel analysis, where not only the inlet velocity could be different form the one used in the CFD predictions, but it usually varies along the axial length. Therefore, the model has to be made applicable to any flow conditions to be simulated by the subchannel code, or in other worlds, the CFD predictions for the lateral velocity have to be scaled to the actual subchannel conditions. The scaled lateral velocity V * can be further used for calculation of the force F _ to be added to the subchannel code lat SG momentum equation: F lat _ SG I t & SCH * = = mlat V (6.14) The scaling involves the definition of the ratio of the lateral velocity as predicted by the CFD code and the inlet axial velocity in the CFD model, the so-called spacer grid lateral convection factor: CFD V f lat _ SG =. (6.15) U CFD inlet 140

159 It is dimensionless parameter that gives the information how the magnitude of lateral velocity depends on the magnitude of the inlet velocity. The spacer grid lateral convection factor is a function of the axial distance from the grid. During the evaluation of the subchannel crossflow m& SCH lat, the F-COBRA-TF donor cell logic and upwind discretization approach have to be taken into account. Implying such a scaling procedure will reduce the required CFD pre-calculations to modeling of the sample geometries only Verification of the Proposed Directed Crossflow Model The functionality of the new model was verified against CFD simulations. A 2 2 channels model of FOCUS TM spacers was developed at AREVA NP GmbH. It consists of four geometrically identical subchannels arranged in a 2 2 array. The fluid in all four subchannels is water at temperature of 300 C and inlet axial velocity of 5 m/s. There are no heated walls. The fluid properties remain constant along the axial length. The spacer grid configuration is such that each subchannel contains a pair of two rotated and mirrored mixing vanes, which create intra-channel swirl downstream of their top edges and directed crossflow between adjacent subchannels with meandering patterns. The mixing vanes configuration is shown in Figure 50. 3D views of the FOCUS TM spacer is given in Figure 51. The chosen fluid conditions assure no diffusive effects due temperature gradient and therefore lateral flows are driven only by convective processes. The model is summarized in Table 7. In total four CFD calculations were performed, in which the mixing vane angle varied from 10 to 40 degree. The lateral (UW) velocities were extracted at every 10 mm axial distance. The CFD results for flow distribution are given in Table E-1 through Table E-3 of Appendix E. It was 141

160 observed that immediately downstream of the grid the lateral flow structures exhibit swirling flow created by the mixing vanes. Because the mixing vanes were mirrored, the swirls in any two neighboring subchannels are rotating in opposite directions and thus creating a crossflow through the gaps. The magnitude of the swirl, and respectively the magnitude of the crossflow, is decreasing further downstream of the spacer. Larger is the mixing vane angle, stronger is the crossflow. Figure 50: Mixing vanes configuration in the 2 2 FOCUS TM model Figure 51: 3D views of the FOCUS TM spacer 142

161 Table 7: Description of the 2x2 channels model used in the STAR-CD calculations Thermal Hydraulic Analyses of Flow and Heat Transfer Coupled Subchannel Analyses STAR-CD Calculation Characterization of Run Objective Model Boundary Conditions Properties Method coupled 2 x 2 subchannels channels with equal inlet velocities and temperatures mirrord and rotated mixing vanes to study flow distribution with cross flow net mass transfer between the subchannels by directed crossflow rod diameter pitch 9.5 mm 12.7 mm length 540 mm Inlet velocity 5 m/s strip thickness of 0.4 mm, vane angle 10, 20, 30, and 40 Outlet Gaps between rods Walls Specific heat Solver Discretization Outlet / Pressure condition symmetry condition no-slip, adiabatic, smooth Temperature at inlet 300 C Turbulence at inlet Intensity 5%, length 2 mm Density kg/m³ Lam. Viscosity Thermal conductivity e-5 kg/m/s 0.56 W/m²/K 4457,3333 J/kg/K Simple, CG + AMG Upwind Accuracy Turbulence standard k-ε, wall fucnction typical cell dimension 0.3 mm From the axial distribution of the lateral velocities, shown in Figure E-1 through Figure E-4 of Appendix E, it is seen that for small declination angles (10 degrees) lateral velocities through all the gaps are equal in magnitude and have same distribution over the axial length. However, for the larger angles the distribution is not longer symmetrical. Lateral velocities through the east and south gaps have similar qualitative and quantitative behavior. One very interesting finding is the change of the velocity direction (sign) at 30/36 hydraulic diameters downstream of the mixing vanes. Lateral velocities through the west and north gaps also have similar magnitude and axial distribution, but there is no change of the sign. Table E-2 and Table E-3 of Appendix E show the 143

162 lateral velocity field further downstream of the spacer. The asymmetry effect might be caused by a migration of the swirling flow away from the center of the subchannel when the flow is developing downstream of the vanes. For example (Table E-2), in the north-east and south-east subchannels the centers of swirling flow move away from the east gap leading to less crossflow through it. At the same time, in the north-west and the north-east gap the swirls move toward the north gap and thus creating crossflow through that gap. Nevertheless that such an effect might be characterized as a numerical problem of the CFD calculations, very similar experimental results were reported by Conner (Conner, M. E. et al., 2004). As above mentioned, the axial distributions of the lateral velocity over one spacer grid span were not symmetrical for large declination angles. However, for the following studies the lateral velocities w ere averaged over the four gaps and a single value was used in the performed analyses. The CFD predictions for the lateral velocity and the lateral mass flux are shown in Figure 52 and Figure 53. The lateral convection factors f lat _ SG, evaluated with Equation 6.15, are plotted in Figure 54. In these figures the length is extended to 3 m, which corresponds to the heated length of the 5 5 rod bundle with FOCUS TM spacer, which will be used later for validation of the model. There are five spacer grids instrumented along the length as depicted in Figure

163 Lateral Velocity CFD Velocity, m/s 2,00 1,75 1,50 1,25 1,00 0,75 0,50 0,25 0,00 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 Axial elevation, m 10 deg 20 deg 30 deg 40 deg Figure 52: CFD predictions for the lateral velocity for different mixing vane angles Lateral Mass Flux CFD Mass flux, kg/m 2 s deg 20 deg 30 deg 40 deg Axial elevation, m Figure 53: CFD predictions for the lateral mass flux for different mixing vane angles 145

164 Lateral Convection Factor F, - lat_conv deg 20 deg 30 deg 40 deg Axial position, m Figure 54: Lateral convection factor for different mixing vane angles EOHL 0.04 m m m 3m m m m BOHL Figure 55: Schematic of the spacers positions in the 5x5 bundle with FOCUS TM spacer 146

165 The data exchange between the CFD code and the subchannel code is similar to one described in Section An interface module was developed, which 1) contains detailed information for the lateral convection factor in a 2D table format; 2) contains additional information for the orientation of the directed crossflows in regard to the global coordinate system; and 3) maintains the exchange between the CFD data base and F-COBRA-TF. Again, for the purposes of routine safety analyses, the code can be supplied with sets of data representing spacer designs that are currently used. For new design studies, an experienced user can create a new data set based on more recent CFD calculations. The flow chart of the directed crossflow modeling and examples for the obtained CFD data sets of the lateral convection factor are given in Appendix F. F-COBRA-TF simulations of the 2 2 channel model of FOCUS TM spacer were carried out. The predicted lateral velocity and mass flux are shown in Figure 56 and Figure 57. It can be seen that the proposed methodology is able to reproduce the axial variation of the lateral mass flux between the adjacent subchannels in both qualitative and quantitative manners. The obtained results demonstrate the functionality of the proposed methodology and therefore the model was implemented in the latest version F-COBRA-TF for simulation of directed crossflow created by different velocity deflectors. The validation of the new modeling is presented in the next section. 147

166 Lateral Velocity F-COBRA-TF y,m/s locit Ve 2,00 1,75 1,50 1,25 1,00 0,75 0,50 0,25 10 deg 20 deg 30 deg 40 deg 0,00 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 Axial elevation, m Figure 56: F-COBRA-TF predictions for the lateral velocity for different mixing vane angles Lateral Mass Flux F-COBRA-TF /m 2 s Mas s flux, k g deg 20 deg 30 deg 40 deg Axial elevation, m Figure 57: F-COBRA-TF predictions for the lateral mass flux for different mixing vane angles 148

167 6.2.4 Validation of the Proposed Directed Crossflow Model Mixing experiments performed with SIEMENS Test Section 53 (DTS53) were used for validation of the proposed model. The tests were conducted at the Columbia University, New York in 1990 for SIEMENS KWU (AREVA NP GmbH) PWR test section TDS53. The bundle description and measured data for are available in Vogel, Chr. et al., Description of the DTS53 Experiment In total twenty-one tests were performed in a 5 5 rod bundle array. The bundle geometry is summarized in Table 8. The radial power distribution was nonuniform: the sixteen peripheral rods had a relative power of 0.94 and the nine internal rods had a relative power of The axial power distribution was uniform. The operational conditions are given in Table 9 and Table 10. The bund le was equipped with FOCUS TM spacer g rids with straight inlet edges, oval dimples, and diagonally oriented springs. The s trips have thickness of mm and height of 40 mm. Split m ixing vanes were attached at the upper edge of the strip. There are five spacers along the heated l ength equidi stantly distributed with a span of 545 mm ( see Figure 55). The experimental data include exit subchannel fluid temperatures in a 6 6 matrix and differential pressure drop measurements. The uncertainties of the temperature measurements are reported being between 0.61 a nd 1.0 K for the absolute temperature in the range of 205 ºC to 343 ºC ( Fighe tti, C. et al., 1990). If the measured temperature exceeded the saturation temperature by 5 degrees, it was set to a negative value in the data base. The total error in absolute pressure measurements is reported being ± 0.41 bars. 149

168 Table 8: Geometrical characteristics of test section DTS53 Parameter Value Lattice 5 5 Number of heater rods 25 Number of guide tubes 0 Pitch, m Heater rod outside diameter, m Heated length, m 3 Rod to wall clearance, m Corner radius, m Bundle flow area, m Table 9: Range of conditions for test section DTS53 Parameter Range Exit pressure, bar Fluid inlet temperature, ºC Average mass flux, kg/m 2 -s Bundle power, kw Table 10: Tests operational conditions Test Inlet Flow Rate, Inlet Enthalpy, Bundle Power, Exit Pressure, Inlet Temperature, ºC kg/s kj/kg kw bars

169 F-COBRA-TF Model F-COBRA-TF model of the 5 5 bundle was developed. It is a full bundle model that consists of 36 subchannels, each divided into 75 equidistant axial nodes of 40 mm height. Geometrical characteristics are given in Table 11. A schematic of the model is shown in Figure 58 and the mixing vanes arrangement and meandering flow patterns established in the bundle are illustrated in Figure 59. Inlet boundary conditions of flow rate and enthalpy and exit boundary conditions of pressure are applied. The spacer grids effects are m odeled as velocity head losses in a vertical flow. An average value of 1.12 for the pressure loss coefficient, as provided in the tests specification, is applied to all subchannels. Experimental conditions and the bundle geometry ar e expected to result in a lateral mass flux caused by 1) turbulent mixing due to density and void fraction gradients; 2) diversion crossflow due to lateral pressure gradients; and 3) directed crossflow due to velocity deflection on the mixing vanes surfaces. Turbulent mixing is modeled using a single-phase mixing coefficient, as predicted with the correlation by Rogers and Rosehart (Rogers, J. T. and Rosehart, R. G., 1972) and Beus model (Beus, S. G., 1970 ) for enhanced two-phase turbulent mixing. The directed crossflow model requires additional input information for the orientation (sign) of the directed crossflow. The F-COBRA-TF logic for lateral flows assumes a positive flow from a low-numbered subchannel to a high-numbered subchannel. If the crossflow has an opposite direction it is considered negative. Therefore the orientation of the directed crossflow created by the 151

170 mixing vanes has to be specified in advance. This information is supplied by an additional input file (dirct_data.inp in Figure F-1 of Appendix F). A negative sign following the gap numbers in Figure 58 indicates that the crossflow is directed from a high-numbered subchannel to a low-numbered subchannel, and vise versa, a positive sign indicates that the crossflow is directed from a lownumbered subchannel to a high-numbered subchannel. Another required input is the declination angle of the mixing vanes. For the FOCUS TM spacer it is 22 degrees. Table 11: Geometrical characteristics of the F-COBRA-TF model Corner Subchannel Flow area, m Wetted perimeter, m Gap width to side subchannel, m Gap length to side subchannel, m Side Subchannel Flow area, m Wetted perimeter, m Gap width to corner subchannel, m Gap length to corner subchannel, m Gap width to side subchannel, m Gap length to side subchannel, m Gap width to internal subchannel, m Gap length to internal subchannel, m Internal Subchannel Flow area, m Wetted perimeter, m Gap width to side subchannel, m Gap length to side subchannel, m Gap width to internal subchannel, m Gap length to internal subchannel, m

171 Figure 58: Schematic of the F-COBRA-TF 5 5 model of DTS53 mixing test bundle Figure 59: Mixing vanes arrangement and meandering flow patterns in the 5x5 bundle with FOCUS spacer TM 153

172 F-COBRA-TF Results F-COBRA-TF calculations of the TDS53 experiments were carried out utilizing four different modeling options: OPTION 1: The spacer grid effects are modeled by pressure losses in a vertical flow. A pressure loss coefficient of 1.12 is applied to all subchannels. The turbulent mixing is modeled with the correlation by Rogers and Rosehart for the singlephase mixing coefficient (Rogers, J. T. and Rosehart, R. G., 1972) and Beus model for two-phase mixing (Beus, S. G., 1970). OPTION 2: The spacer grid effects are modeled by pressure losses in a vertical flow and a directed crossflow modeled for all the gaps. A pressure loss coefficient of 1.12 is applied to all subchannels. The turbulent mixing is modeled with the correlation by Rogers and Rosehart for the singlephase mixing coefficient (Rogers, J. T. and Rosehart, R. G., 1972) and Beus model for two-phase mixing (Beus, S. G., 1970) OPTION 3: The spacer grid effects are modeled by pressure losses in a vertical flow and a directed crossflow modeled for the internal gaps only (gaps between internal subchannels). A pressure loss coefficient of 1.12 is applied to all subchannels. The turbulent mixing is modeled with the correlation by Rogers and Rosehart for the single- phase mixing coefficient (Rogers, J. T. and Rosehart, R. G., 1972) and Beus model for two-phase 154

173 mixing (Beus, S. G., 1970). OPTION 4: The spacer grid effects are modeled by pressure losses in a vertical flow. A pressure loss coefficient of 1.12 is applied to all subchannels. The turbulent mixing is modeled by a single-phase mixing coefficient of 0.04, which is a value found by fitting the COBRA 3CP results to the experimental data. The reason for introducing Option 3 is that the CFD data for the lateral velocity were evaluated only for the particular configuration of 2 2 array of identical subchannels. In our case, 5 5 bundle, those correspond to the four central subchannels. There is no CFD data currently available for the other geometrical configurations found in the simulated 5 5 bundle (internal-to-side subchannels, side-to-side subchannels, and corner-to-side subchannels). The reason for introducing Option 4 is to compare the results obtained with the new model to the ones obtained with the current approach used in AREVA NP GmbH. An automatic procedure, the so-called 5 5 mixing test matrix, for input decks generation, code execution, and extraction of the necessary output information was created for the DTS53 mixing experiments. The F-COBRA-TF predictions for the mixture temperature at the subchannels exits were compared to the measured data. For each test point (the so-called run) the mean values and the standard deviations of the absolute temperature difference T calc T exp and the temperature Tcalc T differen ce relative to the temperature rise along the heated length out in T T exp exp exp were calculated as follows: 155

174 Mean value of the absolute temperature differences : abs T n N abs Tn abs n= 1 T =, where N T = T T (6.18) abs n calc exp n abs T n Standard deviation of the absolute temperature differences : N abs abs ( Tn T ) abs 1 2 σ = (6.19) N 1 n= 1 rel T n Mean value of the relative temperature differences : N = T n T rel n 1 calc T rel exp T =, where Tn = (6.20) out in N T T exp exp n rel T n Standard deviation of the relative temperature differences : N n= 1 rel ( Tn T ) N rel 1 2 σ = (6.21) 1 where n is the number of analyzed test points (runs). Statistical analyses were performed for four data sets: 1) All subchannels; 2) Peripheral subchannels only; 3) All internal subchannels; 4) Four central subchannels only. Results are given in Table 12 through Table 19. Table 20 shows the temperature differences 156

175 ( T calc Texp ) subchannel _ i for each subchannel i averaged over the calculated test points. There is no value given for the first subchannel, because only two measured points are available for this subchannel. Results can be summarized as follows: 1. The original F-COBRA-TF models, which do not simulate the change in the lateral momentum due to velocity deflection, mispredict the fluid temperature distribution at the bundle exit with 3.5 ºC in average. There is a strong overprediction for the central region of the bundle and underprediction for the peripheral region. This is an indication that the lateral transfer is underestimated by the code: the fluid surrounding the more heated rods in the central region is not redistributed to the less heated peripheral subchannels. 2. Applying an additional force calculated by Equation 6.14 to the all lateral momentum cells, regardless of their location in the computational domain (Option 2), results in an improvement of the overall prediction, but not for the peripheral region, where the calculated fluid temperature becomes significantly overpredicted. In other words, the hotter fluid from the central part is overforced to the bundle periphery. These results are not unexpected. We have applied a force, which was calculated using lateral convection factor derived from CFD pre-calculations for geometry corresponding to four central subchannels, to a very different configuration of adjacent subchannels. At the same time, there is an impressive improvement for the central subchannels: the mean value of the absolute temperature differences is reduced from 6.8ºC in average to only 1.7ºC in average. 3. Learning the lesson from the above discussed results, in the third set of evaluations (Option 3) the force was applied only to the gaps connecting internal-to-internal subchannels. Since, there 157

176 are no CFD pre-calculations for the corner-to-side, side-to-side, and side-to-internal subchannels configurations, no force was applied to those gaps. Of course, this is not a truly physical approach, but it will assure that incorrectly calculated rates of transverse momentum change will be not applied to the subchannel equations. As it was expected, the results show no significant change in the code predictions for the internal and central subchan nels, as compared to the Option 2, but the agreement with the experimental d ata for the peripheral subch annels is improved. 4. In the forth set of eva luations (O ption 4 ) the modeling approach u sed by AREVA NP GmbH for simulation of the DTS53 experiments was utilized: the crossflow effects were modeled by an e nhanced mixing coeffic ient of 0.04 for both single- and two-phase flow conditions; this value was found by fitting the COBRA 3CP results to the experimental data. It can be seen that this approach gives a worse agreement with the experimental data comparing to Option 3. The validation of the proposed modeling of directed cros sflow in rod bundles against AREVA NP GmbH DTS53 mixing experiments shows very promising results. Nevertheless that the new model was partially applied, due to the lack of full set of CFD dat a, it already gives better representation of the flow distr ibution insi de rod bundles than the recently used metho dology of simulating convective lateral transfers with an enhanced turbulent mixing. This indicates that the two effects, turbulent mixing and convective mixing, have to be modeled separately in the momentum equations of the subchannel codes. Additionally, the computational performance and efficiency of the modified code version was investigated. Comparisons of the code temporal convergence are given in Figure 60. It can be seen that the new model does not result in a prolonged CPU time. Performed stability analyses showed no distortions in the code convergence on mass and heat 158

177 balance due to the new modeling (Figure 61 and Figure 62). Table 12: Statistical analyses for da ta set 1: all subchannels. Mean value and standard deviation of absolute temperature differences Run Number OPTION 1 OPTION 2 Original F-COBRA- D irected Crossflow TF Models through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRAβ = TF Models, 0.04 Mean Standard Mean Standard Mean Standard Mean Standard Value Deviation Value Deviation Value Deviation Value Deviation average

178 Table 13: Statistical analyses for data set 2: peripheral subchannels only. Mean value and standard deviation o f absolute temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation average

179 Table 14: Statistical analyses for data set 3: internal subchannels. Mean value and standard deviation of absolute temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation average

180 Table 15: Statistical analyses for data set 4: central subchannels only. Mean value and standard deviation of absolute temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation average

181 Table 16: Statistical analyses for data set 1: all subchannels. Mean value and standard deviation of relative temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation 8 6.9% 5.1% 6.1% 4.7% 5.4% 4.6% 5.6% 4.0% 9 6.3% 4.4% 5.8% 4.7% 5.0% 4.3% 5.2% 4.2% % 4.7% 6.4% 5.5% 5.6% 5.3% 6.1% 4.9% % 4.3% 6.3% 5.3% 5.4% 4.9% 5.8% 4.8% % 4.4% 6.1% 5.0% 5.3% 4.8% 5.6% 4.7% % 4.2% 5.8% 4.9% 4.9% 4.4% 5.3% 4.5% % 5.5% 8.6% 8.9% 7.7% 7.2% 8.0% 8.3% % 5.1% 7.5% 7.7% 6.4% 6.1% 6.9% 7.1% % 4.0% 6.3% 4.2% 5.4% 3.7% 5.7% 3.9% % 3.8% 5.9% 4.4% 5.1% 4.1% 5.4% 4.0% % 3.9% 5.9% 4.6% 5.2% 4.4% 5.4% 3.8% % 4.6% 6.1% 4.8% 5.5% 4.3% 5.8% 4.2% % 4.0% 4.9% 2.7% 4.0% 2.6% 4.5% 2.1% % 4.0% 4.9% 2.7% 4.0% 2.4% 4.5% 2.1% % 4.8% 5.6% 4.0% 4.8% 4.0% 5.2% 3.7% % 4.5% 6.1% 4.5% 5.2% 4.2% 5.7% 3.8% % 4.4% 6.2% 4.3% 5.2% 4.2% 5.6% 3.7% % 4.4% 5.1% 3.1% 4.3% 3.1% 4.8% 2.7% % 4.1% 4.8% 2.2% 3.9% 2.5% 4.3% 1.9% % 4.4% 5.1% 3.2% 4.3% 3.1% 5.1% 2.6% % 4.5% 5.4% 3.6% 4.7% 3.5% 5.3% 3.2% average 6.5% 5.9% 5.1% 5.5% 163

182 Table 17: Statistical analyses for data set 1: peripheral subchannels only. Mean value and standard deviation o f relative temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation 8 4.6% 2.8% 8.4% 5.2% 6.9% 5.3% 7.0% 4.4% 9 5.0% 3.1% 7.8% 5.5% 6.4% 5.4% 6.5% 5.2% % 3.0% 8.8% 6.4% 7.3% 6.4% 7.5% 6.0% % 3.5% 8.6% 5.8% 7.0% 5.7% 7.5% 5.5% % 4.0% 8.5% 5.6% 6.9% 5.8% 7.4% 5.6% % 4.0% 7.9% 5.5% 6.3% 5.4% 6.8% 5.5% % 5.4% 11.8% 10.6% 9.8% 8.8% 10.5% 10.1% % 5.1% 10.2% 9.1% 8.4% 7.3% 9.3% 8.5% % 4.2% 7.6% 4.8% 6.2% 4.5% 6.7% 4.7% % 3.5% 7.6% 5.1% 6.0% 5.2% 6.4% 4.9% % 3.2% 7.5% 5.6% 6.0% 5.6% 6.4% 4.8% % 2.3% 7.7% 5.7% 6.0% 5.0% 6.3% 4.8% % 3.4% 5.5% 3.0% 3.8% 3.0% 4.5% 2.4% % 3.8% 5.5% 2.9% 3.9% 2.7% 4.6% 2.3% % 3.3% 6.5% 4.7% 5.0% 4.3% 5.4% 4.0% % 3.3% 7.6% 5.4% 5.9% 5.1% 6.4% 4.6% % 3.5% 7.5% 5.3% 5.8% 4.9% 6.3% 4.5% % 3.6% 5.6% 3.7% 4.0% 3.3% 4.7% 2.9% % 3.5% 4.9% 2.2% 3.0% 2.2% 3.8% 1.6% % 3.0% 6.2% 3.8% 4.5% 3.6% 5.2% 3.0% % 2.8% 6.0% 4.1% 4.7% 3.5% 5.0% 3.2% average 5.6% 7.5% 5.9% 6.4% 164

183 Table 18: Statistical analyses for data set 1: internal subchannels. Mean value and standard deviation of relative temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peripheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation Mean Value Standard Deviation 8 9.5% 5.9% 3.5% 2.3% 3.6% 2.7% 4.0% 2.9% 9 7.9% 5.3% 3.4% 1.5% 3.3% 1.5% 3.7% 1.8% % 5.7% 3.6% 2.2% 3.5% 2.6% 4.4% 2.5% % 4.9% 3.3% 2.1% 3.3% 2.3% 3.6% 2.4% % 4.8% 3.2% 1.6% 3.2% 1.5% 3.5% 1.7% % 4.5% 3.2% 1.8% 3.1% 1.7% 3.4% 1.7% % 5.5% 4.7% 3.5% 5.1% 3.4% 5.0% 3.9% % 5.2% 4.0% 3.0% 3.9% 2.7% 4.0% 3.2% % 4.0% 4.7% 2.6% 4.5% 2.1% 4.6% 2.2% % 4.3% 4.1% 2.3% 4.2% 2.1% 4.2% 2.1% % 4.6% 4.1% 2.1% 4.2% 2.2% 4.5% 2.0% % 5.6% 4.7% 3.4% 5.0% 3.7% 5.3% 3.6% % 4.5% 4.3% 2.3% 4.2% 2.3% 4.5% 2.0% % 4.2% 4.4% 2.4% 4.2% 2.2% 4.5% 2.0% % 5.6% 4.7% 3.2% 4.6% 3.9% 5.0% 3.5% % 5.4% 4.7% 2.8% 4.5% 3.2% 4.9% 2.8% % 5.2% 4.8% 2.7% 4.7% 3.2% 5.0% 2.8% % 4.9% 4.7% 2.6% 4.5% 3.0% 4.9% 2.5% % 4.5% 4.6% 2.2% 4.6% 2.5% 4.8% 2.1% % 5.0% 4.1% 2.4% 4.2% 2.8% 4.9% 2.3% % 5.1% 4.8% 3.1% 4.8% 3.5% 5.5% 3.3% average 7.5% 4.2% 4.1% 4.5% 165

184 Table 19: Statistical analyses for data set 1: central subchannels only. Mean value and standard deviation of relative temperature differences Run Number OPTION 1 Original F-COBRA- TF Models OPTION 2 Directed Crossflow through All Gaps OPTION 3 No Directed Crossflow through Peri pheral Gaps OPTION 4 Original F-COBRA- TF Models, β = 0.04 Mean Value Standard Deviation Mean Standard Value Dev iation Me an Va lue Standard Deviation Mean Value Standard Deviation % 3.2 % 2.5% 1.3% 2.8 % 1.6% 3.8% 2.7% % 3.5% 2.3% 0.9% 2.3% 1.1% 3.1% 2.7% % 3.5% 2.3% 1.6% 2.5% 1.9% 5.0% 2.9% % 2.8 % 1.7% 0.5% 1.8% 0.7% 2.2% 2.1% % 3.2 % 2.1% 0.5 % 2.2 % 0.7% 2.6% 2.2% % 2.6 % 1.7% 1.2 % 1.6 % 1.2% 1.9% 1.4% % 4.8 % 3.1% 1.3 % 3.1 % 1.8% 3.2% 3.5% % 4.5 % 2.9% 1.2 % 2.8 % 1.6% 2.4% 3.0% % 4.0 % 3.2% 2. 4% 3.1 % 2.0% 2.5% 1.8% % 3.8 % 2.7% 1. 8% 2.6 % 1.7% 2.4% 1.9% % 4.0 % 2.4% 1. 8% 2.4 % 1.9% 2.9% 2.2% % 3.2% 2.5% 1.7% 2.8% 2.1% 4.2% 2.8% % 4.2 % 2.6% 2.6% 2.6% 2.5% 2.8% 2.1% % 4.1 % 2.6% 2.4% 2.6% 2.3% 2.7% 2.1% % 4.5 % 2.9% 1. 7% 2. 9% 2.2% 3.6% 2.9% % 4.1 % 2.6% 1. 6% 2.7 % 1.7% 3.2% 2.1% % 4.6 % 3.0% 2. 0% 3.0 % 1.9% 3.2% 2.4% % 4.4 % 2.8% 2. 4% 2. 7% 2.5% 3.0% 2.3% % 4.6 % 3.1% 2. 8% 3. 0% 2.7% 2.9% 2.5% % 3.3 % 2.3% 1. 8% 2. 8% 2.3% 4.7% 2.9% % 3.0% 3.7% 2.5% 4.4% 2.6% 6.1% 2.7% average 11.7% 2.7% 2.6% 3.3% 166

185 Table 20: Statistical analyses: Temperature differences for each subchannel i averaged over the calculated test points N ( Tcalc Texp ) subchannel _ i OPTION 1: n= 1 N n/a N ( Tcalc Texp ) subchannel _ i OPTION 2: n= 1 N n/a N ( Tcalc T exp ) subchannel _ i OPTION 3: n=1 N n/a N ( Tcalc Texp ) subchannel _ i OPTION 4: n= 1 N n/a

186 CPU time per time step, s Code Convergence time step standard model spacer grid model Time step number Figure 60: Comparison of the code temporal convergence when modeling directed crossflow Mass Balance 100 standard model spacer grid model Deviation from steady state, % Time, s Figure 61: Comparison of the code convergence on mass balance when modeling directed crossflow 168

187 Heat Balance 100 standard model spacer grid model Devi ation f rom steady state, % Time, s Figure 62: Comparison of the code convergence on heat balance when modeling directed crossflow 169

188 6.3 Concluding Remarks Most of the subchannel codes do not have advanced mechanistic models for evaluation of the lateral flow rates caused by a change of the axial velocity vector into a certain direction. A very coarse approach is commonly used: the contribution of the lateral convection to the crossflow is approximated by artificially increasing the single-phase mixing coefficient to calculate a crossflow with a magnitude sufficient to reproduce experimental results of the available mixing tests. To overcome the above discussed modeling deficiency, the new generation subchannel codes must separate the treatment of the diffusive spacer grid effects and the convective spacer grid effects. A new methodology for modeling of the directed crossflow created by spacers based on CFD analyses was proposed. The required modifications of the subchannel code F-COBRA-TF were presented. The results of the model validation against experimental data confirm the new model applicability for design studies and safety evaluations. 170

189 CHAPTER 7 CONCLUSIONS Due to its comprehensive modeling features, the thermal-hydraulic subchannel code COBRA- used for LWR safety margins evaluations and design analyses. Under the name F- TF is widely COBRA-TF and in the framework of a joint research project between PSU and AREVA NP GmbH the code has undergone through an extensive validation/verification and qualification program. To make the F-COBRA-TF code applicable for industrial applications, the code programming, numerics, and basic models were improved. The current version of F-COBRA-TF is considered to be a good base for implementation of new modeling capabilities. In order to enable the code for industrial applications including LWR safety margins evaluation s and design analyses, the code modeling capabilities related to the spacer grid effects were revised and substantially improved. The state-of-the-art in the modeling of the spacer grid effects on thermal-hydraulic performance of the flow in LWR rod bundles employs numerical experiments performed by computational fluid dynamics calculations. The capabilities of the CFD codes are usually being validated against mock-up tests. Once validated, the CFD predictions are then used for improvement and development of more sophisticated subchannel codes models. Because of the involved computational cost, CFD codes can not be yet used for full bundle predictions, while subchannel codes equipped with advanced physics are a powerful tool for LWR safety and design analyses. The unique contributions of this PhD research are seen as development, implementation, and 171

190 qualification of an innovative spacer grid model utilizing CFD results within the framework of a subchannel analysis code. The most important outcomes of the performed research are: Based on an extensive literature review and theoretical comparative analyses of the existing F-COBRA-TF conservation equations and the full Reynolds-averaged Navier- Stokes equations the missing physics on the subchannel-level modeling and the phenomena directly influenced by spacer grids were identified. Models for some of the missing phenomena in the current spacer grid modeling in the subchannel analysis codes were developed. Those are the spacer grid effects on the mass, heat, and momentum exchange mechanisms such as turbulent mixing and the lateral flow patterns created by specific configurations of the grid structural elements (directed crossflow). A methodology was developed for off-line coupling between the CFD code STAR-CD and the subchannel code F-COBRA-TF. The developed coupling scheme is flexible in axial mesh overlays. It is developed in a way to be easily adapted to other CFD/subchannel codes. Separate modeling of the spacer grid effects on the diffusive and on the convective processes was proposed and tested. The implemented models do not affect the code convergence and do not result in prolonged CPU times. The implemented directed cross-flow modeling capabilities were successfully validated against experimental data. As a future work, models for the intra-subchannel swirl and the single-phase pressure losses 172

191 in transverse direction have to be developed. The intra-subchannel swirl created by the split vanes improves the heat transfer from the rod surface to the liquid. The swirl has only a local convective effect that cannot be taken into account at a subchannel level. The heat transfer enhancement by swirling flow can be quantified by means of CFD calculations. The idea is using CFD prediction for the velocity curl to evaluate a surface or volume average tangential velocity that will be added to the axial velocity vector. The increasing axial velocity will result in an enhanced heat transfer. The dependence of the swirl intensity of the vane angle can be correlated and a decay function can be defined. Further, when two-phase conditions are considered, there are two other effects that should be addressed: formation of bubbles pockets next to the rod surfaces and increase of deposition rate by the swirl. In the axial direction the pressure losses due to spacers are already modeled in F-COBRA-TF by applying spacer grid loss coefficients. As described in Chapter 2, along with the wall drag coefficients they define explicit factors that multiply the liquid and vapor flow rates. In the transverse direction the pressure losses due to spacers may be modeled by following the F-COBRAuid friction on the spacer surfaces, at an input specified location, can be defined. The horizontal TF logic for the horizontal pressure loss coefficient at a given gap. An additional term, due to the fl spacer loss coefficients may be determined from experimental data or CFD calculations. The question is how significant in magnitude are such pressure losses. 173

192 REFERENCES AEA Technology Engineering Software ltd., (1999): CFX-TASCflow Computational Fluid Dynamics Software AEA Technology Oxfordshire, (1997): CFX International, CFX-4.2 Solver Akiyama, Y. et al., (1995): Void Fraction Measurement of PWR Fuel Assembly and Improvement of PWR Core Analysis, Proceedings: Third International Seminar on Subchannel Analysis (ISSCA-3), Stockholm, Sweden Allaire, G. (1995): Solving Linear Systems in FLICA-4, a Thermal-Hydraulic Code for 3-D Transient Computations, d Proceedings: Internat. Math. Comp. Mtg., Portland, OR, Avramova, M.N. et al., (2002): Comparative Analysis of PWR Core Wide and Hot Channel Calculations, Transactions from ANS 2002Winter Meeting, Washington DC Avramova, M.N. et al., (2003a): COBRA-TF PWR Core Wide and Hot Subchannel Calculations, Transactions from ANS 2003 Annual Meeting, San Diego, CA, USA Avramova, M.N., (2003b): COBRA-TF Development, Qualification, and Application to LWR Analysis, MS Thesis, The Pennsylvania State University Avramova, M.N. et al., (2003c): PWR MSLB Simulations using COBRA-TF Advanced Thermal- Hydraulic Code, Transactions from ANS 2003 Winter Meeting, New Orleans, Louisiana, USA Avramova, M.N., (2004a): F-COBRA-TF 1.2: Source Modification Report. Modifications from Version 1.2a to Version 1.2b: Unformatted Input Structure, Dump/Restart Option, and SI Units, (RDFMG SIM-MA 008(04) rev.0) Avramova, M.N., (2004b): F-COBRA-TF 1.2: Source Modification Report. Automated Input Deck Cross-Checking Procedure, (RDFMG SIM-MA 010(04) rev.0) Avramova, M.N., (2005a): F-COBRA-TF 1.03: Source Modification Report. Implementation of Krylov subspace methods for solution of the F-COBRA-TF linear system of pressure equations, RDFMG SIM-MA 010(05) rev.0 Avramova, M.N., (2005b): Progress Report: F-COBRA-TF Development and Qualification, (RDFMG PR-MA 06(05)) Avramova, M.N., (2006): Verification Matrix of F-COBRA-TF 1.02b. AREVA Technical Report A1C Avramova, M.N. et al., (2006a): Improvements and Applications of COBRA-TF for Stand-Alone and Coupled LWR Safety Analyses, Proceedings: PHYSOR 2006, Vancouver, Canada Biasi, L. et al., (1967): Studies on Burnout, Part 3, Energia Nucleate, 14(9),

193 Bajorek, S.M. and Young, M.Y., (1998): Assessment and Qualification of WCOBRA/TRAC- MOD7A heat Transfer Coefficients for Blowdown Dispersed Flow Film Boiling, Proceedings: Sixth International Conference on Nuclear Engineering (ICONE-6), San Diego, CA, USA Beus, S.G. (1970): A two-phase turbulent mixing model for flow in rod bundles. Bettis Atomic Power Laboratory, WAPD-T-2438 Campbell, R.L. et al., (2005): Computational Fluid Dynamics Prediction of Grid Spacer Thermal- Hydraulic Performance with Comparison to Experimental Results, Nuclear Technology, 149, Caraghiaur, D. et al., (2004): Detailed Pressure Drop Measurements in Single- and Two-Phase Adiabatic Air-Water Turbulent Flows in Realistic BWR Fuel Assembly geometry with Spacer Grids, Proceedings: Sixth International Conference on Nuclear Thermal Hydraulics, Operation and Safety (NUTHOS-6), Nara, Japan Chen, J.C., (1963): A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow, ASME 63-HT-34, American Society of Mechanical Engineers Chen, X.M. and Andersen, J.G.M., (1997a): Prediction of Test Rod Temperature during a Transient Dryout, Proceedings: Fourth International Seminar on Subchannel Analysis (ISSCA- 4), Tokyo, Japan Chen, X.M. and Andersen, J.G.M., (1997b): Prediction of Cross Sectional Void Distribution in a BWR Fuel Bundle Configuration, Proceedings: Eighth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-8), Vol.3, Kyoto, Japan Chen, X.M. and Andersen, J.G.M., (1999): Dynamics in BWR Fuel Bundles during Transients, Proceedings: Ninth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-9), San Francisco, CA, USA Chu, K.H. and Shiralkar, B.S., (1993): Study of Spacer Effect on Critical Power by COBRAG Based on a Two-Fluid and Multi-Field Model, Proceedings: Second International Seminar on Subchannel Analysis (ISSCA-1), Palo Alto, CA, USA (EPRI TH ) Conner, M.E. et al., (2004): Lateral Flow Field Behavior Downstream of Mixing Vanes in a Simulated Nuclear Fuel Rod Bundle, Proceedings of ICAPP 04, Pittsburg, PA, USA Cuervo, D. et al., (2004): Improving the Computation Efficiency of COBRA-TF for LWR Safety Analysis of Large Problems, Proceedings: PHYSOR 2004, Chicago, USA Cuervo, D. et al., (2005): Implementation and Performance of Krylov Methods for the Solution of Two-Fluid Hydrodynamics Equations in the COBRA-TF Code, Proceedings: M&C 2005, Avignon, France, Cui, X.-Z. and Kim K.-Y., (2003): Three-Dimensional Analysis of Turbulent Heat Transfer and Flow through Mixing Vane in a Subchannel of Nuclear Reactor, Journal of Nuclear Science and Technology, 40, No10,

194 Demmel, J.W. et al., (1999): A Supernodal Approach to Sparse Partial Pivoting, SIAM J. Matrix Anal. Appl., 20 (3),pp Dittus, F.W. and Boelter, L.M.K., (1930): Heat Transfer in Automobile Radiators of Tubular Type, University of California, Berkeley Publ. Eng. 2, 13, Downar, T. and Joo, H. (2001): A Preconditioned Krylov Method for Solution of the Multi-dimensional, Two-fluid Hydrodynamics Equations, Annals of Nuclear Energy, 28, pp Drew, D.A. and Lahey, R.T. (1979): An Analytical Derivation of a Sub-Channel Void Drift Model, Trans. Am. Nucl. Soc. (ANS), Vol. 33 Ergun, S. et al., (2005a): Modification to COBRA-TF to Model Dispersed Flow Film Boiling with Two Flow, Five Field Eulerian - Eulerian Approach, Transactions from ANS 2005 Winter Meeting, Washington DC, USA Ergun, S., (2005b): Modeling of Dispersed Flow Film Boiling and Spacer Grid Effects on Heat Transfer with Two-Flow, Five-Field Eulerian-Eulerian Approach, PhD Thesis, The Pennsylvania State University Faya, A.J.G. (1979): Development of a Method for BWR Sub-Channel Analysis. Ph.D. thesis, Massachusetts Institute of Technology (MIT) Fighetti, C. et al., (1990): Error analysis of SIEMENS Critical Heat Flux (CHF) Tests, CU/HTRF-90-04, June, 1990 Frepoli, C., et al., (2001a): COBRA-TF Simulation of BWR Bundle Dry Out Experiment, Proceedings: Ninth International Conference on Nuclear Engineering (ICONE9), Nice, France Frepoli, C. et al., (2001b): Modeling of Annular Film Dry Out with COBRA-TF, Proceedings: Ninth International Conference on Nuclear Engineering (ICONE9), Nice, France Glueck, M. and Kollmann, T. (2005): Application and Visualization Capability of the Sub- Channel Code F-COBRA-TF, Proceedings: Annual Meeting on Nuclear Technology, Nuremberg, Germany Glueck, M., (2005a): Validation Matrix F-COBRA-TF 1.2b. AREVA Technical Report A1C Glueck, M., (2005b): Modeling of Turbulent Mixing and Void Drift in Sub-Channel Analysis (overview over approaches in open literature). AREVA Technical Report A1C Glueck, M. (2006): A New Individual Film Model in the Sub-Channel Code F-COBRA-TF, Annual Meeting on Nuclear Technology, Aachen, Germany Gonzalez-Santalo, J.M. and Griffith, P. (1972): Two-Phase Flow Mixing in Rod Bundle Sub- Channels. ASME Winter Annual Meeting, New York, November

195 Griffith P. et al., (1977): PWR Blowdown Heat Transfer, Thermal and Hydraulic Aspects of Nuclear Reactor Safety, American Society of Mechanical Engineers, New York, Vol.1, Gu C-Y et al., (1993): 3-D Flow Analyses for Design of Nuclear Fuel Spacer, Proceedings: Second International Seminar on Subchannel Analysis (ISSCA-2), Palo Alto, CA, USA Herkenrath, H. et al., (1979): Experimental Investigation of the Enthalpy and Mass Flow Distribution between Sub-Channels in BWR Cluster Geometry (PELCO-S), Joint Research Center Ispra Establishment-Italy Holowach, M.J. et al., (2002): Improving Flow Modeling in Transient Reactor Safety Analysis Computer Codes: Eighth International Conference on Nuclear Engineering (ICONE-8), Arlington, VA, USA Hoshi, M. et al., (1998): Cross Flow of PWR Mixed Core II Evaluation for Staggered Mixing Vane Grid, Proceedings: Sixth International Conference on Nuclear Engineering (ICONE-6), San Diego, CA, USA Hotta, A. et al., (2004): A Modified Equilibrium Void Distribution Model Applicable for Conventional Square and Tight Lattice BWR Fuel Bundles. Proceedings: Sixth International Conference on Nuclear Thermal Hydraulics, Operations and Safety (NUTHOS-6), Nara, Japan Hotta, A., (2005): Preliminary Results of Exercise-1 in NUPEC BFBT Benchmark based on NASCA, NUPEC Benchmark 2 nd Workshop, University Park, PA, USA Ikeda, K., et al., (1998): Cross Flow of PWR Mixed Core I Measurement and CFD Prediction, Proceedings: Sixth International Conference on Nuclear Engineering (ICONE-6), San Diego, CA, USA Ikeno, T., (2001): An Application of the Model of Flow Pulsation to the Rod Gap in the Nuclear Fuel Assembly, Proceedings: Flow Modeling and Turbulence Measurements (FMTM2001), Ikeno, T., (2005): Computational Model for Turbulent Flow around a Grid Spacer with Mixing Vane, Proceedings: Eleventh International Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) In, W.K. et al., (2001): Numerical Study of Coolant Mixing Caused by the Flow Deflectors in a Nuclear Fuel Bundle, Nuclear Technology, 134, Ingesson, L. (1969): Heat Transfer between Sub-Channels in a Rod Bundle. AE-RL-1125 Janssen, E., (1971): Two-Phase Flow and Heat Transfer in Multi-Rod GEAP AEC Research and Development Report Geometries Final Report, Jeong, H., (2004): Evaluation of Turbulent Mixing between Sub-Channels with a CFD Code, Proceedings: Proceedings: Sixth International Conference on Nuclear Thermal Hydraulics, Operation and Safety (NUTHOS-6), Nara, Japan 177

196 Jeong, J.-J. et al., (1999): Development of a Multi-Dimensional Thermal-Hydraulic System Code, MARS 1.3.1, Annals of Nuclear Energy, 26, Jeong, J.-J. et al., (2004): Development of Subchannel Analysis Capability of the Best-Estimate Multi-Dimensional System Code, MARS 3.2, Proceedings: Korean Nuclear Society 2004 Spring Meeting, Kyundju, Korea Jeong, J.-J. et al., (2005a): Prediction of Two-Phase Flow Distributions in Rod Bundles Using the Best-Estimate System Code MARS, Proceedings: Eleventh International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Avignon, France Jeong, J. J., et al., (2005b): Activities of KAERI BFBT Benchmark Team Using MATRA, nd MARS(COBRA-TF) and CFX, NUPEC Benchmark 2 Workshop, University Park, PA, USA Kano, K. et al., (2002): Turbulent Mixing Rate between Adjacent Subchannels in a Vertical 2x3 Rod Channel, Proceedings of The 5 th JSME-KSME Fluids Engineering Conference, Nagoya, Japan, Nov Kano, K. et al., (2003): Flow Distribution and Slug Flow Characteristics for Hydraulically Equilibrium Air-Water Two-phase Flow in a Vertical 2x3 Rod Bundle, Proceedings of ASME FEDSM 03 4 th ASME-JSME Joint Fluids Engineering Conference, Honolulu, Hawaii, USA Kappes, Ch. (2006): CFD Simulationen zur Bestimmung von β SP (in German), AREVA working documentation, BD/FEET/2006/942 Karoutas, C.Y. et al., (1995): 3-D Flow Analyses for Design of Nuclear Fuel Spacer, Proceedings: Seventh International Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH- 7), Saratoga, New York Kawahara, A. et al., (2004): Experiment and Analysis of Air-Water Two-Phase Flow Redistribution due to Void Drift between Subchannels for Hydrodynamic Non-Equilibrium Flow, Proceedings of The 6 th International Conference on Nuclear Thermal Hydraulics Operations and Safety (NUTHOS-6), Nara, Japan Kelly, J.E. (1980): Development of a Two-Fluid, Two-Phase Model for Light Water Reactor subchannel analysis. Ph.D. thesis, Massachusetts Institute of Technology (MIT) Kelly, J.E., et al., (1981): THERMIT-2: A Two-Fluid Model for Light Water Reactor Subchannel Transient Analysis, Energy Laboratory Report No. MIT-EL , MIT Kelly, J.E. and Kazimi, M.S. (1980): Development of the Two-Fluid Multidimensional Code THERMIT for LWR Analysis, AIChE Symposium Series 199, Vol.76 Kim, S. and Park, G.-S., (1997): Estimation of Anisotropic Factor and Turbulent Mixing Rate Based on the Flow Pulsation Phenomenon, Nuclear Technology, 117, Kim, S. and Chung, B.J., (2001): A Scale Analysis of the Mixing Rate for Various Prandtl Number Flow Fields in Rod Bundles, Nuclear Engineering and Design, 205,

197 Kim, K.-Y. and Seo J-W., (2005): Numerical Optimization for the Design of a Spacer Grid with Mixing Vanes in a Pressurized Water Reactor Fuel Assembly, Nuclear Technology, 149, Kronenberg, J. et al., (2003): COBRA-TF - a Core Thermal-Hydraulic Code: Validation against GE 3x3 Experiment, Annual Meeting on Nuclear Technology 2003, Proceedings, ISSN , pp Krulikowski, T.E., (1997): Separation of Diversion Crossflow Effects from Other Mixing Effects within the Thermal Diffusion Coefficient, MS Paper, The Pennsylvania State University Kuldip, S. and Pierre, C.C.St., (1973): Two-Phase Mixing for Annular Flow in Simulated Rod Bundle Geometries, Nuclear Science and Engineering, Vol. 50, Lahey, R. T. et al., (1970): Two-phase flow and heat transfer in multi-rod geometries: Subchannel and Pressure Drop Measurements in Nine-Rod Bundle for Diabatic and Adiabatic Conditions, GEAP AEC Research and Development Report Lahey, R.T. and Moody, F.J. (1993): The Thermal Hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society (ANS) Lee, S.Y. et al., (1992): COBRA/RELAP5: A Merged Version of COBRA-TF and RELAP5/MOD3 Codes, Nuclear Technology, 99, Levy, S. (1963): Prediction of Two-Phase Pressure Drop and Density Distribution from Mixing Length Theory, Journal of Heat Transfer, no. 5 (1963), pp Loftus, M.J. et al., (1982): PWR FLECHT SEASET 21-Rod Bundle Flow Blockage Task Data and Analysis Report, NRC/EPRI/Westinghouse-11 McClusky, H.L. et al., (2002): Development of Swirling Flow in a Rod Bundle Subchannel, Journal of Fluids Engineering, 124, Mishima, K. and Ishii, M. (1984): Flow Regime Transition Criteria for Upward Two-Phase Flow in Vertical Tubes. Int. J. Heat Mass Transfer, vol. 27, no. 5, pp Möller, S.V., (1991): On Phenomena of Turbulent Flow through Rod Bundles, Experiments Thermal Fluid Science, 4, 25 Murao, T. et al., (1993): Improvement and Application of Subchannel Analysis Codes for Advanced Light Water Reactors, Proceedings: Second International Seminar on Subchannel Analysis (ISSCA-1), Palo Alto, CA, USA (EPRI TH ) Naitoh, M. et al., (2002): Critical Power Analysis with Mechanistic Models for Nuclear Fuel Bundles, (I) Models and Verifications for Boiling Water Reactor Application, Journal of Nuclear Science and Technology, 39, No 1, Neykov, B. et al., (2005): NUPEC BWR Full-Size Fine-Mesh Bundle Test (BFBT) Benchmark. Volume 1: Specifications, NEA/NSC/DOC 179

198 Ninokata, H. et al., (2001): Development of the NASCA Code for Predicting Transient BT Phenomena in BWR Rod Bundles. NEA / CSNI / R(2001)2, vol. 2. Ninokata, H., et al. (2004a): Current Status of Generalized Boiling Transition Model Development Applicable to a Wide Variety of Fuel Bundle Geometry, Proceedings: Sixth International Conference on Nuclear Thermal Hydraulics, Operations and Safety (NUTHOS-6), Nara, Japan Ninokata, H., (2004b): Two-Phase Flow Modeling in the Rod Bundle Subchannel Analysis, Proceedings: Advances in the Modeling Methodologies of Two-Phase Flows, Lyon, France Nordsveen, M. et al., (2003): The MONA Subchannel Analysis Code Part A: Model and Description, Proceedings: Tenth International Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-10), Seoul, Korea Okubo, T. et al., (1997): Recent Activities on Subchannel Analysis at JAERI, Proceedings: Fourth International Seminar on Subchannel Analysis (ISSCA-4), Tokyo, Japan Park, C.E. et al., (2005): Extended COBRA-TF and Its Application to Non-LOCA Analysis, Trans. of ANS 2005 Winter Meeting, Washington DC, USA Paik, C. Y. et al., (1985): Analysis of FLECHT SEASET 163-Rod Blocked Bundle Data using COBRA-TF, NRC/EPRI/Westinghouse-12 Ratnayake, R.K., (2003): Entrainment and Deposition Modeling of Liquid Films with Applications for BWR Fuel Rod Dryout, PhD Thesis, The Pennsylvania State University Rehme, K., (1992): The Structure of Turbulence in Rod Bundles and the Implications on Natural Mixing between Subchannels, International Journal of Heat and Mass Transfer, 35, 567 Rogers, J. T. and Rosehart, R. G., (1972): Mixing by Turbulent Interchange in Fuel Bundles, Correlations and Inferences, ASME, 72-HT-53 Rogers, J.T. and Tahir, A.E.E. (1975): Turbulent Interchange Mixing in Rod Bundles and the Role of Secondary Flows. ASME, Heat Transfer Conference. Rosal, E.R. et al., (2003): The Pennsylvania State University and U.S. Nuclear Regulatory Commission Rod Bundle Heat Transfer Facility, Proceeding: Sixth ASME-JSME Thermal Engineering Joint Conference Rowe, D.S. and Angle, C.W. (1967): Crossflow Mixing between Parallel Flow Channels during Boiling. Part II: Measurement of Flow Enthalpy in Two Parallel Channels. BNWL-371 (Part II) Rowe, D.S. and Angle, C.W. (1969): Crossflow Mixing between Parallel Flow Channels during Boiling. Part III: Effect of Spacers on Mixing between Two Channels. BNWL-371 (Part III) Rowe, D.S. et al., 1974: Implications Concerning Rod Bundle Crossflow Mixing Based on Measurements of Turbulent Flow Structure, International Journal of Heat and Mass Transfer, 17, 180

199 407 Rudzinski, K.F. et al., (1972): Turbulent Mixing for Air-Water Flows in Simulated Rod Bundle Geometries. The Canadian Journal of Chemical Engineering, vol. 50 Saad, Y., (2000) Iterative Methods for Sparse Linear Systems, 2nd ed. Sadatomi, M. et al., (1994): Flow Redistribution due to Void Drift in Two-Phase Flow in a Multiple Channel Consisting of Two Subchannels, Nuclear Engineering and Design, Vol. 148, Sadatomi, M. et al., (1996): Prediction of the Single-Phase Turbulent Mixing Rate between Two Parallel Sub-Channels using a Sub-Channel Geometry Factor. Nuclear Engineering and Design, vol. 162, pp Sadatomi, M. et al., (2003): Two-Phase Void Drift Phenomena in a 2x3 Rod Bundle (Flow Redistribution Data and Their Analysis, Proceedings of The 10 th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-10), Seoul, Korea Sadatomi, M., (2004): Study of Single- and Two-Phase Fluid Transfer between Subchannels at Kumamoto University, Proceedings of The 6 th International Conference on Nuclear Thermal Hydraulics Operations and Safety (NUTHOS-6), Nara, Japan Sato, Y. (1992): Cross flow of Gas-Liquid Mixture between Sub-Channels. In: Sub-channel analysis in nuclear reactors. Proc. of the Int. Seminar on Sub-channel Analysis ISSCA 92 (Eds.: Ninokata, H. and Aritomi, M.), The Institute of Applied Energy and The Atomic Energy Society, Japan. Sato, Y. and Sadatomi, M.,: Two-Phase Gas-Liquid Flow Distributions in Multiple Channels, DYNAMICS OF TWO-PHASE FLOWS, CRC Press Schell, H., 2006: Co-operation between AREVA NP GmbH and Penn State University. Assessment Concerning F-COBRA-TF Development, (A1C ), AREVA NP GmbH, Erlangen, Germany Shen, Y.F. et al., (1991): An Investigation of Crossflow Mixing Effect Caused by Grid Spacer with Mixing Blades in a Rod Bundle, Nuclear Engineering and Design, 125, Shirai, H. and Ninokata, H., (2001): Prediction of the Equilibrium Two-Phase Flow Distributions in Inter-Connected Subchannel Systems, Nuclear Science and Technology, Vol. 38 No.6, Shirai, H. et al., (2004): A Strategy of Implementation of the Improved Constitutive Equations for the Advanced Subchannel Code, Proceedings: Sixth International Conference on Nuclear Thermal Hydraulics, Operations and Safety (NUTHOS-6), Nara, Japan Shiralkar, B.S., and Chu, K.H., (1992) Recent Trends in Subchannel Analysis, Subchannel Analysis in Nuclear Reactors: Proceedings of the International Seminar on Subchannel Analysis (ISSCA 92), Tokyo, Japan 181

200 Solis, J. et al., (2004): Multi-level methodology in parallel computing environment for evaluating BWR safety parameters, Nuclear Technology, Vol. 146, 3, CDadapco Group: STAR-CD Version 3.26 Stewart, C.W. et al., (1977): COBRA-IV: The Model and the Method. BNWL-2214, NRC-4 Sugawara, S. (1990): Droplet Deposition and Entrainment Modeling Based on the Three-Field Model, Nuclear Engineering and Design, 122, Sugawara, S. et al., (1991): Sub-channel analysis by the FIDAS code based on the three-fluid model. Nuclear Engineering and Design, vol. 132, pp Taitel, Y. et al., (1980): Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes. AIChE Journal, vol. 26, no. 3, pp Takeuchi, K. et al., (1998): Subcooled Flooding Predictions by WCOBRA/TRAC for UPI Tests and UPI Plants in LOCA, Proceedings: Sixth International Conference on Nuclear Engineering (ICONE-6), San Diego, CA, USA Tippayakul, C. et al., (2007): Investigations on Monte Carlo Based Coupled Core Calculations, Proceedings of ICAPP 06, Nice, France Thurgood, M. J., et al., (1983): COBRA/TRAC A Thermal-Hydraulic Code for Transient Analysis of Nuclear Reactor Vessel and Primary Coolant Systems, NUREG/CR-3046 Turner, J. and Doster, J. (1991): Performance of the conjugate gradient-like algorithms in transient two-phase subchannel analysis, ANS 1991 Winter Meeting, San Francisco, CA, USA VIPRE-02: A Two-Fluid Thermal-Hydraulic Code for Reactor Core and Vessel Analysis, Volume 1: Mathematical Modeling and Solution Methods, TR V1 Research Project, Final Report, June 1994 Vogel, Chr. et al.,(1991): SIEMENS Test Section 53 (TDS53) Description of Experiments, KWU BT23, 1991, e243. Wallis, G.B. (1969): One-Dimensional Two-Phase Flow. Mc-Graw-Hill, New York. Wang, J., and Cao, L.,: Experimental Research for Sub-cooled Boiling Mixing between Subchannels in a Bundle Windecker, G. and Anglart, H., (2001): Phase Distribution in a BWR Fuel Assembly and Evaluation of a Multidimensional Multifield Model, Nuclear Technology, 134, Wong, S. and Hochreiter, L.E., (1981): Analysis of the FLECHT SEASET Unblocked Bundle Steam Cooling and Boiloff Tests, NRC/EPRI/Westinghouse-8 Würtz, J. (1978): An Experimental and Theoretical Investigation of Annular Steam-Water Flow in 182

201 Tubes and Annuli at 30 to 90 Bar, RISO Report No 372 Yadigaroglu, G., and Maganas, A., (1994): Equilibrium Quality and Mass Flux Distributions in an Adiabatic Three Subchann el Test Section, Nuclear Technology, Vol. 112, Yamanouchi, A., (1968): Effect of CoreSpray Cooling in Transient State After Loss-of-Cooling Acciident, Jornal of Nuclear Science and Technology 5, 11, pp Yao, S.C. et al., (1982): Heat Transfer Augmentati on in Rod Bundles near Grid Spacers, Journal of Nuclear Science and Technology, 104 Yoo, Y.J. et al., (1999): Development of a Subchannel Analysis Code MATRA Applicable to PWRs and ALWRs, Journal of the Korean Nuclear Society, vol. 31, No 3, pp Ziabletsev, D. et al., (2004): Development of PWR Integrated Safety Analysis Methodology Using Multi-Level Coupling Algorithm, Nuclear Science and Engineering, Vol.148, 3, Ziabletsev, D., and Böer, R., (2000): Implementation and Initial Verification of the Coupling of COBRA-TF with the PANBOX Code System, Work Report (A1C ), Siemens KWU, Erlangen, Germany Zuber, N. et al, (1961): The Hydraulics Crisis in Pool Boiling of Saturated and Subcooled Liquids, Part II, No.27, in International Developments in Heat Transfer, International Heat Transfer Conference, Boulder, Colorado 183

202 APPENDIX A CFD RESULTS FOR THE 2 1 CASE Table A-1: Temperature field distribution at different strap thickness Sub- Model No strips Temperature Distribution at the Outlet [Kelvin] Temperature Distribution over the Subchannels Centroids Line [Kelvin] 0.4 mm 0.6 mm 184

203 Table A-2: Turbulent viscosity, vertical velocity, and temperature field distribution at the gap region at different strap thickness Sub- Turbulent Viscosity at the Vertical Velocity at the Gap Temperature at the Gap Model Gap Region [Pa-s] Region [m/s] Region [Kelvin] 0.3 mm 0.4 mm 0.6 mm 185

204 Sub- Model 0.3 mm Table A-3: Vertical velocity distribution at different strap thickness Vertical Velocity at the Strip Location [m/s] Vertical Velocity at the Outlet [m/s] 0.6 mm 186

205 Sub- Model 0.4 mm Table A-4: Turbulent viscosity distribution at different strap thickness Turbulent Viscosity at the Strip Location Turbulent Viscosity at the Outlet [Pa-s] [Pa-s] 0.6 mm 187

206 Sub- Model Table A-5: Temperature field distribution at different vane angles Declination Angle of 20 degrees Declination Angle of 50 degrees Temperature Distribution over the Gap Region [Kelvin] Temperature Distribution at the Outlet [Kelvin] Temperature Distribution at the Vanes Location [Kelvin] 188

207 Table A-6: Turbulent viscosity distribution at different vane angles Sub- Model Declination Angle of 20 degrees Declination Angle of 50 degrees Turbulent Viscosity Distribution over the Gap Region [Pa-s] Turbulent Viscosity Distribution at the Outlet [Pa-s] Turbulent Viscosity at the Vanes Location [Pa-s] 189

208 Sub- Model Table A-7: Pressure field distribution at different vane angles Mixing Vanes Declination of 20 degrees Mixing Vanes Declination of 50 degrees Pressure Field Above the Vanes [Pa] Pressure Field at the Vanes Location [Pa] Sub-Model Table A-8: Turbulent Viscosity Distribution over the Subchannels Centroids Line Mixing Vanes Declination of 20 degrees Turbulent Viscosity Distribution over the Subchannels Centroids Line [Pa-s] 190

209 APPENDIX B CFD RESULTS FOR THE ULTRAFLOW TM SPACER Table B-1: Flow pattern at different altitudes (UV velocity component, m/s) At the Tip of the Vanes 31.6 mm Downstream of the Tips mm Downstream of the Tips mm Downstream of the Tips 191

210 Table B-2: Temperature distribution at different altitudes (in Kelvin) At the Tip of the Vanes mm Downstream of the Tips mm Downstream of the Tips 192

211 Table B-3: Turbulent viscosity at different altitudes (in Pa-s) At the Tip of the Vanes 31.6 mm Downstream of the Tips mm Downstream of the Tips mm Downstream of the Tips 193

212 APPENDIX C CFD DATA FOR THE MIXING COEFFICIENT MULTIPLIER Table C-1: Description of the format of the additional input deck with the CFD data for the mixing multiplier Input Variable Description N1 number of entrees for the 1 st independent Total number of axial positions variable N2 number of entrees for the 2 nd independent Total number of different mixing vane variable angles N3 number of entrees for the 3 rd independent Dummy variables N4 number of entrees for the 4 th independent Dummy variables NSET number of data sets to be read st N2_1 1 entree of the 2 independent variable th N2_n n entree of the 2 independent variable V_N1 entree of the independent variable N1 nd nd Corresponds to the number of different subchannel configurations 1 st value of the vane angle n th value of the vane angle i th axial position V_Nn_1 value of the dependent variable at a Spacer multiplier for the 1 st vane angle given combination of N1 and Nn_1 at the i th axial position V_Nn_n value of the dependent variable at a Spacer multiplier for the n th vane angle given combination of N1 and Nn_n at the i th axial position 194

213 Table C-2: Example for the CFD data set for the 2 1 case **************************************************** * 2D table for the spacer multiplier **************************************************** * N1 N2 N * NSET 1 * N2_1 N2_2 N2_3 N2_4 N2_ * V_N1 V_N2_1 V_N2_2 V_N2_3 V_N2_4 V_N2_ N

214

215 Table C-3: Example for the CFD data set for ULTRAFLOW TM spacer **************************************************** * 2D table for the spacer multiplier **************************************************** * N1 N2 N3 N * NSET 1 * N2_1 N2_ * * V_N1 V_N2_1 V_N2_2 *

216

217 Spacer Grid Multiplier Θ SG XSCHEM VDRIFT IXFLOW = 2 or 3 YES SG_MULTIPLIER XSCHEM solves F-COBRA-TF conservation equations VDRIFT calculates turbulent mixing and void drift source terms IXFLOW input flag for modeling of the enhanced turbulent mixing and directed crossflow IXFLOW = 2 only enhanced turbulent mixing modeling will be activated; IXFLOW = 3 both modeling options will be activated SG_MULTIPLIER evaluates spacer grid multiplier Θ SG test_sg_mult Reads the CFD data set input file sg_mult_data Calls the interpolation subroutine Defines the spacer grid multiplier for the mixing coefficient Axial height of the F-COBRA-TF momentum cell and Mixing vanes angle Spacer grid multiplier for the given height and angle as defined after linear Interpolation Subroutine Performs linear interpolation between values given in the CFD data set Writes the evaluated spacer grid multiplier in an additional output file test_sg_mult.out test_sg_mult.out Figure C-1: Flow chart of the modeling of the enhan ced turbulent mixing due to mixing vanes 199

218 APPENDIX D EVALUATION OF THE TRANSVERSE MOMENTUM CHANGE BY MEANS OF CFD PREDICTIONS FOR THE VELOCITY CURL C andidate 1: Knowing the velocity curl in a lateral plane, r v v z y ( v) = curl v =, (A.1) x y z a body force can be calculated as F = ( v) vx ρ A x, (A.2) where v x is the axial velocity in the fluid domain and ρ is its density as both calculated by F- COBRA-TF, A is the area on which the force is acting and x is the axial dimension of the domain for a particular case. We can assume that the area A is equal to A = πr 2, where R is the distance between the center of the subchannel and the rod surface (see Figure D-1). R Figure D-1: Schematic of the model for evaluation of the lateral momentum change by velocity curl 200

219 The momentum change I & in the latera l direction y over a time interval t is then defined as: I I & lat = F = ( v) vx ρ A x. t (A.3) Candidate 2: The pressure gradient over the radius R in Figure D-1 can be given as P = ρω R + ρ g h (A.4) gravity centrofugal force where ρ is the density of the medium; R is the distance between the center of the subchannel and the rod surface; ω is the angular velocity; and g is the gravitational constant. Neglecting the gravity term and using the relation between the angular velocity ω and the velocity curl, ( v) ω =, the pressure gradient becomes P = ρω R = ρ ( v) R, (A.5) Then the lateral momentum change by the force acting on the fluid at the gap area (lateral area A lat S x, where S is the rod-to-rod distance) due to the pressure gradient = ij ij P will be I I& 1 lat = F = P Alat = ρ 2 2 ( v) R Sij x. (A.6) t 8 201

220 APPENDIX E CFD RESULTS FOR THE FOCUS TM SPACER Table E-1: Lateral (UW) velocities field immediately downstream of the mixing vanes 10 degree, local maximum of m/s 20 degree, local maximum of m/s 30 degree, local maximum of m/s 40 degree, local maximum of m/s 202

221 Table E-2: Lateral velocity field further downstream of the spacer 20 degree m 30 degree m 40 degree m 203

222 Table E-3: Lateral velocities field at the position of velocity inversion 20 degree m 30 degree m 40 degree m 204

DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS MODELS FOR NUCLEAR REACTOR APPLICATIONS

DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS MODELS FOR NUCLEAR REACTOR APPLICATIONS DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS MODELS FOR NUCLEAR REACTOR APPLICATIONS Henry Anglart Royal Institute of Technology, Department of Physics Division of Nuclear Reactor Technology Stocholm,

More information

The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering

The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering DEVELOPMENT AND IMPLEMENTATION OF CFD-INFORMED MODELS FOR THE ADVANCED SUBCHANNEL CODE CTF A Dissertation

More information

COMPARISON OF COBRA-TF AND VIPRE-01 AGAINST LOW FLOW CODE ASSESSMENT PROBLEMS.

COMPARISON OF COBRA-TF AND VIPRE-01 AGAINST LOW FLOW CODE ASSESSMENT PROBLEMS. COMPARISON OF COBRA-TF AND VIPRE-01 AGAINST LOW FLOW CODE ASSESSMENT PROBLEMS A. Galimov a, M. Bradbury b, G. Gose c, R. Salko d, C. Delfino a a NuScale Power LLC, 1100 Circle Blvd., Suite 200, Corvallis,

More information

CFD SIMULATION OF SWIRL FLOW IN HEXAGONAL ROD BUNDLE GEOMETRY BY SPLIT MIXING VANE GRID SPACERS. Mohammad NAZIFIFARD

CFD SIMULATION OF SWIRL FLOW IN HEXAGONAL ROD BUNDLE GEOMETRY BY SPLIT MIXING VANE GRID SPACERS. Mohammad NAZIFIFARD CFD SIMULATION OF SWIRL FLOW IN HEXAGONAL ROD BUNDLE GEOMETRY BY SPLIT MIXING VANE GRID SPACERS Mohammad NAZIFIFARD Department of Energy Systems Engineering, Energy Research Institute, University of Kashan,

More information

CFD ANANLYSIS OF THE MATIS-H EXPERIMENTS ON THE TURBULENT FLOW STRUCTURES IN A 5x5 ROD BUNDLE WITH MIXING DEVICES

CFD ANANLYSIS OF THE MATIS-H EXPERIMENTS ON THE TURBULENT FLOW STRUCTURES IN A 5x5 ROD BUNDLE WITH MIXING DEVICES CFD ANANLYSIS OF THE MATIS-H EXPERIMENTS ON THE TURBULENT FLOW STRUCTURES IN A 5x5 ROD BUNDLE WITH MIXING DEVICES Hyung Seok KANG, Seok Kyu CHANG and Chul-Hwa SONG * KAERI, Daedeok-daero 45, Yuseong-gu,

More information

Application of System Codes to Void Fraction Prediction in Heated Vertical Subchannels

Application of System Codes to Void Fraction Prediction in Heated Vertical Subchannels Application of System Codes to Void Fraction Prediction in Heated Vertical Subchannels Taewan Kim Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea. Orcid: 0000-0001-9449-7502

More information

USE OF CFD TO PREDICT CRITICAL HEAT FLUX IN ROD BUNDLES

USE OF CFD TO PREDICT CRITICAL HEAT FLUX IN ROD BUNDLES USE OF CFD TO PREDICT CRITICAL HEAT FLUX IN ROD BUNDLES Z. E. Karoutas, Y. Xu, L. David Smith, I, P. F. Joffre, Y. Sung Westinghouse Electric Company 5801 Bluff Rd, Hopkins, SC 29061 karoutze@westinghouse.com;

More information

Validation of Traditional and Novel Core Thermal- Hydraulic Modeling and Simulation Tools

Validation of Traditional and Novel Core Thermal- Hydraulic Modeling and Simulation Tools Validation of Traditional and Novel Core Thermal- Hydraulic Modeling and Simulation Tools Issues in Validation Benchmarks: NEA OECD/US NRC NUPEC BWR Full-size Fine-mesh Bundle Test (BFBT) Benchmark Maria

More information

TABLE OF CONTENTS CHAPTER TITLE PAGE

TABLE OF CONTENTS CHAPTER TITLE PAGE v TABLE OF CONTENTS CHAPTER TITLE PAGE TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS LIST OF APPENDICES v viii ix xii xiv CHAPTER 1 INTRODUCTION 1.1 Introduction 1 1.2 Literature Review

More information

CFD Simulation of Sodium Boiling in Heated Pipe using RPI Model

CFD Simulation of Sodium Boiling in Heated Pipe using RPI Model Proceedings of the 2 nd World Congress on Momentum, Heat and Mass Transfer (MHMT 17) Barcelona, Spain April 6 8, 2017 Paper No. ICMFHT 114 ISSN: 2371-5316 DOI: 10.11159/icmfht17.114 CFD Simulation of Sodium

More information

THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF MECHANICAL AND NUCLEAR ENGINEERING

THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF MECHANICAL AND NUCLEAR ENGINEERING THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF MECHANICAL AND NUCLEAR ENGINEERING CODE-TO-CODE VERIFICATION OF COBRA-TF AND TRACE ADRIAN MICHAEL LEANDRO SPRING 2016 A thesis submitted

More information

Investigation of CTF void fraction prediction by ENTEK BM experiment data

Investigation of CTF void fraction prediction by ENTEK BM experiment data Investigation of CTF void fraction prediction by ENTEK BM experiment data Abstract Hoang Minh Giang 1, Hoang Tan Hung 1, Nguyen Phu Khanh 2 1 Nuclear Safety Center, Institute for Nuclear Science and Technology

More information

A VALIDATION OF WESTINGHOUSE MECHANISTIC AND EMPIRICAL DRYOUT PREDICTION METHODS UNDER REALISTIC BWR TRANSIENT CONDITIONS

A VALIDATION OF WESTINGHOUSE MECHANISTIC AND EMPIRICAL DRYOUT PREDICTION METHODS UNDER REALISTIC BWR TRANSIENT CONDITIONS A VALIDATION OF WESTINGHOUSE MECHANISTIC AND EMPIRICAL DRYOUT PREDICTION METHODS UNDER REALISTIC BWR TRANSIENT CONDITIONS O. Puebla Garcia * Royal Institute of Technology 10691, Stockholm, Sweden opuebla@deloitte.es

More information

APPLICATION OF THE COUPLED THREE DIMENSIONAL THERMAL- HYDRAULICS AND NEUTRON KINETICS MODELS TO PWR STEAM LINE BREAK ANALYSIS

APPLICATION OF THE COUPLED THREE DIMENSIONAL THERMAL- HYDRAULICS AND NEUTRON KINETICS MODELS TO PWR STEAM LINE BREAK ANALYSIS APPLICATION OF THE COUPLED THREE DIMENSIONAL THERMAL- HYDRAULICS AND NEUTRON KINETICS MODELS TO PWR STEAM LINE BREAK ANALYSIS Michel GONNET and Michel CANAC FRAMATOME Tour Framatome. Cedex 16, Paris-La

More information

The Pennsylvania State University. The Graduate School. College of Engineering COBRA-TF ANALYSIS OF RBHT STEAM COOLING EXPERIMENTS.

The Pennsylvania State University. The Graduate School. College of Engineering COBRA-TF ANALYSIS OF RBHT STEAM COOLING EXPERIMENTS. The Pennsylvania State University The Graduate School College of Engineering COBRA-TF ANALYSIS OF RBHT STEAM COOLING EXPERIMENTS A Thesis in Nuclear Engineering by James P. Spring 2008 James P. Spring

More information

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6 Lectures on Nuclear Power Safety Lecture No 6 Title: Introduction to Thermal-Hydraulic Analysis of Nuclear Reactor Cores Department of Energy Technology KTH Spring 2005 Slide No 1 Outline of the Lecture

More information

A PWR HOT-ROD MODEL: RELAP5/MOD3.2.2Y AS A SUBCHANNEL CODE I.C. KIRSTEN (1), G.R. KIMBER (2), R. PAGE (3), J.R. JONES (1) ABSTRACT

A PWR HOT-ROD MODEL: RELAP5/MOD3.2.2Y AS A SUBCHANNEL CODE I.C. KIRSTEN (1), G.R. KIMBER (2), R. PAGE (3), J.R. JONES (1) ABSTRACT FR0200515 9 lh International Conference on Nuclear Engineering, ICONE-9 8-12 April 2001, Nice, France A PWR HOT-ROD MODEL: RELAP5/MOD3.2.2Y AS A SUBCHANNEL CODE I.C. KIRSTEN (1), G.R. KIMBER (2), R. PAGE

More information

PREDICTION OF MASS FLOW RATE AND PRESSURE DROP IN THE COOLANT CHANNEL OF THE TRIGA 2000 REACTOR CORE

PREDICTION OF MASS FLOW RATE AND PRESSURE DROP IN THE COOLANT CHANNEL OF THE TRIGA 2000 REACTOR CORE PREDICTION OF MASS FLOW RATE AND PRESSURE DROP IN THE COOLANT CHANNEL OF THE TRIGA 000 REACTOR CORE Efrizon Umar Center for Research and Development of Nuclear Techniques (P3TkN) ABSTRACT PREDICTION OF

More information

CFD Analysis for Thermal Behavior of Turbulent Channel Flow of Different Geometry of Bottom Plate

CFD Analysis for Thermal Behavior of Turbulent Channel Flow of Different Geometry of Bottom Plate International Journal Of Engineering Research And Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 13, Issue 9 (September 2017), PP.12-19 CFD Analysis for Thermal Behavior of Turbulent

More information

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow

More information

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

More information

Analysis of the Cooling Design in Electrical Transformer

Analysis of the Cooling Design in Electrical Transformer Analysis of the Cooling Design in Electrical Transformer Joel de Almeida Mendes E-mail: joeldealmeidamendes@hotmail.com Abstract This work presents the application of a CFD code Fluent to simulate the

More information

Research Article CFD Modeling of Boiling Flow in PSBT 5 5Bundle

Research Article CFD Modeling of Boiling Flow in PSBT 5 5Bundle Science and Technology of Nuclear Installations Volume 2012, Article ID 795935, 8 pages doi:10.1155/2012/795935 Research Article CFD Modeling of Boiling Flow in PSBT 5 5Bundle Simon Lo and Joseph Osman

More information

Fluid Dynamics Exercises and questions for the course

Fluid Dynamics Exercises and questions for the course Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r

More information

An Essential Requirement in CV Based Industrial Appliances.

An Essential Requirement in CV Based Industrial Appliances. Measurement of Flow P M V Subbarao Professor Mechanical Engineering Department An Essential Requirement in CV Based Industrial Appliances. Mathematics of Flow Rate The Scalar Product of two vectors, namely

More information

Title: Development of a multi-physics, multi-scale coupled simulation system for LWR safety analysis

Title: Development of a multi-physics, multi-scale coupled simulation system for LWR safety analysis Title: Development of a multi-physics, multi-scale coupled simulation system for LWR safety analysis Author: Yann Périn Organisation: GRS Introduction In a nuclear reactor core, different fields of physics

More information

Application of Computational Fluid Dynamics to the Flow Mixing and Heat Transfer in Rod Bundle

Application of Computational Fluid Dynamics to the Flow Mixing and Heat Transfer in Rod Bundle Tenth International Conference on Computational Fluid Dynamics (ICCFD10), Barcelona, Spain, July 9-13, 2018 ICCFD10-045 Application of Computational Fluid Dynamics to the Flow Mixing and Heat Transfer

More information

Chapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI.

Chapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Chapter 10: Boiling and Condensation 1 1 Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Objectives When you finish studying this chapter, you should be able to: Differentiate between evaporation

More information

THERMAL HYDRAULIC REACTOR CORE CALCULATIONS BASED ON COUPLING THE CFD CODE ANSYS CFX WITH THE 3D NEUTRON KINETIC CORE MODEL DYN3D

THERMAL HYDRAULIC REACTOR CORE CALCULATIONS BASED ON COUPLING THE CFD CODE ANSYS CFX WITH THE 3D NEUTRON KINETIC CORE MODEL DYN3D THERMAL HYDRAULIC REACTOR CORE CALCULATIONS BASED ON COUPLING THE CFD CODE ANSYS CFX WITH THE 3D NEUTRON KINETIC CORE MODEL DYN3D A. Grahn, S. Kliem, U. Rohde Forschungszentrum Dresden-Rossendorf, Institute

More information

Application of computational fluid dynamics codes for nuclear reactor design

Application of computational fluid dynamics codes for nuclear reactor design Application of computational fluid dynamics codes for nuclear reactor design YOU Byung-Hyun 1, MOON Jangsik 2, and JEONG Yong Hoon 3 1. Department of Nuclear and Quantum Engineering, Korea Advanced Institute

More information

MEASUREMENT OF LAMINAR VELOCITY PROFILES IN A PROTOTYPIC PWR FUEL ASSEMBLY. Sandia National Laboratories b. Nuclear Regulatory Commission

MEASUREMENT OF LAMINAR VELOCITY PROFILES IN A PROTOTYPIC PWR FUEL ASSEMBLY. Sandia National Laboratories b. Nuclear Regulatory Commission MEASUREMENT OF LAMINAR VELOCITY PROFILES IN A PROTOTYPIC PWR FUEL ASSEMBLY S. Durbin a, *, E. Lindgren a, and A. Zigh b a Sandia National Laboratories b Nuclear Regulatory Commission Abstract Laminar gas

More information

CONVECTION HEAT TRANSFER

CONVECTION HEAT TRANSFER CONVECTION HEAT TRANSFER THIRD EDITION Adrian Bejan J. A. Jones Professor of Mechanical Engineering Duke University Durham, North Carolina WILEY JOHN WILEY & SONS, INC. CONTENTS Preface Preface to the

More information

CONVECTION HEAT TRANSFER

CONVECTION HEAT TRANSFER CONVECTION HEAT TRANSFER SECOND EDITION Adrian Bejan J. A. Jones Professor of Mechanical Engineering Duke University Durham, North Carolina A WILEY-INTERSCIENCE PUBUCATION JOHN WILEY & SONS, INC. New York

More information

Turbulent Boundary Layers & Turbulence Models. Lecture 09

Turbulent Boundary Layers & Turbulence Models. Lecture 09 Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects

More information

ASSESSMENT OF CTF BOILING TRANSITION AND CRITICAL HEAT FLUX MODELING CAPABILITIES USING THE OECD/NRC BFBT AND PSBT BENCHMARK DATABASES

ASSESSMENT OF CTF BOILING TRANSITION AND CRITICAL HEAT FLUX MODELING CAPABILITIES USING THE OECD/NRC BFBT AND PSBT BENCHMARK DATABASES NURETH14-153 ASSESSMENT OF CTF BOILING TRANSITION AND CRITICAL HEAT FLUX MODELING CAPABILITIES USING THE OECD/NRC BFBT AND PSBT BENCHMARK DATABASES Maria Avramova 1 and Diana Cuervo 2 1 The Pennsylvania

More information

MECHANISTIC MODELING OF TWO-PHASE FLOW AROUND SPACER GRIDS WITH MIXING VANES

MECHANISTIC MODELING OF TWO-PHASE FLOW AROUND SPACER GRIDS WITH MIXING VANES MECHANISTIC MODELING OF TWO-PHASE FLOW AROUND SPACER GRIDS WITH MIXING VANES B. M. Waite, D. R. Shaver and M. Z. Podowski Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic

More information

2017 Water Reactor Fuel Performance Meeting September 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jeju Jeju Island, Korea

2017 Water Reactor Fuel Performance Meeting September 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jeju Jeju Island, Korea ACE/ATRIUM 11 Mechanistic Critical Power Correlation for AREVA NP s Advanced Fuel Assembly Design K. Greene 1, J. Kronenberg 2, R. Graebert 2 1 Affiliation Information: 2101 Horn Rapids Road, Richland,

More information

Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition

Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition Sādhanā Vol. 40, Part 2, April 2015, pp. 467 485. c Indian Academy of Sciences Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition RAMBIR BHADOURIYA,

More information

EasyChair Preprint. Numerical Simulation of Fluid Flow and Heat Transfer of the Supercritical Water in Different Fuel Rod Channels

EasyChair Preprint. Numerical Simulation of Fluid Flow and Heat Transfer of the Supercritical Water in Different Fuel Rod Channels EasyChair Preprint 298 Numerical Simulation of Fluid Flow and Heat Transfer of the Supercritical Water in Different Fuel Rod Channels Huirui Han and Chao Zhang EasyChair preprints are intended for rapid

More information

Boundary-Layer Theory

Boundary-Layer Theory Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22

More information

CFD SIMULATION OF THE DEPARTURE FROM NUCLEATE BOILING

CFD SIMULATION OF THE DEPARTURE FROM NUCLEATE BOILING CFD SIMULATION OF THE DEPARTURE FROM NUCLEATE BOILING Ladislav Vyskocil and Jiri Macek UJV Rez a. s., Dept. of Safety Analyses, Hlavni 130, 250 68 Husinec Rez, Czech Republic Ladislav.Vyskocil@ujv.cz;

More information

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127 C ONTENTS Preface xviii Nomenclature xxvi CHAPTER ONE BASICS OF HEAT TRANSFER 1 1-1 Thermodynamics and Heat Transfer 2 Application Areas of Heat Transfer 3 Historical Background 3 1-2 Engineering Heat

More information

COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF A V-RIB WITH GAP ROUGHENED SOLAR AIR HEATER

COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF A V-RIB WITH GAP ROUGHENED SOLAR AIR HEATER THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp. 963-972 963 COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF A V-RIB WITH GAP ROUGHENED SOLAR AIR HEATER by Jitesh RANA, Anshuman SILORI, Rajesh MAITHANI *, and

More information

EVALUATION OF FOUR TURBULENCE MODELS IN THE INTERACTION OF MULTI BURNERS SWIRLING FLOWS

EVALUATION OF FOUR TURBULENCE MODELS IN THE INTERACTION OF MULTI BURNERS SWIRLING FLOWS EVALUATION OF FOUR TURBULENCE MODELS IN THE INTERACTION OF MULTI BURNERS SWIRLING FLOWS A Aroussi, S Kucukgokoglan, S.J.Pickering, M.Menacer School of Mechanical, Materials, Manufacturing Engineering and

More information

On the transient modelling of impinging jets heat transfer. A practical approach

On the transient modelling of impinging jets heat transfer. A practical approach Turbulence, Heat and Mass Transfer 7 2012 Begell House, Inc. On the transient modelling of impinging jets heat transfer. A practical approach M. Bovo 1,2 and L. Davidson 1 1 Dept. of Applied Mechanics,

More information

ENGINEERING OF NUCLEAR REACTORS. Fall December 17, 2002 OPEN BOOK FINAL EXAM 3 HOURS

ENGINEERING OF NUCLEAR REACTORS. Fall December 17, 2002 OPEN BOOK FINAL EXAM 3 HOURS 22.312 ENGINEERING OF NUCLEAR REACTORS Fall 2002 December 17, 2002 OPEN BOOK FINAL EXAM 3 HOURS PROBLEM #1 (30 %) Consider a BWR fuel assembly square coolant subchannel with geometry and operating characteristics

More information

Table of Contents. Preface... xiii

Table of Contents. Preface... xiii Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...

More information

CFD-Modeling of Boiling Processes

CFD-Modeling of Boiling Processes CFD-Modeling of Boiling Processes 1 C. Lifante 1, T. Frank 1, A. Burns 2, E. Krepper 3, R. Rzehak 3 conxita.lifante@ansys.com 1 ANSYS Germany, 2 ANSYS UK, 3 HZDR Outline Introduction Motivation Mathematical

More information

Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems

Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Arthur T. Johnson, PhD, PE Biological Resources Engineering Department

More information

International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May ISSN

International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May ISSN International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 28 CFD BASED HEAT TRANSFER ANALYSIS OF SOLAR AIR HEATER DUCT PROVIDED WITH ARTIFICIAL ROUGHNESS Vivek Rao, Dr. Ajay

More information

ENGR Heat Transfer II

ENGR Heat Transfer II ENGR 7901 - Heat Transfer II External Flows 1 Introduction In this chapter we will consider several fundamental flows, namely: the flat plate, the cylinder, the sphere, several other body shapes, and banks

More information

Development of twophaseeulerfoam

Development of twophaseeulerfoam ISPRAS OPEN 2016 NUMERICAL STUDY OF SADDLE-SHAPED VOID FRACTION PROFILES EFFECT ON THERMAL HYDRAULIC PARAMETERS OF THE CHANNEL WITH TWO-PHASE FLOW USING OPENFOAM AND COMPARISON WITH EXPERIMENTS Varseev

More information

CFD SIMULATIONS OF THE SPENT FUEL POOL IN THE LOSS OF COOLANT ACCIDENT

CFD SIMULATIONS OF THE SPENT FUEL POOL IN THE LOSS OF COOLANT ACCIDENT HEFAT2012 9 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 16 18 July 2012 Malta CFD SIMULATIONS OF THE SPENT FUEL POOL IN THE LOSS OF COOLANT ACCIDENT Lin Y.T., Chiu

More information

EFFECT OF DISTRIBUTION OF VOLUMETRIC HEAT GENERATION ON MODERATOR TEMPERATURE DISTRIBUTION

EFFECT OF DISTRIBUTION OF VOLUMETRIC HEAT GENERATION ON MODERATOR TEMPERATURE DISTRIBUTION EFFECT OF DISTRIBUTION OF VOLUMETRIC HEAT GENERATION ON MODERATOR TEMPERATURE DISTRIBUTION A. K. Kansal, P. Suryanarayana, N. K. Maheshwari Reactor Engineering Division, Bhabha Atomic Research Centre,

More information

The effect of momentum flux ratio and turbulence model on the numerical prediction of atomization characteristics of air assisted liquid jets

The effect of momentum flux ratio and turbulence model on the numerical prediction of atomization characteristics of air assisted liquid jets ILASS Americas, 26 th Annual Conference on Liquid Atomization and Spray Systems, Portland, OR, May 204 The effect of momentum flux ratio and turbulence model on the numerical prediction of atomization

More information

Flow analysis in centrifugal compressor vaneless diffusers

Flow analysis in centrifugal compressor vaneless diffusers 348 Journal of Scientific & Industrial Research J SCI IND RES VOL 67 MAY 2008 Vol. 67, May 2008, pp. 348-354 Flow analysis in centrifugal compressor vaneless diffusers Ozturk Tatar, Adnan Ozturk and Ali

More information

Research Article Analysis of Subchannel and Rod Bundle PSBT Experiments with CATHARE 3

Research Article Analysis of Subchannel and Rod Bundle PSBT Experiments with CATHARE 3 Science and Technology of Nuclear Installations Volume 22, Article ID 23426, pages doi:.55/22/23426 Research Article Analysis of Subchannel and Rod Bundle PSBT Experiments with CATHARE 3 M. Valette CEA

More information

Computational and Experimental Studies of Fluid flow and Heat Transfer in a Calandria Based Reactor

Computational and Experimental Studies of Fluid flow and Heat Transfer in a Calandria Based Reactor Computational and Experimental Studies of Fluid flow and Heat Transfer in a Calandria Based Reactor SD Ravi 1, NKS Rajan 2 and PS Kulkarni 3 1 Dept. of Aerospace Engg., IISc, Bangalore, India. ravi@cgpl.iisc.ernet.in

More information

FIELD TEST OF WATER-STEAM SEPARATORS FOR THE DSG PROCESS

FIELD TEST OF WATER-STEAM SEPARATORS FOR THE DSG PROCESS FIELD TEST OF WATER-STEAM SEPARATORS FOR THE DSG PROCESS Markus Eck 1, Holger Schmidt 2, Martin Eickhoff 3, Tobias Hirsch 1 1 German Aerospace Center (DLR), Institute of Technical Thermodynamics, Pfaffenwaldring

More information

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel *1 Hüseyin Kaya, 2 Kamil Arslan 1 Bartın University, Mechanical Engineering Department, Bartın, Turkey

More information

Steady and Unsteady Computational Results of Full Two Dimensional Governing Equations for Annular Internal Condensing Flows

Steady and Unsteady Computational Results of Full Two Dimensional Governing Equations for Annular Internal Condensing Flows Steady and Unsteady Computational Results of Full Two Dimensional Governing Equations for Annular Internal Condensing Flows R. Naik*, S. Mitra, A. Narain and N. Shankar Michigan Technological University

More information

Modeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics!

Modeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics! http://www.nd.edu/~gtryggva/cfd-course/! Modeling Complex Flows! Grétar Tryggvason! Spring 2011! Direct Numerical Simulations! In direct numerical simulations the full unsteady Navier-Stokes equations

More information

Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders

Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders A. Jugal M. Panchal, B. A M Lakdawala 2 A. M. Tech student, Mechanical Engineering Department, Institute

More information

ENERGY PERFORMANCE IMPROVEMENT, FLOW BEHAVIOR AND HEAT TRANSFER INVESTIGATION IN A CIRCULAR TUBE WITH V-DOWNSTREAM DISCRETE BAFFLES

ENERGY PERFORMANCE IMPROVEMENT, FLOW BEHAVIOR AND HEAT TRANSFER INVESTIGATION IN A CIRCULAR TUBE WITH V-DOWNSTREAM DISCRETE BAFFLES Journal of Mathematics and Statistics 9 (4): 339-348, 2013 ISSN: 1549-3644 2013 doi:10.3844/jmssp.2013.339.348 Published Online 9 (4) 2013 (http://www.thescipub.com/jmss.toc) ENERGY PERFORMANCE IMPROVEMENT,

More information

Heat Transfer Modeling using ANSYS FLUENT

Heat Transfer Modeling using ANSYS FLUENT Lecture 1 - Introduction 14.5 Release Heat Transfer Modeling using ANSYS FLUENT 2013 ANSYS, Inc. March 28, 2013 1 Release 14.5 Outline Modes of Heat Transfer Basic Heat Transfer Phenomena Conduction Convection

More information

A Study on Hydraulic Resistance of Porous Media Approach for CANDU-6 Moderator Analysis

A Study on Hydraulic Resistance of Porous Media Approach for CANDU-6 Moderator Analysis Proceedings of the Korean Nuclear Society Spring Meeting Kwangju, Korea, May 2002 A Study on Hydraulic Resistance of Porous Media Approach for CANDU-6 Moderator Analysis Churl Yoon, Bo Wook Rhee, and Byung-Joo

More information

COMPUTATIONAL FLOW ANALYSIS THROUGH A DOUBLE-SUCTION IMPELLER OF A CENTRIFUGAL PUMP

COMPUTATIONAL FLOW ANALYSIS THROUGH A DOUBLE-SUCTION IMPELLER OF A CENTRIFUGAL PUMP Proceedings of the Fortieth National Conference on Fluid Mechanics and Fluid Power December 12-14, 2013, NIT Hamirpur, Himachal Pradesh, India FMFP2013_141 COMPUTATIONAL FLOW ANALYSIS THROUGH A DOUBLE-SUCTION

More information

PREFACE. Julian C. Smith Peter Harriott. xvii

PREFACE. Julian C. Smith Peter Harriott. xvii PREFACE This sixth edition of the text on the unit operations of chemical engineering has been extensively revised and updated, with much new material and considerable condensation of some sections. Its

More information

INTERNAL FLOW IN A Y-JET ATOMISER ---NUMERICAL MODELLING---

INTERNAL FLOW IN A Y-JET ATOMISER ---NUMERICAL MODELLING--- ILASS-Europe 2002 Zaragoza 9 11 September 2002 INTERNAL FLOW IN A Y-JET ATOMISER ---NUMERICAL MODELLING--- Z. Tapia, A. Chávez e-mail: ztapia@imp.mx Instituto Mexicano del Petróleo Blvd. Adolfo Ruiz Cortines

More information

Investigation of Flow Profile in Open Channels using CFD

Investigation of Flow Profile in Open Channels using CFD Investigation of Flow Profile in Open Channels using CFD B. K. Gandhi 1, H.K. Verma 2 and Boby Abraham 3 Abstract Accuracy of the efficiency measurement of a hydro-electric generating unit depends on the

More information

Simplified Model of WWER-440 Fuel Assembly for ThermoHydraulic Analysis

Simplified Model of WWER-440 Fuel Assembly for ThermoHydraulic Analysis 1 Portál pre odborné publikovanie ISSN 1338-0087 Simplified Model of WWER-440 Fuel Assembly for ThermoHydraulic Analysis Jakubec Jakub Elektrotechnika 13.02.2013 This work deals with thermo-hydraulic processes

More information

NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL CYCLONE

NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL CYCLONE Applied Mathematics and Mechanics (English Edition), 2006, 27(2):247 253 c Editorial Committee of Appl. Math. Mech., ISSN 0253-4827 NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL

More information

CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE

CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE In this chapter, the governing equations for the proposed numerical model with discretisation methods are presented. Spiral

More information

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic

More information

INTRODUCTION TO CATALYTIC COMBUSTION

INTRODUCTION TO CATALYTIC COMBUSTION INTRODUCTION TO CATALYTIC COMBUSTION R.E. Hayes Professor of Chemical Engineering Department of Chemical and Materials Engineering University of Alberta, Canada and S.T. Kolaczkowski Professor of Chemical

More information

FLOW CHARACTERISTICS IN A VOLUTE-TYPE CENTRIFUGAL PUMP USING LARGE EDDY SIMULATION

FLOW CHARACTERISTICS IN A VOLUTE-TYPE CENTRIFUGAL PUMP USING LARGE EDDY SIMULATION FLOW CHARACTERISTICS IN A VOLUTE-TYPE CENTRIFUGAL PUMP USING LARGE EDDY SIMULATION Beomjun Kye Keuntae Park Department of Mechanical & Aerospace Engineering Department of Mechanical & Aerospace Engineering

More information

Application of a Helmholtz resonator excited by grazing flow for manipulation of a turbulent boundary layer

Application of a Helmholtz resonator excited by grazing flow for manipulation of a turbulent boundary layer Application of a Helmholtz resonator excited by grazing flow for manipulation of a turbulent boundary layer Farzin Ghanadi School of Mechanical Engineering The University of Adelaide South Australia, 5005

More information

Unsteady RANS and LES Analyses of Hooper s Hydraulics Experiment in a Tight Lattice Bare Rod-bundle

Unsteady RANS and LES Analyses of Hooper s Hydraulics Experiment in a Tight Lattice Bare Rod-bundle Unsteady RANS and LES Analyses of Hooper s Hydraulics Experiment in a Tight Lattice Bare Rod-bundle L. Chandra* 1, F. Roelofs, E. M. J. Komen E. Baglietto Nuclear Research and consultancy Group Westerduinweg

More information

COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics

COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid

More information

CFD study for cross flow heat exchanger with integral finned tube

CFD study for cross flow heat exchanger with integral finned tube International Journal of Scientific and Research Publications, Volume 6, Issue 6, June 2016 668 CFD study for cross flow heat exchanger with integral finned tube Zena K. Kadhim *, Muna S. Kassim **, Adel

More information

SIMULATION OF THERMAL CHARACTERISTICS OF RADIATORS USING A POROUS MODEL. YETSAN Auto Radiator Co. Inc Çorum, Turkey NOMENCLATURE

SIMULATION OF THERMAL CHARACTERISTICS OF RADIATORS USING A POROUS MODEL. YETSAN Auto Radiator Co. Inc Çorum, Turkey NOMENCLATURE Proceedings of CONV-14: Int. Symp. on ConvectiveHeatandMass Transfer June8 13, 2014, Turkey CONV-14 176 SIMULATION OF THERMAL CHARACTERISTICS OF RADIATORS USING A POROUS MODEL Kadir G. Güler 1,2 and BarbarosÇetin

More information

AN UNCERTAINTY ESTIMATION EXAMPLE FOR BACKWARD FACING STEP CFD SIMULATION. Abstract

AN UNCERTAINTY ESTIMATION EXAMPLE FOR BACKWARD FACING STEP CFD SIMULATION. Abstract nd Workshop on CFD Uncertainty Analysis - Lisbon, 19th and 0th October 006 AN UNCERTAINTY ESTIMATION EXAMPLE FOR BACKWARD FACING STEP CFD SIMULATION Alfredo Iranzo 1, Jesús Valle, Ignacio Trejo 3, Jerónimo

More information

The Pennsylvania State University The Graduate School IMPROVEMENT OF COBRA-TF FOR MODELING OF PWR COLD- AND HOT-LEGS DURING REACTOR TRANSIENTS

The Pennsylvania State University The Graduate School IMPROVEMENT OF COBRA-TF FOR MODELING OF PWR COLD- AND HOT-LEGS DURING REACTOR TRANSIENTS The Pennsylvania State University The Graduate School IMPROVEMENT OF COBRA-TF FOR MODELING OF PWR COLD- AND HOT-LEGS DURING REACTOR TRANSIENTS A Dissertation in Nuclear Engineering by Robert K. Salko c

More information

Fluid Flow, Heat Transfer and Boiling in Micro-Channels

Fluid Flow, Heat Transfer and Boiling in Micro-Channels L.P. Yarin A. Mosyak G. Hetsroni Fluid Flow, Heat Transfer and Boiling in Micro-Channels 4Q Springer 1 Introduction 1 1.1 General Overview 1 1.2 Scope and Contents of Part 1 2 1.3 Scope and Contents of

More information

NUMERICAL METHOD FOR THREE DIMENSIONAL STEADY-STATE TWO-PHASE FLOW CALCULATIONS

NUMERICAL METHOD FOR THREE DIMENSIONAL STEADY-STATE TWO-PHASE FLOW CALCULATIONS ' ( '- /A NUMERCAL METHOD FOR THREE DMENSONAL STEADY-STATE TWO-PHASE FLOW CALCULATONS P. Raymond,. Toumi (CEA) CE-Saclay DMT/SERMA 91191 Gif sur Yvette, FRANCE Tel: (331) 69 08 26 21 / Fax: 69 08 23 81

More information

Prediction of Critical Heat Flux (CHF) for Vertical Round Tubes with Uniform Heat Flux in Medium Pressure Regime

Prediction of Critical Heat Flux (CHF) for Vertical Round Tubes with Uniform Heat Flux in Medium Pressure Regime Korean J. Chem. Eng., 21(1), 75-80 (2004) Prediction of Critical Heat Flux (CHF) for Vertical Round Tubes with Uniform Heat Flux in Medium Pressure Regime W. Jaewoo Shim and Joo-Yong Park Department of

More information

Theoretical and Experimental Studies on Transient Heat Transfer for Forced Convection Flow of Helium Gas over a Horizontal Cylinder

Theoretical and Experimental Studies on Transient Heat Transfer for Forced Convection Flow of Helium Gas over a Horizontal Cylinder 326 Theoretical and Experimental Studies on Transient Heat Transfer for Forced Convection Flow of Helium Gas over a Horizontal Cylinder Qiusheng LIU, Katsuya FUKUDA and Zheng ZHANG Forced convection transient

More information

HEAT TRANSFER CAPABILITY OF A THERMOSYPHON HEAT TRANSPORT DEVICE WITH EXPERIMENTAL AND CFD STUDIES

HEAT TRANSFER CAPABILITY OF A THERMOSYPHON HEAT TRANSPORT DEVICE WITH EXPERIMENTAL AND CFD STUDIES HEAT TRANSFER CAPABILITY OF A THERMOSYPHON HEAT TRANSPORT DEVICE WITH EXPERIMENTAL AND CFD STUDIES B.M. Lingade a*, Elizabeth Raju b, A Borgohain a, N.K. Maheshwari a, P.K.Vijayan a a Reactor Engineering

More information

Investigation of Jet Impingement on Flat Plate Using Triangular and Trapezoid Vortex Generators

Investigation of Jet Impingement on Flat Plate Using Triangular and Trapezoid Vortex Generators ISSN 2395-1621 Investigation of Jet Impingement on Flat Plate Using Triangular and Trapezoid Vortex Generators #1 Sonali S Nagawade, #2 Prof. S Y Bhosale, #3 Prof. N K Chougule 1 Sonalinagawade1@gmail.com

More information

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

AGITATION AND AERATION

AGITATION AND AERATION AGITATION AND AERATION Although in many aerobic cultures, gas sparging provides the method for both mixing and aeration - it is important that these two aspects of fermenter design be considered separately.

More information

Comparison Of Square-hole And Round-hole Film Cooling: A Computational Study

Comparison Of Square-hole And Round-hole Film Cooling: A Computational Study University of Central Florida Electronic Theses and Dissertations Masters Thesis (Open Access) Comparison Of Square-hole And Round-hole Film Cooling: A Computational Study 2004 Michael Glenn Durham University

More information

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 7, p (July 2004)

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 7, p (July 2004) Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 7, p. 765 770 (July 2004) TECHNICAL REPORT Experimental and Operational Verification of the HTR-10 Once-Through Steam Generator (SG) Heat-transfer

More information

Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow

Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow Sutardi 1, Wawan A. W., Nadia, N. and Puspita, K. 1 Mechanical Engineering

More information

Simulating Interfacial Tension of a Falling. Drop in a Moving Mesh Framework

Simulating Interfacial Tension of a Falling. Drop in a Moving Mesh Framework Simulating Interfacial Tension of a Falling Drop in a Moving Mesh Framework Anja R. Paschedag a,, Blair Perot b a TU Berlin, Institute of Chemical Engineering, 10623 Berlin, Germany b University of Massachusetts,

More information

Laboratory of Thermal Hydraulics. General Overview

Laboratory of Thermal Hydraulics. General Overview Visit of Nuclear Master Students Laboratory of Thermal Hydraulics General Overview Horst-Michael Prasser December 04, 2009 Paul Scherrer Institut Main Goals Development of analytical and experimental methods

More information

Effect of roughness shape on heat transfer and flow friction characteristics of solar air heater with roughened absorber plate

Effect of roughness shape on heat transfer and flow friction characteristics of solar air heater with roughened absorber plate Advanced Computational Methods in Heat Transfer IX 43 Effect of roughness shape on heat transfer and flow friction characteristics of solar air heater with roughened absorber plate A. Chaube 1, P. K. Sahoo

More information

Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks

Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks by Waqar Ahmed Khan Athesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree

More information

The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering

The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering SPACER GRID INDUCED HEAT TRANSFER ENHANCEMENT IN A ROD BUNDLE UNDER REFLOOD CONDITIONS A Dissertation

More information

Onset of Flow Instability in a Rectangular Channel Under Transversely Uniform and Non-uniform Heating

Onset of Flow Instability in a Rectangular Channel Under Transversely Uniform and Non-uniform Heating Onset of Flow Instability in a Rectangular Channel Under Transversely Uniform and Non-uniform Heating Omar S. Al-Yahia, Taewoo Kim, Daeseong Jo School of Mechanical Engineering, Kyungpook National University

More information