Efficient Viscosity and Thermal Conductivity Formulation for Scale-Resolved Hypersonic Flow Simulations

Under high-enthalpy conditions, the calculation of transport properties such as viscosity and thermal conductivity needs to account for nonequilibrium effects, including vibrational nonequilibrium and the dissociation of molecules. Current models require computationally intensive mixing rules and are limited to certain temperature ranges. With scale-resolving simulation becoming more commonplace, there is a need for efficient formulations that can cover a wide range of temperatures. In this contribution, a simplified formulation is proposed for the viscosity and thermal conductivity of air in the temperature range 100–9000 K. Thermal conductivity is decomposed into ro-translational and vibrational contributions for molecular species. The predictions are applicable to both equilibrium and nonequilibrium conditions. For equilibrium air, the predictions are typically within a few percent of reference data. An application to a transitional mixing layer, starting with partially dissociated air at a temperature of 6000 K, is presented. The mixing layer is simulated with a high-order finite difference method and undergoes inflectional instability and transition to turbulence. With the new method the transport properties are within 2.2% of reference values, while the reduced complexity means that the simulations are substantially faster.