Acoustic receptivity of the boundary layer over parabolic bodies at angles of attack

Abstract

The effect of angle of attack on the acoustic receptivity of the boundary layer over two-dimensional parabolic bodies is investigated using a spatial solution of the Navier–Stokes equations. The free stream is decomposed into a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) and Erturk & Corke (2001) in which the solution for the basic flow and linearized perturbation flow are solved separately. Different angles of incidence of the body are investigated for three leading-edge radii Reynolds numbers. For each, the angle of attack ranges from $0^{\circ}$ to past the angle where the mean flow separates. The results then document the effect of the angle of incidence on the leading-edge receptivity coefficient ($K_{{\hbox{\scriptsize{\it LE}}}}$), and in the case of the mean flow separation, on the amplitude of Tollmien–Schlichting (T-S) waves at the linear stability Branch II location ($K_{II}$). For angles of attack before separation, we found that the leading-edge receptivity coefficient, $K_{{\hbox{\scriptsize{\it LE}}}}$, increased with angle of incidence which correlated with an increase in the pressure gradient at the physical leading edge. When a separation zone formed at larger angles of incidence, it became a second site of receptivity with a receptivity coefficient that exceeded that of the leading edge. This resulted in dramatic growth of the T-S waves with Branch II amplitudes more than 100 times larger than those at angles just before separation, and 1000 times more than those at $0^{\circ}$ angle of attack.