## Direct Numerical Simulation of Liquid-Gas-Solid Flows Based on the Lattice Boltzmann Method

### Direkte Numerische Simulation von Flüssig-Gas-Feststoff-Strömungen basierend auf der Lattice Boltzmann-Methode

Please always quote using this URN: urn:nbn:de:bvb:29-opus4-87191
• Liquid-gas-solid three-phase flows play an important role in nature and industrial applications. In this thesis, a direct numerical simulation technique for liquid-gas-solid flows is presented. The model is based on the lattice Boltzmann method for hydrodynamics, a free surface volume-of-fluid approach for liquid-gas interface tracking, and a Lagrangian rigid body representation of solid particles. The theory of the free surface lattice Boltzmann method is developed in detail, including an analysis of lattice Boltzmann boundary conditions for free surfaces, a comparison of different volume-of-fluid surface tension models, and an analysis of the overall method accuracy. Finally, a couplingLiquid-gas-solid three-phase flows play an important role in nature and industrial applications. In this thesis, a direct numerical simulation technique for liquid-gas-solid flows is presented. The model is based on the lattice Boltzmann method for hydrodynamics, a free surface volume-of-fluid approach for liquid-gas interface tracking, and a Lagrangian rigid body representation of solid particles. The theory of the free surface lattice Boltzmann method is developed in detail, including an analysis of lattice Boltzmann boundary conditions for free surfaces, a comparison of different volume-of-fluid surface tension models, and an analysis of the overall method accuracy. Finally, a coupling to the Lagrangian rigid body simulation is presented to extend the method to liquid-gas-solid flows. The method is applied to simulate bubble-particle interaction in a containing liquid. Thus, simulations of gas bubbles within particle suspensions become possible. As a test case, a bubble-induced mixing process of up to 178486 fully resolved particles is simulated. Thanks to the scalability of the method on parallel computers, arbitrarily complex setups are possible, if sufficient resources are provided. The thesis is completed with a self-contained introduction to the lattice Boltzmann method for hydrodynamics. The consistency of the method with the incompressible Navier-Stokes equation is studied by means of Chapman-Enskog analysis.