On the Use of Linear Acoustic Multiports to Predict Whistling in Confined Flows
Mikael Karlsson
Mats Åbom
Abstract
The use of linear acoustic multiport models to analyse the existence of flow driven instabilities, that is – self-sustained oscillators or whistles – is addressed. By combining the scattering and reflection matrices for a system and searching for eigenfrequencies (zeros)
in the critical half-plane, the existence of exponentially growing instabilities can be determined. In practice, the available frequency domain data are only known along the real axis; then the search for zeros may be done via the so-called Nyquist stability criterion generalized to an N-degree
of freedom system. The method has been validated by two test cases, a T-junction and a Herschel-Quincke tube. In both cases, the occurrence and the frequencies of the self-sustained oscillations were correctly predicted.