Finite element modelling of sheared flow effects on the radiation characteristics of acoustic sources in a circular duct

Abstract

The recent interest in propeller noise generation, stimulated by development of new propeller types for commerical propjets, has generated a need for the ability of measure the noise characteristics of propellers. However, wind tunnel noise measurements are affected by reflections from the wind tunnel walls. Computer codes predicting the free-field noise of a propeller and its noise field in a circular wind tunnel allow validating the use of wind tunnel measurements to predict free-field noise characteristics. A wind tunnel contains flow which is uniform in the duct axial direction, but can vary in the radial direction. It can be shown that a third-order differential equation governs the acoustic pressure field for such a duct containing radially sheared subsonic flow. This third-order problem is then posed as a coupled pair of equations which are second-order in terms of acoustic density and first-order in terms of an artificial variable which represents the effects of the flow being sheared. It is shown that this form of the problem allows a natural extension of the existing numerical solution techniques for non-sheared flow. The sheared flow problem is presented, and a finite element method is developed to yield a solution for propeller-type acoustic forces. The finite element code and method are refined with numerical experiments, and results are presented for a specific propeller and duct geometry. Good agreement is shown between this method and an alternate approach to the sheared flow problem using a piecewise constant representation of the velocity in the boundary layer. This validates both the numerical methods.