Direct numerical simulation of moderate-Reynolds-number flow past arrays of rotating spheres

Abstract

Direct numerical simulations with an immersed boundary-lattice Boltzmann method are used to investigate the effects of particle rotation on flows past random arrays of mono-disperse spheres at moderate particle Reynolds numbers. This study is an extension of a previous study of the authors [Q. Zhou and L.-S. Fan, “Direct numerical simulation of low-Reynolds-number flow past arrays of rotating spheres,” J. Fluid Mech. 765, 396–423 (2015)] that explored the effects of particle rotation at low particle Reynolds numbers. The results of this study indicate that as the particle Reynolds number increases, the normalized Magnus lift force decreases rapidly when the particle Reynolds number is in the range lower than 50. For the particle Reynolds number greater than 50, the normalized Magnus lift force approaches a constant value that is invariant with solid volume fractions. The proportional dependence of the Magnus lift force on the rotational Reynolds number (based on the angular velocity and the diameter of the spheres) observed at low particle Reynolds numbers does not change in the present study, making the Magnus lift force another possible factor that can significantly affect the overall dynamics of fluid-particle flows other than the drag force. Moreover, it is found that both the normalized drag force and the normalized torque increase with the increase of the particle Reynolds number and the solid volume fraction. Finally, correlations for the drag force, the Magnus lift force, and the torque in random arrays of rotating spheres at arbitrary solids volume fractions, rotational Reynolds numbers, and particle Reynolds numbers are formulated.