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

Transcription

1 The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering THE DEVELOPMENT OF A THERMAL HYDRAULIC FEEDBACK MECHANISM WITH A QUASI-FIXED POINT ITERATION SCHEME FOR CONTROL ROD POSITION MODELING FOR THE TRIGSIMS-TH APPLICATION A Dissertation in Nuclear Engineering by Veronica V. Karriem 2016 Veronica V. Karriem Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2016

2 ii The dissertation of Veronica Karriem was approved* by the following: Maria Avramova Chair of Committee Adjunct Professor in Nuclear Engineering Dissertation Advisor Kostadin Ivanov Adjunct Professor in Nuclear Engineering Kenan Ünlü Professor in Nuclear Engineering Director of Radiation Science and Engineering Centre Brenden Heidrich Special Member Research Capability Scientist at the Nuclear Science User Facilities Idaho National Laboratory Gabeba Baderoon Associate Professor of Women's, Gender and Sexuality studies and African Studies Arthur Motta Professor of Nuclear Engineering and Material Science and Engineering Chair of the Nuclear and Engineering Program *Signatures are on file in the Graduate School

3 iii ABSTRACT Nuclear reactor design incorporates the study and application of nuclear physics, nuclear thermal hydraulic and nuclear safety. Theoretical models and numerical methods implemented in computer programs are utilized to analyze and design nuclear reactors. The focus of this PhD study's is the development of an advanced high-fidelity multi-physics code system to perform reactor core analysis for design and safety evaluations of research TRIGA-type reactors. The fuel management and design code system TRIGSIMS was further developed to fulfill the function of a reactor design and analysis code system for the Pennsylvania State Breazeale Reactor (PSBR). TRIGSIMS, which is currently in use at the PSBR, is a fuel management tool, which incorporates the depletion code ORIGEN-S (part of SCALE system) and the Monte Carlo neutronics solver MCNP. The diffusion theory code ADMARC-H is used within TRIGSIMS to accelerate the MCNP calculations. It manages the data and fuel isotopic content and stores it for future burnup calculations. The contribution of this work is the development of an improved version of TRIGSIMS, named TRIGSIMS-TH. TRIGSIMS-TH incorporates a thermal hydraulic module based on the advanced sub-channel code COBRA-TF (CTF). CTF provides the temperature feedback needed in the multi-physics calculations as well as the thermal hydraulics modeling capability of the reactor core. The temperature feedback model is using the CTF-provided local moderator and fuel temperatures for the cross-section modeling for ADMARC-H and MCNP calculations. To perform efficient critical control rod calculations, a methodology for applying a control rod position was implemented in TRIGSIMS-TH, making this code system a modeling and design tool for future core loadings. The new TRIGSIMS-TH is a computer program that interlinks various other functional reactor analysis tools. It consists of the MCNP5, ADMARC-H, ORIGEN-S, and CTF. CTF was

4 iv coupled with both MCNP and ADMARC-H to provide the heterogeneous temperature distribution throughout the core. Each of these codes is written in its own computer language performing its function and outputs a set of data. TRIGSIMS-TH provides an effective use and data manipulation and transfer between different codes. With the implementation of feedback and control- rod-position modeling methodologies, the TRIGSIMS-TH calculations are more accurate and in a better agreement with measured data. The PSBR is unique in many ways and there are no off-the-shelf codes, which can model this design in its entirety. In particular, PSBR has an open core design, which is cooled by natural convection. Combining several codes into a unique system brings many challenges. It also requires substantial knowledge of both operation and core design of the PSBR. This reactor is in operation decades and there is a fair amount of studies and developments in both PSBR thermal hydraulics and neutronics. Measured data is also available for various core loadings and can be used for validation activities. The previous studies and developments in PSBR modeling also aids as a guide to assess the findings of the work herein. In order to incorporate new methods and codes into exiting TRIGSIMS, a re-evaluation of various components of the code was performed to assure the accuracy and efficiency of the existing CTF/MCNP5/ADMARC-H multi-physics coupling. A new set of ADMARC-H diffusion coefficients and cross sections was generated using the SERPENT code. This was needed as the previous data was not generated with thermal hydraulic feedback and the ARO position was used as the critical rod position. The B 4 C was re-evaluated for this update. The data exchange between ADMARC-H and MCNP5 was modified. The basic core model is given a flexibility to allow for various changes within the core model, and this feature was implemented in TRIGSIMS-TH. The PSBR core in the new code model can be expanded and changed. This allows the new code to be used as a modeling tool for design and analyses of future code loadings.

5 v The CTF code can be used as a thermal hydraulic stand-alone modeling code. The TRIGSIMS-TH code generates and expands channel thermal hydraulic input model that is capable of analyzing the flow in and around the core construct. The tool can be used to analyze future changes such as the safety analysis of the D 2 O tank changes. The TRIGSIMS-TH code system is an automated tool. Using a generalized input, -it will generate all the needed code-specific input files for the various applications.

6 vi TABLE OF CONTENTS List of Figures... ix List of Tables... xiii List of Abbreviations... xv Acknowledgements... xvi Chapter 1 Introduction Background of the PSBR reactor facility The PSBR reactor PSBR fuel inventory, burnup and analysis tool Objective of this work Synopsis... 8 Chapter 2 Literature Review Current PSBR code system PSBR-related studies Calculation tools Codes used for PSBR analysis Review of related codes Review of coupled codes Thermal hydraulic modeling General review Reviews on critical rod height Nuclear Data Control rod absorber material Chapter 3 Theoretical models and numerical methods Introduction Nuclear Reactor Core Design Terminology Core design process Main parameters for core design Intent and deliverables Computational analysis tools Neutron transport methods and codes Thermal hydraulic methods and codes PSBR description PSBR core TRIGA fuel Application of the PSBR... 37

7 vii 3.5 TRIGSIMS and TRIGSIMS-TH Capabilities of TRIGSIMS and TRIGSIMS-TH Codes in TRIGSIMS-TH Cross sections Other supplementing theory Design of the core loading B 4 C in Control rods Thermal hydraulic feedback Chapter 4 Methodological and modeling developments TRIGSIMS-TH control system Temperature feedback methods Illustration of the thermal hydraulic feedback effects The thermal hydraulic feedback implementation MCNP/CTF coupling ADMARC-H/CTF coupling Pseudo material approach Partially inserted control rods Application of perturbation theory Control rod position method using a quasi-fixed point iteration scheme Thermal hydraulics methodology TRIGSIMS-TH Core Modeling parameters Moderator surrounding the core Conclusion on the methods and models Chapter 5 Results and Findings MCNP/CTF coupling Critical control rod search Validation of critical rod search method Core reactivity estimation from calculations ADMARC-H for acceleration of control rod search method Thermal hydraulic of the PSBR Core Application of power rise with thermal hydraulic feedback AMARCH/CTF coupling Development of core expansion Graphite elements added New type of fuel elements Improvements of the core design parameters Control elements Homogenized cross sections results Continuous energy cross section application Moderator for the core design TRIGSIMS-TH application to CTF Thermal hydraulics as a standalone tool Summary of results Chapter 6 TRIGSIMS-TH Core Design Application

8 6.1 Core loading design scenario Addition of graphite elements A new core layout Core loading design scenario Core design scenario Description of the fuel Analysis Core design scenario 4: Analysis of the core with a D 2 O tank A comparison with and without D 2 O tank Thermal Hydraulics comparison with D 2 O tank Chapter 7 Conclusion and future work Conclusion Proposal for future work Modify the D 2 O input Transient analysis with CTF/ADMARC-H Using the TRIGSIMS-TH to investigate the thermal hydraulic properties of the fuel Addition of a in-core experimental tube within TRIGSIMS-TH Appendix Additional information Measured data Core loading diagrams used in this thesis SERPENT calculations compared with MCNP calculations B 4 C calculations MCNP standard deviation MCNP5 Convergence of the PSBR TRIGSIMS -TH model Normalization factors REFERENCES viii

9 ix LIST OF FIGURES Figure 1-1 PSBR TRIGA Core... 5 Figure 2-1 Current TRIGSIMS layout Figure 3-1 Basic analyses and parameters for nuclear reactor core design Figure 3-2 Core loading configuration Figure 3-3 A typical TRIGA fuel element Figure 3-4 CTF Cartesian coordinate system Figure 3-5 Scalar Mesh cell, axial Figure 3-6 Scalar mesh, transverse Figure 3-7 Homogenization of TRIGA fuel Figure 4-1 Diagram of TRIGSIMS-TH code platform Figure 4-2 Illustration of homogeneous and heterogeneous temperature distributions Figure 4-3 Typical radial temperature distribution at 1MW power [K] Figure 4-4 1MW axial temperature distribution [K] Figure 4-5 A typical sub-channel for CTF Figure 4-6 Illustration of the coupling methodology Figure 4-7 Flow diagram of MCNP/CTF coupling Figure 4-8 Flow diagram of ADMARC-H/CTF couple Figure 4-9 S-curve for control rods Figure 4-10 Flow diagram of the control rod method Figure 4-11 illustration of the quasi fixed point iteration Figure 4-12 Developing of a full core CTF model Figure 4-13 CL56 diagram Figure 4-14 CL54 diagram Figure 5-1 Reference core diagram... 79

10 x Figure 5-2 Temperature distribution for CL Figure 5-3 Temperature distribution for CL Figure 5-4 Temperature distribution for CL53H Figure 5-5 Iterative control rod position search of CL Figure 5-6 Iterative control rod position search for CL Figure 5-7 CL56 AT 700kW power, with Xe adjusted Figure 5-8 CL54 at 800kW power Figure 5-9 CL56 estimation of reactivity loss value Figure 5-10 CL56, with ADMARC-H to accelerate Figure 5-11 Reactivity loss with power increase/control rod withdrawal for CL Figure 5-12 Reactivity loss with power increase for CL Figure 5-13 CL56 average temperature increase for the i-17 rod corresponding to reactivity loss measurements Figure 5-14 CL54 average temperature increase for i-16 corresponding to reactivity loss measurements Figure 5-15 Temperature distribution for coolant surrounding the numbered rods Figure 5-16 Temperature increase with power increase for the indicated rods Figure 5-17 Comparison of CL56 and CL54 flux distribution Figure 5-18 Thermal flux distribution for CL Figure 5-19 Normalized average power distribution for CL Figure 5-20 Normalized average power distribution for CL Figure 5-21 Diagram ADMARC-H/CTF-MCNP-CTF couple for position step Figure 5-22 MCNP/CTF/ADMARC-H coupling Figure 5-23 Illustration of core expansion Figure 5-24 Homogenized fuel/clad/water region Figure 5-25 Illustration of the two input geometries: MCNP and SERPENT

11 xi Figure 5-26 Pseudo material difference (K eff results) Figure 5-27 CL53 no-graphite diagram Figure 5-28 CL graphite elements Figure 5-29 CL54 diagram Figure 5-30 Comparison with and without D 2 O tank to the CL56 design at 1 MW power Figure 5-31 Comparison of average power for the D 2 O tank calculation Figure 5-32 CTF input changes for "standalone" calculations Figure 5-33 Thermal hydraulics results: velocity of channels 112 to 131 for CL Figure 5-34 Thermal Hydraulic results: Temperature distribution for CL Figure 5-35 Results of the mass flow rate across the gaps (cross flow) Figure 5-36 Illustration of the cross flow results Figure 5-37 Illustration of the flow around the channel Figure 6-1 CL56 and CL56- adjusted Figure 6-2 Comparison of the CL56 and CL56_adjusted Figure 6-3 Comparison of CL56 and CL56-adjusted average power distributions Figure 6-4 CL56_adjusted- flux [neutrons/cm 2 -s] across the core Figure 6-5 CL56-flux [neutrons/cm 2 -s] across the core Figure 6-6 Flux [neutrons/cm 2 -s] results from reshuffling of core elements Figure 6-7 Illustration of CL54 and CL54_shuffled Figure 6-8 Comparison of CL54 vs CL54-shuffled Figure 6-9 Difference in element power between CL54_shuffled vs. CL Figure 6-10 Percent Difference in Temperature for CL54_shuff and CL Figure 6-11 CL /20 LEU convergence results Figure 6-12 Temperature distribution of the 30/20 LEU fuel Figure 6-13 Three cases to express the use of the CTF standalone model

12 Figure 6-14 The % difference in power distribution for the D 2 O tank shapes compared no tank Figure 6-15 Illustration of the cross flow data for the channels adjacent to D 2 O to the center of the core Figure A- 1 CL54 Core loading diagram Figure A- 2 CL53H core loading diagram (includes the position for graphite) Figure A-3 Comparison of the K eff values after each burnup step Figure A- 4 Model for burnup of B 4 C Figure A- 5 Shannon fission source entropy convergence check Figure A- 6 Shannon fission source entropy convergence check Figure A- 7 Convergence check of the k eff values using different skipped cycles xii

13 xiii LIST OF TABLES Table 2-1 B 4 C components as used previously Table 3-1 Comparison of old and new TRIGSIMS Table 5-1 Measured results compared with calculated TRIGSIMS-TH results Table 5-2 Comparison of calculated to measured values for power levels less than 1MW Table 5-3 Data from calculations Table 5-4 Reactivity control comparisons for CL Table 5-5 Reactivity control comparisons for CL Table 5-6 Thermal hydraulic results for core loadings at 1MW power Table 5-7 Core excess reactivity in $ for various core loadings Table 5-8 Addition of 10 graphite elements Table 5-9 Theoretical B 4 C number densities Table 5-10 Control Rod Absorber Combinations Table 5-11 Comparisons of control rod position for B 4 C cases Table 5-12 SERPENT vs. MCNP Results for CL Table 5-13 Comparison with previous cross sections using CL53 in ADMARC-H code Table 5-14 CL53 at 1MW- comparison using ADMARC-H code with feedback Table 5-15 Comparison with previous cross sections using CL54 in ADMARC-H code Table 5-16 CL54 at 1 MW- comparison using ADMARC-H code with feedback Table 5-17 Comparison with previous cross sections using CL56 in ADMARC-H code Table 5-18 CL56 at 1MW- comparison using ADMARC-H code with feedback Table 5-19 The effects of the adjustment of the water surrounding the core Table 5-20 Estimation of reactivity for CL56 +D 2 0 tank Table 5-21 Analysis of the hotter elements in CL Table 6-1 estimating CL54 to CL54_shuffled reactivity

14 xiv Table 6-2 Fuel comparisons Table 6-3 CL56 with and without D 2 O tank Table 6-4 D 2 O tank comparisons Table A- 1Measured data Table A- 2 Decrease in B 4 C number densities effect

15 xv LIST OF ABBREVIATIONS ARI ARO B 4 C CL CTF CFD D 2 O ENDF MCNP ORIGEN-S PSBR TRIGA TRIGSIMS-TH All rods in All rods out Boron Carbide Core loading Cobra (COolant Boiling in Rod Array) - thermal fluids Computational Fluid dynamics Deuterium dioxide Evaluated Nuclear Data Files Monte Carlo N-Particle Oak Ridge Isotope GENeration Pennsylvania State Breazeale reactor Training, Research, Isotopes, General Atomic TRIGA SIMULATOR S with thermal hydraulics

16 xvi ACKNOWLEDGEMENTS I would like to thank Dr. Avramova for her support over the past years. Thank you for your unwavering encouragement, to complete this work. Thank you, Dr. Ivanov, for the opportunity and support in my studies. A special thanks to my thesis reviewers especially Dr. Ünlü and Dr. Heidrich, for their input in my studies. I have learned so much from your experiences and knowledge that was shared by our monthly meetings. Thank you Dr. Bederoon, for the time spend as my reviewer, and for the moral support, you give me when we interact. To my husband Zain, who has been my support in both academic and personal life. I appreciate your patience and encouragement through this period. My kids Lynn, Zayn and Hannah, hope my unending studies will benefit your lives in the future. This journey has been a long and unyielding. Thanks to everyone who supported me through this time.

17 1 Chapter 1 Introduction The primary purpose of nuclear reactor design is to ensure the safe and economic operations of nuclear reactors. A nuclear reactor is a complex physical system which involves multiple- and interacting physical phenomena with the most important being neutronics and thermal hydraulics. Neutronics involves the calculation of the neutron distribution in the reactor, from which the reactor power distribution in the core is determined. Heat deposits into the fuel as results of the fission reactions propagating throughout the fuel to its surface and is being removed by the reactor coolant. Nuclear reactor core design entails the simulation of these processes, which ensures that the power density limits in the fuel are within design limits and that the fuel cladding temperature limit is not exceeded. This ultimately ensures that the fuel integrity is not compromised. At non-zero power conditions, neutronics and thermal hydraulics interactions occur simultaneously, i.e. the neutronics and thermal hydraulic processes are intricately connected. The simulation of this multi-physics problem is quite complex and computationally involved. In the past, the pre-traditional approach of the nuclear design techniques treated the neutronics and the thermal hydraulics analyses as isolated simulations that were coupled through state dependent parameters and boundary conditions. The order of the operator for neutronics (transport/diffusion) and the thermal hydraulics (sub-channel/system codes) may also vary. This pre-traditional simplified neutronics and thermal hydraulics analysis approach resulted in a computationally efficient methodology (short run times) and therefore allowed for many design repetitions to occur in a short amount of time so that the optimum reactor core design can be determined.

18 2 The Pennsylvania State Breazeale Reactor (PSBR) or PSBR TRIGA (Training Research Isotope, General Atomic) is a 1MWth research reactor [1] housed at the Radiation Science and Engineering Centre (RSEC) at The Pennsylvania State University (PSU). This reactor facility is used for irradiation purposes as well as research and teaching. The reactor core design for this facility is performed with the code system TRIGSIMS (TRIGA SIMulator S). The TRIGSIMS code system is a fuel management and core analysis code currently in use at the RSEC facility. The aim of this PhD work is to improve the code system TRIGSIMS. TRIGSIMS [2], which is an interface program, connects Monte Carlo N-Particle (MCNP) transport code, to ORIGEN-S burnup code for fuel depletion. A nodal diffusion code, ADMARC- H, was included in this multi-tool platform, to aid in the acceleration of the MCNP calculation. TRIGSIMS however lacked a very important aspect of reactor design studies, i.e., the temperature feedback, associated with the increase of fuel temperature with power. TRIGA reactors utilize hydride fuel, meaning that the fuel and (hydrogen) moderator are in close proximity. The effect of temperature increase has an effect on the core reactivity. In this work, the thermal hydraulic code COBRA-TF (CTF) was incorporated for temperature feedback predictions. The new TRIGSIMS, referred to herein as TRIGSIMS-TH, is now an advanced highfidelity multi-physics tool. The addition of a control-rod-height-methodology in TRIGSIMS-TH has made this software a design tool. What this entails is, the code can be used to design a new core loading complete with critical rod position for a critical reactor at different power levels. This method was only possible with the addition of the feedback method to the core design. The CTF code is coupled with MCNP and ADMARC-H in an automated calculation sequence. Temperature feedback is applied to both system functions ensuring an even higher expected accuracy in the calculation.

19 3 The thermal hydraulic code CTF part of TRIGSIMS-TH can also be used as a stand-alone thermal-hydraulic analysis tool. This addition allows for the safety analysis of a reactor core layout to be performed, as well as the analysis to investigate the coolant flow in the case of upgrades and changes in reactor design. Various other changes and upgrades of the code, to enhance its capabilities, were introduced. A new set of homogenized few-group cross sections were generated with the Monte Carlo code, SERPENT for ADMARC-H calculations. MCNP, ADMARC-H and TRIGSIMS have been previously validated for PSBR applications [2]. CTF was also validated using measured data from PSBR [3]. The validation of the TRIGSIMS-TH code system has been performed in this PhD study through the analyses of various core layouts by comparing the calculated results with the measured data for core loadings (CL), CL56, CL54, and CL53. The effective use of the developments incorporated in TRIGSIMS-TH code system was demonstrated in analyses to various core loadings. The results and findings of this work are presented in this thesis. 1.1 Background of the PSBR reactor facility The PSBR is the first licensed university research reactor in the USA. The operating license for this reactor was received in The PSBR is a Mark-III type TRIGA research reactor. The reactor core is movable and is situated in an oval pool above the ground. This is a light water cooled reactor, which operates at a steady state power of 1MW and is capable of an approximately 2000MW thermal pulse [1], [4]. The original reactor at the RSEC was a Material Testing Reactor (MTR), which used plate type fuel suspended and mounted on a grid plate. At this time, the focus of the facility was

20 4 on nuclear theory applications and characterization of half-lives and radioactive emissions from radioactive isotopes. In 1965, a TRIGA reactor replaced it [5]. Though the PSBR was not the first facility to change to TRIGA type reactor fuel, it was the first to convert its fuel from highenriched uranium (HEU) type to low enriched uranium (LEU) type of TRIGA fuel [1]. The original maximum operating power of the MTR was 100kWt. This was changed to 1MWth with the installation of the TRIGA. The RSEC facility has the following functionality. It has two Co-60 gamma-ray irradiation facilities. One is a pool irradiator, which is a vertical dry tube surrounded by Co-60 sources close to the bottom of the pool and the second is a dry irradiation facility. The RSEC has a hot cell laboratory, which can handle curies. There is a neutron beam laboratory, which is the most used facility. Collimated neutron beams which are thermalized by D 2 O (deuterium oxide or heavy water ) moderator. The reactor facility also hosts a radio-chemistry teaching and research facility, a radio-nuclear application facility and a nuclear security education lab to provide student with hands on experience with radiation detection, source technology etc. [1], [5]. Possible changes are expected for the PSBR facility. Changes to improve the usability of the beam port facility are investigated [5]. This includes the change to the D 2 O tank used in mitigating the neutron beam in the beam ports. All this adds to the need for a core design and a computer simulation code that accurately calculates the neutron population in the core. 1.2 The PSBR reactor The PSBR TRIGA reactor core consists of a uniform lattice of fuel elements in a fixed hexagonal shape configuration positioned between two grids plates - see Figure 1-1[1]. The reactor core is open and exposed inside the pool, with no pumps to drive the coolant through the fuel elements. Cooling of the reactor is through natural convection.

21 5 Figure 1-1 PSBR TRIGA Core The core reactivity is controlled with control rods. The control rods utilized in the PSBR are three fuel follower type and one air follower type with B 4 C as the absorber material. Currently, there are two types of TRIGA fuel elements loaded in the reactor. Both are less than 20 percent enriched uranium TRIGA fuel. They are 8.5 wt% (8.5 weight percent of uranium) and 12 wt% (12 weight percent of uranium) of type UZrH 1.6 (Uranium Zirconium hydride) fuel. The long life of these fuels and the short burn cycles allows for completely mixed burn-up of core elements. Each core loading is a reshuffling of burned fuel elements. Keeping registry of the burned elements number densities is important for further use of the fuel elements. For this inventory account, a reliable fuel management tool is needed. 1.3 PSBR fuel inventory, burnup and analysis tool The TRIGSIMS code system, currently used at the PSBR, is a fuel management, analysis and burnup computer program. The current core layout is written into an input file and the TRIGSIMS code system creates various inputs for various other programs. This code system is

22 6 essentially a program that manipulates data needed for input values of three other code systems. These codes are MCNP5, ORIGEN-S, and the nodal diffusion code ADMARC-H. A detailed explanation of these codes will follow in chapter 3. The MCNP and ADMARC-H are used for neutronic analysis, to calculate the needed criticality as well as power and neutron flux distributions used in the burnup of the fuel elements. ORIGEN-S calculates the depletion of the fuel elements. At each step, TRIGSIMS automatically collects and transfer data, write input and output files, and executes these programs, which makes this computer program unique. The result is a burned fuel inventory of each fuel element. Every reactor facility should account for all nuclear materials. This is a method of updating and keeping inventory. The main functions of this tool are fuel management (including burnup) and core analysis. In this work, this function is expanded and the new code system is now a core design and safety analysis tool. The thermal hydraulic code CTF is included in this TRIGSIMS code system. This further developed code system, TRIGSIMS-TH (TRIGSIMS with thermal hydraulics) is an advanced high-fidelity multi-physics tool specifically formulated for PSBR core analysis and design.

23 7 1.4 Objective of this work This work describes the development, validation, and application of the TRIGSIMS-TH code system. TRIGSIMS-TH is a further development of the TRIGSIMS fuel management and analysis code [2]. The TRIGSIMS code system was lacking the very important component of temperature feedback calculations. This is especially a necessity for TRIGA fuel, because of its fuel-to-moderator closeness that has a big effect on the reactivity of the reactor core. For this application, the thermal hydraulic code CTF was used to provide fuel and moderator temperature feedback. TRIGSIMS-TH is now a high-fidelity multi-physics tool. The CTF code is well studied and proved to be applicable for natural convective flow systems [3]. CTF can be used as a safety analysis tool under both steady state and transient calculations. CTF is added in the code system through a multi-physics coupling with MCNP and ADMARC-H. Additionally, CTF can be used as a stand-alone thermal hydraulic analysis tool. A unique methodology to apply control rod position was implemented in TRIGSIMS-TH. The homogenized few-group cross sections used by ADMARC-H were updated with the code SERPENT. Updates on various other functionalities of the TRIGSIMS code were performed such as, reading of data, to make sure that the correct and consistent nuclear data is extracted from the cross section files for both the MCNP and ADMARC-H calculations. The cross section data after all is an essential part of the calculations. TRIGSIMS_TH is an automated code system allowing minimum interference from the user.

24 8 1.5 Synopsis Chapter 2 of this document is a literature review specifically aimed at PSBR related studies. Since this work revolves around the code system of the PSBR, the review will include similar code systems and other related literature that supports this work. Chapter 3 covers the theory (models and methods) involved with this study. The theory includes the reactor core modeling, the code system and the codes used for simulation in this system. The theory will also cover the new developments of the code system. Chapter 4 outlines the various models and methodologies employed in the further development of TRIGSIMS. Chapter 5 presents the results and findings of these PhD studies using the developed TRIGSIMS-TH code system. The Core Loading (CL) designs - CL54 and CL56 - were used for comparison to measured data to evaluate the findings of the PhD developments. Chapter 6 outlines the use and application domains of TRIGSIMS-TH. Four analyses are performed to illustrate the application potential of TRIGSIMS-TH. Chapter 7 summarizes the PhD contributions of the presented work and provides suggestions for future work. Appendix A section gives the needed data and information that assist in the presented work.

25 9 Chapter 2 Literature Review This chapter will present the work and studies related to the PSBR reactor core design and analysis. It will include studies performed for, and code systems used at the PSBR and other TRIGA research reactors as well as the studies, codes, and methods related to this PhD research. 2.1 Current PSBR code system The PhD thesis of Tippayakul [2] describes the development, validation and application of TRIGSIMS code system for the PSBR analysis and core design. It also followed the changes of the reactor core loading pattern and layout over the years. The PSBR has had core changes from having a full core of 8.5 wt% fuel, to a mixed core of 8.5 wt% and 12 wt% fuel elements. The core has had size changes from core loads with 67 fuel elements (CL1) to recent core load of 102 elements and currently to 108 fuel elements (CL56). With future core loadings, we expect a new fuel element, to form part of this already mixed core. We also expect changes with the core layout, such as D 2 O tank changes. Various aspects affect the fuel economy, the cost, and the safety of nuclear reactors in general. It is for these reasons, the careful account of operations and inventory is recorded, and investigated as well as changed if need be. This PhD work herein, directly continue to build on the work done by Tippayakul [2] PSBR-related studies In the recent studies, Ücar [5] performed an analysis on new models and design of the reactor core-moderator-assembly and new beam ports at the facility. This was all part of the

26 10 design to expand the utilization of the PSBR. In order to do this study he had to employ neutronic and thermal hydraulic models of the PSBR. He's study was guided by design limitations and constraints for the new core-moderator assembly with five new beam ports, which he drafted in a3d model.the codes that he used for his analysis were ANSYS FLUENT, a CFD code with ANSYS Gambit mesh generator [5], [6]. He used the TRIGSIMS code system as well as MURE (an MCNP based code). The aim of this study was to maximize the number of beam ports and minimize the hydrogen gamma contamination of the neutron beam in the channeled beam port [5]. The CFD analysis results presented the flow and temperature profiles as well as the average void fraction distribution in the channels. He compared his results with previous analysis from previous studies and measurements. From the MCNP model of the new design D 2 O tank and beam port configuration, he calculated the neutron and gamma flux spectrum at the end of each beam port. He did optimization studies, to calculate the optimum size of the new shape tank and the optimum distance between beam ports and core face. The aim of his work is intended for the future changes and upgrades for the PSBR. In the PhD work of Sahin [7] he used the PSBR facility to perform a dendrochemical study. His work reviewed the environmental effects of tree-ring chemistry that looks at the elemental concentrations of various changes in soil chemistry deposited in the tree -rings. In order to do this study, he performed a detailed coupled neutronic burn-up simulation of the PSBR. The MURE (Monte Carlo Utility for Reactor evaluations) code, which is, and MCNP based code were the main codes used in his study [8], [9]. In his work, he investigated the fission-product buildup effects, and by comparing his model-predictions to the experimental results showed a good agreement. He developed a set of temperature dependent continuous energy cross section using ENDFB-VII data files with NJOY code [10]. He did this in refined temperature intervals of 10K for an extended isotope list. He also applied the Pseudo material approach in his MCNP calculations. All this additions was to make the MCNP calculation more accurate and comparable

27 11 to the measured data. He's results showed the burnup-calculated cores against measured data of core excess reactivity for the years spanning 1965 to He also calculated the control rod worth comparison for these years. After his analysis on control rod worth, indicating the need of adjusting the B 4 C, he did a control rod adjustment to the B 4 C in order to compare the control rod worth measurements to the calculated. Various combinations of the B 4 C absorber material were considered. This was made to the best-fit outcome and he verified his choice of the B 4 C composition with previous core loading patterns. After his success in the calculation to experimental results comparisons, he compared his neutron activation predictions with measurements in the dry irradiation tube. Time dependent analysis of the neutron flux characterization parameters were performed for the PSBR dry irradiation tubes [7], [9]. After verification of neutronic modeling against measured data, he concluded that the MURE libraries and MCNP5 can successfully be applied to predict the neutronic behavior of the PSBR core following the daily operational schedule. The applications of PSBR facility are many and various. In most cases, the reactor core, which is a neutron source, is being used for these applications. In order to perform any research related to PSBR, one needs to have a well-defined reactor core modeling and calculation tool Calculation tools Though the TRIGSIMS is a multi-code system, the main code for execution of criticality calculation is MCNP5. TRIGSIMS, which is described in the thesis of Tippayakkul [2], is a platform where all these codes share information. The TRIGSIMS code system is outlined in the following diagram [2]

28 12 TRIGSIMS Read XS - Continuous energy - diffusion ADMARC-H MCNP Stores data -power/node -isotopic mass -keff Prepares input - ADMARC-H - MCNP MCNP SCALE ORIGEN-S SCALE ORIGEN-S MCNP MCNP Figure 2-1 Current TRIGSIMS layout Figure 2-1 shows the current TRIGSIMS layout: A) TRIGSIMS is the driver of this coupled code system; B) Coupling between neutronics codes MCNP and ADMARC-H (diffusion); C) Coupling with SCALE (ORGENS for depletion) [11] ; D) Nuclear data preparation used by these codes. With the previous upgrade of TRIGSIMS, MCNP5 has become the main core solver [2]. MCNP5 [12] is a general-purpose transport code with no depletion capabilities. For this reason ORIGEN-S [11], that forms part of the SCALE code system, was coupled with MCNP5 to perform the depletion calculations.

29 13 Like MCNP, the ORIGENS input is automatically generated by the interfacing program TRIGSIMS. The contribution [2] of this MCNP/ORIGEN-S coupled methodology is the following: 1) The generation of one-group cross-section burn-up libraries, specifically made for the PSBR fuel cells (8.5 wt%, 12 wt%, and fuel follower control rods), were created with TRITON, a SCALE module. TRITON [13] is a two-dimensional (2D) transport and depletion module for characterization of spent nuclear fuel. 2) Implementing the on-line three-dimensional (3D) burn-up cross-section generation. A set of selected important isotopes was identified, and using the pin-by-pin fluxes and power from MCNP calculation, to calculate the one-group cross-sections for these isotopes. 3) Implementation of the predictor-corrector approach to better predict fuel depletion and number densities. 4) Xenon poison effect modeling, whereby an adjustment is made before the start of each MCNP calculations. This adjustment is to insure that we correct the Xenon number densities to account for the partial day of operation. 5) Axial depletion model was also one of the innovative changes implemented in the TRIGSIMS code. The fuel elements are now divided into several axial nodes, where node-wise calculations for ORIGEN-S, MCNP5, and ADMACR-H are performed. The work performed for the coupled MCNP5/ORIGEN-S depletion model has been a great success. Sensitivity studies to test and validate the code have been conducted for the use with TRIGA reactors. MCNP calculations with its 3D geometry capabilities, uses continuous energy crosssections. These cross sections are available in temperature intervals of 300K, 600K, 900K and 1200K in the MCNP5 data file [2], [7]. All intermediate temperatures are interpolated from a

30 14 refined grid of these sets. The development of such refined grid is an important contribution of Tippayakul [2]. This was accomplished by the addition to the MCNP_DATA, xsdir.file, of a set of continuous cross sections for a list of important isotopes on a grid with a ΔT of 50K from 300K to 900K intervals. The cross section set was generated using the NJOY code [10]. As part of a speedup scheme for MCNP5 criticality calculations, a nodal diffusion code ADMARC-H [14] was coupled to MCNP. The primary idea with this coupling is to pre-generate the initial source distribution used in the MCNP5 code. With this, MCNP will be obtaining a converged fission source distribution with minimum number of inactive cycles (which are not used in the final determination of the k eff results). With this algorithm, the code will reduce its computational time for the MCNP calculation. Tippayakul has done various feasibility studies on optimization of the skipped cycles in order to accelerate the MCNP calculations [2]. The ADMARC-H code, which is a two group, 3D nodal diffusion theory code for hexagonal geometry, previously was studied in. For its use in the PSBR, a set of homogenized cross sections were prepared with the HELIOS-1.6, a 2D transport and depletion lattice physics code [14], [15]. These cross sections are temperature dependent on a grid with ΔT of 100K, burn up dependent between 0 to MWd, and fuel type dependent for 8.5 wt%, 12 wt% and fuel follower control rods. The ADMARC-H code provides the K eff, flux and power distribution in both axial and radial directions. Similar to MCNP and ORIGEN-S, TRIGSIMS manages the input and output of the ADMARC-H code. It formulates the output into a form that is used for MCNP, and with its robust method, should ADMARC-H not execute, TRIGSIMS will assume the axial cosine shape for the initial source distribution for the fuel elements needed in MCNP calculations. Thereafter the calculation will continue without ADMARC-H execution [2].

31 Codes used for PSBR analysis The PSBR is in an open pool facility. There are no pumps to force the flow through the core. It relies completely on natural convection for cooling. The thermal hydraulics of natural convective coolant flows is a challenge for computational simulations. In recent years, number of thermal-hydraulic studies was carried out. Ücar, was able to model the thermal-hydraulics of the PSBR reactor core with the Computational Fluid Dynamics (CFD) code Fluent [5],[6]. Chang [16] performed previous studies with similar codes, for thermal-hydraulics modeling, in His focus was mainly on the flow and fluid temperature predictions in and around the PSBR core. His research included development of CFD models of the PSBR core and pool as well as calculations of the pool temperature and velocity field predictions. Sub-channel code applications to study the PSBR core thermal-hydraulics were also performed and are described in the following references [3], [17]. Various experiments [17] in PSBR were performed and utilized for benchmarking neutronics and thermal-hydraulics modeling of steady state and transient conditions. Benchmark information was collected for coupled neutronic and thermal-hydraulic models and was utilized for the reactor safety analysis. The intended outcome was to formulate benchmark problems for validation of coupled neutronic and thermal-hydraulic codes. Available experimental data can be used to validate the coupled thermal-hydraulic and neutronics models for PSBR. This was demonstrated in the validation of 3D kinetics code STAR coupled with COBRA-IIIC code and using WIMS-D4 to generated cross sections. In 1997, Gougar [18] has performed various studies on the TRIGA thermal-hydraulics. His experimental investigation of the coolant flow in the TRIGA demonstrated complex coolant flow characteristics of the PSBR. In the work subsequent to this, these flow characteristics for the

32 16 thermal-hydraulic model formed a basis for validation of the coolant flow through the core. Studies using COBRA-TF (CTF) [3], [6] indicated that CTF is capable of modeling PSBR thermal-hydraulics and coolant flow characteristics. 2.3 Review of related codes Multi-physics coupling of codes seems to be an increasing trend in reactor design. Currently the traditional multi-physics coupling is well established add validated while the novel high-fidelity multi-physics coupling is being developed and verified. Here we will review recent developments related to both types of multi-physics coupling since those are involved in this PhD research Review of coupled codes The work referenced in [19], [20] was aimed at increasing the accuracy of spatial resolution of core design studies for coupled neutronics (MCNP) and 3D thermal-hydraulic subchannel codes for the analysis of PWR s. Various valuable contributions were made to the MCNP/SUBCHANFLOW coupling scheme. The authors have adopted radial mapping of thermal-hydraulic and neutronic domains. Passing of information was done with script files. For the axial mapping between these codes, the number of cells was kept the same, for radial mapping an average over the cell with a defined formula were used. The variation of node average fuel temperature is used for checking convergence with a certain convergence criteria. For the Doppler broadening of nuclear cross sections, they have implemented the pseudo material mixing approach methodology. Other studies [7],[9] have shown that this approach increases the

33 17 accuracy of the calculations. This pseudo material approach was also extended to the thermal scattering data. Comparisons were shown to demonstrate the effectiveness of this application. In the PhD-work of Espel [21], a coupled system MCNP/CTF was developed along with acceleration methods for the coupled calculations. The coupling of MCNP5/CTF/NEM/NJOY was applied to a simplified 3D 2x2 fuel pin array. The Nodal Expansion Method (NEM) diffusion code is based on a 3D steady state and transient nodal model. Coolant Boiling in Rod Arrays-Two Fluid, COBRA-TF (or simply CTF), is a thermal-hydraulic sub-channel code. NJOY99, which is a nuclear data processing system, converts evaluated nuclear data in the ENDF (Evaluated nuclear data file) [22] format into cross section libraries for different application, including continuous energy Monte Carlo (MCNP). Espel has developed an automated procedure to generate continuous energy temperature dependent cross sections for MCNP calculations. He used interpolation methods for the pre-generated cross section grid. With the application of MCNP-Threads, he was able to parallelize and speed-up the calculations. Reference [23] presents a VVER benchmark analysis using two coupled code systems, DYN3D/RELAP and DYN3D/ATHLET. The authors consider three ways of coupling: 1) An internal coupling, where the thermal-hydraulics of core and system is simulated by the system code and the neutronics calculations are performed by DYN3D; 2) An external coupling, where both neutron kinetics and thermal-hydraulics of the core are simulated with 3D neutronics code (DYN3D) and thermal-hydraulics of the system is calculated by the system code; 3) A parallel coupling option, where core thermal hydraulics and neutronics are run in parallel and the system code provides boundary conditions. DYN3D calculates thermal hydraulics and updates core power. DYN3D (which is similar code to ADMARC-H) has been used in a coupling schemes with thermal hydraulic codes. The paper presents possible ways of coupling DYN3D with these thermal hydraulic codes. Our

34 18 methodology would be the same as the external coupling explained in this work. Their results showed small difference while comparing the two coupling schemes Thermal hydraulic modeling The TRIGSIMS-TH code system utilizes the thermal hydraulic sub-channel code CTF. This code has seen various upgrades and developments. CTF is now an advanced and modernized sub-channel thermal-hydraulics code. The following review describes the studies performed over last years to upgrade this code. Avramova has had various contributions to the CTF code. As part of her Master's thesis [24] she worked on qualification of CTF and its application to LWR analysis. In her PhD thesis [25] a development of a spacer grid model utilizing computational fluid dynamics within a subchannel analysis tool is introduced. Blyth [26] continued this work by using CFD data to improve grid-detected lateral cross flow effects, turbulent mixing and heat transfer enhancement in CTF. Salko [27] as part of the CASL (Consortium of advanced simulation of Light water reactors) project, worked on the development of CTF modeling of full reactor core and its application to cycle depletion. He included new features in the code that address the PWR challenge problem of departure of nucleate boiling and CRUD (deposits) that induces power shift. Parallelization of the software was done to be able to assist in these calculations. The CTF used in this PhD study includes the improvements described in the abovementioned references.

35 General review In addition to multi-physics coupling methodologies developed in this study there are also various other improvements introduced to TRIGSIMS as part of this PhD research. Reviews to illustrate the need for these improvements follow Reviews on critical rod height In [28] it was determined the critical rod height in a benchmark calculation of 3MW TRIGA Mark II. With MCNP4C model, the authors adjusted the control rod bank until it reached k eff of ~1, which took several iterations. The obtained results showed a good agreement with the measured data. The reference [29] is a report that shows a comparison between TRIGAP, a onedimensional, two-group diffusion computer code, and one group perturbation theory to calculate the reactivity worth of the I.T.U. TRIGA reactor. The results were compared with measured data. Their results show that perturbation calculation performed better than the diffusion code. Some studies using neural network methods were done for control rod positioning in PWR. What this entails is the study of computation and measurements of axial flux profiles for various axial positions of the control rods. This study involved calculations for different scenarios and pattern recognition for a given control rod position [30] Nuclear Data There are numerous studies on cross section generation. The accuracy of neutronics methods is largely dependent on the nuclear data that is used this calculation. References [2], [7] discussed cross section generation. In particular, for TRIGA reactors the thermal scattering needs

36 20 to be accounted for in the neutronic calculations. The NJOY tool is used for the cross section processing. The thermal scattering cross sections for hydrogen bound in water and hydrogen bound in zirconium hydride is well-investigated [2] because of their effect on the calculations accuracy. Kraingchaiporn [15] based her thesis on a 3D transport model utilizing 3D multi-group lattice cross-section generation for the PSBR. She used 3D TORT [14], [31] code and produced TRIGA cross sections generated in 2D and 3D geometries, based on CPXSD (Contribution and Point wise Cross section driven) methodology Control rod absorber material Of significance in this work was the investigation of the B 4 C used in the absorber material of the control rod elements. Previous studies [2], [7] has argued over the B 4 C density and weight used in the MCNP model of TRIGSIMS. The Table 2-1 outlines the results of previous work. The control rods reference are the three fuel follower rods, i.e., the safety rod (SA), the regulating rod (RR) and the shim rod (SH) and one air follower transient rod (TR). Table 2-1 B 4 C components as used previously B10(wt%) B11(wt%) C(wt%) Density (g/cm3) CR Reference 1a SA,RR,SH [2] 1b TR 2a SA,RR,SH [7] 2b TR

37 21 The cases in Table 2-1 are trial-and-error estimates formulated and optimized for the code used for those calculations. Analysis is performed in this PhD work on identifying an appropriate estimate of B 4 C.

38 22 Chapter 3 Theoretical models and numerical methods The theoretical models for the work herein cover different single physics phenomena including neutronics (reactor physics) and thermal hydraulics as well as the multi-physics coupling. The methods involved include statistical (Monte Carlo) and deterministic numerical methods. This section provides a short overview of the PSBR core, which design and analysis is the application in interest. The developed in this research TRIGSIMS-TH code system is summarized through a comparison to the previously developed TRIGSIMS code system. 3.1 Introduction A nuclear reactor is a device in which the nuclear fission reaction can be controlled for the purpose of power production as in the case of power reactors or as a neutron source as in the case of research reactors. The safe operation of any reactor relies on ensuring the integrity of the reactor fuel and on preventing the release of potentially harmless radioactive materials, which are produced during the fission process. The two main characteristics, which are taken into account in reactor design, are neutron distribution and heat removal process. The neutron distribution in a reactor determines the nuclear fission power distribution among the fuel elements. In this process, nuclear fission heat is generated in the fuel. The heat energy in the fuel however needs to be transported away from the fuel, to ensure that the fuel does not overheat and compromise its physical integrity. The two main physical phenomena in nuclear reactor design involve neutron transport and heat conduction. The determination of the neutron population and hence the power production in a nuclear reactor is referred to as neutronics, while the simulation of the thermal

39 23 processes in the reactor is known as thermal hydraulics. Both of these areas of simulation are quite complex and in reality they are coupled resulting in a multi-physics problem. There are numerous neutronics and thermal hydraulic codes. Deterministic and Monte Carlo methods are the most common methods to use for neutronic analysis of the reactor core. For thermal hydraulics modeling, there are generally two types of models. The system models cover the primary cooling system of a reactor while the sub-channel models are used for the reactor core. The remainder of this chapter describes the parameters, which are important for reactor core design [32]. More details are provided for the neutronics and thermal hydraulic codes that are used in this work. Figure 3-1 summarizes the most important analyses and parameters related to nuclear reactor core design. 3.2 Nuclear Reactor Core Design Nuclear reactor core design Core analysis Reactor safety analysis Regulatory consideration Reactor physics Numerical analysis Computational methods Core criticality Power Reactivity control Fuel loading Core arrangement Depletion of fuel Figure 3-1 Basic analyses and parameters for nuclear reactor core design

40 Terminology A nuclear reactor is a device to initiate, control and sustain a nuclear fission chain reaction. In order to undergo fission it requires nuclear material of which are fissile and fissionable. Fissile material, such as uranium-235 ( 235 U), is able to sustain a nuclear chain event. Fissionable material such as uranium-238 ( 238 U) is capable of capturing a high-energy neutron and undergoing fission. In many cases such as for the PSBR, to initiate a chain event the reactor requires an external source. A) Neutron Flux Neutron flux is a measure of the total neutron population and has units of, number of neutrons per square cm, per second, i.e., it gives the total number of neutrons traveling in all directions, per unit area, per unit time. This measurable quantity is related to the reactor power by the following equation for thermal reactors: 3.1 where, P is the reactor power (watts), is the thermal neutron flux(neutrons/cm 2 -sec) is the macroscopic fission cross section (cm -1 ) is the volume of the core (cm 3 )

41 25 B) Criticality Criticality is a measure of the balance (gains and losses) of neutrons in the reactor core. The fission process is a chain reaction whereby the neutrons interact with uranium atoms in the fuel. When the reactor reaches its critical condition, we have balance for neutron being produced and lost in the system. In this case the reactor is critical (k eff =1). If the neutron population is increased and the chain reaction produces more neutrons than what are lost, we refer to this as a super critical reactor (k eff >1). When the reactor has less neutrons being produced than are lost, the reactor is subcritical (k eff <1). C) Reactivity After the reactor has reached a critical state, the effective multiplication factor,k eff =1, and if the neutrons are increased, by means of control rod withdrawal as in the case of the PSBR, this departure from criticality is called reactivity insertion. The expression is given as. D) Burnup Burnup is a measure of fuel depletion given in thermal energy, mega-watt days per unit mass, of the initial value of the heavy metal content, metric ton unit, (MWD/MTU). In uraniumfueled reactors, the reactivity changes with burn up are due to: a) 235 U depletion; b) 239 Pu buildup; c) Buildup of other non-fissile isotopes; d) Buildup of thermal neutron absorbing fission products and other fission products. E) Doppler temperature feedback. With increase in power by a control rod withdrawal, the fuel temperature increases. With this the resonance energy peaks of the 238 U broaden, which allows more absorptions of fission neutrons before reaching thermal energies. Hence, the reactivity decreases. This effect is called Doppler broadening. This is a negative effect on reactivity.

42 26 F) Excess reactivity When the control rods are fully extracted from the core, the reactivity increases to, which is the core excess reactivity. The β eff is the effective delayed neutron fraction approximately equal to for the PSBR. The fission neutrons that are born as a direct result of the fission reaction are called prompt neutrons while the neutrons that are released during the decay of fission products are called delayed neutrons. G) Critical rod position This term is used when the control rods are in a position where the neutron chain reaction is sustained (k eff =1). This could be at low power or at 1MW power for the PSBR Core design process The reason for searching an optimal reactor core design is to ensure efficiency with safety in operation. To be able to shut down the reactor safely is a main concern for all nuclear facilities. The fundamental quantities that are evaluated in the nuclear core design calculations are the effective multiplication factor (k eff ) and the neutron flux distribution (Φ). These fundamental quantities are the basis for the fuel management and reactivity control. To find a solution to these quantities requires a solution to the neutron transport equation Main parameters for core design Figure 3-1 shows some of the basic parameters for the PSBR reactor core design addressed in this thesis. A) Nuclear core analysis

43 27 The first requirement is a reactor core model. This is a layout of physical design of the reactor core. It consists of fuel elements, control rods and all other parts that constitute a reactor core including the surrounding water. For this model, all the characteristics of the elements should be known. This includes material properties of the fuel, neutron control elements, water, neutron reflectors or neutron moderators and structures as well as the geometrical layout of these components. B) The nuclear data or cross-sections This is the measured (evaluated) probabilities of various physical interactions involving nuclei of atoms. The quality and application of this data are important. As an example, the PSBR TRIGA operates with a maximum fuel temperature between 400 C (673K) and 540 C(813K) for full power. The data libraries (ENDF7) are generally in sets of 300K, 600K, 900K, and 1200K etc.[22]. Hence, application using only these libraries would result in a less favorable result. C) Numerical and calculation methodologies For most parameters, the physics models exist. The application of the physics modeling is done with numerical approximations. For example, finding a solution to place a control rod in a certain position to give a critical reactor requires both a numerical formulation and a calculation tool to apply this application. D) Tools The computational tools (codes) assist in quantifying the physics by applying numerical formulas. In the case of TRIGSIM-TH, the tools applied in this core design methodology, uses Monte Carlo, which is a statistical approach to solve the neutron transport, i.e., which solves the neutron flux. E) Safety analysis and regulatory requirements Safety of all nuclear facilities is a regulatory mission. This means that the safe operation and use of the facility are regulated and guided. The reason for this is ensure the safety of the

44 28 public. The guides are usually written in the safety analysis report, whereby the reactor facility conforms in operation. Hence, the core design has specific outcomes and guides that need to be attained. An example of one such regulation is the maximum allowed temperature of the TRIGA fuel is not to exceed 1150 C. A safety analysis is performed for a reactor design to ensure that the operation under steady state and transient conditions is safe and conforms to the guidelines [33] Intent and deliverables The aim of this work is to further develop and improve the TRIGSIMS code system to be used as a modern core design and analysis tool. The final goal of this research is to develop a coupled code system that can simulate reactor steady state and transient conditions with reliable accuracy as compared to measured results within the measured uncertainties. The envisioned outcome is a high-fidelity advanced code system that can be used as a safety, analysis and core design tool for PSBR.

45 Computational analysis tools Neutron transport methods and codes There exist two types of computational methods to solve or model the neutron distribution and motion, in the reactor core. Deterministic methods to solve the linear Boltzmann transport equation in a numerical approximation, and stochastic methods, which used a statistical (probabilistic) approach to solving the neutron transport in the core. The ultimate goal in nuclear reactor studies is to determine the density or distribution of neutrons in a volume, moving with certain energy The neutron flux is the quantity that is solved with the neutron transport methods. This quantity is proportional to all the gains and losses of neutrons in a system, which is due to absorption, fission and scattering. 3.2 This is a linear equation for the unknown variable with seven independent variables. In general, this equation is complex, and the existing deterministic codes usually aim to solve or treat the variables in the equation in a certain way. The series expansion method to solving the angular variable, use spherical harmonics. Discrete ordinates methods are an example of the direct numerical solution techniques of the transport equation. Each variable in this transport equation is discretized by changing the

46 30 continuous variable into a set of discrete points. Differential equations are solved using finite difference or discrete ordinates methods and integrals are represented as sums or numerical quadrature formulas. This treatment of variables can be done with various mathematical tools. An example would be the discretizing angular dependences using S n equations or P n equations of which the widely used one-dimensional P 1, Legendre Polynomial is known. The neutron diffusion approximation is a result of a simplification of the neutron transport equation. The formulation of Fick's law, which implies that the neutrons will diffuse in the direction from high to low-density (flux) regions, is given below: 3.3 where is equal to the net number of neutrons that pass per unit time through a unit area perpendicular to the x-direction [35]. The parameter D is the diffusion coefficient. The code ADMARC-H, used in the TRIGSIMS-TH code system, is a diffusionapproximation based code. For this code, the two group diffusion equations are solved, in form given below:, In these equations, the leakage and removal terms are arranged on the left and the source terms on the right. Deterministic computational methods usually give systematic errors, which arise from discretization of time, space, angle and energy phase space of numerical computation, as well as limitations on computation that limits deterministic high-fidelity modeling of three-dimensional

47 31 configurations. Issues such as memory, time, and accuracy are factors in play with modeling and simulation of multi-dimensional problems. The stochastic methods or Monte Carlo calculations use a relatively straightforward approach to complex three-dimensional configurations. The TRIGSIMS code is a MCNP5[41] based and therefore intensive analysis using this method is required in this research. In this work, SERPENT [36], a Monte Carlo code is used for generation of the few-group homogenized cross sections and diffusion coefficients (constants) utilized in the ADMARC-H code. Similar to MCNP, SERPENT has the same basic geometrical structure as an input. It uses universes, cells and surfaces. In addition to that, it has a varied number of surface types with fixed parameter. In particular, for use of the PSBR studies, it contains hexagonal cylinder shape surfaces, with lattices, which are special universes, filled with these surface shapes. This capability makes the code appropriate since the PSBR whole core is shaped in a hexagonal lattice. SERPENT uses set commands to change the outcome of various quantities such as source rate normalization, flux normalization, heating power, power density amongst other. The group constant generation function lets the user decide on the universes to calculate the homogenized group constants. SERPENT can calculate pin power wise distribution in full core calculations Thermal hydraulic methods and codes Similar to the neutronics codes, thermal hydraulics codes can also be divided into two basic classifications. Codes that model the entire system, or plant balance, are called system codes; and codes that focus on various components, such as the reactor core, are called subchannel codes. System codes, such as the well-known RELAP code series, calculate the thermal hydraulic characteristics of the primary loop under both steady and transient operational

48 32 conditions. Sub-channel codes, such as the COBRA code series, have a focus more on the reactor core, and some of these codes may be used for both transient and steady state conditions. Through time, both, these code series have evolved. They incorporate various models and methods of analysis as the need, information and experience have increased. An increased requirement to address hypothetical accident scenarios has influenced the need for more advanced methods and models. The existence of other codes such as WOSUB, THERMIT that are component codes, RETRAN, and TRAC, which are system codes is acknowledged as well [40]. Thermal hydraulic codes solve mass, momentum, and energy conservation equations numerically. CTF general momentum conservation equation for phase k is given as [26], [27]: 3.6 Left Hand Side (LHS) denotes the change of volume momentum over time and three directional advection of momentum terms. Right Hand Side (RHS) denotes the gravitational force, pressure force, viscous shear stress force with wall drag and form losses, a source term due to phase change and entrainment /de-entrainment, interfacial drag source and the momentum source due to turbulence mixing and void drift. The phasic energy conservation equation: 3.7 LHS denotes the change in energy and the advection of energy.

49 33 RHS denotes inter-cell energy exchange due to void drift model and turbulence model, the energy transfer due to phase change, the volumetric wall heat transfer and the fluid cell due to pressure. The general phasic mass conservation equation: 3.8 LHS term denotes change in mass and advection of mass. RHS term denotes mass transfer in and out of phase change k (e.g. evaporation and condensation) and mass transfer due to turbulent mixing and void drift. A more detailed discussion of these equations and their numerical solution methods can be found in the CTF manual [27]. The type of code to use will strongly depend on the area to be analyzed and the capability of the code. For example if the need were to address accident scenario, where we have pump failure and loss of coolant in the reactor core, we would probably use one of the RELAP codes for this analysis. In the case of the PSBR TRIGA reactor, where the reactor is in pool and natural coolant flow circulation governs the system, the need is for a full core sub-channel analysis, which the CTF code is capable of modeling [3]. 3.4 PSBR description PSBR core The PSBR reactor core, is situated at a depth of approximately 18 feet in a reactor pool which contains liters of demineralized water [5]. This filtered water provides the

50 necessary shielding, reflection and cooling for the reactor. A typical core configuration is given in the Figure 3-2. This layout is particular to CL Figure 3-2 Core loading configuration A usual loading pattern would be to load the more reactive fuel elements in the centre of the core. In general, the reactor has a power profile that peaks around the thimble due to the moderating effect of the water hole. The fresher fuel elements and the 12 wt% fuel are located two or three rings out from the central thimble. The four control rods are indicated in green. They include the Safety rod (SA), which usually has a worth exceeding that of the other rods for the reason that it is closer to the center of the core than the identical Shim and Regulating rods. There is also the Shim rod (SH), to make course adjustments in the neutron density; the Regulating rod (RR), for finer adjustment and power regulation and a special air follower rod; and the Transient rod (TR), which is used for square wave and pulse mode operation [5], [45]. Two dry tube irradiation positions are indicated in pink. On certain core ladings, graphite elements are added to

51 35 the core to increase reactivity. These are placed on the outer ring of the reactor to reflect neutrons back toward the fuel. The graphite elements are used if there is a need to increase the flux in the core. The reactor can be loaded with up to approximately 120 elements. Figure 3-2 shows the CL56 with 105 fuel elements and 3 fuel-follower control rods. These elements, fuel and non-fuel, have fixed positions within the core, based on the grid plates, with a pitch (distance between centers of the elements), of cm (1.71in), which is the size used for the core design layout of the calculations TRIGA fuel TRIGA reactors are inherently designed to be safe. This is because of the moderating properties of the zirconium hydride fuel (ZrH 1.6 U) [52]. In short, the uranium is in close contact with the hydrogen, which results in a self-moderating fuel. Figure 3-3 illustrates the TRIGA fuel and its dimentions.

52 36 Figure 3-3 A typical TRIGA fuel element The basic parameter, which allows TRIGA reactors to operate safely during either steady state or transient conditions is the prompt negative temperature feedback coefficient associated with TRIGA fuel and core design. TRIGA reactors are designed in such a way that an increase in temperature of the fuel element will result in a relatively large decrease in reactivity. This effect is constant. This negative temperature coefficient for TRIGA fuel[48] is because of the following: a) Cell and heterogeneous effect: This accounts for 65% of the negative temperature coefficient. With the rise in temperature of the fuel, the hydrogen in the fuel acts like free hydrogen. Neutrons can transfer energy back and forth with the hydrogen. This increases the probability that a thermal neutron in the fuel element will gain energy from an exited state of an oscillating hydrogen atom (0.14eV quanta).

53 37 As the neutron gains energy from ZrH lattice, the thermal neutron spectrum in the fuel shifts to a higher energy (to the right). The fission cross section for 235 U decreases with increasing energy (temperature), so the probability of fission is lower with these higher energy (temperature) neutrons. This is known as spectrum hardening. This effect also increases the mean free path of the neutron. Hence, the probability for a neutron to escape the fuel is higher with increase in temperature. In the water a re-thermalization of these neutrons can occur. As a result, there is a temperature dependent disadvantage factor for the core unit cell, in which the ratio of the absorption in fuel to cell absorption is increased as the fuel temperature decreases. This brings a shift in core neutron balance giving loss of reactivity [4]; b) Doppler broadening effects: This effect contributes approximately 15% to the negative temperature coefficient. The uranium in the fuel elements is approximately 20% 235 U and 80% 238 U. The capture resonances in the 238 U are Doppler-broadened by an increase in fuel temperature, which in turn causes a decrease in the resonance escape probability (p) [4]; c) Core leakage effect: This contributes the rest of the 20% of the negative temperature coefficient. As mentioned in the cell effect about moderated fuel causing the hardening of the spectrum, as the core heats up, the leakage is increased and relatively more captures occur outside of the fuel [4] Application of the PSBR The PSBR is foremost a research reactor. However, other industries (such as business, government, universities etc.) also use the facility for various irradiation and research. It is part of the Radiation Science and Engineering Centre (RSEC) at the PSU campus. The RSEC facility also hosts gamma irradiation facilities, hot cells, the radio-nuclear application laboratory, the

54 38 neutron beam laboratory and other. The reactor facility houses seven-beam ports, but only one is in use at a time. This is one of the shortcomings that are being investigated [5]. Ücar's thesis evaluated a new core moderator facility to enhance the amount of neutrons to the beam ports # 4 and 7. For these studies and facilities, the PSBR provides the neutron source. The calculation of the core, or neutron source, should be accurate. The TRIGSIMS-TH code system is used for this purpose. 3.5 TRIGSIMS and TRIGSIMS-TH Capabilities of TRIGSIMS and TRIGSIMS-TH The following table shows the difference and similarities between the TRIGSIMS [42] and TRIGSISM-TH code systems as well as outlining the capabilities of each. Table 3-1 Comparison of old and new TRIGSIMS TRIGSIMS Automated to read CL-input and create input decks for the following: - MCNP neutronic analysis - ADMARC-H neutronic analysis - ORIGEN-S burnup - No thermal-hydraulic feedback - Predictor-corrector depletion method TRIGSIMS-TH Automated to read CL-input and temperature distribution file and create input decks for the following: - CTF for coupling with MCNP and ADMARC-H - MCNP neutronic analysis with feedback - ADMARC-H neutronic analysis with feedback - ORIGEN-S burnup - CTF full core thermal hydraulics - Predictor-corrector depletion method

55 39 No control method for rod position for a critical reactor power, usually at 38.1cm, or Control rod placement method for a critical reactor at any power level. otherwise it is set in rod position. No core expansion is possible with ADMARC-H However, MCNP is capable of loading any size core No option for graphite elements TRIGSIMS/MCNP could always take on a new fuel as long as the geometry are the Core expansion possible in: MCNP CTF ADMARC-H Graphite elements are now an option in the input TRIGSIMS-TH/MCNP's capabilities are the same as before same TRIGSIMS-TH is a coupling software connecting various codes with information from other codes. The main core design code is MCNP5 [41]. MCNP5 is coupled to CTF, the subchannel analysis code, to provide the thermal hydraulic feedback. The ADMARC-H code is also coupled to CTF. This coupling is intended to accelerate the calculation. The ADMARC-H/CTF coupling is an optional setting on the TRIGSIMS-TH platform. The burn-up code ORIGEN-S (from the SCALE code system) together with its predictor-corrector method is also included in the TRIGSIMS-TH Codes in TRIGSIMS-TH The following theory covers the various functional codes that make up the TRIGSIMS- TH code system.

56 MCNP MCNP is a Monte Carlo code that is based on a statistical sampling process for selection of random numbers, comparable to throwing dice in a gambling casino, hence the name Monte Carlo. In particle transport, the Monte Carlo technique is pre-eminently realistic (a numerical experiment). It consists of essentially following each of many particles from a source throughout its life to its death in some terminal category (absorption, escape, etc.). Probability distributions are randomly sampled using transport data to determine the outcome at each step of its life. A neutron incident on a fissionable material can have a number of outcomes. Each step is recorded (tallied). The possible events that can happen to a neutron are: it can scatter, produce neutrons, fission thereby producing more neutrons, neutrons can be captured, it can leak out of the material, and photons can scatter, leak or be absorbed. This describes one neutron history. So if more and more neutron and photon histories are followed, their distributions will be better known. The quantities of interest are tallied, along with estimates of the statistical precision (or uncertainty) of the results [12]. The MCNP code package is incomplete without the associated nuclear data tables. MCNP uses continuous energy nuclear data libraries. Nuclear data tables exist for neutron interactions, neutron-induced photons, photon interactions, and thermal particle scattering S (α, β). The geometry of MCNP treats an arbitrary 3-dimensional configuration of user-defined materials in geometric cells. MCNP treats geometric cells in a Cartesian coordinate system. We use MCNP to calculate the nuclear criticality, which is the ability to sustain a chain reaction by fission neutrons. This quantity is characterized by k eff, the eigenvalue of the neutron transport equation. In reactor theory, k eff is thought of as the ratio between the numbers of neutrons in successive generations, with the fission process regarded as the birth event that separates generations of neutrons. For critical systems, k eff = 1 and the chain reaction will just

57 41 sustain itself. For subcritical systems, k eff < 1 and the chain reaction will not sustain itself. For supercritical systems, k eff > 1 and the number of fissions in the chain reaction will increase with time. Calculating k eff consists of estimating the mean number of fission neutrons produced in one generation per fission neutron started. A generation is the life of a neutron from birth in fission to death by escape, parasitic capture, or absorption leading to fission. In MCNP, the computational equivalent of a fission generation is a k eff cycle; that is, a cycle is a computed estimate of an actual fission generation. The TRIGSIMS [38] code uses only the track length estimate of cell flux (F4), and the track length estimate for fission energy deposition (F7) tallies. The average particle flux in a cell can be written as: 3.9 Where is the density of particles regardless of their trajectories, at a point defining to be the differential unit of track length and noting that gives: 3.10 where may be thought of as a track length density; thus, the average flux can be estimated by summing track lengths. MCNP has various means of accessing the statistical precision, variance reduction and error estimation of the results for the k eff and flux produced by a calculation. What was found however is that a calculation that converges in all ways does not necessary guarantee high

58 accuracy. Therefore, careful checking of the input and output data is required to make sure what is intended is calculated, with all the needed information CTF COBRA-TF (COolant Boiling in Rod Arrays Two Fluid), a computer code, was developed at the Pacific Northwest National Laboratory. The modified version of COBRA-TF (CTF) used in this work was developed at the Reactor Dynamics and Fuel Modeling Group (RDFMG) [27]. CTF is an advanced sub-channel code for best-estimate thermal-hydraulic analysis of Light Water Reactors (LWRs). It features three fields representation of two-phase flow. It uses a set of nine time-averaged conservation equations written in a semi-implicit form using donor cell differencing for the convective quantities. It is developed for use with either rectangular Cartesian (Figure 3-4) or sub-channel coordinate systems. Figure 3-4 CTF Cartesian coordinate system It can treat both hot wall and normal flow regimes. This allows a three-dimensional treatment of geometries amenable to the description of the Cartesian coordinate system.

59 43 In CTF, the computational momentum cell structure can be illustrated in the figures below. Figure 3-5 Scalar Mesh cell, axial Figure 3-6 Scalar mesh, transverse CTF momentum equations, 3.6, are solved using a staggered difference scheme in which the velocities are obtained at the mesh cell faces and the state variables such as the pressure, density, enthalpy and void fraction are obtained at the cell center. The mesh is characterized by its cross-sectional area, A, its height, Δx, and the width S, of the connection with adjacent mesh cells. This illustration is shown in the Figure 3-5 and Figure 3-6 [24], [27]. CTF can calculate reverse flow, natural circulation, and cross-flow situations. CTF is equipped with sub-cooled boiling wall heat transfer logic, capable of simulating TRIGA conditions i.e., low flow, low pressure, low power and low temperature. CTF automatically makes the transition to single-phase forced convection at low wall superheat and to pool boiling at low flow rate. CTF s wall interfacial friction model is suited for TRIGA properties. CTF s conduction model specifies the conductor geometry and material properties, and solves the conduction equation. The rod model is designed for nuclear fuel rod, heater rods, tubes, and walls. The model

60 44 consists of options for one-dimensional (radial), two-dimensional (radial and axial), and threedimensional heat conduction [27]. CTF gap conductance model dynamically evaluates fuel pellet-clad conductance for a nuclear fuel rod. The model computes changes in the fuel rod structures and fill gas pressure that affect the gap conductance and fuel temperature during a transient. For this CTF model however, the nuclear fuel rod model was not used because of TRIGA fuel being a zirconium hydride fuel is different from the standard LWR fuel. The hrod (for a solid cylinder) geometry option was used, which allowed for the specification of the various material makeup of this fuel [3] ADMARC-H ADMARC-H [2], [14] is a two group, 3D, nodal diffusion code for hexagonal geometry. ADMARC-H code utilizes a set of tabulated pre-generated cross sections for the 3D core calculations. ADMARC-H code calculates the core flux distribution and power distribution in both axial and radial direction. Previously the ADMARC-H cross sections were generated with the HELIOS lattice physics code. Part of the developments included in this work, was to generate a set of few-group homogenized cross sections using the SERPENT code. In the ADMACR-H execution folder, the set of two-group PSBR homogenized cross sections are stored. They are arranged per cell/material type (water cell, graphite cell, B 4 C cell, air cell, 2 fuel types and Fuel follower control rod cell). For each of these cells, they are arranged per temperature intervals (300 K to 900 K) and per burnup (0 to 140,000MWD). An interpolation scheme allows for determining the cross-section values for conditions in between burnup and temperature reference points. However, for the Boron Carbide (B 4 C) there is no burnup or temperature change indicated (only one value throughout the grid).

61 45 The homogenized cross sections and diffusion coefficients that are stored per cell/material type are the following: D 1 - diffusion coefficient for the fast group - Removal cross section for the fast group Production cross section for group 1 Fission cross section for group1 D 2 - Diffusion coefficient for the Thermal group - Removal cross section for the thermal group Production cross section for group 2 Fission cross section for group 2 The group scattering cross-section (down scattering only) These homogenized cross sections and diffusion coefficient will be for an equivalent cell. The equations for the homogenization were given in a previous section. TRIGSIMS writes into an ADMARC-H input file, for each node in the fuel element, depending on burnup, material type and temperature, a set of nine cross sections, as indicated above. ADMARC-H performs two-group diffusion calculations using these cross sections to solve for the flux distribution, k eff and power distribution, on nodal basis. The numerical procedure is an iterative procedure, whereby it solves the two group equations starting with an initial guess of k=1 and source and proceeding to update, substituting down the group and iteratively from one k to the next until convergence is reached.

62 ORIGEN-S (SCALE) ORIGEN-S is a SCALE [11], [49] system module to calculate fuel depletion, actinide transmutation, fission product buildup and decay, and associated radiation source terms. ORIGEN-S (Oak Ridge Isotope GENeration) computes time-dependent concentrations and radiation source terms of a large number of isotopes that are simultaneously generated or depleted, through neutronic transmutation, fission, and radioactive decay. The primary objective in the design of ORIGEN-S is to make it possible for the depletion calculations to utilize multienergy-group cross sections processed from any standard ENDF/B formatted nuclear data library. In determining the time dependence of nuclide concentrations, ORIGEN-S is primarily concerned with developing solutions for the following equation: ORIGEN-S nuclear data libraries include cross sections for three neutron energy groups: a thermal group below ev, a resonance energy group extending up to 1 MeV, and a fast energy group above 1 MeV. The thermal cross section is stored as the effective 2200-m/s values (value at ev). The resonance and fast group cross sections are the flux weighted values for the respective groups. When running ORIGEN-S [49] as a stand-alone module, the user specifies the cross-section weighting factors THERM, RES, and FAST. THERM is used to adjust the 2200-m/s cross sections in the library for a thermal neutron spectrum for the system. RES and FAST are used to weight the resonance and fast group cross sections in forming effective onegroup values. Note that when ORIGEN-S is run with a binary cross-section library the effective one-group cross sections are stored in, and read directly from the binary library. Therefore, the three-group weighting factors do not need to be input in this case. In our application for TRIGSIMS (also TRIGSIMS-TH), we have ORIGEN-S using both: a) The binary library stored (for non-important isotopes), and;

63 47 b) The pre-calculated cross sections by MCNP for PSBR, for the effective cross sections calculations, with the weighting factors THERM, RES and FAST, calculated for the predetermined important isotopes. Having input values for THERM, RES, and FAST, ORIGEN-S then combines these weighting terms with the three-group cross sections to form the effective one-group cross sections, σ eff, used in the calculation of reaction rates based upon the total thermal flux as: In order to preserve the reaction rates, the group cross sections for thermal, resonance and fast regions are calculated by the MCNP code. The update of the three group cross sections to the burnup dependent cross sections library is performed through COUPLE (part the of SCALE module) which is executed before ORIGEN-S.[2] 3.6 Cross sections TRIGSIMS-TH uses two types of neutronic codes: the diffusion code ADMARC-H and the Monte Carlo code, MCNP5. The MCNP5 code uses continuous energy cross sections, which are provided with the code. In addition, a set of continuous energy cross sections were generated specifically for the PSBR design TRIGA fuel. These refined cross section libraries were produced identified "important" isotopes [2]. The ADMARC-H code use homogenized reaction cross section and diffusion coefficients, which was previously generated with the HELIOS code [14], and for this application performed with SERPENT, a Monte Carlo code. The reason for this cross-section library update is to improve accuracy of cross-sections used in 3D diffusion nodal calculations and make them more consistent with Monte Carlo core calculations. The updated library also covers extended ranges of burnup and temperature conditions as well as new cell/material types.

64 48 A) SERPENT SERPENT[36] is a three-dimensional, continuous-energy Monte Carlo reactor physics burnup, calculation code. It is specifically designed for lattice physics applications and can be used for full core calculation. The code uses built-in routines for burnup calculations and is optimized for generating homogenized multi-group constants for deterministic reactor simulator calculations. Among the many capabilities of this code, for this project we are interested in the homogenized reaction cross sections and diffusion coefficients that it produces for various burnup steps of TRIGA fuel. Internal burnup calculation capability allows SERPENT to simulate fuel depletion as a completely stand-alone application. In general, the burnup calculation is a two-step cyclic process. It consists of transport cycle using the Monte Carlo techniques to determine the reaction rates for the neutron induced transmutation. This data is then combined with radioactive constants, and fission yield is read from nuclear data libraries. The Bateman equation [50] is used to describe the isotopic changes and is given as: 3.11 where is the atomic density of the nuclide j, n is the total number of nuclides and are the generalized transmutation coefficients characterizing the rates of neutron-induced reactions and spontaneous radioactive decay. These are kept constant over the burnup step. Secondly, this equation is solved, thereafter-updated material compositions are applied, and procedure is repeated. The standard isotropic diffusion coefficients are calculated in SERPENT through:

65 where the transport cross section given by 3.13 with few group index G given [51]. The cross sections and diffusion coefficients generated are used for the nodal diffusion code ADMARC-H calculations. A typical TRIGA fuel cell consists of four regions indicated in the Figure 3-7. It can be reduced to an equivalent cell of simpler geometry to expedite calculations. The concept of homogenization is to preserve all the reaction rates in the problem from the detailed heterogeneous transport calculation. Figure 3-7 Homogenization of TRIGA fuel A specific challenge to SERPENT is the critical spectrum calculation. Homogenization is carried out at fuel assembly level, in a geometry consisting of infinite lattice identical assemblies. There is no net current over the boundaries, which affect the k-eigenvalue calculation. Scaling of the fission source has an effect on the flux spectrum, which has an effect on the homogenized group constants. To account for this non-physical infinite lattice approximation, a leakage

66 correction is used, which is similar to the one performed in the deterministic lattice physics codes [50]. Development for a Monte Carlo leakage correction is investigated for SERPENT.[51] Other supplementing theory this study. This section handles important theory that though not key points, adds to the nature of Design of the core loading The power density (kw/l), which is defined as the power produced per unit volume of the reactor core, determines the core size. The average power density is given as Ave power density =, with as the average linear heat generation rate ( power per unit length of fuel),, number of fuel rods, the fuel assembly pitch, Q the reactor thermal power [32] The moderator to fuel ratio ( ) relates to the size and shape of the fuel rods to the water surrounding them in the core volume. H/U refers to the amount of hydrogen atoms to in the moderator the amount of Uranium atoms in the fuel ( 235 U and 238 U). Both of these two effects can have an influence on the design of the reactor core loading. Currently the TRIGSIMS code has a formulation when implementing the core loading, it calculates and adds the moderator domain around the reactor core. This effect influences the k eff of the system. Hence, it is of interest to investigate and assess how it is done for various core loadings.

67 B 4 C in Control rods The isotopic composition of natural boron is 18.8% B10, and 81.2% B11. The possible reaction of neutron absorption is given as: + n ; σ = 4010 b + n ; σ = 0.2 b + n ; σ = b Boron-10 has a high neutron capture cross section, hence a high probability that a 10 B atom will pick up a neutron as it collides with the nucleus, in a (n, α) reaction. This probability changes with energy levels. B-10 has the highest chance of picking up thermal neutrons (slow). It has a high thermal conductivity and hence we can expect a relatively even temperature distribution over the control rod. From post irradiation examination, the B 4 C had a burnup of 3.4% for 3000hours burned. The physical properties of Boron carbide (B 4 C) are reference [37], [43], which gives a theoretical density of 2.51g/cm Thermal hydraulic feedback The variation in reactivity due to change in reactor power is called the power coefficient.. This value must usually be small but negative for the stability of the reactor. If the power coefficient is positive, the reactor power will infinitely increase. If the power coefficient is negative, and large (taking the absolute value), the reactor power will not be able to be elevated, which make the reactor hard to operate. Expressing the power coefficient in terms of temperature coefficient, is given by

68 Where is the variation of temperature of the i-th core component due to temperature change. In reality, these are dependent variables but numerically, the physics of the relationship between power-increase, control-rod-position and the temperature of the core elements needs to be determined. An effort to quantify this relation can be done with measured data. This is also different for each core loading. Ideally, an equation, or a method that would be applicable for all core loadings is what is needed for this multi-tool. Another method would be to use perturbation theory, a variation of equation 4.1. This method relies on a previous run core and depends on the size of reactivity inserted.

69 53 Chapter 4 Methodological and modeling developments The theoretical models, numerical methodologies, and computational codes used in the TRIGSIMS-TH are described in this chapter. TRIGSIMS-TH consists of the Monte Carlo code, MCNP5, nodal diffusion code ADMARC-H, neutronics burnup code ORIGEN-S (SCALE) and newly added thermal hydraulics code CTF. 4.1 TRIGSIMS-TH control system Figure 4-1 shows the basic control flow for TRIGSIMS-TH. TRIGSIMS-TH code system is an automated software management tool that couples various neutronics codes with burnup and thermal hydraulic codes. It carries information transfer between codes, prepares the inputs, and controls codes execution. Thereafter, it post-processes the results and extracts the outputs of reactor parameters that are obtained from a core design calculation. The code system is controlled by a single user input file, which outlines the core configuration and a specific application. This input consists of the description of the core design, control rods and other geometrical structures. The position of each entry of the core-loading map is mapped according to MCNP5 input lattice indexing. The fuel element types are specified as well as the isotopic inventory of every axial section of the fuel. The user specifies the calculation option in the input. There is an option to run this code system with or without the ADMARC-H as an acceleration tool. The user can do any number of control rod insertions from ARI (all rods in) to ARO (all rods out). The code is also equipped with a thermal hydraulic module. This code is able to model any core loading (CL) configuration.

70 54 Input document 1. Run criticality calc 2. Run control rod position 3. Run CTF standalone ADMARC-H Yes No admarch/ctf.exe MCNP5.exe TRIGSIMS-TH.exe SCALE.exe Read ADMARC-H Cross sections Read MCNP Cross sections Write Input ADMARC-H Write MNCP Input Run ADMARC-H/ CTF Run MCNP Write ORIGEN-S Input Write CTF Input Run SCALE/ ORIGEN-S CTF.exe Run CTF Figure 4-1 Diagram of TRIGSIMS-TH code platform

71 55 The TRIGSIMS-TH platform is equipped with the following applications: a) A fast running traditional multi-physics code ADMARC-H/CTF with its associated cross-section data files admr.dat; b) The neutron transport code, MCNP5 with its associated continuous energy temperature dependent cross-section MCNP5_DATA file; c) The depletion code ORIGEN-S (SCALE-6 module); d) The thermal-hydraulics sub-channel analysis code CTF. These are all different codes that are coupled through TRIGSIMS-TH, where TRIGSIMS-TH control the data exchange between these programs. There are three run modes for this application. Run-mode1: The first is an input request for a core loading (CL) criticality calculation. That is to calculate the criticality at any power level. This is an integrative process. Run-mode2: This is a control rod position (CRpos) calculation. This calculation allows the user to do any number of CRpos calculations. The CTF is coupled with MCNP for any CRpos. However, CTF requires an input power level (AFLUX). For this application, the measured data was used to create a CRpos vs. Power curve. Run-mode3: This mode request is for a CTF standalone calculation. This mode will run the MCNP initial calculation for a requested power or position step, followed by the CTF execution.

72 Temperature feedback methods In particular, to TRIGA reactors, the steady state calculation depends on each fuel rod, their positions in the core and their characteristics. The fuels generally have a long life, and with each core loading or core shuffle, the burnt elements are moved around and if needed new fuel elements are added in the central part of the core Illustration of the thermal hydraulic feedback effects The new TRIGSIMS-TH applies a fuel axial temperature profile to each individual fuel element as well as a water axial profile for the moderator surrounding each fuel node. The MCNP input is written with five axial fuel nodes each with a material composition and burnup estimate. The temperature of the moderator surrounding the fuel elements is used to determine the density in the MCNP input for each of these nodes. With this application, a heterogeneous application of cross section is given for a single fuel element. These features are new and the development introduced by this PhD work makes the TRIGSIMS-TH code a simulation code for realistic physical applications. Figure 4-2 illustrates the difference of utilized/predicted temperature distributions between the two codes TRIGSIMS and TRIGSIMS -TH.

73 57 Homogenous temperature Heterogeneous temperature resulting from feedback Figure 4-2 Illustration of homogeneous and heterogeneous temperature distributions The TRIGSIMS code reads the temperature for each segment of the element and sorts through the MCNP XS-DIR file in the following way. The code reads the data from the bottom of the file to the top. The generated PSBR cross section data are arranged on a grid with 50 K temperature intervals. Figure 4-3 depicts the core radial pin wise heterogeneous temperature distribution. The PSBR core does not burn with a flat radial core power distribution neither is the core radial flux distribution flat. The temperature peaks around the center of the core are due to the higher power density fuels inserted in those positions. This result stresses the importance of the application of the heterogeneous temperature distribution in the core.

74 58 A Figure 4-3 Typical radial temperature distribution at 1MW power [K] Figure 4-4 shows the temperature distribution inside the core at 1MW power along the axial length of the fuel rods.

75 59 Figure 4-4 1MW axial temperature distribution [K] This is a typical 1MW axial temperature distribution of the core elements across the centerline of the core. This centerline is indicated in Figure 4-3 as line A. This result shows the thimble in the center of the core. The hottest element is in the C ring while the cooler control elements are in the D ring. The E-ring has slightly warmer elements and the F-ring has slightly colder elements. The result indicates also that the bottom of the rods is hotter than the top due to the partially withdrawn control rods. This is a typical result, which TRIGSIMS-TH is able to calculate for each fuel element in the core at nominal power conditions. This result illustrates the capability of capturing the feedback mechanism.

76 The thermal hydraulic feedback implementation In a previous study of CTF assessment for PSBR thermal hydraulic modeling [3] it was found that the code adequately predicts the natural convective flow of the PSBR. For this work, a full core CTF model of the PSBR core was developed. For the feedback mechanism modeling, we have accelerated the CTF full core model calculation by using fewer nodes between the two grid plates. This model was constructed in such a way, that the passing of information between neutronic codes and CTF would be done with minimal averaging in the nodes. TRIGSIMS-TH automatically generates an input deck for the CTF calculation based on the core loading input (CL.inp). Figure 4-5 illustrates a single sub-channel used in the CTF. A B C Figure 4-5 A typical sub-channel for CTF Figure 4-5 shows three rods that form a flow (sub-channel) region and up to six subchannels border a fuel rod. The number of axial nodes was kept to nine. Five, active fuel region nodes plus four top and bottom graphite-region nodes. The letters A, B and C on the Figure, indicate flow region changes because of channel geometry changes. A boundary condition is set between the grid regions to ensure an enthalpy change is produced and a small flow is applied across the axial length of the channel.

77 61 The results produced by CTF are written to an external file. The coupling of MCNP and CTF is as follows: MCNP calculations output axial and radial power profiles, which are then read by TRIGSIMS-TH. TRIGSIMS-TH creates an input for CTF together with the required power level (AFLUX). This updated CTF input, executes and produces a temperature output file. This in turn is read by TRIGSIMS-TH, which updates the cross sections for the next MCNP iteration. The reason for this external coupling scheme is that these two codes are written in different programming languages. The ADMARC-H and CTF however are coupled internally, meaning, TRIGSIMS-TH handles the temperatures from CTF to ADMARC-H and the power profiles from ADMARC-H to CTF with no need of reading external files. The two codes are written as one application. The TRIGSIMS-TH code is able to apply variations in the core design. It is not fixed to the number of fuel elements and neither is it fixed to the type of element in a position. For the standalone model, we have lengthened the sub-channel to include regions above and below the grid plates indicated in Figure 4-5. The feedback mechanism between CTF and both MCNP and ADMARC-H is implemented in the same way. The neutronic codes pass normalized radial and axial power for each fuel element to CTF and CTF supplies the temperature of the core elements as illustrated in Figure 4-6. TRIGSIMS-TH writes a CTF input only once per each iteration. If ADMARC-H is requested in the input, the ADMARC-H/CTF coupling uses the written CTF/MCNP input and updates the power profiles only.

78 62 Figure 4-6 Illustration of the coupling methodology The multi-physics coupling methodologies developed in this PhD thesis for MCNP/CTF and ADMARC-H/CTF are described next MCNP/CTF coupling As shown in Figure 4-1, there are three types of calculations that can be requested from the TRIGSIMS-TH code. Generally, the code is used for criticality calculation with burnup. For this application, the MCNP/CTF coupling method is outlined in the Figure 4-7.

79 63 Read Temperature file Read MCNP_DATA Prepare MCNP input with CRpos No Run MCNP5 Convergence check Extract data Axial pin power and nominal power/pin Prepare for corrector step Prepare CTF input Temperature Of fuel and moderator Yes Yes Run CTF Predictor step ORIGENS Burn fuel Output MCNP End calc and store output data No Figure 4-7 Flow diagram of MCNP/CTF coupling

80 64 This diagram contains the following key information: 1. MCNP This starts with a request written in the input. Run-mode 1 is an iterative criticality calculation. This calculation starts with ARI and a temperature of 300K for fuel and moderator is advisable. Run-mode 2 is a control rod position calculation. This calculation is not iterative and the user can request any control rod position. An appropriate temperature distribution for the control rod position will be calculated. Run-mode 3 is a request for standalone CTF calculation. This comes as a flag in the input. It utilizes MCNP results from run-mode 1 or run-mode 2. Thus, the standalone CTF calculation uses power profiles produced previously by MCNP. 2. CTF The CTF calculation comes after the MCNP calculation. TRIGSIMS-TH extracts the axial power data per node per fuel element from the MCNP output (F7 tallies data). The data are normalized per node per average fuel power. If the request was for run-mode one, the power for CTF (AFLUX) would be the linear power representing the power in the input file. If the runmode is two, the input linear power (AFLUX) will come from a calculated value based on the data from measurements of control rod position vs. power. After the CTF execution, TRIGSIMS- TH will extract the temperature profiles and write it to an external output file. This will be read for the next iteration or power increase if requested. If this is a standalone request, the CTF would terminate its execution after this step. If this is run-mode 2, the CRpos (control rod position) of next input request will be used. TRIGSIMS-TH will read the CTF temperature file, update MCNP cross sections, apply CRpos, and the calculation would continue. If the request is run-mode 1, a convergence check will be done. Reactivity ρ(x) <0.001, and the temperature is checked for elements in the center of the core.

81 65 3. ORIGEN-S This application is coupled with the predictor-corrector application and remains unchanged with the TRIGSIMS-TH ADMARC-H/CTF coupling The ADMARC-H/CTF coupling runs as one internally coupled application. Thereby there is no need to write and read information. The methodology of passing information is similar to that of MCNP/CTF coupling. Since the ADMARC-H calculation takes few seconds to complete, this addition to this platform is an acceleration of the main solver MCNP/CTF. ADMARC-H code calculates axial power profile in seven nodes. This had to be averaged to fit the five axial fuel nodes for the CTF input. This application always precedes the MCNP/CTF calculation if it is called upon. The CTF input is not written for this coupling. The power profiles are applied after the input is read. This coupling passes to MCNP/CTF coupling updated fission source, power and temperature distributions for the core. The chapters that follow will outline the effectiveness of this methodology. The developed coupling mechanisms is shown in Figure 4-8

82 66 Input shows ADMARC-H Read Temperature file Write ADAMRC-H input Run ADMARC-H ADMARC-H.EXE Prepare ADMARC-H (New cross section adjust CRpos Pass Axial pin powers and Nominal powers No Write Temperature of fuel and moderator file RUN ctf Convergence check Yes MCNP follows Output Crpos and updated temperature file Figure 4-8 Flow diagram of ADMARC-H/CTF couple

83 67 This application can accompany any run-mode as described in the previous section. The control rod methodology for run-mode 1 is based on the same calculations. In the coupled methodology, ADMARCH and CTF are written in one application. Hence, the data is transferred directly and updates are done directly to the codes. Since ADMARC-H runs after MCNP/CTF coupling, the CTF input is not rewritten, but rather just updated. Figure 4-8 shows the coupling method between CTF and ADMARC-H. This is very similar to that of MCNP, except that ADMARC-H is preceded by MCNP, the control rod position is passed to the MCNP next iteration, and a CTF temperature output file is written for the follow up calculation by MCNP Pseudo material approach Grid with interval of 50K for the continuous cross sections, generated by NJOY and further interpolated for exact temperature of interest, is utilized for MCNP calculations [2]. The interpolation methodology is called pseudo material approach and uses an upper and lower bound averaging scheme. TRIGSIMS-TH is able to write an MCNP input file with atom fraction densities for each fuel node, for each fuel element, and for each uranium isotope. For the atom fraction of the material obeying lower temperature, we have: 4.1 for the higher temperature material in the mixture we have: 4.2

84 By using the pseudo material mixing approach[19], we obtain the following cross section mixture: 68 At the end of the calculation, the code reformulates and combines the atom fraction for each uranium isotope. This is needed for the burnup step Partially inserted control rods The PSBR TRIGA reactor is operated with partially inserted control rods. Normal operation with critical full power of 1MW is not the same for each core loading. They can vary between 7.5 inches to 13 inches withdrawn above the bottom of the core; depending on how much fuel, (uranium) is loaded in the core. The lack of a control rod search methodology for a critical reactor condition was one of the shortcomings of the previous code system TRIGSIMS. TRIGSIMS applied an ARO assumption for the 1MW critical rod position. In this work, the use of perturbation theory was found to be applicable for an iterative, automated control rod search. The methodology that was developed in this work is described in this section Application of perturbation theory Usually any small change in the geometry of the core or composition creates relatively small changes in the core multiplication factor, which in turn requires changes in the control rod position. With small changes, the application of perturbation theory can be used for determining the relative reactivity worth of partially inserted control rods for TRIGA reactors. Generally, perturbation theory is not recommended for tight fuel lattices [32], with large number of elements

85 p(x)/p(h) 69 to achieve a uniform power distribution. Neither can it be used to give meaningful estimates of absolute control rod worth. The equation derived from the one-group first order perturbation theory [32][35] is outlined as follows: which is the worth of a partially inserted control rod bank as a function of the distance inserted. This equation is normally represented by an S-curve as shown in Figure 4-9: Fully Withdrawn 0.5 Fully inserted x/h Figure 4-9 S-curve for control rods The maximum change in reactivity occurs when the end of the control rod is in the center of the reactor. Towards the ends, the change in reactivity is smaller. It is this smaller region that is of interest for our calculations. The PSBR TRIGA reactor is normally operated around 1MW, the calculated ρ (H) (which represent the results of a critical rod position), is used in a search (tolerance iteration) to calculate the control rod position using the equation 4.4. The search involves both the x (CR position) value as well as the ρ(x) (the change in reactivity) value. In order for this application to work effectively, the heterogeneous temperature distribution has to be applied to the reactivity calculation of the core.

86 70 This application is part of the CTF/ADMARC-H coupling and MCNP/CTF coupling Control rod position method using a quasi-fixed point iteration scheme This method runs on the premise that the core remains subcritical below the x/h=0.5 of the S curve in Figure 4-9. The criticality calculation starts after the core has reached the halfway mark. Generally, the reactor becomes source critical around the 7.5" (19.05cm) position, which changes for different cores and could be less if the core has many fresh fuel elements. The method utilizes the previous k eff result of a MCNP calculation. Converts this k eff values to the associated reactivity, updates and repeats the calculation. It is essentially a nested loop iteration. It starts with an initial guess of control rod position of 1cm and a reactivity at x position, ρ(x), value of The iteration process is time consuming and depending on how far the control rod is moved from the initial critical rod position to the full power critical position. It can be anywhere between 8 iterations to about 25 iterations. In these cases the ADMARC-H code can be used for more efficient iteration process with MCNP just used for final fine-tuning. Figure 4-10 shows the flow of this method.

87 71 A=2*pi, rowy=a*(rowx/rowh) B=2*pi*x/H - sin(2*pi*x/h) xx=b-sin(b) Input 1 Criticality calc ARI CALC At core tempearture =300K Update input with new CRpos Initial guess CRpos=1 rowx=0.001 Run MCNP Get keff Set rowx=rowx+rowkeff*0.1 Tollkeff <0.002 No Tol= ARI Keff rowh TOL>0.001 Yes Calc A, B, xx Increase CRpos Or Decrease Crpos By 0.1 Yes Crpos found No TOL= rowy-xx Tol Check Figure 4-10 Flow diagram of the control rod method

88 72 The mathematical formulation in Figure 4-10 could be described as a quasi-fixed-point (semi-fixed-point or non-linear fixed-point) iteration scheme. Fixed-point iteration is of the following form: g(x0) g(x1) g(x2) x1 x2 x3... x This method starts with an initial guess x 0, convert F(x)=0 into x=g(x), then iterate, x i+1 = g(x i ), i = 0,1,2,3..., where the iteration will continue if convergence ( x i+1 -g(x 0 ) < tol) is not met. The quasi fixed-point iteration is illustrated by the Figure This is the mathematical formulation of the iteration scheme used in Figure 4-10 for the control rod positioning methodology. g(xi) g(x12) y(p(2)) y(p(x1)) g(x11 g(x10 p(x 0) p(x 1) x11 x12 x13 x2 x1 x2 x3 x Figure 4-11 illustration of the quasi fixed point iteration

89 73 This iteration starts with an initial guess for x 0, and one for p(x 0 ), and then it uses a fixedpoint iteration between x 0 and x 1, to get a value for x 1 corresponding to g(x 0 ), such that x 1 - g(x 0 ) <tol1. If tolerance is reached, then for that x1 value there is p(x 1 ), such that y(p(x 2 )) is calculated and results in a tolerance check between g(x 1 )-p(x 1 ) <tol2.~ If the tolerance is not reached then F(g(x 0 )) is updated and a next search between x1 and x2 using fixed point iteration is started to obtain x 2 =g(x 1 ) and F(xi)=f(x i, y(p(x i )). 4.4 Thermal hydraulics methodology CTF forms part of the coupling methodology and is used for thermal hydraulic feedback. As a request from the user, the code can also write out a standalone input deck. Though we say standalone thermal-hydraulic, this code will still require the neutronics to set the axial and radial power distribution for a particular requested power level. The MCNP calculation will be executed and then the expanded CTF input deck will be written. A standalone calculation is useful to analyze specific thermal hydraulic details. CTF calculates many different thermal hydraulic parameters and with this standalone option of the full core, we can refine the output for information needed for the PSBR safety analysis. Details such as, axial temperature distribution for the fuel, clad and coolant regions, mass flows and velocities can be analyzed. We can test design limits of the core by increase in power beyond the normal, and estimate quantities such as the Critical Heat Flux (CHF), and the Departure from Nucleate Boiling (DNB).

90 74 Figure 4-12 Developing of a full core CTF model Figure 4-12 is a CTF input layout for a PSBR full core calculation. It indicates a typical manner of dividing the reactor core in triangular sub-channels, gaps and rods. Channels, gaps and rods have to be input sequentially, which requires a fixed layout of the core. What this means is that spaces and dry tubes are treated as non-fueled rods in this structure. Hence, no power will apply to these regions. Thus, the input structure for a regular 110-place holder is as indicated. The pink shows non-fueled rods and the yellow indicates potential open spaces. However, this is not fixed, as the user can load fuel elements in these positions as well. If a core loading input adds more elements to the core layout, as indicated in the figure, the TRIGSIMS-TH code will place those elements into the side channels as additional channels. The code will assign a power profile to the fueled elements and the non-fuel elements will have zero power. As indicated in the Figure 4-12, a D 2 O tank can be added to the neutronics calculation. This usually comes as input request (D 2 O-flag), whereby TRIGSIMS-TH will add the geometry of the D 2 O tank to the geometry of the current core layout. This tank is added as an unheated

91 75 conductor data. Which means TRIGSIMS-TH will have to make changes to the input deck for these additional cards. The addition of the D 2 O tank adds another channel to the core layout and another eight more gaps to the current design. The value of this addition to the CTF application of the core loading with the D 2 O tank is that TRIGSIMS-TH can now be used to do analysis on changes of the D 2 O tank design as shown in Ücar's [5] thesis. His proposal for an enclosure that covers half the core can be analyzed with regard to safety and optimal design of the reactor core. 4.5 TRIGSIMS-TH Core Modeling parameters There are a few parameters in the core model, which determine the outcome of a calculation. Some of them are discussed next. The geometry of the core includes the fuel and control rod elements, each with their own isotopic content. They are placed on a grid in a hexagonal layout with a fixed inter-element spacing (pitch). Each element or structure is surrounded with light water and the system has no forced cooling. The code accounts for the isotopic content of the fuel. Since this is hydride fuel, part of moderation of the fast neutrons is done in the fuel. The core design has to account for this as well as for the fact that the absorber material, B 4 C, has a big influence on the results. The assumptions that are made to ensure efficient calculations are not generic Moderator surrounding the core The moderator to fuel ratio in the core relates to the size and shape of the fuel rods and the water surrounding the fuel.

92 76 The application of the TRIGSIMS-TH geometry input is fixed. The water surrounding the core is added in a fixed methodology with the assumption that the core geometry is always fixed. i.e., the top half of the core is the same as the bottom half and all the cells are filled as shown in the CTF model Figure However, the core loading design is variable. More or less fuel elements are used in the core layout depending on the needs of a particular core loading. CL54 has 100 fuel elements, whereas CL56 has a 108 fuel elements. Yet we find that the water surrounding the CL54 is more than that of CL56 (see Figures 4-13 and 4-14). Maximum radius Figure 4-13 CL56 diagram Maximum radius Figure 4-14 CL54 diagram

93 77 Figure 4-13 and Figure 4-14 show the MCNP models for calculation of criticality for CL56 and CL54. The maximum radius plus 4 times the pitch size determines the outside radius of the calculation domain. The code runs a loop to determine the maximum radius using the MCNP cell entries as within the x and y domain, with an adjustment on the x. This method of determining the core maximum radius resulted in some cores being over moderated. In the current TRIGSIMS-TH code, this model is adjusted by applying a ratio of the fuel used in the core model to the fuel used in a full core model as shown in Figure 4-1. The neutron absorbing material, B 4 C, in the control elements was analyzed using various core loadings. Previous combinations of the density and composition were compared to theoretical compositions and densities. The best possible fit analyzed was used in the TRIGSIMS- TH code. 4.6 Conclusion on the methods and models Changes to a code system require good insight to the working of each of the codes. There are five codes with five applications that are housed within the TRIGSIMS-TH. Each one has a function to fulfill. These codes are written in different languages. Changes were induced in the TRIGSIMS, MCNP, ADMARC-H and CTF codes. The depletion code, though it was not changed, was affected due to the upgrades in the other codes. Each change has a function either to enhance the codes capability or to make the code more applicable for the current core loading and future core loadings. The methods applied have been analyzed and the results obtained are presented in the following chapter.

94 78 Chapter 5 Results and Findings This chapter presents the results and findings of the work accomplished in this thesis in the following order. 1. Validation of the implementation of the feedback-mechanism for the highfidelity multi-physics coupling within the TRIGSIMS-TH code system, which involves the neutronics code MCNP, and the thermal hydraulics code CTF. These two codes are the main solving codes, and the focus of this task is to ensure that the coupling was done correctly. 2. Validation of the control rod position search method. This was a needed development for the TRIGSIMS-TH code system, as there is a need for a method to relate the control rod position to the power level. 3. A summary of the thermal hydraulics analyses and results of the PSBR core using the TRIGSIMS-TH code is presented. 4. Application of power increase (with control rod withdrawal) using TRIGSIMS- TH to access reactivity loss was shown and compared with measured results. 5. The results of TRIGSIMS-TH for analysis of additions to the core layout, such as graphite rods, are presented. 6. Quantification findings of improvements introduced on the predictions of core design parameters are given. These improvements include a best estimate of B 4 C in the control elements, new SERPENT-based homogenized cross sections for the ADMARC-H code, pseudo material application for MCNP-based multiphysics calculations, and core moderation changes are given.

95 79 7. The results of the modeling of D 2 O tank with the CTF code and the coupled mechanism are presented. 8. The findings of using the CTF as a standalone code are discussed. 9. Conclusions of the applications of various developments and improvements are summarized. The validation was performed with measured data obtained from the PSBR operation for core loadings, CL 53H and G (with core map given in Figure A- 2), CL54 (with core map Figure A- 1) and CL 56 (with core map given in Figure 3-2). The core maps show where each fuel element, control element and dry irradiation tube are placed in the core layout A C B Figure 5-1 Reference core diagram

96 80 Figure 5-1 gives the basic core map of a PSBR core loading. The indicated numbers and letters in the figure are used as references for latter discussions. The term "ring" refers to the following. The ring B elements surrounds the central water thimble, and then follow C, D, E,F and G rings, radially outward, for the fuel elements. In the Figure 5-1, the letters A, B and C shows the placement of instrumental rods used in calculation and the numbered items are the fuel elements used in the various core loadings. The triangle shapes numbered positions refer to the thermal hydraulic channels used in the CTF results. The elements (fuel and non-fuel) are numbered sequentially from the top to the bottom and from left to right. For this layout, 110 is the last element in the right hand corner. This diagram represents the basic layout used for referencing of different core loadings in this results section. 5.1 MCNP/CTF coupling To show the effective functioning of the coupling methodology with feedback application, the following are the result of full core calculations for CL56, Cl54 and CL53, using TRIGSIMS-TH code. The results were obtained from coupled neutronics/thermal hydraulic (multi-physics) calculations for 1MW power level after iterations to obtain a critical state at a certain control rod position. For these calculations, the control rod position methodology was applied. The results shown in Figures 5-2 through 5-4 are the CTF-predicted full core temperature distributions.

97 Temperature [oc] 81 CL56 at 1MW power, Temperature distribution x y Figure 5-2 Temperature distribution for CL56 The results in Figure 5-2 show that the new instrumetal I-17 rod in position C (as indicated on Figure 5-1) has the highest temperature (539 C). This rod is a new 12 wt% fuel, instrumental rod, and it is expected that it would have a higher power density compared with the other rods in the core. The ring B elements, around the center of the core are 8.5 wt% fuel elements, and the fuel elements with calculated temperatures between 450 C and 500 C (in the C and D ring) are 12 wt% fuel elements.

98 Temperature [oc] 82 CL54 at 1MW power, Temperature distribution x y 50 0 Figure 5-3 Temperature distribution for CL54 The results in the Figure 5-3 show that the temperature of the fuel elements around the center is hotter as compared with CL56. This is because 6 fresh 8.5 wt% fuel elements were placed in these positions. The C-ring elements however still present the hottest core elements, which are 12 wt% elements. The rod I-16, an older instrumental rod, is in position C (as indicated in the reference diagram, Figure 5-1). Maximum temperature of 515 C is calculated at this position.

99 Temperature [oc] 83 CL53 at 1MW power, Temperature distribution x y Figure 5-4 Temperature distribution for CL53H The CL53H results show that the higher temperature elements are around the C ring. Two rods A(227) and B (I-16) (as indicated in Figure 5-1) are calculated to have approximately the same max average temperature of 519 C. B is the instrumental element I-16 used for measurement. All three figures present a similar pattern for the temperature distribution at a 1MW core power. Higher temperatures occur around the C and D ring elements. This is the position where the fuel with highest uranium content is loaded. The predictions of the developed multi-physics

100 84 methodology with feedback mechanisms are compared with measured results. This comparison is presented in Table 5-1. Table 5-1 Measured results compared with calculated TRIGSIMS-TH results Core CL56 CL54 CL53H K eff ± ± ± CR position calculated cm cm cm CR position measured cm cm cm Calculated ave temp C C C Measured ave temp C C C The results using the coupling methodology are comparable to the measured results. As it can be seen from Table 5-1 the TRIGSIMS-TH with temperature feedback modeling is capable of predicting realistic critical states. The control rod position compares well with measured data as well as the average temperature is comparable to that of the measured data. The largest deviation of 20 C is shown for CL56, and this deviation is about 3% of the temperature value. It is not possible to compare results of the TRIGSIMS system to the TRIGSIMS-TH system. The addition of the temperature feedback allows the TRIGSIMS-TH system to calculate a critical state for given core power, which was not previously possible. The results presented in the Table 5-1 verify the coupling methodology for the new temperature feedback mechanism using MCNP/CTF calculations. Measurements are done at the instrumental elements positions only. The results in Table 5-1 can be achieved either by an iterative control rod search method or by power increase method. Ultimately, the code requires a heterogeneous temperature distribution at a certain control rod level. The results display the expected temperature distribution for each core loading. This confirms that the implementation and the execution of the coupling method of CTF to MCNP are correct.

101 Critical control rod search The PSBR operates with partially inserted control rods, i.e., 1MW power has the control rods withdrawn from the core between 20 cm and 33 cm where 38.1 cm is the full length of the absorbing material. The reactor increases power with the control rod withdrawal. By procedure, the operators balance the control rods at the same axial position when the reactor is at full power. The critical control rod search is an algorithm that has been developed in this work. It uses an iterative scheme to find the position where the control rods would be positioned for a critical state at a given power level. The validation of this algorithm is now presented Validation of critical rod search method The calculation starts with an input that contains the desired power level. The iterative scheme will always start at the all rods in position. This is the first calculation that is used to determine placement of the control rods for the next iteration. Each iteration step is followed by a CTF calculation for the desired power level with updated axial and radial power distributions. If the power level is less than 1MW, the Xe number density fraction, currently assumed to be 20% of the equilibrium xenon concentration for all power operations [2], is scaled according to the corresponding power fraction. This application using the TRIGSIMS-TH tool is intended to analyze a full power critical core loading, usually at around 1MW, but it could also be used for analyzing lower and intermediate power levels as well. The validation results are compared with measurements for CL56 at 1MW and 700KW and for CL54 at 1MW and at 800 kw power levels respectively. The aim is to calculate full power at 1MW successfully, but to show the diversity of the tool. For this reason, the results for lower power levels are presented as well.

102 Average fuel Temperature [ Control rod position [cm] 1MW core power with feedback 1 K eff measured k eff = # iterations calculated measured # iterations o C] measured calculated # iterations Figure 5-5 Iterative control rod position search of CL MCNP calculated k eff with standard deviation approximately 50pcm (1σ)

103 Average fuel Temperature [ o C] Control rod position [cm] MW core power with feedback K eff calculated k eff = # iterations calculated measured # iterations measured calculated # iterations Figure 5-6 Iterative control rod position search for CL MCNP calculated k eff with standard deviation approximately 50pcm (1σ)

104 88 Iterative control rod position searches for CL56 and CL54 are shown in Figures 5-5 and 5-6 respectively. The average fuel temperature is taken at the instrumental rod position, the older I-16 for CL54 and new I-17 for CL56.With every iteration, the control rod is either withdrawn or inserted depending on the results from the previous iteration. Each iteration has a neutronics calculation followed by its corresponding thermal hydraulic calculation. The control-rod withdrawal movements are small resulting in more accurate prediction of the position. The critical control rod position for 1 MW power for CL56 was measured at cm (height 1089 units). The average fuel temperature measured at position B was approximately 518 C (~791 F). For CL54, the critical control rod position is measured at 27.23cm (height 1072 units), with the average fuel temperature of 503 C (~776 F). The results indicate that the control rod position has converged as well as the k eff. The temperature difference between the calculation and measurement resulted in a 3 C variation. The temperature for reactivity change at 1MW for CL56 is measured at approximately 0.22 / C for 1 MW power. Thus a 3 C difference constitute to less than 0.01$ reactivity change. This difference is very small to make a notable difference in reactor design. The following result shows the TRIGSIMS-TH capability to use the control rod search method to find a control rod position for CL56 at 700kW and CL54 at 800kW. This calculation shows that not only the code can predict a critical state for full power of 1MW but can also predict a critical core at any other power level. For the 1MW MCNP calculation, the Xe isotopic fraction is adjusted to 20% of the amount indicated in the fuel inventory [2]. However, since these calculations are not full power, this Xenon fraction is scaled by the power fraction, since the Xenon fraction is flux dependent, and hence power dependent, to account for fewer poisons in the fuel during operation. Figure 5-7 shows the results from the control rod search in TRIGSIMS-TH to find a critical core at 700 kw power. Two sets of data are given in this figure. The one is the results from the adjusted Xe fraction (noted in the graph as CL56-Xe) due to lower power

105 Average fuel Temperature [ o C] Control rod position [cm] 89 compared with full amount of Xe (as applied to 1MW power) kW core power with feedback K eff CL56 measured Cl56-Xe-Adj # iterations Cl56 measured Cl56-Xe-Adj # iterations measured CL56 CL56-Xe-Adj # iterations Figure 5-7 CL56 AT 700kW power, with Xe adjusted

106 Average fuel Temperature [ o C] Control rod position [cm] 800kW core power with feedback 1 K eff calculated k eff = # iterations calculated measured # iterations measured calculated # iterations Figure 5-8 CL54 at 800kW power 3 3 MCNP calculated k eff value with standard deviation of approximately 50pcm (1σ)

107 91 The results for the Xe fractioned calculation show a slightly higher control rod position. It is in the region of 0.4 cm, which is not noticeable in the control rod position graph. The temperature graph however indicates a higher overall temperature. Both the Figure 5-7 and Figure 5-8, indicates a convergence in control rod position, a k eff convergence of approximately 1, and temperature convergence. Table 5-2 compares the results of these two calculations. The Xe adjustment is implemented in the TRIGSIMS-TH calculation. Table 5-2 Comparison of calculated to measured values for power levels less than 1MW Parameter Calculated Measured Difference CL56 AT 700kW Control rod height 25.44cm 25.93cm 0.49 cm Temperature I C 442 C 3 C CL54 AT 800kW Control rod height 26.5cm 26.04cm 0.46 cm Temperature I C 460 C 6 C The results shown in the Table 5-2 indicate a difference in control rod position of approximately 0.5 cm for both cases. This is a 1.8% variance, which resulted in a temperature variance as well. In general, the result shows a good agreement, validating the code TRIGSIMS- TH capability for use in critical core calculations Core reactivity estimation from calculations With every startup of a new core loading, and every year therafter, the worth of the control rods is measured. This is to ensure that there is enough reactivity worth in the control rods

108 Reactivity loss 92 to shut reactor down. Using the TRIGSIMS-TH tool, the user can calculate and approximate expected core reactivity. The section demonstrated the criticality calculation result of an iterative scheme to obtain a full power critical rod position for each core loading. Using these results one can calculate the difference in reactivity between all rods in and critical state, which will constitute the reactivity change in the system. Figure 5-9, shows the calculation for the estimation of reactivity loss value given in the Table 5-3. Reactivity loss estimation for CL56 K eff Iterations keff Figure 5-9 CL56 estimation of reactivity loss value Table 5-3 summarizes the calculated data for the CL56 and CL54. The ARI is a taken at a 300K temperature. The reactivity loss at 1MW power can be calculated from the k eff data. The excess reactivity is the reactivity change from critical rod position to ARO position. Table 5-4 and Table 5-5 shows the estimated results for control rod worth for CL56 and CL54 respectively.

109 93 Table 5-3 Data from calculations CL56 CL54 ARI ± ± Reactivity loss [$] 3.44 ± ± 0.07 ARO at 1MW ± ± Table 5-4 Reactivity control comparisons for CL56 CL56 Calculated Measured Reactivity [$] Reactivity [$] Worth removed ± Reactivity loss 3.44 ± Core excess reactivity 5.64 ± TOTAL ± Table 5-5 Reactivity control comparisons for CL54 CL54 Calculated Measured Reactivity [$] Reactivity [$] Worth removed ± Reactivity loss 3.81 ± Worth remaining 6.24 ± TOTAL ± The reactivity loss calculation for CL56 is performed with 15 iterations and that for CL54 is performed with 11 iterations.

110 Control rod position Keff ADMARC-H for acceleration of control rod search method The ADMARC-H code can be used with the control rod search method to accelerate the control rod search for control rod position of the critical core. This is an option of the calculation. The ADMARC-H/CTF pre-run an iterative loop, to bring the rod and temperature up to a certain level, the code passes the control rod position and temperature distribution over to the MCNP/CTF coupled code. The findings of this addition to the control rod search method will follow. This method will eliminate approximately five iterations of the MCNP calculations. The accuracy of this method depends on the initial ARI value calculated MW core power with feedback calculated measured # iterations calculated measured ADMARC-H MCNP # iterations Figure 5-10 CL56, with ADMARC-H to accelerate

111 95 Comparing to Figure 5-10 to Figure 5-5, the addition of ADMARC-H in the calculation shows a big variation in result and this could be as a result of the heterogeneity of the partially rodded nodes that are not properly incorporated into the nodal calculation involving large homogenous nodes (control rod cusping). This will need to be further investigated. The convergence, with the ADMARC-H addition, is reached faster. 5.3 Thermal hydraulic of the PSBR Core Table 5-6 presents obtained results of the thermal hydraulics analysis of the core loadings CL56, CL54, and CL53H calculated in the previous section. The layout of the core elements of these core loadings are given in Figure 3-2, Figure A- 1 and Figure A- 2 Table 5-6 Thermal hydraulic results for core loadings at 1MW power Results CL56 CL54 CL53H Hottest fuel element I-17 I-16 i-i- I-161II16 Proposed hottest channel Clad temperature of hottest 133 C C C elements[ C] Coolant maximum temperature in 60 C 51 C 62 C hot channel [ C] Ave fuel temperature in hot 539 C C C channel[ C] Ave heat flux in hot channel 1.52 x 10 5 b/h-ft x 10 5 b/h-ft x 10 5 b/h-ft 2 Ave mass flow rate in hot channel lb/s 0.195lb/s 0.112lb/s Ave Coolant velocity in hot chan 0.115m/s 0.168m/s m/s

112 96 The thermal hydraulic results are calculated with the coupled MCNP/CTF TRIGSIMS- TH code. The hottest channel is the channel with the highest calculated surface heat flux and highest enthalpy in the core. In the case of CL53H, the hot channel does not have the highest temperature in the core. In fact, this particular core loading, present several possibilities for the hottest channel. 5.4 Application of power rise with thermal hydraulic feedback This is one of the modes in which the TRIGSIMS-TH can be used. With this method, the user can request a control rod position, giving a specific temperature distribution; it will bypass the power input and perform a criticality calculation for the requested control rod position. This method will allow the user to input various control rod positions. The power (AFLUX) needed for the CTF input will be calculated for each control rod position. This is not an iterative calculation, as the functionality is not to attain a critical rod position. As part of control and operation at the PSBR, reactivity measurements of each core are performed. Control rod worth measurements are done to ensure the core excess reactivity is within safety margin ( $ 7.00), shutdown margin limits are met ( $0.25) and the transient rod reactivity is within limits ( $3.50). One of the requirements to the control rod system at every reactor facility is to be able to shut down the reactor safely [44]. For this reason, reactivity loss data from measurements are recorded for each core loading. Using the TRIGSIMS-TH code system with the thermal hydraulic feedback mechanism, one can simulate the reactivity loss measurements.

113 Reactivity Loss [$] CL56 Reactivity loss with control rod withdrawal calculated measured Control rod withdrawal[cm] Figure 5-11 Reactivity loss 4 with power increase/control rod withdrawal for CL56 The result shown in Figure 5-11 is a comparison of reactivity loss with power increase (control rod withdrawal). This is an automated calculation, whereby within each step both the CTF and MCNP are updated. A new CTF and a new MCNP input are written at every step. The results give a good indication of the capability of the code. To get a better fit to this measured data, the calculation would have to have smaller intervals between reactivity steps or iteration at each step will have to be performed. Iterating will require more calculations, more time, and more memory. In general, the reactivity changes are higher at the end and the beginning of the control 4 MCNP calculations with variance of approximately 50pcm (1σ)

114 Reactivity Loss [$] rod withdrawal. From the measured data, you can see that the reactivity differences are also not the same for every core loading CL54 Reactivity loss with control rod withdrawal calculated measured Control rod withdrawal[cm] Figure Reactivity loss with power increase for CL54 Figure 5-12 shows reactivity loss with power increase for CL54. A positive increase shows that at each step the temperature feedback adds to reactivity loss. For this type of calculation the results is good. Although to measure it properly, smaller steps are required. Table A- 1 gives the measured power coefficient and temperature difference per power change for the CL56 and CL54. From the measured data of these core loadings, the average 5 MCNP calculation variance of approximately 50pcm(1σ)

115 99 measured power coefficient of reactivity is approximately equal to 0.24 /kw at higher power level and 0.48 /kw for lower power levels. For these type of calculations, this will indicate, that if we want the reactivity difference to be within (for example; k=0.9995), it will result in a reactivity of 0.07$. This will constitute a power change of approximately kw, for the higher power levels and kw for lower power levels. For these calculations, the steps of power rise will have to be smaller than the above stated (14.58 kw and kw). Thus, the effect of over power at the lower intervals indicated in the figures above is because of the power steps being too high at the lower temperatures. The following Figure 5-13 and Figure 5-14 show the corresponding temperature increase for each of the data points in Figure 5-11 and Figure 5-12 for reactivity loss calculations. This calculated data is the average temperature calculated for the five axial nodes of the fuel rod, whereas the average temperature for measured data is between the highest and lowest of the data from instrumental rod measurements at a certain axial position. CL56 uses I-17 and CL54 uses I- 16 instrumental fuel rods. For these two core loadings, the positions of the instrumental rods are the same, i.e. the expected hot channel in the core loading.

116 Temperature [ o C] CL56 Temperature increase with control rod withdrawal Measured Calculated Control rod position [cm] Figure 5-13 CL56 average temperature increase for the i-17 rod corresponding to reactivity loss measurements The temperature change is a result of the change in reactivity due to power increase. The results show a positive increase, as we would like the calculation to confirm. For 1 MW power level the measured and calculated results show a good agreement. However, there is a difference compared to the measured data for this system. CTF calculates the radial temperature distribution across the fuel rod, and axial temperature distribution across the fuel length of the fuel element. What is chosen to be an average value in measurement, does not always corresponds to a calculated average. The measured temperature difference for reactivity change is given in Table A- 1.

117 Temperature [oc] CL54 Average temperature with control rod withdrawal calculated measured Control rod withdrawal[cm] Figure 5-14 CL54 average temperature increase for i-16 corresponding to reactivity loss measurements This result was not possible with the TRIGSIMS system. The system could apply only one single temperature per structure-type in the core. Figure 5-13 and Figure 5-14, are consistent in comparison to the measured data. The reactivity per change in temperature for measured data is given in Table A- 1. The figures show an average temperature difference in the mid to bottom region of about C. With a temperature /power difference of 0.3 C /kw this temperature, difference results in a notable difference in reactivity.

118 Temperature [ o C] CL56 Temperature increase with power increase for the coolant i Power [kw] Figure 5-15 Temperature distribution for coolant surrounding the numbered rods Figure 5-15 shows results from the CTF output. These are the values carried over from one power step to the next. The results are as expected. The graph shows a steady increase in temperature with each step of the power rise. The calculation shows that the left side of the core is cooler than the right side. The I-17 rod (C) is the rod used for measurements and the channel between I-17 and rod 44 (indicated in Figure 5-1) is the channel used for measurements.

119 Temperature [ o C] 600 CL56 Temperature increase with power increase i measured Power [kw] Figure 5-16 Temperature increase with power increase for the indicated rods In Figure 5-16 the measured values indicated are for the channel 2 of the I-17 instrumental rod and the data from calculations was taken from the node number 3 (middle). Each node is 3in long. The difference between calculated and measured data is approximately 30 C in the center of the graph. At the 900 kw to 1 MW power, we have good agreement. The results show a variance of 0.30$ for the change in reactivity at the mid section of the power region. Thirty cents is a notable change in reactivity. At 900kW to 1MW, there is good agreement, but at lower power levels, the difference is quite significant. A possible reason for this could be the application of the thermal conductivity and specific heat capacity application in the CTF input has

120 Thermal flux in fuel elements[neutrons/s]) 104 a linear application. However, the temperature profile for the reactor does not display a linear profile. Further investigation is needed for this application. x Thermal flux distribution in core elements CL54 CL Elements numered 36 to 47 Figure 5-17 Comparison of CL56 and CL54 flux distribution Figure 5-17 shows a flux distribution calculated for the fuel elements 36 to 48 as indicated in Figure 5-1 for CL54 and CL56. CL54 has an overall higher flux distribution in the around the centre central thimble. CL54 has fresh 8.5wt% fuel at this position. The peak noticed in the centre is as results of the high thermalization of the neutrons because of the water in the thimble. Fast neutrons produced by the B-ring fuel elements are well thermalized in the extra water in the central thimble, hence the peak at the elements directly adjacent to the centre. This information can be extracted from the MCNP output files. The following graphs show the total flux distribution across the core.

121 105 Neutrons/cm 2 -s x x Figure 5-18 Thermal flux distribution for CL56 The thermal flux in the center of the core is calculated at 3.6 neutrons/cm 2 -s. Thermal flux around the edge is around 1.3 x neutrons/cm 2 -s. The results for CL54 would be approximately the same as indicated above. In general, the core configuration for these core loadings are intended to produce similar flux and power profiles.

122 Average power distribution Average power distribution for CL Core Elements numbered Figure 5-19 Normalized average power distribution for CL56 Figure 5-19 shows the average power distribution in the core for a 1 MW critical core for CL56 and Figure 5-20 for CL54. The results of CL56 and CL54 for the power distribution show that the power distribution in CL54 is higher in the center of the core. The power peak of above 1.6 indicated for CL56 is occurring in the new instrumental element, I-17, loaded for this core loading.

123 Average power distribution Average power distribution for CL54 1MW Core Elements numbered Figure 5-20 Normalized average power distribution for CL54 The two core loadings, CL54 and CL56, have a control rod position for a 1 MW critical power reactor of about the same values (27.23 cm and cm). The TRIGSIMS-TH tool is useful in this way. The user will be able to design and analyze different cores. The CL56 and CL54 have different sizes, for the same power at about the same control rod position, producing a higher power density in the center in the case of CL54.

124 AMARCH/CTF coupling The ADMARC-H code was added to the TRIGSIMS system to generate the initial fission source distribution of the MCNP calculation, thereby accelerating the MCNP calculation [2]. The code sequence was made automated in the sense that the input of the code is written by TRIGSIMS based on the initial core loading input for TRIGSIMS. What this means is that TRIGSIMS will apply the position of the control rod as it is indicated in the core loading input. ADMARC-H by itself is also a core analysis tool for the PSBR core simulation. The code is able to display power distribution, flux distribution and k eff value of the core configuration. These capabilities are still valid within the upgraded code system (TRIGSIMS-TH). The coupling of CTF to ADMARC-H is used to provide realistic initial fission source distribution as well as thermal-hydraulic parameters distributions. This approach is very useful since ADMARC-H/CTF converges very quickly and the information it provides help to accelerate MCNP/CTF calculations. ADMARC-H/CTF might be used to efficiently estimate initial critical control position for a given power level while the fine-tuning could be performed with MCNP/CTF. In the results of power rise, the CTF/ADMARC-H couple is executed together with MCNP/CTF couple. ADMARC-H/CTF MCNP CTF Figure 5-21 Diagram ADMARC-H/CTF-MCNP-CTF couple for position step

125 Reactivity difference [$] 109 For normal power increase step-calculation, the workflow of the ADMARC-H code within TRIGSIMS code system has not changed, the only difference here is that between ADMARC-H and MCNP the CTF code calculates the temperature of the fuel and moderator. Thereafter MCNP's cross-sections are updated. For the MCNP/CTF coupling, we have shown that the reactivity loss calculation required smaller steps or an iterative procedure on each step. The iterative procedure with MCNP/CTF is not practical because of the time and computer memory requirements for each MCNP calculation. 2.5 CL54 Comparison MCNP and ADMARCH ADMARCH MCNP Power [KW] Figure MCNP/CTF/ADMARC-H coupling 6 MCNP calculations: reactivity ±1σ

126 110 Figure 5-22 shows two sets of data. One is the result from ADMAC-H/CTF and the other from MCNP/CTF. The results presented in Figure 5-22 are obtained in automation where the control rod position is declared in the TRIGSIMS input file. With each step, ADMARC-H/CTF is followed by MCNP/CTF. Instead of having numerous smaller steps we can have ADMARC- H/CTF coupled calculations to save time. Table 5-7 shows a comparison of the ADMARC-H results to those of MCNP. The results are calculated with a temperature of 300K for both the ARI and ARO. It should be noted however, that for TRIGA reactors, the power is changed with the extraction of the control rods, and changing the power changes the reactivity of the core, hence the ARO calculation at 300K is not physical. Table 5-7 Core excess reactivity in $ for various core loadings Core Loading MCNP ADMARC-H/Serpent ARI -6.70± CL56 ARO ± Total ± ARI ± CL54 ARO ± Total ± ARI ± CL53H ARO ± Total ± Both the MCNP and ADMARC-H calculations show a good agreement at the ARI calculations. The previously developed cross sections [2], shows results in good agreement at the

127 111 ARO calculations because this is where the control rods was placed for evaluating full power. One of upgrades in the TRIGSIMS system was to apply the measured control rod setting instead of ARO as used in the TRIGSIMS-TH code system for a critical rod position. With the application of the thermal hydraulic feedback mechanism to TRIGSIMS-TH, the critical rod position at 1MW corresponded well with k eff =1. This will be discussed in the next subsection. 5.6 Development of core expansion For versatility of usage of this new code, the capability of a core expansion can now be done within limits. The MCNP and CTF have the flexibility to allow variations of the coreloading pattern. The addition of graphite elements and the new fuel, 30/20 LEU, can now be inserted into the core. Figure 5-23 is an illustrates the core expansion positions. Figure 5-23 Illustration of core expansion Graphite elements added The TRIGSIMS-TH is now equipped with rod entries for graphite. Graphite rods are used at various TRIGA facilities as reflector elements [7], [45]. A reason for this is to increase the k eff of the reactor, hence, require fewer fuel elements, or extending the life of the fuel or locally to increase the flux near the dry tubes for irradiation purposes. Table 5-8 gives results for the addition of 10 graphite elements to the CL53G.

128 112 Table 5-8 Addition of 10 graphite elements Power [KW] Difference in reactivity [$] ± ± ± ± ±0.09 The addition of the 10 graphite elements has resulted in a decrease of ~$0.21 in reactivity loss calculations (or increase in reactivity).the reactivity is calculated using the equation New type of fuel elements The TRIGSIMS-TH code uses a predefined geometry input for all the elements. This means, the size of each element has a fixed geometry that TRIGSIM-TH uses to write the various inputs. The isotopic composition is the only degree of freedom for various inputs. Since the new 30/20 LEU fuel are geometrically the same as the 8.5 wt% and 12 wt% fuel, the only requirements for calculating this new fuel in MCNP is to have the correct composition and density for the fuel. In the next chapter, an analysis of this fuel in the TRIGSIMS-TH will be performed using the control rod search methodology. 5.7 Improvements of the core design parameters With the further development of the code system including the addition of CTF and a control rod methodology, there was a need for the following improvements:

129 113 1) New homogenized diffusion coefficients and cross sections were prepared for ADMARC-H calculations. The previous cross sections were generated for the system with no feedback and no control rod placement. Full power calculations were previously performed at ARO. 2) The temperature-dependent continuous energy cross sections previously developed by Tippayakul [2] proved to be sufficient. With the addition of the pseudo material approach and cross section ordering, a more accurate calculation is achieved. 3) The material composition and density of B 4 C used in the control rod elements was a concern raised by previous studies [2], [7], which needed to be addressed Control elements The information about the material composition for the neutron absorbing material B 4 C (Boron Carbide) used in previous studies is not consistent. Each study has used a different set of composition and densities. The known composition of the natural form of B 4 C is given in Table 5-9 [37], [46]. Table 5-9 Theoretical B 4 C number densities Density [g/cc] C 12 (wt%) B 10 (wt%) B 11 (wt%) Previous PSBR work [2], [7] used different combination of these isotopes. The evaluation of core models did not allow using the theoretical material isotopic of the B 4 C hence the variation in data.

130 114 For the aim of creating a tool that predicts control rod placement with feedback for a critical rod position, there is a need to determine the real composition of the neutron absorber in the control rods in order to have accurate calculations. The tool is automated, and data for standard inputs such as control rods are fixed in the program. We know from previous studies that the neutron absorber material composition greatly affects the outcome of the calculations. For this study, calculations of various combinations of the B 4 C were assessed. The following table shows the result of possible combinations used in previous studies and a current combination used in TRIGSIMS-TH. Table 5-10 Control Rod Absorber Combinations Case #1 ARI #2 ARI #3 ARI #4 ARI #5 ARI Combination of B 4 C -K eff CL53 CL54 CL ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Density [g/cm3] SA/SH /RG TR Isotopic Concentration [wt%] 10 B 11 B 12 C % 62.80% 21% % 15.75% 80% % 15.75% 80% % 15.75% 80% % 62.80% 21% #6 ARI R1 critical rod position - K eff

131 115 Table 5-10 presents different isotopic combinations of the B 4 C absorbing material in the control rods. Previous studied have applied a density and isotope weight to work for the system they used. Using the current TRIGSIMS-TH code system to calculate the different cases for ARI position at 300K temperature has delivered the results in Table The theoretical value case #1, shows each of the combinations under-predicted compared with the measured data shown in case #6. The previous used combination (case #2), referred to in the thesis of Tippayakul [2] as a possible combination, has shown an over prediction in CL56, CL54 and CL53. The combination (case #3) was used by Tippayakul [2], where he has used a combination of previously used and a theoretical value, has shown an over prediction of CL56 and CL54. The combination #4 used by Sahin[7], has worked for his MURE system, but for this TRIGSIMS-TH it shows an over prediction in all the core loadings. The TRIGSIMS code is equipped with this combination. The combination #5 indicates closest agreement to the measured data. This combination is applied to TRIGSIMS-TH. Using the control rod methodology described in Section 5.2, the following results show the critical control rod position for nominal power of 1MW for these combinations. Table 5-11 Comparisons of control rod position for B 4 C cases Rod position CL54 CL56 Measured #5 1073(27.25cm) 1089(27.66cm) #3 [2] 27.82cm 27.14cm #4[7] 27.99cm 26.49cm # cm 27.50cm The result in Table 5-11 is for a critical core with control rod search with position placement for 1MW power core design. The results shows that the combination for #5 applied to

132 the TRIGSIMS-TH delivers a more comparable result to the measured data for CL56, whereas for CL54, all the combinations are approximately 2% higher Homogenized cross sections results The cross sections and diffusion coefficients for the ADMARC-H code were previously calculated with the HELIOS code [2]. With the addition of the thermal-hydraulic code for temperature feedback, the previous cross sections were no longer applicable because the crosssection modeling, especially in terms of instantaneous thermal-hydraulic dependencies, was not done properly. As mentioned before, the accuracy of a calculation is significantly dependent on the nuclear data being used. For these cross sections, the fuel elements were burned as a single fuel cell. The following depicts the calculation result representing an 8.5 wt% uranium and a 12 wt% uranium fuel element. For this calculation, reflective boundary conditions were used. Homogenization was done over fuel, clad, water and Zr rod region as indicated in Figure Figure 5-24 Homogenized fuel/clad/water region

133 117 The criticality calculation for a single fuel cell results in a k inf >>1. For this release of the SERPENT code, SERPENT is consistent with criticality calculation in the case where the k=1. When the system is far from critical, the fission neutron population is either over (k<1) or under estimated (k>1). The result is that the neutron spectrum becomes biased, which may affect the energy spectrum and results [36], [51]. Deterministic lattice transport codes use leakage models to overcome this problem. This has been applied also in SERPENT but not in MCNP. Figure A-3 shows a comparison of the burnup of SERPENT compared to MCNP/ORIGEN-S burnup of a single fuel cell. The results show differences in the k eff calculated with this two systems, for each of the burnup steps, which are result from the fact that SERPENT uses a leakage model and MCNP not. Figure 5-25 compares the TRIGSIMS/MCNP to SERPENT input visualizations for the CL4. The core is comprised of 85 fresh 8.5wt% fuel elements. Four control rods with B 4 C as indicated in Table 5-9. Figure 5-25 Illustration of the two input geometries: MCNP and SERPENT The control rods are in position ARI; the core has the same moderator amount surrounding the core model. The results for this comparison are given in the table below. The

134 118 reference #1 is for a rod next to the central thimble on the B-ring, the reference #2 is for a rod in the middle of the core and reference #3 is for a rod on the periphery. Table 5-12 SERPENT vs. MCNP Results for CL4 Area calculated MCNP SERPENT K eff ± ± Fission Neutron Production [neutrons/cm 2 -s] Reference #1 Reference #2 Reference # x x x x x x 10 8 The following results show the comparison of the previously used HELIOS cross section (XS) compared with the newly generated SERPENT cross sections (XS) in the ADMARC-H code. The TRIGSIMS CL53, CL54 and CL56 are used to verify the results. Table 5-13 Comparison with previous cross sections using CL53 in ADMARC-H code CL53 HELIOS XS SERPENT XS Temp 300K 600K 900K 300k 600K 900K ARI MW ARO Total reactivity at (300K)= $ Total reactivity at (300K)=$18.28

135 119 Table 5-14 CL53 at 1MW- comparison using ADMARC-H code with feedback CL53 HELIOS XS SERPENT XS 1 MW Table 5-15 Comparison with previous cross sections using CL54 in ADMARC-H code CL54 HELIOS XS SERPENT XS Temp 300K 600K 900K 300k 600K 900K ARI MW ARO Total reactivity at (300K)= $16.86 Total reactivity at (300K)=$18.45 Table 5-16 CL54 at 1 MW- comparison using ADMARC-H code with feedback CL54 HELIOS XS SERPENT XS 1MW Table 5-17 Comparison with previous cross sections using CL56 in ADMARC-H code CL56 HELIOS XS SERPENT XS Temp 300K 600K 900K 300k 600K 900K ARI MW ARO Total reactivity at (300K)= $15.86 Total reactivity at (300K)=$17.26

136 120 Table 5-18 CL56 at 1MW- comparison using ADMARC-H code with feedback CL56 HELIOS XS SERPENT XS 1MW Table 5-13, Table 5-15 and Table 5-17 show the comparison of previously used cross sections for ADMARC-H generated with the HELIOS code. The cross sections are generated to fit a system. In this case, the TRIGSIMS code did not have feedback and temperature of the core was one temperature. What you will find is that with a homogenous temperature across the core, the k eff will not approach one for a critical core. The comparison of the two sets of cross sections shows a different trend. At ARI, the HELIOS produced cross sections are far off from the measured and expected K eff value. The code system did not have a control rod methodology and a 1 MW critical core was taken as ARO in the system. There are however a systematic difference in the difference in all three cases. The total reactivity difference is approximately 1.57$, for all three cases. Table 5-14, Table 5-16 and Table 5-18 compares the results of a 1 MW rod position for the three core loadings. These results include feedback. Using a heterogeneous temperature distribution at certain control rod positions, the results are in favor of the SERPENT produced cross sections. SERPENT-based results are closer to a K eff of 1 at a 1 MW power level Continuous energy cross section application The temperature-dependent continuous cross sections produced for the TRIGSIMS [2] are found to be adequate for the purpose of TRIGSIMS-TH applications. Smaller intervals of temperature grid of were shown [7] that the refinement to the data improves the accuracy of calculations. The current MCNP generated cross sections, for selected isotopes, are from 300K to 900K in

137 121 steps of 50K intervals. To apply a refinement for higher accuracy, the implementation of pseudo material approach was applied to the cross sections between temperature intervals for the uranium isotopes. The application of pseudo material approach is a way of manipulating cross section data in the case where the intervals are not refined enough. Figure 5-26 shows the difference of this contribution to the calculation Pseudo compared to non-pseudo K eff No Pseudo with Pseudo k eff = #Iteration Figure 5-26 Pseudo material difference (K eff results 7 ) influence. The results show that there is a minor influence, but does not confirm a positive 7 K eff results were calculated to approximately 50pcm (1σ)

138 122 The way of using the cross section can influence the outcome of the calculation. The TRIGSIMS code reads the cross section file xsdir.file stored in the MCNP_DATA folder for MCNP5. The cross sections previously made by Tippayakul [2], with smaller temperature intervals is also loaded into this file. The code reads the cross sections from bottom to top. Therefore is it important to have your choice of cross section table located at the bottom of the list. This applies to the thermal neutron scattering data as well. The choice for cross section search should be to go through the list of "important" isotopes (psbr900) to make the choice there before the code moves over to ENDF7, etc. The tolerance is given as 25K for the temperature choice. An addition to the search of cross sections method is that the code now also makes a choice between the ENDF7 selections for choices not covered by the PSBR cross sections. The code will search and depending on the temperature and it is closest to the choice. The previous cross section selection method was on a loop of order of first occurrence. This was never a problem because the feedback was not modeled and the code only had a few choices Moderator for the core design The TRIGSIMS-TH code system writes the MCNP input. Because it is automated, certain entries are fixed. The original core loadings have a certain size and usually only filled with the usual elements, i.e., the fuel, the control rods and the dry irradiation tubes. CL54 is a core loading that has a difference in geometry. With fewer elements, the core is not shaped in the usual hexagonal shape. TRIGSIMS however apply a moderator input around the core as for the usual method. This result in a typical core loading as the CL56, with its hexagonal shape. The current method of fuel to moderator cells in TRIGSIMS/MCNP is depicted in the following Figure 5-27, Figure 5-28 Figure 5-29 and Figure 4-13 of the core loadings CL53, CL53+graphite, CL54, CL56 respectively. A maximum radius is determined based on the longest

139 123 distance of the MCNP entry. However, this was only done for a positive entry. It was assumed that the core is completely symmetrical, top half entry to be the same as bottom half; hence, the search is in one direction. Also with the addition of a graphite element around the outside, the code would take as part of the core entry. The result would be that different cores would be given a moderator amount based on the maximum radius, which over estimate smaller cores. Maximum radius Figure 5-27 CL53 no-graphite diagram Max radius Figure 5-28 CL graphite elements These two cores have the same amount of fuel, but the moderator is different.

140 124 Maximum radius Figure 5-29 CL54 diagram For the CL54 and CL56 (see Figure 4-13), there is a difference of 5 rods, yet the water surrounding CL54 is more than that of CL56. Table 5-19 shows the results of the TRIGSIMS-TH, comparing the adjustment that was made to the maximum radius value. The code will assess whether the entries are fuel or non-fuel elements and will consider only the fuel elements in the search for maximum radius. Once the maximum radius is found, the value is further adjusted to reduce the radius. The fractional part of the number of fuel elements to the fully loaded diagram (110 elements) is applied. This application has shown an improvement on the results. Table 5-19 The effects of the adjustment of the water surrounding the core. Core loading TRIGSIMS/MCNP Adjusted TRIGSIMS/MCNP difference [$] CL53G ± ± ± 014 CL53G+10graphite ± ± ± 0.14 CL ± ± ± 0.16 CL ± ± ± 0.13

141 TRIGSIMS-TH application to CTF The thermal hydraulic feedback with CTF was implemented with the following criteria in mind: a) the core layout had to allow for fuel and non-fuel elements; b) the ability to expand the core by adding elements to the outer core layout; c) the addition of the D 2 O tank in the input had to be inserted as a restriction to the side of the core; d) CTF input had to be developed to accommodate different modes for running CTF, i.e., the expansion of the deck will write out the core elements with an axial length of 35.66in instead of 25.66in, that certain cards are added, also the addition of the D 2 O, which changes the input at various places. Table 5-20 shows the MCNP results for estimating reactivity calculations for CL56 with D 2 O tank. The reactivity loss is an estimate from calculated results using control rod search method, and the worth remaining is the addition of reactivity loss and calculated excess reactivity. Table 5-20 Estimation of reactivity for CL56 +D 2 0 tank CL56+ D 2 O Calculated Measured Reactivity [$] Reactivity [$] Worth removed ± Reactivity loss 2.64 ± Worth remaining ± TOTAL ±

142 126 The results for ARI (worth removed) calculation for the CL56+ D 2 O tank is approximately 0.70$ lower than the measured results. Figure 5-30 shows the comparison of CL56 with and without the D 2 O tank attached to its core. This option in the input adds a standard size rectangular tank in the MCNP geometry that in this design comes in close proximity to the fuel elements indicated as 1 to 8 in Figure The thermal hydraulics for the core loading had to be expanded to create the restriction in the flow due to the D 2 O in path of cross flow. This addition also forms part of the iterative scheme to find the control rod search for a critical reactor.

143 Temperature[ oc] Ave Power Normalised ave power/rod D 2 O nod 2 O Fuel elements 600 Temperature comparison with D2O and without 500 D 2 O nod 2 O Fuel + non-fuel elements Figure 5-30 Comparison with and without D 2 O tank to the CL56 design at 1 MW power

144 %Difference 128 The results from this comparison confirm the expected flow restriction, with the result that the average power in the Elements 1 to 8 has been increased by approximately 11-15% due to the flow restriction. This power increase is due to the reflection of leaked neutrons from the D 2 O.The difference in the power however gets smaller toward the center of the core. The fuel temperature at these elements 1 to 8 is also higher with a maximum increase of 8%. To ensure a 1 MW power for the CL56 + D 2 O, the positions of control rods were adjusted as expected in the iteration scheme and the rod position settled at approximately 25.9cm (there is no data available for control rod position at a 1 MW power for CL56+ D 2 O tank). The water temperature surrounding these elements is also higher by approximately 5 % (17 C) compared to the CL56 with no D 2 O Ave Power comparison of CL56 with and without the D 2 O tank Fuel elements Figure 5-31 Comparison of average power for the D 2 O tank calculation Figure 5-31shows the difference (D 2 O - no-d 2 O) in power distribution is for a CL56 with a D 2 O tank with and without a tank. It shows that the biggest difference is within the first three

145 rows of the core. This calculation shows a positive difference on the front core elements with a negative difference in the other core elements seen here in the graph Thermal hydraulics as a standalone tool TRIGSIMS-TH with the addition of the CTF code is able to run full core thermal hydraulic calculations of the PSBR reactor core. As part of the coupling methodology to both MCNP and ADMARC-H, a shortened version of the input is used. Essentially, for the use as thermal hydraulic feedback, the need to include flow above and below the grids is unnecessary. In addition, to minimize the time for computation, a short version of the input is introduced. As a "standalone" method, the input for the CTF code is changed. Figure 5-32 depicts the flow channel changes for this input. Top grid A B Bottom grid Figure 5-32 CTF input changes for "standalone" calculations

146 130 Diagram-A represents the flow pattern for the CTF input used in the coupling methodologies of TRIGSIMS-TH code. This flow region consists of nine nodes covering an axial length of inches, representing the flow between the top and bottom grid plates only. The boundary conditions are set at the beginning and end of this flow volume to create the needed pressure difference for the core calculation. CTF has five nodes to represent the active fuel region, which corresponds to the five nodes used in MCNP. With this, further averaging is not needed and this result in minimizing the uncertainty. Diagram B represents the extension of the flow for the "standalone" CTF method. With the extended input, the CTF code is now a thermal hydraulic modeling tool. The flow extends to beyond the top and bottom grid plates. The bottom grid is a solid structure with small holes not big enough to allow much flow to pass. Both the top and bottom grid plates create a pressure difference (core ΔP) across the core axial fuel length. The geometry variation across the vertical length of the flow creates the variation in the momentum areas, continuity areas and wetted perimeters. What these changes mean for our flow pattern, is that we not only have a flow that moves vertically but also across the gaps of the channels (cross flow). The model in Diagram B uses much smaller calculation cells (nodes). This input has seventy-one nodes that starts from the bottom below the grid and extends to the top above the top grid plate. The axial length in this model is inches (0.92m) which includes the fuel region of 15 inches. To create a realistic (physical) scenario for this input, the initial flow rate is set very close to zero (0.0001). The initial channel temperature is set at 73 F (23 C). Local channel pressure losses are used within the grid domain. The pressure at the bottom grid is bigger than at the top due to the almost complete flow restriction in the vertical channel at this position. Figure 5-33 shows the results of the thermal hydraulic analysis of a 1 MW thermal power for CL56. TRIGSIMS-TH generates the CTF input, after the MCNP neutronics calculation has

147 Axial length of the flow channel [in] been performed. TRIGSIMS-TH/MCNP provides the axial power distribution tables as well as the calculated radial power distribution for full core calculation top grid Active fuel region bottom grid Velocity [m/s] centre Channels Figure 5-33 Thermal hydraulics results: velocity of channels 112 to 131 for CL56 The results in Figure 5-33 represent the flow channels that run from left to right through the center of the core. These channels are indicated in Figure 5-1. It also shows the axial velocity

148 132 of the coolant in the indicated channels. The inlet channel starts at the bottom (1) and ends on top (35.66 in). Positive flow is upward. The result reflects the inlet having zero flow (0 velocities) at node 1 and shows both negative and positive velocity results. Channel 131, is a channel on the far right side (outer side) of the core. The result for this channel shows a negative velocity of the fluid in part of the active region. This shows the flow is downward below 23-inch mark and upward above this. The channel 124 has the highest upward velocity among presented results. This channel is between three of the hottest fuel elements in the core resulting in a channel with higher temperature, creating a lower density at the upper region, resulting in a faster upward flow. The maximum velocity in the active fuel region is 0.128m/s. This value corresponds to the calculated result with ANSYS code [5]. Figure 5-33 also shows the results above the top grid plate with both the center channel and the hottest channel reaching upward velocity of 0.17 m/s. The figure shows the restriction in the flow at the top and bottom grid plates. The area above the bottom grid and the area below the top grid has a bigger flow area. In these regions, an almost stagnant or steady equivalent speed is achieved in all the channels, which is what is expected in this region, as the nominal flow area is almost 3 times that of the channel in-between the fuel. The high speed above the top grid plate is also as expected. Based on Bernoulli's principle, increase in speed of fluid will occur simultaneously with decrease in pressure or a decrease in the fluid s potential energy. Figure 5-34 shows the results of analysis obtained for full core temperature distribution in and around the core.

149 Axial length of the flow channe [in] Top grid Active fuel region 10 5 Bottom grid Temperature of the fluid [ C] channels Figure 5-34 Thermal Hydraulic results: Temperature distribution for CL56

150 134 The CTF calculation results indicated in the Figure 5-34 show that the temperature distribution in the core for a 1MWth reactor power operation under steady state condition decrease with increase of radius. The hotter channels are around the center of the core. This is because of the loading pattern where the high power density elements are inserted around the central thimble in the B, C and D rings. The power peaks around this region in the core, therefore the fuel is hotter, resulting in hotter channels. Channel 130, shown in Figure 5-34, is a cooler channel. The maximum temperature for this outside channel is around C. The hottest channel in the results is either channel 124 or channel 122 depending on where the measurement is taken along the axial length. Channel 122 is on the centre and we have shown in the previous figure that the velocity in center is lower than the velocity in channel 124. The channel 122 is bigger channel and get cross flow from all directions. Hence, the channel fluid is hotter at the top half than the bottom half compared with channel 124. Hence, for the channel 122, it appears hotter for part of the channel, but it does not contain the hottest fuel element. One of the main goals of thermal hydraulic design for safety analysis is to ensure that the thermal limitation of the core thermal hydraulics is not exceeded. The fuel rod having the maximum power output is the "hot" fuel rod. The "hot" channel in the core is usually is the coolant channel in which the core heat flux and enthalpy rise is a maximum. Usually this is analyzed by increasing the core conditions to reach the operational limitations. Hence, to establish the "hot "channel, "hot" rod further analysis needs to be done. These analyses can be done with the new TRIGSIMS-TH. The results in Figure 5 33 show that in the maximum fluid temperature in the active fuel region of the channel is approximately 60 C for the channels around the center of the core. Ücar [5] shows the measured temperature in this location (for CL53H) to be around 59 C. From the results obtained from the CTF output file, under steady state conditions, the "hot" channel for this core loading is the channel between rods I-17 (highest heat flux of 1.52 x

151 b/h-ft 2 ), rod 220 (heat flux of 1.20 x 10 5 b/h-ft 2 ) and rod 226 ((heat flux of 1.39 x 10 5 b/h-ft 2 ). The highest channel temperature is approximately 60 C. A few channels around the center have high enthalpies (108 btu/lbm). This is the channel indicated as channel 125. Table 5-21 gives details from the full core calculations using the extended core model to analyze the hotter fuel elements. Table 5-21 Analysis of the hotter elements in CL56 Parameter Rods 46 (I-17) 47 (210) 56 (I-2) 57 (226) Fuel Temp-Mid[ C] Fuel Surf Temp (max) [ C] Measured average Temperature for CL56 at 1MW is 518 C, hottest Temperature is 527 C The instrumental rod I-17 was used for measurements. The results from calculations were taken from node 39 (which is at in axial length from the bottom of an axial length of 35.66in). The data was taken off center, at approximately 0.22 in radius from the center of the fuel rod. The CTF input allows for eight radial temperature distributions, which includes the center Zr-rod, five fuel radial sections a gap region and an outer clad region [3]. This temperature results can be retrieved from the output file called T_hrod.out. The PSBR core is cooled with natural convection. Because of the complexities of this type of flow, the core flow dynamics has been a topic of interest to analyze [6], [16], [18], [39]. The following graph displays the core fluid flow for the 1 MW power of CL56.

152 Axial nodes Mass flow rate [oz/sec] Gaps Figure 5-35 Results of the mass flow rate across the gaps (cross flow) Centre Figure 5-36 Illustration of the cross flow results

153 137 The Figure 5-35 shows the result of the cross flow across the gaps bordering the channels shown in Figure The Figure 5-36 is an illustration (interpretation) of this flow pattern s results shown in Figure The vertical channel velocity results give the inner core channel an upward flow rate and the outer channels have part flow downward. The cross flow results show the inner channels flow transverse inward in the direction of the center. The end channels have the bottom flow inward and the middle to upper part of the flow pattern in the direction of the outside of the core. Similar to the flow from bottom to the top, the driving force of the flow is the change in pressure from channel-i to channel-j horizontally; enthalpy change is due to change in temperature and the upward-flow, which creates a pressure drop at the bottom of the core. A simplification illustration of this explanation is shown in Figure Upward flow due to increase of temp and ΔP Inflow of colder water creates a drop in pressure and enthalpy, creates an in-flow Figure 5-37 Illustration of the flow around the channel

154 Summary of results The further development of TRIGSIMS to TRIGSIMS-TH has provided the following results: A) The addition of CTF to the TRIGSIMS code was applied in a coupling methodology to both the MCNP and ADMARC-H code. This was done successfully and the Figure 5-2, Figure 5-3 and Figure 5-4 show the temperature distributions of this coupling methodology for the MCNP/CTF calculations. The results are as expected and compare well with measured data, which validates the methodology. Table 5-1 gives the desired values for this calculation at 1 MW power distribution. With feedback, the calculation gives the desired k eff value of one and the control rod positions compare well with measured data. The ADMARC-H calculation is used as an acceleration method. Comparing the k eff value at 1MW, we have a good agreement. For ARI our values are close to measured data. B) A control rod search method was added into the TRIGSIMS-TH code. The PSBR is operated with partially inserted control rods and has full power (1 MW) at approximately 12''-13'' rod insertion. A method to find the control rod position at a required condition was needed for a new core loading. Previously the TRIGSIMS code used ARO as a default position. The results of this addition are shown in Figure 5-5, Figure 5-6, Figure 5-7 and Figure 5-8. What these results have shown is that this iterative procedure will give you a height close to the measured control rod position. These results show a very good comparison to the measured results, verifying the methodology of the control rod search algorithm. This method was implemented successfully. C) An important new analysis feature added to the TRIGSIMS-TH code is the ability to have a standalone thermal hydraulics module with an expanded core geometry. That is, an input larger than the geometry used for the condensed CTF/MCNP coupled input deck that will allow the user to use CTF as an analysis tool. With a request given in the input, TRIGSIMS-TH will run

155 139 a MCNP calculation, update and write an expanded geometry CTF input deck, and run the application. This will provide the user with the tool to perform various analyses. The section 5.5 in this chapter describes such an analysis for the CL56. TRIGSIMS-TH also has an option to add to the input a D 2 O tank model. This feature was extended to the CTF model as well. Thus if the user wants to model the core loading with the D 2 O Tank in place, a request is made in the input of TRIGSIMS-TH and both the MCNP and the CTF will be loaded with the necessary geometry changes to do coupled and standalone calculations with the D 2 O tank geometry. The results for these features in TRIGSIMS-TH have delivered results well comparable to measured data. D) In addition to these main developments of the TRIGSIMS-TH code, various other upgrades and changes was done to make this code system well developed for the feedback mechanism, for the design changes and overall to make this code a core design and analysis tool. Overall, all the changes gave positive results and demonstrated successful implementation. The application of the TRIGSIMS-TH as an analysis and design tool is presented in the next chapter.

156 140 Chapter 6 TRIGSIMS-TH Core Design Application This chapter describes the use of the TRIGSIMS-TH code for different studies. The following four scenarios were calculated /simulated. 1. CL56 with changes on the periphery of the core to include graphite elements and an expansion of the core 2. CL54, inserting the six fresh fuel elements currently in this core loading on a different location, not in the center as it is usually done. This is performed to demonstrate the ability of the code to design new core loading and extracting data, to define the core. 3. CL54, inserting the six fresh 30/20 LEU fuel around the central thimble. 4. CL56 is analyzed using the standalone thermal hydraulic expanded geometry capability, to show the effect of the D 2 O tank addition in the core loading as well as the thermal hydraulic analysis ability. 6.1 Core loading design scenario 1 The following application shows a comparison of two cores, CL56 and CL56_adjusted. CL56_adjusted uses the core elements of CL56, then rearranging the outer ring of elements and adding, 8 graphite elements to this core loading. This application shows the TRIGSIMS-TH versatility in the ability to expand the core. The expansion of the core includes a ring of elements where these elements include fuel and non-fuel elements. The core expansion is applicable to both MCNP and CTF.

157 Addition of graphite elements In the preceding chapter, the addition of graphite elements has shown to make a difference especially on the flux distribution in the vicinity where it was placed. A 20 reactivity insertion for approximately 10 elements is what is expected. TRIGSIMS-TH code allows the user to place these elements at any position in the core. In the next example, these elements were used in a new core layout design A new core layout The following illustration compares the two cores for analysis. Fuel Figure 6-1 CL56 and CL56- adjusted Graphite The Figure 6-1 is the CL56 and CL56_adjusted which is CL56 but with a rearanging of elements in the G-ring as well as the addition of 8 graphite elements. It is a larger core with 118

158 Control rod position[cm] Keff 142 elements (fuel and non-fueled). The calculation is a criticality calculation of 1 MW power, which includes the thermal hydraulic feedback at every adjustemnt of control rod. The results obtained by comparing CL56 and CL56_adjusted are shown in Figure Keff and Control rod position comparison adjusted 1mw cl # Iteration adjusted measured cl # Iteration Figure 6-2 Comparison of the CL56 and CL56_adjusted The results between the two core loadings show an insignificant difference in the control rod placement of a 1 MW core power for this comparison. The core contains the same fuel elements and the addition of the graphite elements.

159 Average power distribution Average power distribution 143 1MW avearge power distribution 1.5 A x 5 1MW avearge power distribution y B x 5 y Figure 6-3 Comparison of CL56 and CL56-adjusted average power distributions

160 144 Figure 6-3 indicates that the core loadings show minor but yet visible difference in power distributions. A and B represent the results for average power distribution of a 1 MW critical core power, where A is the adjusted core loading CL56, and B is the CL56. The peak power is at the same position, though with A the inner power is more spread because of the range of elemental distribution being further, compared with B where the inner core elements have higher peak values. The following results in Figures 6-4 and 6-5 show the comparison of thermal flux across the cores.

161 145 Figure 6-4 CL56_adjusted- flux [neutrons/cm 2 -s] across the core Figure 6-5 CL56-flux [neutrons/cm 2 -s] across the core

162 Flux Flux 146 The changes are minor and the affected regions are on the sides where the changes occurred, i.e., on the edges where the thermalization of the neutrons is less because the core is wider and graphite elements are inserted. The following graphs will show that those thermal neutrons are creating higher number of neutrons absorbed in the core elements, situated on the edge of the core. 10 x Comparison of flux distribution in the first and second row CL56-Adjusted CL # rods x CL56-Adjusted CL # rods Figure 6-6 Flux [neutrons/cm 2 -s] results from reshuffling of core elements Using the exact same core (CL56), it is not expected to observe huge differences. The calculation result in Figure 6-6 shows an increase in flux values of approximately 11% around the edge where the DT1 and DT2, dry tubes, are situated. Thus, the developments implemented to the TRIGSIMS-TH code made it a useful tool to measure the degree of change in core design when performing analyses.

163 Core loading design scenario 2 The customary operational approach of loading the PSBR reactor is to insert the higher power density fuel around the central thimble (B-ring for 8.5wt% and C,D -ring for 12 wt% fuel). Hence, new fuel will initially be inserted into around the central thimble. CL54 has six fresh 8.5 wt% fuel elements in the B-ring. For this analysis, the six fresh elements will be inserted into a position closer to the edge of the core. The following diagrams illustrate the position changes of the two core layouts. The CL54 with changes to the fresh fuel elements is referred to as CL54_shuffled. Figure 6-7 Illustration of CL54 and CL54_shuffled Figure 6-7 shows CL54 and CL54_shuffled, which contains the same elements except for the interchange of elements indicated in the positions shown in yellow (6 fresh 8.5 wt%). Figure 6-8 shows the results of criticality calculation at 1 MW power using the TRIGSIMS-TH code.

164 MW core power with feedack 1 k eff Average fuel Temperature [ o C] Control rod position [cm] # iterations CL54-shuf k eff CL # iterations CL54-SHUF average CL54 Measured # iterations CL54-shuf average temp CL54 Figure 6-8 Comparison of CL54 vs CL54-shuffled The comparison of the changes indicated in Figure 6-8 shows a clear difference in all three parameters calculated. The k eff value took longer to converge (17 iterations compared with

165 ). The control rod position is much higher for the 1MW power core loadings for CL54_ shuffled (31.1 cm) as compared with cm measured (27.9 cm calculated) for CL54. In addition, these changes affected the temperature of the core. The CL54_shuffled is calculated at average of 517 C as compared with 502 C calculated (507 C measured) for CL54. The following results show the difference in power distribution for these two core loadings Central Thimble Fuel elements Figure 6-9 Difference in element power between CL54_shuffled vs. CL54 Since both cores are for a 1 MW power, there is a redistribution in power. The six positive peaks indicated in Figure 6-9 (values above 10% difference), are the fresh fuel, which replaced partially burned fuel elements. The reactivity estimation of the two cores is shown in Table 6-1.

166 150 Table 6-1 estimating CL54 to CL54_shuffled reactivity CL54_Shuffled [$] CL54 [$] Measured [$] ARI-worth removed 1MW Power Defect Reactivity loss[$] ARO from 1MW Excess reactivity[$] (0.944 ± ) 8.47 ( ± ) 7.59 ( 0.952) ± ± ( ± ) 1.17 ( ± ) (1.015 ) = = Total reactivity[$] ± ± Figure 6-10 shows the thermal hydraulic comparison of the two core loadings. Figure 6-10 Percent Difference in Temperature for CL54_shuff and CL54

167 151 If we compare the calculated results from Table 6-1 and Figure 6-10 the following observations could be made. The two core loadings CL54 and CL54_shuffled contain the same elements. CL54_shuffled has the six fresh 8.5wt% fuel in a different position (not in the center as in CL54). The difference of this change has delivered an overall higher reactivity of approximately 1.2$. The reactivity of TRIGA reactors are mainly due to the temperature changes of the fuel and the moderator. The Figure 6-10 shows a temperature increase in most elements in the core. The results shows, up to 8% higher fuel temperature for the fresher fuel and an overall 2-4% increase of temperature for the C&D-ring 12 wt% fuel elements. Temperature-induced reactivity is the highest contributor of reactivity change in TRIGA reactors. The Figure 6-9 indicated a 10-17% increase in power over the elements of higher density power (six fresh fuel elements). The estimated control rod reactivity loss value is 1.5$ higher than the CL54 value. What this means for this core configuration is: The reactivity loss from ARI to 1MW power is higher because a bigger span of core elements has higher temperatures, resulting in a higher negative temperature coefficient. The power distribution in Figure 6-9, shows there is a decrease in power around the center core elements, hence, the flux, which normally peaks around the center (as in the CL54 case), has a lower peak, and the flux toward the area where the fresh fuel is inserted is higher. ARI reactivity difference is 0.79$. The core CL54_shuffled is more reactive, than CL54.

168 Core design scenario 3 This section outlines the findings of the addition of a new 30/20 (30 weight percent uranium. 20% enriched) LEU (Low enriched) TRIGA fuel to the already mixed core loading. For these findings there is no measured data as this fuel has not yet been loaded into the core. To study the characteristics of this new fuel is exactly why the use of this TRIGSIMS-TH tool is necessity Description of the fuel The 30/20 LEU TRIGA fuel, have the same geometrical specifications as the standard TRIGA fuel design but differ in material composition as shown in Table 6-2. Table 6-2 Fuel comparisons TYPE 30/20 LEU 8.5wt% & 12wt% Weight % Erbium U-235 [g/element] & Enrichment < 20% < 20% Lifetime [MWd] (8.5wt%) All these three fuel types are less than 20% enriched in 235 U. Table 6-2 shows that there are many differences and quite few similarities. There is no erbium in the standard TRIGA fuel elements. The 30/20 LEU fuel contains about 0.9 wt% of the burnable poison erbium, which also enhances the prompt negative temperature coefficient. The erbium mixed in with the fuel does

169 153 not change the fuels characteristics. The effect of this erbium to the fuel is that the fuel can have a higher enrichment of uranium, like in the 30/20 LEU [54]. Measurements of the thermal conductivity for these fuels were found to be the same, and that the thermal conductivity is independent of the uranium content of the fuel. The density of the 30/20 LEU fuel was calculated using the uranium mass content of g [55] Analysis This section is an analysis of CL54 with the addition of six 30/20 LEU fuel elements instead of the six 8.5 wt% fresh fuel. The loading pattern is as usual and the heavy uranium content fuel is positioned around the center thimble. Using the control rod search methodology to find the critical core at 1 MW power gives the following results. Figure 6-11 gives the k eff convergence with its corresponding control rod position convergence and average fuel temperature convergence results. This result is purely for analysis purposes and does not have a validating information to support the findings. This example of analysis is for the purpose to shows the versatility of the control rod method and the results that can be calculated using the TRIGSIMS-TH code systems.

170 154 Average fuel Temperature [ Control rod position [cm] MW core power with feedack 1 K eff calculated k eff = # iterations calculated average estimated # iterations o C] calculated average estimated # iterations Figure 6-11 CL /20 LEU convergence results

171 155 Figure 6-11 gives the results and show a convergence of the iterative process at about 18 iterations. The convergence shows a k eff of approximately one at a control rod position of 24 cm and an average 30/20 LEU fuel temperature of 594 C. For this core, the highest fuel temperature is in the 30 wt% fuel elements, which is what is expected. The following results show the temperature distribution as predicted by CTF for the middle section of this core loading. Figure 6-12 shows the full core fuel average temperature distribution for a critical core CL /20 LEU fuel elements. Figure 6-12 Temperature distribution of the 30/20 LEU fuel

172 Core design scenario 4: Analysis of the core with a D 2 O tank The CL56 is analyzed with and without D 2 O tank. This has been an option with the TRIGSIMS code. The user enters the flag for the addition of the D 2 O tank to the MCNP input. TRIGSIMS writes this addition in the MCNP input, i.e., the geometry input is changed and the input CL56 is illustrated in Figure If the flag is set for D 2 O tank, the TRIGSIMS-TH will write a CTF input, adding in the needed additions for flow restriction as a result of the geometry change. An unheated conductor is added to the CTF core model, representing the D 2 O tank. The geometry of the adjacent channels is also changed. As part of the MCNP/CTF coupled calculation in the TRIGSIMS-TH code, the input of this CTF, now containing the unheated conductor, is also done with shortened channels with fewer nodes to speed up the calculation. Hence, this calculation is also possible with the iterative coupling and control rod positioning methodology A comparison with and without D 2 O tank tank. Table 6-3 summarizes the findings of comparison of core analysis with and without D 2 O Table 6-3 CL56 with and without D 2 O tank With drum D 2 O With crescent D 2 O Without D 2 O K eff tank tank tank ARI ± ± ± MW ± ± ± Control rod pos (1MW) 25.8 cm 23.8 cm 27.5 cm

173 157 The results shown in Table 6-3 indicate a difference in reactivity of 0.98$ at ARI( for the drum). The measured reactivity difference is approximately 0.42$. Thus, there is a variance of approximately 56 Since the TRIGSIMS-TH gives us a more accurate account of the temperature distribution as well as the power distribution and flux distribution, the studies for the modification of the D 2 O tank [5] could be done with more accuracy. The thermal hydraulic analysis results for the core with and without D 2 O tank addition is given in the next subsection Thermal Hydraulics comparison with D 2 O tank The following analysis is a typical illustration of how to use the standalone method for CTF application. In this example, the CTF parameters are examined for 3 cases, i.e., without D 2 O tank, with current drum shape D 2 O tank and with a crescent shaped tank. Figure 6-13 shows the MCNP representation of these cases. Figure 6-13 Three cases to express the use of the CTF standalone model It was shown in the previous chapter, Figure 5-30, that the addition of the D 2 O tank creates higher power around the first few rows of fuel elements (directly adjacent to the tank).

174 %Difference compared with no-tank 158 This is an effect of the energy spectrum shift due to the D 2 O's effective moderation properties and the reflection of the neutrons that would have been lost. Figure 6-14 shows the MCNP results of the power distribution as a comparison of D 2 O tanks (drum and crescent), compared with no- D 2 O tank Drum compare to crescent shape tank: Difference in Power distribution Elements drum crescent Figure 6-14 The % difference in power distribution for the D 2 O tank shapes compared no tank The results shows the new proposed crescent shape will result in a power with an approximate maximum of 16% higher, compared with drum shape, around the front of the reactor where the tank is situated. This increased power resulted in the temperature increase for the elements adjacent to the tank. The power profiles used for the CTF calculation were prepared through the TRIGSIMS-TH criticality calculation indicated as mode 1. After attaining the control rod position with the temperature distribution for that 1MW power, the TRIGSIMS-TH is used with mode 2, flagging the extended CTF model.

175 159 The following result uses the CTF "stand-alone" application, and expanded option of the core thermal hydraulic input, to analyze the flow and temperature for the various cases. The comparison shown in Table 6-4 includes the following: a) No D 2 O tank; b) A drum shaped tank, as it is in the current TRIGSIMS (drum1); c) A crescent shape as suggested in the thesis of Ücar [5]. The rods used for this analysis is the rod 4, directly adjacent to the tanks, the rod 13, which is next to rod 4, but toward the center, and rod 46 which is the I-17 instrumental rod, which is close to the center (see Figures 3-2 & 5-1).The channels used in this examples are the channels adjacent to these rods. Table 6-4 gives the results for max fuel temperature in channel, the maximum coolant temperature in the channel adjacent to the indicated rods and max channel velocity. Table 6-4 D 2 O tank comparisons D 2 O Tank Configuration Rod Fuel temp [ C] Max-Channel temp [ C] Max-Velocity[m/s] none Drum crescent & none Drum crescent

176 160 none Drum (I-17) crescent The cross flows for no-d 2 O tank to the CL56 are shown in Figure The cross flows for restriction of the flows due to the Drum shape tank is depicted in the following diagram Figure Figure 6-15 Illustration of the cross flow data for the channels adjacent to D 2 O to the center of the core The findings for this analysis are: 1) The D 2 O tank shape has a neutronic effect. It creates a higher localized power in the fuel elements. The drum shape shows a fuel temperature for rod 4 of 11% higher than no-d 2 O results. The crescent shape shows a higher fuel temperature of 6%. The flow at the adjacent channel for the crescent shape is different compared with the drum shape. A small velocity in the

177 161 centre of the channel is calculated due to both upward top and downward bottom flow. The rods 13 and 46 for the crescent shape have higher temperatures compared with drum and no drum. 2) The heating of the fluid channel is a result of the fuel temperature (with conduction from the clad to the water), the cross flow between adjacent channels because of the enthalpy differences, and pressure differences and convection. 3) The cross flow illustration is very similar to that of the core without D 2 O. The bottom of the fuel region has an inward flow while the top shows an outward flow. For the crescent shape around the edge (at rod#4) of the core adjacent to the tank, the flow is only inward. 4) The crescent shape produces a higher fluid temperature in the centre and a velocity twice as high compared with the drum shape. The fuel temperature is raised to ~19%. Hence, the crescent shape will affect both the flow and the neutronics of the core reactivity. This result was presented as an illustration of the use of the CTF tool as a standalone analysis tool.

178 162 Chapter 7 Conclusion and future work 7.1 Conclusion The PhD contributions of this work are for the further developments of the TRIGSIMS fuel management and analysis tool. These developments include: 1) Establishing a multi-physics coupling methodology, which provide the needed thermal hydraulic feedback to the core analysis tool TRIGSIMS-TH. The addition of the best estimate, advance sub-channel analysis code, CTF, is now automated in TRIGSIMS-TH to provide the temperature predictions for the MCNP criticality calculations. TRIGSIMS-TH gives the MCNP input a heterogeneous temperature distribution. The coupling was also extended to the ADMARC-H code, which serves as an acceleration method for the MCNP calculation. The results from the coupling methodology were compared with measured data from various coreloadings. The findings were that the coupling of the CTF to MCNP was done successfully. The ADMARC-H coupling with CTF though successfully done, the results could be improved. 2) Implementation of a critical control rod position search methodology was a needed addition to the TRIGSIMS-TH code. Partially inserted control rods for a critical reactor (at various power levels) can now be set and predicted with this method. The methodology is based on the perturbation theory and computationally applied using a quasi-fixed iteration scheme. This idea is unique and novel, and could only be attained with a thermal hydraulic feedback method and the TRIGSIMS-TH code system. The results was compared with measured data and found to be implemented successfully. 3) Development of the ADMARC-H homogenized cross section library, which models thermal-hydraulic feedback instantaneous dependencies. The diffusion coefficient and crosssection was developed using SERPENT, a Monte Carlo code. The results of the ADMARC-H,

179 163 diffusion code, with the newly generated cross sections delivered better results compared with previous cross sections; however, there is room for improvements. 4) The addition of CTF to the TRIGSIMS-TH code has broadened the functionality of this code system. TRIGSIMS-TH is now a design tool that could be used for safety analysis. Formulation of a standalone model for CTF in TRIGSIMS-TH code involves a methodology that includes both the neutronics and thermal hydraulics. In an automated system, the code is able to perform the feedback mechanism by passing the needed neutronic parameters to the CTF code. The CTF input for the standalone method will be extended (smaller and more nodes including area above the grids) with information that can be calculated. The addition of a D 2 O tank as part of the MCNP and now the CTF input could be added not only in this standalone model but also in criticality calculation with iterations. This automated system was implemented successfully. 5) Various functional upgrades were made to enhance the codes capability or to correct parameters for calculations. This includes; the addition of graphite elements as an option in the code input for MCNP. A reassessment of the B 4 C used in the calculations. The application of pseudo material approach and a reformulation to continuous energy cross section search mechanism for the MCNP input. The moderator surrounding the core is adjusted for the number of fuel elements. All these have shown an improvement to the previous results. The results from improved calculations were validated against measured data form core loadings CL65, CL54, CL53. The results were in a good agreement with the measured data at most applications applied, though various shortcomings was identified. The conclusion of the part of the work i.e., the multi-physics coupling was done successfully. The implementation of the control rod search method has delivered with successful results. The TRIGSIMS-TH code system with this control rod search method and thermal hydraulic feedback is now a complete design tool for future core loadings. The method was used in analyses to show how the code can be used as well as to show the versatility and applicability of this development. The thermal hydraulic code

180 164 CTF, that is now part of TRIGSIMS-TH code system, makes this a safety analysis tool. With this development, various design limitations and safety and control issues can be analyzed. The final product of this PhD work is a code system that works effectively, and is able to analyze, design, burn and manage the PSBR reactor core. 7.2 Proposal for future work Modify the D 2 O input With the aim to modify the D 2 O tank, the MCNP and CTF inputs for tank shape will have to be adjusted to fit the shape of the proposed tank. The current shape of the tank is rectangular. For a horseshoe, or crescent, as it was proposed [5], the modification could also be done with minimal code correction. Using the code as it is, for analysis on the shapes can also be done with just a few CTF input changes. CTF is set up to give a basic core input. This input can be incorporated with or without the D 2 O tank. CTF is also set up as a standalone thermal hydraulics analysis tool with extended flow channels that goes above and below the grid plates. This addition is very useful for analysis of the flow with restriction such as a modified D 2 O tank that encloses the core Transient analysis with CTF/ADMARC-H The TRIGSIMS and the TRIGSIMS-TH codes are currently set to perform steady state and depletion calculations. With the addition of CTF, the thermal hydraulic module, the TRIGSIMS-TH code is now able to perform transient calculations. Both the codes CTF and ADMARC-H are equipped to do transient calculation. Further studies and modifications to the

181 165 ADMARC-H code is needed to make this possible. The control rod movement modeling and the application using control rod method requires the development of rod cusping methodology[53]. This deficiency was seen in the results for ADMARC-H feedback mechanism Using the TRIGSIMS-TH to investigate the thermal hydraulic properties of the fuel The results show the need to reevaluate the material properties of the CTF fuel rod model (especially the thermal conductivity and specific heat capacity). Now with the feedback mechanism and control rod position search and the thermal hydraulics component, the code can be used for much more investigations. Thus, analyses that are more detailed require finer assessment of important parameters. The heat capacity (C p ) and thermal conductivity (K) of the various material properties in the fuel and water might not be linear [3]. Now with the TRIGSIMS-TH tool this can now be analyzed and appropriate changes in the CTF fuel rod model can be implemented to take into account the burnup and burnable poisons Addition of a in-core experimental tube within TRIGSIMS-TH The thesis of Sahin [7], have shown the use of the in-core irradiation of samples at the dry irradiation tubes. This type of experiments can be calculated with samples for various materials or other uses. For this addition to the TRIGSIMS-TH, there ought to be a fixed sample caddy (or tube-insert) that needs to become part of the MCNP geometry. This could be made as an optional addition similar to the graphite elements and D 2 O tank in the TRIGSIMS-TH. The TRIGSIMS-TH code has already the capability to include any material specific isotopic inventory. All that is needed is to add a fixed geometry that will include the geometry of the

182 sample insert that goes into the dry irradiation tubes. This addition to the TRIGSIMS-TH makes the use of the code versatile and more useful. 166

183 167 Appendix Additional information Measured data Table A- 1Measured data Power Δρ P ΔT(F) ΔT/ΔP [kw] [c] [ C] [c/kw] [ C/kW] CL CL CL

184 Table A- 1Measured data gives the power coefficient and temperature difference of the reactor per change in power. The power coefficient, is an aggregate showing the change in reactor reactivity per unit change in reactor power. The reactivity of the system decreases as the power increase, hence the negative power coefficient. As per the thesis of Tippayakul [2], the measurements taken had some degree of uncertainty. This uncertainty was not known. However, comparing the in-hour and rod-drop measurements for control rod worth, the standard deviation was assumed approximately to be 10%. Core loading diagrams used in this thesis Figure A- 1and Figure A- 2 show the core loading configurations used in the thesis to provide the measured core results. These figures show the core design, the fuel elements 12 wt% and 8.5 wt%, the, control rods, the dry irradiation tubes and the position where the source is inserted into the core. The core-loading diagram for CL56 is given in Figure 3-2.

185 169 Figure A- 1 CL54 Core loading diagram Figure A- 2 CL53H core loading diagram (includes the position for graphite)

186 170 SERPENT calculations compared with MCNP calculations Figure A-3 shows the burnup calculation of the MCNP compared with the SERPENT calculation for a single pin (fuel element). The results are in steps of 143 days, which is the equivalent of 5 MWD/MTU per step. The burnup steps are equally spaced which is an indication that the error is consistent throughout the calculation. Serpent vs MCNP, keff per burnup step serpent mcnp Figure A-3 Comparison of the K eff values after each burnup step B 4 C calculations Assessment of the burnup of the B 4 C in the core The following analysis shows the results of the effect of reducing the number densities of the control rod neutron absorbing material B 4 C. The number densities were calculated by the SERPENT code. The code burnup was done with the model shown in Figure A- 4

187 171 Figure A- 4 Model for burnup of B 4 C The B 4 C rod is centered between six of the fresh 12 wt% fuel. The calculation was done at various burnup intervals. Table A- 2 shows the results of the MCNP5 calculation for various core conditions and burnup days. The number density of the B 4 C is indicated in Table 5-9. The core loading used is CL56. This result shows the effect of the burned B 4 C on the k eff calculation. The differences are for conditions at 300K and 900K are negligible. Table A- 2 Decrease in B 4 C number densities effect Condition days k eff ARI at 300K ± ARI at 300K (reference) No burnup of B4C ± ARI at 900K ± ARI at 900K ± ARI at 900K(reference) No burnup of the B4C ±