Computation and analysis of high-speed lifting-body flows based on nonlinear coupled constitutive relations

Near-space high-speed flows involve cross-scale effects spanning from continuum regimes to rarefied regimes. Conventional linear constitutive relations based on Newton's law of viscosity and Fourier's law of heat conduction are inadequate for accurately describing the stress-heat flux nonlinear coupling effect under nonequilibrium conditions. In this paper, the nonlinear coupled constitutive relations (NCCR) were solved using a hybrid iterative method which combines the advantages of fixed-point iteration and Newton iteration. The governing equations were discretized by a finite-volume method on structured grids, and the LU-SGS implicit scheme was employed to accelerate convergence. Comparative computations and analyses between the NCCR model and the Navier-Stokes(N-S) equations were performed for the HyTRV lifting-body vehicle over a range of altitudes (30, 60, 90 km), Mach numbers (5–20), and angles of attack (0°–20°). The results indicate that at altitudes of 30 km and 60 km, the primary flowfield structures and surface pressure coefficient distributions predicted by the two models are in good agreement, suggesting that the flow remains in the near-continuum regime and the nonlinear correction of NCCR is weak. At 90 km and Mach 20, the pressure and heat-flux peaks predicted by NCCR are notably lower than those of the N-S solutions, and the discrepancies further increase with angle of attack, highlighting the growing importance of rarefaction effects and nonlinear coupled constitutive modifications. The NCCR model naturally reduces to the N-S linear constitutive results in the near-continuum regime, while providing more reasonable predictions through nonlinear coupled constitutive relations in regions with significant nonequilibrium effects. The findings of this study can serve as a reference for the aerodynamic and aerothermodynamic evaluation of high-speed lifting-body vehicles across a broad range of altitudes and Mach numbers.