Analysis of particle wakes for PIEP modeling in Euler-Lagrange simulations

To aid in the understanding and modeling of microscale physics, particle resolved direct numerical simulations have become more prevalent in recent years. From these simulations, models can be developed to approximate the microscale inter-phase forces, Reynolds stresses, and residual stresses. The typical approach is to model these properties as functions of the macroscale Reynolds number and particle volume fraction, accounting for the average effect of microscale contributions. Instead, this study accounts for the effects of each neighbor directly. We define a linearly superposable wake (LSW), which when added for all the particles best captures microscale properties of a DNS. The LSW is then used to model the inter-phase forces, Reynolds stresses, and residual stresses in the pairwise interaction expended point-particle (PIEP) framework. This particle based view allows for more precise approximations. In the dilute volume fraction limit, the inter-phase force model approaches the PIEP model based on an isolated particle wake. However, at higher volume fractions, LSW is now calculated using regression applied to DNS data.