Turbulent skin-friction drag reduction with hairy surfaces

Turbulent skin-friction drag reduction with hairy surfaces is investigated by direct numerical simulation (DNS) in turbulent channel flow, in which the channel walls are covered by uniform arrays of rigid or flexible filaments. The studies were performed using a lattice Boltzmann–immersed boundary method, with the filament dynamics modeled using the one-dimensional Euler–Bernoulli beam equation. The tension force was computed implicitly to enforce the inextensibility constraint of the filaments. Simulations were performed in turbulent channel flows at a bulk Reynolds number of Re_b=7200, corresponding to a friction Reynolds number of Re_τ0∼223. Filaments of height equal to 4 to 16 in base-flow wall units, implanted at uniform spacings of 1/2 to 4 filament heights, were investigated across a wide range of dimensionless bending rigidities (2×10^-6≤ K_b^*(≡ K_b /((ρ_s - ρ_fε) u_b² h²) ≤10^-4), density ratios (30 ≤ ρ_s/(ρ_fε) ≤ 1000) and Cauchy numbers (0 ≤ Ca (≡ ρ_f u_τ0² d h³ / K_b) ≤ 40), where K_b is the bending rigidity, u_b is the bulk velocity, h is the filament height, u_τ0 is the friction velocity in the base turbulent channel flow, ρ_f is the fluid density, and ρ_s and ε denote the linear density and hydrodynamic area of the filament, respectively. At high bending rigidities, the filaments behave as roughness elements and increase the drag. However, at lower bending rigidities, the filaments disrupt the near-wall turbulence, suppress the turbulence production and reduce the drag. Over the wide range of filament heights, spacings, bending rigidities, density ratios and Cauchy numbers investigated, the optimal filament configuration was found to always correspond to configurations where the characteristic time of the filament, T_fil, was of the same order as the eddy turnover time of the largest eddies in the turbulent channel flow, H/u_τ0, with the filaments implanted at separations of 1 filament height. Highest drag reductions of ~8% were achieved at T_fil u_τ0/H ~1.5. These results highlight a passive mechanism for skin-friction reduction, with potential applications in flow control using engineered surfaces covered with flexible filaments.