Turbulent skin-friction drag reduction with flexible roughness

The dynamics of wall-bounded turbulence in the presence of flexible roughness is investigated by direct numerical simulation in turbulent channel flow, with surface roughness elements consisting of rigid or flexible filamentous structures, uniformly implanted on both channel walls. The studies were performed using lattice Boltzmann, immersed-Boundary methods. The dynamics of the filaments was tracked by solving the dynamic Euler-Bernoulli beam equation. Simulations were performed in turbulent channel flows at a bulk Reynolds number of Re_b=7200, corresponding to a friction Reynolds number of Re_τ~ 221 in a `base' turbulent channel flow with smooth, no-slip walls. Filamentous structures of height and spacings of 4-16 in base-flow wall-units were investigated, at dimensionless bending rigidities of 10^-6 ≤ K^*_b ≤ 10^-4, dimensionless stretching coefficients of 0.1 ≤ K^*_s ≤ 1, and density ratios of ρ_s/(ε_{s ρ}f)≈100 and 700, where ρ_s and ε_s are the linear density and hydrodynamic area of the filament, respectively. It is observed that, while for higher bending rigidities the filaments simply act as roughness elements, for lower bending rigidities, the presence of the filaments can disrupt the energy exchanges between the mean flow and turbulence and lead to drag reduction. Drag reductions of ~5% have been obtained to date for filaments with height and spacings of 8 in base-flow wall-units at the lowest bending rigidities. The highest drag reductions are obtained when the characteristic time scale of the filaments is of the same order as the inverse of the mean strain rate and the time scale of energy containing eddies in the near wall region, and the filaments have O(1) deformations. For such flows, the kinetic energy that would have normally gone into production of turbulence is redirected into the filaments, whereby it is transported to the viscous sublayer and dissiapted through viscous dissipation.