Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-18T07:05:22.267Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  26 July 2005

O. M. HADDAD
Affiliation:
Department of Mechanical Engineering Jordan University of Science & Technology, PO Box 3030, Irbid 22110, Jordanhaddad@just.edu.jo
E. ERTURK
Affiliation:
Gebze Institute of Technology, Energy Systems Engineering Department, Gebze, Kocaeli 41400, Turkeyercanerturk@eng.bahcesehir.edu.tr
T. C. CORKE
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USAtcorke@nd.edu

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.

Type
Papers
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)