Computation of Heat Flux in Hypersonic Flow with a Cartesian Mesh Using Near-Wall Resolution

Abstract

A hybrid solution methodology is developed to solve laminar hypersonic flow with a Cartesian mesh approach. The hybrid grid consisting of a Cartesian mesh together with an unstructured prism layer near the wall to capture the large gradients close to the surface is used for the near wall viscous resolution. The prism layer is generated by extruding the panels formed by the intersection of the Cartesian grid and the body and is stitched with the outer Cartesian mesh away from the wall for solving axi-symmetric flows. For three dimensional flows, since the prism layer cells are not stitched to the outer Cartesian mesh, the inviscid solution is carried out first for background Cartesian mesh and later this solution is mapped to the extruded prism layer cells and laminar Navier-Stokes solution is carried out for the prism layer cells alone. The developed solver gives an unstructured prism layer solution near the wall and standard Cartesian mesh solution away from the wall. This hybrid solution methodology is validated against the experimentally measured heat flux data and could predict the heat flux with good accuracy. The present methodology thus enables the computation of a viscous solution using a Cartesian mesh based approach.