Density waves and fluctuations in three-dimensional granular poiseuille flow

Abstract

In the present thesis, the gravity driven granular Poiseuille flow has been probed via event-driven simulations in three dimensions between two infinite parallel plates. A monodisperse system of “rough” inelastic hard spheres interacting via hard core potential has been used. The normal coefficient of restitution (e) and the tangential coefficient of restitution (β) are the two basic governing parameters of the collision process. The influence of particle volume fraction (φ), particle roughness (β) and inelasticity (e) on various micro-structural features (velocity distribution functions, correlations, etc.) and macro-structural features (density waves, velocity, density and temperature profiles, etc.) has been probed in the rapid flow regime. The Boltzmann limit (φ = 0.01) of the granular Poiseuille flow has been inves- tigated in detail. By probing the local velocity distribution functions (VDFs) for a range of e and β, it is found that the particle roughness plays an important role in the deviation of VDFs from the Gaussian distribution. The translational and rotational VDFs can differ significantly from each other depending on the values of e and β. The density correlation was found to be negligible for any values of β and e in the Boltzmann limit; however, significant “directional” correlations be- tween translational and rotational velocities were observed for all values of β. For a moderately dense flow (φ = 0.1), we observed the formation of dense plugs and density waves. As in the case of Boltzmann limit, the VDFs are found to be signif- icantly affected by the particle roughness as well as by inelastic dissipation. The pair correlation function shows that the system has a liquid-like structure around the channel centerline where the particles are flowing in the form of density waves. It is found that there are strong directional correlations over the whole channel width which increases with increasing dissipation. For any value of β, the spatial velocity correlations are found to be the largest for the streamwise velocity. A limited set of results on VDFs and correlations for a very dense flow (φ = 0.5) has been qualitatively compared with recent experiments in a similar setup. The vii present work indicates that orientational correlations should be incorporated in the theoretical models of granular flows. The formation of density waves has been examined for a single density (φ = 0.15), and different steady state forms of density variations have been observed. The nature of such density waves has been analysed using the Fourier analysis of the coarse-grained density field. It is found that the density-waves and structure formations can be controlled by varying the system size. The density-wave appears to persist in larger computational domains, and increasing the channel dimensions simply permit additional wave numbers to be realized. At small values of the channel width W/d and the aspect-ratio L/W, the system develops a plug flow. The system develops an S-shaped wavy flow at intermediate values of W/d and further there is a formation of slugs and a combination of these structures. With decreasing dissipation, the steady wave structure no longer persists but results in the formation of slugs if L/W is large enough. The effect of three dimensionality has been studied and it is found that the availability of the third dimension signif- icantly influences the formation of the density waves. The particle motion in the observed three-dimensional structures indicates the presence of vorticity, an im- portant consideration for granular flows, which would enhance mixing of granular materials.