© 2009 Amrit David Patel - University of...

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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 REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2009

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© 2009 Amrit David Patel

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To my Mother and Father for their perpetual love and support and to Jessica for her

encouragement and understanding

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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 grateful.

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 member. I thank the members

of the University 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 Regulatory 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.

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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 Modelling 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

3.2.1.1 Adaptation of UFTR refueling model ..........................................................23 3.2.1.2 Criticality calculation for fixed source generation .......................................25

3.2.2 Development of PENTRAN Models ......................................................................27 3.2.2.1 Single bundle study ......................................................................................27 3.2.2.2 Source specification and spatial meshing selection .....................................27 3.2.2.3 Effect of angular quadrature set order ..........................................................29 3.2.2.4 Effect of homogenization .............................................................................29

3.2.2.5 GMIX: Cross-section library development and source spectrum ................31

3.2.2.6 Results ..........................................................................................................33

3.2.2.7 Application of the bundle study to full scale model .....................................35

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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 4.1.3.1 Determination of the maximum biological dose-equivalent rate .................67

4.2 Speedup and Parallel Processing Efficiency Using PENTRAN .......................................68 4.3 Scalar Flux Convergence ..................................................................................................70

5 CONCLUSIONS AND FUTURE WORK .............................................................................93

LIST OF REFERENCES ...............................................................................................................95

BIOGRAPHICAL SKETCH .........................................................................................................97

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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



3-7 Summary of full-core cases. ..............................................................................................59

4-1 Calculated biological dose-equivalent rate conversion factors based on BUGLE-96

energy group structure. ......................................................................................................92

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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 (#/cm3-s) within the UFTR core (MCNP5 1-σ uncertainty <

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 (#/cm2-s) for group 15

(1.920E+00

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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 distribution 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 UFTR 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 distribution (#/cm2-s) in the fuel region for group 15

(1.920E+00

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4-11 Group 15 3-D flux distributions (#/cm2-s) in the graphite region. (A) MCNP5 flux

distribution, (B) MCNP5 1-σ statistical uncertainty, (C) PENTRAN flux distribution,

and (D) PENTRAN/MCNP5 relative differences..............................................................77

4-12 Neutron flux distribution (#/cm2-s) in the graphite region for group 15

(1.920E+00

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4-26 Neutron flux distribution (#/cm2-s) in the shield tank region for group 42

(5.043E-06

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Abstract of Thesis Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Master of Science

DETAILED NEUTRON FLUX CHARACTERIZATION OF THE EXPERIMENTAL SHIELD

TANK FACILITY AT THE UFTR

By

Amrit David Patel

May 2009

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

management 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 would 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 accurate solutions at

significantly reduced computational time as compared to the Monte Carlo calculations.

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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. This 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 are to reduce the amount of high-level waste by using the spent nuclear fuel and

addressing 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 stress on the issues that come along with

Yucca Mountain, the selected geological repository located in Nevada, built 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 researchers, 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: Can we develop a non-destructive

methodology which can accurately identify isotopic content 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 way to assay spent nuclear fuel experimentally.

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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 interrogate 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 fields within the shield tank.

The goal of this work does not deal with the 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, this work discusses

an effective methodology 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 Core Region

The UFTR is a 100 KWt graphite-moderated, water-cooled/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 fuel bundles and giving a bird’s eye view of the reactor components. The reactor core

contains six aluminum boxes, and each box can hold a maximum of four fuel bundles. Each fuel

bundle consists of 14 fuel plates (0.51 mm in thickness); the fuel meat is made of U3Si2-Al at an

enrichment of 19.75 wt%, and the cladding is 6061 aluminum alloy. Presently, the two boxes on

the east side of the core contain two “dummy” bundles without fuel; both bundles are located on

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

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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 Shield Tank

As 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 dimensions. 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 experimentation. 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.

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Figure 1-1. Dimensions of the UFTR.

Figure 1-2. Side and aerial view of the UFTR.

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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,

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In the above equation we are interested in solving for which represents the

angular group flux for the gth

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 solved analytically, we turn to the 3-D discrete ordinates

(Sn) PENTRAN (Parallel Environment Neutral-particle TRANsport) code system [2, 3].

2.2 Modelling With PENTRAN

The PENTRAN code system is developed to solve 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 the 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. Therefore, the 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 important 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.

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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 length 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 most important aspects of model 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 PENTRAN 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

angular 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 decomposition strategy is quite

effective in speeding up problems by increasing the rate of inner iteration 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

often 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 each spatial domain is solved

on one processor; this can significantly lower memory demands per processor. The speedup from

spatial decomposition is also advantageous if implemented properly.

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When using spatial decomposition in parallel jobs, it is crucial to consider the parallel load

imbalance. 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. According 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 equally 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 problem, 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 imbalance.

Consequently, the boundary data 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

between processors, large lags can occur in the calculation therefore causing the model to be

computationally inefficient. With this description in mind the load imbalance can be practically

defined as the number of fine meshes on the processor with the most coarse meshes divided by

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the number of fine meshes on the processor with the least fine meshes. Therefore, as implied by

previous statements, the closer the load imbalance is to unity, the more efficient the parallel

calculation will be.

The parallel load imbalance is considered 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, cross-section

data, and variable decomposition play very important roles and will be further discussed in the

context of the models developed for this work.

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CHAPTER 3

METHODOLOGY

In this chapter, the MCNP5 and PENTRAN modelling methodology is explained. The

discussion begins with an introduction of the computer systems by which the calculations in this

work were made possible. Also, the MCNP5 fixed source development, used in both PENTRAN

and MCNP5 full-core models, is discussed in addition to an important bundle study that provides

modelling insight for the subsequent full-core models. Finally, the full-core PENTRAN models

are fully described along with the reasoning for choosing the different cases of this study.

3.1 Particle Transport and Distributed Computing (PTDC) Laboratory

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. The entirety of the particle transport simulations were performed using

the parallel computational clusters at the University of Florida Transport Theory Group

(UFTTG) PTDC lab, which is managed by the UFTTG.

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

the entire system. Likewise, another 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

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of DDRAM for the entire system. The Bohr cluster is used for the large models 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 the most efficient way possible. It will be

demonstrated 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, statistical 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 Models

Due to the capability of the Monte Carlo method to solve complex 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 MCNP5’s statistical method is not

necessarily the ideal method for reaching our goal of characterizing neutron flux efficiently

throughout our model. However, MCNP5 fits well to 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.

3.2.1.1 Adaptation of UFTR refueling model

Between 2005 and 2006, the UFTR went through refueling of the reactor core due to a

U.S. Department of Energy (DOE) Program to convert existing research reactor fuel from Highly

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Enriched Uranium (HEU) fuel to Low Enriched Uranium (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 fission 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 distribution 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,

the 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 and the upper portion of

the tank. Therefore, a model that mirrors the actual PENTRAN model is desired to minimize

model differences when comparing PENTRAN flux distributions to MCNP5 flux distributions.

In summary, the detailed MCNP5 model is used strictly for the generation of the fixed source for

use in the full-core models of this study.

The MCNP5 modelled 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 these figures are compared with those in Figure 1-1 and Figure 1-2, it is

apparent that this 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 reasons for this are: 1) because

physically, it is not likely that neutrons leaving the model at the chosen boundaries will have

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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.

3.2.1.2 Criticality calculation for fixed source generation

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 throughout 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 energy using a Watt fission spectrum [4]. To achieve

a statistically reliable source distribution, we have used 800 cycles, 50,000 histories/cycle, and

100 skipped cycles. To tally fission source density, for each fuel plate, 100 meshes were defined

(5 across the width of the plate, 1 representing the thickness, and 20 axially).

Figure 3-3 shows the calculated 3-D fission neutron density (#/cm3-s) throughout the six

fuel boxes. Note that the 1-σ statistical uncertainty associated with these results is less than

~3.5%. This calculation was performed using the Einstein PC-cluster with 16 processors.

To generate the multi-group fission neutron source distribution 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,

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,

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 compares the multi-group

fission spectrum as generated by the cross-section mixing code GMIX [9], to be discussed in

more depth later in this chapter, and the independently verified spectrum as calculated by using

the above equation by numerically integrating 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 accurate treatment of GMIX due to isotope and enrichment dependency

when generating the spectrum.

The MCNP5 code can use the fission neutron source distribution and the fission spectrum

to create a multi-group fission neutron source distribution for performing 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 computation 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 efficient fixed source simulation.

The designs of the full-core MCNP5 models were discussed in detail in Section 3.2.1.1. In

the following discussions of the PENTRAN code system and model development for the single

bundle study, concurrent MCNP5 models were constructed with the same geometric

configurations and material specifications for comparison purposes. Since the scope of the

bundle models are relatively small and since they are computationally inexpensive to run, only

criticality calculations are performed with the created MCNP5 models. Since the basis of this

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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 Models

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].

3.2.2.1 Single bundle study

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 accelerate these smaller calculations in order to gain insight

into modelling choices for the larger, computationally taxing model, which includes the entire

core and shield tank regions. In this section, the foundation for choices 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 models in the study is shown in Figure 3-5; blue regions indicate water

gaps, green is the aluminum fuel plate cladding, and red is the fuel meat.

3.2.2.2 Source specification and spatial meshing selection

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 Section

3.2.1.2. Although the fixed source in PENTRAN is defined differently than the source used in

MCNP5, the same spatially-dependent fission-neutron density distribution is used.

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In PENTRAN, the source is defined with a given spatial mesh defined by the user. This

mesh does not have to be the same as that of the physical model. PENTRAN effectively projects

the defined source onto the specified mesh 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 which can lead to inaccurate results.

Therefore, the best choice is to simply align the source mesh 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 meshes, 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 define such a spatially

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, one must be concerned 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 in

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/source 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 studied 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 center 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 selected meshing scheme provides a load imbalance as close to one as

possible since this parameter drastically affects computational efficiency; this is not important in

this single bundle model, but it is important for large models containing a significantly larger

number of fine spatial meshes, and will be discussed more in depth in following chapters.

Several cases were performed with different meshing types, from very fine to very coarse,

to study the effect on the flux distributions. The goal was to obtain the coarsest meshing scheme

possible that essentially gives the same result as the heterogeneous reference case taken to give

the correct solution and having a very fine mesh resolution. Along with this study, it is necessary

to determine the appropriate order of the angular quadrature set.

3.2.2.3 Effect of angular quadrature 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 shown that a lower

quadrature order is most appropriate due to the diffusive nature of the problem. With this said,

the PENTRAN bundle model explores the impact of S4, S6, and S8 quadrature sets with the goal

of finding the quadrature order that best characterizes flux behavior with the fewest number of

directions.

3.2.2.4 Effect of homogenization

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 scale 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

source 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 able to homogenize the fuel region in order to significantly 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 model 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 along 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 spatial 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 201,600 fine

meshes per bundle. That is to say if we used this 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 all 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 coarse 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 the 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 information that previously caused flux asymmetries is not used in model construction.

If acceptable accuracy is achieved, homogenization provides a significant reduction of fine

meshes.

It is quite obvious that the detail of the aforementioned heterogeneous case is not only

unnecessary for the overall objective at hand (i.e. characterization of the shield tank) since we

are not so concerned with very detailed flux distributions within the core region, but it is

computationally impractical to calculate a solution for 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 can be postulated that the flux distributions in the distant

region of interest (i.e. the shield tank) will be accurate. Although compromising the exact shape

of PENTRAN flux distributions 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 problem

at hand.

3.2.2.5 GMIX: Cross-section library development and source spectrum

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

are 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 cases of this study, BUGLE-96 is used. The BUGLE-96 library contains

infinitely diluted 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-

sections for up to a P5/P7 anisotropic scattering order; it also contains response cross-sections for

several reactions. A maximum P3 anisotropic scattering order was chosen for all PENTRAN

models in this study again because of the diffusive nature of the problem. BUGLE-96 is a cross-

section library that is commonly used for shielding calculations and therefore was appropriate for

use with the PENTRAN models of this study. The 47-group neutron energy structure is given in

Table 3-1 [8].

Once BUGLE-96 was chosen, the 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 library

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 Maxwellian fission

spectrum, as appropriate to the various nuclides, over different energy intervals and is shown in

Figure 3-4.

33

3.2.2.6 Results

Using PENTRAN, the 47-group, 3-D flux distributions for the four different bundle cases

are calculated. 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 the Einstein PC-cluster.

For the remaining cases, angular domain decomposition was performed by processing 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 238 fine meshes along this axis and it uses an S8 quadrature set. Case 2 is also an S8 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 homogenized source.

The following two PENTRAN cases use the same meshing scheme, but have S6 (Case 3) and S4

(Case 4) quadrature sets.

Note the similarity in computation time for Cases 2 and 3. Typically, it would be expected

that Case 3 would be faster since 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 the 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-σ 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 to Figure 3-11 indicates

that all the PENTRAN cases agree within the Monte Carlo 1-σ statistical uncertainty.

Figure 3-12, showing the flux result for group 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

modelling the entire core.

The energy behavior 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 while group 46 is underestimating. The group 46 behavior is consistent

with the other homogeneous PENTRAN cases, however group 47 is not. This observation 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 behavior is likely due to the BUGLE-

96 cross-sections which do not accurately characterize the physics 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 with an S4 quadrature set (Case 4) is only 3.9 minutes (using 8 processors) which is

significantly lower than other cases, especially, the heterogeneous S8 PENTRAN case (Case 1)

which required ~217 minutes (using 14 processors, load imbalance of 28) of computation 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 imbalance.

3.2.2.7 Application of the bundle study to full scale model

Using the single bundle study and applying the conclusions, it is straightforward to model

the full-core and adjacent shield tank region. The core region is based on the homogenization of

the fuel region and an S4 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 mixture, 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 the 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, this

36

modelling 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 the fuel and the

shield tank (about 50 cm), and can be considered insignificant to the flux contribution at the tank.

There 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 symmetry of the geometry along the center

of the model along the x-z plane. In the actual UFTR, the geometry is exactly symmetric with the

exception of the eastern-most pair of control blades. Due to their location toward the farther end

of the reactor core relative 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-core 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 regions analogous to the

actual full-core UFTR model except that only the extent of the active fuel height was considered

along the z-axis. The 3-D spatial mesh distribution can be seen in Figure 3-18; note that this is

simply a cutout of the fuel, graphite, and water regions 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 south bank of fuel bundles is used; however, the 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 symmetry along the x-z core mid-plane.

In order to demonstrate that a fully reflective boundary condition is appropriate for the full-

core model, a 3-D multi-group flux comparison was made in the fuel, graphite, and water regions

of these two three-region models. The graphite region comparison 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 regions 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 distribution 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 simplicity of the model, it is seen that the row of fuel bundles 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 box.

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 should 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 of the most importance due to spatial location,

and in these regions, no physical simplifications 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 comparable 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 source 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 S4 quadrature set was selected as the first case since the bundle study showed that this

was adequate. However, this did not guarantee that S4 was adequate 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 quadrature 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 calculations up to S10 quadrature order were

performed, but there was negligible difference between S8 and S10 cases. In order to come to this

conclusion, an effective relative difference was calculated. This was done by calculating relative

differences between S4 and S6, S6 and S8, and S8 and S10 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 S4 and S6 cases, 3.06% between

S6 and S8 cases, and 1.29% between S8 and S10 cases. Based on this 1.29% effective relative

difference, it was determined that an S8 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, graphite, and shield tank regions are of the

order of the material’s respective average mean-free path along the x and y axes; however, the

water channel within the fuel bundles, 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

the 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 the 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 neutron density (#/cm3-s) within the UFTR core (MCNP5 1-σ uncertainty <

3.5%).

44

Figure 3-4. The GMIX generated and verified Watt fission spectra.

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Energy Group

Fra

cti

on

of

Fis

sio

n S

ou

rce

Ne

utr

on

s P

er

En

erg

y G

rou

p

GMIX Numerically Integrated Watt

45

Figure 3-5. The x-y plane view of a typical UFTR 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 distribution (#/cm

2-s) for group 15

(1.920E+00

49


2-s) for group 30

(2.606E-02

50


2-s) for group 42

(5.043E-06

51


2-s) for group 47

(0

52

Figure 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).

53

Figure 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).

54

Figure 3-18. 3-D spatial mesh distribution used in the symmetry study (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 distribution for the full-core UFTR 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).

57

Table 3-1. BUGLE-96 broad energy group structure

BUGLE-96 Broad

Group Upper 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+06 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

Number of

Processors Decomposition

Time

(hours) Speedup

1 Heterogeneous S8 221,340 14 ang=2, spa=7 3.62 1.00

2 Homogeneous S8 26,040 8 ang=8 0.30 12.07



58

Table 3-3. Mesh 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

1.951 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)


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

- - - -



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



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 S4 407,544 24 spa=24 1.16

2 S6 407,544 24 spa=24 2.13

3 S8 407,544* 24 spa=24 2.77

- S10 407,544 24 spa=24 3.98

4 S8 143,784 24 spa=24 0.81

5 S8 284,240 24 spa=24 1.66

6 S8 571,520 24 spa=24 3.16

*68,964 fine meshes if only considering a shield tank depth up to x=-15 cm

60

CHAPTER 4

RESULTS AND ANALYSIS

4.1 Full-Core Neutron Flux Distributions

As in the results of the previously discussed bundle study, 47-group 3-D flux distributions

were obtained for various cases of the full, partially homogenized core, using PENTRAN with

various quadrature sets 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 graphite

(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 3.2.2.7) as seen

in Table 3-3; Case 1 uses an S4 quadrature set, Case 2 uses an S6 quadrature set, and Case 3 uses

an S8 quadrature set.

As discussed in Chapter 3 (Section 3.2.2.7), by increasing the quadrature order to S8, it was

instructive to look at the effect of increasing 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 of 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 averaged mean-free paths that correspond to each mesh

dimension for each material. This provides a quantitative view of how the mesh sizes are

decreasing in relation to the respective material average mean-free path.

Case 7 is the MCNP5 benchmark case. This case is considered to a depth of only 15 cm

into the shield tank region along the x-axis since tally quantities are scarcely obtained past this

depth and since statistics 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 section is the fuel region along the x-axis at y≈93 cm and z≈60 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. All figures shown in

this section and Section 4.1.2, pertaining to the graphite region, have maximum MCNP5 1-σ

statistical uncertainties that are less than 10%; figures discussed in Section 4.1.3 contain 1-σ

statistical uncertainties in the range of 0% to 42%.

Upon examination of the flux distributions in Figure 4-1and Figure 4-2, there is agreement

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 follow 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 single 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 those meshes lie. This sampling method causes artificial

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spikes to occur 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 for likely no gain

except the smoothing of the observed spikes. Since 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 behavior is merely a side effect of the modelling choice.

Furthermore, the spatial dependence of the source on the plate level becomes less and less

important as neutrons travel farther from the core and closer to the shield tank. Since there are

nearly 20 mean-free paths (based on the graphite average mean-free path) between the shield

tank and fuel region, five meshes seem to suffice for this application. This also accounts for the

oscillatory behavior seen in the results section of the bundle study for MCNP5 flux 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 similar

behavior. In Cases 4, 5, and 6, where there are more meshes along any given direction, there are

naturally more accurate flux shapes as seen more prominently in Cases 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 another 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 peaks for the

three fuel boxes (each containing a 2 x 2 array of four bundles).

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If we look at the flux plots for energy groups in the thermal range in Figure 4-5 to Figure

4-8, there is good agreement, mostly 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 thermal 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 further 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 in this section.

Figures include 1-D flux distributions (at the core mid-planes; y≈76 cm, z≈60 cm) as well as 3-D

flux representations to show a broader trend. All presented PENTRAN 3-D flux distributions

correspond to the S8 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 increasingly important, up to a certain point, at which

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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 the “ray effects” which occur when the quadrature order is too low.

Increasing to S6 in Case 2 shows improvement, but still there is some identifiable oscillatory

behavior. By Case 3, there is agreement with the Case 7 MCNP5 results at the interface of the

shield tank, most noticeably in Figure 4-10. The PENTRAN models with increased numbers 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 shows the group 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-σ statistical uncertainties and the relative 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 behavior of the group 35 flux distributions,

a similar contour is seen between MCNP5 and PENTRAN fluxes and MCNP5 1-σ statistical

uncertainty is low (all are less than 10%). However, the relative difference 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). Figure

4-15 and Figure 4-16, showing 1-D flux distributions for groups 30 and 35, respectively, both

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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 distributions and relative difference mapping.

What differs between (D) of this 3-D contour plot and the previous plots is the 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 deficient. If the cross-sections are deficient, it is expected that

there would be a constant relative difference as a function of position along the x-axis. Increasing

the number of fine meshes from Case 3 to 6 appears to cause no change in the PENTRAN

solution.

4.1.3 Shield Tank

Figure 4-22 to Figure 4-29 give a 1-D representation of neutron flux distributions in the

shield tank region calculated to a depth of 15 cm along the x-axis shown at the core mid-planes.

The MCNP5 results were obtained after completion of 2.8 x 108 histories using 14 processors in

parallel with the Einstein PC-Cluster; this equates to over 90 hours of elapsed 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

uncertainties; 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.

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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 following a similar trend to those of

PENTRAN.

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 group 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 this disagreement, which apparently comes from inadequate cross-section 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 S8

quadrature case with the reference meshing scheme and complete tank depth along the x-axis)

and MCNP5 for four locations along the 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 differences

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 4-31to Figure 4-33 , MCNP5 relative errors are large

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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 eight orders of magnitude to ~2,000 (#/cm2-s); at x≈-150 cm, the group 47 flux is

calculated as ~1 (#/cm2-s), essentially nothing.

Based on the above results, the S8 PENTRAN case with the reference meshing scheme

(~400,000 fine meshes) has shown to provide acceptable results. An S8 quadrature set was shown

to eliminate the ray effects seen in the other S4 and S6 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 gain in accuracy when compared to the S8 reference case. Very good agreement

© 2009 Amrit David Patel - University of...

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