Taylor vortices between almost cylindrical boundaries

Eagles, P. M.; Eames, K.

doi:10.1007/bf00036721

Cited by 17 publications

(4 citation statements)

References 5 publications

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“…2, only the intensity and not the pattern of the flow is affected by and Ta. For a straight outer cylinder, the wavelength of the vortex flow is found to be always equal to the wavelength of the inner cylinder, as was also observed in experiments involving sinusoidal forcing [5,10]. This is in analogy with the flow inside a gap with spatially ramped end condition.…”

Section: Resultssupporting

confidence: 55%

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Pattern formation in weakly forced Taylor-Couette flow

Khayat

2004

Phys. Rev. E

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Low-inertia vortex formation and pattern selection are examined for axisymmetric Taylor-Couette flow with spatially modulated cylinders. The forcing is arbitrary but remains periodic. The modulation amplitude is assumed to be small, and a regular perturbation expansion is used to determine the flow field at small to moderately large Taylor numbers (below the critical threshold). It is found that the presence of a weak modulation leads unambiguously to the emergence of steady Taylor-vortex flow even at vanishingly small Taylor number. This situation is closely reminiscent of the effect of end plates, and the consequent onset of imperfect bifurcation. The vortex structure is found to have the same periodicity as the forcing when only one of the cylinders is modulated, or when the modulations are commensurate. For incommensurate modulations, the vortex pattern is quasiperiodic, with regions of almost purely azimuthal flow. When the counter-rotation speed of the outer cylinder increases, the original vortices are gradually replaced by new ones that end up spanning the entire gap width, and in turn break up into two vortices resulting in two rows of vortices commensurate with each cylinder modulation. It is also shown that, for any modulation amplitude, the forcing wave number that generates the most intense vortex flow for a given Taylor number varies monotonically with Ta, but always reaches the critical value predicted by linear stability analysis for straight cylinders, regardless of which cylinder is modulated.

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Section: Resultssupporting

confidence: 55%

“…Two successive groups are separated by zones of a rapid decay of the strength of vortices, leading to an almost purely azimuthal flow in these zones. The situation is reminiscent of the predictions of Eagles and Eames [10] for slowly varying cylinders (see their Figs. 2 and 3).…”

Section: Resultsmentioning

confidence: 91%

Pattern formation in weakly forced Taylor-Couette flow

Khayat

2004

Phys. Rev. E

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“…Work on extended (i.e., periodic or random) radius variation includes experimental work [ 8 – 19 ], while related work on the effect of localized radius variation has been reported in [ 20 – 22 ]. The most detailed of the experimental investigations are those of [ 8 ] and [ 9 ] (see [ 5 ] for a detailed review of previous work).…”

Section: Flowmentioning

confidence: 99%

Flow control through the use of topography

Cotrell¹,

Kearsley²

2007

J. Res. Natl. Inst. Stand. Technol.

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In this work, optimal shaft shapes for flow in the annular space between a rotating shaft with axially-periodic radius and a fixed coaxial outer circular cylinder, are investigated. Axisymmetric steady flows in this geometry are determined by solving the full Navier-Stokes equations in the actual domain. A measure of the flow field, a weighted convex combination of the volume averaged square of the L2-norm of the velocity and vorticity vectors, is employed. It has been demonstrated that boundary shape can be used to influence the characteristics of the flow field, such as its velocity component distribution, kinetic energy, or even vorticity. This ability to influence flow fields through boundary shape may be employed to improve microfluidic mixing or, possibly, to minimize shear in biological applications.

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“…Although this problem is of interest in several practical contexts, with particular relevance to mixing, and is obviously of fundamental significance, little work has been devoted to its investigation, especially at the theoretical level. Besides work on the effect of localized radius variation [9,10], the only work on extended (periodic or random) radius variation known to us is the experimental work by Koschmieder [11], Ikeda and Maxworthy [12], and Painter and co-workers [13,14]. More recently, Khayat and coworkers examined theoretically the effect of cylinder spatial modulation on the onset of vortex flow, covering both Newtonian [15,16] and viscoelastic [17] fluids.…”

Section: Introductionmentioning

confidence: 99%

Effect of weak geometrical forcing on the stability of Taylor-vortex flow

Pan

Khayat

2008

J. Phys.: Conf. Ser.

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Abstract. Linear stability analysis of fully developed axisymmetric steady and spatially modulated Taylor-Couette flow is carried out in the narrow-gap limit. The inner cylinder is sinusoidally modulated and rotating, while the outer cylinder is straight and at rest. The modulation amplitude is assumed to be small, and the base steady flow is determined using a regular perturbation expansion of the flow field coupled to a variable-step finite-difference scheme. The disturbance flow equations are derived within the framework of Floquet theory and solved using a nonlinear two-point boundary-value approach. In contrast to unforced Taylor-Couette flow, only vortical base flow is possible in the forced case. It is found that the forcing tends to generally destabilize the base flow, especially around the critical point. Both the critical Taylor number and wavenumber are found to decrease essentially linearly with modulation amplitude.

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Taylor vortices between almost cylindrical boundaries

Cited by 17 publications

References 5 publications

Pattern formation in weakly forced Taylor-Couette flow

Pattern formation in weakly forced Taylor-Couette flow

Flow control through the use of topography

Effect of weak geometrical forcing on the stability of Taylor-vortex flow

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