The Inertance of a Smooth-Edged Orifice

Three analytical models for the potential flow through a smooth-edged orifice are discussed and the prediction of the acoustical inertance obtained from these models is compared with experimentally determined values of orifice inertance as a function of the ratio of wall thickness to orifice diameter. It is shown that the simple hyperbolic wall model predicts corrections for wall thickness which are of the wrong order of magnitude for thin-walled orifices and are inaccurate for thick-walled orifices. An improved model, consisting of the super-position of a hyperbolic flow field and a ring vortex, is used to represent an orifice boundary with finite curvature at the throat and finite thickness. By matching either the curvature or the wall thickness of an orifice, upper and lower bounds for the inertance are obtained. By adding another singularity in the potential flow analysis, both the curvature at the throat and the wall thickness of the actual orifice can be matched, and the values predicted by this model are in good agreement with the experimental results.