the development of a thermal hydraulic feedback …
TRANSCRIPT
The Pennsylvania State University
The Graduate School
Department of Mechanical and Nuclear Engineering
THE DEVELOPMENT OF A THERMAL HYDRAULIC FEEDBACK MECHANISM
WITH A QUASI-FIXED POINT ITERATION SCHEME FOR CONTROL ROD
POSITION MODELING FOR THE TRIGSIMS-TH APPLICATION
A Dissertation in
Nuclear Engineering
by
Veronica V. Karriem
2016 Veronica V. Karriem
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2016
ii
The dissertation of Veronica Karriem was approved* by the following:
Maria Avramova
Chair of Committee
Adjunct Professor in Nuclear Engineering
Dissertation Advisor
Kostadin Ivanov
Adjunct Professor in Nuclear Engineering
Kenan Ünlü
Professor in Nuclear Engineering
Director of Radiation Science and Engineering Centre
Brenden Heidrich
Special Member
Research Capability Scientist at the Nuclear Science User Facilities
Idaho National Laboratory
Gabeba Baderoon
Associate Professor of Women's, Gender and Sexuality studies
and African Studies
Arthur Motta
Professor of Nuclear Engineering and Material Science and Engineering
Chair of the Nuclear and Engineering Program
*Signatures are on file in the Graduate School
iii
ABSTRACT
Nuclear reactor design incorporates the study and application of nuclear physics, nuclear
thermal hydraulic and nuclear safety. Theoretical models and numerical methods implemented in
computer programs are utilized to analyze and design nuclear reactors. The focus of this PhD
study's is the development of an advanced high-fidelity multi-physics code system to perform
reactor core analysis for design and safety evaluations of research TRIGA-type reactors.
The fuel management and design code system TRIGSIMS was further developed to
fulfill the function of a reactor design and analysis code system for the Pennsylvania State
Breazeale Reactor (PSBR). TRIGSIMS, which is currently in use at the PSBR, is a fuel
management tool, which incorporates the depletion code ORIGEN-S (part of SCALE system) and
the Monte Carlo neutronics solver MCNP. The diffusion theory code ADMARC-H is used within
TRIGSIMS to accelerate the MCNP calculations. It manages the data and fuel isotopic content
and stores it for future burnup calculations.
The contribution of this work is the development of an improved version of TRIGSIMS,
named TRIGSIMS-TH. TRIGSIMS-TH incorporates a thermal hydraulic module based on the
advanced sub-channel code COBRA-TF (CTF). CTF provides the temperature feedback needed
in the multi-physics calculations as well as the thermal hydraulics modeling capability of the
reactor core. The temperature feedback model is using the CTF-provided local moderator and fuel
temperatures for the cross-section modeling for ADMARC-H and MCNP calculations. To
perform efficient critical control rod calculations, a methodology for applying a control rod
position was implemented in TRIGSIMS-TH, making this code system a modeling and design
tool for future core loadings.
The new TRIGSIMS-TH is a computer program that interlinks various other functional
reactor analysis tools. It consists of the MCNP5, ADMARC-H, ORIGEN-S, and CTF. CTF was
iv
coupled with both MCNP and ADMARC-H to provide the heterogeneous temperature
distribution throughout the core. Each of these codes is written in its own computer language
performing its function and outputs a set of data. TRIGSIMS-TH provides an effective use and
data manipulation and transfer between different codes. With the implementation of feedback and
control- rod-position modeling methodologies, the TRIGSIMS-TH calculations are more accurate
and in a better agreement with measured data.
The PSBR is unique in many ways and there are no “off-the-shelf” codes, which can
model this design in its entirety. In particular, PSBR has an open core design, which is cooled by
natural convection. Combining several codes into a unique system brings many challenges. It also
requires substantial knowledge of both operation and core design of the PSBR. This reactor is in
operation decades and there is a fair amount of studies and developments in both PSBR thermal
hydraulics and neutronics. Measured data is also available for various core loadings and can be
used for validation activities. The previous studies and developments in PSBR modeling also
aids as a guide to assess the findings of the work herein.
In order to incorporate new methods and codes into exiting TRIGSIMS, a re-evaluation
of various components of the code was performed to assure the accuracy and efficiency of the
existing CTF/MCNP5/ADMARC-H multi-physics coupling. A new set of ADMARC-H diffusion
coefficients and cross sections was generated using the SERPENT code. This was needed as the
previous data was not generated with thermal hydraulic feedback and the ARO position was used
as the critical rod position. The B4C was re-evaluated for this update. The data exchange between
ADMARC-H and MCNP5 was modified. The basic core model is given a flexibility to allow for
various changes within the core model, and this feature was implemented in TRIGSIMS-TH. The
PSBR core in the new code model can be expanded and changed. This allows the new code to be
used as a modeling tool for design and analyses of future code loadings.
v
The CTF code can be used as a thermal hydraulic stand-alone modeling code. The
TRIGSIMS-TH code generates and expands channel thermal hydraulic input model that is
capable of analyzing the flow in and around the core construct. The tool can be used to analyze
future changes such as the safety analysis of the D2O tank changes.
The TRIGSIMS-TH code system is an automated tool. Using a generalized input, -it will
generate all the needed code-specific input files for the various applications.
vi
TABLE OF CONTENTS
List of Figures .......................................................................................................................... ix
List of Tables ........................................................................................................................... xiii
List of Abbreviations ............................................................................................................... xv
Acknowledgements .................................................................................................................. xvi
Chapter 1 Introduction ............................................................................................................. 1
1.1 Background of the PSBR reactor facility ................................................................... 3 1.2 The PSBR reactor ....................................................................................................... 4 1.3 PSBR fuel inventory, burnup and analysis tool ......................................................... 5 1.4 Objective of this work ................................................................................................ 7 1.5 Synopsis ..................................................................................................................... 8
Chapter 2 Literature Review .................................................................................................... 9
2.1 Current PSBR code system ........................................................................................ 9 2.1.1 PSBR-related studies ....................................................................................... 9 2.1.2 Calculation tools .............................................................................................. 11
2.2 Codes used for PSBR analysis ................................................................................... 15 2.3 Review of related codes ............................................................................................. 16
2.3.1 Review of coupled codes ................................................................................. 16 2.3.2 Thermal hydraulic modeling ........................................................................... 18
2.4 General review ........................................................................................................... 19 2.4.1 Reviews on critical rod height ......................................................................... 19 2.4.2 Nuclear Data .................................................................................................... 19 2.4.3 Control rod absorber material.......................................................................... 20
Chapter 3 Theoretical models and numerical methods ............................................................ 22
3.1 Introduction ................................................................................................................ 22 3.2 Nuclear Reactor Core Design..................................................................................... 23
3.2.1 Terminology .................................................................................................... 24 3.2.2 Core design process ......................................................................................... 26 3.2.3 Main parameters for core design ..................................................................... 26 3.2.4 Intent and deliverables .................................................................................... 28
3.3 Computational analysis tools ..................................................................................... 29 3.3.1 Neutron transport methods and codes ............................................................. 29 3.3.2 Thermal hydraulic methods and codes ............................................................ 31
3.4 PSBR description ....................................................................................................... 33 3.4.1 PSBR core ....................................................................................................... 33 3.4.2 TRIGA fuel ..................................................................................................... 35 3.4.3 Application of the PSBR ................................................................................. 37
vii
3.5 TRIGSIMS and TRIGSIMS-TH ................................................................................ 38 3.5.1 Capabilities of TRIGSIMS and TRIGSIMS-TH ............................................. 38 3.5.2 Codes in TRIGSIMS-TH ................................................................................ 39
3.6 Cross sections ............................................................................................................. 47 3.7 Other supplementing theory ....................................................................................... 50
3.7.1 Design of the core loading .............................................................................. 50 3.7.2 B4C in Control rods ......................................................................................... 51 3.7.3 Thermal hydraulic feedback ............................................................................ 51
Chapter 4 Methodological and modeling developments .......................................................... 53
4.1 TRIGSIMS-TH control system .................................................................................. 53 4.2 Temperature feedback methods ................................................................................. 56
4.2.1 Illustration of the thermal hydraulic feedback effects ..................................... 56 4.2.2 The thermal hydraulic feedback implementation ............................................ 60 4.2.3 MCNP/CTF coupling ...................................................................................... 62 4.2.4 ADMARC-H/CTF coupling ............................................................................ 65 4.2.5 Pseudo material approach ................................................................................ 67
4.3 Partially inserted control rods .................................................................................... 68 4.3.1 Application of perturbation theory .................................................................. 68 4.3.2 Control rod position method using a quasi-fixed point iteration scheme ........ 70
4.4 Thermal hydraulics methodology .............................................................................. 73 4.5 TRIGSIMS-TH Core Modeling parameters ............................................................... 75
4.5.1 Moderator surrounding the core ...................................................................... 75 4.6 Conclusion on the methods and models ..................................................................... 77
Chapter 5 Results and Findings ............................................................................................... 78
5.1 MCNP/CTF coupling ................................................................................................. 80 5.2 Critical control rod search .......................................................................................... 85
5.2.1 Validation of critical rod search method ......................................................... 85 5.2.2 Core reactivity estimation from calculations ................................................... 91 5.2.3 ADMARC-H for acceleration of control rod search method .......................... 94
5.3 Thermal hydraulic of the PSBR Core ........................................................................ 95 5.4 Application of power rise with thermal hydraulic feedback ...................................... 96 5.5 AMARCH/CTF coupling ........................................................................................... 108 5.6 Development of core expansion ................................................................................. 111
5.6.1 Graphite elements added ................................................................................. 111 5.6.2 New type of fuel elements ............................................................................... 112
5.7 Improvements of the core design parameters ............................................................. 112 5.7.1 Control elements ............................................................................................. 113 5.7.2 Homogenized cross sections results ................................................................ 116 5.7.3 Continuous energy cross section application .................................................. 120 5.7.4 Moderator for the core design ......................................................................... 122 5.7.5 TRIGSIMS-TH application to CTF ................................................................ 125
5.8 Thermal hydraulics as a standalone tool .................................................................... 129 5.9 Summary of results .................................................................................................... 138
Chapter 6 TRIGSIMS-TH Core Design Application ............................................................... 140
viii
6.1 Core loading design scenario 1 .................................................................................. 140 6.1.1 Addition of graphite elements ......................................................................... 141 6.1.2 A new core layout ........................................................................................... 141
6.2 Core loading design scenario 2 .................................................................................. 147 6.3 Core design scenario 3 ............................................................................................... 152
6.3.1 Description of the fuel ..................................................................................... 152 6.3.2 Analysis ........................................................................................................... 153
6.4 Core design scenario 4: Analysis of the core with a D2O tank .................................. 156 6.4.1 A comparison with and without D2O tank ...................................................... 156 6.4.2 Thermal Hydraulics comparison with D2O tank ............................................. 157
Chapter 7 Conclusion and future work .................................................................................... 162
7.1 Conclusion ................................................................................................................. 162 7.2 Proposal for future work ............................................................................................ 164
7.2.1 Modify the D2O input ...................................................................................... 164 7.2.2 Transient analysis with CTF/ADMARC-H ..................................................... 164 7.2.3 Using the TRIGSIMS-TH to investigate the thermal hydraulic properties
of the fuel.......................................................................................................... 165 7.2.4 Addition of a in-core experimental tube within TRIGSIMS-TH .................... 165
Appendix Additional information ........................................................................................... 167
Measured data .................................................................................................................. 167 Core loading diagrams used in this thesis ........................................................................ 168 SERPENT calculations compared with MCNP calculations ........................................... 170 B4C calculations ............................................................................................................... 170 MCNP standard deviation ................................................................................................ 172 MCNP5 Convergence of the PSBR TRIGSIMS -TH model ........................................... 172 Normalization factors ....................................................................................................... 175
REFERENCES ........................................................................................................................ 176
ix
LIST OF FIGURES
Figure 1-1 PSBR TRIGA Core ................................................................................................ 5
Figure 2-1 Current TRIGSIMS layout ..................................................................................... 12
Figure 3-1 Basic analyses and parameters for nuclear reactor core design ............................. 23
Figure 3-2 Core loading configuration..................................................................................... 34
Figure 3-3 A typical TRIGA fuel element ............................................................................... 36
Figure 3-4 CTF Cartesian coordinate system .......................................................................... 42
Figure 3-5 Scalar Mesh cell, axial ........................................................................................... 43
Figure 3-6 Scalar mesh, transverse ......................................................................................... 43
Figure 3-7 Homogenization of TRIGA fuel ............................................................................ 49
Figure 4-1 Diagram of TRIGSIMS-TH code platform ............................................................ 54
Figure 4-2 Illustration of homogeneous and heterogeneous temperature distributions ........... 57
Figure 4-3 Typical radial temperature distribution at 1MW power [K] .................................. 58
Figure 4-4 1MW axial temperature distribution [K] ................................................................ 59
Figure 4-5 A typical sub-channel for CTF ............................................................................... 60
Figure 4-6 Illustration of the coupling methodology ............................................................... 62
Figure 4-7 Flow diagram of MCNP/CTF coupling ................................................................. 63
Figure 4-8 Flow diagram of ADMARC-H/CTF couple .......................................................... 66
Figure 4-9 S-curve for control rods ......................................................................................... 69
Figure 4-10 Flow diagram of the control rod method .............................................................. 71
Figure 4-11 illustration of the quasi fixed point iteration ........................................................ 72
Figure 4-12 Developing of a full core CTF model .................................................................. 74
Figure 4-13 CL56 diagram ....................................................................................................... 76
Figure 4-14 CL54 diagram ....................................................................................................... 76
Figure 5-1 Reference core diagram .......................................................................................... 79
x
Figure 5-2 Temperature distribution for CL56 ........................................................................ 81
Figure 5-3 Temperature distribution for CL54 ........................................................................ 82
Figure 5-4 Temperature distribution for CL53H ..................................................................... 83
Figure 5-5 Iterative control rod position search of CL56 ........................................................ 86
Figure 5-6 Iterative control rod position search for CL54 ....................................................... 87
Figure 5-7 CL56 AT 700kW power, with Xe adjusted ............................................................ 89
Figure 5-8 CL54 at 800kW power ........................................................................................... 90
Figure 5-9 CL56 estimation of reactivity loss value ................................................................ 92
Figure 5-10 CL56, with ADMARC-H to accelerate ................................................................ 94
Figure 5-11 Reactivity loss with power increase/control rod withdrawal for CL56 ................ 97
Figure 5-12 Reactivity loss with power increase for CL54 .................................................... 98
Figure 5-13 CL56 average temperature increase for the i-17 rod corresponding to
reactivity loss measurements............................................................................................ 100
Figure 5-14 CL54 average temperature increase for i-16 corresponding to reactivity loss
measurements ................................................................................................................... 101
Figure 5-15 Temperature distribution for coolant surrounding the numbered rods ................. 102
Figure 5-16 Temperature increase with power increase for the indicated rods ....................... 103
Figure 5-17 Comparison of CL56 and CL54 flux distribution ................................................ 104
Figure 5-18 Thermal flux distribution for CL56 ...................................................................... 105
Figure 5-19 Normalized average power distribution for CL56 ............................................... 106
Figure 5-20 Normalized average power distribution for CL54 .............................................. 107
Figure 5-21 Diagram ADMARC-H/CTF-MCNP-CTF couple for position step ..................... 108
Figure 5-22 MCNP/CTF/ADMARC-H coupling ................................................................... 109
Figure 5-23 Illustration of core expansion ............................................................................... 111
Figure 5-24 Homogenized fuel/clad/water region ................................................................... 116
Figure 5-25 Illustration of the two input geometries: MCNP and SERPENT ......................... 117
xi
Figure 5-26 Pseudo material difference (Keff results) .............................................................. 121
Figure 5-27 CL53 no-graphite diagram ................................................................................... 123
Figure 5-28 CL53 +10 graphite elements ................................................................................ 123
Figure 5-29 CL54 diagram ....................................................................................................... 124
Figure 5-30 Comparison with and without D2O tank to the CL56 design at 1 MW power ..... 127
Figure 5-31 Comparison of average power for the D2O tank calculation ................................ 128
Figure 5-32 CTF input changes for "standalone" calculations ................................................ 129
Figure 5-33 Thermal hydraulics results: velocity of channels 112 to 131 for CL56 ............... 131
Figure 5-34 Thermal Hydraulic results: Temperature distribution for CL56 .......................... 133
Figure 5-35 Results of the mass flow rate across the gaps (cross flow) .................................. 136
Figure 5-36 Illustration of the cross flow results .................................................................... 136
Figure 5-37 Illustration of the flow around the channel .......................................................... 137
Figure 6-1 CL56 and CL56- adjusted ...................................................................................... 141
Figure 6-2 Comparison of the CL56 and CL56_adjusted ........................................................ 142
Figure 6-3 Comparison of CL56 and CL56-adjusted average power distributions ................. 143
Figure 6-4 CL56_adjusted- flux [neutrons/cm2-s] across the core .......................................... 145
Figure 6-5 CL56-flux [neutrons/cm2-s] across the core ........................................................... 145
Figure 6-6 Flux [neutrons/cm2-s] results from reshuffling of core elements ........................... 146
Figure 6-7 Illustration of CL54 and CL54_shuffled ................................................................ 147
Figure 6-8 Comparison of CL54 vs CL54-shuffled ................................................................. 148
Figure 6-9 Difference in element power between CL54_shuffled vs. CL54 ........................... 149
Figure 6-10 Percent Difference in Temperature for CL54_shuff and CL54............................ 150
Figure 6-11 CL54+6 30/20 LEU convergence results ............................................................. 154
Figure 6-12 Temperature distribution of the 30/20 LEU fuel .................................................. 155
Figure 6-13 Three cases to express the use of the CTF standalone model .............................. 157
xii
Figure 6-14 The % difference in power distribution for the D2O tank shapes compared no
tank ................................................................................................................................... 158
Figure 6-15 Illustration of the cross flow data for the channels adjacent to D2O to the
center of the core .............................................................................................................. 160
Figure A- 1 CL54 Core loading diagram ................................................................................. 169
Figure A- 2 CL53H core loading diagram (includes the position for graphite) ....................... 169
Figure A-3 Comparison of the Keff values after each burnup step ........................................... 170
Figure A- 4 Model for burnup of B4C ...................................................................................... 171
Figure A- 5 Shannon fission source entropy convergence check 1 ......................................... 173
Figure A- 6 Shannon fission source entropy convergence check 2 ......................................... 174
Figure A- 7 Convergence check of the keff values using different skipped cycles ................... 174
xiii
LIST OF TABLES
Table 2-1 B4C components as used previously ........................................................................ 20
Table 3-1 Comparison of old and new TRIGSIMS ................................................................. 38
Table 5-1 Measured results compared with calculated TRIGSIMS-TH results ...................... 84
Table 5-2 Comparison of calculated to measured values for power levels less than 1MW .... 91
Table 5-3 Data from calculations ............................................................................................. 93
Table 5-4 Reactivity control comparisons for CL56 ............................................................... 93
Table 5-5 Reactivity control comparisons for CL54 ............................................................... 93
Table 5-6 Thermal hydraulic results for core loadings at 1MW power ................................... 95
Table 5-7 Core excess reactivity in $ for various core loadings .............................................. 110
Table 5-8 Addition of 10 graphite elements ............................................................................ 112
Table 5-9 Theoretical B4C number densities ........................................................................... 113
Table 5-10 Control Rod Absorber Combinations .................................................................... 114
Table 5-11 Comparisons of control rod position for B4C cases ............................................... 115
Table 5-12 SERPENT vs. MCNP Results for CL4 ................................................................. 118
Table 5-13 Comparison with previous cross sections using CL53 in ADMARC-H code ....... 118
Table 5-14 CL53 at 1MW- comparison using ADMARC-H code with feedback ................... 119
Table 5-15 Comparison with previous cross sections using CL54 in ADMARC-H code ...... 119
Table 5-16 CL54 at 1 MW- comparison using ADMARC-H code with feedback................. 119
Table 5-17 Comparison with previous cross sections using CL56 in ADMARC-H code ....... 119
Table 5-18 CL56 at 1MW- comparison using ADMARC-H code with feedback ................... 120
Table 5-19 The effects of the adjustment of the water surrounding the core........................... 124
Table 5-20 Estimation of reactivity for CL56 +D20 tank ........................................................ 125
Table 5-21 Analysis of the hotter elements in CL56 ............................................................... 135
Table 6-1 estimating CL54 to CL54_shuffled reactivity ......................................................... 150
xiv
Table 6-2 Fuel comparisons ..................................................................................................... 152
Table 6-3 CL56 with and without D2O tank ............................................................................ 156
Table 6-4 D2O tank comparisons ............................................................................................. 159
Table A- 1Measured data ......................................................................................................... 167
Table A- 2 Decrease in B4C number densities effect ............................................................... 171
xv
LIST OF ABBREVIATIONS
ARI All rods in
ARO All rods out
B4C Boron Carbide
CL Core loading
CTF Cobra (COolant Boiling in Rod Array) - thermal fluids
CFD Computational Fluid dynamics
D2O Deuterium dioxide
ENDF Evaluated Nuclear Data Files
MCNP Monte Carlo N-Particle
ORIGEN-S Oak Ridge Isotope GENeration
PSBR Pennsylvania State Breazeale reactor
TRIGA Training, Research, Isotopes, General Atomic
TRIGSIMS-TH TRIGA SIMULATOR S with thermal hydraulics
xvi
ACKNOWLEDGEMENTS
I would like to thank Dr. Avramova for her support over the past years. Thank you for
your unwavering encouragement, to complete this work. Thank you, Dr. Ivanov, for the
opportunity and support in my studies. A special thanks to my thesis reviewers especially Dr.
Ünlü and Dr. Heidrich, for their input in my studies. I have learned so much from your
experiences and knowledge that was shared by our monthly meetings. Thank you Dr. Bederoon,
for the time spend as my reviewer, and for the moral support, you give me when we interact.
To my husband Zain, who has been my support in both academic and personal life. I
appreciate your patience and encouragement through this period. My kids Lynn, Zayn and
Hannah, hope my unending studies will benefit your lives in the future.
This journey has been a long and unyielding. Thanks to everyone who supported me
through this time.
1
Chapter 1
Introduction
The primary purpose of nuclear reactor design is to ensure the safe and economic
operations of nuclear reactors. A nuclear reactor is a complex physical system which involves
multiple- and interacting physical phenomena with the most important being neutronics and
thermal hydraulics. Neutronics involves the calculation of the neutron distribution in the reactor,
from which the reactor power distribution in the core is determined. Heat deposits into the fuel as
results of the fission reactions propagating throughout the fuel to its surface and is being removed
by the reactor coolant. Nuclear reactor core design entails the simulation of these processes,
which ensures that the power density limits in the fuel are within design limits and that the fuel
cladding temperature limit is not exceeded. This ultimately ensures that the fuel integrity is not
compromised.
At non-zero power conditions, neutronics and thermal hydraulics interactions occur
simultaneously, i.e. the neutronics and thermal hydraulic processes are intricately connected. The
simulation of this multi-physics problem is quite complex and computationally involved. In the
past, the pre-traditional approach of the nuclear design techniques treated the neutronics and the
thermal hydraulics analyses as isolated simulations that were coupled through state dependent
parameters and boundary conditions. The order of the operator for neutronics (transport/diffusion)
and the thermal hydraulics (sub-channel/system codes) may also vary. This pre-traditional
simplified neutronics and thermal hydraulics analysis approach resulted in a computationally
efficient methodology (short run times) and therefore allowed for many design repetitions to
occur in a short amount of time so that the optimum reactor core design can be determined.
2
The Pennsylvania State Breazeale Reactor (PSBR) or PSBR TRIGA (Training Research
Isotope, General Atomic) is a 1MWth research reactor [1] housed at the Radiation Science and
Engineering Centre (RSEC) at The Pennsylvania State University (PSU). This reactor facility is
used for irradiation purposes as well as research and teaching. The reactor core design for this
facility is performed with the code system TRIGSIMS (TRIGA SIMulator S). The TRIGSIMS
code system is a fuel management and core analysis code currently in use at the RSEC facility.
The aim of this PhD work is to improve the code system TRIGSIMS.
TRIGSIMS [2], which is an interface program, connects Monte Carlo N-Particle (MCNP)
transport code, to ORIGEN-S burnup code for fuel depletion. A nodal diffusion code, ADMARC-
H, was included in this multi-tool platform, to aid in the acceleration of the MCNP calculation.
TRIGSIMS however lacked a very important aspect of reactor design studies, i.e., the
temperature feedback, associated with the increase of fuel temperature with power.
TRIGA reactors utilize hydride fuel, meaning that the fuel and (hydrogen) moderator are
in close proximity. The effect of temperature increase has an effect on the core reactivity. In this
work, the thermal hydraulic code COBRA-TF (CTF) was incorporated for temperature feedback
predictions. The new TRIGSIMS, referred to herein as TRIGSIMS-TH, is now an advanced high-
fidelity multi-physics tool.
The addition of a control-rod-height-methodology in TRIGSIMS-TH has made this
software a design tool. What this entails is, the code can be used to design a new core loading
complete with critical rod position for a critical reactor at different power levels. This method was
only possible with the addition of the feedback method to the core design.
The CTF code is coupled with MCNP and ADMARC-H in an automated calculation
sequence. Temperature feedback is applied to both system functions ensuring an even higher
expected accuracy in the calculation.
3
The thermal hydraulic code CTF part of TRIGSIMS-TH can also be used as a stand-alone
thermal-hydraulic analysis tool. This addition allows for the safety analysis of a reactor core
layout to be performed, as well as the analysis to investigate the coolant flow in the case of
upgrades and changes in reactor design.
Various other changes and upgrades of the code, to enhance its capabilities, were
introduced. A new set of homogenized few-group cross sections were generated with the Monte
Carlo code, SERPENT for ADMARC-H calculations.
MCNP, ADMARC-H and TRIGSIMS have been previously validated for PSBR
applications [2]. CTF was also validated using measured data from PSBR [3]. The validation of
the TRIGSIMS-TH code system has been performed in this PhD study through the analyses of
various core layouts by comparing the calculated results with the measured data for core loadings
(CL), CL56, CL54, and CL53.
The effective use of the developments incorporated in TRIGSIMS-TH code system was
demonstrated in analyses to various core loadings. The results and findings of this work are
presented in this thesis.
1.1 Background of the PSBR reactor facility
The PSBR is the first licensed university research reactor in the USA. The operating
license for this reactor was received in 1955. The PSBR is a Mark-III type TRIGA research
reactor. The reactor core is movable and is situated in an oval pool above the ground. This is a
light water cooled reactor, which operates at a steady state power of 1MW and is capable of an
approximately 2000MW thermal pulse [1], [4].
The original reactor at the RSEC was a Material Testing Reactor (MTR), which used
plate type fuel suspended and mounted on a grid plate. At this time, the focus of the facility was
4
on nuclear theory applications and characterization of half-lives and radioactive emissions from
radioactive isotopes. In 1965, a TRIGA reactor replaced it [5]. Though the PSBR was not the first
facility to change to TRIGA type reactor fuel, it was the first to convert its fuel from high-
enriched uranium (HEU) type to low enriched uranium (LEU) type of TRIGA fuel [1]. The
original maximum operating power of the MTR was 100kWt. This was changed to 1MWth with
the installation of the TRIGA.
The RSEC facility has the following functionality. It has two Co-60 gamma-ray
irradiation facilities. One is a pool irradiator, which is a vertical dry tube surrounded by Co-60
sources close to the bottom of the pool and the second is a dry irradiation facility. The RSEC has
a hot cell laboratory, which can handle 100-350 curies. There is a neutron beam laboratory, which
is the most used facility. Collimated neutron beams which are thermalized by D2O (deuterium
oxide or “heavy water”) moderator. The reactor facility also hosts a radio-chemistry teaching and
research facility, a radio-nuclear application facility and a nuclear security education lab to
provide student with hands on experience with radiation detection, source technology etc. [1], [5].
Possible changes are expected for the PSBR facility. Changes to improve the usability of
the beam port facility are investigated [5]. This includes the change to the D2O tank used in
mitigating the neutron beam in the beam ports. All this adds to the need for a core design and a
computer simulation code that accurately calculates the neutron population in the core.
1.2 The PSBR reactor
The PSBR TRIGA reactor core consists of a uniform lattice of fuel elements in a fixed
hexagonal shape configuration positioned between two grids plates - see Figure 1-1[1]. The
reactor core is open and exposed inside the pool, with no pumps to drive the coolant through the
fuel elements. Cooling of the reactor is through natural convection.
5
Figure 1-1 PSBR TRIGA Core
The core reactivity is controlled with control rods. The control rods utilized in the PSBR
are three fuel follower type and one air follower type with B4C as the absorber material.
Currently, there are two types of TRIGA fuel elements loaded in the reactor. Both are less than 20
percent enriched uranium TRIGA fuel. They are 8.5 wt% (8.5 weight percent of uranium) and 12
wt% (12 weight percent of uranium) of type UZrH1.6 (Uranium Zirconium hydride) fuel. The
long life of these fuels and the short burn cycles allows for completely mixed burn-up of core
elements. Each core loading is a reshuffling of burned fuel elements. Keeping registry of the
burned elements number densities is important for further use of the fuel elements. For this
inventory account, a reliable fuel management tool is needed.
1.3 PSBR fuel inventory, burnup and analysis tool
The TRIGSIMS code system, currently used at the PSBR, is a fuel management, analysis
and burnup computer program. The current core layout is written into an input file and the
TRIGSIMS code system creates various inputs for various other programs. This code system is
6
essentially a program that manipulates data needed for input values of three other code systems.
These codes are MCNP5, ORIGEN-S, and the nodal diffusion code ADMARC-H. A detailed
explanation of these codes will follow in chapter 3. The MCNP and ADMARC-H are used for
neutronic analysis, to calculate the needed criticality as well as power and neutron flux
distributions used in the burnup of the fuel elements. ORIGEN-S calculates the depletion of the
fuel elements.
At each step, TRIGSIMS automatically collects and transfer data, write input and output
files, and executes these programs, which makes this computer program unique. The result is a
burned fuel inventory of each fuel element. Every reactor facility should account for all nuclear
materials. This is a method of updating and keeping inventory.
The main functions of this tool are fuel management (including burnup) and core
analysis. In this work, this function is expanded and the new code system is now a core design
and safety analysis tool. The thermal hydraulic code CTF is included in this TRIGSIMS code
system. This further developed code system, TRIGSIMS-TH (TRIGSIMS with thermal
hydraulics) is an advanced high-fidelity multi-physics tool specifically formulated for PSBR core
analysis and design.
7
1.4 Objective of this work
This work describes the development, validation, and application of the TRIGSIMS-TH
code system. TRIGSIMS-TH is a further development of the TRIGSIMS fuel management and
analysis code [2]. The TRIGSIMS code system was lacking the very important component of
temperature feedback calculations. This is especially a necessity for TRIGA fuel, because of its
fuel-to-moderator closeness that has a big effect on the reactivity of the reactor core. For this
application, the thermal hydraulic code CTF was used to provide fuel and moderator temperature
feedback. TRIGSIMS-TH is now a high-fidelity multi-physics tool.
The CTF code is well studied and proved to be applicable for natural convective flow
systems [3]. CTF can be used as a safety analysis tool under both steady state and transient
calculations. CTF is added in the code system through a multi-physics coupling with MCNP and
ADMARC-H. Additionally, CTF can be used as a stand-alone thermal hydraulic analysis tool. A
unique methodology to apply control rod position was implemented in TRIGSIMS-TH. The
homogenized few-group cross sections used by ADMARC-H were updated with the code
SERPENT. Updates on various other functionalities of the TRIGSIMS code were performed such
as, reading of data, to make sure that the correct and consistent nuclear data is extracted from the
cross section files for both the MCNP and ADMARC-H calculations. The cross section data after
all is an essential part of the calculations.
TRIGSIMS_TH is an automated code system allowing minimum interference from the
user.
8
1.5 Synopsis
Chapter 2 of this document is a literature review specifically aimed at PSBR related
studies. Since this work revolves around the code system of the PSBR, the review will include
similar code systems and other related literature that supports this work.
Chapter 3 covers the theory (models and methods) involved with this study. The theory
includes the reactor core modeling, the code system and the codes used for simulation in this
system. The theory will also cover the new developments of the code system.
Chapter 4 outlines the various models and methodologies employed in the further
development of TRIGSIMS.
Chapter 5 presents the results and findings of these PhD studies using the developed
TRIGSIMS-TH code system. The Core Loading (CL) designs - CL54 and CL56 - were used for
comparison to measured data to evaluate the findings of the PhD developments.
Chapter 6 outlines the use and application domains of TRIGSIMS-TH. Four analyses are
performed to illustrate the application potential of TRIGSIMS-TH.
Chapter 7 summarizes the PhD contributions of the presented work and provides
suggestions for future work.
Appendix A section gives the needed data and information that assist in the presented
work.
9
Chapter 2
Literature Review
This chapter will present the work and studies related to the PSBR reactor core design
and analysis. It will include studies performed for, and code systems used at the PSBR and other
TRIGA research reactors as well as the studies, codes, and methods related to this PhD research.
2.1 Current PSBR code system
The PhD thesis of Tippayakul [2] describes the development, validation and application
of TRIGSIMS code system for the PSBR analysis and core design. It also followed the changes
of the reactor core loading pattern and layout over the years. The PSBR has had core changes
from having a full core of 8.5 wt% fuel, to a mixed core of 8.5 wt% and 12 wt% fuel elements.
The core has had size changes from core loads with 67 fuel elements (CL1) to recent core load of
102 elements and currently to 108 fuel elements (CL56). With future core loadings, we expect a
new fuel element, to form part of this already mixed core. We also expect changes with the core
layout, such as D2O tank changes. Various aspects affect the fuel economy, the cost, and the
safety of nuclear reactors in general. It is for these reasons, the careful account of operations and
inventory is recorded, and investigated as well as changed if need be.
This PhD work herein, directly continue to build on the work done by Tippayakul [2].
2.1.1 PSBR-related studies
In the recent studies, Ücar [5] performed an analysis on new models and design of the
reactor core-moderator-assembly and new beam ports at the facility. This was all part of the
10
design to expand the utilization of the PSBR. In order to do this study he had to employ neutronic
and thermal hydraulic models of the PSBR. He's study was guided by design limitations and
constraints for the new core-moderator assembly with five new beam ports , which he drafted in
a3D model .The codes that he used for his analysis were ANSYS FLUENT, a CFD code with
ANSYS Gambit mesh generator [5], [6]. He used the TRIGSIMS code system as well as MURE
(an MCNP based code). The aim of this study was to maximize the number of beam ports and
minimize the hydrogen gamma contamination of the neutron beam in the channeled beam port
[5]. The CFD analysis results presented the flow and temperature profiles as well as the average
void fraction distribution in the channels. He compared his results with previous analysis from
previous studies and measurements. From the MCNP model of the new design D2O tank and
beam port configuration, he calculated the neutron and gamma flux spectrum at the end of each
beam port. He did optimization studies, to calculate the optimum size of the new shape tank and
the optimum distance between beam ports and core face. The aim of his work is intended for the
future changes and upgrades for the PSBR.
In the PhD work of Sahin [7] he used the PSBR facility to perform a dendrochemical
study. His work reviewed the environmental effects of tree-ring chemistry that looks at the
elemental concentrations of various changes in soil chemistry deposited in the tree -rings. In order
to do this study, he performed a detailed coupled neutronic burn-up simulation of the PSBR. The
MURE (Monte Carlo Utility for Reactor evaluations) code, which is, and MCNP based code were
the main codes used in his study [8], [9]. In his work, he investigated the fission-product buildup
effects, and by comparing his model-predictions to the experimental results showed a good
agreement. He developed a set of temperature dependent continuous energy cross section using
ENDFB-VII data files with NJOY code [10]. He did this in refined temperature intervals of 10K
for an extended isotope list. He also applied the Pseudo material approach in his MCNP
calculations. All this additions was to make the MCNP calculation more accurate and comparable
11
to the measured data. He's results showed the burnup-calculated cores against measured data of
core excess reactivity for the years spanning 1965 to 2012. He also calculated the control rod
worth comparison for these years. After his analysis on control rod worth, indicating the need of
adjusting the B4C, he did a control rod adjustment to the B4C in order to compare the control rod
worth measurements to the calculated. Various combinations of the B4C absorber material were
considered. This was made to the best-fit outcome and he verified his choice of the B4C
composition with previous core loading patterns. After his success in the calculation to
experimental results’ comparisons, he compared his neutron activation predictions with
measurements in the dry irradiation tube. Time dependent analysis of the neutron flux
characterization parameters were performed for the PSBR dry irradiation tubes [7], [9]. After
verification of neutronic modeling against measured data, he concluded that the MURE libraries
and MCNP5 can successfully be applied to predict the neutronic behavior of the PSBR core
following the daily operational schedule.
The applications of PSBR facility are many and various. In most cases, the reactor core,
which is a neutron source, is being used for these applications. In order to perform any research
related to PSBR, one needs to have a well-defined reactor core modeling and calculation tool.
2.1.2 Calculation tools
Though the TRIGSIMS is a multi-code system, the main code for execution of criticality
calculation is MCNP5. TRIGSIMS, which is described in the thesis of Tippayakkul [2], is a
platform where all these codes share information. The TRIGSIMS code system is outlined in the
following diagram [2]
12
TRIGSIMS
Stores data
-power/node
-isotopic mass
-keff
Read XS
- Continuous energy
- diffusion
Prepares input
- ADMARC-H
- MCNP
MCNP
MCNPSCALE
ORIGEN-S
SCALE
ORIGEN-SMCNP
MCNP
ADMARC-H
Figure 2-1 Current TRIGSIMS layout
Figure 2-1 shows the current TRIGSIMS layout:
A) TRIGSIMS is the driver of this coupled code system;
B) Coupling between neutronics codes MCNP and ADMARC-H (diffusion);
C) Coupling with SCALE (ORGENS for depletion) [11] ;
D) Nuclear data preparation used by these codes.
With the previous upgrade of TRIGSIMS, MCNP5 has become the main core solver [2].
MCNP5 [12] is a general-purpose transport code with no depletion capabilities. For this reason
ORIGEN-S [11], that forms part of the SCALE code system, was coupled with MCNP5 to
perform the depletion calculations.
13
Like MCNP, the ORIGENS input is automatically generated by the interfacing program
TRIGSIMS. The contribution [2] of this MCNP/ORIGEN-S coupled methodology is the
following:
1) The generation of one-group cross-section burn-up libraries, specifically made for the
PSBR fuel cells (8.5 wt%, 12 wt%, and fuel follower control rods), were created with
TRITON, a SCALE module. TRITON [13] is a two-dimensional (2D) transport and
depletion module for characterization of spent nuclear fuel.
2) Implementing the on-line three-dimensional (3D) burn-up cross-section generation. A
set of selected “important” isotopes was identified, and using the pin-by-pin fluxes
and power from MCNP calculation, to calculate the one-group cross-sections for
these isotopes.
3) Implementation of the predictor-corrector approach to better predict fuel depletion
and number densities.
4) Xenon poison effect modeling, whereby an adjustment is made before the start of
each MCNP calculations. This adjustment is to insure that we correct the Xenon
number densities to account for the partial day of operation.
5) Axial depletion model was also one of the innovative changes implemented in the
TRIGSIMS code. The fuel elements are now divided into several axial nodes, where
node-wise calculations for ORIGEN-S, MCNP5, and ADMACR-H are performed.
The work performed for the coupled MCNP5/ORIGEN-S depletion model has been a
great success. Sensitivity studies to test and validate the code have been conducted for the
use with TRIGA reactors.
MCNP calculations with its 3D geometry capabilities, uses continuous energy cross-
sections. These cross sections are available in temperature intervals of 300K, 600K, 900K and
1200K in the MCNP5 data file [2], [7]. All intermediate temperatures are interpolated from a
14
refined grid of these sets. The development of such refined grid is an important contribution of
Tippayakul [2]. This was accomplished by the addition to the MCNP_DATA, xsdir.file, of a set
of continuous cross sections for a list of “important isotopes” on a grid with a ΔT of 50K from
300K to 900K intervals. The cross section set was generated using the NJOY code [10].
As part of a speedup scheme for MCNP5 criticality calculations, a nodal diffusion code
ADMARC-H [14] was coupled to MCNP. The primary idea with this coupling is to pre-generate
the initial source distribution used in the MCNP5 code. With this, MCNP will be obtaining a
converged fission source distribution with minimum number of “inactive cycles” (which are not
used in the final determination of the keff results). With this algorithm, the code will reduce its
computational time for the MCNP calculation. Tippayakul has done various feasibility studies on
optimization of the skipped cycles in order to accelerate the MCNP calculations [2].
The ADMARC-H code, which is a two group, 3D nodal diffusion theory code for
hexagonal geometry, previously was studied in . For its use in the PSBR, a set of homogenized
cross sections were prepared with the HELIOS-1.6, a 2D transport and depletion lattice physics
code [14], [15]. These cross sections are temperature dependent on a grid with ΔT of 100K, burn
up dependent between 0 to 140 000MWd, and fuel type dependent for 8.5 wt%, 12 wt% and fuel
follower control rods. The ADMARC-H code provides the Keff , flux and power distribution in
both axial and radial directions.
Similar to MCNP and ORIGEN-S, TRIGSIMS manages the input and output of the
ADMARC-H code. It formulates the output into a form that is used for MCNP, and with its
robust method, should ADMARC-H not execute, TRIGSIMS will assume the axial cosine shape
for the initial source distribution for the fuel elements needed in MCNP calculations. Thereafter
the calculation will continue without ADMARC-H execution [2].
15
2.2 Codes used for PSBR analysis
The PSBR is in an open pool facility. There are no pumps to force the flow through the
core. It relies completely on natural convection for cooling. The thermal hydraulics of natural
convective coolant flows is a challenge for computational simulations.
In recent years, number of thermal-hydraulic studies was carried out. Ücar, was able to
model the thermal-hydraulics of the PSBR reactor core with the Computational Fluid Dynamics
(CFD) code Fluent [5],[6]. Chang [16] performed previous studies with similar codes, for
thermal-hydraulics modeling, in 2004. His focus was mainly on the flow and fluid temperature
predictions in and around the PSBR core. His research included development of CFD models of
the PSBR core and pool as well as calculations of the pool temperature and velocity field
predictions.
Sub-channel code applications to study the PSBR core thermal-hydraulics were also
performed and are described in the following references [3], [17]. Various experiments [17] in
PSBR were performed and utilized for benchmarking neutronics and thermal-hydraulics
modeling of steady state and transient conditions. Benchmark information was collected for
coupled neutronic and thermal-hydraulic models and was utilized for the reactor safety analysis.
The intended outcome was to formulate benchmark problems for validation of coupled neutronic
and thermal-hydraulic codes. Available experimental data can be used to validate the coupled
thermal-hydraulic and neutronics models for PSBR. This was demonstrated in the validation of
3D kinetics code STAR coupled with COBRA-IIIC code and using WIMS-D4 to generated cross
sections.
In 1997, Gougar [18] has performed various studies on the TRIGA thermal-hydraulics.
His experimental investigation of the coolant flow in the TRIGA demonstrated complex coolant
flow characteristics of the PSBR. In the work subsequent to this, these flow characteristics for the
16
thermal-hydraulic model formed a basis for validation of the coolant flow through the core.
Studies using COBRA-TF (CTF) [3], [6] indicated that CTF is capable of modeling PSBR
thermal-hydraulics and coolant flow characteristics.
2.3 Review of related codes
Multi-physics coupling of codes seems to be an increasing trend in reactor design.
Currently the traditional multi-physics coupling is well established add validated while the novel
high-fidelity multi-physics coupling is being developed and verified. Here we will review recent
developments related to both types of multi-physics coupling since those are involved in this PhD
research.
2.3.1 Review of coupled codes
The work referenced in [19], [20] was aimed at increasing the accuracy of spatial
resolution of core design studies for coupled neutronics (MCNP) and 3D thermal-hydraulic sub-
channel codes for the analysis of PWR’s. Various valuable contributions were made to the
MCNP/SUBCHANFLOW coupling scheme. The authors have adopted radial mapping of
thermal-hydraulic and neutronic domains. Passing of information was done with script files. For
the axial mapping between these codes, the number of cells was kept the same, for radial mapping
an average over the cell with a defined formula were used. The variation of node average fuel
temperature is used for checking convergence with a certain convergence criteria. For the
Doppler broadening of nuclear cross sections, they have implemented the pseudo material mixing
approach methodology. Other studies [7],[9] have shown that this approach increases the
17
accuracy of the calculations. This pseudo material approach was also extended to the thermal
scattering data. Comparisons were shown to demonstrate the effectiveness of this application.
In the PhD-work of Espel [21] , a coupled system MCNP/CTF was developed along with
acceleration methods for the coupled calculations. The coupling of MCNP5/CTF/NEM/NJOY
was applied to a simplified 3D 2x2 fuel pin array. The Nodal Expansion Method (NEM) diffusion
code is based on a 3D steady state and transient nodal model. Coolant Boiling in Rod Arrays-Two
Fluid, COBRA-TF (or simply CTF), is a thermal-hydraulic sub-channel code. NJOY99, which is
a nuclear data processing system, converts evaluated nuclear data in the ENDF (Evaluated
nuclear data file) [22] format into cross section libraries for different application, including
continuous energy Monte Carlo (MCNP). Espel has developed an automated procedure to
generate continuous energy temperature dependent cross sections for MCNP calculations. He
used interpolation methods for the pre-generated cross section grid. With the application of
MCNP-Threads, he was able to parallelize and speed-up the calculations.
Reference [23] presents a VVER benchmark analysis using two coupled code systems,
DYN3D/RELAP and DYN3D/ATHLET. The authors consider three ways of coupling:
1) An internal coupling, where the thermal-hydraulics of core and system is simulated by
the system code and the neutronics calculations are performed by DYN3D;
2) An external coupling, where both neutron kinetics and thermal-hydraulics of the core
are simulated with 3D neutronics code (DYN3D) and thermal-hydraulics of the
system is calculated by the system code;
3) A parallel coupling option, where core thermal hydraulics and neutronics are run in
parallel and the system code provides boundary conditions.
DYN3D calculates thermal hydraulics and updates core power. DYN3D (which is similar
code to ADMARC-H) has been used in a coupling schemes with thermal hydraulic codes. The
paper presents possible ways of coupling DYN3D with these thermal hydraulic codes. Our
18
methodology would be the same as the external coupling explained in this work. Their results
showed small difference while comparing the two coupling schemes.
2.3.2 Thermal hydraulic modeling
The TRIGSIMS-TH code system utilizes the thermal hydraulic sub-channel code CTF.
This code has seen various upgrades and developments. CTF is now an advanced and
modernized sub-channel thermal-hydraulics code. The following review describes the studies
performed over last years to upgrade this code.
Avramova has had various contributions to the CTF code. As part of her Master's thesis
[24] she worked on qualification of CTF and its application to LWR analysis. In her PhD thesis
[25] a development of a spacer grid model utilizing computational fluid dynamics within a sub-
channel analysis tool is introduced. Blyth [26] continued this work by using CFD data to
improve grid-detected lateral cross flow effects, turbulent mixing and heat transfer enhancement
in CTF.
Salko [27] as part of the CASL (Consortium of advanced simulation of Light water
reactors) project, worked on the development of CTF modeling of full reactor core and its
application to cycle depletion. He included new features in the code that address the PWR
challenge problem of departure of nucleate boiling and CRUD (deposits) that induces power shift.
Parallelization of the software was done to be able to assist in these calculations.
The CTF used in this PhD study includes the improvements described in the above-
mentioned references.
19
2.4 General review
In addition to multi-physics coupling methodologies developed in this study there are
also various other improvements introduced to TRIGSIMS as part of this PhD research. Reviews
to illustrate the need for these improvements follow.
2.4.1 Reviews on critical rod height
In [28] it was determined the critical rod height in a benchmark calculation of 3MW
TRIGA Mark II. With MCNP4C model, the authors adjusted the control rod bank until it reached
keff of ~1, which took several iterations. The obtained results showed a good agreement with the
measured data.
The reference [29] is a report that shows a comparison between TRIGAP, a one-
dimensional, two-group diffusion computer code, and one group perturbation theory to calculate
the reactivity worth of the I.T.U. TRIGA reactor. The results were compared with measured data.
Their results show that perturbation calculation performed better than the diffusion code.
Some studies using neural network methods were done for control rod positioning in
PWR. What this entails is the study of computation and measurements of axial flux profiles for
various axial positions of the control rods. This study involved calculations for different scenarios
and pattern recognition for a given control rod position [30].
2.4.2 Nuclear Data
There are numerous studies on cross section generation. The accuracy of neutronics
methods is largely dependent on the nuclear data that is used this calculation. References [2], [7]
discussed cross section generation. In particular, for TRIGA reactors the thermal scattering needs
20
to be accounted for in the neutronic calculations. The NJOY tool is used for the cross section
processing. The thermal scattering cross sections for hydrogen bound in water and hydrogen
bound in zirconium hydride is well-investigated [2] because of their effect on the calculations
accuracy. Kraingchaiporn [15] based her thesis on a 3D transport model utilizing 3D multi-group
lattice cross-section generation for the PSBR. She used 3D TORT [14], [31] code and produced
TRIGA cross sections generated in 2D and 3D geometries, based on CPXSD (Contribution and
Point wise Cross section driven) methodology.
2.4.3 Control rod absorber material
Of significance in this work was the investigation of the B4C used in the absorber
material of the control rod elements. Previous studies [2], [7] has argued over the B4C density and
weight used in the MCNP model of TRIGSIMS. The Table 2-1 outlines the results of previous
work. The control rods reference are the three fuel follower rods, i.e., the safety rod (SA), the
regulating rod (RR) and the shim rod (SH) and one air follower transient rod (TR).
Table 2-1 B4C components as used previously
B10(wt%) B11(wt%) C(wt%) Density (g/cm3) CR Reference
1a
1b
15.6
3.91
62.8
15.75
21.6
80.34
2.49
1.89
SA,RR,SH
TR
[2]
2a
2b
3.18
3.18
12.82
12.82
84
84
2.50
1.13
SA,RR,SH
TR
[7]
21
The cases in Table 2-1 are trial-and-error estimates formulated and optimized for the
code used for those calculations. Analysis is performed in this PhD work on identifying an
appropriate estimate of B4C.
22
Chapter 3
Theoretical models and numerical methods
The theoretical models for the work herein cover different single physics phenomena
including neutronics (reactor physics) and thermal hydraulics as well as the multi-physics
coupling. The methods involved include statistical (Monte Carlo) and deterministic numerical
methods. This section provides a short overview of the PSBR core, which design and analysis is
the application in interest. The developed in this research TRIGSIMS-TH code system is
summarized through a comparison to the previously developed TRIGSIMS code system.
3.1 Introduction
A nuclear reactor is a device in which the nuclear fission reaction can be controlled for
the purpose of power production as in the case of power reactors or as a neutron source as in the
case of research reactors. The safe operation of any reactor relies on ensuring the integrity of the
reactor fuel and on preventing the release of potentially harmless radioactive materials, which are
produced during the fission process. The two main characteristics, which are taken into account in
reactor design, are neutron distribution and heat removal process. The neutron distribution in a
reactor determines the nuclear fission power distribution among the fuel elements. In this process,
nuclear fission heat is generated in the fuel. The heat energy in the fuel however needs to be
transported away from the fuel, to ensure that the fuel does not overheat and compromise its
physical integrity.
The two main physical phenomena in nuclear reactor design involve neutron transport
and heat conduction. The determination of the neutron population and hence the power
production in a nuclear reactor is referred to as neutronics, while the simulation of the thermal
23
processes in the reactor is known as thermal hydraulics. Both of these areas of simulation are
quite complex and in reality they are coupled resulting in a multi-physics problem. There are
numerous neutronics and thermal hydraulic codes. Deterministic and Monte Carlo methods are
the most common methods to use for neutronic analysis of the reactor core. For thermal
hydraulics modeling, there are generally two types of models. The system models cover the
primary cooling system of a reactor while the sub-channel models are used for the reactor core.
The remainder of this chapter describes the parameters, which are important for reactor
core design [32]. More details are provided for the neutronics and thermal hydraulic codes that
are used in this work. Figure 3-1 summarizes the most important analyses and parameters related
to nuclear reactor core design.
3.2 Nuclear Reactor Core Design
Nuclear reactor core design
Core analysisReactor safety analysis
Regulatory consideration
Reactor physics
Numerical analysis
Computational methods
Core criticality
Power
Reactivity control
Fuel loading
Core arrangement
Depletion of fuel
Figure 3-1 Basic analyses and parameters for nuclear reactor core design
24
3.2.1 Terminology
A nuclear reactor is a device to initiate, control and sustain a nuclear fission chain
reaction. In order to undergo fission it requires nuclear material of which are fissile and
fissionable. Fissile material, such as uranium-235 (235
U), is able to sustain a nuclear chain event.
Fissionable material such as uranium-238 (238
U) is capable of capturing a high-energy neutron
and undergoing fission. In many cases such as for the PSBR, to initiate a chain event the reactor
requires an external source.
A) Neutron Flux
Neutron flux is a measure of the total neutron population and has units of, number of
neutrons per square cm, per second, i.e., it gives the total number of neutrons traveling in all
directions, per unit area, per unit time. This measurable quantity is related to the reactor power by
the following equation for thermal reactors:
3.1
where,
P is the reactor power (watts),
is the thermal neutron flux(neutrons/cm2-sec)
is the macroscopic fission cross section (cm-1
)
is the volume of the core (cm3)
25
B) Criticality
Criticality is a measure of the balance (gains and losses) of neutrons in the reactor core.
The fission process is a chain reaction whereby the neutrons interact with uranium atoms in the
fuel. When the reactor reaches its critical condition, we have balance for neutron being produced
and lost in the system. In this case the reactor is critical (keff=1). If the neutron population is
increased and the chain reaction produces more neutrons than what are lost, we refer to this as a
super critical reactor (keff>1). When the reactor has less neutrons being produced than are lost, the
reactor is subcritical (keff<1).
C) Reactivity
After the reactor has reached a critical state, the effective multiplication factor ,keff=1, and
if the neutrons are increased, by means of control rod withdrawal as in the case of the PSBR, this
departure from criticality is called reactivity insertion. The expression is given as .
D) Burnup
Burnup is a measure of fuel depletion given in thermal energy, mega-watt days per unit
mass, of the initial value of the heavy metal content, metric ton unit, (MWD/MTU). In uranium-
fueled reactors, the reactivity changes with burn up are due to:
a) 235
U depletion;
b) 239
Pu buildup;
c) Buildup of other non-fissile isotopes;
d) Buildup of thermal neutron absorbing fission products and other fission products.
E) Doppler temperature feedback.
With increase in power by a control rod withdrawal, the fuel temperature increases. With
this the resonance energy peaks of the 238
U broaden, which allows more absorptions of fission
neutrons before reaching thermal energies. Hence, the reactivity decreases. This effect is called
Doppler broadening. This is a negative effect on reactivity.
26
F) Excess reactivity
When the control rods are fully extracted from the core, the reactivity increases to
, which is the core excess reactivity. The βeff is the effective delayed neutron
fraction approximately equal to 0.007 for the PSBR. The fission neutrons that are born as a direct
result of the fission reaction are called prompt neutrons while the neutrons that are released
during the decay of fission products are called delayed neutrons.
G) Critical rod position
This term is used when the control rods are in a position where the neutron chain reaction
is sustained (keff=1). This could be at low power or at 1MW power for the PSBR.
3.2.2 Core design process
The reason for searching an optimal reactor core design is to ensure efficiency with safety
in operation. To be able to shut down the reactor safely is a main concern for all nuclear facilities.
The fundamental quantities that are evaluated in the nuclear core design calculations are
the effective multiplication factor (keff) and the neutron flux distribution (Φ). These fundamental
quantities are the basis for the fuel management and reactivity control. To find a solution to these
quantities requires a solution to the neutron transport equation.
3.2.3 Main parameters for core design
Figure 3-1 shows some of the basic parameters for the PSBR reactor core design
addressed in this thesis.
A) Nuclear core analysis
27
The first requirement is a reactor core model. This is a layout of physical design of the
reactor core. It consists of fuel elements, control rods and all other parts that constitute a reactor
core including the surrounding water. For this model, all the characteristics of the elements
should be known. This includes material properties of the fuel, neutron control elements, water,
neutron reflectors or neutron moderators and structures as well as the geometrical layout of these
components.
B) The nuclear data or cross-sections
This is the measured (evaluated) probabilities of various physical interactions involving
nuclei of atoms. The quality and application of this data are important. As an example, the PSBR
TRIGA operates with a maximum fuel temperature between 400°C (673K) and 540°C(813K) for
full power. The data libraries (ENDF7) are generally in sets of 300K, 600K, 900K, and 1200K
etc.[22]. Hence, application using only these libraries would result in a less favorable result.
C) Numerical and calculation methodologies
For most parameters, the physics models exist. The application of the physics modeling is
done with numerical approximations. For example, finding a solution to place a control rod in a
certain position to give a critical reactor requires both a numerical formulation and a calculation
tool to apply this application.
D) Tools
The computational tools (codes) assist in quantifying the physics by applying numerical
formulas. In the case of TRIGSIM-TH, the tools applied in this core design methodology, uses
Monte Carlo, which is a statistical approach to solve the neutron transport, i.e., which solves the
neutron flux.
E) Safety analysis and regulatory requirements
Safety of all nuclear facilities is a regulatory mission. This means that the safe operation
and use of the facility are regulated and guided. The reason for this is ensure the safety of the
28
public. The guides are usually written in the safety analysis report, whereby the reactor facility
conforms in operation. Hence, the core design has specific outcomes and guides that need to be
attained. An example of one such regulation is the maximum allowed temperature of the TRIGA
fuel is not to exceed 1150 °C. A safety analysis is performed for a reactor design to ensure that
the operation under steady state and transient conditions is safe and conforms to the guidelines
[33].
3.2.4 Intent and deliverables
The aim of this work is to further develop and improve the TRIGSIMS code system to be
used as a modern core design and analysis tool. The final goal of this research is to develop a
coupled code system that can simulate reactor steady state and transient conditions with reliable
accuracy as compared to measured results within the measured uncertainties.
The envisioned outcome is a high-fidelity advanced code system that can be used as a
safety, analysis and core design tool for PSBR.
29
3.3 Computational analysis tools
3.3.1 Neutron transport methods and codes
There exist two types of computational methods to solve or model the neutron
distribution and motion, in the reactor core. Deterministic methods to solve the linear Boltzmann
transport equation in a numerical approximation, and stochastic methods, which used a statistical
(probabilistic) approach to solving the neutron transport in the core.
The ultimate goal in nuclear reactor studies is to determine the density or distribution of
neutrons in a volume, moving with certain energy
The neutron flux is
the quantity that is solved with the neutron transport methods. This quantity is proportional to all
the gains and losses of neutrons in a system, which is due to absorption, fission and scattering.
3.2
This is a linear equation for the unknown variable with seven independent
variables . In general, this equation is complex, and the existing
deterministic codes usually aim to solve or treat the variables in the equation in a certain way.
The series expansion method to solving the angular variable, use spherical harmonics.
Discrete ordinates methods are an example of the direct numerical solution techniques of
the transport equation. Each variable in this transport equation is discretized by changing the
30
continuous variable into a set of discrete points. Differential equations are solved using finite
difference or discrete ordinates methods and integrals are represented as sums or numerical
quadrature formulas. This treatment of variables can be done with various mathematical tools. An
example would be the discretizing angular dependences using Sn equations or Pn equations of
which the widely used one-dimensional P1, Legendre Polynomial is known.
The neutron diffusion approximation is a result of a simplification of the neutron
transport equation. The formulation of Fick's law, which implies that the neutrons will diffuse in
the direction from high to low-density (flux) regions, is given below:
3.3
where is equal to the net number of neutrons that pass per unit time through a unit
area perpendicular to the x-direction [35]. The parameter D is the diffusion coefficient.
The code ADMARC-H, used in the TRIGSIMS-TH code system, is a diffusion-
approximation based code. For this code, the two group diffusion equations are solved, in form
given below:
, 3.4
3.5
In these equations, the leakage and removal terms are arranged on the left and the source
terms on the right.
Deterministic computational methods usually give systematic errors, which arise from
discretization of time, space, angle and energy phase space of numerical computation, as well as
limitations on computation that limits deterministic high-fidelity modeling of three-dimensional
31
configurations. Issues such as memory, time, and accuracy are factors in play with modeling and
simulation of multi-dimensional problems.
The stochastic methods or Monte Carlo calculations use a relatively straightforward
approach to complex three-dimensional configurations. The TRIGSIMS code is a MCNP5[41]
based and therefore intensive analysis using this method is required in this research.
In this work, SERPENT [36], a Monte Carlo code is used for generation of the few-group
homogenized cross sections and diffusion coefficients (constants) utilized in the ADMARC-H
code. Similar to MCNP, SERPENT has the same basic geometrical structure as an input. It uses
universes, cells and surfaces. In addition to that, it has a varied number of surface types with fixed
parameter. In particular, for use of the PSBR studies, it contains hexagonal cylinder shape
surfaces, with lattices, which are special universes, filled with these surface shapes. This
capability makes the code appropriate since the PSBR whole core is shaped in a hexagonal lattice.
SERPENT uses set commands to change the outcome of various quantities such as source rate
normalization, flux normalization, heating power, power density amongst other. The group
constant generation function lets the user decide on the universes to calculate the homogenized
group constants. SERPENT can calculate pin power wise distribution in full core calculations.
3.3.2 Thermal hydraulic methods and codes
Similar to the neutronics codes, thermal hydraulics codes can also be divided into two
basic classifications. Codes that model the entire system, or plant balance, are called system
codes; and codes that focus on various components, such as the reactor core, are called sub-
channel codes.
System codes, such as the well-known RELAP code series, calculate the thermal
hydraulic characteristics of the primary loop under both steady and transient operational
32
conditions. Sub-channel codes, such as the COBRA code series, have a focus more on the reactor
core, and some of these codes may be used for both transient and steady state conditions. Through
time, both, these code series have evolved. They incorporate various models and methods of
analysis as the need, information and experience have increased. An increased requirement to
address hypothetical accident scenarios has influenced the need for more advanced methods and
models. The existence of other codes such as WOSUB, THERMIT that are component codes,
RETRAN, and TRAC, which are system codes is acknowledged as well [40].
Thermal hydraulic codes solve mass, momentum, and energy conservation equations
numerically.
CTF general momentum conservation equation for phase k is given as [26], [27]:
3.6
Left Hand Side (LHS) denotes the change of volume momentum over time and three
directional advection of momentum terms.
Right Hand Side (RHS) denotes the gravitational force, pressure force, viscous shear
stress force with wall drag and form losses, a source term due to phase change and entrainment
/de-entrainment, interfacial drag source and the momentum source due to turbulence mixing and
void drift.
The phasic energy conservation equation:
3.7
LHS denotes the change in energy and the advection of energy.
33
RHS denotes inter-cell energy exchange due to void drift model and turbulence model,
the energy transfer due to phase change, the volumetric wall heat transfer and the fluid cell due to
pressure.
The general phasic mass conservation equation:
3.8
LHS term denotes change in mass and advection of mass.
RHS term denotes mass transfer in and out of phase change k (e.g. evaporation and
condensation) and mass transfer due to turbulent mixing and void drift.
A more detailed discussion of these equations and their numerical solution methods can
be found in the CTF manual [27].
The type of code to use will strongly depend on the area to be analyzed and the capability
of the code. For example if the need were to address accident scenario, where we have pump
failure and loss of coolant in the reactor core, we would probably use one of the RELAP codes
for this analysis. In the case of the PSBR TRIGA reactor, where the reactor is in pool and natural
coolant flow circulation governs the system, the need is for a full core sub-channel analysis,
which the CTF code is capable of modeling [3].
3.4 PSBR description
3.4.1 PSBR core
The PSBR reactor core, is situated at a depth of approximately 18 feet in a reactor pool
which contains 270 000 liters of demineralized water [5]. This filtered water provides the
34
necessary shielding, reflection and cooling for the reactor. A typical core configuration is given in
the Figure 3-2. This layout is particular to CL56.
Figure 3-2 Core loading configuration
A usual loading pattern would be to load the more reactive fuel elements in the centre of
the core. In general, the reactor has a power profile that peaks around the thimble due to the
moderating effect of the water hole. The fresher fuel elements and the 12 wt% fuel are located
two or three rings out from the central thimble. The four control rods are indicated in green. They
include the Safety rod (SA), which usually has a worth exceeding that of the other rods for the
reason that it is closer to the center of the core than the identical Shim and Regulating rods. There
is also the Shim rod (SH), to make course adjustments in the neutron density; the Regulating rod
(RR), for finer adjustment and power regulation and a special air follower rod; and the Transient
rod (TR), which is used for square wave and pulse mode operation [5], [45]. Two dry tube
irradiation positions are indicated in pink. On certain core ladings, graphite elements are added to
35
the core to increase reactivity. These are placed on the outer ring of the reactor to reflect neutrons
back toward the fuel. The graphite elements are used if there is a need to increase the flux in the
core. The reactor can be loaded with up to approximately 120 elements. Figure 3-2 shows the
CL56 with 105 fuel elements and 3 fuel-follower control rods. These elements, fuel and non-fuel,
have fixed positions within the core, based on the grid plates, with a pitch (distance between
centers of the elements), of 4.354 cm (1.71in), which is the size used for the core design layout of
the calculations.
3.4.2 TRIGA fuel
TRIGA reactors are inherently designed to be safe. This is because of the moderating
properties of the zirconium hydride fuel (ZrH1.6U) [52]. In short, the uranium is in close contact
with the hydrogen, which results in a self-moderating fuel. Figure 3-3 illustrates the TRIGA fuel
and its dimentions.
36
Figure 3-3 A typical TRIGA fuel element
The basic parameter, which allows TRIGA reactors to operate safely during either steady
state or transient conditions is the prompt negative temperature feedback coefficient associated
with TRIGA fuel and core design. TRIGA reactors are designed in such a way that an increase in
temperature of the fuel element will result in a relatively large decrease in reactivity. This effect
is constant. This negative temperature coefficient for TRIGA fuel[48] is because of the following:
a) Cell and heterogeneous effect:
This accounts for 65% of the negative temperature coefficient. With the rise in
temperature of the fuel, the hydrogen in the fuel acts like free hydrogen. Neutrons can
transfer energy back and forth with the hydrogen. This increases the probability that a
thermal neutron in the fuel element will gain energy from an exited state of an oscillating
hydrogen atom (0.14eV quanta).
37
As the neutron gains energy from ZrH lattice, the thermal neutron spectrum in the fuel
shifts to a higher energy (to the right). The fission cross section for 235
U decreases with increasing
energy (temperature), so the probability of fission is lower with these higher energy (temperature)
neutrons. This is known as “spectrum hardening”. This effect also increases the mean free path
of the neutron. Hence, the probability for a neutron to escape the fuel is higher with increase in
temperature. In the water a re-thermalization of these neutrons can occur. As a result, there is a
temperature dependent disadvantage factor for the core unit cell, in which the ratio of the
absorption in fuel to cell absorption is increased as the fuel temperature decreases. This brings a
shift in core neutron balance giving loss of reactivity [4];
b) Doppler broadening effects:
This effect contributes approximately 15% to the negative temperature coefficient. The
uranium in the fuel elements is approximately 20% 235
U and 80% 238
U. The capture resonances in
the 238
U are Doppler-broadened by an increase in fuel temperature, which in turn causes a
decrease in the resonance escape probability (p) [4];
c) Core leakage effect:
This contributes the rest of the 20% of the negative temperature coefficient. As
mentioned in the cell effect about moderated fuel causing the hardening of the spectrum, as the
core heats up, the leakage is increased and relatively more captures occur outside of the fuel [4].
3.4.3 Application of the PSBR
The PSBR is foremost a research reactor. However, other industries (such as business,
government, universities etc.) also use the facility for various irradiation and research. It is part of
the Radiation Science and Engineering Centre (RSEC) at the PSU campus. The RSEC facility
also hosts gamma irradiation facilities, hot cells, the radio-nuclear application laboratory, the
38
neutron beam laboratory and other. The reactor facility houses seven-beam ports, but only one is
in use at a time. This is one of the shortcomings that are being investigated [5]. Ücar's thesis
evaluated a new core moderator facility to enhance the amount of neutrons to the beam ports # 4
and 7.
For these studies and facilities, the PSBR provides the neutron source. The calculation of
the core, or neutron source, should be accurate. The TRIGSIMS-TH code system is used for this
purpose.
3.5 TRIGSIMS and TRIGSIMS-TH
3.5.1 Capabilities of TRIGSIMS and TRIGSIMS-TH
The following table shows the difference and similarities between the TRIGSIMS [42]
and TRIGSISM-TH code systems as well as outlining the capabilities of each.
Table 3-1 Comparison of old and new TRIGSIMS
TRIGSIMS TRIGSIMS-TH
Automated to read CL-input and create
input decks for the following:
- MCNP neutronic analysis
- ADMARC-H neutronic analysis
- ORIGEN-S burnup
- No thermal-hydraulic feedback
- Predictor-corrector depletion method
Automated to read CL-input and temperature
distribution file and create input decks for the
following:
- CTF for coupling with MCNP and ADMARC-H
- MCNP neutronic analysis with feedback
- ADMARC-H neutronic analysis with feedback
- ORIGEN-S burnup
- CTF full core thermal hydraulics
- Predictor-corrector depletion method
39
No control method for rod position for a
critical reactor power, usually at 38.1cm, or
otherwise it is set in rod position.
Control rod placement method for a critical reactor
at any power level.
No core expansion is possible with
ADMARC-H
However, MCNP is capable of loading any
size core
Core expansion possible in:
MCNP
CTF
ADMARC-H
No option for graphite elements Graphite elements are now an option in the input
TRIGSIMS/MCNP could always take on a
new fuel as long as the geometry are the
same
TRIGSIMS-TH/MCNP's capabilities are the same
as before
TRIGSIMS-TH is a coupling software connecting various codes with information from
other codes. The main core design code is MCNP5 [41]. MCNP5 is coupled to CTF, the sub-
channel analysis code, to provide the thermal hydraulic feedback. The ADMARC-H code is also
coupled to CTF. This coupling is intended to accelerate the calculation. The ADMARC-H/CTF
coupling is an optional setting on the TRIGSIMS-TH platform. The burn-up code ORIGEN-S
(from the SCALE code system) together with its predictor-corrector method is also included in
the TRIGSIMS-TH.
3.5.2 Codes in TRIGSIMS-TH
The following theory covers the various functional codes that make up the TRIGSIMS-
TH code system.
40
3.5.2.1 MCNP
MCNP is a Monte Carlo code that is based on a statistical sampling process for selection
of random numbers, comparable to throwing dice in a gambling casino, hence the name “Monte
Carlo”. In particle transport, the Monte Carlo technique is pre-eminently realistic (a numerical
experiment). It consists of essentially following each of many particles from a source throughout
its life to its death in some terminal category (absorption, escape, etc.). Probability distributions
are randomly sampled using transport data to determine the outcome at each step of its life. A
neutron incident on a fissionable material can have a number of outcomes. Each step is recorded
(tallied). The possible events that can happen to a neutron are: it can scatter, produce neutrons,
fission thereby producing more neutrons, neutrons can be captured, it can leak out of the material,
and photons can scatter, leak or be absorbed. This describes one neutron history. So if more and
more neutron and photon histories are followed, their distributions will be better known. The
quantities of interest are tallied, along with estimates of the statistical precision (or uncertainty) of
the results [12].
The MCNP code package is incomplete without the associated nuclear data tables.
MCNP uses continuous energy nuclear data libraries. Nuclear data tables exist for neutron
interactions, neutron-induced photons, photon interactions, and thermal particle scattering S (α,
β). The geometry of MCNP treats an arbitrary 3-dimensional configuration of user-defined
materials in geometric cells. MCNP treats geometric cells in a Cartesian coordinate system.
We use MCNP to calculate the nuclear criticality, which is the ability to sustain a chain
reaction by fission neutrons. This quantity is characterized by keff, the eigenvalue of the neutron
transport equation. In reactor theory, keff is thought of as the ratio between the numbers of
neutrons in successive generations, with the fission process regarded as the birth event that
separates generations of neutrons. For critical systems, keff = 1 and the chain reaction will just
41
sustain itself. For subcritical systems, keff < 1 and the chain reaction will not sustain itself. For
supercritical systems, keff > 1 and the number of fissions in the chain reaction will increase with
time. Calculating keff consists of estimating the mean number of fission neutrons produced in one
generation per fission neutron started. A generation is the life of a neutron from birth in fission to
death by escape, parasitic capture, or absorption leading to fission. In MCNP, the computational
equivalent of a fission generation is a keff cycle; that is, a cycle is a computed estimate of an
actual fission generation.
The TRIGSIMS [38] code uses only the track length estimate of cell flux (F4), and the
track length estimate for fission energy deposition (F7) tallies. The average particle flux in a cell
can be written as:
3.9
Where is the density of particles regardless of their trajectories, at
a point defining to be the differential unit of track length and noting that gives:
3.10
where may be thought of as a track length density; thus, the average flux can be
estimated by summing track lengths.
MCNP has various means of accessing the statistical precision, variance reduction and
error estimation of the results for the keff and flux produced by a calculation. What was found
however is that a calculation that converges in all ways does not necessary guarantee high
42
accuracy. Therefore, careful checking of the input and output data is required to make sure what
is intended is calculated, with all the needed information.
3.5.2.2 CTF
COBRA-TF (COolant Boiling in Rod Arrays – Two Fluid), a computer code, was
developed at the Pacific Northwest National Laboratory. The modified version of COBRA-TF
(CTF) used in this work was developed at the Reactor Dynamics and Fuel Modeling Group
(RDFMG) [27].
CTF is an advanced sub-channel code for best-estimate thermal-hydraulic analysis of
Light Water Reactors (LWRs). It features three fields representation of two-phase flow. It uses a
set of nine time-averaged conservation equations written in a semi-implicit form using donor cell
differencing for the convective quantities.
It is developed for use with either rectangular Cartesian (Figure 3-4) or sub-channel
coordinate systems.
Figure 3-4 CTF Cartesian coordinate system
It can treat both hot wall and normal flow regimes. This allows a three-dimensional
treatment of geometries amenable to the description of the Cartesian coordinate system.
43
In CTF, the computational momentum cell structure can be illustrated in the figures
below.
Figure 3-5 Scalar Mesh cell, axial
Figure 3-6 Scalar mesh, transverse
CTF momentum equations, 3.6, are solved using a staggered difference scheme in which
the velocities are obtained at the mesh cell faces and the state variables such as the pressure,
density, enthalpy and void fraction are obtained at the cell center. The mesh is characterized by its
cross-sectional area, A, its height, Δx, and the width S, of the connection with adjacent mesh
cells. This illustration is shown in the Figure 3-5 and Figure 3-6 [24], [27].
CTF can calculate reverse flow, natural circulation, and cross-flow situations. CTF is
equipped with sub-cooled boiling wall heat transfer logic, capable of simulating TRIGA
conditions i.e., low flow, low pressure, low power and low temperature. CTF automatically
makes the transition to single-phase forced convection at low wall superheat and to pool boiling
at low flow rate.
CTF’s wall interfacial friction model is suited for TRIGA properties. CTF’s conduction
model specifies the conductor geometry and material properties, and solves the conduction
equation. The rod model is designed for nuclear fuel rod, heater rods, tubes, and walls. The model
44
consists of options for one-dimensional (radial), two-dimensional (radial and axial), and three-
dimensional heat conduction [27].
CTF gap conductance model dynamically evaluates fuel pellet-clad conductance for a
nuclear fuel rod. The model computes changes in the fuel rod structures and fill gas pressure that
affect the gap conductance and fuel temperature during a transient. For this CTF model however,
the nuclear fuel rod model was not used because of TRIGA fuel being a zirconium hydride fuel is
different from the standard LWR fuel. The hrod (for a solid cylinder) geometry option was used,
which allowed for the specification of the various material makeup of this fuel [3].
3.5.2.3 ADMARC-H
ADMARC-H [2], [14] is a two group, 3D, nodal diffusion code for hexagonal geometry.
ADMARC-H code utilizes a set of tabulated pre-generated cross sections for the 3D core
calculations. ADMARC-H code calculates the core flux distribution and power distribution in
both axial and radial direction. Previously the ADMARC-H cross sections were generated with
the HELIOS lattice physics code. Part of the developments included in this work, was to generate
a set of few-group homogenized cross sections using the SERPENT code.
In the ADMACR-H execution folder, the set of two-group PSBR homogenized cross
sections are stored. They are arranged per cell/material type (water cell, graphite cell, B4C cell, air
cell, 2 fuel types and Fuel follower control rod cell). For each of these cells, they are arranged per
temperature intervals (300°K to 900°K) and per burnup (0 to 140,000MWD). An interpolation
scheme allows for determining the cross-section values for conditions in between burnup and
temperature reference points. However, for the Boron Carbide (B4C) there is no burnup or
temperature change indicated (only one value throughout the grid).
45
The homogenized cross sections and diffusion coefficients that are stored per
cell/material type are the following:
D1 - diffusion coefficient for the fast group
- Removal cross section for the fast group
– Production cross section for group 1
– Fission cross section for group1
D2 - Diffusion coefficient for the Thermal group
- Removal cross section for the thermal group
– Production cross section for group 2
– Fission cross section for group 2
– The group scattering cross-section (down scattering only)
These homogenized cross sections and diffusion coefficient will be for an equivalent cell.
The equations for the homogenization were given in a previous section.
TRIGSIMS writes into an ADMARC-H input file, for each node in the fuel element,
depending on burnup, material type and temperature, a set of nine cross sections, as indicated
above. ADMARC-H performs two-group diffusion calculations using these cross sections to
solve for the flux distribution, keff and power distribution, on nodal basis. The numerical
procedure is an iterative procedure, whereby it solves the two group equations starting with an
initial guess of k=1 and source and proceeding to update, substituting down the group and
iteratively from one k to the next until convergence is reached.
46
3.5.2.4 ORIGEN-S (SCALE)
ORIGEN-S is a SCALE [11] , [49] system module to calculate fuel depletion, actinide
transmutation, fission product buildup and decay, and associated radiation source terms.
ORIGEN-S (Oak Ridge Isotope GENeration) computes time-dependent concentrations and
radiation source terms of a large number of isotopes that are simultaneously generated or
depleted, through neutronic transmutation, fission, and radioactive decay. The primary objective
in the design of ORIGEN-S is to make it possible for the depletion calculations to utilize multi-
energy-group cross sections processed from any standard ENDF/B formatted nuclear data library.
In determining the time dependence of nuclide concentrations, ORIGEN-S is primarily
concerned with developing solutions for the following equation:
ORIGEN-S nuclear data libraries include cross sections for three neutron energy groups:
a thermal group below 0.625 eV, a resonance energy group extending up to 1 MeV, and a fast
energy group above 1 MeV. The thermal cross section is stored as the effective 2200-m/s values
(value at 0.0253 eV). The resonance and fast group cross sections are the flux weighted values for
the respective groups. When running ORIGEN-S [49] as a stand-alone module, the user specifies
the cross-section weighting factors THERM, RES, and FAST. THERM is used to adjust the
2200-m/s cross sections in the library for a thermal neutron spectrum for the system. RES and
FAST are used to weight the resonance and fast group cross sections in forming effective one-
group values. Note that when ORIGEN-S is run with a binary cross-section library the effective
one-group cross sections are stored in, and read directly from the binary library. Therefore, the
three-group weighting factors do not need to be input in this case. In our application for
TRIGSIMS (also TRIGSIMS-TH), we have ORIGEN-S using both:
a) The binary library stored (for non-important isotopes), and;
47
b) The pre-calculated cross sections by MCNP for PSBR, for the effective cross sections
calculations, with the weighting factors THERM, RES and FAST, calculated for the pre-
determined ”important isotopes”.
Having input values for THERM, RES, and FAST, ORIGEN-S then combines these
weighting terms with the three-group cross sections to form the effective one-group cross
sections, σeff, used in the calculation of reaction rates based upon the total thermal flux as:
In order to preserve the reaction rates, the group cross sections for thermal, resonance and
fast regions are calculated by the MCNP code. The update of the three group cross sections to the
burnup dependent cross sections library is performed through COUPLE (part the of SCALE
module) which is executed before ORIGEN-S.[2]
3.6 Cross sections
TRIGSIMS-TH uses two types of neutronic codes: the diffusion code ADMARC-H and
the Monte Carlo code, MCNP5. The MCNP5 code uses continuous energy cross sections, which
are provided with the code. In addition, a set of continuous energy cross sections were generated
specifically for the PSBR design TRIGA fuel. These refined cross section libraries were produced
identified "important" isotopes [2].
The ADMARC-H code use homogenized reaction cross section and diffusion
coefficients, which was previously generated with the HELIOS code [14], and for this application
performed with SERPENT, a Monte Carlo code. The reason for this cross-section library update
is to improve accuracy of cross-sections used in 3D diffusion nodal calculations and make them
more consistent with Monte Carlo core calculations. The updated library also covers extended
ranges of burnup and temperature conditions as well as new cell/material types.
48
A) SERPENT
SERPENT[36] is a three-dimensional, continuous-energy Monte Carlo reactor physics
burnup, calculation code. It is specifically designed for lattice physics applications and can be
used for full core calculation. The code uses built-in routines for burnup calculations and is
optimized for generating homogenized multi-group constants for deterministic reactor simulator
calculations. Among the many capabilities of this code, for this project we are interested in the
homogenized reaction cross sections and diffusion coefficients that it produces for various burnup
steps of TRIGA fuel. Internal burnup calculation capability allows SERPENT to simulate fuel
depletion as a completely stand-alone application.
In general, the burnup calculation is a two-step cyclic process. It consists of transport
cycle using the Monte Carlo techniques to determine the reaction rates for the neutron induced
transmutation. This data is then combined with radioactive constants, and fission yield is read
from nuclear data libraries. The Bateman equation [50] is used to describe the isotopic changes
and is given as:
3.11
where is the atomic density of the nuclide j, n is the total number of nuclides and
are the generalized transmutation coefficients characterizing the rates of neutron-induced
reactions and spontaneous radioactive decay. These are kept constant over the burnup step.
Secondly, this equation is solved, thereafter-updated material compositions are applied, and
procedure is repeated.
The standard isotropic diffusion coefficients are calculated in SERPENT through:
49
3.12
where the transport cross section given by
3.13
with few group index G given [51].
The cross sections and diffusion coefficients generated are used for the nodal diffusion
code ADMARC-H calculations.
A typical TRIGA fuel cell consists of four regions indicated in the Figure 3-7. It can be
reduced to an equivalent cell of simpler geometry to expedite calculations. The concept of
homogenization is to preserve all the reaction rates in the problem from the detailed
heterogeneous transport calculation.
Figure 3-7 Homogenization of TRIGA fuel
A specific challenge to SERPENT is the critical spectrum calculation. Homogenization is
carried out at fuel assembly level, in a geometry consisting of infinite lattice identical assemblies.
There is no net current over the boundaries, which affect the k-eigenvalue calculation. Scaling of
the fission source has an effect on the flux spectrum, which has an effect on the homogenized
group constants. To account for this non-physical infinite lattice approximation, a leakage
50
correction is used, which is similar to the one performed in the deterministic lattice physics codes
[50]. Development for a Monte Carlo leakage correction is investigated for SERPENT.[51]
3.7 Other supplementing theory
This section handles important theory that though not key points, adds to the nature of
this study.
3.7.1 Design of the core loading
The power density (kW/l), which is defined as the power produced per unit volume of the
reactor core, determines the core size. The average power density is given as
Ave power density =
,
with as the average linear heat generation rate ( power per unit length of
fuel), , number of fuel rods, the fuel assembly pitch, Q the reactor thermal power [32]
The moderator to fuel ratio (
) relates to the size and shape of the fuel rods to the water
surrounding them in the core volume. H/U refers to the amount of hydrogen atoms to in the
moderator the amount of Uranium atoms in the fuel (235
U and 238
U). Both of these two effects can
have an influence on the design of the reactor core loading. Currently the TRIGSIMS code has a
formulation when implementing the core loading, it calculates and adds the moderator domain
around the reactor core. This effect influences the keff of the system. Hence, it is of interest to
investigate and assess how it is done for various core loadings.
51
3.7.2 B4C in Control rods
The isotopic composition of natural boron is 18.8% B10, and 81.2% B11. The possible
reaction of neutron absorption is given as:
+ n
; σ = 4010 b
+ n
; σ = 0.2 b
+ n
; σ = 0.005 b
Boron-10 has a high neutron capture cross section, hence a high probability that a 10
B
atom will pick up a neutron as it collides with the nucleus, in a (n, α) reaction. This probability
changes with energy levels. B-10 has the highest chance of picking up thermal neutrons (slow). It
has a high thermal conductivity and hence we can expect a relatively even temperature
distribution over the control rod. From post irradiation examination, the B4C had a burnup of
3.4% for 3000hours burned. The physical properties of Boron carbide (B4C) are reference [37],
[43], which gives a theoretical density of 2.51g/cm3.
3.7.3 Thermal hydraulic feedback
The variation in reactivity due to change in reactor power is called the power coefficient.
. This value must usually be small but negative for the stability of the reactor. If the
power coefficient is positive, the reactor power will infinitely increase. If the power coefficient is
negative, and large (taking the absolute value), the reactor power will not be able to be elevated,
which make the reactor hard to operate.
Expressing the power coefficient in terms of temperature coefficient,
is given
by
52
3.14
Where
is the variation of temperature of the i-th core component due to
temperature change.
In reality, these are dependent variables but numerically, the physics of the relationship
between power-increase, control-rod-position and the temperature of the core elements needs to
be determined. An effort to quantify this relation can be done with measured data. This is also
different for each core loading. Ideally, an equation, or a method that would be applicable for all
core loadings is what is needed for this multi-tool. Another method would be to use perturbation
theory, a variation of equation 4.1 . This method relies on a previous run core and depends on the
size of reactivity inserted.
53
Chapter 4
Methodological and modeling developments
The theoretical models, numerical methodologies, and computational codes used in the
TRIGSIMS-TH are described in this chapter. TRIGSIMS-TH consists of the Monte Carlo code,
MCNP5, nodal diffusion code ADMARC-H, neutronics burnup code ORIGEN-S (SCALE) and
newly added thermal hydraulics code CTF.
4.1 TRIGSIMS-TH control system
Figure 4-1 shows the basic control flow for TRIGSIMS-TH. TRIGSIMS-TH code system
is an automated software management tool that couples various neutronics codes with burnup and
thermal hydraulic codes. It carries information transfer between codes, prepares the inputs, and
controls codes’ execution. Thereafter, it post-processes the results and extracts the outputs of
reactor parameters that are obtained from a core design calculation. The code system is controlled
by a single user input file, which outlines the core configuration and a specific application. This
input consists of the description of the core design, control rods and other geometrical structures.
The position of each entry of the core-loading map is mapped according to MCNP5 input lattice
indexing. The fuel element types are specified as well as the isotopic inventory of every axial
section of the fuel. The user specifies the calculation option in the input. There is an option to run
this code system with or without the ADMARC-H as an acceleration tool. The user can do any
number of control rod insertions from ARI (all rods in) to ARO (all rods out). The code is also
equipped with a thermal hydraulic module. This code is able to model any core loading (CL)
configuration.
54
Input document
1. Run criticality calc
2. Run control rod position
3. Run CTF standalone
ADMARC-H
Yes No
Read
ADMARC-H
Cross
sections
Write Input
ADMARC-H
Read MCNP
Cross
sections
Write MNCP
Input
Run MCNP
Write CTF
Input
Run CTF
Write
ORIGEN-S
Input
Run SCALE/
ORIGEN-S
Run ADMARC-H/
CTF
Figure 4-1 Diagram of TRIGSIMS-TH code platform
TRIGSIMS-TH.exe
SCALE.exe MCNP5.exe admarch/ctf.exe
CTF.exe
55
The TRIGSIMS-TH platform is equipped with the following applications:
a) A fast running traditional multi-physics code ADMARC-H/CTF with its associated
cross-section data files admr.dat;
b) The neutron transport code, MCNP5 with its associated continuous energy temperature
dependent cross-section MCNP5_DATA file;
c) The depletion code ORIGEN-S (SCALE-6 module);
d) The thermal-hydraulics sub-channel analysis code CTF.
These are all different codes that are coupled through TRIGSIMS-TH, where
TRIGSIMS-TH control the data exchange between these programs. There are three run modes for
this application.
Run-mode1: The first is an input request for a core loading (CL) criticality calculation.
That is to calculate the criticality at any power level. This is an integrative process.
Run-mode2: This is a control rod position (CRpos) calculation.
This calculation allows the user to do any number of CRpos calculations.
The CTF is coupled with MCNP for any CRpos. However, CTF requires an input
power level (AFLUX).
For this application, the measured data was used to create a CRpos vs. Power
curve.
Run-mode3: This mode request is for a CTF standalone calculation. This mode will run
the MCNP initial calculation for a requested power or position step, followed by the CTF
execution.
56
4.2 Temperature feedback methods
In particular, to TRIGA reactors, the steady state calculation depends on each fuel rod,
their positions in the core and their characteristics. The fuels generally have a long life, and with
each core loading or core shuffle, the burnt elements are moved around and if needed new fuel
elements are added in the central part of the core.
4.2.1 Illustration of the thermal hydraulic feedback effects
The new TRIGSIMS-TH applies a fuel axial temperature profile to each individual fuel
element as well as a water axial profile for the moderator surrounding each fuel node. The MCNP
input is written with five axial fuel nodes each with a material composition and burnup estimate.
The temperature of the moderator surrounding the fuel elements is used to determine the density
in the MCNP input for each of these nodes. With this application, a heterogeneous application of
cross section is given for a single fuel element. These features are new and the development
introduced by this PhD work makes the TRIGSIMS-TH code a simulation code for realistic
physical applications. Figure 4-2 illustrates the difference of utilized/predicted temperature
distributions between the two codes TRIGSIMS and TRIGSIMS -TH.
57
Figure 4-2 Illustration of homogeneous and heterogeneous temperature distributions
The TRIGSIMS code reads the temperature for each segment of the element and sorts
through the MCNP XS-DIR file in the following way. The code reads the data from the bottom of
the file to the top. The generated PSBR cross section data are arranged on a grid with 50 K
temperature intervals. Figure 4-3 depicts the core radial pin wise heterogeneous temperature
distribution. The PSBR core does not burn with a flat radial core power distribution neither is the
core radial flux distribution flat. The temperature peaks around the center of the core are due to
the higher power density fuels inserted in those positions. This result stresses the importance of
the application of the heterogeneous temperature distribution in the core.
Homogenous temperature
Heterogeneous temperature
resulting from feedback
58
Figure 4-3 Typical radial temperature distribution at 1MW power [K]
Figure 4-4 shows the temperature distribution inside the core at 1MW power along the
axial length of the fuel rods.
A
59
Figure 4-4 1MW axial temperature distribution [K]
This is a typical 1MW axial temperature distribution of the core elements across the
centerline of the core. This centerline is indicated in Figure 4-3 as line A. This result shows the
thimble in the center of the core. The hottest element is in the C ring while the cooler control
elements are in the D ring. The E-ring has slightly warmer elements and the F-ring has slightly
colder elements. The result indicates also that the bottom of the rods is hotter than the top due to
the partially withdrawn control rods. This is a typical result, which TRIGSIMS-TH is able to
calculate for each fuel element in the core at nominal power conditions. This result illustrates the
capability of capturing the feedback mechanism.
60
4.2.2 The thermal hydraulic feedback implementation
In a previous study of CTF assessment for PSBR thermal hydraulic modeling [3] it was
found that the code adequately predicts the natural convective flow of the PSBR. For this work, a
full core CTF model of the PSBR core was developed. For the feedback mechanism modeling,
we have accelerated the CTF full core model calculation by using fewer nodes between the two
grid plates. This model was constructed in such a way, that the passing of information between
neutronic codes and CTF would be done with minimal averaging in the nodes. TRIGSIMS-TH
automatically generates an input deck for the CTF calculation based on the core loading input
(CL.inp). Figure 4-5 illustrates a single sub-channel used in the CTF.
Figure 4-5 A typical sub-channel for CTF
Figure 4-5 shows three rods that form a flow (sub-channel) region and up to six sub-
channels border a fuel rod. The number of axial nodes was kept to nine. Five, active fuel region
nodes plus four top and bottom graphite-region nodes. The letters A, B and C on the Figure,
indicate flow region changes because of channel geometry changes. A boundary condition is set
between the grid regions to ensure an enthalpy change is produced and a small flow is applied
across the axial length of the channel.
A
B
C
B
C
61
The results produced by CTF are written to an external file. The coupling of MCNP and
CTF is as follows: MCNP calculations output axial and radial power profiles, which are then read
by TRIGSIMS-TH. TRIGSIMS-TH creates an input for CTF together with the required power
level (AFLUX). This updated CTF input, executes and produces a temperature output file. This in
turn is read by TRIGSIMS-TH, which updates the cross sections for the next MCNP iteration.
The reason for this external coupling scheme is that these two codes are written in different
programming languages. The ADMARC-H and CTF however are coupled internally, meaning,
TRIGSIMS-TH handles the temperatures from CTF to ADMARC-H and the power profiles from
ADMARC-H to CTF with no need of reading external files. The two codes are written as one
application. The TRIGSIMS-TH code is able to apply variations in the core design. It is not fixed
to the number of fuel elements and neither is it fixed to the type of element in a position.
For the standalone model, we have lengthened the sub-channel to include regions above
and below the grid plates indicated in Figure 4-5. The feedback mechanism between CTF and
both MCNP and ADMARC-H is implemented in the same way. The neutronic codes pass
normalized radial and axial power for each fuel element to CTF and CTF supplies the
temperature of the core elements as illustrated in Figure 4-6. TRIGSIMS-TH writes a CTF input
only once per each iteration. If ADMARC-H is requested in the input, the ADMARC-H/CTF
coupling uses the written CTF/MCNP input and updates the power profiles only.
62
Figure 4-6 Illustration of the coupling methodology
The multi-physics coupling methodologies developed in this PhD thesis for MCNP/CTF
and ADMARC-H/CTF are described next.
4.2.3 MCNP/CTF coupling
As shown in Figure 4-1, there are three types of calculations that can be requested from
the TRIGSIMS-TH code. Generally, the code is used for criticality calculation with burnup. For
this application, the MCNP/CTF coupling method is outlined in the Figure 4-7.
63
Read Temperature file
Read MCNP_DATA
Prepare MCNP input with CRpos
Run MCNP5
Extract data
Axial pin power
and nominal
power/pin
Prepare CTF
input
Run CTF
Temperature
Of fuel and
moderator
Convergence
check
Yes
No
Output
MCNP
ORIGENS
Burn fuel
Prepare for
corrector step
Predictor step
End calc
and store
output data
Yes
No
Figure 4-7 Flow diagram of MCNP/CTF coupling
64
This diagram contains the following key information:
1. MCNP
This starts with a request written in the input. Run-mode 1 is an iterative criticality
calculation. This calculation starts with ARI and a temperature of 300K for fuel and moderator is
advisable. Run-mode 2 is a control rod position calculation. This calculation is not iterative and
the user can request any control rod position. An appropriate temperature distribution for the
control rod position will be calculated. Run-mode 3 is a request for standalone CTF calculation.
This comes as a flag in the input. It utilizes MCNP results from run-mode 1 or run-mode 2. Thus,
the standalone CTF calculation uses power profiles produced previously by MCNP.
2. CTF
The CTF calculation comes after the MCNP calculation. TRIGSIMS-TH extracts the
axial power data per node per fuel element from the MCNP output (F7 tallies data). The data are
normalized per node per average fuel power. If the request was for run-mode one, the power for
CTF (AFLUX) would be the linear power representing the power in the input file. If the run-
mode is two, the input linear power (AFLUX) will come from a calculated value based on the
data from measurements of control rod position vs. power. After the CTF execution, TRIGSIMS-
TH will extract the temperature profiles and write it to an external output file. This will be read
for the next iteration or power increase if requested. If this is a standalone request, the CTF would
terminate its execution after this step. If this is run-mode 2, the CRpos (control rod position) of
next input request will be used. TRIGSIMS-TH will read the CTF temperature file, update MCNP
cross sections, apply CRpos, and the calculation would continue. If the request is run-mode 1, a
convergence check will be done. Reactivity ρ(x) <0.001, and the temperature is checked for
elements in the center of the core.
65
3. ORIGEN-S
This application is coupled with the predictor-corrector application and remains
unchanged with the TRIGSIMS-TH.
4.2.4 ADMARC-H/CTF coupling
The ADMARC-H/CTF coupling runs as one internally coupled application. Thereby
there is no need to write and read information. The methodology of passing information is similar
to that of MCNP/CTF coupling. Since the ADMARC-H calculation takes few seconds to
complete, this addition to this platform is an acceleration of the main solver – MCNP/CTF.
ADMARC-H code calculates axial power profile in seven nodes. This had to be averaged
to fit the five axial fuel nodes for the CTF input.
This application always precedes the MCNP/CTF calculation if it is called upon. The CTF input is
not written for this coupling. The power profiles are applied after the input is read. This coupling
passes to MCNP/CTF coupling updated fission source, power and temperature distributions for
the core. The chapters that follow will outline the effectiveness of this methodology.
The developed coupling mechanisms is shown in Figure 4-8
66
Input shows
ADMARC-H
Read
Temperature
file
Write
ADAMRC-H
input
Run
ADMARC-H
RUN ctf
Pass
Axial pin powers
and
Nominal powers
Write Temperature
of fuel and
moderator
file
Convergence
check
No
Yes
Prepare
ADMARC-H
(New cross section
adjust CRpos
Output Crpos
and updated
temperature file
MCNP follows
Figure 4-8 Flow diagram of ADMARC-H/CTF couple
ADMARC-H.EXE
67
This application can accompany any run-mode as described in the previous section. The
control rod methodology for run-mode 1 is based on the same calculations. In the coupled
methodology, ADMARCH and CTF are written in one application. Hence, the data is transferred
directly and updates are done directly to the codes. Since ADMARC-H runs after MCNP/CTF
coupling, the CTF input is not rewritten, but rather just updated. Figure 4-8 shows the coupling
method between CTF and ADMARC-H. This is very similar to that of MCNP, except that
ADMARC-H is preceded by MCNP, the control rod position is passed to the MCNP next
iteration, and a CTF temperature output file is written for the follow up calculation by MCNP.
4.2.5 Pseudo material approach
Grid with interval of 50K for the continuous cross sections, generated by NJOY and
further interpolated for exact temperature of interest, is utilized for MCNP calculations [2]. The
interpolation methodology is called pseudo material approach and uses an upper and lower bound
averaging scheme. TRIGSIMS-TH is able to write an MCNP input file with atom fraction
densities for each fuel node, for each fuel element, and for each uranium isotope. For the atom
fraction of the material obeying lower temperature, we have:
4.1
for the higher temperature material in the mixture we have:
4.2
68
By using the pseudo material mixing approach[19], we obtain the following cross section
mixture:
4.3
At the end of the calculation, the code reformulates and combines the atom fraction for
each uranium isotope. This is needed for the burnup step.
4.3 Partially inserted control rods
The PSBR TRIGA reactor is operated with partially inserted control rods. Normal
operation with critical full power of 1MW is not the same for each core loading. They can vary
between 7.5 inches to 13 inches withdrawn above the bottom of the core; depending on how
much fuel, (uranium) is loaded in the core. The lack of a control rod search methodology for a
critical reactor condition was one of the shortcomings of the previous code system TRIGSIMS.
TRIGSIMS applied an ARO assumption for the 1MW critical rod position.
In this work, the use of perturbation theory was found to be applicable for an iterative,
automated control rod search. The methodology that was developed in this work is described in
this section.
4.3.1 Application of perturbation theory
Usually any small change in the geometry of the core or composition creates relatively
small changes in the core multiplication factor, which in turn requires changes in the control rod
position. With small changes, the application of perturbation theory can be used for determining
the relative reactivity worth of partially inserted control rods for TRIGA reactors. Generally,
perturbation theory is not recommended for tight fuel lattices [32], with large number of elements
69
to achieve a uniform power distribution. Neither can it be used to give meaningful estimates of
absolute control rod worth.
The equation derived from the one-group first order perturbation theory [32][35] is out-
lined as follows:
4.4
which is the worth of a partially inserted control rod bank as a function of the distance
inserted. This equation is normally represented by an S-curve as shown in Figure 4-9:
Figure 4-9 S-curve for control rods
The maximum change in reactivity occurs when the end of the control rod is in the center
of the reactor. Towards the ends, the change in reactivity is smaller. It is this smaller region that is
of interest for our calculations. The PSBR TRIGA reactor is normally operated around 1MW, the
calculated ρ (H) (which represent the results of a critical rod position), is used in a search
(tolerance iteration) to calculate the control rod position using the equation 4.4. The search
involves both the x (CR position) value as well as the ρ(x) (the change in reactivity) value.
In order for this application to work effectively, the heterogeneous temperature
distribution has to be applied to the reactivity calculation of the core.
0 0.5 110
0.5
1
x/H
p(x
)/p
(H)
Fully inserted
Fully Withdrawn
70
This application is part of the CTF/ADMARC-H coupling and MCNP/CTF coupling.
4.3.2 Control rod position method using a quasi-fixed point iteration scheme
This method runs on the premise that the core remains subcritical below the x/H=0.5 of
the S curve in Figure 4-9. The criticality calculation starts after the core has reached the halfway
mark. Generally, the reactor becomes source critical around the 7.5" (19.05cm) position, which
changes for different cores and could be less if the core has many fresh fuel elements.
The method utilizes the previous keff result of a MCNP calculation. Converts this keff
values to the associated reactivity, updates and repeats the calculation. It is essentially a nested
loop iteration. It starts with an initial guess of control rod position of 1cm and a reactivity at x
position, ρ(x), value of 0.001. The iteration process is time consuming and depending on how far
the control rod is moved from the initial critical rod position to the full power critical position. It
can be anywhere between 8 iterations to about 25 iterations. In these cases the ADMARC-H code
can be used for more efficient iteration process with MCNP just used for final fine-tuning. Figure
4-10 shows the flow of this method.
71
Input 1
Criticality calc
ARI CALC
At core tempearture =300K
Initial guess
CRpos=1
rowX=0.001
Tol=0.0011
ARI Keff
rowH
No
Yes
Calc A,
B, xx
TOL=
rowY-xx
Tol Check
Increase CRpos
Or
Decrease Crpos
By 0.1
Update input
with new CRpos
Run MCNP
Get keff
Set
rowX=rowX+rowkeff*0
.1
Tollkeff
<0.002
Yes
Crpos found
No
A=2*pi, rowY=A*(rowx/rowH)
B=2*pi*x/H - sin(2*pi*x/H)
xx=B-sin(B)
TOL>0.001
Figure 4-10 Flow diagram of the control rod method
72
The mathematical formulation in Figure 4-10 could be described as a quasi-fixed-point
(semi-fixed-point or non-linear fixed-point) iteration scheme. Fixed-point iteration is of the
following form:
This method starts with an initial guess x0, convert F(x)=0 into x=g(x) , then iterate, xi+1
= g(xi) , i = 0,1,2,3..., where the iteration will continue if convergence (|xi+1 -g(x0)|< tol) is not
met.
The quasi fixed-point iteration is illustrated by the Figure 4-11. This is the mathematical
formulation of the iteration scheme used in Figure 4-10 for the control rod positioning
methodology.
Figure 4-11 illustration of the quasi fixed point iteration
x1 x2 x3........ x
y(p(2))
y(p(x1))
g(x0)
g(x2)
g(x1)
g(xi)
x11 x12 x13 x2
x1 x2 x3 x
p(x0)
p(x1)
g(x10
)
g(x12)
g(x11
)
73
This iteration starts with an initial guess for x0, and one for p(x0), and then it uses a fixed-
point iteration between x0 and x1, to get a value for x1 corresponding to g(x0), such that |x1-
g(x0)|<tol1. If tolerance is reached, then for that x1 value there is p(x1), such that y(p(x2)) is
calculated and results in a tolerance check between |g(x1)-p(x1)|<tol2.~0.001. If the tolerance is
not reached then F(g(x0)) is updated and a next search between x1 and x2 using fixed point
iteration is started to obtain x2=g(x1) and F(xi)=f(xi, y(p(xi)).
4.4 Thermal hydraulics methodology
CTF forms part of the coupling methodology and is used for thermal hydraulic feedback.
As a request from the user, the code can also write out a standalone input deck. Though we say
standalone thermal-hydraulic, this code will still require the neutronics to set the axial and radial
power distribution for a particular requested power level. The MCNP calculation will be executed
and then the expanded CTF input deck will be written. A standalone calculation is useful to
analyze specific thermal hydraulic details. CTF calculates many different thermal hydraulic
parameters and with this standalone option of the full core, we can refine the output for
information needed for the PSBR safety analysis. Details such as, axial temperature distribution
for the fuel, clad and coolant regions, mass flows and velocities can be analyzed. We can test
design limits of the core by increase in power beyond the normal, and estimate quantities such as
the Critical Heat Flux (CHF), and the Departure from Nucleate Boiling (DNB).
74
Figure 4-12 Developing of a full core CTF model
Figure 4-12 is a CTF input layout for a PSBR full core calculation. It indicates a typical
manner of dividing the reactor core in triangular sub-channels, gaps and rods. Channels, gaps and
rods have to be input sequentially, which requires a fixed layout of the core. What this means is
that spaces and dry tubes are treated as non-fueled rods in this structure. Hence, no power will
apply to these regions. Thus, the input structure for a regular 110-place holder is as indicated.
The pink shows non-fueled rods and the yellow indicates potential open spaces. However, this is
not fixed, as the user can load fuel elements in these positions as well.
If a core loading input adds more elements to the core layout, as indicated in the figure,
the TRIGSIMS-TH code will place those elements into the side channels as additional channels.
The code will assign a power profile to the fueled elements and the non-fuel elements will have
zero power.
As indicated in the Figure 4-12, a D2O tank can be added to the neutronics calculation.
This usually comes as input request (D2O-flag), whereby TRIGSIMS-TH will add the geometry
of the D2O tank to the geometry of the current core layout. This tank is added as an unheated
75
conductor data. Which means TRIGSIMS-TH will have to make changes to the input deck for
these additional cards. The addition of the D2O tank adds another channel to the core layout and
another eight more gaps to the current design.
The value of this addition to the CTF application of the core loading with the D2O tank is
that TRIGSIMS-TH can now be used to do analysis on changes of the D2O tank design as shown
in Ücar's [5] thesis. His proposal for an enclosure that covers half the core can be analyzed with
regard to safety and optimal design of the reactor core.
4.5 TRIGSIMS-TH Core Modeling parameters
There are a few parameters in the core model, which determine the outcome of a
calculation. Some of them are discussed next.
The geometry of the core includes the fuel and control rod elements, each with their own
isotopic content. They are placed on a grid in a hexagonal layout with a fixed inter-element
spacing (pitch). Each element or structure is surrounded with light water and the system has no
forced cooling. The code accounts for the isotopic content of the fuel. Since this is hydride fuel,
part of moderation of the fast neutrons is done in the fuel. The core design has to account for this
as well as for the fact that the absorber material, B4C, has a big influence on the results. The
assumptions that are made to ensure efficient calculations are not generic.
4.5.1 Moderator surrounding the core
The moderator to fuel ratio in the core relates to the size and shape of the fuel rods and
the water surrounding the fuel.
76
The application of the TRIGSIMS-TH geometry input is fixed. The water surrounding
the core is added in a fixed methodology with the assumption that the core geometry is always
fixed. i.e., the top half of the core is the same as the bottom half and all the cells are filled as
shown in the CTF model Figure 4-12. However, the core loading design is variable. More or less
fuel elements are used in the core layout depending on the needs of a particular core loading.
CL54 has 100 fuel elements, whereas CL56 has a 108 fuel elements. Yet we find that the water
surrounding the CL54 is more than that of CL56 (see Figures 4-13 and 4-14).
Figure 4-13 CL56 diagram
Figure 4-14 CL54 diagram
Maximum radius
Maximum radius
77
Figure 4-13 and Figure 4-14 show the MCNP models for calculation of criticality for
CL56 and CL54. The maximum radius plus 4 times the pitch size determines the outside radius of
the calculation domain. The code runs a loop to determine the maximum radius using the MCNP
cell entries as within the x and y domain, with an adjustment on the x. This method of
determining the core maximum radius resulted in some cores being over moderated. In the
current TRIGSIMS-TH code, this model is adjusted by applying a ratio of the fuel used in the
core model to the fuel used in a full core model as shown in Figure 4-1.
The neutron absorbing material, B4C, in the control elements was analyzed using various
core loadings. Previous combinations of the density and composition were compared to
theoretical compositions and densities. The best possible fit analyzed was used in the TRIGSIMS-
TH code.
4.6 Conclusion on the methods and models
Changes to a code system require good insight to the working of each of the codes. There
are five codes with five applications that are housed within the TRIGSIMS-TH. Each one has a
function to fulfill. These codes are written in different languages. Changes were induced in the
TRIGSIMS, MCNP, ADMARC-H and CTF codes. The depletion code, though it was not
changed, was affected due to the upgrades in the other codes. Each change has a function either to
enhance the codes capability or to make the code more applicable for the current core loading and
future core loadings. The methods applied have been analyzed and the results obtained are
presented in the following chapter.
78
Chapter 5
Results and Findings
This chapter presents the results and findings of the work accomplished in this thesis in
the following order.
1. Validation of the implementation of the feedback-mechanism for the high-
fidelity multi-physics coupling within the TRIGSIMS-TH code system, which
involves the neutronics code MCNP, and the thermal hydraulics code CTF.
These two codes are the main solving codes, and the focus of this task is to
ensure that the coupling was done correctly.
2. Validation of the control rod position search method. This was a needed
development for the TRIGSIMS-TH code system, as there is a need for a method
to relate the control rod position to the power level.
3. A summary of the thermal hydraulics analyses and results of the PSBR core
using the TRIGSIMS-TH code is presented.
4. Application of power increase (with control rod withdrawal) using TRIGSIMS-
TH to access reactivity loss was shown and compared with measured results.
5. The results of TRIGSIMS-TH for analysis of additions to the core layout, such as
graphite rods, are presented.
6. Quantification findings of improvements introduced on the predictions of core
design parameters are given. These improvements include a best estimate of B4C
in the control elements, new SERPENT-based homogenized cross sections for
the ADMARC-H code, pseudo material application for MCNP-based multi-
physics calculations, and core moderation changes are given.
79
7. The results of the modeling of D2O tank with the CTF code and the coupled
mechanism are presented.
8. The findings of using the CTF as a standalone code are discussed.
9. Conclusions of the applications of various developments and improvements are
summarized.
The validation was performed with measured data obtained from the PSBR operation for
core loadings, CL 53H and G (with core map given in Figure A- 2), CL54 (with core map Figure
A- 1) and CL 56 (with core map given in Figure 3-2). The core maps show where each fuel
element, control element and dry irradiation tube are placed in the core layout.
Figure 5-1 Reference core diagram
C 36 37 38 39 A 41 42
B
44 45 46 47
112 116 120 122 124 128 131
1 2 3 4 5 6 7 8
13
80
Figure 5-1 gives the basic core map of a PSBR core loading. The indicated numbers and
letters in the figure are used as references for latter discussions. The term "ring" refers to the
following. The ring B elements surrounds the central water thimble, and then follow C, D, E,F
and G rings, radially outward, for the fuel elements.
In the Figure 5-1, the letters A, B and C shows the placement of instrumental rods used in
calculation and the numbered items are the fuel elements used in the various core loadings. The
triangle shapes numbered positions refer to the thermal hydraulic channels used in the CTF
results. The elements (fuel and non-fuel) are numbered sequentially from the top to the bottom
and from left to right. For this layout, 110 is the last element in the right hand corner. This
diagram represents the basic layout used for referencing of different core loadings in this results’
section.
5.1 MCNP/CTF coupling
To show the effective functioning of the coupling methodology with feedback
application, the following are the result of full core calculations for CL56, Cl54 and CL53, using
TRIGSIMS-TH code. The results were obtained from coupled neutronics/thermal hydraulic
(multi-physics) calculations for 1MW power level after iterations to obtain a critical state at a
certain control rod position. For these calculations, the control rod position methodology was
applied. The results shown in Figures 5-2 through 5-4 are the CTF-predicted full core temperature
distributions.
81
Figure 5-2 Temperature distribution for CL56
The results in Figure 5-2 show that the new instrumetal I-17 rod in position C (as
indicated on Figure 5-1) has the highest temperature (539°C). This rod is a new 12 wt% fuel,
instrumental rod, and it is expected that it would have a higher power density compared with the
other rods in the core. The ring B elements, around the center of the core are 8.5 wt% fuel
elements, and the fuel elements with calculated temperatures between 450°C and 500 °C (in the C
and D ring) are 12 wt% fuel elements.
0
5
10
15
20
25
30
1234567891011
0
500
CL56 at 1MW power , Temperature distribution
y x
Tem
pera
ture
[oC
]
50
100
150
200
250
300
350
400
450
500
82
Figure 5-3 Temperature distribution for CL54
The results in the Figure 5-3 show that the temperature of the fuel elements around the
center is hotter as compared with CL56. This is because 6 fresh 8.5 wt% fuel elements were
placed in these positions. The C-ring elements however still present the hottest core elements,
which are 12 wt% elements. The rod I-16, an older instrumental rod, is in position C (as indicated
in the reference diagram, Figure 5-1). Maximum temperature of 515°C is calculated at this
position.
0
5
10
15
20
25
30
1234567891011
0
500
CL54 at 1MW power , Temperature distribution
yx
Tem
pera
ture
[oC
]
0
50
100
150
200
250
300
350
400
450
500
83
Figure 5-4 Temperature distribution for CL53H
The CL53H results show that the higher temperature elements are around the C ring. Two
rods A(227) and B (I-16) (as indicated in Figure 5-1) are calculated to have approximately the
same max average temperature of 519°C. B is the instrumental element I-16 used for
measurement.
All three figures present a similar pattern for the temperature distribution at a 1MW core
power. Higher temperatures occur around the C and D ring elements. This is the position where
the fuel with highest uranium content is loaded. The predictions of the developed multi-physics
0
5
10
15
20
25
30
1234567891011
0
500
CL53 at 1MW power , Temperature distribution
y x
Tem
pera
ture
[oC
]
0
50
100
150
200
250
300
350
400
450
500
84
methodology with feedback mechanisms are compared with measured results. This comparison is
presented in Table 5-1.
Table 5-1 Measured results compared with calculated TRIGSIMS-TH results
Core CL56 CL54 CL53H
Keff 1.00003±0.00057 0.99938±0.00055 1.00049±0.00049
CR position calculated 27.50 cm 27.25 cm 32.56 cm
CR position measured 27.66 cm 27.23 cm 32.56 cm
Calculated ave temp 539.3°C 515.5°C 519.7°C
Measured ave temp 518.1°C 507.2°C 520.4°C
The results using the coupling methodology are comparable to the measured results. As it
can be seen from Table 5-1 the TRIGSIMS-TH with temperature feedback modeling is capable of
predicting realistic critical states. The control rod position compares well with measured data as
well as the average temperature is comparable to that of the measured data. The largest deviation
of 20°C is shown for CL56, and this deviation is about 3% of the temperature value.
It is not possible to compare results of the TRIGSIMS system to the TRIGSIMS-TH
system. The addition of the temperature feedback allows the TRIGSIMS-TH system to calculate a
critical state for given core power, which was not previously possible. The results presented in the
Table 5-1 verify the coupling methodology for the new temperature feedback mechanism using
MCNP/CTF calculations. Measurements are done at the instrumental elements positions only.
The results in Table 5-1 can be achieved either by an iterative control rod search method or by
power increase method. Ultimately, the code requires a heterogeneous temperature distribution at
a certain control rod level. The results display the expected temperature distribution for each core
loading. This confirms that the implementation and the execution of the coupling method of CTF
to MCNP are correct.
85
5.2 Critical control rod search
The PSBR operates with partially inserted control rods, i.e., 1MW power has the control
rods withdrawn from the core between 20 cm and 33 cm where 38.1 cm is the full length of the
absorbing material. The reactor increases power with the control rod withdrawal. By procedure,
the operators balance the control rods at the same axial position when the reactor is at full power.
The critical control rod search is an algorithm that has been developed in this work. It uses an
iterative scheme to find the position where the control rods would be positioned for a critical state
at a given power level. The validation of this algorithm is now presented.
5.2.1 Validation of critical rod search method
The calculation starts with an input that contains the desired power level. The iterative
scheme will always start at the all rods in position. This is the first calculation that is used to
determine placement of the control rods for the next iteration. Each iteration step is followed by a
CTF calculation for the desired power level with updated axial and radial power distributions. If
the power level is less than 1MW, the Xe number density fraction, currently assumed to be 20%
of the equilibrium xenon concentration for all power operations [2], is scaled according to the
corresponding power fraction. This application using the TRIGSIMS-TH tool is intended to
analyze a full power critical core loading, usually at around 1MW, but it could also be used for
analyzing lower and intermediate power levels as well. The validation results are compared with
measurements for CL56 at 1MW and 700KW and for CL54 at 1MW and at 800 kW power levels
respectively. The aim is to calculate full power at 1MW successfully, but to show the diversity of
the tool. For this reason, the results for lower power levels are presented as well.
86
Figure 5-5 Iterative control rod position search of CL561
1 MCNP calculated keff with standard deviation approximately 50pcm (1σ)
0 2 4 6 8 10 12
0.96
0.98
1
1.021MW core power with feedback
Kef
f
# iterations
0 2 4 6 8 10 120
10
20
30
Co
ntr
ol
rod
po
siti
on
[cm
]
# iterations
0 2 4 6 8 10 120
200
400
600
Av
era
ge f
uel
Tem
pera
ture
[
oC
]
# iterations
measured
calculated
calculated
measured
measured
keff
=1
87
Figure 5-6 Iterative control rod position search for CL542
2 MCNP calculated keff with standard deviation approximately 50pcm (1σ)
0 1 2 3 4 5 6 7 8 9 10 110.94
0.96
0.98
1
1.021MW core power with feedback
Kef
f
# iterations
0 1 2 3 4 5 6 7 8 9 10 110
10
20
30
Co
ntr
ol
rod
po
siti
on
[cm
]
# iterations
0 1 2 3 4 5 6 7 8 9 10 110
100
200
300
400
500
600
Av
erag
e fu
el T
emp
erat
ure
[ o C
]
# iterations
calculated
measured
measured
calculated
calculated
keff
=1
88
Iterative control rod position searches for CL56 and CL54 are shown in Figures 5-5 and
5-6 respectively. The average fuel temperature is taken at the instrumental rod position, the older
I-16 for CL54 and new I-17 for CL56.With every iteration, the control rod is either withdrawn or
inserted depending on the results from the previous iteration. Each iteration has a neutronics
calculation followed by its corresponding thermal hydraulic calculation. The control-rod
withdrawal movements are small resulting in more accurate prediction of the position. The
critical control rod position for 1 MW power for CL56 was measured at 27.66 cm (height 1089
units). The average fuel temperature measured at position B was approximately 518°C (~791°F).
For CL54, the critical control rod position is measured at 27.23cm (height 1072 units), with the
average fuel temperature of 503°C (~776°F). The results indicate that the control rod position has
converged as well as the keff. The temperature difference between the calculation and
measurement resulted in a 3°C variation. The temperature for reactivity change at 1MW for CL56
is measured at approximately 0.22¢/°C for 1 MW power. Thus a 3°C difference constitute to less
than 0.01$ reactivity change. This difference is very small to make a notable difference in reactor
design.
The following result shows the TRIGSIMS-TH capability to use the control rod search
method to find a control rod position for CL56 at 700kW and CL54 at 800kW. This calculation
shows that not only the code can predict a critical state for full power of 1MW but can also
predict a critical core at any other power level. For the 1MW MCNP calculation, the Xe isotopic
fraction is adjusted to 20% of the amount indicated in the fuel inventory [2]. However, since
these calculations are not full power, this Xenon fraction is scaled by the power fraction, since the
Xenon fraction is flux dependent, and hence power dependent, to account for fewer poisons in the
fuel during operation. Figure 5-7 shows the results from the control rod search in TRIGSIMS-TH
to find a critical core at 700 kW power. Two sets of data are given in this figure. The one is the
results from the adjusted Xe fraction (noted in the graph as CL56-Xe) due to lower power
89
compared with full amount of Xe (as applied to 1MW power).
Figure 5-7 CL56 AT 700kW power, with Xe adjusted
0 2 4 6 8 10 12 14 160.95
0.96
0.97
0.98
0.99
1
1.01
700kW core power with feedback
Kef
f
# iterations
0 2 4 6 8 10 12 14 160
5
10
15
20
25
30
35
Co
ntr
ol
rod
po
siti
on
[cm
]
# iterations
0 2 4 6 8 10 12 14 160
100
200
300
400
500
Av
erag
e fu
el T
emp
erat
ure
[ o C
]
# iterations
Cl56
measured
Cl56-Xe-Adj
measured
CL56
CL56-Xe-Adj
CL56
measured
Cl56-Xe-Adj
90
Figure 5-8 CL54 at 800kW power3
3 MCNP calculated keff value with standard deviation of approximately 50pcm (1σ)
0 1 2 3 4 5 6 7 8 9 100.94
0.96
0.98
1
1.02
800kW core power with feedbackK
eff
# iterations
0 1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
Co
ntr
ol
rod
po
siti
on
[cm
]
# iterations
0 1 2 3 4 5 6 7 8 9 10
100
200
300
400
500
Av
erag
e fu
el T
emp
erat
ure
[ o C
]
# iterations
calculated
measured
measured
calculated
calculated
keff
=1
91
The results for the Xe fractioned calculation show a slightly higher control rod position.
It is in the region of 0.4 cm, which is not noticeable in the control rod position graph. The
temperature graph however indicates a higher overall temperature. Both the Figure 5-7 and Figure
5-8 , indicates a convergence in control rod position, a keff convergence of approximately 1, and
temperature convergence.
Table 5-2 compares the results of these two calculations. The Xe adjustment is
implemented in the TRIGSIMS-TH calculation.
Table 5-2 Comparison of calculated to measured values for power levels less than 1MW
Parameter Calculated Measured Difference
CL56 AT 700kW
Control rod height 25.44cm 25.93cm 0.49 cm
Temperature I-17 439°C 442°C 3°C
CL54 AT 800kW
Control rod height 26.5cm 26.04cm 0.46 cm
Temperature I-16 466°C 460°C 6 °C
The results shown in the Table 5-2 indicate a difference in control rod position of
approximately 0.5 cm for both cases. This is a 1.8% variance, which resulted in a temperature
variance as well. In general, the result shows a good agreement, validating the code TRIGSIMS-
TH capability for use in critical core calculations.
5.2.2 Core reactivity estimation from calculations
With every startup of a new core loading, and every year therafter, the worth of the
control rods is measured. This is to ensure that there is enough reactivity worth in the control rods
92
to shut reactor down. Using the TRIGSIMS-TH tool, the user can calculate and approximate
expected core reactivity. The section 5.2.1 demonstrated the criticality calculation result of an
iterative scheme to obtain a full power critical rod position for each core loading. Using these
results one can calculate the difference in reactivity between all rods in and critical state, which
will constitute the reactivity change in the system. Figure 5-9 , shows the calculation for the
estimation of reactivity loss value given in the Table 5-3.
Figure 5-9 CL56 estimation of reactivity loss value
Table 5-3 summarizes the calculated data for the CL56 and CL54. The ARI is a taken at
a 300K temperature. The reactivity loss at 1MW power can be calculated from the keff data. The
excess reactivity is the reactivity change from critical rod position to ARO position. Table 5-4
and Table 5-5 shows the estimated results for control rod worth for CL56 and CL54 respectively.
-1
0
1
2
3
4
5
0.953
0.963
0.973
0.983
0.993
1.003
0 2 4 6 8 10 12 14 16
Rea
ctiv
ity l
oss
Kef
f
Iterations
Reactivity loss estimation for CL56
keff
93
Table 5-3 Data from calculations
CL56 CL54
ARI 0.95356 ±0.00062 0.94951 ±0.00047
Reactivity loss [$] 3.44 ± 0.08 3.8112 ± 0.07
ARO at 1MW 1.01563 ±0.00059 1.01731±0.00053
Table 5-4 Reactivity control comparisons for CL56
CL56 Calculated Measured
Reactivity [$] Reactivity [$]
Worth removed -6.63 ± 0.088 -6.77
Reactivity loss 3.44 ± 0.08 3.18
Core excess reactivity 5.64 ± 0.1659 5.85
TOTAL 12.27 ± 0.25 12.62
Table 5-5 Reactivity control comparisons for CL54
CL54 Calculated Measured
Reactivity [$] Reactivity [$]
Worth removed -7.21 ± 0.067 -7.18
Reactivity loss 3.81 ± 0.07 3.72
Worth remaining 6.24 ± 0.15 5.83
TOTAL 13.45 ± 0.217 13.01
The reactivity loss calculation for CL56 is performed with 15 iterations and that for CL54
is performed with 11 iterations.
94
5.2.3 ADMARC-H for acceleration of control rod search method
The ADMARC-H code can be used with the control rod search method to accelerate the
control rod search for control rod position of the critical core. This is an option of the calculation.
The ADMARC-H/CTF pre-run an iterative loop, to bring the rod and temperature up to a certain
level, the code passes the control rod position and temperature distribution over to the
MCNP/CTF coupled code. The findings of this addition to the control rod search method will
follow. This method will eliminate approximately five iterations of the MCNP calculations. The
accuracy of this method depends on the initial ARI value calculated.
Figure 5-10 CL56, with ADMARC-H to accelerate
0 5 10 150.95
0.96
0.97
0.98
0.99
1
1.011MW core power with feedback
Keff
# iterations
0 5 10 150
5
10
15
20
25
30
Co
ntr
ol
rod
po
siti
on
# iterations
calculated
measured
calculated
measured
ADMARC-H MCNP
95
Comparing to Figure 5-10 to Figure 5-5, the addition of ADMARC-H in the calculation
shows a big variation in result and this could be as a result of the heterogeneity of the partially
rodded nodes that are not properly incorporated into the nodal calculation involving large
homogenous nodes (control rod cusping). This will need to be further investigated. The
convergence, with the ADMARC-H addition, is reached faster.
5.3 Thermal hydraulic of the PSBR Core
Table 5-6 presents obtained results of the thermal hydraulics analysis of the core loadings
CL56, CL54, and CL53H calculated in the previous section. The layout of the core elements of
these core loadings are given in Figure 3-2, Figure A- 1 and Figure A- 2
Table 5-6 Thermal hydraulic results for core loadings at 1MW power
Results CL56 CL54 CL53H
Hottest fuel element I-17 I-16 i-I- I-161II16
Proposed hottest channel 125 129 145
Clad temperature of hottest
elements[°C]
133°C 132.7°C 131.6°C
Coolant maximum temperature in
hot channel [°C]
60°C 51°C 62°C
Ave fuel temperature in hot
channel[°C]
539°C 511.11°C 527.78°C
Ave heat flux in hot channel 1.52 x 105 b/h-ft
2 1.45 x 10
5 b/h-ft
2 1.34 x 10
5
b/h-ft2
Ave mass flow rate in hot channel 0.116 lb/s 0.195lb/s 0.112lb/s
Ave Coolant velocity in hot chan 0.115m/s 0.168m/s 0.0944m/s
96
The thermal hydraulic results are calculated with the coupled MCNP/CTF TRIGSIMS-
TH code. The hottest channel is the channel with the highest calculated surface heat flux and
highest enthalpy in the core. In the case of CL53H, the hot channel does not have the highest
temperature in the core. In fact, this particular core loading, present several possibilities for the
hottest channel.
5.4 Application of power rise with thermal hydraulic feedback
This is one of the modes in which the TRIGSIMS-TH can be used. With this method, the
user can request a control rod position, giving a specific temperature distribution; it will bypass
the power input and perform a criticality calculation for the requested control rod position. This
method will allow the user to input various control rod positions. The power (AFLUX) needed for
the CTF input will be calculated for each control rod position. This is not an iterative calculation,
as the functionality is not to attain a critical rod position.
As part of control and operation at the PSBR, reactivity measurements of each core are
performed. Control rod worth measurements are done to ensure the core excess reactivity is
within safety margin (≤$ 7.00), shutdown margin limits are met (≥$0.25) and the transient rod
reactivity is within limits (≤$3.50). One of the requirements to the control rod system at every
reactor facility is to be able to shut down the reactor safely [44]. For this reason, reactivity loss
data from measurements are recorded for each core loading. Using the TRIGSIMS-TH code
system with the thermal hydraulic feedback mechanism, one can simulate the reactivity loss
measurements.
97
Figure 5-11 Reactivity loss4 with power increase/control rod withdrawal for CL56
The result shown in Figure 5-11 is a comparison of reactivity loss with power increase
(control rod withdrawal). This is an automated calculation, whereby within each step both the
CTF and MCNP are updated. A new CTF and a new MCNP input are written at every step. The
results give a good indication of the capability of the code. To get a better fit to this measured
data, the calculation would have to have smaller intervals between reactivity steps or iteration at
each step will have to be performed. Iterating will require more calculations, more time, and more
memory. In general, the reactivity changes are higher at the end and the beginning of the control
4 MCNP calculations with variance of approximately 50pcm (1σ)
20 21 22 23 24 25 26 27 280
0.5
1
1.5
2
2.5
3
3.5CL56 Reactivity loss with control rod withdrawal
Rea
ctiv
ity
Lo
ss [
$]
Control rod withdrawal[cm]
calculated
measured
98
rod withdrawal. From the measured data, you can see that the reactivity differences are also not
the same for every core loading.
Figure 5-12 5Reactivity loss with power increase for CL54
Figure 5-12 shows reactivity loss with power increase for CL54. A positive increase
shows that at each step the temperature feedback adds to reactivity loss. For this type of
calculation the results is good. Although to measure it properly, smaller steps are required.
Table A- 1 gives the measured power coefficient and temperature difference per power
change for the CL56 and CL54. From the measured data of these core loadings, the average
5MCNP calculation variance of approximately 50pcm(1σ)
19 20 21 22 23 24 25 26 27 280
0.5
1
1.5
2
2.5
3
3.5
4CL54 Reactivity loss with control rod withdrawal
Rea
ctiv
ity
Lo
ss [
$]
Control rod withdrawal[cm]
calculated
measured
99
measured power coefficient of reactivity is approximately equal to 0.24¢/kW at higher power
level and 0.48¢/kW for lower power levels. For these type of calculations, this will indicate, that
if we want the reactivity difference to be within 0.0005 (for example; k=0.9995), it will result in a
reactivity of 0.07$. This will constitute a power change of approximately 29.16 kW, for the
higher power levels and 14.58 kW for lower power levels. For these calculations, the steps of
power rise will have to be smaller than the above stated (14.58 kW and 29.16 kW). Thus, the
effect of over power at the lower intervals indicated in the figures above is because of the power
steps being too high at the lower temperatures.
The following Figure 5-13 and Figure 5-14 show the corresponding temperature increase
for each of the data points in Figure 5-11 and Figure 5-12 for reactivity loss calculations. This
calculated data is the average temperature calculated for the five axial nodes of the fuel rod,
whereas the average temperature for measured data is between the highest and lowest of the data
from instrumental rod measurements at a certain axial position. CL56 uses I-17 and CL54 uses I-
16 instrumental fuel rods. For these two core loadings, the positions of the instrumental rods are
the same, i.e. the expected hot channel in the core loading.
100
Figure 5-13 CL56 average temperature increase for the i-17 rod corresponding to
reactivity loss measurements
The temperature change is a result of the change in reactivity due to power increase. The
results show a positive increase, as we would like the calculation to confirm. For 1 MW power
level the measured and calculated results show a good agreement. However, there is a difference
compared to the measured data for this system. CTF calculates the radial temperature distribution
across the fuel rod, and axial temperature distribution across the fuel length of the fuel element.
What is chosen to be an average value in measurement, does not always corresponds to a
calculated average. The measured temperature difference for reactivity change is given in Table
A- 1.
20 21 22 23 24 25 26 27 280
100
200
300
400
500
600
CL56 Temperature increase with control rod withdrawal
Tem
pera
ture
[oC
]
Control rod position [cm]
Measured
Calculated
101
Figure 5-14 CL54 average temperature increase for i-16 corresponding to reactivity loss
measurements
This result was not possible with the TRIGSIMS system. The system could apply only
one single temperature per structure-type in the core. Figure 5-13 and Figure 5-14, are consistent
in comparison to the measured data. The reactivity per change in temperature for measured data is
given in Table A- 1. The figures show an average temperature difference in the mid to bottom
region of about 30-50°C. With a temperature /power difference of 0.3°C /kW this temperature,
difference results in a notable 26-43¢ difference in reactivity.
19 20 21 22 23 24 25 26 27 280
100
200
300
400
500
600CL54 Average temperature with control rod withdrawal
Tem
per
atu
re [o
C]
Control rod withdrawal[cm]
calculated
measured
102
Figure 5-15 Temperature distribution for coolant surrounding the numbered rods
Figure 5-15 shows results from the CTF output. These are the values carried over from
one power step to the next. The results are as expected. The graph shows a steady increase in
temperature with each step of the power rise. The calculation shows that the left side of the core
is cooler than the right side. The I-17 rod (C) is the rod used for measurements and the channel
between I-17 and rod 44 (indicated in Figure 5-1) is the channel used for measurements.
100 200 300 400 500 600 700 800 900 100025
30
35
40
45
50
55
60CL56 Temperature increase with power increase for the coolant
Tem
pera
ture
[oC
]
Power [kW]
38
39
40
41
42
43-i17
44
103
Figure 5-16 Temperature increase with power increase for the indicated rods
In Figure 5-16 the measured values indicated are for the channel 2 of the I-17
instrumental rod and the data from calculations was taken from the node number 3 (middle). Each
node is 3in long. The difference between calculated and measured data is approximately 30°C in
the center of the graph. At the 900 kW to 1 MW power, we have good agreement. The results
show a variance of 0.30$ for the change in reactivity at the mid section of the power region.
Thirty cents is a notable change in reactivity. At 900kW to 1MW, there is good agreement, but at
lower power levels, the difference is quite significant. A possible reason for this could be the
application of the thermal conductivity and specific heat capacity application in the CTF input has
0 100 200 300 400 500 600 700 800 900 10000
100
200
300
400
500
600CL56 Temperature increase with power increase
Tem
pera
ture
[oC
]
Power [kW]
36
37
38
39
40
41
42
43-i17
44-210
measured
104
a linear application. However, the temperature profile for the reactor does not display a linear
profile. Further investigation is needed for this application.
Figure 5-17 Comparison of CL56 and CL54 flux distribution
Figure 5-17 shows a flux distribution calculated for the fuel elements 36 to 48 as
indicated in Figure 5-1 for CL54 and CL56. CL54 has an overall higher flux distribution in the
around the centre central thimble. CL54 has fresh 8.5wt% fuel at this position. The peak noticed
in the centre is as results of the high thermalization of the neutrons because of the water in the
thimble. Fast neutrons produced by the B-ring fuel elements are well thermalized in the extra
water in the central thimble, hence the peak at the elements directly adjacent to the centre. This
information can be extracted from the MCNP output files.
The following graphs show the total flux distribution across the core.
36 38 40 42 44 46 480.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4x 10
13 Thermal flux distribution in core elements
Th
erm
al
flu
x i
n f
uel
ele
men
ts[n
eu
tro
ns/
s])
Elements numered 36 to 47
CL54
CL56
105
Figure 5-18 Thermal flux distribution for CL56
The thermal flux in the center of the core is calculated at 3.6 neutrons/cm2-s. Thermal flux
around the edge is around 1.3 x 1013
neutrons/cm2-s.
The results for CL54 would be approximately the same as indicated above. In general, the core
configuration for these core loadings are intended to produce similar flux and power profiles.
0
20
40
60
80
100
0
20
40
60
80
100
0
1
2
3
4
x 1013
0
0.5
1
1.5
2
2.5
3
3.5
x 1013Neutrons/cm
2-s
106
Figure 5-19 Normalized average power distribution for CL56
Figure 5-19 shows the average power distribution in the core for a 1 MW critical core for
CL56 and Figure 5-20 for CL54. The results of CL56 and CL54 for the power distribution show
that the power distribution in CL54 is higher in the center of the core. The power peak of above
1.6 indicated for CL56 is occurring in the new instrumental element, I-17, loaded for this core
loading.
0 20 40 60 80 100 1200.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Average power distribution for CL56
Core Elements numbered 1-108
Av
erag
e p
ow
er d
istr
ibu
tio
n
107
Figure 5-20 Normalized average power distribution for CL54
The two core loadings, CL54 and CL56, have a control rod position for a 1 MW critical
power reactor of about the same values (27.23 cm and 27.66 cm). The TRIGSIMS-TH tool is
useful in this way. The user will be able to design and analyze different cores. The CL56 and
CL54 have different sizes, for the same power at about the same control rod position, producing a
higher power density in the center in the case of CL54.
0 20 40 60 80 100 1200.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Average power distribution for CL54
Core Elements numbered 1-103
Av
erag
e p
ow
er d
istr
ibu
tio
n
1MW
108
5.5 AMARCH/CTF coupling
The ADMARC-H code was added to the TRIGSIMS system to generate the initial fission
source distribution of the MCNP calculation, thereby accelerating the MCNP calculation [2]. The
code sequence was made automated in the sense that the input of the code is written by
TRIGSIMS based on the initial core loading input for TRIGSIMS. What this means is that
TRIGSIMS will apply the position of the control rod as it is indicated in the core loading input.
ADMARC-H by itself is also a core analysis tool for the PSBR core simulation. The code is able
to display power distribution, flux distribution and keff value of the core configuration. These
capabilities are still valid within the upgraded code system (TRIGSIMS-TH).
The coupling of CTF to ADMARC-H is used to provide realistic initial fission source
distribution as well as thermal-hydraulic parameters distributions. This approach is very useful
since ADMARC-H/CTF converges very quickly and the information it provides help to
accelerate MCNP/CTF calculations. ADMARC-H/CTF might be used to efficiently estimate
initial critical control position for a given power level while the fine-tuning could be performed
with MCNP/CTF. In the results of power rise, the CTF/ADMARC-H couple is executed together
with MCNP/CTF couple.
ADMARC-H/CTF
MCNP
CTF
Figure 5-21 Diagram ADMARC-H/CTF-MCNP-CTF couple for position step
109
For normal power increase step-calculation, the workflow of the ADMARC-H code
within TRIGSIMS code system has not changed, the only difference here is that between
ADMARC-H and MCNP the CTF code calculates the temperature of the fuel and moderator.
Thereafter MCNP's cross-sections are updated. For the MCNP/CTF coupling, we have shown
that the reactivity loss calculation required smaller steps or an iterative procedure on each step.
The iterative procedure with MCNP/CTF is not practical because of the time and computer
memory requirements for each MCNP calculation.
Figure 5-22 6 MCNP/CTF/ADMARC-H coupling
6 MCNP calculations: reactivity ±1σ
0 100 200 300 400 500 600 700 800 900 10000
0.5
1
1.5
2
2.5CL54 Comparison MCNP and ADMARCH
Reacti
vit
y d
iffe
ren
ce [
$]
Power [KW]
ADMARCH
MCNP
110
Figure 5-22 shows two sets of data. One is the result from ADMAC-H/CTF and the other
from MCNP/CTF. The results presented in Figure 5-22 are obtained in automation where the
control rod position is declared in the TRIGSIMS input file. With each step, ADMARC-H/CTF is
followed by MCNP/CTF. Instead of having numerous smaller steps we can have ADMARC-
H/CTF coupled calculations to save time.
Table 5-7 shows a comparison of the ADMARC-H results to those of MCNP. The
results are calculated with a temperature of 300K for both the ARI and ARO.
It should be noted however, that for TRIGA reactors, the power is changed with the
extraction of the control rods, and changing the power changes the reactivity of the core, hence
the ARO calculation at 300K is not physical.
Table 5-7 Core excess reactivity in $ for various core loadings
Core Loading MCNP ADMARC-H/Serpent
CL56
ARI -6.70±0.08 -6.557
ARO 7.412 ±0.08 10.579
Total 14.532 ±0.16 17.316
CL54
ARI -7.26 ± 0.07 -6.9840
ARO 7.074 ±0.07 10.78
Total 14.33 ±0.14 17.76
CL53H
ARI -8.5471 ± 0.067 -9.00
ARO 5.4548 ± 0.067 8.681
Total 14.00 ± 0.134 17.681
Both the MCNP and ADMARC-H calculations show a good agreement at the ARI
calculations. The previously developed cross sections [2], shows results in good agreement at the
111
ARO calculations because this is where the control rods was placed for evaluating full power.
One of upgrades in the TRIGSIMS system was to apply the measured control rod setting instead
of ARO as used in the TRIGSIMS-TH code system for a critical rod position. With the
application of the thermal hydraulic feedback mechanism to TRIGSIMS-TH, the critical rod
position at 1MW corresponded well with keff=1. This will be discussed in the next subsection.
5.6 Development of core expansion
For versatility of usage of this new code, the capability of a core expansion can now be
done within limits. The MCNP and CTF have the flexibility to allow variations of the core-
loading pattern. The addition of graphite elements and the new fuel, 30/20 LEU, can now be
inserted into the core. Figure 5-23 is an illustrates the core expansion positions.
Figure 5-23 Illustration of core expansion
5.6.1 Graphite elements added
The TRIGSIMS-TH is now equipped with rod entries for graphite. Graphite rods are used
at various TRIGA facilities as reflector elements [7], [45]. A reason for this is to increase the keff
of the reactor, hence, require fewer fuel elements, or extending the life of the fuel or locally to
increase the flux near the dry tubes for irradiation purposes.
Table 5-8 gives results for the addition of 10 graphite elements to the CL53G.
112
Table 5-8 Addition of 10 graphite elements
Power [KW] Difference in reactivity [$]
300
0.226±0.09
700
0.2045±0.09
800 0.2051±0.09
900
0.194±0.09
1000 0.2112±0.09
The addition of the 10 graphite elements has resulted in a decrease of ~$0.21 in reactivity
loss calculations (or increase in reactivity).The reactivity is calculated using the equation
5.6.2 New type of fuel elements
The TRIGSIMS-TH code uses a predefined geometry input for all the elements. This
means, the size of each element has a fixed geometry that TRIGSIM-TH uses to write the various
inputs. The isotopic composition is the only degree of freedom for various inputs. Since the new
30/20 LEU fuel are geometrically the same as the 8.5 wt% and 12 wt% fuel, the only
requirements for calculating this new fuel in MCNP is to have the correct composition and
density for the fuel. In the next chapter, an analysis of this fuel in the TRIGSIMS-TH will be
performed using the control rod search methodology.
5.7 Improvements of the core design parameters
With the further development of the code system including the addition of CTF and a
control rod methodology, there was a need for the following improvements:
113
1) New homogenized diffusion coefficients and cross sections were prepared for
ADMARC-H calculations. The previous cross sections were generated for the system with no
feedback and no control rod placement. Full power calculations were previously performed at
ARO.
2) The temperature-dependent continuous energy cross sections previously developed by
Tippayakul [2] proved to be sufficient. With the addition of the pseudo material approach and
cross section ordering, a more accurate calculation is achieved.
3) The material composition and density of B4C used in the control rod elements was a
concern raised by previous studies [2], [7], which needed to be addressed.
5.7.1 Control elements
The information about the material composition for the neutron absorbing material B4C
(Boron Carbide) used in previous studies is not consistent. Each study has used a different set of
composition and densities. The known composition of the natural form of B4C is given in Table
5-9 [37], [46].
Table 5-9 Theoretical B4C number densities
Density [g/cc] C12 (wt%) B10(wt%) B11(wt%)
2.52 0.216 0.156 0.628
Previous PSBR work [2], [7] used different combination of these isotopes. The evaluation
of core models did not allow using the theoretical material isotopic of the B4C hence the variation
in data.
114
For the aim of creating a tool that predicts control rod placement with feedback for a
critical rod position, there is a need to determine the real composition of the neutron absorber in
the control rods in order to have accurate calculations. The tool is automated, and data for
standard inputs such as control rods are fixed in the program.
We know from previous studies that the neutron absorber material composition greatly
affects the outcome of the calculations. For this study, calculations of various combinations of the
B4C were assessed.
The following table shows the result of possible combinations used in previous studies
and a current combination used in TRIGSIMS-TH.
Table 5-10 Control Rod Absorber Combinations
Case
Combination of B4C -Keff Density [g/cm3] Isotopic Concentration
[wt%]
CL53 CL54 CL56 SA/SH
/RG TR
10B
11B
12C
#1 ARI 0.93556 0.94597 0.94953
2.49 2.49 15.60% 62.80% 21% ±0.00044 ±0.00052 ±0.00052
#2 ARI 0.95125 0.96439 0.96719
1.8855 1.8855 3.91% 15.75% 80% ±0.00041 ±0.00053 ±0.00057
#3 ARI 0.94032 0.958 0.96162
1.8855 2.49 3.91% 15.75% 80% ±0.00052 ±0.00053 ±0.00053
#4 ARI 0.95189 0.96319 0.966
2.5 1.13 3.91% 15.75% 80% ±0.00052 ±0.00054 ±0.00053
#5 ARI 0.94115 0.9495 0.95329
1.7 1.7 15.60% 62.80% 21% ±0.00040 ±0.00051 ±0.00050
#6 ARI 0.94393 0.94974 0.95262 R1 critical rod position - Keff
115
Table 5-10 presents different isotopic combinations of the B4C absorbing material in the
control rods. Previous studied have applied a density and isotope weight to work for the system
they used. Using the current TRIGSIMS-TH code system to calculate the different cases for ARI
position at 300K temperature has delivered the results in Table 5-10. The theoretical value case
#1, shows each of the combinations under-predicted compared with the measured data shown in
case #6. The previous used combination (case #2), referred to in the thesis of Tippayakul [2] as a
possible combination, has shown an over prediction in CL56, CL54 and CL53. The combination
(case #3) was used by Tippayakul [2], where he has used a combination of previously used and a
theoretical value, has shown an over prediction of CL56 and CL54. The combination #4 used by
Sahin[7], has worked for his MURE system, but for this TRIGSIMS-TH it shows an over
prediction in all the core loadings. The TRIGSIMS code is equipped with this combination. The
combination #5 indicates closest agreement to the measured data. This combination is applied to
TRIGSIMS-TH.
Using the control rod methodology described in Section 5.2, the following results show
the critical control rod position for nominal power of 1MW for these combinations.
Table 5-11 Comparisons of control rod position for B4C cases
Rod position CL54 CL56
Measured #5 1073(27.25cm) 1089(27.66cm)
#3 [2]
27.82cm 27.14cm
#4[7] 27.99cm 26.49cm
#5 27.89cm 27.50cm
The result in Table 5-11 is for a critical core with control rod search with position
placement for 1MW power core design. The results shows that the combination for #5 applied to
116
the TRIGSIMS-TH delivers a more comparable result to the measured data for CL56, whereas for
CL54, all the combinations are approximately 2% higher.
5.7.2 Homogenized cross sections results
The cross sections and diffusion coefficients for the ADMARC-H code were previously
calculated with the HELIOS code [2]. With the addition of the thermal-hydraulic code for
temperature feedback, the previous cross sections were no longer applicable because the cross-
section modeling, especially in terms of instantaneous thermal-hydraulic dependencies, was not
done properly. As mentioned before, the accuracy of a calculation is significantly dependent on
the nuclear data being used.
For these cross sections, the fuel elements were burned as a single fuel cell. The
following depicts the calculation result representing an 8.5 wt% uranium and a 12 wt% uranium
fuel element. For this calculation, reflective boundary conditions were used. Homogenization was
done over fuel, clad, water and Zr rod region as indicated in Figure 5-23.
Figure 5-24 Homogenized fuel/clad/water region
117
The criticality calculation for a single fuel cell results in a kinf >>1. For this release of the
SERPENT code, SERPENT is consistent with criticality calculation in the case where the k=1.
When the system is far from critical, the fission neutron population is either over (k<1) or under
estimated (k>1). The result is that the neutron spectrum becomes biased, which may affect the
energy spectrum and results [36], [51]. Deterministic lattice transport codes use leakage models
to overcome this problem. This has been applied also in SERPENT but not in MCNP. Figure A-3
shows a comparison of the burnup of SERPENT compared to MCNP/ORIGEN-S burnup of a
single fuel cell. The results show differences in the keff calculated with this two systems, for each
of the burnup steps, which are result from the fact that SERPENT uses a leakage model and
MCNP not.
Figure 5-25 compares the TRIGSIMS/MCNP to SERPENT input visualizations for the
CL4. The core is comprised of 85 fresh 8.5wt% fuel elements.
Four control rods with B4C as indicated in Table 5-9.
Figure 5-25 Illustration of the two input geometries: MCNP and SERPENT
The control rods are in position ARI; the core has the same moderator amount
surrounding the core model. The results for this comparison are given in the table below. The
118
reference #1 is for a rod next to the central thimble on the B-ring, the reference #2 is for a rod in
the middle of the core and reference #3 is for a rod on the periphery.
Table 5-12 SERPENT vs. MCNP Results for CL4
Area calculated MCNP SERPENT
Keff 0.93084 ± 0.00077 0.93044 ± 0.00086
Fission Neutron
Production
[neutrons/cm2-s]
Reference #1 1.01 x 10
8 1.13 x 10
8
Reference #2 5.7x 10
8 7.295 x 10
8
Reference #3 2.76 x 10
8 2.33 x 10
8
The following results show the comparison of the previously used HELIOS cross section
(XS) compared with the newly generated SERPENT cross sections (XS) in the ADMARC-H
code. The TRIGSIMS CL53, CL54 and CL56 are used to verify the results.
Table 5-13 Comparison with previous cross sections using CL53 in ADMARC-H code
CL53 HELIOS XS SERPENT XS
Temp 300K 600K 900K 300k 600K 900K
ARI 0.928700 0.903065 0.9170641 0.9370 0.8845 0.924668
1MW 1.037264 1.013478 1.025051 1.05803 1.00543 1.04503
ARO 1.043420 1.019757 1.031156 1.0647 1.01216 1.051655
Total reactivity at (300K)= $16.904 Total reactivity at (300K)=$18.28
119
Table 5-14 CL53 at 1MW- comparison using ADMARC-H code with feedback
CL53 HELIOS XS SERPENT XS
1 MW 1.00929 0.99832
Table 5-15 Comparison with previous cross sections using CL54 in ADMARC-H code
CL54 HELIOS XS SERPENT XS
Temp 300K 600K 900K 300k 600K 900K
ARI 0.939355 0.91382 0.927845 0.94905 0.8969 0.93651
1MW 1.03752 1.01357 1.025275 1.06168 1.00966 1.048178
ARO 1.05649 1.032842 1.04407 1.0817 1.02981 1.0681
Total reactivity at (300K)= $16.86 Total reactivity at (300K)=$18.45
Table 5-16 CL54 at 1 MW- comparison using ADMARC-H code with feedback
CL54 HELIOS XS SERPENT XS
1MW 1.01230 1.00046
Table 5-17 Comparison with previous cross sections using CL56 in ADMARC-H code
CL56 HELIOS XS SERPENT XS
Temp 300K 600K 900K 300k 600K 900K
ARI 0.942209 0.91672 0.93078 0.953392 0.900979 0.94109
1MW 1.038725 1.014800 1.026766 1.06200 1.00957 1.049098
ARO 1.05607 1.032424 1.043972 1.08030 1.02790 1.06726
Total reactivity at (300K)= $15.86 Total reactivity at (300K)=$17.26
120
Table 5-18 CL56 at 1MW- comparison using ADMARC-H code with feedback
CL56 HELIOS XS SERPENT XS
1MW 1.01305 1.00249
Table 5-13, Table 5-15 and Table 5-17 show the comparison of previously used cross
sections for ADMARC-H generated with the HELIOS code. The cross sections are generated to
fit a system. In this case, the TRIGSIMS code did not have feedback and temperature of the core
was one temperature. What you will find is that with a homogenous temperature across the core,
the keff will not approach one for a critical core. The comparison of the two sets of cross sections
shows a different trend. At ARI, the HELIOS produced cross sections are far off from the
measured and expected Keff value. The code system did not have a control rod methodology and a
1 MW critical core was taken as ARO in the system. There are however a systematic difference in
the difference in all three cases. The total reactivity difference is approximately 1.57$, for all
three cases.
Table 5-14, Table 5-16 and Table 5-18 compares the results of a 1 MW rod position for
the three core loadings. These results include feedback. Using a heterogeneous temperature
distribution at certain control rod positions, the results are in favor of the SERPENT produced
cross sections. SERPENT-based results are closer to a Keff of 1 at a 1 MW power level.
5.7.3 Continuous energy cross section application
The temperature-dependent continuous cross sections produced for the TRIGSIMS [2] are found
to be adequate for the purpose of TRIGSIMS-TH applications. Smaller intervals of temperature
grid of were shown [7] that the refinement to the data improves the accuracy of calculations.
The current MCNP generated cross sections, for selected isotopes, are from 300K to 900K in
121
steps of 50K intervals. To apply a refinement for higher accuracy, the implementation of pseudo
material approach was applied to the cross sections between temperature intervals for the uranium
isotopes. The application of pseudo material approach is a way of manipulating cross section data
in the case where the intervals are not refined enough. Figure 5-26 shows the difference of this
contribution to the calculation.
Figure 5-26 Pseudo material difference (Keff results7)
The results show that there is a minor influence, but does not confirm a positive
influence.
7 Keff results were calculated to approximately 50pcm (1σ)
0 1 2 3 4 5 6 7 8 9 100.94
0.95
0.96
0.97
0.98
0.99
1
1.01Pseudo compared to non-pseudo
Kef
f
#Iteration
No Pseudo
with Pseudo
keff
=1
122
The way of using the cross section can influence the outcome of the calculation. The
TRIGSIMS code reads the cross section file xsdir.file stored in the MCNP_DATA folder for
MCNP5. The cross sections previously made by Tippayakul [2], with smaller temperature
intervals is also loaded into this file. The code reads the cross sections from bottom to top.
Therefore is it important to have your choice of cross section table located at the bottom of the
list. This applies to the thermal neutron scattering data as well. The choice for cross section
search should be to go through the list of "important" isotopes (psbr900) to make the choice there
before the code moves over to ENDF7, etc. The tolerance is given as 25K for the temperature
choice. An addition to the search of cross sections method is that the code now also makes a
choice between the ENDF7 selections for choices not covered by the PSBR cross sections. The
code will search and depending on the temperature and it is closest to the choice. The previous
cross section selection method was on a loop of order of first occurrence. This was never a
problem because the feedback was not modeled and the code only had a few choices.
5.7.4 Moderator for the core design
The TRIGSIMS-TH code system writes the MCNP input. Because it is automated,
certain entries are fixed. The original core loadings have a certain size and usually only filled
with the usual elements, i.e., the fuel, the control rods and the dry irradiation tubes. CL54 is a
core loading that has a difference in geometry. With fewer elements, the core is not shaped in the
usual hexagonal shape. TRIGSIMS however apply a moderator input around the core as for the
usual method. This result in a typical core loading as the CL56, with its hexagonal shape. The
current method of fuel to moderator cells in TRIGSIMS/MCNP is depicted in the following
Figure 5-27, Figure 5-28 Figure 5-29 and Figure 4-13 of the core loadings CL53,
CL53+graphite, CL54, CL56 respectively. A maximum radius is determined based on the longest
123
distance of the MCNP entry. However, this was only done for a positive entry. It was assumed
that the core is completely symmetrical, top half entry to be the same as bottom half; hence, the
search is in one direction. Also with the addition of a graphite element around the outside, the
code would take as part of the core entry. The result would be that different cores would be given
a moderator amount based on the maximum radius, which over estimate smaller cores.
Figure 5-27 CL53 no-graphite diagram
Figure 5-28 CL53 +10 graphite elements
These two cores have the same amount of fuel, but the moderator is different.
Maximum radius
Max radius
124
Figure 5-29 CL54 diagram
For the CL54 and CL56 (see Figure 4-13), there is a difference of 5 rods, yet the water
surrounding CL54 is more than that of CL56.
Table 5-19 shows the results of the TRIGSIMS-TH, comparing the adjustment that was
made to the maximum radius value. The code will assess whether the entries are fuel or non-fuel
elements and will consider only the fuel elements in the search for maximum radius. Once the
maximum radius is found, the value is further adjusted to reduce the radius. The fractional part of
the number of fuel elements to the fully loaded diagram (110 elements) is applied. This
application has shown an improvement on the results.
Table 5-19 The effects of the adjustment of the water surrounding the core.
Core loading TRIGSIMS/MCNP
Adjusted
TRIGSIMS/MCNP
difference [$]
CL53G 0.93264 ± 0.00046 0.93576 ± 0.00056 0.45 ± 014
CL53G+10graphite 0.93615 ± 0.00045 0.93804 ± 0.00052 0.27 ± 0.14
CL54 0.94698 ± 0.00062 0.94956 ±0.00047 0.37 ± 0.16
CL56 0.95273 ± 0.00044 0.95329 ± 0.00050 0.08 ± 0.13
Maximum radius
125
5.7.5 TRIGSIMS-TH application to CTF
The thermal hydraulic feedback with CTF was implemented with the following criteria in
mind:
a) the core layout had to allow for fuel and non-fuel elements;
b) the ability to expand the core by adding elements to the outer core layout;
c) the addition of the D2O tank in the input had to be inserted as a restriction to the
side of the core;
d) CTF input had to be developed to accommodate different modes for running
CTF, i.e., the expansion of the deck will write out the core elements with an axial
length of 35.66in instead of 25.66in, that certain cards are added, also the
addition of the D2O, which changes the input at various places.
Table 5-20 shows the MCNP results for estimating reactivity calculations for CL56 with
D2O tank. The reactivity loss is an estimate from calculated results using control rod search
method, and the worth remaining is the addition of reactivity loss and calculated excess reactivity.
Table 5-20 Estimation of reactivity for CL56 +D20 tank
CL56+ D2O Calculated Measured
Reactivity [$] Reactivity [$]
Worth removed -5.63 ± 0.08 -6.36
Reactivity loss 2.64 ±0.08 --
Worth remaining 6.996 ± 0.16 6.66
TOTAL 12.626 ± 0.24 13.02
126
The results for ARI (worth removed) calculation for the CL56+ D2O tank is
approximately 0.70$ lower than the measured results.
Figure 5-30 shows the comparison of CL56 with and without the D2O tank attached to its
core. This option in the input adds a standard size rectangular tank in the MCNP geometry that in
this design comes in close proximity to the fuel elements indicated as 1 to 8 in Figure 6-13. The
thermal hydraulics for the core loading had to be expanded to create the restriction in the flow
due to the D2O in path of cross flow. This addition also forms part of the iterative scheme to find
the control rod search for a critical reactor.
127
Figure 5-30 Comparison with and without D2O tank to the CL56 design at 1 MW power
0 20 40 60 80 100 1200.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Normalised ave power/rod
Av
e P
ow
er
Fuel elements
0 20 40 60 80 100 1200
100
200
300
400
500
600
Temperature comparison with D2O and without
Tem
per
atu
re[
oC
]
Fuel + non-fuel elements
D2O
noD2O
D2O
noD2O
128
The results from this comparison confirm the expected flow restriction, with the result
that the average power in the Elements 1 to 8 has been increased by approximately 11-15% due to
the flow restriction. This power increase is due to the reflection of leaked neutrons from the
D2O.The difference in the power however gets smaller toward the center of the core. The fuel
temperature at these elements 1 to 8 is also higher with a maximum increase of 8%. To ensure a 1
MW power for the CL56 + D2O, the positions of control rods were adjusted as expected in the
iteration scheme and the rod position settled at approximately 25.9cm (there is no data available
for control rod position at a 1 MW power for CL56+ D2O tank). The water temperature
surrounding these elements is also higher by approximately 5 % (17°C) compared to the CL56
with no D2O.
Figure 5-31 Comparison of average power for the D2O tank calculation
Figure 5-31shows the difference (D2O - no-D2O) in power distribution is for a CL56 with
a D2O tank with and without a tank. It shows that the biggest difference is within the first three
1
2
3 4 5
6 7 8
9 10 11 12
13
14
15
16
17
18 19 20
21 22 23
24
25
26
27
28
29
30
31
32 33
34
35
36
37
38
39
40
41 42 43 44
45
46
47
48 49 50
51 52 53 54
55 56
57
58
59
60 61
62
63
64
65
66
67 68 69
70
71 72 73
74 75 76
77
78 79
80
81 82
83
84
85
86
87
88
89
90 91
92
93
94 95
96 97 98
99
100
101 102
103 104 105
106 107
108
-10
-5
0
5
10
15
20
%D
iffe
ren
ce
Fuel elements
Ave Power comparison of CL56 with and without the D2O tank
129
rows of the core. This calculation shows a positive difference on the front core elements with a
negative difference in the other core elements seen here in the graph.
5.8 Thermal hydraulics as a standalone tool
TRIGSIMS-TH with the addition of the CTF code is able to run full core thermal
hydraulic calculations of the PSBR reactor core. As part of the coupling methodology to both
MCNP and ADMARC-H, a shortened version of the input is used. Essentially, for the use as
thermal hydraulic feedback, the need to include flow above and below the grids is unnecessary. In
addition, to minimize the time for computation, a short version of the input is introduced.
As a "standalone" method, the input for the CTF code is changed. Figure 5-32 depicts the
flow channel changes for this input.
A B
Figure 5-32 CTF input changes for "standalone" calculations
Bottom grid
Top grid
130
Diagram-A represents the flow pattern for the CTF input used in the coupling
methodologies of TRIGSIMS-TH code. This flow region consists of nine nodes covering an axial
length of 25.66 inches, representing the flow between the top and bottom grid plates only. The
boundary conditions are set at the beginning and end of this flow volume to create the needed
pressure difference for the core calculation. CTF has five nodes to represent the active fuel
region, which corresponds to the five nodes used in MCNP. With this, further averaging is not
needed and this result in minimizing the uncertainty.
Diagram B represents the extension of the flow for the "standalone" CTF method. With
the extended input, the CTF code is now a thermal hydraulic modeling tool. The flow extends to
beyond the top and bottom grid plates. The bottom grid is a solid structure with small holes not
big enough to allow much flow to pass. Both the top and bottom grid plates create a pressure
difference (core ΔP) across the core axial fuel length. The geometry variation across the vertical
length of the flow creates the variation in the momentum areas, continuity areas and wetted
perimeters. What these changes mean for our flow pattern, is that we not only have a flow that
moves vertically but also across the gaps of the channels (cross flow). The model in Diagram B
uses much smaller calculation cells (nodes). This input has seventy-one nodes that starts from the
bottom below the grid and extends to the top above the top grid plate. The axial length in this
model is 35.66 inches (0.92m) which includes the fuel region of 15 inches. To create a realistic
(physical) scenario for this input, the initial flow rate is set very close to zero (0.0001). The initial
channel temperature is set at 73°F (23°C). Local channel pressure losses are used within the grid
domain. The pressure at the bottom grid is bigger than at the top due to the almost complete flow
restriction in the vertical channel at this position.
Figure 5-33 shows the results of the thermal hydraulic analysis of a 1 MW thermal power
for CL56. TRIGSIMS-TH generates the CTF input, after the MCNP neutronics calculation has
131
been performed. TRIGSIMS-TH/MCNP provides the axial power distribution tables as well as
the calculated radial power distribution for full core calculation.
Figure 5-33 Thermal hydraulics results: velocity of channels 112 to 131 for CL56
The results in Figure 5-33 represent the flow channels that run from left to right through
the center of the core. These channels are indicated in Figure 5-1. It also shows the axial velocity
0
5
10
15
20
25
30
35
40
-0.100 -0.050 0.000 0.050 0.100 0.150 0.200 0.250 0.300
Axia
l le
ngth
of
the
flow
chan
nel
[in
]
Velocity [m/s]
112 116 120 centre 124 128 131
bottom grid
top grid
Active fuel region
Channels
132
of the coolant in the indicated channels. The inlet channel starts at the bottom (1) and ends on top
(35.66 in). Positive flow is upward.
The result reflects the inlet having zero flow (0 velocities) at node 1 and shows both
negative and positive velocity results. Channel 131, is a channel on the far right side (outer side)
of the core. The result for this channel shows a negative velocity of the fluid in part of the active
region. This shows the flow is downward below 23-inch mark and upward above this.
The channel 124 has the highest upward velocity among presented results. This channel
is between three of the hottest fuel elements in the core resulting in a channel with higher
temperature, creating a lower density at the upper region, resulting in a faster upward flow. The
maximum velocity in the active fuel region is 0.128m/s. This value corresponds to the calculated
result with ANSYS code [5].
Figure 5-33 also shows the results above the top grid plate with both the center channel
and the hottest channel reaching upward velocity of 0.17 m/s. The figure shows the restriction in
the flow at the top and bottom grid plates. The area above the bottom grid and the area below the
top grid has a bigger flow area. In these regions, an almost stagnant or steady equivalent speed is
achieved in all the channels, which is what is expected in this region, as the nominal flow area is
almost 3 times that of the channel in-between the fuel. The high speed above the top grid plate is
also as expected. Based on Bernoulli's principle, increase in speed of fluid will occur
simultaneously with decrease in pressure or a decrease in the fluid’s potential energy.
Figure 5-34 shows the results of analysis obtained for full core temperature distribution in
and around the core.
133
Figure 5-34 Thermal Hydraulic results: Temperature distribution for CL56
0
5
10
15
20
25
30
35
40
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
Axia
l le
ngth
of
the
flow
chan
ne
[in
]
Temperature of the fluid [°C]
122 124 126 128 130 channels
Top grid
Bottom grid
Active fuel region
134
The CTF calculation results indicated in the Figure 5-34 show that the temperature
distribution in the core for a 1MWth reactor power operation under steady state condition
decrease with increase of radius. The hotter channels are around the center of the core. This is
because of the loading pattern where the high power density elements are inserted around the
central thimble in the B, C and D rings. The power peaks around this region in the core, therefore
the fuel is hotter, resulting in hotter channels.
Channel 130, shown in Figure 5-34, is a cooler channel. The maximum temperature for
this outside channel is around 38-40°C. The hottest channel in the results is either channel 124 or
channel 122 depending on where the measurement is taken along the axial length. Channel 122 is
on the centre and we have shown in the previous figure that the velocity in center is lower than
the velocity in channel 124. The channel 122 is bigger channel and get cross flow from all
directions. Hence, the channel fluid is hotter at the top half than the bottom half compared with
channel 124. Hence, for the channel 122, it appears hotter for part of the channel, but it does not
contain the hottest fuel element. One of the main goals of thermal hydraulic design for safety
analysis is to ensure that the thermal limitation of the core thermal hydraulics is not exceeded.
The fuel rod having the maximum power output is the "hot" fuel rod. The "hot" channel in the
core is usually is the coolant channel in which the core heat flux and enthalpy rise is a maximum.
Usually this is analyzed by increasing the core conditions to reach the operational limitations.
Hence, to establish the "hot "channel, "hot" rod further analysis needs to be done. These analyses
can be done with the new TRIGSIMS-TH.
The results in Figure 5 33 show that in the maximum fluid temperature in the active fuel
region of the channel is approximately 60°C for the channels around the center of the core. Ücar
[5] shows the measured temperature in this location (for CL53H) to be around 59°C.
From the results obtained from the CTF output file, under steady state conditions, the
"hot" channel for this core loading is the channel between rods I-17 (highest heat flux of 1.52 x
135
105 b/h-ft
2), rod 220 (heat flux of 1.20 x 10
5 b/h-ft
2) and rod 226 ((heat flux of 1.39 x 10
5 b/h-ft
2 ).
The highest channel temperature is approximately 60°C. A few channels around the center have
high enthalpies (108 btu/lbm). This is the channel indicated as channel 125.
Table 5-21 gives details from the full core calculations using the extended core model to
analyze the hotter fuel elements.
Table 5-21 Analysis of the hotter elements in CL56
Parameter Rods
46 (I-17) 47 (210) 56 (I-2) 57 (226)
Fuel Temp-Mid[°C]
538 507 513 527
Fuel Surf Temp (max) [°C]
[°C]
133 130 131 132
Measured average Temperature for CL56 at 1MW is 518°C, hottest Temperature is 527°C
The instrumental rod I-17 was used for measurements. The results from calculations were
taken from node 39 (which is at 18.79 in axial length from the bottom of an axial length of
35.66in). The data was taken off center, at approximately 0.22 in radius from the center of the
fuel rod. The CTF input allows for eight radial temperature distributions, which includes the
center Zr-rod, five fuel radial sections a gap region and an outer clad region [3]. This temperature
results can be retrieved from the output file called T_hrod.out.
The PSBR core is cooled with natural convection. Because of the complexities of this
type of flow, the core flow dynamics has been a topic of interest to analyze [6], [16], [18], [39].
The following graph displays the core fluid flow for the 1 MW power of CL56.
136
Figure 5-35 Results of the mass flow rate across the gaps (cross flow)
Figure 5-36 Illustration of the cross flow results
0
10
20
30
40
50
60
70
80
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Ax
ial
no
des
Mass flow rate [oz/sec]
174 175 176 177 178 179 180 181
Centre
Gaps
137
The Figure 5-35 shows the result of the cross flow across the gaps bordering the channels shown
in Figure 5-33. The Figure 5-36 is an illustration (interpretation) of this flow pattern’s results
shown in Figure 5-35. The vertical channel velocity results give the inner core channel an upward
flow rate and the outer channels have part flow downward. The cross flow results show the inner
channels flow transverse inward in the direction of the center. The end channels have the bottom
flow inward and the middle to upper part of the flow pattern in the direction of the outside of the
core. Similar to the flow from bottom to the top, the driving force of the flow is the change in
pressure from channel-i to channel-j horizontally; enthalpy change is due to change in
temperature and the upward-flow, which creates a pressure drop at the bottom of the core.
A simplification illustration of this explanation is shown in Figure 5-37.
Figure 5-37 Illustration of the flow around the channel
Inflow of colder water creates a drop in
pressure and enthalpy, creates an in-flow
Upward flow due to
increase of temp and
ΔP
138
5.9 Summary of results
The further development of TRIGSIMS to TRIGSIMS-TH has provided the following
results:
A) The addition of CTF to the TRIGSIMS code was applied in a coupling methodology
to both the MCNP and ADMARC-H code. This was done successfully and the Figure 5-2, Figure
5-3 and Figure 5-4 show the temperature distributions of this coupling methodology for the
MCNP/CTF calculations. The results are as expected and compare well with measured data,
which validates the methodology. Table 5-1 gives the desired values for this calculation at 1 MW
power distribution. With feedback, the calculation gives the desired keff value of one and the
control rod positions compare well with measured data.
The ADMARC-H calculation is used as an acceleration method. Comparing the keff value
at 1MW, we have a good agreement. For ARI our values are close to measured data.
B) A control rod search method was added into the TRIGSIMS-TH code. The PSBR is
operated with partially inserted control rods and has full power (1 MW) at approximately 12''-13''
rod insertion. A method to find the control rod position at a required condition was needed for a
new core loading. Previously the TRIGSIMS code used ARO as a default position. The results of
this addition are shown in Figure 5-5, Figure 5-6, Figure 5-7 and Figure 5-8. What these results
have shown is that this iterative procedure will give you a height close to the measured control
rod position. These results show a very good comparison to the measured results, verifying the
methodology of the control rod search algorithm. This method was implemented successfully.
C) An important new analysis feature added to the TRIGSIMS-TH code is the ability to
have a standalone thermal hydraulics module with an expanded core geometry. That is, an input
larger than the geometry used for the condensed CTF/MCNP coupled input deck that will allow
the user to use CTF as an analysis tool. With a request given in the input, TRIGSIMS-TH will run
139
a MCNP calculation, update and write an expanded geometry CTF input deck, and run the
application. This will provide the user with the tool to perform various analyses. The section 5.5
in this chapter describes such an analysis for the CL56.
TRIGSIMS-TH also has an option to add to the input a D2O tank model. This feature was
extended to the CTF model as well. Thus if the user wants to model the core loading with the
D2O Tank in place, a request is made in the input of TRIGSIMS-TH and both the MCNP and the
CTF will be loaded with the necessary geometry changes to do coupled and standalone
calculations with the D2O tank geometry. The results for these features in TRIGSIMS-TH have
delivered results well comparable to measured data.
D) In addition to these main developments of the TRIGSIMS-TH code, various other
upgrades and changes was done to make this code system well developed for the feedback
mechanism, for the design changes and overall to make this code a core design and analysis tool.
Overall, all the changes gave positive results and demonstrated successful implementation.
The application of the TRIGSIMS-TH as an analysis and design tool is presented in the
next chapter.
140
Chapter 6
TRIGSIMS-TH Core Design Application
This chapter describes the use of the TRIGSIMS-TH code for different studies. The
following four scenarios were calculated /simulated.
1. CL56 with changes on the periphery of the core to include graphite elements and
an expansion of the core
2. CL54, inserting the six fresh fuel elements currently in this core loading on a
different location, not in the center as it is usually done. This is performed to
demonstrate the ability of the code to design new core loading and extracting
data, to define the core.
3. CL54, inserting the six fresh 30/20 LEU fuel around the central thimble.
4. CL56 is analyzed using the standalone thermal hydraulic expanded geometry
capability, to show the effect of the D2O tank addition in the core loading as well
as the thermal hydraulic analysis ability.
6.1 Core loading design scenario 1
The following application shows a comparison of two cores, CL56 and CL56_adjusted.
CL56_adjusted uses the core elements of CL56, then rearranging the outer ring of elements and
adding, 8 graphite elements to this core loading. This application shows the TRIGSIMS-TH
versatility in the ability to expand the core. The expansion of the core includes a ring of elements
where these elements include fuel and non-fuel elements. The core expansion is applicable to
both MCNP and CTF.
141
6.1.1 Addition of graphite elements
In the preceding chapter, the addition of graphite elements has shown to make a
difference especially on the flux distribution in the vicinity where it was placed. A 20¢ reactivity
insertion for approximately 10 elements is what is expected. TRIGSIMS-TH code allows the user
to place these elements at any position in the core. In the next example, these elements were used
in a new core layout design.
6.1.2 A new core layout
The following illustration compares the two cores for analysis.
Figure 6-1 CL56 and CL56- adjusted
The Figure 6-1 is the CL56 and CL56_adjusted which is CL56 but with a rearanging of
elements in the G-ring as well as the addition of 8 graphite elements. It is a larger core with 118
Fuel
Graphite
142
elements (fuel and non-fueled). The calculation is a criticality calculation of 1 MW power, which
includes the thermal hydraulic feedback at every adjustemnt of control rod.
The results obtained by comparing CL56 and CL56_adjusted are shown in Figure 6-2.
Figure 6-2 Comparison of the CL56 and CL56_adjusted
The results between the two core loadings show an insignificant difference in the control
rod placement of a 1 MW core power for this comparison. The core contains the same fuel
elements and the addition of the graphite elements.
0 5 10 15 20 250.95
0.96
0.97
0.98
0.99
1
1.01
# Iteration
Kef
f
Keff and Control rod position comparison
0 5 10 15 20 250
5
10
15
20
25
30
Co
ntr
ol
rod
po
siti
on
[cm
]
# Iteration
adjusted
1mw
cl56
adjusted
measured
cl56
143
Figure 6-3 Comparison of CL56 and CL56-adjusted average power distributions
0
5
10
15
20
25
1
2
34
5
67
8
910
11
0
0.5
1
1.5
1MW avearge power distribution
yx
Avera
ge p
ow
er
dis
trib
ution
0
5
10
15
20
25
123
4567
891011
0
0.5
1
1.5
1MW avearge power distribution
y
x
Avera
ge p
ow
er
dis
trib
ution
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
A
B
144
Figure 6-3 indicates that the core loadings show minor but yet visible difference in power
distributions. A and B represent the results for average power distribution of a 1 MW critical core
power, where A is the adjusted core loading CL56, and B is the CL56. The peak power is at the
same position, though with A the inner power is more spread because of the range of elemental
distribution being further, compared with B where the inner core elements have higher peak
values.
The following results in Figures 6-4 and 6-5 show the comparison of thermal flux across
the cores.
145
Figure 6-4 CL56_adjusted- flux [neutrons/cm2-s] across the core
Figure 6-5 CL56-flux [neutrons/cm2-s] across the core
146
The changes are minor and the affected regions are on the sides where the changes occurred, i.e.,
on the edges where the thermalization of the neutrons is less because the core is wider and
graphite elements are inserted. The following graphs will show that those thermal neutrons are
creating higher number of neutrons absorbed in the core elements, situated on the edge of the
core.
Figure 6-6 Flux [neutrons/cm2-s] results from reshuffling of core elements
Using the exact same core (CL56), it is not expected to observe huge differences. The
calculation result in Figure 6-6 shows an increase in flux values of approximately 11% around the
edge where the DT1 and DT2, dry tubes, are situated. Thus, the developments implemented to the
TRIGSIMS-TH code made it a useful tool to measure the degree of change in core design when
performing analyses.
0 5 10 15 20 254
6
8
10x 10
12
# rods
Flu
x
Comparison of flux distribution in the first and second row
0 5 10 15 20 254
6
8
10
12
14
x 1012
Flu
x
# rods
CL56-Adjusted
CL56
CL56-Adjusted
CL56
147
6.2 Core loading design scenario 2
The customary operational approach of loading the PSBR reactor is to insert the higher
power density fuel around the central thimble (B-ring for 8.5wt% and C,D -ring for 12 wt% fuel).
Hence, new fuel will initially be inserted into around the central thimble. CL54 has six fresh 8.5
wt% fuel elements in the B-ring. For this analysis, the six fresh elements will be inserted into a
position closer to the edge of the core. The following diagrams illustrate the position changes of
the two core layouts. The CL54 with changes to the fresh fuel elements is referred to as
CL54_shuffled.
Figure 6-7 Illustration of CL54 and CL54_shuffled
Figure 6-7 shows CL54 and CL54_shuffled, which contains the same elements except
for the interchange of elements indicated in the positions shown in yellow (6 fresh 8.5 wt%).
Figure 6-8 shows the results of criticality calculation at 1 MW power using the TRIGSIMS-TH
code.
148
Figure 6-8 Comparison of CL54 vs CL54-shuffled
The comparison of the changes indicated in Figure 6-8 shows a clear difference in all
three parameters calculated. The keff value took longer to converge (17 iterations compared with
2 4 6 8 10 12 14 16 180.94
0.96
0.98
1
1.02
1MW core power with feedackk
eff
# iterations
2 4 6 8 10 12 14 16 180
5
10
15
20
25
30
35
Co
ntr
ol
rod
po
siti
on
[cm
]
# iterations
2 4 6 8 10 12 14 16 180
100
200
300
400
500
600
Av
erag
e fu
el T
emp
erat
ure
[ oC
]
# iterations
CL54-SHUF
average
CL54
Measured
CL54-shuf
keff
CL54
CL54-shuf
average temp
CL54
149
12). The control rod position is much higher for the 1MW power core loadings for CL54_
shuffled (31.1 cm) as compared with 27.23 cm measured (27.9 cm calculated) for CL54. In
addition, these changes affected the temperature of the core. The CL54_shuffled is calculated at
average of 517 °C as compared with 502°C calculated (507°C measured) for CL54. The
following results show the difference in power distribution for these two core loadings.
Figure 6-9 Difference in element power between CL54_shuffled vs. CL54
Since both cores are for a 1 MW power, there is a redistribution in power. The six
positive peaks indicated in Figure 6-9 (values above 10% difference), are the fresh fuel, which
replaced partially burned fuel elements.
The reactivity estimation of the two cores is shown in Table 6-1.
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
82
85
88
91
94
97
10
0
10
3
Fuel elements 1-105
Central Thimble
150
Table 6-1 estimating CL54 to CL54_shuffled reactivity
CL54_Shuffled [$] CL54 [$] Measured [$]
ARI-worth removed (0.944 ±0.00056) 8.47 (0.94951 ±0.00047) 7.59 ( 0.952) 7.18
1MW Power Defect
Reactivity loss[$]
5.33062±1.36 3.8112±0.74 3.72
ARO from 1MW (1.00826 ±0.00053 ) 1.17 (1.01643±0.00050) 2.309 (1.015 ) 2.11
Excess reactivity[$] 5.33+1.17 = 6.50 3.8112+2.309 = 6.12 5.83
Total reactivity[$] 14.97 ± 1.49 13.71 ± 0.82 13.01
Figure 6-10 shows the thermal hydraulic comparison of the two core loadings.
Figure 6-10 Percent Difference in Temperature for CL54_shuff and CL54
151
If we compare the calculated results from Table 6-1 and Figure 6-10 the following
observations could be made. The two core loadings CL54 and CL54_shuffled contain the same
elements. CL54_shuffled has the six fresh 8.5wt% fuel in a different position (not in the center as
in CL54). The difference of this change has delivered an overall higher reactivity of
approximately 1.2$. The reactivity of TRIGA reactors are mainly due to the temperature changes
of the fuel and the moderator. The Figure 6-10 shows a temperature increase in most elements in
the core. The results shows, up to 8% higher fuel temperature for the fresher fuel and an overall
2-4% increase of temperature for the C&D-ring 12 wt% fuel elements. Temperature-induced
reactivity is the highest contributor of reactivity change in TRIGA reactors. The Figure 6-9
indicated a 10-17% increase in power over the elements of higher density power (six fresh fuel
elements). The estimated control rod reactivity loss value is 1.5$ higher than the CL54 value.
What this means for this core configuration is:
The reactivity loss from ARI to 1MW power is higher because a bigger span of
core elements has higher temperatures, resulting in a higher negative temperature
coefficient.
The power distribution in Figure 6-9, shows there is a decrease in power around
the center core elements, hence, the flux, which normally peaks around the center
(as in the CL54 case), has a lower peak, and the flux toward the area where the
fresh fuel is inserted is higher.
ARI reactivity difference is 0.79$. The core CL54_shuffled is more reactive, than
CL54.
152
6.3 Core design scenario 3
This section outlines the findings of the addition of a new 30/20 (30 weight percent
uranium. 20% enriched) LEU (Low enriched) TRIGA fuel to the already mixed core loading. For
these findings there is no measured data as this fuel has not yet been loaded into the core. To
study the characteristics of this new fuel is exactly why the use of this TRIGSIMS-TH tool is
necessity.
6.3.1 Description of the fuel
The 30/20 LEU TRIGA fuel, have the same geometrical specifications as the standard
TRIGA fuel design but differ in material composition as shown in Table 6-2 .
Table 6-2 Fuel comparisons
TYPE 30/20 LEU 8.5wt% & 12wt%
Weight % Erbium 0.9 0.0
U-235 [g/element] 162 39 & 56.32
Enrichment < 20% < 20%
Lifetime [MWd] 3000 100 (8.5wt%)
8 9.5
All these three fuel types are less than 20% enriched in 235
U. Table 6-2 shows that there
are many differences and quite few similarities. There is no erbium in the standard TRIGA fuel
elements. The 30/20 LEU fuel contains about 0.9 wt% of the burnable poison erbium, which also
enhances the prompt negative temperature coefficient. The erbium mixed in with the fuel does
153
not change the fuels characteristics. The effect of this erbium to the fuel is that the fuel can have a
higher enrichment of uranium, like in the 30/20 LEU [54]. Measurements of the thermal
conductivity for these fuels were found to be the same, and that the thermal conductivity is
independent of the uranium content of the fuel. The density of the 30/20 LEU fuel was calculated
using the uranium mass content of 750.16g [55].
6.3.2 Analysis
This section is an analysis of CL54 with the addition of six 30/20 LEU fuel elements
instead of the six 8.5 wt% fresh fuel. The loading pattern is as usual and the heavy uranium
content fuel is positioned around the center thimble. Using the control rod search methodology to
find the critical core at 1 MW power gives the following results.
Figure 6-11 gives the keff convergence with its corresponding control rod position convergence
and average fuel temperature convergence results. This result is purely for analysis purposes and
does not have a validating information to support the findings. This example of analysis is for the
purpose to shows the versatility of the control rod method and the results that can be calculated
using the TRIGSIMS-TH code systems.
154
Figure 6-11 CL54+6 30/20 LEU convergence results
0 2 4 6 8 10 12 14 16 18
0.96
0.98
1
1.021MW core power with feedack
Kef
f
# iterations
0 2 4 6 8 10 12 14 16 180
10
20
30
Co
ntr
ol
rod
po
siti
on
[cm
]
# iterations
0 2 4 6 8 10 12 14 16 180
200
400
600
800
Av
era
ge f
uel
Tem
pera
ture
[
oC
]
# iterations
calculated
average estimated
calculated
average estimated
calculated
keff
=1
155
Figure 6-11 gives the results and show a convergence of the iterative process at about 18
iterations. The convergence shows a keff of approximately one at a control rod position of 24 cm
and an average 30/20 LEU fuel temperature of 594°C. For this core, the highest fuel temperature
is in the 30 wt% fuel elements, which is what is expected.
The following results show the temperature distribution as predicted by CTF for the
middle section of this core loading.
Figure 6-12 shows the full core fuel average temperature distribution for a critical core
CL54 +6 30/20 LEU fuel elements.
Figure 6-12 Temperature distribution of the 30/20 LEU fuel
156
6.4 Core design scenario 4: Analysis of the core with a D2O tank
The CL56 is analyzed with and without D2O tank. This has been an option with the
TRIGSIMS code. The user enters the flag for the addition of the D2O tank to the MCNP input.
TRIGSIMS writes this addition in the MCNP input, i.e., the geometry input is changed and the
input CL56 is illustrated in Figure 4-12. If the flag is set for D2O tank, the TRIGSIMS-TH will
write a CTF input, adding in the needed additions for flow restriction as a result of the geometry
change.
An unheated conductor is added to the CTF core model, representing the D2O tank. The
geometry of the adjacent channels is also changed. As part of the MCNP/CTF coupled calculation
in the TRIGSIMS-TH code, the input of this CTF, now containing the unheated conductor, is also
done with shortened channels with fewer nodes to speed up the calculation. Hence, this
calculation is also possible with the iterative coupling and control rod positioning methodology.
6.4.1 A comparison with and without D2O tank
Table 6-3 summarizes the findings of comparison of core analysis with and without D2O
tank.
Table 6-3 CL56 with and without D2O tank
Keff
With drum D2O
tank
With crescent D2O
tank
Without D2O
tank
ARI 0.95988 ± 0.00062 0.96944 ± 0.00069 0.95359 ± 0.00062
1MW 0.99986 ± 0.00056 1.00029 ± 0.00061 1.000003 ± 0.00058
Control rod pos (1MW) 25.8 cm 23.8 cm 27.5 cm
157
The results shown in Table 6-3 indicate a difference in reactivity of 0.98$ at ARI( for the
drum). The measured reactivity difference is approximately 0.42$. Thus, there is a variance of
approximately 56¢
Since the TRIGSIMS-TH gives us a more accurate account of the temperature
distribution as well as the power distribution and flux distribution, the studies for the modification
of the D2O tank [5] could be done with more accuracy. The thermal hydraulic analysis results for
the core with and without D2O tank addition is given in the next subsection.
6.4.2 Thermal Hydraulics comparison with D2O tank
The following analysis is a typical illustration of how to use the standalone method for
CTF application. In this example, the CTF parameters are examined for 3 cases, i.e., without D2O
tank , with current drum shape D2O tank and with a crescent shaped tank. Figure 6-13 shows the
MCNP representation of these cases.
Figure 6-13 Three cases to express the use of the CTF standalone model
It was shown in the previous chapter, Figure 5-30, that the addition of the D2O tank
creates higher power around the first few rows of fuel elements (directly adjacent to the tank).
158
This is an effect of the energy spectrum shift due to the D2O's effective moderation properties and
the reflection of the neutrons that would have been lost. Figure 6-14 shows the MCNP results of
the power distribution as a comparison of D2O tanks (drum and crescent), compared with no-
D2O tank.
Figure 6-14 The % difference in power distribution for the D2O tank shapes compared no tank
The results shows the new proposed crescent shape will result in a power with an
approximate maximum of 16% higher, compared with drum shape, around the front of the reactor
where the tank is situated. This increased power resulted in the temperature increase for the
elements adjacent to the tank. The power profiles used for the CTF calculation were prepared
through the TRIGSIMS-TH criticality calculation indicated as mode 1. After attaining the control
rod position with the temperature distribution for that 1MW power, the TRIGSIMS-TH is used
with mode 2, flagging the extended CTF model.
-20
-15
-10
-5
0
5
10
15
20
25
30
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106
%D
iffe
rence
com
par
ed w
ith n
o-t
ank
Elements
Drum compare to crescent shape tank: Difference in Power
distribution
drum crescent
159
The following result uses the CTF "stand-alone" application, and expanded option of the
core thermal hydraulic input, to analyze the flow and temperature for the various cases. The
comparison shown in Table 6-4 includes the following:
a) No D2O tank;
b) A drum shaped tank, as it is in the current TRIGSIMS (drum1);
c) A crescent shape as suggested in the thesis of Ücar [5].
The rods used for this analysis is the rod 4, directly adjacent to the tanks, the rod 13,
which is next to rod 4, but toward the center, and rod 46 which is the I-17 instrumental rod, which
is close to the center (see Figures 3-2 & 5-1).The channels used in this examples are the channels
adjacent to these rods. Table 6-4 gives the results for max fuel temperature in channel, the
maximum coolant temperature in the channel adjacent to the indicated rods and max channel
velocity.
Table 6-4 D2O tank comparisons
D2O Tank
Configuration
Rod Fuel temp [°C] Max-Channel temp
[°C]
Max-Velocity[m/s]
none
4
384.77 54.78 -0.179
Drum1 425.47 47.61 0.119
crescent 407.97 45.42 0.076 & -0.070
none
13
370.86 52.17 0.04
Drum1 341.26 54.67 0.119
crescent 423.73 53.38 0.119
160
none
46
(I-17)
473.79 61.06 0.082
Drum1 445.97 56.39 0.082
crescent 561.06 57.38 0.24
The cross flows for no-D2O tank to the CL56 are shown in Figure 5-36. The cross flows
for restriction of the flows due to the Drum shape tank is depicted in the following diagram –
Figure 6-14.
Figure 6-15 Illustration of the cross flow data for the channels adjacent to D2O to the
center of the core
The findings for this analysis are:
1) The D2O tank shape has a neutronic effect. It creates a higher localized power in the
fuel elements. The drum shape shows a fuel temperature for rod 4 of 11% higher than no-D2O
results. The crescent shape shows a higher fuel temperature of 6%. The flow at the adjacent
channel for the crescent shape is different compared with the drum shape. A small velocity in the
161
centre of the channel is calculated due to both upward top and downward bottom flow. The rods
13 and 46 for the crescent shape have higher temperatures compared with drum and no drum.
2) The heating of the fluid channel is a result of the fuel temperature (with conduction
from the clad to the water), the cross flow between adjacent channels because of the enthalpy
differences, and pressure differences and convection.
3) The cross flow illustration is very similar to that of the core without D2O. The bottom
of the fuel region has an inward flow while the top shows an outward flow. For the crescent shape
around the edge (at rod#4) of the core adjacent to the tank, the flow is only inward.
4) The crescent shape produces a higher fluid temperature in the centre and a velocity
twice as high compared with the drum shape. The fuel temperature is raised to ~19%.
Hence, the crescent shape will affect both the flow and the neutronics of the core
reactivity.
This result was presented as an illustration of the use of the CTF tool as a standalone
analysis tool.
162
Chapter 7 Conclusion and future work
7.1 Conclusion
The PhD contributions of this work are for the further developments of the TRIGSIMS
fuel management and analysis tool. These developments include:
1) Establishing a multi-physics coupling methodology, which provide the needed thermal
hydraulic feedback to the core analysis tool TRIGSIMS-TH. The addition of the best estimate,
advance sub-channel analysis code, CTF, is now automated in TRIGSIMS-TH to provide the
temperature predictions for the MCNP criticality calculations. TRIGSIMS-TH gives the MCNP
input a heterogeneous temperature distribution. The coupling was also extended to the
ADMARC-H code, which serves as an acceleration method for the MCNP calculation. The
results from the coupling methodology were compared with measured data from various core-
loadings. The findings were that the coupling of the CTF to MCNP was done successfully. The
ADMARC-H coupling with CTF though successfully done, the results could be improved.
2) Implementation of a critical control rod position search methodology was a needed
addition to the TRIGSIMS-TH code. Partially inserted control rods for a critical reactor (at
various power levels) can now be set and predicted with this method. The methodology is based
on the perturbation theory and computationally applied using a quasi-fixed iteration scheme. This
idea is unique and novel, and could only be attained with a thermal hydraulic feedback method
and the TRIGSIMS-TH code system. The results was compared with measured data and found to
be implemented successfully.
3) Development of the ADMARC-H homogenized cross section library, which models
thermal-hydraulic feedback instantaneous dependencies. The diffusion coefficient and cross-
section was developed using SERPENT, a Monte Carlo code. The results of the ADMARC-H,
163
diffusion code, with the newly generated cross sections delivered better results compared with
previous cross sections; however, there is room for improvements.
4) The addition of CTF to the TRIGSIMS-TH code has broadened the functionality of
this code system. TRIGSIMS-TH is now a design tool that could be used for safety analysis.
Formulation of a standalone model for CTF in TRIGSIMS-TH code involves a methodology that
includes both the neutronics and thermal hydraulics. In an automated system, the code is able to
perform the feedback mechanism by passing the needed neutronic parameters to the CTF code.
The CTF input for the standalone method will be extended (smaller and more nodes including
area above the grids) with information that can be calculated. The addition of a D2O tank as part
of the MCNP and now the CTF input could be added not only in this standalone model but also in
criticality calculation with iterations. This automated system was implemented successfully.
5) Various functional upgrades were made to enhance the codes capability or to correct
parameters for calculations. This includes; the addition of graphite elements as an option in the
code input for MCNP. A reassessment of the B4C used in the calculations. The application of
pseudo material approach and a reformulation to continuous energy cross section search
mechanism for the MCNP input. The moderator surrounding the core is adjusted for the number
of fuel elements. All these have shown an improvement to the previous results.
The results from improved calculations were validated against measured data form core
loadings CL65, CL54, CL53. The results were in a good agreement with the measured data at
most applications applied, though various shortcomings was identified. The conclusion of the part
of the work i.e., the multi-physics coupling was done successfully. The implementation of the
control rod search method has delivered with successful results. The TRIGSIMS-TH code system
with this control rod search method and thermal hydraulic feedback is now a complete design tool
for future core loadings. The method was used in analyses to show how the code can be used as
well as to show the versatility and applicability of this development. The thermal hydraulic code
164
CTF, that is now part of TRIGSIMS-TH code system, makes this a safety analysis tool. With this
development, various design limitations and safety and control issues can be analyzed.
The final product of this PhD work is a code system that works effectively, and is able to
analyze, design, burn and manage the PSBR reactor core.
7.2 Proposal for future work
7.2.1 Modify the D2O input
With the aim to modify the D2O tank, the MCNP and CTF inputs for tank shape will have
to be adjusted to fit the shape of the proposed tank. The current shape of the tank is rectangular.
For a horseshoe, or crescent, as it was proposed [5], the modification could also be done with
minimal code correction. Using the code as it is, for analysis on the shapes can also be done with
just a few CTF input changes. CTF is set up to give a basic core input. This input can be
incorporated with or without the D2O tank. CTF is also set up as a standalone thermal hydraulics
analysis tool with extended flow channels that goes above and below the grid plates. This
addition is very useful for analysis of the flow with restriction such as a modified D2O tank that
encloses the core.
7.2.2 Transient analysis with CTF/ADMARC-H
The TRIGSIMS and the TRIGSIMS-TH codes are currently set to perform steady state
and depletion calculations. With the addition of CTF, the thermal hydraulic module, the
TRIGSIMS-TH code is now able to perform transient calculations. Both the codes CTF and
ADMARC-H are equipped to do transient calculation. Further studies and modifications to the
165
ADMARC-H code is needed to make this possible. The control rod movement modeling and the
application using control rod method requires the development of rod cusping methodology[53].
This deficiency was seen in the results for ADMARC-H feedback mechanism.
7.2.3 Using the TRIGSIMS-TH to investigate the thermal hydraulic properties of the fuel
The results show the need to reevaluate the material properties of the CTF fuel rod model
(especially the thermal conductivity and specific heat capacity). Now with the feedback
mechanism and control rod position search and the thermal hydraulics component, the code can
be used for much more investigations. Thus, analyses that are more detailed require finer
assessment of important parameters. The heat capacity (Cp) and thermal conductivity (K) of the
various material properties in the fuel and water might not be linear [3]. Now with the
TRIGSIMS-TH tool this can now be analyzed and appropriate changes in the CTF fuel rod model
can be implemented to take into account the burnup and burnable poisons.
7.2.4 Addition of a in-core experimental tube within TRIGSIMS-TH
The thesis of Sahin [7], have shown the use of the in-core irradiation of samples at the
dry irradiation tubes. This type of experiments can be calculated with samples for various
materials or other uses. For this addition to the TRIGSIMS-TH, there ought to be a fixed sample
caddy (or tube-insert) that needs to become part of the MCNP geometry. This could be made as
an optional addition similar to the graphite elements and D2O tank in the TRIGSIMS-TH. The
TRIGSIMS-TH code has already the capability to include any material specific isotopic
inventory. All that is needed is to add a fixed geometry that will include the geometry of the
166
sample insert that goes into the dry irradiation tubes. This addition to the TRIGSIMS-TH makes
the use of the code versatile and more useful.
167
Appendix
Additional information
Measured data
Table A- 1Measured data
Power
[kW]
ΔρP
[c]
ΔT(F)
[°C]
[c/kW]
ΔT/ΔP
[°C/kW]
CL56
100 28 57.65 -0.56 1.153
200 23 40.8 -0.46 0.816
500 32 51.2 -0.32 0.512
700 26 33.15 -0.26 0.3315
800 22 28.4 -0.22 0.284
900 22 24.7 -0.22 0.247
CL54
100 29 52.05 -0.58 1.05
200 22 39.85 -0.44 0.797
500 34 48.2 -0.34 0.482
700 28 31.1 -0.28 0.311
800 26 26.3 -0.26 0.263
900 26 23.35 -0.26 0.2335
CL53
100 24 79.2 -0.48 1.584
200 18 31.9 -0.36 0.638
168
500 30 40.8 -0.30 0.48
700 23 29.6 -0.23 0.296
800 22 29.0 -0.22 0.290
900 21 26.1 -0.21 0.261
Table A- 1Measured data gives the power coefficient and temperature difference of the
reactor per change in power. The power coefficient, is an aggregate showing the change in reactor
reactivity per unit change in reactor power. The reactivity of the system decreases as the power
increase, hence the negative power coefficient.
As per the thesis of Tippayakul [2], the measurements taken had some degree of
uncertainty. This uncertainty was not known. However, comparing the in-hour and rod-drop
measurements for control rod worth, the standard deviation was assumed approximately to be
10%.
Core loading diagrams used in this thesis
Figure A- 1and Figure A- 2 show the core loading configurations used in the thesis to
provide the measured core results. These figures show the core design, the fuel elements 12 wt%
and 8.5 wt%, the, control rods, the dry irradiation tubes and the position where the source is
inserted into the core. The core-loading diagram for CL56 is given in Figure 3-2 .
169
Figure A- 1 CL54 Core loading diagram
Figure A- 2 CL53H core loading diagram (includes the position for graphite)
170
SERPENT calculations compared with MCNP calculations
Figure A-3 shows the burnup calculation of the MCNP compared with the SERPENT
calculation for a single pin (fuel element). The results are in steps of 143 days, which is the
equivalent of 5 MWD/MTU per step. The burnup steps are equally spaced which is an indication
that the error is consistent throughout the calculation.
Figure A-3 Comparison of the Keff values after each burnup step
B4C calculations
Assessment of the burnup of the B4C in the core
The following analysis shows the results of the effect of reducing the number densities of
the control rod neutron absorbing material B4C. The number densities were calculated by the
SERPENT code. The code burnup was done with the model shown in Figure A- 4
1.38
1.40
1.42
1.44
1.46
1.48
1.50
0 0.5 1 1.5 2 2.5 3 3.5
Serpent vs MCNP, keff per burnup step
serpent
mcnp
171
Figure A- 4 Model for burnup of B4C
The B4C rod is centered between six of the fresh 12 wt% fuel. The calculation was done
at various burnup intervals.
Table A- 2 shows the results of the MCNP5 calculation for various core conditions and
burnup days. The number density of the B4C is indicated in Table 5-9. The core loading used is
CL56. This result shows the effect of the burned B4C on the keff calculation. The differences are
for conditions at 300K and 900K are negligible.
Table A- 2 Decrease in B4C number densities effect
Condition days keff
ARI at 300K 363.69 0.95017±0.00048
ARI at 300K (reference) No burnup of B4C 0.95064±0.00045
ARI at 900K 163 0.99834±0.00046
ARI at 900K 406 0.99759±0.00050
ARI at 900K(reference) No burnup of the B4C 0.99752±0.00047
172
MCNP standard deviation
The calculations of TRIGSIMS-TH tool revolve around the MCNP5 code. MCNP is a
statistical code that determines the neutron distribution in the reactor. Thus the results that is
produced from this code is an approximation (statistical estimate), which lies within a certain
confidence interval. This interval is determined by the particle histories followed (tracked). A
larger sample size will deliver a better estimate. Suppose MCNP yields a successive random
variable x with a sample mean;
0.1
where N is the number of histories and is random walks, or scores. MCNP results are
given as where is the standard deviation. MCNP estimate S, which is given by
, which is the estimated standard deviation, and
, where S the standard
deviation is estimated as [47].
It is important to note that accuracy refers to how close to the true physical value the
value comes, and the difference between the true value and the sample mean is the statistical
error, which is usually unknown. MCNP refers only to the precision of the results and not to the
accuracy [12]. The defaulted confidence interval is given as σ (68%), and throughout this thesis
calculation, this is the confidence interval used.
MCNP5 Convergence of the PSBR TRIGSIMS -TH model
The TRIGSIMS-TH code uses MCNP5 as the main neutronics solver. The two most
important aspects for a criticality calculation are to ensure that all the material in the design
problem is sampled and that a fundamental eigenvalue (keff) is reached before or during an active
cycle. MCNP has statistical checks that will ensure both are achieved. It is advisable that the user
173
check both the fission source entropy (Shannon entropy source distribution) and the keff, track
length for convergence.
The following results shows convergence results for the CL56.Using a batch size of 5000
neutrons. The results were taken at 1MW power distribution.
The results have indicated that using a 3D grid to sample the Shannon source entropy
convergence check was passed, and that the cycle 4 is the first cycle having fission source
entropy within 1 standard deviation of average entropy distribution (given as 4.4) which is also
indicated in the Figure A- 5. Showing the Hsrc (cycle n+1) vs Hsrc (cycle n).
Figure A- 5 Shannon fission source entropy convergence check 1
The followings Figure A- 6 and Figure A- 7 compare the convergence of keff and Hsrc
source distribution data. It is favorable that the source converges before the keff.
4.30
4.35
4.40
4.45
4.50
4.55
4.30 4.35 4.40 4.45 4.50 4.55 4.60
Hsr
c (c
ycl
e-n
+1)
Hsrc (cycle n)
174
Figure A- 6 Shannon fission source entropy convergence check 2
Figure A- 7 Convergence check of the keff values using different skipped cycles
The results from Figure A- 6 shows that the fission source entropy has indeed converged
before the keff value. The keff value has seen convergence around 100 cycles. Thus, using 5000
neutrons/cycle, a minimum 400 cycles would be advised for this calculation. The thesis of
Tippyakul [2], has explicitly investigated the skipped cycles as means of speed up. He has found
that the high number of skipped cycles can be reduced if more accurate approximation of initial
fission source is utilized. Using initial fission source from nodal diffusion results reduces the
number of skipped cycles and saves up to 8.5% of the time to calculate a PSBR model.
4.30
4.35
4.40
4.45
4.50
4.55
4.60
0 100 200 300 400 500 600
Hsr
c
cycle
0.990
0.992
0.994
0.996
0.998
1.000
1.002
0 100 200 300 400 500 600
Kef
f
cycles 50 skipped …
175
Normalization factors
Criticality calculation normalization:
For a steady state power of 1 MW the following are the normalization factors used for the
MCNP calculation herein (i.e. the flux, f4 tallies and fmesh ) .
0.2
Thus for P watts of power, one needs 3.467 x 1010
P fissions per second. This power level
produces 3.467 x 1010
x P x ν neutron/sec. (ν~2.41 fissions/neutron).[41]
For the criticality normalization, the value 8.36 x 1016
neutrons/sec is the multiplying
factor for a 1MW power.
176
REFERENCES
[1] RSEC, Radiation Science and Engineering Website: www.engr.psu.edu, Celebrating 60
years of Nuclear research at Penn State (Article)
[2] Tippayakul, C., (2006): Development of practical fuel management system for PSBR
based on advanced three-dimensional Monte Carlo coupled depletion methodology, Thesis
for Doctor of Philosophy
[3] Karriem, V., (2011): PSBR core design studies of the D2O tank design and new LEU fuel
utilization, MS Thesis, Pennsylvania State University.
[4] IAEA, website (ansn.iaea.org) for Education and Training, Nuclear safety and security,
TRIGA reactor characteristics
[5] Ücar, D.,(2013):Modeling and design of a new core-moderator assembly and neutron
beam ports for the Penn State Breazeale nuclear Reactor (PSBR), Thesis for Doctor of
Philosophy
[6] Ücar, D. et al,(2012) : Thermal hydraulic analysis of the new Penn State Breazaeale
reactor core design using ANSYS Fluent code., ANS paper (June 2012)
[7] Sahin, D., (2012): Tracing footprints of environmental events in tree ring chemistry using
nuclear activation analysis, Thesis for Doctor of Philosophy
[8] Sahin, D.,et al, (2012) : Modeling transient mechanisms for Penn State Breazeale nuclear
reactor core neutronic analysis., ANS paper (June 2012)
[9] Sahin ,D. et al, 2015; Neutronic analysis of the the PSBR using a burnup-coupled MCNP
simulation with MURE, Nuclear Technology, Volume 194
177
[10] MacFarlane, R.E, (1999): NJOY 99.0 Code system for producing pointwise and
multigroup neutron and photon cross sections from ENDF/B data., Los Alamos National
Laboratory
[11] Scale5.1 RSICC code package CCC-732
[12] X-5 Monte Carlo Team, (2003) : "MCNP - A General N-Particle Transport Code, Version
5 - Volume I: Overview and Theory", LA-UR-03-1987, Los Alamos National Laboratory
[13] De Hart, M., (2004): “TRITON a two-dimensional depletion sequence for characterization
of spent nuclear fuel”, Oak Ridge National Laboratory.
[14] Kraingchairporn,N, (2001): Advanced fuel management system (AFMS) for PSBR., MS
Thesis, Pennsylvania State University
[15] Kraingchairporn, N., (2006): Transport model based on 3-D cross section generation for
TRIGA core analysis. PhD thesis, Pennsylvania State University.
[16] Chang, J.E., (2004): Thermal Hydraulic Modeling of the Pennsylvania State University
Breazeale Nuclear Reactor , Thesis of Doctor of Philosophy Chang, J.E., (2004): Thermal
Hydraulic Modeling of the Pennsylvania State University Breazeale Nuclear Reactor,
[17] Feltus,M.,et al, (1999) : Three dimensional coupled kinetics/thermal hydraulic benchmark
TRIGA experiments. Annals of Nuclear Energy 27 (2000) 771-790
[18] Gougar, H.D., (1997): Development and modeling of coolant flow control in the Penn
State Breazeale Reactor, Thesis for Master of Science.
[19] Ivanov, A., et al, (2012) : Optimization of a coupling scheme between MCNP5 and
SUBCHANFLOW for high fidelity modeling of LWR reactors. PHYSOR paper
178
[20] Ivanov, A.,et al, (2013): High fidelity simulation of conventional and innovative LWR
with the coupled Monte Carlo thermal hydraulic system MCNP-SUBCHANFLOW,
Nuclear engineering and design 262:264-275
[21] Puente-Espel, F., (2010): High accuracy modeling for advance nuclear reactor core design
using Monte Carlo based coupled calculations. PhD thesis, Pennsylvania State University
[22] National Nuclear data Centre; website, http://www.nndc.bnl.gov/endf/
[23] Kozmenkov,Y.,et al : V1000CT-1 Benchmark analyses with the DYN3D/RELA5 and
DYN3D/ATHLET coupled code systems.
[24] Avramova, M.N, (2003): COBRA-TF Development, qualification and application to LWR
Analysis, MS Thesis, Pennsylvania State University
[25] Avramova, M.N., (2007): Development of an innovative spacer grid model utilizing
Computational Fluid Dynamics within a sub-channel analysis tool, Thesis for Doctor of
Philosophy
[26] Blyth,T., (2014): Improvement of Cobra-TF sub-channel thermal hydraulic (CTF) using
computational fluid dynamics, CASL-U-2015-0002-000
[27] Salko,R., et al, (2015): COBRA-TF sub-channel thermal-hydraulic code (CTF) theory
manual,CASL-U-2015-0054-000
[28] Huda,M., et al: Monte Carlo simulation of the 3MW TRIGA MARK II benchmark
experiments
[29] Saygin, H., (1998): A comparison between the results of perturbation theory and TRIGAP
for the reactivity worth calculations of fuel elements, Annals of nuclear energy, Vol 25,
No14, pp:1133-1140 section generation for TRIGA core analysis. PhD thesis,
Pennsylvania State University.
179
[30] Garis, N., et al, (1998) : Determination of PWR control rod position by core physics and
neural network methods., Nuclear Technology, vol.123
[31] DOORS 3.2, 2003; One, two and three-dimensional discrete ordinates neutron/proton
transport code system, Oak Ridge National Laboratory
[32] Oka,Y.(2010): Nuclear reactor design, An advanced course in Nuclear Engineering
,Tokyo, Japan
[33] Safety Analysis Report 2005; Safety Analysis Report for the renewal of license R-2 for the
Breazeale Nuclear Reactor , PSBR, RSEC
[34] Duderstadt, J, Hamilton, L., 1976: Book, Nuclear Reactor Analysis
[35] Lamarsh, J.R., et al, (2001): Introduction to Nuclear Engineering, Third Edition.
[36] Leppanen, J., (2009): SERPENT - a Continuous-energy Monte Carlo Reactor Physics
Burnup Calculation code, RSICC computer code collection, Oak Ridge National
Laboratory.
[37] Ursu, I., (1985):Physics and technology of nuclear materials, Pergamon (publisher)
[38] TRIGSIMS Manuel, Prepared by RDFMG
[39] Wargon, M, (2015): Safety analysis of the new core moderator assembly for the Penn
State Breazeale Reactor, PSU, MS thesis.
[40] Kazimi, M.,et al, (1980): A condensed review of nuclear reactor thermal hydraulic
computer codes for two-phase flow analysis. Report no MIT-EL 79-018.
[41] X-5 Monte Carlo team, 2001: MCNP5-A General Monte Carlo N-Particle Transport Code,
Version 5, Volume II: User's Guide
[42] TRIGSIMS manual, maintained at the RSEC,PSU
180
[43] Simnad,M., Nuclear reactor materials and fuels reactor thermal-hydraulic computer codes
for two phase flow analysis, MIT
[44] Docket No 50-005 (2009): Facility Operating License R-2, Technical Specification for the
Pennsylvania State University Breazeale Reactor.
[45] Radiation Center, OSU, 2007; Safety analysis report for the conversion of the Oregon state
TRIGA reactor from HEU to LEU Fuel
[46] Tombakoglu,M.,(2001): Control rod worth evaluation of TRIGA MARK II, reactor,
Nuclear Energy in Central Europe
[47] Brown, F., (2011): "K-effective of the World" and other concerns for the Monte Carlo
eigenvalue calculations, Nuclear Science and Technology, Vol.2,pp 738-742
[48] TRIGA Nuclear Reactors, GENERAL ATOMICS, http://ga.com
[49] Gauld, I, et al,(2006): ORIGEN-S: Scale system module to calculate Fuel depletion,
actinide transmutation, fission product buildup and decay and associated radiation.
[50] Fridman, E. et al, (2011): On the use of the SERPENT Monte Carlo code for few-group
cross section generation, Annals of Nuclear Energy
[51] Dorval,E., et al, (2014) : Monte Carlo current-based diffusion coefficients: Application to
few-group constants generation in SERPENT, Annals of Nuclear Energy
[52] Hawley,S.,et al,(1982): Credible Accident analyses for TRIGA and TRIGA-Fueled
Reactors, Pacific Northwest National Laboratory
[53] Kibog, L.,et al.,1998; Correction of control rod cusping effect using one dimensional fine
mesh flux profiles. Proceedings of Korean Nuclear Society Autumn Meeting, Korea
181
[54] Docket no 50-163, NUREG-1282, (1987): Safety Evaluation Report on High-Uranium
content, Low-Enriched Uranium Zirconium hydride fuels of TRIGA reactors, USNRC
[55] Bess, J., et al, (2011): Fresh-Core reload of the Neutron radiography (NRAD) reactor with
Uranium (20)-Erbium-Zirconium-Hydride fuel. INL
VITA Veronica V. Karriem
Veronica Karriem was born on May 23, 1972 in Cape Town, South Africa. She attended
the University of the Western Cape, in South Africa, for her Bachelor of Science degree.
Thereafter she attended the University of South Africa (UNISA) for further studies. The focus of
her degree was Physics. Her career path in South Africa was varied. She worked in the local
industries, at UNISA and at the South African nuclear energy corporation (NECSA). Together
with her husband and kids, she moved to the United States in 2008, where she endeavored to do
graduate studies at Pennsylvania State University. Serving as graduate assistant in the Nuclear
Engineering Department and being involve with research and design modeling of the PSBR
TRIGA has been a great learning experience for her. She completed her Masters degree in 2011.
Soon after this, she continued with her PhD studies, which now comes to a completion.