Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Abstract

A statistically stationary homogeneous isotropic turbulent flow modified by 64 small fixed non-Stokesian spherical particles is considered. The particle diameter is approximately twice the Kolmogorov length scale, while the particle volume fraction is 0.001. The Taylor Reynolds number of the corresponding unladen flow is 32. The particle-laden flow has been obtained by a direct numerical simulation based on a discretization of the incompressible Navier-Stokes equations on 64 spherical grids overset on a Cartesian grid. The global (space-and time-averaged) turbulence kinetic energy is attenuated by approximately 9 %, which is less than expected. The turbulence dissipation rate on the surfaces of the particles is enhanced by two orders of magnitude. More than 5 % of the total dissipation occurs in only 0.1 % of the flow domain. The budget of the turbulence kinetic energy has been computed, as a function of the distance to the nearest particle centre. The budget illustrates how energy relatively far away from particles is transported towards the surfaces of the particles, where it is dissipated by the (locally enhanced) turbulence dissipation rate. The energy flux towards the particles is dominated by turbulent transport relatively far away from particles, by viscous diffusion very close to the particles, and by pressure diffusion in a significant region in between. The skewness and flatness factors of the pressure, velocity and velocity gradient have also been computed. The global flatness factor of the longitudinal velocity gradient, which characterizes the intermittency of small scales, is enhanced by a factor of six. In addition, several point-particle simulations based on the Schiller-Naumann drag correlation have been performed. A posteriori tests of the point-particle simulations, comparisons in which the particle-resolved results are regarded as the standard, show that, in this case, the point-particle model captures both the turbulence attenuation and the fraction of the turbulence dissipation rate due to particles reasonably well, provided the (arbitrary) size of the fluid volume over which each particle force is distributed is suitably chosen.

Point-Particle DNS and LES of Particle-Laden Turbulent flow - a state-of-the-art review

“…This method has been used to calculate the force on a single, fixed particle in decaying homogeneous isotropic turbulence [7, 24]. Very recently this method has been applied to analyze homogeneous isotropic turbulent flow around an array of 64 fixed spherical particles [111] with a size equal to twice the Kolmogorov length and a particle volume fraction of 0.001. Extension of this method to moving particles is not straightforward due to collisions that occur and lead to overlap of the spherical grid of one particle with another particle.…”

“…Also, the way in which the two-way coupling force should be applied in point-particle simulations can be found from particle-resolved simulations. An example of this can be found in the recent paper on particle-resolved DNS of the flow around a fixed array of particles in homogeneous isotropic turbulence by Vreman [111]. There it was found that the agreement with point-particle DNS can substantially be improved by distributing the two-way coupling force in the point-particle DNS over a larger volume than usually chosen.…”

“…Recently, particle-resolved simulations with 10,000 particles in turbulent channel flow have been performed by means of the immersed boundary method [78]. Also, progress can be seen in the development of numerical methods for particle-resolved simulations with body-fitted grids [111]. As has recently been observed by Prosperetti [82], this progress marks the beginning of a golden age of science in the area of particulate flows, or more general, multiphase flows.…”

Meshfree modeling of a fluid‐particle two‐phase flow with an improved SPH method

“…Glowinski et al developed a distributed Lagrange multiplier/fictitious domain method (DLM/FDM), and Turek et al and Wan and Turek presented a finite element fictitious boundary method (FE‐FBM) to solve particulate flow problems. Recently, Vreman applied the overset grid method to study particle‐laden pipe flows . This method is based on two sets of background meshes, ie, a fixed mesh for fluid and a body‐fitted mesh for each particle.…”

“…Recently, Vreman applied the overset grid method to study particle-laden pipe flows. 12,13 This method is based on two sets of background meshes, ie, a fixed mesh for fluid and a body-fitted mesh for each particle. In Vreman's works, the velocities and pressures on different background grids are coupled by third-order Lagrange interpolations.…”