Transitional boundary-layer response to wall vibrations

Abstract

The effects of wall vibration on the development of Tolimien-Schlichting (T-S) waves in a transitional flat-plate boundary layer are considered. Theoretically, the dynamic interaction between T-S waves and velocity perturbations induced by the vibrating wall is demonstrated through the kinetic energy balance of velocity perturbations. For a compliant wail, the response of T-S waves to velocity perturbations induced by the vibrating wall has been studied for various phase angles between the T-S wave veiocity and the wall velocity, and for various amplitudes of the wail vibration. Experimentally, T-S waves are induced by a vibrating wire located in the upstream portion of the wail. The downstream portion Is vibrated at the same frequency as that of the wire and the phase between the two oscillations can be varied. Depending on the phase angle, the T-S waves may be either amplified or attenuated, even if the wavelengths do not coincide. Notation c = w / a = c, + ici c, = phase veiocity ci = amplification coefficient H = shape parameter of boundary layer = 6,/6, p = instantaneous pressure 0 = time mean vressure q = kinetic energy of velocity perturbations = U12 4-&I2 I Rea, = Reynolds number = U,6,/v t = time U, v = instantaneous velocity components 0, F = time mean velocities U', U' = perturbations velocities U, = velocity outside of boundary layer xi,xj = space coordinates P:=cuZ+icuRe(l-c) 6 = boundary layer thickness 6 1 = displacement thickness = momentum thickness 4, a, w = amplitude, wave number and frequency of stream function perturbation Y = kinematic viscosity p = density $ = stream function C = perturbation velocity rotational = &//ay -&'/ax

Excitation of instabilies in a Blasius boundary layer by surface vibration

“…Further experimental evidence was provided by Gilev (1984) who also showed that transition due to TS instability could be delayed by damping the artificially forced TS wave by a phase-shifted excitation of the vibrating surface. This behaviour was also observed during the experiment of Kim et al (1994) but the similarity of this control technique with the Kramer-type compliant surfaces inspired by dolphin skin, in Kramer (1960), Kramer (1961) and Landahl (1962) is yet to be determined. Through tighter fluid and structure coupling Carpenter and co-workers (1984Carpenter and co-workers ( ), (1985Carpenter and co-workers ( ), (1986Carpenter and co-workers ( ), (1997Carpenter and co-workers ( ) and (2003 drew a more conclusive picture of the evolution of instability modes on compliant surfaces where it was demonstrated that the spatial extent played an important role too in the amplification or decay of the TS wave.…”