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1 DETAILED NEUTRON FLUX CHARACTERIZATION OF THE EXPERIMENTAL SHIELD TANK FACILITY AT THE UFTR By AMRIT DAVID PATEL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIRE MENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 200 9
2 200 9 Amrit David Patel
3 To my Mother and Father for their perpetual love and support and to Jessica for her encouragement and understa nding
4 ACKNOWLEDGMENTS I would like to give special acknowledgement to my mother who has always supported me in my pursuit of education and I would like to especially give thanks and credit to her for getting me to this point in my life I also want to acknowledge my father who instilled a sense of responsibility in me to always strive and do my best when it comes to my education. To my other family members who have showed constant support and pride in my pursuit of higher education, I am also very grat eful. Dr. Alireza Haghighat, my advisor, deserves great thanks for his aid Without him I would not have been able to finish or even start this work. I also extend great thanks to Dr. Glenn Sjoden for all of his help and who served as my other committee me mber. I thank the members of the U niversity of Florda Transport Theory Group who were there to help me with any questions or problems that I encountered, namely Dr. Ce Yi and Mike Wenner. I thank the Oak Ridge National Laboratory and the U.S. Nuclear Regul atory Commission who funded this work. Last, but not least, I want to thank Jessica Harrington for her moral support when times were tough and also without whom I could not have completed this work.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 ABSTRACT ................................ ................................ ................................ ................................ ... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 13 1.1 Background ................................ ................................ ................................ ....................... 13 1.1 Motivation of Work ................................ ................................ ................................ .......... 13 1.2 University of Florida Training Reactor ................................ ................................ ............ 14 1.2.1 Reactor Core Region ................................ ................................ .............................. 14 1.2.2 Experimental Shield Tank ................................ ................................ ...................... 15 2 THEORY ................................ ................................ ................................ ................................ 17 2.1 Neutron Transport Equation ................................ ................................ ............................. 17 2.2 Mode l ling With PENTRAN ................................ ................................ ............................. 18 3 METHODOLOGY ................................ ................................ ................................ ................. 22 3.1 Particle Transport and Distributed Computing (PTDC) Laboratory ................................ 22 3.2 Computational Methods ................................ ................................ ................................ .... 23 3.2.1 Development of MCNP5 Models ................................ ................................ ........... 23 220.127.116.11 A daptation of UFTR refueling model ................................ .......................... 23 18.104.22.168 Criticality calculation for fixed source generation ................................ ....... 25 3.2.2 Development of PENTRAN Mod els ................................ ................................ ...... 27 22.214.171.124 Single bundle study ................................ ................................ ...................... 27 126.96.36.199 Source specification and spatial meshing selection ................................ ..... 27 188.8.131.52 Effect of angular quadrature set order ................................ .......................... 29 184.108.40.206 Effect of homogenization ................................ ................................ ............. 29 220.127.116.11 GMIX: Cr oss section library development and source spectrum ................ 31 18.104.22.168 Results ................................ ................................ ................................ .......... 33 22.214.171.124 Application of the bundle study to full scale mode l ................................ ..... 35
6 4 RESULTS AND ANALYSIS ................................ ................................ ................................ 60 4.1 Full Core Neutron Flux Distributions ................................ ................................ .............. 60 4.1.1 Fuel ................................ ................................ ................................ ......................... 61 4.1.2 Graphite ................................ ................................ ................................ .................. 63 4.1.3 Shield Tank ................................ ................................ ................................ ............. 65 126.96.36.199 D etermination of the maximum biological dose equivalent rate ................. 67 4.2 Speedup and Parallel Processing Efficiency Using PENTRAN ................................ ....... 68 4.3 S calar Flux Convergence ................................ ................................ ................................ .. 70 5 CONCLUSIONS AND FUTURE WORK ................................ ................................ ............. 93 LIST OF REFERENCES ................................ ................................ ................................ ............... 95 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ......... 97
7 LIST OF TABLES page 3 1 BUGLE 96 broad energy group structure ................................ ................................ .......... 57 3 2 Summary of bundle study cases. ................................ ................................ ........................ 57 3 3 Mesh sizes of reference UFTR full core PENTRAN model (Case 3) ............................... 58 3 4 Mesh sizes of UFTR full core PENTRAN model (Case 4) ................................ ............... 58 3 5 Mesh sizes of UFTR full core PENTRAN model (Case 5) ................................ ............... 58 3 6 Mesh sizes of UFTR full core PENTRAN model (Case 6) ................................ ............... 59 3 7 Summary of full core cases. ................................ ................................ .............................. 59 4 1 Calculated biological dose equivalent rate conversion factors based on BUGLE 96 energy group structure. ................................ ................................ ................................ ...... 92
8 LIST OF FIGURES page 1 1 Dimensions of the UFTR. ................................ ................................ ................................ .. 16 1 2 Side and aerial view of the UFTR. ................................ ................................ ..................... 16 3 1 The MCNP5 simplified model of the UFTR (x z slice). ................................ ................... 41 3 2 The MCNP5 simplified model of the UFTR (x y slice). ................................ ................... 42 3 3 Fission neutron density (#/cm 3 s) within the UFTR core (MCNP5 1 3.5%). ................................ ................................ ................................ ................................ 43 3 4 The GMIX generated and verified Watt fission spectra. ................................ ................... 44 3 5 The x y plane view of a typical UFTR fuel bundle at mid height showing the spatial mesh distribution. ................................ ................................ ................................ ............... 45 3 6 The x y plane view of a typical UFTR fuel bundle at mid height showing the spatial source distribution. ................................ ................................ ................................ ............. 46 3 7 The x y plane view of a homogenized UFTR fuel bundle at mid height showing the spatial source distribution. ................................ ................................ ................................ 47 3 8 Bundle normalized neutron flux distribution (#/cm 2 s) for group 15 (1.920E+00
9 3 16 The 3 D spatial mesh distribution for the full core UFTR model (colors correspond to material regions as follows: red fuel, blue graphite, green water). ....................... 52 3 17 An x y slice of the full core UFTR model typical for all fuel containing axial levels (colors correspond to material regions as follows: red fuel, pink graphite, green water). ................................ ................................ ................................ ................................ 53 3 18 3 D spatial mesh d istribution used in the symmetry study (colors correspond to material regions as follows: red fuel, blue graphite, green water). ........................... 54 3 19 Flux relative differences in the graphite region for the symmetry study within the thermal, epithermal, and fast energy ranges. A) group 47, B) group 30, C) group 15, and D) group 4. ................................ ................................ ................................ .................. 55 3 20 3 D spatial mesh distribution for the full core UF TR model using a reflective boundary condition at the x z core mid plane (colors correspond to material regions as follows: red fuel, blue graphite, green water). ................................ ...................... 56 4 1 Neutron flux dis tribution (#/cm 2 s) in the fuel region for group 15 (1.920E+00
10 4 11 Group 15 3 D flux distributions (#/cm 2 s) in the graphite region. (A) MCNP5 flux distribution, (B) MCNP5 1 and (D) PENTRAN/MCNP5 relative differences. ................................ ............................. 77 4 12 Neutron flux dist ribution (#/cm 2 s) in the graphite region for group 15 (1.920E+00
11 4 26 Neutron flux distribution (#/cm 2 s) in the shield tank region for group 42 (5.043E 06
12 Abstract of T hesis Presented to the Graduate Sch ool of the University of Florida in Partial Fulfillment of the Requirements for the Degree of M aster of S cience DETAILED NEUTRON FLUX CHARACTERIZATION OF THE EXPERIMENTAL SHIELD TANK FACILITY AT THE U FTR By Amrit Davi d Patel May 200 9 Chair: Alireza Haghighat Major: Nuclear Engineering Sciences The Global Nuclear Energy Partnership (GNEP) is an international program, sponsored by the U.S. Department of Energy domestically, of which an important aspect is to improve m anagement of spent nuclear fuel. Part of this management would include characterization of spent nuclear fuel, a process that is commonly performed through destructive testing The work done in this study provides support for the design of a tool which wou ld allow characterization of spent fuel based on a combination of non destructive testing and simulation in a radiologically safe environment. We investigated a methodology for neutron flux characterization of the experimental shield tank facility at the University of Florida Training Reactor (UFTR) for future development of a fuel burn up reconstruction device. Utilizing both 3 D Monte Carlo and 3 D deterministic particle transport codes, multi group neutron flux distributions are calculated. The accuracy and efficiency of the PENTRAN code based on flux distributions throughout the reactor core and graphite reflector regions are assessed and further compared with MCNP5 results It is demonstrated that the deterministic PENTRAN code package achieves accurat e solutions at significantly reduced computational time as compared to the Monte Carlo calculations
13 CHAPTER 1 INTRODUCTION 1.1 Background The Global Nuclear Energy Partnership (GNEP) is an international initiative which is headed by the Department of Energy in the U. S. Th is program interfaces with the Advanced Fuel Cycle Initiative (AFCI) which is the research and development component supporting the evolving technology that will recycle spent nuclear fuel from commercial power generation. The objectives a re to reduce the amount of high level waste by using the spent nuclear fuel and address ing many non proliferation concerns. From a high level waste storage standpoint, the implications of a program like GNEP are profound. Successful implementation would put less stre ss on the issues that come along with Yucca Mountain, the selected geological repository located in Nevada buil t for long term storage of high level waste Further, it eliminates the projected limitations on storage capacity and environmental impacts, not to mention the non proliferation benefits due to the removal of the plutonium from the spent nuclear fuel. This work discusses a study, of which the results will eventually be used by other researcher s in assaying spent nuclear fuel at the University of Florida. 1.1 Motivation of Work Currently, destructive methods and associated computer codes are available to assess the contents of spent nuclear fuel, but the question is : C an we develop a non destructive methodology which can accurately identify isotopic co ntent of the fuel? Assaying an actual bundle of spent nuclear fuel elements can be quite a challenge since these bundles are very radioactive and therefore become a very complicated safety hazard. It is therefore necessary to develop a practical and safe w ay to assay spent nuclear fuel experimentally.
14 To accomplish this task, researchers at the University of Florida Department of Nuclear and Radiological Engineering (UF NRE) propose a burn up reconstruction device. The basic idea is to be able to interroga te a spent fuel bundle, which is to be submersed in water, with passive and active detection systems. To implement either system, it is essential to determine the neutron and gamma field s within the shield tank. The goal of this work does not deal with th e explicit design of the burn up reconstruction device but rather seeks to define the aforementioned neutron flux distribution that will be used as the known source for subsequent studies and experimentation. Therefore, t his work discusses a n effective me thodology for the neutron flux characterization of the experimental shield tank facility at the University of Florida Training Reactor (UFTR). 1.2 University of Florida Training Reactor 1.2.1 Reactor C ore R egion The UFTR is a 100 KW t graphite moderated, water coole d/moderated Argonaut design with various experimental facilities arranged on the perimeter of the reactor core in addition to three vertical experimental ports. Figure 1 1 shows a schematic of the UFTR with dimensions Figure 1 2 further illustrates important regions of the UFTR by showing the relative location of The reactor core contains six aluminum boxes, and each box can hold a m aximum of four fuel bundles. Each fuel bundle consists of 14 fuel plates (0.51 mm in thickness); the fuel meat is made of U 3 Si 2 Al at an enrichment of 19.75 wt%, and the cladding is 6061 aluminum alloy. Presently, t he two boxes on the east side of the core the outermost corners of the east side of the core. The reactor is controlled by means of four control blades (3 safety blades and 1 regulating blade) of swing arm type. The blades are mounted on the side of the core and swing downward
15 through the core between the fuel boxes. Each control blade is encased in a magnesium shroud and has a cadmium insert at the tip [ 1 ] 1.2.2 Experimental S hield T ank A s previously mentioned, there are several experimental facilities associated with the UFTR. The one of interest in this study is the shield tank located at the west side of the facility. It is approximately 13.5 ft high and 5 ft by 5ft along the other dim ensions. The shield tank is an ideal environment to house the burn up reconstruction device because it is a good shield for radiation to the surrounding environment and also because it is large enough to accommodate several sizes of objects for experimenta tion The shield tank is such a good neutron shield due to its moderating capabilities that it does make the problem quite complicated for characterizing the neutron flux throughout it accurately and efficiently; however the following chapters discuss how this was accomplished.
16 Figure 1 1 Dimensions of the UFTR Figure 1 2 Side and aerial view of the UFTR
17 CHAPTER 2 THEORY 2.1 Neutron Transport Equation In order to obtain the desired neutron flux distributions, a formulation is needed that models the proper physics of neutron population behavior. We turn to the Linear Boltzmann Equation (LBE) which includes all of the necessary and applicable terms for obtaining the desired neutron flux distributions. The LBE can be written in many forms, but for the purpose of this thesis, we utilize the 3 D Cartesian Boltzmann transport equation in multi group form as shown below [ 2 ] where
18 In the above equation we are interested in solving for which represents the angular group flux fo r the g th energy group. If these angular fluxes are summed over the angular variables and the scalar flux, can be determined This is the quantity of interest. Since this balance equation cannot be solv ed analytically, we turn to the 3 D discrete ordinates (S n ) PENTRAN (Parallel Environment Neutral particle TRANsport) code system [ 2 3 ] 2.2 Model l ing With PENTRAN The PENTRAN code system is developed to so lve the linear Boltzman equation numerically for particle transport problems of all types. As alluded to earlier the reason for using the deterministic PENTRAN code is that it is necessary to determine a detailed multi group flux distribution throughout t he model, and the Monte Carlo calculations generally require significant computation time especially for tallying detailed 3 D regions Also, Monte Carlo calculations do not inherently give 3 D multi group flux distributions for the entire model. Therefor e, th e Monte Carlo calculation is used to examine the accuracy of the deterministic predictions at select locations. It is important to understand some basic principles used in designing a model using PENTRAN. The first thing that should be realized is the more spatial meshes in the problem, the more time it will take to solve the problem. The physical scope of the model developed in this study is quite large for use with the PENTRAN code (unless larger supercomputers are readily available) so it is importa nt that the number of meshes in the problem is minimized without compromising solution accuracy. Additionally, the source specification is critical in obtaining meaningful answers since the source term is what drives the solution in a fixed source problem. This means that spatial meshing should be adequately detailed for regions containing source.
19 The quadrature set which by selection determines the number of directions along which the LBE is to be solved, and plays a role in solution accuracy and the len gth of time it will take to solve a given problem. The objective here is to use the lowest quadrature order possible, and hence the fewest directions, in order to obtain meaningful results. Cross section data is also one of the m ost important aspects of m odel design Neutron cross sections should be of an appropriate anisotropic scattering order and mixed from an appropriate cross section library. Finally, it is essential for a problem of this scope to use parallel processing which is at the heart of why P ENTRAN was chosen for solving this problem. The PENTRAN code system allows energy, space, and /or angular decomposition allowing the user to utilize multiple processors for calculations. The most effective ways of utilizing this feature is the use of the an gular and spatial decomposition. The angular decomposition works by solving the Boltzmann transport equation for different directions on different processors. During the calculation, this information is summed to obtain scalar flux values. This decompositi on strategy is quite effective in speeding up problems by increasing the rate of inner i teration convergence, but does not save much in terms of memory used per processor. The memory demands can be quite large for problems with many spatial meshes and will oft en exceed the amount available. This is where spatial decomposition is the most effective. The spatial decomposition allows groups of fine meshes, known as coarse meshes, to be divided up among several processors available (i.e. memory partitioning) and e ach spatial doma in is solved on one processor; t his can significantly lower memory demands per processor The speedup from spatial decomposition is also advantageous if implemented properly.
20 When using spatial decomposition in parallel jobs, it is crucial to consider the parallel load im balance. This value can be thought of as a measure of the parallel efficiency for a given problem. It is first instructive to briefly differentiate between a fine and coarse mesh in the context of PENTRAN model generation. A ccording to convention, a coarse mesh is a grouping of fine meshes that generally contains a single material. Each defined coarse mesh can only have a single fine mesh density. When using parallel processing with spatial decomposition, coarse meshes are eq ually divided among the processors according to the specified decomposition in order from one to the number of coarse meshes in the problem. The basic idea is that when each processor is allotted a number of coarse meshes for solving a problem, there is a possibility more often than not, that the total number of fine meshes assigned to a processor is different among all of the processors. This is due to the fact that each coarse mesh is independent, from a calculational standpoint, from all others in the pr oblem, and therefore each coarse mesh can have its own distinct mesh density. Essentially, this allowance proves quite useful when setting up the model since different material regions will have different properties neutronically (e.g. mean free path) and hence variable meshing densities between coarse meshes become convenient. When the difference in number of fine meshes per processor is not significant, the problem can be considered optimal as far as parallel load im balance Consequently, the boundary dat a needed on the processors can be transferred between processors efficiently, precluding the necessity of waiting, or lagging between processors with otherwise large numbers of fine meshes. So, if there are large differences in the numbers of fine meshes b etween processors, large lags can occur in the calculation therefore causing the model to be computationally inefficient. With this description in mind the load im balance can be practically defined as the number of fine meshes on the processor with the mos t coarse meshes divided by
21 the number of fine meshes on the processor with the least fine meshes. Therefore, as implied by previous statements, the closer the load im balance is to unity, the more efficient the parallel calculation will be. The parallel loa d im balance is consi dered for the large scale model in this study and it is essential to ensure that this number is approximately one and preferably less than or equal to about 10. So in summary, the source definition, spatial meshing, quadrature order, c ross section data, and variable decomposition play very important roles and will be further discussed in the context of the models developed for this work.
22 CHAPTER 3 METHODOLOGY In this chapter, the MCNP5 and PENTRAN mode l ling methodology is explained. The discussio n begins with an introduction of the computer systems by which the calculations in this work were made possible. Also, t he MCNP5 fixed source development, used in both PENTRAN and MCNP5 full core models, is discussed in addition to an important bundle stud y that provides mode l ling insight for the subsequent full core models. Finally, the full core PENTRAN models are fully described along with the reasoning f or choosing the different cases of this study. 3.1 Particle Transport and Distributed Computing (PTDC) Lab oratory Since the main goal of this work is to show that accurate assessment of the neutron flux as a function of energy at various positions throughout the UFTR core and experimental shield tank can be achieved through computer simulation, it is important to specify the systems on which this work was performed. T he entirety of the particle transport simulations were performed using the parallel computational clusters at the University of Florida Transport Theory Grou p ( UFTTG ) PTDC lab which is managed by the U FTTG The main cluster used is designated as Einstein and it contains eight nodes, each containing two processors; the processors are AMD Dual Opteron processors at 2.4 GHz. Each node contains 4096 MB of DDRAM on a 533 MHz system bus for a total of 32 GB of DDRAM for t he entire system. Likewise, an other cluster, named Chadwick, contains eight nodes, each containing two processors; these processors are Dual Intel Xeon processors at 2.4 GHz. Also, Chadwick has 4096 MB of DDRAM present for each node on a 533 MHz system bus The most recent addition to the laboratory is the Bohr cluster which contains six nodes, each containing 4 processors. Each processor contains 4096 MB of DDRAM for a total of 96 GB
23 of DDRAM for the entire system. The Bohr cluster is use d for the large mo dels in this study to obtain greater speedups The work here explores the benefit of using a parallel computing architecture versus the traditional single processor when performing computationally expensive calculations. The objective is to achieve an accurate solution, but in th e most efficient way possible. It will be d emonstrate d that a real world problem can be solved in reasonable time relative to the breadth and scope of the solution goals. The choice of solution method, st atistical or deterministic, plays an important role in efficiency and overall quality of the neutron flux solutions and is now discussed in further detail. 3.2 Computational Methods 3.2.1 Development of MCNP5 M odels Due to the capability of the Monte Carlo method to solve com plex particle transport problems accurately, it was decided that the Monte Carlo Neutral Particle (MCNP) series developed by Los Alamos National Laboratory in the United States would serve as the computational benchmarking tool. In particular, the primary version used for this study was MCNP version 5 or MCNP5 [ 4 ] It is recognized that method is not necessarily the ideal method for reaching our goal of characterizing neutron flux e fficiently thro ughout our model. However, MCN P 5 fits well t o serve as a benchmarking tool due to the convenience of its detailed 3 D space and multi group energy mesh tally capabilities and the evident robustness of the code 188.8.131.52 Adaptation of UFTR r efueling m odel Between 20 05 and 2006 the UFTR went through refueling of the reactor core due to a U S Department of Energy (DOE) P rogram to convert existing research reactor fuel from H igh ly
24 E nrich ed U ranium (HEU) fuel to L ow E nrich ed U ranium (LEU) fuel. During this time several extensive models were created to aid in the analysis of this undertaking. A model of the reactor core and surrounding regions was developed for analysis purposes using MCNP5 [ 5 6 ] In the current study the model has been altered to include tallying for creation of a detailed fiss ion source density distribution for fixed source modelling in addition to the shield tank. This model, as seen in Figure 1 2 provides all of the important physical components of the reactor system to ensure that the fission source is accurately characterized. Originally, this model was designed to be used for flux distributi on comparison with PENTRAN full core models. However since a criticality calculation is being performed, the transport process is rather inefficient for a deep penetration problem and thus this model is used only for proper characterization of a fixed source for use in the subsequent MCNP5 design. Furthermore, t he scope of the full core PENTRAN models does not consider detail such as the heterogeneous core and control blades and does not include regions including concrete an d the upper po rtion of the tank. T heref ore, a model tha t mirrors the actual PENTRA N model is desired to minimize model differences when comparing PENTRAN flux distributions to MCNP5 flux distributions. I n summary, the detailed MCNP5 model is used strictly for the generation of the f ixed source for use in the full core models of this study. The MCNP5 modell ed core including the shield tank that was created for subsequent fixed source calculations for comparison with PENTRAN model flux distributions is shown in Figure 3 1 and Figure 3 2 If thes e figures are compared with those in Figure 1 1 and Figure 1 2 it is apparent that th is fixed source MCNP5 model does not include the graphite to the right of the fuel, the concrete, and a limited portion of the shield tank. The reason s for this are : 1) because physically it is not likely that neutrons leaving the model at the chosen boundaries w ill have
25 significant impacts on the fluxes that are calculated within ~ 7 10 mean free paths of the boundaries ( and since we are interested in the central regions of the model consequently where the fluxes are the highest, this is not of concern ) 2) limiting the scope of the geometry in MCNP5 provides some acceleration since computation time is not being wasted tracking neutrons that do not significantly contribute to fluxes in the regions of interest, and 3) to ensure that the MCNP5 model is similar to the geometry of the PENTRAN model so that comparisons become more meaningful. 184.108.40.206 Criticality c alculation for f ixed s ource g eneration To calculate a detailed flux distribution throughout the reactor model, we have partitioned the calculation into two parts: 1 ) determination of the fission neutron source density and 2 ) determination of the neutron flux througho ut the reactor model. The determination of the detailed fission neutron source density distribution is discussed below To determine a fission neutron density distribution we perform a criticality calculation using MCNP5 that samples fission neutron energ y using a Watt fission spectrum [ 4 ] To achieve a statistically reliable source distribution, we have used 800 cycles, 5 0 000 histories/cycle, and 1 0 0 s kipped cycles. To tally fission source density, for each fuel p late, 100 meshes were defined (5 across the width of the plate, 1 representing the thickness, and 20 axially). Figure 3 3 s hows the calculated 3 D fission neutron density ( #/cm 3 s ) throughout the six fuel boxes. Note that the 1 ~ 3.5%. This calculation was performed using the Einstein PC cluster with 16 processo rs. To generate the multi group fission neutron source distrib ution for a fixed source using MCNP5, and additionally for deterministic calculations, we have generated a multi group fission spectrum based on the continuous energy Watt spectrum formulation [ 7 ] The continuous energy form is given as
26 and the multi group form is obtained by integrating this equation over the energy widths of the 47 groups in the BUGLE 96 cross section library [ 8 ] Figure 3 4 compare s the multi group fission spectr um as generated by the cross section mixing code GMIX [ 9 ] t o be discussed in more depth later in this chapter and the independently verified spectrum as calculat ed by using the above equation by numerically integra ting over the respective energy group widths of the BUGLE 96 group structure It is noted that the spectra in Figure 3 4 are not identical, but this is explained by the more acc urate treatment of GMIX due to isotope and enrichment dependency when generating the spectrum The MCNP5 code can u se the fission neutron source distribution and the fission spectrum to create a multi group fission neutron source di stribution for perfo rming fixed source calculations. Again, a major benefit of this process, that is, first performing a criticality calculation and then a fixed source calculation compared to only performing a criticality calculation, is that significant reduction of computa tion time can be achieved for the problem at hand because we are assuming we have a properly converged source obtained from the criticality calculation In other words, any subsequent calculations can be performed by using the more computationally ef ficien t fixed source simulation. The designs of the full core MCNP5 models were discussed in detail in Section 220.127.116.11 In the following discussions o f the PENTRAN code system and model development for the single bundle study concu rrent MCNP5 models were constructed with the same geometric configurations and material specifications for comparison purposes. Sinc e the scope of the bundle models are rel atively small and since they are computationally inexpensive to run, only criticalit y calculati ons are performed w ith the creat ed MCNP5 mode l s Since the basis of this
27 work is the use of PENTRAN with MCNP5 used as a benchmarking tool, the intricacies of MCNP5 model development are not discussed and are also precluded by the much simpler input specification. 3.2.2 Development of PENTRAN M odels Creating the PENTRAN input decks is tedious and difficult to generate from scratch. With the help of a pre processing code, however, this turns model creation into a relatively simple task. PENMSH Express or PENMSHXP is the code developed for this task and was the application used to assemble all PENTRAN input decks in this work [ 10 ] 18.104.22.168 Single b undle s tudy In order to arrive at a computationally efficient PENTRAN full core model, it is instructive to first properly characterize the source term and determine a proper quadrature set for subsequent calculations. By looking at a small scale model of a single UFTR fuel bundle, we are able to use parallel processing to accel erate these smaller calculations in order to gain insight into model l ing choices for the large r, computationally taxing model, which include s the entire core and shield tank regions In this section, the foundation for choic es made in the final full scale model of the UFTR core and shield tank are developed. The spatial mesh distribution for one of the heterogeneous model s in the study is shown in Figure 3 5 ; blue regions indicate water gaps, green i s the aluminum fuel plate cladding, and red is the fuel meat. 22.214.171.124 Source s pecification and s patial m eshing s election The method by which the source is defined for the PENTRAN bundle models is based on the previously discussed methodology For this bundle study a unique source distribution was defined for specific application; however the process is exactly the same as discussed in S ection 126.96.36.199 Although the fixed sourc e in PENTRAN is defined differently than th e source used in MCNP5 th e same spatially dependent fission neutron density distribution is used.
28 In PENTRAN, the source is defi ned with a given spatial mesh d efined by the user. This mesh does not have to be the same as that of the physical model. PENTRAN effectively proje cts the defined s ource onto the specified m esh for the physical model defined by the user. This fact plays an important role when selecting the spatial mesh of the model because a poor choice could result in an improper spatial definition of the source w hich can lead to inaccurate results. Therefore, the best choice is to simply align the source m esh with the physical model so that no approximation is made. However, for large models such as the one in this study with relatively fine source meshe s, this is not possible if a computationally efficient model is desired because the greater the number of meshes, the longer it takes to solve the problem ; processor memory requirements also become an issue Furthermore, it is not necessary to d efine such a s patially exact source term in a relatively large model such as the UFTR for example due to the fact that the shield tank is distanced by an optically thick graphite region and since the focus of this study is not in the core region. However, o ne must be conce rned with preserving the relative shape and magnitude of the flux throughout the source region of the model to ensure consistency with actual behavior If the source magnitude and shape is significantly inaccurate due to coarse meshing this will be seen i n other regions of the model. This can possibly be an issue in the fuel region, where for example, the probability of interaction is very high within thermal groups. If spatial meshing is coarse relative to the thermal group mean free paths in the fuel/so urce region, it is possible that thermal groups will not be properly characterized. This is a concern in the full core applications since thermal flux dominates in all regions of the model. In summary, the meshing selection must be carefully chosen and stu died looking at the shape of fluxes in the region and comparing them to the benchmark and also ensuring that the total source is conserved in cases where projection
29 occurs. Figure 3 6 gives the spatial source distribution at the c enter of one of the fuel bundle mesh configurations studied. Notice that this particular configuration shows symmetry along the x and y axes; depending on the meshing selection, this might or might not be the case. It is also important to ensure the select ed meshing scheme provides a load im balance as close to one as possible since this parameter drastically a ffects computational efficiency; this is not important in this single bundle model, but it is important for large models containing a significantly la rge r number of fine spatial meshes and will be discussed more in depth in following chapter s Several cases were performed with different meshing types from very fine to very coarse to study the effect on the flux distributions The goal wa s to obtain t he coarsest meshing scheme possible that essentially gives the same result as the heterogeneous reference case taken to give the correct solutio n and having a very fine mesh resolution. Along with this study, it is necessary to determine the appropriate order of the angular quadrature set 188.8.131.52 Effect of angular q uadrature set order Since the full core problem is classified as a deep penetration shielding problem dominated primarily by scattering reactions within graphite and water, it can be s hown that a low er quadrature order is most appropriate due to the diffusive nature of the problem. With this said, the PENTRAN bundle model explores the impact of S 4 S 6 and S 8 quadrature sets with the goal of finding the quadrature order that best characterizes flux be havior with the fewest number of directions. 184.108.40.206 Effect of h omogenization In the same manner that studying the way the source projects onto the spatial meshing grid and the effect that quadrature has on the calculation, it was thought that due to the large sca le of the full core and shield tank model, that there would be great gains in model efficiency if the model was homogenized.
30 In the context of this study homogenization refers to the fuel boxes. Concurrent with this, homogenization of the source was also performed to study the behavior of the flux local to the source to ensure that the total source is conserved irrespective of the coarseness of the selected meshing density ; it was found that source homogenization is not necessarily required for total sourc e conservation or flux distribution accuracy but depending on the spatial mesh distribution it might be When applying the results of this single bundle study, it will definitely be beneficial to be abl e to homogenize the fuel region in order to signific antly reduce the amount of spatial meshes of the problem and therefore drastically improve the computational efficiency. Fine mesh reduction through material homogenization in this study is one of the most important steps toward creation of an efficient m odel and therefore it is emphasized. For example, we can look at the bundle case to better understand the effect of homogenization In the Figure 3 5 a mesh configuration was put together specifying two meshes per fuel plate alon g the y axis and 30 total meshes along the x axis In order to do this in a heterogeneous configuration, it is necessary to define a very fine sp atial meshing along the y axis, in this case 224 fine meshes among 14 coarse meshes With 30 fine meshes in the axial direction also, this gives 2 01 6 00 fine meshes per bundle. That is to say if we used thi s configuration within the full core model for each bundle, there would be over 4. 4 million meshes which is only characterizing the fuel region, not to mention a ll of the surrounding graphite and the shield tank. Figure 3 7 shows the spatial source distribution for a homogenized fuel material and source configuration containing 31x28x30 meshes for a total of 624,960 fine meshes. This is a reduction in total meshes per bundle of nearly a factor of 8 compared to the previously discussed case. It is also noteworthy to mention that concurrent with the fact that the fuel plate thickness is so thin (0.51 mm), differences in material and/or coar se mesh boundary positions from actual
31 positions on the order of fractions of a millimeter have shown to cause drastic effects in flux results in this bundle study, namely in the form of asymmetries. This slight mismatch of coordinates has an effect on how t he source is projected and shows how careful one must be when choosing a meshing scheme when local behavior is important in the source region In this problem, this coordinate mismatch is not apparent since homogenization is used and the boundary in formation that previously caused flux asymmetries is not used in model construction. If acceptable accuracy is achieved, h omogenization provides a significant reduction of fine meshes It is quite obvious that the detail of the aforementioned heterogeneous case i s not only unnecessary for the overall objective at hand (i.e. characterization of the shield tank) since we are not so con cerned with very detailed flux distributions within the core region, but it is computationally imp ractical to calculate a solution fo r a model containing millions of meshes. As long as the total source can be shown to be conserved, and the source distribution is shown to be adequately modeled it c an be postulated that the flux distributions in the distant region of interest (i.e. the s hield tank) will be accurate. Although compromising the exact shape of PENTRAN flux d istributions in the regions local to the source this methodology will prove very useful in obtaining accurate results in reasonable amounts of time for the full scale pro blem at hand. 220.127.116.11 GMIX: Cross s ection l ibrary d evelopment and s ource s pectrum This section is intended to further elaborate on the use of GMIX as previously mentioned in the discussion regarding the MCNP5 model. In MCNP5, the continuous energy cross sections a re used from the standard ENDF/B VI [ 11 ] library and this is a very straightforward input specification for the user. For a deterministic code such as PENTRAN, the specification is slightly more of a challenge because a problem specific library must be generated and with
32 model homogenization in the fuel region, care must be taken in constructing it due to the numerous materials that compose the mixture First, a calculation appropriate library must be selected; in the c ases of this study, BUGLE 96 is used. The BUGLE 96 library contains infinitely dilute d cross sections for 120 nuclides with a concrete weighting flux It contains 47 neutron energy groups and 20 gamma energy groups for transport simulations and has cross s ections for up to a P 5 /P 7 anisotropic scattering order; it also contains response cross sections for several reactions. A maximum P 3 anisotropic scattering order was chosen for all PENTRAN models in this study again because of the diffusive nature of the p roblem BUGLE 96 is a cross section library that is commonly used for shieldi ng calculations and therefore was appropriate for use with the PENTR AN models of this study. The 47 group neutron energy structure is given in Table 3 1 [ 8 ]. Once BUGLE 96 was chosen, t he GMIX code was used to generate the cross section library containing the appropriately mixed cross sections for the materials in the PENTRAN cases GMIX was recently developed as part of an effort for the generation of problem dependent cross section libraries for deterministic transport codes. This problem specific l ibrary contains neutron and/or gamma macroscopic cross section data for various materials/mixtures in the problem GMIX also conveniently outputs the fission spectrum based on the given fissionable materials. Again, as previously mentioned in the discussion of the MCNP5 models the GMIX output fission spectrum is based on integrating the isotope dependent Watt or Ma xwellian fission spectrum as appropriate to the various nuclides, over different energy intervals a nd i s s hown in Figure 3 4
33 18.104.22.168 Results Using PENTRAN, the 47 group 3 D flux distributions for the four different bundle cases are cal culated. All cases use a constant meshing along the x and z axes containing 31 and 30 fine meshes, respectively. The reference heterogeneous case (Case 1) uses a strategy incorporating both angular and spatial decomposition and utilizing 14 processors on t he Einstein PC cluster. For the remaining cases angular domain decomposition w as performed by p rocessing one octant per processor on the Einstein PC cluster. The MCNP5 calculation was performed on the same cluster using 16 processors Table 3 2 outlines some PENTRAN model parameters and computation times. In Figure 3 8 to Figure 3 14 the normalized flux distributions for various thermal, epithermal, and fast energy groups are compared ; the selection of energy groups presented is chosen to illustrate the overall trends in the respective spectral ranges. Case 1 represents the reference case which is very finely meshed containing 42 coarse meshes along the y axis for a total of 23 8 fine meshes along this axis and it uses an S 8 quadrature set. Case 2 is also an S 8 case; however it is homogenized and uses a uniform meshing consisting of only one coarse mesh along the y axis with 28 fine meshes. All of the homogenized cases use a hom ogenized source. The following two PENTRAN cases use the same meshing scheme but have S 6 ( Case 3) and S 4 ( Case 4 ) quadrature set s Note the similarity in computation time for Case s 2 and 3. Typically, it would be expected that Case 3 would be faster sinc e there are less directions to solve for; however, due to the increased number of iterations needed to achieve convergence for Case 3, it took about the same time as the more detailed Case 2 which converged in fewer iterations. The final case Case 5, is t he reference MCNP5 calculation that is in a heterogeneous configuration. This case is a criticality calculation containing a superimposed mesh tally that
34 records the flux in the corresponding regions as a function of energy group. All flux results reported have 1 relative errors less that 10% and the computation time (wall time) was 1.20 hours. Looking at the fast and epithermal flux distributions Figure 3 8 t o Figure 3 11 indicate s that all the PENTRAN cases agree within the Monte Carlo 1 Figure 3 12 showi ng the flux result for g roup 42 also shows that fluxes are in agreement. There is some slight difference seen in the relative magnitudes, however it is not of considerable concern because : 1) the relative differences are less than ~10% and 2) as with all low energy neutrons within the source region, they will be of low importance to the shield tank region when model l ing the entire core. The energy be havior is interesting for the fluxes in energy groups 46 and 47 shown in Figure 3 13 and Figure 3 14 respectively, for the homogenized PENTRAN cases. It appears from the MCNP5 results that for group 47, the homogenized results overestimate fluxes and the group 46 homogenized results underestimate fluxes. If the two groups are summed, however, the results between MCNP5 and homogenized PENTRAN are consistent as seen in Figure 3 15 Interestingly, the reference heterogeneous PENTRAN case (Case 1) shows agreement with MCNP5 group 47 fluxes wh ile group 46 is underestimating. The group 46 behavior is consistent with the other homogeneous PENTRAN cases however group 47 is not This obse rvation of the homogenized models showing a slight overestimation of flux magnitudes for group 47 might be an effect of material homogenization. However, since group 46 is consistently differing between all of the PENTRAN models and the MCNP5 model, this b ehavior is likely due to the BUGLE 96 cross sections which do not accurately characterize the phy sics of the problem properly for thermal groups, especially group 46 and group 47 ; this is also possibly due to using a cross
35 section library that does not include thermal upscattering cross sections In the next chapter discussing the full core model we will further examine the issues with these lowest two energy groups. It is important to note that the computational cost of the PENTRAN homogeneous calculation wi th an S 4 quadrature set (Case 4) is only 3.9 min utes (using 8 processors) which is significantly lower than other cases, especially, the heterogeneous S 8 PENTRAN case (Case 1) which required ~ 217 min utes (using 14 processors load im balance of 28 ) of compu tation time (factor of ~56 speedup ). The speedup seen in Cases 2 through 4 compared to Case 1 is somewhat misleading, however, since Case 1 was not optimized as far as minimizing the load im balance. 22.214.171.124 Application of the bundle study to full scale m odel Usin g the single bundle study and applying the conclusions, it is straightforward to model the full core and adjacent s hield tank region. The core region is based on the homogenization of the fuel region and a n S 4 quadrature order serves as the starting point for the quadrature study as found appropriate by the bundle study. Figure 3 16 shows the 3 D spatial meshing distribution for the UFTR full core PENTRAN model including the shield tank. The red regions are the homogenized fuel mix ture, the green regions above and below the red represent the water in the bundle channel, the blue is the graphite reflector, and the green wall at the end represents a lower portion of the shield tank. Figure 3 17 shows a 2 D x y slice of the PENTRAN core which shows the spatial mesh distribution and core dimensions for axial levels containing fuel The cadmium tipped control blades, which have the most noticeable effect on thermal neutrons in the system, have been removed from t he model in an attempt to further simplify it. The original eigenvalue calculation for generation of the source included the control blades, therefore they are indirectly represented in the current fixed source definition. Furthermore, t his
36 model l ing choice should not be of concern in the fixed source transport of neutrons because the probability of thermal neutrons (the ones not being absorbed by the control blades) reaching the shield tank are quite minimal due to the expanse amount of graphite between th e fuel and the shield tank (about 50 cm) and can be considered insignificant to the flux contribution at the tank. T here are also benefits from a load balancing perspective because the control blades cut through the core along the y axis and extend through the height of the fuel. This forces the creation of very small coarse meshes in the model in order to characterize these control blades causing potential for a significant load imbalance or granularity issues The next simplification was chosen due to the sym metry of the geometry along the center of the model along the x z plane. In the actual UFTR, the geometry is exactly symmetric wi th the exception of the eastern most pair of control blades. Due to their location toward the farther end of the reactor core r elative to the shield tank and the fact that the control blades only affect the thermal region of the neutron energy spectrum, it is reasonable to argue that using a reflective boundary condition at the x z core mid plane will not be an issue in the full c ore model in the regions of the graphite and shield tank, and even in the majority of the fuel region. In order to substantiate this claim, two simple three region PENTRAN models were created and compared. These models include fuel, graphite, and water re gion s analogous to the actual full core UFTR model except that only the extent of the active fuel height was considered along the z axis T he 3 D spatial mesh distribution can be seen in Figure 3 18 ; note that this is simply a cut out of the fuel, graphite, and water region s as seen in Figure 3 16 In one of the models, the source in the north bank of fuel bundles is used and in the other model, the source from the sou th bank of fuel bundles is used ; howeve r t he south is reflected over the x z mid plane so it resembles the source from the north bank of bundles. Performing the
37 transport calculations for these models should therefore produce similar 3 D multi group flux distributions if in fact there is mirror symme try along the x z core mid plane. In order to demonstrate that a fully reflective boundary condit ion is appropriate for the full core model, a 3 D multi group flux comparison was made in the fuel, graphite, and water region s of these two three region model s The graphite region compar ison is shown in Figure 3 19 in which fractional relative differences are given as a function of 3 D position for four different energy groups along the BUGLE 96 neutron energy spectrum; the other regi ons exhibit similar differences, that is on average between 1% and 3% relative differences. Since these differences are so low, it is concluded that the use of a symmetry condition at the x z core mid plane is appropriate for this study. The mesh dist ribu tion for the reference full core model, which serves as the basis for the cases in this study is shown in Figure 3 20 Note that the shield tank has been extended to include the entire depth allowing the entire lower part of the water tank to be modeled The source used for all of the subsequent full core models is the fixed source located in the northern bank of fuel bundles generated from the initial MCNP5 full core model that performs a criticality calculation. To further increase the sim plicit y of the model, it is seen that the row of fuel bundle s has been combined into a single region. As an important note, during the homogenization process, special care was taken to conserve the materials within the fuel meat, fuel cladding, and fuel bo x. Displacing the small graphite regions ( between fuel bundles ) with homogenized fuel material is also a helpful simplification which precludes the need to create unnecessary coarse meshes and hence more fine meshes. Although this is not physically correct, the simplification sh ould have no noticeable impact of the flux distribution at the water tank due to the fixed source transport in
38 which the fission process is not being modeled Furthermore, those neutrons coming from the bundles closest to the water tank can be seen to be o f the most importance due to spatial location and in these regions, no physical simplif ications are made aside from material homogenization. In the single bundle study using a meshing scheme of 31x28x30 meshes for a single bundle, this gave good results c omparable to the most detailed case. This was used as the basis for the full core models but was adjusted in order to slightly minimize the number of meshes characterizing the fuel region. Therefore a meshing scheme of 186x56x39 was initially used to span the length of six bundles in the x axis direction and two bundles in the y axis direction. While this meshing scheme was formulated according to reasoning based on the results of the bundle study, it was thought that such detail was unnecessary in this so urce region since detailed flux distributions were not of particular interest to the study. Therefore a meshing scheme of 21x5x39 was chosen roughly based on the average mean free path in the fuel ( ~2 cm as seen from previous MCNP5 studies ). An S 4 quadrat ure set was selected as the first case since the bundle study showed that this was adequate. However, this d id not guarantee that S 4 wa s adeq uate for the more detailed full core model especially when characterizing behavior of higher energy neutrons which stream from the fuel region and past the graphite region. To ensure that an appropriate quadratur e set was selected for the full core models, the order was increased until a negligible change was achieved in flux distribution results. A series of calculati on s up to S 10 quadrature order w ere performed, but there was negligible difference between S 8 and S 10 cases. In order to come to this conclusion, an effective relative difference was calculated. This was done by calculating relative differences between S 4 and S 6 S 6 and S 8 and S 8 and S 10 cases for the 1 D flux distribution plots in the graphite region (plots in Section 4.1.2 ) for each position. Then, an average relative
39 difference was calculated based on energy group. If these group wise relative difference averages are then averaged, an effective relative difference based on quadrature order is calculated. This effective relative difference is 7.46% between S 4 and S 6 cases, 3.06% between S 6 and S 8 cases, and 1.29% between S 8 an d S 10 cases. Based on this 1.29% effective relative difference it was determined that an S 8 quadrature set was appropriate for the final full core model. Like the fuel region, the meshing schemes for the graphite and water regions of the model were also initially roughly based on using the average mean free path. The average graphite mean free path is about 2.9 cm and for water it is about 0.36 cm. Table 3 3 through Table 3 6 contain mesh sizes used in the various full core model cases. The next step in the process of establishing the final full core model was to ensure that there were no numerical issues in using the reference meshing as given in Table 3 3 ; this means ensuring that flux distribution inaccuracies were not present based on the spatial meshing being too coarse. The strategy for the meshing study was to double the number of fine meshes between cases (by multiplying the number of fine meshes along each direction by the same factor) several times looking for changes in flux shape and magnitude particularly in the graphite region. A summary of the full core cases can be found in Table 3 7 It should be noted that mesh sizes of the fuel, graphi te, and shield tank regions are of the average mean free path along the x and y axes; however the water channel within the fuel bundle s, above and below the homogenized fuel region is meshed much coarser than the shield tank region. This is due to the relative importance of this region of the problem and fine meshing of these regions would unnecessarily add more meshes to a region that is of minimal interest in this particular study. Accordingly, to ease memory requirements,
40 t he number of meshes along the axial height of the model was decreased, thus deviating from the established mean free path rule. This was found to be acceptable due to the fact that the axial flux changes were much less sensitive than along the x and y axes of t he model.
41 Figure 3 1 The MCNP5 simplified model of the UFTR ( x z slice).
42 Figure 3 2 The MCNP5 simplified model of the UFTR ( x y slice)
43 Figure 3 3 Fission n eutron d ensity (#/cm 3 s) within the UFTR c ore ( MCNP5 1 < 3.5%).
44 Figure 3 4 The GMIX generated and verified Watt fission spectra
45 Figure 3 5 The x y plane view of a typical UF TR fuel bundle at mid height showing the spatial mesh distribution
46 Figure 3 6 The x y plane view of a typical UFTR fuel bundle at mid height showing the spatial source distribution.
47 Figure 3 7 The x y plane view of a homogenized UFTR fuel bundle at mid height showing the spatial source distribution.
48 Figure 3 8 Bundle normalized neutron flux distribu tion ( # / cm 2 s ) for group 15 ( 1.920E+00
49 Figure 3 10 Bundle normalized neutron flux distribution (#/cm 2 s) for group 30 (2.606E 02
50 Figure 3 12 Bundle normalized neutron flux distribution (#/cm 2 s) for group 4 2 (5.043E 06
5 1 Figure 3 14 Bundle normalized neutron flux distribution (#/cm 2 s) for group 47 (0
52 Figure 3 16 The 3 D sp atial mesh distribution for the full core UFTR model (colors correspond to material regions as follows: red fuel, blue graphite, green water)
53 Figure 3 17 An x y sli ce of the full core UFTR model t ypical for all fuel containing axial levels (colors correspond to material regions as follows: red fuel, pink graphite, green water)
54 Figure 3 18 3 D spatial mesh distribution used in the symmetry st udy (colors correspond to material regions as follows: red fuel blue graphite, green water )
55 A B C D Figure 3 19 Flux relative differences in the graphite region for the symmetry study within the thermal, epithermal, and fast energy ranges A) group 47, B) group 30, C ) group 15, and D) group 4.
56 Figure 3 20 3 D spatial mesh distributi on for the full core UFTR model using a reflective boundary condi tion at the x z core mid plane (colors correspond to material regions as follows: red fuel, blue graphite, green water)
57 Table 3 1 BUGLE 96 broad energy group structure BUGLE 96 Broad Group Upp er Energy (eV) BUGLE 96 Broad Group Upper Energy (eV) 1 1.73E+07 25 2.97E+05 2 1.42E+07 26 1.83E+05 3 1.22E+07 27 1.11E+05 4 1.00E+07 28 6.74E+04 5 8.61E+06 29 4.09E+04 6 7.41E+06 30 3.18E+04 7 6.07E+06 31 2.61E+04 8 4.97E+06 32 2.42E+04 9 3.68E+0 6 33 2.19E+04 10 3.01E+06 34 1.50E+04 11 2.73E+06 35 7.10E+03 12 2.47E+06 36 3.35E+03 13 2.37E+06 37 1.58E+03 14 2.35E+06 38 4.54E+02 15 2.23E+06 39 2.14E+02 16 1.92E+06 40 1.01E+02 17 1.65E+06 41 3.73E+01 18 1.35E+06 42 1.07E+01 19 1.00E+06 43 5 .04E+00 20 8.21E+05 44 1.86E+00 21 7.43E+05 45 8.76E 01 22 6.08E+05 46 4.14E 01 23 4.98E+05 47 1.00E 01 24 3.69E+05 Table 3 2 Summary of bundle study cases. Case Type Quadrature Fine Meshes Numb er of Processors Decomposition Time (hours) Speedup 1 Heterogeneous S 8 221 340 14 ang=2, spa=7 3.62 1.00 2 Homogeneous S 8 26 040 8 ang=8 0.30 12.07 3 Homogeneous S 6 26 040 8 ang=8 0.30 12.07 4 Homogeneous S 4 26 040 8 ang=8 0.064 56.56
58 Table 3 3 Me sh sizes of reference UFTR full core PENTRAN model ( Case 3 ) Material Mesh Size (cm) Mesh Size/Avg MFP X Y Z X Y Z Graphite 2.625 2.540 2.000 0.910 0.881 0.693 2.634 2.667 2.170 0.913 0.925 0.752 1.9 51 2.500 2.083 0.676 0.867 0.722 H2O 1.000 1.016 2.000 2.763 2.807 5.526 1.026 1.627 2.834 4.496 1.000 2.083 2.763 5.756 Fuel 2.508 2.667 1.280 1.361 2.170 1.107 Table 3 4 Mesh sizes of UFTR full core PENTRAN model ( Case 4 ) Material Mesh Size (cm) Mesh Size/Avg MFP X Y Z X Y Z Graphite 2.083 2.016 1.587 0.722 0.699 0.550 2.091 2.117 1.722 0.725 0.734 0.597 1.549 1.984 1.654 0.537 0.688 0.573 H2O 0.794 0.806 1.587 2.193 2.228 4.386 0.814 1.292 2.249 3.568 0.794 1.654 2.193 4.569 Fuel 1.991 2.117 1.016 1.080 1.722 0.879 Table 3 5 Mesh sizes of UFTR full core PENTRAN model ( C ase 5 ) Material Mesh Size (cm) Mesh Size/Avg MFP X Y Z X Y Z Graphite 1.654 1.600 1.260 0.573 0.555 0.437 1.659 1.680 1.367 0.575 0.583 0.474 1.229 1.575 1.312 0.426 0.546 0.455 H2O 0.630 0.640 1.260 1.740 1.768 3.481 0.646 1.025 1.785 2.832 0.630 1.312 1.740 3.626 Fuel 1.580 1.680 0.806 0.857 1.367 0.697
59 Table 3 6 Mesh sizes of UFTR full core PENTRAN model ( Case 6 ) Material Mesh Size (cm) Mesh Size/Avg MFP X Y Z X Y Z Graphite 1.313 1.270 1.000 0.455 0.440 0.347 1.317 1.334 1.085 0.457 0.462 0.376 0.976 1.250 1.042 0.338 0.433 0.361 H2O 0.500 0.508 1.000 1.381 1.404 2.763 0.513 0.814 1.417 2.248 0.500 1.042 1.381 2.878 Fuel 1.254 1.334 0. 640 0.680 1.085 0.553 Table 3 7 Summary of full core cases Case Quadrature Fine Meshes Number of Processors Decomposition Time (hours) 1 S 4 407,544 24 spa=24 1.16 2 S 6 407,544 24 spa=24 2.13 3 S 8 407 544* 24 spa=24 2.77 S 10 407,544 24 spa=24 3.98 4 S 8 143,784 24 spa=24 0.81 5 S 8 284,240 24 spa=24 1.66 6 S 8 571,520 24 spa=24 3.16 *68,964 fine meshes if only considering a shield tank depth up to x= 15 c m
60 CHAPTER 4 RESULTS AND ANALYS IS 4.1 Full Core Neutron Flux Distributions As in the results of the prev iously discussed bundle study, 47 group 3 D flux distribution s w ere obtained for various cases of the full, partially homogenized core, using PENTRAN with various quadrature set s and also with MCNP5. Flux distributions from the three distinct regions of the core are presented in order to show comparisons characterizing the full extent of the core for each of the cases studied The regions consist of the fuel (x = 50 cm to 103 cm), the graphi te (x=0 cm to 50 cm), and the shield tank regions (x= 15 cm to 0 cm); the 15 cm shield tank depth is used for comparison purposes only, the final model includes flux distributions for the full extent of the shield tank along the x axis ( 105 cm to 0 cm). A similar energy group selection as shown in the bundle study results section is used for demonstration There are seven cases shown for each 1 D flux distribution plot. Case 1 to Case 3 is based on the reference mesh distribution as previously discussed in Chapter 3 (Section 126.96.36.199 ) as seen in Table 3 3 ; Case 1 uses an S 4 quadrature set, Case 2 uses an S 6 quadrature set, and Case 3 uses an S 8 quadrature set. As discussed in Chapter 3 (Section 188.8.131.52 ), b y increasing the quadrature order to S 8 it was instructive to look at the effect of increa sing the fine mesh densities (and consequently reducing the sizes of the fine meshes) of the various coarse meshes while keeping the quadrature set constant. It was decided that the number of fine meshes in the reference meshing scheme (~70,000 fine meshes if not considering the shield tank from x= 150 cm to x= 15 cm ) would be doubled (~144,000 fine meshes) then increased by a factor o f four (~284,000 fine meshes) and then by a factor of eight ( ~ 572,000) ; Case 4, 5, and 6 correspond to these latter three meshing schemes, respectively. Table 3 3 to Table 3 6 in addition to giving the various mesh dimensions,
61 provides the fraction of the energy average d mean free paths that correspond to each mesh dimension for each material. This provides a qua ntitative view of how the mesh sizes are decreasing i n relatio n to the respective material average mean free path Case 7 is the MCNP5 bench mark case. This case is considered to a depth of only 15 cm in to the shield tank region along the x axis since tally quantities are scarcely obtained past this depth and since stat istics are poor due to the small chance of neutron survival in the random walk process of the Monte Carlo method 4.1.1 Fuel The particular fuel region being analyzed in the figures (reference Figure 3 17 for visual aid) of this secti on is the fuel region along the x axis at y cm and z cm ( core axial mid plane). The source term is located in the fuel region and therefore it is expected that there is agreement between the two solution methods especially within this region Al l figures shown in this section and Section 4.1.2 pe rtaining to the graphite regio n, have maximum MCNP5 1 statistical uncertainties t hat are less than 1 0 % ; figures discussed in Section 4.1.3 contain 1 statistical uncertainties in the range of 0% to 42%. Upon examination of the flux distributions in Figure 4 1 and Figure 4 2 there is agree ment between the two solution methods. Note the depressed flux toward the right side of the graphs; this behavior is due to the presence of the dummy bundle which contains no fuel and therefore no source term. The flux shapes between MCNP5 and PENTRAN foll ow similar trends in that the peaks and valleys correspond to the same positions. Oscillatory behavior of the flux in the areas where peaks occur in the overall shape are caused by the way the source was defined, which is with five meshes representing a si ngle fuel plate along the x axis for neutron sampling in the MCNP5 models. Since five points were essentially specified for the neutron sampling, we see a spike where the center points of th os e meshes lie. This sampling method causes artificial
62 spikes to o ccur due to the fact that the volume source being modeled is based on a collection of point sources However, since there are 308 plates with 100 meshes representing one plate, a finer meshing scheme would likely have a more detailed source specification f or likely no gain except the smoothing of the observed spikes. S ince the goal is not the characterization of the fuel region but the characterization of the shield tank these spikes are rather inconsequential to the overall goal of this work. The behavio r is merely a side effect of the mode l ling choice. Furthermore, the spatial dependence of the source on the plate level becomes less and less important as neutr ons travel farther from the core and closer to the shield tank Since there are nearly 20 mean fr ee paths (based on the graphite average mean free path) between the shield tank and fuel region, five meshes seem to suffice for this application. T his also accounts for the oscillatory behavior seen in the results section of the bundle study for MCNP5 flu x distributions Upon examination of the different cases in Figure 4 1 and Figure 4 2 we see that the lower quadrature order cases (Case 1 and 2) and the higher quadrature order case ( Case 3 ) show simil ar behavior. In Case s 4, 5, and 6 w h ere there are more meshes along any given direction, there are naturally more accurate flux shape s as seen more prominently in Case s 5 and 6 which nicely move with the peaks and valleys of the Case 7 MCNP5 distribution Figure 4 3 and Figure 4 4 correspond to flux distributions calculated in the epithermal energy range. Excellent agreement is seen for this range of the spectrum ; all cases seem to converge onto one anot her revealing no apparent gain by moving to higher quadrature order and increasing the mesh density As with the plots shown above in the faster end of the spectrum, the regions with local peaking are those containing fuel bundles; there are three main pea ks for the three fuel boxes (each containing a 2 x 2 array of four bundles).
63 If we look at the flux plots for energy groups in the thermal range in Figure 4 5 t o Figure 4 8 there is good agreement, mostl y less than 10% relative difference ; the exception is group 46. The group 46 flux distribution is some cause for concern. Going back to the bundle study, we saw that the group 46 flux distribution was underestimating for all PENTRAN cases, even the finely meshed heterogeneous case. This shows that the apparent inaccuracy of this group flux distribution is not caused by material homogenization or fine mesh coarseness and is evidently a cross section issue Although these thermal groups are not of particular importance to the fixed source transport of neutrons from the fuel to the shield tank due to the low chance of actually reaching this region they become increasingly important as higher energy neutrons approaching the shield tank region scatter down to th ermal energies. This is an issue since the majority of the flux in the shield tank comes from these bottom two groups. Furthermore, in the next section looking at the graphite region between the core and the shield tank, other issues arise that possibly fu rther degrade the quality of the PENTRAN solution for group 46 and 47. 4.1.2 Graphite The graphite region between the fuel and shield tank is characterized i n this section Figures include 1 D flux distributions (at the core mid planes; y cm, z cm) a s well as 3 D fl ux representations to show a broader trend. All presented PENTRAN 3 D flux distributions correspond to the S 8 reference meshing case. The comparisons for the faster groups, as seen in Figure 4 9 and Figure 4 10 show the impact of the higher quadrature orders. Fast neutrons are highly mono directional in the graphite region; this means, to have survived, most of the contribution to the respective fast group flux distributions (such as group 4 and 7 as seen in Figure 4 9 and Figure 4 10 respectively ) is from uncollided neutrons. This means that for higher energy neutrons, the number of directions (which is determined by the quadrature order) is increasingl y important up to a certain point at which
64 increasing the quadrature order does little with respect to increased solution accuracy Case 1, with the fewest directions shows a somewhat oscillatory behavior in the flux distribution which can be identified as ray effects which occur when the quadrature order is too low. Increasing to S 6 in Case 2 shows improvement, but still there is some identifiable oscillatory behavior. By Case 3, there is agreement with the Case 7 MCNP 5 results at the interface of the shield tank most noticeably in Figure 4 10 The PENTRAN models with increased number s of meshes corresponding to distributions in Cases 4 to 6, do not provide any observable improvement in solution compared to Case 3 Figure 4 11 show s the g roup 15 3 D flux distribution for the graphite region bounded in the axial direction by the height of the fuel region, for PENTRAN and MCNP5. Also given are the MCNP5 1 statistical uncertaint ies and the relativ e differences between the PENTRAN and MCNP5 results Looking at (D) in Figure 4 11 it is apparent that the relative differences are primarily less than 15%, however there are significant differences at the model boundaries (not at the reflective boundary) between 40% and 70%. This is not detrimental since the region of interest lies primarily at the central portion of the shield tank where fluxes are highest. Figure 4 12 and Figure 4 13 are 1 D flux distributions at the lower end of the fast spectrum There is excellent agreement for all cases in these figures with relative errors mostly less than 10% Looking at Figure 4 14 characterizing the 3 D beh avior of the group 35 flux distribution s a similar contour is seen between MCNP5 and PENTRAN fluxes and MCNP5 1 uncertainty is low (all are less than 10%) However, the relative differ ence mapping has changed and is now more uniform Relative differences are mostly less than 10% and again increase toward the model boundary along the north face of the region (+y direction in the figure). Fi gure 4 15 and Figure 4 16 showing 1 D flux distributions for groups 30 and 35 respectively, both
65 consistently show relative differences less than 10 % which is in agreement with Figure 4 14 (D). Again, all cases are in agreement. Figure 4 17 represents the group 47 3 D flux distribution s and relative difference mapping. What differs between (D) of this 3 D contour p lot and the previous plots is th e increasing relative differences with increasing distance from the fuel region as the shield tank wall is approached. This implies that there is conflict between the PENTRAN and MCNP5 flux shapes along the x axis. Figure 4 18 and Figure 4 19 groups 42 and 45 respectively, show very good agreement among all cases; relative differences are all less than 10%. Figure 4 20 and Figure 4 21 groups 46 and 47 respectively, show noticeable disagreement. Since the relative differences between the PENTRAN and MCNP5 flux distributions are increasing toward the shield tank it would seem likely that there is a numerical issue in the calculation as opposed to the idea that the cross sections for groups 46 and 47 are defici ent. If the cross sections are d eficient it is expected that there would be a constant relative difference as a function of position along the x axis I ncreasing the number of fine meshes from Case 3 to 6 appears to cause no change in the PENTRAN solution. 4.1.3 Shield T ank Figure 4 22 to Figure 4 29 give a 1 D representation of neutron flux distributions in the shield tan k region calculated to a depth of 15 cm along the x axis s hown at the core mid planes. The MCNP5 results were obtained after completion of 2 8 x 10 8 histories using 14 processors in parallel with the Einstein PC Cluster; this equates to over 90 hours of el apsed wall time. In Figure 4 22 and Figure 4 23 showing group 15 and group 20 flux distributions in the fast regime, it is immediately apparent that there are tally scoring issues and large statistical u ncertainti es; however MCNP5 fluxes follow a similar trend to the PENTRAN fluxes despite the unphysical nature of the MCNP5 results. All of the PENTRAN cases are in agreement
66 The epithermal flux distributions of Figure 4 24 and Figure 4 25 show the same trend as the fast flux distributions; specifically MCNP5 results indicate tally scoring issues and large statistical uncertainties with MCNP5 flux distributions follow ing a similar trend to those of PEN TRAN. The thermal group flux distributions, namely group 42 in Figure 4 26 and group 45 in Figure 4 27 show excellent agreement in two groups that actually have some acceptable statistical uncertainties The PENTRAN g roup 46 and 47 flux distributions, Figure 4 28 and Figure 4 29 respectively, are again in disagreement with MCNP5 ; statistical uncertainty is apparently not the cause of the problem due to the fact that 46 and 47 are the bottom two energy groups As in the graphite region, there is some flux shape disagreement (seen as differing slopes on the logarithmic scale) although less pronounced than in the graphite region. Whatever the cause of thi s disagreement which a pparently come s from inadequate cross s ection data throughout the full core model for group 46 and group 47 there is more than an order of magnitude difference in the bottom two groups between PENTRAN and MCNP5 flux distributions. Figure 4 30 to Figure 4 33 show the neutron flux spectrum from PENTRAN (the S 8 quadrature case with the reference meshing scheme and complete tank depth along the x axis ) and MCNP5 for four locations along t he x axis in the shield tank at 0.25, 4.75, 10.25, and 14.75 cm, respectively Figure 4 34 shows the neutron flux spectrum from PENTRAN only at x= 100.5 cm. As expected group 46 and 47 fluxes dominate for all positions with di fferences between PENTRAN and MCNP5 becoming more evident with increasing depth into the shield tank. Figure 4 30 actually shows excellent agreement between the two spectra for many groups (when MCNP5 data is present). For Figure 4 31 to Figure 4 33 MCNP5 relative errors are large
67 causing the shape of the spectra to be somewhat inconsistent ; lack of data is also seen for many groups. Looking at Figure 4 34 at x= 100.5 cm, the shape of the spectra is still basically the same as seen at the shield tank wall. The magnitude of the group 47 flux at this location has dropped almost eig ht orders of magnitude to ~2,000 (#/cm 2 s) 150 cm, the group 47 flux is calculated as ~ 1 (#/cm 2 s) essentially nothing. Based on the above results, the S 8 PENTRAN case with the reference meshing scheme (~ 40 0,000 fine meshes) has shown to provide ac ceptable results. An S 8 quadrature set was shown to eliminate the ray effects seen in the other S 4 and S 6 cases with the same meshing scheme. It was also seen that increasing the number of meshes by factors of two, four, and eight provided no appreciable g ain in accuracy when compared to the S 8 reference case. Very good agreement was shown among groups characteristic of the thermal, epithermal, and fast energy regimes in all materials regions (except at model boundaries) with the exception of group s 46 and 47 which sho wed disagreement for all particular regions of interest T his disagreement is most likely attributable to the fact that the BUGLE 96 group 46 and 47 flux weighted cross section s are not suitable for this study 184.108.40.206 Determination of the maximum bio logical dose equivalent rate The 3 D multi group flux distributions in the shield tank can be multiplied by biological dose equivalent rate factors to obtain a dose rate estimate based on International Commission for Radiological Protection Publication 21 (ICRP 21) neutron flux to dose conversion factors. Appendix H of the MCNP5 manual gives a table based on these factors in units of (rem/hr)/ ( #/cm 2 s) [ 4 ] It is recommended that log log interpolation be performed wh en exact data is not given in the table; accordingly, this interpolation was done graphically using Figure 4 35 which was constructed based on the table in the MCNP5 manual providing the ICRP 21 conversion factors.
68 A conservative approach was taken in calculating the dose equivalent rate. As seen in Figure 4 35 there are three main energy ranges over which a curve ( the dotted line) has been overlaid to conservatively appro ximate the dose conversion factors corresponding to the BUGLE 96 energy group structure These three broad groups range from 0 MeV to ~0.01 MeV (thermal), ~0.01 MeV to ~1 MeV (epithermal), and greater than ~1 MeV (fast). In the thermal and fast ranges, the conversion factors are assumed to be approximately constant with the largest conversion factor in the range being used to characterize the respective ranges. In the epithermal range, the conversion factors show a strong dependence on energy. Again a conse rvative approach is take n in estimating the dose conversion factor in the epithermal range by using the dose conversion factor corresponding to the u pper energy bound of each group as opposed to an average Table 4 1 shows the dose conversion factors for the 47 group BUGLE 96 structure as read from Figure 4 35 Applying the conversion factors in Table 4 1 to the 1 D multi group flux distributions in the shield tank at the core mid planes (where the flux is the highest), the group dependent biological dose equivalent rates are calculated. Summing these group wise dose rates, an estimate of the spectrum weighted total biological dose eq uivalent rate is obtained as a function of shi eld tank depth along the x axis; this is shown in Figure 4 36 As seen from Figure 4 36 the estimated biological dose equival ent rate at the outer tank wall (x=0 cm) is ~0.4 mrem/hr. 4.2 Speedup and Parallel Processing Efficiency Using PENTRAN The benefit of using a deterministic code such as PENTRAN is that it provides scalar flux information for the entire model inherently once a calculation is completed As long as the flux converges for an appropriately specified tolerance and proper c onsideration is taken in model prepar ation, PENTRAN is very useful for detailed 3 D multi group flux characterization.
69 Additionally, parallel proce ssing capabilities allow larger, more detailed, problems to be modeled in an otherwise limited capacity. The MCNP5 methodology has been proven to be robust but due to the statistical nature of the Monte Carlo process, complications can arise with statist ical significance in regions which are optically thick where few tallies are being scored as seen in the shield tank region ; this is especially true for higher energy neutrons. Without detailed variance reduction, large real world problems can become compu tationally expensive Therefore, PENTRAN is the preferred code for this application and MCNP5 is used as a benchmark in a somewhat limited capacity. The MCNP5 computation times are not listed in the following sections since MCNP5 ultimately is not going to be used for the detailed 3 D multi group characterization of the shield tank and since the current computation time is unknown for achieving statistically significant results It was already stated that over 90 hours of computation time (with 14 processors) were used and still there was un certainty to the flux results seen in the shield tank. The total computation time for the reference S 8 PENTRAN calculation including the entire 150 cm x axis tank depth was 2.77 hours on 24 processors As disc ussed previously, Table 3 2 gives a summary of the model attribut es for dedicated parallel jobs. Of paramou nt importance for this work was maximizing computational efficiency while at the same time obtaining a 3 D 47 group neutron flux characterization of as much as the lower shield tank region as possible. Applying the findings ascertained from the bundle study, a homogeneous fuel region was used for the full scale PENTRAN models of the UFTR core and shield tank. Model homogenizat ion helped with memory requirements by allowing the fuel region to be characterized with fewer meshes as compared with a heterogeneous configuration while still maintaining flux distribution accuracy
70 Th e analysis (i.e. combinations of different spatial mesh sizes and angular quadrature orders) performed on these six PENTRAN cases prompted the conclusion that the reference S 8 case contain ing 144 coarse meshes, ~ 40 0 000 fine meshes, and 1 6 axial levels was the best mode l ling choice. Substantial work was do ne with this model to minimize the load im balance in an effort to maximize the computational efficiency for use with a parallel computing environment Originally, t his model was segmented into 1 6 axial coarse meshes i n order to fully utilize spatial decomp osition on either the Einstein or Chadwick PC Cluster When the Bohr PC Cluster became available, 24 processors were able to be used for use for a given problem. This worked out well with the 16 level, 144 coarse mesh design since the 24 processor cluster was also able to be fully utilized with th e selected model configuration. Since the model was designed to use a symmetric boundary condition along the x z core mid plane effectively reducing the number of fine meshes in half memory requirements were not of concern for the 407,544 fine mesh model As discussed in Section 2.2 the parallel load im balance w as kept low to minimize proces sor communication lag. The load im balance was calculated to be 1. 54 which is reasonable considering the extent of the problem being modeled and the varying coarse mesh densities. 4.3 Scalar Flux Convergence The angular flux convergence is important in establi shing validity to results in any particular model. If fluxes are not converging in a certain region this may indicate problems with meshing or other mode l ling considerations such as quadrature set. For the full scale model, an inner iteration convergence to lerance of 0.005 was used. Figure 4 37 gives information about coarse mesh convergence as a function of coarse mesh position for group 47 In the reference S 8 model, all groups converged except for group 47 of which 82% of the coa rse meshes exceeded the convergence tolerance as seen visually in Figure 4 37 The red color in Figure 4 37
71 represents regions that exceeded the inner iteration tolerance of 0.005 and the blue regions rep resent those that have converged for group 47; the maximum value is 0.0159. The fact that the fuel region coarse meshes converged for group 47 may explain why results seem accurate for group 47 flux distributions in the fuel region However, f lux convergen ce does not guarantee that fluxes are accurate This is seen in the group 46 flux distribution s which proved to be inaccurate throughout the entire model compared to the MCNP5 benchmark despite meeting the convergence criteria. For this reason, it cannot b e argued with complete certainty that the PENTRAN group 47 flux distribution s disagree with MCNP5 based on not me eting the convergence tolerance; however it is a possible explanation.
72 Figure 4 1 Ne utron flux distribution (#/cm 2 s) in the fuel region for group 1 5 (1.920E+00
73 Figure 4 3 Neutron flux distribution (#/cm 2 s) in the fuel region for group 30 (2.606E 02
74 Figure 4 5 Neutron flux distribution (#/cm 2 s) in the fuel region for group 42 (5.043E 06
75 Figure 4 7 Neutron flux distribution (#/cm 2 s) in the fuel region for group 46 ( 1.000E 07
76 Figure 4 9 Neutron flux distribution (#/cm 2 s) in the graphite region for group 4 (8.607E+00
77 A B C D Figure 4 11 Group 15 3 D flux distributions (#/cm 2 s) in the graphite region. (A) MCNP5 flux distribution (B) MCNP5 1 (C) PENTRAN flux distribution, and (D) PENTRAN/MCNP5 relative differences
78 Figure 4 12 Neutron flux distribution (#/cm 2 s) in the graphite region for group 15 (1.920E+00
79 A B C D Figure 4 14 Group 35 3 D flux distributions (#/cm 2 s) in the graphite region. (A) MCNP5 flux distribution (B) MCNP5 1 (C) PENTRAN flux distribution, and (D) PENTRAN/MCNP5 relative differences
80 Fi gure 4 15 Neutron flux distribution (#/cm 2 s) in the graphite region for group 30 (2.606E 02
81 A B C D Figure 4 17 Group 47 3 D flux distributions (#/c m 2 s) in the graphite region. (A) MCNP5 flux distribution (B) MCNP5 1 (C) PENTRAN flux distribution, and (D) PENTRAN/MCNP5 relative differences
82 Figure 4 18 Neutron flux distri bution (#/cm 2 s) in the grap hite region for group 42 (5.043E 06
83 Figure 4 20 Neutron flux distribution (#/cm 2 s) in the graphite region for group 46 ( 1.000E 07
84 Figure 4 22 Neu tron flux distribution (#/cm 2 s) in the shield tank region for group 15 (1.920E+00
85 Figure 4 24 Neutron flux distribution (#/cm 2 s) in the shield tank region for group 30 (2.606E 02
86 Figure 4 26 Neutron flux distribution (#/cm 2 s) in the shield tank region for group 42 (5.043E 06
87 Figure 4 28 Neu tron flux distribution (#/cm 2 s) in the shield tank region for group 46 (1.000E 07
88 Figure 4 30 Neutron flux (#/cm 2 s) spectra at x= 0.25 cm at core mid planes. Figure 4 31 Neutron flux (#/cm 2 s) spectra at x= 4 7 5 cm at core mid planes.
89 Figure 4 32 Neutron flux (#/cm 2 s) spectra at x= 1 0.25 cm at core mid planes. Figure 4 33 Neutron flux (#/cm 2 s) spectra at x= 14 7 5 cm at core mi d planes.
90 Figure 4 34 Neutron flux (#/cm 2 s) spectra at x= 100. 5 cm at core mid planes. Figure 4 35 Flux to dose conversion factors as a function of neutr on energy.
91 Figure 4 36 Biological dose equivalent rate as a function of x axis position in the shield tank at the core mid planes.
92 Figure 4 37 Group 47 c onvergence as a function of coarse mesh for the full core model (blue represents the fuel region) Table 4 1 Calculated biological dose equivalent rate conversion factors based on BUGLE 96 energy group stru cture Energy Group Conv ersion Factor (rem/hr) 34 47 4.55E 06 33 4.80E 06 32 5.00E 06 31 6.80E 06 30 1.00E 05 29 1.20E 05 28 2.70E 05 27 3.00E 05 26 4.80E 05 25 5.70E 05 24 7.00E 05 23 8.00E 05 22 1.00E 04 19 21 1.30E 04 1 18 1.30E 04
93 CHAPTER 5 CONC LUSIONS AND FUTURE WORK The objective of this work was to obtain a benchmarked, 3 D multi group neutron flux distribution in the shield tank of the UFTR for future use in the design of a burn up reconstruction device. Adding to that, the other major goal was to develop an efficient model providing the detailed flux solution in a reasonable amount of computation time The PENTRAN code system was chosen for mode l ling of this detailed distribution due to : 1) ability of the deterministic code to provide the flu x solution inherently upon successful completion of an adequately converged model, 2) parallel processing capabilities, and 3) the adaptive differencing scheme. The PENTRAN code system has also been successful in the benchmarking of many real world neutral particle transport applications. MCNP5 wa s chosen as the code system for the determination of the fission source distribution and for benchmarking the PENTRAN results due to the widespread use of the code in the nuclear sciences field. Chapter s 3 and 4 discussed the methodology developed in order to increase PENTRAN model efficiency. This was achieved mostly by material homogenization to minimize fine meshes in the fuel region development of a variable mesh ing scheme use of an appropriate quadrature set ( c hosen as S 8 ), and using symmetry by implementing a reflective boundary condition at the x z core mid planes Furthermore, efficiency was achieved by utilizing as much processing power as was available ( 24 processors of the Bohr PC Cluster) while minimizing the parallel load im balance (1. 54 ) of the system. As seen in Chapter 4, overall agreement between PENTRAN and MCNP5 cases can be seen between flux distributions in all regions of the UFTR core and nearby regions with the exceptions of group 46 and 47 C haracte rization of the shield tank proved to be troublesome with the benchmark MCNP5 cases because of statistical significance and tally underscoring; however,
94 PENTRAN showed agreement with MCNP5 overall group wise trends throughout the shield tank. F or active sp ent fuel interrogation, the burn up reconstruction device should be placed as close to the shield tank wall as possible in order to maximize the flux seen by the device Hopefully, the region modeled give s an idea of what kind of fluxes can be expected for various energies of interest as a function of 3 D space, but more benchmarking data is needed to completely validate the developed PENTRAN model. Future Work and Improvements This study has several aspects that need to be studied further. This work was in tended to be a benchmarking problem; however, the integrity of MCNP5 results is somewhat questionable within the shield tank region One thing that could be done is to develop a more statistically significant MCNP5 characterization of the shield tank Use of the code A 3 MCNP would be a great tool and could be a very useful aid for this task by employing effective variance reduction methods [ 12 ] In support of more benchmarking, experimental analysis, possibly using Neut ron Activation Analysis ( NAA ) techniques could also be obtained throughout the major regions of interest in the shield tank To resolve differences between PENTRAN and MCNP5 for group 46 and 47 flux distributions, a problem specific cross section library c ould be generated from the SCALE [ 13 ] 238 fine group neutron cross section library using the DEV XS methodology [ 9 ] developed at the University of Florida Finally, for a m ore complete characterization of the shield tank gamma ray transport shou ld be included in order to fully provide useful information for future implementation by other researchers.
95 LIST OF REFERENCES  HAGHIGHAT, A. SJODEN, S., VERNETSON, W., BACIAK, J., ANGHAIE. S. Submittal report to cover analyses of U niversity of F lorida T raining R eactor ( UFTR ) conversion from HEU to LEU Technical report, University of Florida, 2005. [2 ] SJODEN, G. HAGHIGHAT, A., PENTRAN Code System User's Guide to Version 9.4X.1 Serie s HSW Technologies LLC, 2008, Parallel Distributed Decomposition of Discrete Ordinates (S n ) in 3 D Cartesian Geometry. [3 ] SJODEN, G. HAGHIGHAT, A., P ENTRAN A 3 D C artesian parallel S n code with angular, energy, and spatial decomposition, in Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing in Nuclear Applications volume II, pages 1267 1276, Saratoga Springs, NY, 1997.  X 5 MONTE CARLO TEAM MCNP: A General Monte Carlo N Particle Transport Code, Version 5 LA UR 03 1987 2004. [5 ] DIONNE, B. et al., A detailed neutronics comparison between the U niversity of F lorida T raining R eactor ( UFTR ) current HEU and proposed LEU core, in Proceedings of the PHYSOR ANS Topical Meeting Vancouver, BC, Canada, 2006.  HAGHIGHAT, A. DIONNE, B., SJODEN, G., BA CIAK, J., VERNETSON, W., MATOS, J., Methodologies and related issues U niversity of F lorida HEU to LEU fuel conversion project, in Proceedings of the 48th Annual INMM Meeting Tucson, AZ, USA, 2007.  LAMARSH, J. R., Introduction to Nuclear Engineering Addison Wesley Publishing Company, Reading, MA, USA, 2 edition, 1983.  WHITE, J. E. INGERSOLL, D.T., SLATER, C.O., ROUSSIN, R.W. B UGLE 96: A revised multigroup cross section library for LWR applications based on ENDF / B VI release 3, in American Nuclear Society Radiation Protection & Shielding Topical Meeting Falmo uth, MA, USA, 1996, Oak Ridge National Laboratory. [9 ] MOCK, T. MANALO, K., PLOWER, T., SJODEN, G., DEV XS: A Cross Section Development Primer for PENTRAN/PENBURN Version 2.0 FINDS, 2007.  YI, C., PENMSH Express Manual Transport Theory Group at University of Florida Nuclear and Radiological Engineering Department, 2007, A Mesh Generator to Build PENTRAN Input Deck.  CROSS SECTION EVALUATION WORKING GROUP, E NDF / B VI summary documentation, BNL NCS 17541 ( ENDF 201), Technical report, National Nuclear Data Center, Brookhaven Nat ional Laboratory, Upton, NY, 1991.  WAGNER, J. C. HAGHIGHAT, A. A 3 MCNP: Automatic Adjoint Accelerated MCNP User's Manual Oak Ridge National Laboratory and The Pennsylvania State University Department of Nuclear & Mechanical Engineering, Oak Ridge, TN, USA, version 1.0i, 2000.
96  SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluations, ORNL/TM 2005/39 version 5.1, vols. i iii, 2006, Available from Radiation Safety Information Computational Center at Oak Ridge Na tional Laboratory as CCC 732.
BIOGRAPHICAL SKETCH Amrit Davi d Patel was born in Albany, GA in 1984. He moved to Apopka, FL in 1988 There he graduated from Apopka High School in 2002. He was accepted to the University of Florida upon completion of high s chool and obtained a b Nuclear and Radiological Engineering in 2006. During his undergraduate years, he interned with Southern Nuclear Company ( Birmingham, AL ) under the B oiling Water Reactor core analysis group. Whil e completing his graduate studies in nuclear engineering, he also interned with the U.S. Nuclear Regulatory Commission (NRC) in Washington D.C. which lead to a permanent position with the Office of New Reactors in the Reactor Systems branch. During graduat e school, Amrit was awarded a fellowship by the U.S. N uclear Regulatory Commission