Anisotropy Perspective of Supersonic Turbulent Boundary Layer with Non-adiabatic Wall Temperature

In many high-speed applications, the wall temperature does not match the adiabatic or recovery temperature. This non-adiabatic condition strengthens the coupling between the energy and momentumequations, leading to significant changes in the boundary-layer structure. Adetailed understanding of these high-speed flows with non-adiabatic walls is still developing, and new scaling laws and models are still evolving, as the traditional scaling laws, which are applicable for adiabatic cases, do not hold in this regime. In this work, we present a modal Discontinuous Galerkin Implicit Large Eddy Simulation of a Mach 4 flow over a zero-pressure gradient turbulent boundary layer of a flat plate using our in-house code Multiscale Ionized Gas. The flat plate wall temperature is set to a recovery-to-wall temperature ratio of 0.75 to represent nominal conditions for high-speed vehicles and wind tunnels. Advantages of the modal Discontinuous Galerkin Implicit Large Eddy Simulation method are shown, and the results for the turbulent kinetic energy (TKE) budget terms are compared with those of Direct Numerical Simulation results. The results show a good match with DNS results, and hence, the modal Discontinuous Galerkin Implicit Large Eddy Simulation method is presented as a new and alternative approach to simulate these type of high speed flows with non-adiabatic walls, to reduce computational time as compared to DNS, while capturing flow physics with sufficient accuracy. Various insights into the flow physics are deduced from the TKE budget terms. A linear barycentric map is used to gain insights into the flow’s anisotropy, which is relevant for understanding the dimensionality of turbulent kinetic energy at various parts of the flow. The barycentric map analysis is compared with an Anisotropy-Invariant Map analysis, and the advantages of the barycentric map are discussed.