Effects of the air layer of an idealized superhydrophobic surface on the slip length and skin-friction drag

2016 ◽  
Vol 790 ◽  
Author(s):  
Taeyong Jung ◽  
Haecheon Choi ◽  
John Kim
Keyword(s):  
Drag Reduction ◽  
Skin Friction ◽  
Superhydrophobic Surface ◽  
Slip Length ◽  
Joint Probability ◽  
Turbulent Channel Flow ◽  
Water Interface ◽  
Friction Drag ◽  
Recirculating Flow ◽  
Air Water Interface

The anisotropy of the slip length and its effect on the skin-friction drag are numerically investigated for a turbulent channel flow with an idealized superhydrophobic surface having an air layer, where the idealized air–water interface is flat and does not contain the surface-tension effect. Inside the air layer, both the shear-driven flow and recirculating flow with zero net mass flow rate are considered. With increasing air-layer thickness, the slip length, slip velocity and percentage of drag reduction increase. It is shown that the slip length is independent of the water flow and depends only on the air-layer geometry. The amount of drag reduction obtained is in between those by the empirical formulae from the streamwise slip only and isotropic slip, indicating that the present air–water interface generates an anisotropic slip, and the streamwise slip length ($b_{x}$) is larger than the spanwise one ($b_{z}$). From the joint probability density function of the slip velocities and velocity gradients at the interface, we confirm the anisotropy of the slip lengths and obtain their relative magnitude ($b_{x}/b_{z}=4$) for the present idealized superhydrophobic surface. It is also shown that the Navier slip model is valid only in the mean sense, and it is generally not applicable to fluctuating quantities.

Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces

2015 ◽  
Vol 783 ◽  
pp. 448-473 ◽  
Author(s):  
J. Seo ◽  
R. García-Mayoral ◽  
A. Mani
Keyword(s):  
Drag Reduction ◽  
Numerical Simulations ◽  
Superhydrophobic Surface ◽  
Stagnation Pressure ◽  
Direct Numerical Simulations ◽  
Superhydrophobic Surfaces ◽  
Water Interface ◽  
System Parameters ◽  
Wide Range ◽  
Air Water Interface

Superhydrophobic surfaces can entrap gas pockets within their grooves when submerged in water. Such a mixed-phase boundary is shown to result in an effective slip velocity on the surface, and has promising potential for drag reduction and energy-saving in hydrodynamic applications. The target flow regime, in most such applications, is a turbulent flow. Previous analyses of this problem involved direct numerical simulations of turbulence with the superhydrophobic surface modelled as a flat boundary, but with a heterogeneous mix of slip and no-slip boundary conditions corresponding to the surface texture. Analysis of the kinematic data from these simulations has helped to establish the magnitude of drag reduction for various texture topologies. The present work is the first investigation that, alongside a kinematic investigation, addresses the robustness of superhydrophobic surfaces by studying the load fields obtain from data from direct numerical simulations (DNS). The key questions at the focus of this work are: does a superhydrophobic surface induce a different pressure field compared to a flat surface? If so, how does this difference scale with system parameters, and when does it become significant that it can deform the air–water interface and potentially rapture the entrapped gas pockets? To this end, we have performed DNS of turbulent channel flows subject to superhydrophobic surfaces over a wide range of texture sizes spanning values from $L^{+}=6$ to $L^{+}=155$ when expressed in terms of viscous units. The pressure statistics at the wall are decomposed into two contributions: one coherent, caused by the stagnation of slipping flow hitting solid posts, and one time-dependent, caused by overlying turbulence. The results show that the larger texture size intensifies the contribution of stagnation pressure, while the contribution from turbulence is essentially insensitive to $L^{+}$. The two-dimensional stagnation pressure distribution at the wall and the pressure statistics in the wall-normal direction are found to be self-similar for different $L^{+}$. The scaling of the induced pressure and the consequent deformations of the air–water interface are analysed. Based on our results, an upper bound on the texture wavelength is quantified that limits the range of robust operation of superhydrophobic surfaces when exposed to high-speed flows. Our results indicate that when the system parameters are expressed in terms of viscous units, the main parameters controlling the problem are $L^{+}$ and a Weber number based on inner dimensions; We obtain good collapse when all our results are expressed in wall units, independently of the Reynolds number.

scholarly journals Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing

2016 ◽  
Vol 802 ◽  
pp. 553-582 ◽  
Author(s):  
Davide Gatti ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Skin Friction ◽  
Travelling Waves ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Friction Drag ◽  
Reduction Techniques ◽  
Controlled Flow ◽  
Friction Drag Reduction

This paper examines how increasing the value of the Reynolds number $Re$ affects the ability of spanwise-forcing techniques to yield turbulent skin-friction drag reduction. The considered forcing is based on the streamwise-travelling waves of spanwise-wall velocity (Quadrio et al., J. Fluid Mech., vol. 627, 2009, pp. 161–178). The study builds upon an extensive drag-reduction database created via direct numerical simulation of a turbulent channel flow for two fivefold separated values of $Re$, namely $Re_{\unicode[STIX]{x1D70F}}=200$ and $Re_{\unicode[STIX]{x1D70F}}=1000$. The sheer size of the database, which for the first time systematically addresses the amplitude of the forcing, allows a comprehensive view of the drag-reducing characteristics of the travelling waves, and enables a detailed description of the changes occurring when $Re$ increases. The effect of using a viscous scaling based on the friction velocity of either the non-controlled flow or the drag-reduced flow is described. In analogy with other wall-based drag-reduction techniques, like riblets for example, the performance of the travelling waves is well described by a vertical shift of the logarithmic portion of the mean streamwise velocity profile. Except when $Re$ is very low, this shift remains constant with $Re$, at odds with the percentage reduction of the friction coefficient, which is known to present a mild, logarithmic decline. Our new data agree with the available literature, which is however mostly based on low-$Re$ information and hence predicts a quick drop of maximum drag reduction with $Re$. The present study supports a more optimistic scenario, where for an airplane at flight Reynolds numbers a drag reduction of nearly 30 % would still be possible thanks to the travelling waves.

scholarly journals Sustained drag reduction in a turbulent flow using a low-temperature Leidenfrost surface

2016 ◽  
Vol 2 (10) ◽  
pp. e1600686 ◽  
Author(s):  
Dhananjai Saranadhi ◽  
Dayong Chen ◽  
Justin A. Kleingartner ◽  
Siddarth Srinivasan ◽  
Robert E. Cohen ◽  
...  
Keyword(s):  
Drag Reduction ◽  
Skin Friction ◽  
Superhydrophobic Surface ◽  
Pressure Fluctuations ◽  
Slip Boundary Condition ◽  
Superhydrophobic Surfaces ◽  
Friction Drag ◽  
Slip Boundary ◽  
Large Water ◽  
High Reynolds

Skin friction drag contributes a major portion of the total drag for small and large water vehicles at high Reynolds number (Re). One emerging approach to reducing drag is to use superhydrophobic surfaces to promote slip boundary conditions. However, the air layer or “plastron” trapped on submerged superhydrophobic surfaces often diminishes quickly under hydrostatic pressure and/or turbulent pressure fluctuations. We use active heating on a superhydrophobic surface to establish a stable vapor layer or “Leidenfrost” state at a relatively low superheat temperature. The continuous film of water vapor lubricates the interface, and the resulting slip boundary condition leads to skin friction drag reduction on the inner rotor of a custom Taylor-Couette apparatus. We find that skin friction can be reduced by 80 to 90% relative to an unheated superhydrophobic surface for Re in the range 26,100 ≤ Re ≤ 52,000. We derive a boundary layer and slip theory to describe the hydrodynamics in the system and show that the plastron thickness is h = 44 ± 11 μm, in agreement with expectations for a Leidenfrost surface.

scholarly journals Base flow modulations for skin-friction drag reduction

2011 ◽  
Vol 318 (3) ◽  
pp. 032008 ◽  
Author(s):  
Jens H M Fransson ◽  
Alessandro Talamelli
Keyword(s):  
Drag Reduction ◽  
Skin Friction ◽  
Base Flow ◽  
Friction Drag ◽  
Friction Drag Reduction
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