Laminar boundary layer receptivity to transverse structural vibration

The development of stimulate Tollmien-Schlichting waves in a boundary layer as a result of forced leading edge vibration is discussed. The results of two major sets of experiments are presented. A “stable” case was used to isolate the forcing function imposed by the vibrating leading edge, and the development of the stimulated response of the Tollmien-Schlichting wave in the boundary layer due to leading edge vibration was investigated in the “unstable case”. The leading edge vibration was the only disturbance introduced in the laminar boundary layer. The characteristics of the disturbance were such that the global plate vibration levels were at least 25 times less than those of the leading edge tip vibration. This leading edge vibration can be interpreted as the inhomogeneous boundary conditions imposed on the fluid dynamic problem, and gives rise to an acoustic wave in the test duct. However, the oscillatory velocity field imposed by the leading edge mode is negligible compared to the oscillatory velocity field imposed by the leading edge vibration. The velocity oscillations imposed by the acoustic wave mode are not the cause of instability because the velocity profiles at x≤150 mm do not resemble a Stokes shear wave. The experiments were perfomed with the stagnation point of the flow incident on the leading edge located slightly below the tip of the leading edge. No flow separation was observed . The experimental results are compared with a set of results obtained by Chiu and Norton, for which the stagnation point was located slightly above the tip of the leading edge. The experimental results in the present case reveal that, prior to reaching branch I of the neutral stability curve, the boundary layer response to leading edge vibration is independent of the location of the stagnation point of the flow incident of the leading edge. However, comparison with the stimulated response shows that the development of the Tollmien-Schlichting wave is drastically affected by the change in the location of the stagnation point from a position slightly above the tip of the leading edge to that slightly below the tip of the leading edge. This can be attributed to the upstram movement of the region of adverse pressure gradient when the stagnation point is moved from a position above the tip of the leading edge to that slightly below it.