Improvement of the Viscous Penalty Method for Particle-Resolved Simulations

Mohamed-Amine Chadil,Stéphane Vincent,Jean-Luc Estivalèzes

doi:10.4236/ojfd.2019.92012

Abstract

A numerical study of the parameters controlling the viscous penalty method is investigated to better set up Particle-Resolved Direct Numerical Simulations (PR-DNS) of particulate flows. Based on this analysis, improvements of the methods are proposed in order to reach an almost second order convergence in space. The viscous penalty method is validated in Stokes regime by simulating a uniform flow past a fixed isolated cylinder. Moreover, it is also utilized in moderate Reynolds number regime for a uniform flow past a square configuration of cylinder and compared in terms of friction factor to the well-known Ergun correlation.

Highlights

The motion of rigid particles interacting with a carrier fluid is a very active research area that is commonly found in the fields of environment and industrial processes
The numerical simulation of resolved-scale particle motion is a highly developed field of research mainly based on fixed structured grids, as unstructured meshes adapted to the particle motion are difficult to design in three dimensions and CPU time consuming [1]
Among the wide variety of fictitious domain approaches, i.e. particles are treated as immersed interfaces on a fixed mesh, we can cite the numerical methods based on Lattice Boltzmann models [2] [3] [4] [5] [6] and the approaches that uses the Navier-Stokes equations, such as the Immersed Boundary Method (IBM) of Uhlmann [7] [8], the PURe-IBM approach of Tenneti et al [9], the Distributed Lagrangian Method (DLM) of Glowinski and co-workers [10] [11] and the Implicit Tensorial Penalty Method (ITPM) of Vincent et al [12] [13], called viscous penalty method

Summary

Introduction

The motion of rigid particles interacting with a carrier fluid is a very active research area that is commonly found in the fields of environment and industrial processes. We can cite fluidized beds and chemical engineering, material manufacturing and design, sand dynamics, beach erosion under wave impact or nano-particle impact on human health. The simulation of such real problems is based on the use of Eulerian-Eulerian or Eulerian-Lagrangian models that require knowledge of constitutive laws for drag, lift, torque, collisions or heat transfers for the fluid-particle interactions. The numerical simulation of resolved-scale particle motion is a highly developed field of research mainly based on fixed structured grids, as unstructured meshes adapted to the particle motion are difficult to design in three dimensions and CPU time consuming [1]. Among the wide variety of fictitious domain approaches, i.e. particles are treated as immersed interfaces on a fixed mesh, we can cite the numerical methods based on Lattice Boltzmann models [2] [3] [4] [5] [6] and the approaches that uses the Navier-Stokes equations, such as the Immersed Boundary Method (IBM) of Uhlmann [7] [8], the PURe-IBM approach of Tenneti et al [9], the Distributed Lagrangian Method (DLM) of Glowinski and co-workers [10] [11] and the Implicit Tensorial Penalty Method (ITPM) of Vincent et al [12] [13], called viscous penalty method

Objectives

Methods

Findings

Conclusion