Permeability and effective slip in confined flows transverse to wall slippage patterns

2016 ◽  
Vol 28 (8) ◽  
pp. 082002 ◽  
Author(s):  
Avinash Kumar ◽  
Subhra Datta ◽  
Dinesh Kalyanasundaram
Author(s):  
Avinash Kumar ◽  
Subhra Datta ◽  
Dinesh Kalyanasundaram

Even Newtonian liquids are now known to slip past suitably engineered surfaces, such as those exhibiting super-hydrophobicity. Through friction reduction, such surfaces have potential to significantly reduce the required the motive power to drive confined flows. Studies of unconfined shear flows over such surfaces have revealed that patterned slipping surfaces are intrinsically inferior to the less realizable uniformly slipping surfaces in terms of the fluid slip velocity generated per unit pattern-averaged shear stress. In this study, a spectrally accurate semianalytical approach is used to assess the friction-reduction performance of several alternate ways of confining the flow over a patterned surface. Fluid permeates by pressure differential through a channel with plate-like walls. One of the plates forming the channel is kept fixed throughout the study to have a sinusoidal slip pattern, while the second plate can be non-slipping, uniformly slipping and patterned identically to the first surface. The gap between the plates, the degree of slip and pattern waveform parameters can be varied between limits not restricted by the model. Significantly different behaviours in permeability and the effective degree of slip of the first plate arise from the differences in patterning on the second plate.


Author(s):  
Andrea Catarsi ◽  
Davide Fioriti ◽  
Mauro Mameli ◽  
Sauro Filippeschi ◽  
Paolo Di Marco

1984 ◽  
Author(s):  
P. Kotidis ◽  
P. Chaviaropoulos ◽  
K. D. Papailiou

The development of transverse velocity profile is directly related to the development of secondary vorticity. In the internal aerodynamics case with potential external flow, although vorticity remains confined inside the viscous shear layer, secondary vorticity induced velocities exist outside of it. If the secondary vorticity field is known, the induced secondary velocity field is well approximated following Hawthorne’s classical analysis. In the present work, the above analysis is used to separate the velocity field in the transverse plane into a potential and a rotational part. In the case of confined flows, the rotational part is confined inside the viscous shear layer, while the potential part occupies the whole flow field. This last part is the consequence of the “displacement” effects of the shear layer in the transverse plane. Therefore, the present work allows a re-examination of the flow two-zone model (separation of the flow field in a viscous and an inviscid part) in confined flows. On the other hand, the limitations of Hawthorne’s theory are examined, while a parallel analysis is presented for the case where the secondary vorticity distribution varies not only along the blade height, but also circumferentially.


2014 ◽  
Vol 747 ◽  
pp. 186-217 ◽  
Author(s):  
S. Türk ◽  
G. Daschiel ◽  
A. Stroh ◽  
Y. Hasegawa ◽  
B. Frohnapfel

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.


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