Using discrete element modelling (DEM) and breakage experiments to model the comminution action in a tumbling mill

Includes abstract.Includes bibliographical references (leaves 147-153).The Discrete Element Method (DEM) is a powerful modelling tool that characterises the system at the individual particle level. This makes it particularly well suited for simulating tumbling mills whose charge is principally individual particles (steel balls, rocks and fines). The use of DEM to simulate tumbling mills has proliferated since the early 1990s and been successfully employed to predict important milling parameters such as charge motion, power draw, liner wear and impact energy distribution. The ultimate aim of any model of the tumbling mill is to predict the product of the milling process. Current DEM simulations of the tumbling mill however do not simulate the breakage of the particles and as such can not directly predict the product. In order to predict the performance of industrial-scale tumbling mills, laboratory-scale mills are used to experimentally obtain data, which is then scaled up using black box mathematical models. In this thesis a tumbling mill model that utilises the power of DEM to provide the mechanical environment and the energies available for breakage is proposed. The incorporation of DEM eliminates the need to scale up because DEM is able to simulate the actual industrial-scale device. Data from breakage experiments on the ore being treated is also incorporated into the model to determine the breakage functions. Population balance techniques are applied in the mathematical framework of the model to predict the product of the comminution process. In order to test the proposed tumbling mill model, DEM simulations of a 1.695m diameter pilot SAG mill using charge based on actual operation data were performed and analysed. Results from the DEM simulation and Drop Weight Tester breakage experiments were then used in the proposed tumbling mill model to predict the evolution of the product size distribution

Viscoelastic behavior in discrete element method realized by interparticle Maxwell-Zener model

The discrete element method describes the motion of granular structures numerically. Each particle is considered as a discrete element. Combining springs and dashpot for the normal contact forces, viscoelastic behavior represented by rheological models is realized via a nonlinear Maxwell–Zener model in a dynamic routine. For individual contacts and large particle structures, this model is compared to the Hertzian contact model for elastic behavior and studied with respect to rate dependence and the effect of model parameters

Development of GPU-based SPH Framework for Hydrodynamic Interactions With Non-spherical Solid Debris

일본의 후쿠시마 사고 이후 원자로 중대 사고에 대한 연구의 필요성과 대처 능력 확보에 대한 중요성이 점점 증가하고 있다. 사고 시 발생할 수 있는 노심 용융물 거동에 대한 평가는 용융물-콘크리트 상호작용(MCCI, Molten Core Concrete Interaction)과 증기 폭발로부터의 원자로 노심 냉각성 및 건전성에 따른 재임계 측면에서 매우 중요하다. 특히 OPR 1000의 경우, 사전 충수 조건(Wet cavity condition)을 기본적인 원자로 외벽 냉각 대응 전략으로 채택함으로써 핵연료-냉각재 상호작용(FCI, Fuel Coolant Interaction) 반응이 필연적으로 발생하는 것으로 알려져 있다. [Jin, 2014] FCI 현상은 임의 형태의 핵연료 고체 파편물과 냉각재의 상호작용뿐만 아니라, 냉각재 비등 현상 등도 포함하는 다유체, 다상 현상으로 그 현상이 매우 복잡하다. 이 과정에서 원자로 건물 하부에 고체 파편물이 퇴적되어 잔해 층이 형성되고, 그 냉각성에 따라 사고의 다음 진행 상황에 영향을 줄 수 있다. 이러한 비구형 고체 파편물 거동에 대한 이해를 위해 강체 개념을 적용한 고체 해석 체계는 좋은 접근법이 될 수 있다. 따라서 본 연구에서는 유체와 고체 간 수력학적 상호작용 해석을 위해 입자유체동역학(SPH, Smoothed Particle Hydrodynamics) 기법과 강체역학(RBD, Rigid Body Dynamics) 기법을 연계하여 라그랑지안 해석 체계를 구축하였다. 완화입자유체동역학 기법은 해석 유체를 유한개의 입자로 표현함으로써 유동을 해석하는 라그랑지안 해석 기법 중 하나이다. 개별 입자들의 움직임으로 유동을 해석하므로 비선형의 대류항에 대한 계산이 필요 없으며, 입자가 추가되거나 사라지지 않는 한 해석 계의 전체 질량은 자동으로 보존된다. 이러한 라그랑지안 기법의 특성으로 SPH 방법은 자유 표면 유동, 다유체 유동, 다상 유동, 형태 변화가 큰 유동 등에 대해 해석 장점을 갖는다. 본 연구에서는 SPH 기법을 적용한 in-house SOPHIA 코드를 사용하여 비압축 다상 유동 해석을 수행하였으며, 벤치마크 데이터와의 비교에서 좋은 검증 해석 결과를 보였다. 강체역학은 외력에 의해 형태가 변하지 않는 강체의 개념을 이용하여 고체의 병진 운동과 회전 운동을 해석하는 연구 분야이다. 본 연구에서는 이산요소법(DEM, Discrete Element Method) 분야에서 오랜 시간 동안 널리 사용되고 검증되었던 Hertz-Mindlin 충돌 모델을 적용하여 강체 간 충돌 해석을 구현하였다. 강체는 유한개의 입자들로 표현할 수 있으며, 강체 간 충돌은 각 강체를 구성하고 있는 입자쌍의 작은 중첩을 기반으로 계산된다. 본 연구에서는 입자기반의 강체역학 해석 코드를 이용하여 단일 강체 및 다중 강체 충돌에 대해 검증 해석을 수행하였으며, 해석해 및 벤치마크 데이터 결과와 잘 일치함을 확인하였다. 원자력 분야에서 발생할 수 있는 비구형 고체와 유체간 상호작용 해석을 위해 앞서 설명한 SPH 기법과 강체역학 연계 해석 코드를 개발하였다. 본 연구에서 적용한 완전 해상 방식(Fully resolved approach)은 유체-고체의 상이 분리되어 있고, 제 1 원리를 만족하므로 고체의 형상에 따른 상관식과 표면 적분이 필요하지 않다는 장점이 있다. 또한 고체 경계면에서의 정확한 압력 계산을 위해 유체 입자 정보를 기반으로 노이만 압력 경계 조건을 적용하였다. 본 연구에서는 이러한 해상 방식의 유체-강체 연계 해석 코드를 이용하여 비구형 고체와 유체의 수력학적 상호작용에 대한 검증 해석을 수행하였으며, 선행된 실험과의 비교에서 좋은 결과를 보였다. 유동 해석을 위해 본 연구에 적용한 SPH 방법에서는 수식들이 매우 선형적이고 외연적(Explicit)으로 계산을 수행하기 때문에 각 입자에 대한 계산이 독립적으로 수행되어도 문제가 없다. 따라서 SPH 방법은 계산 병렬화에 최적화된 방법으로 잘 알려져 있으며, 대규모 고해상도 해석을 위해 이는 필수적이다. 또한 입자 기반의 강체 계산을 위해서는 효율적인 계산 알고리즘이 필요하다. 따라서 본 연구에서는 대규모 계산과 높은 연산 효율성을 위해 그래픽처리장치(GPU, Graphic Processing Unit)를 이용하여 계산 병렬화를 수행하였으며, 이를 이용한 다중 고체와 유체의 상호작용 해석에서 좋은 계산 성능을 확인하였다. 본 연구에서 수행한 비구형 고체와 유체의 수력학적 상호작용을 위한 GPU 기반의 SPH 해석 코드 개발 연구를 통해 원자로 중대사고 시 발생할 수 있는 냉각재와 핵연료 고체 파편물의 수력학적 상호작용 뿐만 아니라, 고체 파편물 간 역학적 상호작용에 대해 효율적인 해석 체계를 개발하였다. 이를 통해 습식 공동(wet cavity)에서 발생하는 핵연료 고체 파편물의 퇴적 작용, 쓰나미 사고로 인한 해안 구조물의 수력학적 상호작용, 그리고 침수 사고 시 원자로 건물 내 부유물의 거동 등 원자력 분야에서 발생할 수 있는 다양한 고체-유체의 수력학적 상호작용에 대한 해석적 연구에 적용하고 기여할 수 있을 것으로 기대한다.Since the Fukushima accident, the necessity for researches on severe accidents and the importance of securing the ability to cope with the accidents have been increasing. The evaluation of the molten core behavior that may occur during the accident is very important in terms of re-criticality according to the coolability and integrity of the reactor core from the MCCI (Molten Core Concrete Interaction) and steam explosion. In the case of OPR 1000, especially, FCI (Fuel Coolant Interaction) is known to occur unconditionally because the wet cavity condition has been adopted as a basic strategy for ex-vessel cooling. [Jin, 2014] FCI is a highly complicated phenomenon, which includes multi-fluid, multi-phase interaction between the arbitrary shape of solid debris and coolant as well as coolant boiling. In this process, the debris bed is formed at the bottom of the containment, and its coolability influences the next phase of the accident. For the understanding on the solid debris behavior, a solid system with a rigid body can be a good approach for the non-spherical solid debris analysis. Therefore, in this study, Smoothed Particle Hydrodynamics (SPH) method and Rigid Body Dynamics (RBD) are coupled in a fully Lagrangian manner for the hydrodynamic interactions between fluid and solid. Smoothed Particle Hydrodynamics (SPH) is one of the Lagrangian-based analysis methods which represents the fluid flow as a finite number of particles. Since the flow is analyzed by the motion of individual particles, there is no need to calculate the nonlinear convective term, and the total mass of the system is automatically conserved as long as particles are not added or removed. Through these Lagrangian nature, it is well known that the SPH method is effective for the free surface flow, multi-fluid and multi-phase flow, and highly deformable flow. In this study, the incompressible multi-phase flow analysis has been performed using the in-house SPH code, SOPHIA code, and V&V simulation results showed good agreement with the benchmark data. Rigid Body Dynamics (RBD) is a research field that analyses the translation and rotation of a solid body by using the concept that a rigid body doesn’t change its shape by external forces. In this study, the collision calculation between rigid bodies is implemented by applying the Hertz-Mindlin contact force model commonly used and verified for a long time in the Discrete Element Method (DEM) field. A rigid body can be expressed as a group of finite particles, and the contact forces between solid bodies are calculated based on the small overlap of the particle pairs. Using the particle-based RBD analysis code implemented in this study, V&V simulations on single- and multi- rigid body collisions have been performed and showed good agreement with the analytical solution and the benchmark data. To analyze the hydrodynamic interactions between non-spherical solids and fluids that can occur in the nuclear field, the integrated code has been developed by coupling RBD with SPH code. Since a fully resolved approach adopted in this study as a phase coupling method satisfies the 1st principle and the fluid-solid phase is entirely separated from each other, there is no need for the surface integral and empirical correlations depending on the solid geometry. In addition, the Neumann pressure boundary condition is implemented for accurate pressure estimation at the solid interface using the fluid particle properties. By applying the resolved SPH-RBD coupled code, V&V simulations were carried out on the hydrodynamic interactions of non-spherical solid-fluid and showed good agreement with the experimental data. In the SPH method, since the numerical expression are highly linear and the calculations are performed explicitly, there is no problem even if the calculations for each particle are performed independently. Therefore, the SPH is well known as an optimized method for parallelization, and it is essential for large scale high-resolution simulations. In addition, an efficient computational algorithm is required for particle-based rigid body calculation. In this study, therefore, the parallelization was performed using a Graphical Processing Unit (GPU) for large-scale calculations and high computational efficiency, and it showed a good performance in analyzing the interactions of a large number of solids and fluids particles. Through the researches on the development of a GPU-based SPH framework for the hydrodynamic interaction of non-spherical solids and fluids in this study, an efficient analysis system has been developed for not only the hydrodynamic interaction of solid corium debris with coolant but also the mechanical interaction between solid debris which can occur at the severe accidents in the nuclear reactor. By using this, it is expected that the integrated code will contribute to analytical researches on various accident scenarios that may occur in the nuclear field such as solid fuel debris sedimentation in the wet cavity, hydrodynamic interactions with coastal structures caused by the Tsunami, and the behavior of floating objects in the reactor building at the flooding accident, etc.Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Previous Studies 3 1.2.1 Numerical Studies on FCI Premixing Jet Breakup 3 1.2.2 Numerical Studies on Fluid-Solid Coupling with RBD 4 1.3 Objectives and Scope 5 Chapter 2 Smoothed Particle Hydrodynamics (SPH) 9 2.1 SPH Overview 9 2.1.1 Basic Concept of SPH 9 2.1.2 SPH Particle Approximation 10 2.1.3 SPH Kernel Function 12 2.1.4 SPH Governing Equations 13 2.2 SPH Multi-phase Models 16 2.2.1 Normalized Density Approach 16 2.2.2 Treatments for Multi-phase Flow 17 2.2.3 Surface Tension Force Model 18 2.3 SPH Code Implementation 20 2.3.1 Nearest Neighbor Particle Search (NNPS) 20 2.3.2 Algorithm of SPH Code 21 2.3.3 Time Integration 21 2.3.4 GPU Parallelization 22 Chapter 3 Rigid Body Dynamics (RBD) 30 3.1 RBD Overview 30 3.2 Collision Models of Rigid Body 31 3.2.1 Monaghan Boundary Force (MBF) Model 31 3.2.2 Ideal Plastic Collision Model 33 3.2.3 Impulse-based Boundary Force (IBF) Model 35 3.2.4 Penalty-based Contact Model 37 3.2.5 Determination of Collision Model 40 3.3 Algorithm of RBD 41 3.3.1 Calculation of Rigid Body Information 41 3.3.2 Contact Detection 42 3.3.3 Contact Normal Calculation 42 3.3.4 Contact Force Calculation 45 3.3.5 Summation of Rigid Body Particles 46 3.3.6 Time Integration 47 3.4 GPU Parallelization 48 3.4.1 Algorithm 1: Atomic Operation 49 3.4.2 Algorithm 2: Sorting 50 3.5 Code V&V Simulations 51 3.5.1 Conservation of Momentum & Angular Momentum 51 3.5.2 Conservation of Kinetic Energy in Elastic Collision 52 3.5.3 Bouncing Block 53 3.5.4 Sliding Block on a Slope 55 3.5.5 Collapse of Stacked Multi-body 57 Chapter 4 Two-way Coupling of SPH-RBD 75 4.1 Resolved Approach 75 4.2 Governing Equations 75 4.2.1 Solid Phase 75 4.2.2 Fluid Phase 78 4.3 Algorithm of SPH-RBD Code 78 4.4 Code V&V Simulations 81 4.4.1 Karman Vortex Problem 81 4.4.2 Water Entry 84 4.4.3 Sinking & Rotating Body 85 4.4.4 Floating & Falling Body 85 4.4.5 Collapse of Stacked Multi-body with Fluid 87 4.4.6 Code Application to Non-spherical Debris Sedimentation 89 Chapter 5 Conclusion 110 5.1 Summary 110 5.2 Recommendations 112 Nomenclature 114 Bibliography 117 국문 초록 127박

Micromechanics of hot mix asphalt material formulation and numerical simulation

Hot Mix Asphalt (HMA), a highway and airfield pavement material, is heterogeneous, granular, and composite. It is traditionally modeled as a homogeneous material using continuum mechanics or semi-empirical methods. As a result, the above models either neglect or over-simply component reactions, failing to predict field performance problems resulting from particle segregation. This research presents micromechanical modeling, a novel approach that accounts for the components. A micromechanical model is developed for HMA by modeling it as an assembly of asphalt cement coated particles. The asphalt cement is modeled as a viscoelastic material. To represent asphalt cement, several viscoelastic elements (i.e. Maxwell, Kelvin-Voigt, and Burgers\u27 elements) were considered. From these viscoelastic elements the Burgers\u27 element is shown to be most representative of asphalt binder behavior based on mechanical responses and comparisons with physical experimental results. The model for HMA, ASBAL, is based on the TRUBAL program, a Discrete Element Method (DEM), with Burgers\u27 element. Monotonic and cyclic tests were simulated to observe the ability of the model to predict the mechanical behavior of HMA. During these simulations the physical values of microscopic input parameters were varied to determine how each contributes to the overall behavior of HMA. Then, the ASBAL model was used to simulate a mechanical test with x-ray tomography to accurately predict residual stresses of the laboratory sample after compaction, the initial modulus, stress levels throughout the test, and number of contacts within HMA matrix. Using the master curve and the time-temperature superposition theory the input parameters for the Burgers\u27 element at different temperatures were calculated. Using those input parameters, the mechanical responses of HMA at different temperatures were simulated. Results show that at higher temperatures the strength and initial stiffness values are a fraction of those found at lower temperatures. Hence the ASBAL model predicts the temperature softening of HMA that contributes to the rutting of HMA. The micromechanical model simulates the discrete mechanical behavior of HMA and hence can be used to develop performance based tests for HMA

다상유동 및 고체 파편물의 수력학적 거동 해석을 위한 GPU 기반의 SPH-DEM 연계해석 코드 개발

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 에너지시스템공학부, 2020. 8. 김응수.In the late phase severe accident of LWR, the massive corium releases out of the reactor pressure vessel (RPV) and falls to the coolant if the In-Vessel Retention (IVR) strategy fails. The melt jet can be fragmented into debris particles based on the assumption that the ex-vessel pool is sufficiently deep. It is known that there are various three-phase flow issues associated with the fragmented debris particles under the influence of phase change of cavity coolant. In such cases, the vapor phase forms a sharp and dynamic interface with the liquid phase while the transient relocation behavior of debris particles is the main concern. Thus, coupling Lagrangian-based multi-phase CFD techniques and Discrete Element Method (DEM) can be an effective approach in terms of numerical modeling of such behaviors. In this respect, an integrated numerical code for incompressible 3-phase flow has been developed in this study by two-way phase coupling of multi-phase Smoothed Particle Hydrodynamics (SPH) and DEM model. Smoothed Particle Hydrodynamics (SPH) is one of the best-known meshless CFD methods in which the fluid system is represented as the finite number of Lagrangian particles. The SPH code developed in this study proposes a new density estimation model and improves the surface tension model for accurate simulation of incompressible two-phase flow behavior. The demonstration of its applicability has been performed through several V&V simulations including multi-phase dam-break and sloshing simulations. Discrete Element Method (DEM) is a direct simulation method for a rigid body that can analyze the translation, rotation, and collision behavior of solid particles in detail. The soft-sphere collision model with Hertz-Mindlin contact force equations is adopted for developed DEM code in this study. To precisely estimate the wall boundary interactions of bed-formed debris particles, a versatile wall boundary model is newly proposed in this study that also covers the sliding and rolling behavior of solid particles. The inter-particle collision behavior and sliding & rolling motion of particles are well proven in several V&V cases. The numerical code system for incompressible 3-phase flow is newly developed by two-way phase coupling of the above two models (SPH-DEM). The unresolved coupling approach between two methods was adopted for the analysis of the overall behavior of particulate solid debris. The fundamental validation of the phase coupled model was performed for both single-particle behavior and particulate granular flow such as dam-breaking motion of particle-fluid. The SPH-DEM coupled code in this study has been parallelized based on Graphical Process Unit (GPU) in order to overcome the inherent efficiency problem of the Lagrangian-based numerical method. Parallel mapping and reduction are applied for solving discretized summation equations of each SPH particle, solving contact force equations for each DEM particle, and also for solving coupling equations between SPH and DEM particles. The efficiency of code parallelization was evaluated through the scalability analysis based on the benchmark calculation. Finally, the simulation of the vapor-driven leveling behavior of spherical solids was performed as a case study to demonstrate the applicability of the developed code. The time-variant surface shape of solid particles was compared with the benchmark experiments both qualitatively and quantitatively. The effect of gas flow rate on the tendency of leveling behavior also has been analyzed. The developed numerical system in this study is expected to be a good alternative for the simulation of such phenomena that were difficult to handle with traditional numerical methods since the numerical schemes used in the code have a high potential for simulation of complicated physics with highly deformable geometry. In addition, this validated code system can contribute to hydrodynamic modeling studies for severe accident technology by performing numerical experiments on conditions that hard to be conducted on a laboratory scale.가압경수로 중대사고 후기 과정에서 핵연료 용융물 노내 억류 전략의 실패로 용융 핵연료가 용기 바깥쪽 침수 공동으로 재배치되면, 공동의 깊이나 제트의 속도 등의 조건에 따라 핵연료 파편화가 발생할 수 있다. 이러한 핵연료 파편물에서 발생하는 붕괴열에 의해 냉각재의 상변화가 이루어지면, 이상유동 자연대류와 고체 파편물이 공존하는 3상유동 시스템이 된다. 핵연료 용융물의 제트 파쇄, 하강 및 퇴적, 평탄화 등 일련의 과정에서 다양한 형태의 파편물 3상 냉각 거동이 발생할 수 있으며, 핵연료 파편물의 붕괴열이 충분히 제거되지 못하면 파편물의 응집 및 재용융이 발생할 수 있다. 중대사고 완화의 관점에서 이러한 3상 냉각 거동에 대한 상세한 이해가 필요하지만, 이상유동 자연대류, 이상유동 열전달, 고화, 용융, 비등, 유동-입자 상호작용 등을 포함하는 거동 자체의 복잡성으로 인해 관련 현상들의 예측 및 평가는 큰 불확실성을 내포하고 있다. 전통적인 핵연료 파편물을 포함한 3상 거동 해석은 다른 중대사고 해석과 마찬가지로 경험적 방법론에 의존한 보수적인 접근 방법이나 고체 입자와 이상 유체를 모두 연속체로 가정하는 다유체 모델을 기반으로 이루어졌다. 최근에는 이러한 방법론들이 가지는 본질적인 한계를 극복하고자 고체 입자들 사이의 충돌이나 회전을 별개로 다루는 이산요소법(Discrete Element Method, DEM)과 격자 기반의 오일러리안 전산유체해석(CFD) 기법을 연계하는 형태로 서로 간의 상호작용을 해석하는 연구들이 많이 이루어지고 있다. 한편, 최근에는 하드웨어 및 소프트웨어의 성능이 비약적으로 좋아지면서 격자(Grid)에 기반하지 않고 질점 하나하나의 움직임을 따라가면서 유동에 대한 지배방정식을 해석하는 라그랑지안 유체 해석기법의 응용이 늘어나고 있다. 라그랑지안 해석 기법에서는 다상유동 해석 시에 액체와 기체 두 상을 완전히 별개의 영역으로 해상하여 지배방정식을 풀기 때문에 계면 마찰력이나 항력, 양력 등에 대한 별도의 상관식 없이 제 1 원리 기반으로 유동을 해석할 수 있어, 이상유동에 대한 보다 근본적인 해석이 가능하다. 핵연료 파편물의 생성 및 3상 냉각 거동과 관련된 현상들은 대부분 기체 상의 생성이나 이상유동 자연대류에 영향을 받는 현상들로 액체 기체 사이의 인터페이스가 복잡하고 역동적인 경향이 있기 때문에, 액체-기체 다상유동에 효과적인 라그랑지안 기반의 유체해석 기법과 강체 이산요소법(DEM)을 연계하면 효과적인 3상 유동 해석 체계를 구축할 수 있다. 하지만, 핵연료 파편물을 포함한 3상 냉각 거동과 관련하여 라그랑지안 입자 기반 유체해석 기법을 활용한 연구는 세계적으로도 아직 수행된 바가 없다. 이러한 필요성에 따라, 본 연구에서는 대표적인 입자 기반의 유체해석 방법론 중 하나인 완화입자유체동역학(Smoothed Particle Hydrodynamics, SPH) 기법과 강체의 충돌, 병진, 회전 운동을 직접적으로 다루는 이산요소법(DEM)의 연계를 통해 고체 입자를 포함한 3상 유동 해석을 위한 라그랑지안 해석 체계를 구축하였다. 고체 입자와 유체 사이의 연계는 mm 이하의 스케일을 가지는 핵연료 파편물의 형상적 특성을 고려하여 두 상 사이의 겹침을 허용하여 운동량 교환을 모델링하는 비해상(unresolved) 방식으로 이루어졌다. 또한, SPH 유체 모델, DEM 강체 모델, SPH-DEM 연계 모델 각각에 대한 검증을 다양한 스케일에서 다양한 실험 연구들과의 비교를 통해 수행하였다. 한편, 완화입자유체동역학(SPH) 기법과 이산요소법(DEM) 모델은 라그랑지안 해석 기법의 특성상 컴퓨터 성능의 비약적인 발전에도 불구하고 오일러리안 해석 기법에 비해 계산 효율 및 시간에 대한 상대적인 제약이 존재한다. 특히 액체-기체의 이상유동 해석을 다룰 경우 기체 상의 밀도가 작기 때문에 라그랑지안 유체해석 기법에서는 더 작은 시간 간격이 요구된다. 이에 본 연구에서는 그래픽 처리 장치 (Graphics Processing Unit, GPU)를 활용하여 SPH 해석, DEM 해석, SPH-DEM 연계 해석이 모두 각 라그랑지안 질점에 대해 동시에 수행될 수 있도록 GPU 기반의 연계코드 병렬화 및 가속화를 수행하였다. 마지막으로 개발한 라그랑지안 기반의 3상유동 해석 체계의 유용성 입증을 위해 원자로 중대사고 후기 과정에서 발생할 수 있는 핵연료 파편물 층(debris bed)의 평탄화(self-leveling) 거동에 대한 검증 해석을 수행하였다. 시간에 따른 파편물 층 표면의 형상 변화를 타 기관에서 수행된 기체주입 실험과 비교하는 형태로 검증이 이루어졌다. 분석 결과, 본 연구에서 개발한 SPH-DEM 연계해석 코드가 고체 입자 상을 포함한 수력학적 3상 거동을 정량적으로, 정성적으로 잘 해석하는 것을 확인하였다. 본 연구에서 개발한 라그랑지안 기반의 SPH-DEM 3상유동 해석 체계는 원자로 중대사고의 해석적 관점에서 기존의 수치해석 기법들이 다루기 어려웠던 현상들에 대한 대안 또는 상호 보완의 역할을 할 수 있다. 또한, 본 연구에서 개발한 코드는 제 1원리 기반의 물리 법칙을 기반으로 유동 및 강체의 거동을 해석하기 때문에 실험으로 구현하기 어려운 조건이나 스케일에 대한 수치적 재현이 가능하고, 이를 바탕으로 기존의 스케일링 법칙을 검증하거나 실험 결과가 없는 영역에서 수치 데이터를 생성하여 기존의 상관식을 개선하는데 활용할 수 있다. 이러한 점에서 본 연구는 원자로 중대사고의 해석이나 안전성 평가와 관련하여 불확실성을 저감하는데 기여한다.Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Previous Studies 3 1.2.1 Numerical Studies on Particulate Debris Bed 3 1.2.2 SPH-DEM Phase Coupling 4 1.3 Objectives and Scope 5 Chapter 2 Fluid Phase: Smoothed Particle Hydrodynamics 8 2.1 Smoothed Particle Hydrodynamics (SPH) 9 2.1.1 SPH Particle Approximation 9 2.1.2 SPH Particle Approximation of Derivatives 10 2.1.3 Kernel Function 11 2.1.4 Accuracy of SPH Approximation 12 2.1.5 Governing Equations for Incompressible Flow 14 2.2 Multi-phase SPH Governing Equations 16 2.2.1 Treatment of Multi-Phase Flow 16 2.2.2 Normalized Density Model 18 2.2.3 Continuum Surface Force (CSF) Model 19 2.3 Implementation of SPH Model 21 2.3.1 Algorithm of SPH Code 21 2.3.2 Nearest Neighboring Particles Searching (NNPS) 22 2.3.3 Time Integration 23 2.4 V&V Simulations 24 2.4.1 Rayleigh-Taylor Instability 25 2.4.2 Bubble Terminal Velocity 25 2.4.3 Dam-Break Simulation 25 2.4.4 Centralized Sloshing Simulation 26 Chapter 3 Solid Phase: Discrete Element Method 45 3.1 Discrete Element Method (DEM) 46 3.2 DEM Contact Force 47 3.2.1 Soft-sphere Contact Model 47 3.2.2 Contact Force Model 48 3.2.3 Hertz-Mindlin Contact Force Model 49 3.3 Wall Boundary Conditions 52 3.3.1 Versatile Wall Boundary Model 52 3.3.2 Particle Collision with the Wall 54 3.3.3 Sliding and Rolling on the Wall Boundary 56 3.4 DEM Implementation Algorithm 57 3.4.1 Contact Detection 58 3.4.2 Estimation of Relative Velocity 59 3.4.3 Calculation of Contact Force 60 3.4.4 Wall Boundary Conditions and Time Integration 60 3.5 V&V and Simulations 61 3.5.1 Conservation of Momentum and Angular Momentum 62 3.5.2 Conservation of Energy in Elastic Collision 63 3.5.3 V&V Simulations for Wall Boundary Model 63 3.5.4 Granular Collapse of Spherical Particles 64 Chapter 4 Two-way Phase Coupling of SPH and DEM 76 4.1 Unresolved Coupling of SPH and DEM 76 4.2 Governing Equations 78 4.2.1 SPH Particles: Locally Averaged N-S Equations 78 4.2.2 DEM Particles: Coupling Forces Acting on Solid Particles 80 4.2.3 SPH Particles: Reaction Force from Momentum Exchange 82 4.3 Algorithm of SPH-DEM Coupled Model 83 4.4 V&V Simulations for SPH-DEM Coupled Model 84 4.4.1 Single DEM Particle Behavior 85 4.4.2 Pressure Drop through Packed Bed 87 4.4.3 Granular Flow in Liquid: 3D Dam-Break 89 Chapter 5 GPU Parallelization of Coupled SPH-DEM Code 103 5.1 Parallelization of Governing Equations 104 5.1.1 GPU-based Parallelization 104 5.1.2 Parallelization of SPH-DEM Governing Equations 104 5.2 Parallelization of NNPS and Contact Detection 105 5.3 Results of GPU Parallelization 107 5.3.1 Speedup in Computation Time 107 5.3.2 Parallelization Factors 107 Chapter 6 Code Application to Vapor-Driven Leveling Behavior of Spherical Debris 113 6.1 Self-Leveling Behavior of Debris Bed 114 6.1.1 Self-Leveling Issue in LWR 114 6.1.2 Self-Leveling Behavior in Terms of Debris Coolability 114 6.2 Benchmark Experiment 116 6.3 SPH-DEM Simulation Setup 118 6.3.1 Properties and Simulation Conditions 118 6.3.2 Sequence of SPH-DEM Leveling Simulation 120 6.3.3 Determination of Inclined Angle 121 6.4 Validation Results and Discussions 121 6.4.1 SPH-DEM Simulation Results 121 6.4.2 Validation Result 122 6.4.3 Effect of Gas Flow Rate 122 Chapter 7 Summary 129 7.1 Summary 129 7.2 Recommendations 131 References 134 국문 초록 142Docto

Development of a discrete element model with moving realistic geometry to simulate particle motion in a Mi-Pro granulator

This paper presents the implementation of a methodology incorporating a 3D CAD geometry into a 3D Discrete Element Method (DEM) code; discussing some of the issues which were experienced. The 3D CAD model was discretised into a finite element mesh and the finite wall method was employed for contact detection between the elements and the spherical particles. The geometry was based on a lab scale Mi-Pro granulator. Simulations were performed to represent dry particle motion in this piece of equipment. The model was validated by high speed photography of the particle motion at the surface of the Mi-Pro�s clear bowl walls. The results indicated that the particle motion was dominated by the high speed impeller and that a roping regime exists. The results from this work give a greater insight into the particle motion and can be used to understand the complex interactions which occur within this equipment

Wear and impact analysis of granular materials using Discrete Element Method simulations

Wear models for abrasion, ductile erosion, brittle erosion and combined erosion are implemented into a Discrete Element Method program utilising the linear spring dashpot model. A linear damage model is developed, implemented and then applied to an industrial case study through which it is found to predict wear accurately and provide a good insight into the improvement based on material change using the abrasion models. Four methods of creating energy based modelling were created for specific use inside DEM and contrasted with known wear models to assess what mechanisms they may potentially replicate. Through use with DEM, this allows use with a Single Element Failure criteria which can rapidly assess a variety of material changes inside a system to take steps to de-risk potential industrial trials. Design changes were made to assess the effects on both wear/energy models and provide predictions for causes and possible side effects. The effect of particle kinetics were assessed with respect to angle of impact, mass flow rate and coefficient of restitution to determine how this impacts wear modelling in DEM

On investigation of contact models in DEM simulation of rockfalls

Simulation of rockfall allows us to protect infrastructures and forests along rock slopes against the impacts of rockfall. In this thesis, a computer program based on 3D Discrete Element Method (DEM) is developed by the author for rockfall simulation and fundamental investigation of physics of a rockfall event. Each rock is modeled as a sphere and impact surfaces are generated by numbers of 3D triangles. Contacts in DEM between objects are modeled using a mass-damper model. Different contact models of DEM produce different contact stiffnesses for springs and therefore different contact forces. Since contact forces have essential effect on dynamic behaviour of particles; hence a comparative study is performed to investigate the effect of each contact model on dynamic of rocks contacts. The five chosen contact models are: linear model, Hertz-Mindlin, Ng model, elastic-inelastic power function model and combination of Hertz model and Ng model (Hertz-Ng model). Energy in linear, Hertz-Mindlin, Hertz-Ng and Ng model is dissipated using linear normal and shear dashpots. Also, the coefficient of restitution is a concept that defines the energy level of a rock after contact with a surface. To relate the concept of coefficient of restitution and damping ratio for each contact model, the correlations of damping ratio and coefficient of restitution are determined for contact of a spherical rock and horizontal wall as well as the correlation of coefficient of restitution and damping ratio for sloped walls for linear contact model. An has developed a 2D elastic-inelastic power function for modeling of normal contact of rocks and surfaces. In this research, 3D modeling of this contact model is produced, and the effects of the input parameters on dynamic behaviours of a rock are studied and the correlation between transition force and coefficient of restitution is determined. Finally, for a 3D slope, a sensitivity analysis is performed and the effect of seven input parameters on horizontal travel distance of a rock is investigated. [ Show less ] You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer Translations powered by LEC

A GPGPU implementation of the discrete element method applied to modeling the dynamic particulate environment inside a tumbling mill

Includes bibliographical references.Tumbling mills have been an integral part of the comminution circuit for more than a century. With the advent of better computing, discrete element modeling (DEM) has taken on the challenge to model the dynamic particulate environment inside these devices in the search for understanding and hence improving the process of the size reduction of ore. This process represents a large percentage of the energy consumption of a mine. In this work, a discrete element modeling tool was built on a GPU-based platform to perform simulations on a single commodity hardware PC. With a view to elucidating the governing mechanisms inside such devices, the extreme capabilities of the GPU are utilised to provide performance and accurate simulation. The simulation environment offers control that can never be achieved in an experimental setup. Notwithstanding, when agreement with physical experiment is achieved, confidence can be gained in the computational results. In this work the foundations and framework for a large scale GPU based discrete element modeling tool have been built with an emphasis on strict physics requirements, rather than on performance or appearance. In this regard we demonstrate the validity of the GPU implementation of a Hertz-Mindlin-based contact model