Aeroacoustic Attenuation Performance of a Helmholtz Resonator with a Rigid Baffle Implemented in the Presence of a Grazing Flow

To broaden its’ effective frequency range and to improve its transmission loss performance, a modified design of a Helmholtz resonator is proposed and evaluated by implementing a rigid baffle in its cavity. Comparison is then made between the proposed design and the conventional one by considering a rectangular duct with the resonator implemented in the presence of a mean grazing flow. For this, a linearized 2D Navier-Stokes model in frequency domain is developed. After validated by benchmarking with the available experimental data and our experimental measurements, the model is used to evaluate the effects of (1) the width Lp of the rigid baffle, (2) its implementation location/height Hg, (3) its implementation configurations (i.e., attached to the left sidewall or right sidewall), (4) the grazing mean flow Mu (Mach number), and (5) the neck shape on a noise damping effect. It is shown that as the rigid baffle is attached in the 2 different configurations, the resonant frequencies and the maximum transmission losses cannot be predicted by using the classical theoretical formulation ω2=c2S/VLeff, especially as the grazing Mach number Mu is greater than 0.07, i.e., Mu>0.07. In addition, there is an optimum grazing flow Mach number corresponding to the maximum transmission loss peak, as the width Lp is less than half of the cavity width Dr, i.e., Lp/Dr≤0.5. As the rigid plate width is increased to Lp/Dr=0.75, one additional transmission loss peak at approximately 400 Hz is produced. The generation of the 12 dB transmission loss peak at 400 Hz is shown to attribute to the sound and structure interaction. Finally, varying the neck shape from the conventional one to an arc one leads to the dominant resonant frequency being increased by approximately 20% and so the secondary transmission loss peak by 2-5 dB. The present work proposes and systematically studies an improved design of a Helmholtz resonator with an additional transmission loss peak at a high frequency, besides the dominant peak at a low frequency.

The Acoustic Impedance of a Vibrating Annular Piston Located on a Flat Rigid Baffle Around a Semi-Infinite Circular Rigid Cylinder

The axisymmetric problem of acoustic impedance of a vibrating annular piston embedded into a flat rigid baffle concentrically around a semi-infinite rigid cylindrical circular baffle has been undertaken in this study. The Helmholtz equation has been solved. The Green’s function valid for the zone considered has been used for this purpose. The influence of the semi-infinite cylindrical baffle on the piston’s acoustic impedance has been investigated. The acoustic impedance has been presented in both forms: integral and asymptotic, both valid for the steady harmonic vibrations. Additionally, the acoustic impedances of the piston with and without the cylindrical baffle have been compared to one another. In the case without the cylindrical baffle some earlier results have been used.

ASYMPTOTIC APPROXIMATION OF THE MODAL ACOUSTIC IMPEDANCE OF A CIRCULAR MEMBRANE

The Neumann boundary value problem of the Helmholtz equation of a vibrating circular membrane embedded into a flat rigid baffle is solved. The membrane is excited asymmetrically and radiates acoustic waves into the half-space above the baffle. A set of elementary asymptotic equations for modal radiation self-impedance and mutual impedance is presented. The equations are necessary for numerical computations of the radiated active and reactive acoustic power including the acoustic attenuation. A few equations available in the literature are collected. All the missing equations have been obtained using the methods of analysis of contour integral and stationary phase. The presented equations cover a wide frequency band, with the exception of the lowest frequencies and the frequencies close to coincidence.