Effect of helical corrugations on the low Reynolds number flow in a tube

Wang, C. Y.

doi:10.1002/aic.10817

Cited by 17 publications

(16 citation statements)

References 13 publications

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“…36. Wang 23 reports that for Stokes flow through a straight, twisting tube with wavy walls, the axial pressure gradient is independent of ⑀ to first order when the helical pitch is infinite, that is, the cross section does not twist, as is the case here. Note that other researchers, including Dean himself, use the maximum pipe velocity in determining C, which produces C = 4, see for example Refs.…”

Section: A 0 : Straight Pipe With Wavy Wallsmentioning

confidence: 82%

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Steady flow through a curved tube with wavy walls

Peterson

2010

Physics of Fluids

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The problem of fully developed steady flow of an incompressible Newtonian fluid through a mildly curved tube with wavy walls of small amplitude-to-wavelength ratio around the tube circumference is solved via a perturbation solution. Dean's original solution for tubes with circular cross-section is used as the foundation to solve the current regular perturbation problem. In general, the wavy walls are found to mitigate the effect of a given term in Dean's expansion. For instance, the first order effect of the wavy walls is to reduce the strength of the secondary flow vortices and minimize the reduction of the volumetric flow rate caused by the curvature. A related effect is a general reduction in the average axial and circumferential wall shear stresses. The local wall shear stress, however, increases at the points of maximum incursion of the protrusions into the flow and decreases in the valleys between the protuberances. The general form of the solution for an arbitrary number of protuberances is presented to first order in the geometric perturbation and to fourth order in the Dean number.

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Section: A 0 : Straight Pipe With Wavy Wallsmentioning

confidence: 82%

“…Stokes flow in straight circular tubes with small amplitude protuberances has recently been studied by Wang. 23,24 In Ref. 23 the tube cross section has wavy walls and the tube twists along its length producing helical corrugations.…”

Section: Introductionmentioning

confidence: 99%

Steady flow through a curved tube with wavy walls

Peterson

2010

Physics of Fluids

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“…Ng and Wang [42] discussed the effects of both longitudinal and transverse wall corrugations on the [43] discussed the effects of near-wall slip induced by surface roughness on the pressure rise and flow rate of a single rotating-disk viscous micropump operating with Newtonian water. Wang [44] studied the low Reynolds number flow in a tube with helical corrugations. The effects of wall corrugations on EOF through a wavy microchannel were investigated by Shu et al [45].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates

Buren

Jian

2015

Electrophoresis

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In this paper, 2D electromagnetohydrodynamic (EMHD) flow in a microparallel channel with slightly transverse corrugated walls is investigated using perturbation method. The corrugations of the two walls are presented by periodic sinusoidal waves with small amplitudes. The perturbation solutions of the stream function and a relation between flow rate and roughness are obtained. It is shown that the flow rate always decreases due to the wall corrugations irrespective of the phase difference. For prescribed Hartmann number and wave number of the wavy walls, the flow resistance increases as the phase difference between the wall corrugations increases. The effect of corrugation on the flow rate decreases with Hartmann number. With the increase of wave number, the effects of corrugations on the flow rate increase. The phase difference of wall corrugations becomes unimportant when the wave number is greater than 4. The obtained results for the flow rates as a function of the applied current are in qualitative agreement with the existing experimental results.

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“…Wang [3] carried out a perturbation analysis for tubes with small-amplitude sinusoidal corrugations of arbitrary pitch in lowReynolds-number inertial flow and confirmed the existence of an optimal pitch. Pozrikidis [4] performed a complementary perturbation expansion for Stokes flow in tubes with arbitrary crosssection in the limit of large pitch, and presented numerical solutions obtained by a finite-element method for an assortment of geometries up to second-order in the helical wave number.…”

Section: Introductionmentioning

confidence: 75%

Stokes flow through a twisted tube with square cross-section

Pozrikidis

2015

European Journal of Mechanics - B/Fluids

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Effect of helical corrugations on the low Reynolds number flow in a tube

Cited by 17 publications

References 13 publications

Steady flow through a curved tube with wavy walls

Steady flow through a curved tube with wavy walls

Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates

Stokes flow through a twisted tube with square cross-section

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