Scaling Analysis of the Osu High Temperature Test Facility During a Pressurized Conduction Cooldown Event Using Relap5- 3D

AN ABSTRACT OF THE THESIS OF

Juan A. Castañeda for the degree of Master of Science in Nuclear Engineering presented on May 21, 2014. Tittle: SCALING ANALYSIS OF THE OSU HIGH TEMPERATURE TEST FACILITY DURING A PRESSURIZED CONDUCTION COOLDOWN EVENT USING RELAP5- 3D

Abstract approved:

Brian G. Woods

In early 2000, the Generation IV International Forum (GIF) was created to perform research and development for the next generation nuclear systems. Among the selected nuclear systems was the Very High Temperature Gas-Cooled Reactor (VHTR). Then in 2008, the U.S. Department of Energy (DOE) decided that the Next Generation Nuclear Plant (NGNP) would be the VHTR. The VHTR was chosen because it has the capability to produce electricity, hydrogen and may be used for other high-temperature process heat applications. In support of licensing and validation of the VHTR, Oregon State University was tasked to develop a high temperature apparatus that will be able to capture the thermal fluids phenomena of the VHTR and perform integral effects tests for validation of existing safety codes. The design has been called the High Temperature Test Facility (HTTF), which is a scaled design of the Modular High Temperature Gas-Cooled Reactor (MHTGR). The objective of this study was to investigate the ability of the HTTF to simulate the Pressurized Conduction Cooldown (PCC) Event during the natural circulation phase in the MHTGR. This was achieved with the aid of a thermal hydraulic systems code, RELAP5-3D.

SCALING ANALYSIS OF THE OSU HIGH TEMPERATURE TEST FACILITY DURING A PRESSURIZED CONDUCTION COOLDOWN EVENT USING RELAP5-3D by Juan A. Castañeda

A THESIS Submitted to Oregon State University

in partial fulfillment of the requirements for the degree of

Master of Science

Presented May 21, 2014 Commencement June 2014

Master of Science thesis of Juan A. Castañeda presented on May 21, 2014.

APPROVED:

______Major Professor, representing Nuclear Engineering

______Head of the Department of Nuclear Engineering and Radiation Health Physics

______Dean of the Graduate School

I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request.

______Juan A. Castañeda, Author

ACKNOWLEDGEMENTS

The author would like to express his appreciation to all those who somehow contribute to the success of this project. I wish to begin acknowledging and thanking my advisor, Dr. Brian Woods, for giving me the opportunity to work under his guidance. The professional development that I have experienced under his guidance and the willingness to assist me at the times when I needed it the most is invaluable. I greatly appreciate for what he has done and for preparing me for my future outcomes as an engineer. I also would like to express my appreciation to Dr. Wade Marcum for always being willing to answer questions related to my work and providing guidance throughout my graduate studies. Also, I would like to thank Dr. Todd Palmer for taking the time from his busy schedule to be part of my committee and providing valuable feedback through my thesis defense. Also, in no particular order, I would like to express my appreciations to my fellow graduate students Matt Hertel, Jordan Cox, Luke Harmon, Mike Holton, Trever Howard, Mario Gomez, Ruirui Liu, Renae Lenhof, Jackson Harter and Etienne Mullen for their support and encouragement throughout my graduate studies. I also would like to recognize and express my appreciations to Dr. Kathryn Higley for giving me the opportunity to attain my graduate studies at OSU. The knowledge and the learning that I have experience in my short time at OSU are unmatched. I also wish to acknowledge and thank my undergraduate professors, Dr. David Simpson, Dr. Nathaniel Greene and Dr. Nazafarin Fallahian for expressing your trust and guiding me into the right direction to pursue further education. Finally, I would like to thank my parents, Luis and Gilda, and my sister, Evelyn, whose love and support have given me the courage and perseverance to believe in myself in order to chase my dreams.

TABLE OF CONTENTS

Page

1 INTRODUCTION ...... 1 1.1 Overview ...... 2 1.1.1 The MHTGR ...... 3 1.1.2 The HTTF ...... 8 1.2 Motivation of Study ...... 11 1.3 Research Objectives ...... 12 1.4 Assumptions ...... 13 1.5 Limitations ...... 13 1.6 Overview of the Following Chapters ...... 14 2 LITERATURE REVIEW ...... 15 2.1 Postulated Accident Scenarios ...... 15 2.1.1 Loss of Forced Convection Accidents ...... 16 2.1.2 Reactivity, Steam Water Ingress and Plant Coupling Events ...... 17 2.2 The Pressurized Conduction Cooldown Event ...... 18 2.3 Previous Relevant Literatures ...... 20 3 HTTF SCALING PARAMETERS ...... 28 3.1 Single-Phase Natural Circulation Loop Scaling Analysis ...... 28 3.2 Single-Phase Fluid Natural Circulation Loop Scaling Ratios ...... 32 3.3 Primary Loop Resistance ...... 35 3.4 Structural Materials Heat Transfer ...... 36 3.5 HTTF Design Specifications ...... 43 3.5.1 Scaling Choices ...... 43 3.5.2 Natural Circulation Design Specifications ...... 44 3.5.3 Structural Materials Design Specifications ...... 46 3.5.4 HTTF Scaling Ratios ...... 51 4 DESCRIPTION OF THE RELAP5-3D MODELS ...... 55 4.1 The MHTGR ...... 55

TABLE OF CONTENTS (Continued)

Page

4.2 The HTTF ...... 59 4.3 Benchmarking of the Models at Steady-State ...... 64 5 PCC EVENT SIMULATIONS AND RESULTS ...... 74 5.1 Scenario 1: PCC Event with SG Heat Removal ...... 75 5.1.1 Case 1 Specifics ...... 75 5.1.2 Case 1 Results ...... 75 5.2 Scenario 2: PCC Event with SG and Cross-Duct Vessel Break ...... 82 5.2.1 Case 2 Specifics ...... 82 5.2.2 Case 2 Results ...... 84 5.3 Scenario 3: PCC Event with an Isolated Reactor Vessel ...... 89 5.5.1 Case 3 Specifics ...... 89 5.5.2 Case 3 Results ...... 91 5.4 Scenarios Conclusion ...... 95 6 HTTF SENSITIVITY STUDIES ...... 98 6.1 Methods to Preserved Similarity in the HTTF ...... 98 6.1.1 Reducing Natural Convection ...... 99 6.1.2 Core Power Increased ...... 100 6.1.3 Reducing Rate of Decay Power ...... 102 6.1.4 Modified RCCS Heat Removal System ...... 103 6.1.5 Emissivity Decreased ...... 105 6.1.6 Results of Sensitivity Studies for HTTF parameters to Control ...... 105 6.2 Sensitivity Studies of the In-Vessel Solid Structures ...... 108 7 CONCLUSIONS AND FUTURE WORK ...... 114 7.1 PCC Event with SG/Heat-Exchanger Heat Removal ...... 114 7.2 PCC Event with a Cross-Duct Vessel Break ...... 114 7.3 PCC Event with an Isolated Reactor Pressure Vessel ...... 115 7.4 Sensitivity Analysis ...... 115 7.5 Future Work Suggestion………………………………………………………………………………………….116

TABLE OF CONTENTS (Continued)

Page BIBLIOGRAPHY ...... 117 APPENDICES ...... 120 APPENDIX A - DESIGN PARAMETERS ...... 121 A.1 MHTGR Design Parameters ...... 121 A.2 HTTF Design Parameters ...... 129 APPENDIX B – MATERIAL PROPERTIES ...... 138 B.1 Tables of Thermal Conductivities ...... 138 B.2 Tables of Volumetric Heat Capacities ...... 145 APPENDIX C – DECAY CORE POWER CURVES ...... 151 C.1 MHTGR Decay Curve ...... 151 C.2 HTTF Decay Curve ...... 154

LIST OF FIGURES

Figure Page

Figure 1-1: The General Atomics Proposed NGNP Reactor Module [6] ...... 3 Figure 1-2: The MHTGR Steam Generator Arrangement [6] ...... 4 Figure 1-3: The General Atomics Proposed NGNP Primary System Flow Diagram [19] ...... 5 Figure 1-4: Cross Sectional view of the MHTGR Reactor Core [19] ...... 7 Figure 1-5: The MHTGR Reactor Cavity Cooling System [6] ...... 8 Figure 1-6: The High Temperature Test Facility Reactor Vessel ...... 9 Figure 1-7: The High Temperature Test Facility Ceramic Core ...... 10 Figure 1-8: The High Temperature Test Facility...... 11 Figure 2-1: Single-phase Natural Circulation during a PCC Event. [5] ...... 19 Figure 3-1: Conduction and Radiation Heat Transfer Geometry of the HTTF Core. [5] ...... 37 Figure 4-1: Nodalization of the MHTGR RELAP5-3D model ...... 56 Figure 4-2: RELAP5-3D Nodalization Definitions ...... 57 Figure 4-3: The Unit Cell of the MHTGR Core Channel. [10] ...... 58 Figure 4-4: Nodalization of the HTTF RELAP5-3D model ...... 61 Figure 4-5: The Unit Cell of the HTTF Core Channel. [10] ...... 62 Figure 4-6: The Predicted Primary Loop Temperature Profile of the PSID, MHTGR and HTTF...... 68 Figure 4-7: The Predicted Primary Loop Pressure of the MHTGR RELAP5-3D Model compared against the PSID values...... 69 Figure 4-8: The Predicted Primary Loop Pressure of the HTTF RELAP5-3D Model and the Design Value...... 69 Figure 4-9: The Steam Generator and the U-tube Heat-exchanger temperature distributions along the primary and secondary loops of the MHTGR and HTTF RELAP5-3D models...... 71 Figure 4-10: The Predicted Radial Temperature Profile of the MHTGR and HTTF...... 73 Figure 5-1: The MHTGR heat balance results from the PSID compared to the MHTGR heat balance results from RELAP5-3D during a PCC event...... 76 Figure 5-2: The peak fuel temperature of the MHTGR and the HTTF during a PCC event with the availability of the steam generator to remove decay heat...... 77

LIST OF FIGURES (Continue)

Figure Page

Figure 5-3: The MHTGR and HTTF helium temperature at core inlet during a PCC event with the availability of the SG to remove reactor decay heat...... 78 Figure 5-4: The MHTGR heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system...... 79 Figure 5-5: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system...... 80 Figure 5-6: The helium mass flow rate of the MHTGR during a PCC event with the availability of the steam generator to remove reactor decay heat...... 81 Figure 5-7: The helium mass flow rate of the HTTF during a PCC event with the availability of the steam generator to remove reactor decay heat...... 81 Figure 5-8: Nodalization of the MHTGR RELAP5-3D model for the PCC event with a cross-duct vessel break...... 83 Figure 5-9: Nodalization of the HTTF RELAP5-3D model for the PCC event with a cross-duct vessel break...... 83 Figure 5-10: The peak fuel temperature of the MHTGR and HTTF during a PCC event with a cross-duct vessel break the availability of the SG to remove decay heat...... 85 Figure 5-11: The MHTGR and HTTF helium temperature at core inlet during a PCC event with the availability of the SG to remove reactor decay heat...... 85 Figure 5-12: The MHTGR heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system...... 86 Figure 5-13: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system...... 87 Figure 5-14: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system...... 88 Figure 5-15: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system...... 88 Figure 5-16: Nodalization of the HTTF RELAP5-3D model for the PCC event with an isolated reactor pressure vessel...... 90

LIST OF FIGURES (Continue)

Figure Page

Figure 5-17: Nodalization of the HTTF RELAP5-3D model for the PCC event with an isolated reactor pressure vessel...... 90 Figure 5-18: The peak fuel temperature of the MHTGR and the HTTF with an isolated reactor pressure vessel during a PCC event with ...... 91 Figure 5-19: The MHTGR and HTTF helium temperature at core inlet with an isolated reactor pressure vessel during a PCC event...... 92 Figure 5-20: The MHTGR heat balance with an isolated reactor pressure vessel during a PCC event with ...... 93 Figure 5-21: The HTTF heat balance with an isolated reactor pressure vessel during a PCC event with ...... 93 Figure 5-22: The MHTGR helium mass flow rate with an isolated reactor pressure vessel during a PCC event...... 94 Figure 5-23: The HTTF helium mass flow rate with an isolated reactor pressure vessel during a PCC event...... 95 Figure 6-1: Nodalization of the HTTF RELAP5-3D model with an opened loop during the PCC event...... 100 Figure 6-2: The Predicted Radial Temperature Profile of the MHTGR, the HTTF Base Model and the HTTF model with an initial increase of 50% in core power...... 102 Figure 6-3: Nodalization of the HTTF RELAP5-3D model with a modified RCCS design for the PCC event with an isolated reactor pressure vessel...... 103 Figure 6-4: The Predicted Radial Temperature Profile of the MHTGR, the HTTF base model and the modified HTTF RCCS model...... 105 Figure 6-5: The peak fuel temperatures of the MHTGR and HTTF sensitivity analyses during the natural circulation phase of the PCC event...... 107 Figure 6-6: The peak fuel temperatures of the MHTGR and HTTF during the PCC event to analyze the sensitivity results for the in-vessel solid structures ...... 112

LIST OF TABLES

Table Page

Table 3-1: The HTTF design scaling specification ratios...... 51 Table 3-2: The HTTF natural circulation loop design scaling specification ratios...... 52 Table 3-3: The HTTF in-vessel solid structural material scaling ratios...... 52 Table 3-4: Initial Conditions of the HTTF. [19] ...... 54 Table 4-1: The MHTGR in-vessel solid material properties...... 59 Table 4-2: The HTTF in-vessel solid material properties...... 63 Table 4-3: The Steady-State RELAP5-3D predicted values of the thermal-hydraulics parameters of interest of the MHTGR. [5] ...... 64 Table 4-4: The Steady-State RELAP5-3D predicted values of the thermal-hydraulics parameters of interest of the HTTF...... 66 Table 5-1: Description of the scenarios of the PCC event...... 74 Table 5-2: Design specifications and distortions of the in-vessel solid structures scaling ratios in the MHTGR and HTTF...... 97 Table 6-1: Parameters that could be control in the HTTF...... 98 Table 6-2: The Steady-State RELAP5-3D predicted values of the thermal-hydraulics parameters of interest of the HTTF with core power increase of 50%...... 101 Table 6-3: The HTTF Steady-State RELAP5-3D calculations of the thermal-hydraulics parameters of interest using the modified RCCS model...... 104 Table 6-4: Calculation Matrix Summary for the sensitivity studides of the parameters that could be manipulated in the HTTF...... 106 Table 6-5: The design specifications and scaling ratios of the in-vessel solid structures of the HTTF...... 108 Table 6-6: The design specifications and scaling ratios of the in-vessel solid structures of the HTTF...... 110

SCALING ANALYSIS OF THE OSU HIGH TEMPERATURE TEST FACILITY DURING A PRESSURIZED CONDUCTION COOLDOWN EVENT USING RELAP5-3D

1 INTRODUCTION

The current concerns of global warming and the production of low-carbon electricity at stable and competitive cost has been a challenge to the energy sector for the last couple of decades. Nuclear technology could be a solution to this problem, however past nuclear incidents, such as Chernobyl, Three-Mile Island and the most recent, Fukushima Diiachi, has placed a negative perception on the public. As a result, the U.S. Department of Energy and other international organizations have started research and development into advanced nuclear reactor technologies. [1] Consequently, the Generation IV International Forum (GIF) was created to perform research and development for the next generation nuclear systems. [1] The GIF in their “Technology Roadmap” identified four goals needed to satisfy the fourth generation of advanced nuclear energy: 1) sustainability, 2) safety and reliability, 3) economic competitiveness and 4) proliferation resistance and physical protection. [2] The objective is to enhance technologies that excel in these four areas. In 2002 the GIF identified six nuclear systems that would satisfy their Generation IV requirements: The Gas-Cooled Fast Reactor (GFR), Lead-Cooled Fast Reactor (LFR), Molten Salt Reactor (MSR), Sodium-Cooled Fast Reactor (SFR), Supercritical-Water-Cooled Reactor (SCWR) and the Very-High-Temperature Reactor (VHTR). [2] In the United States, this new effort is coordinated by the Department of Energy (DOE). In 2008, the DOE decided that the Next Generation Nuclear Plant (NGNP) would be the Very High Temperature Gas-Cooled Reactor (VHTR).The VHTR was chosen because it has the capability to produce electricity and hydrogen. The VHTR can also provide high-temperature process heat that can be used as a substitute for the burning of fossil fuels for a wide range of commercial applications. [3] [4]

The U.S. Nuclear Regulatory Commission (NRC) is assigned with the licensing and regulation of new nuclear technology. Since the VHTR is a new nuclear system with unproven technology, the NRC will need to revise its requirements for licensing the VHTR. [4] Therefore, the Energy Policy Act of 2005 (EPAct 2005) recognized the need for an alternative strategy for the licensing of the VHTR. [3] [4] This strategy includes the use of analytical tools currently applied to Light Water Reactors (LWR), as well as using experimental data develop by the individual applicant and domestic and international organizations.[3] [4] Also, since the technology still under the development phase, changes to the licensing strategy may be necessary. [4] [5] With the need of analytical tools, the NRC developed an agreement between Oregon State University (OSU), Texas A&M University (TAMU), and the University of Michigan (UM) “to study the thermal hydraulics and reactor physics of the VHTR”. [5] The agreement involves the research and development of coupled reactor physics techniques, separate and integral effects tests and the study of gas reactor thermal fluids phenomena. [5] Oregon State University was tasked to develop a “high temperature apparatus” [5] that will be able to capture the thermal fluids phenomena of the VHTR and perform integral effects tests for existing safety code validation. [5] The apparatus has been called the High Temperature Test Facility (HTTF), which is a scaled design of the Modular High Temperature Gas-Cooled Reactor (MHTGR). [5] The HTTF will be able to conduct tests and provide data for the Depressurized Conduction Cool-down (DCC) event. In addition, to a limited extent, the HTTF will be able to simulate the Pressurized Conduction Cool-down (PCC) event. [5]

1.1 Overview

Gas-cooled reactors have been around for a long time. One of the earliest developments began in the United Kingdom (UK) with the experimental “Dragon” reactor design in 1964. [6] The Peach Bottom Unit 1 and Fort Saint-Vrain (FSV) were built in the U.S. in 1966, using the prismatic design approach. The AVR was built in Germany in 1961, using the pebble bed idea. Germany also built the Thorium High-

Temperature Reactor (THTR-300) in 1983. Recently, the High Temperature Test Reactor (HTTR) was built in Japan and the High Temperature Reactor (HTR-10) in China in 1998. [6] Because information is available to the public, the Modular High Temperature Gas-Cooled Reactor (MHTGR) was chosen as a point design for this project. [10]

1.1.1 The MHTGR

The idea for the MHTGR began in 1984 with the idea of a “simpler, safer’ nuclear power plant. The idea was to develop a design that contains passive systems, but that can also stay economically competitive. [7] The GA’s MHTGR consists of a reactor pressure vessel on one side and the steam generator on the other side. Figure 1 shows a schematic of the MHTGR reactor module. [6]

Figure 1-1: The General Atomics Proposed NGNP Reactor Module [6]

The single steam generator vessel contains a once-through helically coiled steam generator bundle and an electrical driven-motor pump, called the “circulator”. The steam- generator thermal center is located below that of the reactor core as shown on Figure 1-1. The steam generator is a vertically oriented up-flow boiling, cross-counter flow and tube heat exchanger as shown on Figure 1-2. It utilizes multiple helically coiled tube bundles to remove 352 MWth of heat from the primary system. In addition, the steam generator vessel is designed to enable easy accessibility into the steam-generator tube bundle through the removal of the upper vessel head. [6]

Figure 1-2: The MHTGR Steam Generator Arrangement [6]

The MHTGR is a single-phase helium gas cooled reactor. Helium was chosen as its primary coolant due to being an inert gas (does not chemically react) and having minimal reactivity effects. Figure 1-3 shows a diagram of the flow path of helium and illustrates how heat is added and removed within the primary system during normal operations.

Figure 1-3: The General Atomics Proposed NGNP Primary System Flow Diagram [19]

Helium coolant discharges from the circulator and flows to the reactor vessel in the cold duct of the cross-duct vessel, flows up between the reactor vessel and the core

6 barrel into the upper plenum, down through the core into the lower plenum, through the hot duct of the cross-duct vessel, down through the steam-generator bundle, then up through the annular region between the steam-generator bundle and steam generator vessel and back into the inlet of the helium circulator. On the secondary coolant side, feedwater enters from the bottom of the steam-generator vessel, flows up through the once-through helical coil tube bundle and exits as superheated steam at the top of the Steam Generator bundle. [6] [19] The MHTGR reactor graphite core consists of the annular active core surrounded by inner and outer reflector elements. The graphite allows high heat capacity and structural stability at very high temperatures. The active core consists of hexagonal graphite fuel elements that contain holes for fuel compacts and coolant channels for helium flow. The fuel elements are stacked on top of each other to form columns in a hexagonal annular configuration. Figure 1-4 shows a cross-sectional view of the MHTGR reactor core. [6] The fuel compacts consists of refractory coated fuel particles, identified as Tristructural-Isotropic (TRISO), which retains its fission products at much higher temperatures. During an accident event, the low power density (5.9 W/cm3) and the annular core design, allows a passive mode of heat removal from the core to maintain maximum fuel temperatures below 1,600 ○C. The fuel is also designed with a negative temperature coefficient of reactivity, which shuts down the reactor above normal operating temperatures. [6] [10] [19]

Figure 1-4: Cross Sectional view of the MHTGR Reactor Core [19]

Consequentially, the MHTGR contains an un-insulated steel reactor vessel that is surrounded by a natural circulation of air in the Reactor Cavity Cooling System (RCCS). The RCCS is a safety related system that passively removes decay heat from the core during accident conditions. During an accident scenario, heat is mainly removed by conduction through the graphite reflector and by convection and thermal radiation from the reactor vessel to the RCCS. [19] A schematic representing the Reactor Cavity Cooling System is shown on figure 1-5.

Overall, the MHTGR operates at a full core power of 350 MWth with a reactor pressure vessel inlet and outlet temperatures of approximately 259 ○C and 687 ○C respectively. The primary loop is pressurized to approximately 6.38 MPa with a coolant flow rate of 157 kg/s. [19]

Figure 1-5: The MHTGR Reactor Cavity Cooling System [6]

1.1.2 The HTTF

The High Temperature Test Facility (HTTF) is a thermal-hydraulic test facility that has been scaled to be full temperature and reduced pressure (~1/8th) of that of the MHTGR and will operate at a maximum power of 2.2 MW, supplied by graphite electrical heater rods. It’s a 1/4th in height, length and diameter; with a 1/16th flow area of the MHTGR and consequentially 1/64th in volume. It maintains the approximate flow channel size, but scales down number of flow channels from the MHTGR. Figure 1-6 shows a schematic of the HTTF reactor vessel. [8]

Figure 1-6: The High Temperature Test Facility Reactor Vessel

The working fluid of the HTTF can be helium, nitrogen, or any other fluid that does not oxidize graphite. Due to the scaling methodology, the prismatic graphite core was replaced with a ceramic core that scales the thermal resistance through the core internals. [5] The core configuration for the HTTF is different than the MHTGR. Hexagonal ceramic blocks representing the active core and inner and outer reflectors are stacked on top of each other. The electrical heater rods and coolant channels are located within the active core. An image of one block of the ceramic core is shown on Figure 1-7.

Figure 1-7: The High Temperature Test Facility Ceramic Core

As discussed, the HTTF is expected to provide experimental data for validation of existing system safety codes and near-term multi-physics computer codes. [5] The apparatus has been designed to model the behavior of the Depressurized Conduction Cooldown (DCC) event and, to a limited extent, it will also be able to simulate the Pressurized Conduction Cooldown (PCC) event using the appropriate coolant or boundary conditions. In addition, the HTTF has the potential to explore phenomena during normal operations. [8] During normal operations the flow pattern in the reactor vessel of the HTTF is very similar to that of the MHTGR. However, as helium flows out of the concentric region of the cross-duct vessel, helium flows up through the U-tube heat-exchanger of the HTTF, and then flows down through the circulator and back to the outer annulus of the cross-duct vessel. The thermal center of the U-tube heat-exchanger of the HTTF is located approximately above that of the reactor core. The elevation differences between

11 the HTTF heat-exchanger and the MHTGR steam-generator could have a potential impact on the flow characteristics of the primary loop, especially during the natural circulation phase of the Pressurized Conduction Cooldown (PCC) event. An image of the integral test facility is shown in Figure 1-8.

REACTOR VESSEL

U-TUBE HEAT-EXCHANGER

CIRCULATOR

Figure 1-8: The High Temperature Test Facility.

1.2 Motivation of Study

The primary motivation of this study is to analyze the scaling distortions that may occur during the natural circulation phase of the PCC event in the OSU HTTF. Due to the

12 design concept of the MHTGR, natural circulation is not expected to exist through the primary side of the steam generator. However, due to the fact that the thermal center of the heat exchanger in the HTTF is higher than the thermal center of the core, there is a possibility that the helium coolant will be able to circulate throughout the u-tube heat- exchanger (Figure 1-8). The ultimate motivation of this study is to inform and provide simulation results of the thermal fluid phenomena of the VHTR during the PCC event. At a later date, this work may be used for the design and licensing perspective of the gas reactors. Once the HTTF is built, it will be able to provide experimental data for the validation of existing system safety codes. Therefore, the results from this work would need to be validated against the experimental results.

1.3 Research Objectives

The primary objective of this study is to investigate the ability of the HTTF to simulate the Pressurized Conduction Cooldown (PCC) Event in the MHTGR. This will be determined with the aid of a thermal hydraulic systems code, RELAP5-3D. The general objectives of this analysis are shown below.

 A development of two RELAP5-3D models, one for the MHTGR and one for the HTTF.  Derivation of scaling parameters during the PCC event to determine the initial conditions of the HTTF RELAP5 model.  Numerical simulations of the PCC event and a comparison of the following figures of merit: o Radial temperature profile during steady-state calculations o Peak fuel temperatures o Primary system temperatures, pressures and mass flow-rates o System heat balance  Compare and quantify potential distortions between the model and the prototype

 Sensitivity analysis of parameters that can be manipulated in the HTTF and an analysis of the properties of the in-vessel solid structures  Discussions of the ability of the HTTF to simulate the PCC event

1.4 Assumptions

Throughout this analysis, several assumptions have been made in order to simplify the challenges of the problem. First of all, it is assumed that the thermal- hydraulic systems code, RELAP5-3D, is capable of simulating the MHTGR and HTTF during the phenomena of interest, such as steady-state conditions and transient events. It is also assumed that any operating characteristics and physical dimensions for the MHTGR are true and accurate, since the information will be used to capture the phenomena of interest. [10] In addition, the Preliminary Safety Information Document developed by General Atomics estimates that the maximum amount of the flow through the bypass region is 11%. This information was assumed to be true for both the MHTGR and HTTF models; therefore the flow area of the core was increased by 11% in both models. [19] Finally, no internal heat generation by gamma heating is modeled, which indicates that all of the core power is directly deposited into the fuel or heater rod.

1.5 Limitations

Throughout this study, RELAP5-3D Version 4.0.3 is used for all computational modeling and is the primary contributor of limitation throughout the analysis. RELAP5-3D, being a lumped parameter code, is highly dependent on the discretization of the system, which limits the spatial resolution of its nodalization and determines average variables throughout its volumes. This indicates that any phenomena occurring at smaller scale than the discretized volume or heat structures will not be captured during the event. [10]

In addition, the results of this study are limited to the thermal-hydraulic empirical correlations and sub-models of the code. Such correlations could include flow regimes, non-equilibrium effects and forced heat transfer through heat structures, which limits the results to some degree of uncertainties. In addition, keeping in mind the discretization of the system and the empirical correlations of the code, this analysis is limited to the uncertainties that could potentially exist within the code. Finally, since the reduced scale facility is still not complete and experimental validation has not been attained, this study is limited to the results obtained from the numerical simulation during a PCC event.

1.6 Overview of the Following Chapters

The literature review is presented in chapter two. In this chapter, the postulated accident scenarios of the VHTR will be presented. This section will transition into the description of the Pressurized Conduction Cooldown (PCC) event and will introduce some of the previous work achieved in this area. Chapter three will give provide the derivation of the scaling parameters, in order to determine the initial conditions of the HTTF during a PCC event. Chapter four will describe the MHTGR and HTTF RELAP5-3D models. In addition, a benchmark between the models at steady-state conditions will be provided. Chapter five will provide the results, discussions and comparison of possible distortions of the numerical simulations during the PCC event. Chapter six presents several sensitivity analyses to determined what can be done in the facility in order to better simulate the PCC event. This chapter will also quantify the distortions in the in-vessel solid structures of the HTTF. Lastly, chapter seven will provide the conclusion and ending remarks concerning the reduced scaled facility and its ability to simulate the PCC event. This chapter will also provide future possibilities of work and an outline of how the RELAP5-3D models could be improved.

2 LITERATURE REVIEW

Up to this time, there has been a wide range of research concerning the VHTR. Most of the literature regarding the Pressurized Conduction Cooldown (PCC) event involves the use of computational tools and systems codes. This chapter outlines the literature review and is broken down into three sections. The first section will provide an overview of the postulated accidents scenarios that could occur in the VHTR, as identified by the NRC PIRT panel. The second section will introduce the PCC event and the different phenomena of interest. The last section will provide an overview of past investigations related to the HTGR and PCC event.

2.1 Postulated Accident Scenarios

As mentioned earlier, the HTTF will provide experimental data for validation of existing safety system codes and will demonstrate the design and safety concept of the VHTR. The HTTF has been designed to provide data for a depressurized loss of forced convection (D-LOFC) event, but to a limited extent, it will also be able to provide data for a pressurized loss of forced convection (P-LOFC) event. [5] It is important to understand the different types of scenarios that could occur in the VHTR. A report developed by the U.S. NRC, “Next generation Nuclear Plant Phenomena Identification and Ranking Tables (PIRTs)”, identified the most important accidents scenarios that could occur in the VHTR. [5] [17] The Phenomena Identification and Ranking Table (PIRT) is a strategy that provides a convenient method of evaluation for the NRC’s research and development (R&D) needs, concerning the NGNP phenomena. [17] The PIRT process allows the identification of events and ranks them according to their importance, since it is impossible to preserve all similarities between the model and the prototype. It includes a nine-step process that is described in detail in “Volume 1 of the NRC’s NGNP PIRT”. [17] Five areas of interest were acknowledged while conducting the PIRT process: 1) Accident analysis and thermal-fluids (including neutronics), 2) fission product transport

16 and dose, 3) high temperature materials, 4) graphite and 5) process heat and hydrogen production. These phenomena were further broken down into six categories of postulated accident scenarios and they are described as follows, [17]

1. Pressured Loss Of Forced Convection Accident 2. Depressurized Loss of Forced Convection Accident 3. Depressurized Loss of Forced Convection Accident with Air Ingress 4. Reactivity Induced Transient (Including events involving ATWS) 5. Steam-Water Ingress Events 6. Process Plant Coupling Events

2.1.1 Loss of Forced Convection Accidents

A loss of forced convection (LOFC) accident occurs when forced circulation of the helium coolant is lost and reduces the ability of the system to remove decay heat. Several areas of importance during this accident include the RCCS behavior and ability to remove decay heat and circulation of air in the reactor cavity. [5] [17] During a LOFC event, heat is primarily removed through conduction within the core and radiation from the vessel walls. In which case, the P-LOFC accident and the D-LOFC accident are often called the Pressurized Conduction Cooldown (PCC) Event and Depressurized Conduction Cooldown (DCC) Event respectively. [5] The Pressurized Conduction Cooldown (PCC) Event is typically initiated by a loss of forced flow throughout the primary system from a circulator shutdown or a break between the inlet/outlet of the cross-duct vessel. In either case the pressure of the system remains intact. [11] During a PCC event, onset of natural circulation occurs and a flow reversal initiates. Several areas of concern during this event involves, hot helium coolant flowing out of the top of the core and radiation heat transfer from the core into the upper vessel head. Both of these events could lead to very high temperatures in the upper plenum. The PCC event will be discussed in detail in the next section. [5] [11]

The Depressurized Conduction Cooldown (DCC) Event occurs with a break in the boundary of the system, which depressurizes the system and releases helium coolant into the cavity. [5] The DCC event is sometimes comparable to a Loss of Coolant Accident in LWRs [20], where a small or large break could occur. If the break is small enough, there is a possibility that no air may enter the system. However, if the break is large enough, air may enter the system and potentially cause damage and oxidize the graphite. As oxidation occurs, it impacts the integrity of the core and its support structures, and may lead to further oxidation of the graphite fuel, which could potentially release fission products. [5] [10] [20]

2.1.2 Reactivity, Steam Water Ingress and Plant Coupling Events

Reactivity induced transient events include accidents involving anticipated transient without scram (ATWS). Often times, this accident includes a LOFC event with failure of the reactor protection system to actuate. This event is very important in the pebble bed design, since induced reactivity could arise due to the movement of the pebbles in an earthquake. [17] The initial thought for steam-water ingress events included the consequence of a Steam Generator Tube Rapture. Consequentially, this event would lead to steam-water entering the primary system. However, since the systems are still under conceptual design and most current VHTR designs use the “direct gas-turbine brayton cycle for power production, accidents involving steam/water ingress contained very low probability” [27] and have been eliminated by the PIRT panel. As result, the HTTF will not be collecting data for this event. [17] One of the key features of the VHTR is the potential of non-power related processes, such as the production of hydrogen. The PIRT panel decided to include auxiliary and process-plants events, since not much information has been collected for this type of events. These types of accident scenarios typically involve chemical releases from the heat-process plant and gasses that could influence the reactor. [17] Again, the HTTF will not be providing data for plant coupling, reactivity or steam-water ingress events. The HTTF has been strictly designed to provide data for the DCC event.

However, with specified boundary conditions, the HTTF could potentially provide data for the PCC event as well.

2.2 The Pressurized Conduction Cooldown Event

The PCC event is a scenario where forced circulation is lost, but the pressure of the system remains close to normal operations and no depressurization or air ingress exists. The PCC event is caused by a circulator shutdown or a break within the system, such as between the inlet and outlet the cross-duct vessel [5] [11]. There are several phenomena of concern during the PCC event; therefore it is important to understand the progression of the accident. During normal operations forced helium coolant flows in the downward direction through the core into the lower plenum. However, when forced circulation is lost, the helium continues to flow in the downward direction through the core until the inertia forces are overcome by the resistance of the flow and frictional forces [5]. At this point, the helium begins to heat up and expands, where buoyancy forces allow the gas to flow in the upward direction through the core. Consequently, a flow reversal occurs and onset of natural circulation initiates. If the core is assumed to contain one single channel, then as onset of natural circulation occurs, the helium will now enter the bottom of the core from the lower plenum; it will flow through the core and will be heated by the decay heat of the core. Helium will continue to flow upward into the upper plenum and down through the annular region of the core barrel and the reactor vessel. In this region, the helium will be cooled by natural convection by the inner surface of the vessel wall, and then thermal radiation from the outside surface of the reactor vessel wall. The helium will continue to flow downward exiting the reactor vessel and into the steam generator or heat-exchanger, where it will further be cooled. Figure 2-1 shows a representation of the natural circulation of the helium coolant during a PCC event. [5]

Figure 2-1: Single-phase Natural Circulation during a PCC Event. [5]

In reality, the MHTGR will contain thousands of core channels; some will be hotter than others and some will be cooler. This indicates that flow reversal is not expected to occur in all channels at the same time, and some channels may not even reverse at all. It is expected that the flow in the hotter channels of the core will reverse first and the flow in the cooler channels will not reverse. If this occurs, then the helium coolant will flow up through the hotter channels, exiting the top of the core, flowing back through the cooler channels, exiting the bottom of the core and eventually flowing up through the hotter channels again. This phenomenon is called intra-core recirculation and

20 it is what is expected to occur in the MHTGR because the heat sink was designed at a lower elevation than the thermal center of the core. However, due to the fact that the thermal center of the heat exchanger in the HTTF is higher than the thermal center of the core, there is a possibility that the helium coolant will have different circulation patterns throughout the HTTF u-tube heat-exchanger. There are several phenomena of interest during the PCC event. Because some core channels will be hotter than others with different amount of power, hot gas jets with different velocities and temperatures are expected to exit the top of the core, which consequently could impinge into the upper vessel head. In addition, there is going to be plenty of radiation heat transfer from the top of the core into the inner surface of the upper vessel head. These two phenomena’s could have significant thermal stress into the upper vessel head. [5] In addition, as forced circulation is lost, the system’s ability to remove heat decreases; therefore the temperature in in-vessel solid structures, fuel and reactor vessel are expected to increase. As the temperature increases, so does the pressure. Consequently, if the pressure increases enough, there may be a possibility that the system will over-pressurize, which could actuate the pressure relief valves, turning the PCC event into DCC event. [5] Even though there may be many phenomena of interest during the PCC event, this study concentrates on the integral aspects of the system. This study involves the natural circulation phase and the ability of the RCCS to remove decay heat during a PCC event.

2.3 Previous Relevant Literatures

Shultz et al. in 2010 performed several thermal-hydraulic analyses using RELAP5-3D models. [26] The objective of the study was to investigate how the core responded to conduction cool-down events. Comparisons of steady-state calculations were performed first, and then transient simulations were calculated. The geometrical information used to develop the MHTGR model was obtained from the Preliminary Safety Information Document (PSID) [19]. The models included the core, reflectors, coolant channels, the cavity and the RCCS. The core was modeled by three rings and

21 several channels representing the total flow area of the core. Conduction and radiation was also modeled to better represent the design concepts. Temperature and pressure boundary conditions were applied in the inlet and outlet of the cross-duct vessel. [26] The analysis included results for the PCC event and was modeled by maintaining the system’s pressure at normal operation and forcing a sixty second forced circulation coast-down to onset of natural circulation. By forcing the system to 60-sec forced flow coast-down, the peak fuel temperature initially decrease since the forced circulation was enough to remove some of the stored energy in the core. Afterwards, the peak fuel temperature increased to a maximum and then slowly started to decrease. The behavior of the reactor vessel temperature and the RCCS heat removal followed closely the trend of the peak-fuel temperature. [26] Shultz also did several sensitivity calculations with a lower pressure boundary condition and different bypass flow percent area. It was discovered that with a lower pressure boundary condition, the peak fuel temperature tends to increase and the reactor vessel temperature slightly decreased. In addition, the reactor pressure vessel temperatures slightly increased as the bypass flow area increased. [26] The HTTF was modeled by using the same base MHTGR model. [26] During steady state calculations, it was observed that the core temperature decreased and the reflector temperatures increased. Additionally, the flow in the bypass area changed from turbulent to laminar, causing a decrease in the convective heat transfer, hence reflector temperatures increased. The PCC event was simulated with the initial 10% power reduction and held constant until the normal 350 MW decay power curved dropped down to 10%, and then it followed the normal decay curve. It was observed that the peak fuel temperature was higher due to the initial higher temperatures in the reflector regions. Additionally, the temperature in the reactor vessel increased as well. [26] The second approached to model the HTTF was by applying reduced scaling factors to the base MHTGR model and changing the thermal properties from graphite to ceramic material. It was found that the temperature in the in-vessel solid structures were significantly higher than the prototype. The reason for this is that laminar flow developed, which reduced the ability of the system to remove decay heat via convection.

During the PCC event simulation, it was found that the peak fuel temperature significantly increased due to higher initial temperatures. [26] In 2013, Aldridge performed a scaling study of the Oregon State High Temperature Test Facility during a depressurized conduction cool-down (DCC) event using RELAP5-3D models. [10] The objective of the study was to evaluate the scaling ratios and quantify possible distortions in the test facility. Consequently, the study also involved the Integral Effects Test (IET) during the natural circulation of the molecular diffusion phase, which is same single-phase natural circulation loop scaling analysis used for the PCC event. [10] During the scaling analysis of the “as-built HTTF” ratios, it was discovered that some of the geometrical parameters and thermal properties for the HTTF did not satisfy the designed ratios, specifically the thermal conductivities of the permanent side reflectors (PSR) and the pressure vessel. In addition, distortions in the heat loss ratio during the natural circulation phase were also found. Since radiation is a surface phenomenon and the HTTF was scaled according to the volume in the core, it was expected that the HTTF would lose a large amount of heat through the reactor vessel wall. This showed that the HTTF would develop distortions, with lower temperatures, thus losing temperature similarity during the steady-state calculations and transient events. [10] Furthermore, two RELAP5 models were developed, one for the MHTGR and one for the HTTF. The models were very similar to the ones developed by Shultz et al. [26], but one single core-channel approach was used. The models consisted of the core, in- vessel solid structures, cavity, RCCS and boundary conditions at the inlet and outlet of the cross-duct vessel. Conduction and radiation were also modeled to better represent the design concepts. Aldridge’s models are described in detail in chapter 4, since they provided the starting point for this study. [10] Comparisons of the RELAP5-3D models at steady-state were performed first. During steady-state calculations it was observed that the HTTF was unable to predict temperature similarity for the in-vessel solid structures. The reason for this was that the scaling ratios of the thermal conductivities were not conserved, especially in the PSR and

23 reactor pressure vessel, which lead to distortions in the radial temperature profile of the HTTF compared to the MHTGR. [10] During the natural circulation phase of the IET, a large deviation in the Richardson number was found, which indicated that buoyancy forces were not well captured in the HTTF. The reason for this was that form loss coefficients were adjusted for the core to obtain a 1:2 velocity ratio. However, by doing so, similarity in the fiction ratio was lost, which lead to higher friction losses. [10] As for the thermal response, the HTTF couldn’t predict the radial temperature profile of the in-vessel solid structures during the natural circulation phase. The HTTF temperatures were much lower than the MHTGR. The reason for this was because the heat loss to power ratio was much higher in the HTTF than the MHTGR. The studies further analyzed that the diffusion coefficient were independent of pressure. However, RELAP uses the “Colburn-Hougen” correlation to find the diffusion coefficient, which is inversely proportional to the pressure. In addition, the analysis also indicated that an increase in the initial core power of the HTTF could potentially allow the in-vessel solid structures to heat up and resemble the results of the MHTGR. [10] A study by King, B. M., in 2012 analyzed the temperature distribution and the impinging of hot jets in the upper plenum during a pressurized conduction cooldown (PCC) event. [11] The primary objective of the study was the behavior of the gas flow into the upper plenum given boundary conditions of the PCC event. An analytical scaling analysis of the PCC was performed to develop the initial conditions of the velocity of the core channels. This was achieved with the use of the loop momentum balance equation, which determined several non-dimensional parameters: The Froude number, Reynolds number and ratio of inlet plenum length to flow channel diameter (L/D). During the analytical work, it was found that the HTTF Froude and Reynolds numbers did not match the ones for the MHTGR and distortions were expected because of the L/D ratio. [11] Models of computational fluid dynamics StarCCM+ were developed for both, the MHTGR and the HTTF, and were used to simulate the PCC mixing in the upper plenum. Both models consisted of a 1/12th slice of the upper plenum with different geometrical configurations for the MHTGR and HTTF. Simulations of different percent of channels flowing upward to see the effects into the upper plenum were performed. In all

24 simulations, it was determined that the hottest gas jets entered the upper plenum from the inner channels of the core at 1,000 K for both models. [11] For the 25% upflow, the jets diffused radially as they travel upward and reached the upper plenum wall at 990 K for the MHTGR, 960 K for the helium in the HTTF and 960 K for nitrogen in the HTTF. For the 50% upflow, the jets diffused radially as they travel upward and reached the upper plenum wall at 1,000 K for the MHTGR, 980 K for the helium in the HTTF and just below 1,000 K for nitrogen in the HTTF. Very different phenomena occurred for the 100% upflow. For the MHTGR, as the jets diffused through the upper plenum, the gas jets diverged into the lower side of the upper plenum with a temperature of 1,000 K. As for the HTTF, the helium coolant diverges into the center of the upper plenum, but continues to the top of the upper plenum with temperatures of 980 K. As for the nitrogen coolant in the HTTF, the gas jets moved towards the outer region of the upper plenum, but stopped before coming in contact with the walls. [11] King, B. M. concluded that distortions were seen because of the non-dimensional parameters. The HTTF flow area was scaled by maintaining the individual channel area and reducing the number of channels in the core. The relationship results approximately with 4x higher L/D ratio between the MHTGR and HTTF. This relationship resulted in the Froude number being scaled correctly; however from the analysis it was concluded that distortions in the Reynolds number would appear and a gas with properties that would allow the velocity to match the Reynolds number was needed. [11] In 2006, Haque developed an analysis of the VHTR during Pressurized Conduction Cooldown (PCC) and Depressurized Conduction Cooldown (DCC) events using the thermal-hydraulics code THERMIX. [12] The code THERMIX was used to develop numerical simulations for the HTR with pebble-bed fuel, where the results were validated against experimental data. As modifications were added to the code, new simulations were performed for the GT-HTR with prismatic fuel. These calculations were compared against results obtained from other codes during the “CRP-3 benchmark problem”, which resulted with good comparison. [12] Haque used the code to develop simulations for the GT-MHR Pu-Burner and the VHTR. During normal operations the helium coolant in the GT-MHR Pu-Burner enters the core at 490 0C and exits at 850 0C. The helium coolant in the VHTR design enters the

25 core at 490 0C and exits at 1,000 0C. Both design consisted of a RCCS with a boundary temperature condition of 65 0C in the cooling tubes. [12] During the transient events, the DCC event consisted of a break in the boundary of the primary system followed by a reactor scram, loss of forced convection and a rapid depressurization of the system. It was assumed that the pressure of the system was 1 bar following the blowdown. As for the PCC event, a reactor scram occurred as loss of forced convection was lost, where the system’s pressure remained intact. The pressure of the system was assumed to be 55 bar. In both events, it was expected that decay heat from the core is mostly removed via conduction and radiation. [12] The first analysis consisted of comparing the results in the GT-MHR Pu-Burner design against the calculations obtained in the CRP-3 program. The peak fuel temperature and the reactor pressure vessel temperatures were compared for both events, the DCC and PCC. The calculations for the DCC case gave reasonable results with small deviations. As for the PCC event, the calculations did not give reasonable results. It was concluded that the differences were due to distinct computational methods, material properties, or different modeling techniques. [12] The second analysis performed consisted of the VHTR design, which contained higher core outlet temperatures during normal operations. During the DCC event, the peak fuel temperature reached 1587 0C, which was slightly lower than the fuel design limit of 1600 0C. During this event, the system is depressurized to 1 bar, which leads to lower gas density and low buoyancy forces. Therefore, natural convection was negligible in this event and the primary mechanisms of heat removal were due to conduction and radiation. [12] As for the PCC event, natural circulation of the helium coolant developed. With a pressurized system, a high helium density developed and buoyancy forces reversed the circulation of the helium as forced circulation was lost. As a result, cold helium gas entered the bottom of the core, rose upward through the core as the gas expanded. The helium then transferred energy to the upper regions of the core and flow downward through the cooler channels of the core. As a result, natural convection took placed and cold regions of the top of the core heated up and the lower regions cooled down. At the same time, conduction within the core components and radiation heat transfer to the

RCCS was taken place. The peak fuel temperature was approximately ~1200 0C, 350 0C lower than the DCC event. The reason for this is that during the DCC event, natural convection did not take place, which means that less heat was transfer out of the core. [12] In 2005, Ball, S. performed several sensitivity studies concerning the gas turbine modular high-temperature gas-cooled reactor (GT-MHR) and the pebble bed modular reactor (PBMR) during several P-LOFC events. [27] The analysis was performed with the thermal-hydraulics code Graphite Reactor Severe Accident Code (GRSAC) developed by Oak Ridge national Laboratory [28]. The GRSA contained a 3-D thermal- hydraulics model for the core, reactor vessel, shutdown cooling system (SCS) and a reactor cavity cooling system (RCCS). The 3-D, hexagonal geometry of the core allowed the studied of detailed temperature distribution in the axial and radial directions. In addition, GRSA has the capability of performing P-LOFC events with or without scram. [27] The P-LOFC event in the GT-MHR assumed a flow coast-down and an instantaneous reactor scram, with an operational RCCS. The peak fuel temperature was 1290 C at 24 hrs. The maximum vessel temperature was 509 C at 72 hrs. It was concluded that the concern during this event is not the peak fuel temperature, but the distribution of the fuel temperature along the axial level. During a P-LOFC the peak fuel temperature shifted to the top of the core, which gave higher temperatures near the top of the reactor cavity. In addition, the parameter most likely to affect the success of this event was the emissivity of the reactor vessel. With a small reduction of 25% in the emissivity, the peak fuel temperature increase only by 7 C, while the reactor vessel temperature increased by a large amount of 37 C. [27] A P-LOFC event in the GT-MHR with an ATWS event was also investigated. This accident assumed a flow coast-down with failure of reactor scram. During the first 30 hours of the scenario, the results were very similar to the P-LOFC with scram, since the temperature feedback coefficient was strong enough to insert negative reactivity into the reactor. However, re-criticality occurred at about 32 hours and the peak fuel temperature started to increase till the point where it exceeded the 1600 C limit. The GRSAC code was able to predict significant fuel failure after the first 2 days during the

27 event. It was concluded that core re-criticality occurred as a consequence of the sensitivity of the core to the fuel and moderator temperature reactivity feedback coefficients. [27]

3 HTTF SCALING PARAMETERS

In order for the HTTF to simulate important flow and heat transfer phenomena of the MHTGR during the PCC event, adequate initial boundary conditions must be determined. [5] This chapter presents the analytical derivation of the single-phase natural circulation loop scaling analysis during a PCC event.

3.1 Single-Phase Natural Circulation Loop Scaling Analysis

As mentioned earlier, in a PCC event, the onset of natural circulation begins as buoyancy forces overcome frictional and inertial forces. Control volume balance equations can be written for each component within the system. However, several general assumptions were made during this analysis: 1) The flow is one-dimensional along the loop axis, 2) the fluid properties are assumed to be uniform at each cross-section of the loop, 3) the fluid is incompressible, 4) the pressure drop in the core is the dominant resistance within the loop, 5) any viscous dissipation forces are assumed negligible and 6) any expansion effects and oxidation energy release are not applicable to this analysis, since the loop is intact and no air ingress exists in the PCC event. [5] Using the assumptions stated above, where the flow is treated as incompressible and the mass flow rate at every cross-section for the “ith” component along the loop is constant, then the gas mixture continuity equation can be determine as shown below. [5]

̇ ̇ (3-1)

Then an integrated loop momentum balance equation can be determined as shown below.

̇ ∑ [ ] ( )

(3-2)

̇ ̇ ( ) ∑ [ ( ) ( ) ] ( )

The terms on the right hand side of the equation represents the friction and form losses, the acceleration due to the change in the heated gas density and thermal expansion across the core. Similarly, an energy balance equation can be obtained as shown below. [5]

(3-3)

In this equation, the rate of change of energy in the coolant is balanced against the energy added as the coolant flows across the core, the energy lost from the system, the energy stored in the components and the energy removed by the steam generator. [5] Each of the terms in the loop momentum and energy equations can be normalize using initial boundary conditions. Therefore, the dimensionless parameters are given as follows,

(3-4 )

∑ [ ( ) ( ) ]

{∑ [ ( ) ( ) ]} (3-5 )

{∑ [ ( ) ( ) ]}

̇ ̇ ̇ ̇ ̇ (3-6 ) ̇

(3-7 )

( ) ( ) (3-8 )

( ) ( ) (3-9)

( ) ( ) (3-10)

( ) ( ) (3-11)

( ) ( ) (3-12)

( ) (3-13) ( )

( ) [ ] ( ) ( ) [ ] (3-14) ( ) ( ) [ ] ( )

( ) (3-15) ( )

( )

( ) ( ) ( ) ( ) (3-16) ( )

( )

( ) ( ) ( ) ( ) (3-17) ( )

( )

( ) ( ) ( ) ( ) ( 3-18) ( )

( )

( ) ( ) ( ) ( ) (3-19) ( )

The normalized characteristic length used the height between the thermal centers of the steam generator and the core, as shown below. [5]

(3-20)

The characteristic density difference is taken as the difference between the helium density at core inlet (H) temperature and outlet (C) temperature, as shown below.

( ) ( ) ( )

(3-21)

( ) ( ) ( )

Using the above dimensionless parameters, equations (3-4) through (3-21) and substituting them into equations (3-2) and (3-3), then dimensionless momentum and energy balance equations for the system loop can be determined,

̇ ( ) (3-22)

( ̇ ) {∑ [ ( ) ( )]} ̇

(3-23) ( ) ( ) ( )

( ) ( )

Where the coefficients to the above non-dimensional loop momentum and energy balance equations represent the single-phase fluid natural circulation loop scaling ratios for the PCC event and they are presented in the next section.

3.2 Single-Phase Fluid Natural Circulation Loop Scaling Ratios

The Loop Reference Geometry Ratio for natural circulation during a PCC event is given by,

∑ [ ] ∑ [ ] (3-24)

Where the reference length is given by,

(3-25)

The loop Richardson number ratio,

( ) (3-26)

The primary loop resistance number ratio for natural circulation during a PCC event is given by,

∑ [ ( ) ( ) ] (3-27) ( )

The Ratio of Specific Heats for natural circulation during a PCC event is given by,

( ) (3-28) ( )

The Loop Peclet Number Ratio for natural circulation during a PCC event is given by,

( ) ( ) ( 3-29) ( )

The Heat Loss Ratio for natural circulation during a PCC event is given by,

( ) (3-30) ( ) ( ) ( )

The Stored Energy Transport Ratio for natural circulation during a PCC event is given by,

( ) (3-31) ( ) ( ) ( )

The Loop Core Power Ratio for natural circulation during a PCC event is given by,

( ) (3-32) ( ) ( ) ( )

The Loop Steam Generator Energy Removal Ratio for natural circulation during a PCC event is given by,

( ) (3-33) ( ) ( ) ( )

The Loop Time Scale Ratio for natural circulation during a PCC event is given by,

∑ [ ] ∑[ ] (3-34)

In the dimensionless system loop momentum equation, equation (3-22), if the time dependent term is set to zero, the dimensionless numbers are set to one and the pressure drop due to acceleration is assumed negligible, then a steady-state solution can be determined. This leads to similarity between the Richardson number and loop resistance number as shown below. [5]

(3-35)

Furthermore, if an energy balance across the core is used (equation 3-36) and a coefficient of thermal expansion to describe the change in density due to local fluid heating across the core is used (equation 3-36), then the loop Richardson Number can be express as a function of core power as shown in equation 3-38.

̇ ̇ (3-36)

( ) (3-37)

̇ (3-38)

Then, by substituting the above equation (3-38) into equation (3-35), one obtains the velocity of natural circulation as shown below.

⁄ ̇ [ ] (3-39)

3.3 Primary Loop Resistance

The major contributor to flow resistance in the primary loop of the MHTGR during the PCC event is the core and the steam generator. However, if a break exists within the concentric region of the hot and cold cross duct vessel, the primary contributor to flow resistance will be the core and the break. The pressure drop for the core and the steam generator consists of frictional and form losses, and for the break, the pressure drop consists only of form losses. [5] If gas expansion is assumed negligible, the pressure drop through the core, through the steam generator and through the cross duct vessel break can be determined, as shown below.

[ ] (3-40)

[ ] (3-41)

(3-42)

Furthermore, by using the above definitions of pressure drop and applying them into the integrated loop momentum balance equation at steady-state and ignoring thermal expansion, then the pressure drop through the core and the steam generator can be found as shown below.

[ ] [( ) ] (3-43)

If a break exists, then the pressure drop through the core and the cross duct vessel break can be found as shown below.

[ ] [( ) ] (3-44)

Equation (3-43) and equation (3-44) can further be simplified if the property of the fluid is similar.

[ ] [ ] (3-45)

[ ] [ ] (3-46)

In the HTTF, the use of orifices will allow the modeler to obtain the desired pressure drop across the primary loop to satisfy the above equations. [5]

3.4 Structural Materials Heat Transfer

This section presents the scaling analysis of the radial and axial heat conduction. The radiation heat transfer of the core barrel and the vessel’s exterior surface is also presented. Figure 3-1 shows the radial heat transfer geometry of the HTTF. At the center

(point zero), there is not heat generation since no active fuel exist. This region represents the inner ceramic reflector. Heat can only be transfer to this region by conduction from the core region (red zone). The core transfers heat radially towards the outer reflector (zone 2 to 3) and heat is further conducted through the PSR and the core barrel. From the core barrel, heat is radiated along the up-comer coolant channels into the inner surface of the reactor vessel. Heat travels radially along the vessel walls and is radiated outwardly through the cavity and into the RCCS.

Cavity RCCS

Coolant Channels

Figure 3-1: Conduction and Radiation Heat Transfer Geometry of the HTTF Core. [5]

If the density of the solid is assumed constant, then the heat transfer through the regions of the inner reflector, outer reflector, and core barrel can be described by the following heat equation. [5]

( ) ( ) (3-47)

Since the core contains heat generation, then heat transfer through the core can be described by the following equation.

( ) ( ) (3-48)

From the above equations, non-dimensionless parameters can be developed.

(3-49)

(3-50)

(3-51)

(3-52)

(3-53)

(3-54)

( ) (3-55) ( )

Then the non-dimensionalized equations that describe the heat-transfer during the natural circulation phase during the PCC event through the inner reflector, outer reflector, core barrel and reactor vessel can be described in the following equation.

( ) ( ) (3-56)

The non-dimensional heat-equation for the core region can be described in the following equation.

( ) ( ) ( ) (3-57)

The time scale and the PCC event natural circulation radial and axial Fourier Number Ratios and the core power ratio are shown below.

(3-58)

(3-59)

(3-60)

( ) (3-61)

Radiation boundary conditions can be applied to the outside of the core barrel wall and the inner side of the reactor vessel as long as convection heat transfer is assumed negligible as shown in the following equations.

| ( ) (3-62)

| ( ) (3-63)

The cavity heat transfer is different from the heat transfer in the inside of the reactor vessel, which indicates that a different boundary condition at the outer surface of the reactor vessel wall must be applied as shown below.

| ( ) ( ) (3-64)

If additional non-dimensionless parameters of quartic temperature difference and single temperature difference are used as shown below,

( ) ( ) (3-65)

( ) ( ) (3-66)

( ) ( ) (3-67)

Then by applying the previous dimensionless parameters from equation (3-49) through (3-51), non-dimensional boundary conditions for the core barrel can be obtained as shown below.

| ( ) (3-68)

(3-69) ( )

The outside of the vessel wall can be described in the following equation.

| ( ) ( ) (3-70)

In the above equation, the natural circulation Biot Number Ratio and Modified Boltzmann Number Ratio were used, and they are shown below respectively.

(3-71) ( )

(3-72) ( )

It is expected that the flow through the coolant channels during the natural circulation phase will be dominated by natural convection. The natural convection through the core channels can be described by a boundary condition shown below.

| ( ) (3-73)

Non-dimensional parameters can be developed for the above equation as shown below.

( ) ( ) (3-74)

(3-75)

| ( )( ) (3-76)

( ) (3-77)

The following equation shows the natural convection on the surface of vertical plate, which is “Churchill-Chu” correlation. [18]

( ) (3-78)

[ ( ) ] { }

In the above equation, the natural circulation channel Rayleigh Number Ratio and the Prandtl Number Ratio were applied, and they are shown below respectively.

( ) (3-79) ( )

( ) (3-80) ( )

3.5 HTTF Design Specifications

Similarity criteria for the natural circulation phase during a PCC event were presented in the previous section. These similarity criteria will be used to determine the operating and initial boundary conditions of the HTTF. Several parameters have already been chosen in the scaling report [5] in order to obtain all the necessary scaling ratios for the design of the HTTF. The rest of the scaled ratios will be presented in this chapter. [5]

3.5.1 Scaling Choices

The requirements of kinematic similarity and friction/form loss similarity have been imposed on this scaling analysis as shown below.

( ) (3-81)

( ) (3-82)

In addition, the Elevation/Length and Diameter scaling ratios have been imposed within the facility as shown below.

( ) (3-83)

( ) (3-84)

From the lengths and diameter scaling ratios, a cross sectional area and the volume scaling ratio can be obtained as shown below.

( ) (3-85)

( ) (3-86)

Additionally, a restriction on the pressure has been applied in the facility, due to economics and safety limits. [5] The scaling ratio for pressure is shown below.

( ) (3-87)

Also, it is desired for the HTTF to be a full temperature facility within the primary system. [5]

( ) (3-88)

3.5.2 Natural Circulation Design Specifications

This section identifies the scaling design specifications for the HTTF during the natural circulation phase in a PCC event. Temperature similarity and the use of helium as a coolant will be assumed during this analysis. The vessel internal lengths and areas can be determined by using the natural circulation geometry ratio from equation (3-24) as shown below.

∑ [ ] → ( ) ( ) (3-89)

∑ [ ] → ( ) ( ) (3-90)

The core inlet velocity can be determined using the natural circulation velocity from equation (3-39). From that equation, if temperature, gas concentration, and friction and form loss similarity is assumed, the following simplification is allowed as shown below.

⁄ ⁄ ̇ ̇ [ ] [ ] [ ] (3-91)

In addition, if the natural circulation core power ratio is used, from equation (3-32), and the previous similarities are used (temperature, gas concentration, and friction and form losses similarities), then a relationship for the core power scaling is obtained as shown below.

[ ̇ ] [ ] (3-92)

Then by combining equation (3-91) and (3-92), the core inlet velocity ratio can be determined as shown below.

⁄ [ ] [( ) ] (3-93)

If the primary contributor to pressure drop during a PCC event is assumed to be through the core and temperature and gas composition similarity is conserved, the pressure drop ratio can be obtained from the resistance number from equation (3-27) as shown below.

[ ] [( ) ] [( ) ] (3-94)

The core decay power can be obtained by assuming temperature similarity and by assuming that the gas specific heat is only a function of temperature, it leads to the following core power density scaling ratio.

[ ] [ ] (3-95)

Then, by using the definition of core power density and volume, the scaled core power can be determined as shown below.

[ ̇ ] [ ] (3-96)

The initial condition for the mass flow rate can be determined assuming temperature similarity during normal operations as shown on the following equation,

̇ [ ] [ ] (3-97) ̇ ( )

Using the same assumption of temperature similarity and by assuming that the gas specific heat is only a function of temperature, the scale initial condition of mass flow rate is shown below.

[ ̇ ] [ ̇ ] (3-98)

The time scaling for the natural circulation phase during a PCC event can be determined using equation (3-34). The natural circulation time ratio is shown below.

( ) [ ] (3-99)

3.5.3 Structural Materials Design Specifications

This section presents the structural materials design specifications used for heat transfer in HTTF. The thermal storage properties of the core and the reactor vessel material can be found by the initial heat storage ratio as shown below.

( ) [ ̇ ] [ ] (3-100)

Assuming temperature and specific heat similarity, the structural materials volumetric heat capacity can be determine, as shown below.

[( ) ] [ ] (3-101)

The thermal diffusivity of the reflectors can be found by setting the Fourier Number Ratio equal to one.

[ ] [ ]

(3-102)

Further simplification of the above equation, yields the thermal diffusivity of the inner and outer reflectors.

[ ] [ ]

(3-103)

The thermal conductivity scaling ratios of the inner and outer reflectors can be found by using the definition of thermal diffusivity and solving for the thermal conductivity.

[ ] [( ) ( ) ] (3-104)

The thermal diffusivity of the core barrel is set by the same way as it was determined for the reflectors. Using the Fourier number ratio and setting it equal to one.

[ ] [ ]

(3-105)

Further simplification of the above equation, yields the thermal diffusivity for the core barrel.

[ ] [ ] (3-106)

The core barrel thermal conductivity can be found by setting the modified Boltzmann number ratio equal to one, as shown below.

(3-107) ( )

Assuming temperature similarity, then the core barrel thermal conductivity to emissivity scaling ratio can be determined as shown below.

( ) [ ] [ ] (3-108) ( )

In addition, if the emissivity is assumed to be similar, the core barrel thermal conductivity can be determined.

[( ) ] [ ] (3-109)

The thermal diffusivity and thermal conductivity of the HTTF vessel can be found the same way as it was determined for the core barrel. The thermal diffusivity is determined by setting the HTTF vessel Fourier number equal to one.

[ ] [ ] (3-110)

The facility vessel thermal conductivity can be found by the modified Boltzmann number ratio as shown below.

(3-111) ( )

Assuming temperature similarity, then the facility vessel thermal conductivity to emissivity scaling ratio can be determined as shown below.

( ) [ ] [ ] (3-112) ( )

In addition, if the emissivity is assumed to be similar, the facility vessel thermal conductivity can be found.

[( ) ] [ ] (3-113)

The thermal diffusivity of the core can be found by setting the Core Fourier Number Ratio equal to one.

[ ] [ ] (3-114)

Further simplification of the above equation, yields the thermal diffusivity of the prismatic core.

[ ] [ ] (3-115)

The core thermal conductivity is determined by setting the core power density number ratio to one.

( ) (3-116)

By assuming temperature similarity and further simplification of the above equation, the core thermal conductivity can be determined as shown below.

( ) ( ) [ ] [ ] (3-117)

The emissivity of the core is found by setting the modified Boltzmann Number ratio equal to one.

(3-118) ( )

Then by assuming temperature similarity, the core emissivity ratio is given by the following equation.

( ) [ ] [ ] (3-119)

The core heat transfer coefficient scaling ratio can be found by setting the Biot’s number ratio equal to one.

(3-120) ( )

Then the core heat transfer coefficient scaling ratio can be determined, as shown on the following equation.

( ) [ ] [ ] (3-121)

Note that the heat-transfer coefficient in the above equation only depends on the thermal-conductivity of the core, since the HTTF channel diameter was scaled with the same length as the MHTGR.

3.5.4 HTTF Scaling Ratios

This section presents a summary of all the design scaling ratios derived throughout the chapter. The HTTF scaling design choice ratios are summarized on Table 3-1. The scaling ratios for the natural circulation phase are summarized on Table 3-2. Lastly, the scaling ratios for the structural materials are summarized in table 3-3.

Table 3-1: The HTTF design scaling specification ratios.

Characteristic Choice Scaling Ratio Definition Scale Ratio

Kinematic ( ) 1:1

Resistance ( ) 1:1

Length/Height ( ) 1:4

Diameter ( ) 1:4

Cross-Sectional Area ( ) 1:16

Volume ( ) 1:64

Temperature ( ) 1:1

Initial Pressure ( ) 1:8

Table 3-2: The HTTF natural circulation loop design scaling specification ratios.

Natural Circulation Loop Scaling Ratios Definitions Scale Ratio

Pressure Drop [ ] [( ) ] 1:32

⁄ Core Inlet Velocity ( ) [ ] 1:2

Core Power Density ( ) 1:4 [ ]

Core Power ( ) ( ) 1:256 ̇

Initial Mass Flow Rate ( ̇ ) [ ] 1:256 ̇

Time Scale ( ) [ ] 1:2

Table 3-3: The HTTF in-vessel solid structural material scaling ratios.

Characteristic Scaling Ratio Definition Scale Ratio

Heat Storage [ ] [ ]

Thermal Diffusivity [ ] [ ] Reflectors

Thermal Conductivity ( ) ( ) [ ] [ ]

Reflectors

Thermal Diffusivity Core [ ] [ ] Barrel

Thermal Conductivity [( ) ] [( ) ] Core Barrel

Thermal Diffusivity [ ] [ ] Vessel

Thermal Conductivity [( ) ] [( ) ] Vessel

Thermal Diffusivity Core [ ] [ ]

Thermal Conductivity ( ) ( ) [ ] [ ] Core

Emissivity [ ] [ ]

Core Channel Heat ( ) [ ] [ ] Transfer Coefficient

The structural material scaling parameters are not part of the initial conditions for the HTTF RELAP5-3D model because it was design according to how the reduced facility was actually built. However, they are used as a point of reference to determine and quantify possible distortions that may exist during the simulations. By using the HTTF scaling design specification ratios and the MHTGR parameters provided by the Preliminary Safety Information Document (PSID), the initial conditions of the natural circulation phase for the HTTF during a PCC event are summarized on Table 3-4.

Table 3-4: Initial Conditions of the HTTF. [19]

MHTGR Scale HTTF Design Parameter PSID Value Ratio Value

Temperature (○C)

Reactor Vessel Inlet 259.0 1:1 259.0

Reactor Vessel Outlet 687.0 1:1 687.0

SG Bundle Inlet 685.6 1:1 686.6

SG Bundle Outlet 255.0 1:1 256.2

Peak Fuel Temperature 771.0 1:1 772.0

Pressure (MPa)

Reactor Vessel Inlet 6.38 1:8 0.7974

Reactor Vessel Outlet 6.32 1:7.94 0.7955

SG Bundle Inlet 6.31 1:7.94 0.7954

SG Bundle Outlet 6.29 1:7.92 0.7948

Mass Flow Rate (Kg/s)

Primary System 157.0 1:256 0.613

Heat Balance (MW)

Core 350.0 1:256 1.367

RCCS Loss 0.718 1:256 0.0028

SG Heat Removal 352.2 1:256 1.376

4 DESCRIPTION OF THE RELAP5-3D MODELS

This chapter presents the description and nodalization of the MHTGR and HTTF RELAP5-3D models. The Preliminary Safety Information Document (PSID) [19] provided the design parameters for the MHTGR model. The design parameters for the HTTF were taken from the available design drawings and information documents provided by OSU.

4.1 The MHTGR

The MHTGR RELAP5-3D model simulates the primary loop, secondary loop and the RCCS of the MHTGR. As mentioned earlier, the MHTGR contains a reactor vessel and steam-generator (SG) vessel, with a once-through helical coil SG. A nodalization diagram for the MHTGR model is given in Figure 4-1. The primary system is nodalized with volume numbers #1xx. Volume #140 represents the circulator with a time-dependent junction that sets the flow rate of the primary system during steady-state calculations. The flow rate of the time-dependent junction is controlled by a proportional-integral control variable that monitors the temperature of the reactor vessel outlet. Volume #142 is a branch that represents the circulator discharged plenum that connects into the inlet of the cold duct (Volume #143). Volume #143 connects to the cold-duct of the MHTGR (Volume #144). Volume #103 is a branch that connects the cold duct into the Metallic Core Support Structure (MCSS) (Volume #104). Volume #104 connects into the up-comer riser channels (Volume #105) and the MHTGR helium-gap between the core barrel and the reactor vessel wall. Volume #105 connects to Volume #106, which models the upper-plenum. The upper-plenum is a branch that connects into Volume #107, the Metallic Plenum Element (MPE) and the upper reflector of the MHTGR. [10] The core channels, developed as a “single channel approach”, are represented by Volume #109 and connect to Volume #111, the lower reflector. Volume #112 represents a branch that models the lower plenum and connects into the hot cross-duct vessel (Volume #122). The hot-duct connects into the elbow of the hot-duct (Volume #123) that eventually connects into the inlet plenum of the SG

(Volume #124). The helium coolant that flows through the SG tube-bundle is represented by Volume #126 and connects into the SG outlet plenum (Volume #130). Volume #132 models the annular region between the steam-generator bundle and steam generator vessel and connects into the inlet plenum of the circulator (Volume # 134). [10] [19]

301

106

107

109 105 116 300

140

142

-> 134 ->

->->-> 111 -> -->

-> ->

-> 143 144 ->

<- <-- <-- <-- 123 122 -> 112

-> 103 -> -->

124 ->

-> 204 205 ->

-> -> --> --> 104 --> --> --> --> -->

304

132 126 203

-> 130 201

-> 200

Figure 4-1: Nodalization of the MHTGR RELAP5-3D model

The secondary system is nodalized with volumes #2xx. Volume #200 models the inlet pressure and temperature boundary conditions of the feed-water and discharges into Volume #201. Between those two volumes, a time-dependent junction sets the flow rate of the secondary loop and is controlled by a proportional-integral control variable that monitors the temperature of the circulator in the primary loop. The Steam-Generator tube bundle is represented by Volume #203, and is divided into three parts with distinct geometries: 1) Economizer/Evaporator/Super-Heater (EES), 2) Finishing Super-heater (FS) and 3) EES/FS Transition. Volume #204 models the “expansion loop tubes” with super-heater steam that connects into the main steam line (MSL) boundary condition (Volume #205). [6] [19] The reactor cavity is nodalized with volumes #3xx. Volumes #301 and #304 control the boundary conditions of the RCCS at atmosphere pressure. Volume #300 models the cavity of the RCCS. The location of the heat-structures and conduction/radiation enclosure sub-models of the MHTGR can be found by using figure 4-2.

Primary Coolant System

Secondary Coolant System

RCCS System

Upper Plenum HS

Inner Reflector HS

Core HS

Outer Reflector/PSR/Core Barrel HS

Core Barrel Coolant Channel HS

Reactor Vessel HS

RCCS HS

SG/Heat-Exchanger HS

Conduction

Thermal Radiation

Circulator TDJ

Figure 4-2: RELAP5-3D Nodalization Definitions

The geometry of the core heat-structures for the MHTGR was developed by using a “sub-channel” approach [10] [23]. This was achieved by converting the geometrical configuration of the unit cell from hexagonal to cylindrical geometry. The center coolant channel and the surrounding fuel compact cross-sectional areas are conserved during this process. [10] Figure 4-3 represents a figure of the MHTGR core unit cell conversion.

Figure 4-3: The Unit Cell of the MHTGR Core Channel. [10]

The core uses a chopped cosine axial power profile at 350 MW. The unit cell fuel compact is assumed to be the default UO2, the pre-built fuel properties of RELAP5. The graphite uses irradiated H-451 thermal properties, irradiated to 3.0 dpa. [10] [23] The inner and outer reflectors uses the same graphite properties, irradiated H-451, and they thermally conduct heat within the core by using the conduction enclosure sub- model provided by RELAP5-3D.The permanent side reflector (PSR) is also made of graphite and is assumed to contain the properties of un-irradiated Stackpole-2020. [10] The core barrel is allowed to thermally radiate into the inside of the reactor vessel wall by using the radiation enclosure sub-model provided by RELAP5-3D. The outside of the reactor vessel wall also thermally radiates into the RCCS heat-structure by using the radiation enclosure model [10] [19]. The emissivity of the core barrel and reactor

59 vessel is assumed to be 0.85, while the RCCS emissivity is assumed to be 0.80. The RCCS heat-structure contains a constant temperature of 40 0C on the non-radiating side (right side of heat structure) [10] [19]. Table 4-1 shows a summary of the solid material properties for the MHTGR with their respective average values. Appendix A.1 gives a summary of all the MHTGR RELAP5-3D parameters.

Table 4-1: The MHTGR in-vessel solid material properties.

Parameter MHTGR Material [ ] [ ]

Inner Reflector H-451 Graphite, Irradiated Fluence=3.0 30.78 3.05E+06

H-451 Graphite, Irradiated Fluence=3.0 Core 27.54 3.09E+06 & UO2

Outer Reflector H-451 Graphite, Irradiated Fluence=3.0 32.15 2.85E+06

PSR Stackpole 2020 Graphite, unirradiated 55.5 2.63E+06

Core Barrel Alloy 800H 16.3 3.66E+06

SA533 Grade B, Class-1 Manganese- Reactor Vessel 47.9 4.55E+06 Molybdenum Steel Allow

4.2 The HTTF

The HTTF RELAP5-3D model is very similar of the MHTGR model. The main differences are the piping configuration on the SG vessel side and the U-tube heat- exchanger. A nodalization diagram for the HTTF model is given in Figure 4-4. The primary system of the HTTF is nodalized with volume numbers #1xx. Volume #140 represents the circulator with a time-dependent junction that sets the flow rate of the primary system during steady-state calculations. The flow rate of the time-

60 dependent junction is controlled by a proportional-integral control variable that monitors the temperature of the reactor vessel outlet. Volume #142 is a pipe that represents the circulator discharged that connects into the inlet of the cold duct (Volume #144). Volume #103 is a branch that connects the cold duct into Volume #104. The Lower Core Support Structure (LCSS) is represented by Volume #104 and connects into the up-comer riser channels (Volume #105) between the core barrel and the reactor vessel. Volume #105 connects to the upper plenum (Volume #106). The upper-plenum is a branch that connects into Volume #107, the upper reflector of the HTTF. [10] The HTTF core sub- channels also use the “single-channel” approach and are represented by Volume #109. Volume #109 connects to Volume #111, the lower reflector. Volume #112 represents a branch that models the lower plenum. [10] The lower plenum connects into the hot cross- duct vessel (Volume #122). The hot-duct connects into the elbow of the hot-duct (Volume #123) that eventually connects into the inlet plenum of the U-tube heat- exchanger (Volume #124). The U-tube heat-exchanger is model by Volume # 126, with half of the volumes having a vertical angle of 900 and the other half with vertical angle of -900. Volume #126 discharges into the outlet plenum of the heat-exchanger (Volume #128). Volume #132 models the piping configuration that connects into the inlet of the circulator.

106 301

<-- <-- <-- <-- ->

-> 215 <-- <-- <-- <-- <-- 209 208 107

-> -> -> ->

-> 200 202 <- <- <- <- <- ->

203 205 126 126 205 109 105 300

-> --> --> --> --> --> --> --> -> --> -->

-> 128 124

-> ->

<- <- <- <- <- <- ->

-> -> 111 123

--> <-- <- 122 112 132 --> -->

143 144 103 ->

-> ->

<-- -> 140 --> 104 --> 304 142

Figure 4-4: Nodalization of the HTTF RELAP5-3D model

The secondary system of the HTTF is nodalized with volumes #2xx. Volume #200 models the inlet pressure and temperature boundary conditions of the feed-water and discharges into Volume #202. Between those two volumes, a time-dependent junction sets the flow rate of the secondary loop (during steady-state calculations) and is controlled by a proportional-integral control variable that monitors the temperature of the circulator in the primary loop. Volume #203 models the annular region of the heat- exchanger between the inner and the outer shells of the heat-exchanger. Volume #203 discharges into the lower plenum of the heat-exchanger above the tube-sheet. Volume #205 models the upcomer of the heat-exchanger tube bundle. Volume #208 models the

62 upper steam plenum of the heat-exchanger and connects into Volume #209. Volume #215 represents the MSL boundary condition of the HTTF. The reactor cavity of the HTTF is nodalized with volumes #3xx. Volumes #301 and #304 control the atmosphere pressure boundary conditions of the RCCS. Volume #300 models the cavity of the RCCS. [10] Just like the MHTGR, the location of the HTTF heat-structures and conduction/radiation enclosure sub-models of the HTTF can be found by using figure 4-2. The core heat-structures for the HTTF also use the core sub-channel approach. [10] [23]. However, the cross-sectional area of the unit cell is conserved differently, since the HTTF contains the heater-rod in the center surrounded by six coolant channels. Figure 4-5 represents a figure of the HTTF core unit cell conversion.

Figure 4-5: The Unit Cell of the HTTF Core Channel. [10]

The HTTF core uses a chopped cosine axial power profile at 1.367 MW (1:256 scaling parameter) and is assumed to contain the properties of un-radiated H-451 graphite. [10] The inner and outer reflectors are made of Greencast-94F ceramic and the PSR uses Thor-80 ceramic. [10] [23]

As with the MHTGR, the inner and outer reflectors of the HTTF thermally interconnect within the core by using the conduction enclosure sub-model provided by RELAP5-3D. The core barrel is allowed to thermally radiate into the inside of the reactor vessel wall, and then radiates outwardly into the RCCS heat-structure by using the radiation enclosure sub-model provided by RELAP5-3D. [10] The emissivity of the core barrel is assumed to be 0.54 (lightly oxide stainless-steel, SS-304) and the emissivity of the reactor vessel is assumed to be 0.22 (typical clean stainless-steel, SS-304) [24] The temperature of the RCCS heat-structure on the non-radiating side is controlled by a control variable that uses a proportional-integral controller to monitor the amount of heat loss by the reactor vessel during steady-state calculations. The temperature and heat proportionalities, along with other steady-state parameters will be discuss in the next section. Table 4-2 shows a summary of the HTTF in-vessel solid materials properties with their respective average values and Appendix A.2 gives a summary of all the HTTF RELAP5-3D parameters.

Table 4-2: The HTTF in-vessel solid material properties.

Parameter HTTF Material [ ] [ ]

Inner Reflector Greencast-94F Core Ceramic 2.65 3.54E+06

Greencast-94F Core Ceramic Core & 10.55 3.50E+06 H-451 Uniradiated Radial Direction

Outer Reflector Greencast-94F Core Ceramic 2.95 3.44E+06

PSR Thor-80 PSR Ceramic 6.71 2.65E+06

Core Barrel SS-304 19.7 4.19E+06

Reactor Vessel SS-304 18.3 4.19E+06

4.3 Benchmarking of the Models at Steady-State

The MHTGR and HTTF RELAP5-3D models are run to converge upon steady- state results to compare them, representing the normal operations of both models. In addition, the steady-state results are used as initial conditions to simulate the necessary transient events in the following chapter. The MHTGR is benchmarked against normal operation conditions provided by the PSID. [19]. The HTTF is benchmark against the scaling parameters developed in Chapter 3. The form loss coefficients for each model, across each segment are manually adjusted in order to achieve the correct frictional and form losses in each of the primary systems. Table 4-2 and table 4-3 show the steady- state results of the MHTGR and HTTF RELAP5-3D models respectively.

Table 4-3: The Steady-State RELAP5-3D predicted values of the thermal-hydraulics parameters of interest of the MHTGR. [5]

MHTGR MHTGR % Parameter PSID RELAP Error Value Value Temperature (○C) Reactor Vessel Inlet 259.0 259.0 B.C. Reactor Vessel Outlet 687.0 687.0 B.C. SG Bundle Inlet 685.6 686.6 0.14% SG Bundle Outlet 255.0 256.2 0.45% Circulator Inlet 255.0 256.1 0.43% Circulator Outlet 258.8 259.2 0.15% Feed-water Inlet 193 193.0 B.C. Steam-line Outlet 541 557.8 3.60% Peak Fuel Temperature 771 772.0 0.13% Pressure

RPV Inlet (MPa) 6.3766 6.3589 -0.50% RPV Outlet (MPa) 6.3215 6.3048 -0.50% Core Pressure Drop (KPa) 34.500 33.61 -2.58%

SG Bundle Inlet (MPa) 6.3146 6.2976 -0.50% SG Bundle Outlet (MPa) 6.2946 6.2787 -0.49% SG Pressure Drop (KPa) 20.00 18.92 -5.40% Feed-water Inlet (MPa) 20.70 20.70 B.C. Steam-line Outlet (MPa) 17.30 17.36 0.33% 2nd. System SG P-Drop (KPa) 3.40 3.33 -2.01% Mass Flow Rate (Kg/s)

Primary System 157.0 156.6 -0.31% Secondary System 137.4 131.6 -4.19% Heat Balance (MW)

Core 350.0 350.0 B.C. Circulators 3.1 N/A N/A RCCS Loss 0.718 0.727 -1.17% Heat to SG 352.2 349.1 -0.90%

As expected, the temperatures in the primary loop of the MHTGR are well matched against the PSID (within 1% error), since active-control time dependent junctions are used. The time-dependent junctions are controlled by proportional-integral control variables that monitor the temperature of the inlet plenum of the circulator and the outlet of the reactor vessel. Furthermore figure 4-6 shows the similarity of the temperature profile within the primary loop of the MHTGR compared against the PSID values. The predicted peak fuel temperature of the MHTGR is also well matched against the PSID value, within 0.13%. Additionally as expected, the feed-water inlet temperature is matched against the PSID since it is given a set boundary condition. The predicted main steam-line temperature deviates within 3.1% to the PSID value. This occurs since a lower mass flow rate is desired, which gives the steam time to heat up to higher temperatures. Nonetheless, the temperatures are still well matched to the desired values. The pressure of the primary system is within 0.28% lower than the values in the PSID. This occurs because the model did not contain any source of pressure controller in the primary system. As expected, the core and the SG pressure drop are lower than the

PSID values, 2.58% and 5.4% respectively. Nonetheless, the pressures similarity is conserved against the desired values as shown on figure 4-7. The mass flow rate of the primary system is 0.31% lower than the PSID value, which indicates that it is well matched to the desired value. The mass flow rate of the secondary system is 4.19% lower than the desired value, since a lower heat removal from the steam generator is needed in order to accommodate for the heat that is not added by the circulator. Since the MHTGR RELAP5-3D model did not contain a circulator, it is anticipated that the steam generator removes less heat from the system in order to achieve heat balance. As expected, the SG heat removal is 0.90% less than the desired value. The heat loss to the RCCS is 1.17% less than the PSID. Therefore, the heat balance is conserved within the system (within 3% error).

Table 4-4: The Steady-State RELAP5-3D predicted values of the thermal-hydraulics parameters of interest of the HTTF.

HTTF HTTF Designed RELAP Distortion Parameter Designed RELAP Ratio Ratio % Value Value Temperature (○C)

Reactor Vessel Inlet 259.0 259.0 1:1 1:1.000 B.C. Reactor Vessel Outlet 687.0 687.0 1:1 1:1.000 B.C. SG Bundle Inlet 685.6 686.9 1:1 1:0.998 0.19% SG Bundle Outlet 255.0 258.5 1:1 1:0.987 1.33% Circulator Inlet 255.0 258.5 1:1 1:0.987 1.33% Circulator Outlet 258.8 259.3 1:1 1:0.998 0.19% Feed-water Inlet N/A 20.0 N/A N/A N/A Steam-line Outlet N/A 186.3 N/A N/A N/A Peak Fuel Temperature 771 752.8 1:1 1:1.02 -2.43% Pressure (MPa)

RPV Inlet 0.79708 0.7987 1:8 1:7.98 0.19% RPV Outlet 0.79567 0.7972 1:7.94 1:7.93 0.19% Core Pressure Drop (KPa) 1.078 1.088 1:32 1:31.7 -0.94%

SG Bundle Inlet 0.796 0.797 1:7.94 1:7.92 0.19% SG Bundle Outlet 0.795 0.796 1:7.92 1:7.91 0.16% SG Pressure Drop (KPa) 0.919 0.857 1:32 1:31.4 1.88% Feed-water Inlet N/A 0.207 N/A N/A B.C. Steam-line Outlet N/A 0.202 N/A N/A N/A 2nd. System P-Drop (KPa) N/A 5.7 N/A N/A N/A Mass Flow Rate (Kg/s)

Primary System 0.613 0.6094 1:256 1:257 -0.33% Secondary System N/A 0.4910 N/A N/A N/A Heat Balance (MW)

Core 1.367 1.367 1:256 1:256 B.C. Circulators N/A N/A N/A N/A N/A RCCS Loss (KW) 2.805 2.817 1:256 1:255 0.42% Heat to SG 1.376 1.361 1:256 1:259 -1.07%

As expected, the temperatures in the primary loop of the HTTF are well match against the designed ratios (within 3% deviation), since active control time dependent junctions are used to control the temperatures. The time-dependent junctions are controlled by proportional-integral control variables that monitor the temperature of the inlet plenum of the circulator and the outlet of the reactor vessel. Furthermore, figure 4-6 shows the temperature profile within the primary loop of the HTTF compared against the MHTGR and PSID values. As shown from the figure, temperature similarity in the fluid is preserved for the HTTF. The peak fuel temperature is well matched to the desired value by a distortion of only 2.41% less than the predicted value. Since the HTTF contains a completely different secondary system compared to the MHTGR, there are no scaling ratios for the main feed- water and the main-steam line. Nonetheless, the temperature in the feed-water line of the HTTF, 22 0C, is much lower than the MHTGR, 193 0C. This indicates that during a transient event, if the HTTF heat-exchanger and the MHTGR SG are used as a source to remove heat from the primary loop, then similarities in the thermal-fluids properties will not be conserved.

The pressures within the primary system of the HTTF are well match, within 0.19% of the desired value. The pressure drop across the core is also well matched against the designed ratio. However, the pressure drop across the steam generator deviates within 27% of the design ratio. This is because additional sensitivity analysis is needed in order to achieve the correct form coefficient. Nonetheless, pressure similarity across the primary loop of the HTTF is conserved as shown on figure 4-8. The mass flow rate of the primary system is 0.35% lower than the designed ratio, which indicates that is well match (within 3% deviation), to the desired value. Again, since the secondary loop is not part of the scaling analysis, there is no scaling ratio for the flow rate in the secondary system. Since the heat added to the primary system by the circulator is not included in the HTTF RELAP model, it is anticipated that the U-tube heat exchanger removes less heat from the system in order to achieve heat balance. As expected, the heat-exchanger removes 1.07% less than the desired value. The heat loss to the RCCS is only 0.42% higher than the design ratio. Therefore, the heat loss to the RCCS is also well matched to the desired value. A slightly higher heat loss by the RCCS will lead to lower temperatures in the fuel of the HTTF compared to the MHTGR.

Figure 4-6: The Predicted Primary Loop Temperature Profile of the PSID, MHTGR and HTTF.

Figure 4-7: The Predicted Primary Loop Pressure of the MHTGR RELAP5-3D Model compared against the PSID values.

Figure 4-8: The Predicted Primary Loop Pressure of the HTTF RELAP5-3D Model and the Design Value.

As mentioned, the HTTF contains a completely different secondary system to that of the MHTGR. The HTTF contains a U-tube heat-exchanger, while the MHTGR contains a once-through helically coil steam generator. Figure 4-9 shows the temperature profile distribution along the primary and secondary side of the MHTGR’ steam generator and HTTF’s heat-exchanger. The red line on the figure indicates the helium coolant temperature distribution across the steam generator of the MHTGR. The blue line indicates the temperature of the feed-water and super-heated steam of the MHTGR. As expected, the helium coolant in the MHTGR enters the SG with a high temperature and exits at a low temperature, while the feed-water enters helically coil tubes with a low temperature and exits as super-heater steam. As for the HTTF, the green line indicates the helium coolant temperature distribution across the U-tube heat-exchanger and the purple line indicates the temperature of the feed-water and the steam. As expected, the helium coolant enters with a high temperature and exits at low temperature. The feed-water in the HTTF enters at a low temperature and exits as steam with high temperatures. Even though distinct phenomena occur within the heat-sinks, the point of interest is the temperature similarity in the inlet and outlet of the primary loops. Nonetheless, the primary loop inlet/outlet temperatures for both models are well matched to the desired values.

Figure 4-9: The Steam Generator and the U-tube Heat-exchanger temperature distributions along the primary and secondary loops of the MHTGR and HTTF RELAP5-3D models.

Figure 4-10 shows the predicted radial temperature profile of the in-vessel solid materials at the axial level where the peak temperature occurs. The figure further illustrates that the HTTF is capable of meeting temperature similarities within the core as long as the properties of the material are chosen correctly and the boundary conditions are properly selected. The core material properties chosen for the HTTF is ceramic. The reason for this is that ceramic contains a very low thermal-conductivity (~2.6 W/m-0C) compared to graphite (~30.1 W/m-0C) in the MHTGR. Consequently with small deviations, this allows temperature similarity to be maintained within the core region as shown on the figure. Furthermore, the temperature at the center of the inner reflector of the HTTF is well matched (within 3% deviation) to the MHTGR, within 2.47%. The peak fuel temperature is only 2.48% less of the MHTGR and the outer reflector is approximately 8.0% less compared to the predicted value. This indicates that the HTTF is able to

72 maintain temperature similarity within the core and reflector regions during steady state calculations. However, the temperature of the HTTF radially deviates at the core barrel and reactor vessel. The reason for this is that the dimensions and thickness at these regions were not properly scaled and were chosen according to the sizes that were commercially available. [5] As for the temperature at the wall of the reactor vessel and the RCCS, unique boundary conditions are chosen. Because in the HTTF scaling analysis [5], the decay core power is scaled according to the volume, the surface area is not conserved. This means that too much radiation heat leakage occurs on the reactor vessel wall, since radiation is dependent on the surface area. To accommodate for this heat loss, the HTTF contains insulated cooling panels and a piping configuration with water flowing inside of them. This insulation system allows additional thermal resistance through the RCCS. However, because of the complexibility and geometrical configurations, the actual RCCS in the facility was not modeled in the HTTF RELAP5-3D model. Instead, the RCCS is model as a simplified single heat-structure that contains a high temperature boundary condition to accommodate for radiation heat loss. As previously discussed, the temperature on the non-radiating side of the RCCS wall is controlled by a control variable that uses a proportional-integral controller that monitors the heat-rate of the outside of the reactor vessel wall during steady-state calculations. This allows the heat loss to be monitored according to the scaled value given in table 4-2 (1:256). In other words, if the reactor vessel wall is giving off too much heat, the temperature on the RCCS wall increases, and if the reactor vessel wall is not losing sufficient amount of heat, then the temperature of the RCCS wall decreases. This is why the RCCS temperature in the HTTF is much larger compared to the MHTGR. Consequently, this also disturbs the behavior of the reactor vessel wall, thus in some cases negative heat-flux along the axial level of the reactor vessel wall can be found. This means that the convective heat-transfer coefficient may be negative and heat may be push back into the up-comer coolant channels, between the core barrel and the reactor vessel wall. Subsequently, higher temperature could affect the end results of a transient event, where temperatures inside the reactor pressure vessel are expected to increase.

Figure 4-10: The Predicted Radial Temperature Profile of the MHTGR and HTTF.

Some conclusion can be made for each model during steady-state analysis. The MHTGR model is able to calculate the thermal-fluid properties of interest from the PSID. The HTTF model is also able to calculate the correct thermal-fluid properties of interest according to the scaling ratios. This indicates that similarities in the thermal-fluid properties are conserved for both models. However during a PCC event, if the HTTF heat-exchanger is used as a method to remove decay heat from the primary system, similarities in the thermal-fluid properties and the system’s heat-balance may be lost. In addition, the high temperatures in the RCCS of the HTTF may also lead to distortions in the thermal-fluid properties during a transient event. The reason for this is that as the primary system cools down and the high temperature boundary condition is kept on the RCCS wall, then heat may have an opportunity to flow back into the primary loop due to convection and conduction in the reactor vessel wall.

5 PCC EVENT SIMULATIONS AND RESULTS

The previous chapter presented the calculations at steady-steady for the MHTGR and HTTF models. This chapter presents the results of the simulations of the PCC event. To reiterate, the models were run to converge upon steady-state and transients were then calculated starting from the end of steady state, at time zero. All simulations assumed an instantaneous loss of flow accident (LOFA) by circulator shutdown with a successful reactor protection system (RPS) actuation and the availability of the RCCS. The decay power curve used for the MHTGR was taken using the information from [25] and extrapolated values were found using a curve fit approximation. The same decay heat curve was used for the HTTF with a scaled ratio of 1:256 and a time ratio of 1:2. The decay curves can be found in Appendix B. The MHTGR uses a temperature boundary condition of 40 0C in the non-radiating side of the RCCS. As for the HTTF, the control variable that controls the temperature on the RCCS is set to a constant value. This means that the RCCS is given the temperature found during steady-state calculations (~246 0C). Both models are run for a total simulation time of 30 days and the results and comparison are shown in the following sections. A summary of the various scenarios explored is presented in Table 5-1.

Table 5-1: Description of the scenarios of the PCC event.

Scenario # Scenario Description

MHTGR PCC Events Scenario 1.a LOFA with SG Scenario 2.a LOFA with SG and Cross-Duct Vessel Break Scenario 3.a LOFA with an Isolated Reactor Vessel HTTF PCC Events Scenario 1.b LOFA with SG Scenario 2.b LOFA with Heat-Exchanger and Cross-Duct Vessel Break Scenario 3.b LOFA with an Isolated Reactor Vessel

5.1 Scenario 1: PCC Event with SG Heat Removal

5.1.1 Case 1 Specifics

This scenario assumes a loss of forced convection by circulator shutdown. In addition, the SG and Heat-exchanger are available to remove decay heat from the core. In order to simulate the PCC event, several changes were made to the nodalization of the MHTGR and HTTF models. The time dependent junction that simulates the constant flow rate of the circulator was deleted and a single junction was added. The addition of the single junction stops the forced flow in the primary loop and allows the helium coolant to behave according to the thermal-fluid phenomena in the primary system. The initial flow rate of the single junction is assumed to be the mass flow rate obtained from steady-state calculations. As for the SG and the heat-exchanger heat removal, the time dependent junction that controls the feedwater mass flow rate in the secondary system was given a constant flow rate, according to the value found during steady-state calculations.

5.1.2 Case 1 Results

The first figure (Figure 5-1) shows the results of the MHTGR heat balance found in the PSID compared to the heat balance results obtained from MHTGR RELAP5-3D model. The figure further illustrates that the results obtained from the MHTGR RELAP5- 3D model are closely related to the results obtained from the PSID. The heat removed by the RCCS in the RELAP5-3D model (red dotted line) overcomes the decay curve (blue solid line) around 50 hours. While the heat removed by the RCCS in the PSID overcomes the decay curve around 90 hours. The reason for this is because the decay curve in the PSID contains slightly higher values than the ones found in the RELAP5-3D model. The decay curved used in the RELAP5-3D model were taken from [25], which is a more recent decay heat curve approximation.

Figure 5-1: The MHTGR heat balance results from the PSID compared to the MHTGR heat balance results from RELAP5-3D during a PCC event.

Figure 5-2 presents the calculated peak fuel temperature for the MHTGR and the HTTF during the PCC event with the steam generator and heat-exchanger available to remove reactor decay heat. During the first few seconds of the scenario (not shown on the figure) the MHTGR and HTTF followed the same trend because of reactor scram. Afterwards, the trends diverged and the figure further illustrates that the HTTF is unable to predict the peak fuel temperature of the MHTGR. The MHTGR peak fuel temperature continued to increase because the system’s ability to remove decay heat decreased in consequence to the loss of forced convection. The temperature continued to rise until reaching its maximum value of 990 0C, around 24 hours, and then slowly decreased as the system’s heat removal mechanisms exceeded the reactor decay heat. As for the HTTF, the peak fuel temperature initially decreased and continued to decrease throughout the rest of the scenario. This is because the HTTF in-vessel solid structures are unable to

77 retain the heat and the HTTF heat-exchanger effectively removed much more heat than the MHTGR (figure 5-5).

Figure 5-2: The peak fuel temperature of the MHTGR and the HTTF during a PCC event with the availability of the steam generator to remove decay heat.

The predicted helium coolant temperature at the core inlet of the MHTGR and the HTTF are shown on figure 5-4. During normal operations, cold helium coolant enters the top of the core and exits as hot helium at the bottom of the core. However, at the onset of natural circulation (figure 5-5 and 5-6), the flow is reversed and cold helium enters the bottom of the core (core outlet) and exits as hot helium at the top of the core (core inlet). Both cases followed the same trend since natural convection was effective in removing heat from core to the core inlet. The hot helium then flows to the upper plenum and down through the coolant riser channels, where helium is cool down by natural convection in the reactor vessel wall. Additional heat is removed from the helium as it continued to flow through the steam generator/heat-exchanger and back again to the core outlet.

Figure 5-3: The MHTGR and HTTF helium temperature at core inlet during a PCC event with the availability of the SG to remove reactor decay heat.

The MHTGR heat balance is shown on figure 5-4. Initially, the RCCS heat removal slightly drops (not seen on the figure) as the core power was reduced. This enabled the steam generator to remove a small amount of decay heat at the beginning of the scenario. However, as the scenario progressed, the temperature of the core and the in- vessel solid material increases, which results an increase in the radiation heat transfer from the reactor vessel to the RCCS. Additional decay heat is then removed as the helium coolant flows down through the coolant riser channel.

Figure 5-4: The MHTGR heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system.

The HTTF heat balance is shown on figure 5-5. The RCCS in the HTTF is able to remove decay heat at a much faster rate than the MHTGR, since the time ratio is 1:2. In contrast to the heat removed by the SG in the MHTGR, the HTTF heat-exchanger is able to remove considerable amount of heat at the beginning of the scenario. The reason for this is because the HTTF feedwater temperature (22 0C) is much cooler than the MHTGR. Consequently, the primary system is cooled down to the point where the RCCS no longer removes decay heat from the system; instead it adds heat to the system (negative values on the figure) and the HTTF heat-exchanger removes the additional heat. This is because of the high temperature (246 0C) boundary condition on the non- radiating side of the RCCS found during steady-state calculations. The actual reduced- facility will not behave like this, since it will contain a special cooling system through the RCCS.

Figure 5-5: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system.

Figure 5-6 and figure 5-7 shows the mass flow rate of the helium coolant for the MHTGR and HTTF respectively. The negative mass flow rate on the figures indicates that the systems’ experienced onset of natural circulation and flow reversal. Both models reached natural circulation within two seconds in the scenario. The figures further illustrates that the HTTF mass flow rate scaling ratio flow is approximately 1:33.3, where it should have scaled to 1:256. This indicates that the HTTF developed a much higher mass flow rate, which further increases the ability of the system to remove decay heat from the core.

Figure 5-6: The helium mass flow rate of the MHTGR during a PCC event with the availability of the steam generator to remove reactor decay heat.

Figure 5-7: The helium mass flow rate of the HTTF during a PCC event with the availability of the steam generator to remove reactor decay heat.

5.2 Scenario 2: PCC Event with SG and Cross-Duct Vessel Break

5.2.1 Case 2 Specifics

This scenario models the PCC event with a circulator shut down and a break in the inlet/outlet of the cross-duct vessel. This scenario also assumes that the SG and heat- exchanger are available. The break in the cross-duct vessel was chosen because the most likely failure area in the MHTGR is associated with the seals and bellows, which are located in the elbow of the hot-duct. The results of this break would lead a leakage into the area of the cold gas. [19] Again, in order to simulate this scenario, several changes were made to the nodalization of the models. The time dependent junction that controls the circulator flow rate was deleted and a single junction was added. The feedwater time dependent junction is given the constant flow rate value found during steady-state calculations. The cross-duct vessel break is modeled with a conservative assumption of an “instantaneous break”. For the MHTGR, a single junction was added between Volume #143 and Volume #123. As for the HTTF, the break is between Volume #122 and Volume #143. The nodalization of the MHTGR and HTTF models for the PCC event with a cross-duct vessel break are shown on figure 5-8 and 5-9 respectively.

301

106

107

109 105 116 300

140

142

-> 134 ->

->->-> 111 >> >> -> -->

-> 143 144 ->

>> >> <- <-- <-- <-- 123 122 -> 112

-> 103 -> -->

124 ->

-> 204 205 ->

-> -> --> --> 104 --> --> --> --> -->

304

132 126 203

-> 130 201

-> 200

Figure 5-8: Nodalization of the MHTGR RELAP5-3D model for the PCC event with a cross-duct vessel break.

106 301

-> ->

<-- <-- <-- <-- <-- ->

-> ->

<- -> 215 <-- <-- <-- <-- <-- 209 208 107

-> ->

-> -> -> -> ->

200 202 -> <- <- <- <- <- ->

-> -> ->

203 205 126 126 205 109 105 300

<- -> -> ->

--> --> -> --> --> --> --> --> -> --> -->

-> 128 124

-> -> ->

-> ->

<- <- <- <- <- <- <- ->

-> -> 111

123

-> ->

<< --> <-- <-

>> 122 112 132 >> << --> -->

143 144 -> 103 -> -> ->

<-- -> 140 --> 104 --> 304 <-- 142

Figure 5-9: Nodalization of the HTTF RELAP5-3D model for the PCC event with a cross-duct vessel break.

5.2.2 Case 2 Results

Figure 5-10 presents the peak fuel temperature for the MHTGR and the HTTF during the PCC event with a cross-duct vessel break and the availability of the steam generator to remove decay heat. Again, the figure shows that the HTTF is unable to predict the peak fuel temperature of the MHTGR. The MHTGR peak fuel temperature is much lower during this scenario compared to the previous scenario because additional heat is being removed from the core as a consequence of a higher mass flow rate in the helium coolant. The reason for this is because stagnant helium developed on the steam generator side of the primary loop (Volume #124 through Volume #142 from figure 5-8). This results in the helium having a shorter path to travel throughout the loop, hence the “loop length” decreases and the mass flow rate of the system increases. This phenomenon can be explained analytically from Equation 3-2, the integrated loop momentum balance equation. The left term of the equation represents the inertial term and the right side contains the frictional and form losses. With a smaller “loop length” and the friction and form losses from the steam generator avoided, then by conservation of momentum, the helium mass flow rate in the system increases. The MHTGR and the HTTF helium temperatures at the core inlet are shown on figure 5-11. Once again, the HTTF is unable to predict the helium temperature in the primary system because of the in-vessel solid structures are unable to retain heat as well as the MHTGR, which results in a large amount of heat loss from the system.

Figure 5-10: The peak fuel temperature of the MHTGR and HTTF during a PCC event with a cross-duct vessel break the availability of the SG to remove decay heat.

Figure 5-11: The MHTGR and HTTF helium temperature at core inlet during a PCC event with the availability of the SG to remove reactor decay heat.

The MHTGR heat balance is shown on figure 5-12.The figure illustrates that the steam generator is unable to remove decay heat from the system because of the stagnant helium. The RCCS heat removal was effective and cooldown the reactor for the rest of the scenario. Figure 5-13 represents the heat balance of the HTTF. As expected, the HTTF heat-exchanger did not behaved as the MHTGR and was able to remove decay heat from the core. In addition, around 16 hours in the scenario, the HTTF helium coolant experienced several instabilities in the mass flow rate and the natural circulation seized. This indicates that heat removal due to natural convection decreased, which enabled conduction and thermal radiation to become the dominant decay heat removal mechanisms.

Figure 5-12: The MHTGR heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system.

Figure 5-13: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system.

Figure 5-14 shows the mass flow rate of the MHTGR. This figure further illustrates the passive safety mechanism of heat removal in the MHTGR. Typically “intra-core” natural circulation develops during a PCC event. However, since the MHTGR RELAP-3D model contains only one channel in the core, natural circulation developed at the location of the break and the hot helium never reached the steam generator. The stagnant cold helium stayed in the steam generator side with very small amount of mixing occurring at the location of the break. As for the HTTF, very different phenomena occurred as shown on figure 5-15. The flow rate in heat-exchanger of the HTTF continued its normal forced circulation pattern as the transient initiated. The oscillations seen on the figure is likely due to instabilities in the flow of the helium coolant, as the coolant velocity is trying to shift from one direction to another one through the u-tube heat-exchanger.

Figure 5-14: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system.

Figure 5-15: The HTTF heat balance during a PCC event with the availability of the steam generator to remove reactor decay heat from the primary system.

5.3 Scenario 3: PCC Event with an Isolated Reactor Vessel

5.5.1 Case 3 Specifics

Scenario 3 consists of a PCC event with a circulator shutdown and an isolated reactor pressure vessel. This means that the steam generator and heat exchanger were excluded from this event and the helium coolant cannot flow towards the SG/heat- exchanger side of the primary system. It is assumed that as the circulator seizes and the reactor trip occurs, the reactor vessel is instantaneously isolated. Again, in order to simulate this event, changes were made to the nodalization of the models. The time dependent junction that controls the circulator flow rate was replaced by a single junction and the feedwater time dependent junction is given the constant flow rate value found during steady state calculations. The MHTGR reactor pressure vessel is isolated by using a single junction between volume #143 and volume #123. As for the HTTF, the reactor vessel is isolated by adding a single junction between Volume #143 and Volume #122. In addition, two valves were closed to block the flow towards the SG side of the primary loop. The MHTGR valves are located between Volumes #123 and #124 and Volumes #143 and #142. The HTTF valves are located between Volumes #143 and #142 and Volumes #122 and #123. Figure 5-16 and 5-17 shows the nodalization of the MHTGR and HTTF as isolated reactor pressure vessels.

301

106

107

109 105 116 300

111

>> >> -> -->

-> 143 144 ->

>> >> <- <-- <-- <-- 123 122 -> 112

-> 103 ->

-> --> --> 104 --> --> --> --> --> 304

Figure 5-16: Nodalization of the HTTF RELAP5-3D model for the PCC event with an isolated reactor pressure vessel.

106 301

107

109 105 300

-> 111

<< << --> <-- <-

>> 122 112

<< << --> -->

143 144 -> 103 -> ->

--> --> 304 104

Figure 5-17: Nodalization of the HTTF RELAP5-3D model for the PCC event with an isolated reactor pressure vessel.

5.5.2 Case 3 Results

The peak fuel temperatures for the MHTGR and HTTF during a PCC event with an isolated reactor vessel are shown in figure 5-18. Even with the exclusion of the SG and the heat-exchanger, the HTTF is unable to predict the peak fuel temperature of the MHTGR. The MHTGR peak fuel temperature is slightly lower than the previous scenario since a higher mass flow rate developed, which enables the helium coolant to remove more heat from the core through natural convection. As for the HTTF, the peak fuel temperature is also lower than the previous scenario because of a higher mass flow rate.

Figure 5-18: The peak fuel temperature of the MHTGR and the HTTF with an isolated reactor pressure vessel during a PCC event with

Figure 5-19 shows the MHTGR and the HTTF helium temperatures at the core inlet. Once again, the HTTF is unable to predict the coolant temperature because of the rapid loss of heat from the primary system to the RCCS. However, both models were able

92 to capture the same trend since cold helium enters the bottom of the core and exits as hot helium.

Figure 5-19: The MHTGR and HTTF helium temperature at core inlet with an isolated reactor pressure vessel during a PCC event.

The MHTGR and HTTF heat balance are shown on figure 5-20 and figure 5-21 respectively. With the reactor vessel isolated, the only way heat can be removed from the primary system is through the RCCS. Comparing the peak of the RCCS trend for both models, the HTTF removes heat at an approximately ratio of 1:140, where it should have been 1:256. This indicates that the HTTF removed much more heat than the MHTGR at a faster rate. The reason for this could be due to the combination of different phenomena’s occurring at the same time, such as heat removal due to natural convection, possible distortions in the in-vessel solid structures or the additional surface area found on the vessel wall of the HTTF.

Figure 5-20: The MHTGR heat balance with an isolated reactor pressure vessel during a PCC event with

Figure 5-21: The HTTF heat balance with an isolated reactor pressure vessel during a PCC event with

Figure 5-22 and figure 5-23 shows the mass flow rate for the MHTGR and the HTTF respectively. The figures show that the MHTGR, as well as the HTTF were able to develop a natural circulation loop along the reactor vessel. By comparing the mass flow rate in both figures, the HTTF scaling ratio is approximately 1:150, where it should have been 1:256. Again, this indicates that the HTTF developed a higher mass flow rate than the MHTGR, which enabled the HTTF to remove more heat in the form of natural convection.

Figure 5-22: The MHTGR helium mass flow rate with an isolated reactor pressure vessel during a PCC event.

Figure 5-23: The HTTF helium mass flow rate with an isolated reactor pressure vessel during a PCC event.

5.4 Scenarios Conclusion

Three scenarios of the PCC event were executed for the MHTGR and HTTF. Scenario 1 consisted of a LOFA by circulator shutdown with the availability of the SG and heat-exchanger to removed reactor decay heat. It was observed that the HTTF was unable to capture the same phenomena as the MHTGR. The HTTF heat-exchanger removed a considerable amount of decay heat, which cooled down the system to the point where the RCCS temperature boundary condition was unsuccessful. Scenario 2 consisted of a loss of forced convection with a break within the inlet and outlet of the cross-duct vessel and the availability of the SG and heat-exchanger to remove decay heat. Again, different phenomena occurred in the HTTF compared to the MHTGR. While the MHTGR developed stagnant cold helium coolant in the SG, the helium coolant in the HTTF heat-exchanger continued the normal circulation conditions. Scenario 1 and

96 scenario 2 showed that the PCC event in the HTTF cannot be modeled by using the heat- exchanger and must be simulated with an isolated reactor pressure vessel. The results for a PCC event with an isolated reactor pressure vessel were presented in scenario 3. This event proved that even with an isolated reactor pressure vessel, the HTTF was unable to predict the phenomena of interest of the MHTGR. The reason for this is most likely due to the combination of different phenomena’s occurring at the same time. This could include the higher mass flow rate that the HTTF developed during the simulation, possible distortions found in the scaling ratios of the in-vessel solid structures or the additional surface area found in the vessel wall of the HTTF. By analyzing the scaling ratios (Table 3-3) and the material properties for both systems (Table 4-1 and Table 4-2) it is evident that the HTTF may contain several distortions in the thermal conductivities, volumetric heat capacities and thermal diffusivities of the materials. Table 5-2 shows the material properties average values in both the MHTGR and HTTF, the design scaling ratios, the average “as-built” ratios and the distortion factors found in the HTTF. By observing the parameters in the reflector regions, on average the thermal conductivity scaled down to ~1:11, which means it is approximately five to six times larger. The volumetric heat capacity is also too high, however by definition; this quantity measures the ability of the material to store thermal energy, therefore it helps the reflector regions retain their heat, which gives the HTTF an advantage in the overall transient. Then, by analyzing the thermal diffusivity (ratio of conductance to storage) of the reflectors, the HTTF stores thermal energy better than it conducts, therefore the transient should proceed slower throughout the reflectors. However, due to the fact that the other quantities (such as the core) conduct better than storing the thermal energy, this may lead to the deviations seen in the earlier results.

Table 5-2: Design specifications and distortions of the in-vessel solid structures scaling ratios in the MHTGR and HTTF.

Thermal Conductivity Design As Built Distortion KMHTGR KHTTF [ ⁄ ] Ratio Ratio Factor Inner Reflector 30.78 2.65 1:64 1:11.6 0.8 Core 27.54 10.5 1:64 1:2.61 1.0 Outer Reflector 32.15 2.95 1:64 1:10.9 0.8 PSR 55.5 6.71 1:64 1:8.3 0.9 Core Barrel 16.3 19.7 1:4 1:0.8 0.8 Reactor Vessel 47.9 18.3 1:4 1:2.6 0.3

Volumetric Heat Design As Built Distortion Capacity [ ] [ ] Ratio Ratio Factor [ ⁄ ] Inner Reflector 3.05E+06 3.54E+06 1:8 1:0.9 0.9 Core 3.09E+06 3.50E+06 1:8 1:0.9 0.9 Outer Reflector 2.85E+06 3.44E+06 1:8 1:0.8 0.9 PSR 2.63E+06 2.65E+06 1:8 1:1.0 0.9 Core Barrel 3.66E+06 4.19E+06 1:8 1:0.9 0.9 Reactor Vessel 4.55E+06 4.19E+06 1:8 1:1.1 0.9

Thermal Diffusivity Design As Built Distortion [ ⁄ ] αMHTGR αHTTF Ratio Ratio Factor

Inner Reflector 1.01E-05 7.49E-07 1:8 1:13.5 -0.7 Core 8.93E-06 3.01E-05 1:8 1:2.96 0.6 Outer Reflector 1.13E-05 8.58E-07 1:8 1:13.2 -0.6 PSR 2.11E-05 2.53E-06 1:8 1:8.3 0.04 Core Barrel 4.46E-06 4.70E-06 1:8 1:0.9 0.9 Reactor Vessel 1.05E-05 4.37E-06 1:8 1:2.4 0.7

6 HTTF SENSITIVITY STUDIES

This chapter presents several sensitivity studies that were performed for the HTTF during the natural circulation phase of the PCC event. The first section presents several methods that could be applied in the HTTF in order to preserve temperature similarity against the MHTGR. The second part of this analysis involves a sensitivity study of the properties of the in-vessel solid structures of the HTTF. The scenarios presented for all sensitivity studies are identical to “Scenario 3” from the previous chapter. The events are initiated by a loss of flow accident by circulator shutdown and an instantaneous reactor trip with an isolated reactor pressure vessel. All simulations used the same HTTF steady-state model and calculations, unless otherwise stated in the problem.

6.1 Methods to Preserved Similarity in the HTTF

The primary purpose of these sensitivity studies is to indicate several methods that could be manipulated in the HTTF in order to preserve temperature similarity during the PCC event. Some of the parameters that can be controlled in the HTTF are shown on Table 6-1.

Table 6-1: Parameters that could be control in the HTTF.

Method # Criterion

Additional form loses to reduce the mass flow rate of the helium 1. coolant during the natural circulation phase.

Initially increasing the core power to allow the in-vessel solid 2. structures to heat up.

Decreasing the rate of the decay core power to slow down the 3. phenomenon of interest in the HTTF and allow it to behave as the MHTGR.

RCCS model that allows the same temperature boundary condition as 4. the MHTGR.

Decreasing the Emissivity Coefficient of the Reactor Pressure Vessel 5. and RCCS walls in order to reduce radiation heat transfer.

The following sections present additional details to the criterions and the changes that were applied to the HTTF RELAP5 model.

6.1.1 Reducing Natural Convection

Additional form losses can be obtained in the HTTF through the use of orifices. The addition of form loses reduces the mass flow rate of the helium coolant in the system, therefore decreasing the amount of heat-removal through natural convection. In addition, if the heat removal due to convection is still too high, then there is a possibility to completely stop the mass flow rate of the coolant by simulating the scenario without connecting the two ends in the inlet and outlet of the cross-duct vessel. Therefore, the helium coolant in the system becomes completely “stagnant” and the only modes of heat removal are through conduction and radiation. Figure 6-1 shows the nodalization of the HTTF RELAP model for this specific scenario. The figure illustrates that Volume #122 and Volume #143 are not connected, and with a single-core channel approached, the helium coolant cannot develop natural circulation. Keep in mind that the HTTF contains many core channels and natural circulation is expected to develop within the core.

100

106 301

107

109 105 300

-> 111

-> 122 --> 122 <-- <- 112

--> -->

143 144 -> 103 -> ->

-> --> 104 --> 304

Figure 6-1: Nodalization of the HTTF RELAP5-3D model with an opened loop during the PCC event.

6.1.2 Core Power Increased

There is a possibility that by initially increasing the core power during the steady state calculations, it could give the in-vessel solid structures enough time to allow the materials to heat-up to the point where temperature similarity could be maintain during the transient event. This sensitivity analysis was done by arbitrarily increasing the core power during steady-state calculations and the decay power by 50%. The results of the steady-state calculations are presented in Table 6-2.

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Table 6-2: The Steady-State RELAP5-3D predicted values of the thermal-hydraulics parameters of interest of the HTTF with core power increase of 50%.

HTTF HTTF Designed RELAP Distortion Parameter Designed RELAP Ratio Ratio % Value Value Temperature (○C)

Reactor Vessel Inlet 259.0 259.0 1:1 1:1.00 B.C. Reactor Vessel Outlet 687.0 687.0 1:1 1:1.00 B.C. Peak Fuel Temperature 771 788.0 1:1 1:0.98 2.16% Pressure (MPa)

RPV Inlet 0.7974 0.7987 1:8 1:7.98 0.19% RPV Outlet 0.7957 0.7972 1:7.94 1:7.93 0.19% Core Pressure Drop (KPa) 1.078 1.087 1:32 1:31.7 -0.95% Mass Flow Rate (Kg/s)

Primary System 0.613 0.612 1:256 1:255.8 0.07% Heat Balance (MW)

Core 1.367 2.05 1:256 1:172 33.0% RCCS Loss (KW) 2.805 2.81 1:256 1:255 0.01%

The results from the above table are very similar to the ones obtain from the base model (Chapter 4). The difference that was expected is in the peak fuel temperature, since the core power was increased by 50%, therefore it allowed the in-vessel solid structures to heat up. Figure 6-2 shows the peak radial temperature profile. As expected, the inner reflector and the peak fuel temperatures increased. However, the rest of the materials were unable to obtain higher temperatures. This indicates temperature similarity will be lost during the natural circulation phase of the PCC event.

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Figure 6-2: The Predicted Radial Temperature Profile of the MHTGR, the HTTF Base Model and the HTTF model with an initial increase of 50% in core power.

6.1.3 Reducing Rate of Decay Power

From the previous results, it was observed that the HTTF tends to lose heat rapidly when compared to the MHTGR. This is due to the 1:2 scaling ratio. The rate of decay power can easily be manipulated by the operator in the facility. By decreasing the rate of the decay power, there is a possibility that it would give the HTTF enough time to behave as the MHTGR during a transient event. For this analysis, the decay power curve was modified by multiplying the “decay-time” by a factor of 2, therefore making the curve independent of time with a 1:1 scaling ratio and with a decay power scaling ratio of 1:256.

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6.1.4 Modified RCCS Heat Removal System

Because of the simplified RCCS heat structure in the HTTF RELAP5 model, a high temperature boundary condition was needed to maintain heat-balance in the system during steady-state calculations. A more detailed RCCS was developed in order to maintain the same temperature boundary condition as the MHTGR (40.0 0C). The new RCCS model was designed with two heat structures with an air gap in the middle. The mass flow rate of the air is controlled by a proportional-integral control variable that monitors the amount of heat-flux that the reactor vessel wall radiates. In addition, it was assumed that the RCCS is made of an arbitrarily insulated material, instead of stainless- steel. Figure 6-3 shows the nodalization of the HTTF with the modified RCCS.

106 301 321

-> ->

107

-> ->

-> A I R

109 105 300 320

G A P

-> ->

-> 111

-> ->

<< << --> <-- <-

>> 122 122 112

<< << --> -->

-> ->

143 144 ->

-> 103 -> ->

-> --> 104 --> 304 324

Figure 6-3: Nodalization of the HTTF RELAP5-3D model with a modified RCCS design for the PCC event with an isolated reactor pressure vessel.

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The new HTTF model was run to converge upon steady-state results. Table 6-3 shows the results for the steady-state calculations and figure 6-4 shows the predicted radial temperature profile of the in-vessel solid materials at the axial level where the peak temperature occurs.

Table 6-3: The HTTF Steady-State RELAP5-3D calculations of the thermal-hydraulics parameters of interest using the modified RCCS model.

HTTF HTTF Designed RELAP Distortion Parameter Designed RELAP Ratio Ratio % Value Value Temperature (○C)

Reactor Vessel Inlet 259.0 258.9 1:1 1:1.00 B.C. Reactor Vessel Outlet 687.0 687.0 1:1 1:1.00 B.C. Peak Fuel Temperature 771 752.7 1:1 1:1.02 -2.43% Pressure (MPa)

RPV Inlet 0.7974 0.7974 1:8 1:7.98 0.001% RPV Outlet 0.7957 0.7957 1:7.94 1:7.93 0.001% Core Pressure Drop (KPa) 1.078 1.105 1:32 1:31.2 2.43% Mass Flow Rate (Kg/s)

Primary System 0.6133 0.6128 1:256 1:255.4 0.23% Heat Balance (MW)

Core 1.367 1.367 1:256 1:256 B.C. RCCS Loss (KW) 2.805 2.805 1:256 1:256 0.02%

Again, the results are very similar to the ones obtain from the base model (Chapter 4), with the exception of the temperature gradient in the RCCS. With the addition of an insulated material and the air gap, the thermal resistance across the RCCS was drastically increased to maintain the same temperature boundary condition as the MHTGR.

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Figure 6-4: The Predicted Radial Temperature Profile of the MHTGR, the HTTF base model and the modified HTTF RCCS model.

6.1.5 Emissivity Decreased

There is a possibility that the emissivity coefficient in the reactor vessel walls can be decreased with the addition of insulators or by using “typical-clean” and “highly polished” surfaces. Since radiation is a surface phenomenon, then by decreasing the emissivity coefficient, the radiation heat transfer from the reactor vessel to the RCCS can be reduced. For this analysis, the emissivity coefficient of the reactor vessel wall and the RCCS was arbitrarily chosen to be 0.22 (typical clean stainless-steel, SS-304) [24].

6.1.6 Results of Sensitivity Studies for HTTF parameters to Control

Table 6-4 shows a summary of the calculation matrix for the sensitivity studies and figure 6-5 shows the results of the peak fuel temperatures for the sensitivity studies calculations.

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Table 6-4: Calculation Matrix Summary for the sensitivity studides of the parameters that could be manipulated in the HTTF.

Criterion Name Criterion Description

Natural Convection The primary loop of the system was not connected at the inlet Reduced and outlet of the cross-duct vessel.

Core Power The initial core power and the core decay power were increased Increased by 50%. The time in the decay curve was slowed down by multiplying it Rate of Decay by two. Therefore the decay power curve is independent of time Power Decreased and depends only on the power scaling ratio of 1:256. A new RCCS was added to the HTTF with the same temperature Modified RCCS boundary condition as the MHTGR, (400C). The emissivity coefficient of the reactor vessel wall and the Emissivity RCCS was arbitrarily chosen to be 0.22 (typical clean stainless- Decreased steel, SS-304) [24]

From the figure, there are two dotted lines, the one with the higher temperature throughout the transient represents the peak fuel temperature of the MHTGR Base Model (Scenario 3) and the one below it represents the peak fuel temperature of the HTTF Base Model (Scenario 3). The blue line represents the peak fuel temperature for the case where the inlet and outlet cross-duct vessel are not connected, an “opened” loop. The main purpose of this scenario was to completely immobilize the helium coolant to eliminate heat transfer due to natural convection. The green line represents the case where the initial core power was increased for the purpose to allow the in-vessel solid structures to heat up. Initially, this method responded satisfactory with higher temperatures in the materials, however as the transient progressed, the structures start to cool down and the trend stayed slightly above the peak fuel temperature of the base model. The red line represents the case where the rate of decay heat is reduced. The main purpose of this method was to slow down the phenomenon of interest in the transient to

107 allow it to behave as the MHTGR; however the peak fuel temperature only stayed slightly above from the base model. The purple line represents the modified RCCS model. Initially, the trend behaves almost identical to the base model of the HTTF. However, as the transient progressed, the peak fuel temperature starts to rapidly decrease due to the lower temperature boundary condition in the non-radiating side of the RCCS. Therefore, this case verifies that the high temperature boundary condition chosen for the base model to preserved heat-balance during steady-state calculations was satisfactory.

Figure 6-5: The peak fuel temperatures of the MHTGR and HTTF sensitivity analyses during the natural circulation phase of the PCC event.

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The yellow line represents the reduction of the emissivity coefficient. The main purpose of this method was to reduce radiation heat transfer from the reactor vessel wall. This trend illustrates that with slightly smaller emissivity coefficient, the radiation heat transfer decreases, which decreases the amount of heat removal by the RCCS. Consequentially, slightly higher peak fuel temperatures are obtained. From the above methods, it can be observed that the most effective method to increase the peak fuel temperature in the HTTF throughout the transient is by reducing the mass flow rate of the helium coolant, which then reduces heat removal by natural convection. Also, there is a possibility that the combination of different methods could be apply to the HTTF in order to allow the facility to behave as the MHTGR.

6.2 Sensitivity Studies of the In-Vessel Solid Structures

The sensitivity studies presented in this section involve changes in the scaling ratios of the ceramic material properties of the HTTF. From Table 5-2 it was observed that distortions exists due to the improper “as-built” scaling ratios of the thermal conductivity, volumetric heat capacity and the thermal diffusivity of the in-vessel solid structures. Therefore, by using this analogy and the design scaling ratios, the correct design properties for the ceramic material can be found, as shown in Table 6-5.

Table 6-5: The design specifications and scaling ratios of the in-vessel solid structures of the HTTF.

Thermal As Built Design Design As Built Conductivity KMHTGR KHTTF KHTTF Ratio Ratio [ ⁄ ] Inner Reflector 30.78 2.65 0.5 1:64 1:11.6 Core 27.54 10.55 0.4 1:64 1:2.61 Outer Reflector 32.15 2.95 0.5 1:64 1:10.9 PSR 55.5 6.71 0.9 1:64 1:8.3 Core Barrel 16.3 19.7 4.1 1:4 1:0.8 Reactor Vessel 47.9 18.3 12.0 1:4 1:2.6

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Volumetric Heat As Built Design Design As Built Capacity [ ] [ ] [ ] Ratio Ratio [ ⁄ ]

Inner Reflector 3.05E+06 3.54E+06 3.81E+05 1:8 1:0.9 Core 3.09E+06 3.50E+06 3.86E+05 1:8 1:0.9 Outer Reflector 2.85E+06 3.44E+06 3.56E+05 1:8 1:0.8 PSR 2.63E+06 2.65E+06 3.28E+05 1:8 1:1.0 Core Barrel 3.66E+06 4.19E+06 4.57E+05 1:8 1:0.9 Reactor Vessel 4.55E+06 4.19E+06 5.69E+05 1:8 1:1.1

Thermal As Built Design Design As Built Diffusivity Ratio Ratio [ ⁄ ]

Inner Reflector 1.01E-05 7.49E-07 1.26E-06 1:8 1:13.5 Core 8.93E-06 3.01E-05 1.12E-06 1:8 1:2.96 Outer Reflector 1.13E-05 8.58E-07 1.41E-06 1:8 1:13.2 PSR 2.11E-05 2.53E-06 2.64E-06 1:8 1:8.3 Core Barrel 4.46E-06 4.70E-06 5.57E-07 1:0.9 0.9 Reactor Vessel 1.05E-05 4.37E-06 1.32E-06 1:2.4 0.7

After observing the main cause for distortions in the in-vessel solid structures of the HTTF, three new simulations were prepared in the HTTF RELAP5-3D model.

(1) The first run involves changes in the thermal conductivity of the ceramic material in the HTTF. The thermal conductivity of the inner reflector, outer reflector and the PSR were adjusted to match the design values. Changes in the ceramic material also affect the core region (Table 6-6).

(2) The second simulation involves changes in the volumetric heat capacity of the ceramic material. Due to the fact that the volumetric heat capacity in the reflector regions of the HTTF is higher than what is supposed to be (i.e. helps the HTTF store its thermal energy), there was no reason to actually scale

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down, since it would lose temperature similarity even more. Therefore, the volumetric heat capacity of the ceramic materials in the reflectors, the core region and the PSR were arbitrarily increased (by a factor of two) to simply observed the changes in the peak fuel temperature.

(3) The third simulation involves changes in both, the thermal conductivity and volumetric heat capacity to scale the ceramic material of the HTTF to the design thermal diffusivity coefficient. This was achieved by adjusting the reflectors, the core region and PSR to the design values of thermal conductivity and volumetric heat capacity.

Table 6-6 shows a summary of the calculation matrix for these specific cases and figure 5-24 shows the results of the peak fuel temperatures.

Table 6-6: The design specifications and scaling ratios of the in-vessel solid structures of the HTTF.

Simulation #1: Modified Thermal Conductivity As Built Design Modified KHTTF KHTTF KHTTF

(1) Inner Reflector 2.65 0.5 0.5 Thermal Conductivity Core 10.55 0.4 1.69 Outer Reflector 2.95 0.5 0.5 PSR 6.71 0.9 0.9

Simulation #2: Modified Volumetric Heat Capacity

As Built Design Modified

[ ] [ ] [ ]

(2) Volumetric Inner Reflector 3.54E+06 3.81E+05 7.08E+06 Heat Capacity Core 3.50E+06 3.86E+05 6.65E+06 Outer Reflector 3.44E+06 3.56E+05 7.08E+06 PSR 2.65E+06 3.28E+05 5.30E+06

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Simulation #3: Modified Thermal Diffusivity As Built Design Modified

KHTTF KHTTF KHTTF (3) Inner Reflector 2.65 0.5 0.5 Thermal Conductivity Core 10.55 0.4 1.69 Outer Reflector 2.95 0.5 0.5 PSR 6.71 0.9 0.9

As Built Design Modified

[ ] [ ] [ ] (3) Volumetric Inner Reflector 3.54E+06 3.81E+05 3.69E+05 Heat Capacity Core 3.50E+06 3.86E+05 3.67E+05 Outer Reflector 3.44E+06 3.56E+05 3.69E+05 PSR 2.65E+06 3.28E+05 3.28E+05

As Built Design Modified

[ ] [ ] [ ] (3) Thermal Inner Reflector 7.49E-07 1.26E-06 1.35E-06 Diffusivity Core 3.01E-06 1.12E-06 4.61E-06 Outer Reflector 8.58E-07 1.41E-06 1.35E-06 PSR 2.53E-06 2.64E-06 2.74E-06

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Figure 6-6: The peak fuel temperatures of the MHTGR and HTTF during the PCC event to analyze the sensitivity results for the in-vessel solid structures

Again from the above figure, two dotted lines are shown, one representing the peak fuel temperature of the MHTGR and the other one representing the peak fuel temperature of the HTTF base model. The blue line represents changes in the thermal conductivity of the ceramic material in the HTTF. In this case, the thermal conductivity was decreased, which increases the thermal diffusivity ratio. Hence, the HTTF stores thermal energy better than it conducts, which leads to higher temperatures as shown on the figure. The red line represents changes to the volumetric heat capacity. The volumetric heat capacity was arbitrary increased the by a factor of two, which decreased the thermal diffusivity and allowed the transient to behave slower than the previous results as shown on the figure. For this case, the HTTF successfully stored its thermal energy and allowed

113 higher peak fuel temperatures in the overall transient when compared to the HTTF base model. The green line represents changes in the thermal conductivity and the volumetric heat capacity to correctly scale the thermal diffusivity values (average) in the ceramic material. Correctly scaling the thermal diffusivity in the ceramic material increases the values in all the regions, including the core (table 6-6). As the thermal diffusivity increases, the HTTF is able to conduct thermal energy better than storing it. This allows the transient to behave faster, which resulted in lower temperatures as shown on the figure.

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7 CONCLUSIONS AND FUTURE WORK

The purpose of this study was to demonstrate the ability of the HTTF to simulate the natural circulation phase during the PCC event compared to the MHTGR. The thermal–hydraulics code RELAP5-3D was used throughout this assessment to investigate the thermal-fluid phenomena during three distinct scenarios. In addition, several sensitivity analyses were performed to quantify the distortions that appeared in the calculations of the HTTF.

7.1 PCC Event with SG/Heat-Exchanger Heat Removal

The first scenario assumed an instantaneous loss of flow accident by circulator shutdown with a successful reactor protection system actuation. In addition, the MHTGR steam generator and the HTTF heat-exchanger were available to removed decay heat from the primary system. Due to the different heat-sink designs, it was observed that the HTTF was unable to capture the same phenomena as the MHTGR. The HTTF heat- exchanger removed a considerable amount of decay heat, cooling the system too fast compared to the MHTGR.

7.2 PCC Event with a Cross-Duct Vessel Break

The second scenario is identical to the previous one, except a break within the inlet and outlet of the cross-duct vessel occurred. Again, due to the different heat-sink design concepts, the HTTF was unable to predict the phenomena of interest in the MHTGR. The MHTGR developed a circulation through the reactor vessel and the break with stagnant cold helium coolant in the steam generator vessel of the primary system. The HTTF also developed a circulation loop through the reactor vessel and the cross-duct vessel break. However, the helium coolant in the HTTF heat-exchanger continued its normal circulation patterns, which disturbed the system and enabled additional heat removal.

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7.3 PCC Event with an Isolated Reactor Pressure Vessel

The third scenario assumed a loss of flow accident by circulator shutdown with a successful reactor protection system actuation. However, this scenario assumed an isolated reactor pressure vessel. This event proved that even with an isolated reactor pressure vessel, the HTTF was unable to predict the phenomena of interest of the MHTGR. The reason for this is most likely due to the combination of different phenomena’s occurring at the same time. This could include the higher mass flow rate that the HTTF developed during the simulation, possible distortions found in the scaling ratios of the in-vessel solid structures or the additional surface area found in the vessel wall of the HTTF.

7.4 Sensitivity Analysis

Due to the deviations found in the previous scenarios, several sensitivity studies were needed in order to answer the question “why the HTTF was unable to predict the phenomena of interest of the MHTGR?” The first set of sensitivity studies provided several methods that could be applied to the reduced facility in order to bridge the gap of deviations between the models. During this analysis it was observed that by reducing heat transfer due to natural convection and an increased in the core power, the deviations in the results between the HTTF and MHTGR can be overcome. The second sensitivity analysis consisted of modifications in the material properties of the in-vessel solid structures. The main purpose of the analysis was to analyze and quantify possible the distortions that may exist between the material properties of the models.

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7.5 Future Work Suggestion

The analysis presented predicts the thermal-fluid phenomenon of the HTTF during the natural circulation phase of the PCC event. The main goal of the HTTF is to provide data that can be used by the “NRC for experimental validation of existing system safety codes and near-term multi-physics computer codes” [5]. Once the reduced scaled facility is complete, the results from this analysis can be verified against the provided experimental data to determine the capabilities of RELAP5-3D to capture the phenomenon of interest in the MHTGR during the PCC event. Further analysis of this work involves the use of other gases to improve the overall transient in the PCC event. Similarities improvements in parameters such as the Density ratio, Peclet number and the Reynolds number could be obtained with the use of nitrogen as a working fluid because of the reduced pressure facility. The HTTF and MHTGR RELAP5-3D models were limited to one single core channel. However, during the PCC event, it is expected that “intra-core” circulation will exist. During this circulation, all channels in the core may not reverse at the same time. The addition of multiple channels in the core for both models needs to be developed to better estimate the flow characteristics of the event. In addition, it is not expected that RELAP5-3D will be able to capture the mixing occurring in the upper plenum due to hot jets exiting the core during the PCC event. However, with the addition of multiple core channels, the velocity of the hot jets can be calculated to improve the initial condition of previous studies dealing with inlet plenum mixing. Similarly, radiation heat transfer from the core to the upper plenum was not modeled throughout this analysis. It could be beneficial to include this phenomenon to the RELAP5-3D models to determine if there are any biases in the calculations. Furthermore, it was assumed that the HTTF contains a chopped cosine power profile. However, it is anticipated that the HTTF will attained a more-like uniform power profile and it would be beneficial to perform future analysis using the correct power shape.

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BIBLIOGRAPHY

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APPENDICES

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APPENDIX A - DESIGN PARAMETERS

A.1 MHTGR Design Parameters

MHTGR HYDRO-DYNAMIC COMPONENTS

)

Area (m

Length (m)

Vertical Angle (

Component Name

Reynolds F/R Loss

Horizontal Angle (

RELAP Component

Hydraulic Diameter (m)

RELAP Component Type

Reactor Vessel System (1)(2)(3)(4)(5)(9)(10) Reactor Vessel 103 branch 1.225 1.077 -90 0 1.171 0 Inlet Plenum Lower Core 104 branch 5.944 1.186 0 0 1.229 0 Support *z coord 0.254 27.745 90 -- 5.944 0 105 pipe Upcomer

105-01 1.548 1.212 90 0 0.251 -- 105-02 1.982 1.212 90 0 0.251 -- 105-03 to 0.793 1.212 90 0 0.251 -- 105-12 105-13 1.189 1.212 90 0 0.251 -- 105-14 0.396 1.212 90 0 0.251 -- 106 branch 5.944 7.227 0 180 3.034 0 Upper Plenum Upper 107 pipe Reflector 107-01 0.396 1.497 -90 0 0.016 0.335 107-02 1.189 1.497 -90 0 0.016 0.335 Core Inlet 108 sngljun -- 1.497 ------0 Junction 109 pipe Core

109-01 0.793 1.497 -90 0 0.016 0.335 109-02 0.793 1.497 -90 0 0.016 0.335 109-03 0.793 1.497 -90 0 0.016 0.335 109-04 0.793 1.497 -90 0 0.016 0.335 109-05 0.793 1.497 -90 0 0.016 0.335 109-06 0.793 1.497 -90 0 0.016 0.335

122

MHTGR HYDRO-DYNAMIC COMPONENTS

)

ngle (

Area (m

Length (m)

Vertical Angle (

Component Name

Reynolds F/R Loss

Horizontal A

RELAP Component

Hydraulic Diameter (m)

RELAP Component Type Reactor Vessel System (1)(2)(3)(4)(5)(9)(10) 109-07 0.793 1.497 -90 0 0.016 0.335 109-08 0.793 1.497 -90 0 0.016 0.335 109-09 0.793 1.497 -90 0 0.016 0.335 109-10 0.793 1.497 -90 0 0.016 0.335 Core Outlet 110 sngljun -- 1.497 ------0 Junction Lower 111 snglvol 1.982 1.497 -90 0 0.016 -- Reflector 112 branch 4.851 0.473 0 180 0.061 0 Lower Plenum *z coord 0.900 2.549 -90 -- 0.061 0 116 pipe Helium Gap

116-01 1.548 4.542 -90 0 0.457 -- 116-02 1.982 4.542 -90 0 0.457 -- 116-03 to 0.793 4.542 -90 0 0.457 -- 116-12 116-13 1.189 4.542 -90 0 0.457 -- 116-14 0.396 4.542 -90 0 0.457 -- Steam Generator Primary Side (2) (9) 122 pipe Hot Duct

122-01 to 0.688 1.119 0 180 1.194 -- 122-10 Hot Duct 123 branch 1.194 1.119 0 180 1.194 -- Elbow *z coord 1.194 1.119 90 -- 1.194 -- SG Inlet 124 pipe -- Plenum 124-01 0.927 1.423 -90 0 1.346 -- 124-02 3.048 1.423 -90 0 1.346 -- 126-03 1.402 9.200 -90 0 2.591 -- 125 sngljun -- 3.636 ------Junction to SG 126 pipe Primary SG

126-01 to 0.144 3.636 -90 0 0.599 0.335 126-06 126-07 to 0.457 3.833 -90 0 1.103 0.335 126-10

123

MHTGR HYDRO-DYNAMIC COMPONENTS

)

Area (m

Length (m)

Vertical Angle (

Component Name

Reynolds F/R Loss

Horizontal Angle (

RELAP Component

Hydraulic Diameter (m)

RELAP Component Type Steam Generator Primary Side (2) (9) 126-11 to 0.197 3.636 -90 0 0.599 0.335 126-50 SG Outlet 130 branch 3.901 5.746 0 180 2.706 -- Plenum 132 pipe SG Annulus

132-01 to 1.055 1.375 90 0 0.231 -- 132-10 132-11 to 2.225 1.375 90 0 0.231 -- 132-12 133 sngljun -- 1.375 ------Circulator Inlet 134 pipe 90 0 Plenum 134-01 0.927 1.375 90 0 0.231 -- 134-02 1.194 1.375 90 0 0.334 -- 134-03 to 0.535 1.375 90 0 1.740 -- 134-10 Circulator 140 branch 3.901 2.540 0 0 3.215 -- Blades Circulator 141 tmdpjun -- 2.239 ------Junction Source Circulator 142 snglvol 3.975 10.580 -90 0 3.112 -- Outlet Plenum 143 branch 1.194 1.119 0 0 0.432 Cold Duct Inlet

*z coord 1.803 0.741 -90 -- 0.432

144 pipe 1.194 Cold Duct

144-01 to 0.688 1.077 0 0 0.432 -- 144-10 Steam Generator (Secondary Side) (2) Feed-Water 200 tmdpvol 10 100 0 0 0.612 -- Source SG Lower 201 tmdpjun -- 0.294 ------Plenum (2nd) 202 snglvol 2.794 0.294 90 0 0.612 -- 203 pipe dZ Secondary SG

203-01 to 3.665 0.098 3.07 0 0.019 0.197 203-40

124

MHTGR HYDRO-DYNAMIC COMPONENTS

)

Area (m

Length (m)

Vertical Angle (

Component Name

Reynolds F/R Loss

Horizontal Angle (

RELAP Component

Hydraulic Diameter (m)

RELAP Component Type Steam Generator (Secondary Side) (2) 203-41 to 0.457 0.098 90.0 0 0.019 0.457 203-44 203-45 to 2.676 0.098 3.07 0 0.019 0.144 203-50 Main Steam 204 branch 2.794 0.338 90 0 0.656 -- Line Steam Line 205 tmdpvol 10 100 0 0 0.656 -- Sink Reactor Cavity System(2)(6)(9)(10) 301 tmdpvol 1 100 -90 0 11.28 -- Cavity Source Cavity Source 302 tmdpjun -- 114.32 ------Junction 300 pipe

300-01 1.172 90.194 -90 0 6.177 -- 300-02 1.172 90.194 -90 0 6.177 -- 300-03 1.172 90.194 -90 0 6.177 -- 300-04 0.396 90.194 -90 0 6.177 -- 300-05 1.189 90.194 -90 0 6.177 -- 300-06 0.793 90.194 -90 0 6.177 -- 300-07 0.793 90.194 -90 0 6.177 -- 300-08 0.793 90.194 -90 0 6.177 -- 300-09 0.793 90.194 -90 0 6.177 -- 300-10 0.793 90.194 -90 0 6.177 -- 300-11 0.793 90.194 -90 0 6.177 -- 300-12 0.793 90.194 -90 0 6.177 -- 300-13 0.793 90.194 -90 0 6.177 -- 300-14 0.793 90.194 -90 0 6.177 -- 300-15 0.793 90.194 -90 0 6.177 -- 300-16 1.982 90.194 -90 0 6.177 -- 300-17 1.548 90.194 -90 0 6.177 -- 300-18 0.666 90.194 -90 0 6.177 -- 300-19 0.666 90.194 -90 0 6.177 -- 300-20 0.666 90.194 -90 0 6.177 -- 300-21 0.666 90.194 -90 0 6.177 -- 303 sngljun -- 114.32 ------0 Cavity Outlet 304 tmdpvol 1 100 -90 0 11.28 -- Cavity Sink

125

MHTGR HYDRO-DYNAMIC COMPONENTS

Roughness for all SS components (7): 2.0 15.9 Roughness for all graphite components (7):

Conversion Factors:

1 Pa = 1.450377e-4 psi

degF = (9/5)*(degK -273.15)+32

= 1.8*degK - 459.67

1 lbm = 0.453592 kg

1 kg/m^3 = 0.0624 lb/ft^3

1 Kelvin = 273.15 Cel

REFERENCES:

(1) OSU-HTTF-000000-ETRAN-001-R0 Modular High Temperature Gas Reactor (MHTGR) Design Parameters (2) Preliminary Safety Information Document (PSID) for the Standard MHTGR (3) OSU-HTTF-000000-ETRAN-001-R0-S01 (GA Meeting Slides from 12/02/09) (4) OSU-HTTF-000000-ETRAN-001-R0-S11 (GA Action Items from Dec 1&2 Meeting) (5) Prismatic Coupled Neutronics/Thermal Fluids Transient Benchmark of the MHTGR-350 MW Core Design Benchmark Definition (6) F.M. White, Fluid Mechanics, 5th Edition, 2003 (7) Y. Tung;et.al., Effects of Graphite Surface Roughness on Bypass Flow Computations for an HTGR,INL/CON-11-21340 (8) OSU-HTTF-000000-ETRAN-013-R0-S1 (9) Incropera, Dewit Bergman, Lavine. HEAT AND MASS TRANSFER. Seventh Edititon, Wiley (10)Aldridge, R.J. Scaling Study of the Depressurized Conduction Cooldown Event in the High Temperature Test Facility Using RELAP5-3D/ATHENA.

126

MHATGR HEAT STRUCTURES

metry

Number

Geo Condition Condition

Length (m) Length (m)

Left Surface

Right Surface

Left Boundary Left Boundary

Heat Structure

Coordinate (m) Coordinate (m)

Right Boundary Right Boundary

Primary System (1)(2)(3)(4)(5)(10) 1051

1051-01 Cylinder 3.2 3.2004 105-01 116-14 1.548 1.548 1051-02 Cylinder 3.2 3.2004 105-02 116-13 1.982 1.982 1051-03 105-03 to 105- 116-12 to to Cylinder 3.2 3.2004 0.793 0.793 12 116-03 1051-12 1051-13 Cylinder 3.2 3.2004 105-13 116-02 1.189 1.189 1051-14 Cylinder 3.2 3.2004 105-14 116-01 0.396 0.396 1061 Sphere 3.15 3.201 106-01 0 0.5 0.5

Conduction 1070 Cylinder 0 0.825 Symmetric 0.396 0.396 to 1071 Conduction 1071 Cylinder 0.0078 0.0178 107-01 2747. 2747. to 1072 116- Conduction 1072 Cylinder 1.75 3.048 01/Radiatio 0.396 0.396 from 1071 n to 1113 1073 Cylinder 0.0078 0.0178 107-02 0 8243. 8243.

116- Conduction 1074 Cylinder 1.75 3.048 02/Radiatio 1.189 1.189 from 1073 n to 1113 Conduction 1075 Cylinder 0 0.8250 Symmetric 1.189 1.189 to 1073 Conduction 1090 Cylinder 0 0.8250 Symmetric 0.793 0.793 to 1091 1091

Conduction 1091-01 Cylinder 0.0078 0.0178 109-01 5495. 5495. to 1092 Conduction 1091-02 Cylinder 0.0078 0.0178 109-02 5495. 5495. to 1092 Conduction 1091-03 Cylinder 0.0078 0.0178 109-03 5495. 5495. to 1092 Conduction 1091-04 Cylinder 0.0078 0.0178 109-04 5495. 5495. to 1092 Conduction 1091-05 Cylinder 0.0078 0.0178 109-05 5495. 5495. to 1092 Conduction 1091-06 Cylinder 0.0078 0.0178 109-06 5495. 5495. to 1092 Conduction 1091-07 Cylinder 0.0078 0.0178 109-07 5495. 5495. to 1092 Conduction 1091-08 Cylinder 0.0078 0.0178 109-08 5495. 5495. to 1092 Conduction 1091-09 Cylinder 0.0078 0.0178 109-09 5495. 5495. to 1092 Conduction 1091-10 Cylinder 0.0078 0.0178 109-10 5495. 5495. to 1092

127

MHATGR HEAT STRUCTURES

Number

Geometry Condition Condition

Length (m) Length (m)

Left Surface

Right Surface

Left Boundary Left Boundary

Heat Structure

Coordinate (m) Coordinate (m)

Right Boundary Right Boundary

Primary System (1)(2)(3)(4)(5)(10) 116-03 to Conduction 116- 1092 Cylinder 1.75 3.048 0.793 0.793 from 1091 12/Radiatio n to 1113 Conduction 1010 Cylinder 0 0.8250 Symmetric 1.982 1.982 to 1111 Conduction 1111 Cylinder 0.0078 0.0178 111-01 13739 1373 to 1112 116- Conduction 1112 Cylinder 1.75 3.048 13/Radiatio 1.982 1.982 from 1111 n to 1113 1113

116- 300- 0.396 1113-01 Cylinder 3.277 3.411 01/Radiation 04/Radiatio 0.396 5 from 1072 n to 2041 116- 300- 1113-02 Cylinder 3.277 3.411 02/Radiation 05/Radiatio 1.189 1.189 from 1074 n to 2041 300-06 to 1113-03 116-03 to 116- 300- to Cylinder 3.277 3.411 12/Radiation 0.793 0.793 15/Radiatio 1113-12 from 1092 n to 2041 116- 300- 1113-13 Cylinder 3.277 3.411 13/Radiation 16/Radiatio 1.982 1.982 from 1112 n to 2041 300- 1113-14 Cylinder 3.277 3.411 116-14 17/Radiatio 1.548 1.548 n to 2041 RCCS System(2)(3)(4)(10) 2041

2041-01 Rectangu 300-21 to 300- 21.68 to 0 0.0254 T=40 oC 21.683 lar 18 26 2041-04 300- Rectangu 50.40 2041-05 0 0.0254 17/Radiation T=40 oC 50.402 lar 25 from 1113 300- Rectangu 64.54 2041-06 0 0.0254 16/Radiation T=40 oC 64.541 lar 14 from 1113 2041-07 300-15 to 300- Rectangu 25.81 to 0 0.0254 06/Radiation T=40 oC 25.817 lar 65 2041-16 from 1113 300- Rectangu 38.72 2041-17 0 0.0254 05/Radiation T=40 oC 38.725 lar 48 from 1113

128

MHATGR HEAT STRUCTURES

Number Number Number Number Number Number Number Number Number

Heat Structure Heat Structure Heat Structure Heat Structure Heat Structure Heat Structure Heat Structure Heat Structure Heat Structure RCCS System (2)(3)(4)(10) 300- Rectangu 12.90 2041-18 0 0.0254 04/Radiation T=40 oC 12.908 lar 83 from 1113 2041-19 Rectangu 300-03 to 300- 38.14 to 0 0.0254 T=40 oC 38.146 lar 01 63 2041-21 Steam Generator (2)(3)(4) 2203 2203-01 203-50 to 203- 126-01 to to 2203- Cylinder 55.69 65.405 55.69 65.41 45 126-06 05 2203-06 203-44 to 203- 126-07 to to 2203- Cylinder 9.5129 11.172 9.51 11.17 41 126-10 10 2203-11 203-40 to 203- 126-11 to to Cylinder 76.264 89.572 76.26 89.57 01 126-50 220350

129

A.2 HTTF Design Parameters

HTTF HYDRODYNAMIC COMPONENTS

)

Area (m

Length (m)

Vertical Angle (

Component Name

Horizontal Angle (

RELAP Component

Reynolds Forward Loss

Hydraulic Diameter (m)

RELAP Component Type Primary System (1)(2)(3)(4)(5)(13) Cold Duct 103 branch 0.356 0.045 -90 0 0.239 0.0 Junction Lower Core 104 branch 1.486 0.207 0 0 0.514 0.86 Support *z coord 0.178 1.734 90 -- 1.486 0.86 105 pipe Upcomer

105-01 0.340 0.284 90 0 0.114 0.86 105-02 0.198 0.284 90 0 0.114 0.86 105-03 0.305 0.284 90 0 0.114 0.86 105-04 to 0.198 0.284 90 0 0.114 0.86 105-13 105-14 0.102 0.284 90 0 0.114 0.86 105-15 0.279 0.284 90 0 0.114 0.86 Upper 106 branch 1.486 0.672 0 180 0.925 0.86 Plenum Upper 107 pipe Reflector 107-01 0.279 0.083 -90 0 0.015 0.66 107-02 0.102 0.083 -90 0 0.015 0.66 Core In 108 sngljun -- 0.083 ------0.66 Junction 109 pipe Core

109-01 0.198 0.083 -90 0 0.015 0.76 109-02 0.198 0.083 -90 0 0.015 0.76 109-03 0.198 0.083 -90 0 0.015 0.76 109-04 0.198 0.083 -90 0 0.015 0.76 109-05 0.198 0.083 -90 0 0.015 0.76 109-06 0.198 0.083 -90 0 0.015 0.76 109-07 0.198 0.083 -90 0 0.015 0.76 109-08 0.198 0.083 -90 0 0.015 0.76 109-09 0.198 0.083 -90 0 0.015 0.76 109-10 0.198 0.083 -90 0 0.015 0.76

130

HTTF HYDRODYNAMIC COMPONENTS

)

Area (m

Length (m)

Vertical Angle (

Component Name

Horizontal Angle (

RELAP Component

Reynolds Forward Loss

Hydraulic Diameter (m)

RELAP Component Type Primary System (1)(2)(3)(4)(5)(13) Core Out 110 sngljun -- 0.083 ------0.66 Junction Lower 111 pipe Reflector 111-01 0.305 0.083 -90 0 0.015 0.655 111-02 0.198 0.097 -90 0 0.025 0.105 Lower 112 branch 1.213 0.135 0 180 0.088 3.66 Plenum *z coord 0.222 0.735 -90 -- 0.088 3.66 122 pipe Hot Duct

122-01 0.137 0.07 0 180 0.298 0.003 122-02 to 0.132 0.07 0 180 0.298 0.003 122-08 124 122-09 0.235 0.07 0 180 0.298 0.003 122-10 0.254 0.07 0 180 0.298 0.003 122-11 0.381 0.07 0 180 0.298 0.003 123 branch 0.600 0.051 90 0 0.254 0.000 Elbow SG Inlet 124 pipe Plenum 124-01 0.146 0.051 90 0 0.254 0.001 124-02 0.548 0.106 45 90 0.254 0.001 124-03 0.051 0.106 90 0 0.260 0.001 124-04 0.083 0.047 90 0 0.018 0.001 Junc: SG 125 sngljun -- 0.047 ------0.001 Inlet 126-01 to 126 0.048 0.047 90 0 0.018 0.005 Primary SG 126-05 126-06 to 0.059 0.047 90 0 0.018 0.005 126-25 126-26 to 0.040 0.047 90 0 0.018 0.005 126-30 126-31 to 0.040 0.047 -90 0 0.018 0.005 126-35 126-36to 0.059 0.047 -90 0 0.018 0.005 126-55 126-56 to 0.048 0.047 -90 0 0.018 0.005 126-60

131

HTTF HYDRODYNAMIC COMPONENTS

)

Area (m

Length (m)

Vertical Angle (

Component Name

Horizontal Angle (

RELAP Component

ydraulic Diameter (m)

Reynolds Forward Loss

RELAP Component Type Primary System (1)(2)(3)(4)(5)(13) Junc: SG 127 sngljun -- 0.047 ------0.001 Outlet SG Inlet 128 pipe Plenum 124-01 0.146 0.047 90 0 0.018 0.001 124-02 0.548 0.106 45 90 0.130 0.001 124-03 0.051 0.032 90 0 0.203 0.001 124-04 0.083 0.032 90 0 0.203 0.001 Single 131 sngljun -- 0.032 ------0.001 Junction 132 pipe To Pump

132-01 0.819 0.032 -90 0 0.203 0.001 132-02 1.048 0.032 -57.8 -90 0.203 0.001 132-03 0.203 0.032 -57.8 -90 0.203 0.001 132-04 0.413 0.032 0 180 0.203 0.001 140 branch 1.294 0.369 0 -90 0.254 0.000 Circulator Circulator 141 tmdpjun -- 0.029 ------Junction 142 pipe

Discharge 142-01 0.787 0.029 0 0 0.394 0.00 Pipe 142-02 1.401 0.029 90 0 0.394 0.00 142-03 0.787 0.029 0 180 0.394 0.00 142-04 0.490 0.029 0 90 0.394 0.00 143 branch 0.191 0.032 0 0 0.056 0.00 Duct In 144 pipe Cold Duct

144-01 to 0.161 0.068 0 0 0.111 0.00 144-07 144-08 to 0.159 0.045 0 0 0.076 0.00 144-10 Secondary Steam Generator (11)(12)(13)

Feed-Water 199 tmdpvol 1 1 0 0 2.08 Source

Feed Water 200 tmdpjun ------Flow 201 pipe FW Pipe

132

HTTF HYDRODYNAMIC COMPONENTS

)

onent Type

Area (m

Length (m)

Vertical Angle (

Component Name

Horizontal Angle (

RELAP Component

Reynolds Forward Loss

Hydraulic Diameter (m)

RELAP Comp Primary System (1)(2)(3)(4)(5)(13) 201-01 to 0.19812 0.050 0.03 0.11 201-03

FW Isolation 202 valve ------Valve

FW 203 pipe Downcomer

203-01 0.345 0.050 -90 0 0.06 1.0 203-02 0.199 0.050 -90 0 0.06 1.0 203-03 1.178 0.050 -90 0 0.06 2.5 203-04 to 0.04763 0.050 -90 0 0.06 1.0 203-08

SG Multi- 204 mtpljun ------1.5 Junction

205-01 to Secondary 205 0.048 0.178 90 0 0.05 3.4 205-05 SG 205-06 to 0.059 0.178 90 0 0.05 3.4 205-25 205-26 to 0.040 0.178 90 0 0.05 3.4 205-30 Single 207 sngljun ------1.0 Junction

208 207-01 0.305 0.232 90 0 0.54 1.0 Above Tubes 207-02 0.508 0.141 90 0 0.42 1.0 207-03 0.051 0.232 90 0 0.54 1.0 Steam 209 branch 0.543 0.106 90 0 0.20 1.0 Plenum

MS Isolation 210 valve ------Valve

Steam Line 205 tmdpvol 1 1 0 0 2.08 Sink

133

HTTF HYDRODYNAMIC COMPONENTS

)

ponent

Area (m

Length (m)

Vertical Angle (

Component Name

Horizontal Angle (

RELAP Com

Reynolds Forward Loss

Hydraulic Diameter (m)

RELAP Component Type Reactor Cavity System(6)(14) Cavity 301 tmdpvol 1.0 1000 -90 0 35.7 -- Source Cavity 302 tmdpjun -- 4.824 ------Source Junction 300 pipe

300-01 0.279 4.824 -90 0 1.2 -- Cavity Pipe 300-02 0.102 4.824 -90 0 1.2 -- 300-03 0.198 4.824 -90 0 1.2 -- 300-04 0.198 4.824 -90 0 1.2 -- 300-05 0.198 4.824 -90 0 1.2 -- 300-06 0.198 4.824 -90 0 1.2 -- 300-07 0.198 4.824 -90 0 1.2 -- 300-08 0.198 4.824 -90 0 1.2 -- 300-09 0.198 4.824 -90 0 1.2 -- 300-10 0.198 4.824 -90 0 1.2 -- 300-11 0.198 4.824 -90 0 1.2 -- 300-12 0.198 4.824 -90 0 1.2 -- 300-13 0.305 4.824 -90 0 1.2 -- 300-14 0.198 4.824 -90 0 1.2 -- 300-15 0.340 4.824 -90 0 1.2 -- 303 sngljun -- 0.000 ------0.0 Cavity Outlet

304 tmdpvol 1.000 1.000 -90 0 11.3 -- Cavity Sink

134

HTTF HYDRODYNAMIC COMPONENTS

REFERENCES:

(1) HTTF_ASSM

(2) HTTF-414XXX_LowerPleunum

(3) HTTF-415XXX_Core

(4)HTTF-413XXX_LowerHead

(5)HTTF-411XXX_UpperHead

(6)HTTF-710XXX_VesselCavity

(7) F.M. White, Fluid Mechanics, 5th Edition, 2003

(8) OSU-HTTF-000000-ETRAN-013-R0-S1

(9) HTTF_Ceramic_Fab_V5

(10) J.M. Kelly, Calculations in Support of HTTF Design, HTTF

Steering Committee Meeting, November 8,2011 (11) HTTF-M1 (12) 25838 Rev AB (13) 26100-PCS-100 REV 1 CROSSOVER (14)Aldridge, R.J. Scaling Study of the Depressurized Conduction Cooldown

Event in the High Temperature Test Facility Using RELAP5-3D/ATHENA.

135

HTTF HEAT STRUCTURES

oordinate (m)

Heat Structure Number

Left Surface Length (m)

Left Boundary Condition

Right Surface Length (m)

Right Boundary Condition

Heat Structure Description Heat Structure Description

Left Boundary Coordinate (m)

Right Boundary C

Primary System (1)(2)(3)(4)(5)(14) Upper 1061 Sphere 0.80 0.82 0.5 0.5 106-01 0 Plenum Shroud

Inner Upper 1070 Cylinder 0 0.21 0.28 0.28 Symtri Symtri Reflector #1

Inner Upper 1075 Cylinder 0 0.21 0.10 0.10 Symtri Symtri Reflector #2

Inner 1090 Cylinder 0 0.21 0.20 0.20 Symtri Symtri Reflector Core

Inner Lower 1110 Cylinder Reflector 1110-01 0 0.21 0.30 0.30 Symtri Symtri 1110-02 0 0.21 0.20 0.20 Symtri Symtri

Upper 1071 Cylinder 0.007 0.03 144 144 107-01 Reflector #1

Upper 1073 Cylinder 0.007 0.03 52.4 52.4 107-02 Reflector #2

1091 Cylinder Core 1091-01 0.007 0.03 102 102 1091-01

1091-02 0.007 0.03 102 102 1091-02

1091-03 0.007 0.03 102 102 1091-03

1091-04 0.007 0.03 102 102 1091-04

1091-05 0.007 0.03 102 102 1091-05

1091-06 0.007 0.03 102 102 1091-06

1091-07 0.007 0.03 102 102 1091-07

1091-08 0.007 0.03 102 102 1091-08

1091-09 0.007 0.03 102 102 1091-09

1091-10 0.007 0.03 102 102 1091-10

136

HTTF HEAT STRUCTURES

(m)

Heat Structure Number

Left Surface Length (m)

Left Boundary Condition

Right Surface Length (m)

Right Boundary Condition

Heat Structure Description Heat Structure Description

Left Boundary Coordinate (m)

Right Boundary Coordinate Primary System (1)(2)(3)(4)(5)(14) Lower 1111 Cylinder Reflector 1111-01 0.007 0.03 157 157 111-01

1111-02 0.007 0.03 38 38 111-02 Upper Reflector #1 1072 Cylinder 0.438 0.76 0.28 0.28 105-15 to Core Barrel(PSR)

Upper Reflector #2 1074 Cylinder 0.438 0.76 0.10 0.10 105-14 to Core Barrel (PSR)

105-13 to Core to Core 1092 Cylinder 0.438 0.76 0.20 0.20 105-04 Barrel (PSR)

Lower Reflector to 1112 Cylinder Core Barrel (PSR) 1112-01 0.438 0.76 0.30 0.30 105-03

1112-02 0.438 0.76 0.20 0.20 105-02

Reactor 1113 Cylinder Vessel

105- 300- 15/Radiati 01/Radiati 1113-01 0.819 0.87 0.28 0.28 on from on to 1072 2041

105- 300- 14/Radiati 02/Radiati 1113-02 0.819 0.87 0.10 0.10 on from on to 1074 2041

137

HTTF HEAT STRUCTURES

dinate (m)

Heat Structure Number

Left Surface Length (m)

Left Boundary Condition

Right Surface Length (m)

Right Boundary Condition

Heat Structure Description Heat Structure Description

Left Boundary Coordinate (m)

Right Boundary Coor Primary System (1)(2)(3)(4)(5)(14)

105- 300- 1113-03 13/Radiati 03/Radiati to 1113- 0.819 0.87 0.20 0.20 on from on to 12 1092 2041

105- 300- 03/Radiati 13/Radiati 1113-13 0.819 0.87 0.30 0.30 on from on to 1112 2041

105- 300- 02/Radiati 14/Radiati 1113-14 0.819 0.87 0.20 0.20 on from on to 1112 2041 300- 15/Radiati 1113-15 0.819 0.87 0.34 0.34 105-01 on to 2041 RCCS System(2)(3)(4)(14) Rectangu RCCS 2041 lar Structure 2041-01 0 0.03 2.7 2.7 1.84 Arbitrarily 2041-02 0 0.03 1.0 1.0 1.84 Arbitrarily 2041-03 to 2041- 0 0.03 1.9 1.9 1.84 Arbitrarily 12 2041-13 0 0.03 3.0 3.0 1.84 Arbitrarily 2041-14 0 0.03 1.9 1.9 1.84 Arbitrarily 2041-15 0 0.03 3.3 3.3 1.84 Arbitrarily SG (11)(12)(13) 1113 Cylinder 0.009 0.01 0.50 0.54 0.02 205-01 SG HS 0.009 0.01 0.62 0.66 0.02 205-06

0.009 0.01 0.42 0.45 0.02 205-26

0.009 0.01 0.42 0.45 0.02 205-30

0.009 0.01 0.62 0.66 0.02 205-25

0.009 0.01 0.50 0.54 0.02 205-05

138

APPENDIX B – MATERIAL PROPERTIES

B.1 Tables of Thermal Conductivities

SA533 GRADE B, CLASS 1 MANGANESE-MOLYBDENUM STEEL ALLOY

Temperature Thermal Conductivity (K) k(W/m-K) 290.000 51.5338 300.789 51.4943 330.732 51.1111 369.887 50.5747 425.165 49.8851 496.567 48.9655 637.066 46.9732 719.983 45.7471 770.655 44.9808 860.482 43.4483 904.244 42.7586 950.309 41.9923 977.948 41.4559 1042.440 40.1533 1088.505 39.2337 1150.693 38.0077 1180.636 37.3946 1203.668 36.9349

139

ALLOY 800H

Temperature Thermal Conductivity (K) k(W/m-K) 293.15 11.5 373.15 13.0 473.15 14.7 573.15 16.3 673.15 17.9 773.15 19.5 873.15 21.1 973.15 22.8 1073.15 24.7 1173.15 27.1 1273.15 31.9

SS-304 (Stainless-Steel 304)

Temperature Thermal Conductivity (K) k(W/m-K) 100 11.449 200 13.161 300 14.841 400 16.489 500 18.105 600 19.689 700 21.241 800 22.761 900 24.249 1000 25.705 1100 27.129 1200 28.521 1300 29.881 1400 31.209 1500 32.505

140

H-451 GRAPHITE IRRADIATED FLUENCE=3.0 RADIAL DIRECTION

Temperature Thermal Conductivity (K) k(W/m-K) 297.7135556 29.41557206 317.2555556 29.41557206 411.7094444 30.78389115 493.1350000 31.46787762 506.1633333 31.46787762 587.5888889 32.83602364 600.6172222 32.83602364 688.5566667 32.15203717 708.0988889 32.15203717 792.7816667 32.15203717 809.0666667 32.15203717 890.4944444 31.46787762 906.7777778 31.46787762 991.4611111 31.46787762 1007.744444 30.78389115 1085.911111 30.09973161 1102.200000 30.78389115 1183.622222 29.41557206 1206.422222 29.41557206 1291.105556 30.09973161 1307.388889 30.78389115 1392.072222 34.88832920 1405.100000 35.57248875 1496.300000 45.14968395 1509.327778 45.83367042 1587.494444 53.35856005 1603.783333 52.67457358 1694.977778 51.30642756 1717.777778 51.30642756 1799.200000 49.93828154 1812.233333 49.25412200 1890.400000 47.88597598 1906.683333 47.88597598 1991.366667 46.51782996 2004.394444 45.83367042 2036.966667 46.51782996

141

STACK 2020 GRAPHITE UNIRRADIATED RADIAL DIRECTION

Temperature Thermal Conductivity (K) k(W/m-K) 290.0000000 62.20362491 525.8866667 63.84196809 592.2388889 60.33999889 604.9994444 60.07069653 699.4238889 55.76064716 709.6322222 55.49134479 796.4011111 52.25885103 806.6088889 51.72007323 893.3777778 48.75688183 906.1388889 48.48757947 995.4611111 46.06316588 1005.666667 45.79369044 1092.433333 43.09997448 1105.194444 42.83067212 1199.622222 40.13695616 1212.377778 40.13695616 1291.494444 37.98184494 1304.255556 37.71254258 1396.127778 35.55743135 1406.333333 35.28812899 1495.655556 33.40249321 1508.416667 33.40249321 1595.183333 31.24755506 1610.494444 30.97807962 1623.255556 30.70877725 1636.016667 30.43930181 1646.222222 30.43930181 1658.983333 30.16999945 1674.294444 29.90069708 1689.611111 29.63122164

142

THOR-80 PSR CERAMIC

Temperature Thermal Conductivity (K) k(W/m-K) 300 6.50712281 350 6.52307231 400 6.54342181 450 6.56817131 500 6.59732081 550 6.63087031 600 6.66881981 650 6.71116931 700 6.75791881 750 6.80906831 800 6.86461781 850 6.92456731 900 6.98891681 950 7.05766631 1000 7.13081581 1050 7.20836531 1100 7.29031481 1150 7.37666431 1200 7.46741381 1250 7.56256331 1300 7.66211281 2600 7.66211281

143

INCONEL 625

Temperature Thermal Conductivity (K) k(W/m-K) 204 12.5 316 14.1 427 15.7 538 17.5 649 19.0 760 20.8 871 22.8 982 25.2

GREENCAST-94F CORE CERAMIC

Temperature Thermal Conductivity (K) k(W/m-K) 300 7.3820458 400 6.0806622 500 5.0349819 600 4.2166710 700 3.5973961 800 3.1488236 900 2.8426199 1000 2.6504514 1100 2.5439845 1200 2.4948856 1300 2.4748212 1400 2.4554577 1500 2.4084614 1600 2.3054989 1700 2.1182364 1800 1.8183405 1900 1.3774775 2600 1.3774775

144

H-451 UNIRRADIATED RADIAL DIRECTION

Temperature Thermal Conductivity (K) k(W/m-K) 287.9425000 126.5556700 300.9706000 125.1875240 330.2839000 123.1352185 353.0828000 121.7670724 366.1111000 120.3989264 379.1394000 119.0307804 398.6811000 117.6626344 411.7094444 116.9784748 454.0505556 112.8740368 538.7333333 105.3491472 607.1311111 99.87639001 685.2994444 93.03548685 701.5850000 91.66734083 789.5244444 86.87874324 805.8094444 86.19475676 887.2333333 80.72199962 903.5222222 79.35385360 988.2055556 75.93340202 1001.233333 75.24941555 1092.427778 69.09249886 1118.483333 67.72435284 1199.911111 63.61991479 1219.450000 62.93575525 1284.594444 60.88362276 1304.133333 60.19946321 1395.333333 57.46317118 1493.044444 55.41086561 1587.494444 53.35856005 1603.783333 52.67457358 1717.777778 51.30642756 1799.200000 49.93828154 1890.400000 47.88597598 1906.683333 47.88597598 1991.366667 46.51782996 2004.394444 45.83367042 2095.594444 45.14968395

145

B.2 Tables of Volumetric Heat Capacities

SA533 GRADE B, CLASS 1 MANGANESE-MOLYBDENUM STEEL ALLOY

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 309.5485 3610954.0 342.1155 3684861.0 376.5980 3771694.0 401.5020 3839883.0 424.4910 3906899.0 453.2270 3996154.0 485.7940 4104667.0 522.1920 4235183.0 550.9280 4345104.0 600.7360 4549985.0 627.5560 4667842.0 660.1230 4818038.0 713.7630 5082346.0 748.2460 5263378.0 792.3070 5507353.0 834.4530 5754018.0 878.5140 6025794.0 930.2380 6362986.0 968.5520 6625409.0 991.5410 6788042.0 1001.119 6856947.0

ALLOY 800H

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) Constant 3.657E+06

146

H-451 GRAPHITE IRRADIATED FLUENCE=3.0 RADIAL DIRECTION

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 306.950 1289312 334.749 1421340 376.448 1621826 435.521 1890771 484.170 2047249 522.394 2184170 633.591 2487347 710.039 2668273 821.236 2849198 925.483 2971450 1078.38 3123039 1196.53 3206159 1557.92 3382195 1804.63 3460442 2009.65 3504447 2183.40 3533783 2367.57 3558230 2527.41 3577805 2673.36 3587584 2784.56 3602252 2909.65 3612031 2982.63 3621810

147

STACK 2020 GRAPHITE UNIRRADIATED RADIAL DIRECTION

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 290.000 1187346 308.508 1317405 322.689 1378902 356.723 1534695 370.903 1612591 402.101 1751985 444.643 1944668 475.840 2075872 521.218 2223469 560.924 2375161 614.811 2510441 708.403 2727743 819.013 2904034 887.080 3006527 989.181 3121319 1176.37 3273011 1306.83 3350903 1411.76 3408308 1556.41 3473901 1681.20 3514895 1837.18 3555906 1961.97 3584600 2169.01 3625593 2359.03 3658398 2512.18 3674792 2682.35 3695298 2807.14 3703486 2926.26 3711692 2980.15 3719897

148

SS-304 (STAINLESS-STEEL 304)

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 100 2.15E+06 200 3.18E+06 273 3.63E+06 500 4.27E+06 700 4.50E+06 1500 6.00E+06

THOR-80 PSR CERAMIC

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 298 1.69E+06 300 1.70E+06 400 2.13E+06 500 2.40E+06 600 2.58E+06 700 2.72E+06 800 2.83E+06 900 2.89E+06 1000 2.96E+06 1100 3.01E+06 1200 3.06E+06 1300 3.10E+06 1400 3.14E+06 1500 3.17E+06 1600 3.20E+06 1700 3.23E+06 1800 3.26E+06 1900 3.28E+06 2600 3.28E+06

149

INCONEL 625

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 204 3.85E+06 316 4.06E+06 427 4.31E+06 538 4.52E+06 649 4.77E+06 760 4.98E+06 871 5.23E+06 982 5.44E+06 1093 5.65E+06

GREENCAST-94F CORE CERAMIC

Temperature Volumetric Heat Capacity 3 (K) ρcp(J/m -K) 298 2.24E+06 300 2.26E+06 400 2.75E+06 500 3.01E+06 600 3.18E+06 700 3.30E+06 800 3.40E+06 900 3.47E+06 1000 3.54E+06 1100 3.59E+06 1200 3.64E+06 1300 3.68E+06 1400 3.71E+06 1500 3.74E+06 1600 3.77E+06 1700 3.80E+06 1800 3.82E+06 1900 3.84E+06 2600 3.84E+06

150

H-451 UNIRRADIATED RADIAL DIRECTION

151

APPENDIX C – DECAY CORE POWER CURVES

C.1 MHTGR Decay Curve

MHTGR Decay Heat Curve (t = 0, P = 350 MW)

Decay Heat Decay Heat Time(days) Time(s) (%) (MW)

0.00000 6.4263% 0.0 22.4920000 1.16E-05 6.0080% 1.0 21.0280000 2.31E-05 5.6990% 2.0 19.9466452 3.47E-05 5.4885% 3.0 19.2097448 4.63E-05 5.3126% 4.0 18.5939908 5.79E-05 5.1800% 5.0 18.1300000 6.94E-05 5.0503% 6.0 17.6761036 8.10E-05 4.9432% 7.0 17.3012168 9.26E-05 4.8523% 8.0 16.9829080 0.000104 4.7734% 9.0 16.7070040 0.000116 4.7040% 10.0 16.4640000 0.000231 4.2160% 20.0 14.7560000 0.000347 3.9275% 30.0 13.7463048 0.000463 3.7349% 40.0 13.0720984 0.000579 3.5920% 50.0 12.5720000 0.000694 3.4663% 60.0 12.1319948 0.000810 3.3634% 70.0 11.7720116 0.000926 3.2768% 80.0 11.4688256 0.001042 3.2023% 90.0 11.2078848 0.001157 3.1370% 100.0 10.9795000 0.001273 3.0790% 110.0 10.7765688 0.001389 3.0270% 120.0 10.5945844 0.001505 2.9800% 130.0 10.4298896 0.001620 2.9371% 140.0 10.2796896 0.001736 2.8977% 150.0 10.1418016 0.001852 2.8613% 160.0 10.0144908 0.001968 2.8275% 170.0 9.89635680 0.002083 2.7961% 180.0 9.78625400 0.002199 2.7666% 190.0 9.68323280 0.002315 2.7390% 200.0 9.58650000 0.002431 2.7128% 210.0 9.49487880 0.002546 2.6881% 220.0 9.40833600 0.002662 2.6647% 230.0 9.32637800

152

MHTGR Decay Heat Curve (t = 0, P = 350 MW)

Decay Heat Decay Heat Time(days) Time(s) (%) (MW) 0.002778 2.6425% 240.0 9.2485780 0.002894 2.6213% 250.0 9.1745640 0.003009 2.6011% 260.0 9.1040116 0.003125 2.5819% 270.0 9.0366340 0.003241 2.5635% 280.0 8.9721792 0.003356 2.5458% 290.0 8.9104220 0.003472 2.5289% 300.0 8.8511628 0.011574 1.9450% 1000.0 6.8075000 0.023148 1.5990% 2000.0 5.5965000 0.034722 1.4045% 3000.0 4.9156960 0.046296 1.2810% 4000.0 4.4835000 0.057870 1.1938% 5000.0 4.1783460 0.069444 1.1270% 6000.0 3.9445000 0.081019 1.0758% 7000.0 3.7652133 0.092593 1.0333% 8000.0 3.6165084 0.104167 0.9972% 9000.0 3.4902240 0.115741 0.9660% 10000.0 3.3810000 0.231481 0.7950% 20000.0 2.7825000 0.347222 0.7098% 30000.0 2.4844183 0.462963 0.6550% 40000.0 2.2925000 0.578704 0.6138% 50000.0 2.1481610 0.694444 0.5820% 60000.0 2.0370000 0.810185 0.5556% 70000.0 1.9445816 0.925926 0.5337% 80000.0 1.8679213 1.041667 0.5151% 90000.0 1.8028146 1.157407 0.4990% 100000.0 1.7465000 1.273148 0.4839% 110000.0 1.6937830 1.388889 0.4706% 120000.0 1.6470468 1.504630 0.4586% 130000.0 1.6051933 1.620370 0.4478% 140000.0 1.5673918 1.736111 0.4380% 150000.0 1.5330000 1.851852 0.4289% 160000.0 1.5012607 1.967593 0.4206% 170000.0 1.4720451 2.083333 0.4129% 180000.0 1.4450208 2.199074 0.4057% 190000.0 1.4199147 2.314815 0.3990% 200000.0 1.3965000 2.430556 0.3922% 210000.0 1.3728357 2.546296 0.3859% 220000.0 1.3506460 2.662037 0.3799% 230000.0 1.3297780 2.777778 0.3743% 240000.0 1.3101005

153

MHTGR Decay Heat Curve (t = 0, P = 350 MW)

Decay Heat Decay Heat Time(days) Time(s) (%) (MW) 2.893519 0.3690% 250000.00 1.2915000 3.009259 0.3642% 260000.00 1.2745340 3.125000 0.3595% 270000.00 1.2584188 3.240741 0.3552% 280000.00 1.2430826 3.356481 0.3510% 290000.00 1.2284618 3.472222 0.3470% 300000.00 1.2145000 3.587963 0.3429% 310000.00 1.2000330 3.703704 0.3389% 320000.00 1.1861896 3.819444 0.3351% 330000.00 1.1729246 3.935185 0.3315% 340000.00 1.1601974 4.050926 0.3280% 350000.00 1.1479713 4.166667 0.3246% 360000.00 1.1362132 4.224537 0.3230% 365000.00 1.1305000 5.000000 0.3050% 432000.00 1.0676009 10.00000 0.2411% 864000.00 0.8437587 15.00000 0.2101% 1296000.0 0.7352594 20.00000 0.1905% 1728000.0 0.6668492 25.00000 0.1766% 2160000.0 0.6182008 30.00000 0.1660% 2592000.0 0.5810987 40.00000 0.1506% 3456000.0 0.5270320 50.00000 0.1396% 4320000.0 0.4885836 60.00000 0.1312% 5184000.0 0.4592607

154

C.2 HTTF Decay Curve

HTTF Decay Heat Curve (T = 1:2, P = 1:256)

Time(s) Decay Heat (MW)

0.0 0.08785938 0.5 0.08214063 1.0 0.07791658 1.5 0.07503807 2.0 0.07263278 2.5 0.07082031 3.0 0.06904728 3.5 0.06758288 4.0 0.06633948 4.5 0.06526173 5.0 0.06431250 10.0 0.05764063 15.0 0.05369650 20.0 0.05106288 25.0 0.04910938 30.0 0.04739060 35.0 0.04598442 40.0 0.04480010 45.0 0.04378080 50.0 0.04288867 55.0 0.04209597 60.0 0.04138510 65.0 0.04074176 70.0 0.04015504 75.0 0.03961641 80.0 0.03911910 85.0 0.03865764 90.0 0.03822755 95.0 0.03782513 100.0 0.03744727 105.0 0.03708937 110.0 0.03675131 115.0 0.03643116 120.0 0.03612726 125.0 0.03583814 130.0 0.03556255 135.0 0.03529935

155

HTTF Decay Heat Curve (T = 1:2, P = 1:256)

Time(s) Decay Heat (MW) 140.0 0.03504758 145.0 0.03480634 150.0 0.03457485 500.0 0.02659180 1000.0 0.02186133 1500.0 0.01920194 2000.0 0.01751367 2500.0 0.01632166 3000.0 0.01540820 3500.0 0.01470786 4000.0 0.01412699 4500.0 0.01363369 5000.0 0.01320703 10000.0 0.01086914 15000.0 0.00970476 20000.0 0.00895508 25000.0 0.00839125 30000.0 0.00795703 35000.0 0.00759602 40000.0 0.00729657 45000.0 0.00704224 50000.0 0.00682227 55000.0 0.00661634 60000.0 0.00643378 65000.0 0.00627029 70000.0 0.00612262 75000.0 0.00598828 80000.0 0.00586430 85000.0 0.00575018 90000.0 0.00564461 95000.0 0.00554654 100000.0 0.00545508 105000.0 0.00536264 110000.0 0.00527596 115000.0 0.00519445 120000.0 0.00511758 125000.0 0.00504492 130000.0 0.00497865 135000.0 0.00491570 140000.0 0.00485579 145000.0 0.00479868

156

HTTF Decay Heat Curve (T = 1:2, P = 1:256)

Time(s) Decay Heat (MW) 150000.0 0.00474414 155000.0 0.00468763 160000.0 0.00463355 165000.0 0.00458174 170000.0 0.00453202 175000.0 0.00448426 180000.0 0.00443833 182500.0 0.00441602 216000.0 0.00417032 432000.0 0.00329593 648000.0 0.00287211 864000.0 0.00260488 1080000.0 0.00241485 1296000.0 0.00226992 1728000.0 0.00205872 2160000.0 0.00190853 2592000.0 0.00179399

157