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.