Safety Analysis of a Compact Integral Small Light Water Reactor

Zhiyuan Cheng

B. Eng. Nuclear Science and Engineering (2018) Fudan University

SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING

AT THE

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Signature of Author……………………………………………………………... Zhiyuan Cheng Department of Nuclear Science and Engineering May 11, 2020 Certified by: …………………………………………………………………… Koroush Shirvan Assistant Professor of Nuclear Science and Engineering Thesis Supervisor Certified by: …………………………………………………………………… Emilio Baglietto Associate Professor of Nuclear Science and Engineering Thesis Reader

Accepted by ...….….……...... …………………………………………………………

Ju Li, Ph.D. Battelle Energy Alliance Professor of Nuclear Science and Engineering Professor of Materials Science and Engineering Chair Department Committee on Graduate Students

Safety Analysis of a Compact Integral Small Light Water Reactor

by Zhiyuan Cheng Submitted to the Department of Nuclear Science and Engineering on May 11, 2020 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Nuclear Science and Engineering

Abstract

Small modular reactors (SMRs) hold great promise in meeting a diverse market while reducing the risk of delays during nuclear construction compared to large gigawatt-sized reactors. However, due to lack of economy of scale, their capital cost needs to be reduced. Increasing the compactness or power density of the nuclear island is one way to reduce capital cost. This work first assesses the transient analysis of a compact integral small light water reactor to examine its safety performance. Subsequently, a parametric optimization study with the goal of increasing its power density (i.e. improve its market competitiveness) while maintaining safety is performed. A model of the reactor is established using RELAP5/3.3gl, with reference to the

features of Nuward SMR. Nuward is a compact 170 MWe Pressurized Water Reactor, whose key features include the use of Compact Steam Generators and a large water tank in which the containment submerges for passive heat removal.

A transient analysis of the reference reactor after Loss of Flow Accident, Station Blackout, and Loss of Coolant Accident is carried out. Following all three accidents, the integrity of the fuel and the reactor is maintained. The passive cooling system is estimated to provide 12 – 13 days of grace period. The parametric optimization study indicates that the size of the tank can be reduced to half and still maintain sufficient margin to both short-term and long-term safety goals after all three transients with an estimated grace period of 7 – 8 days. In addition, the configuration of the passive safety system can be rearranged to reduce the size of the containment to 76% of the reference design without affecting its safety performance.

By increasing the coolant enthalpy change, which also results in a higher thermal efficiency, the electrical output of the reference design can be enhanced by 44% without major design changes. If the number of pumps in the vessel are increased by 2, the electrical output can be enhanced by 102% while satisfying all safety criteria. The uprated power that satisfies a 72- hour grace period requires a tank size that is 32.5% of the reference design. Such compact and simplified nuclear steam supply system can partially address the lack of economy of scale for the reference SMR and improve its market competitiveness.

Thesis supervisor: Koroush Shirvan Title: Assistant Professor of Nuclear Science and Engineering

Acknowledgements

I would like to thank Prof. Koroush Shirvan for the opportunity to work with him and his continuous guidance throughout my thesis, Prof. Emilio Baglietto and Prof. Jacopo Buongiorno for their support on this project, Dr. Xu Wu and Dr. Wei Li for the help on RELAP model development.

I would also like to thank EDF for funding this project. I would also like to thank Laurent Amice and all the EDF staff who provided information and feedback throughout the project.

Lastly, I would like to thank all my family and friends for their moral support and encouragement.

Table of contents

Abstract ...... 2 Acknowledgements ...... 3 List of Figures ...... 6 List of Tables ...... 10 Chapter 1. Introduction ...... 12 1.1 Motivation ...... 12 1.2 Nuward reactor design ...... 15 1.3 Thesis objective and outline ...... 20 Chapter 2 Methodology ...... 22 2.1 RELAP model development ...... 22 2.1.1 RELAP model of the core ...... 24 2.1.2 RELAP model of the steam generators ...... 28 2.1.3 RELAP model of the pumps ...... 31 2.1.4 RELAP model of the pressurizer ...... 33 2.1.5 RELAP model of the pipes and pressure vessel ...... 34 2.1.6 RELAP model of the secondary side ...... 35 2.1.7 RELAP model of the containment ...... 35 2.1.8 RELAP model of the safety system ...... 36 2.2 Steady-state simulation result ...... 43 Chapter 3. Transient analysis ...... 46 3.1 Overview of transient analysis ...... 46 3.2 LOFA transient analysis ...... 46 3.3 SBO transient analysis ...... 51 3.4 LOCA transient analysis ...... 56 Chapter 4 Optimization study ...... 65 4.1 General description ...... 65 4.2 Passive safety system optimization ...... 66 4.3 Steam generator alternative ...... 78 4.4 Power uprating ...... 86 4

4.4.1 Power uprating approaches ...... 86 4.4.2 Transient analysis with uprated power ...... 90 Chapter 5 Conclusion and future work ...... 99 5.1 Conclusion ...... 99 5.2 Future work...... 100 Appendix ...... 102 PCHE benchmarking in RELAP ...... 102 References ...... 110

List of Figures

Figure 1-1 Design concept for one unit of the Nuward SMR

Figure 1-2 Four-reactor configuration of the Nuward SMR

Figure 1-3 Cross section of the Nuward reactor pressure vessel

Figure 2-1 Simplified schematic of Nuward SMR for RELAP model development

Figure 2-2 RELAP model of the Nuward SMR

Figure 2-3 Heat flux along fuel rod of the average core, the hottest assembly and the hottest pin

Figure 2-4 RELAP model of the core

Figure 2-5 SCRAM reactivity feedback in the RELAP model

Figure 2-6 Channel geometry compact steam generators (a) Areva design; (b) PCHE

Figure 2-7 Example of spool-type pump with mixed flow hydraulics

Figure 2-8 Volumes of steam and liquid in the RELAP model of the pressurizer

Figure 2-9 Equivalent water tank RELAP model with only one ANNULUS component

Figure 2-10 Simulation result over 2000 seconds of the model shown in Figure 2-9

Figure 2-11 Equivalent water tank RELAP model with two ANNULUS components

Figure 2-12 Simulation result over 2000 seconds of the model shown in Figure 2-11

Figure 2-13 Schematic of the reactor vessel, safety condenser and water tank

Figure 2-14 RELAP simulation of nominal operation: (a) pressure in the reactor vessel; (b)core inlet and outlet temperature

Figure 2-15 Centerline temperature distribution along fuel rod of the average core, the hottest assembly and the hottest pin

Figure 3-1 RELAP simulation result of the reference reactor following LOFA. (a) core outlet temperature; (b) reactor pressure vessel pressure; (c) reactor power; (d) primary coolant mass flow rate;(e) critical heat flux ratio of the core; (f) water tank temperature

Figure 3-2 RELAP simulation result of the reference reactor following SBO. (a) peak cladding temperature; (b) pressure in reactor vessel

Figure 3-3 Water tank temperature rise after SBO with and without natural circulation

Figure 3-4 Natural circulation mass flow rate after SBO

Figure 3-5 Water tank temperature after SBO

Figure 3-5 RELAP simulation result of the reference reactor following LOCA. (a) reactor thermal power; (b) break discharge rate; (c) break void fraction; (d) pressure in reactor vessel; (e) accumulator injection mass flow rate; (f) peak cladding temperature; (g) core outlet void fraction; (h) containment pressure

Figure 3-6 Water tank temperature after LOCA

Figure 4-1 Different setups of the safety condenser and the water tank. (a) original design; (b) water tank with half of the original volume; (c) condenser with lower inlet

Figure 4-2 Alternative setups of the safety condenser. (a) No condenser; (b) condenser submerged in the water tank.

Figure 4-3 SBO transient RELAP simulation results for the reference design, a modified design with water tank half of its original size and a modified design with lower inlet of the safety condenser. (a) peak cladding temperature; (b) pressure in the vessel; (c) days before boiling in the tank

Figure 4-4 Void fraction in the upper half of the water tank after an SBO transient

Figure 4-5 Onset of bulk boiling and the uncovering of the condenser after SBO for the reference design, modified design with water tank half of its original size and modified design with lower inlet of the safety condenser

Figure 4-6 LOCA transient RELAP simulation results for the reference design, a modified design with water tank half of its original size and a modified design with

lower inlet of the safety condenser. (a) Pressure in the vessel; (c) peak containment pressure

Figure 4-7 Schematic of the steam generators in the reactor vessel. Blue blocks represent the safety CSGs and red the CSGs for normal operation. The orange circle represents the core. (a) 8 rectangular CSGs; (b) 8 PCHEs; (c)8 + 2 additional safety PCHEs

Figure 4-8 Comparison between models adopting rectangular CSG and PCHE after SBO (LOFA). (a) CHFR in the core; (a) pressure in reactor vessel; (b) peak cladding temperature; (c) pressure in the safety system.

Figure 4-9 Mass flow rate instability in PCHE

Figure 4-10 Comparison between models adopting rectangular CSG and PCHE after LOCA.(a) pressure in reactor vessel; (b) pressure in the containment; (c) core outlet void fraction

Figure 4-11 Comparison between Nuward and EPR coolant temperatures

Figure 4-12 Schematic of the reactor coolant pumps in the core. (a) six-pump setup; (b) eight-pump setup

Figure 4-13 Simulation results after SBO for two models of uprated core: 1. only increase coolant enthalpy change, resulting in a thermal output of 681MW; 2. increase coolant enthalpy change and the number of reactor coolant pumps, resulting in a thermal output of 956MW. (a) thermal power; (b) primary coolant flow rate; (c) peak cladding temperature; (d) water tank performance

Figure 4-14 Simulation results after LOCA for two models of uprated core: (a) pressure in the reactor vessel; (b) pressure in the containment; (c) void fraction at core outlet

Figure 4-15 Grace periods after SBO for different water tank heights

Figure A-1 KAIST PCHE test facility

Figure A-2 Geometry of the PCHE channels (a) cross section of one basic unit; (b) flow path of the hot channel (left) and cold channel (right)

Figure A-3 RELAP model of the KAIST PCHE test facility

Figure A-4 Steady state pressure drop in PCHE at different mass flow rate. (a) Comparison between KAIST experiment and RELAP simulation results; (b) calculated pressure drop curves with various void fraction models

Figure A-5 Density wave oscillation in the low mass flow rate region in RELAP

Figure A-6 Two-phase instability in PCHE at different mass flow rate. (a) RELAP simulation results; (b) KAIST experiment results

List of Tables

Table 1-1 Current SMRs offered by various vendors/countries and their development status

Table 1-2 Design parameters of Nuward SMR

Table 2-1 Core parameters of Nuward SMR

Table 2-2 Reactor kinetic parameters of the reference SMR

Table 2-3 SCRAM reactivity feedback in the RELAP model

Table 2-4 Parameters of the steam generators modeled in RELAP

Table 2-5 Parameters of the pump in RELAP

Table 2-6 Parameters of the pressurizer modeled in RELAP

Table 2-7 Parameters of the pipes and pressure vessel components in RELAP

Table 2-8 Parameters of the secondary side modeled in RELAP

Table 2-9 Parameters of the containment modeled in RELAP

Table 2-10 Parameters of the water tank in the reference SMR

Table 2-11 RELAP Simulation result of nominal operation

Table 3-1 Timeline of events for LOFA transient

Table 3-2 Timeline of events for SBO transient

Table 3-3 Timeline of events for LOCA transient

Table 4-1 Transient performances after SBO and LOCA for all five designs

Table 4.2 Comparison between the rectangular CSG and PCHE

Table 4-3 Steady-state simulation results for the uprated reactor

Table 4-4 Steady-state simulation results for the uprated reactor with additional pumps.

Table 4-5 Safety performance of the uprated core after SBO and LOCA

Table 4-6 Short-term safety performance of the optimized after SBO and LOCA

Table A-1 Properties of the hydraulic components of the cold side in RELAP

Table A-2 Properties of the hot side fluid in the KAIST test facility

Chapter 1. Introduction

1.1 Motivation

The 21st century is at a profound energy crossroad where we need to drastically reduce the emission of greenhouse gases while maintaining and expanding economic growth. This challenge calls for a revolution in the power sector, which will play a vital role in deep decarbonization. A new electrical generation system that comprises of a variety of low- or zero- carbon technologies needs to be deployed in order to serve growing loads and simultaneously reduce emission. While there are a number of candidates in the green energy category, research has shown that with the presence of nuclear, which has the capability of generating a large amount of dispatchable electricity, the cost of achieving decarbonization will be lowered greatly. Therefore, nuclear energy must play an essential role in this battle.

However, investment in nuclear is stalled in many countries nowadays. Besides public concerns about severe accidents (especially after the Fukushima accident in 2011), a deep-lying cause for the rejection of nuclear energy is its high cost. Since the design and construction of the early commercial nuclear power in the 1950s, the power of reactor units has grown from less than 100 MWe to nearly 2000 MWe. With capital costs nowadays ranging from $2,000/kW to $6,000/kW in different countries, a thousand megawatts plant would mean a multi-billion-dollar investment. Although with corresponding economies of scale, larger units are able to bring down the unit cost of electricity after being built, further expansion of nuclear energy is hindered by this high capital investments and associated risks in terms of project financing, potential construction delays and cost overruns.

Small reactors could be a breakthrough. Parallel to the development of large-scale nuclear power units, small power reactors have been built to serve diverse purposes throughout the decades, such as neutron sources, ships or aircrafts propulsion, 12

power supply for remote military sites, etc., and the industry has accumulated considerable experience in its design and construction. “Small” here refers to power rating. Typically, a reactor with power rating from approximately 10 to 300 MWe is defined as small (Carelli and Ingersoll, 2014). Although relative to large light water reactors, small reactors lack economies of scale, this disadvantage could be balanced by the economies of multiples and accelerated learning, which is highlighted in small modular reactors (SMRs), where the unit assembly is compact and integral and can be assembled from one or several submodules. Of course, in order to realize such economics attributes, the cost of factory and multiple orders from the market is needed. With simplified and innovative design, small reactors have the potential to reduce capital investments and risks. Besides economic viability, most modern small reactors are designed with a high level of passive or inherent safety in the event of malfunction, further attracting the industry’s attention across the world.

Current SMR designs under construction or consideration include light water- cooled reactor, which is the majority, high-temperature gas-cooled reactor, as well as liquid-metal cooled reactors with fast neutron spectrum. Table 1-1 lists SMR designs offered by various countries and vendors and their development status.

Table 1-1 Current SMRs offered by various vendors/countries and their development status (IAEA, 2005; IAEA, 2018). Power Reactor Vendor Country Status (MWe) Light water reactor Detailed design VBER-300 200 OKBM Russia nearly completed NuScale Power NuScale 60 USA Licensing stage LLC SMR-160 160 Holtec USA Conceptual design

ACP100 100 CNNC China Under construction

Flexblue 160 DCNS Group France Conceptual design

KLT-40S 35 OKBM Russia Operating

SMART 100 KAERI South Korea Licensed

Nuward 2*170 consortium France Conceptual design Expected to enter RITM-200 50 OKBM Russian operation in 2020 Construction CAREM 25 CNEA/INVAP Argentina resumed in 2020 Westinghouse 225 Westinghouse USA Conceptual design SMR VK-300 300 Atomstroyexport Russia Detailed design Pre-licensing BWR-X300 300 Ge-Hitachi USA review Gas cooled-reactors

EM2 240 General Atomics USA Conceptual design

HTR-PM 2*105 INET China Under construction

Sodium cooled-reactors

PRISM 311 GE-Hitachi USA Detailed design

G4M 25 Gen4 Energy USA Conceptual design

4S 10 Toshiba Japan Detailed design

Lead cooled-reactors

BREST 300 Atomenergoprom Russia Detailed design

SVBR-100 100 OKB Gidropress Russia Detailed design

Molten salt reactors Terrestrial Licensing planned Integral MSR 192 Canada Energy in 2020s

Most of the small modular reactors listed above are in the conceptual design phase. Non-water-cooled reactors, such as lead fast reactor, would not be expected to enter the market before 2050 (MIT, 2018). More mature concepts, such as light water- based reactors, are expected to be technologically ready for commercialization by 2030, and they are the subject of this thesis. The French Nuward reactor is chosen as a reference design. It is a compact integral light water reactor with passive safety features. The basic design of Nuward is expected to be completed between 2022 and 2025, and construction of a demonstration unit is scheduled for 2030, the

construction of which is expected to take three years (WNN, 2019). The following subchapter will describe the features of Nuward in detail.

1.2 Nuward reactor design

Nuward, a fully integrated Pressurized Water Reactor (PWR), is jointly developed

by CEA, EDF, Naval Group and TechnicAtome. It is a 170 MWe pressurized water

reactor with UO2 fuel. All main components, including the reactor pressure vessel, the accumulators and the safety condenser are within the steel containment (Figure 1-1). The integrated unit is submerged in a large volume of water (Figure 1-2) to provide passive cooling in accident scenarios. Multi-unit configuration of identical reactors in a same nuclear island is plausible and will provide the operator with the flexibility of construction and operation.

Figure 1-1 Design concept for one unit of the Nuward SMR [Image from (WNN, 2019)]

Figure 1-2 Four-reactor configuration of the Nuward SMR. Each module is submerged in a water tank [Image from (TechnicAtome, 2019)].

The design philosophy of the Nuward SMR is to generate power that is: (i) affordable: all components can be shipped conveniently and only the containment will be likely to need on-site assembly, thus lowering the cost. (ii) Flexible: two more configurations are available, and the system can be easily adapted to the power required by the grid. (iii) Protected against natural and human hazards: the reactor will be underground, and the nuclear island is protected under an artificial mound. (iv) Safe: for design basis accidents, the passive heat removal system can operate for at least 7 days without external heat sink or power supply.

Figure 1-3 Cross section of the Nuward reactor pressure vessel [Image from http://www.nuclearenergy.polimi.it/elsmor/]

These goals are imbedded in specific design features. For instance, as shown in Figure 1-2, the reactor core, control rod drive mechanisms, steam generators and pressurizer are all integrated within the reactor pressure vessel. To enable such compactness, Nuward utilizes Compact Steam Generators (CSGs). Six CSGs will be functioning under normal operation, while two will perform heat removal under accident scenarios. The use of CSG for SMRs was first proposed by Shirvan et al

in 2009 and utilized again to design a passive 170 MWe reactor for the French Naval Group (Shirvan et al., 2016). This integral vessel allows for pre-manufacture and helps reaching the goal of affordability.

The safety systems of Nuward are passive and simplified. The design includes a two-train passive heat removal system that transfers the decay heat from the core to the water surrounding the containment using natural circulation. Inside the vessel, design efforts have been made to reduce the size of the pipes connected to the vessel so as to limit the size of LOCA to 30mm diameter. The small diameter of possible pipe break eliminates large break LOCA from design basis and leads to a limited water loss during the LOCA. A set of two redundant low-pressure safety injection accumulators provides the make-up of water inventory inside the vessel. The steel containment submerged in the pool serves as the third barrier of defense- in-depth and it is protected against hydrogen risk in DBAs by passive recombiners. More detailed information about the steam generators, the safety system, as well as other major components of the reactor can be found in Table 1-2 (TechnicAtome, 2019).

Table 1-2 Design parameters of Nuward SMR Parameter Value Unit

Overview

Coolant Light water /

Moderator Light water /

Neutron spectrum Thermal /

Thermal Power 540 per module MWt

Electrical Power 170 per module MWe

Efficiency 31.5 %

Type of cycle Rankine /

Plant design life >60 Years

Plant availability 92 % 8800 for 4-reactor Plant footprint m2 configuration Mode of operation Base and load-following Seismic design (peak ground 0.25 g acceleration) Core

Number of assemblies 69 or 76 /

Assembly type 17×17 /

Fuel type UO2 rod

Enrichment <5 wt%

Power density ~70 kW/L

Fuel cycle length 24 or 36 months

Discharge burnup <60 MWd/kg Main reactivity control Internal Control Rod Drive mechanism Mechanism (CRDM) Burnable absorber strategy Burnable poison

Soluble absorber strategy No soluble boron

Reactor coolant system

Cooling mode Forced convection

Operating pressure 15 MPa

Core coolant inlet temperature 280 oC Core coolant outlet 307 oC temperature Mean temperature rise across 27 oC core Steam generators

Type Plate steam generator

Number 6 (normal operation)

+ 2 (safety)

Transport weight 5 t

Coolant pump

Number 6

Reactor pressure vessel Inner diameter of cylindrical 4000 mm shell Total inner height 13500 mm

Transport weight 310 t

Primary containment Metallic compact containment. Type No pressure resistant civil work. Shape Cylindrical

Dimensions 15/16 m

Safety system

Residual heat removal system Passive

Safety injection systems Passive /reactor- Core damage frequency 1×10-5 year /reactor- Large early release frequency Practical elimination year Collective occupational human- 0.1 radiation exposure Sv/year 0 for Design-Basis Accidents (DBAs) Operator action time hours 0.5 for beyond design-basis accidents 7 days grace period without Design goal for DBAs external power or heat sink

1.3 Thesis objectives and outline

Using the key elements of Nuward as the reference design, this thesis will build a computerized model of an integral small light water reactor and perform safety analysis. Based on the results, a parametric optimization study will be carried out. The goal is to further reduce the size of the reactor and hence increase the power density while satisfying the same safety goals, thus making it more economically competitive.

The focus of the analysis will be on thermal hydraulic and safety performance, and the computational tool of choice is RELAP5/3.3gl (Reactor Excursion and Leak Analysis Program), a simulation tool developed by Idaho National Laboratory (INL) that allows users to model the coupled behavior of the coolant system and the core for operational transients and postulated accidents. The operation of the reference reactor will be simulated in RELAP5, and the performance of the safety system under various transients will be assessed.

Chapter 2 of this paper will describe a RELAP5 model of Nuward. The model will include the reactor pressure vessel, the primary loop, the secondary loop, the steam generators, the pressurizer, the accumulator, the water tank, etc. The steady-state operation of the reactor will be simulated and compared with design parameters. Particularly, this chapter will focus on the CSG performance and discuss its usage in nuclear systems. Chapter 3 will present the results of transient analysis. Three accident scenarios, LOFA, SBO and LOCA will be simulated using RELAP5. LOFA is initiated by the loss of electrical power to all the pumps. During SBO, the plant will lose all electrical power, with the pump and turbine ceasing to function. LOCA is induced by the largest possible rupture in the coolant pipe. The short-term and long-term performance of the safety system will be evaluated and discussed. Chapter 4 will present the parametric optimization study based on previous results. A sensitivity analysis will be carried out following the transient simulations. The contribution of the chosen design parameters to the safety of the reactor in the

accident scenarios will be assessed. Subsequently, the optimization results will guide the design process to improve the reference SMR’s performance. This will be achieved by reducing the size of the reactor pool and/or containment and increasing its power output while guaranteeing safety. Chapter 5 will describe main conclusions and provides recommendation for future work that can be implemented to improve the analysis.

Chapter 2 Methodology

2.1 RELAP model development

A RELAP model of the reference SMR is developed in order to assess its performance, especially that of the safety system under transient conditions. The detailed design of Nuward is proprietary, thus the model is established using public information and careful assumptions. As listed in Table 1-2, important geometric and operation parameters are available, including power output, containment size and inlet/outlet temperatures. Figure 1-1 and Figure 1-2 indicate how components are positioned and connected.

A simplified schematic of one reactor unit including only major components is shown in Figure 2-1, which will serve as the basis of the RELAP model. The water tank surrounds the containment and allows for passive cooling. Inside the reactor pressure vessel are the core, six steam generators (drawn as one equivalent steam generator), two safety steam generators (drawn as one equivalent), six pumps (drawn as two equivalents) and the pressurizer. A safety condenser is placed in the

Figure 2-1 Simplified schematic of Nuward SMR for RELAP model development 22

containment, one side of which is connected with the safety steam generators and the other with the water tank. Two accumulators (drawn as one equivalent) are placed in the containment for passive injection and are positioned above the core level.

Other important inputs, such as the ones concerning the design of the CSGs and the reactor coolant pumps are obtained via informed assumption and extrapolation. In this way, different components are added and ultimately, they have evolved into a complete reactor model, as shown in Figure 2-2.

Figure 2-2 RELAP model of the Nuward SMR

2.1.1 RELAP model of the core

The core of the Nuward SMR can adopt either a 69- or 76-assembly configuration. The vendors currently select the 69-assembly configuration, with the prospect of upgrading to 76 in the future. Core height is scaled from the design layout to be 2.2 , and the geometric properties of typical PWR rods are used in the RELAP model,𝑚𝑚 as shown in Table 2-1. The power distribution along the rod has a chopped cosine shape with an estimated peaking factor of 1.45. Assembly and pin peaking factors are assumed to be 1.3 and 1.1 respectively, resulting in an overall peaking factor of approximately 2. Heat flux distribution in the average core, the hot assembly and the hot pin are shown in Figure 2-3. The average heat flux for each of them is 451 kW/m , 586 kW/m and 645 kW/m respectively. 2 2 2

UO2 is used as the fuel with zirconium cladding. The thermal conductivity and heat capacity of UO2 with regard to temperature are specified in RELAP in the form of General Table. The thermal properties of zirconium cladding and helium gas in the gap are assumed to be constant and are specified in the RELAP input file too.

In order to assess the core performance and explore design limits, core is divided into three parts in the RELAP model representing the average core, the hot assembly and the hot pin, where each is a PIPE component with the same length and different surface areas and hydraulic diameters. A heat structure is assigned to each PIPE to represent reactor power. Different amounts of power are calculated using the peaking factors. Cross flow between channels is enabled in the heat structure, which enhances mixing and flattens the temperature and mass flow rate among the channels. Correspondingly, the heat transfer mode of rod bundles with crossflow is selected in RELAP.

Table 2-1 Core parameters of Nuward SMR

Parameters Value Parameters Value

Core height 2.2 Axial power distribution Chopped cosine

Pellet diameter 7.84 × 10𝑚𝑚 Axial power peaking factor 1.45 −3 Gap thickness 8.32 × 10 𝑚𝑚 Hot assembly peaking factor 1.3 −5 Clad thickness 5.73 × 10 𝑚𝑚 Hot pin peaking factor 1.1 −3 Rod diameter 9.16 × 10 𝑚𝑚 Core peaking factor 2.07 −3 𝑚𝑚

Figure 2-3 Heat flux along fuel rod of (i) average core, (ii) hot assembly, (iii) hot pin

Figure 2-4 RELAP model of the core

As information regarding spacer grid in the core is not available, a honeycomb type spacer is assumed. There are several models to calculate the effective loss coefficient of a spacer grid including In (In et al., 2002), de Stordeur (de Stordeur, 1961) and Rehme (Rehme, 1972) correlations. These three models result in loss coefficient in rage of 0.1 to 0.6. A loss coefficient of 0.36 is assumed for the simulations.

For reactor kinetics, the POINT kinetic type and SEPARABL feedback type is chosen in RELAP, meaning that reactor kinetics feedback due to moderator fluid density, void fraction weighted moderator fluid temperature and volume average fuel temperature is assumed to be separable. The table below lists some kinetic parameters. No reactivity coefficients are assumed in the model to obtain a conservative result for the selected transients.

Table 2-2 Reactor kinetic parameters of the reference SMR

Parameters Value Initial reactivity 0.0 / 243.1 −1 Product 𝛽𝛽yield𝜆𝜆 factor 1.0𝑠𝑠 U239 yield factor 0.7

When shutting down the reactor, the same reactivity worth for control rods as the Westinghouse PWR is assumed, as shown in Table 2-3 or Figure 2-5. This table is entered as the SCRAM signal in RELAP input and will be triggered in transient scenarios. The complete insertion of negative reactivity is done in about 5 seconds. Since the core of Nuward SMR is smaller than traditional PWRs and is designed with one control rod cluster per assembly, the 5-second insertion time and the assumed reactivity insertion are conservative estimates.

Table 2-3 SCRAM reactivity feedback in the RELAP model

Time (s) Reactivity ($)

0.00 0.00

0.80 0.00

1.50 0.00

2.00 -0.217

2.50 -0.318

3.00 -1.012

3.50 -2.891

3.60 -4.336

3.70 -7.227

3.80 -10.11

4.00 -12.29

4.25 -13.3

4.50 -13.95

5.00 -14.45

1 × 10 -14.45 6

Figure 2-5 SCRAM reactivity feedback in the RELAP model

2.1.2 RELAP model of the steam generators

The Nuward SMR utilizes CSGs that can be placed entirely inside the reactor vessel. As the detailed design of the steam generators is proprietary information, the RELAP model adopted the CSG disclosed by Areva (Haratyk, 2015), while Another design, the PCHE designed by HeatricTM will also be taken into consideration and discussed in the optimization study.

Figure 2-6 (a)

Figure 2-5 (a)

Figure 2-6 (b) Figure 2-6 Channel geometry compact steam generators (a) Areva design; (b) PCHE (Haratyk, 2015)

The Areva CSG is a diffusion-bonded plate-type CSG. The plates are made of a titanium alloy (TA6V) and can sustain up to 10 MPa pressure difference between each other for normal operation. Straight vertical channels are used in the heat exchanger for reliability and inspectability concerns, and the channels are connected to each other within a plate so that cross flow between channels can occur. The cross-section of the channels is rectangular, each with a flow area of 8 mm2, as shown in Figure 2-6 (a). With over 20,000 rectangular micro-channels,

this type of diffusion bonded CSGs can provide high power density with lower pressure drop and maintenance requirements.

The Heatric PCHE is also a type of compact steam generators. It is formed by the diffusion-bonding of stacked rectangular plates with chemically etched semicircular channels as the flow paths. The channels of PCHE are smaller than that of the rectangular CSGs, with a flow area of 1.57 mm2 and hydraulic diameter of 1.2 mm. Thanks to the diffusion-bonding technology and the resulting large heat transfer area over volume ratio, PCHE has high integrity, high power density and low pressure drop. It first entered the market in the 1980s and has been used in various industries, such as refrigeration, hydrocarbon processing and petrochemical, while attracting growing attention from the nuclear industry as well. Institutions such as Idaho National Laboratory (INL), Korea Advanced Institute of Science and Technology (KAIST) and MIT have published papers investigating its potential. However, experience on using PCHE under boiling water is limited, as the small channels may be more prone to two-phase instabilities. A RELAP model of the PCHE will be discussed in Chapter 4 along with discussion on the possibility and implication of replacing the rectangular CSG with PCHE.

In RELAP, the six CSGs are modeled as one with an equivalent size and heat transfer surface area for simplicity. The equivalent steam generator is modeled as two individual PIPE components as the primary and secondary sides, connected by a heat structure to establish heat transfer. The primary side PIPE is oriented vertically with upward flow, while the secondary PIPE has the same placement with downward flow.

Total height of the steam generator is estimated from the schematics to be 2.5 m, with a header area assumed to be 0.5 m in height at both ends and the heat transfer region in the middle. The optimal size of the CSG needs to be iterated to find maximum power density and corresponding smallest volume. For the initial model, a power density of 90.53 MW/m3 calculated in previous study (Haratyk, 2015) is

adopted. Therefore, with six steam generators generating a total thermal power of 540 MW, each will have a volume of approximately 1 m3. Combining this with knowledge of the height and geometry, the total number of channels is calculated to be 28818, giving a cross sectional area of 1.26 m2.

For heat transfer, the convective boundary condition is used for both PIPEs. The heat structure is divided into 10 nodes vertically, while horizontally 5 radial meshes are established, with material defined by a constant heat capacity and thermal conductivity. RELAP uses Chen’s correlation for two-phase heat transfer (INL, 2015). However, it is noteworthy that experiments have shown existing heat transfer correlations insufficient in describing heat transfer in CSGs due to the small hydraulic diameter of the channels, especially for two-phase flow. In these small, confined mini-channels, bubbles coalesce easily and may introduce dryout earlier (Sardeshpande et al, 2013). On the other hand, the same confinement effect tends to flatten the bubbles and reduce the thickness of liquid film, thus boosting the evaporation process. Therefore, the overall effect that small channels have on heat transfer is uncertain. This will be more carefully discussed in the Appendix with experimental benchmark. Modification to the default heat transfer correlation is possible in RELAP by adjusting the parameters fouling factor and local boiling – the former imposes a multiplication factor on heat transfer coefficient and the latter is the ratio between local and average heat flux. In the initial model, both parameters are set as default.

Table 2-4 Parameters of the steam generators modeled in RELAP

Parameter Value Channel properties Hydraulic diameter 2.66 × 10 m −3 Channel area 8 mm Number of channels 288182 CSG properties Cross section 1.26 m 2 30

Header height 0.5 m Heated region height 1 m Total height 1.5 m Header friction loss = 0.1

𝑓𝑓 𝐾𝐾

2.1.3 RELAP model of the pumps

The reference SMR has six reactor coolant pumps (RCP) located inside the pressure vessel. The spool-type pump designed by Westinghouse is adopted here as reference since the actual pump used in Nuward is not disclosed. This type of pump was used in the IRIS (International Reactor Innovative and Secure) reactor, an integral PWR with 335 power output, which is comparable to Nuward

(Kujawski, 2002). The spool𝑀𝑀 𝑊𝑊type𝑒𝑒 RCP motor and pump impeller consist of two concentric cylinders, where the outer ring is the stator and the inner ring is the rotor that carries high specific speed pump impellers. It has several advantages over traditional RCPs, including the fact that it can be located entirely inside the reactor vessel. Furthermore, the use of high temperature motor windings and bearing materials can eliminate the need for cooling water and the associated small piping connections. Other characteristics include low head, high flow rate, medium inertia/coastdown, and flow run-out capability which will reduce the consequences of LOFAs. The current defined pump flow rate and developed head are:

• pump flow: 588.4 kg/s;

• developed head: 24m

The spool-type pump is suitable for an integral small reactor like Nuward and should be similar to the actual design.

Figure 2-7 Example of spool-type pump with mixed flow hydraulics (Kujawski, 2002)

In RELAP, the six RCPs are modeled as one equivalent PUMP component and it is located below the steam generators, as shown in the schematic. Pump specifications are considered based on calculated mass flow rate and the design limit of spool-type pumps. A 5% margin from the design value is adopted for conservative analysis. Other specifications, such as flow area and friction coefficients, are based on typical pump data and the IRIS design. Table 2-5 lists some important parameters.

Table 2-5 Parameters of the pump in RELAP.

Parameters Value Rated velocity 140 rad/s Rated flow 5.0 m /s 3 Rated head 22.8 m Rated torque 1.28 Pa × m 3 Moment of inertia 1.43 kg × m 2

2.1.4 RELAP model of the pressurizer

The pressurizer of the Nuward reactor is inside the pressure vessel and is located at its highest point. The detailed design of the pressurizer is not disclosed. From the schematic, its height is estimated to be 3.5 meters. In RELAP, it is modeled as a PIPE component as shown in Figure 2-8, the top half of which is filled with steam and the bottom half liquid. The pressurizer is connected to a relief valve, modeled as a VALVE component in RELAP. Initially, the pressure in the system is set to be 15 MPa. Using control variables, the VA LV E component controls the pressure during simulation. When the pressure rises above 15.4 MPa, the valve opens and reduces the pressure of the system. The valve closes again once the pressure reaches below 14.98 MPa to maintain the pressure. This VA LVE component is further connected to a TIME DEPENDENT VOLUME component filled with air at the fixed pressure of 1.5 atm that represents the containment boundary.

Table 2-6 Parameters of the pressurizer modeled in RELAP Parameter Value Pressure 15 MPa Total volume 36 m 3 Steam portion Height 1.875 m Volume 16 m Quality 100%3 Liquid portion Height 1.875 m Volume 20 m 2 Quality 0% 3

Figure 2-8 Volumes of steam and liquid in the RELAP model of the pressurizer

2.1.5 RELAP model of the pipes and pressure vessel

Components in the reactor pressure vessel of Nuward are positioned and connected based on the schematic. The riser, modeled as PIPE component, is located above the core and connects with the steam generators at its outlet. The pressurizer is connected to the top of the riser to control the pressure on the primary side. Pumps are located below the steam generators and connected to downcomer, modeled as an ANNULUS, which leads to the volume of water below the core, at bottom of the pressure vessel, modeled as a PIPE. These parts are all connected with the BRANCH component. The total height of the pressure vessel is modeled to be 13.5 . The table below is the height and volume of different components in

RELAP.𝑚𝑚

Table 2-7 Parameters of the pipes and pressure vessel components in RELAP Component RELAP model Height (m) Volume ( ) 𝟑𝟑 Bottom of vessel PIPE 2.5 4.09 𝐦𝐦 Core PIPE 2.2 3.95 Riser PIPE 4.9 9.62 Steam generators PIPE 2.5 2.00 (primary side, 6+2) Pressurizer PIPE 3.75 36.08 Downcomer ANNULUS 6.9 22.89

2.1.6 RELAP model of the secondary side

Since the Nuward design, much like many SMRs, does not rely on any auxiliary cooling during LOCA or SBO, then the secondary side, including the turbine and the feedwater line, is not included in the RELAP model. Instead, TIME DEPENDENT VOLUMEs are used to represent the turbine and the feedwater inventory, and a TIME DEPENDENT JUNCTION is used to control feedwater inlet. VALVEs are used to connect between these components and the secondary side of the steam generators. These are trip valves, and they are closed at the onset of transient to simulate the loss of feedwater.

The secondary side design of Nuward is not publicly available. In this study, the secondary side pressure is assumed to be 7MPa, and the feedwater temperature and steam outlet temperature are adjusted accordingly to meet the target reactor thermal power. The table below includes the parameters of the secondary side.

Table 2-8 Parameters of the secondary side modeled in RELAP Parameter Value Pressure 7.0 MPa Feedwater temperature 227 oC Feedwater mass flow rate 300 kg/s Steam outlet temperature 286 oC

2.1.7 RELAP model of the containment

The containment of the reactor is assumed to be filled with air along with a water inventory at the bottom. In RELAP, this is modeled with two ANNULUS components. Their volumes are calculated by subtracting the volume of the known components inside the containment. Initially, the containment pressure is set at 1.5 bar, as it is placed underwater. A heat structure is established between the water tank and the containment air. Since Nuward shares many similar design features 35

including overall size as the compact PWR SMR designed by Shirvan et al, 2014, same containment design pressure (9 bar) and thickness (5 cm) is assumed. Table 2-9 lists some main parameters of the containment.

In order to simulate the LOCA transient, a VALVE is placed inside the containment, connecting between the downcomer and the containment. It will open to simulate a break that pushes primary coolant into the containment and initiate LOCA.

Table 2-9 Parameters of the containment modeled in RELAP Parameter Value Initial pressure 1.5 bar Design pressure 9 bar Containment air volume 860 m3 Containment water volume 72 m3 Wall thickness 0.05 m

2.1.8 RELAP model of the safety system

2.1.8.1 Safety steam generators

The two safety steam generators are modeled as one equivalent component in RELAP. It consists of two PIPEs representing the primary and secondary side and a heat structure between them. At the onset of transient, primary coolant flow is diverted to the safety steam generators. The detailed mechanism of this transition in Nuward is unclear based on provided information, but a RELAP approximation enabled by trip valves is adopted to meet the design expectations. VA LV E components are placed between the riser and the CSGs. Using control variables, when a transient takes place, the VALVE connected with the safety CSGs opens instantaneously while the one connected with the normal CSGs gradually closes during the first 20 seconds following the transient to avoid a surge in temperature. It is noted that only one of the two safety steam generators are assumed to be 36

working in accident scenarios to obtain a conservative result. Therefore, the size and heat transfer area of the equivalent RELAP component are adjusted accordingly in transient analysis to represent only one safety CSG.

2.1.8.2 Safety condenser

In the Nuward reactor, a safety condenser is placed in the containment, one side of which is connected with the secondary side of the safety steam generators and the other with the water tank. The water drawn from the tank cools the safety CSG and therefore removes residual heat after transient. Similar to the CSGs, the safety condenser is modeled with one PIPE component and one ANNULUS component connected by a heat structure. As the safety condenser is placed in the top half of the containment, a PIPE oriented upwards connects the outlet of the secondary side of the safety CSG and the inlet of the hot side of the condenser. Scaling from the schematic, the condenser is sized to be approximately 3m in height. The surface area is 150 m2 and the pipes connecting to the condenser have a diameter of 30 mm, according to the design parameters of Nuward. The pressure of the safety condenser is set to be the same as the secondary side, at 7MPa.

It is noteworthy that two-phase flow with small mass flux and low pressure is likely to occur in the safety condenser during residual heat removal. Experiments have shown that such flow is prone to instabilities (Johnston, 2001). In the meantime, the cold side of the safety condenser, connected to the water tank, relies on natural circulation, which is sensitive to initial conditions in RELAP and tends to cause instabilities as well. Loss coefficients are therefore imposed on the component junctions in the model to avoid instabilities.

2.1.8.3 Water tank

The size of the water tank is scaled from Figure 1-1b to be a 20 × 20 × 20 m cubic with a 15 × 16 cylindrical hollow (the containment) in the middle. As the reactor will be build underground, the pressure at the surface of the water tank is slightly higher than the atmosphere, at 1.5 × 10 Pa. The initial temperature is as 5 low as 20 to ensure effective cooling.

℃ Table 2-10 Parameters of the water tank in the reference SMR.

Parameter Value Height 20 m Volume 5173 m 3 Pressure at the surface 1.5 × 10 Pa 5 Pressure at the bottom 3.5 × 10 Pa 5 Temperature 20

℃ The water tank is connected with the safety condenser, which draws water from the bottom of the tank and exhausts to the middle. As the incoming water has a higher temperature, natural circulation is introduced.

If one ANNULUS component is used in the model, natural circulation is non- existent due to RELAP5 modeling limitation. For verification, Figure 2-9 shows a simplified equivalent model of the water tank, with the properties of the inlet flow set to be similar to that from the safety condenser. The result shows that only three mesh points experienced temperature change, and the temperature rise of the hottest node is in 2000 seconds. In order to model natural circulation, two identical annuli are9℃ used, each with 20 m in height but 2500 m in volume. The 3 condenser draws water from one of these “half annuli” and exhausts into another, therefore introducing natural circulation in the water tank. For verification, Figure 2-11 shows a simplified model of this setup. Parameters other than the two half tanks are set to be the same as that in Figure 2-9. Throughout the same time span

of 2000 seconds, the temperature rise is significantly lower, and all the mesh points of the annuli have similar trends, as shown in Figure 2-12.

Figure 2-9 Equivalent water tank RELAP model with only one ANNULUS component.

Figure 2-10 Simulation result over 2000 seconds of the model shown in Figure 2-9

Figure 2-11 Equivalent water tank RELAP model with two ANNULUS components.

Figure 2-12 Simulation result over 2000 seconds of the model shown in Figure 2-11

2.1.8.4 Accumulators

Nuward has two passive accumulators in the containment as part of the emergency core cooling system (ECCS). In case of a loss of coolant accident (LOCA), when the pressure in the reactor vessels decreases to below a certain pressure, the accumulators will automatically inject water into the vessel. Each accumulator contains of water at the bottom and nitrogen at the top. In RELAP, the two accumulators are modeled as one equivalent PIPE. The pressure inside the accumulators is set to be the same as the injection pressure, and the initial temperature is 25oC for effective cooling. The accumulators are then connected to a relief valve, the other end of which leads to the downcomer. This is modeled with a VALVE component and control variables. When the pressure in the vessel drops below the injection pressure, water in the accumulator will be pushed into the vessel, fulfilling passive injection. The diameter of the injection line pipe is set to be 5cm, with reference to typical PWR values.

2.1.8.5 Relative elevation and positions

The positions of the components inside the reactor vessel are shown in Figure 1-2. RELAP modelling in this matter is straightforward, as it is a closed loop inside the vessel and the number of pipes has been greatly reduced in the Nuward design. For the safety system, however, the relative elevation and position of components requires more careful examination as it is very important in natural circulation.

As shown in Figure 2-13, the bottom of the water tank is at the same level as the bottom of the reactor vessel, while its upper part exceeds the top of the vessel. The safety condenser is placed in a way that its bottom is at the same level as the inlet of the secondary side of the safety CSGs. The condenser draws water from a point slightly higher than the midplane of the tank and discharges to the top. As the condenser is 3m in height, the elevation between the inlet and outlet is assumed to 41

be 4m from the schematic. The bottom of the accumulator is placed on the same plane as the top of the downcomer.

Figure 2-13 Schematic of the reactor vessel, safety condenser and water tank (Chenais & Douveneau 2020)

2.2 Steady-state simulation result

The previous section described the initial RELAP model of the reference reactor. Modifications and improvements are made along the way to better account for the design details of the reactor. With the model developed according to the description above, a RELAP simulation of the plant during nominal operation is performed. The system reached steady state after around 20 seconds and continued to run until 200 seconds. Figures 2-14 showed the pressure in the reactor pressure vessel and the safety system, as well as the inlet and outlet temperature of the core. All of them agree well with the target design values. Figure 2-15 shows the temperature profile along the fuel rod centerline in the average core, the hot assembly and the hot pin. The maximum temperature in the hot pin is 890oC, which is well below

the UO2 melting point. More detailed simulation results are listed in Table 2-11. Overall, the simulation result is very similar to design values.

Figure 2-14 (a)

Figure 2-14 (b) Figure 2-14 RELAP simulation of nominal operation. (a) pressure in the reactor vessel; (b)core inlet and outlet temperature

Figure 2-15 Centerline temperature distribution along fuel rod of (i) average core, (ii) hot assembly, (iii) hot pin

Table 2-11 RELAP Simulation result of nominal operation. RELAP5 Designed values Parameters results (TechnicAtome et al, 2019) Thermal power (MW) 540 540

Pressurizer pressure (MPa) 15.01 15.00

Core inlet temperature (oC) 280 280

Core outlet temperature (oC) 307 307

Primary side mass flow rate (kg/s) 3142 3142

Core pressure drop (kPa) 42

SG secondary side pressure (MPa) 7.02 /

Steam outlet temperature (oC) 286 /

Secondary side mass flow rate (kg/s) 300 /

Chapter 3. Transient analysis

3.1 Overview of transient analysis

This chapter will analyze the safety performance of the reference SMR after three transients: LOFA, SBO and LOCA. The following three subsections will describe the sequence of events for each of these transients, how they were modeled in RELAP, short-term and long-term simulation results and their safety indication. In order to obtain more conservative results, only one safety steam generator is assumed to be functioning after the transient. In the RELAP model, this means that only half of the original surface area is available for heat transfer.

3.2 LOFA transient analysis

LOFA is initiated by the loss of electrical power to the pump. After the pumps trip, there is an immediate decrease in primary coolant mass flow rate and a rapid increase in its temperature. Control variables are defined to monitor the core inlet and outlet temperature. When the temperature difference reaches 118% of the nominal value, SCRAM is triggered. This initiation limit is assumed to be the same as the Westinghouse IRIS plant (Ricotti, 2002). Subsequently, valves on the safety side open, and the two safety steam generators remove heat from the reactor through the safety condenser via heat exchange with water drawn from the water tanks. Feedwater valve gradually closes after the six steam generators for nominal operation cease to function and the flow is diverted to the safety CSG. The sequence of events is shown in Table 3-1. The switching of the normal CSGs to safety CSGs is assumed to occur instantaneously upon the SCRAM signal.

Table 3-1 Timeline of events for LOFA transient

Event Trigger Nominal operation = 0 s

Pump loses power 𝑡𝑡= 200 s

SCRAM > 118%𝑡𝑡 × , Safety system opens 𝛥𝛥𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 SCRAM 𝛥𝛥time𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 Complete loss of feedwater SCRAM time +20 s

Figure 3-1 (a)

Figure 3-1 (b)

Figure 3-1 (c)

Figure 3-1 (d)

Figure 3-1 (e)

Figure 3-1 (f)

It is noteworthy that since the reference reactor completely relies on passive heat removal with no emergency feedwater system, the long-term effect for the LOFA transient is very similar to that of station blackout, as once the pump is tripped and SCRAM signal is triggered, there will no longer be any electric power source for residual heat removal. Therefore, for the LOFA transient, more emphasis is laid on the short-term effect as the long-term effect will be covered in the next subsection.

Figure 3-2(a) shows the change in core outlet temperature. Typically, upon pump trip the SCRAM signal is assumed with few seconds delay. In this simulation two conservative assumptions were made. First, as mentioned, no reactivity feedback is assumed, thus upon core heat up, reactor power does not decrease and remains constant. Second, the SCRAM signal is triggered once the nominal core temperature rise (27oC) reaches its 118% nominal value (32oC). This happened 2.2S seconds after the pump trips. Following SCRAM, core outlet temperature begins to steadily decrease. Throughout the simulation, void fraction in the core remains 0, meaning that there is no boiling and the core is covered at all time.

Figure 3-1(b) shows the change in primary side pressure following LOFA transient. There is an initial increase in pressure when the pump loses power because of the temperature rise in the core as a result of loss of flow. Afterwards, the pressure in the vessel steadily decreases. 800 seconds after the transient, the pressure will have decreased from the nominal 15 MPa to approximately 12 MPa.

When the SCRAM signal is triggered, a total reactivity of -$14.5 is inserted into the core in 5 seconds. The reactor power therefore sees a sharp decrease to decay heat shortly after the transient. Mass flow rate on the primary side decreases rapidly immediately following LOFA to one-third of the nominal value before steadily decrease. By 800 seconds after the accident, the primary coolant mass flow rate is approximately 300 kg/s. The minimum critical heat flux ratio (CHFR) in the core is 3.55, which occurs 3.5 seconds after the transient. Afterwards, CHFR increases. Overall, the ratio stays well above the typical PWR limit of 1.3 by utilizing the

built-in look-up tables in RELAP and therefore boiling crisis will likely not occur in the core after LOFA. The very high value of CHFR before the transient is attributed to the lower core average temperature and power density, compared to conventional PWR. The temperature of the water tank increases as it cools the reactor. Due to the large amount of water, this increase is slow – 1.5oC in the first 800 seconds after the transient and will become even slower as decay heat decreases over time. This will be discussed more in detail in the analysis of the SBO transient.

3.3 SBO transient analysis

Station blackout is the loss of all offsite electrical power, which causes the pumps and the turbine to trip. Since the turbine is not modeled in RELAP and the reactor relies completely on passive heat removal, the timeline of events in the SBO transient is very similar to that of the LOFA transient. The only difference is that a SCRAM signal is assumed to be imposed two seconds after the initiation of the accident. Therefore, more emphasis will be laid on the long-term effect, especially that of the passive safety system. Nuward reactor is designed with the goal that it is has at least a 7-day grace period without external power or heat sink following a DBA. Whether this goal can be achieved relies greatly on the presence of water in the water tank to effectively remove decay heat. Therefore, a parameter that will receive the most attention and examination here is the temperature of the water in the water tank.

As in LOFA, after the initiation of the transient, flow in the primary side switches from the path for nominal operation to the safety system and the feedwater line gradually loses water. The table below shows the timeline of events.

Table 3-2 Timeline of events for SBO transient

Event Trigger Nominal operation = 0 s

Plant loses power 𝑡𝑡= 200 s SCRAM 𝑡𝑡 = 202 Safety system opens SCRAM𝑡𝑡 time𝑠𝑠 Complete loss of feedwater SCRAM time +20 s

Following the transient, the peak cladding temperature (PCT) first decreases rapidly to about 280 oC, then steadily drops further. As no spike occurs after the transient, PCT stays well below the limit, thus the integrity of the cladding is not challenged. Depressurization after SBO is steady. As shown in the LOFA analysis, pressure in the reactor pressure vessel decreases rapidly in the first hour to 10 MPa. The depressurization slows down afterwards and stabilizes around 9.5 MPa, as shown in Figure 3.2 (b).

Figure 3-2 (a)

Figure 3-2 (b)

Figure 3-2 RELAP simulation result of the reference reactor following SBO. (a) peak cladding temperature; (b) pressure in reactor vessel

To investigate the performance of the passive safety system, the average temperature of the water tank is examined. As described in section 2.1.7.3, natural circulation can be enabled in the water tank by dividing it into two halves and creating a flow path. A case where the water tank is modeled as a single PIPE component (i.e. no natural circulation) is also simulated, and the result is presented in Figure 3.3, along with the final model with two-component water tank. Without enforcing natural circulation, temperature change in water tank almost doubles. Therefore, it is essential that the two-component water tank is adopted to obtain realistic outcome. However, the establishment of natural circulation in RELAP is very sensitive to initial conditions and simulation timestep and it is prone to oscillations. After numerous trials, the timestep immediately after the transient is fixed at 1.0 × 10 s and an initial temperature difference of 90oC between the −4 cold side of the condenser and the water tank is introduced. The natural circulation mass flow rate stabilizes at 110kg/s after some oscillations immediately after the transient, as shown in Figure 3-4.

Figure 3-3 Water tank temperature rise after SBO with and without natural circulation.

Figure 3-4 Natural circulation mass flow rate after SBO

As the simulation progresses, it becomes difficult to find the appropriate timestep to eliminate the instabilities and the simulation tends to abort itself. This error is 54

not physical but rather the limitation of RELAP. The reactor system is relatively simple after the transient, as all active parts are no longer functioning, and the decay heat is ultimately transferred entirely to the water tank. Therefore, a MATLAB model for this simplified system is established to evaluate the performance of the water tank after the RELAP model becomes too laborious to function. This is especially helpful in the sensitivity analysis in the next chapter, when many simulation runs are necessary. Typically, the MATLAB model is adopted 1 × 10 4 × 10 s, or 1 – 5 days after the transient. 5 5 − The input parameters of the MATLAB model are initial time, timestep and initial temperature, or average temperature of the water tank when the RELAP simulation terminates. Water tank is treated as a whole in the model, with an assigned volume. Total heat transferred to the tank is equal to decay heat, which is a function of time. At every timestep, the temperature rise in the water tank is calculated:

Q T =

Δ 𝑝𝑝 where density and heat capacity a𝑉𝑉𝑉𝑉re 𝐶𝐶obtained from the steam table. In the next timestep, 𝜌𝜌new density and heat𝐶𝐶𝑝𝑝 capacity are acquired under the newly increased temperature and the temperature rise is calculated again until it reaches boiling temperature. The combined result of the RELAP and MATLAB model on the water tank temperature is shown in Figure 3-5. The two parts transition smoothly. The average water tank temperature reaches the boiling point of 125oC (under the average pressure of the tank underground) 7.54 days after the transient. It is noteworthy that some surface boiling may already be present, at the top region of the tank is closer to the inlet and has smaller pressure. However, the bulk boiling is not expected to begin after this simulated result. Therefore, the design goal of a 7-day grace period after DBA is satisfied.

Figure 3-5 Water tank temperature after SBO

3.4 LOCA transient analysis

Nuward SMR has made design efforts to reduce the pipes connected to the vessel so as to limit the size of LOCA to 30 mm in diameter. In this way, large break LOCA is not possible in the reactor. Therefore, this section is dedicated to the analysis of small break LOCA (SBLOCA).

It is noteworthy that that there is no definitive path of development of events following a SBLOCA in PWRs. The design of the reactor and the geometry and location of the break may dramatically change the post-SBLOCA scenarios. In Three Mile Island, for instance, the use of once-through steam generators had a drastic effect on the impact of SBCLOA. SMRs rely on the larger water inventory in the integral vessel to balance the loss of inventory by switching from U-tube to once-through steam generators. Other factors affecting SBLOCA include the break size, the core bypass size, operator interactions, etc. 56

SBLOCA is triggered by a break in the primary side. To simulate the safety performance at the worst-case scenario, a break of 30 mm is chosen in RELAP. A valve with the corresponding area connecting the downcomer and the containment will open to initiate the transient. The SCRAM signal is imposed two seconds later, the safety system is put into use simultaneously, and the loss of feedwater is completed 20 seconds later. Because of the break, the reactor pressure vessel will experience a rapid decrease in pressure following the initiation of the transient. When the pressure on the primary side is lower than 15 bar , the passive accumulators begin injecting water into the vessel. The table below is the timeline of events for a LOCA transient.

LOCA analysis will focus on the short-term effect, such as break discharge, peak cladding temperature and peak containment pressure. Long-term performance – whether the water tank is able to sustain throughout the 7-day grace period will also be considered.

Table 3-3 Timeline of events for LOCA transient

Event Trigger Nominal operation = 0 s

Break in downcomer 𝑡𝑡= 200 s SCRAM 𝑡𝑡 = 202 Safety system opens SCRAM𝑡𝑡 time𝑠𝑠 Injection from the accumulator < 15 bar

Complete loss of feedwater SCRAM𝑃𝑃 time +20 s

Figure 3-5 (a)

Figure 3-5 (b)

Figure 3-5 (c)

Figure 3-5 (d)

Figure 3-5 (e)

Figure 3-5 (f)

Figure 3-5 (g)

Figure 3-5 (h)

Following the accident, the SCRAM signal initiates, and the reactor vessel internal control rods drops down to insert a negative reactivity. Figure 3-5 (a) shows the change in core thermal power. It decreases rapidly to decay heat level after the transient.

The break discharge mass flow rate and void fraction are shown in Figure 3-5 (b) and (c) respectively. Immediately after the transient, the mass flow rate reaches its maximum at 80 kg/s. The flow is subcooled at this stage. Flow rate decreases as the vessel depressurizes. When the pressure meets the saturation pressure with regard to the coolant temperature at the point, the flow becomes a two-phase mixture. Eventually, the transient progresses to the blow-down phase, where the discharge is mostly steam and the flow rate becomes very small. In both figures, there is fluctuation in both two-phase and blow-down periods. This is mainly caused by the accumulator injection, and the added numerical and physical instabilities in RELAP for two-phase mixture at low pressure.

As there is no automatic depressurization system (ADS), the vessel depressurizes following its natural curve as mass and energy are lost from the break. Approximately 1200 seconds after the transient, the pressure in the pressure vessel decreases to the same as it is in the containment and remains steady. When the pressure in the vessel has dropped below 15 bar, the accumulator is activated, and it injects cold water into the primary system by gravity. This takes places 546 seconds after the transient. The peak mass flow rate from the accumulator is 38kg/s.

With the core power dropped to decay heat level, there is a sharp decrease in PCT, which first decreases rapidly from nominal values to about 275 oC, then steadily drops further. The NRC limit for PCT is 2200oF, or 1204 oC. Throughout the transient, the core remains covered and PCT stays well below the limit even for the hottest pin, thus the integrity of the cladding is maintained.

As the transient progresses, the core outlet heats up due to both depressurization and decay heat. It reaches saturation approximately 200 seconds after the onset of 62

the transient. In a verification simulation for AP1000 during SBLOCA, Westinghouse chose a void fraction limit of = 90% as the indicator of the onset of core dryout (Wang et al, 2013). As shownα in Figure 3-5 (f), the maximum core outlet void fraction stays below the limit throughout the simulation, except at one point, which will not endanger core safety.

Due to the coolant with high temperature discharged into the sealed containment, pressure inside increases following LOCA. The peak containment pressure is around 4.3 bar, which occurs 100 seconds into the transient, below the 9-bar limit.

Water tank temperature is examined to see if the 7-day grace period can be satisfied after LOCA. As spikes and instabilities are more likely to occur in LOCA, RELAP aborts itself earlier than that in SBO analysis. The MATLAB model is adopted three hours into the simulation. Bulk boiling in the water tank after LOCA begins 7.34 days after the transient, that is to say that the safety goal can be reached in this

Figure 3-6 Water tank temperature after LOCA.

scenario too. Since no core uncover was experienced after LOCA, the grace period should be close to that of SBO as supported by the derived values. 63

In general, the transient analysis proves the reference model capable of performing residual heat removal. After either SBO or LOCA, the reactor is free from any potential structural damage or core melt. With the passive safety system, the 7-day grace period without any outside heat sink or power source can be achieved. Of course, detailed sensitivity and uncertainty analysis should be performed to verify the simulation results in the future.

Chapter 4 Optimization study

4.1 General description

Results from the transient analysis indicate that the current design satisfies the safety goal of 7-day grace period. For a small reactor to succeed, however, a high level of safety is not the only contributing factor. Due to considerably smaller economies of scale, small reactors need to find innovative ways to further reduce capital investments and risks.

The reference reactor has indeed adopted strategies to make itself competitive in the market. For instance, the integral containment is 5 times smaller than that of AP1000, which already adopts a compact design compared with traditional PWRs. This can help simplify manufacturing and lower the cost. The reference SMR also has a simple and fully passive safety system that eliminates the need for safety- grade electric power supply.

At the same time, however, there is still room for improvement in cost and risk reduction. Certain safety features prove to be conservative. For example, the water tank will not start boiling until more than 7 days after a station blackout transient. Since passive heat removal will not cease to function or noticeably degrade until the water evaporates to a point where the safety condenser is no longer submerged, which will take considerably more time, the grace period will be much longer than the design goal of 7 days.

Another design parameter that could improve the reference reactor’s economic performance is its cycle efficiency. The current Nuward design has a thermal output at 540 MW and an electrical power at 170 MW, which translates to a thermal efficiency of 31.5%. This is not a competitive number because modern PWR plants often have efficiencies around 33% and some more advanced models are designed with a higher number – EPR (European Pressurized Reactor) for instance, has an

efficiency of 36% (Kadak, 2017). If innovations on the power conversion system can be made to raise the efficiency, cost of electricity in dollar per kilowatt can be further reduced.

In this chapter, optimization pathways will be discussed with the goal of increasing power density while maintaining safety performance. This includes uprating the power, making modifications on the design of the water tank, safety condenser, pumps, steam generators, etc. while the fundamental features of the reference plant will remain unchanged.

4.2 Passive safety system optimization

This section focuses on the optimization of the water tank and the safety condenser in the passive safety system. Five optimization alternatives are considered with the goal of reducing the size of the system while maintaining safety performance.

1. Reduce the size of the tank. The current amount of water in the tank more than adequate for residual heat removal during the expected 7-day grace period. Therefore, a smaller tank will be sufficient to meet the goal. Potentially, this can reduce the cost associated with tank construction

2. Lower the condenser inlet. The condenser currently draws water from a point near the midplane of the water tank. Installation would be made easier if the inlet is lowered to allow the condenser to draw water from the bottom of the tank, but more gravitational pressure drop needs to be overcome for natural circulation to take place.

3. Eliminate the condenser. There are two loops in the passive safety system of the reference SMR, one connecting the secondary side of the safety steam generator and the condenser, the other the condenser and the water tank. This may be simplified by adopting a one-loop system, where the safety

CSGs directly draw water from the tank. This way, the size and cost of construction will be lowered.

4. Submerge the safety condenser in the water tank. In the current design, there are two loops in the safety condenser to cool the safety CSGs. The condenser can be moved out of the containment and cooled directly by the water that it submerges in. This is similar to the strategy adopted by the NuScale SMR (NuScale Power, 2017). This alternative will potentially have the same effect in passive cooling, as all the residual heat is ultimately transferred to the water tank either way, but it can reduce the size of the containment or the tank. Exactly how much reduction can be achieved by this alternative depends on the detailed information on the sizes and positions of components in the containment. Based on the size of the condenser and the schematic of the reference design in Figure 2-1, it is assumed that the containment diameter can reduce from 16 m to 14 m, which will result in a ~25% reduction in the containment volume.

5. Reduce the size of the tank and submerge the condenser. If the fourth alternative proves capable of residual heat removal beyond the designed 7- day grace period, a smaller tank may be sufficient too.

Figure 4-1 shows the cross-sectional view of the reactor. Components presented here include the pressure vessel, the containment, the safety condenser and the water tank. In Figure 4-1 (b), the water tank volume is reduced to half of its original value. The surface area of the tank remains the same, while the height is changed from 20 m to 10 m, covering only the top half of the containment. In Figure 4-1 (c), the inlet of the condenser is lowered by 8 m, making the elevation between inlet and outlet increase from 4 m to 12 m. Figure 4-2 shows the two alternative designs concerning the safety condenser. Figure 4-2 (a) corresponds to the third alternative design described above, and Figure 4-2 (b) the fourth.

Figure 4-1 (a)

Figure 4-1 (b)

Figure 4-1 (c) Figure 4-1 Different setups of the safety condenser and the water tank. (a) original design; (b) water tank with half of the original volume; (c) condenser with lower inlet 68

Figure 4-2 (a)

Figure 4-2 (b) Figure 4-2 Alternative setups of the safety condenser. (a) No condenser; (b) condenser submerged in the water tank.

A sensitivity study of the five modified designs is performed to compare their performance during transients with that of the reference design. LOFA, SBO and LOCA transients are simulated in RELAP to evaluate whether the modified designs can reach the safety goals. The timeline of events for both transients are the same as described in Chapter 3. The Areva rectangular CSGs are used, and only one of the safety CSGs is assumed to function during transient.

The third design alternative, where there is no safety condenser, is immediately eliminated. It is extremely difficult to provide effective cooling with this design. Flow in the secondary side of the safety CSGs is small and oscillating, and the passive safety system is therefore not able to cool the reactor following the transient, causing a large spike in the temperature and pressure of the primary coolant that exceeds safety limits. The other four alternatives are examined in detail.

For station blackout, both short-term and long-term effects are examined. PCT in the hottest pin immediately after the transient is checked to determine if the integrity of the fuel rod is maintained. Depressurization of the vessel and temperature rise in the water tank indicate the long-term performance of the passive cooling system.

For LOCA, emphasis is laid on the short-term effect. PCT in the hottest pin and peak containment pressure will be examined to determine whether the integrity of the reactor is maintained. Core void fraction will be looked at in case of boiling crisis. The depressurization in the reactor vessel and the coolant discharge rate are largely determined by the size, shape and location of the break, thus the changes in the passive safety system have little impact on them.

Figure 4-3 shows the RELAP simulation results after SBO for the reference design and the four modified versions. For short-term effect, all of the modified designs have similar performance to the original model. PCT experiences a sharp drop of 50oC after the onset of the transient in all designs. When the condenser is submerged, decrease in PCT is lower than when the condenser is in the containment, but it stays below the safety limit throughout the transient as well, thus the integrity of the cladding is maintained. Depressurization after SBO is steady and the pressure is stabilized 1 – 2 hours after the transient, although pressure at the end of the simulation is slightly different for the four designs. Theoretically, the original design and the design with a submerged full

condenser are capable of removing heat and depressurizing the vessel most efficiently and design with half the volume of the water tank least. The simulations show corresponding results. The pressure at the end of the un in the reactor vessel after depressurization in the latter case is higher than the former by 0.4 MPa.

For long-term effect of residual heat removal, the time it takes for bulk boiling to begin in the water tank for all the design alternatives are shown in Figure 4- 3 (c). When the condenser with lower inlet is adopted, the capability of the passive safety system is slightly lower, shortening the days before boiling from 7.54 days to 7.33 days. This difference is, however, miniscule, and they both satisfy the design goal of 7-day grace period with a considerable margin. When the condenser is submerged in the tank, the onset of boiling is slightly postponed to 7.82 days. This may be explained by the fact that direct cooling of the condenser is more effective than adopting a natural circulation loop. Reducing the size of the water tank to half has a significant impact, with bulk boiling now starting only 4.65 days after the transient for the condenser in containment and 4.92 days for the submerged condenser. However, as long as the condenser is still covered by water, the passive safety system will function to remove decay heat from the core. It is therefore worthwhile to extend the analysis beyond the starting point of bulk boiling in the water tank.

Figure 4-3 (a)

Figure 4-3 (b)

Days before boiling in SBO

lower-inlet 7.33

full-size 7.54

half-size 4.65 independent condenser

full-size 7.82

half-size 4.92 condenser in tank in condenser

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

Figure 4-3 (c)

A MATLAB model extending the one described in Chapter 3.3 to two-phase mixture is established to examine how long it takes before the water in the tank evaporates to a point where the top of the condenser, which is at the one-fourth tank height from the top, becomes uncovered. The mathematical equivalent for this scenario used in the model is when the upper half of the water tank has a void fraction of larger than 0.95. The homogeneous equilibrium model is used in the calculation of the void fraction:

1 = 1 1 + α 𝑔𝑔 − 𝑥𝑥 𝜌𝜌 𝑓𝑓 where is the quality, and the densit𝑥𝑥 𝜌𝜌ies of saturated vapor and liquid

respectively.𝑥𝑥 𝜌𝜌𝑔𝑔 𝜌𝜌𝑓𝑓

Figure 4-4 Void fraction in the upper half of the water tank after an SBO transient.

Water tank performance after SBO

full-size 13.11 7.82

half-size 8.02 4.92 condenser in tank in condenser

lower-inlet 12.48 7.33

full-size 12.69 7.54

7.81 condenser in contain. in condenser half-size 4.65

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

condenser uncovered bulk boiling

Figure 4-4 shows the simulation result for the half-size water tank with condenser in containment. The condenser will remain covered until 7.8 days after an SBO transient, meaning that the safety goal of 7-day grace period is still satisfied even with a water tank only half of its original size. The same simulation is performed for the other designs to find out their maximum capability of passive heat removal after transient. For a full-size water tank, the condenser will remain covered 5 days after boiling begins. Therefore, the better estimate of the grace period is 12 – 13 days instead of 7 days for these two designs. Again, no sensitivity or uncertainty quantification has been performed in this study as these estimates should be taken as preliminary.

Following a LOCA transient, the discharge and depressurization processes are similar for all the designs, thus only the change of reactor vessel pressure is shown here for reference. When the condenser is submerged, the depressurization curve is slightly different, but the pressure drops to containment pressure around the same time – 1200 seconds after the transient.

The peak containment pressure varies, due to the heat transfer between the containment and the water tank. When using a full-size tank, the peak containment pressure is 4.3 bar regardless of where the safety condenser is located, which occurs 100 seconds into the transient. For a half-size tank, the peak pressure is 7.3 bar. Compared with the 9-bar reference limiting pressure of the DCNS reactor, there is still a margin. Therefore, integrity of the containment can be maintained, and fission products retained with the half-size condenser.

The heating up of the water tank after LOCA is more rapid than that after SBO immediately following the transient. After break discharge flow rate has decreased to negligible and the system stabilized, the long-term effect of the passive safety system has a similar performance to that of SBO. With a full-size water tank, the grace period is 11 – 12 days and with a half-size, 6, regardless of where the condenser is located.

Figure 4-6 (a)

Figure 4-6 (b)

Figure 4-6 LOCA transient RELAP simulation results for the reference design, a modified design with water tank half of its original size and a modified design with lower inlet of the safety condenser. (a) Pressure in the vessel; (c) peak containment pressure.

Table 4.1 shows the sensitivity analysis result regarding the four alternative designs on their safety performance. The check mark indicates that the design has reached safety criteria – a PCT below 1204oC, a core void fraction of smaller than 0.9, and a peak containment pressure lower than 9 bars respectively. When using the full-size water tank, all safety criteria can be met. The grace period after the transient falls between 11 – 13 days, depending on how the safety condenser is installed. It is longer than the Nuward goal (7 days) and comparable to the passive cooling ability of NuScale (beyond 7 days). When using the half-size water tank, all criteria are met except that the condenser will be uncovered 6 days after the transient. Although this is slightly shorter than the goal of Nuward, it has nevertheless proved its long-term passive cooling capabilities, and should be sufficiently safe for commercial SMRs.

Table 4-1 Transient performances after SBO and LOCA for all five designs.

SBO LOCA

Depress. Grace Core void Peak contain. Grace PCT PCT of vessel period fraction pressure period

✓ Original (9.8MPa 12.69 ✓ 12.15 ✓ ✓ ✓ (4.3 bar) after 3h) Condenser ✓ in contain., (10.2MPa 7.81 ✓ 6.09 ✓ ✓ ✓ (7.3 bar) half tank after 3h) Condenser ✓ in contain., (9.9MPa 12.48 ✓ 11.83 ✓ ✓ ✓ (4.3 bar) lower inlet after 3h)

Condenser ✓ (9.8MPa 13.11 ✓ 12.65 submerged ✓ ✓ ✓ (4.3 bar) after 3h) Condenser ✓ submerged, (9.8MPa 8.02 ✓ 6.23 ✓ ✓ ✓ (7.7 bar) half tank after 3h)

4.3 Steam generator alternative

The rectangular CSG is used in the reference model. Another possible candidate for the steam generator in a small reactor is the PCHE. The general features of the PCHE are described in Chapter 2.1.2. The Heatric PCHE has horizontal semicircular channels with a flow area of 1.57 mm2 and hydraulic diameter of 1.2 mm. Thanks to higher heat transfer area to volume ratio, PCHE has higher power density compared to the rectangular CSG currently used in the model and can thus potentially make the reactor more compact, or remove higher thermal power from the integral vessel.

To test whether PCHE can be adopted in the design, a RELAP model is built and a steady state simulation is run. Like in the reference model, the six steam generators for normal operation and the two safety steam generators are modeled as two pairs of PIPE components respectively, each connected between themselves with a heat structure. Parameters were tested to find the size of PCHE that can produce the same amount of power as the rectangular CSG. Table 4-2 shows the geometry of the PCHE and a comparison between steady state simulation between the models adopting the two types of steam generators.

PCHE has a larger power density and larger heat transfer coefficients on both sides over the rectangular CSG. On the primary side, the pressure drop in the rectangular CSG is slightly smaller than that of PCHE. This is due to the fact that there is an upward flow in the primary side of the CSG, making the gravitational pressure drop to be negative, while in PCHE the flow is horizontal. On the secondary side, the pressure drop in PCHE smaller than that of the rectangular CSG. Both models are able to reach steady-state simulation and the designed values. As noted by previous studies, the prediction of boiling crisis, particularly for the PCHE with semicircular channels in horizontal flow is subject to much uncertainty and the table

values should be treated as preliminary (Shirvan et al, 2012).

Table 4.2 Comparison between the rectangular CSG and PCHE

Rectangualar CSG PCHE

# of channels 26020 132580

Power 90 MWth 90 MWth

Geometry

Heated length 1.5 m 0.3 m

Volume (no headers) 1.17 m3 0.37 m3

Power density 76.9 MW/m3 243.2 MW/m3

Primary side

Mass flow rate 3142 kg/s 3142 kg/s

Inlet temperature 280 oC 280 oC

Outlet temperature 307 oC 307 oC

Inlet pressure 15.0 MPa 15.0 MPa

Pressure drop 21 kPa 23 kPa Heat transfer 11470 W/m2K 44296 W/m2K coefficient Secondary side

Mass flow rate 300 kg/s 300 kg/s

Inlet temperature 227 oC 227 oC

Outlet temperature 286 oC 286 oC

Outlet pressure 7.0 MPa 7.0 MPa

Pressure drop 4.4 kPa 1.7 kPa Heat transfer 35271 W/m2K 40873 W/m2K coefficient

Using the geometric specifications calculated above, schematics of the steam generators in the reactor vessel are made, as shown in Figure 4-7. Both the CSGs for normal operations and the safety CSGs are included. A total of eight steam generators surround the core. Thanks to its compactness, the PCHEs spread sparsely in the vessel. It is therefore possible to increase the surface area of existing PCHEs if this is needed to work under uprated power. It is also possible to maintain

Figure 4-7 (a) Figure 4-7 (b)

Figure 4-7 (c)

its current size but install additional safety PCHEs if necessary, as shown in Figure 4-7 (c). For rectangular CSGs, the current size is close to their spatial limit in the reactor vessel.

Transient analysis following LOFA, SBO and LOCA is also carried out to examine PCHE’s impact on the safety performance. The timelines of events for both transients are the same as described in Chapter 3. In both scenarios, only one of the two safety PCHEs are assumed to be working in order to obtain a conservative result.

As the accident timeline and consequences are very similar for LOFA and SBO in this reactor, who relies on passive removal with no emergency feedwater system, the discussion of the two is merged. In general, PCHE demonstrates very similar performance to rectangular CSG. The minimum CHFR after LOFA in the core is 4.15, higher than CSG. This is due to the fact than PCHEs are smaller and provide a longer effective height to establish natural circulation which reduces the rate of decrease in flow. No boiling crisis will occur after the transient. The pressure in reactor vessel, peak cladding temperature and pressure in the safety system all show similar trends to the reference design with rectangular CSG. For long-term effect, when PCHE is used, the water tank starts boiling 7.49 days after the transient and the reactor has a grace period of 12.56 days, showing only a miniscule difference between rectangular CSG.

Figure 4-8 (a)

Figure 4-8 (b)

Figure 4-8 (c)

Figure 4-8 (d)

Figure 4-8 Comparison between models adopting rectangular CSG and PCHE after SBO (L OFA ) . (a) CHFR in the core; (a) pressure in reactor vessel; (b) peak cladding temperature; (c) pressure in the safety system.

PCHE is expected to experience more flow instabilities due to its small channels and non-conventional geometry. As shown in Figure 4-9, instability of the mass flow rate indeed occurs in the two-phase flow in the safety condenser when using PCHE. This will be discussed in detail in the Appendix.

Figure 4-9 Mass flow rate instability in PCHE

Following LOCA, PCHE demonstrates similar performance to rectangular CSG as well. As shown in Figure 4-10 (a), the depressurization process has almost the same trend and stabilizes at containment pressure around the same time (1200 s). Peak pressure in the containment is 4.3 bar when PCHE is used, same as the rectangular CSG result. The overall core void fraction is higher by approximately 0.1 with PCHE, and there is more fluctuation in the steam blow-down phase. However, only at a few instants is void fraction larger than 0.9. In terms of long-term cooling, using PCHE does not affect the grace period after LOCA.

Figure 4-10 (a)

Figure 4-10 (b) 84

Figure 4-10 (c)

Figure 4-10 Comparison between models adopting rectangular CSG and PCHE after LOCA. (a) pressure in reactor vessel; (b) pressure in the containment; (c) core outlet void fraction.

In general, replacing the rectangular CSG with PCHE has little impact on the safety either the short- or long-term performance of the safety system. Both designs would prove capable of passive heat removal after SBO or LOCA. PCHE has a higher power density and consequently smaller size, thus is has the potential of increasing the surface area or the number of steam generators in the case of power uprate. However, PCHE has yet to be extensively tested with two-phase flow while the existing experiments (Shin et al, 2017) and the simulation in this study show that it is more prone to instabilities. In addition, the existing correlations for pressure drop and CHF calculation may not be applicable to channels as small as those in PCHE and to a lesser degree, the rectangular CSGs. This will be discussed in the Appendix to better evaluate the prospect of adopting PCHE in the reactor.

4.4 Power uprating

The previous two sections mainly discussed ways of enhancing the compactness of the reactor, either – for instance – by reducing water tank size or adopting a more compact steam generator. With the goal of increasing power density in mind, this section will be dedicated to the power uprating of the reference reactor. First, the approaches of uprating the power, both thermal and electrical, will be examined. A transient analysis of the uprated model under SBO and LOCA will then be carried out. Lastly, the safety indications of the analysis will be discussed and a model with maximum power to volume ratio that satisfies the safety criteria will be proposed.

4.4.1 Power uprating approaches

The reference reactor has a thermal power of 540 MW and an electrical power of 170MW. The governing parameters, namely the enthalpy change across core and the efficiency, are both lower than the typical values for commercial PWR. The motivation for these lower values is discussed explicitly by Halimi and Shirvan, 2020. They are primarily driven by managing high peaking factors as the consequence of boron-free operation and the target to achieve longer than normal fuel cycle lengths. In both cases, the design targets can be relaxed, especially with the elimination of fuel limiting accidents including large break LOCA and rod ejection accident and therefore, there is room for improvement on both ends. In fact, in the study by Halimi and Shirvan, the feasibility of uprating an SMR similar to the reference core by a factor of 2 from neutronic and thermal-hydraulic point- of-view was confirmed.

In terms of thermal power, the designed coolant inlet temperature is 280oC and the outlet is 307oC, marking a difference of 27oC. This number is relatively small compared with the reference reactor’s larger-scale counterparts. AP-1000, for example, has the same inlet temperature but the temperature rise across core is 41oC. EPR, a design that stemmed from the same French roots as the reference

reactor, has an inlet temperature of 296oC and an outlet of 330oC (Framatome, 2005). EPR also has a higher efficiency of 36% compared with the 31.5% efficiency of the reference reactor.

The uprated core will use EPR parameters as reference. Two uprating approaches are proposed:

1. Increase thermal power by using EPR inlet and outlet temperatures and increasing primary coolant flow rate.

2. Same as 1 but assume EPR efficiency, which translates to increased feedwater flow rate.

Figure 4-11 Comparison between Nuward and EPR coolant temperatures.

To find the maximum allowed power under the two approaches, RELAP models are built in which several parameters, including primary and secondary flow rates, are iterated to achieve steady state operation. In the models, rectangular CSGs are used and the water tank and safety condenser adopt the reference design. Table 4- 3 shows the steady-state simulation results.

Table 4-3 Steady-state simulation results for the uprated reactor

Original design Approach #1 Approach #2

Thermal power 540 MW 681 MW 681 MW

Efficiency 31.5% 31.5% 36%

Electric power 170 MW 215 MW 245 MW

Increase in electric power / 26% 44%

Primary coolant flow rate 3142 kg/s 3354 kg/s 3354 kg/s

Coolant inlet temperature 280 oC 296 oC 296 oC

Coolant outlet temperature 307 oC 330 oC 330 oC

Feedwater flow rate 300 kg/s 378 kg/s 385 kg/s Secondary inlet 227 oC 227 oC 230 oC temperature Steam outlet temperature 286 oC 286 oC 293 oC

Steam pressure 7.0 MPa 7.0 MPa 7.8 MPa

The first approach is able to increase the electrical power by 26%, from 170 MWe

to 215 MWe. The second approach requires the secondary side pressure to increase from 7.0 to 7.8 MPa in order to match up with efficiency. This way, it can increase

the electrical power by 44% to 245 MWe.

The limiting factor for both of the approaches is the primary coolant flow rate. Spool-type pumps are used in the reference design, as described in Chapter 2. This type of pump has a maximum mass flow rate of 588.4 kg/s. Since there are six pumps in the vessel, considering a 5% margin, the primary coolant flow rate cannot exceed 3354 kg/s. Therefore, the thermal power of the reactor cannot be further increased. A solution to this problem is to increase the number of pumps if there is enough room in the reactor vessel.

A schematic of the pumps in the vessel is shown in Figure 4-12 (a). The diameter of the pump is assumed to be 0.75 m. If add two more pumps into the vessel, as shown in Figure 4-12 (b), the minimum distance between two pumps will be 0.2 88

m, sufficient to avoid pumps hitting each other due to vibration or maintenance. This way, the maximum primary coolant mass flow rate can be increased to 4472 kg/s.

Figure 4-12 (a) Figure 4-12 (b)

Figure 4-12 Schematic of the reactor coolant pumps in the core. (a) six-pump setup; (b) eight-pump setup

Considering the additional pumps, two more approaches to uprate the power are put forward:

1. Increase thermal power by using EPR inlet and outlet temperatures and maximum primary coolant flow rate.

2. Same as 1 but assume EPR efficiency.

The steady-state results are shown in Table 4-4.

Table 4-4 Steady-state simulation results for the uprated reactor with additional pumps.

Original design Approach #3 Approach #4

Thermal power 540 MW 956 MW 956 MW

Efficiency 31.5% 31.5% 36%

Electric power 170 MW 301 MW 344 MW

Increase in electric power / 77% 102%

Primary coolant flow rate 3142 kg/s 4472 kg/s 4472 kg/s

Coolant inlet temperature 280 oC 296 oC 296 oC Coolant outlet 307 oC 330 oC 330 oC temperature Feedwater flow rate 300 kg/s 530 kg/s 541 kg/s Secondary inlet 227 oC 227 oC 230 oC temperature Steam outlet temperature 286 oC 286 oC 293 oC

Steam pressure 7.0 MPa 7.0 Mpa 7.8 MPa

With the increased primary coolant mass flow rate, feedwater flow rates are increased dramatically in both cases to match with the power. The third approach is able to increase the electrical power by 77% to 301 MWe and the fourth approach can double the electrical power to 344 MWe. It is noted that it was found that the reference rectangular CSGs were able to accommodate the higher power density without degradation in performance, such as lower steam outlet temperature.

4.4.2 Transient analysis with uprated power

SBO and LOCA transient analysis are carried out to see evaluate the uprated reactor’s safety performance. The timeline of events for both transients are the same as described in Chapter 3. In both scenarios, only one of the two safety CSGs are assumed to function in order to obtain a conservative result.

The short-term effect of the transients on thermal power and core mass flow rate will be examined, as they have different initial values from the previous analysis. Parameters that indicate the performance of the safety system, such as peak cladding temperature, safety condenser uncovering time, core outlet void fraction, etc. will also be included.

For SBO (LOFA), after the SCRAM signal, core thermal power falls rapidly to decay heat level for the two uprated models after a 2-second delay. MCHFR for the uprated cores are 1.63 and 1.39 respectively, meaning that in both cases, boiling crisis will not occur. As it can be seen, now the uprated core has similar core average temperature and power density as a standard PWR, the MCHFR values are far closer to 1.0 which motivates future best estimate analysis. The primary coolant mass flow rate decreases rapidly as well following the SCRAM. When two additional pumps are used in the vessel and the steady-state mass flow rate is higher, its decrease after the transient is slower before reducing to approximately 50 kg/s like in the original model and the increased enthalpy model 2000 seconds post- transient. In terms of short-term effect, the peak cladding temperature decreases continuously after SBO for the uprated core, as shown in Figure 4-13 (c). For long- term cooling, the water tank can perform passive heat removal up to 9.69 days for the 681MWth core, when no pumps are added. If uprate the thermal output to

956MWth, the safety system can sustain for a grace period of 6.61 days.

Figure 4-13 (a)

Figure 4-13 (b)

Figure 4-13 (c)

Water tank performance after SBO for uprated core

6.61 ∆h↑ + 8 pumps 3.99

9.69 ∆h↑ + 6 pumps 5.81

12.69 original 7.54

0 2 4 6 8 10 12 14

condenser uncovered bulk boiling

Figure 4-13 (d)

Figure 4-14 shows the performance of the uprated core after LOCA. The depressurization of the reactor vessel first experiences a rapid fall immediately after the break in the primary loop. Afterwards, the decrease in pressure is at first slower when the thermal power is higher, but they eventually all converge to containment level. Peak containment pressure is 4.3 bar for both cases, same as the original value. There are more noticeable fluctuations and spikes when the power is uprated, but they all stayed well below the limiting pressure of 9 bar. The core outlet void fraction is shown on Figure 4-14 (c). The amount of steam produced in the core can be calculated by:

Q W = +

93ℎ𝑓𝑓 𝑓𝑓 Δℎ𝑖𝑖𝑖𝑖

where W is the steam generation rate in kg/s, Q is the decay heat, the latent heat under certain pressure and the inlet subcooling (Kukitaℎ 𝑓𝑓et𝑓𝑓 al., 1990;

Welter et al., 2005). For the upratedΔℎ core,𝑖𝑖𝑖𝑖 Q is higher. However, as shown in Figure 4-14 (a), the pressure in the vessel is also higher for the uprated core for the majority of the time, making the latent heat also higher than in the reference design. Under the influence of these two factors, the void fraction at the outlet is similar to the original model. For both power uprating approaches, only at a few instants is void fraction larger than 0.9, which will not have large negative impact on the safety of the core. In terms of long-term cooling, the performance of the passive safety system is similar to that of SBO. The grace period for the 681 MWth core is around 9 days, and for the 956 MWth core, it is around 6 days, still much longer than current operating PWRs.

The same transient analysis is performed for the alternative design where the condenser is submerged in the tank, as it has been proved to prolong the grace period. In general, when the core is uprated to either 681 MWth or 956 MWth if more pumps are employed, the short-term effects of SBO or LOCA can be successfully coped with by the safety system. All safety criteria can be met with considerable margin – a PCT below 1204oC, a void core void fraction of smaller than 0.9, and a peak containment pressure lower than 9 bar, as shown in Table 4.5.

In terms of long-term safety, the grace period for the 681 MWth core is around 9 days, satisfying the Nuward design goal. For the 956 MWth core, although the 6- day grace period is shorter than the goal, it is sufficiently long for a passive safety system.

Figure 4-14 (a)

Figure 4-14 (b)

Figure 4-14 (c)

Figure 4-14 Simulation results after LOCA for two models of uprated core: 1. 681MW thermal output; 2. 956MW thermal output 4.1.1(a) pressure Safety in the analysis reactor vessel with; (b) upratedpressure in powerthe containment ; (c) void fraction at core outlet

Table 4-5 Safety performance of the uprated core after SBO and LOCA.

LOFA SBO LOCA

Depress. Grace Core void Peak contain. Grace MCHFR PCT PCT of vessel period fraction pressure period

Original 3.55 12.69 12.15 ✓ ✓ ✓ ✓ ✓ Condenser 9.69 9.07 681 in contain. ✓ ✓ ✓ ✓ ✓ MW 1.63 Condenser core 9.86 9.15 submerged ✓ ✓ ✓ ✓ ✓ Condenser 6.61 6.11 956 in contain. ✓ ✓ ✓ ✓ ✓ MW 1.39 Condenser core 6.83 6.23 submerged ✓ ✓ ✓ ✓ ✓

According to the Nuclear Regulatory Commission (NRC), nuclear power plants should strengthen SBO mitigation capability for design basis and beyond design basis external events. Detailed recommendations include: (1) establishment of a minimum coping time of 8 hours, (2) preparation of the equipment, procedure, and training necessary to implement an extended SBO coping time of 72 hours for core and spent fuel pool (SFP) cooling, (3) establishment of pre-plan and pre-stage offsite resources to support uninterrupted core and SFP cooling. In order to find the minimum size of the passive heat removal system, a safety goal for the uprated small reactor is set based on NRC recommendations: a 72-hour grace period after SBO without external heat sink or power supply.

Using the 956 MWth core and the condenser submerged, the height of the water tank is adjusted to find its minimum size. With each height, a RELAP model is built. SBO simulation is ran in RELAP for 105 seconds and the MATLAB model is used subsequently to determine the time when the top of the condenser is uncovered. The timeline of events for SBO is the same as described in Chapter 3. The Areva rectangular CSG is used, and only one of the two safety CSGs is assumed to be functioning during the transient for a conservative result.

In the sensitivity analysis in Chapter 4.1, reducing the tank size to half approximately shortens the grace period by 60%. Therefore, at the first attempt, tank height of 10 m was chosen. Models with tank height of 8 m and 12 m were run simultaneously. Figure 4-15 shows the simulation results. When is water tank is 8 m in height, it still takes 3.5 days, or 84 hours, before the passive heat removal ceases to function. However, when the tank height is reduced to 6 m, the grace period is shortened to 2.88 days, or 69 hours. Finally, when the tank height is 6.5 m, the grace period is exactly 72 hours, and thus this is the minimum height of the water tank.

Figure 4-15 Grace periods after SBO for different water tank heights

A LOCA simulation is run for the optimized reactor model with a water tank height of 6.5 m to see if safety criteria are met. All the results show the same trends as the previous transient analysis. The table below shows the short-term effects of SBO and LOCA on this model. In general, both the short-term and long-term safety of the reactor are guaranteed.

Table 4-6 Short-term safety performance of the optimized after SBO and LOCA.

LOFA MCHFR 1.37 Continuous decrease, PCT o SBO below the 1204 C limit Depressurization of vessel Continuous decrease PCT Continuous decrease, below limit LOCA Core void fraction Below the 0.9 limit except at few points Peak containment pressure 8.6 bar, below the 9-bar limit

Chapter 5 Conclusions and future work

5.1 Conclusions

This work performs safety analysis for a compact integral small light water reactor during LOFA, SBO and LOCA. A parametric optimization study to reduce the reference reactor size and increase its power output while meeting safety goals is also performed.

With reference to the Nuward SMR, a RELAP model of the reactor is established and steady-state operation is achieved in agreement with the target design parameters. Following LOFA and SBO (the timeline of events for both transients and their outcomes are almost identical, as the reactor relies completely on passive heat removal), PCT experiences a continuous decrease and CHFR stays well above safety limit, with an MCHFR of 3.55. Following LOCA, no core uncover is experienced, containment pressure stays below the reference 9-bar limit, and PCT is below the 1204 oC-limit at all time. A grace period, where there is no external heat sink or power supply is estimated to be 12 – 13 days.

In the subsequent parametric study, changes in the configurations of the passive safety system are proposed. Transient analysis of these alternative designs indicates:

1. Reducing the tank size to half shortens the grace period to 7 – 8 days, which is sufficiently safe for commercial reactors, and can reduce cost in tank construction.

2. Submerging the condenser in the water tank prolongs the grace period by 10 hours, and can reduce the size of the containment to 76% of the reference design.

The possibility of replacing the rectangular CSG with PCHE is discussed. While having little impact on the safety performance, PCHE has a power density of 316% of the CSG. Potentially it can improve the compactness of the reactor or remove more thermal power from the vessel. However, instability is observed in RELAP and previous studies 99

point to the fact that existing empirical models may not be accurate in describing two- phase flow dynamics in such small channels. Therefore, the more rigorous study is needed if PCHE is to be used in the reactor.

By increasing the coolant enthalpy change which can also result in a higher thermal efficiency with reference to EPR values, the electrical output can be enhanced by 44% of the reference reactor without major design changes. Transient analysis is performed under this design and all parameters are within the safety limit. The grace period of this design is 9 – 10 days. Further uprating the power is limited by the maximum allowed flow rate in the RCPs. It is estimated that 2 more pumps can fit into the vessel, increasing the total number of RCPs to 8. With the increased primary coolant mass flow rate, the electrical output can be enhanced by 102%. All parameters meet the safety criteria after transients and the grace period of this design is 6 – 7 days. In order to find the most compact configuration with this uprated power that satisfies safety criteria of 72-hour grace period post-SBO, design parameters are iterated. It is found that the height of the water tank can be reduced from 20 m to 6.5 m (i.e. 1/3 of the original volume) with all parameters below the safety limit after transients. The significant increase in the power density of the nuclear systems should improve the economic performance of the reference design. Therefore, the optimized design demonstrates the potential to address the lack of economy of scale for small reactors and significantly improve operation and maintenance cost on a per kWh basis.

5.2 Recommended future work

To simulate a hydraulic system that relies on natural circulation in RELAP, the selection of timestep is crucial. Currently, the initial timestep of 1 × 10 s is selected −4 as a stable natural circulation flow can be established under this setup. Alternative timestep selection and methodologies can be explored to investigate its effect on the simulation result.

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In the model, the diversion of primary coolant from the normal operation CSGs to the safety CSGs is achieved by valves and control variables in RELAP. Currently, the flow path to the safety CSGs open simultaneously with the SCRAM signal, while the closure of the normal operation path and feedwater supply is gradual and takes 20 seconds. This is a reasonable setup after discussion with the vendor. However, the initial instants following a transient are crucial to effective heat removal. If a more detailed design is available, the model should be updated to revisit the transient analysis.

The lack of experimental data on two-phase flow in small channels is mentioned in this work. Existing empirical models may not be able to accurately predict two-phase behavior and instabilities are more likely to occur. This should raise a concern if PCHEs are used in the reactor, and to a lesser degree, rectangular CSGs. Due to the limitation of the models, RELAP results may not be entirely reliable without appropriate verification and validation.

In the optimization study, the possibility of increasing the number of steam generators (if PCHEs are used) and RCPs is discussed. Based on current information regarding the sizes of components in vessel, such changes are feasible. However, in the actual design, the piping configuration may be complicated, which would potentially hinder the prospect of adding new components. Therefore, this section should be revisited when more information is available.

The increase in core power density has impact on other parts of the design process, including fuel performance. While this study addressed the system wide response and the detailed neutronics and thermal hydraulics were performed as part of a separate study (Halimi and Shirvan, 2020), a fuel performance study should also be performed to verify feasibility of operation at such high power density (~125 kW/L).

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Appendix

PCHE benchmarking in RELAP

The use of PCHE as the steam generators in SMRs has been proposed by institutes such as MIT and KAIST to leverage the advantages in size and efficiency. However, two- phase flow heat transfer and transport phenomena in channels with such small hydraulic diameter are quite different from conventional large channels. For instance, there are concerns that channel blockage resulting from fouling and corrosion may be more severe in small channels. In addition, the accurate prediction of two-phase flow and heat transfer in such geometries may fail to be represented by existing models. Therefore, whether the RELAP model of PCHE can successfully capture its features and predict its performance needs to be verified with experimental data.

KAIST has constructed a test facility to study the thermal hydraulics of PCHEs in order to utilize them as steam generators. The objective of their experiment was to (1) identify the occurrence of instability under two-phase and superheated steam flow in PCHE, and (2) obtain pressure drop characteristics of PCHE and analyze them using different models. In this Appendix, a RELAP model of the facility is established to compare the experimental and simulation results.

Figure A-1 shows the schematic of the test facility. It consists of two parts: a primary side (red) that transfers heat from a heater and a secondary side (green) that draws water from a tank and condenses the heated steam. To imitate the behavior of the steam generator in a nuclear reactor, the maximum temperature of the fluid will reach 300oC, which requires a minimum pressure of 9 MPa. In order to reduce the cost and risk of high-pressure experiments, heat transfer oil that can stably heat up to designed temperatures under atmospheric pressure is used in the primary loop. The heater can supply a constant output of up to 100 kW. The hot side is heated until it reaches 300 oC at 1 bar, and the pump that circulates the heat transfer oil works up to 2.5 m /hr. Water 3 is the working fluid of the secondary side, which consists of a water storage tank, a 102

PCHE with a throttling valve and a water return line. During the experiment, this side will have water with mass flow rates ranging from 1 to 33 kg/min. At the PCHE outlet, the water becomes a saturated mixture or superheated steam. It is condensed and collected in the loop and will return to the inlet at the designated temperature. A throttling valves is installed to reduce instability and obtain steady-state results. When investigating the occurrence of two-phase instability, the degree of opening of the valve is adjusted accordingly.

Figure A-2 shows the geometry of the PCHE channels in the test facility. One basic unit is composed of two semicircular channels, in which the hot heat transfer oil flow, and one circular channel, in which flows the water. There are 2112 hot channels and 1056 cold channels in total. The outer wall of the PCHE is wrapped with a steel plate and insulated to prevent heat losses. The hot side adopts a zigzag shaped channel, while the simplest straight channels are used in the cold side to minimize pressure drop and reduce fouling.

A simplified RELAP model of the test facility is established. Since the subject of this study is solely the thermal-hydraulic characteristics of the PCHE, many components, such as the storage tank, pumps and the entire hot side, are eliminated and are represented by general tables or boundary conditions in the RELAP code. The model only includes the cold side, which is composed of two TIME DEPENDENT VOLUMES as the water inlet and outlet, a TIME DEPENDENT JUNCTION that controls the flow rate, a PIPE representing the PCHE and a SINGLE JUNCTION for connection, as shown in Figure A-3. The throttling valve is represented by an inlet form loss coefficient in the PIPE component. Table A-1 shows some important parameters for these hydraulic components calculated from KAIST publication. A heat structure is imposed on the PIPE component. Its left boundary condition is connected with the hydraulic volumes of the PIPE, while the right boundary is described by general tables to represent the hot side. Table A-2 shows the properties of the hot side fluid.

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Figure A-1 KAIST PCHE test facility [Image from (Shin, 2017)]

Figure A-2 (a) Figure A-2 (b)

Figure A-2 Geometry of the PCHE channels (Shin, 2017) (a) cross section of one basic unit; (b) flow path of the hot channel (left) and cold channel (right)

Figure A-3 RELAP model of the KAIST PCHE test facility

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Table A-1 Properties of the hydraulic components of the cold side in RELAP

Parameter Value

PCHE total Area 3.66 × 10 m −3 2 Channel Hydraulic Diameter 2.10 × 10 m −3 PCHE Length 0.6 m

Mass flow rate 0.017 0.55 kg/s

PCHE form loss coefficient 50 – 260−

Table A-2 Properties of the hot side fluid in the KAIST test facility

Parameter Value

Viscosity 4.98 × 10 Pa s −4 Density 691 kg/s ∙

Specific heat 2893 kJ/(kg K)

Thermal conductivity 0.11 W/(m ∙K)

Reynold’s number 713088 ∙

Prandtl’s number 12.8

Dittus-Boelter correlation can be used here to calculate the heat transfer coefficient of the hot side:

Nu = 0.023Re . Pr . = 3066 0 8 0 4

Nu = = 2.70 × 10 W/(m K) 𝐾𝐾 5 2 ℎ ∙ 𝐷𝐷 Other boundary conditions include an initial temperature of 300oC and a constant heat flux of 1.46 × 10 W/m , since the power output of the hot side is at 100 kW. A 4 2 complete set of conditions that defines the model in the same way as the test facility is therefore established.

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Two tests performed on the KAIST test facilities are carried out in RELAP following the same procedure:

1. Steady state pressure drop across PCHE at different mass flow rate. This is to test whether the Lockhard-Martinelli model used in RELAP can capture the characteristics of two-phase flow in small channels.

2. Flow instability at different mass flow rate. This is to test whether the instability in the RELAP simulation with PCHE, as mentioned in Chapter 4, is in accordance with the physical instabilities seen in experiment.

For test 1, the form loss coefficient is set as 260 to obtain steady-state result. The secondary side pressure is 5.5 bar and the PCHE inlet temperature is 85oC. The tested flow rate ranges from 2 to 24 kg/min. Figure A-4 (a) shows the comparison between KAIST experimental result and RELAP simulation result. When the mass flow rate is as high as 24 kg/min, the PCHE outlet is still subcooled. At this point, the two results agree with each other. However, in the two-phase region, the experimental result shows a higher pressure drop in general.

Figure A-4 (b) is extracted from KAIST publication and it shows how accurately different void fraction models predict the pressure drop in PCHE. As shown in both Figure A-4(a) and (b), the pressure drop calculated using Lockhart-Martinelli model is lower than experimental result in general. Among the six models, Thom’s correlation (1964) is shown to be the closest to experimental data. However, it is very likely that the authors made an error when calculating the void fraction. In an attempt to reproduce Figure A-4 (b), Thom’s correlation proved to be no better than Baroczy or Lockhart- Martinelli.

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Figure A-4 (a) Figure A-4 (b) Figure A-4 Steady state pressure drop in PCHE at different mass flow rate. (a) Comparison between KAIST experiment and RELAP simulation results; (b) calculated pressure drop curves with various void fraction models by KAIST [Image from (Shin, 2017)]

For test 2, a form loss coefficient of 50 is chosen to investigate the instabilities. As shown in Figure A-5, instabilities occur in RELAP when the mass flow rate is low. The instability in the figure is identified as density wave oscillation (DWO). The average fluid velocity is 0.67 m/s. The channel length in the RELAP model is 0.6 m, thus the residence time is 0.9 s. The period of the oscillation shown below is around 1.5 s, which is on the same order of magnitude as twice the residence time. As mass flow rate increases, the flow becomes stable. DWO is also identified in the low mass flow rate region in the KAIST experiment.

Figure A-5 Density wave oscillation in the low mass flow rate region in RELAP

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The amplitude of DWO at different mass flow rates is shown on Figure A-6. In RELAP, instability occurs when the mass flow rate is lower than 6 kg/min, while in the KAIST experiment, the first steady state result is at a mass flow rate of 5.5 kg/min. DWO amplitude for both simulation and experiment is large when the mass flow rate is smaller than 3 kg/min and becomes smaller as the mass flow rate increases. In general, RELAP simulation result on two-phase instability is in agreement with the experimental data.

Figure A-6 (a) Figure A-6 (b)

Figure A-6 Two-phase instability in PCHE at different mass flow rate. (a) RELAP simulation results; (b) KAIST experiment results [Image from (Shin, 2017)]

In summary, compared with experimental data, RELAP underestimates the pressure drop in PCHE. This could mean that RELAP is not accurate in predicting natural circulation in the reactor when PCHE is used as well. The void fraction models tested by KAIST and this study, including homogeneous, Zivi, Baroczy, Thom, Turner-Wallis and Lockhart-Martinelli, all fail to agree with experimental result. In terms of two- phase instability, or DWO in particular, RELAP produces similar results as the KAIST experiment. Both the simulation and the experiment show that instability may be significant in PCHE, especially when the mass flow rate is low.

Although the preliminary results provide some insight into the potential challenges of utilizing PCHE in nuclear reactors, more rigorous study needs to be carried out. There are new experimental studies on two-phase flow in small channels. For instance, 108

Kromer (2019) investigated experimentally the use of a microchannel heat exchanger in the Integral Inherently Safe Light Water Reactor, the results of which could aid the further validation of PCHE in reactor for this study.

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