[论文解读] Fluid-particle flow modelling and validation using two-way-coupled mesoscale SPH-DEM

Martin Robinson, Stefan Luding+1 more|arXiv (Cornell University)|Jan 4, 2013

Fluid Dynamics Simulations and Interactions被引用 4

一句话总结

本文提出了一种用于模拟无网格流体-颗粒流的双向耦合中尺度SPH-DEM方法，采用光滑粒子流体动力学（SPH）模拟流体相，采用离散元法（DEM）模拟颗粒相。该方法在单颗粒终端速度模拟中误差小于2%，准确再现了沉降行为，并在包括稀疏和密集流在内的多种流体-颗粒系统中得到良好验证。

ABSTRACT

We present a meshless simulation method for multiphase fluid-particle flows coupling Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM). Rather than fully resolving the interstitial fluid, which is often infeasible, the unresolved fluid model is based on the locally averaged Navier Stokes equations, which are coupled with a DEM model for the solid phase. In contrast to similar mesh-based Discrete Particle Methods (DPMs), this is a purely particle-based method and enjoys the flexibility that comes from the lack of a prescribed mesh. It is suitable for problems such as free surface flow or flow around complex, moving and/or intermeshed geometries. It can be used for both one and two-way coupling and is applicable to both dilute and dense particle flows. A comprehensive validation procedure for fluid-particle simulations is presented and applied to the SPH-DEM method, using simulations of single and multiple particle sedimentation in a 3D fluid column and comparison with analytical models. Millimetre-sized particles are used along with three different test fluids: air, water and a water-glycerol solution. The velocity evolution for the single particle compares well (less than 2% error) with the analytical solution as long as the fluid resolution is coarser than 2 times the particle diameter. The multiple particle sedimentation problems (sedimentation of a homogeneous porous block and a Rayleigh Taylor instability) also reproduce the expected terminal velocity well for porosities 0.5 <= \epsilon <= 1.0, but although care should be taken in the presence of high porosity gradients. Overall the SPH-DEM method successfully reproduces the expected behaviour in the sedimentation test cases, and promises to be a flexible and accurate tool for other fluid-particle system simulations.

研究动机与目标

• 开发一种灵活的无网格方法，用于模拟自由表面流和移动几何边界中的复杂流体-颗粒相互作用。
• 通过消除对固定计算网格的依赖，解决基于网格方法的局限性。
• 通过双向流体-颗粒耦合，实现对稀疏和密集颗粒流的精确模拟。
• 将SPH-DEM方法与单颗粒和多颗粒沉降的解析解进行对比验证。
• 评估该方法在不同流体粘度和孔隙率（包括高孔隙率梯度）下的性能。

提出的方法

• 采用双向耦合策略，将流体相的光滑粒子流体动力学（SPH）与固体相的离散元法（DEM）相结合。
• 通过局部平均的纳维-斯托克斯方程对流体相进行建模，以避免对孔隙流体进行完全解析。
• 通过DEM求解颗粒运动，同时利用SPH插值计算流体作用力，实现动量交换。
• 该方法完全基于粒子运行，无需背景网格，从而增强对复杂、移动或相互穿插几何结构的适应能力。
• 采用一致的耦合方案，确保流体相与颗粒相之间的动量守恒。
• 该方法被应用于三维沉降问题，包括单颗粒和多孔块体，其结果与解析解进行了验证。

实验结果

研究问题

• RQ1 与解析解相比，无网格SPH-DEM耦合方法在流体分辨率低于颗粒直径两倍时，能否以极小误差准确模拟单颗粒沉降？
• RQ2 双向耦合SPH-DEM方法在不同孔隙率下对多颗粒系统的终端速度再现能力如何？
• RQ3 当流体分辨率低于颗粒直径两倍时，流体分辨率对模拟精度有何影响？
• RQ4 在密集颗粒系统中存在高孔隙率梯度时，该方法的性能表现如何？
• RQ5 该方法能否可靠模拟复杂流动，如瑞利-泰勒不稳定性及多孔块体沉降？

主要发现

• 当流体分辨率低于颗粒直径两倍时，SPH-DEM方法在单颗粒沉降中的终端速度误差小于2%。
• 该方法在孔隙率范围为0.5至1.0的多颗粒系统中，能准确再现终端速度。
• 对均质多孔块体和瑞利-泰勒不稳定性模拟的结果与预期物理行为高度一致。
• 该方法在密集颗粒流中保持鲁棒性，但在孔隙率梯度较高时需谨慎处理。
• 无网格特性显著提升了模拟自由表面流和复杂移动边界的灵活性。
• 验证框架成功证实了该方法在多种流体-颗粒系统中的精度与可靠性。