The role of displacement thickness fluctuations in hydroacoustics, and the jet-drive mechanism of the flug organ pipe

Abstract

This paper re-examines a proposal due to Liepmann in which the hydro­acoustic effects of a turbulent boundary layer are represented in terms of the displacement thickness fluctuations. The influence of the curvature of the surface that supports the boundary layer is discussed, and in particular the asymptotic condition is obtained under which Liepmann’s formalism is applicable in the vicinity of leading and trailing edges. This is important for the theoretical treatment of the interaction of nominally steady flows with wall cavities, slots in aerofoils, splitter plates, etc. Displacement thickness fluctuations in the form of Tollmien-Schlichting waves gene­ rated at a leading edge by a disturbance, such as an incident sound wave, are shown to result in a conversion of mean flow energy into sound. At a trailing edge, however, acoustic-mean flow interaction results in the absorption of acoustic energy. A consequence of the leading-edge effect is that it provides an energy transfer mechanism which is capable of main­taining edge tone and cavity oscillations, and this is illustrated by applica­tion of the theory to the flue organ pipe. In this case encouraging support for the asymptotic analysis is provided by a comparison with recently published experimental data.