Method of Submerged Stokeslets for Slip Flow About Ensembles of Particles

2008 ◽  
Vol 8 (7) ◽  
pp. 3790-3801
Author(s):  
Shunliu Zhao ◽  
Alex Povitsky
Keyword(s):  
Boundary Conditions ◽  
Self Assembly ◽  
Slip Flow ◽  
Chemical Vapor ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Singularity Method ◽  
Low Reynolds Number Flows ◽  
Micro Pump

A boundary singularity method with submerged Stokeslets is applied to the low Reynolds number flows about a set of spheres. Newtonian fluid is considered with no slip or partial slip boundary conditions at the wall. The validity of the method for Stokes flows about representative sets of spheres is investigated. The considered cases include (i) a uniform flow about a stationary set of particles typical for filtration and chemical vapor deposition, (ii) a flow induced by particles moving toward each other typical for self-assembly processes and (iii) a flow induced by spinning particles typical for micro-pump applications. The dependence of the flowfield on the number of Stokeslets is investigated in order to establish the needed number of Stokeslets. Comparison of flow field for the no-slip (Kn = 0) and partial-slip boundary conditions (Kn = 0.1) shows that the partial slip at the particles' surface significantly affect the velocity field and pressure distribution.

Implementation of partial slip boundary conditions in an open-source finite-volume-based computational library

2019 ◽  
Vol 39 (4) ◽  
pp. 377-387 ◽  
Author(s):  
Célio Fernandes ◽  
Luís Lima Ferrás ◽  
Florian Habla ◽  
Olga Sousa Carneiro ◽  
João Miguel Nóbrega
Keyword(s):  
Boundary Conditions ◽  
Open Source ◽  
Analytical Solutions ◽  
Plug Flow ◽  
Flow Distribution ◽  
Polymer Processing ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Extra Stress Tensor

Abstract This paper reports the implementation of slip boundary conditions in the open-source computational library OpenFOAM. The linear and nonlinear Navier slip laws, which are newly implemented in this paper, can be used both for Newtonian and viscoelastic constitutive models. For the former case, the Couette flow assumption near the wall is employed, and for the latter, the cell-centered extra-stress tensor components are linearly extrapolated to the wall. The validation is performed by comparing the numerical results obtained for Newtonian and simplified Phan-Thien-Tanner constitutive model fluids in Couette and Poiseuille flows, with existing analytical solutions. The results obtained using different slip factors were shown to be in agreement with the analytical solutions, even for the most extreme cases where the slip factor is high enough to induce a plug flow pattern for the velocity field. The newly implemented boundary conditions are also used to study the influence of slip in polymer processing, namely in the production of an extruded profile. The results obtained show that the developed slip boundary conditions are able to deal with complex geometrical problems, and are an important tool to support the search of a balanced flow distribution in the design of profile extrusion dies.

scholarly journals Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Swirling Flow ◽  
Velocity Profiles ◽  
Partial Slip ◽  
Injection Velocity ◽  
Slip Boundary Conditions ◽  
Slip Boundary

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

scholarly journals Dynamics of a bilayer membrane with membrane-solvent partial slip boundary conditions

2018 ◽  
Vol 16 (3) ◽  
pp. 186-191 ◽  
Author(s):  
Kento Yasuda ◽  
Ryuichi Okamoto ◽  
Shigeyuki Komura ◽  
Jean-Baptiste Fournier
Keyword(s):  
Boundary Conditions ◽  
Bilayer Membrane ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Slip Boundary

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

Numerical investigation of flow around a structure using Navier-slip boundary conditions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sang-Do Choi ◽  
Tae-Soo Eum ◽  
Eun Taek Shin ◽  
Chang Geun Song
Keyword(s):  
Boundary Conditions ◽  
Slip Length ◽  
Lift Coefficient ◽  
Vortex Formation ◽  
Slip Condition ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Navier Slip ◽  
Slip Boundary

Purpose Complicated motion of vortex is frequently observed in the wake of islands. These kinds of swirling fluid cause the trap of sediments or pollutants, subsequently inducing the dead zone, odor or poor water quality. Therefore, the understanding of flow past a circular cylinder is significant in predicting water quality and positioning the immersed structures. This study aims to investigate the flow properties around a structure using Navier-slip boundary conditions. Design/methodology/approach Boundary conditions are a major factor affecting the flow pattern because the magnitude of flow detachment on a surface can redistribute the tangential stress on the wall. Therefore, the authors performed an analysis of laminar flow passing through a circular structure to investigate the effect of boundary conditions on the flow pattern. Findings The authors examined the relationship between the partial-slip boundary conditions and the flow behavior at low Reynolds number past a circular cylinder considering velocity and vorticity distributions behind the cylinder, lift coefficient and Strouhal number. The amplitude of lift coefficient by the partial slip condition had relatively small value compared with that of no-slip condition, as the wall shear stress acting on the cylinder became smaller by the velocity along the cylinder surface. The frequency of the asymmetrical vortex formation with partial slip velocity was increased compared with no-slip case due to the intrinsic inertial effect of Navier-slip condition. Originality/value The ability to engineer slip could have dramatic influences on flow, as the viscous dominated motion can lead to large pressure drops and large axial dispersion. By the slip length control, no-slip, partial-slip and free-slip boundary conditions are tunable, and the velocity distributions at the wall, vortex formation and wake pattern including the amplitude of lift coefficient and frequency were significantly affected by slip length parameter.

Gaseous Slip Flow Mixed Convection in Vertical Microducts With Constant Axial Energy Input

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Arman Sadeghi ◽  
Mostafa Baghani ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Cross Sections ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Slip Boundary Conditions ◽  
First Order ◽  
Slip Boundary

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.

scholarly journals EFFECTS OF SLIP ON THE VON KÁRMÁN SWIRLING FLOW AND HEAT TRANSFER IN A POROUS MEDIUM

2015 ◽  
Vol 39 (2) ◽  
pp. 357-366 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Disk Surface ◽  
Partial Slip ◽  
Fluid Temperature ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Porosity Parameter ◽  
Flow And Heat Transfer

Numerical solutions are obtained for the fully coupled and highly nonlinear system of differential equations, arising due to the steady Kármán flow and heat transfer of a viscous fluid in a porous medium. The conventional no-slip boundary conditions are replaced by partial slip boundary conditions owing to the roughness of the disk surface. Combined effects of the slip λ and porosity γ parameters on the momentum and thermal boundary layers are studied in detail. Both parameters produce the same effects on the mean velocity profiles, such that all velocity components are reduced by increasing either λ or γ. The temperature slip factor β has a dominating influence on the temperature profiles by decreasing the fluid temperature in the whole domain. The porosity parameter strongly decreases the heat transfer coefficient at the wall for low values of β and tends to an asymptotical limit around 0.1 for β ≃ 10. The porosity parameter γ increases the moment coefficient at the disk surface, which is found to monotonically decrease with λ.

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