Receptivity of a Supersonic Boundary Layer to Acoustic Disturbances

Abstract

The boundary layer receptivity process generated by the interaction of 3-D slow and fast acoustic disturbances with a blunted flat plate, is numerically investigated at a freestream Mach number of 3.5, and at a high Reynolds number of 39 * 10 6 /m. The computations are performed with and without a 2-D isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially nonoscillatory scheme for space discretization and using the third-order total-variation-diminishing Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien-Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the freestream disturbances for the slow and fast waves, respectively. It was also revealed that a small isolated roughness element does not enhance the receptivity process for the given nose bluntness.