Gas flow through static particle arrangements with a channel: Resolved simulations and analytic considerations

Abstract

Fractures of particle assemblies happen frequently in dense gas-solid systems leading to a notable heterogeneity in the particle configuration, especially in case of cohesive powders and non-spherical particle interlocking. In this work, we investigate the influence of such heterogeneities on the hydrodynamic drag by studying the idealized case of a random arrangement of spheres with a channel-like void region. More specifically, we introduce this heterogeneity to a homogeneous particle arrangement by shifting apart two bulk regions, such that a void channel divides particle bulk. Single-relaxation-time lattice Boltzmann simulations were performed to resolve fluid flow through such arrested particle configurations and calculate the corresponding gas-particle momentum exchange and pressure drop. The calculated drag forces acting on the solids for random sphere arrangement are in good agreement with previously reported results of Hill et al. (2001b), Tenneti et al. (2011), and Tang et al. (2015). However, the overall momentum exchange obtained for configurations containing a heterogeneity is significantly lower. Obviously, the channel allows for a by-passing of a considerable amount of the flow leading to a reduced overall pressure drop and thereby underestimating the minimum fluidization velocity in a fluidized bed. Based on these direct numerical simulations, we examine the overall pressure drop dependence on the characteristic length scale (i.e. width) of the channel-like heterogeneity $L_c$, the superficial Reynolds number (30 $⩽$ Re $⩽$ 300), and the solid volume fraction in the dense (i.e. bulk) region (0.4 $⩽{\varphi }_p⩽$ 0.55). The width of the channel is varied within the order of magnitude of particle diameter $D_p$ (1 $⩽L_c/D_p⩽4.36$), decreasing an overall solid volume fraction (0.25 $⩽\varphi ⩽$ 0.55). In addition to the numerical simulations, we derive (semi)-analytic correlations for the dense bulk region as well as for the channel. As the simulations range from laminar to transitional flow, providing a single pressure drop correlation is very challenging. Therefore, we estimate the channel pressure drop with the appropriate correlations selected according to calculated superficial Reynolds number. For laminar flow, we achieved a good agreement between a combined (i.e. bulk and channel) analytical prediction of overall pressure drop and our resolved numerical simulation. In the transitional regime, the pressure drop values are more difficult to predict, with the better agreement as we approach the turbulent regime. We believe that this work can act as a basis for the development of future drag laws accounting for channel-like sub-grid heterogeneities.