747 research outputs found
Three-Dimensional Smoothed Particle Hydrodynamics Simulation for Liquid Droplet with Surface Tension
We provide a basic method of Smoothed Particle Hydrodynamics (SPH) to
simulate liquid droplet with surface tension in three dimensions. Liquid
droplet is a simple case for surface tension modeling. Surface tension works
only on fluid surface. In SPH method, we simply apply the surface tension on
the boundary particles of liquid. The particle on the 3D boundary was detected
dynamically using Free-Surface Detection algorithm. The normal vector and
curvature of the boundary surface were calculated simultaneously with 3D
boundary surface reconstruction using Moving Least-Squares (MLS) method. Before
the reconstruction, the coordinate system was transformed into a local
coordinate system. Afterwards, the surface tension force which depends on
curvature of the surface, was calculated and applied on the boundary particles
of the droplet. We present the simulation result of droplet motion with gravity
force. By using the basic method of SPH for fluid modeling, and a combination
of 3D Free-Surface Detection algorithm with MLS method, we can simulate droplet
phenomena with expected result.Comment: 9 pages, 4 figure, Selected Paper from the International Symposium on
Computational Science 201
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곡νλΆ, 2020. 8. κΉμμ.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.κ°μκ²½μλ‘ μ€λμ¬κ³ νκΈ° κ³Όμ μμ ν΅μ°λ£ μ©μ΅λ¬Ό λ
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μ¦μ μν΄ μμλ‘ μ€λμ¬κ³ νκΈ° κ³Όμ μμ λ°μν μ μλ ν΅μ°λ£ ννΈλ¬Ό μΈ΅(debris bed)μ ννν(self-leveling) κ±°λμ λν κ²μ¦ ν΄μμ μννμλ€. μκ°μ λ°λ₯Έ ννΈλ¬Ό μΈ΅ νλ©΄μ νμ λ³νλ₯Ό ν κΈ°κ΄μμ μνλ 기체주μ
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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
κ΅λ¬Έ μ΄λ‘ 142Docto
Smoothed Particle Hydrodynamics for Navier-Stokes Fluid Flow Application
The aim of this publication is to introduce the particle based computational fluid dynamics (CFD) method smoothed particle hydrodynamics (SPH) and introduce an applicable and valid SPH implementation for practical cases. For this purpose, current research approaches are combined regarding performance and numerical stability. The principles of the method, the mathematical basics and the discretization of the Navier-Stokes equations are clarified. Furthermore, the implementation of method-specific boundary conditions, wall, inlet and outlet, as well as several correction procedures and a surface tension setup into the present code framework are described. The advantages and validity of the method are shown based on different cases. The free surface fluid behavior of a dam break is compared to experimental data of the time dependent water level of selected positions. A Karman vortex street is validated by its Strouhal number for different Reynolds numbers. The frequency of an oscillating drop is analysed and compared to the analytical solution. The SPH is utilized for pipe flows influenced by a backward facing step and shows an expected qualitative flow field
Pairwise Force SPH Model for Real-Time Multi-Interaction Applications
In this paper, we present a novel pairwise-force smoothed particle hydrodynamics (PF-SPH) model to allow modeling of various interactions at interfaces in real time. Realistic capture of interactions at interfaces is a challenging problem for SPH-based simulations, especially for scenarios involving multiple interactions at different interfaces. Our PF-SPH model can readily handle multiple kinds of interactions simultaneously in a single simulation; its basis is to use a larger support radius than that used in standard SPH. We adopt a novel anisotropic filtering term to further improve the performance of interaction forces. The proposed model is stable; furthermore, it avoids the particle clustering problem which commonly occurs at the free surface. We show how our model can be used to capture various interactions. We also consider the close connection between droplets and bubbles, and show how to animate bubbles rising in liquid as well as bubbles in air. Our method is versatile, physically plausible and easy-to-implement. Examples are provided to demonstrate the capabilities and effectiveness of our approach
Enhanced SPH modeling of free-surface ο¬ows with large deformations
The subject of the present thesis is the development of a numerical solver to
study the violent interaction of marine flows with rigid structures.
Among the many numerical models available, the Smoothed Particle
Hydrodynamics (SPH) has been chosen as it proved
appropriate in dealing with violent free-surface flows. Due to its
Lagrangian and meshless character it can naturally handle breaking waves and
fragmentation that generally are not easily treated by standard methods. On
the other hand, some consolidated features of mesh-based methods, such as
the solid boundary treatment, still remain unsolved issues in the SPH
context.
In the present work a great part of the research activity has been devoted
to tackle some of the bottlenecks of the method. Firstly, an enhanced SPH
model, called delta-SPH, has been proposed. In this model, a proper numerical diffusive
term has been added in the continuity equation in order to remove the spurious
numerical noise in the pressure field which typically affects the weakly-compressible SPH
models. Then, particular attention has been paid to the development of suitable
techniques for the enforcement of the boundary conditions. As for the free-surface, a
specific algorithm has been designed to detect free-surface particles and
to define a related level-set function with two main targets: to allow the
imposition of peculiar conditions on the free-surface and to analyse and
visualize more easily the simulation outcome (especially in 3D cases).
Concerning the solid boundary treatment, much effort has been spent to
devise new techniques for handling generic body geometries with an adequate
accuracy in both 2D and 3D problems. Two different techniques have been
described: in the first one the standard ghost fluid method has been
extended in order to treat complex solid geometries. Both free-slip and
no-slip boundary conditions have been implemented, the latter being a quite
complex matter in the SPH context. The proposed boundary treatment proved
to be robust and accurate in evaluating local and global loads, though it
is not easy to extend to generic 3D surfaces.
The second technique has been adopted for these cases.
Such a technique has been developed in the context of Riemann-SPH methods
and in the present work is reformulated in the context of the standard SPH scheme.
The method proved to be robust in treating complex 3D
solid surfaces though less accurate than the former.
Finally, an algorithm to correctly initialize the SPH simulation in the case of generic
geometries has been described. It forces a resettlement of the fluid particles
to achieve a regular and uniform spacing even in complex configurations. This
pre-processing procedure avoids the generation of spurious currents due to
local defects in the particle distribution at the beginning of the simulation.
The delta-SPH model has been validated against several problems
concerning fluid-structure interactions. Firstly, the capability of the
solver in dealing with water impacts has been tested by simulating a
jet impinging on a flat plate and a dam-break flow against a vertical
wall. In this cases, the accuracy in the prediction of local loads and of
the pressure field have been the main focus. Then, the viscous flow around
a cylinder, in both steady and unsteady conditions, has been simulated
comparing the results with reference solutions. Finally, the generation
and propagation of 2D gravity waves has been simulated. Several
regimes of propagation have been tested and the results
compared against a potential flow solver.
The developed numerical solver has been applied to several cases of
free-surface flows striking rigid structures and to the problem of the
generation and evolution of ship generated waves. In the former case, the
robustness of the solver has been challenged by simulating 2D and 3D water impacts
against complex solid surfaces. The numerical outcome have been compared
with analytical solutions, experimental data and other numerical results
and the limits of the model have been discussed.
As for the ship generated waves, the problem has been firstly studied
within the 2D+t approximation, focusing
on the occurrence and features of the breaking bow waves. Then, a
dedicated 3D SPH parallel solver has been developed to tackle the simulation
of the entire ship in constant forward motion. This simulation is quite demanding in
terms of complexities of the boundary geometry and computational resources
required. The wave pattern obtained has been compared against experimental
data and results from other numerical methods, showing in both the cases a fair
and promising agreement
Toward the development of a virtual spray test-rig using the Smoothed Particle Hydrodynamics method
In this work we present the numerical simulation of air-assisted liquid atomization at high pressure us-
ing the Smoothed Particle Hydrodynamics (SPH) method. Different post-processing tools are applied to
facilitate the comparison with experimental observations. This allows to quantitatively validate the nu-
merical method against the experiment, in terms of (i) frequency of the KelvinβHelmholtz instability that
develops on the jet surface, and (ii) statistical distribution of the jet intact length. The qualitative com-
parison also shows a good prediction of the jet global instability and of the fragmented liquid lumps,
with regards to length and time scales. In addition, the post-processing tools also give access to the local
parameters of the generated spray in the vicinity of the nozzle, which are not easily accessible in a real
experiments. Using these tools, 1D profiles and 2D maps of the liquid phase properties such as the vol-
ume fraction, the droplet concentration, the Sauter Mean Diameter (SMD) and the droplet sphericity are
presented. Because of the Lagrangian nature of the SPH method, it is also possible to monitor the whole
atomization cascade as a causal tree, from the primary instabilities to the spray characteristics. This tree
contains various information such as the fragmentation spectrum and the breakup activity, which are
of great interest for researchers and engineers. Hence, the capability of the Smoothed Particle Hydrody-
namics (SPH) method for simulating air-assisted atomization at high ambient pressure is demonstrated
as well as its applicability to realistic configurations. This is a first step towards the development of a
complete virtual spray test-rig
Development of GPU-based SPH Framework for Hydrodynamic Interactions With Non-spherical Solid Debris
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Έμ¬ μ©μ΅λ¬Ό κ±°λμ λν νκ°λ μ©μ΅λ¬Ό-μ½ν¬λ¦¬νΈ μνΈμμ©(MCCI, Molten Core Concrete Interaction)κ³Ό μ¦κΈ° νλ°λ‘λΆν°μ μμλ‘ λ
Έμ¬ λκ°μ± λ° κ±΄μ μ±μ λ°λ₯Έ μ¬μκ³ μΈ‘λ©΄μμ λ§€μ° μ€μνλ€. νΉν OPR 1000μ κ²½μ°, μ¬μ μΆ©μ 쑰건(Wet cavity condition)μ κΈ°λ³Έμ μΈ μμλ‘ μΈλ²½ λκ° λμ μ λ΅μΌλ‘ μ±νν¨μΌλ‘μ¨ ν΅μ°λ£-λκ°μ¬ μνΈμμ©(FCI, Fuel Coolant Interaction) λ°μμ΄ νμ°μ μΌλ‘ λ°μνλ κ²μΌλ‘ μλ €μ Έ μλ€. [Jin, 2014] FCI νμμ μμ ννμ ν΅μ°λ£ κ³ μ²΄ ννΈλ¬Όκ³Ό λκ°μ¬μ μνΈμμ©λΏλ§ μλλΌ, λκ°μ¬ λΉλ± νμ λ±λ ν¬ν¨νλ λ€μ 체, λ€μ νμμΌλ‘ κ·Έ νμμ΄ λ§€μ° λ³΅μ‘νλ€. μ΄ κ³Όμ μμ μμλ‘ κ±΄λ¬Ό νλΆμ κ³ μ²΄ ννΈλ¬Όμ΄ ν΄μ λμ΄ μν΄ μΈ΅μ΄ νμ±λκ³ , κ·Έ λκ°μ±μ λ°λΌ μ¬κ³ μ λ€μ μ§ν μν©μ μν₯μ μ€ μ μλ€. μ΄λ¬ν λΉκ΅¬ν κ³ μ²΄ ννΈλ¬Ό κ±°λμ λν μ΄ν΄λ₯Ό μν΄ κ°μ²΄ κ°λ
μ μ μ©ν κ³ μ²΄ ν΄μ 체κ³λ μ’μ μ κ·Όλ²μ΄ λ μ μλ€. λ°λΌμ λ³Έ μ°κ΅¬μμλ μ 체μ κ³ μ²΄ κ° μλ ₯νμ μνΈμμ© ν΄μμ μν΄ μ
μμ 체λμν(SPH, Smoothed Particle Hydrodynamics) κΈ°λ²κ³Ό κ°μ²΄μν(RBD, Rigid Body Dynamics) κΈ°λ²μ μ°κ³νμ¬ λΌκ·Έλμ§μ ν΄μ 체κ³λ₯Ό ꡬμΆνμλ€.
μνμ
μμ 체λμν κΈ°λ²μ ν΄μ μ 체λ₯Ό μ νκ°μ μ
μλ‘ ννν¨μΌλ‘μ¨ μ λμ ν΄μνλ λΌκ·Έλμ§μ ν΄μ κΈ°λ² μ€ νλμ΄λ€. κ°λ³ μ
μλ€μ μμ§μμΌλ‘ μ λμ ν΄μνλ―λ‘ λΉμ νμ λλ₯νμ λν κ³μ°μ΄ νμ μμΌλ©°, μ
μκ° μΆκ°λκ±°λ μ¬λΌμ§μ§ μλ ν ν΄μ κ³μ μ 체 μ§λμ μλμΌλ‘ 보쑴λλ€. μ΄λ¬ν λΌκ·Έλμ§μ κΈ°λ²μ νΉμ±μΌλ‘ SPH λ°©λ²μ μμ νλ©΄ μ λ, λ€μ 체 μ λ, λ€μ μ λ, νν λ³νκ° ν° μ λ λ±μ λν΄ ν΄μ μ₯μ μ κ°λλ€. λ³Έ μ°κ΅¬μμλ SPH κΈ°λ²μ μ μ©ν in-house SOPHIA μ½λλ₯Ό μ¬μ©νμ¬ λΉμμΆ λ€μ μ λ ν΄μμ μννμμΌλ©°, λ²€μΉλ§ν¬ λ°μ΄ν°μμ λΉκ΅μμ μ’μ κ²μ¦ ν΄μ κ²°κ³Όλ₯Ό 보μλ€.
κ°μ²΄μνμ μΈλ ₯μ μν΄ ννκ° λ³νμ§ μλ κ°μ²΄μ κ°λ
μ μ΄μ©νμ¬ κ³ μ²΄μ λ³μ§ μ΄λκ³Ό νμ μ΄λμ ν΄μνλ μ°κ΅¬ λΆμΌμ΄λ€. λ³Έ μ°κ΅¬μμλ μ΄μ°μμλ²(DEM, Discrete Element Method) λΆμΌμμ μ€λ μκ° λμ λ리 μ¬μ©λκ³ κ²μ¦λμλ Hertz-Mindlin μΆ©λ λͺ¨λΈμ μ μ©νμ¬ κ°μ²΄ κ° μΆ©λ ν΄μμ ꡬννμλ€. κ°μ²΄λ μ νκ°μ μ
μλ€λ‘ ννν μ μμΌλ©°, κ°μ²΄ κ° μΆ©λμ κ° κ°μ²΄λ₯Ό ꡬμ±νκ³ μλ μ
μμμ μμ μ€μ²©μ κΈ°λ°μΌλ‘ κ³μ°λλ€. λ³Έ μ°κ΅¬μμλ μ
μκΈ°λ°μ κ°μ²΄μν ν΄μ μ½λλ₯Ό μ΄μ©νμ¬ λ¨μΌ κ°μ²΄ λ° λ€μ€ κ°μ²΄ μΆ©λμ λν΄ κ²μ¦ ν΄μμ μννμμΌλ©°, ν΄μν΄ λ° λ²€μΉλ§ν¬ λ°μ΄ν° κ²°κ³Όμ μ μΌμΉν¨μ νμΈνμλ€.
μμλ ₯ λΆμΌμμ λ°μν μ μλ λΉκ΅¬ν κ³ μ²΄μ μ μ²΄κ° μνΈμμ© ν΄μμ μν΄ μμ μ€λͺ
ν SPH κΈ°λ²κ³Ό κ°μ²΄μν μ°κ³ ν΄μ μ½λλ₯Ό κ°λ°νμλ€. λ³Έ μ°κ΅¬μμ μ μ©ν μμ ν΄μ λ°©μ(Fully resolved approach)μ μ 체-κ³ μ²΄μ μμ΄ λΆλ¦¬λμ΄ μκ³ , μ 1 μ리λ₯Ό λ§μ‘±νλ―λ‘ κ³ μ²΄μ νμμ λ°λ₯Έ μκ΄μκ³Ό νλ©΄ μ λΆμ΄ νμνμ§ μλ€λ μ₯μ μ΄ μλ€. λν κ³ μ²΄ κ²½κ³λ©΄μμμ μ νν μλ ₯ κ³μ°μ μν΄ μ 체 μ
μ μ 보λ₯Ό κΈ°λ°μΌλ‘ λ
Έμ΄λ§ μλ ₯ κ²½κ³ μ‘°κ±΄μ μ μ©νμλ€. λ³Έ μ°κ΅¬μμλ μ΄λ¬ν ν΄μ λ°©μμ μ 체-κ°μ²΄ μ°κ³ ν΄μ μ½λλ₯Ό μ΄μ©νμ¬ λΉκ΅¬ν κ³ μ²΄μ μ 체μ μλ ₯νμ μνΈμμ©μ λν κ²μ¦ ν΄μμ μννμμΌλ©°, μ νλ μ€νκ³Όμ λΉκ΅μμ μ’μ κ²°κ³Όλ₯Ό 보μλ€.
μ λ ν΄μμ μν΄ λ³Έ μ°κ΅¬μ μ μ©ν SPH λ°©λ²μμλ μμλ€μ΄ λ§€μ° μ νμ μ΄κ³ μΈμ°μ (Explicit)μΌλ‘ κ³μ°μ μννκΈ° λλ¬Έμ κ° μ
μμ λν κ³μ°μ΄ λ
립μ μΌλ‘ μνλμ΄λ λ¬Έμ κ° μλ€. λ°λΌμ SPH λ°©λ²μ κ³μ° λ³λ ¬νμ μ΅μ νλ λ°©λ²μΌλ‘ μ μλ €μ Έ μμΌλ©°, λκ·λͺ¨ κ³ ν΄μλ ν΄μμ μν΄ μ΄λ νμμ μ΄λ€. λν μ
μ κΈ°λ°μ κ°μ²΄ κ³μ°μ μν΄μλ ν¨μ¨μ μΈ κ³μ° μκ³ λ¦¬μ¦μ΄ νμνλ€. λ°λΌμ λ³Έ μ°κ΅¬μμλ λκ·λͺ¨ κ³μ°κ³Ό λμ μ°μ° ν¨μ¨μ±μ μν΄ κ·Έλν½μ²λ¦¬μ₯μΉ(GPU, Graphic Processing Unit)λ₯Ό μ΄μ©νμ¬ κ³μ° λ³λ ¬νλ₯Ό μννμμΌλ©°, μ΄λ₯Ό μ΄μ©ν λ€μ€ κ³ μ²΄μ μ 체μ μνΈμμ© ν΄μμμ μ’μ κ³μ° μ±λ₯μ νμΈνμλ€.
λ³Έ μ°κ΅¬μμ μνν λΉκ΅¬ν κ³ μ²΄μ μ 체μ μλ ₯νμ μνΈμμ©μ μν GPU κΈ°λ°μ SPH ν΄μ μ½λ κ°λ° μ°κ΅¬λ₯Ό ν΅ν΄ μμλ‘ μ€λμ¬κ³ μ λ°μν μ μλ λκ°μ¬μ ν΅μ°λ£ κ³ μ²΄ ννΈλ¬Όμ μλ ₯νμ μνΈμμ© λΏλ§ μλλΌ, κ³ μ²΄ ννΈλ¬Ό κ° μνμ μνΈμμ©μ λν΄ ν¨μ¨μ μΈ ν΄μ 체κ³λ₯Ό κ°λ°νμλ€. μ΄λ₯Ό ν΅ν΄ μ΅μ 곡λ(wet cavity)μμ λ°μνλ ν΅μ°λ£ κ³ μ²΄ ννΈλ¬Όμ ν΄μ μμ©, μ°λλ―Έ μ¬κ³ λ‘ μΈν ν΄μ ꡬ쑰물μ μλ ₯νμ μνΈμμ©, κ·Έλ¦¬κ³ μΉ¨μ μ¬κ³ μ μμλ‘ κ±΄λ¬Ό λ΄ λΆμ λ¬Όμ κ±°λ λ± μμλ ₯ λΆμΌμμ λ°μν μ μλ λ€μν κ³ μ²΄-μ 체μ μλ ₯νμ μνΈμμ©μ λν ν΄μμ μ°κ΅¬μ μ μ©νκ³ κΈ°μ¬ν μ μμ κ²μΌλ‘ κΈ°λνλ€.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 doesnβt 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
κ΅λ¬Έ μ΄λ‘ 127λ°
An improved SPH scheme for cosmological simulations
We present an implementation of smoothed particle hydrodynamics (SPH) with
improved accuracy for simulations of galaxies and the large-scale structure. In
particular, we combine, implement, modify and test a vast majority of SPH
improvement techniques in the latest instalment of the GADGET code. We use the
Wendland kernel functions, a particle wake-up time-step limiting mechanism and
a time-dependent scheme for artificial viscosity, which includes a high-order
gradient computation and shear flow limiter. Additionally, we include a novel
prescription for time-dependent artificial conduction, which corrects for
gravitationally induced pressure gradients and largely improves the SPH
performance in capturing the development of gas-dynamical instabilities. We
extensively test our new implementation in a wide range of hydrodynamical
standard tests including weak and strong shocks as well as shear flows,
turbulent spectra, gas mixing, hydrostatic equilibria and self-gravitating gas
clouds. We jointly employ all modifications; however, when necessary we study
the performance of individual code modules. We approximate hydrodynamical
states more accurately and with significantly less noise than standard SPH.
Furthermore, the new implementation promotes the mixing of entropy between
different fluid phases, also within cosmological simulations. Finally, we study
the performance of the hydrodynamical solver in the context of radiative galaxy
formation and non-radiative galaxy cluster formation. We find galactic disks to
be colder, thinner and more extended and our results on galaxy clusters show
entropy cores instead of steadily declining entropy profiles. In summary, we
demonstrate that our improved SPH implementation overcomes most of the
undesirable limitations of standard SPH, thus becoming the core of an efficient
code for large cosmological simulations.Comment: 21 figures, 2 tables, accepted to MNRA
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