COMPRESSIBLE COUETTE FLOW AND ITS HEAT TRANSFER UNDER VIBRATIONAL NONEQUILIBRIUM EFFECTS

Most of the new-generation hypersonic cruise vehicles have sharp leading edges and thin wings, and the flow and heat transfer downstream the stagnation point are characterized by the strong shear effects and significant nonequilibrium effects. Because of the demand on the total heat load prediction and the experimental data identification, there is an increasing engineering interest in the strongly sheared nonequilibrium flow and aerodynamic heating problems. In this paper, the theoretical modeling method, as well as the direct simulation Monte Carlo (DSMC) method, is used to study the aerodynamic force and heating performance of the compressible Couette flow under the vibrational nonequilibrium effects. Firstly, based on the reference temperature method, a theoretical formula of the reference temperature for the compressible Couette flow is deduced under the calorically perfect gas model. Then, analyses are conducted of the vibrational nonequilibrium effects on the reference temperature and the Reynolds analogy. The dimensionless criterion for the vibrational nonequilibrium effects is proposed, and the criterion is further employed to design formulas for prediction of the skin-friction and heat transfer. Finally, the theoretical results are validated and calibrated by the DSMC results. Both the analytical and numerical results in this study indicate that, the vibrational nonequilibrium effects reduce the skin-friction of the compressible Couette flow, but meanwhile, the Reynolds analogy is still valid as long as the analogy ratio is corrected to take into account of the vibrational energy transfer. The present study could enrich our understanding of the vibrational nonequilibrium shear flow, and specifically, the nonequilibrium flow criterion could be extended to investigate more practical aerodynamic heating problems which significantly involve the thermal nonequilibrium effects.