Structure-dependent drag in gas-solid flows studied with direct numerical simulation

Quantification of drag F is critical to the simulation of gas-solid flows in both discrete particle models and two-fluid models. It is commonly accepted that for homogeneous flow the drag is a function of solid volume fraction phi and particle Reynolds number Rep (based on the mean slip velocity and particle radius). However, its adequacy for heterogeneous flows encountered more frequently is in debate yet. In this work, we reveal the strong structural dependence of the drag in both a simple case of two particles and a typical case with stepwise heterogeneity, demonstrating the necessity for a structure-dependent drag description. To quantify such dependence, flow past idealized static suspensions with linear heterogeneity is studied first, which confirms a general form F(Re-p,phi,vertical bar del phi vertical bar,theta) suggested previously, where theta is the angle between the gradient del phi and the mean slip velocity. In the studied range of 5 < Re-p < 30, F depends linearly on Re-p for a given static particle configuration. However, the concrete expressions are yet to be found. Then for dynamic gas-solid suspension, large-scale simulations enabled by supercomputing systems reveal a much more complicated dependence: on one hand, the drag coefficients on individual particles scatter even in the absence of distinct heterogeneity: and on the other hand, with the presence of distinct heterogeneity, the drag predicted by Wen and Yu (1966) deviates significantly from the simulation value in both direction and magnitude. A purely bottom-up statistical approach to establish a drag correlation in this case seems difficult and a theoretical elucidation is needed. (C) 2014 Elsevier Ltd. All rights reserved.