safety analysis of the new core-moderator assembly …

The Pennsylvania State University

The Graduate School

Department of Mechanical and Nuclear Engineering

SAFETY ANALYSIS OF THE NEW CORE-MODERATOR ASSEMBLY FOR

THE PENN STATE BREAZEALE NUCLEAR REACTOR

A Thesis in

Nuclear Engineering

by

Matthew Wargon

©2015 Matthew Wargon

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

August 2015

ii

The thesis of Matthew Wargon was reviewed and approved* by the following:

Kenan Ünlü

Professor of Mechanical and Nuclear Engineering

Director of Radiation Science and Engineering Center

Thesis Advisor

Maria Nikolova Avramova

Associate Professor of Nuclear Engineering

Brenden Heidrich

NSUF R&D Infrastructure Lead

Nuclear Science User Facilities

Idaho National Laboratory

Arthur Motta

Chair of Nuclear Engineering

Professor of Nuclear Engineering and Materials Science and Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

In the ever-evolving world of nuclear engineering, new technology is constantly

being discovered and developed to further benefit mankind. New technology is

introduced every day, which can be used to perform new, exciting, and innovative

research. The Penn State Breazeale Reactor at the Radiation Science and Engineering

Center is no exception to wanting to be at the forefront of nuclear science and technology.

The facility currently has plans that call for a major expansion and overhaul of its current

neutron beam lab facility, which include a new core-moderator assembly and new

neutron beam ports. Past analyses have completed the design and some analysis of this

new core and moderator tank assembly, but the work has not yet been finalized. Before

installation of the core-moderator assembly, the thermal-hydraulic behavior of this new

system must be analyzed.

The goal of this work is to use a combination of MCNP6 and RELAP5-3D®to

confirm the results of prior analyses of this new core-moderator assembly, and to

generate a safety analysis report. MCNP6 will be used to calculate relevant neutronic

core parameters, and RELAP5-3D® will be used to perform a thermal-hydraulic safety

analysis of the system. The results of the thermal-hydraulic safety analysis were chiefly

compared to the work of Dr. Dündar Uçar, the original designer of the new assembly.

After comparing the results of the RELAP5-3D®analysis to past work and in-core

measurements, it was concluded that the RELAP5-3D®results were sufficiently accurate,

and the past work can also be confirmed as accurate. While Dr. Uçar’s work was not

able to calculate a sufficient fuel temperature, a proper value was calculated in RELAP5-

3D® that is considered a good match when compared to previous experimental

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measurements. This work shows that, at least from a steady-state standpoint, the

proposed new design for PSBR will operate safely under all normal conditions.

v

List of Abbreviations ............................................................................................................ vii

List of Figures ........................................................................................................................ viii List of Tables ............................................................................................................................. x

Acknowledgments .................................................................................................................. xi Chapter 1: Introduction ......................................................................................................... 1 1.1 Motivation .................................................................................................................................... 2 1.2 Thesis Structure ......................................................................................................................... 6

Chapter 2: Literature Review .............................................................................................. 8 2.1 Relevant Past Work from PSU ................................................................................................ 8 2.1.1 MS Thesis of Veronica Karriem ...................................................................................................... 8 2.1.2 PhD Dissertation of Dr. Dündar Uçar ........................................................................................ 11

2.2 Relevant Past Work from Outside of PSU ....................................................................... 15 2.2.1 MS Thesis of Wade Marcum ......................................................................................................... 16

2.3 PSBR Safety Analysis Report ............................................................................................... 19 2.4 Review of the Computational Tools .................................................................................. 20 2.4.1 RELAP5-‐3D .......................................................................................................................................... 20 2.4.2 MCNP6 ................................................................................................................................................... 21

Chapter 3: The PSBR Facility and Experimental Setup ............................................ 22 3.1 Use of the Facility .................................................................................................................... 22 3.2 Past Core: 53H .......................................................................................................................... 31 3.3 Current Core: 56 ...................................................................................................................... 31 3.4 Proposed Future Core: NBL ................................................................................................. 34

Chapter 4: Thermal-‐Hydraulic Models of the PSBR Facility .................................. 36 4.1 Steady-‐State RELAP5-‐3D®Models ..................................................................................... 36 4.1.1 Single-‐Channel RELAP5-‐3D®Model ......................................................................................... 37 4.1.2 Coolant Source and Sink ................................................................................................................. 39 4.1.3 Cold Leg (Downcomer) ................................................................................................................... 41 4.1.4 Horizontal Connection .................................................................................................................... 41 4.1.5 Hot Leg ................................................................................................................................................... 42 4.1.6 Hot Leg Heat Structure ................................................................................................................... 45

4.2 CHF Correlations ..................................................................................................................... 50 4.2.1 Bernath CHF Correlation ............................................................................................................... 52 4.2.2 AECL-‐UO CHF Lookup Tables ...................................................................................................... 53

Chapter 5: Steady-‐State RELAP5-‐3D®Simulation Results ...................................... 55 5.1 Results and Comparison of PSBR Core 53H ................................................................... 56 5.2 Results and Comparison of Current PSBR Core 56 ...................................................... 58 5.3 Results and Comparison of Proposed Future Core NBL ............................................. 61

Chapter 6: Conclusion and Future Work ...................................................................... 68 6.1 Conclusion ................................................................................................................................. 68 6.2 Future Work .............................................................................................................................. 71

Works Cited ............................................................................................................................ 72

Appendix A: Sample RELAP5-‐3D® Input Deck for PSBR Core 53H ..................... 74 Appendix B: MATLAB Transient Pulse Script ............................................................. 90

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Appendix C: RELAP5-‐3D® Transient Control Block Sample .................................. 92

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List of Abbreviations

CFD computational fluid dynamics CHF critical heat flux HEU high-enriched uranium LEU low-enriched uranium NBL Neutron Beam Lab RSEC Radiation Science and Engineering Center PSBR Penn State Breazeale Reactor PSU The Pennsylvania State University SAR safety analysis report USNRC United States Nuclear Regulatory Commission OSTR Oregon State TRIGA Reactor TRIGA Training, Research, Isotopes, General Atomics DNBR departure from nucleate boiling ratio MDNBR minimum departure from nucleate boiling ratio

viii

List of Figures

Figure 1: Current configuration of beam lines top-down view. [4] ................................... 3 Figure 2: Axial location of current beam lines. [4] ............................................................ 4 Figure 3: Proposed new moderator tank and beam line configuration. [4] ....................... 5 Figure 4: A rudimentary new moderator tank and core design as postulated by Karriem.

[6] .............................................................................................................................. 10 Figure 5: New moderator tank design as seen in AutoCAD. [7] ..................................... 12 Figure 6: New top and bottom grid plates designed for the new moderator tank. [7] ..... 12 Figure 7: Hypothetical flow field in and around the reactor in its current configuration.

[7] .............................................................................................................................. 14 Figure 8: Hypothetical flow field in and around the reactor in its proposed new

configuration. [7] ...................................................................................................... 14 Figure 9: Single (hot) channel model with no cross-flow next to a two-channel model

with cross-flow. [8] ................................................................................................... 17 Figure 10: Sensitivity study of relation between equilibrium quality and mass flux to

CHF. [8] .................................................................................................................... 19 Figure 11: View of the PSBR reactor pool with cutaways. [9] ....................................... 23 Figure 12: TRIGA fuel element diagram. [9] .................................................................. 25 Figure 13: Diagram of an instrumented TRIGA fuel element. [9] .................................. 27 Figure 14: Operating orientations of the three normal control rods. [9] .......................... 29 Figure 15: The transient control rod. [9] .......................................................................... 30 Figure 16: Loading pattern for Core 53H. ....................................................................... 32 Figure 17: MCNP6 generated map of XY axis of Core 53H. .......................................... 32 Figure 18: Loading pattern for Core 56. .......................................................................... 33 Figure 19: MCNP6 generated map of XY axis of Core 56. ............................................. 33 Figure 20: MCNP6 generated map of XY axis of Core 53H coupled to the proposed new

moderator tank. ......................................................................................................... 35 Figure 21: Block diagram of the Core 53H RELAP5-3D®model (not to scale). ............ 38 Figure 22: Nodalization of hot-channel pipe component. ............................................... 42 Figure 23: Graphical representation of hot channel and flow area. ................................. 44 Figure 24: Cross-section of a single radius of the hot-channel heat structure. ................ 45 Figure 25: Parametric study of gas gap thickness. ........................................................... 49 Figure 26: Graphical representation of the general pool boiling curve showing CHF. [17]

................................................................................................................................... 52 Figure 27: Axial bulk fluid temperature as calculated by Dr. Uçar. [7] .......................... 55 Figure 28: Axial bulk fluid temperature profile of Core 53H, calculated by RELAP5-3D.

................................................................................................................................... 57 Figure 29: CHF ratio along the heated length of the fuel rod in Core 53H, calculated by

RELAP5-3D. ............................................................................................................. 58 Figure 30: Axial bulk fluid temperature profile of Core PSBR 56, calculated by

RELAP5-3D. ............................................................................................................. 60 Figure 31: CHF ratio along the heated length of the fuel rod in PSBR Core 56, calculated

by RELAP5-3D. ........................................................................................................ 60

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Figure 32: CHF ratio along the heated length of the fuel rod of the same conditions as Dr. Ucar, calculated by RELAP5-3D®for future core. ................................................... 63

Figure 33: Axial bulk fluid temperature profile of the technical specification limits, calculated by RELAP5-3D®for the future core. ...................................................... 64

Figure 34: CHF ratio along the heated length of the fuel rod in the technical specification limits, calculated by RELAP5-3D®for the future core. ........................................... 65

Figure 35: Temperature rise in the hot channel for all simulations. ................................ 66 Figure 36: Bernath CHFR for all simulations. ................................................................. 67

x

List of Tables

Table 1: Summary of RELAP5-3D®models. .................................................................. 37 Table 2: Geometric dimensions of the coolant source/sink. ............................................ 38 Table 3: Coolant source/sink initial temperature and pressure. ....................................... 39 Table 4: Geometric specifications of the cold leg. .......................................................... 39 Table 5: Hot channel pipe component lengths. ................................................................ 39 Table 6: Hot-channel geometric specifications. ............................................................... 39 Table 7: Axial power shape for Core 53H. ...................................................................... 43 Table 8: Radial power shape for Core 53H. .................................................................... 46 Table 9: Node locations and materials inside hot-channel heat structure. ....................... 47 Table 10: RELAP5-3D®simulation results as compared to prior work. ......................... 56 Table 11: RELAP5-3D®results compared to a fuel temperature measurement from the

current core. .............................................................................................................. 59 Table 12: RELAP5-3D®results from proposed core compared to results from Dr. Uçar.

................................................................................................................................... 61 Table 13: RELAP5-3D®results from the technical specification limit simulation of the

proposed Core NBL. ................................................................................................. 62 Table 14: MDNBR value of each core for each CHF correlation. .................................. 66

xi

Acknowledgments

First and foremost I would like to thank Dr. Kenan Ünlü for his support, advice,

and guidance throughout my time as a graduate student at Penn State. Without his

support, none of this work could have been possible, and I am very grateful for that. I

would also like to thank the rest of the staff at the Radiation Science and Engineering

center for their support throughout this process. I would also like to express my sincerest

gratitude to Dr. Brenden Heidrich, without whom this work would certainly not have

been completed.

I would also like to acknowledge the other members of my research group, for

keeping me from on track, and helping me reach my goal. Finally, I would not have

made it through graduate school without the help of my best friends, Mike, Seth, Aaron,

and Erica from keeping me from going crazy, and my family who have always pushed

me to be the best that I can be, no matter what I do.

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Chapter 1: Introduction

Since the construction of the man-made nuclear reactor at the Chicago Pile 1 in

1942, hundreds of reactors have been built worldwide [1]. Of these hundreds of reactors,

there are two major categories: power reactors and research and test reactors. The first

category, power reactors, is what is commonly thought of as nuclear reactors. These are

used to generate electricity by spinning a turbine-generator with steam generated by

passing water through the reactor core. There are currently 435 commercial nuclear

power reactors in operation today with about 70 new units under construction worldwide

[2]. While power reactors can be dual-use technology, such as generating hydrogen or

purifying water, the main focus of the current worldwide fleet of nuclear power reactors

is to generate electrical power. Research reactors, of which there are currently 240 in

operation worldwide, are used for a myriad of other purposes, such as research and

training, materials testing, or the production of radioisotopes for medicine and industry

[3]. Materials testing reactors, such as the Jules Horowitz Reactor currently being built in

Cadarache, France, are used to test the influence of and reaction to radiation fields on

materials, specifically those used in nuclear reactor components. Radioisotope

production reactors are used to generate isotopes that are useful in industrial or medical

settings such as the generation of molybdenum-99 from neutron activation of

molybdenum-98 for use in obtaining technetium-99m, an important medical isotope used

in diagnosis or treatments of various medical conditions. Research and training reactors

are used to perform all other functions that a nuclear reactor can fill with its unique

properties.

2

The research and training type of research reactor is of particular interest in the

university setting due to the sub-group’s long list of capabilities. In addition to training

students through class work and formal operator training, research and training reactors

can be used for many research purposes. This list includes, but is not limited to, studies

utilizing neutrons, studies utilizing gammas, irradiations, and isotope production.

Research and training reactors are thus quite valuable, especially if they can be optimized

to their fullest extent.

The Radiation Science and Engineering Center (RSEC) at PSU houses the Penn

State Breazeale Reactor (PSBR), which is a TRIGA Mark-3 research and training reactor.

The PSBR is used both for training students and reactor operators, and for research and

isotope production. The reactor has been in operation in its current form since 1965, and

current plans call for upgrading the reactor to extend its utility and value far into the

future.

1.1 Motivation

The PSBR was originally built as and began operations in 1955 as an

open-pool materials test reactor. This reactor used aluminum-clad, plate-type high-

enriched uranium (HEU) fuel during its short life span. The core was suspended from a

bridge above the 71,000-gallon pool, which was attached to rails and allowed the core to

traverse the pool. When originally built in 1955, the PSBR was fitted with seven neutron

beam-ports that would be used to perform different studies that utilized neutrons. The

entrance to these beam ports is in heavy water (D2O) moderator tank so that the core

could be moved and coupled as shown in Figure 1. Figure 2 shows the axial beam port

3

arrangement. In 1965, the PSBR was converted to its new and still current operating

state as a TRIGA Mark-3 reactor. The TRIGA reactor, which stands for Training,

Research, Isotopes, General Atomics, is described by General Atomics as being the most

widely used non-power nuclear reactor on the planet with 66 units installed worldwide

[4]. Unfortunately, when the core conversion project was finished, only two of the seven

neutron beam lines (#4 and #7) were at an adequate position to be used when coupled

with the new TRIGA core. The TRIGA® fuel is 15 inches tall versus the 24 inch tall

MTR fuel. Only one beam port was properly aligned after the core conversion.

Figure 1: Current configuration of beam lines top-down view. [4]

4

Figure 2: Axial location of current beam lines. [4]

The new Neutron Beam Laboratory (NBL) project at the PSBR aims to regain

much of the functionality lost when the core was converted to a TRIGA. The goal of the

project is to implement a new D2O moderator tank with five replacement neutron beam

ports including a cold neutron source with three neutron guides as shown in Figure 3.

These new ports in the new D2O moderator tank would be optimized for use with the

current TRIGA core, thus attaining peak efficiency. The beams would also lead to a

brand new NBL, which would employ all of the currently used neutron beam techniques

plus new ones that the current system does not utilize.

5

Figure 3: Proposed new moderator tank and beam line configuration.

[4]

The goal of this work is to perform a safety analysis of the reactor core using

RELAP5-3D®in its proposed new conditions to qualify the final stages of the project.

Previous design work has been completed on this project by Veronica Karriem, a fellow

graduate student, and Dr. Dündar Uçar of PSU in their MS thesis and PhD dissertation

respectively. The past work was based on studies performed on Core 53H of the PSBR.

Karriem used a subchannel code (COBRA-TF) for her studies, and Dr. Uçar mainly used

a computational fluid dynamics (CFD) code (ANSYS FLUENT 14.5) in his work. This

project aims to confirm the past work performed by showing similar results in RELAP5-

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3D, an industry standard thermal-hydraulics safety analysis code, while subsequently also

confirming the models using data from the current operating core of PSBR, Core 56.

Once this is done, the RELAP5-3D®models will be used to predict the safety of the new

core assembly utilized in the NBL project.

1.2 Thesis Structure

This thesis is comprised of six chapters. The following briefly outlines the major

goals of each chapter.

Chapter 2 contains a comprehensive literature review of the major works used to

complete this work. The highlights of this section are the review of the PhD dissertation

of Dr. Uçar for the design and analysis of the new core, the MS thesis of Wade Marcum

of Oregon State University for modeling guidelines, and the PSU Safety Analysis Report

for its limiting technical specifications of the PSBR. These three documents were used

extensively in this work along with some others also detailed in this chapter.

Chapter 3 thoroughly describes the PSBR facility. Being a research and training

reactor, PSBR has quite a number of uses, many of which are relevant to the end goal of

this study as outlined in this chapter. Chapter 3 continues with descriptions of the three

different core configurations (Core 53H, Core 56, and NBL) used in this study.

Chapter 4 discusses the three major models used in this study. The steady-state

RELAP5-3D®model, which is based off of an output deck from Oregon State University,

is described in great detail because it is the main basis for the study. A MATLAB model

also adapted from OSU is described here as a tool to create a pulse transient. Finally, the

transient RELAP5-3D®model is explained.

7

Chapter 5 contains the results of all of the steady-state experiments and models

used for this work and subsequent comparisons of all the data.

Chapter 6 provides a summary of the work and draws some conclusions, and

descriptions of future work that could be performed along with this study and the

previous ones.

8

Chapter 2: Literature Review

This chapter will serve to highlight the documents that were deemed extremely

important to this study. Some are previous work performed both at PSU and other

universities, and one is a technical document defining the allowable operations conditions

of the PSBR. Finally, this chapter will conclude with a review of the computational tools

used throughout this work.

2.1 Relevant Past Work from PSU

As previously mentioned, there are two works previously performed at PSU that

directly relate to this project. The first is the MS thesis of Karriem, and the second is the

PhD dissertation of Dr. Uçar. Both of these are integral to the successful completion of

the new NBL project as a whole, and the completion of this thesis.

2.1.1 MS Thesis of Veronica Karriem

The MS work of Karriem from 2011 had three major portions: designing a

COBRA-TF model of the PSBR TRIGA reactor, core-design studies for the new D2O

tank design, and low-enriched uranium (LEU) fuel utilization studies. [5] The studies

relating to the new D2O tank and the COBRA-TF model designs are relevant to this work.

This study exclusively used COBRA-TF, which was developed and is maintained

by the Reactor Dynamics and Fuel Management Group at Penn State. COBRA-TF is a

9

three field-two fluid, best-estimate, thermal-hydraulics code used for reactor sub-channel

analysis.

The first main goal of modeling was to characterize the core-wide coolant

temperature, and the fuel temperature of the hot-element, which for Core 53H, was a

standard TRIGA fuel element with three thermocouples embedded in the fuel meat and

used as an input to the reactor system. A major relevant part of this work was in the

COBRA-TF modeling portion; a study was performed on the fuel/clad gap. The size and

composition of the fuel/clad gap used in the model, which is different in TRIGA fuel than

in commercial nuclear power plant fuel, was found through sensitivity studies. These

studies have subsequently been taken into account for this work’s RELAP5-3D®models.

The final model calculated values 10% over the measured values, which was deemed a

success.

A rudimentary model was also created of a new moderator tank design. This tank,

as shown in Figure 4, was just a simple design that was meant to cover the core face and

a portion of the sides to restrict the flow. This tank was designed before Dr. Uçar

performed his rigorous design process, so the same level of detail that was included in his

analysis is not available.

10

Figure 4: A rudimentary new moderator tank and core design as postulated by Karriem. [6]

Karriem’s study of a new moderator tank design also tested the effects of

changing the thickness of the top and bottom grid plates and a feasibility study for a

possible power upgrade. An important take-away from her work is that the interior of the

core sees relatively little cross-flow from the periphery, and most cooling in the interior

of the core is dominated by vertical flow caused by conduction from the fuel elements.

This is important because it supports the assertion that a single-channel model of the hot

fuel element/hot channel is sufficiently conservative for this analysis (see below).

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2.1.2 PhD Dissertation of Dr. Dündar Uçar

In his PhD dissertation in 2013, Modeling and Design of a New Core-Moderator

Assembly and Neutron Beam Ports for the Penn State Breazeale Nuclear Reactor (PSBR),

Dr. Uçar’s scope was to model and design a new reactor core-moderator assembly and

new neutron beam ports. [6] Having such a wide range of tasks to accomplish, Dr. Uçar

used many different computational tools:

• MCNP5

• ANSYS Fluent

• Gambit

• TRIGSIMS

• MURE, a Burned Coupled MCNP simulation tool.

The first major task was to design and optimize the shape and size of a new core-

moderator assembly. The design process was conducted with constraints on the “excess

reactivity of the core, the tower design to support the new top and bottom grid plates, the

gamma contamination problem in the beam port facilities, and reduction of cross-flow

rate into the core due to the new moderator shape.” [6] (Page 52) After an optimization

process the new moderator tank was chosen to be a crescent shape as shown in Figure 5

and the new top and bottom grid plates can be seen which accommodate the new

moderator tank in Figure 6.

12

Figure 5: New moderator tank design as seen in AutoCAD. [7]

Figure 6: New top and bottom grid plates designed for the new moderator tank. [7]

13

The crescent shape of the moderator tank was ultimately chosen because of how

well it coupled neutronically to the reactor core. The final design specifications have a

48.2 cm tall tank resting 0.6 cm away from the core face. The design couples tighter to

the sides of the core, and blocks flow to the front. The current design has the tank only

obscuring flow on the front face, while the new design covers the front and some portion

of two of the remaining five sides. The hypothetical flow field in and around the reactor,

as shown in Figure 7, would subsequently be modified to something closer to what is

shown in Figure 8 because of the lack of possible flow to the periphery of the front and

side faces of the core. Because of this, ANSYS Fluent was used to analyze the new

design and determine the new potential flow fields, coolant temperatures, and fuel

temperatures in steady-state situations.

14

Figure 7: Hypothetical flow field in and around the reactor in its current configuration. [7]

Figure 8: Hypothetical flow field in and around the reactor in its proposed new configuration. [7]

15

The ANSYS Fluent CFD model utilized modeled Core 53H at 1 MWth power

coupled to the new moderator tank for Dr. Uçar’s study. Heat generation rates were

found using the in-house neutronics and depletion coupled-code TRIGSIMS and were

applied to the outside surface of the cladding. Inner fuel temperatures were back-

calculated analytically using equations provided by General Atomics using the bulk fluid

temperatures calculated by the CFD model. The maximum bulk fluid temperature in the

hot channel was found to be 88°C, the predicted cladding temperature was 175°C, and

the predicted peak fuel temperature was 482°C. The values determined from the CFD

and analytical calculations were then compared with experimental values from the actual

Core 53H and values from the previous work of Karriem’s MS thesis. The work deemed

the general design complete regardless of the fact that the bulk fluid temperature was

increased somewhat.

2.2 Relevant Past Work from Outside of PSU

While Dr. Uçar and Karriem’s work provided a solid base on which to begin this

thesis, it was also deemed appropriate to look outside the realm of PSU to gauge was type

of relevant work has been performed out of the university. Because of the close working

relationship between the director of the Oregon State TRIGA reactor and the director of

the PSBR, it was directed that this thesis take a similar direction as work performed at

Oregon State University in 2008 for their license amendment to the NRC.

16

2.2.1 MS Thesis of Wade Marcum

In 2008, Marcum performed a safety analysis of the Oregon State TRIGA reactor

in support of the facility efforts to cooperate with the Reduced Enrichment for Research

and Training Reactors (RERTR) program [8]. The RERTR effort at Oregon State called

for swapping out all of the HEU fuel in the reactor and replacing it with LEU fuel, so a

safety analysis was warranted. The goals of the analysis were identified as,

• “Calculate natural circulation flow rates, coolant temperatures, and fuel

temperatures as a function of core power for both the current HEU and proposed

LEU.

• For steady state and pulsed operation, calculate peak values of fuel temperature,

clad temperature, surface heat flux, critical heat flux ratio (CHFR), and

temperature profiles.

• Perform accident analyses for accident scenarios identified in the OSTR safety

analysis report (SAR).” [8] (Page 2)

RELAP5-3D®v2.4.2 was used for all of the thermal-hydraulics modeling for this

project. Three RELAP5-3D®models were developed for this application: a single “hot”

channel model, a two-channel model with a hot channel and the rest of the core lumped

in an average condition, and an eight-channel model that included the hot channel and

seven other lumped average channels. Of particular importance to this thesis is the

study’s theoretical justification for using a single-channel model. It is stated that the

single (hot) channel is assumed to be the location in the core of the highest power density

and smallest flow area and will contain the highest coolant temperature in the core. A

17

two-channel model containing the hot channel and the second hottest channel was then

compared to the hot channel as shown in Figure 9.

Figure 9: Single (hot) channel model with no cross-flow next to a two-channel model with cross-flow. [8]

Because all flow is driven by natural circulation, the flow rate between the two

channels are the same, and it can be stated that through diffusion of Sub-channel 2 into

18

Sub-channel 1, the exit bulk coolant temperature will be lower with two channels than

with one, and so on. This means that the lack of cross-flow in the single-channel model

will cause the temperature in the sub-channel to be conservatively higher than if there

was a more detailed model with cross-flow.

Marcum also specifically conducted a study using different Critical Heat Flux

(CHF) correlations to test their applicability and documented the results. Along with the

study of CHF correlation applicability, the effects of a single-channel model were also

examined with respect to CHF and its reliance on cross-flow. CHF can broadly be

defined as a function of mass flux, equilibrium quality, and absolute pressure. The

TRIGA reactor is an open-pool type reactor; the pressure at any given location is mostly

governed by the hydrostatic pressure head at that point. Because of this, the effects of

absolute pressure on CHF were not examined because the absolute pressure should

remain relatively unchanged between a single- or multi-channel model. A sensitivity

study was then performed in which an equivalent change in equilibrium quality had a

much larger effect on CHF than those of mass flux as shown in Figure 10. This figure

shows the percent change in CHF value per percent change in equilibrium quality (red

data set), as well as the percent change in CHF value per percent change in mass flux

(blue data set). The data in Figure 10 further proves that a single-channel model is

sufficiently conservative over a more detailed multi-channel model for this analysis.

Marcum proceeded through the process of modeling and analyzing both steady-state and

transient (pulse) scenarios of the Oregon State reactor, of which a very similar

methodology will be used here.

19

Figure 10: Sensitivity study of relation between equilibrium quality and mass flux to CHF. [8]

2.3 PSBR Safety Analysis Report

The current incarnation of the PSBR SAR was used for the renewal of License

R-2 in December 2005. The SAR is one of the documents sent to and certified by the

USNRC to renew the reactor’s license, clearly stating its binding legal technical

specifications. The document is quoted throughout this thesis whenever a technical

specification regarding the PSBR is needed [8].

20

2.4 Review of the Computational Tools

Throughout this thesis, two computational tools, RELAP5-3D®and MCNP6, will

be used extensively. The following section will give a brief overview of these two tools.

2.4.1 RELAP5-‐3D

RELAP5-3D®v 4.1.2 will be used for all of the thermal-hydraulic analysis in this

thesis. As described in the RELAP5-3D®code manual,

The RELAP5-3D®code has been developed for best-estimate transient simulation of light water reactor coolant systems during postulated accidents. The code models the coupled behavior of the reactor coolant system and the core for loss of coolant accidents (LOCA) and operational transients such as anticipated transient without scram, loss of offsite power (LOOP), loss of feed-water, and loss of flow. A generic modeling approach is used that permits simulating a variety of thermal-hydraulic systems. Control systems and secondary system components are included to permit modeling of plant controls, turbines, condensers, and secondary feed-water systems…. The RELAP5-3D®code is based on a nonhomogeneous and nonequilibrium model for the two-phase system that is solved by a fast, partially implicit numerical scheme to permit economical calculation of system transients. [9]

The code is developed at Idaho National Lab under sponsorship of the US Department of

Energy, the USNRC, members of the International Code Assessment and Applications

Program, members of the Code Applications and Maintenance Program, and members of

the International RELAP5 Users Group. RELAP5-3D®will be used to model the PSBR

core for both steady-state and transient (pulsed) conditions.

21

2.4.2 MCNP6

MCNP6 will be used for all of the neutronics analysis in this thesis. It is

described in the code manual as “a general-purpose, continuous energy, generalized-

geometry, time-dependent, Monte Carlo radiation-transport code designed to track many

particle types over broad ranges of energies” [10]. MCNP6 will be used to obtain the

axial and radial power shape necessary for RELAP5-3D®to properly generate heat in the

fuel.

22

Chapter 3: The PSBR Facility and Experimental Setup

3.1 Use of the Facility

In its current incarnation as a Mark-3 TRIGA reactor, the PSBR has quite a few

practical uses. Current operating facilities include: Neutron Irradiation, Neutron

Imaging, Neutron Activation Analysis, Radioactive Isotope Production, Neutron

Transmission Measurement, Nuclear Detector Testing and Calibration, Radiation Effects

Testing on Materials and Electronics, and Gamma Irradiation. The facility is also used to

teach academic, corporate, and government users how to safely carry out experiments

utilizing the RSEC’s facilities; provide undergraduate and graduate demonstrations,

nuclear engineering laboratory classes, and research opportunities; and provide tours,

workshops, and training to public and professional users, pre-college and college-level

students, and educators [11]. The new NBL project would greatly increase the utility of

the reactor by adding a Triple-Axis Spectrometer, Prompt Gamma Activation Analysis,

Neutron Depth Profiling, Time-of-Flight Neutron Depth Profiling, and Neutron Powder

Diffraction to the RSEC [6]. The PSBR facility, as shown in Figure 11, is comprised of a

71,000-gallon pool of filtered de-ionized water that can be separated into two halves by a

removable gate. If one section of the pool needs to be drained for maintenance or

inspection, the entire reactor bridge, including the suspension tower and reactor core

suspended below it, can be moved along rails across the pool.

23

Figure 11: View of the PSBR reactor pool with cutaways. [9]

The core of the PSBR is comprised of approximately100 fuel elements, four

control rods, two air-filled dry tubes, a source, and a water-filled central thimble. A

TRIGA fuel element, shown in Figure 12, is unlike a typical commercial power plant fuel

rod. The fuel itself is made of uranium zirconium hydride, which is a dispersion of

uranium in a zirconium hydride matrix. The zirconium hydride lattice inside which the

uranium is dispersed, acts as a moderator inside the fuel element. The amount of

uranium in the fuel can vary; but, in the case of PSBR, there is a mixture of 8.5 weight

24

percent (w/o) and 12 w/o fuel elements, both enriched to 19.75 % uranium-235 (LEU).

There is also a quarter-inch diameter zirconium rod in the center of each fuel element.

During the fabrication of the fuel, a quarter-inch hole is left in the center to help facilitate

the hydriding process. After fuel fabrication is finished, the zirconium rod is inserted into

the hole to fill the space. It is the special properties of this fuel material that allows a

TRIGA reactor to operate in the way it does. Specifically, this type of fuel contains an

extremely large prompt negative reactivity coefficient. According to the PSBR SAR, the

approximate make-up of the prompt negative temperature coefficient is: 65% from the

“cell effect,” 15% from Doppler broadening of uranium-238 resonances, and 20% from

temperature dependent moderation and leakage associated with the water. [8] The “cell

effect” can best be described as the phenomenon as follows:

The rise in temperature of the hydride increases the probability that a thermal neutron in the fuel element will gain energy from an excited state of an oscillating hydrogen atom in the lattice. As neutrons gain energy from the ZrH [zirconium hydride] their mean free path is increased appreciably…. Since the average chord length in the fuel element is comparable with a mean free path, the probability of escape from the fuel element before capture is increased. In the water (where the temperature remains relatively constant) the neutrons are rapidly rethermalized so that the capture and escape probabilities are relatively insensitive to the energy with which the neutron enters the water. The heating of the moderator mixed with the fuel thus causes the spectrum to harden more in the fuel than in the water. As a result, there is a temperature-dependent disadvantage factor for the unit cell in the core which decreases the ratio of absorptions in the fuel to total-cell absorptions as the fuel element temperature is increased. This change in disadvantage factor brings about a shift in the core neutron balance, giving a loss of reactivity, and is termed the cell effect. [12]

This unique property dominates the prompt fuel reactivity feedback and allows for such

operation as pulsing transients, in which a transient control rod is rapidly ejected from the

core.

25

Figure 12: TRIGA fuel element diagram. [9]

As shown in Figure 12, a TRIGA fuel element is further comprised of two

graphite reflectors, both above and below the active fuel region, stainless steel cladding

around the fuel and graphite reflectors, a stainless steel spacer at the top of the upper

graphite, and stainless steel top and bottom end-fixtures. The graphite reflectors are

simply used to increase neutronic efficiency in the fuel element by reflecting neutrons

26

back down into the active fuel. Stainless steel is currently used on all active fuel as the

cladding. General Atomics originally manufactured TRIGA fuel elements with

aluminum cladding; however it proved too stiff to withstand repeated pulsing in the fuel.

It is postulated that there is in fact a fuel/clad gap filled with gas in TRIGA elements.

Not all elements seem to have the same size gap, and the composition of the gap gas is

unknown. Further study of the gap will be examined in Chapter 4. As shown in Figure

13, certain special fuel elements known as instrumented elements also exist within the

core. These fuel elements contain three thermocouples within the active fuel region of

the fuel element and electronic wiring leading out of the top of the element. These fuel

elements are used to monitor live the temperature of the fuel in the core and are often

placed in strategic position throughout the core (e.g., the peak fuel element) so that the

peak fuel temperature of the core can always be accurately known.

27

Figure 13: Diagram of an instrumented TRIGA fuel element. [9]

28

There are four control rods in the PSBR core: the safety rod, the shim rod, the

regulating rod, and the transient rod. The safety, shim, and regulating rods are all

structurally the same and are used simply for reactor control—all can be moved

independently. As shown in Figure 14, these rods consist of three main zones: a 15-inch

borated graphite absorbing region, a 15-inch fueled region, and graphite reflecting

regions on the top and bottom of the rods; the entire rod is clad in stainless steel in the

same way as the fuel. When fully inserted, the borated graphite region of these rods lines

up with the active fuel region of the fuel elements in the core. When partially or fully

withdrawn, a fueled region comprised of 8.5 w/o fuel follows the borated graphite region

of the control rods. The fourth control rod, the transient rod, as shown in Figure 15, is

markedly different from the other three. While it can also be used for safety and control

in normal steady-state operation, it can also be pneumatically driven from the core to

perform pulses and square waves. These operation modes are unique to TRIGA reactors

that are made possible by their inherent safety qualities as previously mentioned.

29

Figure 14: Operating orientations of the three normal control rods. [9]

30

Figure 15: The transient control rod. [9]

31

3.2 Past Core: 53H

The following will include the modeling and analysis of three different core

loadings of the PSBR. The first of these, Core 53H, as shown in Figure 16 as a core

loading diagram and Figure 17 as an MCNP6 plot, is the core that was analyzed by Uçar

in his previous work. The purpose of modeling and re-analyzing this core is to match the

results that Uçar achieved in his CFD analysis with RELAP5-3D. Matching Uçar’s

results will not only serve to further validate his work, but will help to confirm the

RELAP5-3D®models used in this analysis for the future core.

3.3 Current Core: 56

The second core that will be modeled and analyzed is the current core loading of

the PSBR, Core 56, as shown in Figure 18 as a core loading diagram and Figure 19 as an

MCNP6 plot. Core 56 is useful to this analysis because as the current core loading,

relevant neutronic and thermal-hydraulic data are both readily available, and simple to

sample. This leads to the core loading providing ample data with which to further verify

the RELAP5-3D®simulation models.

32

Figure 16: Loading pattern for Core 53H.

Figure 17: MCNP6 generated map of XY axis of Core 53H.

33

Figure 18: Loading pattern for Core 56.

Figure 19: MCNP6 generated map of XY axis of Core 56.

34

3.4 Proposed Future Core: NBL

The third and final core that will be modeled and analyzed is a mockup of the

future core for use with the proposed new moderator tank. As with the analysis

performed by Uçar, Core 53H will be used as a stand-in for the actual core loading.

Figure 20 shows an MCNP6 generated model of Core 53H coupled to the proposed

moderator tank as designed by Uçar. It consists of the same core model as shown in Core

53H with the face 0.6 cm from the tank. The beam ports and their components have been

removed, so only the moderator in the proposed new moderator tank will have an effect

on the core neutronics. Neither this model nor that of the bare Core 53H include the

graphite reflector rods as shown in Figure 16 because they were removed in Uçar’s

analysis to reduce core excess reactivity, and weren’t used in the new moderator tank

plan.

35

Figure 20: MCNP6 generated map of XY axis of Core 53H coupled to the proposed new moderator tank.

36

Chapter 4: Thermal-‐Hydraulic Models of the PSBR Facility

As previously mentioned, a large portion of the modeling for this work is based

on that previously done by Dr. Marcum. He created several RELAP5-3D®models for his

analysis of the OSTR. Because of the relatively small size of the TRIGA community,

especially operating at universities, a network of communication exists between different

TRIGA operating facilities. A RELAP5-3D®output file (which contains an echo of the

input) used in Marcum’s analysis was obtained by the PSBR for use in aiding this current

analysis. The steady-state and subsequently transient pulse models that it is built off of in

this analysis are thus directly adapted from Dr. Marcum’s work.

4.1 Steady-‐State RELAP5-‐3D®Models

The following section will detail the steady-state RELAP5-3D®deck used for

modeling Core 53H. Because of the relative complexity of the model, the only major

differences between the model of Core 53H, Core 56, and the NBL core are the power

provided to the heat structure and the axial and radial power shapes generated from

MCNP6 mesh tallies. Therefore, the model described for the reminder of Section 4.1

should be treated as representative of all four models. Table 1 shows a summary of the

changes made in relation to the base model of Core 53H.

37

Table 1: Summary of RELAP5-3D®models.

4.1.1 Single-‐Channel RELAP5-‐3D®Model

Section 2.2.1 previously documented Marcum’s work in proving that a single-

channel model was conservative and sufficient for use in the current analysis. As shown

in Figure 21, the single-channel model for Core 53H is quite simple, consisting only of

ten separate components, which will be detailed below.

Model Changes from Base Model (CL 53H) CL 53H Base model as described.

CL 56 Axial and radial power shapes in fuel changed to match MCNP6 tallies

Power in fuel rod increased to 17.31 kW from 16.6 kW

CL53H w/ New D2O Tank matching Dr. Ucar Axial and radial power shapes in fuel changed to match MCNP6 tallies

CL53H w/ New D2O Tank Tech Spec Limits Axial and radial power shapes in fuel changed to match MCNP6 tallies

Power in fuel rod increased to 24 kW from 16.6 kW

38

Figure 21: Block diagram of the Core 53H RELAP5-3D®model (not to scale).

Table 2: Geometric dimensions of the coolant source/sink.

Dimension Specification Flow Area 0.005595 ft

Length 3.28083 ft (1 m) Hydraulic Diameter 0.058151 ft

39

Table 3: Coolant source/sink initial temperature and pressure.

Initial Condition Specification Pressure 21.9254 (psia)

Temperature 140.0 F

Table 4: Geometric specifications of the cold leg.

Dimension Specification Flow Area 0.005595 ft2 Length 2.07541 ft

Hydraulic Diameter 0.058151 ft

Table 5: Hot channel pipe component lengths.

Hot Channel Pipe Component Length (ft) Lower Core Grid Plate 0.25

Lower Graphite Reflector 0.31 Fuel (*20) 0.0625

Upper Graphite Reflector 0.21333 Upper Core Grid Plate 0.052083

Table 6: Hot-channel geometric specifications.

Dimension Specification Fuel Element Outside Diameter 1.47 in

Fuel Element Pitch 1.7 in Flow Area 0.005595 ft

Hydraulic Diameter 0.058151 ft Fuel Rod Roughness 0.000007

Bottom Grid Plate Form Loss 1.293 Top Grid Plate Form Loss 0.861

4.1.2 Coolant Source and Sink

The model of Core 53H does not contain a complete closed hydraulic loop,

instead opting for the use of a coolant source (Component 100) and coolant sink

(Component 104) at the start and end of the model respectively. The only difference

40

between the source and the sink is that one is at the beginning of the model and supplies

coolant to the system, and the other is at the end of the model and removes coolant from

the system. Therefore, the following description of the source, while not mentioning the

sink, will also fully pertain to the coolant sink.

The coolant source is modeled as a horizontal (0º inline) time-dependent volume,

which allows it to conform to the needs of the model. The geometric parameters of this

component are relatively irrelevant to the function of the model, so they have been

normalized to the values shown in Table 2 for simplicity’s sake, as was done by Dr.

Marcum. The flow area and hydraulic diameter were chosen as the same values used in

the hot channel, and the length of the time-dependent volume was chosen simply because

it is a standard unit of length.

The initial pressure and temperature of the coolant source were chosen to

introduce the most conservative assumptions available to the model and were in fact used

consistently in all components of the model. Table 3 shows the values used for the

pressure and temperature initial conditions. The initial pressure of the system was

calculated from the hydrostatic pressure head above the location of the model in the core.

The source and sink were modeled directly above the location of the top grid plate of the

core, which is approximately 16 2/3 feet (5.08 m) below the surface of the water.

Accordingly, converting this water column height into hydrostatic pressure head and

adding the atmospheric contribution to pressure for a final result in absolute pressure

determined the initial pressure of the system. The initial temperature of the system was

set as the technical specification limit for bulk fluid temperature. Because by definition

the hot channel will always be a significantly hotter than the bulk fluid temperature,

41

starting the hot channel at the technical specification limit for the bulk fluid temperature

(140 ºC) [8] will allow for the peak hot-channel temperature to be that much hotter.

4.1.3 Cold Leg (Downcomer)

The first component that follows the source is the cold leg (Component 101),

alternatively called the downcomer. While not a component that physically exists in the

PSBR, the cold leg is necessary for the proper operation of the RELAP5-3D®model.

Because the reactor operates with pressure-driven natural convection as its primary

coolant-flow mechanism, the model needs a way to properly supply flow without using a

pump. The cold leg was modeled as a vertical (90º incline) pipe with the same geometric

specification as the hot leg (shown in Table 4; see Table 3 for the initial conditions). The

cold leg helps to drive flow to the connection and hot leg simply because flow will be

driven downwards through the pipe by gravity and fed through the connection. Having

the same dimensions as the hot leg allows the system to reach an equilibrium between the

driving flow forces of gravity in the cold leg and natural convection in the hot channel.

4.1.4 Horizontal Connection

The first component that comes after the cold leg is the horizontal (0º incline)

connection (Component 102). This is another non-physical component that is used to

facilitate the modeling process in RELAP5-3D. The horizontal connection is used to

connect the cold leg to the hot leg. This component is horizontal, which means it incurs

no gravitational loading, and it has a roughness value of 0, so it also does not incur any

frictional loading. Therefore, this component does not have any effects on the flow other

42

than directing it to the proper location. (For the geometric specifications for this

component, see Table 2. For its initial conditions, see Table 3.)

4.1.5 Hot Leg

The final component in the model before the coolant sink is the vertical (90º

incline) hot leg (Component 103). The hot leg is the portion of interest in the model. It

was modeled using a pipe with 24 volumes as shown in Figure 22.

Figure 22: Nodalization of hot-channel pipe component.

43

Table 7: Axial power shape for Core 53H.

Node Axial Power Shape 1 0.034521 2 0.035703 3 0.041118 4 0.046382 5 0.050059 6 0.054181 7 0.057248 8 0.059954 9 0.061424 10 0.062029 11 0.062109 12 0.061248 13 0.060408 14 0.057233 15 0.053951 16 0.050397 17 0.046492 18 0.040265 19 0.034162 20 0.031118

The geometric length specifications for the hot-channel pipe are shown in Table 5.

All 20 of the fuel volumes are the same length, so fuel will only be listed once and

assumed to account for all 20 volumes. Table 7 shows the values used for the axial power

shape for Core 53H.

The rest of the geometric specifications for the hot-channel pipe are shown in

Table 6. The flow area was calculated using Equation 1 and is visualized in Figure 23.

The hot element (for Core 53H) was I-16, which is shown in the center of the figure. The

hot sub-channel, Channel R in the figure, is shaded in red. The flow area around one fuel

element is comprised of exactly two times the area of Channel R. The hydraulic diameter

was subsequently calculated using the standard equation shown in Equation 2.

44

𝐴!" = 2 ∗34 𝑃! −

𝜋𝐷!"#$% !"#$!

8 ,𝑤ℎ𝑒𝑟𝑒 𝑃 = 𝑓𝑢𝑒𝑙 𝑟𝑜𝑑 𝑝𝑖𝑡𝑐ℎ (1)

𝐷! =4 ∗ 𝐴!"𝑃!

,𝑤ℎ𝑒𝑟𝑒 𝑃! = 𝑤𝑒𝑡𝑡𝑒𝑑 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 (2)

Figure 23: Graphical representation of hot channel and flow area.

Throughout the entire RELAP5-3D®model, material roughness is only used in

one location: along the length of the fuel rods. Marcum identified the most likely

roughness of the stainless steel cladding (see Table 5). He also identified likely values

45

and ranges of the form losses that the flow would incur entering the lower grid plate and

exiting the upper grid plate (see Table 5).

4.1.6 Hot Leg Heat Structure

The only heat structure in the model is that of the fuel element in the hot channel.

Figure 24 shows a cross-section of a single radius of the heat structure. Table 8 shows

the radial power shape used for Core 53H.

Figure 24: Cross-section of a single radius of the hot-channel heat structure.

46

Table 8: Radial power shape for Core 53H.

Node Radial Power Shape 1 0 2 0.044381574 3 0.044589445 4 0.044576506 5 0.04488536 6 0.045134018 7 0.045360736 8 0.045773385 9 0.046183784 10 0.046662254 11 0.047268148 12 0.047943238 13 0.048743221 14 0.049708881 15 0.050801965 16 0.052272819 17 0.053903443 18 0.055950937 19 0.058469305 20 0.06161157 21 0.06577941 22 0 23 0

The fuel element was modeled as previously described in Section 3.1: a

zirconium rod in the center surrounded by uranium zirconium hydroxide fuel, with a

fuel/clad gap and stainless steel cladding. As shown, a single node is used to model the

zirconium rod, followed by 20 nodes of uranium zirconium hydroxide fuel, a single node

for the fuel/clad gap, and a single node for the stainless steel cladding. Because the fuel

material is clearly of most interest to this study, it is the most nodalized material. Table 9

shows the location of the right edge of each mesh point. The left edge of the zirconium

rod is at 0 feet.

47

Table 9: Node locations and materials inside hot-channel heat structure.

Node Material Right Edge Location (ft) 1 Zirconium 0.0104 2 Uranium Zirconium Hydroxide 0.0116 3 Uranium Zirconium Hydroxide 0.0141 4 Uranium Zirconium Hydroxide 0.0166 5 Uranium Zirconium Hydroxide 0.0190 6 Uranium Zirconium Hydroxide 0.0215 7 Uranium Zirconium Hydroxide 0.0239 8 Uranium Zirconium Hydroxide 0.0264 9 Uranium Zirconium Hydroxide 0.0289 10 Uranium Zirconium Hydroxide 0.0313 11 Uranium Zirconium Hydroxide 0.0338 12 Uranium Zirconium Hydroxide 0.0363 13 Uranium Zirconium Hydroxide 0.0388 14 Uranium Zirconium Hydroxide 0.0412 15 Uranium Zirconium Hydroxide 0.0437 16 Uranium Zirconium Hydroxide 0.0462 17 Uranium Zirconium Hydroxide 0.0486 18 Uranium Zirconium Hydroxide 0.0511 19 Uranium Zirconium Hydroxide 0.0536 20 Uranium Zirconium Hydroxide 0.0561 21 Uranium Zirconium Hydroxide 0.0585 22 Gap Gas 0.058584666 23 Stainless Steel 0.060251333

As previously mentioned, a short study was performed to determine and produce

an adequate model value for the fuel/clad gap. Generally, when a fresh TRIGA fuel

element is shipped, it either has no fuel/clad gap or a very small one. When a fuel

element is initially pulsed, the fuel material will expand due to extreme thermal gradients

in the fuel. When the fuel material expands, it pushes the stainless steel cladding along

with it. [13] After the pulse transient is completed and the fuel has cooled, it will

contract to roughly its initial dimension, while the cladding will have plastically

deformed. An experiment to study the fuel temperature after different pulses was

48

conducted and documented in the PSU SAR, which shows this effect. [8] After each

successive pulse of large reactivity insertion value, the cladding will be stretched to a

larger outer diameter. Because of this phenomenon, it is difficult to characterize the

fuel/clad gap size of a fuel element that has been in continuous operation, and thus seen

thousands of pulses over the years. The fact that determining a precise fuel/clad gap

thickness is not possible experimentally without taking extreme measures allows for the

determination of the gap thickness to be used a good model calibration tool. Figure 25

shows the results of a study to determine the optimal gap thickness for Core 53H and

subsequently the rest of this study. The gap was increased in different increments

between 0.0001 inches (0.00254 mm) and 0.001 inches (0.0254 mm), and the

temperature in the fuel at the thermocouple instrumentation was plotted along with the

temperature at the outer diameter of the cladding. The red line on the figure shows the

average value read from the thermocouples (520.4ºC (793.55 K)), taken from data

recorded from Core 53H in July 2011. The figure shows that a gas gap thickness of

0.00026 inches (0.006604 mm) nearly overlaps with the experimental value at 527.97ºC

(801.12 K). This value was subsequently used for all models for the duration of this

work.

49

Figure 25: Parametric study of gas gap thickness.

The final important components of the hot-channel heat structure are the axial and

radial power shape within the fuel. These two components take the input power level and

accurately distribute it within the geometry of the fuel. It is well-known that the axial

power shape within a fuel element will roughly resemble a cosine curve centered about

the axial center of the element, and the radial power shape will roughly resemble and

exponential curve increasing from the center of the element to the outer radius. To obtain

precise values for these power shapes, MCNP6 mesh tallies were utilized. The tallies

were setup to independently obtain the fission rate in 20 axial nodes and 20 radial nodes

in the hot element. The mesh tally values were then normalized to the total value such

that the sum of the normalized values was one.

While the core orientation is markedly different between the PSBR and OSTR,

the composition and makeup of the materials in the fuel element are the same. Therefore,

50

the thermal conductivity and heat capacity values for the uranium zirconium hydroxide

and zirconium used in this model are the same as those used and documented by Marcum

[7]. All thermal property data used for the gas-gap material and stainless steel material

are the default values stored by RELAP5-3D.

4.2 CHF Correlations

One of the most important measures of safety of a water-cooled system operating

at high temperatures is that the system remains operating below its CHF. In the case of

the PSBR, the CHF mechanism of note is departure from nucleate boiling, which is

defined succinctly by the USNRC as, “The point at which the heat transfer from a fuel

rod rapidly decreases due to the insulating effect of a steam blanket that forms on the rod

surface when the temperature continues to increase” [14]. As shown in Figure 26, CHF

is the local maximum on the Pool Boiling curve before which is nucleate boiling, and

after which is transition boiling. To determine the proximity to theoretical CHF in a

given situation, empirical correlations are often employed. Because the empirical nature

of these correlations causes them to have a range of applicability that may not precisely

apply to all situations, it is common to use multiple correlations to analyze a single

situation to be certain of the results. This analysis will employ the use of three CHF

correlations in an attempt to prove the safety of the system. An analysis was performed

at Argonne National Laboratory to explore steady state CHF analysis in TRIGA reactors.

[15] This analysis employed the code used for TRIGA steady state CHF analysis by

General Atomics, STAT (a proprietary thermal-hydraulics code used by General Atomics

for TRIGA reactor anaylsis), as well as RELAP5, and compared the results of the two

codes using multiple different CHF correlations. Of general importance to this work is

51

the study’s analysis of the Bernath CHF correlation, and the 1986 and 2006 AECL-UO

CHF Lookup Tables. While the study concludes that the 2006 AECL-UO is the best

choice for of all available CHF correlations, it also notes that it should not be used alone

because “the amount of measured data is insufficient to determine a definitive conclusion

as to the power level at which CHF occurs.” [15] This conclusion, while a good

endorsement for the use of the 2006 Lookup Tables, suggests that it would be

advantageous to also use other correlations to confirm safe results, which in this case will

be the 1986 Lookup Tables and the Bernath correlation.

52

Figure 26: Graphical representation of the general pool boiling curve showing CHF. [17]

4.2.1 Bernath CHF Correlation

The Bernath correlation, which is often used in TRIGA analysis, combines

previous experimental data provided by both William McAdams and Columbia

University. “Both sets of experiments were at low pressure and measured CHF for

53

subcooled boiling in annuli” [15], making the Bernath correlation seem to be a good fit—

at least in theory—for TRIGA reactor analysis. The Bernath calculated heat flux can be

calculated using Equations 3–6. The Bernath equation is not included in RELAP5-3D, so

it was calculated by hand.

𝑄𝐴 !"

= ℎ!" 𝑇!,!" − 𝑇! (3)

ℎ!" = 10890𝐷!

𝐷! + 𝐷!+ 𝑠𝑙𝑜𝑝𝑒 𝑉 (4)

𝑠𝑙𝑜𝑝𝑒 =48𝐷!!.!

𝑖𝑓 𝐷! ≤ 0.1 𝑓𝑡 (5𝑎)

𝑠𝑙𝑜𝑝𝑒 = 90+10𝐷! 𝑖𝑓 𝐷! > 0.1 𝑓𝑡 (5𝑏)

𝑇!,!" = 57𝑙𝑛𝑃 − 54𝑃

𝑃 + 15 −𝑉4 (6)

𝑊ℎ𝑒𝑟𝑒 𝑄𝐴 !"

𝑖𝑠 𝑡ℎ𝑒 𝐶𝐻𝐹 ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 𝑖𝑛 𝑝𝑐𝑢

𝐹𝑡! ∗ ℎ𝑟

4.2.2 AECL-‐UO CHF Lookup Tables

RELAP5-3D®natively uses a table lookup method to calculate CHF. D. C.

Groeneveld, S. C. Cheng, and T. Doan developed the default method, known as the

54

“1986 AECL-UO Critical Heat Flux Lookup Table”. [16] The correlation uses eight “k-

factors” (hydraulic factor, bundle factor, grid spacer factor, heated length factor, axial

power factor, horizontal factor, vertical flow factor, and pressure out-of-range factor) to

calculate a multiplier, which is then used in conjunction with a value found in the lookup

table. RELAP5-3D®also includes an option to change the default CHF correlation to

“The 2006 AECL-UO CHF Look-Up Table”. [17] Both the 1986 and 2006 tables were

used in conjunction with RELAP5-3D®in this work.

55

Chapter 5: Steady-‐State RELAP5-‐3D®Simulation Results

This chapter will present the results of the steady state RELAP5-3D®simulations

and offer comparisons of said results to both past work and data taken from the PSBR. A

sample RELAP5-3D®input deck is shown in Appendix A. The axial bulk fluid

temperature profile in Dr. Uçar’s CFD hot element is shown in Figure 27. This figure

will be compared to a similar profile from each different simulation. It is important while

reviewing the results to know that the technical specification limitations state that the

steady-state fuel temperature limit is 1150ºC, the loss of coolant accident temperature

limit is 950ºC, and the clad outer temperature limit is 500ºC. [8]

Figure 27: Axial bulk fluid temperature as calculated by Dr. Uçar. [7]

56

5.1 Results and Comparison of PSBR Core 53H

As previously discussed, Core 53H is what Karriem modeled, and is also what the

proposed NBL was based off of by Dr. Uçar. Thus, there is a larger amount of earlier

data for this section. The RELAP5-3D®simulation for this run was performed using the

same initial conditions, including the same initial temperature at the entrance to the

channel of 32ºC, a system pressure of 1.5 atm, the same general geometry, and a power

peaking factor of 1.72, yielding a rod power of 16.6 kW. Table 10 shows the fluid

temperature at the core center and 12.7 cm above the core center, as well as the fuel

temperature at the instrumentation location in the element. The data included in the table

are from measurements taken of Core 53H, calculations performed in COBRA-TF by

Karriem, and calculations from RELAP5-3D. As described by Dr. Uçar, the fluid

measurements were taken in the hot channel (Channel R) with a thermocouple housed in

an aluminum tube. Of particular note is the nearly flawless agreement between the

measured fuel temperature and the RELAP5-3D®predicted fuel temperature in this

instance.

Table 10: RELAP5-3D®simulation results as compared to prior work.

All values in ºC Measurement CTF Prediction RELAP5-‐3D®Prediction Fluid at Core Center 58.00 54.00 55.18 Fluid 12.7 cm above Core Center 59.30 66.00 71.60 Fuel Temperature 533.7 311.36 527.83

Figures 28 and 29 show the axial bulk fluid temperature profile and the CHF

calculations respectively. Figure 28 includes the bulk fluid temperature along the entire

length of the hot channel from the lower grid plate to the upper grid plate. Figure 29

57

includes the CHF ratio along all 20 nodes of the heated length of the fuel rod as

calculated by all three CHF correlations, along with a line indicating a CHF ratio value of

one, which indicates departure from nucleate boiling.

Figure 28: Axial bulk fluid temperature profile of Core 53H, calculated by RELAP5-3D.

58

Figure 29: CHF ratio along the heated length of the fuel rod in Core 53H, calculated by RELAP5-3D.

The profile in Figure 28 compares favorably with that of Figure 27. It shows a

temperature profile of roughly the same shape, but of roughly lower value (about 10 ºC

lower), as would be expected for Core 53H, without the moderator tank providing extra

moderation. Figure 29 shows all three CHF correlations predicting a CHF ratio well

above 1.0 for the entire heated length of the fuel, thus predicting CHF not to occur in

these conditions.

5.2 Results and Comparison of Current PSBR Core 56

PSBR Core 56, the current operating core, was not analyzed by Dr. Uçar or

Karriem, but it still provides more data that can be used to judge the worthwhile of the

RELAP5-3D®simulations. The RELAP5-3D®simulation for this run was performed

using the same initial conditions, including the same initial temperature at the entrance to

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the channel of 32ºC, a system pressure of 1.5 atm, the same general geometry as Core

53H, but with a power peaking factor of 1.83, yielding a rod power of 17.1831 kW.

Table 11 shows the fluid temperature at the core center and 12.7 cm above the core center

as well as the fuel temperature at the instrumentation location in the element. The data

included in the table are from measurements taken of Core 56 and calculations from

RELAP5-3D. Thermocouple data was not readily available for the fluid temperature in

the hot channel of Core 56, so it was omitted.

Table 11: RELAP5-3D®results compared to a fuel temperature measurement from the current core.

All values in ºC Measurement RELAP5-‐3D®Prediction Fluid at Core Center — 55.83

Fluid 12.7 cm above Core Center — 72.46 Fuel Temperature 518.1 547.04 Clad Temperature — 132.74






one, which indicates departure from nucleate boiling.

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Figure 30: Axial bulk fluid temperature profile of Core PSBR 56, calculated by RELAP5-3D.

Figure 31: CHF ratio along the heated length of the fuel rod in PSBR Core 56, calculated by RELAP5-3D.

61

The profile in Figure 30 compares favorably with that of Figure 27. It shows a

temperature profile of roughly the same shape, but of roughly lower value (about 10 ºC

lower), as would be expected for Core 56 and similar to PSBR Core 53H, without the

moderator tank providing extra moderation. Figure 31 shows all three CHF correlations

predicting a CHF ratio well above 1.0 for the entire heated length of the fuel, thus

predicting CHF not to occur in these conditions.

5.3 Results and Comparison of Proposed Future Core NBL

The simulation of the proposed future Core NBL was slightly different than the

previous two. Because the goal of this analysis is to prove the safe operation of the core

assembly, two different inputs were created: one with the exact same conditions as Dr.

Uçar, and another with conditions mimicking the technical specification limits, initial

bulk fluid temperature of 60ºC and a pin power of 24.7 kW. Table 12 shows the fluid

temperature at the core center and 12.7 cm above the core center, as well as the fuel

temperature at the instrumentation location in the element in the simulation that matches

Dr. Uçar’s data., and Table 13 shows the same data from the simulation of the technical

specification limits.

Table 12: RELAP5-3D®results from proposed core compared to results from Dr. Uçar.

All values in ºC CFD Prediction RELAP5-‐3D®Prediction Fluid at Core Center 65.42 55.20

Fluid 12.7 cm above Core Center 78.88 71.57 Fuel Temperature 482 527.31 Clad Temperature 174.85 132.11

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Table 13: RELAP5-3D®results from the technical specification limit simulation of the proposed Core NBL.

All values in ºC RELAP5-‐3D®Prediction Fluid at Core Center 81.89

Fluid 12.7 cm above Core Center 97.26 Fuel Temperature 703.77 Clad Temperature 136.95






one, which indicates departure from nucleate boiling. Figures 33 and 34 show the same

data, but from the simulation at the technical specification limits.

63

Figure 31: Axial bulk fluid temperature profile of the same conditions as Dr. Uçar, calculated by RELAP5-3D®for future core.

Figure 32: CHF ratio along the heated length of the fuel rod of the same conditions as Dr. Ucar, calculated by RELAP5-3D®for future core.

64

The profile in 31 compares favorably with that of Figure 27. Figure 32 shows all

three CHF correlations predicting a CHF ratio well above 1.0 for the entire heated length

of the fuel, thus predicting CHF not to occur in these conditions.

Figure 33: Axial bulk fluid temperature profile of the technical specification limits, calculated by RELAP5-3D®for the future core.

65

Figure 34: CHF ratio along the heated length of the fuel rod in the technical specification limits, calculated by RELAP5-3D®for the future core.

The profile in Figure 33 compares favorably with that of Figure 27. Figure 34

shows all three CHF correlations predicting a CHF ratio well above 1.0 for the entire

heated length of the fuel, thus predicting CHF not to occur in these conditions.

Additional information can be taken from the comparison of these two cases to

each other. In dividing the CHFR of the nominal case by that of the technical

specification limit case, a ratio between 1.5 and 2.3 can be found of all locations for all

three correlations. This shows that some safety margin is (as expected) lost when the

core is operating at the technical specification limit of bulk fluid temperature and power,

but it is a relatively constant value. Table 14 shows a summary of all of the minimum

departure from nucleate boiling ratio (MDNBR) values from each core and each

correlation. MDNBR is the lowest DNBR that is calculated along the length of the

channel, and thus the most important value. The table shows the general trend of the

66

Bernath correlation being the most conservative, followed by the 2006 Lookup Table and

the 1986 Lookup Table. This trend helps to confirm the results from [15], which also

strengthens the conclusions used for this work.

Table 14: MDNBR value of each core for each CHF correlation.

Correlation Core 53H Core 56 Nominal New Core Tech Spec Limit New Core Bernath 2.72 2.63 3.79 1.78 AECL-‐UO 1986 7.88 7.56 7.93 4.46 AECL-‐UO 2006 6.53 6.27 6.57 3.74

Figures 35 and 36 show a final summary of some of the most important technical

parameters. Figure 35 shows the temperature rise in the hot channel for all four scenarios

overlaid to help show that the trend is the same in all scenarios. Figure 36 is similar in

that it attempts to achieve the same effect, but for the CHFR of the Bernath correlation.

Figure 35: Temperature rise in the hot channel for all simulations.

67

Figure 36: Bernath CHFR for all simulations.

68

Chapter 6: Conclusion and Future Work

6.1 Conclusion

The RSEC is planning a major expansion project to the NBL facility at the PSBR.

Among other things, this project will see the installation of a new heavy water neutron

moderation tank, which will couple with a new core design. The thermal hydraulics

calculations for this project were partially analyzed by Karriem using CTF, and the full

design was created and analyzed by Dr. Uçar using MCNP, TRIGSIMS, and ANSYS

Fluent for CFD. The main goal of this work was to model the same scenario as Dr. Uçar,

and confirm the results of his analysis.

A thorough literature review was performed to determine what work has been

performed, and a set a proper course of action for the current study at hand. A short

review was also given to the two major analysis tools for this work: MCNP6 and

RELAP5-3D®. A description was then given for the three major core configurations that

were simulated for this work: the past PSBR Core 53H, which was simulated by Karriem,

the current PSBR Core 56, and the proposed new core with the proposed new moderator

tank, which was simulated by Dr. Uçar. The next major section detailed the development

and use of the RELAP5-3D® simulation models. The models were adapted from a

model given to the PSBR by the OSTR, after it performed a similar analysis on their

reactor. A different model was developed for each of the different core configurations.

The results from the RELAP5-3D® simulations, in general, showed very good

agreement with both past simulations and measurement. First, the shape of the axial bulk

69

fluid temperature plots on all of the simulations matched that of Dr. Uçar quite well.

Uçar achieved a slightly higher peak temperature on his plot (about 85 ºC) than all of the

simulations other than the technical specification limit moderator tank run (about 75 ºC);

however, this can be attributed to slight model differences, which seem to uniformly

decrease the temperature. The reason that the technical specification limit simulation

temperature (about 97 ºC) is higher than Dr. Uçar’s is because this simulation was meant

to be the very edge of the operating range of the hot element, which was far higher than

that of what Dr. Uçar was simulating.

Tables 10–12 show the raw data of the simulations, which can be used to gauge

the relative precision of the different models. Table 10 shows a nearly identical fluid

temperature at the center of the core between the measurement, Karriem’s simulation,

and the RELAP5-3D®simulation. The fluid above the core was calculated by RELAP5-

3D® to be nearly 12ºC hotter than the measurement, and 7ºC hotter than the COBRA-TF

calculation, but this is only a relatively small and conservative source of error. The only

significant source of error in the simulation of PSBR Core 53H was that of the fuel

temperature, in which the RELAP5-3D® simulation was 1.1% lower than that of the

measurement, while the COBRA-TF calculation was 52.6% lower. This discrepancy can

possibly be caused by the unrefined nature of the CTF model, which was created before

more precise measurements were taken. The only measurement data from PSBR Core 56

was a fuel temperature measurement, as shown in Table 11. The RELAP5-3D® results

were similar to that of PSBR Core 53H, although slightly hotter (about 20 C), which was

expected from a similar rod in a similar channel with more power. The RELAP5-3D®

calculated fuel temperature was found to be 5.43% higher than that of the measurement,

70

which is another conservative error within the realm of acceptance. The results from the

technical specification limit simulation do not have any direct measurement or other

simulation to be compared to, but they still follow the same trend as the other simulations,

and the cladding and fuel temperature fall well below their limit, which indicates that the

new NBL core will still operate safely, even at its maximum operating limit.

Finally, the simulation of the new NBL core matching that of Dr. Uçar’s work can

be examined. Dr. Uçar’s calculated fluid temperatures are about 10 ºC higher than the

RELAP5-3D®temperatures. This is considered to be acceptable because it is not a

significant difference, and there are known issues with Dr. Uçar’s calculated

temperatures, which are discussed in the following. The issue comes when comparing

the fuel temperature and clad temperature between the two simulations. Dr. Uçar

calculated the fuel temperature to be 482ºC and the clad temperature to be 174.85ºC,

while RELAP5-3D® calculated the fuel temperature to be 527ºC, and the clad

temperature to be 132.11ºC. In his CFD simulation, Dr. Uçar did not actually model the

full fuel rod, instead opting to model a cladding outside of the boundary and applying a

heat flux to the boundary to simulate the fuel. Because of this, his fuel temperature

needed to be hand calculated using the bulk fluid temperature as a starting point and

using conduction and convection equations. This hand calculation was highly dependent

on constant values of the gap heat transfer coefficient and the thermal conductivity values.

Dr. Uçar notes in his dissertation that his calculated fuel temperature was significantly

lower than the 540ºC measured in the fuel rod, and this discrepancy was most likely

caused by the use of the hand calculation and constant values used therein. In light of

this discrepancy, it can be reasonably stated that because of the general agreement to both

71

past calculations and measured values, the RELAP5-3D® simulations can be deemed an

accurate representation of the PSBR, and Dr. Uçar’s original design analysis can be

validated.

6.2 Future Work

While this work completed its stated goal of confirming Dr. Uçar’s original

analysis, additional future work has been identified. A transient pulsing analysis should

be completed using RELAP5-3D® for the PSBR. Such work was originally intended to

be part of this analysis, but a lack of additional resources did not allow for this to be

completed. Currently, a detailed prompt fuel temperature coefficient and full modeling

methodology do not exist, and would need to be developed for the completion of this

analysis. Appendix B shows a MATLAB script originally developed by Marcum for use

with the OSTR and adapted for use with the PSBR that determines relevant thermal-

hydraulic parameters such as power and fuel temperature during a pulse. This script

could be used in future work to continue analyzing the PSBR for this project. Appendix

C shows a RELAP5-3D®input block consisting of six control variables, which can be

used in conjunction to recreate a pulse as a function of time in RELAP5-3D. These

resources set a solid base for future work to be completed for a transient RELAP5-

3D®analysis of the PSBR.

72

Works Cited

[1] Argonne National Laboratory. (2014, May) Argonne's Nuclear Science and Technology Legacy. [Online]. http://www.ne.anl.gov/About/cp1-pioneers/

[2] World Nuclear Association. (2015, February) Nuclear Power in the World Today. [Online]. http://www.world-nuclear.org/info/Current-and-Future-Generation/Nuclear-Power-in-the-World-Today/

[3] World Nuclear Organization. (2015, April) Research Reactors. [Online]. http://www.world-nuclear.org/info/Non-Power-Nuclear-Applications/Radioisotopes/Research-Reactors/

[4] General Atomics. TRIGA® Nuclear Reactors. [Online]. http://www.ga.com/triga [5] K. Unlu, Budget Justintification for "New Core-Moderator Assembly and Neutron

Beam Ports Development and Installation at the Radiation Science and Engineering Center (RSEC)".

[6] V. Karriem, PSBR Core Design Studies of the D2O Tank Design and New LEU Fuel Utilization. University Park, PA, USA: The Pennsylvania State University, 2011.

[7] D. Ucar, Modeling And Design Of A New Core-Moderator Assembly And Neutron Beam Ports For The Penn State Breazeale Nuclear Reactor (PSBR). State College, PA, USA: The Pennsylvania State University, 2013.

[8] W. Marcum, Thermal Hydraulic Analysis of the Oregon State TRIGA© Reactor Using RELAP5-3D. Corvallis, OR, USA: The Oregon State University, 2008.

[9] PSBR Staff, "Safety Analysis Report for Renewal of License R-2 for the Breazeale Nuclear Reactor," Radiation Science and Engineering Center, Breazeale Nuclear Reactor, State College, Safety Analysis Report 2005.

[10] The RELAP5-3D®Code Development Team, RELAP5-3D®Code Manual Volume 1: Code Structure, System Models and Soluion Methods, 2013.

[11] John T. Goorley et al., MCNP6™ USER'S Manual, Denise B. Pelowitz, Ed. Los Alamos, NM, USA: Los Alamos National Laboratory, 2013.

[12] Radiation Science and Engineering Center. (2009) Radiation Science and Engineering Center. [Online]. http://www.rsec.psu.edu/

[13] M. T. Simnad, F. C. Foushee, and G. B. West. (1975, January) Fuel Elements for Pulsed TRIGA® Research Reactor.

[14] S. H. Levine, G. C. Geisler, and R. E. Totenbier, TEMPERATURE BEHAVIOR OF 12 WT.& U TRIGA Fuel, 1993.

[15] Nuclear Regulatory Commission. (2015, Mar.) U.S. NRC. [Online]. http://www.nrc.gov/reading-rm/basic-ref/glossary/departure-from-nucleate-boiling-dnb.html

[16] E. E. Feldman. (2007, Dec.) Fundamental Approach to TRIGA Steady-State Thermal-Hydraulic CHF Analysis. [Online]. http://www.ipd.anl.gov/anlpubs/2008/03/61351.pdf

[17] Wikipedia. [Online]. https://upload.wikimedia.org/wikipedia/en/4/49/Boiling_Curve.jpg

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[18] D. C. Groeneveld, S. C. Cheng, and T. Doan, "AECL-UO Critical Heat Flux Lookup Table," Heat Transfer Engineering, vol. 7, pp. 46-62, 1986.

[19] D. C. Groeneveld et al., "The 2006 CHF Look-Up Table," Nuclear Engineering and Design, vol. 237, pp. 1909-1922, 2007.

74

Appendix A: Sample RELAP5-‐3D® Input Deck for PSBR Core 53H

= psbr neutron beam lab project * =============================================================================== * PSBR New Neutron Beam Lab Assembly Project * * The Pennsylvania State University * * By: Matt Wargon * * 2014/2015 * * =============================================================================== * Description: * * The following model describes a single (hot) channel of the Penn State * * Breazeale Nuclear Reactor. The current model is representative of a steady * * state 1 MWth (16.6 KWth in the hot pin) core. This model represents core * * 53H. This core is being used a benchmark for the code against CFD calcs. * * =============================================================================== * Initial Conditions: * * Average Temperature: ~89.6 F (Same temperature as Dr. Ucar) * * Fluid Flow: ~0.1 ft/s * * Fluid Quality: ~0.0 * * Core Power: 1.0 MW * * Pressure: 21.9254 psia (14.7 psi + 7.2254 psi = 16 2/3 feet) * *=============================================================================== * Problem type and option *===============================================================================

75

*crdno prob type option 100 new transnt * *=============================================================================== * Units selection *=============================================================================== *crdno input output 102 british si * *=============================================================================== * noncondensible gas species *=============================================================================== *crdno gas type 110 nitrogen * *=============================================================================== * Timestep control cards *=============================================================================== *crdno End Min dt Max dt ctrl Minor Ed Major Ed Restart 201 400.0 1.0-7 1.0 3 10 10 3000 * *=============================================================================== * Minor Edit Call Outs *=============================================================================== 301 htpowg 3030001 302 htpowg 3030002 303 htpowg 3030003 304 htpowg 3030004 305 htpowg 3030005 306 htpowg 3030006 307 htpowg 3030007 308 htpowg 3030008 309 htpowg 3030009 310 htpowg 3030010 311 htpowg 3030011 312 htpowg 3030012 313 htpowg 3030013 314 htpowg 3030014

76

315 htpowg 3030015 316 htpowg 3030016 317 htpowg 3030017 318 htpowg 3030018 319 htpowg 3030019 320 htpowg 3030020 * *=============================================================================== * Component Data *=============================================================================== * Component 100 * Coolant Source *------------------------------------------------------------------------------- * crdno name type 1000000 Source tmdpvol * crdno Area Length Vol h-ang v-ang delz 1000101 0.005595 3.28083 0.0 0.0 0.0 0.0 * crdno rough HD ctl 1000102 0.0 0.058151 0000000 * crdno ctl 1000200 3 * crdno time pressure temp 1000201 0.0 21.9254 89.6 1000202 5000.0 21.9254 89.6 * *------------------------------------------------------------------------------- * Component 200 * Junction 100->101 *------------------------------------------------------------------------------- * crdno name type 2000000 jun200 sngljun * crdno from to area floss rloss flag 2000101 100010002 101010001 0 0 0 00000000 * crdno ctl flowf flowg velj 2000201 1 0.1 0.0 0 * *------------------------------------------------------------------------------- * Component 101 * Downcomer *------------------------------------------------------------------------------- * crdno name type 1010000 dwncmr pipe * crdno nv 1010001 1

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* crdno Area Vol # 1010101 0.005595 1 * crdno Length Vol # 1010301 2.12542 1 * crdno V-Ang Vol # 1010601 -90.0 1 * crdno delz Vol # 1010701 -2.12542 1 * crdno rough hdy Vol # 1010801 0.0 0.058151 1 * crdno ctl Vol # 1011001 0000010 1 * crdno ctl pressure temp Vol # 1011201 3 21.9254 89.6 0 0 0 1 * *------------------------------------------------------------------------------- * Component 201 * Junction 101->102 *------------------------------------------------------------------------------- * crdno name type 2010000 jun201 sngljun * crdno from to area floss rloss flag 2010101 101010002 102010001 0 0 0 00000000 * crdno ctl flowf flowg velj 2010201 1 0.1 0.0 0 * *------------------------------------------------------------------------------- * Component 114 * Horizontal Connector *------------------------------------------------------------------------------- * crdno name type 1020000 Hconnect pipe * crdno nv 1020001 1 * crdno Area Vol # 1020101 0.005595 1 * crdno Length Vol # 1020301 3.28083 1 * crdno V-Ang Vol # 1020601 0.0 1 * crdno delz Vol # 1020701 0.0 1 * crdno rough hdy Vol # 1020801 0.0 0.058151 1 * crdno ctl Vol # 1021001 0000010 1

78

* crdno ctl pressure temp Vol # 1021201 3 21.9254 89.6 0 0 0 1 * *------------------------------------------------------------------------------- * Component 202 * Junction 102->103 *------------------------------------------------------------------------------- * crdno name type 2020000 jun202 sngljun * crdno from to area floss rloss flag 2020101 102010002 103010001 0 0 0 00000000 * crdno ctl flowf flowg velj 2020201 1 0.1 0.0 0 * *------------------------------------------------------------------------------- * Component 103 * B-Ring Hot Channel *------------------------------------------------------------------------------- * crdno name type 1030000 bringsc pipe * crdno nv 1030001 24 * crdno Area Vol # 1030101 0.005595 1 1030102 0.005595 2 1030103 0.005595 3 1030104 0.005595 4 1030105 0.005595 5 1030106 0.005595 6 1030107 0.005595 7 1030108 0.005595 8 1030109 0.005595 9 1030110 0.005595 10 1030111 0.005595 11 1030112 0.005595 12 1030113 0.005595 13 1030114 0.005595 14 1030115 0.005595 15 1030116 0.005595 16 1030117 0.005595 17 1030118 0.005595 18 1030119 0.005595 19 1030120 0.005595 20 1030121 0.005595 21 1030122 0.005595 22 1030123 0.005595 23

79

1030124 0.005595 24 * crdno Length Vol # 1030301 0.25 1 1030302 0.286667 2 1030303 0.0625 3 1030304 0.0625 4 1030305 0.0625 5 1030306 0.0625 6 1030307 0.0625 7 1030308 0.0625 8 1030309 0.0625 9 1030310 0.0625 10 1030311 0.0625 11 1030312 0.0625 12 1030313 0.0625 13 1030314 0.0625 14 1030315 0.0625 15 1030316 0.0625 16 1030317 0.0625 17 1030318 0.0625 18 1030319 0.0625 19 1030320 0.0625 20 1030321 0.0625 21 1030322 0.0625 22 1030323 0.286667 23 1030324 0.052083 24 * crdno V-Ang Vol # 1030601 90.0 1 1030602 90.0 2 1030603 90.0 3 1030604 90.0 4 1030605 90.0 5 1030606 90.0 6 1030607 90.0 7 1030608 90.0 8 1030609 90.0 9 1030610 90.0 10 1030611 90.0 11 1030612 90.0 12 1030613 90.0 13 1030614 90.0 14 1030615 90.0 15 1030616 90.0 16 1030617 90.0 17 1030618 90.0 18 1030619 90.0 19

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1030620 90.0 20 1030621 90.0 21 1030622 90.0 22 1030623 90.0 23 1030624 90.0 24 * crdno delz Vol # 1030701 0.25 1 1030702 0.286667 2 1030703 0.0625 3 1030704 0.0625 4 1030705 0.0625 5 1030706 0.0625 6 1030707 0.0625 7 1030708 0.0625 8 1030709 0.0625 9 1030710 0.0625 10 1030711 0.0625 11 1030712 0.0625 12 1030713 0.0625 13 1030714 0.0625 14 1030715 0.0625 15 1030716 0.0625 16 1030717 0.0625 17 1030718 0.0625 18 1030719 0.0625 19 1030720 0.0625 20 1030721 0.0625 21 1030722 0.0625 22 1030723 0.286667 23 1030724 0.052083 24 * crdno rough hdy Vol # 1030801 0.000007 0.058151 1 1030802 0.000007 0.058151 2 1030803 0.000007 0.058151 3 1030804 0.000007 0.058151 4 1030805 0.000007 0.058151 5 1030806 0.000007 0.058151 6 1030807 0.000007 0.058151 7 1030808 0.000007 0.058151 8 1030809 0.000007 0.058151 9 1030810 0.000007 0.058151 10 1030811 0.000007 0.058151 11 1030812 0.000007 0.058151 12 1030813 0.000007 0.058151 13 1030814 0.000007 0.058151 14 1030815 0.000007 0.058151 15

81

1030816 0.000007 0.058151 16 1030817 0.000007 0.058151 17 1030818 0.000007 0.058151 18 1030819 0.000007 0.058151 19 1030820 0.000007 0.058151 20 1030821 0.000007 0.058151 21 1030822 0.000007 0.058151 22 1030823 0.000007 0.058151 23 1030824 0.000007 0.058151 24 * crdno floss rloss Jun # 1030901 1.293 0.0 1 1030902 0.0 0.0 2 1030903 0.0 0.0 3 1030904 0.0 0.0 4 1030905 0.0 0.0 5 1030906 0.0 0.0 6 1030907 0.0 0.0 7 1030908 0.0 0.0 8 1030909 0.0 0.0 9 1030910 0.0 0.0 10 1030911 0.0 0.0 11 1030912 0.0 0.0 12 1030913 0.0 0.0 13 1030914 0.0 0.0 14 1030915 0.0 0.0 15 1030916 0.0 0.0 16 1030917 0.0 0.0 17 1030918 0.0 0.0 18 1030919 0.0 0.0 19 1030920 0.0 0.0 20 1030921 0.0 0.0 21 1030922 0.0 0.0 22 1030923 0.861 0.0 23 * crdno ctl Vol # 1031001 0000000 1 1031002 0000000 2 1031003 0000000 3 1031004 0000000 4 1031005 0000000 5 1031006 0000000 6 1031007 0000000 7 1031008 0000000 8 1031009 0000000 9 1031010 0000000 10 1031011 0000000 11 1031012 0000000 12

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1031013 0000000 13 1031014 0000000 14 1031015 0000000 15 1031016 0000000 16 1031017 0000000 17 1031018 0000000 18 1031019 0000000 19 1031020 0000000 20 1031021 0000000 21 1031022 0000000 22 1031023 0000000 23 1031024 0000000 24 * crdno ctl Jun # 1031101 00000000 1 1031102 00000000 2 1031103 00000000 3 1031104 00000000 4 1031105 00000000 5 1031106 00000000 6 1031107 00000000 7 1031108 00000000 8 1031109 00000000 9 1031110 00000000 10 1031111 00000000 11 1031112 00000000 12 1031113 00000000 13 1031114 00000000 14 1031115 00000000 15 1031116 00000000 16 1031117 00000000 17 1031118 00000000 18 1031119 00000000 19 1031120 00000000 20 1031121 00000000 21 1031122 00000000 22 1031123 00000000 23 * crdno ctl pressure temp Vol # 1031201 3 21.9254 89.6 0 0 0 1 1031202 3 21.9254 89.6 0 0 0 2 1031203 3 21.9254 89.6 0 0 0 3 1031204 3 21.9254 89.6 0 0 0 4 1031205 3 21.9254 89.6 0 0 0 5 1031206 3 21.9254 89.6 0 0 0 6 1031207 3 21.9254 89.6 0 0 0 7 1031208 3 21.9254 89.6 0 0 0 8 1031209 3 21.9254 89.6 0 0 0 9

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1031210 3 21.9254 89.6 0 0 0 10 1031211 3 21.9254 89.6 0 0 0 11 1031212 3 21.9254 89.6 0 0 0 12 1031213 3 21.9254 89.6 0 0 0 13 1031214 3 21.9254 89.6 0 0 0 14 1031215 3 21.9254 89.6 0 0 0 15 1031216 3 21.9254 89.6 0 0 0 16 1031217 3 21.9254 89.6 0 0 0 17 1031218 3 21.9254 89.6 0 0 0 18 1031219 3 21.9254 89.6 0 0 0 19 1031220 3 21.9254 89.6 0 0 0 20 1031221 3 21.9254 89.6 0 0 0 21 1031222 3 21.9254 89.6 0 0 0 22 1031223 3 21.9254 89.6 0 0 0 23 1031224 3 21.9254 89.6 0 0 0 24 * crdno ctl 1031300 1 * crdno flowf flowg velj Jun # 1031301 0.1 0.0 0.0 1 1031302 0.1 0.0 0.0 2 1031303 0.1 0.0 0.0 3 1031304 0.1 0.0 0.0 4 1031305 0.1 0.0 0.0 5 1031306 0.1 0.0 0.0 6 1031307 0.1 0.0 0.0 7 1031308 0.1 0.0 0.0 8 1031309 0.1 0.0 0.0 9 1031310 0.1 0.0 0.0 10 1031311 0.1 0.0 0.0 11 1031312 0.1 0.0 0.0 12 1031313 0.1 0.0 0.0 13 1031314 0.1 0.0 0.0 14 1031315 0.1 0.0 0.0 15 1031316 0.1 0.0 0.0 16 1031317 0.1 0.0 0.0 17 1031318 0.1 0.0 0.0 18 1031319 0.1 0.0 0.0 19 1031320 0.1 0.0 0.0 20 1031321 0.1 0.0 0.0 21 1031322 0.1 0.0 0.0 22 1031323 0.1 0.0 0.0 23 * *------------------------------------------------------------------------------- * Component 203 * Junction 103->104 *-------------------------------------------------------------------------------

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* crdno name type 2030000 jun203 sngljun * crdno from to area floss rloss flag 2030101 103240002 104010001 0 0 0 00000000 * crdno ctl flowf flowg velj 2030201 1 0.1 0.0 0 * *------------------------------------------------------------------------------- * Component 104 * Coolant Sink *------------------------------------------------------------------------------- * crdno name type 1040000 Sink tmdpvol * crdno Area Length Vol h-ang v-ang delz 1040101 0.005595 3.28083 0.0 0.0 0.0 0.0 * crdno rough HD ctl 1040102 0.0 0.058151 0000000 * crdno ctl 1040200 103 * crdno time pressure temp 1040201 0.0 21.9254 89.6 1040202 5000.0 21.9254 89.6 * *=============================================================================== * Heat Structures *=============================================================================== * Heat Structure 303 * B-Ring Core Single Channel *------------------------------------------------------------------------------- * crdno no.hs no.m.p geo s.s.flg left 13030000 20 24 2 0 0.0 * crdno meshflg fmt 13030100 0 1 * crdno intvl rt.cor 13030101 1 0.010417 13030102 1 0.011647 13030103 1 0.014108 13030104 1 0.016601 13030105 1 0.019062 13030106 1 0.021522 13030107 1 0.023983 13030108 1 0.026476 13030109 1 0.028937 13030110 1 0.031398

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13030111 1 0.033858 13030112 1 0.036352 13030113 1 0.038812 13030114 1 0.041273 13030115 1 0.043733 13030116 1 0.046227 13030117 1 0.048688 13030118 1 0.051148 13030119 1 0.053609 13030120 1 0.056102 13030121 1 0.058563 13030122 1 0.058584666 13030123 1 0.060251333 * crdno comp # intvl 13030201 1 1 13030202 2 21 13030203 3 22 13030204 4 23 * crdno source intvl 13030301 0.000000 1 13030302 0.044381574 2 13030303 0.044589445 3 13030304 0.044576506 4 13030305 0.04488536 5 13030306 0.045134018 6 13030307 0.045360736 7 13030308 0.045773385 8 13030309 0.046183784 9 13030310 0.046662254 10 13030311 0.047268148 11 13030312 0.047943238 12 13030313 0.048743221 13 13030314 0.049708881 14 13030315 0.050801965 15 13030316 0.052272819 16 13030317 0.053903443 17 13030318 0.055950937 18 13030319 0.058469305 19 13030320 0.06161157 20 13030321 0.06577941 21 13030322 0.000000 22 13030323 0.000000 23 * crdno temp intvl 13030401 150.0 24 * crdno lftvol incr b.c sacode safac h.s.no 13030501 0 0 0 1 0.0625 1

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13030502 0 0 0 1 0.0625 2 13030503 0 0 0 1 0.0625 3 13030504 0 0 0 1 0.0625 4 13030505 0 0 0 1 0.0625 5 13030506 0 0 0 1 0.0625 6 13030507 0 0 0 1 0.0625 7 13030508 0 0 0 1 0.0625 8 13030509 0 0 0 1 0.0625 9 13030510 0 0 0 1 0.0625 10 13030511 0 0 0 1 0.0625 11 13030512 0 0 0 1 0.0625 12 13030513 0 0 0 1 0.0625 13 13030514 0 0 0 1 0.0625 14 13030515 0 0 0 1 0.0625 15 13030516 0 0 0 1 0.0625 16 13030517 0 0 0 1 0.0625 17 13030518 0 0 0 1 0.0625 18 13030519 0 0 0 1 0.0625 19 13030520 0 0 0 1 0.0625 20 * crdno rtvol incr b.c sacode safac h.s.no 13030601 103030000 10000 1 1 0.0625 1 13030602 103040000 10000 1 1 0.0625 2 13030603 103050000 10000 1 1 0.0625 3 13030604 103060000 10000 1 1 0.0625 4 13030605 103070000 10000 1 1 0.0625 5 13030606 103080000 10000 1 1 0.0625 6 13030607 103090000 10000 1 1 0.0625 7 13030608 103100000 10000 1 1 0.0625 8 13030609 103110000 10000 1 1 0.0625 9 13030610 103120000 10000 1 1 0.0625 10 13030611 103130000 10000 1 1 0.0625 11 13030612 103140000 10000 1 1 0.0625 12 13030613 103150000 10000 1 1 0.0625 13 13030614 103160000 10000 1 1 0.0625 14 13030615 103170000 10000 1 1 0.0625 15 13030616 103180000 10000 1 1 0.0625 16 13030617 103190000 10000 1 1 0.0625 17 13030618 103200000 10000 1 1 0.0625 18 13030619 103210000 10000 1 1 0.0625 19 13030620 103220000 10000 1 1 0.0625 20 * crdno s.type s.mult dir.lft dir.rt h.s.no 13030701 100 0.034521 0 0 1 13030702 100 0.035703 0 0 2 13030703 100 0.041118 0 0 3 13030704 100 0.046382 0 0 4 13030705 100 0.050059 0 0 5

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13030706 100 0.054181 0 0 6 13030707 100 0.057248 0 0 7 13030708 100 0.059954 0 0 8 13030709 100 0.061424 0 0 9 13030710 100 0.062029 0 0 10 13030711 100 0.062109 0 0 11 13030712 100 0.061248 0 0 12 13030713 100 0.060408 0 0 13 13030714 100 0.057233 0 0 14 13030715 100 0.053951 0 0 15 13030716 100 0.050397 0 0 16 13030717 100 0.046492 0 0 17 13030718 100 0.040265 0 0 18 13030719 100 0.034162 0 0 19 13030720 100 0.031118 0 0 20 * crdno hdy htdlthfwd htdlthrv h.s.no 13030901 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 1 13030902 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 2 13030903 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 3 13030904 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 4 13030905 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 5 13030906 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 6 13030907 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 7 13030908 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 8 13030909 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 9 13030910 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 10 13030911 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 11 13030912 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 12 13030913 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 13 13030914 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 14 13030915 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 15 13030916 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 16 13030917 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 17 13030918 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 18 13030919 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 19 13030920 0.0 10.0 10.0 0.0 0.0 0.0 0.0 1.0 20 * *=============================================================================== * General Tables *=============================================================================== * Time Table 100 * Core Power *------------------------------------------------------------------------------- * crdno name

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20210000 power * crdno Time Power(MW) 20210001 0.0 0.0166 20210002 20.0 0.0166 20210003 50.0 0.0166 20210004 100.0 0.0166 20210005 150.0 0.0166 20210006 5000.0 0.0166 * *=============================================================================== * Heat Structure Thermal Property Data *=============================================================================== * Zirconium Pin *------------------------------------------------------------------------------- * crdno type th.con.ct vol.ht.cap 20100100 tbl/fctn 1 1 * crdno temp (F) th.con 20100101 -99.4 0.004045 *(Btu/s-ft-F) 20100102 260.6 0.003467 20100103 620.6 0.003322 20100104 980.6 0.003467 20100105 1340.6 0.003804 20100106 1700.6 0.004173 20100107 2240.6 0.004622 * * crdno temp (F) ht.cap 20100151 -99.4 25.862257 *(Btu/ft3-F) 20100152 260.6 29.388929 20100153 620.6 31.544117 20100154 980.6 33.503379 20100155 1340.6 35.462640 20100156 1700.6 33.699305 20100157 2240.6 33.699305 * *------------------------------------------------------------------------------- * Fuel *------------------------------------------------------------------------------- * crdno type th.con.ct vol.ht.cap 20100200 tbl/fctn 1 2 * crdno th.con 20100201 0.00282228 *(Btu/s-ft-F) * crdno l.temp.limit u.temp.limit A0 A1 20100251 32.0 10000.0 30.4178 0.034543 0 0 0 0 0 *(Btu/ft3-F) *

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*------------------------------------------------------------------------------- * Gap *------------------------------------------------------------------------------- * crdno type 20100300 gap * *------------------------------------------------------------------------------- * Stainless Steel Cladding *------------------------------------------------------------------------------- * crdno type 20100400 s-steel * .*----------------------- end of input -----------------------------------------

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Appendix B: MATLAB Transient Pulse Script

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Numerical Solutions of Point Reactor Kinetics Equations % % By: Wade Marcum and altered by Matt Wargon for use with PSBR% % % % "Integration Factor Method" % % % % This program is built to give the user the ability to solver the % % the point reactor kinetics equations using integration factor method. % % % % Note: Constants hard-coded are refered to for U-235 specifically % %============================================================% clear all clc fprintf('1) Functional Reactivity Coefficient\n2) Constant Reactivity Coefficient'); which=input('\nWhich Coefficient [1-2]?: '); % LEU MOL if which==1 beta=0.007; alphaT=inline('1.320E-07*T+1.161E-05', 'T'); %alphaT=inline('0.8*4.228E-07*T+0.8*4.584E-05', 'T'); %alphaT=inline('4.228E-07*T+4.584E-05', 'T'); L=38.0E-6; Cp0=83645.1; Cp1=170.98; end if which==2 beta=0.007; alphaT=9.5E-5; L=38E-6; Cp0=83645.1; Cp1=170.98; end % Implementing the Core Configuration Information to the U-235 properties %-------------------------------------------------------------------------------------------------------% L=L; % mean neutron generation time hl=[54.51 21.84 6 2.23 0.496 .179]; % half lifes for 6 groups dc=log(2)./hl; % decay constants for 6 groups betai=[.038 .213 .188 .407 .128 .026]; % Relative Yield beta=beta; % average delayed neutron fraction bi=betai.*beta; % delayed neutron fraction for each group Cp0=Cp0; % Specific Heat Constant

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Cp1=Cp1; % Specific Heat Slope % Time-step Solution Parameters %-------------------------------------------------------------------------------------------------------% finish=.15; % end of t interval sec step=1E-5; % time step size sec count=finish/step+1; % # of steps that will be taken t=(0:count); % Iteration Number ttime(1)=0; for tt=2:count+1 ttime(tt)=ttime(tt-1)+step; end % System Parameter inputs %-------------------------------------------------------------------------------------------------------% Power=100; dollars=2.50; Temp=60; rho=dollars*beta; % Solving Using integration factor %-------------------------------------------------------------------------------------------------------% for i=1:6 C(i)=(bi(i))/(dc(i)*L*(1-rho(1)))*Power(1); end for j=1:count-1 A=(rho(j)-beta)/(L*(1-rho(j))); % Power Calculation Power(j+1)=(Power(j)*exp(A*step)+((sum(C))/A)*(exp(A*step)-1)); % Precurser Calculation for i=1:6 C(i)=C(i)*exp(-dc(i)*step)+(Power(j)+Power(j+1))*(1/2)*(bi(i)/(L*(1-rho(j))))*(1-exp(-dc(i)*step))/dc(i); end % Temperature Calculation X=(step)*(Power(j+1)+Power(j))/2; Y=Cp0*Temp(j)+(1/2)*Cp1*(Temp(j))^2; c=-1*(X+Y); a=(Cp1)/2; b=Cp0; Temp(j+1)=(-b+sqrt(b^2-4*a*c))/(2*a); % Reactivity Calculation if which==2 rho(j+1)=rho(j)-alphaT*(Temp(j+1)-Temp(j)); else rho(j+1)=rho(j)-alphaT(Temp(j+1))*(Temp(j+1)-Temp(j)); end end trace=1.83*Temp;

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Appendix C: RELAP5-‐3D® Transient Control Block Sample

******************************* * Control Blocks * ******************************* * * name type scale ival iflag limit 20500100 "exp" poweri -1.0 0.0 0 0 * input param power 20500101 cntrlvar 4 2 * * name type scale ival iflag limit 20500300 "sum" sum 1.0 0.0 0 0 * a0 scale name param 20500301 -0.05871 1.0 time 0 * * name type scale ival iflag limit 20500400 "divide" mult 145.349 0.0 0 0 * input param 20500401 cntrlvar 3 * * name type value 20500500 "e" constant 2.71828 * * name type scale ival iflag limit 20500600 "trace" powerx 8.40889E7 0.0 0 0 * input param input param 20500601 cntrlvar 5 cntrlvar 1

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