Hydrodynamic forces on assemblies of non-spherical particles: orientation and voidage effects

This work provides a recipe for creating drag, lift and torque closures for static assemblies of axisymmetric, non-spherical particles. Apart from Reynolds number $Re$ and solids volume fraction $\epsilon_s$, we propose four additional parameters to characterize the flow through non-spherical particle assemblies. Two parameters consider the mutual orientations of particles (the orientation tensor eigenvalues $S_1$ and $S_2$) and two angles represent the flow direction (polar and azimuthal angles $\alpha$ and $\beta$). Interestingly, we observe that the hydrodynamic forces on the particles are independent of the mutual particle orientations. Rather, the most important parameter representing the particle configuration itself is the incident angle $\phi$ of the individual particles with respect to the incoming flow. Moreover, we observe that our earlier finding of sine-squared scaling of drag for isolated particles (Sanjeevi & Padding 2017) holds on average even for a multiparticle system in both the viscous and inertial regimes. Similarly, we observe that the average lift for a multiparticle system follows sine-cosine scaling, as is observed for isolated particles. Such findings are very helpful since the pressure drop of a packed bed or porous media can be computed just with the knowledge of orientation distribution of particles and their drag at $\phi=0^\circ$ and $\phi=90^\circ$ for a given $Re$ and $\epsilon_s$. With the identified dependent parameters, we propose drag, lift and torque closures for multiparticle systems.