The interaction between the supersonic boundary layer on an infinitely thin plate and acoustic waves is investigated on the basis of direct numerical simulation for Mach 2 incident flow. The parametric numerical investigations of the disturbances generated within the boundary layer by an acoustic wave arbitrarily oriented in space are for the first time performed. The calculations are carried out for different angles of incidence and sliding (in the latter case the wave vector is parallel to the plate surface) and frequencies. The main calculations are performed for the Reynolds numbers slightly greater than the critical values of the loss of stability. It is established that the velocity disturbance amplitude in the boundary layer is several times greater than that of outer acoustic wave. At small incidence and sliding angles the oscillation intensity increases with increase in the Reynolds number. At fairly large values of these angles the Reynolds-number-dependences of the disturbance amplitude contain maxima which are displaced toward the leading edge of the plate with increase in the angle. For a fixed point on the plate and a fixed frequency there exist critical sliding and incidence angles, at which the disturbances generated in the boundary layer are maximum. The excitation of oscillations in the boundary layer by a sound wave is more effective if the plate is irradiated from above. On the basis of the calculations performed at different frequencies it is shown that the location of a minimum in the dependence of the generated velocity disturbances coincides at a good accuracy with the position of the lower branch of the neutral stability curve.

Theoretical investigation of the flat-plate binary-mixture compressible boundary-layer at free-stream Mach number M=2 under the injection of heavy gas sulfur hexafluoride (SF₆) has been performed. It was assumed that this foreign gas which is possible to use for wind tunnel experiments have been introduced into the boundary layer of air through the permeable surface at normal direction to it. It was found that weak distributed injection of the gas only slightly influence boundary layer streamwise velocity and temperature profiles however gives significant increase to the mixture density near the wall. Linear stability characteristics of such binary-mixture boundary-layer have been studied. It is established that action of heavy gas injection is similar to the action of wall cooling and leads to an increase of boundary-layer stability and therefore to laminar-turbulent transition delay. Estimate of the influence of injection on the position of transition by means of e^N-method has been performed. Principal possibility to noticeable increase of the transition Reynolds number by means of a heavy gas injection has been established.

Theoretical investigation of the linear stability of the flat-plate binary-mixture compressible boundary-layer at free-stream Mach number M=3 has been performed. It was assumed that foreign gases of various molecular mass have been introduced in the boundary layer of air through the permeable surface. It is found that weak distributed injection of a lighter gas destabilizes the flow. It is established that action of a heavy gas injection on the boundary-layer is similar to the action of wall cooling and leads to an increase of boundary-layer stability and to laminar-turbulent transition delay. Estimate of the influence of injection on the position of transition by means of the known e N -method has been performed. Principal possibility to double the transition Reynolds number by means of a heavy gas injection has been revealed.

Stability of a subsonic boundary layer with heat supply into its narrow band is studied. The maximum length of the stable boundary layer in the case of heat supply is found to be approximately three times smaller as compared to the case of a thermally insulated wall without heat supply. The frequency range of disturbances and their growth rates are approximately doubled. In contrast to the case without heat supply, three-dimensional disturbances are the most rapidly growing disturbances. In the case of a heated wall, the growth rate of disturbances decreases after heat supply into the boundary layer, which may lead to an increase in the length of the laminar region of the boundary layer.

The paper presents a study of a supersonic boundary layer while heat supply to the layer’s narrow internal region. Calculations were performed for a flow with Mach number M = 2 and the dimensionless temperature (normalized to the temperature at a layer boundary edge T_w = 3.9 (630 K). It was demonstrated that heat supply causes a twofold increase in the 2D disturbance increments, while the frequency range expands by factor of three with a heat-insulated plate (zero heat input) taken as a reference. For a heated plate (with T_w = 3.9), the heat input into this layer delays the disturbance growth; that is, this facilitates the boundary layer stabilization and the disturbance increments reduce by almost four times. Along with 2D waves, the oblique waves were investigated in this paper. It was found that for low-frequency disturbance, we observe an intense growth of 3D (oblique) waves. Meanwhile, 2D disturbances enhance for a high-frequency range. These facts comply with the numerous data on boundary layer stability. However, these factors for boundary layer stability become less significant in the case of heat input to the supersonic boundary layer (compared with the zero heat input). The study also observes the longitudinal structures with a downstream decay. The heat supply makes these structures decrement lower in the supersonic boundary layer (meaning a slower decay). The results for the study of boundary layer disturbance are compared to similar data for the flow with M ≪ 1.