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<p>We investigate the interaction between two miniature Helmholtz resonators (HRs), separated in the streamwise direction, and a grazing turbulent boundary layer (TBL). This study aims to understand how the resonators modify the velocity fluctuations in the grazing flow, with the goal of informing the design of surface features capable of deterministically influencing turbulence dynamics. By building on the study of&#xa0;Hassanein et al. (Phys Rev Fluids 9(11):114610, 2024), the model for the resonator-turbulence interaction, for a single HR, will be explored for multiple resonators. The grazing turbulent flow is studied experimentally using time-resolved planar particle image velocimetry; the resonators themselves are embedded in the wall beneath a TBL at a friction Reynolds number of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Re_\tau \approx 2000\)</EquationSource> </InlineEquation> and are tuned so that their resonance frequency coincides with the peak of the wall-pressure spectrum. Three streamwise separation distances are considered. At resonance, the streamwise-separated HRs exhibit minimal interaction, producing an amplification pattern resembling independent HR units. At sub-resonant frequencies, the energy of streamwise velocity fluctuations is reduced downstream of the second orifice, with attenuation increasing as the separation distance decreases. We hypothesise that this attenuation arises from an increase in the phase velocity of pressure fluctuations above the resonators, which dephases the resonator-induced velocity (driven by pressure exciting the resonator) and the velocity fluctuation in the incoming flow. These findings, combined with a fundamental understanding of passive resonator-induced modifications to wall impedance, provide guidance for designing arrays of resonators to manipulate turbulence.</p>

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Interaction of Two Streamwise-Separated Miniature Helmholtz Resonators with a Grazing Turbulent Boundary Layer

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  • 发表日期：

    2026年5月20日

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  • Abdelrahman Hassanein,
  • Davide Modesti,
  • Woutijn J. Baars

摘要

We investigate the interaction between two miniature Helmholtz resonators (HRs), separated in the streamwise direction, and a grazing turbulent boundary layer (TBL). This study aims to understand how the resonators modify the velocity fluctuations in the grazing flow, with the goal of informing the design of surface features capable of deterministically influencing turbulence dynamics. By building on the study of Hassanein et al. (Phys Rev Fluids 9(11):114610, 2024), the model for the resonator-turbulence interaction, for a single HR, will be explored for multiple resonators. The grazing turbulent flow is studied experimentally using time-resolved planar particle image velocimetry; the resonators themselves are embedded in the wall beneath a TBL at a friction Reynolds number of \(Re_\tau \approx 2000\) and are tuned so that their resonance frequency coincides with the peak of the wall-pressure spectrum. Three streamwise separation distances are considered. At resonance, the streamwise-separated HRs exhibit minimal interaction, producing an amplification pattern resembling independent HR units. At sub-resonant frequencies, the energy of streamwise velocity fluctuations is reduced downstream of the second orifice, with attenuation increasing as the separation distance decreases. We hypothesise that this attenuation arises from an increase in the phase velocity of pressure fluctuations above the resonators, which dephases the resonator-induced velocity (driven by pressure exciting the resonator) and the velocity fluctuation in the incoming flow. These findings, combined with a fundamental understanding of passive resonator-induced modifications to wall impedance, provide guidance for designing arrays of resonators to manipulate turbulence.