Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals

Hoffmann, Christian; Altmeyer, Sebastian; Pinter, A.; Lücke, M.

doi:10.1088/1367-2630/11/5/053002

Cited by 34 publications

(35 citation statements)

References 20 publications

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“…An example of the strong end effects in Taylor-Couette systems is found by comparing the transition between Taylor and spiral vortices when axially periodic [48] and physical no-slip boundary conditions [49] are used. It is expected that end effects will decrease with the increase of , although they will influence the dynamics even in systems with very large [34,50].…”

Section: Discussionmentioning

confidence: 99%

Dynamics of axially localized states in Taylor-Couette flows

Lopez

Marqués

2015

Phys. Rev. E

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We present numerical simulations of the flow confined in a wide gap Taylor-Couette system, with a rotating inner cylinder and variable length-to-gap aspect ratio. A complex experimental bifurcation scenario differing from the classical Ruelle-Takens route to chaos has been experimentally reported in this geometry. The wavy vortex flow becomes quasiperiodic due to an axisymmetric very low frequency mode. This mode plays a key role in the dynamics of the system, leading to the occurrence of chaos via a period-doubling scenario. Further increasing the rotation of the inner cylinder results in the appearance of a new flow pattern which is characterized by large amplitude oscillations localized in some of the vortex pairs. The purpose of this paper is to study numerically the dynamics of these axially localized states, paying special attention to the transition to chaos. Frequency analysis from time series simultaneously recorded at several points has been applied in order to identify the flow transitions taking place. It has been found that the very low frequency mode is essential to explain the behavior associated with the different transitions towards chaos including localized states.

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Section: Discussionmentioning

confidence: 99%

Dynamics of axially localized states in Taylor-Couette flows

Lopez

Marqués

2015

Phys. Rev. E

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“…In his groundbreaking paper on Newtonian fluids in 1923, Taylor showed that when the angular velocity of the inner cylinder is increased above a certain threshold, (Taylor number), the Couette flow becomes unstable and a secondary steady state characterized by axisymmetric toroidal vortices, known as Taylor vortex flow (TVF), emerges [1]. Subsequently increasing the angular speed of the cylinder the system undergoes a progression of instabilities which lead to states with greater spatio-temporal complexity, such as wavy vortex flow and spiral vortex flow [2,3]. The TCF at low angular velocities, remains steady and purely azimuthal known as circular Couette flow (CCF).…”

Section: Introductionmentioning

confidence: 99%

“…A comprehensive glossary of dynamic situations of the flow of the Newtonian fluids between coaxial cylinders is recently collected by Hoffmann et al both theoretically and experimentally [3]. The exchange of stability based on the variation of a control parameter among the known flows, i.e., CCF, TVF, SPI (spiral TVF), wavy vortex flow (WVF), and wavy spiral vortex flow (WSPI) are explained in their work.…”

Section: Introductionmentioning

confidence: 99%

“…The pseudoplastic model adopted here has proved to be a good representative of the nonlinear fluid [12]. As for the truncation level, a similar approach taken in [2,3,6,9,14] is adopted in the Fourier representation for the flow field in the present study. Such levels of truncation have also been historically and widely used for the conservation, Navier-Stokes and energy equations (see, for example, [22][23][24]).…”

Section: Introductionmentioning

confidence: 99%

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Flow pattern and stability of pseudoplastic axial Taylor–Couette flow

Ashrafi

Hazbavi

2012

International Journal of Non-Linear Mechanics

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“…A comprehensive glossary of dynamic situations of the flow of the Newtonian fluids between coaxial cylinders is recently collected by Hoffmann et al both theoretically and experimentally [4]. The exchange of stability based on the variation of a control parameter among known flows i.e., CCF, TVF, SPI (spiral TVF), wavy vortex flow (WVF), and wavy spiral vortex flow (WSPI) is explained in their work.…”

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confidence: 99%

Order in chaotic pseudoplastic flow between coaxial cylinders

Ashrafi

2011

Arch Appl Mech

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Order is found within the chaotic nonlinear flow between rotating coaxial cylinders. The flow stability analysis is carried out for a pseudoplastic fluid through bifurcation diagram and Lyapunov exponent histogram. The fluid is assumed to follow the Carreau-Bird model, and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear-thinning effects increase. The emergence of the vortices corresponds to the onset of a supercritical bifurcation, which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram. 810 N. Ashrafi range of excited spatio-temporal scales. In order to assess the effect of the smaller length scales on the flow, a high resolution of the flow field is needed. It is by now well established that low-order dynamical systems can be a viable alternative to conventional numerical methods for the linear and nonlinear flows [2,3]. Despite the severe degree of truncation in the formulation of these models, some of the basic qualitative elements of the onset of Taylor vortices and destabilization of the cellular structure can be recovered using low-order dynamical systems.A number of studies have been directed on the issue of CCF of Newtonian fluids in the finite gaps between rotating cylinders. A comprehensive glossary of dynamic situations of the flow of the Newtonian fluids between coaxial cylinders is recently collected by Hoffmann et al both theoretically and experimentally [4]. The exchange of stability based on the variation of a control parameter among known flows i.e., CCF, TVF, SPI (spiral TVF), wavy vortex flow (WVF), and wavy spiral vortex flow (WSPI) is explained in their work. It is resulted that the wavy structures appearing via a secondary bifurcation out of Taylor vortex flow and out of spiral vortex flow, respectively, mediate transitions between Taylor and spiral vortices and vice versa. Many of these findings are also predictable by the low-dimensional approach taken in the present study, for the case of non-Newtonian flows. This approach was originally used in the seminal work of Lorenz to investigate the stability of Rayleigh-Bernard convection problem [5]. Later, Kuhlmann [3] extended the method to the TVF of Newtonian fluids in the narrow gap, followed by the work of Berger [6] to cover finite gaps and Ashrafi and Khayat for the narrow gap flow of weakly shear-thinning fluids [2].Flow computations of nonlinear fluid flows, especially the TVF, require extra ca...

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Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals

Cited by 34 publications

References 20 publications

Dynamics of axially localized states in Taylor-Couette flows

Dynamics of axially localized states in Taylor-Couette flows

Flow pattern and stability of pseudoplastic axial Taylor–Couette flow

Order in chaotic pseudoplastic flow between coaxial cylinders

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