AEROACOUSTIC RESPONSE OF A SLIT-SHAPED DIAPHRAGM IN A PIPE AT LOW HELMHOLTZ NUMBER, 2: UNSTEADY RESULTS

In a companion paper the quasi-steady aeroacoustic behavior of diaphragms which prevails for low Strouhal number but Mach number of order unity was discussed. The complementary case of a small Mach number and a Strouhal number of order unity is now considered. In this case, a two-dimensional numerical method is used to predict the Strouhal-number dependence of the coefficients of the scattering matrix. The numerical method solves the two-dimensional incompressible flow equations by means of the vortex-blob method. The quality of the numerical results is investigated by comparing results of Howeʹs energy formulation with results obtained by an integral formulation to calculate the pressure difference across the diaphragm. The predictions of the coefficients are compared with experimental measurements carried out at LAUM. It is shown that the low- and high-frequency behavior are quite well predicted, while for intermediate frequencies a deviation between numerical simulations and experimental measurements is observed. While this is not yet fully understood it is expected to be related to whistling induced by the finite thickness of the diaphragm in the experiments.