Coarse-grained methods have been widely used in simulations of gas-solid
fluidization. However, as a key parameter, the coarse-graining ratio,
and its relevant scaling law is still far from reaching a consensus. In
this work, a scaling law is developed based on a similarity analysis,
and then it is used to scale the multi-phase particle-in-cell (MP-PIC)
method, and validated in the simulation of two bubbling fluidized beds.
The simulation result shows this scaled MP-PIC can reduce the errors of
solids volume fraction and velocity distributions over a wide range of
coarse-graining ratios. In future, we expect that a scaling law with
consideration of the heterogeneity inside a parcel or numerical particle
will further improve the performance of coarse-grained modeling in
simulation of fluidized beds.