Theoretical and numerical analysis of drag force at the interface between the dilute and dense phases

Abstract

Resolving the sharp interface between the dilute and dense phases in gas–solid flows is a bottleneck in fine-grid simulations. This study addresses this issue through the theoretical analysis of an infinite gas–structure interface with arbitrary flow directions. The drag force at the interface is decomposed into three parts: the homogeneous drag forces of the dilute and dense regions and a stress divergence difference term. All the three parts are expressed as the functions of the solid volume fractions, particle Reynolds numbers, and stress divergences of the interface grid and its adjacent grids. The developed theoretical drag models at the interface are verified and improved based on particle-resolved direct numerical simulations (PR-DNSs) of flows past plug-like structures. The models are then tested against PR-DNSs of flows past bubble-containing, spherical, ellipsoidal structures. They yield significantly better performance than the traditional Beetstra et al.'s model [Beetstra et al., “Drag force of intermediate Reynolds number flow past mono‐ and bidisperse arrays of spheres,” AIChE J. 53(2), 489–501 (2007)].