[Paper Review] Turbulent skin-friction reduction by wavy surfaces

Sacha Ghebali, S. I. Chernyshenko+1 more|arXiv (Cornell University)|May 4, 2017

Fluid Dynamics and Turbulent Flows36 references21 citations

TL;DR

This study investigates passive skin-friction drag reduction in turbulent channel flows using skewed wavy walls to emulate the shear-strain effects of a Spatial Stokes Layer (SSL) without active actuation. Direct numerical simulations show a net drag reduction of up to 0.5% due to a 2% friction drag reduction, offset by a 1.3% pressure drag penalty, with the transverse shear strain remaining approximately Reynolds-number independent when scaled in wall units.

ABSTRACT

Direct numerical simulations of fully-developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow, and leading to a reduction in the turbulent skin-friction drag. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag reduction of about 0.5%. The friction-drag reduction is shown to behave approximately quadratically for small wave slopes and then linearly for higher slopes, whilst the pressure-drag penalty increases quadratically. Unlike in the SSL case, there is a region of increased turbulence production over a portion of the wall, above the leeward side of the wave, thus giving rise to a local increase in dissipation. The transverse shear-strain layer is shown to be approximately Reynolds-number independent when the wave geometry is scaled in wall units.

Motivation & Objective

• To explore passive, geometrically induced drag reduction in turbulent boundary layers using wavy walls as a substitute for active in-plane wall motions.
• To assess whether wavy walls can emulate the transverse shear-strain profile of a Spatial Stokes Layer (SSL), known to reduce skin friction.
• To quantify the trade-off between friction-drag reduction and pressure-drag penalty in wavy-wall configurations.
• To evaluate the Reynolds-number dependence of the shear-strain profile and drag reduction performance when wall geometry is scaled in wall units.
• To identify dominant mechanisms limiting performance, including localized turbulence production and phase variation effects.

Proposed method

• Direct numerical simulations (DNS) of fully developed turbulent channel flows with wavy walls are performed using a spectral/hp element method with high spatial and temporal resolution.
• The wavy wall is oriented at an angle θ to the mean flow direction, generating a spanwise pressure gradient that induces spanwise flow and transverse shear strain.
• The wall geometry is scaled in wall units (e.g., A⁺, λ⁺) to assess Reynolds-number independence of the shear-strain profile.
• Drag components—friction and pressure—are computed and compared against a baseline plane channel flow with identical mesh and domain size.
• Grid convergence studies are conducted at Reτ = 360 to assess numerical accuracy and sensitivity of drag reduction estimates.
• Turbulence production and dissipation terms are analyzed to identify localized instabilities and energy transfer mechanisms near the leeward side of the wave.

Experimental results

Research questions

• RQ1 Can a passive wavy wall geometry effectively emulate the transverse shear-strain profile of a Spatial Stokes Layer (SSL) in turbulent channel flow?
• RQ2 How does the net drag reduction vary with wave height, wavelength, and flow angle, and what is the optimal configuration?
• RQ3 To what extent is the shear-strain profile and drag reduction performance independent of Reynolds number when wall geometry is scaled in wall units?
• RQ4 What are the dominant mechanisms limiting drag reduction, particularly in terms of turbulence production and pressure drag?
• RQ5 How do localized increases in turbulence production above the leeward side of the wave affect overall energy dissipation and performance?

Key findings

• The transverse shear-strain profile above the wavy wall closely resembles that of a Spatial Stokes Layer (SSL), validating the emulation strategy.
• Friction-drag reduction scales approximately quadratically for small wave slopes and linearly for higher slopes, while pressure-drag penalty increases quadratically with wave height.
• A net drag reduction of approximately 0.5% is estimated at Reτ ≈ 360 for a configuration with A⁺ ≈ 20, λ⁺ ≈ 920, and θ = 70°, based on the finest grid resolution.
• The shear-strain profile is approximately Reynolds-number independent when wall geometry is scaled in wall units, indicating robustness across Reynolds numbers.
• A localized peak in turbulence production is observed above the leeward side of the wave, contributing to increased dissipation and counteracting drag reduction.
• The performance of the wavy wall is limited by a combination of quadratic pressure drag and localized turbulence intensification, which degrades the benefit from friction reduction.