Bifurcation phenomena in Taylor-Couette flow in a very short annulus

Pfister, G.; Schmidt, Heiko; Cliffe, K. A.; Mullin, T.

doi:10.1017/s0022112088001491

Cited by 85 publications

(77 citation statements)

References 19 publications

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“…Instabilities (Swinney & Gollub 1981;Pfister & Rehberg 1981;Pfister et al 1988;Chandrasekhar 1981;Drazin & Reid 1981;Busse 1967), nonlinear dynamics and chaos (Lorenz 1963;Ahlers 1974;Behringer 1985;Dominguez-Lerma et al 1986;Strogatz 1994), pattern formation (Andereck et al 1986;Cross & Hohenberg 1993;Bodenschatz et al 2000), and turbulence (Siggia 1994;Grossmann & Lohse 2000;Kadanoff 2001;Lathrop et al 1992b;Ahlers et al 2009;Lohse & Xia 2010) have been studied in both TC and RB and both numerically and experimentally. The main reasons behind the popularity of these systems are, in addition to the fact that they are closed systems, as mentioned previously, their simplicity due to the high amount of symmetries present.…”

Section: Optimal Taylor-couette Flow: Radius Ratio Dependencementioning

confidence: 99%

Optimal Taylor–Couette flow: radius ratio dependence

et al. 2014

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Taylor-Couette flow with independently rotating inner (i) & outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Re i = 9.5 · 10 3 and Re o = 5 · 10 3 , corresponding to Taylor numbers of up to T a = 10 8 for four different radius ratios η = r i /r o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T 3 C) setup, reach Reynolds numbers of up to Re i = 2 · 10 6 and Re o = 1.5 · 10 6 , corresponding to T a = 5 · 10 12 for η = 0.714−0.909. Effective scaling laws for the torque J ω (T a) are found, which for sufficiently large driving T a are independent of the radius ratio η. As previously reported for η = 0.714, optimum transport at a non-zero Rossby number Ro = r i |ω i − ω o |/[2(r o − r i )ω o ] is found in both experiments and numerics. Ro opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between T a ∼ 3 · 10 8 and T a ∼ 10 10 , Ro opt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Ro opt are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

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Section: Optimal Taylor-couette Flow: Radius Ratio Dependencementioning

confidence: 99%

Optimal Taylor–Couette flow: radius ratio dependence

et al. 2014

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“…Since the pioneering work by Benjamin [7,8,9], TCI in finite size cylinders have been studied in detail with stationary outer cylinders [10,11,12,13,14,15,16,17,18,19,20], and with rotating outer cylinders [21]. In our TCI-stable flows, the outer cylinder must rotate.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Investigation of Circulation in Short Cylinders

Kageyama

Goodman

et al. 2004

J. Phys. Soc. Jpn.

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In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at Re ≤ 3200 agrees remarkably well with experiment at Re ∼ 10 6 . This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings.

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“…Furthermore, the flow behavior in the short cylinders has been the subject of numerous theoretical, experimental and numerical studies (Hall, (1982); Lücke et al, (1984); Aitta et al, (1985); Heinrichs et al,(1986); Pfister et al, (1988); Nakamura et al,(1990Nakamura et al,( , 1989; Cliffe et al, (1992); Toya et al, (1994); Linek and Ahlers, (1998); Mullin et al, (2002); Czarny et al, (2002); Furusawa et al, (2002); , Lopez and Marques, (2003); Watanabe and Toya, 2012)). Recently, Deng et al, (2009) presented an experimental and numerical study on the onset of Taylor vortices in short cylinders with an aspect ratio of 5.17.…”

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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Bifurcation phenomena in Taylor-Couette flow in a very short annulus

Cited by 85 publications

References 19 publications

Optimal Taylor–Couette flow: radius ratio dependence

Optimal Taylor–Couette flow: radius ratio dependence

Numerical and Experimental Investigation of Circulation in Short Cylinders

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

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