A Scaling Method for Modal Sound Propagation in Annular Ducts

Abstract

The interaction between stationary and rotating components is a major source of the noise emission of aircraft engines. Within the engine, the generated sound propagates in discrete pressure patterns, so-called spinning modes. In order to develop noise reduction technologies for these acoustic components, numerical as well as experimental investigations are carried out. In many cases however, the test rigs are geometrically and thermodynamically scaled in comparison to the turbomachines used in aircraft engines. The objective of this paper is to provide an analytical method to investigate the effect of scaling on the major properties of modal sound propagation in symmetric hard-walled annular ducts with a superimposed uniform axial flow. The potential of generating similar sound propagation properties in two ducts is assessed. For these purposes, the magnitude of the dominating modal group velocity vector, the corresponding axial component, and the angle relative to the duct axis are expressed in terms of the dimensionless parameters Mach number, Helmholtz number, and hub-to-tip ratio. In addition, the corresponding quantities of the wave vector are considered. With respect to these properties, it is shown that for a constant hub-to-tip ratio, modal sound propagation in two annular ducts is similar if the Mach number and Helmholtz number are identical.