An acoustic criterion for the whistling of orifices in pipes

Whistling due to vortex shedding has been extensively studied in the case of cylinders in cross-flows, of flow separation above cavities and of shear layers with flow impingement feedback. Less attention has been given to pressure drop devices in piping systems, which are known to generate high noise levels due to single tones in gas systems, and even in water systems. Based on recent work of Auregan et Starobinski (1999), an experimental criterion is proposed to evaluate the whistling ability of a pressure drop device in the presence of plane waves acoustic feedback. The idea of the criterion can be summarized as follows: if for a given combination of incident pressure waves, the amount of acoustic power scattered is higher than the incident one, the pressure drop device behaves as an acoustic amplifier, so that whistling can occur if the adequate acoustic boundary conditions are met. The main advantage of this criterion is that it depends only on the acoustic scattering matrix of the device, rather than on the acoustics of the surrounding pipe. Results obtained in an air test rig with an inner diameter of 3 cm, a Mach number varying from 10^-3 to 10^-1 and a Reynolds number varying from 10 ³ to 10⁵ are reported for single hole orifices. Basing the Strouhal number on the thickness of the orifice and on the average velocity through the hole, thin single hole orifices with sharp angles appear to whistle at Strouhal numbers close to 0.2. Furthermore, it is shown that a thin orifice with a downstream bevel is prone to whistling, whereas the same orifice with the bevel upstream cannot whistle.