Transition in a Supersonic Boundary Layer Due to Acoustic Disturbances

The boundary layer receptivity process due to the interaction of three-dimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. The computations are performed with and without two-dimensional 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 non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) 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 free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.