Beyond classical similitude: group theoretic extrapolation of hypersonic stagnation-point boundary layers
Motivated by the need to extrapolate the results from ground-based experiments to the conditions of high-speed flight, we present the Lie equivalence symmetry analysis of the hypersonic stagnation-point boundary layers. We demonstrate the application of the equivalence symmetry on the set of coupled ODEs which are physically relevant in hypersonics. By allowing the property laws to transform along with the independent and dependent variables, the invariants derived within the similarity-reduced stagnation-point ODE formulation identify families of non-linear maps that can be used to extrapolate the laboratory-scale predictions to flight. In practice, implementing these maps requires the laboratory-scale ODE solution together with the lab- and flight-side thermochemical property data, which are generally available from existing databases. The maps are derived for the similarity-reduced non-dimensional temperature across the boundary layer and are shown to {collapse with independently computed flight solutions} for a range of relevant cases.