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Numerical modeling of the receptivity of a two-dimensional flat-plate boundary layer to entropy disturbances is carried out at the freestream Mach number M∞ = 6. Low-intensity perturbations considered are in the form of temperature spots of various shapes and with different initial positions downstream of the shock. They are shown to be able to generate unstable disturbances in the boundary layer. This receptivity mechanism is relatively weak as compared with the receptivity to acoustic waves. When the entropy perturbations are introduced upstream of the bow shock, they first pass across the shock. Downstream of the shock this interaction generates acoustic waves which, in turn, penetrate into the boundary layer thus exciting unstable disturbances of a considerably greater amplitude than the temperature spots. Thus, the bow shock can change the receptivity mechanism.

Transition prediction of the supersonic boundary layer on a cone with small angle of attack and Mach number 3.5 is investigated under the consideration of receptivity to slow acoustic waves, as the acoustic waves are the main environmental disturbances in a conventional, i.e. non-quiet, wind tunnel. It is shown that the e-N method can still yield fairly satisfactory results in comparison with those obtained in wind tunnel experiments, provided that the boundary layer receptivity to slow acoustic waves is properly taken into account, including the dependence of the amplitude of disturbances on the frequency and stream-wise location. Neither the conventional e-N method nor the improved e-N method can yield correct result of transition prediction, because the receptivity mechanisms considered there are not in accord with the real situation in the wind tunnel.

Receptivity of a high-speed boundary layer on a flat plate to acoustic disturbances is investigated using a combined numerical and asymptotic approach. The leading-edge receptivity problem is discussed with emphasis on physical mechanisms associated with scattering and diffraction of acoustic waves. Analytical solutions provide insight into the interplay of these mechanisms as a function of the angle of incidence of external acoustic waves. The theoretical predictions are in good agreement with the wind-tunnel experimental data of Maslov et al. obtained at free-stream Mach number 6. The leading-edge receptivity model is incorporated into the multiple-modes method to account for the inter-modal exchange downstream from the leading edge. This combined modelling resembles basic features of the direct numerical simulation of Ma & Zhong. A comparative analysis of the leading-edge receptivity and the inter-modal exchange associated with non-parallel effects is presented. The theory allows fast evaluation of the receptivity coefficients and clarifies the physics of the receptivity process. The theoretical results may guide further direct numerical simulations and experimental studies of boundary layer receptivity at supersonic and hypersonic speeds.

Two-dimensional direct numerical simulation (DNS) of receptivity to acoustic disturbances radiating onto a flat plate with a sharp leading edge in the Mach 6 free stream is carried out. Different angles of incidence of fast and slow acoustic waves are considered. DNS results are compared with theoretical modeling of leading-edge receptivity and downstream propagation of boundary-layer disturbances.

Receptivity of supersonic boundary layer to acoustic disturbances interacting with a blunt leading edge of a flat plate is studied using a combined asymptotic and numerical approach. A relationship between the receptivity coefficients for sharp and blunt leading edges is established using the concept of effective length. For the case of receptivity to fast acoustic waves at free-stream Mach number 6, it is shown that even small bluntness leads to significant decreasing of the receptivity level. Nomenclature C = coupling coefficient E = receptivity coefficient F = frequency parameter L = streamwise length scale ef l = effective length b l = wavelength coefficient M = freestream Mach number p = pressure disturbance r = nose radius ** Re /

At present it is generally accepted that laminar-turbulent transition in boundary layer is connected with the loss of stability of the initially laminar flow and the receptivity phenomena. The problem of receptivity mechanisms for supersonic boundary layers still needs a serious consideration. The first attempt of theoretical investigation of the interaction of acoustic waves and the supersonic boundary layer was made in [6] on the basis of stability theory. Some theoretical papers appeared recently which studied the role of the leading edge in receptivity of supersonic boundary layer to external acoustic waves [1-3]. The generation of unstable waves in the boundary layer was found to depend on the inclination angle of acoustic wave. We note, that conclusions of [2, 3] need experimental verification.