Topology Optimization of Capillary, Two-Phase Flow Problems (Communications in Computational Physics, 2017)
This paper presents topology optimization of capillary, the typical two-phaseflow with immiscible fluids, where the level set method and diffuse-interface modelare combined to implement the proposed method. The two-phase flow is described bythe diffuse-interface model with essential no slip condition imposed on the wall, wherethe singularity at the contact line is regularized by the molecular diffusion at the interfacebetween two immiscible fluids. The level set method is utilized to express thefluid and solid phases in the flows and the wall energy at the implicit fluid-solid interface.Based on the variational procedure for the total free energy of two-phase flow, theCahn-Hilliard equations for the diffuse-interface model are modified for the two-phaseflow with implicit boundary expressed by the level set method. Then the topology optimizationproblem for the two-phase flow is constructed for the cost functional withgeneral formulation. The sensitivity analysis is implemented by using the continuousadjoint method. The level set function is evolved by solving the Hamilton-Jacobianequation, and numerical test is carried out for capillary to demonstrate the robustnessof the proposed topology optimization method. It is straightforward to extend thisproposed method into the other two-phase flows with two immiscible fluids.