Drag correlation for micro spherical particles at finite Reynolds and Knudsen numbers by lattice Boltzmann simulations

The drag coefficient of particles is an important parameter for predicting the transport properties of particle-laden flows. For a sphere immersed in continuum flows, the drag coefficient is typically related to the Reynolds number (Re), and when the rarefaction effect involved, it is then presented as a function of the Knudsen number (Kn). In this work, a new drag coefficient correlation for spherical particles is proposed based on direct numerical simulations, which well considers both the influences of finite Reynolds (0.1≤Re≤3.5) and Knudsen numbers (0.1≤Kn≤1). The simulations are performed using the lattice Boltzmann method coupled with an improved effective relaxation time model to account for the effect of finite Kn. The results show that the classical Cunningham-type correlation is not sufficient as Re>0.1, which can underestimate the drag coefficient with a maximum error about 27.1% at Kn=0.1 and 4.2% at Kn=1.0. Moreover, the drag coefficient expressions cannot be obtained by simply combining the formulas with pure slip and inertial effects considered separately, which usually overestimate the drag coefficient.