Correlation formulae for local momentum and heat transfer in hypersonic transitional flows

Near-space hypersonic vehicles encounter significant rarefaction effects during the flight through the atmosphere, causing the classical Navier–Stokes–Fourier (NSF) equations to break down and posing challenges for the evaluation of surface drag and heat flux. In this paper, the nonlinear momentum and heat transfer in a hypersonic transitional boundary layer are analysed based on the generalized hydrodynamic equations (GHE), and the generality of the derived formulae is also discussed. The leading transport relations are obtained by estimating the relative orders of the various terms in GHE according to the hypersonic flow and boundary-layer requirements. Local non-equilibrium parameters characterising the shear non-equilibrium effect ( $K_\sigma$ ) and thermal-gradient non-equilibrium effect ( $K_q$ ) are introduced, and a set of correlation formulae for local surface pressure, shear stress and heat flux are proposed as corrections to continuum-based solutions. The correction function depends only on the non-equilibrium parameters $K_\sigma$ and $K_q$ , and the continuous solutions can be either analytical formulae or NSF simulation results. This enables us to predict the surface aerothermodynamics with enhanced accuracy while still using the solutions of the NSF equations. The proposed formulae are carefully verified by comparing with direct simulation Monte Carlo (DSMC) results of different hypersonic rarefied flows, including flat-plate, sharp-wedge, cylinder and blunt-cone flows, and partial experimental data are also given. The results demonstrate that the proposed formulae can significantly enhance the accuracy of the continuum-based solutions, and show good agreement with DSMC simulations and experimental measurements in the near-continuum regime.