Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number

TL;DR

This study investigates how the effectiveness of spanwise forcing techniques for reducing turbulent skin-friction drag diminishes at higher Reynolds numbers using DNS, revealing parameter shifts that may sustain net energy savings.

Contribution

It provides new insights into the Reynolds number dependence of drag reduction performance and identifies optimal parameter shifts that mitigate performance loss at higher Re.

Findings

Drag reduction decreases with Re, but at a slower rate when optimal parameters shift.

Optimal forcing parameters change with Re, becoming less sensitive to Re at higher values.

Potential for positive net energy savings at large Re due to energy-efficient forcing.

Abstract

A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number $Re$. We consider active, predetermined strategies based on spanwise forcing (oscillating wall and streamwise-traveling waves applied to a plane channel flow), and explore via Direct Numerical Simulations (DNS) up to $Re_\tau=2100$ the rate at which their performance deteriorates as $Re$ is increased. To be able to carry out a comprehensive parameter study, we limit the computational cost of the simulations by adjusting the size of the computational domain in the homogeneous directions, compromising between faster computations and the increased need of time-averaging the fluctuating space-mean wall shear-stress. Our results, corroborated by a few full-scale DNS, suggest a scenario where drag reduction degrades with $Re$ at a rate that varies according to the parameters of the wall forcing. In agreement with already available information, keeping them at their low-$Re$ optimal value produces a relatively quick decrease of drag reduction. However, at higher $Re$ the optimal parameters shift towards other regions of the parameter space, and these regions turn out to be much less sensitive to $Re$. Once this shift is accounted for, drag reduction decreases with $Re$ at a markedly slower rate. If the slightly favorable trend of the energy required to create the forcing is considered, a chance emerges for positive net energy savings also at large values of the Reynolds number.