Sustainable Drag Reduction in Turbulent Taylor-Couette Flows by Depositing Sprayable Superhydrophobic Surfaces

Abstract

We demonstrate a reduction in the measured inner wall shear stress in moderately turbulent Taylor-Couette flows by depositing sprayable superhydrophobic microstructures on the inner rotor surface. The magnitude of reduction becomes progressively larger as the Reynolds number increases up to a value of 22% at Re=8.0×10[superscript 4]. We show that the mean skin friction coefficient C[subscript f] in the presence of the superhydrophobic coating can be fitted to a modified Prandtl–von Karman–type relationship of the form (C[subscript f]/2)[[superscript -1/2] = Mln (Re(C[subscript f]/2)[[superscript 1/2]) + N + (b/Δr)Re(C[subscript f]/2)[superscript 1/2] from which we extract an effective slip length of b ≈ 19 μm. The dimensionless effective slip length b[superscript +] = b/δ[subscript ν], where δ[subscript ν] is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as b[[superscript +] ~ Re[superscript 1/2] in the limit of high Re.