Towards the simulations of inertial dense particulate flows with a volume-averaged lattice Boltzmann method. (30th April 2018) - Höcker, Stephan B.; Trunk, Robin; Dörfler, Willy; Krause, Mathias J.
Abstract: The simulation of dense particulate flows offers a series of challenges, including the modelling of particle-particle and fluid-particle interaction, complex heterogeneous structures in the particulate phase and the displacement of fluid by particles. A common approach to incorporate the latter into the governing equations of the fluid phase is given by the volume-averaged Navier–Stokes (VANS) equations which have been extensively researched in combination with finite volume methods. Multiple lattice Boltzmann (LB) schemes for the VANS equations have been suggested, yet only one study, relying on the use of non-physical force terms, investigated the schemes' applicability to test cases with non-homogeneous particle concentrations. Furthermore, no such scheme has yet been used in a dense Euler–Euler model. In this paper, we first introduce a novel lattice Boltzmann method (LBM) for the VANS equations which relies on an adaptation of the streaming step, while requiring no additional forcing terms. Second, we combine the method with an advection-diffusion LBM to obtain a simple multiphase model, which forms a first step towards an Euler–Euler model for dense particulate flows. It takes the phases' volume fractions and simple drag forces into consideration but neglects some inter-particle and hydrodynamic forces as well as turbulence. The LBM's convergence to the VANS equations is investigated in four test cases with analytical solutions, two of which contain spatially or temporally fluctuating particle concentrations. The combined multiphase model is validated using a Rayleigh–Taylor instability test case.