Analysis of sound attenuation in a duct with a solid or porous splitter

The equivalent singularity method is developed for the analysis of sound propagation in a duct with a thin solid or point-reacting porous splitter of a finite streamwise length. The method consists in representing the splitter by a singular plane of pressure dipoles and mass sources, distributions of which are determined so that the boundary condition at the splitter surfaces is satisfied. The boundary condition is expressed in terms of two admittance parameters giving relations between pressures and normal displacements of fluid particles at the upper and lower surfaces of the splitter. Computed results are presented to illustrate the dependence of the sound power transmitted through the splitter section on the acoustic properties, length and location of the splitter and the flow Mach number. A principal cause of the sound attenuation due to a splitter is found to be the conversion of the acoustic energy into the wake vortex energy convected downstream. A solid splitter or a porous splitter of small admittance shows tuning effects—with a peak or multiple peaks in the attenuation spectrum. The tuning frequencies can be controlled by the splitter location.