A simplified steady-state mesoscale drag model with an analytical solution for fluidized beds

Abstract

Mesoscale structures have an essential impact on hydrodynamics and heat/mass transfer and hence should be considered in drag modeling. However, there is a lack of generalized drag coefficient expressions taking into account mesoscale effects for fluidized beds. In this study, a simplified steady-state mesoscale drag model which can be solved analytically was proposed by simplifying sub-system drag forces and cluster diameter equation. Thus, two new generalized expressions for mesoscale drag coefficient used to simulate fluidized beds were obtained by deriving the analytical solution of the simplified steady-state mesoscale drag model. The sensitivity of the heterogeneity index Hd of the new drag model to material properties and operating gas velocity was analyzed, and the results showed that Hd was most sensitive to dp and Ug, followed by ρp and μg, and least sensitive to ρg. As a preliminary validation, new drag coefficient expressions were incorporated into two-fluid model simulations of realistic fluidized beds. Noteworthy, the relative errors of axial solid volume fraction using the new Drag A for bubbling, turbulent and circulating fluidized beds, which were 7.41%, 12.51% and 12.80%, respectively, were the smallest compared to that using other drag models. The simulation results proved the accuracy and generality of the new simplified steady-state mesoscale drag model.