Streamwise-traveling waves of spanwise wall velocity for turbulent drag reduction

TL;DR

This paper investigates how sinusoidal spanwise wall velocity waves, traveling at different speeds, can significantly reduce or increase turbulent drag, offering insights into more efficient flow control techniques.

Contribution

It introduces a generalized wave-based forcing method that encompasses known drag reduction techniques and explores the effects of wave speed and direction on turbulence and drag.

Findings

Slow forward-traveling waves cause large drag reduction and can relaminarize flow.

Fast waves can increase drag, while very fast waves reduce drag again.

Backward-traveling waves consistently reduce drag regardless of speed.

Abstract

Waves of spanwise velocity imposed at the walls of a plane turbulent channel flow are studied by Direct Numerical Simulations. We consider sinusoidal waves of spanwise velocity which vary in time and are modulated in space along the streamwise direction. The phase speed may be null, positive or negative, so that the waves may be either stationary or traveling forward or backward in the direction of the mean flow. Such a forcing includes as particular cases two known techniques for reducing friction drag: the oscillating wall technique (a traveling wave with infinite phase speed) and the recently proposed steady distribution of spanwise velocity (a wave with zero phase speed). The traveling waves alter the friction drag significantly. Waves which slowly travel forward produce a large reduction of drag, that can relaminarize the flow at low values of the Reynolds number. Faster waves yield a totally different outcome, i.e. drag increase. Even faster waves produce a drag reduction effect again. Backward-traveling waves instead lead to drag reduction at any speed. The traveling waves, when they reduce drag, operate in similar fashion to the oscillating wall, with an improved energetic efficiency. Drag increase is observed when the waves travel at a speed comparable with that of the convecting near-wall turbulence structures. A diagram illustrating the different flow behaviors is presented.