Multiscale approach to fully resolved boundary layers using adaptive grids

Abstract

Bubbly flows are omnipresent in most industrial processes. Often the intended use of such processes is to facilitate efficient mass and heat transfer for reactive flows. Mass and heat transfer coupled with fluid flow in gas-liquid systems gives rise to multiscale transport phenomena. Because of large Schmidt and (possibly) Prandtl numbers in the liquid phase the concentration and temperature boundary layers are much thinner than the momentum boundary layers. When using fully resolved CFD modeling on an uniform grid, these small scales would demand an overall refinement which requires an immense computational effort. Here, however, a hybrid mesh approach is used which couples a fixed Cartesian grid for the hydrodynamics and a tree structure based mesh, which can be adaptively refined for heat and mass transfer. Tree based adaptive refinements commonly suffer from low order accurate numerical schemes. A higher order finite volume scheme on a parallel tree data structure for solving the convection-diffusion equation has been implemented using an implicit formulation. The resulting set of linear algebraic equation are then solved with AMG class of matrix solvers. This approach presents a solution to resolve the fine boundary layers of scalar transport for realistic range of Schmidt and Prandtl numbers. The present study will demonstrate the robustness of this framework to capture sharp boundary layers in fairly simple analytical flow fields. A detailed comparison is performed with overall refined simulations on multi core parallel architectures.