Acoustic Power Calculation in Deep Cavity Flows: A Semiempirical Approach

Abstract

Acoustic power generated by turbulent flow over a coaxial side branch (deep cavity) resonator mounted in a rectangular duct is calculated using a semiempirical approach. Instantaneous flow velocity is decomposed into an irrotational acoustic component and vorticity-bearing hydrodynamic field. The total velocity at several phases of the acoustic oscillation cycle is measured using digital particle image velocimetry. The acoustic velocity field is numerically calculated. The emphasis is on the effect of the accurate geometry representation for the acoustic field modeling on the calculated acoustic power. Despite the generally low levels of acoustic radiation from the coaxial side branches, when the main duct is incorporated into the model for calculation of the acoustic velocity, the acoustic velocity exhibits substantial horizontal (streamwise) components in the vicinity of the cavity corners. This streamwise acoustic velocity correlates with hydrodynamic horizontal velocity fluctuations, thus contributing to the calculated acoustic power. Spatial structure and strength of the acoustic source change as the distance between the side branches varies. Global quantitative imaging approach is used to characterize the transformation of the acoustic source structure in terms of patterns of instantaneous and phase-averaged flow velocity, vorticity, and streamline topology as well as time-averaged acoustic power.