Tangential-Velocity Gradient at Stagnation-Point Boundary-Layer Edge for Hypersonic Spheres

This paper presents a new theoretical approach for accurately evaluating the tangential velocity gradient at the stagnation-point boundary-layer (BL) edge, a key parameter for predicting stagnation point heat flux. Traditional methods often use inviscid stagnation point values, which this study shows can introduce significant errors in practical scenarios. Both the BL edge and inviscid tangential velocity gradients decrease with increasing thermochemistry. Higher viscosity increases the difference between these gradients for a given gas model but reduces the disparity between edge values across different gas models. Additionally, neither the edge nor inviscid stagnation point values show significant thermochemical nonequilibrium effects, and nonequilibrium values are well approximated by equilibrium values. The proposed approach derives the BL edge tangential velocity gradient by considering the linear variation of the inviscid gradient along the stagnation streamline, the absence of BL displacement, and the ratio of BL thickness to shock standoff distance, Formula: see text, for which a new analytical expression including real-gas effects is developed. Validation is performed using two-dimensional axisymmetric Navier–Stokes simulations across a range of gas models, gas mixtures, and high-enthalpy freestream conditions for both cold (300 K) and hot (2000 K) walls. This approach significantly improves theoretical prediction accuracy.