Evaluation of the Oscillation Velocity in the Neck of the Helmholtz Resonator in Nonlinear Regimes

Abstract

Methods for measuring the acoustic characteristics of orifices have been reviewed. Comparison of three methods for evaluating of oscillation velocity in the neck of the Helmholtz resonator are presented. The first method is measurements in an impedance tube with the two-microphone method, the second is based on measuring the sound pressure in the resonator chamber, and the third is based on direct measurements of bias flow with a Pitot tube. The results of measuring the oscillation velocity in the neck of the Helmholtz resonator are presented, and show that these methods are in good agreement only within linear acoustics, but they lead to different results in nonlinear regimes characterized by high sound pressure levels.

Comparison of Semi-Empirical Impedance Models for Locally-Reacting Acoustic Liners in a Wide Range of Sound Pressure Levels

“…Subsequent semi-empirical impedance models proposed by other authors refined the description of the main physical effects occurring in resonators under various conditions, as well as the empirical data (end correction, oscillation velocity in the resonator neck, discharge coefficient, etc.) [13][14][15][16][17][18][19][20][21][22][23][24].…”

Investigations into the Approaches of Computational Fluid Dynamics for Flow-Excited Resonator Helmholtz Modeling within Verification on a Laboratory Benchmark

“…The role of panoramic methods based on visualization in studying the characteristics of acoustic and hydrodynamic fields in the Helmholtz resonator problem should be mentioned, additionally. Thus, in [19], studies of the parameters of resonance modes inside a resonator excited in an impedance pipe using fog visualization in a laser sheet was combined with the measurements of pneuma gauges and microphones. The fog visualization allowed a clear demonstration for the first time that resonance is caused by the disruption of a single discrete vortex from the edge of the orifice, which moves along it during one cycle of oscillations (the first mode) in studies of the flow-excited Helmholtz resonator ( [10]).…”

“…In this regard, attempts to use simplified approaches to describe Helmholtz resonators excited by flows have been made from the very beginning of the use of CFD methods. For example, in [19], a certain intermediate approximation was used between the conditions of a compressible and incompressible medium for the Navier-Stokes equations, and in [20] a numerical procedure based on the kinetic equation, combined with the RNG turbulence model, is applied. In this case, it was possible to obtain good qualitative agreement; however, the calculated amplitudes of pressure pulsations could be lower (up to 20 dB, see [19]), and in [20] a special coefficient was even introduced to reduce the free flow velocity by 15/22 times compared to parameters of the experimental studies in [10] to demonstrate agreement between the calculated pressure values in the resonator and the experimental data.…”

“…For example, in [19], a certain intermediate approximation was used between the conditions of a compressible and incompressible medium for the Navier-Stokes equations, and in [20] a numerical procedure based on the kinetic equation, combined with the RNG turbulence model, is applied. In this case, it was possible to obtain good qualitative agreement; however, the calculated amplitudes of pressure pulsations could be lower (up to 20 dB, see [19]), and in [20] a special coefficient was even introduced to reduce the free flow velocity by 15/22 times compared to parameters of the experimental studies in [10] to demonstrate agreement between the calculated pressure values in the resonator and the experimental data. This was explained by the difficulties of adequately reproducing the velocity distribution in the boundary layer, the thickness of which affects the effective velocity of the shear layer.…”