Simulation of two-phase dynamics using lattice Boltzmann method (LBM)

In this dissertation, a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model), is proposed for the simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. Bulk regions of the two phases are governed by a non-ideal equation of state (for example, the van der Waals equation of state), whereas an artificial near-critical equation of state is applied in the interfacial region. The interfacial equation of state is described by a double well density dependence of the free energy. The continuity of chemical potential is enforced at the interface boundaries. Using the AILB model, large density and viscosity ratios of the two phases can be simulated. The model is able to quantitatively capture the coexistence curve for the van der Waals equation of state for different temperatures. Moreover, spatially varying viscosities can be simulated by choosing the relaxation time as a function of local density.;Suitable velocity and density (pressure) boundary conditions are also developed for the particle distribution functions in the framework of the proposed model. Boundary conditions for both the 2D as well as 3D domains are developed and relationships to evaluate unknown distribution functions are explicitly provided. Based on the Cahn's wetting theory, physics governing the wall-fluid interactions is also developed in the framework of the AILB model. Using it, any specified contact angle (ranging from 0o to 180o) can be simulated at the walls of the domain. The proposed AILB model and the Lee-Fischer LB model are evaluated on several simple problems which involve interactions between two phases of a fluid and, between two phases and solid walls. Some of these problems in the order of increasing complexity are: the simulation of multi-fluid Poiseuille-Couette flow, specifying static bubbles/droplets in a periodic domain, two-bubble or two-drop coalescence, single rising bubble, break-up of a drop/bubble due to shearing walls, specifying different equilibrium contact angles on the surfaces, dynamics of drop/bubble in contact with a surface, etc.;In addition, a simulation methodology based on the Peng-Robinson (P-R) equation of state has been devised in the LB framework. The developed P-R model can accurately predict phase-coexistence curve for water and steam at different system temperatures and allows simulation of phases with varying density/viscosity ratios.;Thermal effects in the AILB model are simulated by employing a separate distribution function responsible for tracking the temperature dynamics. A phenomenological model to simulate evaporation and condensation is also developed in the framework of the proposed model. The thermal model is able to qualitatively capture the bubble growth and shrinking dynamics due to the variations in surrounding bulk temperatures.;For the numerical analyses using the LBM, a computer code is developed to solve problems in both 2D and 3D. The code can run on a single processor PC as well as on a parallel cluster. The code has been written in FORTRAN90 language and incorporates MPI paradigm for parallelization.