Acoustic impedance of circular orifice backed with sound-absorbing material in the presence of grazing flow

• A numerical approach based on solving frequency-domain LNSEs is proposed to determine the acoustic impedance of the orifice backed with sound-absorbing material in the presence of grazing flow . • The non-dimensional acoustic impedance of a circular orifice in the presence of grazing flow and sound-absorbing material is obviously affected by orifice diameter. • An expression for the acoustic impedance of an orifice that accurately considers the combined effects of sound-absorbing material and vortex-sound interaction has been proposed, which is useful for engineering design of dissipative silencers. To comprehensively consider the influences of vortex-sound interaction and sound-absorbing material, a numerical approach based on three-dimensional (3-D) frequency-domain linearized Navier-Stokes equations (LNSEs) is proposed to accurately determine the acoustic impedance of a circular orifice backed with sound-absorbing material in the presence of grazing flow. The sound-absorbing material is treated as an equivalent fluid. The computations are performed in three steps: (1) time-averaged flow variables are computed by steady-state computational fluid dynamics (CFD) simulation and then mapped into acoustic mesh, (2) sound pressure is obtained by solving frequency-domain LNSEs and converted into the input acoustic impedance in the presence of grazing flow, and (3) input acoustic impedance in the absence of flow is evaluated by using frequency-domain LNSEs and subtracted from input acoustic impedance in the presence of flow to determine the non-dimensional acoustic impedance. The effects of Mach number, flow resistivity, thickness of sound-absorbing material, porosity, thickness of the plate, and diameter of the orifice on the non-dimensional acoustic impedance of the orifice are investigated in detail. Through parameter analysis and the curve-fitting method, an acoustic impedance formula is proposed for a circular orifice backed with sound-absorbing material in the presence of grazing flow. The flow-induced resistance and end correction calculated by using the proposed acoustic impedance formulae show reasonable agreements with the measurements, which verifies the accuracy of the present model. As an application, the transmission losses of straight-through perforated tube dissipative mufflers are predicted by using the present acoustic impedance formulae as well as published models and compared with the measurements. Excellent agreements between the transmission loss predictions and measurements further validate the accuracy of the proposed acoustic impedance formulae.