Decomposition of the mean friction drag on a NACA4412 airfoil under uniform blowing/suction

TL;DR

This study uses the RD identity to analyze how uniform blowing and suction affect the mean friction drag on a NACA4412 airfoil, revealing scale-specific turbulence contributions and their independence from Reynolds number and control intensity.

Contribution

It introduces an application of the RD identity combined with empirical mode decomposition to decompose and understand the effects of blowing and suction on turbulent drag over an airfoil.

Findings

Blowing enhances large-scale turbulence contributions on the suction side.

Suction suppresses large-scale motions and enhances small-scale turbulence.

Statistics related to drag generation are Reynolds number independent.

Abstract

The application of drag-control strategies on canonical wall-bounded turbulence, such as periodic channel and zero- or adverse-pressure-gradient boundary layers, raises the question of how to describe control effects consistently for different reference cases. We employ the RD identity (Renard & Deck, J. Fluid Mech., 790, 2016, pp. 339-367) to decompose the mean friction drag and investigate the control effects of uniform blowing and suction applied to a NACA4412 airfoil at chord Reynolds numbers Re_c=200,000 and 400,000. The connection of the drag reduction/increase by using blowing/suction with the turbulence statistics (including viscous dissipation, turbulence-kinetic-energy production, and spatial growth of the flow) across the boundary layer, subjected to adverse or favorable pressure gradients, are examined. We found that the peaks of the statistics associated with the friction-drag generation exhibit good scaling in either inner or outer units throughout the boundary layer. They are also independent of the Reynolds number, control scheme, and intensity of the blowing/suction. The small- and large-scale structures are separated with an adaptive scale-decomposition method, i.e. empirical mode decomposition (EMD), aiming to analyze the scale-specific contribution of turbulent motions to friction-drag generation. Results unveil that blowing on the suction side of the airfoil is able to enhance the contribution of large-scale motions and to suppress that of small-scales; on the other hand, suction behaves contrarily. The contributions related to cross-scale interactions remain almost unchanged with different control strategies.