| A finite volume numerical method is introduced to perform the direct numerical simulation for two-phase immiscible and incompressible fluids. The Navier-Stokes equation is discretized by the staggered mesh spatially and advected temporally with the 4th order Runge-Kutta scheme. CFL conditions involving the effect from the convective term, viscous term, stiff source term and heat transfer are applied to meet the stringent limitation on the time step. Energy equation is coupled with the Navier-Stokes equation when the study of heat transfer is included. The interface separating the fluids is treated implicitly using a finite thickness, which constrained the numerical instabilities within the interface, by the level set method. The topology change and location of the interface are captured by advecting the smooth level set function with the 5th order WENO algorithm. Re-initialization of the signed distance function is executed at the designated time steps to ensure the mass conservation. The surface tension effect is modelled with the Continuum Surface Force (CSF) model and the numerical spurious error is corrected by the modified curvature calculation. The validated method is used to study the dynamics of single and multiple bubble/droplet movements influenced by different viscosity, density ratio and surface tension effect. The application of this method is further extended to investigate the binary Rayleigh-Benard convection in two-dimensional and three-dimensional geometries. The complex nonequilibrium of the system is well captured and compared with the linear stability analysis. Discussion and explanation for the driving mechanism and pattern of energy transportation of the two-phase Rayleigh-Benard convection are presented with the predicted results. |
