Slip Length–Based Boundary Condition for Modeling Drag Reduction Devices

AIAA Journal ◽  
2018 ◽  
Vol 56 (9) ◽  
pp. 3478-3490 ◽  
Author(s):  
Benedetto Mele ◽  
Renato Tognaccini
Keyword(s):  
Boundary Condition ◽  
Drag Reduction ◽  
Slip Length

Hydrodynamic slippage of water at surfaces

2017 ◽  
Author(s):  
E. Charlaix ◽  
L. Bocquet
Keyword(s):  
Boundary Condition ◽  
Molecular Mechanisms ◽  
Slip Length ◽  
Molecular Simulations ◽  
Short Review ◽  
Solid Surfaces ◽  
Experimental Investigations

The boundary condition (B.C.) for hydrodynamic flows at solid surfaces is usually assumed to be that of no slip. However a number of molecular simulations and experimental investigations over the last two decades have demonstrated violations of the no-slip B.C., leading to hydrodynamic slippage at solid surfaces. In this short review, we explore the molecular mechanisms leading to hydrodynamic slippage of water at various surfaces and discuss experimental investigations allowing us to measure the so-called slip length

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.

Turbulent flow over superhydrophobic surfaces with streamwise grooves

2014 ◽  
Vol 747 ◽  
pp. 186-217 ◽  
Author(s):  
S. Türk ◽  
G. Daschiel ◽  
A. Stroh ◽  
Y. Hasegawa ◽  
B. Frohnapfel
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Secondary Flow ◽  
Slip Length ◽  
Laminar Flows ◽  
Superhydrophobic Surfaces ◽  
Mean Velocity ◽  
Effective Slip Length ◽  
Effective Slip

AbstractWe investigate the effects of superhydrophobic surfaces (SHS) carrying streamwise grooves on the flow dynamics and the resultant drag reduction in a fully developed turbulent channel flow. The SHS is modelled as a flat boundary with alternating no-slip and free-slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. In all computations, a constant pressure gradient condition is employed, so that the drag reduction effect is manifested by an increase of the bulk mean velocity. To capture the flow properties that are induced by the non-homogeneous boundary conditions the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. It is observed that the alternating no-slip and free-slip boundary conditions lead to the generation of Prandtl’s second kind of secondary flow characterized by coherent streamwise vortices. A mathematical relationship between the bulk mean velocity and different dynamical contributions, i.e. the effective slip length and additional turbulent losses over slip surfaces, reveals that the increase of the bulk mean velocity is mainly governed by the effective slip length. For a small spanwise periodicity of the streamwise grooves, the effective slip length in a turbulent flow agrees well with the analytical solution for laminar flows. Once the spanwise width of the free-slip area becomes larger than approximately 20 wall units, however, the effective slip length is significantly reduced from the laminar value due to the mixing caused by the underlying turbulence and secondary flow. Based on these results, we develop a simple model that allows estimating the gain due to a SHS in turbulent flows at practically high Reynolds numbers.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

2002 ◽  
Author(s):  
Derek C. Tretheway ◽  
Luoding Zhu ◽  
Linda Petzold ◽  
Carl D. Meinhart
Keyword(s):  
Boundary Condition ◽  
Shear Rate ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Bounce Back

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9–L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1−P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

scholarly journals SUPERHYDROPHOBIC SURFACES FOR DRAG REDUCTION

2014 ◽  
Author(s):  
Alessandro Bottaro
Keyword(s):  
Drag Reduction ◽  
Slip Length ◽  
Superhydrophobic Surfaces ◽  
Transition To Turbulence ◽  
Effective Coupling ◽  
Instability Waves ◽  
Low Surface Energy ◽  
Apparent Slip ◽  
Energy Material ◽  
Relevant Length Scale

Properties of superhydrophobic materials are examined in light of their possible use for drag reduction in naval applications. To achieve superhydrophobicity a low-surface-energy material must be structured so as to minimize the liquid-solid interactions. The crucial aspect is that of maintaining a layer of gas in between the (rough) wall and the liquid, and this can be achieved by hierarchical micro- and nano-structuring of the solid surface, to ensure a sufficiently large apparent slip of the fluid at the wall, thus reducing skin friction. The behavior of the liquid is quantified by a slip length; recent results have shown that this length can be as large as 400 μm. As far as transition to turbulence is concerned, we show that superhydrophobic surfaces are effective (i.e. they delay the onset of travelling instability waves) only in channels with characteristic dimensions of a few millimeters. Conversely, when the fluid flow has already attained a turbulent state, the gain in term of drag reduction can be very significant also in macroscopic configurations. This occurs because the relevant length scale of the boundary layer is now the thickness of the viscous sub-layer, which can be of magnitude comparable to the slip length, so that an effective coupling emerges. Finally, some procedures to produce superhydrophobic surfaces are examined, in light of the possible application of such innovative coatings on the hull of ships.

Numerical Simulation of Fluid Slip at a Hydrophobic Surface

Volume 4 ◽  
2004 ◽  
Author(s):  
Takao Fujita ◽  
Keizo Watanabe
Keyword(s):  
Boundary Condition ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Drag Reduction ◽  
Hydrophobic Surface ◽  
Friction Reduction ◽  
Water Repellent ◽  
Two Dimensional ◽  
Hydrophobic Property ◽  
Flow Past

Laminar drag reduction is achieved by using a hydrophobic surface. In this method, fluid slip is applied at the hydrophobic surface. An initial experiment to clarify for a laminar skin friction reduction was conducted using ducts with a highly water-repellent surface. The surface has a fractal-type structure with many fine grooves. Fluid slip at a hydrophobic surface has been analyzed by applying a new wet boundary condition. In this simulation, an internal flow is assumed to be a two-dimensional laminar flow in a rectangular duct and an external flow is assumed to be a two-dimensional laminar flow past a circular cylinder. The VOF technique has been used as the method for tracking gas-liquid interfaces, and the CSF model has been used as the method for modeling surface tension effects. The wet boundary condition for the hydrophobic property on the surface has been determined from the volume ratio in contact with water near the surface. The model with a stable gas-liquid interface and the experimental results of flow past a circular cylinder at Re = 250 without growing the Karman vortex street are made, and these results show that laminar drag reduction occurring due to fluid slip can be explained in this model.

Fluid Slip of Flow Past a Hydrophobic Wall Sphere

2004 ◽  
Author(s):  
Takao Fujita ◽  
Keizo Watanabe
Keyword(s):  
Boundary Condition ◽  
Drag Reduction ◽  
Flow Visualization ◽  
Flow Characteristics ◽  
Flow Patterns ◽  
Liquid Interface ◽  
Solid Boundary ◽  
Stress Boundary Condition ◽  
Sphere Drag ◽  
Stress Boundary

The possibility of fluid slip has received considerable attention in recent years. Laminar drag reduction is achieved by using a hydrophobic wall with fluid slip. Fluid slip is closely related to the gas-liquid interface formed at a solid surface with many fine grooves. The friction generated by the solid boundary is modified considerably because the gas-liquid interface provides a zero-shear stress boundary condition. The purpose of this study is to experimentally clarify the flow characteristics and drag reduction of a hydrophobic wall sphere by visualizing flow and by measuring the drag. In addition, the flow patterns were numerically analyzed by applying a wet boundary condition for fluid slip. The flow visualization results showed that the Vortex Loop was not exist at Re < 400 in the hydrophobic wall sphere and the separation point moved downstream compared with that of a conventionally smooth sphere. Drag reduction occurred in the flow and the maximum drag reduction ratio was 14.6% at Re=93.2. In this simulation, the flow patterns for the numerical simulation results agreed with those of the flow visualization results.

Predictions of the effective slip length and drag reduction with a lubricated micro-groove surface in a turbulent channel flow

2019 ◽  
Vol 874 ◽  
pp. 797-820 ◽  
Author(s):  
Jaehee Chang ◽  
Taeyong Jung ◽  
Haecheon Choi ◽  
John Kim
Keyword(s):  
Aspect Ratio ◽  
Drag Reduction ◽  
Numerical Simulations ◽  
Channel Flow ◽  
Slip Length ◽  
Turbulent Channel Flow ◽  
Solid Substrate ◽  
Direct Numerical Simulations ◽  
Effective Slip ◽  
Lubricant Viscosity

We perform direct numerical simulations of a turbulent channel flow with a lubricated micro-grooved surface to investigate the effects of this surface on the slip characteristics at the interface and the friction drag. The interface between water and lubricant is assumed to be flat, i.e. the surface-tension effect is neglected. The solid substrate, where a lubricant is infused, is composed of straight longitudinal grooves. The flow rate of water inside the channel is maintained constant, and a lubricant layer under the interface is shear driven by the turbulent water flow above. A turbulent channel flow with a superhydrophobic (i.e. air-lubricated) surface having the same solid substrate configuration is also simulated for comparison. The results show that the drag reduction with the liquid-infused surface highly depends on the lubricant viscosity as well as the groove width and aspect ratio. The amounts of drag reduction with the liquid-infused surfaces are not as good as those with superhydrophobic surfaces, but are still meaningfully large. For instance, the maximum drag reduction by the heptane-infused surface is approximately 13 % for a rectangular groove whose spanwise width and depth in wall units are 12 and 14.4, respectively, whereas a superhydrophobic surface with the same geometry results in a drag reduction of 21 %. The mean slip length normalized by the viscosity ratio and groove depth depends on the groove aspect ratio. The ratio of fluctuating spanwise slip length to the streamwise one is between 0.25 (ideal surface without groove structures) and 1 (i.e. isotropic slip), indicating that the slip is anisotropic. Using the Stokes flow assumption, the effective streamwise and spanwise slip lengths are expressed as a function of groove geometric parameters and lubricant viscosity. We also suggest a predictive model for drag reduction with the heptane-lubricated surface by combining the predicted effective slip lengths with the drag reduction formula used for riblets (Luchini et al., J. Fluid Mech., vol. 228, 1991, pp. 87–109). The predicted drag reductions are in good agreements with those from the present and previous direct numerical simulations.

Dispersion due to Electroosmotic Flow Through a Circular Tube With Axial Step Changes of Zeta Potential and Hydrodynamic Slippage

2013 ◽  
Author(s):  
Qi Zhou ◽  
Chiu-On Ng
Keyword(s):  
Boundary Condition ◽  
Zeta Potential ◽  
Dispersion Coefficient ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Axial Position ◽  
Hydrodynamic Dispersion ◽  
Lubrication Approximation ◽  
Slip Boundary ◽  
Zeta Potentials

The hydrodynamic dispersion of a neutral non-reacting solute due to steady electro-osmotic flow in a circular channel with longitudinal step changes of zeta potential and hydrodynamic slippage is analyzed in this study. The channel wall is periodically micro-patterned along the axial position with alternating slip-stick stripes of distinct zeta potentials. Existing studies on electrically driven hydrodynamic dispersion are based on flow subject to either the no-slip boundary condition on the capillary surface or the simplification of lubrication approximation. Taking wall slippage into account, a homogenization analysis is performed in this study to derive the hydrodynamic dispersion coefficient without subject to the long-wave constraint of the lubrication approximation, but for a general case where the length of one periodic unit of wall pattern is comparable with the channel radius. The flow and the hydrodynamic dispersion coefficient are calculated numerically, using the packages MATLAB and COMSOL, as functions of controlling parameters including the period length of the wall pattern, the area fraction of the slipping region (EOF-suppressing) in a periodic unit, the ratio of the two zeta potentials, the intrinsic hydrodynamic slip length, the Debye parameter, and the Péclet number. The dispersion coefficient is found to show notable, non-monotonic in certain situations, dependence on these controlling parameters. It is noteworthy that the introduction of hydrodynamic slippage will generate much richer behaviors of the hydrodynamic dispersion than the situation with no-slip boundary condition, as slippage interacts with zeta potentials in the EOF-suppressing and EOF-supporting regions (either likewise or oppositely charged).

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