On the Mechanism of Turbulence Suppression and Skin Friction Drag Reduction with Hairy Surfaces

DNS studies (Akhavan & Lee, 2023) and experiments (Takata et al., 1996) have both shown that a uniform carpet of flexible filaments, of appropriate physical characteristics, implaneted on the inner walls of a pipe or a channel flow can lead to turbulence suprression and skin-friction drag reduction. In DNS studies performed in turbulent channel flows at a bulk Reynolds number of Re_b=7200 (Re_τ0≈223), with flexible filaments of height 4 ≤ h⁺⁰ ≤ 16 (in base flow wall units), diameter of d^{^+0}≈1, filament height to spacing ratios of 1/4 ≤ h/s ≤ 2, canopy soldities of 0.025 ≤ λ (≡ h d / s²) ≤ 0.5, filament to fluid density ratios of 30 ≤ ρ_r (≡ ρ_s/ρ_f ε ) ≤ 1000, and Cauchy numbers of Ca (≡ ρ_f u_τ0² d h³ / K_b) = 0, 5, 10, 20, 30, 40, it was found that the magnitude of drag reduction is primarily determined by the ratio of the timescale of the filaments, T_fil , to the eddy turnover time of the largest turbulent eddies in the channel, H/u_Τ0. The highest drag reductions of DR ≈ 8% were observed at T_fil H / u_τ0 ≈ 1.5, with filament spacings equal to the filamet height, h/s=1. While in the past, it has been suggested that the filaments suppress the production of turbulence through a spectral shortcut mechanism, in which the energy of the largest turbulent eddies is redirected into the motion of the filaments, we find no such spectral shortcut mechanism at work. Instead, we find that the filaments suppress the turbulence by disrupting the pressure-strain correlations, thus resulting in accumulation of the turbulence kinetic energy in the streamwise component of the velocity, and a concomitant reduction in the Reynolds shear stress, turbulence production and streamwise vorticity fluctuations. Examination of the pre-multiplied spectra reveals that these effects are most pronounced at the largest turbulent scales and extend to wall-normal distances far beyond the height of the filaments. Reexamination of the mechanism of DR with polymer additives and spanwise wall oscillations reveals that a similar disruption of the pressure-strain correlations is also present in DR with these agents, suggesting that targeting the pressure-strain correlations may be a path to more effective passive DR technologies.