A non-linear dynamical system approach to finite amplitude Taylor-Vortex flow of shear-thinning fluids

2004 ◽  
Vol 45 (3) ◽  
pp. 321-340 ◽  
Author(s):  
Zhenyu Li ◽  
Roger E. Khayat
Keyword(s):  
Dynamical System ◽  
System Approach ◽  
Vortex Flow ◽  
Shear Thinning ◽  
Finite Amplitude ◽  
Taylor Vortex ◽  
Linear Dynamical System ◽  
Dynamical System Approach ◽  
Shear Thinning Fluids ◽  
Taylor Vortex Flow

scholarly journals Taylor-vortex flow in shear-thinning fluids

2019 ◽  
Vol 100 (2) ◽  
Author(s):  
S. Topayev ◽  
C. Nouar ◽  
D. Bernardin ◽  
A. Neveu ◽  
S. A. Bahrani
Keyword(s):  
Vortex Flow ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Thinning Fluids ◽  
Taylor Vortex Flow

scholarly journals Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

2021 ◽  
Vol 933 ◽  
Author(s):  
S. Topayev ◽  
C. Nouar ◽  
J. Dusek
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Vortex Flow ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Thinning Fluids ◽  
Taylor Vortex Flow ◽  
Viscous Shear ◽  
Taylor Couette ◽  
Shear Thinning Fluid

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is $\eta = R_1/R_2=0.4$ . The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at ${Re} = 5.28 \, {Re}_c$ . At ${Re} = 6.9 \, {Re}_c$ , the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

On wavy instabilities of the Taylor-vortex flow between corotating cylinders

1988 ◽  
Vol 188 ◽  
pp. 585-598 ◽  
Author(s):  
Masato Nagata
Keyword(s):  
Vortex Flow ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Taylor Vortex ◽  
Axisymmetric Solution ◽  
Boundary Flow ◽  
Taylor Vortex Flow ◽  
Average Rotation ◽  
The One ◽  
Outflow Boundary

At least four wavy instabilities are found numerically by analysing the linear stability of Taylor-vortex flow (TVF) in the limit of a small gap between two concentric cylinders which rotate differentially in the same direction. Two of the wavy instabilities, including the one leading to conventional wavy vortex (WVF), have the same axial wavelength as TVF at the onset of instability, while the other two are characterized by subharmonic modes with axial wavelengths twice as long as those of TVF. The two subharmonic instabilities appear to correspond to the wavy-inflow-boundary flow (WIB) and the wavy-outflow-boundary flow (WOB) observed in the experiment of Andereck, Liu & Swinney (1986). The phase velocities, measured in the rotating frame of reference, of all the wavy instabilities are non-zero at the onset except that the phase velocity of WVF vanishes in the region where the average rotation rate Ω of the cylinders is small. By using this simple bifurcation property of WVF for small Ω, time-independent finite-amplitude non-axisymmetric solution branches bifurcating from TVF are followed numerically. The most interesting findings are that some of the solution branches cross the line Ω = 0, producing three-dimensional nonlinear solutions in plane Couette flow.

Finite-amplitude Taylor-vortex flow of viscoelastic fluids

1999 ◽  
Vol 400 ◽  
pp. 33-58 ◽  
Author(s):  
ROGER E. KHAYAT
Keyword(s):  
Vortex Flow ◽  
Axisymmetric Flow ◽  
Viscoelastic Fluids ◽  
Axial Direction ◽  
Finite Amplitude ◽  
Dynamical Behaviour ◽  
Galerkin Projection ◽  
Taylor Vortex ◽  
Fluid Elasticity ◽  
Taylor Vortex Flow

The influence of inertia and elasticity on the onset and stability of Taylor-vortex flow (TVF) is examined for an Oldroyd-B fluid. The Galerkin projection method is used to obtain the departure from Couette flow (CF). Only axisymmetric flow is examined. The solution is capable of capturing the dynamical behaviour observed experimentally for viscoelastic fluids in the inertio-elastic and purely elastic ranges. For flow with dominant inertia, the bifurcation picture is similar to that for a Newtonian fluid. However, transition from CF to TVF is oscillatory because of fluid elasticity. Steady TVF sets in, via supercritical bifurcation, as Re reaches a critical value, Rec. The critical Reynolds number decreases with fluid elasticity, and is strongly influenced by fluid retardation. As elasticity exceeds a critical level, a subcritical bifurcation emerges at Rec, similar to that predicted by the Landau–Ginzburg equation. It is found that slip along the axial direction tends to be generally destabilizing. The coherence of the formulation is established under steady and transient conditions through comparison with exact linear stability analysis, experimental measurements, and flow visualization. Good agreement is obtained between theory and the measurements of Muller et al. (1993) in the limit of purely elastic overstable TVF.

Centrifugal instabilities of circumferential flows in finite cylinders: nonlinear theory

1980 ◽  
Vol 372 (1750) ◽  
pp. 317-356 ◽  
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Perturbation Expansion ◽  
Direct Consequence ◽  
Finite Amplitude ◽  
Taylor Vortex ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
Axisymmetric Disturbances ◽  
Finite Cylinders

In an earlier paper, Blennerhassett & Hall (1979) investigated the linear stability of the flow between concentric cylinders of finite length. The inner cylinder was taken to rotate, while the outer cylinder was fixed. Furthermore, the end walls rotated such that the flow was purely circumferential. In this paper the finite amplitude development of the unstable disturbances to the flow is considered. It is found that the usual perturbation expansion of nonlinear stability theory must be modified if the cylinders are not infinitely long. The bifurcation to a Taylor vortex flow in finite cylinders is shown to be two-sided. The latter effect is shown to be a direct consequence of the finiteness of the cylinders and by taking the cylinders to be very long, we recover the results obtained previously for the infinite problem. The interaction of the two most dangerous modes of linear theory is also investigated. For certain values of the length of the cylinders the initial finite amplitude Taylor vortex flow is shown to become unstable to another class of axisymmetric disturbances. The effect of perturbing the end conditions towards the no-slip conditions appropriate to most experimental configurations is also discussed. Some discussion of the instability problem in very long cylinders with fixed ends is given.

Taylor-Vortex Flow: A Dynamical System

SIAM Review ◽  
1986 ◽  
Vol 28 (3) ◽  
pp. 315-342 ◽  
Author(s):  
J. T. Stuart
Keyword(s):  
Dynamical System ◽  
Vortex Flow ◽  
Taylor Vortex ◽  
Taylor Vortex Flow

Non-linear dynamical system approach to behavior modeling

1999 ◽  
Vol 15 (7-8) ◽  
pp. 349-364 ◽  
Author(s):  
Siome Goldenstein ◽  
Edward Large ◽  
Dimitris Metaxas
Keyword(s):  
Dynamical System ◽  
System Approach ◽  
Behavior Modeling ◽  
Linear Dynamical System ◽  
Dynamical System Approach ◽  
Non Linear

Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach

1995 ◽  
Vol 38 (2) ◽  
pp. 121-129 ◽  
Author(s):  
J.L. Hernández ◽  
R. Biscay ◽  
J.C. Jimenez ◽  
P. Valdes ◽  
R.Grave de Peralta
Keyword(s):  
Dynamical System ◽  
System Approach ◽  
Linear Dynamical System ◽  
Dynamical System Approach ◽  
Non Linear ◽  
Eeg Recordings
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