Numerical Simulations of Short- and Long-Range Interaction Forces in Turbulent Particle-Laden Gas Flows

Abstract

The main objective of this work is to study the effects of distance-dependent interactions in turbulent gas-particle flows using an Euler–Lagrange simulation approach. The turbulent gas flow is accounted for via Direct Numerical Simulation to the Kolmogorov scale using a spectral method to solve the Navier–Stokes equations in a cubic computational domain with tri-periodic boundary conditions. This flow simulation is coupled (one-way) with a Lagrangian particle phase solver that performs particle trajectory tracking. Electrostatic forces can be calculated using two different approaches. Firstly, the direct method consists of a sum of all inter-particle interactions for all the particles of the computational domain and their periodic images. However, this purely Lagrangian approach is computationally costly for a large number of particles, therefore another approximative approach is considered. According to it, one can estimate the short-range interactions via a sum of inter-particle interactions within a cut-off distance and the long-range ones via a sum of particle interactions with clusters of particles that, from a distance greater than the cut-off, are “seen” as one pseudo-particle. This method is then adjusted in order to accommodate periodic boundary conditions, which are not trivial in the case of electrostatic interactions as periodicity entails an infinite number of periodic domain images that has to be truncated to a finite number. Simulations are then performed by varying the properties of the particles in terms of diameter, density (Stokes number) and charge (electrostatic Stokes number). Finally, a statistical analysis is performed in order to investigate how the dynamics of the turbulent gas-particle flow are affected by distance-dependent particle–particle interactions, namely electrostatic forces.