Acoustic Impedance of a Helmholtz Resonator at Very High Amplitude

Abstract

The acoustic impedance of a Helmholtz resonator terminating a ten-inch diameter tube has been investigated for sound pressure levels in the resonator of from 100 db to 170 db and for a range of particle velocities in the neck of from 1.3 cm/sec to 1.2×104 cm/sec (rms). Two different mounting orientations showed the same general rise in acoustic resistance and rise in resonant frequency with increasing sound pressure level but gave quite different results in detail.

Acoustic response of Helmholtz dampers in the presence of hot grazing flow

“…11 illustrates the total virtual neck-extension δ for various temperatures of the grazing flow, normalized with the virtual neck-extension at isothermal conditions and small forcing amplitudes δ 0 . The length of the virtual neck changes with the forcing amplitude already at isothermal conditions, which is in line with the findings of Bies and Wilson [12]. At high amplitudes the acoustic displacement is large and the turbulent mixing is strong, causing the decrease of the mass end-correction at both ends of the neck.…”

“…The change of the effective jet diameter was obtained from the isothermal measurements, which is also used to determine the relation between the forcing amplitude and the virtual neckextension δ. In line with the findings of Ingård [11] as well as Bies and Wilson [12], the neck-extension decreases with increasing acoustic amplitude due to turbulent mixing and the associated nonlinear displacement. At an amplitude of jû=u pf j¼1 and isothermal conditions, the total length correction is δ 0 % 8=ð3πÞ0:84D.…”

“…Addressing the problems of the virtual neck-extension and dissipation mechanisms, Ingård [11] suggested design guidelines for acoustic resonators for various geometries. Additionally, similar to Bies and Wilson [12], an amplitude dependence of the damping efficiency was identified. Two mechanisms are responsible for the conversion of acoustic energy into heat: visco-thermal damping at the walls of the neck, which is important at very low amplitudes, and vortex shedding, which is nonlinearly connected to the acoustic velocity amplitude.…”

Acoustic Response of a Helmholtz Resonator Exposed to Hot-Gas Penetration and High Amplitude Oscillations

“…It was found that the resistance of the impedance increases with the amplitude of the acoustic velocity. Similar results were found by Bies and Wilson [4]. Both identified three regions, depending on the acoustic velocity amplitude: a linear regime, which is due to viscothermal damping; an intermediate regime; and a nonlinear regime.…”

“…However, the damping strongly depends on the pressure oscillation amplitude and, despite numerous studies (e.g., Refs. [2][3][4][5][6][7]) on this subject, has not yet been fully understood.…”