Reattachment heating upstream of short compression ramps in hypersonic flow

Abstract

Hypersonic shock-wave/boundary-layer interactions with separation induce unsteady thermal loads of particularly high intensity in flow reattachment regions. Building on earlier semi-empirical correlations, the maximum heat transfer rates upstream of short compression ramp obstacles of angles $$15^{\circ }\leqslant \theta \leqslant 135^{\circ }$$ are here discretised based on time-dependent experimental measurements to develop insight into their transient nature ( $$M_{e}$$ = 8.2–12.3, $$Re_h= 0.17\times 10^{5}$$ – $$0.47\times 10^{5}$$ ). Interactions with an incoming laminar boundary layer experience transition at separation, with heat transfer oscillating between laminar and turbulent levels exceeding slightly those in fully turbulent interactions. Peak heat transfer rates are strongly influenced by the stagnation of the flow upon reattachment close ahead of obstacles and increase with ramp angle all the way up to $$\theta =135^{\circ }$$ , whereby rates well over two orders of magnitude above the undisturbed laminar levels are intermittently measured ( $$q'_\mathrm{max}>10^2q_{u,L}$$ ). Bearing in mind the varying degrees of strength in the competing effect between the inviscid and viscous terms—namely the square of the hypersonic similarity parameter $$(M\theta )^2$$ for strong interactions and the viscous interaction parameter $$\bar{\chi }$$ (primarily a function of Re and M)—the two physical factors that appear to most globally encompass the effects of peak heating for blunt ramps ( $$\theta \geqslant 45^{\circ }$$ ) are deflection angle and stagnation heat transfer, so that this may be fundamentally expressed as $$q'_\mathrm{max}\propto {q_{o,2D}}$$ $$\theta ^2$$ with further parameters in turn influencing the interaction to a lesser extent. The dominant effect of deflection angle is restricted to short obstacle heights, where the rapid expansion at the top edge of the obstacle influences the relaxation region just downstream of reattachment and leads to an upstream displacement of the separation front. The extreme heating rates result from the strengthening of the reattaching shear layer with the increase in separation length for higher deflection angle.