Application of Powell's analogy for the prediction of vortex-pairing sound in a low-Mach number jet based on time-resolved planar and tomographic PIV

This paper describes an experimental investigation by time-resolved planar and tomographic PIV on the sound production mechanism of vortex pairing of a transitional water-jet flow at Re=5000. The shear layer is characterized by axisymmetric vortex rings which undergo pairing with a varicose mode. Three-dimensional measurements show the presence of longitudinal pairs of counter-rotating vortices inducing vortex azimuthal instabilities prior to the breakdown of the vortices. Based on Powell's aeroacoustic analogy, flow structures responsible for noise generation are characterized by the second-time-derivative of the Lamb vector field, which is directly evaluated by planar and tomographic PIV. The analysis of the dynamics of such structures shows peak activity in correspondence of the vortex cores during the leapfrogging, vortex-azimuthal instabities and vortex breakdown mechanism. Under the hypothesis of axisymmetric flow, far field acoustic produced by vortex pairing is predicted by directly applying time-resolved planar PIV data to Powell's acoustic analogy. Pronounced acoustic emission is found during the coalescence of the vortices