The approximate sound power generation associated with the fluctuations of an enclosed acoustically small flow

Abstract

The kinematics of general fluctuating flows are examined. For the sum of any model irrotational and solenoidal fields to exactly equal the actual flow fluctuations throughout a domain, it is sufficient that the irrotational field have the divergence of the flow, the solenoidal field have the vorticity of the flow and that the addition of the two fields equal the flow at the boundary of the domain. An approximate theory is developed. The theory describes the generation of sound power by time stationary fluctuating flows and boundaries in time stationary motion in acoustically small pipes and ducts. The theory is only applicable where sound power is transmitted away from the source region by simple harmonic plane waves propagating in regions of low Mach number flow. The theory exposes the influence of “global rate of momentum change/boundary force imbalances”, “turbulence driven dilatations” and the upstream and downstream impedances on sound power generation. A prediction of the phase of boundary forces acting on the fluid during a particular aeroacoustic resonance is made.