Radiation in a wall jet flow environment

Abstract

An analytical study of sound propagation through a wall jet flow with compliant walls has been carried out. The prime objective of this study is to evaluate the influences of flow convection and refraction due to non-uniform mean flow on sound radiation. Another major aim is to calculate the nature of acoustic attenuation attributable to finite wall admittances. A two-dimensional model is used in the analysis. A simple source distribution is prescribed at the nozzle exit plane. The governing convected wave equation is derived from the conservation equations. The mean flow field required for the analysis is obtained from a combination of experimental data and analytical solutions. The resulting convected wave equation is reduced to an ordinary differential equation by suitable approximations. This equation is solved numerically in terms of modified modes in radial shells. The modified modes are classical eigenfunction solutions modified by the non-uniform mean flow and wall admittances. These modified modes are used with the appropriate matching conditions to yield the solution of the radiated sound field. The results show that the modal expansion procedure can be applied succesfully to investigate the present problem. The non-uniform mean flow reduced the source power output compared to the power output of the given source in a stationary medium. The flow convection and shear refraction produced a significant effect on the sound directivity which showed a steep downstream valley. This is at variance with the view that the sound directivity of blown flap noise is due to the inherent directivity of trailing edge sources. The compliant wall increased the dip of the valley created by the non-uniform flow in most of the cases. The liners had a strong influence on the mode shapes, but did not produce significant acoustic attenuation. The small sound reduction observed in this study implies that the major effects of the liners are hydrodynamic, related to the reduction of source strength.