Time Constants of the Transition between Onset and Decay Reynolds Numbers for the Appearance of Taylor-Couette Flow

AbstractWe numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (${T}^{3} C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$. For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $. An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

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Heat Transfer Enhancement in Axial Taylor-Couette Flow

Heat Transfer: Volume 1 ◽

10.1115/ht2005-72746 ◽

2005 ◽

Cited By ~ 5

Author(s):

S. Gilchrist ◽

C. Y. Ching ◽

D. Ewing

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Nusselt Number ◽

Couette Flow ◽

Reynolds Numbers ◽

Taylor Number ◽

Number Range ◽

Taylor Couette ◽

Number Case ◽

Taylor Couette Flow

An experimental investigation was performed to determine the effect that surface roughness has on the heat transfer in an axial Taylor-Couette flow. The experiments were performed using an inner rotating cylinder in a stationary water jacket for Taylor numbers of 106 to 5×107 and axial Reynolds numbers of 900 to 2100. Experiments were performed for a smooth inner cylinder, a cylinder with two-dimensional rib roughness and a cylinder with three-dimensional cubic protrusions. The heat transfer results for the smooth cylinder were in good agreement with existing experimental data. The change in the Nusselt number was relatively independent of the axial Reynolds number for the cylinder with rib roughness. This result was similar to the smooth wall case but the heat transfer was enhanced by 5% to 40% over the Taylor number range. The Nusselt number for the cylinder with cubic protrusions exhibited an axial Reynolds number dependence. For a low axial Reynolds number of 980, the Nusselt number increased with the Taylor number in a similar way to the other test cylinders. At higher axial Reynolds numbers, the heat transfer was initially independent of the Taylor number before increasing with Taylor number similar to the lower Reynolds number case. In this higher axial Reynolds number case the heat transfer was enhanced by up to 100% at the lowest Taylor number of 1×106 and by approximately 35% at the highest Taylor number of 5×107.

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Turbulent Taylor–Couette Flow at Large Reynolds Numbers*

Journal of Engineering Physics and Thermophysics ◽

10.1007/s10891-016-1488-3 ◽

2016 ◽

Vol 89 (5) ◽

pp. 1247-1254

Author(s):

V. A. Babkin

Keyword(s):

Couette Flow ◽

Reynolds Numbers ◽

Taylor Couette ◽

Taylor Couette Flow

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Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.15 ◽

2018 ◽

Vol 840 ◽

pp. 5-24 ◽

Cited By ~ 6

Author(s):

Junho Park ◽

Paul Billant ◽

Jong-Jin Baik ◽

Jaemyeong Mango Seo

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Couette Flow ◽

Linear Stability Analysis ◽

Reynolds Numbers ◽

Axisymmetric Mode ◽

Stability Threshold ◽

Taylor Couette ◽

The Stability ◽

Taylor Couette Flow

The stably stratified Taylor–Couette flow is investigated experimentally and numerically through linear stability analysis. In the experiments, the stability threshold and flow regimes have been mapped over the ranges of outer and inner Reynolds numbers: $-2000<Re_{o}<2000$ and $0<Re_{i}<3000$, for the radius ratio $r_{i}/r_{o}=0.9$ and the Brunt–Väisälä frequency $N\approx 3.2~\text{rad}~\text{s}^{-1}$. The corresponding Froude numbers $F_{o}$ and $F_{i}$ are always much smaller than unity. Depending on $Re_{o}$ (or equivalently on the angular velocity ratio $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D6FA}_{o}/\unicode[STIX]{x1D6FA}_{i}$), three different regimes have been identified above instability onset: a weakly non-axisymmetric mode with low azimuthal wavenumber $m=O(1)$ is observed for $Re_{o}<0$ ($\unicode[STIX]{x1D707}<0$), a highly non-axisymmetric mode with $m\sim 12$ occurs for $Re_{o}>840$ ($\unicode[STIX]{x1D707}>0.57$) while both modes are present simultaneously in the lower and upper parts of the flow for $0\leqslant Re_{o}\leqslant 840$ ($0\leqslant \unicode[STIX]{x1D707}\leqslant 0.57$). The destabilization of these primary modes and the transition to turbulence as $Re_{i}$ increases have been also studied. The linear stability analysis proves that the weakly non-axisymmetric mode is due to the centrifugal instability while the highly non-axisymmetric mode comes from the strato-rotational instability. These two instabilities can be clearly distinguished because of their distinct dominant azimuthal wavenumber and frequency, in agreement with the recent results of Park et al. (J. Fluid Mech., vol. 822, 2017, pp. 80–108). The stability threshold and the characteristics of the primary modes observed in the experiments are in very good agreement with the numerical predictions. Moreover, we show that the centrifugal and strato-rotational instabilities are observed simultaneously for $0\leqslant Re_{o}\leqslant 840$ in the lower and upper parts of the flow, respectively, because of the variations of the local Reynolds numbers along the vertical due to the salinity gradient.

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Direct numerical simulation of turbulent Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/s0022112007007367 ◽

2007 ◽

Vol 587 ◽

pp. 373-393 ◽

Cited By ~ 99

Author(s):

S. DONG

Keyword(s):

Couette Flow ◽

Dimensional Space ◽

Three Dimensional ◽

Reynolds Numbers ◽

Taylor Vortex ◽

Görtler Vortices ◽

Tilting Angle ◽

Taylor Couette ◽

Gortler Vortices ◽

Taylor Couette Flow

We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Görtler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Görtler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

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Space–time VMS isogeometric analysis of the Taylor–Couette flow

Computational Mechanics ◽

10.1007/s00466-021-02004-6 ◽

2021 ◽

Vol 67 (5) ◽

pp. 1515-1541

Author(s):

Levent Aydinbakar ◽

Kenji Takizawa ◽

Tayfun E. Tezduyar ◽

Takashi Kuraishi

Keyword(s):

Flow Field ◽

Couette Flow ◽

Vortex Flow ◽

Computational Analysis ◽

Reynolds Numbers ◽

High Fidelity ◽

Exact Representation ◽

Taylor Couette ◽

Isogeometric Discretization ◽

Taylor Couette Flow

AbstractThe Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

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Modulated Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/s0022112089002806 ◽

1989 ◽

Vol 208 ◽

pp. 127-160 ◽

Cited By ~ 33

Author(s):

C. F. Barenghi ◽

C. A. Jones

Keyword(s):

Couette Flow ◽

Bifurcation Theory ◽

Modulation Frequency ◽

Low Frequency ◽

Reynolds Numbers ◽

Narrow Gap ◽

Initial Value ◽

Critical Reynolds Numbers ◽

Taylor Couette ◽

Taylor Couette Flow

The onset of instability in temporally modulated Taylor-Couette flow is considered. Critical Reynolds numbers have been found by computing Floquet exponents. We find that frequency modulation of the inner cylinder introduces a small destabilization, in agreement with the narrow-gap theory of Hall and some recent experiments of Ahlers. We review the previous computational literature on this problem, and find a number of contradictory results: the source of these discrepancies is examined, and a satisfactory resolution is achieved. Nonlinear axisymmetric calculations on the modulated problem have been done with an initial value code using a spectral method with collocation. The results are compared satisfactorily with Ahlers' measurements.At low modulation frequency, a large destabilization has been observed in past experiments. We show that this cannot be explained on the basis of perfect bifurcation theory: an analysis of the modulated amplitude equation shows that very small imperfections can substantially affect the behaviour at low frequency by giving rise to ‘transient’ vortices at subcritical Reynolds number. We argue that these ‘transient’ vortices are the source of the large destabilization seen in some experiments. Modelling the imperfections in the initial-value code provides additional confirmation of this effect.

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Optimal Taylor–Couette flow: radius ratio dependence

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.134 ◽

2014 ◽

Vol 747 ◽

pp. 1-29 ◽

Cited By ~ 29

Author(s):

Rodolfo Ostilla-Mónico ◽

Sander G. Huisman ◽

Tim J. G. Jannink ◽

Dennis P. M. Van Gils ◽

Roberto Verzicco ◽

...

Keyword(s):

Couette Flow ◽

Scaling Laws ◽

Reynolds Numbers ◽

Radius Ratio ◽

System Response ◽

Rossby Number ◽

Theoretical Predictions ◽

Taylor Couette ◽

Set Up ◽

Taylor Couette Flow

AbstractTaylor–Couette flow with independently rotating inner ($i$) and outer ($o$) cylinders is explored numerically and experimentally to determine the effects of the radius ratio $\eta $ on the system response. Numerical simulations reach Reynolds numbers of up to $\mathit{Re}_i=9.5\times 10^3$ and $\mathit{Re}_o=5\times 10^3$, corresponding to Taylor numbers of up to $\mathit{Ta}=10^8$ for four different radius ratios $\eta =r_i/r_o$ between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ($\mathrm{T^3C}$) set-up, reach Reynolds numbers of up to $\mathit{Re}_i=2\times 10^6$ and $\mathit{Re}_o=1.5\times 10^6$, corresponding to $\mathit{Ta}=5\times 10^{12}$ for $\eta =0.714\mbox{--}0.909$. Effective scaling laws for the torque $J^{\omega }(\mathit{Ta})$ are found, which for sufficiently large driving $\mathit{Ta}$ are independent of the radius ratio $\eta $. As previously reported for $\eta =0.714$, optimum transport at a non-zero Rossby number $\mathit{Ro}=r_i |\omega _i-\omega _o |/[2(r_o-r_i)\omega _o]$ is found in both experiments and numerics. Here $\mathit{Ro}_{opt}$ is found to depend on the radius ratio and the driving of the system. At a driving in the range between $\mathit{Ta}\sim 3\times 10^{8}$ and $\mathit{Ta}\sim 10^{10}$, $\mathit{Ro}_{opt}$ saturates to an asymptotic $\eta $-dependent value. Theoretical predictions for the asymptotic value of $\mathit{Ro}_{opt}$ 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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