A whistling criterion for two orifices in series

Whistling phenomena in pipe power plants have been observed in the past years. It occurs at pressure drop devices where vortex shedding is established. It generates high noise levels and excessive vibrations. Aurégan and Starobinsky [1] have developed an experimental criterion to predict whistling frequencies of pressure drop devices submitted to plane propagating pressure waves. This criterion estimates the net acoustic power, an acoustic exergy generation indicating that the device behaves as an acoustic amplifier. The corresponding frequencies are potential whistling frequencies. The application of the criterion only requires the determination of the scattering matrix of the device. In previous works, this criterion was applied to different single hole orifices. The purpose of the present study is to apply the criterion to two orifices in series and to verify that the behavior of this system can be predicted from the scattering matrix of each individual orifice and of the straight pipe in-between. Measurements are done on an air test rig with an inner diameter of 3 cm, a Mach number of 2.6 × 10^-2 and a Reynolds number of 10⁴. Different distances between orifices are characterized. The study of the influence of the second orifice on the whistling criterion shows an enhancement of the whistling potential and a shift of the main potential whistling frequency. A fair agreement is found between experimental and predicted results. Characterization of orifices in series is then possible from the coefficients of the scattering matrix of one orifice and an appropriate condition on the distance between the orifices.