Fully resolved scalar transport for high Prandtl number flows using adaptive mesh refinement. (November 2019) - Panda, A.; Peters, E.A.J.F.; Baltussen, M.W.; Kuipers, J.A.M.
Highlights: Novel multiple resolution technique is proposed to resolve scalar boundary layers. Comparison of second order Laplacian operators for quadtrees. Solenoidal velocity interpolations and Z-order curve for dual grid communications. Accurate prediction of Nusselt number is obtained for single/multiple particles. Abstract: In multiphase systems, boundary layers occur at fluid-fluid or fluid-solid interfaces. In a direct numerical simulation, the grid requirements are often dictated by the thickness of these boundary layers. Systems that are characterized by high Prandtl (or Schmidt number) exhibit temperature (or mass) boundary layers that are much thinner than the momentum boundary layers. In this paper, a hybrid computational approach is presented that uses a fixed Cartesian grid for the Navier-Stokes and continuity equations and an adaptive mesh for scalar transport, thus reducing the memory and CPU requirements tremendously while resolving all boundary layers. We describe the key aspects that need to be addressed in this hybrid approach, related to discretization, grid mapping, velocity interpolation along with detailed verification tests. Finally, the robustness and accuracy of our hybrid methodology is demonstrated for forced-convection heat transfer over stationary spherical particles at high Prandtl numbers.