Computation of taylor vortex flow by a transient implicit method

Roquefort, T. Alziary de; Grillaud, Gérard

doi:10.1016/0045-7930(78)90017-8

Cited by 60 publications

(22 citation statements)

References 14 publications

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“…2͑d͔͒. This phenomenon has previously been reported by Lücke, Mihelcic, and Wingerath, 32 Alziary de Roquefort and Grillaud, 33 Pfister and Rehberg, 34 and others. 3,4 Based on the linear stability analysis reported by Chandrasekhar, 35 the critical Reynolds number for an infinite annulus with a radius ratio of ϭ0.5 is Re c ϭ68.2.…”

Section: A Isothermal Flows (Gr‫)0؍‬supporting

confidence: 73%

Taylor–Couette flow with buoyancy: Onset of spiral flow

Kuo

Ball

1997

Physics of Fluids

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Numerical simulations of the effects of buoyancy on the stability and morphology of Taylor-Couette flow have been conducted. The three-dimensional equations of motion are discretized using a hybrid Chebyshev collocation/Fourier spectral method. The problem geometry consists of an air-filled vertical annulus with radius ratio, ϭr i /r o ϭ0.5 ͑where r i and r o are the inner and outer radii, respectively͒, and aspect ratio, ΓϭL/(r o Ϫr i )ϭ10 ͑where L is the height of the annulus͒. The flow is generated by combined heating and rotation of the inner cylinder. Results for various values of the Reynolds number, Re, and Grashof number, Gr, show several bifurcations of the system. The most notable change in flow structure with increasing rotational effects is the onset of spiral flow in certain parameter ranges. Compared to existing analytical and experimental results, the current numerical results show good agreement.

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Section: A Isothermal Flows (Gr‫)0؍‬supporting

confidence: 73%

Taylor–Couette flow with buoyancy: Onset of spiral flow

Kuo

Ball

1997

Physics of Fluids

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“…The vortices developed from the endboundaries, by the Ekman pumping, induced the formation of next vortices that propagate toward the center of fluid column which can be seen at Ta = 35.2. As Taylor number is further increased, the cells propagate towards the center region until it fills completely the fluid column when Taylor number reaches the critical value, Tac1= 42, in which 10 vortices form along the axis of rotation showing a good overall agreement with the numerical results of Alziary de Roquefort and Grillaud, (1978) and Leng et al, (2014) for the same geometrical parameters.When the Taylor number reaches the critical value, Tac2=59, the cells begin to oscillate in the circumferential direction corresponding to the onset of wavy mode (WVF). Further, the adjacent vortices are not independent and the waves have an S-shape.…”

Section: Fig 3 Various Flow Regimes In the Finite-length Geometrysupporting

confidence: 73%

“…He indicated that the bottom and top ends of the cylinders have significant effects on the flow patterns. Furthermore, Alziary de Roquefort and Grillaud, (1978) have employed a finite difference method to analyze the flow behavior in finite length annulus, Γ=10. They noted that the cellular vortices appear in the vicinity of the mid-plane and that for Re/Rec between 0.97 and 1.17 the vortex intensity increased rapidly.…”

Section: Introductionmentioning

confidence: 99%

On the Onset of Taylor Vortices in Finite-Length Cavity Subject to a Radial Oscillation Motion

Lalaoua

Bouabdallah

2016

JAFM

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Taylor-Couette flow (TCF) is an important template for studying various mechanisms of the laminarturbulent transition of rotating fluid in enclosed cavity. It is also relevant to engineering applications like bearings, fluid mixing and filtration. Furthermore, this flow system is of potential importance for development of bio-separators employing Taylor vortices for enhancement of mass transfer. The fluid flowing in the annular gap between two rotating cylinders has been used as paradigm for the hydrodynamic stability theory and the transition to turbulence. In this paper, the fluid in an annulus between short concentric cylinders is investigated numerically for a three dimensional viscous and incompressible flow. The inner cylinder rotates freely about a vertical axis through its centre while the outer cylinder is held stationary and oscillating radially. The main purpose is to examine the effect of a pulsatile motion of the outer cylinder on the onset of Taylor vortices in the vicinity of the threshold of transition, i.e., from the laminar Couette flow to the occurrence of Taylor vortex flow. The numerical results obtained here show significant topological changes on the Taylor vortices. In addition, the active control deeply affects the occurrence of the first instability. It is established that the appearance of the Taylor vortex flow is then substantially delayed with respect to the classical case; flow without control.

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“…Ekman boundary layers cause the fluid near the boundary to spiral preferentially inwards for any nonzero rotation rate, and the Taylor vortices to develop first in the boundary layer, moving smoothly into the bulk of the fluid as R approaches R c -this has been observed in experiments [9] and in calculations [10]. In the words of Benjamin [7], 'no precise critical value of R exists for the onset of cellular motion'.…”

Section: Introductionmentioning

confidence: 94%

Boundary effects and the onset of Taylor vortices

Rucklidge

Champneys

2004

Physica D: Nonlinear Phenomena

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It is well established that the onset of spatially periodic vortex states in the TaylorCouette flow between rotating cylinders occurs at the value of Reynolds number predicted by local bifurcation theory. However, the symmetry breaking induced by the top and bottom plates means that the true situation should be a disconnected pitchfork. Indeed, experiments have shown that the fold on the disconnected branch can occur at more than double the Reynolds number of onset. This leads to an apparent contradiction: why should Taylor vortices set in so sharply at the Reynolds number predicted by the symmetric theory, given such large symmetry-breaking effects caused by the boundary conditions? This paper offers a generic explanation. The details are worked out using a Swift-Hohenberg pattern formation model that shares the same qualitative features as the Taylor-Couette flow. Onset occurs via a wall mode whose exponential tail penetrates further into the bulk of the domain as the driving parameter increases. In a large domain of length L, we show that the wall mode creates significant amplitude in the centre at parameter values that are O(L −2 ) away from the value of onset in the problem with ideal boundary conditions. We explain this as being due to a Hamiltonian Hopf bifurcation in space, which occurs at the same parameter value as the pitchfork bifurcation of the temporal dynamics. The disconnected anomalous branch remains O(1) away from the onset parameter since it does not arise as a bifurcation from the wall mode.

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Computation of taylor vortex flow by a transient implicit method

Cited by 60 publications

References 14 publications

Taylor–Couette flow with buoyancy: Onset of spiral flow

Taylor–Couette flow with buoyancy: Onset of spiral flow

On the Onset of Taylor Vortices in Finite-Length Cavity Subject to a Radial Oscillation Motion

Boundary effects and the onset of Taylor vortices

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