Numerical Modeling of the Interaction between a Supersonic Boundary Layer and an Acoustic Wave

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.