Influence of a weak adverse pressure gradient on the generation of tonal protuberance noise in a laminar boundary layer

Abstract When a two-dimensional protuberance is placed in an unstable laminar boundary layer at moderate Reynolds numbers, tonal noise can be generated by an acoustic feedback-loop mechanism, not unlike that in case of the trailing-edge noise of an airfoil. In this paper, the generation of tonal protuberance noise was examined experimentally, focusing on the influence of the weak adverse pressure gradient on the critical protuberance height for the onset of tonal noise. It was shown that the weak adverse pressure gradient could cause the critical protuberance height to decrease, while the frequencies of tonal noise were little changed in the present experimental condition. At the onset condition for the tonal noise, the separation bubble formed just upstream of the protuberance was found to be almost the same size in both the zero- and weak adverse-pressure-gradient boundary layers, despite of the difference in the instability nature in the absence of the protuberance. A linear stability analysis revealed that the separation bubble could amplify disturbances by a factor of one hundred or more within a short distance (several times the boundary-layer thickness) at the onset condition. Such rapid disturbance growth was requisite for the sustenance of the feedback-loop mechanism even for the adverse-pressure-gradient case at least in the present Reynolds number range.