Drag reduction of turbulent boundary layer flow with traveling wavy wall on flexible rubber sheet

An effect of a traveling wavy wall deformation generated on a flexible rubber sheet for the drag reduction of turbulent boundary layer flow was investigated. The traveling wave was generated by oscillating the upstream end of the rubber sheet in the wall-normal direction using a piezoelectric actuator so that the wave travels in the streamwise direction. The parameters of the traveling wave, e.g., amplitude, wavelength, and wave speed, are given in the range where fully developed turbulent flows could be relaminarized in Nakanishi et al. [“Relaminarization of turbulent channel flow using traveling wave-like wall deformation,” Int. J. Heat Fluid Flow 35, 152–159 (2012)] and Mamori et al. [“Effect of the parameters of traveling waves created by blowing and suction on the relaminarization phenomena in fully developed turbulent channel flow,” Phys. Fluids 26, 015101 (2014)]. A two-component laser Doppler velocimetry was used to measure the streamwise and the wall-normal velocities. The flow was measured at two streamwise points where the Reynolds numbers based on the momentum thickness without control were 620 and 880. The momentum in the boundary layer was evaluated using the von Kármán momentum integral equation considering the momentum defect, the fluctuating momentum, and the pressure gradient in the boundary layer. The total drag between the measurement points quantified by the momentum equation was reduced by 9.4% due to the traveling wave. The modification of the turbulence was discussed in terms of a velocity fluctuation decomposed into periodic and random components. The wavy wall directly induced the periodic forcing in the near-wall region while secondarily reducing the turbulent fluctuation in the wide range of the boundary layer. The reduced turbulent fluctuations result in a reduction in the momentum defect, which contributes to the reduction in the drag quantified by the momentum equation.