Influence of global rotation and Reynolds number on the large-scale features of a turbulent 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.

Download Full-text

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.634 ◽

2017 ◽

Vol 831 ◽

pp. 330-357 ◽

Cited By ~ 5

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.

Download Full-text

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.

Download Full-text

Effect of the number of vortices on the torque scaling in Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.213 ◽

2014 ◽

Vol 748 ◽

pp. 756-767 ◽

Cited By ~ 31

Author(s):

B. Martínez-Arias ◽

J. Peixinho ◽

O. Crumeyrolle ◽

I. Mutabazi

Keyword(s):

Reynolds Number ◽

Aspect Ratio ◽

Couette Flow ◽

Scaling Laws ◽

Taylor Vortex ◽

Large Radius ◽

Aspect Ratios ◽

Taylor Vortex Flow ◽

Taylor Couette ◽

Taylor Couette Flow

AbstractTorque measurements in Taylor–Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque–speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

Download Full-text

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.

Download Full-text

Bursting dynamics due to a homoclinic cascade in Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/s0022112008003418 ◽

2008 ◽

Vol 613 ◽

pp. 357-384 ◽

Cited By ~ 25

Author(s):

J. ABSHAGEN ◽

J. M. LOPEZ ◽

F. MARQUES ◽

G. PFISTER

Keyword(s):

Numerical Simulations ◽

Couette Flow ◽

Large Scale ◽

Nonlinear Dynamical Systems ◽

Low Frequency ◽

Accumulation Point ◽

Infinite Length ◽

Phase Dynamics ◽

Taylor Couette ◽

Taylor Couette Flow

Transitions between regular oscillations and bursting oscillations that involve a bifurcational process which culminates in the creation of a relative periodic orbit of infinite period and infinite length are investigated both experimentally and numerically in a short-aspect-ratio Taylor–Couette flow. This bifurcational process is novel in that it is the accumulation point of a period-adding cascade at which the mid-height reflection symmetry is broken. It is very rich and complex, involving very-low-frequency states arising via homoclinic and heteroclinic dynamics, providing the required patching between states with very different dynamics in neighbouring regions of parameter space. The use of nonlinear dynamical systems theory together with symmetry considerations has been crucial in interpreting the laboratory experimental data as well as the results from the direct numerical simulations. The phenomenon corresponds to dynamics well beyond the first few bifurcations from the basic state and so is beyond the reach of traditional hydrodynamic stability analysis, but it is not fully developed turbulence where a statistical or asymptotic approach could be employed. It is a transitional phenomenon, where the phase dynamics of the large-scale structures (jets of angular momentum emanating from the boundary layer on the rotating inner cylinder) becomes complicated. Yet the complicated phase dynamics remains accessible to an analysis of its space–time characteristics and a comprehensive mechanical characterization emerges. The excellent agreement between the experiments and the numerical simulations demonstrates the robustness of this complex bifurcation phenomenon in a physically realized system with its inherent imperfections and noise. Movies are available with the online version of the paper.

Download Full-text

Microbubbly drag reduction in Taylor–Couette flow in the wavy vortex regime

Journal of Fluid Mechanics ◽

10.1017/s0022112008001183 ◽

2008 ◽

Vol 608 ◽

pp. 21-41 ◽

Cited By ~ 45

Author(s):

KAZUYASU SUGIYAMA ◽

ENRICO CALZAVARINI ◽

DETLEF LOHSE

Keyword(s):

Reynolds Number ◽

Drag Reduction ◽

Couette Flow ◽

Physical Mechanism ◽

Dilute Suspensions ◽

Fluid Coupling ◽

Taylor Couette ◽

The Individual ◽

Reynolds Number Dependence ◽

Taylor Couette Flow

We investigate the effect of microbubbles on Taylor–Couette flow by means of direct numerical simulations. We employ an Eulerian–Lagrangian approach with a gas–fluid coupling based on the point-force approximation. Added mass, drag, lift and gravity are taken into account in the modelling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1%, zero Weber number and bubble Reynolds number ≲10) induce a robust statistically steady drag reduction (up to 20%) in the wavy vortex flow regime (Re=600–2500). The Reynolds number dependence of the normalized torque (the so-called torque reduction ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. Conf. Ser. vol. 14, 2005, p. 143). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When it is neglected, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified. Movies are available with the online version of the paper.

Download Full-text