Empirical model of the acoustic impedance of a circular orifice in grazing mean flow

Although there are many analytical and empirical models for orifice impedance, the predicted acoustical performance when adopting any one of them sometimes shows a large discrepancy with the measured result in some cases. In order to obtain a new practical and precise empirical impedance model under grazing flow conditions, the acoustic impedance of circular orifices has been measured with a variation of the involved parameters under very carefully tested and controlled measurement conditions. The parameters involved in determining the acoustic impedance of an orifice are comprised of the orifice diameter, orifice thickness, perforation ratio, mean flow velocity, and frequency. The range of involved parameters is chosen to cover the practical data span of perforates in typical exhaust systems of internal combustion engines. The empirical impedance model is obtained by using nonlinear regression analysis of the various results of the parametric tests. The proposed empirical model of orifice impedance, with a very high correlation coefficient, is applied to the prediction of the transmission loss of concentric resonators, which have geometric configurations typical of acoustically short and long through-flow resonators. By comparing the measured and predicted results, in which the predictions are made by employing many previous orifice impedance models as well as the present model, it is confirmed that the proposed orifice impedance model yields the most accurate prediction among all other existing impedance models.