Theoretical derivation and a priori validation of a new scalar variance-based sub-grid drag force model for simulation of gas-solid fluidized beds

A novel sub-grid drag force model is proposed for coarse-grid Euler-Euler simulation of gas-solid fluidized beds. Starting from a transport equation for the drift velocity, an equilibrium condition is used as a basis to derive a new algebraic drift velocity model. The sub-grid correlations that show up are closed by a large-eddy PDF approach inspired from LES of turbulent reacting flows. The new analytical model only depends on the resolved slip velocity and on a few sub-grid moments of the solid volume fraction. Then, a conditional averaging procedure shows that the new model can be properly captured by a simple functional expression that only requires a closure for the sub-grid variance of the solid volume fraction. A priori validation studies show that the drift velocity is predicted with high accuracy (R-2 > 0.90) for a large range of filter widths and for both Geldart A and Geldart B particles.