Development of a Heterogeneous Drag Model for Gas-Solid Flows Based on Particle-Resolved Direct Numerical Simulations

The conventional drag models commonly used in gas-solid flow are mainly developed based on the system of random and homogeneous distribution of particles. Since the existence of particle clusters and bubbles in fluidized beds have a pronounced influence on the interaction between fluid and particles, the effect of heterogeneity on drag force in fixed beds at low Reynolds numbers is studied with particle-resolved direct numerical simulation (PR-DNS). Two kinds of inhomogeneous structures are studied in this paper: (i) the linear spatial distribution of solid volume fraction, (ii) the simple stepwise heterogeneous structure formed with dilute phase and dense phase. Our PR-DNS results show that though the drag coefficient agrees well with the BVK (Beetstra et al. AIChE J. 2007) model at dense or dilute phase with a certain gradient of volume fraction, obvious deviation occurs in the latter configuration, especially near the interface between dense and dilute phase.

Further focus on the drag force at the stepwise heterogeneous structures, the PR-DNS results suggest that: (i) the drag coefficient decrease if the gas flow is perpendicular to the gradient of the volume fraction while increase if gas flow is parallel to the gradient; (ii) the deviations between the PR-DNS results and the homogenous drag model increase with the increasing of the filtered grid size at the same gradient of the volume fraction; (iii) the drag curves versus solid concentration vary with gradient of the volume fraction at the same filtered grid size. Based on these results, a heterogamous drag coefficient model considering the solid volume fraction, particle Reynolds numbers, filtered grid size, flow direction, and the gradient of volume fraction is developed. Note that, no consistency rule could be observed when the filter grid size is one particle diameter or below, which indicates the proposed drag model no longer applies at this situation.

Furthermore, the proposed new drag model is validated with a serial of PR-DNS of gas-solid flows with obvious clusters. Our proposed drag model could obtain not only the well-known drag reduction but also the local drag increasing due to the local heterogeneity. The further validation of the new drag model in large scale simulations using CFD-DEM or TFM will be our future work.