The Pennsylvania State University. The Graduate School. College of Engineering INVESTIGATION OF COUPLED CODE PRESSURIZED WATER REACTOR

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1 The Pennsylvania State University The Graduate School College of Engineering INVESTIGATION OF COUPLED CODE PRESSURIZED WATER REACTOR SIMULATIONS USING CTF WITH SOLUBLE BORON TRACKING A Thesis in Nuclear Engineering by Mark B. Biery 2013 Mark B. Biery Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2013

2 The thesis of Mark B. Biery was reviewed and approved* by the following: Maria N. Avramova Assistant Professor of Nuclear Engineering Thesis Advisor Kostadin N. Ivanov Distinguished Professor of Nuclear Engineering Arthur T. Motta Professor of Nuclear Engineering and Materials Science and Engineering Chair of the Department of Nuclear Engineering *Signatures are on file in the Graduate School. ii

3 ABSTRACT For long term reactivity control over a nuclear reactor core fuel cycle, pressurized water reactors make use of chemical shim in the form of soluble boron added to the coolant water. While soluble boron allows for even reactivity control and more uniform fuel burn-up, maintaining uniform distribution of the boron is important to prevent localized transients. Transients that are caused by a local disturbance in the concentration of boron are classified as boron dilution transients. While many studies have been performed to study these types of transients, the choice of existing codes available to simulate soluble boron transport have required tradeoffs to be made. Popularly used system codes such as RELAP5-3D can only simulate one-dimensional boron transport with comparatively simple physical models which neglect important physical characteristics of boron transport in the fluid such as mixing due to cross flow between channels and turbulence effects. On the other extreme, Computational Fluid Dynamics (CFD) codes are capable of modeling boron transport with very high fidelity, but most CFD codes still require a large amount of computational resources to simulate a realistic physical model. Recent work by members of The Pennsylvania State University, Department of Mechanical and Nuclear Engineering, Reactor Dynamics and Fuel Management Group has helped to fill this capability gap. The result is an improvement to the Penn State version of COBRA-TF, PSU CTF by employing a newly developed boron tracking model. The resulting version of CTF is known as CTF-BTM. The implemented boron tracking model uses a Modified Godunov method to solve the boron transport field equation. Although the CTF boron tracking model was rigorously tested at the time it was developed, it has not yet been used in coupled thermal hydraulics and neutronics simulations, which is the aim of this study. iii

4 The objective of this study is to continue the validation and qualification of the boron tracking model used in CTF-BTM. This is accomplished by first coupling CTF-BTM to the nodal diffusion-based neutronics code NEM. Part II and Part III of the 2007 OECD / NEA MOX / UO 2 Core Transient Benchmark are then used to validate the coupled code at Hot-Full Power (HFP) conditions and Hot-Zero Power (HZP) conditions. Close agreement to the benchmark solutions is achieved in both cases. Between the boron tracking and non-boron tracking code versions, the results at HZP were nearly identical with a 0.01 ppm difference of predicted critical boron and a 0.33% deviation from the benchmark reference solution. At HFP conditions, the differences introduced by the boron tracking model were more obvious. The boron tracking model result produced a larger deviation from the benchmark reference solution with a 0.61% deviation versus a 0.02% deviation predicted by the non-boron tracking code version. It was concluded that this larger deviation from the benchmark reference solution was due to the fact that the boron tracking model provides a more realistic treatment of the boron transport behavior by allowing the boron concentration to change with moderator density changes and moderator void formation. Although a soluble boron transient benchmark was not available for this particular core model, a systematic approach is used to build upon the successful steady-state benchmarking of the coupled code. For transient verification, a series of steady-state calculations are first carried out to find the effective multiplication factor of the core at varying levels of coolant boron concentration. Using these data to predict the core reactivity change for a prescribed change in inlet boron concentration, a series of inlet boron concentration transient simulations are carried out. The core response to the boron transient is then compared to the predicted reactivity change. Of five cases simulated, it was found that smaller and more rapid changes in reactivity produced a result that more closely matched predicted reactivity. More gradual and larger changes in reactivity caused fuel heating or cooling to occur which introduced Doppler feedback effects. iv

5 Although it proved difficult to produce transient simulation results that exactly matched predicted reactivity changes, deviations from predicted reactivity changes could be explained by changes in fuel temperature corresponding to changes in reactivity introduced by the change in coolant boron concentration. This study then culminates in the execution of a postulated post-small Break Loss Of Coolant Accident (SBLOCA) boron dilution accident and an accompanying sensitivity study. While the scenario is highly idealized in terms of initiating events and assumptions, it provides an example of one of the expected future applications of coupled CTF and three-dimensional neutronics codes in LWR simulations with the introduction of boron tracking capability. In this culminating scenario, a series of simulations are executed where deborated condensate water slugs are inserted into the core. The slugs are formed in the steam generators by condensation following loss of coolant inventory sufficient to maintain natural circulation. In the natural circulation cases, a 1.16 m 3 slug is assumed. Following formation of the condensate mass, natural circulation is assumed to resume, carrying the condensate slug into the core. The location of slug entry is varied from the core periphery to the core center along an expected path of travel in the lower plenum. It is found that, of the locations where the slug was expected to enter, the most limiting location was fuel assembly E3 (sub-channel 158). The limiting case was determined by the peak fuel enthalpy in the hottest fuel node, which in this case peaked at cal/g. This is well below the enthalpy level expected to cause fuel damage. After finding the limiting location of condensate slug entry in the natural circulation cases, the case is simulated again with the condensate slug entering the same location with the same volume, but at forced circulation conditions assuming actuation of the corresponding reactor coolant pump. As expected, the core response was more violent than exhibited in the natural circulation cases with a larger power excursion and peak fuel enthalpy of cal/g. At this v

6 fuel enthalpy level, extensive fuel damage is expected. In the final simulation case, the forced circulation case is executed again, but with a 4 m 3 condensate slug volume. The cross sectional area of the slug remains unchanged which gives the slug a longer length. In this case, the heating of the fuel occurred for a longer period of time due to the longer power excursion event. The peak fuel enthalpy in this case was cal/g with extensive fuel damage expected. Given the assumptions made in the boron dilution accident scenario simulation cases, the formulation used represents worst case boron dilution accident conditions due to the amount of approximations and simplifications used and the level of compensatory conservatism in the formulation. While many studies have been performed elsewhere on boron dilution accidents for currently operating Pressurized Water Reactors (PWRs) this study is one of few focused on boron dilution simulations in a PWR with a MOX/UO 2 core. vi

7 TABLE OF CONTENTS LIST OF ABBREVIATIONS ix LIST OF FIGURES xi LIST OF TABLES xiv NOMENCLATURE xv ACKNOWLEDGMENTS xvii CHAPTER 1: BACKGROUND AND INTRODUCTION Background Introduction Research Objectives Thesis Outline 6 CHAPTER 2: NEM, CTF, AND BORON TRACKING MODEL OVERVIEWS NEM Overview CTF Overview CTF Boron Tracking Model 12 CHAPTER 3: PURDUE MOX / UO 2 CORE MODEL DESCRIPTION Core Model Overview Cross Section Data Discretization and Nodalization Scheme 20 CHAPTER 4: CTF-BTM AND NEM CODE COUPLING Introduction Coupling Methodology Steady-State Solution and Transient Simulation k-search Implementation 27 CHAPTER 5: COUPLED CODE BENCHMARKING AND VERIFICATION Introduction Steady-State Benchmarking at HFP Steady-State Benchmarking at HZP Transient Code Verification Exercises 41 vii

8 CHAPTER 6: BORON DILUTION TRANSIENT SIMULATIONS Introduction Accident Scenario Initiating Events Assumptions and Scenario Formulation Condensate Entrance Sensitivity Study Natural Circulation Extreme Accident Cases Condensate Entry by Forced Circulation Uncertainties Accident Simulation Conclusions 87 CHAPTER 7: CONCLUSIONS Conclusions Recommendations for Continued Work 93 APPENDIX A. PURDUE MOX / UO 2 CORE MAPS 98 APPENDIX B. TRANSIENT TEST RESULTS 102 APPENDIX C. ACCIDENT TRANSIENT RESULTS NAT. CIRCULATION CASES 110 viii

9 LIST OF ABBREVIATIONS BTM CFD CHF COBRA-TF CTF CVCS DeCART EWE GSI HFP HZP IFBA LOCA LWR MNE MOC MOX NEA NEM NRC NSSS Boron Tracking Model Computational Fluid Dynamics Critical Heat Flux COolant in Boiling Rod Arrays Two Fluid Penn State Version of COBRA-TF Chemical and Volume Control System Deterministic Core Analysis based on Ray Tracing Error Weighted Error Generic Safety Issue Hot Full Power Hot Zero Power Integral Fuel Burnable Absorber Loss Of Coolant Accident Light Water Reactor Department of Mechanical and Nuclear Engineering Method Of Characteristics Mixed OXide Nuclear Energy Agency Nodal Expansion Method US Nuclear Regulatory Commission Nuclear Steam Supply System ix

10 OECD PARCS PSU PWE PWR RDFMG RELAP RCP SBLOCA SCRAM Organization for Economic Cooperation and Development Purdue Advanced Reactor Core Simulator The Pennsylvania State University Power Weighted Error Pressurized Water Reactor Reactor Dynamics and Fuel Management Group Reactor Excursion and Leak Analysis Program Reactor Coolant Pump Small Break Loss Of Coolant Accident Safety Control Rod Ax Man (term left over from the early years of nuclear energy denotes full control rod insertion as quickly as possible) TH UO 2 Thermal Hydraulic Uranium Dioxide x

11 LIST OF FIGURES Figure 2.1.1: Example NEMTAB Cross Section Table Figure 2.3.1: Spatial Notation Used to Demonstrate the Modified Godunov Scheme Figure 3.1.1: Purdue MOX Core Loading Pattern (Quarter Core) Figure 4.3.1: Illustration of the Explicit Steady-State Code Coupling Scheme Figure 4.3.2: Coupled Code Transient Time Step Marching Scheme Figure 5.2.1: Quarter Core HFP Radial Power Distribution Figure 5.2.2: Radially Averaged Core HFP Axial Power Distributions Figure 5.2.3: Radially Averaged Core Boron Concentration at Each Axial Level Figure 5.2.4: Radially Averaged Core Boron Density at Each Axial Level Figure 5.3.1: Quarter Core HZP Radial Power Distribution Figure 5.3.2: Radially Averaged Core HZP Axial Power Distributions Figure 5.4.1: HZP Steady-State Multiplication Factor vs. Inlet Boron Concentration Figure 5.4.2: HZP Steady-State Core Reactivity vs. Inlet Boron Concentration Figure 5.4.3: Transient Test Case 1 Core Reactivity vs. Time Figure 5.4.4: Transient Test Case 1 Average Fuel and Moderator Temp. vs. Time Figure 5.4.5: Transient Test Case 1 Inlet Boron Concentration vs. Time Figure 5.4.6: Transient Test Case 2 Core Reactivity vs. Time Figure 5.4.7: Transient Test Case 2 Average Fuel and Moderator Temp. vs. Time Figure 5.4.8: Transient Test Case 2 Inlet Boron Concentration vs. Time Figure 5.4.9: Transient Test Case 3 Core Reactivity vs. Time Figure : Transient Test Case 3 Average Fuel and Moderator Temp. vs. Time Figure : Transient Test Case 5 Core Reactivity vs. Time Figure : Transient Test Case 5 Average Fuel and Moderator Temp. vs. Time Figure 6.2.2: Simplified Diagram of Boron Dilution Due to Reflux Condensation in Post-SBLOCA Conditions Figure 6.3.2: Westinghouse 4-Loop Reactor Vessel Side Cut-Away View Figure 6.3.3: Westinghouse 4-Loop Reactor Vessel Cut-Away View at Nozzle Level Figure 6.4.1: Discretized Possible Condensate Water Slug Entrance Locations Figure 6.4.2: Condensate Water Slug Discretization (assuming 27.5 in diameter) Figure 6.4.5: Case 4 Power Evolution with Time Figure 6.4.6: Case 4 Reactivity Evolution with Time Figure 6.4.7: Case 4 Temperature Evolution with Time Figure : Case 4 Boron Concentration Distribution Prior to Transient Figure : Case 4 Radial Power Distribution at Peak Core Power Figure : Case 4 Axial Power Distribution at Peak Core Power Figure : Case 4 Boron Concentration Distribution at Peak Core Power Figure 6.5.1: Condensate Water Slug Discretization Forced Circulation Case xi

12 Figure 6.5.2: Forced Circulation Case 1 Power Evolution with Time Figure 6.5.3: Forced Circulation Case 1 Log (Base 10) Power Evolution with Time Figure 6.5.5: Forced Circulation Case 1 Radial Power Distribution at Peak Core Power Figure 6.5.6: Forced Circulation Case 1 Axial Power Distribution at Peak Core Power Figure 6.5.7: Forced Circulation Case 1 Boron Concentration Distribution at Peak Core Power Figure 6.5.8: Forced Circulation Case 1 Temperature Evolution with Time Figure 6.5.9: Forced Circulation Case Fuel Temperature Distribution at Time 3 Seconds. 81 Figure : Forced Circulation Case 2 Log (Base 10) Power Evolution with Time Figure A.1: Core Assembly Loading Pattern Figure A.2: NEM Radial Node Pattern Map Figure A.3: Radial CTF Sub-channel Pattern Map Figure A.4: Core Control Rod Bank Map Figure B.1: Transient Test Case 1 Core Reactivity vs. Time Figure B.2: Transient Test Case 1 Average Fuel and Moderator Temp. vs. Time Figure B.3: Transient Test Case 1 Inlet Boron Concentration vs. Time Figure B.4: Transient Test Case 2 Core Reactivity vs. Time Figure B.5: Transient Test Case 2 Average Fuel and Moderator Temp. vs. Time Figure B.6: Transient Test Case 2 Inlet Boron Concentration vs. Time Figure B.7: Transient Test Case 3 Core Reactivity vs. Time Figure B.8: Transient Test Case 3 Average Fuel and Moderator Temp. vs. Time Figure B.9: Transient Test Case 3 Inlet Boron Concentration vs. Time Figure B.10: Transient Test Case 4 Core Reactivity vs. Time Figure B.11: Transient Test Case 4 Average Fuel and Moderator Temp. vs. Time Figure B.12: Transient Test Case 4 Inlet Boron Concentration vs. Time Figure B.13: Transient Test Case 5 Core Reactivity vs. Time Figure B.14: Transient Test Case 5 Average Fuel and Moderator Temp. vs. Time Figure B.15: Transient Test Case 5 Inlet Boron Concentration vs. Time Figure C.1: Case 1 Power Evolution with Time Figure C.2: Case 1 Reactivity Evolution with Time Figure C.3: Case 1 Temperature Evolution with Time Figure C.4: Case 2 Power Evolution with Time Figure C.5: Case 2 Reactivity Evolution with Time Figure C.6: Case 2 Temperature Evolution with Time Figure C.7: Case 3 Power Evolution with Time Figure C.8: Case 3 Reactivity Evolution with Time Figure C.9: Case 3 Temperature Evolution with Time Figure C.10: Case 4 Power Evolution with Time Figure C.11: Case 4 Reactivity Evolution with Time Figure C.12: Case 4 Temperature Evolution with Time Figure C.13: Case 5 Power Evolution with Time Figure C.14: Case 5 Reactivity Evolution with Time Figure C.15: Case 5 Temperature Evolution with Time Figure C.16: Case 6 Power Evolution with Time xii

13 Figure C.17: Case 6 Reactivity Evolution with Time Figure C.18: Case 6 Temperature Evolution with Time Figure C.19: Case 7 Power Evolution with Time Figure C.20: Case 7 Reactivity Evolution with Time Figure C.21: Case 7 Temperature Evolution with Time Figure C.22: Case 8 Power Evolution with Time Figure C.23: Case 8 Reactivity Evolution with Time Figure C.24: Case 8 Temperature Evolution with Time xiii

14 LIST OF TABLES Table 3.1.1: Purdue MOX Core Selected Specifications and Operating Data Table 3.2.2: Tabulated Cross Section Thermal Hydraulic Range Table 5.2.1: Selected HFP Benchmarking k-search Simulation Parameters Table 5.2.2: HFP Benchmarking Overall Results [20] Table 5.3.1: Selected HZP Benchmarking k-search Simulation Parameters Table 5.3.2: HZP Benchmarking Overall Results [20] Table 5.4.1: Overall Transient Verification Reactivity Change Results Table 6.3.2: Original and Modified Inlet Coolant Flow Conditions Table 6.3.1: Selected Boron Dilution Transient Input Conditions (All Cases) Table 6.4.1: Natural Circulation Simulation Cases Executed Table 6.4.2: Natural Circulation Simulation Core Wide Results Summary Table 6.4.3: Hot Fuel Node Peak Results Summary Table 6.5.1: Forced Circulation Core Wide Results Comparison Table 6.5.2: Forced Circulation Hot Fuel Node Results Comparison xiv

15 NOMENCLATURE Variables and Symbols A C Cr D dk G k q R Re S t v x α Δt θ ρ Φ ϕ = Cross Sectional Area = Boron Concentration = Courant Number = Diffusion Coefficient = Delta k (Reactivity) = Mass Flux = Multiplication Factor = Mass Flow Rate = Ratio of Loop and Safety Injection Flow Rates = Reynolds Number = Source Term = Time = Velocity = Cartesian Spatial Coordinate = Void Fraction = Time Increment = Discontinuity Detector = Density = Roe s Superbee Limiter = Limited Diffusion Term xv

16 ω = Yee s Compression Constant Superscripts and Subscripts B Eddy f i in j K L M n p SI Boron Eddy Diffusion Liquid Phase Iteration Index Inlet Spatial Index Node Identifier Node Identifier or Loop Node Identifier Time Index Particle Safety Injection xvi

17 ACKNOWLEDGMENTS I would first like to thank my advisor Dr. Maria Avramova, for her support, advice, invested trust, and encouragement throughout the course of my Masters studies at Penn State. I would also like to thank Dr. Kostadin Ivanov for his support and encouragement during the course of this work. I must also thank Dr. Robert Salko for his valuable technical assistance with CTF. I wish to thank the Pennsylvania State University for providing funding during much of my Masters studies as well as helping me to make a successful transition from life in military service back into civilian life. Finally, I would like to thank my wife Meghan, for putting up with the endless long nights I spent working in the office during this project. Her love, support, understanding, and encouragement were crucial in making this endeavor a successful one. xvii

18 CHAPTER 1 BACKGROUND AND INTRODUCTION 1.1 Background One of the primary reactivity control mechanisms of PWRs is through the introduction of chemical shim to the primary loop coolant. Boric acid (H 3 BO 3 ) is the most common form of chemical shim. The soluble boron that is mixed with the coolant as a result of the addition of chemical shim allows for much more uniform reactivity control and helps to reduce localized neutron flux peaking and core transients. This leads to more uniform fuel burn-up over the core lifetime and improved fuel utilization of the individual fuel assemblies and fuel rods. Despite the advantages, chemical shim reactivity control does have some limitations. First, under nominal conditions, the amount of time required for changing the concentration of boron in the coolant and thus changing the reactivity contribution of the dissolved boron is substantially longer as compared to mechanical control rod movements. To change the soluble boron concentration, the primary coolant must be circulated through the Chemical and Volume Control System (CVCS). Once the coolant enters the CVCS, the boron concentration is either diluted by adding purified water or further concentrated by adding additional boric acid. The time to change the concentration of the boric acid throughout the primary loop takes on the order of minutes to hours depending on the flow rate of the particular CVCS system and the amount of boron concentration change required [1, 2]. Thus chemical shim control is generally used to compensate for longer term changes in core reactivity as fuel burn-up progresses while mechanical control rods are used for short term control of the core [3]. 1

19 The second limitation of chemical shim reactivity control is that, while the soluble boron will remain almost uniformly mixed with the coolant under normal operating conditions due to the forced circulation of the reactor coolant pumps and the turbulent mixing which occurs the primary loop, certain conditions may occur that cause an abnormal and perhaps localized dilution of the coolant. Unlike control rod positions, dilution of soluble boron is more difficult to immediately detect by the plant operator in the main control room since there is generally no instrumentation to directly detect that this is occurring or where in the primary loop it is occurring [2]. Conditions and situations that may cause boron dilution during normal plant conditions are generally well categorized and reliance is placed on operating procedures and technical specifications to reduce the possibility of inadvertent boron dilution [4]. However, the possibility of such an event, known as a boron dilution transient, still exists [5]. During post-accident conditions, the potential for a boron dilution accident is increased. An example, as postulated by the Nuclear Regulatory Commission (NRC) Generic Safety Issue 185 (GSI-185), is such an event occurring during post-loss Of Coolant Accident (post-loca) Conditions [6]. Following a SBLOCA, core boiling will occur for a number of hours until decay heat is sufficiently reduced by safety injection coolant flow. During this time, the coolant inventory may be sufficiently reduced such that natural circulation ceases and the core begins to operate in a boiler and condenser mode. While the core coolant continues boiling, water vapor rising in the hot leg portion of the primary loop (at this stage now only partially filled) may then condense in the steam generators via reflux condensation. In U-tube steam generators, deborated water may then collect on the cold side of the steam generators as well as in the cross over leg between the steam generator outlet and reactor coolant pump inlets and eventually form a large mass of low boron water. If natural circulation is restored in the primary loop or if forced circulation is started, this mass of deborated condensate may enter the core with insufficient mixing to recover the nominal boron concentration. If the mass of condensate is large and dilute 2

20 enough, the resulting positive insertion of reactivity may exceed the reactivity worth of the fully inserted control rods and cause a return to criticality and possibly a reactivity excursion causing fuel damage. In order to accurately model such boron transients, a capability to model the transport and mixing mechanisms is needed. System codes such as Reactor Excursion and Leak Analysis Program (RELAP) are able to model the boron transient in one dimension only [7]. Because of being able to model the boron transient in a single dimension only, system codes such RELAP neglect important physical characteristics of the boron transport such as cross channel mixing from diffusion and turbulence. Computational Fluid Dynamics (CFD) simulations on the other hand, are capable of fully capturing these important features of boron transport. However, the computational cost associated with accurate CFD simulations is still very high. Additionally, experience with coupling CFD with core neutronics codes is still in the early stages compared to coupling with system or sub-channel codes [8, 9]. These deficiencies indicate a capability gap in modeling boron transport. 1.2 Introduction Over the past several years, members of The Pennsylvania State University, Department of Mechanical and Nuclear Engineering (PSU MNE), Reactor Dynamics and Fuel Management Group (RDFMG) have been working to provide higher fidelity boron transport simulations at a reasonable computation cost. The additional capabilities that were added to the Penn State version of the code COolant in Boiling Rod Arrays-Two Fluid (COBRA-TF) or PSU CTF allows boron transport to be simulated in a manner that balances higher spatial and physical accuracy with reasonable computation cost. 3

21 The purpose of this project is to build upon the recent progress made in the implementation and improvement of the capabilities of CTF by benchmarking and employing the improved code in a series of verification studies on a chosen core model. To accomplish this, the code is coupled to the Penn State nodal diffusion code NEM (Nodal Expansion Method) which simulates the core model neutronics response. The resulting coupled code is thus referred to as CTF-BTM / NEM. 1.3 Research Objectives The objective of this thesis is to continue validation of the physical accuracy of the boron tracking model implementation introduced to CTF by applying it to coupled reactor core simulations. A series of benchmarking tests and sensitivity analyses are conducted in order to accomplish this objective. The code is first benchmarked at steady-state. The core model employed for this benchmarking is the Purdue MOX / UO 2 core (also known as the Purdue core model) which is used in the 2007 Organization for Economic Cooperation and Development (OECD) and Nuclear Energy Agency (NEA) Core Transient Benchmark [10]. The Purdue core model is based on a typical Westinghouse 4-loop reactor core that is partially loaded with Mixed Oxide fuel (MOX). This particular blend of Mixed Oxide fuel consists of formerly weapons grade Plutonium that is mixed and down-blended with Uranium. The remaining core loading consists of standard Uranium Dioxide fuel assemblies. This core model is of particular interest in this study due to the large neutron flux gradients expected between the unlike fuel assemblies as well as the decreased effective delayed neutron fraction which characterizes Mixed Oxide fuels. In order to obtain steady-state conditions, Part II and Part III of the benchmark specifications for steady operation are used to formulate the boundary conditions of the core model. A k-search 4

22 subroutine created for the purpose of this project is used to determine the inlet boron concentration boundary condition which yields a critical or steady-state core. Steady-state benchmarking is performed at both Hot Full Power conditions (HFP) and Hot Zero Power conditions (HZP). While many studies have been performed on boron concentration behavior in reactor vessel coolant flow and the resulting core response for various core and plant types, a boron transient scenario and benchmark solution for this UO 2 / MOX core model are not available. Due to the lack of a specific benchmark solution, a number of transient verification exercises are systematically performed using the steady-state benchmarking results as the basis to build upon. Following steady-state benchmark verification of the coupled code, the inlet boron concentration is varied at HZP throughout the operating range of tabulated boron concentrations. The resulting multiplication factors are then tabulated and the reactivity worth of the boron is calculated for these various steady-state calculations. A series of homogeneous boron transients are then conducted. By uniformly inserting a calculated amount of reactivity by changing the inlet boron concentration, the core response is assessed and the behavior verified. Since the reactivity of the core at varying steady-state conditions was already tabulated, an ideal transient simulation should produce a similar change in core reactivity to what was calculated. Once verification of the transient code is achieved, a series of accident simulations are carried out based on the GSI-185 scenario to demonstrate the capabilities of the coupled code and evaluate the core response to such an accident scenario. For these simulations, a heterogeneous boron dilution accident is formulated and the scenario is then simulated using natural circulation conditions as well as forced circulation conditions. Selected parameters are varied such as entry location of the condensate slug and mass flow rate of the coolant. 5

23 1.4 Thesis Outline This thesis is structured to take on a building block approach toward briefly explaining the underlying theory of the reactor simulation codes used, the core model employed, the coupling of the reactor analysis codes, subsequent verification efforts of the coupled code, and finally employment in the coupled code in a practical accident scenario simulation. Chapter 2 outlines the codes employed for this project. An overview of NEM is given first followed by an overview of CTF. The chapter closes with an explanation of the boron tracking model theory and implementation. Chapter 3 details the Purdue core model. An overview of the core makeup, selected specifications, cross section library used, and discretization scheme is given. Chapter 4 discusses the coupling methodology used for CTF-BTM and NEM. Additionally, features added to the implemented coupled code such as k-search and boron transient modeling are described. In Chapter 5, steady-state benchmarking of the coupled code using the k-search methodology is first discussed. The results are compared to the 2007 MOX / UO 2 core transient benchmark results as well as results of the non-boron tracking version of the coupled code. Also in Chapter 5, following steady-state verification using the benchmark, boron reactivity is tabulated by varying inlet boron concentration and obtaining the coupled steady-state multiplication factor at each inlet boron concentration and calculating the resulting reactivity worth for the boron. Then while performing a transient simulation of the core, a known amount of reactivity is homogeneously inserted through increase or decrease of the inlet boron concentration 6

24 and the core response is evaluated. In the absence of a known benchmark solution, this approach is used to verify the transient features of the coupled code. In Chapter 6, the coupled code is employed to simulate a boron dilution transient which is initiated by a post-sbloca boron dilution accident. A number of simulation cases are performed where the condensate slug entrance location is varied. Cases of natural circulation flow rate as well as forced circulation flow rate are simulated. The thesis is concluded in Chapter 7 where the contributions made during this project and recommendations for future work are summarized. 7

25 CHAPTER 2 NEM, CTF, AND BORON TRACKING MODEL OVERVIEWS 2.1 NEM Overview The neutronics code used to conduct this project is the Penn State University version of Nodal Expansion Method (PSU NEM). NEM is a multi-group, three-dimensional nodal diffusion code designed to conduct steady-state and transient neutron kinetics neutronics simulations [11]. As many as seventy neutron energy groups may be simulated although the code can be modified for more energy groups if needed. NEM has the capability to simulate systems in Cartesian, cylindrical, and hexagonal-z coordinate systems. U.S. commercial fuel and core loading designs almost universally use a Cartesian coordinate system in their design. Cylindrical coordinates are generally used for high temperature pebble-bed reactor modeling. The hexagonal coordinate system incorporated into NEM, which will be used for fast breeder reactor and VVER applications, is still under development [12]. A standard scheme of inner and outer iterations is used in NEM to solve the diffusion equations. For the inner iterations, the neutron currents are calculated for each energy group. Once the inner iterations are completed either by converging or reaching a set inner iteration limit, the neutron currents are used to predict neutron fluxes. These neutron fluxes are then used to calculate the new source moments from fission, down-scattering, and up-scattering. For the inner iterations, each node in NEM is simulated using a transverse integrated neutron flux representation and transverse leakage approximation. The transverse integrated flux is represented by one-dimensional polynomial expansion in each dimension of the coordinate 8

26 system used. Partial current formulation is used for the nodal coupling relationships. A response matrix is then solved to update the ongoing partial currents [12]. Cross section data is supplied to NEM in one of two ways. The first method is by use of a polynomial fitting procedure entered directly into the NEM input deck (NEMIN). This is the original implementation used in NEM [13]. The second method, which is the one used for this study, is 4-D linear surface interpolation of cross section tables, which are prepared separately [11]. In this method, each material is given a complete set of cross section tables, consisting of the transport cross section, absorption cross section, fission cross section multiplied by average neutron production (nu-fission), kappa-fission cross section, and scattering cross sections between energy groups. Discontinuity factors, fission spectrum, delayed neutron fraction, and precursor decay constants may also be included. Each table includes data for every combination of the range of thermal hydraulic independent variables tabulated. The entire cross section library is built into a separate input file called NEMTAB. An example table is given in Figure

27 Figure 2.1.1: Example NEMTAB Cross Section Table 2.2 CTF Overview CTF is the Penn State version of the reactor core thermal hydraulics code, COolant in Boiling Rod Arrays Two Fluid, COBRA-TF. COBRA-TF is a sub-channel code originally developed by Pacific Northwest Laboratory under NRC contract [14]. In the years following, COBRA-TF has been adapted for use by the commercial nuclear industry for use in best-estimate accident analysis such as LOCA analyses. The code was acquired by Penn State in the 1990s and, following years of further validation and development, has been used extensively by the Penn State MNE department for LWR simulations and studies. Using the sub-channel formulation approach, CTF solves the mass, momentum, and energy equations across each sub-channel node in three dimensions [15]. A separated flow model is used for independent modeling of the three fields that exist in two-phase flow: continuous liquid, entrained liquid droplets, and vapor. 10

28 CTF uses two sets of flow regime maps for determining energy and momentum transfer. A normal or cold-wall flow regime map is used under most conditions to determine the fluid flow regime. However, CTF benefits from also having a set of hot-wall flow regime maps. This allows the code to model the thermal hydraulic conditions of the system when the wall surface temperature increases beyond the Critical Heat Flux (CHF) temperature. This is especially important for accurate modeling of extreme system conditions, which would be prevalent when simulating accident conditions [15]. CTF also models a number of other phenomena in the fluid flow in order both to solve the basic field equations as well as increase the physical modeling accuracy of the code. These phenomena include wall and phase interface shear, wall and phase interface heat transfer, void drift, turbulent mixing, and entrainment of droplets [15]. While COBRA-TF has been widely used and accepted as a reliable code for best estimate safety analyses, it has suffered from a limitation in that it did not have the ability to model soluble boron transport in the coolant. In order to model this solute transport, system codes with this capability, such as RELAP5-3D, had to be used. Otherwise, full Computational Fluid Dynamics (CFD) simulations had to be conducted. While RELAP can model solute transport, it can only model it in one dimension, which is a source of inaccuracy, especially in PWR cores since full fluid flow communication is possible throughout the core [7]. CFD simulations, while capable of modeling the solute transport and other aspects of the coolant flow with extremely high fidelity, have one major drawback: the amount of computational expense associated with CFD is still extremely high compared to system or sub-channel codes. There was clearly an opportunity for CTF to address this capability gap. Recent work by Ozdemir and PSU RDFMG, has addressed these shortcomings in CTF. As a result, CTF now has the capability to model solute transport, giving the code a boron tracking 11

29 capability. The primary motivation of employing a boron tracking model is to give CTF the capability to model the transport and flow behavior of soluble boron in the coolant flow for transient and accident analyses [16]. 2.3 CTF Boron Tracking Model The underlying theory behind the CTF boron tracking model starts with a review of the past implementation and improvement of solute tracking models in RELAP5-3D. The following assumptions are used for the RELAP5 solute tracking models [7]: 1. Liquid (solvent) properties are not altered by the presence of the solute. 2. Solute is transported only in the liquid phase (solvent) and at the velocity of the liquid phase (solvent). 3. Energy transported by the solute is negligible. 4. Inertia of the solute is negligible. Using these assumptions, RELAP5 employs the following field equation for spatial boron conservation: B 1 B v t A x f A 0 (2.3.1) where, C (2.3.2) B f f B In the RELAP5 code, two solution methods are available to solve the boron conservation field equation. By default, the upward difference scheme is used by the code. The user also has the option of using a second-order accurate Godunov scheme [7]. 12

30 Investigations conducted by Freixa et al into the accuracy of the solution methods employed in RELAP5, first concluded that the upward difference scheme suffers from numerical diffusion due to numerical truncation. It was found that the second-order accurate Godunov scheme significantly reduces the numerical diffusion commonly observed in the upward difference scheme. However, accounting for physical diffusion was still lacking in the original RELAP5 Godunov solution scheme. Using the second-order accurate Godunov solution scheme and introducing an eddy diffusivity term to take flow turbulence into account, a modified Godunov solution scheme was devised by Freixa as follows [17]. Using the assumptions made in the RELAP5 solute tracking model, equation is equivalent to the linearized Burger s equation: B t v p B x B D S x x (2.3.3) where, D = D Eddy = 1.35vRe 7/8 (2.3.4) It is also assumed that the particle velocity, v p is equal to the fluid velocity, v f. This assumption is applied to equation and the equation is converted to integral form: t x B B dv Bv f D da V A 0 (2.3.5) The Godunov scheme is now used to solve equation Figure gives the spatial notation used throughout the solution. 13

31 14 Figure 2.3.1: Spatial Notation Used to Demonstrate the Modified Godunov Scheme [17] Using a similar solution method to that used for the RELAP implementation of the Godunov scheme, the following solution is obtained: n j j L n j j L n L B n L B G A v A G v t 1 1, 1, (2.3.6) where the terms are defined as, M n j B L n j B n j f M n j B L n j B n j f n j v v G, 1,, 1, 2 1/ 1,, 1,, 1, 2 1/ 1, (2.3.7) n j f n j f n j f v v v v 1, 1 1, 2 1/ 1, 2 1 (2.3.8) L L L L n L B L n j B S x t v x 1 2 1,, 1, (2.3.9) M M M M n M B M n j B S x t v x 1 2 1,, 1, (2.3.10) The limited diffusion term is given as, v D C x n j r L 1, 2 min (2.3.11) K L M j - 1 j j + 1 j + 2

32 The cell-centered limited gradient, S L, S L n n (2.3.12) B, M B, L 1 LL r,1 S j1 1 LL r, 1 x j1 The superbee limiter, is given as, r, 1 max 0,min 2r,1,min r,2 (2.3.13) where, S j r (2.3.14) S j1 S j n n B, L B, K x j (2.3.15) S j n n B, L B, K x j (2.3.16) In the compression term, 1 L L, the discontinuity detector, L is defined as, 1 r (2.3.17) 1 r and the parameter is partially defined by the Courant number, Cr L L L L L min Cr, 1Cr (2.3.18) 15

33 For reference, the Courant number is defined as, Cr L v t x L (2.3.19) L The modified Godunov scheme was later implemented in CTF by Ozdemir with the addition of cross flow between sub-channels. The boron solute transient is calculated for both the continuous and entrained droplet fields [16]. The implemented boron tracking algorithm was verified using analytical and CFD solutions, and subsequently validated using measured data. The basic boron tracking algorithm is implemented in CTF such that after calculation of the fluid flow fields in each node, the boron solute flow rate is calculated at each node boundary using the modified Godunov method. Based on the results of the solute flow rate, the boron mass and concentration are determined in each node. The boron tracking model adds two subroutines to CTF and one module to store and exchange variable information for the boron tracking model. The boron tracking model is controlled in the CTF input deck along with the rest of the CTF userdefined parameters. Initial conditions of the boron are defined in Card 1 where the initial boron concentration of the system is uniformly defined. The boron tracking model boundary conditions are defined in Card As with other CTF boundary conditions, forcing functions may be defined for the inlet boron concentration. This allows the user to control the inlet boron with respect to time as the CTF-modeled transient progresses. 16

34 CHAPTER 3 PURDUE MOX / UO 2 CORE MODEL DESCRIPTION 3.1 Core Model Overview The core model used to benchmark and evaluate the CTF-BTM / NEM coupled code is the Purdue MOX / UO 2 core model from the 2007 OECD / NEA PWR MOX / UO 2 Core Transient Benchmark [10]. The intent of this benchmark was to characterize the behavior of reactor cores partially loaded with down-blended, formerly weapons grade Plutonium. Since only one-third of the core is loaded with MOX fuel and the rest of the core loaded with standard UO 2 fuel assemblies, large neutron flux gradients were expected between the unlike fuel assemblies. Additionally, the smaller effective delayed neutron fraction was a concern of such a core loading scheme. This core model is used throughout the current validation study. The Purdue core model is modeled after a Westinghouse four-loop reactor core. It consists of 193 fuel assemblies which include 4.2 wt% and 4.5 wt% standard UO 2 assemblies as well as 4.0 wt% and 4.3 wt% MOX assemblies. The fuel assemblies consist of fresh, once-burned, and twice burned fuel assemblies with burn-up among the fuel assemblies ranging from GWd/tHM to 37.5 GWd/tHM. The core is also enclosed by a single layer of neutron reflector assemblies in the radial and axial directions. The core fuel assembly loading map (quarter core) is shown in Figure Selected core data are listed in Table

35 M4.3% R M4.0% M4.0% 17.5 R M4.3% 17.5 M4.3% 35.0 R M4.0% 22.5 M4.0% M4.3% 20.0 R R M4.3% M4.3% M4.3% 32.5 R M4.0% M4.3% R M4.3% R R R R R R Figure 3.1.1: Purdue MOX Core Loading Pattern (Quarter Core) [10] Table 3.1.1: Purdue MOX Core Selected Specifications and Operating Data Number of Fuel Assemblies 193 Core Full Power Rating [MW thermal ] Nominal Inlet Pressure [MPa] 15.5 Total Core Moderator Mass Flow Rate [kg/sec] HFP Core Average Moderator Temperature [K] HFP Core Average Fuel Temperature [K] HZP Core Average Fuel Temperature [K] Fuel Lattice, Fuel Rods Per Assembly 17 x 17 Square, 264 Control Rod Guide Tubes Per UO 2 Assembly 24 Guide Tubes Per Assembly 1 Active Fuel Length [cm] Assembly Pitch [cm] Pin Pitch [cm] 1.26 Core Load [thm] 81.6 Shutdown Margin [%Δρ]

36 Due to the large flux gradients expected as a result of partially loading the core with MOX assemblies, the benchmark specifies a number of restraints which are imposed on the core loading pattern: 1. MOX fuel assemblies will contain no control rods. 2. No MOX assemblies facing each other. 3. Fresh MOX assemblies will not be loaded into the core periphery. 4. No more than 1/3 of the core will consist of MOX assemblies. 5. MOX assemblies will not contain IFBAs. 3.2 Cross Section Data The cross sections used are the same as those supplied by the PWR MOX / UO 2 Core Transient benchmark [10]. They are two group multi-dimensional tabular cross section libraries, which are homogenized on the assembly level. As described above, multi-dimensional linear surface interpolation is used to calculate the appropriate cross section based on the thermal hydraulic conditions supplied to NEM. The tabulated feedback parameters of the cross sections are moderator density, fuel temperature, and boron concentration. The only exception is the reflector which relies on boron concentration only for this particular cross section library. When the code executes, the cross section data is loaded from a separate input deck called NEMTAB which contains the cross section library. The thermal hydraulic values tabulated in the supplied cross section library are listed in Table

37 Table 3.2.2: Tabulated Cross Section Thermal Hydraulic Range T-H Parameter Minimum Mid-Range Maximum Fuel Temperature [K] Moderator Density [g/cm 3 ] Boron Concentration [ppm] Discretization and Nodalization Scheme The nodalization scheme of the Purdue core model used in NEM includes one node per fuel assembly in the radial directions for a total of 241 radial nodes. Axially, the core is divided into 28 layers, two of which are the top and bottom axial reflectors which are cm thick. For the remaining 26 axial nodes, the active fuel length is divided into 26 equidistant axial nodes. Appendix A, Figure A.2 gives a radial map of the nodalization used in NEM. The CTF model uses one sub-channel per fuel assembly for a total of 193 sub-channels. Although each fuel assembly contains 25 non-fuel rods in addition to the 264 fuel rods, only the fuel rods are modeled in CTF for each sub-channel by using the rod multiplier function. The non-fuel rods are neglected, but still accounted for in the sub-channel area and wetted perimeter. Finally, like the NEM model used, the CTF model divides the active fuel length into 26 axial nodes. Figure A.3 gives the sub-channel map used in the CTF sub-channel discretization. As mentioned before, the core is enclosed by a single layer of neutron reflector assemblies. The supplied reflector cross sections are dependent on boron concentration only and, per the benchmark specifications, the boron concentration of the reflectors is assumed to be uniform and equal to the corresponding inlet boron concentration. The only exception is the reflector in the top axial layer above the core. The boron concentration in these reflector nodes is assumed to be 20

38 equal to the concentration of the fuel nodes directly below them due to the direction of the coolant flowing upward in the core. For these reasons, the reflectors are not explicitly modeled in the CTF sub-channel model that was developed for this core. 21

39 CHAPTER 4 CTF-BTM AND NEM CODE COUPLING 4.1 Introduction The primary reason CTF is typically coupled to deterministic three-dimensional neutronics codes such as NEM for reactor core analysis is that the core power distribution is highly dependent upon the thermal hydraulic behavior. In turn, the thermal hydraulic behavior is dependent upon the power distribution. An accurate analysis requires that the power distribution be continually updated by NEM as CTF recalculates the thermal hydraulic behavior and vice versa. Although some versions of CTF make use of an integral point-kinetics model to calculate the power distribution, the point kinetics model suffers from a critical limitation. If the spatial system behavior is not tightly coupled, the results of the point kinetics model tend to lose accuracy [18]. For large full core simulations, the spatial dependence on power distribution is high enough such that the point kinetics model is not at all suitable for simulation of localized transients such as a control rod ejection or localized entrance of deborated water. Thus, a separate, coupled threedimensional time-dependent neutronics code such as NEM is used for this function. By making an initial guess of the core power distribution, CTF can calculate the corresponding thermal hydraulic feedback parameters. When three-dimensional neutronics codes predict the resulting core power distribution, CTF can be executed again to update the thermal hydraulic parameters. If this process is repeated with steady-state boundary conditions, the thermal hydraulic feedback parameters and power distributions will eventually converge to a steady 22

40 solution. After the thermal hydraulic conditions are converged to a steady-state, transient calculations can then be performed by executing a coupled iteration at each time step. 4.2 Coupling Methodology The coupling scheme employed between CTF-BTM and NEM is an online coupling. Online coupling allows a single set of input decks to be used for the code to execute to completion without further user action. This approach is far more efficient than offline coupling, particularly for systems that require a large amount of coupled iterations to obtain a steady-state solution or if transient simulations will be conducted. An offline coupling would require the user to manually use the results of one code in order to build the input deck and start execution of the next code. For the simulations conducted in this study, an offline coupling is simply impractical due to the large number of coupled iterations which are required. The CTF-BTM / NEM coupled code also uses an explicit coupling. Explicit coupling is easier to accomplish from a programming standpoint in that each code used in the coupling remains mostly independent (for online coupling) or completely separated (for offline coupling). As each code converges, only required information is passed to the other code. Thus minimal changes to the native codes are required. Additionally in this case, only two subroutines need to be introduced to the coupled code in order to coordinate the transfer of data between the two codes. The primary drawback to explicitly coupled codes is that these tend to experience more convergence difficulties than implicitly coupled codes and are less efficient. While implicit coupling tends to be more efficient and inherently more stable, this coupling scheme is far more difficult to accomplish since both codes are combined in such a way that the field equations are all solved as part of a unified system of equations [19]. 23

41 For explicitly coupled codes, one code is designated as the master code and the other as the slave code. In this study, CTF-BTM was designated as the master code for the coupling while NEM was designated as the slave code. CTF-BTM communicates with NEM by passing the spatial distributions of thermal hydraulic feedback variables to NEM when it is called as a subroutine. Fuel (Doppler) temperature, moderator temperature, moderator density, and boron concentration are the feedback variables passed from CTF-BTM to NEM. Following NEM execution, the core power distribution is sent back to CTF and updated for the next CTF iteration. For the purposes of spatial coupling, each fuel assembly node is directly coupled between NEM and CTF-BTM in a one-to-one relationship both in the axial and radial directions. When the coupled code is ready to pass CTF-BTM feedback variables to NEM, they must first be prepared. For fuel temperature, the temperature profile of the node rods is weighted using the temperature at the rod centers and surfaces in the radial and axial directions throughout the sub-channel node. Moderator temperature and density are averaged over all fluid phases present and weighted by void fraction. Boron concentration requires no additional preparation beyond what the boron tracking model itself calculates. Once units are matched for all feedback variables, the feedback data is stored until NEM is ready to start cross section interpolation. Following NEM convergence, the power distribution is passed directly back to the corresponding CTF subchannel node for the next CTF execution. The current developed coupled code gives the user the ability to choose between three coupled execution modes. The coupled code can perform a steady-state solution, a transient simulation, or an automated k-search where the inlet boron concentration boundary condition is varied until a user-specified eigenvalue (multiplication factor) is converged upon. When the coupled code is started, CTF-BTM will initially execute in a stand-alone, quasi-steadystate. This stand-alone execution will continue until the global heat balance and global mass 24

42 balance deviations both achieve a defined maximum value of 0.1%. Once CTF-BTM achieves steady-state convergence, a feedback subroutine is first called to convert the CTF-BTM feedback variables into the units used by NEM as well as to map this information to the discretization scheme used by NEM. The coupled code execution differs between the three execution modes after this point. 4.3 Steady-State Solution and Transient Simulation When the coupled code is executed to find a steady-state solution, the code determines the core state at the current, fixed time and given set of core conditions. In addition to the CTF-BTM and NEM convergence criteria, a set of user-specified coupled convergence criteria are used to determine when coupled steady-state convergence is achieved. The coupled convergence criteria used are the percent change of thermal hydraulic feedback variables between coupled iterations: fuel temperature, moderator temperature, and moderator density. The basic process for the steady-state solution is for CTF-BTM to first calculate the quasi-steadystate solution. Coupled execution then begins when CTF-BTM gives the thermal hydraulic feedback variable information to NEM. NEM will then calculate the core eigenvalue and the power distribution which is sent back to CTF-BTM. This process repeats until the overall coupled convergence criteria are achieved which is the percent change in feedback variables between coupled iterations. The basic coupled steady-state solution process is shown in Figure

43 CTF-BTM Ρ mod,t mod, T fuel, B conc NEM Power Distribution Figure 4.3.1: Illustration of the Explicit Steady-State Code Coupling Scheme For the transient simulation coupled execution mode, the code starts out in the same manner as the steady-state solution coupled execution mode. Once coupled steady-state convergence is achieved, CTF will no longer use the quasi-steady-state convergence criteria prior to calling NEM since these criteria will no longer be valid in a continually changing system. Additionally, a time step marching scheme is employed as shown in Figure Time Step: n Time Step: n+1 CTF-BTM CTF-BTM. T fuel, T mod, ρ mod, B conc Power Distribution T fuel, T mod, ρ mod, B conc Power Distribution NEM NEM Figure 4.3.2: Coupled Code Transient Time Step Marching Scheme In order to control the CTF boundary conditions with time, a set of time-dependent forcing functions can be used as part of the CTF input deck. To define a forcing function, the user enters into CTF Card 13, a set of Cartesian coordinate points used by CTF to determine the time 26

44 behavior of the specified boundary conditions. Between explicitly defined points in time, CTF linearly interpolates to calculate the boundary condition value at that time. Prior to coupling CTF-BTM to NEM, CTF only allowed for a single set of boundary condition forcing functions as part of the CTF input deck. However, since CTF executes in a null-transient mode during coupled steady-state calculations, the amount of CTF time needed to reach a steadystate solution prior to the start of transient can vary. In order to simulate inlet boron concentration transients a new, easier method was needed. This problem was solved by introducing a second set of boundary condition forcing functions which are also defined in the CTF input deck. The second set of forcing functions is only used after coupled steady-state convergence is reached and transient calculations have started. The advantage of using a second set of forcing functions is that the user can start the second set of forcing functions at time zero which is more intuitive. Once the code is ready to begin transient calculations, it will start at time zero defined in the transient forcing functions. Thus, there is no longer a need to estimate the amount of CTF time required to reach the coupled steady-state solution. 4.4 k-search Implementation In the k-search coupled execution mode, the user inputs a desired steady-state multiplication factor. The coupled code then finds the inlet boron boundary condition which yields the userdefined eigenvalue at steady-state. The k-search capability implemented into the coupled code is an original subroutine that controls the k-search process. When the code is executed in the k- Search mode, the NEM cross section data is read to find the upper and lower limits of the tabulated boron concentrations. The code then uniformly sets the inlet boron CTF boundary condition to the maximum tabulated boron concentration, C in,1 and CTF executes in stand-alone 27

45 mode for a sufficient amount of time such that the new boron concentration is allowed to fully propagate throughout the core model. Once enough time has passed and CTF achieves sufficient heat and mass balance, coupled execution begins until a steady-state eigenvalue convergence. The k-search subroutine then stores the first eigenvalue, k 1 that is found and arbitrarily reduces the inlet boron concentration by 10% as an initial estimate to find the user-specified eigenvalue, k search. ΔC in,1 = 0.1 * Maximum Tabulated Boron (4.4.1) C in,2 = C in,1 - ΔC in,1 (4.4.2) The second eigenvalue, k 2 is then found in a similar manner as the first. The value of delta-k between the two eigenvalues is then found using the definition of delta-k: dk 2 k 2 1 (4.4.3) k 2 k * k 1 Next, based on the current eigenvalue, the amount of delta-k remaining, dk remain to reach the userspecified k-search eigenvalue is calculated: dk remain k (4.4.4) search k 2 Based on the change in boron concentration between the first and second guesses (ΔC in,1 ) as well as the values of dk 2 and the dk remain, a linear guess is used to find the next inlet boron concentration, C in,3 : 28

46 dk remain Cin, 2 * Cin,1 dk (4.4.5) 2 C C C (4.4.6) in, 3 in,2 in,2 This process repeats until the k-search converges on the user-specified eigenvalue. The convergence criterion used for the k-search is the same as the k eff -convergence criterion specified in the NEM input deck. 29

47 CHAPTER 5 COUPLED CODE BENCHMARKING AND VERIFICATION 5.1 Introduction In order to confirm that a computational physics program is producing physically valid results, a validation strategy must be employed. Ideally, an analytical solution that encompasses both the desired inputs and outputs of the given program would be used for validation. However, for a system that encompasses multiple, interlinked physical phenomena, such as an LWR core, obtaining an exact analytical solution is impractical. An alternative solution to validation if an analytical solution is not available is the comparison of the program inputs and outputs to a benchmark reference solution. Ideally, a given benchmark solution is based on experimental data. However, another means of developing a benchmark solution is the use of other codes that have been previously validated. Such is the case with the Purdue MOX core model benchmark solutions, which were developed from use of previously validated codes rather than from actual experimental data [10]. The strategy employed to validate the CTF-BTM / NEM coupled code starts with benchmarking against parts of the Purdue MOX / UO 2 Core Transient Benchmark at steady-state conditions. In order to quantify the effect of the addition of the boron tracking model, the results of the CTF- BTM / NEM code are also compared to the non-boron tracking model version of the code. In the non-boron tracking version of the code, the entire core is assumed to have a uniform boron concentration throughout. 30

48 Selected parts of the Purdue MOX / UO 2 Core Transient Benchmark are used to benchmark the CTF-BTM / NEM coupled code. Since the Purdue MOX / UO 2 core model has not been used in any currently operating nuclear power plants, actual measured operating data is not available. Without actual operating data available, the benchmark reference solutions for Part II (steadystate HFP conditions) and Part III (steady-state HZP conditions) were based on the results of the Purdue Advanced Reactor Core Simulator (PARCS) code using two energy groups. The exception is that for Part III, the power distribution reference solution is based on the DeCART solution which uses the Method of Characteristics. The Method of Characteristics is considered to be much more accurate than nodal diffusion methods since it is a neutron transport theory-based solution [10]. Comparison to a benchmark reference solution for validation of the transient capabilities of the coupled code is not possible since a boron transient benchmark solution has not been generated for the Purdue core model. In order to verify the transient operation of the coupled code, the code is first used to calculate the steady-state multiplication factor eigenvalues throughout the range of available inlet boron concentrations at HZP conditions. The resulting steady-state multiplication factors are then used to predict insertions of positive and negative reactivity when the inlet boron concentration is homogeneously varied. When the code is executed in transient mode and the inlet boron concentration varied, the resulting change in core reactivity should match what was predicted using the steady-state results. 5.2 Steady-State Benchmarking at HFP The CTF-BTM / NEM coupled code is first benchmarked at HFP conditions. To accomplish this, the code is set to execute using the k-search coupled execution mode to find the critical inlet 31

49 boron concentration boundary condition. At HFP conditions, the core operates at full power with all control rods fully withdrawn or All Rods Out (ARO). Initial conditions, boundary conditions, and operating parameters are selected to most closely match those that are specified in Part II of the benchmark. Selected operating parameters, initial conditions, boundary conditions, and convergence criteria used in the CTF-BTM and NEM input decks are listed in Table Table 5.2.1: Selected HFP Benchmarking k-search Simulation Parameters Parameter Input Deck Input Value Control Rod States NEM Card 36a ARO NEM Boundary Conditions NEM Card 34 Zero flux in all directions NEM k-convergence Criteria NEM Card k-search Target CTF Card Moderator Mass Flow Rate Boundary Condition (Core-Integrated) [kg/sec] CTF Card (uniform distribution) Linear Power Initial Condition [kw/m] CTF Card Moderator Inlet Enthalpy Boundary Condition [kj/kg] Moderator Outlet Pressure Boundary Condition [MPa] CTF Card 13 CTF Card (uniform distribution) 15.5 (uniform distribution) Moderator Inlet Boron Concentration CTF Card 13 Controlled by k-search Coupled Convergence Criteria (T_Fuel, T_Mod, R_Mod) CTF Card Effective Delayed Neutron Fraction (β) NEM Card As shown in Table 5.2.2, the non-boron tracking version of the CTF/NEM coupled code closely agrees with the predicted critical boron concentration of the benchmark solution with a difference of 0.02%. However, when boron tracking is introduced, the required critical inlet boron concentration decreases and exhibits a greater deviation of 0.61% from the reference solution. 32

50 CODE Table 5.2.2: HFP Benchmarking Overall Results [20] Critical Boron [ppm] Assembly Power Error Core Averaged T/H Conditions Moderator Density [kg/m 3 ] Doppler Temp. [K] Moderator Temp. [K] %PWE %EWE CTF-BTM / NEM CTF / NEM (No BTM) PARCS 2G (REF) REF REF The quarter core radial power distributions for the benchmark reference solution, CTF-BTM / NEM result, and CTF / NEM result (without boron tracking) are given in Figure The axial power distributions for these three cases are given in Figure A B C D E F G H Figure 5.2.1: Quarter Core HFP Radial Power Distribution [20] (Top of Each Cell: Non-Boron Tracking Result / Middle: Boron Tracking Result / Bottom: PARCS 2G Reference Solution) 33

51 Figure 5.2.2: Radially Averaged Core HFP Axial Power Distributions [20] As demonstrated in Table 5.2.2, the boron tracking version of the code produces a larger deviation of predicted critical boron concentration from the benchmark result than the non-boron tracking version. However, the percent Power-Weighted Error (%PWE) and percent Error- Weighted Error (%EWE) improved when the boron tracking model was introduced. Since the non-boron tracking version of the coupled code produced a critical boron concentration that was in close agreement with the benchmark result, it is hypothesized that the larger deviation produced by the boron tracking version of the coupled code is due to fact that the boron density changes with spatial position in the core. This is a physical phenomenon not simulated in the nonboron tracking version since the boron remains uniform regardless of moderator conditions. The change in spatial boron concentration in the axial direction is compared between the two code versions as shown in Figure

52 Figure 5.2.3: Radially Averaged Core Boron Concentration at Each Axial Level In Figure 5.2.4, the radially averaged boron density is calculated for the boron tracking and nonboron tracking results at each axial level. For the boron tracking result, the boron tracking model is used to radially average the boron concentration at each axial level of the CTF model. The radially averaged moderator density is then used to calculate the boron density at each axial level. For the non-boron tracking result, the constant and uniform boron concentration is used with the changing moderator density to calculate the boron density at each axial level. 35

53 Figure 5.2.4: Radially Averaged Core Boron Density at Each Axial Level As demonstrated in Figure 5.2.4, the boron density toward the core inlet and core outlet of the boron tracking result is less than that of the non-boron tracking result. This is due to the fact that the non-boron tracking code version boron density that was calculated is dependent on and directly proportional to the change in moderator density only. The boron tracking result however, starts with a smaller boron concentration at the inlet. From the inlet, as the moderator travels up the core and is rapidly heated, the moderator density decreases, but the boron density decreases at a smaller rate. At the mid-core region, the boron and moderator densities approach proportionality. This initial difference in proportionality is due to the fact that the axial power distribution, and thus the neutron flux, peaks in the axial mid-region of the core. As the boron travels up the core and the moderator density decreases, the boron concentration increases, peaking in the axial mid-region slightly above the axial power peak. This gives the boron in this region a higher effective reactivity worth, therefore the boron concentration 36

54 boundary condition required at the inlet for criticality is less than that of the non-boron tracking result. Near the core outlet, voiding occurs in the moderator as heating continues. This voiding causes the boron density change to become disproportionate to the moderator density change since the moderator density is influenced by the vapor phase. The boron tracking model however does not allow the boron to enter the moderator vapor phase, hence causing this deviation from proportionality again. Although the inlet boron concentration of CTF-BTM / NEM deviates further from the benchmark reference solution than the non-boron tracking version, the cause for the difference is understood with physical explanation. Furthermore, the non-boron tracking version result is a very close match to the benchmark reference solution which uses a simpler, one-dimensional thermal hydraulics model which models mass and energy, but not momentum and boron transport. Therefore it is concluded that the CTF-BTM / NEM coupled code is validated at steady-state HFP conditions. 5.3 Steady-State Benchmarking at HZP The coupled code is next benchmarked at HZP conditions. At HZP conditions, the core operates at 10-4 % power level with the control rod banks fully inserted and the shutdown banks fully withdrawn. The k-search execution mode is used once again to find the critical inlet boron concentration. Selected input conditions are listed in Table

55 Table 5.3.1: Selected HZP Benchmarking k-search Simulation Parameters Parameter Input Deck Input Value Control Rod States NEM Card 36a Control Rods Inserted, Shutdown Banks Withdrawn NEM Boundary Conditions NEM Card 34 Zero flux in all directions NEM k-convergence Criteria NEM Card k-search Target CTF Card Moderator Mass Flow Rate Boundary Condition (Core-Integrated) [kg/sec] CTF Card (uniform distribution) Linear Power Initial Condition [kw/m] CTF Card Moderator Inlet Enthalpy Boundary Condition [kj/kg] Moderator Outlet Pressure Boundary Condition [MPa] CTF Card 13 CTF Card (uniform distribution) 15.5 (uniform distribution) Moderator Inlet Boron Concentration CTF Card 13 Controlled by k-search Coupled Convergence Criteria (T_Fuel, T_Mod, R_Mod) CTF Card Effective Delayed Neutron Fraction (β) NEM Card As shown in Table 5.3.2, there was negligible difference in predicted inlet boron between the boron tracking and non-boron tracking versions of the coupled code. This is largely due to minimal changes in moderator density from the small heat flux as the moderator travels up the core. Both cases of the coupled code indicated reasonable agreement of inlet boron concentration with the reference benchmark solution with a deviation of 0.33% of the two code versions from the reference solution. 38

56 Table 5.3.2: HZP Benchmarking Overall Results [20] CODE Critical Boron [ppm] Assembly Power Error %PWE %EWE CTF-BTM / NEM CTF / NEM (No BTM) PARCS 2G (REF) DeCART* 1265 REF REF *The DeCART Heterogeneous, Method of Characteristics (MOC) Solution in 47 groups was used as the reference solution for the HZP power distribution per the benchmark. The quarter core radial power distributions for the benchmark reference solution, CTF-BTM / NEM result, and CTF / NEM result (without boron tracking) are given in Figure The axial power distributions for these three cases are given in Figure A B C D E F G H Figure 5.3.1: Quarter Core HZP Radial Power Distribution [20] (Top of Each Cell: Non-Boron Tracking Result / Middle: Boron Tracking Result / Bottom: DeCART MOC Reference Solution) 39

57 Figure 5.3.2: Radially Averaged Core HZP Axial Power Distributions [20] As demonstrated in the preceding power distribution results and Table 5.3.2, the calculated power distributions almost exactly agreed between the boron tracking and non-boron tracking coupled code results. There was also closer agreement of both of the CTF / NEM results to the DeCART power distribution result than what was achieved with the PARCS result as indicated by the smaller %PWE and %EWE. The negligible differences between the boron tracking and non-boron tracking versions of the CTF / NEM coupled code were expected due to the smaller amount of heat transfer between fuel rods and moderator. Since minimal heat was added to the moderator, the moderator density does not change appreciably while traveling up the core. This effectively makes the boron concentration uniform throughout the core, which is the assumption made in the non-boron tracking version of CTF / NEM and simulated by the boron tracking model in CTF-BTM / NEM. The close agreement to the reference benchmark solutions supports the conclusion that the CTF- BTM / NEM code is validated for the Purdue core model at steady-state HZP conditions. 40

58 5.4 Transient Code Verification Exercises To verify the CTF-BTM / NEM coupled code for transient simulation of the Purdue MOX core model, a verification methodology was needed since a boron transient benchmark solution is not available. Since the coupled code was successfully validated using the steady-state benchmark portions of the MOX / UO 2 Core Transient Benchmark, a transient verification methodology is adopted that builds upon the steady-state validation results. To conduct the transient verification, HZP conditions are used to help separate moderator and void feedback effects from Doppler feedback effects. This strategy starts with obtaining steady-state solutions of the coupled code by varying the inlet boron concentration throughout the range of cross section tabulated boron concentrations. The steady-state coupled execution mode is used for this purpose and the resulting steady-state multiplication factors are then plotted against inlet boron concentration. Figure gives the resulting plot of inlet boron concentration versus steady-state multiplication factor at HZP conditions. The steady-state multiplication factors are then used to calculate the core reactivity for each inlet boron concentration as plotted in Figure For purposes of reactivity calculations, a core-wide effective delayed neutron fraction (β) of is used as specified in the NEM Card 12 input. 41

59 Figure 5.4.1: HZP Steady-State Multiplication Factor vs. Inlet Boron Concentration Figure 5.4.2: HZP Steady-State Core Reactivity vs. Inlet Boron Concentration 42

60 By using a linear curve fit to the plotted points in Figure 5.4.2, the resulting linear equation should allow for a prediction of core reactivity change following a homogeneous change of inlet boron concentration. However, this prediction would be dependent upon changing the core reactivity before fuel heating or cooling occurs. If the fuel temperature changes, then the core reactivity will be affected by this temperature change in addition to the intended change in reactivity due to the change of moderator boron concentration. Using the results of the already validated steady-state calculations and predicting core reactivity changes in response to homogeneous inlet boron concentration changes, this methodology is used to confirm and validate the transient capability and behavior of the CTF-BTM / NEM coupled code. To carry out this verification strategy, a series of reactivity insertions are first predicted using the steady-state results. The resulting change in core reactivity is then compared to the steady-state result. Five cases are simulated in which the equivalent reactivity worth of the boron is varied as well as the length of time for the inlet boron concentration to change from the initial boundary condition value to the final value corresponding to the reactivity insertion. The results of the five cases are summarized in Table

61 Table 5.4.1: Overall Transient Verification Reactivity Change Results Case Initial Inlet Boron [ppm] Final Inlet Boron [ppm] Inlet Boron Transition Time [sec] Predicted Equivalent Reactivity Change [$] Actual Peak Transient Reactivity Change Simulated [$] Reactivity Error [%] Core Average Dopper Temp. Change At Peak Reactivity [K] For Case 1, the inlet boron is started at just below the HZP critical value before $0.10 of negative reactivity is inserted by increasing the inlet boron concentration over a period of 0.5 seconds. As shown in Figure 5.4.3, the core reactivity initially decreases past -$0.10, producing a negative peak of -$ The reactivity then asymptotically approaches approximately -$0.06 over a long period of time. When the core averaged fuel temperature is examined as shown in Figure 5.4.4, the increase in reactivity following the negative peak and the asymptotic approach of core reactivity to -$0.06 is directly correlated to the fuel temperature decreasing and approaching equilibrium with the moderator temperature. The initial fuel temperature increase indicated in Figure is due to the fact that the inlet boron boundary condition forcing function does not start the planned increase until five seconds into the simulation as indicated by Figure which shows the inlet boron concentration profile with time. Following the increase in boron from time 5 seconds to time 5.5 seconds, the inlet boron is held constant for the rest of the simulation. The fuel heating that was allowed to occur in the first five seconds contributed to the initial undershoot of the core reactivity once the boron concentration increased between times 5 and 5.5 seconds. 44

62 Figure 5.4.3: Transient Test Case 1 Core Reactivity vs. Time (Red Line Indicates Target Reactivity) Figure 5.4.4: Transient Test Case 1 Average Fuel and Moderator Temperatures vs. Time 45

63 Figure 5.4.5: Transient Test Case 1 Inlet Boron Concentration vs. Time An insertion of positive $0.10 reactivity is simulated in Case 2. As indicated in the overall results of Table and in Figure 5.4.6, the simulated reactivity was in close agreement with the predicted change in reactivity with a smaller percent deviation. In this case, due to the small amount of reactivity inserted and the relatively slow rate it was inserted, little heat was added or removed from the fuel as shown in Figure Due to the fact that the change in fuel temperature was relatively small and the reactivity insertion ended at near critical inlet boron concentration, the predicted core reactivity change was more accurate than Case 1 with a smaller deviation between predicted and simulated core reactivity. The amount of time for steady conditions to be obtained was also significantly shorter. For reference, the Case 2 inlet boron concentration profile over time is given in Figure

64 Figure 5.4.6: Transient Test Case 2 Core Reactivity vs. Time (Red Line Indicates Target Reactivity) Figure 5.4.7: Transient Test Case 2 Average Fuel and Moderator Temperatures vs. Time 47

65 Figure 5.4.8: Transient Test Case 2 Inlet Boron Concentration vs. Time For Case 3, Case 4, and Case 5, $0.50 of positive reactivity is inserted into the core starting from an initial reactivity of -$0.60 using the same initial and final boron concentration for all three cases. The difference between these three cases is the amount of time for the boron concentration to change such that $0.50 of reactivity is inserted. As indicated in Table and indicated by the reactivity evolution of Case 3 in Figure 5.4.9, in order to more accurately obtain the target reactivity change in a single insertion, the boron concentration must change in a shorter period of time (2.5 seconds in this case). However, this increase in reactivity in Case 3 decreases again shortly after the boron concentration ramping due to heating of the fuel as shown in the core average temperature profile given in Figure If more time is allowed to pass while the boron concentration changes, the fuel will have more time to increase in temperature, which contributes to a greater reactivity defect due to the prompt Doppler feedback effects. Figure gives the reactivity change over time for Case 5. In Case 48

66 5, much more time is allowed for fuel heating since the boron concentration is gradually changed over the course of 45 seconds as demonstrated in the Case 5 core temperature profile in Figure Since the fuel is given more time to increase in temperature in this case, the reactivity defect is much greater. Figure 5.4.9: Transient Test Case 3 Core Reactivity vs. Time (Red Line Indicates Target Reactivity) 49

67 Figure : Transient Test Case 3 Average Fuel and Moderator Temperatures vs. Time Figure : Transient Test Case 5 Core Reactivity vs. Time (Red Line Indicates Target Reactivity) 50

68 Figure : Transient Test Case 5 Average Fuel and Moderator Temperatures vs. Time A complete set of figures used in the transient verification study is located in Appendix B. For all five cases simulated, these figures include reactivity change with time, inlet boron concentration change with time, and core averaged fuel and moderator temperatures with time. While in some cases the simulated transient reactivity changes did not precisely match the steadystate predicted reactivity changes, the proximate causes for these deviations can be linked to real, physical effects such as Doppler and moderator temperature feedback effects, as well as timedependent versus steady-state neutronics modeling. It is therefore concluded that although reference benchmark solution data for a boron transient is not available for the core model used, the transient simulation of varying inlet boron produces core behaviors that would be expected for an LWR core subjected to these types of reactivity transients. That said, the transient boron simulation portion of the CTF-BTM / NEM coupled code is considered to be verified for the purposes of this study. 51

69 CHAPTER 6 BORON DILUTION TRANSIENT SIMULATIONS 6.1 Introduction In the final phase of this study, the verified CTF-BTM / NEM coupled code is employed in the simulation of a series of boron dilution transients using the Purdue MOX core model. Heterogeneous boron dilution transient scenarios are simulated in order to fully exercise and demonstrate the boron tracking capability of CTF-BTM and the capabilities of the coupled CTF- BTM / NEM code. Following scenario formulation, a series of variations to the scenario are executed. The condensate slug entrance radial location is first varied assuming that a SBLOCA occurred while the reactor was at full power operation. The most limiting radial entrance location is determined from these results and two extreme cases are considered where actuation of a main reactor coolant pump drives a single condensate slug into the core at the most limiting entrance location at a high velocity. 6.2 Accident Scenario Initiating Events The current scenario is largely based on an accident sequence postulated in NRC Generic Safety Issue - 185, Control of Recriticality following Small-Break LOCAs in PWRs [6]. While the reactor is at full power operation, the primary loop boron concentration is approximately 1680 ppm with control rods withdrawn. A simplified, typical Westinghouse 4-Loop NSSS is shown in Figure

70 Cold Leg Figure 6.2.1: Typical Westinghouse 4-Loop NSSS [21] The accident initiates when a break occurs in the primary coolant loop on one of the cold legs. The break is considered to be an S2-sized break of approximately two inches equivalent diameter. The primary loop loses pressurization in a matter of minutes with the superheated coolant flashing to steam. The pressurizer rapidly loses ability to make up for the pressure loss and the depressurization signal triggers the control rods to automatically SCRAM (which is successful) and the main RCPs to trip and begin coast-down. Safety injection flow is started by the safety injection pumps which will remain operable for purposes of this scenario. The break however is a size large enough such that coolant is rapidly lost due to vaporization and spillage 53

71 from the break itself, but still small enough that system pressure is maintained at a reduced level. The remaining system pressure is above the charging pressure of the accumulators, which therefore do not actuate. Following coast-down of the main RCPs, natural circulation begins in the primary loop. Although the reactor is successfully scrammed and brought to a hot shutdown state, fission product decay heat causes the coolant to continue to boil after the initial LOCA. Due to the system remaining partially pressurized above the accumulator charge pressure, safety injection flow rate is reduced and cannot keep up with the loss of coolant inventory due to coolant vaporization and coolant spilling from the break site. After some time, the coolant inventory is sufficiently reduced such that air and vapor get into the steam generator U-tubes causing natural coolant circulation through the primary coolant loops to cease. When natural circulation ceases, the core begins to operate in a boiler and condenser mode. While coolant boiling continues, the water vapor rises and travels in the now partially filled primary coolant loop hot legs. In the steam generators, which are the highest points in the primary loops, reflux condensation occurs as the vapor is cooled by the secondary coolant shell side in the steam generators. The vapor that rises in the loops is distilled. More specifically, as the coolant boils off, the boric acid does not travel with the water vapor. The primary problem postulated in GSI-185 is that the distilled and deborated water vapor would condense in the steam generator U-tubes. Some of the water would run back down the hot leg sides in the U-tubes and mix back in with the borated water, but some would also run down the cold side toward the outlet plena. As the water running down the cold side collects, the added distilled water would cause a decrease in soluble boron concentration. As this condensate mass collects in the steam generator primary outlet plenum, cross over leg, and RCP inlet, the potential for a boron dilution transient is increased [22]. A diagram illustrating this condition is shown in Figure

72 Steam Generator Steam Generator U-Tubes Cold Leg Hot Leg Reactor Vessel Break Site RCP Cross-over Leg Figure 6.2.2: Simplified Diagram of Boron Dilution Due to Reflux Condensation in Post-SBLOCA Conditions [23] 6.3 Assumptions and Scenario Formulation In order to build a post-sbloca boron dilution transient simulation scenario, a number of assumptions and simplifications must be made. Some of these assumptions are due to the limitations of available cross section data while others are required by the difficulty of determining appropriate boundary conditions for the given scenario without detailed experimental data. Where these assumptions or simplifications are made, an effort is made to bias toward conservative input parameters. One obvious problem is the cross section library used for the MOX / UO 2 Core Transient Benchmark. LOCA conditions present a particularly extreme set of thermal hydraulic conditions 55

73 since the primary coolant pressure falls to a fraction of the system nominal operating pressure. Fuel temperatures will also rise significantly due to the nature of the accident itself. While extrapolation outside of the tabulated cross section thermal hydraulic ranges is possible, it is a dangerous practice that can lead to severe errors. Similar problems of limiting tabulated thermal hydraulic range for the cross section library have been encountered in other post-sbloca accident simulation studies. A methodology was adopted by Diamond et al to circumvent the problem of the maximum tabulated moderator density being too low for the conditions presented. Although the primary coolant loop is depressurized, the system pressure boundary condition is artificially raised to match the level of sub-cooling (Δh subcooled ) in the moderator using the lower, tabulated maximum moderator density [24]. At the originally formulated post-loca conditions, the moderator density is calculated to be g/cm 3, which is higher than the maximum tabulated moderator density. Using this method of raising the pressure boundary artificially, the tabulated maximum density, g/cm 3, can be used instead, achieving an equivalent level of sub-cooling and keeping the moderator density within the tabulated cross section range. Table gives a list of the formulated and subsequently modified moderator flow conditions. Table 6.3.2: Original and Modified Inlet Coolant Flow Conditions Flow Condition Original Formulation Modified Formulation Pressure [MPa] T sat [K] h f [kj/kg] T inlet [K] h [kj/kg] Δh subcooled [kj/kg] Another assumption made concerns the inlet boron concentration boundary conditions. As described above, mixing data for this particular system is not available for the transport of the 56

74 deborated condensate from the steam generators to the core inlet since this data is highly sensitive to individual system geometries and flow conditions. Of particular importance is the mixing that would occur in the downcomer regions and lower plenum of the reactor vessel. Traditionally the system codes have been used to model boron transport and mixing in these flow regions, but these codes suffer from limitations as mentioned in Chapter 2. Ideally, detailed experimental data would be available or outputs from a CFD simulation would be available for this specific system geometry. In lieu of this data being available, a number of conservative assumptions are made. For the formulation of the simulation input decks, the initial core thermal power level is set to 2% of nominal to account for post shutdown decay heat. At this power level and pressure, the natural circulation flow rate for a Westinghouse 4-loop NSSS will be approximately 225 kg/sec per loop [25]. Actuation of a single main reactor coolant pump is assumed in a more severe set of forced circulation cases, resulting in the condensate slug entering the core at a higher velocity. For the forced circulation cases, a single RCP will generate a mass flow rate of kg/sec. In all cases, it is assumed that the overall core coolant mass flow rate is uniformly distributed across all core inlet channels. The total core coolant mass flow rate also assumes four safety injection inlets of equal flow rates. To determine the boron concentration of the condensate slug entering the core, it is assumed that when circulation starts, no mixing occurs during transit of the condensate slug through the reactor coolant pump and cold leg. It is then assumed that perfect mixing occurs at the point where the condensate slug moves past the safety injection point in the reactor vessel. Under this assumption, the following equation is used to determine the resultant condensate slug boron concentration after mixing with the safety injection flow [25]: 57

75 C in C SI RC 1 R L (6.3.1) where, q q L R (6.3.2) SI and where, C SI = Boron Concentration of the Safety Injection Flow [ppm] q SI = Safety Injection Flow Rate [kg/sec] C L = Initial Boron Concentration of the Condensate Slug [ppm] q L = Loop Flow Rate [kg/sec] C in = Resultant Condensate Slug Concentration Entering the Core Inlet [ppm] For all trial cases conducted, the initial boron concentration of the condensate slug is assumed to be 0 ppm and the safety injection flow boron concentration 2200 ppm. The inlet location where the condensate slug enters the core is another unknown. Due to the assumptions made that there is no mixing in the reactor vessel downcomer and lower plenum, the exact location of entry is not known. It is assumed that the slug will travel from the cold leg inlet straight downward in the downcomer, and turn upward again in the lower plenum. The upward turn is assumed to direct the slug in a straight line in the direction of the center of the reactor core in the lateral direction. A side cutaway view of the reactor vessel is given in Figure showing the assumed flow path of a condensate water slug. 58

76 Figure 6.3.2: Westinghouse 4-Loop Reactor Vessel Side Cut-Away View [26] (Red Line Represents Assumed Flow Path of Condensate Slug) 59

77 A cut-away downward view of the reactor vessel is shown in Figure For the forced circulation cases simulated, it is assumed that the condensate slug will enter from the lower right cold leg inlet 23 degrees counter-clockwise from the 270 degree direction. The point at which the slug enters the core is varied between the core periphery and the core center for the natural circulation cases. Figure 6.3.3: Westinghouse 4-Loop Reactor Vessel Cut-Away View at Nozzle Level [27] (Red Line Represents Assumed Possible Entry Points for the Condensate Slug) 60

78 Another unknown in the scenario formulation is the shape of the condensate slug. In natural and forced circulation cases, it is assumed that the borated slug that enters the core inlet takes the cross sectional shape of the cold leg pipe in the axial direction, despite the mixing that in reality will occur to some extent in the downcomer and lower plenum of the reactor vessel. This assumption is considered to be a conservative formulation in the absence of detailed mixing data. To determine the most limiting entrance location of the water slug, a sensitivity study is first conducted to determine which core entrance location results in the largest reactivity increase and fuel enthalpy peak. Table gives a selected list of input conditions common across all simulation cases considered. Table 6.3.1: Selected Boron Dilution Transient Input Conditions (All Cases) Parameter Input Deck Input Value Control Rod States NEM Card 36a All Rods In Linear Power Initial Condition [kw/m] CTF Card Inlet Coolant Enthalpy Boundary Condition [kj/kg] CTF Card Outlet Coolant Pressure Boundary Condition [bar] CTF Card Initial System Boron Concentration [ppm] CTF Card Condensate Boron Concentration [ppm] N/A Condensate Entrance Sensitivity Study Natural Circulation For these cases, the transport of the condensate slug is simulated under natural circulation conditions. The natural circulation flow rate in these cases is 225 kg/sec per loop and the safety injection flow rate is 12 kg/sec per loop due to the system pressure [25]. Assuming four safety injection inlets, the total coolant mass flow rate is 948 kg/sec. Using equation 6.3.1, and assuming 61

79 no mixing in the downcomer and lower plenum, the boron concentration of the condensate entering the core inlet is 111 ppm. To determine the most limiting entrance location of the condensate slug, eight cases are simulated in which the entrance locations are varied from the core periphery to the core center region. Based on the assumed path of the condensate travel depicted in Figure 6.3.3, the condensate slugs are centered on the fuel assemblies as shown in the quarter core map in Figure A M4.3% R B M4.0% M4.0% 17.5 R C M4.3% 17.5 M4.3% 35.0 R D M4.0% 22.5 M4.0% M4.3% 20.0 R E R R F M4.3% M4.3% M4.3% 32.5 R G M4.0% M4.3% R R H M4.3% R R R R R R R R Figure 6.4.1: Discretized Possible Condensate Water Slug Entrance Locations (Red Fuel Assemblies Represent Centered Condensate Entrance Locations) 62

80 The condensate slug in each case is assumed to have a circular cross section of the same inner diameter as the cold leg pipes. The resultant boron concentration is discretized in the same manner as the CTF sub-channel discretization using an area-weighted boron distribution to calculate the regional boron concentrations. The inner diameter of the cold leg pipe is specified to be 27.5 inches and the condensate slug is discretized as depicted in Figure assuming the slug is centered on a fuel assembly [21]. Region 1 is the condensate slug boron concentration, which is weighted 0% toward the fully borated water concentration since this region is fully enveloped by the condensate slug. Region 2 is weighted 29.78% toward the fully borated water concentration. Region 3 is weighted 5.26% toward the fully borated water concentration. Region 3 Region 2 Region 1 Region 2 Region 3 Region 1 Region 1 Region 1 Region 3 Region 2 Region 1 Region 2 Region 3 Region 1 = ppm Region 2 = ppm Region 3 = ppm Full Boration = 1680 ppm = Actual Slug Boundary Figure 6.4.2: Condensate Water Slug Discretization (assuming 27.5 in diameter) For the natural circulation cases, the volume of each condensate slug was originally assumed to be approximately 4 m 3 which is the approximate volume of the steam generator outlet plenum, 63

81 cross over leg, and RCP inlet [25]. Due to the low sub-channel velocity at natural circulation conditions, the feedback effects are effective to negatively affect reactivity as the condensate slug moves up the core. The volume of each slug in these cases is therefore reduced such that the axial length of the slug is approximately the same length as the active fuel length of the core in the axial direction in order to reduce computation time. The resultant volume of the slug is therefore 1.16 m 3. For each case, the inlet boron concentration of the slug entrance location is ramped down from time 0.5 seconds to time 1.0 second. The condensate is considered to have entered the core at time 1.0 second. As the slug completes core entry, the inlet boron concentration is ramped back to full borated concentration over 0.5 seconds. The inlet boron concentration returns to full boron concentration at time, seconds. The eight cases simulated for natural circulation conditions are summarized in Table The core-wide results of all seven cases are summarized in Table Table 6.4.1: Natural Circulation Simulation Cases Executed Case Center of Entry Location* Sub-channel ID of Slug Center Condensate Slug Description 1 H4 193 Single Slug 27.5 in Diameter 2 G3 183 Single Slug 27.5 in Diameter 3 F3 171 Single Slug 27.5 in Diameter 4 E3 158 Single Slug 27.5 in Diameter 5 D2 143 Single Slug 27.5 in Diameter 6 C2 128 Single Slug 27.5 in Diameter 7 B1 112 Single Slug 27.5 in Diameter 8 A1 97 Single Slug 27.5 in Diameter * In Reference to Figure

82 Case Table 6.4.2: Natural Circulation Simulation Core Wide Results Summary Maximum Core Reactivity [$] Peak Reactivity Change [$] Maximum Core Averaged Mod Temp [K] Maximum Core Averaged Fuel Temp [K] Maximum Core Power Factor [-] Figures depict the core power evolution, corresponding core reactivity evolution, and core averaged temperature evolution for Case 4 (complete results for all cases are given in Appendix C). In all cases the power evolution initially spikes before falling to a lower level, but Case 4 was found to exhibit greatest power peaking factor. The peak reactivity change for Case 4 is also the highest among the cases simulated with a peak reactivity change of +$ The peak reactivity change is calculated by determining the change in reactivity from the minimum core reactivity prior to the first power spike and the maximum reactivity that follows. 65

83 Figure 6.4.5: Case 4 Power Evolution with Time Figure 6.4.6: Case 4 Reactivity Evolution with Time 66

84 Figure 6.4.7: Case 4 Temperature Evolution with Time As expected, Doppler feedback effects quickly reduce the power level of the core as the positive reactivity is inserted by the condensate slug entering the core. The peak fuel temperature and fuel enthalpy for each case at the hottest node is given in Table Table 6.4.3: Hot Fuel Node Peak Results Summary Case Location of Hottest Fuel Node* Peak Fuel Node Temperature [K] Peak Fuel Node Enthalpy [cal/g] 1 144, , , , , , , , *CTF Radial Sub-channel, Axial Sub-channel (Axial Levels Starting From Bottom of Core) 67

85 Based on the peak fuel enthalpy of the hottest fuel node in each case, the most limiting case is considered to be Case 4 with a peak fuel enthalpy of cal/g in the hot node. The fuel enthalpy level considered to cause fuel damage is about 230 cal/g, which is well above the hot node enthalpy peak found in Case 4. The next concern would be clad damage which is expected to occur at a fuel enthalpy of 170 cal/g, however this is also well above the Case 4 peak [28]. The initial boron concentration distribution, radial power distribution, and axial power distribution are given in Figures 6.4.8, 6.4.9, and , respectively. The initial boron and power factor distributions are then followed by the corresponding plots at time 2.93, which is the time of peak core power during the transient. The radial power distribution, axial power distribution, and boron concentration distribution at the time of peak power are given in Figures , , and respectively. Further analysis of Case 4 confirms that the condensate slug location correlates well to the radial and axial power distributions. At the time of peak core power, the radial peaking occurs in the same region as the condensate entrance location and the axial peaking occurs at the lower axial levels where the condensate is located. The fully inserted control rods and nominal boron concentration in the other core regions not directly affected by the condensate prevent the core wide reactivity from coming near critical in all cases. However, the local core region of the condensate still experiences a power excursion as evidenced by the radial power distribution at peak core power for Case 4 in Figure and the overall core power in Figure Due to the peak reactivity change being less than $1.00, it is concluded that prompt criticality is not attained locally. 68

86 Figure 6.4.8: Case 4 Radial Power Distribution Prior to Transient Figure 6.4.9: Case 4 Axial Power Distribution Prior to Transient 69

87 Figure : Case 4 Boron Concentration Distribution Prior to Transient (Warmer Colors Indicate Higher Boron Concentration) 70

88 Figure : Case 4 Radial Power Distribution at Peak Core Power Figure : Case 4 Axial Power Distribution at Peak Core Power 71

89 Condensate Slug Figure : Case 4 Boron Concentration Distribution at Peak Core Power (Warmer Colors Indicate Higher Boron Concentration) 72

90 6.5 Extreme Accident Cases Condensate Entry by Forced Circulation A more severe boron dilution transient would occur if forced circulation were started by actuation of a RCP. The cause of this actuation could be due to human error or an electrical malfunction of some nature. In any case, the start of a reactor coolant pump would drive the mass of deborated condensate through the cold leg and reactor vessel and into the core at a much higher velocity. The resulting insertion of positive reactivity would be much more rapid and the power level of the core would be able to increase further before prompt feedback reduces the power level again. A set of cases are now simulated where a single condensate slug enters the core at high velocity as a result of being swept into the core by forced circulation. The flow rate of the coolant entering the downcomer from the cold leg of the actuated RCP, is kg/sec, which is the nominal flow rate for the RCP. The safety injection flow rate is still 12 kg/sec due to the higher system pressure. The total mass flow rate of the safety injection flow and the RCP is therefore kg/sec. Using the same assumptions that the boron concentration of the condensate slug exiting the cold leg pipe is 0 ppm and the safety injection boron concentration is 2200 ppm, equations and give a resultant boron concentration of 6.64 ppm for the condensate slug entering the core. The cross-sectional shape of the condensate slug is still assumed to be circular with the same diameter as the cold leg pipe inner diameter. The discretization scheme is the similar to that of the natural circulation cases with only the resultant boron concentrations changing. The discretization of the slug entering the core in this case is shown in Figure

91 Region 3 Region 2 Region 1 Region 2 Region 3 Region 1 Region 1 Region 1 Region 3 Region 2 Region 1 Region 2 Region 3 Region 1 = 6.6 ppm Region 2 = ppm Region 3 = ppm Full Boration = 1680 ppm = Actual Slug Boundary Figure 6.5.1: Condensate Water Slug Discretization Forced Circulation Case Among the natural circulation cases simulated, the core entrance location that resulted in the highest localized fuel enthalpy was when the condensate slug entrance was centered on core position E3 (sub-channel 158). It is this location where the condensate slug will enter in the forced circulation cases. Two forced circulation cases are now executedwith the difference between the two cases being the condensate slug volume. In the first case, the slug volume is the same as the natural circulation cases to determine the impact of the condensate slug entrance velocity being increased. In the second case, the slug volume is increased to 4 m 3 which is the originally formulated slug volume by increasing the slug length. In both cases, the inlet boron concentration ramps down from nominal boron from time 0.5 seconds to 1.0 second with the condensate considered to have entered the core at time 1.0 second. Once the slug has completely entered the core, the inlet boron concentration of the entrance 74

92 location is ramped back to nominal over a period of 0.5 seconds. In Case 1, the inlet boron concentration returns to nominal at time 4.32 seconds. For Case 2, inlet boron concentration returns to nominal at time seconds. Following execution of the first forced circulation case (Case 1), it is found that the power spike was more intense with a peak power factor of at time 1.31 seconds. This larger spike is due to the condensate slug being able to enter further into the core before significant Doppler feedback was able to bring the power level back down again as shown by the power evolution in Figure Due to the large power fluctuations, a semi-log plot of core power is also given in Figure The corresponding core wide reactivity increase was higher, with a peak reactivity of -$20.77, as shown in Figure This corresponds to a peak reactivity change of +$ Although the core wide reactivity remained well below critical, the observed power spike combined with the calculated peak reactivity change suggests that localized prompt criticality was attained in the core region affected by the condensate. 75

93 Figure 6.5.2: Forced Circulation Case 1 Power Evolution with Time Figure 6.5.3: Forced Circulation Case 1 Log (Base 10) Power Evolution with Time 76

94 Figure 6.5.4: Forced Circulation Case 1 Reactivity Evolution with Time The radial power distribution, axial power distribution, and boron concentration distribution at the time of peak core power (time 1.31 seconds) are given in Figures 6.5.5, 6.5.6, and 6.5.7, respectively. As predicted, at the time of peak core power, the condensate slug has entered further into the core than in the natural circulation case which contributed to the more rapid and higher power increase. 77

95 Figure 6.5.5: Forced Circulation Case 1 Radial Power Distribution at Peak Core Power Figure 6.5.6: Forced Circulation Case 1 Axial Power Distribution at Peak Core Power 78

96 Condensate Slug Figure 6.5.7: Forced Circulation Case 1 Boron Concentration Distribution at Peak Core Power (Warmer Colors Indicate Higher Boron Concentration) The core averaged temperature increase of the fuel in this case was much more severe as would be expected. As shown in Figure 6.5.8, at the core-wide level, the core averaged fuel temperature peaked with a temperature of K at time 3 seconds. The moderator temperature peaked soon after with a temperature of K at 3.26 seconds. 79

97 Figure 6.5.8: Forced Circulation Case 1 Temperature Evolution with Time What is more informative though is the fuel temperature distribution in the core as shown in Figure at time 3 seconds. As indicated in the figure, the temperature is extremely hot near the condensate flow region and less so in other core regions, indicating that the core averaged fuel temperature spike is largely due to the power spike in the core region where the condensate travels. 80

98 Condensate Slug Path Figure 6.5.9: Forced Circulation Case Fuel Temperature Distribution at Time 3 Seconds (Warmer Colors Indicate Hotter Fuel Temperature in the Vicinity of the Condensate Path) At the individual node level, the hottest fuel node was radial node 144, axial level 10 with a peak fuel node temperature of K. The fuel enthalpy at this temperature is cal/g, which is high enough to cause extensive fuel damage. However it is also observed that the peak fuel temperature and enthalpy at the node level occurred at the end of the transient at time 12 seconds. Further examination of the hot node fuel temperature indicated that the fuel enthalpy first 81

99 exceeded the fuel damage level of 230 cal/g at time seconds at radial node 144, axial level 12. Once fuel damage begins, much more uncertainty exists since the geometry of the fuel and cladding would likely begin to change as the fuel temperature reaches these more extreme and damaging levels. Forced circulation Case 2 is simulated next. As stated prior, the only difference between the first and second forced circulation case is the condensate slug volume and the resultant length being increased in the second case. As shown in Figures and , the initial phase (first 3.8 seconds) of power evolution is the same as forced circulation Case 1. Similar to Case 1, the power in Case 2 also peaks at a factor of at time 1.31 seconds. Additionally, the peak reactivity change and peak core averaged fuel temperature are also the same as indicated in Figures and Figure 6.5.9: Forced Circulation Case 2 Power Evolution with Time 82

100 Figure : Forced Circulation Case 2 Log (Base 10) Power Evolution with Time Figure : Forced Circulation Case 2 Reactivity Evolution with Time 83

101 Figure : Forced Circulation Case 2 Temperature Evolution with Time The only difference between forced circulation Case 1 and Case 2 is the amount of time the power excursion is allowed to continue and the amount of time the fuel is being heated. At the node level, the hottest fuel node in this case was radial node 144, axial level 9 with a peak fuel node temperature of K which occurred near the end of the simulation at time 11 seconds. The fuel enthalpy at this temperature is cal/g, which again is high enough to cause extensive fuel damage and effectively bring the same end result as the first case. Finally, the core wide results of the two forced circulation cases and natural circulation Case 4 are summarized in Table The hot node location, fuel temperature, and fuel enthalpy among these cases are compared in Table

102 Table 6.5.1: Forced Circulation Core Wide Results Comparison Maximum Core Reactivity [$] Peak Reactivity Change [$] Maximum Core Averaged Mod Temp [K] Maximum Core Averaged Fuel Temp [K] Maximum Core Case Power Factor [-] N4* *Natural Circulation Case 4 Table 6.5.2: Forced Circulation Hot Fuel Node Results Comparison Case Location of Hottest Fuel Node* Peak Fuel Node Temperature [K] Peak Fuel Node Enthalpy [cal/g] 1 144, , N4** 144, *CTF Radial Sub-channel, Axial Sub-channel (Axial Levels Starting From Bottom of Core) **Natural Circulation Case Uncertainties While a boron dilution accident transient was successfully simulated for a combination of scenarios and conditions, a number of uncertainties exist in the results. The most obvious uncertainty is the mixing that the deborated water slug undergoes while transiting from the accumulation points in the steam generator outlet and cross over leg to the core inlet. Without detailed experimental data for the precise system geometry and conditions, a separate set of simulation results are needed in order to accurately model this mixing and transport. Such data could be generated by a CFD simulation. The results of this simulation 85

103 would then be used to determine the inlet locations and concentrations of the deborated water slug and provide a more realistic set of inlet boron boundary conditions rather than the overly conservative boundary conditions used in this study. The resultant CFD data could also be used to provide localized core inlet flow boundary conditions rather than making an idealized assumption of uniformly distributed flow rate, especially in the case of forced circulation. Another source of uncertainty is the cross section data used for the given thermal hydraulic conditions. Although a similar level of coolant subcooling is achieved by adjusting the pressure boundary condition higher, the actual moderator density yielded (which is the maximum tabulated density) is still below that which would be present for the originally formulated post- LOCA conditions shown in Table In the forced circulation case, the limited cross section thermal hydraulic range became a problem again. Although the average core fuel temperature remains within the tabulated range, the hot fuel node temperature indicates that some node fuel temperatures far exceeded the tabulated maximum fuel temperature by a significant amount (over 250% for the peak temperature of the hot fuel node). Although the calculation was able to continue, significant extrapolation of cross section data did occur, which is likely to be an additional source of error. In addition to the uncertainty associated with the fuel temperature from a cross section standpoint, the fuel geometry also likely changed as a result of the extreme temperatures observed in the forced circulation cases. To reduce uncertainties associated with cross section modeling, a cross section library would be built to encompass the full range of accident thermal hydraulic conditions expected. In the less extreme cases, the nodal fuel enthalpies provide insight as to where the hottest fuel temperatures are likely to occur. For a more rigorous safety analysis perspective, a pin-power reconstruction method could be used to determine the individual pin power factor evolutions 86

104 within the hot fuel node. This power factor data could then be used to build a localized CTF simulation case which could then provide more detailed information on peak fuel enthalpy and peak cladding temperature. These results would provide more definitive confirmation that fuel or cladding failure is or is not expected to occur as well as reveal a higher resolution thermal behavior of the fuel during the transient. 6.7 Accident Simulation Conclusions For the preceding accident simulations, a practical application of the boron tracking model used in the CTF-BTM / NEM coupled code is demonstrated. The ten accident scenario cases executed simulate a deborated condensate slug entering the core during post-sbloca conditions. For the assumption that natural circulation is restored and sweeps the condensate into the core, the entrance location of the condensate slug is varied to determine the most limiting entrance location in terms of peak fuel enthalpy and calculated reactivity change. For the natural circulation cases, the most limiting core entrance location was determined to be location E3 (sub-channel 158). The core power was found to peak at time 2.93 seconds at a factor of The peak reactivity change in this location was found to be +$0.932 and the peak fuel enthalpy was found to be cal/g. At this level of peak fuel enthalpy, fuel damage is not expected to occur. In the first forced circulation case, the condensate slug was driven into the core at the same limiting location determined in the natural circulation cases. The resulting reactivity change was more rapid with the core power peaking with a higher power factor of attained at 1.31 seconds. The peak reactivity change was found to be +$1.046 which, in addition to the power 87

105 spike observed, indicates that localized prompt criticality was attained in the vicinity of the condensate slug. Most importantly, the peak fuel enthalpy in the hot fuel node increased to cal/g. At this level of fuel enthalpy, extensive damage to the fuel would have occurred in the affected fuel assemblies. This damage to the fuel would further contribute to the radioactivity already present in containment due to the SBLOCA since the gaseous fission product inventory would be expelled from the fuel rods. The second forced circulation case exhibited the same behavior as the first case with the exception of the amount of time the power excursion was allowed to continue due to the longer condensate slug length. In this case a peak fuel enthalpy of cal/g was obtained in the hot fuel node toward the end of the transient. The end result however, is basically the same as Case 1 since the affected fuel assemblies would suffer significant damage as a result of these transients. Although uncertainties are known to exist and many assumptions and simplifications were made, the level of conservatism used in the scenario model helps to bias the results towards that of a worst case scenario. In reality, mixing of the condensate slug as it is formed in the steam generator and crossover leg will increase the initial boron concentration of the condensate. Furthermore, as the condensate is swept through the cold leg, downcomer, and through the lower plenum of the reactor vessel, some degree of mixing with the fully borated coolant will surely occur and the resultant reactivity insertion would likely not be as severe or as localized. Finally, the reason that GSI-185 was closed by the NRC without extensive follow-up study or mandate of installed countermeasures in existing plants is that the likelihood of such a combination of worst case events occurring to trigger this type of boron dilution accident is extremely low [6]. A narrow range of break sizes is required to create the correct type of post- SBLOCA system conditions that increase the likelihood of this particular dilution transient. For 88

106 forced circulation cases, human error or an electrical control system malfunction would be required to actuate the RCP that sweeps the condensate into the core and completes the chain of initiating events. Natural circulation resumption is more likely, but the comparatively low fluid velocity and fluid mixing would help to mitigate the consequences of such an occurrence with a smaller and more gradual insertion of positive reactivity. 89

107 CHAPTER 7 CONCLUSIONS 7.1 Conclusions In this thesis, the new boron tracking model added to CTF is employed in an explicit coupling of CTF with NEM. This employment of the CTF-BTM / NEM code in a coupling verification study represents the next step in the overall validation and qualification of the boron tracking model which uses the Modified Godunov scheme to simulate boron transport. The coupled code is first validated at steady-state conditions using an implemented k-search algorithm to find the critical boron concentration. At HZP conditions, the inlet boron concentration predicted by both the boron tracking model and assumption of uniform boron closely match, with both versions predicting a greater boron concentration than the reference solution by 0.33%. The predicted HZP power distribution more closely matched the DeCART Method of Characteristics reference solution than the PARCS power distribution. At HFP conditions, the differences between the boron tracking modal and assumption of uniform boron were much more pronounced. The critical inlet boron concentration predicted using the boron tracking model exhibited a greater deviation from the benchmark reference solution than the case of assuming perfectly uniform boron. The boron tracking model predicted an inlet boron concentration 0.61% less than the reference solution versus a 0.02% smaller boron concentration predicted by a uniform boron concentration. This difference is due to the fact that as the moderator density changes, the boron concentration also changes. Since the boron tracking model allows for an independent control of the inlet boron concentration boundary condition from the inlet moderator conditions, the inlet boron required for criticality is reduced. This is due to the fact that as the moderator density decreases, the boron concentration increases and eventually the 90

108 boron concentration becomes directly proportional to the change in moderator density. This phenomenon occurs toward the middle of the axial core height where the neutron flux is greater, thus giving the increased boron concentration in this region a greater reactivity influence. Using a series of coupled, steady-state multiplication factor solutions for varying inlet boron concentrations, these data were used in the verification of the transient CTF-BTM / NEM coupled code. The core reactivity responses were first predicted using the gathered steady-state data. Then a series of five cases were carried out where the inlet boron concentration was homogeneously changed using the transient operation of the coupled code. It was found that in cases where the boron was rapidly changed, the transient core response more closely matched the predicted reactivity response. This was concluded to be due to the temperature change of the fuel in cases where the boron was more gradually increased, causing a fuel temperature reactivity feedback which increased in magnitude as more time was allowed for the fuel temperature to change. The displayed core responses to these reactivity transients were determined to be physically valid and the transient portion of the coupled code was considered to be verified. The study concluded with the formulation and execution of one of the intended uses of the boron tracking model in CTF in a practical application. For post-sbloca conditions, a boron dilution accident is simulated for eight condensate slug entry locations at natural circulation conditions along possible entry locations. It was found that in natural circulation flow Case 4, the slug centered on the fuel assembly located in position E3 (sub-channel 158) produced the highest nodal fuel enthalpy of cal/g and a peak reactivity change of +$ It was concluded that although the core remained subcritical, a localized power excursion did occur. Case 4 was considered to be the most limiting case among the natural circulation cases due to attaining the highest fuel enthalpy peak in the hottest fuel node. 91

109 After determining that Case 4 defined the most limiting location for condensate slug entry, this case was simulated again at forced circulation conditions for two cases. As expected, the resultant reactivity in the forced circulation cases was higher than the natural circulation cases with a peak reactivity change of +$1.046 attained for both forced circulation cases. The large power spike and amount of reactivity change calculated indicate that super-prompt criticality had been attained in the vicinity of the condensate. Moreover, the peak fuel enthalpy in the hot node was extremely high at cal/g and cal/g for Cases 1 and 2, respectively. At this level, fuel damage was predicted to be extensive, but due to a number of uncertainties in the assumptions and cross section modeling, this result is especially prone to error. In all natural circulation cases simulated, the peak reactivity change was kept below $1.00, indicating that localized prompt criticality was not attained. Resumption of natural circulation was concluded to be unlikely to cause fuel damage. In the forced circulation case, the RCP restart was concluded to have caused localized super-prompt criticality and fuel damage in the hot fuel nodes. Given the conservative assumptions used, mixing of the condensate slug with the borated coolant during transport to the core would help to mitigate the effects of such a scenario. The boron transport model added to CTF prior to this study greatly enhanced the overall capabilities of the code. By coupling the code to a three-dimensional nodal diffusion code as was done with the coupling to NEM in this study, the boron tracking model was further verified using a combination of known benchmarking results and a series of transient simulation verification exercises. The application of the CTF boron tracking model in a coupled code application was then successfully demonstrated in a post-sbloca boron dilution transient, indicating that when coupled to a three-dimensional neutronics code, the boron tracking model enables simulation of a class of LWR transients once off limits to CTF which are transients involving changes of coolant boron concentration. Furthermore, transients which have already been simulated by CTF may 92

110 now yield more physically accurate results since uniform boron concentration throughout the core no longer must be assumed. 7.2 Recommendations for Continued Work During the course of work for this thesis study, a number of opportunities for future continued work were identified. This future work would yield additional contributions to the studies of boron transport and reactor core analysis of transients resulting from boron dilution events. For future studies of post-loca transients using the Purdue MOX core model, a new cross section library which encompasses a more extreme range of thermal hydraulic conditions would be desirable. Although a methodology was found to address the moderator density tabulation range being too low for expected post-loca conditions by raising the outlet pressure boundary condition, uncertainties are still believed to exist. This is due to the fact that this work-around only addressed the amount of subcooling in the moderator. The density in the simulation was still lower than expected. Furthermore, in the forced circulation accident case, some fuel node temperatures far exceeded the tabulated fuel temperature range causing cross section extrapolation to occur, which is undesirable. Developing a new set of cross sections with a wider range of thermal hydraulic conditions would alleviate this source of uncertainty. One of the biggest unknowns for the post-sbloca conditions was determining the appropriate boundary conditions at the core inlet. Due to these difficulties, highly idealized boundary conditions were used. Mixing effects prior to the condensate slug entering the core inlet were mostly neglected. Additionally, coolant temperature and velocity distributions were ignored with uniform distributions used instead. 93

111 In future studies, a more realistic set of boundary conditions would help to reduce some of the uncertainties and provide for a more realistic analysis. Ideally, these boundary conditions would be generated from detailed experimental data representing the specific system geometry. A system code such as RELAP or TRACE could be used to provide the inlet boundary conditions, but these codes would face the same challenges of boron transport modeling accuracy that spurred creation of the CTF boron tracking model in the first place. A CFD simulation however, would produce the amount of detail desired to get the most benefit from the improved subchannel boron tracking model in the CTF-BTM / NEM coupled code. Finally, analysis of the coupled code result was able to determine the location and enthalpy of the hottest fuel node during the transient simulations. This analysis would have been more useful if fuel temperature and enthalpy data were able to be extracted at the pin level to provide a better estimate of peak clad temperature and fuel enthalpy. This can be achieved by executing a followup standalone CTF-BTM simulation of only the hot node using the fuel assembly power profile from the coupled code and then performing a pin power reconstruction to determine the individual pin-power levels to use as the CTF inputs. At this level of detail, much greater confidence would be gained as to whether or not fuel and cladding integrity is maintained. 94

112 REFERENCES [1] Areva Nuclear Power, Inc., Evolutionary Power Reactor Design Control Document, Revision 3, (2011). [2] Mitsubishi Heavy Industries, Ltd., US-Advanced Pressurized Water Reactor Design Control Document, Revision 3, (2011). [3] Westinghouse Electric Company, LLC., AP1000 Design Control Document, Revision 19, (2011). [4] United States Nuclear Regulatory Commission, "Resolution of Generic Safety Issues: Issue 22: Inadvertent Boron Dilution Events (NUREG-0933)," Revision 2, (2012). [5] United States Nuclear Regulatory Commission, "Meeting Summary," in Proceedings of the OECD/CSNI Specialists Meeting on Boron Dilution Reactivity Transients, State College, Pennsylvania, (1997). [6] United States Nuclear Regulatory Commission, "Resolution of Generic Safety Issues: Issue 185: Control of Recriticality Following Small-Break LOCAs in PWRs (NUREG-0933)," Revision 0, (2012). [7] The RELAP5 Code Development Team, RELAP5-3D Code Manual, vol. 1, (2001). [8] J. Yan, B. Kochunas and M. Hursin, "Coupled Computational Fluid Dynamics and MOC Neutronic Simulations of Westinghouse PWR Fuel Assemblies with Grid Spacers," in Proceedings of The 14th International Topical Meeting on Nuclear Reactor Thermalhydraulics, Toronto, Canada, NURETH14-254, (2011). [9] J. Hu and Rizwan-uddin, "Coupled Neutronics and Thermal-Hydraulics Simulations Using MCNP and FLUENT," Transactions of the American Nuclear Society, vol. 98, pp , (2008). [10] T. Kozlowski and T. Downar, "PWR MOX/UO2 Core Transient Benchmark: Final Report," Nuclear Energy Agency, Organization for Economic Co-operation and Development, US Nuclear Regulatory Commission, (2007). [11] K. Ivanov, T. Beam and A. Baratta, "Pressurized Water Reactor Main Steam Line Break (MSLB) Benchmark," NEA/NSC/DOC (99) 8, OECD NEA, (1999). 95

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115 APPENDIX A. PURDUE MOX / UO 2 CORE MAPS R R R R R R R R R A R R R 20.0 M4.3% M4.3% R R R B R R M4.3% M4.0% M4.0% M4.3% R R C R 32.5 M4.3% 20.0 M4.3% M4.3% M4.3% M4.3% 32.5 R D R R R R E R 20.0 M4.3% 20.0 M4.0% 37.5 M4.0% 22.5 M4.0% 22.5 M4.0% M4.3% 20.0 R F R M4.3% 35.0 M4.3% M4.3% 17.5 M4.3% 35.0 R G R 17.5 M4.0% 32.5 M4.0% M4.0% M4.0% 17.5 R H R 32.5 M4.3% M4.3% R I R 17.5 M4.0% 32.5 M4.0% M4.0% M4.0% 17.5 R J R M4.3% 35.0 M4.3% M4.3% 17.5 M4.3% 35.0 R K R 20.0 M4.3% 20.0 M4.0% 37.5 M4.0% 22.5 M4.0% 22.5 M4.0% M4.3% 20.0 R L R R R R M R 32.5 M4.3% 20.0 M4.3% M4.3% M4.3% M4.3% 32.5 R FRES N R R M4.3% M4.0% M4.0% M4.3% R R ONC O R R R 20.0 M4.3% M4.3% R R R TWI R R R R R R R R R REFL Figure A.1: Core Assembly Loading Pattern (Refer to Figure for Key) 98

116 Figure A.2: NEM Radial Node Pattern Map 99

117 Figure A.3: Radial CTF Sub-channel Pattern Map CONTROL ROD BANK MAP R R R R R R R R R R R R R R R R R CR-SA CR-B CR-C CR-B CR-SA R R 100 R CR-SC CR-SB CR-SB CR-SC R R R CR-SA CR-D CR-SD CR-D CR-SA R R

118 Figure A.4: Core Control Rod Bank Map 101