Nghiên cứu hiện tượng chuyển pha trong vùng hoạt lò phản ứng

Table 3.26 Average void fraction calculation results with different Nusselt number correlations ...79 Table 3.24 CFX and CTF results comparisons versus experiment void fraction ...80 Ta

BỘ GIÁO DỤC VÀ ĐÀO TẠO

TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI

HOÀNG MINH GIANG

NGHIÊN CỨU HIỆN TƯỢNG CHUYỂN PHA TRONG VÙNG HOẠT

LÒ PHẢN ỨNG

LUẬN ÁN TIẾN SĨ CƠ HỌC

Hà Nội – 2016

LỜI CAM ĐOAN

Văn Hiền

Các số liệu, những kết luận nghiên cứu được trình bày trong luận văn này trung thực và chưa từng được công bố dưới bất cứ hình thức nào

Tôi xin chịu trách nhiệm về nghiên cứu của mình

Nguyễn Đông

BỘ GIÁO DỤC VÀ ĐÀO TẠO

TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI

HOÀNG MINH GIANG

NGHIÊN CỨU HIỆN TƯỢNG CHUYỂN PHA TRONG VÙNG HOẠT

LỜI CAM ĐOAN

Tôi xin cam đoan luận án là công trình nghiên cứu của bản thân tôi dưới

sự hướng dẫn của tập thể giáo viên hướng dẫn

Các kết quả nêu trong luận án là trung thực, không sao chép của bất kỳ công trình nào và chưa từng được công bố trong bất kỳ công trình nào khác

Hà Nội, ngày 27 tháng 4 năm 2016

NGHIÊN CỨU SINH

HOÀNG MINH GIANG Hướng dẫn 1

PGS NGUYỄN PHÚ KHÁNH

Hướng dẫn 2

TS TRẦN CHÍ THÀNH

LỜI CẢM ƠN

Trước hết, tôi xin bày tỏ lòng kính trọng và biết ơn tới: PGS Nguyễn Phú Khánh và TS Trần Chí Thành, những người thày đã trực tiếp hướng dẫn, giúp đỡ tôi trong quá trình học tập và thực hiện luận án

Tôi xin chân thành cảm ơn các thày cô tại Bộ môn Kỹ thuật Hàng không

và Vũ trụ, Viện Cơ khí Động lực; cảm ơn TS Lê Văn Hồng, Viện Năng lượng Nguyên tử Việt Nam, chủ nhiệm đề tài độc lập cấp nhà nước (mã số ĐTĐL.2011-G/82) ―Nghiên cứu, phân tích, đánh giá và so sánh hệ thống công nghệ nhà máy điện hạt nhân dùng lò VVER-1000 giữa các loại AES-91, AES-

92 và AES-2006‖, các đồng nghiệp Hoàng Tân Hưng, Trung tâm An toàn hạt nhân, Nguyễn Hữu Tiệp, Trung tâm Năng lượng hạt nhân, Viện Khoa học và Kỹ thuật hạt nhân đã giúp đỡ, tạo điều kiện để tôi có thể hoàn thành luận án này

Tôi cũng xin trân trọng cảm ơn Ban lãnh đạo Viện Khoa học và Kỹ thuật hạt nhân, Viện đào tạo Sau đại học của Trường Đại học Bách Khoa Hà Nội đã

cử tôi đi đào tạo cũng như tạo điều kiện thuận lợi trong quá trình thực hiện luận

án

Hà nội ngày 27/4/2016 Nghiên cứu sinh

Hoàng Minh Giang

STUDY ON PHASE CHANGE IN THE CORE OF

NUCLEAR REACTOR

TABLE OF CONTENTS

Abbreviations and Nomenclature 8

List of Tables 12

List of Figures 14

Overview 17

Chapter 1 Introduction to research work 19

1.1 Status of nuclear power in the World and Vietnam 19

1.2 Brief overview of nuclear safety 20

1.3 Core thermal hydraulics safety analysis in transient condition 21

1.3.1 Role of void fraction in simulation of two phase flow 24

1.3.2 Experiment overview for bundle of sub channel analysis 25

1.3.3 Void fraction prediction study 26

1.4 VVER technology understanding related to this study 27

1.5 Thesis objectives 29

1.5.1 Studied object 30

1.5.2 Scope of study 30

1.6 Thesis outline 31

Chapter 2 Overview of phase change models in code theories with different scales 33

2.1 Multi code and multi scales approach to PWR thermal hydraulic simulation 33

2.1.1 Neutron codes and thermal hydraulics codes 33

2.1.2 Different scale of thermal hydraulic codes 34

2.1.3 Different thermal hydraulic modeling approaches 36

2.2 Phase change models in system code RELAP5 38

2.3 Phase change models in sub channel code CTF 40

2.3.1 Evaporation and condensation induced by thermal phase change 40

2.3.2 Evaporation and condensation induced by turbulent mixing and void drift 42

2.4 Phase change models in meso scale code CFX 42

2.4.1 Evaporation at the wall 42

2.4.2 Condensation model in bulk of liquid 43

2.5 Conclusions 44

Chapter 3 Phase change models verification and assessment by numerical simulation 45

3.1 Brief information of VVER-1000/V392 45

3.2 Verification of RELAP5 simulation models for VVER-1000/V392 reactor with SAR 47

3.2.1 Nodalization scheme 48

3.2.2 Verification of modeling through steady-state study 48

3.3 CTF models verification and assessment with BM ENTEK tests 51

3.3.1 ENTEK BM facility 51

3.3.2 Modeling by CTF 53

3.3.3 Results and discussions 53

3.4 Verification CFX models with PSBT sub channel tests 59

3.4.1 PSBT test section for single sub channel 60

3.4.2 Mesh generation study 61

3.4.3 Solver convergence study 63

3.4.4 Mesh refinement study 64

3.4.5 Sensitivity study on physical models 68

3.4.6 Assessment of CFX and CTF modeling results in comparison with PSBT single channel 79

3.4.7 Discussion on CTF and CFX void fraction predictions 82

3.4.8 Improvement of CFX void fraction prediction in saturated region 84

3.5 Conclusions 86

Chapter 4 Void fraction prediction in hot channel of VVER-1000/V392 88

4.1 Calculation Diagram 88

4.2 Power distribution calculation by MCNP5 code 90

4.3 LOCAs simulation by RELAP5 code 93

4.4 Void fraction prediction in hot channel during transient by CTF code 96

4.4.1 VVER-1000/V392 void fraction prediction by CTF 96

4.4.2 Discussion on RELAP5 and CTF void fraction predictions 98

4.5 Void fraction prediction in single channel by CFX code 100

4.5.1 Mesh refinement study 101

4.5.2 Void fraction prediction calculated by CFX along sub channel 102

4.6 Void fraction prediction in bundle of channel calculated by CFX code 104

4.7 Conclusions 107

Conclusions and proposals 108

Achievements and new findings given by the thesis 108

Proposal of future work 110

References 112

List of Author’ papers and report 116

Abbreviations and Nomenclature

Abbreviations

VVER-1200/V491 A type of Russia reactor with capability of 1200 MWe

VVER-1000/V392 A type of Russia reactor with capability of 1000 MWe

DID Defend in depth policy in nuclear power plant design

Castellana The 4 x 4 square rod bundle test for fuel rod in Columbia University

(USA)

BM ENTEK The BM Facility at the Research and Development Institute of Power

Engineering (RDIPE; a.k.a., ENTEK and NIKIET) models the forced circulation circuit of RBMK type reactors

RBMK-1000 A type of Russia reactor of 1000 MWe with transliteration of Russian

characters for graphite-moderated boiling-water-cooled channel-type reactor

Corporation (NUPEC, Japan) PWR sub channel and bundle tests

(USA) RELAP5 System code developed by Information Systems Laboratories, Inc

Rockville, Maryland Idaho Falls, Idaho COBRA-TF Coolant-Boiling in Rod Arrays—Two Fluids (COBRA-TF) is a Thermal

Hydraulic (T/H) simulation code designed for Light Water Reactor (LWR) vessel analysis developed by Pacific Northwest Laboratory

RELAP-3D Newest version of RELAP5 with coupling with COBRA-TF

Belene A site for nuclear power plant project in Bulgaria

Ansys CFX A Computational Fluid Dynamics developed by Ansys

0D, 1D, 2D Dimension of spatial averaging

LES Large Eddy Simulation

meso scale The spatial scale with size around 1mm and less simulated with RANS

LBLOCAs Large break for loss of coolant accident

OECD/NRC BFBT UPEC BWR Full-size Fine-mesh Bundle Test (BFBT) Benchmark

αcrit Void fraction corresponding with critical heat flux correlation

Super-heated vapor interfacial area per unit volume (m-1)

C pl Liquid specific heat, constant pressure (J/kg.K)

C pv Vapor specific heat, constant pressure (J/kg.K)

h Vapor saturation enthalpy (J/kg)

h Sub-cooled liquid interface heat transfer coefficient (W/m2.K)

h Sub-cooled vapor interface heat transfer coefficient (W/m2.K)

h Super-heated liquid interface heat transfer coefficient (W/m2.K)

h Super-heated vapor interface heat transfer coefficient (W/m2.K)

h c Chen correlation heat transfer coefficient (W/m2.K)

h Vapor interface heat transfer coefficient (W/m3..K)

h Liquid interface heat transfer coefficient (W/m3..K)

Wall heat transfer to liquid for convection (W)

Qwif , Q boil Wall heat transfer to liquid for vaporization (W)

Liquid density (kg/m3) Vapor density (kg/m3)

Vapor generation from near wall (kg/m3.s) Total Vapor Generation (kg/m3.s)

Γ’’ Evaporation rate (kg/m2.s)

T chf ,T crit Critical heat flux temperature (K)

h nb Nucleate-boiling heat transfer coefficient (W/m2.K)

h fc Forced-convective heat transfer coefficient (W/m2.K

h c Chen correlation heat transfer coefficient (W/m2.K)

g Gravitational acceleration (m/s2)

f Bubble detachment frequency (s-1)

A s Conductor surface area in mesh cell (m2)

Inverse Martinelli factor

𝑞 Volumetric heat transfer from the wall (W/m3)

𝑞 Total wall heat flux (W/m2)

𝑞 Quenching heat flux (W/m2)

𝑞 Evaporative heat flux (W/m2)

𝑞 Convective heat flux (W/m2)

Local mean bubble diameter (m)

Liquid temperature (K)

Mesh-cell area of phase k (m2) Chen suppression factor

Heat transfer per volumetric unit (W/m3)

̅ Mixing mass flux (kg/m3.s)

List of Tables

Table 1.1 Multiple levels of protection from DID approach (source [45]) 20

Table 1.2 Content of Safety Analysis Reports (source [45]) 21

Table 1.3 Castellana 4x4 test characteristics (source [29]) 25

Table 1.4 EPRI 5x5 characteristics for test 74 and test 75(source [29]) 25

Table 1.5 Geometry and power shape for Test Assembly B5, B6, and B7 (Source [1]) 25

Table 2.1 Main characteristics of codes with four different scales (source [11]) 36

Table 2.2 Main characteristics modeling approaches for three main types of single-phase CFD 37

Table 3.1 Main technical characteristics of VVER-1000/V392 (source[36]) 46

Table 3.2 Comparison of steady-state of VVER-1000/V392 48

Table 3.3 Boundary conditions for event number 3 (source [35]) .49

Table 3.4 Chronological sequence of Event 3 from SAR [35] and this study 50

Table 3.5 Setting for base case and sensitivity cases according to test 01 and test 17 53

Table 3.6 Base case void fraction distribution calculations versus experiment for cases at 3MPa .54

Table 3.7 Base case void fraction distribution calculations versus experiment for cases at 7MPa .54

Table 3.8 Deviation of void fraction distribution calculation results versus experiment 55

Table 3.9 Deviation of void fraction distributions on input uncertainties 58

Table 3.10 Maximum deviation of void fraction distribution on input parameters versus base case 58

Table 3.11 Experimental uncertainties on input parameters 60

Table 3.12 Test Conditions for Steady-State Void Measurement of selected runs 61

Table 3.13 Mesh characteristics 62

Table 3.14 y+ predicted by Mesh 1 62

Table 3.15 y+ predicted by Mesh 2 62

Table 3.16 y+ predicted by Mesh 3 63

Table 3.17 Two phase flow model setting 63

Table 3.18 Average void fraction calculations between three meshes and experiment value 64

Table 3.19 Radial distribution of pressure and temperature for different refinement meshes 64

Table 3.20 Radial distribution of velocity and void fraction for different refinement meshes 65

Table 3.21 Average void fraction calculation at given cross section with or without modeling 69

Table 3.22 Calculation results of average void fraction 73

Table 3.23 Average void fraction calculation with different scale of bubble mean diameter 75

Table 3.24 Average void fraction calculation results with different Nref 77

Table 3.25 Average void fraction calculation results with different bubble departure diameters 78

Table 3.26 Average void fraction calculation results with different Nusselt number correlations 79

Table 3.24 CFX and CTF results comparisons versus experiment void fraction 80

Table 3.25 Comparison of CFX and CTF results and experiment void fraction in saturated region 81

Table 3.26 Comparison of CFX and CTF results versus experiment in case of high pressure 81

Table 3.27 Comparison of CFX and CTF results and experiment void fraction 82

Table 3.28 Void fraction and temperature super heating before and after calibration 85

Table 4.1 Main technical characteristics of fuel assembly for VVER-1000/V392 90

Table 4.2 Case studies for void fraction prediction 94

Table 4.3 Boundary condition of LOCA coupled with SBO for analysis 94

Table 4.4 Data related to phase change of interfacial area for case LB01002B at 15s of transient 99

Table 4.5 Cases for void fraction prediction in single channel by CFX 101

Table 4.6 Average void fraction for different meshes 102

Table 4.7 Void fraction prediction by CTF and CFX at downstream of channel at z = 3.48m 102

Table 4.8 Sub cooled selected regions for CFX investigation 105

Table 4.9 Saturated selected regions for CFX investigation 105

List of Figures

Figure 1.1 Nuclear power generation by country in 2013 (source [46]) 19

Figure 1.2 Multiple physical barriers in DID policy (source [45]) 22

Figure 1.3 Heal flux versus temperature difference for pool boiling heat transfers (source [31]) 23

Figure 1.4 Types of boiling flow crisis (source [25]) 23

Figure 1.5 Critical heat flux in uniformly core (source [25]) 24

Figure 1.6 Development of VVER nuclear reactor technology chart [32] 28

Figure 1.7 Multi-scale analysis of reactor thermal hydraulics (source [11]) 29

Figure 1.7 (a) temperature distributions in a cylindrical fuel pin, (b) flow regime 31

Figure 2.1 Relations between MCNP5, system code RELAP5 and component code CTF 33

Figure 2.3 System code capabilities for reactor thermal hydraulics (source [7]) 34

Figure 2.4 Control volume and axial flow area defined in sub channel code 35

Figure 2.6 The tree of two-phase thermal hydraulic modeling approaches (source [11]) 38

Figure 2.7 Schematic of vertical flow regime map in RELAP5(source [19]) 40

Figure 2.8 CTF normal-wall flow regime maps (source [38]) 41

Figure 3.1 Side view of primary system of VVER-1000/V392 (source [36]) 46

Figure 3.2 Primary system and safety system for VVER-1000/V392 (source [37]) 47

Figure 3.3 VVER-1000/V392 nodalization schemes in this study 48

Figure 3.4 (a) Cladding temperature from calculations, (b) Cladding temperature from SAR 51

Figure 3.5 Test section (Heat Release Zone, φ is diameter in mm) 52

Figure 3.6 BM ENTEK modeling by CTF 53

Figure 3.7 Radial void distribution of the test T04 56

Figure 3.8 Cross mass flow due to turbulent mixing and void drift 56

Figure 3.9 Maximum and minimum voiding curves versus experiment 57

Figure 3.10 Maximum and minimum voiding curves versus experiment 57

Figure 3.11 Uncertainty void fraction distributions for test T01 58

Figure 3.12 Test section for central sub channel void distribution measurement (source [1]) 60

Figure 3.13 Cross section of three proposed meshes 62

Figure 3.14 Base line for radial distribution investigation 64

Figure 3.15 S14326 Radial distribution of void fraction 66

Figure 3.16 S16222 Radial distribution of void fraction 66

Figure 3.17 S12211 Radial distribution of void fraction 67

Figure 3.18 S14326 Axial sub channel distribution of void fraction 67

Figure 3.19 S16222 Axial sub channel distribution of void fraction 68

Figure 3.20 S12211 Axial sub channel distribution of void fraction 68

Figure 3.21 S14326 Radial distribution of void fraction of full sub models 70

Figure 3.22 S144411 Radial distribution of void fraction of full sub models 70

Figure 3.23 S12211 Radial distribution of void fraction of full sub models 71

Figure 3.24 S14411 Radial distribution of void fraction of full sub models 71

Figure 3.25 S16222 Radial distribution of void fraction of full sub models 72

Figure 3.26 S14326 Radial distribution of void fraction of full sub models 72

Figure 3.27 S11222 Radial distribution of void fraction with different turbulent 73

Figure 3.28 S16222 Radial distribution of void fraction with different turbulent 74

Figure 3.29 S14326 Radial distribution of void fraction with different turbulent 74

Figure 3.30 S12211 Radial distribution of void fraction with different scale 75

Figure 3.31 S16222 Radial distribution of void fraction with different scale 76

Figure 3.32 S14326 Radial distribution of void fraction with different scale 76

Figure 3.33 (a) Bubble departure size, (b) Heat flux partition with different models 79

Figure 3.34 Temperature distribution along axial and radial channel 84

Figure 3.35 Temperature superheating and void fraction before and after calibration 86

Figure 4.1 Two-phase thermal hydraulic modeling for RELAP5, CTF and CFX 88

Figure 4.2 Geometry of sub channel in VVER-1000/V392 fuel assembly 89

Figure 4.3 VVER-1000/V392 void fraction prediction chart using multi codes and multi scales 90

Figure 4.4 The sixth of core loading pattern and whole core geometry for MCNP5 simulation 91

Figure 4.5 Relative power distribution in the sixth of the whole core 92

Figure 4.6 Distribution of relative power along axial hot channel 93

Figure 4.7 Distribution of relative power in the hot channel 93

Figure 4.8 (a) Whole fuel assembly simulated as hot channel and (b) the active part 95

Figure 4.9 Average void fraction calculated by RELAP5 on exit of active region in hot channel 95

Figure 4.10 Taken twelfth of whole bundle for void fraction prediction .96

Figure 4.11 Cross section of CTF modeling for the selected part of the whole bundle 97

Figure 4.12 Void fraction prediction by CTF and RELAP5 for LBLOCAs 97

Figure 4.13 Void fraction prediction by CTF and RELAP5 for SBLOCAs 98

Figure 4.14 Total vapor generation rate and vapor generation rate near wall 98

Figure 4.15 Total vapor generation rate and vapor generation rate near wall 99

Figure 4.16 Three meshes used to simulate geometry of single channel 101

Figure 4.17 Average void fraction along channel with different meshes 102

Figure 4.18 Axial sub channel void fraction prediction by CFX and CTF 103

Figure 4.19 (a) Overview of mesh (b) Zooming of mesh 105

Figure 4.20 Four cases with specific timing for study by CFX 105

Figure 4.21 Improvement by CFX in left pictures and upper and lower bounds in right pictures 107

Overview

Phase change in the nuclear reactor core is related to safety criteria such as Departure of Nucleate Boiling (DNB) during normal and transient conditions So that, a lot of computer codes with verification and validation against experiment are used to investigation of thermal hydraulics behavior of vertical boiling flow in core channel with system and component scales Until now, even many studies on boiling flow are implemented in CFD scale codes, but their utilization to specific nuclear reactor is not yet applied Thus, the utilization of many codes including CFD scale (Ansys CFX) to investigate void fraction in hot channel of VVER-1000/V392 reactor core is studied in this work Due to VVER-1000/V392 nuclear reactor is a candidate for Ninh Thuan 1 nuclear power project, so that the understanding of VVER’s reactor technologies including research works of this thesis is important to develop competence of nuclear safety in Vietnam

In this thesis, the numerical simulation is used to investigate boiling flow in the core channel

of VVER-1000/V392 reactor with verification and validation against experiment with similar Pressurized Water Reactor conditions

The thesis includes four chapters together a conclusion in the last Chapter 1 mentions about introduction that leads to motivation of this study Chapter 2 presents the methodology related

to multi scale analysis along with the code theories at different scale for RELAP5, CTF and Ansys CFX with focus on phase change models The verification and assessment of modeling used in these codes versus experiment data are presented in chapter 3 The system simulation results are compared with those in SAR documents The assessment of CTF code is implemented by simulation BM ENTEK experiment tests which is an International Standard Benchmark to investigate boiling flow through Russian fuel bundle of RBMK reactor The meso scale code Ansys CFX is verified with PSBT single sub channel which is also an International Standard Benchmark as well Chapter 4 presents the simulation of VVER-1000/V392 by three scales with system, component and CFD codes corresponding with RELAP5, CTF and Ansys CFX, respectively Void fraction in hot channel of the core is predicted by utilization of CTF and Ansys CFX codes

It is summarized several main contributions from the thesis as following:

 It is proposed a reality of best estimate approach in void fraction prediction by utilization of multi codes and multi scale including MCNP5, RELAP5, and CTF for analysis of void fraction behavior in the core during transient

 It is established a procedure of utilization of CTF and Ansys CFX for improvement of void fraction prediction as following: (a) at sub cooled region, corresponding with small bubble flow regime, Ansys CFX results is used; (b) in saturated boiling region, CTF and Ansys CFX void fraction curves along the channel is used as upper bound and lower bound to predict void fraction in the core

 It is found that, in saturated boiling region, the wall boiling model built in Ansys CFX

is incorrectly partitioned heat flux to corresponding parts in convective, quenching and evaporative This issue causes Ansys CFX gives under prediction of void fraction in saturated boiling region It is proposed a calibration for bubble departure diameter and

maximum area fraction to improve void fraction prediction by Ansys CFX in saturated region

Chapter 1 Introduction to research work

1.1 Status of nuclear power in the World and Vietnam

Nuclear technology uses the energy released by splitting the atoms of certain elements After Second World War, nuclear technology turned to peaceful purposes of nuclear fission for power generation Today, as updated in February 2015 [46], the world produces as much electricity from nuclear energy as it did from all sources combined in the early years of nuclear power Civil nuclear power now can boast over 16,000 reactor years of experience and supplies almost 11.5% of global electricity needs The 31 countries host over 435 commercial nuclear power reactors with a total installed capacity of over 375,000 MWe as illustrated in Figure 1.1 About 70 further nuclear power reactors are under construction, equivalent to 20% of existing capacity, while over 160 are firmly planned, and equivalent to half of present capacity

Figure 1.1 Nuclear power generation by country in 2013 (source [46])

After Fukushima accident in 2011, it is needed to improve performance from existing nuclear reactor safety, so that stress test is implemented for every reactor to ensure that it can stand with design extension conditions as it occurred in Fukushima

Nuclear power program in Vietnam was confirmed by National Assembly Decision on November 25, 2009 with a plan to build four nuclear power units Russian VVER technology was selected for the first site and the VVER-1200/V491 and VVER-1000/V392 nuclear reactors were considered as the candidates In parallel with capacity building for nuclear

power infrastructure, Vietnam Atomic Energy Institute (VINATOM) has been assigned to develop technical competence of nuclear safety and, in future, it will become a main Technical Support Organization (TSO) for nuclear safety in Vietnam

1.2 Brief overview of nuclear safety

In any nuclear reactor, nuclear safety includes three primitive principals related to all operational conditions: (a) control of reactivity, (b) heat removal from the core to ultimate heat sink and (c) confinement of fission products in case of accident occurrence Requirements of nuclear safety enforce the utilization of defend in depth (DID) policy in nuclear power plant design In general, defense in depth policy is implemented by multiple levels of protection (Table 1.1) and protection barriers

Table 1.1 Multiple levels of protection from DID approach (source [45])

Level 1 Prevention of abnormal operation and

failures

Conservative design and high quality in construction and operation

Level 2 Control of abnormal operation and

detection of failures

Control, limit & protection systems and other surveillance feature

Level 3 Control of accidents within the design

basis

Engineered safety features and accident procedures

Level 4 Control of severe plant conditions,

including prevention of accident progression and mitigation of the consequences of severe accidents

Complementary measures and accident managements

Level 5 Mitigation of radiological consequences

of significant release of radioactive materials

Off-site emergency response

For PWR reactors at power operation, the barriers confining the fission products are typically: (a) fuel matrix, (b) fuel cladding, (c) boundary of the reactor coolant system, (d) containment system as shown in Figure 1.2 The nuclear utility owner must provide and demonstrate that their technical plan design is satisfied for the safety requirements through safety analysis report (SAR) which is reviewed and approved by nuclear regulatory authorities (NRA) and independent TSO All main issues, related to nuclear safety during plant life time, are mentioned in SAR as illustrated in Table 1.2 Nuclear safety covers a wide range of issues related to the plant including external hazards such as seismic, tsunami, flooding… and internal hazard resulted from failure of structures, systems and components together with human factor that are important to safety In chapter 15 of SAR, thermal hydraulics safety analysis is performed by simulation of different categories of postulated transient and design base accident such as reactivity insertion accident (RIAs), loss of coolant flow (LOFAs) and loss of coolant accident (LOCAs) The main system and other connected systems including reactor coolant system (primary system), secondary system are modeled by system code that

can present the response of safety systems to protect and bring nuclear reactor to safety condition

Table 1.2 Content of Safety Analysis Reports (source [45])

Contents of Safety Analysis Reports

Chapter 1 – Introduction and General Description of Plant

Chapter 2 – Site Characteristics

Chapter 3 – Design of Structures, Components, Equipment, and Systems

Chapter 4 – Reactor

Chapter 5 – Reactor Coolant System and Connected Systems

Chapter 6 – Engineered Safety Features

Chapter 7 – Instrumentation and Controls

Chapter 8 – Electric Power

Chapter 9 – Auxiliary Systems

Chapter 10 – Steam and Power Conversion System

Chapter 11 – Radioactive Waste Management

Chapter 12 – Radiation Protection

Chapter 13 – Conduct of Operations

Chapter 14 – Initial Test Program and ITAAC-Design Certification

Chapter 15 – Accident Analysis

Chapter 16 – Technical Specifications

Chapter 17 – Quality Assurance

Chapter 18 – Human Factors Engineering

Chapter 19 – PSA and Severe Accidents

1.3 Core thermal hydraulics safety analysis in transient condition

It is shown that the second barrier plays a very important role due to the fact that it protects fission product in fuel rod from release to primary system Therefore, the peaking cladding temperature in transient and accident conditions must be satisfied specific acceptance criteria The acceptance criteria introduced by IAEA for transient condition in [21] is briefly formulated as below:

(1) The probability of a boiling crisis anywhere in the core is low This criterion is typically expressed by the requirement that there is a 95% probability at the 95% confidence level that the fuel rod does not experience a departure from nucleate boiling (DNB) The DNB correlation used in the analysis needs to be based on experimental data that are relevant to the particular core cooling conditions and fuel design

(2) The pressure in the reactor coolant and main steam systems is maintained below a prescribed value (typically 110% of the design pressure)

(3) There is no fuel melting anywhere in the core

Figure 1.2 Multiple physical barriers in DID policy (source [45])

Based on the first criteria, core thermal hydraulics is related to boiling crisis during transient condition As mentioned in [31], the relation between heat flux from the wall and temperature difference from wall and fluid for pool boiling heat transfer is illustrated in Figure 1.3 The point ―C‖ in Figure 1.3 is called burnout point due to departure of nucleate boiling (DNB) reached Thus, if heat flux from the wall increases to reach the burnout point (or also called DNB point) and results in a numerous of bubbles which begin to coalesce and clump near heating surface (the vapor covering the surface acts as a heat insulator) The blanket of vapor covering heating surface limits heat transfer from wall to liquid and makes cladding temperature higher that lead to violate acceptance criteria This is known as partial nucleate boiling and must be avoid or must be limited as the first criteria mentioned above in nuclear reactor during normal and transient operation condition, respectively As known in Figure 1.3,

if heat flux reaches the burnout point, heat transfer mode is unstable in transition from nucleate boiling to film boiling with corresponding increase in wall temperature Thus, the boiling crisis, in which cladding temperature increases dramatically, corresponds to a sudden drop in heat transfer coefficient from wall due to change boiling mechanism from nucleate boiling to film boiling The boiling crisis is presented by many names such as burnout, critical heat flux and DNB The boiling crisis in flowing coolant is more complicated than pool boiling due to added effects of forced convection and bubbles clouding that tend to cover heating surface

Figure 1.3 Heal flux versus temperature difference for pool boiling heat transfers (source [31])

The boiling crisis in coolant flow is closely related to flow pattern and void fraction In [25], it

is mentioned about two typical phenomenon of interest in nuclear safety as presented in

Figure 1.4

Figure 1.4 Types of boiling flow crisis (source [25])

The left picture in Figure 1.4 shows the sub cooled or low quality DNB that is caused from detachment of bubble from boundary layer The picture in the right of Figure 1.4 shows the burnout at high quality region that is caused from the liquid film covering heating surface

complicated due to the fact that it depends on many factors such as channel sharp, surface condition, physical properties of the coolant and flow conditions The most popular correlation that ensures critical heat flux not exceeded during core operation is DNB ratio It

is defined by the minimum ratio of the critical heat flux to the heat flux achieved in the core:

For the PWR, the DNBR > 1.3 for insurance of DNB not occurred Figure 1.5 shows the DNBR along axial channel in the uniform core

Figure 1.5 Critical heat flux in uniformly core (source [25])

It is emphasized here that thermal hydraulics safety analysis in transient condition is dealing with finding appropriate correlation that prevent DNB occurring in flow channel of the core Due to DNB occurrence is a very complicated mechanism but it is strictly related to void fraction and flow regime, so that study on void fraction in transient condition is the first step

to approach understanding DNB mechanism

1.3.1 Role of void fraction in simulation of two phase flow

The value of void fraction plays an important role in modeling of two phase flows During solving the conservation equations, the void fraction is calculated Then, the flow regime is defined based on the value of void fraction For example, in CTF code, flow regimes are determined based on the range of void fraction in normal wall models as illustrated in Figure 2.8 of this thesis The normal wall flow regime map includes following flow regimes:

 Small-bubble defined by void fraction below 0.2

 Small-to-large bubble (Slug) defined by void fraction in range (0.2, 0.5)

 Churn/turbulent defined by void fraction in range (0.5 αcrit)

 Annular/mist defined by void fraction greater αcrit

Then each of individual flow regimes of normal wall map, the interfacial area, interfacial drag and interfacial heat transfer are differently defined

1.3.2 Experiment overview for bundle of sub channel analysis

Rod to Wall spacing, in (cm) 0.148 (0.376)

Ratio of heat flux

Assembly Dimensions in x in., (cm x cm) 2.383 x 2.383 (6.053 x 6.053)

 EPRI tests

EPRI 5x5 tests allows for collection of exit flow quantities, as well as rod temperatures near assembly exit The brief information about this test is given in Table 4

Table 1.4 EPRI 5x5 characteristics for test 74 and test 75(source [29])

Rod to Wall spacing (x), in (cm) 0.142 (0.361) 0.130 (0.33)

Rod to Wall spacing (y), in (cm) 0.135 (0.343) 0.135 (0.343)

Assembly Dimensions in x in., (cm x cm) 3.03 x 3.03 (7.7x7.7) 3.03 x 3.03 (7.7x7.7)

 BM ENTEK facility

The BM ENTEK facility [33] allows investigation void fraction along heating channel similar

to Russia RBMK-1000 bundle of fuel rods The channel contains a 7- rod bundle made by stainless steel with rod outer diameter of 13.5 mm, 1.25 mm wall thickness, and 7 m length The bundle is contained within a stainless steel pressure tube (80 mm outer diameter and 5

mm wall thickness) with inner diameter of 49 mm and 10.5 mm wall thickness

 PSBT Void Distribution Measurements

The PSBT facility [1] allows measurement of void fraction in both bundle of rods or in single sub channel Some brief information of PSBT rod bundle is given in Table 1.5

Table 1.5 Geometry and power shape for Test Assembly B5, B6, and B7 (Source [1])

Heater rod outer diameter (mm) 9.50 9.50 9.50

Thimble rod outer diameter

(mm)

Heated rod pitch (mm) 12.60 12.60 12.60 Axial heated length (mm) 3658 3658 3658 Flow channel inner width 64.9 64.9 64.9

Axial power sharp Uniform Cosine Cosine

1.3.3 Void fraction prediction study

The void fraction prediction study is implemented in all scale from system scale ([33], [4]), component scale (rod bundle scale) such as ([26], [38] and [44]) In general, the studies at system scale and component scale focus on verification and assessment of physical model of the codes with experiments For example, Ref [4] present the study on the extent the range of applicability of the RELAP5 code to low-pressure simulations of subcooled boiling in upward vertical flow The study on void fraction distribution by RELAP5 over RBMK fuel channel through the ENTEK BM Test Facility is found in Ref [33] COBRA-TF is released in many versions and is widely used to investigate vertical channel flow A study of COBRA-TF void fraction recalculation using experimental data of both the OECD/NRC BFBT benchmark and in-house tests in AREVA NP’s KATHY loop is presented in [28] The Ref [28] introduces several correlations to correct void fraction based on experiment void fraction derived from measured density Another assessment of the COBRA-TF performance for prediction of sub cooled boiling conditions in heated rod bundles with Light Water Reactors operating conditions is reported in [23] The assessment in the Ref [23] consists of two parts: (a) a comparison of COBRA-TF predictions to data from three heated bundle experiments and (b)

an evaluation of the physics models and constitutive relations within COBRA-TF Some conclusions from this report are related to fluid temperature distribution and wall temperature distribution based on EPRI 5x5 rod bundle tests For the void fraction study, it is shown in Ref [23] that COBRA-TF and COBRA-EN predict similar in the locations within the channel

at which the flow quality is greater than zero Furthermore, COBRA-TF predicts none zero void at near channel inlet, even when the flow quality is predicted to be zero The Ref [26] shows the study of CTF void fraction prediction for PSBT single channel exercises It can be seen that the CTF predictions stay within the error bound of 0.1 void (the CT scanner cross section average void measurements were specified as an uncertainty of 0.03) From the Ref [26], it is observed a tendency that CTF over predict the vapor generation rate, which is due the utilized interfacial drag modeling in CTF

The study presented in [29] do not directly mention about CTF void fraction prediction, but presents simulation of experiments consisting of 5x5 and 4x4 rod bundle geometries Test cases allowed for comparison of void fraction, flow quality, enthalpy, and temperature to experimental values In addition, a 17x17 model of a standard pressurized water reactor fuel assembly was simulated to evaluate turbulent mixing models and heat conduction options in CTF It was found that the heat transfer models in CTF were inappropriate for simulations of subcooled boiling conditions In addition, while the code was able to predict bundle average properties with reasonable accuracy, significant differences were observed between the experimental and computed exit fluid temperature and mass flux for individual sub channels

The study [38] aims at improving a new version of CTF with new features allowing simulating even horizontal two phase flow which is not available in the version before The RELAP-3D and MARS-3D are resulted from coupling RELAP5 with COBRA-TF with purpose of better simulation core and steam generator in nuclear power plant

Recently, an extension of CFD code application for two-phase flow is implemented as a part

of multi-scale of thermal hydraulic safety analysis Two-phase flow CFD used for safety investigations may predict small scale flow processes, which are not seen by system thermal hydraulics codes It is shown that at least six Nuclear Safety Reactor (NSR) problems and many other NRS issues may benefit from study at the CFD scale More detail about CFD code application on NSR problems can be found at [10], [6]

Huge studies on boiling flow at meso scale, a systematic overview of sub models for evaporation and condensation is presented in [41, 42] The investigation boiling flow is typical mentioned in [12, 13, and 14] For instant, Ref [14] present a validation of physical models based on the Bartolomej experiment performed in 2 m long heated tube with the inner diameter of 15.4 mm The validation of boiling sub models such as bubble size at detachment and wall superheat depending on the reference nucleation site density is presented in Ref [13].The study mentioned in Ref [41] focus on the assessment of the heat flux partitioning model in handling the latter physics of subcooled flow boiling In order to achieve closure to the model, the current prevailing approach has always been the utilization of empirical correlations particularly for the active nucleation site density, bubble departure diameter and bubble departure frequency A comprehensive survey of existing empirical correlations is presented to assess the performance of this empirical model In Ref [42] the improved heat flux partitioning model based on determining the active nucleation site density, bubble size and bubble frequency is evaluated for subcooled flow boiling in vertical heated channels at low pressures

In conclusions, the application of CTF to specific simulation is needed to validate with experiment in similar conditions The study on CFD boiling model is still in progress with the application range of sub cooled region In order to adaptation of simulation by CFD code, it is also necessary to validate against appropriate experiments

1.4 VVER technology understanding related to this study

Around several decades ago, the nuclear reactor VVER-1000/V320 is considered as Russian standard reactor of generation II which is built in many places such as Balakovo, South Ukraine, Rostov, Kalinin, and Kozloduy… Recently, the VVER nuclear reactor with advanced technology and safety is developed from the standard design based on application of new nuclear safety feature such as balance between active and passive safety systems The Figure 1.6 shows two branches of new advanced Russian nuclear reactor development carried out by two designers in Russia: Saint Petersburg Atomenergoprom (called Saint Peterburg Designer) and JSC Atomenergoproekt (called Moscow Designer)

Figure 1.6 Development of VVER nuclear reactor technology chart [32]

Taking the role of TSO for nuclear safety, VINATOM is assigned a mission to boost understanding of VVER reactor technologies for the selection of appropriate candidate for Ninh Thuan 1 with advanced technology as well as with highest level of safety After Fukushima accident, an important issue related to nuclear safety is investigation of the VVER reactor candidate in design extension conditions In general, it is recognized that the most challenge for the worst situation is removal decay heat from the core to ultimate heat sink Therefore, the capability of safety passive systems of the VVER-1000/V392 that can delay timing of core damage at least 24 hours in the worst situation is investigated by our research group through the national project (code DTDL.2011-G/82) in the duration 2011-2014:

"Study, analysis and comparison of Technology Systems about the Nuclear Power Plants with the different reactors: VVER-1000 AES 91, AES-92 and AES-2006‖ with financial support from Ministry of Science and Technology (MOST)

The VVER-1200/V491 which is considered as the most potential candidate for Ninh Thuan 1,

is also investigated in the worst case through another national project: "Study the Nuclear Power Plant’s Technology proposed for Ninh Thuan 1 and Ninh Thuan 2 in order to support Basic Design’s Review" (code KC.05.26/11-15) in the duration 2014 -2015.

In design base or design extension conditions, the loss of coolant accidents (LOCAs) and LOCAs with station blackout (SBO) simultaneous occurrence are considered more carefully

in any stress test for new nuclear safety requirements The LOCAs are typically postulated accident with many complicated phenomena in thermal hydraulics such as by pass, boiling and quenching effects which require a lot of correlations from experiment to validate the physical models in computer code Several accidents mentioned above are simulated by system code RELAP5 to analyze whether safety systems responses are met the requirements

or not in our works through the national project (code DTDL.2011-G/82)

With regard to methodology for thermal hydraulics safety analysis, it is recommended several options at system level such as conservative or best estimate methodologies The best estimate methodology with conservative assumption for initial and boundary conditions is now widely applied As mentioned in [9], the best estimate approach aims at providing a detailed realistic description of postulated accident scenarios based on the best available modeling methodologies and numerical strategies sufficiently verified against experimental data from differently scaled separate effect test and integral effect test facilities Based on availability of

codes used in VINATOM, the study is realized by multi code and multi scale utilization to predict void fraction in hot channel of the VVER-1000/V392

For the multi code approach, the initial and boundary conditions for thermal hydraulics codes are provided by neutron codes For example, results from neutron codes such as MCNP5 give the axial channel power distribution for modeling heat structure in RELAP5 MCNP5 also provides the hot channel factor for RELAP5 and radial relative power distribution in a bundle

of fuel rods that allow modeling in component code as COBRA-TF

For the multi scale approach, there are multi scale simulation and multi scale analysis In multi scale simulation, a system code includes a module of component code with 3D simulation at finer scale such as RELAP-3D or MARS-3D that consist of COBRA-TF inside

to treat core modeling in more detail

Figure 1.7 Multi-scale analysis of reactor thermal hydraulics (source [11])

For the multi scale analysis, the output results from larger scale are considered as input for initial and boundary condition in smaller scale Smaller scale with zooming to interested domain can give better results such as values of variables in 3D of the domain Thus, analysis between different scales can give overall picture and also zooming in small spatial domain for detailed investigation as illustrated in Figure 1.7

The materials for this study at system scale are based on the VVER-1000/V392 safety analysis report for technical design phase (called Interim SAR) given by our research group through the national projects (code DTDL.2011-G/82 and KC.05.26/11-15) Due to the fact that SAR is a confident document being approved for Belene nuclear power project (Bulgaria), therefore it is considered as a good reference to compare results for the national project as well as for this study

channel with heating wall is important in thermal hydraulics analysis with a lot of experiments and codes developments Thus, it is proposed a motivation to study void fraction prediction in core of the VVER-1000/V392 nuclear reactor with the goal as following:

 To adopt a procedure of void fraction prediction during transient using multi scale analysis based on the computer codes: MCNP5, RELAP5 and CTF;

 To consider a combination of CTF and Ansys CFX codes to improve void fraction predicted by CTF in specific timing within the transient period

So that the study on phase change in the core of nuclear reactor in this thesis will be limited in void fraction prediction in core of the VVER-1000/V392 nuclear reactor with neutron code MCNP5 and with three different scales thermal hydraulics codes RELAP5, CTF and Ansys CFX

In this study, the consideration of utilization of CTF and CFX codes to improve void fraction prediction in core is a new issue As usually, CTF is used to predict void fraction during transient time It is expected that CFX with at meso scale for void fraction prediction will give

an improvement to predict for steady state in specific timing

In conclusion, it is summarized the thesis objectives as below

1.5.1 Studied object

The void fraction in hot channel of VVER-1000/V392 reactor is predicted with three different scales during 40 seconds of transient condition at the beginning of LOCAs with different break sizes

1.5.2 Scope of study

It is also limited the scope of the study due to complexity of the two phase flow The investigated two phase flow through core sub channels is vertical flow with the specific regime such as bubbly, slug, churn and annular The left picture and the right of Figure 1.7 shows the temperature profile from center of fuel pellet through several segments inside the fuel rod such as outer of fuel pellet (TF), inside cladding (Tc) and outside cladding (Ts), the coolant (TFl) and the flow regime from bubbly to annular flow with corresponding heat transfer modes from the wall

(a) (b)

Figure 1.7 (a) temperature distributions in a cylindrical fuel pin, (b) flow regime

and correspond heat transfer modes (source [31])

1.6 Thesis outline

Thus, the thesis includes four chapters and last with the conclusion Chapter 1 mentions about introduction that leads to motivation of this study with following arguments:

 Status of nuclear power in the World and Vietnam

 Brief overview of nuclear safety

 Core thermal hydraulics safety analysis in transient condition

 VVER technologies understanding in Vietnam related to this study

 Thesis objectives

 Thesis outline

Chapter 2 presents the methodology related to multi scale analysis along with the code theories at different scale for RELAP5, CTF and Ansys CFX with focus on phase change models in several items below:

 Multi scale approach to LWR thermal hydraulic simulation

 System code RELAP5

 Sub channel code CTF

 Meso scale code CFX

 Conclusions

The verification and assessment of modeling used in these codes versus experiment data are presented in chapter 3 The system simulation results are compared with those in SAR documents The assessment of CTF code is implemented by simulation BM ENTEK experiment tests which is an International Standard Benchmark to investigate boiling flow through Russian fuel bundle of RBMK reactor The meso scale code Ansys CFX is verified

with PSBT single sub channel which is an International Standard Benchmark as well Therefore, the main contents of chapter 3 are presented as following:

 Brief information of VVER-1000/V392 nuclear reactor

 Verification of RELAP5 simulation models for VVER-1000/V392 reactor with SAR

 Verification and assessment of CTF models with BM ENTEK experiment tests

 Verification Ansys CFX models with PSBT sub channel experiment tests

 Conclusions

The tasks mentioned in thesis objectives in chapter 1 are described and solved in chapter 4 with following steps:

 Calculation Diagram

 Power distribution calculation by MCNP5 code

 LOCAs simulation by RELAP5 code

 Transient simulation in LOCAs by CTF code

 Transient simulation in LOCAs by CFX code

 Conclusions

Chapter 2 Overview of phase change models in code

theories with different scales

2.1 Multi code and multi scales approach to PWR thermal hydraulic simulation

As mentioned in previous chapter, the best estimate approach aims at providing a detailed realistic simulation of thermal hydraulics behavior based on the best available modeling methodologies sufficiently verified against experimental data from differently scaled separate effect test and integral effect test facilities Therefore, as mentioned in [22], it is utilized as a tendency of the best estimate approach to simulate PWR thermal hydraulics phenomena The use of best estimate (BE) computer codes combined with realistic input data is particularly attractive because it allows for a more precise specification of safety margins and thus leads to greater operational flexibility For the best estimate approach, the two points are aggregated as following:

(a) It is required the best estimate methodologies including physical models in the codes validated with experiment in separate effect tests or integrate effect tests

(b) It is required the realistic input data for the modeling

2.1.1 Neutron codes and thermal hydraulics codes

In this context, the utilization of multi codes mentions about relation between neutron and thermal hydraulics codes It is noticed that neutron codes provide more precise data for thermal hydraulics simulation input For example, the coupling codes allow interactive exchange data between PARCS and RELAP5 codes [19] When this coupling is enabled, the 3-D reactor kinetics calculated by PARCS code, affects to the heat structure modeling for heat source in RELAP5, therefore, the heat source modeling is improved with better initial data and core power is calculated by PARCS instead of RELAP5 Besides the coupling codes between neutron and thermal hydraulics, the utilization of multi codes is an establishment more precise initial and boundary conditions for thermal hydraulics simulation from results of neutron code As illustrated in Figure 2.1, the calculation results by neutron code MCNP5 provide:

(a) Peaking factor for hot channel in order to make input of RELAP5

(b) Axial channel power distribution for input of RELAP5 and CTF

(c) Radial relative power distribution in hot channel for CTF

Figure 2.1 Relations between MCNP5, system code RELAP5 and component code CTF

RELAP5

CTF

MCNP5

 Peaking factor for hot channel

 Axial power distribution

 Radial relative power distribution in hot channel

2.1.2 Different scale of thermal hydraulic codes

In general, as presented in Figure 1.7, multi scale analysis for two phase flow includes four levels as mentioned in [11]: System scale, Component codes, CFD in open medium, Direct Numerical Simulation (DNS) and pseudo-DNS

The system scale aims to describe whole circuits of reactor or a system test facility by system codes System codes, in general, include several modules such as hydro dynamics, heat structure, core kinetic and control system

Figure 2.3 System code capabilities for reactor thermal hydraulics (source [7])

The hydro dynamic module allows simulation of flow path using finite volume method and special components such as pump, valves, heat exchanger Normally, system codes allow modeling primary, secondary system and other connected systems such as safety or axially systems with 1D simulation of flow path Application of system codes is core transient and accident scenarios simulation for safety analysis Thus, the main advantage of system codes is capability of whole system simulation and the main disadvantage is limitation of mesh number For example, RELAP5 code allows number of meshes from 1000 to 10000 Several system codes such as RELAP5, TRAC, TRACE, CATHARE-2, and ATHLET are now widely used

Component scale mentions about codes with capacity of 3D simulation of reactor components such as cores and heat exchanger These codes use the ―porosity‖ concept in the ―porous body‖ approach The popular case is sub channel code such as COBRA-TF used for cores simulation with spatial resolution based on cross section sharp of sub channel size (approximation of 1 cm) The left picture in Figure 2.4 shows how to define a control volume from a sub channel inside a bundle of fuel rod and the right picture illustrates the axial channel conservation equations in a sub channel and transvers momentum equation from sub

channel to sub channel Thus, the flow area of sub channel code is defined by the sharp of fuel rod arrangement

Figure 2.4 Control volume and axial flow area defined in sub channel code

(source [31])

CTF is a version of COBRA-TF developed by Pennsylvania State University with capacity of flow area simulation in the sharp of rectangle or triangle It is noticed that flow area in VVER’s cores is triangle sharp The grid spacer in rod bundle is simulated as pressure drop along axial channel

The scale of CFD in open medium is called as meso scale or average scale (1 millimeter or less) The codes at this scale allow finer description of flows than component codes The turbulent models are used in these codes including Reynolds Averaged Navier Stokes (RANS) or Large Eddy Simulation (LES) The codes at this scale are now widely used including Ansys CFX, FLUENT, NEPTUNE-CFD, STAR-CD and so on These codes allow analysis of a local interested part of domain and allow predicting the fluid temperature field with sufficient time and space resolution for investigating thermal shocks or thermal fatigue

of the reactor structures as illustrated in Figure 2.5

For the scale at Direct Numerical Simulation (DNS) and pseudo-DNS, the characteristic length is defined by the smallest flow feature such as an eddy or a bubble size This length is less than micrometer These codes at this scale allow simulation of small domain such as a region containing a few bubbles or droplets The utilization of DNS gives understanding the local phenomena, therefore, gives information for developing closure relation for macroscopic scale models The DNS codes, in two phase flow, are added the interface tracking technique (ITT) to solve basic fluid equations in order to predict the position and evolution with time of every interface Direct Numerical Simulation (DNS) just solves exact local instantaneous equations without any averaging or filtering In turbulent flow this requires that the nodalization is smaller than the smallest eddies at the Kolmogorov scale η This approach being extremely CPU costly is limited to some investigations of simple problems

In conclusions, it is summarized the characteristics of four types of codes as below

Table 2.1 Main characteristics of codes with four different scales (source [11])

code

CFD in open medium

DNS & DNS

porous 3D

porous 3D &

sub-channel analysis

RANS 3D &

LES type

No model in single-phase

nodes in current

applications

Few 100 nodes About 1000 nodes for 3D Pressure Vessel

103 to 105 106 to 108 106 to 108

operation & all accidental transients

Fuel design (CHF) Heat Exchanger design

(steam generator) Some coupled TH-neutrons transients

Mixing problems

in 1- phase flow:

boron dilution, MSLB, PTS, thermal fatigue, thermal

stripping,…

PTS, CHF in phase flow

2-Basic flow processes: turbulent flow in simple

geometry, boiling, bubbly flow,…

Computer/run

time

Few hours on single processor

Few hours to few

days on single processor Few hours on multi-processor

Several days to several weeks on massively

parallel compute

Several days to several weeks

on massively parallel computer

2.1.3 Different thermal hydraulic modeling approaches

The summary of thermal hydraulics modeling approach of four different scale codes which mentioned above related to several choices is presented [11] as following:

1 Selection between the CFD for open medium and the CFD for porous body by multiplying basic equations by a fluid-solid characteristic function

2 Time averaging or ensemble averaging

3 Space averaging, space integration, or space filtering

And for two-phase flow only:

4 Choice of the number of phases or fields of the model by multiplying basic equations by phase characteristic functions or field characteristic functions

5 Treatment of interface, which can be Deterministic Interface (DI), Filtered Interface (FI) or Statistical Interface (SI)

It is observed that, for single phase flow, only three main types of CFD in open medium may

be identified as shown in the Table 6 The RANS approach for steady flow utilizes time averaging or ensemble averaging for local instantaneous equations (mass momentum and energy) The filter all turbulent eddies and to predict only a mean velocity field is implemented by time averaged equations The two-equation turbulence model with the Boussinesq approximation and a turbulent viscosity are used in RANS (k-ε) model There are

a lot of variations of two-equation turbulence modeling such as k-l, k-ω, SST, RNG-k ε, V2, nonlinear k-ε RANS approach was initially used to simulate steady flow The Unsteady

k-ε-or Transient flow (U-RANS k-ε-or T-RANS) are also applied RANS approach if the time scale of the mean flow is larger than the time scale of the largest eddies

A space filter to basic balance equations are used to simulate the Large Eddy Simulation (LES)

Table 2.2 Main characteristics modeling approaches for three main types of single-phase CFD

simulated

No eddy modeled

Large eddies simulated Small eddies modeled

No eddy simulated (largest scale fluctuations may be simulated in U-RANS & TRANS)

Requirements on dt

&

mesh size δ

δ< η dt< η/uη

f : length scale of filter: in inertial sub range of turbulence spectrum

δ< f dt< f/uf

Steady algorithm possible in steady flow

δ& dt limited by mesh and time convergence for mean flow resolution

The space filter allows simulating large eddies but the effects of smaller eddies have to be modeled The LES family also includes the Detached Eddy Simulation (DES) and Very Large

Eddy Simulation (VLES) Scale Adaptive Simulation (SAS) includes some hybrid methods between U-RANS and LES

The local instantaneous equations without any averaging or filtering are exactly solved by Direct Numerical Simulation (DNS) codes Table 2 shows that, the requirements on the mesh size δ and time step dt depend on the method The RANS type methods require δ and dt limited by mesh and time convergence of mean flow resolution whereas δ must be smaller than the filter scale f in LES or even smaller than the Kolmogorov space and time scales in DNS It is shown that, in practical, these requirements generally induce the increase of meshe number of more than an order of magnitude from RANS to LES or from LES to DNS

The various modeling approaches based on the five choices mentioned above were illustrated

in [11] by Figure 2.6 with four different approaches identified in the domain covered by CFD

in open medium and DNS type codes For the domain covered by system codes and component codes, at least four different approaches are identified Based on Figure 2.6, it is shown that RELAP5 code belongs to column (1D nF) with one dimension simulation and two phase conservation equations Space treatment is applied to many quantitative terms such as temperature, pressure and so on Time treatment is applied to some terms such as velocity and phase characteristic is identified Similarly, CTF code falls in column ―Porous-3D, nF) in Table 6 with requirement of mesh size δf must be greater than equivalent diameter of flow The difference with RELAP5 is characteristics of fluid or solid is applied in CTF

Figure 2.6 The tree of two-phase thermal hydraulic modeling approaches (source [11])

2.2 Phase change models in system code RELAP5

The RELAP5 models include conservation equations for two-phase flow with one dimensional simulation of thermal hydraulics behavior along flow path The detail of RELAP5

conservation equations and its closure models is presented in [19] In general, constitutive

models include: (a) equations of state (material behavior) based on tabular form functions provided by built in steam table and (b) models and correlations (imbedded in code as

functional form) used to treat following issues:

 Interface momentum and interactions

 Interface energy and mass exchange

 Wall momentum exchange

 Wall heat transfer

Thus, the phase change models are related to interface energy and mass exchange and wall heat transfer The vapor generation or condensation [19] in RELAP5 is modeled by phase change induced from heat transfer between interface and wall heat transfer effect:

𝑢 (2.5) The determination of interfacial heat transfer coefficient ( ) for phase p (W/m2•K) and interfacial area per unit volume (m2/m3), , is based on flow regime defined in RELAP5 The flow regime for vertical flow is illustrated as in Figure 2.7 with detail explanation given

in [19]

Figure 2.7 Schematic of vertical flow regime map in RELAP5(source [19])

The two terms and present heat transfer from wall to fluid and vapor, respectively Discussion of phase change near wall is mentioned in [20] based on models and correlations, for example, the near wall evaporation is calculated by following correlation:

2.3 Phase change models in sub channel code CTF

The CTF model includes nine conservation equations and three fields: liquid, vapor and entrained liquid drop The various forms of conservation equations are presented in [5, 9, 24 and 25] However, only Ref [29] takes into account core sub channel geometry To determine closure models for governing equations, the flow regime maps are used to calculate the interfacial transportation terms such as momentum transfer and heat transfer terms

2.3.1 Evaporation and condensation induced by thermal phase change

There are two different types of flow regime maps: ―normal wall‖ map and ―hot wall‖ map The normal wall map is used when the maximum wall surface temperature, Tw, in a given computational mesh cell is below the critical heat flux temperature, Tcrit Then a part of wall adjacent to this mesh cell is expected to be fully wetted The normal wall flow regime map includes the following flow regimes: small bubble; small-to-large bubble (slug); churn/turbulent; and annular/mist