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Development of Dynamic LES-SPH Method for Thermal Ablation Analysis with Turbulent Natural Convection : 전이 및 난류 자연 대류 유동을 동반한 열적 침식 해석을 위한 입자법 기반 동적 대와류 모델 개발

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dc.contributor.advisor김응수-
dc.contributor.author최태수-
dc.date.accessioned2023-11-20T04:18:47Z-
dc.date.available2023-11-20T04:18:47Z-
dc.date.issued2023-
dc.identifier.other000000179595-
dc.identifier.urihttps://hdl.handle.net/10371/196348-
dc.identifier.urihttps://dcollection.snu.ac.kr/common/orgView/000000179595ko_KR
dc.description학위논문(박사) -- 서울대학교대학원 : 공과대학 에너지시스템공학부, 2023. 8. 김응수.-
dc.description.abstractThe primary objective in nuclear severe accident mitigation strategies is to retain and efficiently cool corium to prevent the release of fission products. However, the decay heat generated from corium can lead to thermal ablation of the pressure boundary, compromising structural integrity and potentially leading to the release of fission product into the environment. Prominent examples include RPV ablation in IVR-ERVC strategy, concrete structure breaching in MCCI and thermal erosion of sacrificial material caused by corium jet impingement above core-catcher. The extent of thermal ablation is determined by the flow characteristics of corium and heat flux at boundary. Therefore, a comprehensive understanding of thermal ablation and the behavior of corium is crucial from a severe accident mitigation perspective.

The analysis of turbulent natural convection behavior of corium and thermal ablation has been based on empirical approaches using simulant experiments or conventional computational fluid dynamics (CFD). Researches has been conducted to refine and validate of turbulence models for analyzing the behavior of corium flow, and recently, comprehensive analysis incorporating grid-based phase change analysis has been carried out. Numerical assumptions have been introduced, to simulate phenomena such as transient interface tracking between corium layers and domain deformation due to phase change.

With advancements in hardware and software for large-scale parallel computing, particle-based CFD methods, such as Smoothed Particle Hydrodynamics (SPH), have been applied to nuclear safety analysis. The particle-based CFD methods analyze flow using moving particles with physical quantities making it suitable for analyzing multi-phase, multi-fluid, free surface and phase change effectively.

Thermal ablation and corium thermal flow involve solid-liquid phase change and multi-fluid heat transfer analysis, making the particle-based CFD an effective framework by utilizing advanced phase change model. However, there has been no cases of analysis using sophisticated turbulence models based on particle-based CFD, and therefore, no research on thermal ablation accompanied by turbulent thermal flow.

Therefore, in this study, a turbulence model applicable to transient laminar, transitional, and turbulent flow conditions was developed based on Smoothed Particle Hydrodynamics (SPH), which is a representative particle-based fluid analysis method. By combining the common features of SPH, which uses spatial weight functions, and Large Eddy Simulation (LES), which utilizes spatial filter functions for modeling turbulent flow, a dynamic LES-SPH framework was developed without additional filtering processes. Numerical corrections were applied to SPH discretization to ensure the LES models numerical accuracy when analyzing low Prandtl number fluids, such as corium and liquid metals. Turbulent Prandtl number modeling and the dynamic Vreman model were introduced for this purpose. The capabilities of the developed dynamic LES-SPH model to analyze thermal flow under transitional and turbulent conditions were validated through comparisons with various numerical and experimental studies.

Furthermore, an advanced phase change model based on the Enthalpy-Porosity Model (EPM) was developed to analyze thermal ablation using the SPH method. By incorporating the assumption of porosity effects in the momentum equation, the EPM enabled the analysis of phase change without the need for numerical modification related to viscosity and other properties. The developed SPH phase change model was validated through comparisons with various numerical and experimental studies, confirming its capability to analyze phase interfaces and heat transfer.

To demonstrate the utility of the developed LES-SPH with phase change model, an analysis was conducted on the behavior of corium pool and the thermal ablation of the pressure vessel under in-vessel retention conditions. The thermal ablation of the pressure vessel at different times and locations was compared to CFD and previous SPH approaches. The analysis results confirmed that the dynamic LES-SPH and phase change models developed in this study effectively analyze turbulent corium flow accompanied by thermal ablation.

The particle-based LES-SPH phase change framework developed in this study provides an analysis methodology for phenomena that were difficult to analyze using conventional CFD in the context of nuclear severe accidents. It is expected to complement conventional CFD methods and provide a more comprehensive understanding. Furthermore, rigorous validation and analysis of the developed LES-SPH and phase change models will be conducted to ensure their reliability. This will facilitate the improvement and proposal of correlations in areas without experimental data related to nuclear severe accidents, contributing to the field of nuclear safety.		-
dc.description.abstract원자력 중대사고 완화전략에서는 노심용융물의 노내/노외에서의 효율적인 냉각을 통해 사고 진전 완화 및 핵분열물질의 유출방지를 목표로 한다. 그러나 노심용융물 붕괴열로 인해 압력경계의 열적 침식이 발생하며, 구조건전성로 인해 핵분열 생성물이 노외로 유출될 수 있다. 대표적인 사례로는 노내억류 전략에서 압력용기 용발, 노외억류 전략에서 MCCI 및 코어캐처 희생물질 열적 침식이 있다. 이때 압력경계의 열적 침식 정도는 노심용융물 열유동과 경계에서의 열유속에 의해 결정된다. 따라서 중대사고 완화 관점에서 열적 침식 현상과 상경계에서 노심용융물 거동에 대한 종합적인 이해가 필요하다. 그러나 극한 조건을 동반한 현상의 특징으로 인해, 실험적 해석에는 제한이 있고, 난류 자연대류를 동반한 노심용융물 거동, 고체-액체 상변화, 성층화된 노심용융물간 열유동 등의 거동 자체의 복잡성으로 인해 예측 및 평가에 불확실성이 존재한다.

노심용융물의 난류 자연대류 거동 및 압력경계 열적 침식 해석은 다른 중대사고와 마찬가지로, 모사실험 기반 경험적 접근 방식이나 성층화된 노심용융물 층의 유동특성을 고려한 전통적 전산 유체해석 방법론에 기반하였다. 노심용융물의 거동해석을 위해 고도화된 난류모델 개발 및 검증 연구가 진행되고 있으며, 최근에는 격자기반 상변화 해석을 포함한 종합적인 해석연구가 수행되었다. 이때 성층화된 노심용융물 간 계면변화, 노심용융물의 자유표면 해석 및 상변화로 인한 해석영역의 변형 등의 영향을 모사하기 위해 수치적 가정들이 도입되었다.

한편, 최근 대규모 병렬계산을 위한 장비 및 소프트웨어의 발전에 힘입어, 입자법 기반 전산유체 해석 방법론이 원자력 안전 해석에 적용하는 경우가 늘어나고 있다. 입자법은 격자 기반이 아닌, 물리량을 가진 입자의 움직임을 통해 유동을 해석하여, 다유체/다상 경계를 해석할 수 있으며, 상변화 및 자유표면을 다루는데 강점이 있다.

열적 침식 및 노심용융물 거동 관련 물리현상은 고체-액체 상변화현상으로 인한 해석계면 변형은 물론, 다물질 혼합물인 노심용융물 내에서 밀도차에 의한 성층화로 인한 다유체 열유동 해석등을 포함한다. 이러한 특징 때문에 입자법 기반 상변화 모델을 활용한 전산유체 해석방법론을 통해 효율적인 해석체계를 구축할 수 있다. 그러나 입자법 기반 전산유체 해석 방법론에서는 고도화된 난류모델을 통한 해석이 진행된 사례가 없으며, 따라서 난류 열유동을 동반한 열적 침식에 대한 해석 연구가 진행된 사례가 없다.

따라서, 본 연구에서는 대표적인 입자 기반 유체 해석 방법론인 완화입자유체동역학 (Smoothed Particle Hydrodynamics, SPH) 기반으로, 과도적인 층류, 전이 및 난류 유동 조건에 범용적으로 적용할 수 있는 난류모델을 개발하였다. 공간 가중함수를 활용하는 SPH 차분화 방법과, 공간 필터함수를 활용해 난류 유동 모델링을 수행하는 대와류모델 (Large Eddy Simulation, LES)의 공통점을 이용해, 추가적인 필터링 과정이 필요 없는 LES-SPH 해석체계를 구축하였다. LES 모델의 수치 정확도 확보를 위해, SPH 차분화 수치 보정을 수행하였다. 또한 저 Pr 유체인 노심용융물 및 액체금속 열유동 해석을 위해, 난류 Pr수 모델링 및 동적 Vreman 모델을 도입하였다. 구축된 동적 LES-SPH 모델의 전이 및 난류 조건에서의 열유동 해석 능력 검증은 다양한 수치, 실험 연구들과 비교를 통해 수행되었다.

또한 양해법 SPH 해석체계를 활용한 열적 침식 해석을 위해, 엔탈피-다공성(Enthalpy-Porosity Model, EPM) 모델을 기반으로 상변화 모델을 고도화하였다. 상변화 구간에서 다공성 가정을 활용해 운동량 방정식 구성함으로써, 점성 등의 물성치에 대한 수치적 수정 없이 상변화 해석을 수행할 수 있다. 개발된 SPH 상변화 모델은 다양한 수치, 실험 연구와의 비교검증을 통해 상경계 및 열유동 해석 능력을 검증하였다.

마지막으로 개발된 LES-SPH 기반의 상변화 모델의 유용성 입증하기 위해 원자로 중대사고 완화전략인 노내억류 조건에서 노심용융물의 거동 및 압력용기의 열적 용발에 대한 해석을 수행하였다. 시간 및 위치에 따른 압력용기의 열적 용발 정도를 격자법 전산유체해석 방법론 및 선행 SPH 방법과 비교 검증하였다. 분석 결과, 본 연구에서 개발한 동적 LES-SPH 및 상변화 모델이 열적 침식을 동반한 난류 다유체 유동을 정성적으로 잘 해석하는 것을 확인하였다.

본 연구에서 개발한 입자법 기반 LES-SPH 상변화 해석체계는 원자로 중대사고 관점에서 기존 전산유체해석 기법을 통해 해석하기 어려웠던 현상들에 대한 직접 해석 방법론을 제안하였다는 의의가 있으며, 추후 전통적 유체해석 기법과 상호보완적 역할을 수행할 것으로 기대한다. 또한 개발된 LES-SPH 모델 및 상변화 모델에 대한 보다 엄밀한 검증 및 분석을 통해 신뢰성을 확보할 예정이다. 이를 통해 원자력 중대사고에서 실험결과가 없는 영역에 대한 상관식 개선 및 제안할 수 있으며, 원자력 안전 분야에 기여할 것으로 기대한다.		-
dc.description.tableofcontentsList of Contents

Abastract ⅰ
List of Contest ⅳ
Chapter 1 Introduction 1
1.1. Background and Motivation 1
1.2. Previous Researches 4
1.2.1. Numerical Studies on Phase Change 4
1.2.2. Turbulence-SPH Model 5
1.3. Objective and Scope 6
Chapter 2 Smoothed Particle Hydrodynamics 10
2.1. Smoothed Particle Hydrodynamics 10
2.1.1. Basic Concept of SPH 10
2.1.2. SPH Discretization 11
2.1.3. SPH Consistency and Accuracy 11
2.1.4. Nearest Neighboring Particle Searching 22
2.2. Governing Equation 23
2.2.1. Momentum Equation 23
2.2.2. Energy Equation 14
2.3. Explict Incompressible SPH 14
2.3.1. Projection Time Integration 14
2.3.2. Explicit PPE Analysis in SPH Formulation 16
2.4. Numerical Scheme for SPH Accuracy 17
2.4.1. SPH derivative correction 17
2.4.2. Particle Shifting Scheme 19
2.4.3. Boundary Treatment 20
Chapter 3 Dynamic LES-SPH Model 25
3.1. Optimized SPH Formulation for LES-SPH model 26
3.1.1. Spatial Weighting Function for LES-SPH model 27
3.1.2. SPH Formulation for LES Filtering Operator 28
3.1.3. Improvement of Filtered Derivative Operator 30
3.2. Dynamic LES-SPH model 32
3.2.1. Standard Smagorinsky Model 32
3.2.2. Dynamic Smagorinsky Model 33
3.2.3. Dynamic Vreman Model 35
3.2.4. Turbulent Prandtl Number Modeling 37
3.3. Validation and Verification 39
3.3.1. Benchmark of Lid-driven Flow 39
3.3.2. Transient Lid-driven Flow 39
3.3.3. Turbulent Lid-driven Flow 41
3.3.4. Benchmark of Rayleigh Benard Convection 43
3.3.5. Turbulent Rayleigh Benard Convection 44
Chapter 4 Phase Change Model for SPH 73
4.1. Ethalpy-Based Phase Change Model for SPH 73
4.1.1. PPE Analysis for SPH Phase-Change Model 73
4.1.2. Enthalpy-Porosity Model for Mushy zone 74
4.2. Validation and Verification 76
4.2.1. 2D Stefan Solidification Problem 76
4.2.2. 2D Thermal ablation with natural convection 78
4.2.3. 3D Thermal ablation with transition natural convection 79
Chapter 5 Analysis of IVR-ERVC 97
5.1. Full-Scale Analysis of IVR-ERVC 97
5.1.1. Severe Accident Scenario 97
5.1.2. Initial Condition for IVR-ERVC 98
5.1.3. Simulation Setup 99
5.2. Results and Discussion 99
Chapter 6 Conclusion 109
6.1. Summary 109
6.2. Recommendation for Future Work 112

References 117
Abstract in Korean 129



List of Tables

Table 1.1 CFD researches on thermal ablation and phase change 8
Table 1.2 Pevious SPH researches on turbulence model 9
Table 3.1 RMSE of double filtered derivative method 68
Table 3.2 SPH discretization of DSM in grid filter scale 68
Table 3.3 SPH discretization of DSM in test filter scale 69
Table 3.4 Volume averaging method in DSM model 69
Table 3.5 SPH discretization of DVM in grid filter scale 69
Table 3.6 SPH discretization of DVM in test filter scale 70
Table 3.7 Volume averaging method in DVM model 70
Table 3.8 Global model for turbulent Pr number 71
Table 3.9 Local model for turbulent Pr number 71
Table 3.10 Simulation condition of RB convection 72
Table 3.11 Initial condition of RB convection 72
Table 4.1 EPM application in projection step 94
Table 4.2 EPM application in correction step 94
Table 4.3 Modeling condition for 2D melting simulation 95
Table 4.4 Simluation conditions for gallium thermal ablation 95
Table 4.5 Initial condition for sensitivity study 96
Table 5.1 Chronology of events in severe accident 107
Table 5.2 Material properties of metal layer 107
Table 5.3 Initial condition of metal layer 108
Table 5.4 Material properties of oxide layer 108
Table 5.5 Initial condition of oxide layer 108


List of Figures

Figure 2.1 Lagrangian and Eulerian specification 21
Figure 2.2 SPH interpolation and kernel function 22
Figure 2.3 Link-list algorithm for NNPS 22
Figure 2.4 Dissatisfaction of unity condition near boundary 23
Figure 2.5 Generalized bounadry condition 23
Figure 2.6 EISPH solver Algorithm 24
Figure 3.1 Attenuation factor distribution 47
Figure 3.2 Grid filter and Test filter concept in SPH 47
Figure 3.3 Benchmark for double filtered derivative 48
Figure 3.4 Benchmark for the effect of numerical correction method, spatial resolution and particle distribution 48
Figure 3.5 Benchmark for 1st order derivative accuracy 49
Figure 3.6 Benchmark for derivative accuracy near boundary 50
Figure 3.7 SPH derivative discretization method near wall 50
Figure 3.8 Benchmark results (Rate of Strain) 51
Figure 3.9 DSM concept in energy spectrum 52
Figure 3.10 Turbulent Prandtl number distribution of low-Prantl number fluid 52
Figure 3.11 Dimensionless velocity and temperature distribution in boundary layer at different turbulent Pr number 53
Figure 3.12 Simulation geometry of cubical cavity flow 54
Figure 3.13 Averaged velocity profile at Re=5,000 55
Figure 3.14 RMS velocity profile at Re=5,000 56
Figure 3.15 Streamline with x-directional velocity (SSM) 57
Figure 3.16 Streamline with x-directional velocity (DSM) 58
Figure 3.17 Streamline with x-directional velocity (DVM) 59
Figure 3.18 Averaged velocity profile at Re=12,000 60
Figure 3.19 Skin friction factor at the bottom(Re=12,000) 61
Figure 3.20 RMS velocity profile at Re=12,000 62
Figure 3.21 Streamline with x-directional velocity (SSM) 63
Figure 3.22 Streamline with x-directional velocity (DVM) 64
Figure 3.23 Spectral analysis of simulation results of SSM 65
Figure 3.24 Spectral analysis of simulation results of DVM 65
Figure 3.25 Schematic of Rayleigh-Benard Convection 66
Figure 3.26 Temperature-Density distribution of water 66
Figure 3.27 Averaged Nusselt number distribution over time (inversion parameter of 0.0) 67
Figure 3.28 Averaged Nussetl number distribution over time (inversion parameter of 0.5) 67
Figure 4.1 Phase Change Model 83
Figure 4.2 Compressed particle distribution near boundary 84
Figure 4.3 Mushy zone and porous media 84
Figure 4.4 Schematic of 2D solidification simulation 85
Figure 4.5 The position of phase front in diagonal direction 85
Figure 4.6 The position of phase front over time 86
Figure 4.7 Schematic of 2D melting simulation 86
Figure 4.8 The position of phase front of 2D melting simulation 87
Figure 4.9 Temperature distribution of 2D metling simulation 87
Figure 4.10 Averaged Nusselt number at hot wall surface 88
Figure 4.11 Liquid fraction in entire domain over time 88
Figure 4.12 Schematic of gallium melting experiment 89
Figure 4.13 Phase interface at t=125.0 with various resolutions 89
Figure 4.14 Phase interface at t=225.0 with various resolutions 90
Figure 4.15 Phase interface at t=325.0 with various resolutions 90
Figure 4.16 Liquid fraction at 325.0s with various resolutions 91
Figure 4.17 Normalized liquid fraction 91
Figure 4.18 Phase interface position over time 92
Figure 4.19 Enthalpy-porosity distribution at each time step 92
Figure 4.20 Total Liquid fraction over time 93
Figure 5.1 Initial configuration of IVR-ERVC simulation 102
Figure 5.2 SPH input configuration of IVR-ERVC 102
Figure 5.3 RPV and ablated metal behavior over time 103
Figure 5.4 RPV configuration at 0.0 and 18.0 second 104
Figure 5.5 Total mass of ablated metal over time 104
Figure 5.6 Temperature distribution over time at x=0.0m 105
Figure 5.7 Temperature distribution at the bottom of light metal layer 106
Figure 6.1 Flow chart of future work 116		-
dc.format.extentⅷ, 131-
dc.language.isokor-
dc.publisher서울대학교 대학원-
dc.subjectSmoothed Particle Hydrodynamics-
dc.subjectDynamic Large Eddy Simulation-
dc.subjectThermal Ablation-
dc.subjectTurbulence-
dc.subjectPhase Change-
dc.subject.ddc622.33-
dc.titleDevelopment of Dynamic LES-SPH Method for Thermal Ablation Analysis with Turbulent Natural Convection-
dc.title.alternative전이 및 난류 자연 대류 유동을 동반한 열적 침식 해석을 위한 입자법 기반 동적 대와류 모델 개발-
dc.typeThesis-
dc.typeDissertation-
dc.contributor.AlternativeAuthorTae Soo Choi-
dc.contributor.department공과대학 에너지시스템공학부-
dc.description.degree박사-
dc.date.awarded2023-08-
dc.contributor.major원자핵공학-
dc.identifier.uciI804:11032-000000179595-
dc.identifier.holdings000000000050▲000000000058▲000000179595▲-
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