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Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances
Published online by Cambridge University Press: 27 May 2005
Abstract
Supersonic boundary-layer receptivity to different types of free-stream disturbance is studied for a Mach 4.5 boundary-layer flow over a flat plate by using the approaches of both direct numerical simulation and linear stability theory. This paper is Part 3 of a three-part study of the receptivity of supersonic boundary layers to free-stream disturbances. The present paper investigates receptivity to four types of different free-stream disturbances, i.e. slow and fast acoustic waves, entropy waves, and vorticity waves. A high-order shock-fitting scheme is used in the numerical simulation in order to accurately account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. Numerical results on the generation of fast acoustic waves by free-stream entropy waves or vorticity waves are compared with those of a linear theory. Good agreement is obtained in both wave angles and amplitudes immediately behind the bow shock. It is found that the second-mode receptivity to free-stream slow acoustic waves is several times stronger than that to free-stream fast acoustic waves. This is because free-stream slow acoustic waves can directly induce and interact with the first and second Mack modes, while free-stream fast acoustic waves cannot. Instead, the free-stream fast acoustic waves can only induce and interact with stable mode I waves, which in turn induce unstable Mack modes. In the cases of receptivity to free-stream entropy waves and vorticity waves, it is found that the oblique shock wave created by the displacement of the boundary layer plays an important role because boundary-layer disturbances are mainly induced by fast acoustic waves generated behind the shock by free-stream forcing waves. As a result, mechanisms of the receptivity to free-stream entropy and vorticity waves are very similar to those of the receptivity to free-stream fast acoustic waves.
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- © 2005 Cambridge University Press
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