A priori test of effective drag modeling for filtered two-fluid model simulation of circulating and dense gas-solid fluidized beds

Eulerian two-fluid approach is generally used to simulate gas-solid flows in industrial fluidized beds. Because of limitation of computational resources, simulations of large vessels are usually performed using too coarse mesh to capture the influence of the fine flow scales which can play an important role in the dynamic behaviour of the beds. In particular, neglecting the particle segregation effect at small scale leads to an inadequate modelling of the mean interfacial momentum transfer between phases. Then, an appropriate modelling approach which accounts for influences of unresolved structures has to be proposed for "coarse simulations". For this purpose, computational grids are refined to get mesh-independent results for a dense and a periodic circulating fluidized beds in which statistical quantities do not change with further mesh refinement. These mesh-independent results are filtered by volume averaging and then used to perform a priori analysis on the filtered drag term. Results show that filtered momentum equation can be computed on "coarse simulations" but must take into account the particle to fluid drift velocity due to the subgrid correlation between the local fluid velocity and the local particle volume fraction. In the present paper we propose a model, for subgrid the drift velocity, written in terms of the difference between the averaged of gas velocity weighted by solid volume fraction and the averaged of gas velocity weighted by gas volume fraction. We use a systematic procedure to provide constitutive closures for the subgrid drift velocity and the closure depends of both the filtered solid volume fraction and a characteristic filter size.