A high-order numerical method to study hypersonic boundary-layer instability including high-temperature gas effects

Abstract

Prediction of laminar-turbulent transition is a key factor in the design of the heat shield of vehicles (re-)entering a planetary atmosphere. To investigate the transition by means of numerical simulation, accurate and efficient computational methods are necessary. Here, the compressible Navier–Stokes equations are solved for a gas where properties such as specific heat, thermal conductivity, viscosity, and specific gas constant depend on one or two thermodynamic variables. Our approach models a mixture of perfect gases in local thermodynamic equilibrium. The gas properties are provided either by means of direct calls to a library based on statistical mechanics and kinetic theory or indirectly in the form of look-up tables. In the first part of the paper, our method of handling a high-temperature gas in thermochemical equilibrium is described and verified. In the second part, the method is applied to the investigation of linear and non-linear boundary-layer instability. We carry out numerical simulations for a laminar flat-plate boundary layer at Mach 10 with a small, convectively amplified perturbation for both Earth and Martian atmospheres. Amplification of the perturbations shows favorable agreement with results obtained from linear theory. The secondary instability of the boundary layer in the presence of a large-amplitude two-dimensional wave is investigated. We observe that the non-linear mechanism of fundamental resonance becomes active and leads to a strong increase in amplification of three-dimensional disturbance waves.