Mesoscale structures such as particle clusters have been observed both in experiments and in numerical simulations of circulating fluidized beds. In a numerical simulation, in order to account for the effects of such mesoscale structures, the computational grids have to be fine enough. The use of such fine grids is impractical in engineering applications due to excessive computational costs. To predict the macroscopic behavior of a fluidized bed with reasonable computation cost, they perform a second average over the averaged equations for two-phase flows. A mesoscale inter-phase exchange force is found to be the correlation of the particle volume fraction and the pressure gradient. This force is related to the mesoscale added mass of the two-phase flow. Typically, added mass for particle scale interactions is negligible in gas-solid flows since the gas density is small compared to density of solid particles. However, for a mesoscale structure, such as a bubble, the surrounding media is the mixture of gas and particles. The surrounding fluid density experienced by the mesoscale structure is the density of the surrounding mixture. Therefore, the added mass of a mesoscale structure, such as bubbles, cannot be neglected. The property of this new force is studied based on the numerical simulation of a fluidized bed using high grid resolution. It is shown that this force is important in the region where the particle volume fraction is high. The effects of the inhomogeneity to the interphase drag are also studied.
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