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'Analysis of the pressure fluctuations induced by grazing flow over a Helmholtz resonator

'Analysis of the pressure fluctuations induced by grazing flow over a Helmholtz resonator

Farzin Ghanadi, Maziar Arjomandi, Benjamin S. Cazzolato, Anthony C. Zander (2014)

Journal of Fluids and Structures
under review

Abstract:

Grazing flow over a Helmholtz resonator is a source of pressure fluctuations within its cavity. The flow excitation phenomenon is assumed to be associated with both external pressure fluctuations within the turbulent boundary layer of the grazing flow and the acoustic response of the resonator cavity. In this paper an analytical model has been developed to enable prediction of the amplitude and frequency of the pressure fluctuations within a flow-excited Helmholtz resonator. The model employs a simplified momentum balance equation between the interior and exterior of the resonator. The formulation combines the incompressible and fully developed flow within the resonator neck and compressible flow inside the cavity. For the purpose of validation, results obtained from the model have been compared with experimental values obtained by Ghanadi et al. (2014). It was demonstrated that the analysis provides an accurate representation of the phase and amplitude of the resonator pressure fluctuations. A sensitivity study has been undertaken by changing the main geometrical parameters of the resonator and characteristics of the incoming turbulent boundary layer. The results show that increasing the ratio of the orifice diameter to the momentum thickness from 1 to 40, results in a significant increase in the maximum pressure PSD within the resonator cavity, from 11dB to 32dB. Conversely, when the orifice length is greater than the momentum thickness, pressure fluctuations within the resonator cavity are reduced. It was also demonstrated that increasing Reynolds number amplifies the flow fluctuations within the resonators and if high pressure fluctuations are to be generated then the ratio of the depth to the diameter of the cavity must be in specific range. These investigations assist in identifying the optimal parameters to generate ideal pressure fluctuations within the Helmholtz resonator for the purpose of flow control in the vicinity of the resonator.

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