Start-up and cessation Newtonian Poiseuille and Couette flows with dynamic wall slip

Kaoullas, George; Georgiou, Georgios C.

doi:10.1007/s11012-015-0127-y

Cited by 16 publications

(16 citation statements)

References 33 publications

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“…Equations (34) and (35) can be checked to agree with those deduced by Kaoullas and Georgiou [14], upon omitting the dynamic slip and rectifying some typographical errors in their equations.…”

Section: Couette Flow Between Two Plates With a Depletion Layermentioning

confidence: 69%

“…When the outer cylinder is stationaryÛ 1 = 0 and the two slip lengths are the sameb 0 =b 1 , our problem becomes the one studied by Kaoullas and Georgiou [14] without the dynamic slip. Figure 7 shows the agreement of velocity profiles computed by their and our solutions, thereby validating our equations deduced above.…”

Section: Couette Flow Between Two Plates With a Depletion Layermentioning

confidence: 99%

“…The dashed lines denote the steady-state velocity profiles. The square symbols are results computed by Kaoullas and Georgiou [14].…”

Section: Couette Flow Between Two Plates With a Depletion Layermentioning

confidence: 99%

“…We may check our deduction by comparing with their solution for this problem. Using a dynamic slip model to account for slip relaxation, Kaoullas and Georgiou [14] presented analytical solutions for starting and ceasing Poiseuille and Couette flows in circular and parallel-plate channels. We may also check our solutions, in the case of equal slip lengths on the walls, against those by Kaoullas and Georgiou [14] without the dynamic slip.…”

Section: Introductionmentioning

confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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This paper contains a collection of problems and their analytical solutions for starting flows under the effect of boundary slip in channels of various geometries. The startup flows examined in this work include: (i) plane Couette flow between two plates, (ii) rotary Couette flow between two coaxial cylinders, (iii) Poiseuille flow through a parallel-plate channel, (iv) Poiseuille flow through a rectangular channel, (v) Poiseuille flow through a circular channel, and (iv) Poiseuille flow through an annulus. It is first shown that, using a depletion layer to model the effective slip, the slip length may attain its steady state much faster than the starting flow will do. This supports the use of a constant Navier slip length in the present problems. Transient solutions are derived in the form of eigenfunction expansions, where the eigenvalues are determined, by solving the characteristic equations numerically, as a function of the channel geometry and the slip lengths. From the leading eigenvalue, it is found that the boundary slip will in general lengthen the transient period of a starting flow.

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Section: Couette Flow Between Two Plates With a Depletion Layermentioning

confidence: 69%

Section: Couette Flow Between Two Plates With a Depletion Layermentioning

confidence: 99%

“…The dashed lines denote the steady-state velocity profiles. The square symbols are results computed by Kaoullas and Georgiou [14].…”

Section: Couette Flow Between Two Plates With a Depletion Layermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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“…Using Laplace transform method Khaled and Vafai (2004) obtained an exact analytical solutions of Stokes and Couette flows commenced by sinusoidal motion of a wall with slip boundary conditions. Recently, many works have been devoted to study the effect of dynamic slip boundary condition (Kaoullas & Georgiou, 2013;Damianou et al, 2014;Kaoullas & Georgiou, 2015) (where the slip velocity is a function of previous wall shear stress state) on pressure gradient and velocity profiles in different flows configurations.…”

Section: I|ntroductionmentioning

confidence: 99%

Analytical Solutions for Unsteady Pipe Flows with Slip Boundary Condition

Pillai

Manu

2020

JAFM

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In this paper analytical expressions for time-dependent velocity profiles and pressure gradient are obtained for fully-developed laminar flows with given volume flow-rate conditions in circular pipe flows with slip boundary conditions. The governing equations are solved analytically using the traditional Laplace transform method together with Mellin's inversion formula. The evolution of velocity profiles and pressure gradient for starting and pulsatile flow with slip boundary conditions are analyzed. New simplified expressions and perspectives on velocity and pressure gradient for no-slip and slip flows are obtained from the analytical results. New scalings in starting and pulsatile flows are proposed for pipe flows with no-slip and slip boundary conditions using nondimensional numbers. Special attention is paid to the effect of slip factor and pulsatile flow frequency on the time-dependent skin-friction factor. Finally, by using the starting and pulsating flow results, analytical expressions of velocity and pressure for arbitrary inflow are obtained by approximating the arbitrary volume flow-rate by a Fourier series

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Computing hydrodynamic eigenmodes of channel flow with slip—A highly accurate algorithm

et al. 2022

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The transient start‐up flow solution with slip is a useful tool to verify computational fluid dynamics (CFD) simulations. However, a highly accurate, open‐source black box solution does not seem to be available. Our method provides a fast, automated, and rigorously verified open‐source implementation that can compute the hydrodynamic eigenmodes of a two‐dimensional channel flow beyond the standard floating‐point precision. This allows for a very accurate computation of the corresponding Fourier series solution. We prove that all roots are found in all special cases for the general flow problem with different slip lengths on the channel walls. The numerical results confirm analytically derived asymptotic power laws for the leading hydrodynamic eigenmode and the characteristic timescale in the limiting cases of small and large slip. The code repository including test cases is publicly available (DOI: https://doi.org/10.5281/zenodo.6806351). The Navier slip boundary condition for numerical simulations in OpenFOAM is also publicly available (DOI: https://doi.org/10.5281/zenodo.7037712).

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Start-up and cessation Newtonian Poiseuille and Couette flows with dynamic wall slip

Cited by 16 publications

References 33 publications

Starting flow in channels with boundary slip

Starting flow in channels with boundary slip

Analytical Solutions for Unsteady Pipe Flows with Slip Boundary Condition

Computing hydrodynamic eigenmodes of channel flow with slip—A highly accurate algorithm

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