Analysis of nonlinear transport in hypersonic rarefied nonequilibrium boundary layer and theoretical prediction of surface aerothermodynamics

Accurate and rapid prediction of surface aerothermodynamics is critical for flying vehicle design. Near-space vehicles flying across the atmosphere are significantly affected by rarefied gas effects, which render the conventional Navier-Stokes (N-S) equations invalid and pose challenges to the accurate and efficient prediction of surface aerothermodynamics. In particular, the accurate description of nonlinear transport in the near-wall boundary layer is crucial for aerodynamic predictions. To address this, the present study conducted a theoretical analysis of hypersonic rarefied nonequilibrium boundary layers based on the Grad 13 moment equations (G13) and generalized hydrodynamic equations (GHE), in conjunction with the normal solutions of the Boltzmann model equation for shear flows and the simulation results from the direct simulation Monte Carlo (DSMC) method. The nonequilibrium mechanisms and nonlinear transport characteristics within the boundary layer were investigated, from which the leading transport relations and the parameters characterizing nonequilibrium effects were derived. A set of correlation formulae for local surface pressure, skin friction, and heat flux were developed, and were validated against DSMC simulations for various geometries, including flat plate, blunt plate, blunt wedge, blunt cone, and sphere. The results show that the nonlinear transport functions for each component of stress and heat flux in the boundary layer can be expressed as explicit functions of the shear nonequilibrium parameter K_σ and thermal gradient nonequilibrium parameter K_q. The established correlation formulae significantly improve the traditional N-S predictions and agree well with DSMC results from the continuum to early transitional regimes (K_σ ～1). Notably, these formulae can provide approximate yet accurate estimates of surface aerothermodynamics for the hypersonic transitional flows using only the continuum-based N-S solutions (either analytical or numerical), without solving moment or kinetic equations, thus showing promising prospects for rapid prediction of surface aerothermodynamics on near-space vehicles.