Lattice Boltzmann Simulations of Multiphase Flows

Jeremy Aaron Kolker Horwitz
University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign, 2013


   title={Lattice Boltzmann simulations of multiphase flows},



   school={University of Illinois}


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This thesis is a comprehensive account of my experiences implementing the Lattice Boltzmann Method (LBM) for the purpose of simulating multiphase flows relevant to Air Conditioning and Refrigeration Center (ACRC) applications. Other methodologies have been used to simulate multiphase flow including finite volume based Navier-Stokes solvers. These methods have found reasonable success in simulating multiphase flows. LBM was chosen because of its ability to capture multi-fluid physics including phase-change and interfacial dynamics with relative ease. In addition, the LBM algorithm can be easily parallelized. This allows larger problems to be simulated quicker. Among the multiphase LBM algorithms, we have implemented the Shan-Chen method, the He-Chen method, and an extension to the He-Chen method. We carefully document our methodology and discuss relevant kinetic theory and fluid dynamics. We present results for a number of fundamental flow problems including droplet impingement on solid and liquid surfaces as well as multiphase flow in complex micro-channels. In addition, we examine in great detail the problem of axial droplet migration and deformation in a square-duct at moderate Reynolds number. Our results suggest that the LBM algorithm is capable of simulating a wide range of flows and can accurately capture flow physics provided the density ratio among fluid phases is not large. Because ACRC equipment often harbor high density ratio flows, the standard LBM procedures require modification to accommodate higher density ratio problems. We investigate one such modification to the He-Chen algorithm by introducing a pressure Poisson equation (PPE) to reduce density variation related to compressibility effects.
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