Theory of Local Heat Transfer in Shock/Laminar Boundary-Layer Interactions

Abstract

A fundamental theory of the local heat transfer disturbances in supersonic and hypersonic shock / laminar boundary-layer interaction zones is given, based on an asymptotic nonadiabatic triple-deck model that is formulated using the reference temperature method combined with a total enthalpy form of the energy equation. Analytical and numerical results are presented and compared with experimental heat transfer data for compression corner-generated interactions. The predictions of the theory provide strong support for important but empirical observations on the behavior of interactive heat transfer when separation occurs. NomenclatureFig. 1 M = Mach number Pr = Prandtl number p = static pressure q w = wall heat transfer rate Re L = Reynolds number [ « 2 8 , r`U`L/ms e = total streamline slope along the boundary-layer edge, v e /U`1 uB T = absolute static temperature T t = freestream total temperature, H /C 0 p U`= freestream velocity at edge of incoming boundary layer u, v = velocity components in x, y directions, respectively x, y = streamwise and normal coordinates, respectively b = 2 1) 1/2 2 (Mg = speci c heat ratio d* = displacement thickness variable * d0 = undisturbed boundary-layer displacement thickness Q = ow de ection angle k = 1/2K /l u is l = 0.332, Blasius solution constant m = coef cient of viscosity [ry r = density t w = wall shear stress x = viscous interaction parameter, 3 2 1/2 C M Re REF`L x = uni ed supersonic-hypersonic interaction parameter,M x/b v = viscosity temperature-dependence exponent, m ; T v Presented as Paper 95ADIAB = adiabatic wall conditions B = body surface e = local inviscid ow conditions at boundary-layer edge i.s. = incipient separation REF = based on reference temperature w = wall surface conditions 0 = undisturbed boundary layer ahead of interaction zonè = freestream conditions Superscript = nondimensional variables from triple-deck theory, Eqs. (12-19)