The computational fluid dynamics-discrete element method (CFD-DEM) at the laboratory scale has shown to be effective in capturing the main characteristics of gas-solid flows. The accuracy of gas-solid drag models is critically important for the predictability of simulations on gas-solid fluidized beds. A number of studies have shown that the inhomogeneities have a pronounced effect on the drag in gas-solid systems [1-3]. In this work, direct numerical simulations of flows past fluidized spheres in cubic domain with full-period boundary conditions are performed to investigate the effect of inhomogeneities on the drag at low Reynolds numbers. Two powerful sub-grid quantities have been employed to quantify the extent of inhomogeneities in the literature [3]: the drift flux, measures the correlation between the solid volume fraction and the fluid velocity, and the scalar variance of solid volume fraction, determined by the particle configurations. Due to the unresolved flow structures at the sub-grid scale in CFD-DEM simulations, the drift flux cannot be obtained directly and extra closure for it is required when the drag model based on the drift flux is applied in CFD-DEM simulations. For lack of effective approach to estimate the drift flux perfectly, drag model with the modelled drift flux usually presents an unsatisfactory result in predicting the drag. In terms of the particle configuration and velocity are available in CFD-DEM simulations, a newly defined quantity named the solid drift flux, which is a measure of the correlation between the gas volume fraction and the particle phase velocity, is proposed in this work. Then a new inhomogeneous drag model is developed by taking the effect of both the scalar variance of solid volume fraction and the solid drift flux into consideration. Comparison is made between the newly proposed drag model and prior drag models [4-5]. The results show that the new drag model achieves a good performance for describing the effect of inhomogeneities on the gas-solid drag force, which can be applied in CFD-DEM simulations without any additional closures for sub-grid quantities.
Reference
1. G. Zhou, Q. Xiong, L. Wang, X. Wang, X. Ren, W. Ge. Structure-dependent drag in gas-solid flows studied with direct numerical simulation. Chemical Engineering Science. 2014;116:9-22.
2. X. Chen, N. Song, M. Jiang, T. Ma, Q. Zhou. A microscopic gas-solid drag model considering the effect of interface between dilute and dense phases. International Journal of Multiphase Flow. 2020:103266.
3. G.J. Rubinstein, A. Ozel, X. Yin, J.J. Derksen, S. Sundaresan. Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force. Journal of Fluid Mechanics. 2017;833:599-630.
4. D. Gidaspow. Multiphase flow and fluidization: continuum and kinetic theory descriptions: Academic press; 1994.
5. M.A. van der Hoef, R. Beetstra, J. Kuipers. Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. Journal of Fluid Mechanics. 2005;528:233-254.
