Bicylindrical model of Herschel–Quincke tube-duct system: theory and comparison with experiment and finite element method
Résumé
An analytical three dimensional bicylindrical model is developed in order to take into account the effects of the saddle-shaped area for the interface of a n-Herschel–Quincke tube system with the main duct. Results for the scattering matrix of this system deduced from this model are compared, in the plane wave frequency domain, versus experimental and numerical data and a one dimensional model with and without tube length correction. The results are performed with a two-Herschel–Quincke tube configuration having the same diameter as the main duct. In spite of strong assumptions on the acoustic continuity conditions at the interfaces, this model is shown to improve the nonperiodic amplitude variations and the frequency localization of the minima of the transmission and reflection coefficients with respect to one dimensional model with length correction and a three dimensional model.