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.

Hypersonic vehicles in large airspace and wide speed range have become one of the current research hotspots, and waveriders have attracted significant attention due to their high lift-to-drag ratio and relatively simple shape. However, there is little research on the aerodynamic characteristics of waveriders under high-altitude rarefied conditions. Since the flow field encompasses multiple regimes ranging from continuum to rarefied, the accurate prediction of aerodynamic characteristics remains a considerable challenge. Focusing on the rarefaction effect on aerodynamic characteristics of a waverider model, which is tested in the MARHy rarefied wind tunnel in France, the numerical simulations are performed using Direct Simulation Monte Carlo (DSMC) method, conventional Navier-Stokes (NS) equation, and DSMC data improved Navier Stokes (DiNS) model. By comparing with experiment data, the computational accuracy of the different methods is evaluated. The aerodynamic characteristics of the waverider in the near-continuum regime are analyzed, with particular emphasis on the local rarefaction effects within the flow field and their influence on aerodynamic performance. Furthermore, the effects of Mach number and angle of attack are systematically investigated. The results show that under the experimental conditions of Mach number 20 and Knudsen number 0.01, the error in drag predicted by the conventional NS equation with slip boundary conditions reaches as high as 39.19% compared to experimental data. The DiNS model can reduce this relative error to 3.95% by correcting the linear constitutive relationship; for this waverider, skin friction contributes approximately 97.14% of the total drag. A pronounced shear nonequilibrium effect exists within the boundary layer, which invalidates the linear constitutive relations and causes the conventional NS equations to overpredict the skin friction. In addition, an increase in angle of attack leads to a significant increase in lift coefficient, a significant improvement in lift to drag ratio, and a more pronounced rarefaction effect. As the Mach number increases, the lift coefficient decreases significantly due to deviation from the design conditions, and the lift to drag ratio decreases significantly.