Interaction of an inner-scaled Helmholtz resonator with boundary-layer turbulence

Abstract

We investigate the impact of a single miniature Helmholtz resonator on wall-bounded turbulence using time-resolved planar particle image velocimetry. A particular aim is to explain the mechanism by which a resonator alters the turbulent velocity fluctuations of different scales. A grazing flow configuration is studied in which the resonator is embedded in the wall beneath a turbulent boundary layer at a friction Reynolds number of Reτ≈2300; the resonator is designed so that its resonance frequency matches the peak frequency of the wall-pressure spectrum. It is found that the resonator amplifies velocity fluctuations near its resonance frequency, while it attenuates the energy of subresonance scales. Underlying mechanisms responsible for these changes in energy are discussed in view of the resonator's local impedance condition. It is posited that large-scale velocity fluctuations in the wall-normal velocity, at temporal frequencies below resonance, are subject to a phase-opposed wall-normal velocity perturbation when the TBL flow convects over the resonator's orifice. This yields a decrease of large-scale energy in u′u′¯,-u′v′¯, and v′v′¯. In addition, modifications of the wall-shear stress field downstream of the resonator are addressed. Insights from this research will contribute to the development of surface designs for passive skin-friction control using arrays of miniature resonators.