Numerical study on boundary-layer receptivity with localized wall blowing/suction

Abstract

Most of previous studies focused on the boundary-layer receptivity to the convected disturbances in the free stream interacting with localized wall roughness. Whereas the research on the boundary-layer receptivity induced by localized blowing or localized suction is relatively few. In this paper, we investigate two-dimensional boundary-layer receptivity induced by localized blowing/suction within free-stream turbulence through using direct numerical simulation and fast Fourier transformation. High-order compact finite difference schemes in the y-direction, fast Fourier transformation in the x-direction, and a Runge-Kutta scheme in time domain are used to solve the Navier-Stokes equations. The numerical results show that Tollmien-Schlichting (T-S) wave packets are excited by the free-stream turbulence interacting with localized blowing in the two-dimensional boundary layer, which are superposed by a group of stable, neutral and unstable T-S waves. The dispersion relations, growth rates, amplitude distributions and phase distributions of the excited waves accord well with theoretical solutions of the linear stability theory, thus confirming the existence of the boundary-layer receptivity. And the frequencies of the instability waves are between the upper and lower branches of the neutral stability curves. According to the evolutions of the wave packets, the positions of peaks and valleys are tracked over time to calculate the propagation speed by taking the average. The propagation speeds of the wave packets are approximately one-third of the free-stream velocity, which are in accordance with Dietz's measurements. The propagation speeds of wave packets are also close to the phase speeds of the most unstable waves for the numerical results. The relations of the receptivity response to the forcing amplitude, the blowing intensity, and the blowing width are found to be linear, when the forcing amplitude and the blowing intensity are less than 1% free-steam velocity amplitude and 0.01, respectively. And the maximum amplitudes of the T-S waves can be excited while the blowing length is equal to the resonant wavelength /(TS-FS), where TS is the wave-number of the T-S wave, and FS is the wave-number of the forcing disturbance. These results are similar to those given by Dietz [Dietz A J 1999 J. Fluid Mech. 378 291]. Additionally, T-S waves with the same dispersion relations but opposite phases are generated by localized blowing and localized suction respectively, and the amplitudes of the T-S waves excited by localized blowing are nearly 15% greater than those by localized suction under the same condition. According to this theory, an optimal design of localized suction device is able to enhance or delay the laminar-turbulent transition for turbulent control.