Drag correlations for flow past monodisperse arrays of spheres and porous spheres based on symbolic regression: Effects of permeability

Abstract

An accurate drag correlation accounting for multiscale heterogeneous porous structures is a prerequisite for reliable CFD simulation of fluidized beds. Though particle clusters in fluidized beds are usually modeled as porous particles, particle-resolved direct numerical simulation (PR-DNS), in which monodisperse arrays of spheres are taken as model systems, has been widely used as a first-principle approach to derive drag correlations. This work is to bridge the gap of drag correlations for monodisperse arrays of spheres and porous spheres by considering permeability effects and derive new drag correlations using symbolic regression (SR) methods. Firstly, experimental porous spheres settling data were utilized to identify the most important features affecting drag force using Support Vector Machine (SVM), in which the permeability β was packed up in addition to the solid fraction ϕ and Reynolds numbers Re. A new drag correlation for porous spheres based on ϕ,Re, and β, which has physical terms, high prediction accuracy and correct limiting cases, is automatically generated using SR method. Then, PR-DNS data from open sources were used to distill drag correlations for monodisperse arrays of spheres by incorporating the extra permeability parameter by SR method, demonstrating solid physical basis with high accuracy. It is further shown the SR based on drag correlations for porous spheres and monodisperse arrays of spheres can be reduced to limiting cases of a single solid sphere and Stokes flow. The proposed new drag correlations not only provide a way to use permeability as a simple yet physically sounded parameter to quantify heterogeneous structures in fluidized beds, but also open a venue for directly validating drag correlations obtained purely from PR-DNS simulations with experimental data of flow around porous spheres.