Global effect of local skin friction drag reduction in spatially developing turbulent boundary layer

TL;DR

This study investigates how local skin friction drag reduction techniques in turbulent boundary layers affect the overall flow, introducing a global drag reduction metric and a simple model to predict downstream effects.

Contribution

It introduces a global drag reduction rate and a model linking local control effects to overall flow development in turbulent boundary layers.

Findings

Persistent downstream drag reduction with uniform blowing

Drag increase with turbulence damping downstream

A model relates local and global drag reduction without extensive simulations

Abstract

A numerical investigation of two locally applied drag reducing control schemes is carried out in the configuration of a spatially developing turbulent boundary layer (TBL). One control is designed to damp near-wall turbulence and the other induces constant mass flux in the wall-normal direction. Both control schemes yield similar local drag reduction rates within the control region. However, the flow development downstream of the control significantly differs: persistent drag reduction is found for the uniform blowing case whereas drag increase is found for the turbulence damping case. In order to account for this difference the formulation of a global drag reduction rate is suggested. It represents the reduction of the streamwise force exerted by the fluid on a finite length plate. Furthermore, it is shown that the far downstream development of the TBL after the control region can be described by a single quantity, namely a streamwise shift of the uncontrolled boundary layer, i.e. a changed virtual origin. Based on this result, a simple model is developed that allows relating for the local drag reduction rate to the global one without the need of conducting expensive simulations or measurements far downstream of the control region.