Linear Theory and Experiments for Laminar Bias Flow Impedance: Orifice Shape Effect

Axisymmetric orifices with neck diameter equal to the plate thickness have been investigated. The influence of orifice geometry on the transfer impedance in presence of bias flow was predicted for laminar-flow conditions by means of a compressible Linearized-Navier-Stokes-Equations model. The results are compared to those for an incompressible-flow model and to measurements of the transfer impedance. The effect of confinement on the transfer impedance appears to be negligible for the resistance. The effect of confinement on the inertance (or reactance) can be estimated by means of Fok’s classical result for thin orifices. The experimental results agree qualitatively with the predicted impedances. The Strouhal numbers for minima of the resistance are slightly higher than predicted. Negative minima indicating a whistling potentiality correspond to hydrodynamic modes of the orifice. The predicted inertance is at higher Strouhal numbers significantly larger than the measured one. The results indicate how whistling potentiality of a certain hydrodynamic mode can be promoted. The amplitude of the acoustical forcing was varied permitting to delimit the conditions under which the orifice response is linear. As the acoustic velocity amplitude approaches the steady flow velocity, the whistling potentiality of the orifices disappears.