Circular concentric Helmholtz resonators

Abstract

The effect of specific cavity dimensions of circular concentric Helmholtz resonators is investigated theoretically, computationally, and experimentally. Three analytical models are employed in this study: (1) A two-dimensional model developed to account for the nonplanar wave propagation in both the neck and the cavity; (2) a one-dimensional solution developed for the limit of small cavity length-to-diameter ratio, l/d, representing a radial propagation in the cavity; and (3) a one-dimensional closed-form solution for configurations with large l/d ratios which considers purely axial wave propagation in the neck and the cavity. For low and high l/d, the resonance frequencies determined from the two-dimensional approach are shown to match the one-dimensional predictions. For cavity volumes with l/d>0.1, the resonance frequencies predicted by combining Ingard’s end correction with one-dimensional axial wave propagation are also shown to agree closely with the results of the two-dimensional model. The results from the analytical methods are then compared with the numerical predictions from a three-dimensional boundary element method and with experiments. Finally, these approaches are employed to determine the wave suppression performance of circular Helmholtz resonators in the frequency domain.

Acoustic Attenuation Performance of Circular Expansion Chambers With Extended Inlet/Outlet

“…Thus, while yielding reasonable predictions at lower frequencies, this simplistic approach is expected to deviate from experimental results at higher frequencies. The effect of higher order modes on the acoustic attenuation of some related silencers has received considerable attention, including concentric [2,3] and asymmetric expansion chambers [4±10],¯ow-reversing chambers [11,12], and Helmholtz resonators [13]. For expansion chambers with extended inlet/ outlet, A Ê bom [14] developed, utilizing the mode-matching technique, a general 198 A. SELAMET AND Z. L. JI three-dimensional analytical approach to evaluate the four-pole parameters which incorporated higher order modes and yielding endplates.…”

TLM method and acoustics

“…A plane-wave Gaussian pulse is excited at the beginning of the duct and PML ABCs are imposed at both ends of the duct. A theoretical value for the transmission loss of the system, de"ned as the ratio in dBs of the incident to the transmitted pressure, can be obtained by considering axial plane-wave propagation at the duct, the neck and the cavity and an empirical correction to take into account the volume of #uid near the neck [10]. Figure 12 is a plot of the transmission loss for both the TLM and the theoretical prediction for axial propagation.…”

Step-Scan T-Cell Fourier Transform Infrared Photoacoustic Spectroscopy (FTIR-PAS) for Monitoring Environmental Air Pollutants

“…Furthermore, as T-cell is a kind of novel resonant photoacoustic cell that is being applied in PAS fields [8][9][10][11][12][13], its full theory on photoacoustic signal analysis has not been well developed comprehensively [12]. To explore the step-scan FTIR-PAS signal theoretically, it is valuable to consider the FTIR-PAS theory for regular cylindrical PA cell as the resonance principles of both kinds of cell are similar [12].…”