Frequency-tuned surfaces for passive control of wall-bounded turbulent flow – a resolvent analysis study

Abstract

The potential of frequency-tuned surfaces as a passive control strategy for reducing drag in wall-bounded turbulent flows is investigated using resolvent analysis. These surfaces are considered to have geometries with impedances that permit transpiration and/or slip at the wall in response to wall pressure and/or shear and are tuned to target the dynamically important structures of wall turbulence. It is shown that wall impedance can suppress the modes resembling the near-wall cycle and the very-large-scale motions and the Reynolds stress contribution of these modes. Suppression of the near-wall cycle requires a more reactive impedance. In addition to these dynamically important modes, the effect of wall impedance across the spectral space is analysed by considering varying mode speeds and wavelengths. It is shown that the materials designed for suppression of the near-wall modes lead to gain reduction over a wide range across the spectral space. Furthermore, a wall with only shear-driven impedance is found to suppress turbulent structures over a wider range in spectral space, leading to an overall turbulent drag reduction. Most importantly, the present analysis shows that the drag-reducing impedance is non-unique and the control performance is not sensitive to variations of the surface impedance within a favourable range. This implies that specific frequency bandwidths can be targeted with periodic material design.