Effect of flow on the acoustic length correction factor of a Helmholtz resonator neck at high Strouhal number: A symmetric three-dimensional numerical parametric study

Abstract

The effect of flow on the acoustic length correction factor (ALCF) of a Helmholtz resonator (HR) neck is investigated numerically in order to achieve an expression to calculate the respective flow-acoustic length correction factor (FALCF) as a function dependent on the ratio between the radii of the neck and cavity (up to 0.4) and on the Mach (Ma) number (up to 0.1). The ALCF is of great interest in one-dimensional acoustic applications for achieving better prediction of local effects. In this work, the effects of turbulent flow and radial and axial neck-cavity wave motions are added to improve the one-dimensional HR's resonant frequency prediction model. A symmetric three-dimensional HR model is parameterized and adopted to solve a set of CFD problems (RANS equation and turbulent SST model), with different geometry parameters. The acoustic fluid is air at 20 °C and is considered incompressible. The predictions of the numerical model are validated with experimental studies available in the literature. Different formulations employed to predict the resonance frequency of an HR for the Ma = 0 case are investigated and compared to CFD results as a way to verify its prediction capability related with the HR's geometry. Also, the possibility to obtain the FALCF factor from the neck's acoustic impedance is investigated and compared with the expression derived from the HR's resonance frequency.