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 $\mathrm{Re}=8.0\ifmmode\times\else\texttimes\fi{}1{0}^{4}$. We show that the mean skin friction coefficient ${C}_{f}$ in the presence of the superhydrophobic coating can be fitted to a modified Prandtl--von K\'arm\'an--type relationship of the form $({C}_{f}/2{)}^{\ensuremath{-}1/2}=M\mathrm{ln}\text{ }(\mathrm{Re}({C}_{f}/2{)}^{1/2})+N+(b/\mathrm{\ensuremath{\Delta}}r)\mathrm{Re}({C}_{f}/2{)}^{1/2}$ from which we extract an effective slip length of $b\ensuremath{\approx}19\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. The dimensionless effective slip length ${b}^{+}=b/{\ensuremath{\delta}}_{\ensuremath{\nu}}$, where ${\ensuremath{\delta}}_{\ensuremath{\nu}}$ is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as ${b}^{+}\ensuremath{\sim}{\mathrm{Re}}^{1/2}$ in the limit of high Re.