A multiple-resolution strategy for two phase flow simulations using the phase field method

Abstract

In this work, a multiple-grid Phase Field Method PFM approach has been implemented using a Direct Numerical Simulation DNS. The Continuity equation CE and the Navier-Stokes equations NSE are coupled with second-order Phase Field Method PFM, where one equation is responsible for the description of the interfacial dynamics (Cahn-Hillard equation CHE) and the other one for the surfactant (Cahn-Hillard-like equation), which will not be covered in this thesis, since the mutliple-grid for the surfactant is already implemented. In the turbulence-interface model just the equation for the interface will be expanded and it is validated through two sets of benchmarks. First, a 2D benchmark is completed, where a 2D droplet is exposed in a laminar shear flow. From analytical results and previous numerical and experimental works it is known that a steady-state will be reached after some point. Therefore, the deformation and the steady-state angle will be compared for different viscosity ratios and capillary numbers. Furthermore, a 3D benchmark is obtained. A thin sheet layer is placed in the center of a turbulent channel flow and the breakage and coalescence of this thin sheet layer will be compared to the current internal code, where no expansion for the phase-field is included. Last but not least, a simulation is obtained, where the influence of different grid-resolutions on the mass leakages and the surface area development are compared.