Skin-friction Drag Reduction by Hairy Surfaces in Turbulent Channel Flow

Abstract

One notable feature of wall-bounded turbulent flows is high skin-friction drag. Reducing the turbulent skin-friction drag on engineering surfaces such as oil pipelines, aircrafts, or ships, can lead to significant energy savings and reduction in carbon footprint. Hairy surfaces, inspired by deal fur surfaces and bird feathers, have emerged as a promising approach for skin-friction drag reduction. Despite their promise, no study has yet demonstrated the underlying mechanism of skin-friction drag reduction with hairy surfaces. In this study, turbulent skin-friction drag reduction with hairy surfaces and its physical mechanism were investigated by employing direct numerical simulation (DNS) in turbulent channel flow, with hairy surfaces, uniformly distributed on both channel walls. The simulations were conducted using a lattice Boltzmann, immersed boundary (LB-IB) method. An improved reciprocal interpolation-spreading operations is proposed in order to satisfy the no-slip enforcement on the hairy filaments. The no-slip condition along the hairy filaments was measured by employing the ratio of the velocity of a Lagrangian marker along a hairy filament to the fluid velocity interpolated into that marker. If the ratio is the unity, the no-slip condition is strictly satisfied; in other words, the slip error is indicated by the deviation of this ratio from the unity. In comparison to the previous LB-IB methods that provided the slip error up to O(1000)%, the present LB-IB method ensures better no-slip enforcement on the hairy filaments with the slip error less than ∼ 2%. Due to the improved reciprocity of the interpolation-spreading operations, the present LB-IB method successfully accomplishes better numerical accuracy, stability, and robustness compared to the previously suggested LB-IB methods. A parametric study was performed at a bulk Reynolds number of 7200, corresponding to a friction Reynolds number of approximately 221 in a base turbulent channel flow with smooth, no-slip walls, for various filament parameters such as Cauchy number, filament height-to-spacing ratio, filament height, density ratio between the hairy filament and fluid. When drag reduction was plotted as functions of the individual filament parameters, it did not exhibit consistent trends with respect to each of the filament parameters. However, when plotted against the ratio of the characteristic time scale of the hairy filaments to the time scale of the largest eddies in the base turbulent channel flow, the magnitudes of drag reduction collapsed into a single curve. The maximum drag reduction of 5.4% was obtained at the characteristic time scale ratio of 1.4 − 1.5. Another significant achievement of this study is to reveal the underlying mechanism behind skin-friction drag reduction with hairy surfaces. The mechanism was investigated by examining the modulation of intercomponent/interscale energy transfer through budgets of Reynolds stresses, mean/turbulent kinetic energy budgets, and one-dimensional energy spectra. The mechanism can be attributed to the modulation of intercomponent and interscale energy transfer. Specifically, the presence of hairy filaments leads to a decrease in the pressure-strain correlation, which causes an accumulation of turbulence intensity in the streamwise component while reducing it in the cross-streamwise components. Consequently, the energy that would have been distributed from the streamwise component to the spanwise and wall-normal components is transported to wake scale turbulence by hairy filaments, and the transported energy is eventually dissipated within the viscous sublayer. This study is the first DNS research that demonstrates skin-friction drag reduction with hairy surfaces and reveals its underlying physical mechanism.