Stability of Rotating Couette Flow. II. Comparison with Numerical Results

Snyder, Howard A.

doi:10.1063/1.1692167

Cited by 35 publications

(28 citation statements)

References 11 publications

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“…The relative gap width is h/R 1 =0.1343 Fig.6 Comparison of the theory with the experimental data for the instability condition of TaylorCouette flow 's experiments, R1=6.023 cm, R2=6.281 cm). The data are taken from his Table III [12]. The relative gap width is h/R 1 =0.0428.…”

Section: Resultsmentioning

confidence: 99%

Instability of Taylor–Couette flow between concentric rotating cylinders

Dou

Khoo

Yeo

2008

International Journal of Thermal Sciences

114

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The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. This theory has been strictly derived in our previous works.In our previous studies, the energy gradient theory was demonstrated to be applicable for wallbounded parallel flows. It was found that the critical value of the energy gradient parameter K max at subcritical transition is about 370-389 for wall-bounded parallel flows (which include plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which no turbulence occurs.In this paper, the detailed derivation for the calculation of the energy gradient parameter in the flow between concentric rotating cylinders is provided. The theoretical results for the critical condition of primary instability obtained are in very good agreement with the experiments found in literature. The mechanism of spiral turbulence generation for counter-rotation of two cylinders is also explained using the energy gradient theory. The energy gradient theory can also serve to relate the condition of transition in Taylor-Couette flow to that in plane Couette flow. The latter reasonably becomes the limiting case of the former when the radii of cylinders tend to infinity. It is our contention that the energy gradient theory is possibly universal for analysis of flow instability and turbulent transition, and is valid for both pressure and shear driven flows in both parallel and rotating flow configurations.

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Section: Resultsmentioning

confidence: 99%

Instability of Taylor–Couette flow between concentric rotating cylinders

Dou

Khoo

Yeo

2008

International Journal of Thermal Sciences

114

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“…It would be interesting to conduct systematic studies of the variation of Γ onto the stability and transport properties. The influence of Γ onto the instability threshold, in the case of outer cylinder at rest has been computed by Chandrasekhar [28], Snyder [23]. This is illustrated in Fig.…”

Section: E Influence Of Aspect Ratiomentioning

confidence: 98%

“…The viscosity damps the instability until Re > R c (R Ω , η), corresponding to the transition from the laminar flow to the so-called Taylor vortices flow. Figure 3 displays the numerical data by Snyder [23], providing the stability threshold R c as a function of R Ω for three gap size (η = 0.935, 0.8, 0.2), and illustrates the influence of the curvature on the instability threshold. The experimental data of Prigent et al [18], at η = 0.983 is also reported.…”

Section: Stability Propertiesmentioning

confidence: 99%

Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

et al. 2005

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This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the detailed analysis of the experimental data obtained in several studies of the transition to turbulence and turbulent transport in Taylor-Couette flow. We first introduce a new set of control parameters, based on dynamical rather than geometrical considerations, so that the analysis applies more naturally to rotating shear flows in general and not only to Taylor-Couette flow. We then investigate the transition thresholds in the supercritical and the subcritical regime in order to extract their general dependencies on the control parameters. The inspection of the mean profiles provides us with some general hints on the mean to laminar shear ratio. Then the examination of the torque data allows us to propose a decomposition of the torque dependence on the control parameters in two terms, one completely given by measurements in the case where the outer cylinder is at rest, the other one being a universal function provided here from experimental fits. As a result, we obtain a general expression for the turbulent viscosity and compare it to existing prescription in the literature. Finally, throughout all the paper we discuss the influence of additional effects such as stratification or magnetic fields.

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“…When the constraint that the outer cylinder is stationary (i.e. Re o = 0) is relaxed, the value of Re o plays an important role on Re c (Taylor 1923;Donnelly & Fultz 1960;Coles 1965;Snyder 1968;Andereck et al 1986) as well as on higher order instabilities. A very different behaviour is observed in the co-and counter-rotational regimes, corresponding to Re o > 0 and Re o < 0, respectively.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows

Dutcher

Müller

2009

J. Fluid Mech.

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Spatial and temporal frequency dynamics were experimentally tracked via flow visualization for Newtonian fluids as a function of the inner cylinder Reynolds number (Rei) in the flow between concentric, independently rotating cylinders with a radius ratio of 0.912 and an aspect ratio of 60.7. Eight transitions from laminar to turbulent flow were characterized in detail for a stationary outer cylinder, producing highly resolved space–time and frequency–time plots for wavy, modulated and weakly turbulent states. A previously unreported early-modulated wavy vortex flow was found in our high aspect ratio geometry both with and without the presence of a dislocation. The envelope of stability for this flow state was shown to cross into the co-rotating regime, and is present up to Reo ~ 60, where Reo is the outer cylinder Reynolds number. This early modulation is independent of acceleration in the range 0.18 < dRei/dτ < 2.9, where τ is the time nondimensionalized with a viscous time scale. While many of the flow states have been previously observed in geometries with somewhat different radius ratios, we provide new characterization of transitional structures for Reo = 0 in the range 0 < Re* < 21.4, where Re* = Rei/Rec and Rec is the value of Rei at the primary instability. Special attention has been given to ramp rate. For quasi-static ramps, axisymmetric states are stable over the ranges of Re* = [(0–1.17), > 15.4], states characterized by a single distinct temporal frequency for Re* = [(1.17–1.41), (3.56–5.20), (7.85–15.4)], states with multiple temporal frequencies for Re* = [(1.41–3.56), (5.20–7.85)], and a transition from laminar to weakly turbulent vortices occurs at Re* = 5.49. All flow states are characterized by symmetry/symmetry-breaking features as well as azimuthal and axial wavenumbers.

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Stability of Rotating Couette Flow. II. Comparison with Numerical Results

Cited by 35 publications

References 11 publications

Instability of Taylor–Couette flow between concentric rotating cylinders

Instability of Taylor–Couette flow between concentric rotating cylinders

Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows

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