Boundary layer receptivity mechanisms relevant to laminar flow control.

Abstract

Receptivity processes by which free-stream acoustic waves generate instability waves in boundary layers are investigated. Concentration is placed on mechanisms associated with local regions of short scale variation in wall suction or admittance distribution. These mechanisms are relevant to laminar flow control technology, in which suction is utilized to control the growth of boundary layer instabilities. The receptivity process requires a transfer of energy from the long wavelength of the free-stream disturbance to the short wavelength of the instability wave. In the case of wall suction, this occurs through the unsteady modulation, by the acoustic wave, of the short scale mean flow variation due to the steady wall suction. In the wall admittance mechanism, the boundary condition for the unsteady motion contains a short scale variation which directly scatters energy from the acoustic wave into the instability wave. The latter mechanism does not require a short scale adjustment in the mean boundary layer. Time harmonic, two and three-dimensional interactions are analyzed using the asymptotic, high Reynolds number, triple deck structure. The influence of subsonic compressibility is examined for the case of two-dimensional interactions, and a similarity transform is found which reduces the problem to an equivalent incompressible flow. For three-dimensional interactions, a similarity transform is possible only in the Fourier transform wavenumber space, and in the equivalent two-dimensional problem the frequency is complex. However, in many cases of practical interest, the imaginary component of this frequency is quite small and can be neglected. The acoustic wave orientation and the geometry of the wall suction or admittance distribution are found to significantly influence the amplitude of the generated instability wave. For an isolated, three-dimensional region of wall suction or admittance, instability wave growth is confined to a downstream, wedge shaped region. The saddle point method is utilized to calculate the characteristics of this instability wave pattern. In some ranges of parameter space, two saddle points are found to make comparable contributions. The instability wave pattern in these directions exhibits a beat phenomenon, due to constructive and destructive interference of the contributions from the two saddle points.