An Acoustic Criterion for the Whistling of Orifices in Pipes

Abstract

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 103 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.

Whistling of an orifice in a reverberating duct at low Mach number

“…The arguments of the extradiagonal elements have not been plotted, because their modulus are smaller than 0.1. The transmission and reflection coefficients of the original scattering matrix appear to reasonably fulfill the low Mach number relations, [20][21][22] namely…”

“…In the latter case, the fluid compressibility inside the orifice does not play a significant role, and the four elements of the scattering matrix are no longer independent. [20][21][22] Benefiting from this circumstance, a new set of variables can be introduced, which facilitates the physical understanding of acoustic amplification and of pure tone generation.…”

“…This property is known to be related to the fact that at low Mach numbers, the orifice area can be considered as almost acoustically compact, so that the upstream and downstream acoustic velocities are approximately equal. [20][21][22] From now on, the sums and the differences of the incident and of the scattered propagating pressures shall be used as a new set of variables, keeping in mind that the phenomena of interest are essentially due to the pressure difference terms.…”

Acoustic impedance and hydrodynamic instability of the flow through a circular aperture in a thick plate

“…Next, Moussou et al (2007) investigated experimentally a long pipe fitted with a constriction for a number of values of the constriction ratio and the thickness ratio β. They observe that the conditional instability criterion Z R > 0 (or arg(B) > π/2 using their notation) is verified in a range St L ≈ [0.2, 0.25], again in good agreement with the C1 conditional instability frequency range.…”

Acoustic instability prediction of the flow through a circular aperture in a thick plate via an impedance criterion

“…Fabre et al (2020, § 8). Moussou et al (2007) studied experimentally a long pipe with a constriction for a number of values of the constriction ratio and the thickness ratio. In this study, they identified both the first and second branch of conditionally unstable modes.…”