An Analytical and Numerical Study of Unsteady Channel Flow With Slip

Matthews, Miccal T.; Hastie, Karen M.

doi:10.1017/s1446181112000272

Cited by 5 publications

(27 citation statements)

References 14 publications

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“…After reconciling the normalization scales, the expressions given above can be checked to agree with those presented by Matthews and Hastie [13]. Our expression above for the Fourier coefficientsÂ n is slightly simpler in form than theirs.…”

Section: Poiseuille Flow Through a Parallel-plate Channelmentioning

confidence: 75%

“…As was remarked by Matthews and Hastie [13] and Avramenko et al [11,12], these analytical solutions are valuable for future studies. For one thing, they can be used as benchmarks for numerical simulations, or to validate computational fluid dynamics (CFD) codes.…”

Section: Introductionmentioning

confidence: 73%

“…The problem formulated above and the solution deduced below are essentially the same as those given by Matthews and Hastie [13], but are presented here in terms of the present notation for completeness of this paper. The same problem but under the condition of equal slip lengths on the two walls has been solved by Avramenko et al [11] using Laplace transform.…”

Section: Poiseuille Flow Through a Parallel-plate Channelmentioning

confidence: 99%

“…Our solutions are expressed in a form simpler than theirs. Matthews and Hastie [13] also studied, using Fourier series expansions, start-up pressure-driven flow through a parallel-plate channel with disparate slip lengths on the two plates. We may check our deduction by comparing with their solution for this problem.…”

Section: Introductionmentioning

confidence: 99%

“…On assuming steady and uniform slip lengths, our problems for starting Couette flow between two parallel flat plates and between two coaxial cylinders, and starting pressure-driven flow through a parallel-plate, rectangular, circular, and annular channel are then presented in Sections 3-8. Figures 1,3,6,8,10,13,16 show the definition sketches for these problems.…”

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: Poiseuille Flow Through a Parallel-plate Channelmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 73%

Section: Poiseuille Flow Through a Parallel-plate Channelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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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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Starting Poiseuille Flow in a Circular Tube With Two Immiscible Fluids

Wang

2018

Journal of Fluids Engineering

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Starting flow due to a suddenly applied pressure gradient in a circular tube containing two immiscible fluids is solved using eigenfunction expansions. The orthogonality of the eigenfunctions is developed for the first time for circular composite regions. The problem, which is pertinent to flow lubricated by a less viscous near-wall fluid, depends on the ratio of the radius of the core region to that of the tube, and the ratios of dynamic and kinematic viscosities of the two fluids. In general, a higher lubricating effect will lead to a longer time for the starting transient to die out. The time development of velocity profile and slip length are examined for the starting flows of whole blood enveloped by plasma and water enveloped by air in a circular duct. Owing to a sharp contrast in viscosity, the starting transient duration for water/air flow can be ten times longer than that of blood/plasma flow. Also, the slip length exhibits a singularity in the course of the start-up. For blood with a thin plasma skimming layer, the singularity occurs very early, and hence for the most part of the start-up, the slip length is nearly a constant. For water lubricated by air of finite thickness, the singularity may occur at a time that is comparable to the transient duration of the start-up, and hence, an unsteady slip length has to be considered in this case.

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An Analytical and Numerical Study of Unsteady Channel Flow With Slip

Cited by 5 publications

References 14 publications

Starting flow in channels with boundary slip

Starting flow in channels with boundary slip

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

Starting Poiseuille Flow in a Circular Tube With Two Immiscible Fluids

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