Parametric Study on a Sinusoidal Riblet for Drag Reduction by Direct Numerical Simulation

The direct numerical simulation of fully developed turbulent channel flow with a sinusoidal riblet surface has been carried out at the friction Reynolds number of 110. Lateral spacing of adjacent walls in a sinusoidal riblet is varied sinusoidally in the streamwise direction. The average lateral spacing of a sinusoidal riblet is larger than the diameter of a quasi-streamwise vortex and its wetted area is smaller than that of ordinary straight-type riblets. We investigate the effect of sinusoidal riblet design parameters on the drag reduction rate and flow statistics in this paper. The parametric study shows that the maximum total drag reduction rate is approximately 9.8% at a friction Reynolds number of 110. The riblet induces downward and upward flows in the expanded and contracted regions, respectively, which contribute to periodic Reynolds shear stress. However, the random Reynolds shear stress decreases drastically as compared with the flat surface case, resulting in the reduction of total drag owing to the sinusoidal riblet. We also performed vortex tracking to discuss the motion of the vortical structure traveling over the sinusoidal riblet surface. Vortex tracking and probability analysis for the core of the vortical structure show that the vortical structure is attenuated owing to the sinusoidal riblet and follows the characteristic flow. These results show that the high skin-friction region on the channel wall is localized at the expanded region of the riblet walls. In consequence, the wetted area of the riblet decreases, resulting in the drag-reduction effect.