Velocity profiles, flow structures and scalings in a wide-gap turbulent 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.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.275 ◽

2015 ◽

Vol 774 ◽

pp. 342-362 ◽

Cited By ~ 8

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.

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Fine Scale Structure of High Reynolds Number Taylor-Couette Flow

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2007-37172 ◽

2007 ◽

Author(s):

W. He ◽

M. Tanahashi ◽

T. Miyauchi

Keyword(s):

Reynolds Number ◽

Couette Flow ◽

High Reynolds Number ◽

Flow Fields ◽

Fine Scale ◽

Azimuthal Direction ◽

Taylor Vortices ◽

Taylor Couette ◽

High Reynolds ◽

Taylor Couette Flow

Direct numerical simulation (DNS) has been conducted to investigate turbulence transition process and fine scale structures in Taylor-Couette flow. Fourier-Chebyshev spectral methods have been used for spatial discretization and DNS are conducted up to Re = 12000. With the increase of Reynolds number, fine scale eddies are formed in a stepwise fashion. In relatively weak turbulent Taylor-Couette flow, fine scale eddies elongated in the azimuthal direction appear near the outflow and inflow boundaries between Taylor vortices. These fine scale eddies in the outflow and inflow boundaries are inclined at about −45/135 degree with respect to the azimuthal direction. With the increase of Reynolds number, the number of fine scale eddies increases and fine scale eddies appear in whole flow fields. The Taylor vortices in high Reynolds number organize lots of fine scale eddies. In high Reynolds number Taylor-Couette flow, fine scale eddies parallel to the axial direction are formed in sweep regions between large scale Taylor vortices. The most expected diameter and maximum azimuthal velocity of coherent fine scale eddies are 8 times of Kolmogorov scale and 1.7 times of Kolmogorov velocity respectively for high Reynolds Taylor-Couette flow. This scaling law coincides with that in other turbulent flow fields.

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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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Delaying transition in Taylor–Couette flow with axial motion of the inner cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112097006630 ◽

1997 ◽

Vol 348 ◽

pp. 141-151 ◽

Cited By ~ 19

Author(s):

AREL Y. WEISBERG ◽

IOANNIS G. KEVREKIDIS ◽

ALEXANDER J. SMITS

Keyword(s):

Couette Flow ◽

Outer Cylinder ◽

Stability Diagram ◽

Base Flow ◽

Marginal Stability ◽

Axial Motion ◽

Taylor Vortices ◽

Experimental Apparatus ◽

Taylor Couette ◽

Taylor Couette Flow

Periodic axial motion of the inner cylinder in Taylor–Couette flow is used to delay transition to Taylor vortices. The outer cylinder is fixed. The marginal stability diagram of Taylor–Couette flow with simultaneous periodic axial motion of the inner cylinder is determined using flow visualization. For the range of parameters studied, the degree of enhanced stability is found to be greater than that predicted by Hu & Kelly (1995), and differences in the scaling with axial Reynolds number are found. The discrepancies are attributed to essential differences between the base flow in the open system considered by Hu & Kelly, where mass is conserved over one period of oscillation, and the base flow in the enclosed experimental apparatus, where mass is conserved at all sections at all times.

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Suspension Taylor–Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.291 ◽

2019 ◽

Vol 870 ◽

pp. 901-940 ◽

Cited By ~ 7

Author(s):

Prashanth Ramesh ◽

S. Bharadwaj ◽

Meheboob Alam

Keyword(s):

Reynolds Number ◽

Velocity Field ◽

Couette Flow ◽

Vortex Flow ◽

Travelling Waves ◽

Taylor Vortex ◽

Taylor Vortices ◽

Spiral Vortex ◽

Taylor Couette ◽

Taylor Couette Flow

Flow visualization and particle image velocimetry (PIV) measurements are used to unravel the pattern transition and velocity field in the Taylor–Couette flow (TCF) of neutrally buoyant non-Brownian spheres immersed in a Newtonian fluid. With increasing Reynolds number ($Re$) or the rotation rate of the inner cylinder, the bifurcation sequence in suspension TCF remains same as in its Newtonian counterpart (i.e. from the circular Couette flow (CCF) to stationary Taylor vortex flow (TVF) and then to travelling wavy Taylor vortices (WTV) with increasing $Re$) for small particle volume fractions ($\unicode[STIX]{x1D719}<0.05$). However, at $\unicode[STIX]{x1D719}\geqslant 0.05$, non-axisymmetric patterns such as (i) the spiral vortex flow (SVF) and (ii) two mixed or co-existing states of stationary (TVF, axisymmetric) and travelling (WTV or SVF, non-axisymmetric) waves, namely (iia) the ‘TVF$+$WTV’ and (iib) the ‘TVF$+$SVF’ states, are found, with the former as a primary bifurcation from CCF. While the SVF state appears both in the ramp-up and ramp-down experiments as in the work of Majji et al. (J. Fluid Mech., vol. 835, 2018, pp. 936–969), new co-existing patterns are found only during the ramp-up protocol. The secondary bifurcation TVF $\leftrightarrow$ WTV is found to be hysteretic or sub-critical for $\unicode[STIX]{x1D719}\geqslant 0.1$. In general, there is a reduction in the value of the critical Reynolds number, i.e. $Re_{c}(\unicode[STIX]{x1D719}\neq 0)<Re_{c}(\unicode[STIX]{x1D719}=0)$, for both primary and secondary transitions. The wave speeds of both travelling waves (WTV and SVF) are approximately half of the rotational velocity of the inner cylinder, with negligible dependence on $\unicode[STIX]{x1D719}$. The analysis of the radial–axial velocity field reveals that the Taylor vortices in a suspension are asymmetric and become increasingly anharmonic, with enhanced radial transport, with increasing particle loading. Instantaneous streamline patterns on the axial–radial plane confirm that the stationary Taylor vortices can indeed co-exist either with axially propagating spiral vortices or azimuthally propagating wavy Taylor vortices – their long-time stability is demonstrated. It is shown that the azimuthal velocity is considerably altered for $\unicode[STIX]{x1D719}\geqslant 0.05$, resembling shear-band type profiles, even in the CCF regime (i.e. at sub-critical Reynolds numbers) of suspension TCF; its possible role on the genesis of observed patterns as well as on the torque scaling is discussed.

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Experimental Study of Axial Slit Wall Effect on Taylor-Couette Flow

Volume 2: Fora, Parts A and B ◽

10.1115/fedsm2007-37321 ◽

2007 ◽

Author(s):

Sang-Hyuk Lee ◽

Hyoung-Bum Kim

Keyword(s):

Reynolds Number ◽

Couette Flow ◽

Vortex Flow ◽

Outer Cylinder ◽

Velocity Fields ◽

Taylor Vortex ◽

Stable Mode ◽

Taylor Vortex Flow ◽

Taylor Couette ◽

Taylor Couette Flow

Taylor-Couette flow has been studied extensively and lots of variables which affect the flow instability are being reported. The wall geometry effect of Taylor-Couette flow, however, has been less studied. In this study, we investigated the effect of axial slit of outer cylinder. This kind of configuration can be easily seen in rotating machinery. Particle image velocimetry method was used to measure the velocity fields in longitudinal and latitudinal planes. The index matching method was used to avoid light refraction. The velocity fields between the slit and plain model which has the smooth wall were compared. From the experiments, both models have the same flow mode below Re = 143. The transition from circular Couette flow to plain Taylor vortex flow began at Re = 103, and the next transition to wavy vortex flow occurred at 124. The effect of slit wall appeared when the Reynolds number is larger than Re = 143. Above this Reynolds number, there was no stable mode and plain and wavy Taylor vortex flow randomly appeared.

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Experiments on the Stability of Taylor-Couette Flow With Different Radial Temperature Gradient

ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C ◽

10.1115/fedsm-icnmm2010-30602 ◽

2010 ◽

Author(s):

Dong Liu ◽

Hyoung-Bum Kim

Keyword(s):

Reynolds Number ◽

Temperature Gradient ◽

Couette Flow ◽

Outer Cylinder ◽

Transition Process ◽

Taylor Vortex ◽

Radial Temperature ◽

Buoyant Force ◽

Taylor Couette ◽

Taylor Couette Flow

The effect of the temperature gradient and the presence of slits in the outer cylinders involved in creating a Taylor-Couette flow was investigated by measuring the velocity field inside the gap simultaneously. The slits were azimuthally located along the inner wall of outer cylinder and the number of slits was 18. The results showed that the buoyant force due to the temperature gradient clearly generated the helical flow when the rotating Reynolds number is small. For the plain model, the transition to turbulent Taylor vortex flow is not affected by the temperature gradient considered in this study. In addition, the transition process of 18-slit model was accelerated due to the slit wall. As the temperature gradient became larger, the critical Reynolds number of the transition process decreased.

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Spatio-temporal character of non-wavy and wavy Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/s0022112098008969 ◽

1998 ◽

Vol 364 ◽

pp. 59-80 ◽

Cited By ~ 103

Author(s):

STEVEN T. WERELEY ◽

RICHARD M. LUEPTOW

Keyword(s):

Reynolds Number ◽

Couette Flow ◽

Vortex Flow ◽

Outer Cylinder ◽

Taylor Vortex ◽

Meridional Plane ◽

Azimuthal Wave ◽

Moderate Reynolds Number ◽

Taylor Couette ◽

Taylor Couette Flow

The stability of supercritical Couette flow has been studied extensively, but few measurements of the velocity field of flow have been made. Particle image velocimetry (PIV) was used to measure the axial and radial velocities in a meridional plane for non-wavy and wavy Taylor–Couette flow in the annulus between a rotating inner cylinder and a fixed outer cylinder with fixed end conditions. The experimental results for the Taylor vortex flow indicate that as the inner cylinder Reynolds number increases, the vortices become stronger and the outflow between pairs of vortices becomes increasingly jet-like. Wavy vortex flow is characterized by azimuthally wavy deformation of the vortices both axially and radially. The axial motion of the vortex centres decreases monotonically with increasing Reynolds number, but the radial motion of the vortex centres has a maximum at a moderate Reynolds number above that required for transition. Significant transfer of fluid between neighbouring vortices occurs in a cyclic fashion at certain points along an azimuthal wave, so that while one vortex grows in size, the two adjacent vortices become smaller, and vice versa. At other points in the azimuthal wave, there is an azimuthally local net axial flow in which fluid winds around the vortices with a sense corresponding to the axial deformation of the wavy vortex tube. These measurements also confirm that the shift-and-reflect symmetry used in computational studies of wavy vortex flow is a valid approach.

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