Pattern formation in weakly forced Taylor-Couette flow

Li, Zhenyu; Khayat, Roger E.

doi:10.1103/physreve.69.046305

Cited by 5 publications

(2 citation statements)

References 15 publications

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“…3 that the outflow of the vortex pair occurs at the crest of the modulation of the inner cylinder, and the wavelength of the vortex pattern is equal to the forcing wavelength, as was also observed experimentally by Ikeda and Maxworthy 3 and the theoretical predictions of Li and Khayat. 6 The vortices fill the entire gap between the outer and inner cylinders and extend over the modulated wavelength. This observation is reminiscent of the unforced Taylor vortex flow.…”

Section: B Results and Discussionmentioning

confidence: 99%

Finite-amplitude modulated Taylor-Couette flow

Zhang

Khayat

2006

Physics of Fluids

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The Taylor-Couette flow with finite-amplitude modulated cylinders is examined in this study. A spectral/finite-difference approach is used based on domain transformation. The governing equations are mapped over the rectangular domain, and the flow field is represented spectrally in the axial direction, which, together with the Galerkin projection, led to a system of equations that are solved using a variable step finite-difference discretization. The vortex formation and pattern selection are examined after the validity of the method is established. The inner and outer cylinders are modulated in phase, and are free to co-or counter-rotate at different speed. It is found that the presence of modulation leads to the emergence of steady vortex flow even at vanishingly small Taylor number. The vortex structure is found to have the same periodicity as the forcing, even after the critical Taylor number corresponding to the onset of vortex flow straight cylinders is exceeded. The outer to inner cylinder velocity ratio controls not only the vortex strength and the nonlinearity but also the size, location, and breakup of the vortices. It is also found that the forcing wave number that generates the most intense vortex flow varies slightly with Ta and is different from the critical wave number predicted by linear stability analysis for straight cylinders.

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Section: B Results and Discussionmentioning

confidence: 99%

Finite-amplitude modulated Taylor-Couette flow

Zhang

Khayat

2006

Physics of Fluids

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“…This is also the case for modulated rotating flow, of closer relevance to the current problem of thermal convection. Li and Khayat (2004) showed the existence of intricate steady pattern formation, but limited their formulation to weakly modulated Taylor-Couette flow. Finite amplitude forcing was later considered by Zhang and Khayat (2006).…”

Section: Introductionmentioning

confidence: 99%

Spatially modulated thermal convection

Obé

Khayat

2010

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to investigate the thermal convection inside a spatially modulated domain. Design/methodology/approach -The governing equations are mapped onto an infinite strip, allowing Fourier expansion of the flow and temperature in the streamwise direction. Findings -Similar to Rayleigh-Benard convection, conduction is lost to convection at a critical Rayleigh number, which depends strongly on both the modulation amplitude and the wavenumber. The effect of modulation is found to be destabilizing (stabilizing) for conduction for relatively large (small) modulation wavelength. Oscillatory convection sets in as the Rayleigh number is increased. Originality/value -This paper presents novel results.

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Interaction dynamics of longitudinal corrugations in Taylor-Couette flows

Jaiman

Lim

2018

Physics of Fluids

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In this paper, numerical simulations are performed on the interaction of vortices with a longitudinal corrugated wall in a Taylor-Couette (TC) setting with the inner smooth surface cylinder rotating and the outer corrugated surface cylinder stationary. The motivation of the study is to shed light on how such an interaction affects the drag/torque with respect to two geometric parameters of the corrugations, namely, the wavelength λc* and amplitude A*, where * indicates a normalization by the gap width d. Results show that in the circular Couette flow regime, the secondary vortices induced by the corrugations cause the torque to increase. When λc*<1, there is a linear relationship between torque and λc*, and when λc*>1, there is a steeper increase of torque due to the interaction of the growing secondary vortices and the opposite wall. In the Taylor-vortex flow regime, the interaction between the Taylor vortices and the corrugations produces three distinct behaviors characterized by λc*. As the wavelength increases, our results show that the stronger modulation effects can override the inherent TC flow dynamics, which in turn leads to a wide range of flow structures that can have a significant impact on the resulting drag/torque characteristics. Generally, a torque reduction is achieved when λc*≤1, while forcing the Taylor vortices to stay on the crests of the corrugations can lead to significant improvement in torque reduction. Finally, the geometrical shape of the corrugations mainly alters the wall shear stress distribution on the corrugated wall, with a negligible effect on the flow dynamics when compared to λc*.

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Pattern formation in weakly forced Taylor-Couette flow

Cited by 5 publications

References 15 publications

Finite-amplitude modulated Taylor-Couette flow

Finite-amplitude modulated Taylor-Couette flow

Spatially modulated thermal convection

Interaction dynamics of longitudinal corrugations in Taylor-Couette flows

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