The Herschel–Quincke tube: A theoretical, computational, and experimental investigation

Abstract

A general expression for the transmission loss characteristics of the Herschel-Quincke tube is developed. This relationship eliminates the restrictions on duct cross-sectional area employed in earlier analytical studies. The attenuation of sound by this configuration is also studied computationally in terms of a nonlinear one-dimensional finite-difference model that solves the balance equations of mass, momentum, and internal energy, coupled with the ideal gas equation of state. Transmission loss predictions from both analytical and computational models are then shown to correlate well with experimental data ,acquired from an extended impedance tube setup. INTRODUCTION The Herschel-Ouincke tube is a parallel connection of two pipes having arbitrary lengths and constant, although not necessarily equal, cross-sectional areas. Studies of this configuration date back to Herschel and Quincke's attempts in the 19th century, and Stewart's refinement early in the 20th century (Herschel, 1833; Quincke, 1866; Stewart, 1928; Stewart and Lindsay, 1930). Since then, the configuration has received relatively little attention [see, for example, the classic NACA report (Davis et aL, 1954) for a brief mention and 3177 d. Acoust. Soc. Am. 96 (5), Pt.

Acoustic Behavior of Short Elliptical Chambers With End Central Inlet and End Offset or Side Outlet

“…For the concentric case, the short distance between the inlet and outlet also leads to an acoustic resonant response with less similarity at low frequencies in comparison with the end o!set and side outlet geometries. The concentric con"guration has also been fabricated and its transmission loss has been measured in an extended impedance tube facility described elsewhere [8]. The comparison with the predictions shows a good agreement, as expected.…”

Effects of Numerical Dissipation and Dispersion on Acoustic Predictions From a Time-Domain Finite Difference Technique for Non-Linear Wave Dynamics

“…The imaginary component is the result of odd derivatives in the truncation error and leads to amplitude errors while the real component is due to the even derivative terms and result in phase errors, or numerical dispersion. As indicated by equation (8)…”

“…The investigation focuses on the computational phase and amplitude errors incurred for sinusoidal disturbances propagating in a stationary and inviscid medium. The explicit finite-difference technique of Chapman and co-workers [5,8] is applied for the non-linear balance equations of mass, momentum and energy. This finite difference approach has been used extensively in design tools for automotive intake and exhaust systems [5,9].…”

An efficient FEM-BEM procedure for the multi-frequency acoustical analysis of lined ducts containing passive components

“…The theory is presented in Sections 3 and 4. The last section shows practical applications involving Helmholtz resonators [2] and Herschel-Quincke tubes [3]. The benefit of the present approach is shown both in terms of CPU time and model reduction, when compared to standard FE models.…”