scholarly journals Taylor–Couette turbulence at radius ratio : scaling, flow structures and plumes

2016 ◽  
Vol 799 ◽  
pp. 334-351 ◽  
Author(s):  
Roeland C. A. van der Veen ◽  
Sander G. Huisman ◽  
Sebastian Merbold ◽  
Uwe Harlander ◽  
Christoph Egbers ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Velocity Profiles ◽  
Radius Ratio ◽  
Taylor Number ◽  
Turbulent Regime ◽  
Counter Rotation ◽  
Taylor Couette ◽  
Cylinder Rotation

Using high-resolution particle image velocimetry, we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor–Couette flow for a radius ratio of 0.5 and Taylor number of up to $6.2\times 10^{9}$. The extracted angular velocity profiles follow a log law more closely than the azimuthal velocity profiles due to the strong curvature of this ${\it\eta}=0.5$ set-up. The scaling of the wind Reynolds number with the Taylor number agrees with the theoretically predicted $3/7$ scaling for the classical turbulent regime, which is much more pronounced than for the well-explored ${\it\eta}=0.71$ case, for which the ultimate regime sets in at much lower Taylor number. By measuring at varying axial positions, roll structures are found for counter-rotation while no clear coherent structures are seen for pure inner cylinder rotation. In addition, turbulent plumes coming from the inner and outer cylinders are investigated. For pure inner cylinder rotation, the plumes in the radial velocity move away from the inner cylinder, while the plumes in the azimuthal velocity mainly move away from the outer cylinder. For counter-rotation, the mean radial flow in the roll structures strongly affects the direction and intensity of the turbulent plumes. Furthermore, it is experimentally confirmed that, in regions where plumes are emitted, boundary layer profiles with a logarithmic signature are created.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

scholarly journals Azimuthal velocity profiles in Rayleigh-stable Taylor–Couette flow and implied axial angular momentum transport

2015 ◽  
Vol 774 ◽  
pp. 342-362 ◽  
Author(s):  
Freja Nordsiek ◽  
Sander G. Huisman ◽  
Roeland C. A. van der Veen ◽  
Chao Sun ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Velocity Profiles ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Angular Momentum Transport ◽  
Taylor Couette ◽  
Taylor Couette Flow

We present azimuthal velocity profiles measured in a Taylor–Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of ${\it\eta}=0.716$, an aspect ratio of ${\it\Gamma}=11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. This regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $\mathit{Re}_{S}\sim O(10^{5})$, for both ${\it\Omega}_{i}>{\it\Omega}_{o}>0$ (quasi-Keplerian regime) and ${\it\Omega}_{o}>{\it\Omega}_{i}>0$ (sub-rotating regime), where ${\it\Omega}_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles match the non-vortical laminar Taylor–Couette profile. The deviation from that profile increases as solid-body rotation is approached at fixed $\mathit{Re}_{S}$. Flow super-rotation, an angular velocity greater than those of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that are larger than the torques for the case of laminar Taylor–Couette flow. The quasi-Keplerian profiles are composed of a well-mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor–Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.

Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor–Couette flow

2017 ◽  
Vol 831 ◽  
pp. 330-357 ◽  
Author(s):  
A. Froitzheim ◽  
S. Merbold ◽  
C. Egbers
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Cylinder Wall ◽  
Taylor Vortices ◽  
Wide Gap ◽  
Taylor Couette ◽  
Taylor Couette Flow

Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.

scholarly journals Optimal Taylor–Couette flow: direct numerical simulations

2013 ◽  
Vol 719 ◽  
pp. 14-46 ◽  
Author(s):  
Rodolfo Ostilla ◽  
Richard J. A. M. Stevens ◽  
Siegfried Grossmann ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Angular Velocity ◽  
Couette Flow ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Experimental Result ◽  
Counter Rotation ◽  
Taylor Couette ◽  
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.

scholarly journals Turbulence decay towards the linearly stable regime of Taylor–Couette flow

2014 ◽  
Vol 748 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Reynolds Number ◽  
Accretion Disks ◽  
Outer Cylinder ◽  
Flow State ◽  
Initial State ◽  
Stable Regime ◽  
Turbulence Decay ◽  
Taylor Couette ◽  
Cylinder Rotation ◽  
Damped Oscillator

AbstractTaylor–Couette (TC) flow is used to probe the hydrodynamical (HD) stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC flow are in conflict about the existence of turbulence (cf. Ji et al. (Nature, vol. 444, 2006, pp. 343–346) and Paoletti et al. (Astron. Astroph., vol. 547, 2012, A64)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of subcritical transitions to turbulence when no end plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \lesssim 10^5$ and the radius ratio is $\eta =0.714$. The stabilization causes the system to behave as a damped oscillator and, correspondingly, the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay.

scholarly journals Exploring the phase diagram of fully turbulent Taylor–Couette flow

2014 ◽  
Vol 761 ◽  
pp. 1-26 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Phase Diagram ◽  
Reynolds Number ◽  
Couette Flow ◽  
Parameter Space ◽  
Coriolis Force ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Aspect Ratios ◽  
Cylinder Rotation

AbstractDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.

Heat Transfer Enhancement in Axial Taylor-Couette Flow

2005 ◽  
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.

scholarly journals Periodically driven Taylor–Couette turbulence

2018 ◽  
Vol 846 ◽  
pp. 834-845 ◽  
Author(s):  
Ruben A. Verschoof ◽  
Arne K. te Nijenhuis ◽  
Sander G. Huisman ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Phase Delay ◽  
Amplitude Response ◽  
Numerical Work ◽  
Periodically Driven ◽  
Wide Range ◽  
Rest Time ◽  
Taylor Couette ◽  
The Given

We study periodically driven Taylor–Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_{i}=5\times 10^{5}$). Using particle image velocimetry, we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15\leqslant Wo\leqslant 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal velocity. In agreement with earlier theoretical and numerical work, we find that for large modulation periods the system follows the given modulation of the driving, i.e. the behaviour of the system is quasi-stationary. For smaller modulation periods, the flow cannot follow the modulation, and the flow velocity responds with a phase delay and a smaller amplitude response to the given modulation. If we compare our results with numerical and theoretical results for the laminar case, we find that the scalings of the phase delay and the amplitude response are similar. However, the local response in the bulk of the flow is independent of the distance to the modulated boundary. Apparently, the turbulent mixing is strong enough to prevent the flow from having radius-dependent responses to the given modulation.

scholarly journals Turbulence strength in ultimate Taylor–Couette turbulence

2017 ◽  
Vol 836 ◽  
pp. 397-412 ◽  
Author(s):  
Rodrigo Ezeta ◽  
Sander G. Huisman ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Field Measurements ◽  
Azimuthal Velocity ◽  
Energy Dissipation Rate ◽  
Local Flow ◽  
Kolmogorov Length Scale ◽  
Taylor’S Hypothesis ◽  
Taylor Couette

We provide experimental measurements for the effective scaling of the Taylor–Reynolds number within the bulk $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number $\mathit{Ta}$), in the ultimate regime of Taylor–Couette flow. We define $Re_{\unicode[STIX]{x1D706},bulk}=(\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}}))^{2}(15/(\unicode[STIX]{x1D708}\unicode[STIX]{x1D716}_{bulk}))^{1/2}$, where $\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}})$ is the bulk-averaged standard deviation of the azimuthal velocity, $\unicode[STIX]{x1D716}_{bulk}$ is the bulk-averaged local dissipation rate and $\unicode[STIX]{x1D708}$ is the liquid kinematic viscosity. The data are obtained through flow velocity field measurements using particle image velocimetry. We estimate the value of the local dissipation rate $\unicode[STIX]{x1D716}(r)$ using the scaling of the second-order velocity structure functions in the longitudinal and transverse directions within the inertial range – without invoking Taylor’s hypothesis. We find an effective scaling of $\unicode[STIX]{x1D716}_{\mathit{bulk}}/(\unicode[STIX]{x1D708}^{3}d^{-4})\sim \mathit{Ta}^{1.40}$, (corresponding to $\mathit{Nu}_{\unicode[STIX]{x1D714},\mathit{bulk}}\sim \mathit{Ta}^{0.40}$ for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.40}$) and direct numerical simulations ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.38}$). The resulting Kolmogorov length scale is then found to scale as $\unicode[STIX]{x1D702}_{\mathit{bulk}}/d\sim \mathit{Ta}^{-0.35}$ and the turbulence intensity as $I_{\unicode[STIX]{x1D703},\mathit{bulk}}\sim \mathit{Ta}^{-0.061}$. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor–Reynolds number effectively scales as $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}\sim \mathit{Ta}^{0.18}$ in the present parameter regime of $4.0\times 10^{8}<\mathit{Ta}<9.0\times 10^{10}$.

scholarly journals Flow characteristics analysis of a two-phase suspension between rotating porous cylinders with radial and axial flows

2018 ◽  
Vol 22 (4) ◽  
pp. 1857-1864
Author(s):  
Yu-Chuan Zhu ◽  
Qing-He Xiao ◽  
Ming-Xin Gao ◽  
Qian Liu ◽  
Zhanhong Wan
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Radial Flow ◽  
Outer Cylinder ◽  
Flow Characteristics ◽  
Axial Flow ◽  
Taylor Number ◽  
Two Phase ◽  
Characteristics Analysis ◽  
Correlation Parameters

The flow characteristics problem of the two-phase suspension in the design of filters is presented, and the hydrodynamic stability is carried out to study the flow characteristics of a two-phase suspension between a rotating porous inner cylinder and a concentric, stationary, porous outer cylinder when radial flow and axial flow are present. Linear stability analysis results in an eigenvalue problem that is solved numerically by Wan?s method. The results reveal that the critical Taylor number for the onset of instability is altered by other parameters. For given correlation parameters, increasing the axial Reynolds number increases the critical Taylor number for transition very slightly, the critical Taylor number decreases as the axial Reynolds number becomes negative.

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