Simulation Of The Thermocapillary Convection With Lattice Boltzmann Method

The fluid dynamics problem involving gas-liquid or liquid-liquid interface is widely observed in nature and industrial production. The fluid interface is a thin transition region, the interactive force between molecules behaves macroscopically as the surface tension. In general, the surface tension depends on the interface temperature or concentration. The temperature gradient on the interface results in a gradient of surface tension along the fluid interface, and it drives melt convection, so-called thermocapillary flow.Under microgravity or in micro-scale flow, the gravity and buoyancy effect is greatly reduced, and the thermocapillary flow may become the dominated convection. In thermocapillary flow, the unbalanced surface tension not only drives the convection, but also affects the interface shape, and the coupling between thermocapillary flow and interface deformation makes the numerical simulation to become a challenge in computational fluid dynamics.Based on the Lattice Boltzmann Method(LBM), the numerical method for thermocapillary flow with considering dynamic interface deformation was developed. The two-phase flow was simulated with LBM, the dynamic interface deformation was captured with phase-field method. By using the developed method and code, the thermocapillary migration of drop, the drop’s coalescence, and thermocapillary flow in an annular cavity with two liquid layers were investigated numerically.The main works in this paper are summarized as follows:(1) Firstly, the LBM and the relation with the Navier-Stokes equation were introduced briefly, and the incompressible multi-relaxation-time LBM model was presented. The classical flow problem was simulated by the LBM to valid the model and code.(2) Based on the above LBM model, two kinds of coupling models for isothermal two-phase flow with dynamic interface deformation were developed. The flow fields were obtained from the LBM model, and the interface deformation was captured by the front tracking technique and phase field method, respectively. The parallel programming with OpenMP was implemented for three-dimensional two-phase flow problems.(3) The energy equation was introduced to the LBM model, which is coupled with phase field method, to simulate thermocapillary flow. The LBM was applied to solve the flow field for incompressible binary fluids, and the model was implemented in an axisymmetric form. Both phase field equation and the energy equation were solved with the finite difference method. The continuum surface force model was adopted to compute the normal and tangential surface tension according the order parameter.(4) The thermocapillary migration of drop and the drop’s interaction were simulated numerically. The effects of Marangoni number and Capillary numbers on the drop’s coalescence were investigated. The results indicate that the drop coalescence becomes more difficult with a larger Marangoni number. With increasing Capillary number, the deformation of the leading drop becomes more obvious, the drop coalescence becomes more difficult, and the coalescence time lasts longer.(5) The flow and interface deformation in an annular cavity with two immiscible liquids were investigated. The flow intensities in two liquid layers are reduced with increasing the ratio of kinematic viscosity and density, but the interface deformation becomes more obvious. The Capillary number has little effect on the flow intensities, but the interface deformation becomes more obvious at the larger Capillary number.