scholarly journals Statistics, plumes and azimuthally travelling waves in ultimate Taylor–Couette turbulent vortices

2019 ◽  
Vol 876 ◽  
pp. 733-765
Author(s):  
Andreas Froitzheim ◽  
Rodrigo Ezeta ◽  
Sander G. Huisman ◽  
Sebastian Merbold ◽  
Chao Sun ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Large Scale ◽  
Travelling Waves ◽  
Azimuthal Velocity ◽  
Taylor Vortex ◽  
Small Scale ◽  
Underlying Structure ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Taylor Couette

In this paper, we experimentally study the influence of large-scale Taylor rolls on the small-scale statistics and the flow organization in fully turbulent Taylor–Couette flow for Reynolds numbers up to $Re_{S}=3\times 10^{5}$. The velocity field in the gap confined by coaxial and independently rotating cylinders at a radius ratio of $\unicode[STIX]{x1D702}=0.714$ is measured using planar particle image velocimetry in horizontal planes at different cylinder heights. Flow regions with and without prominent Taylor vortices are compared. We show that the local angular momentum transport (expressed in terms of a Nusselt number) mainly takes place in the regions of the vortex in- and outflow, where the radial and azimuthal velocity components are highly correlated. The efficient momentum transfer is reflected in intermittent bursts, which becomes visible in the exponential tails of the probability density functions of the local Nusselt number. In addition, by calculating azimuthal energy co-spectra, small-scale plumes are revealed to be the underlying structure of these bursts. These flow features are very similar to the one observed in Rayleigh–Bénard convection, which emphasizes the analogies of these systems. By performing a complex proper orthogonal decomposition, we remarkably detect azimuthally travelling waves superimposed on the turbulent Taylor vortices, not only in the classical but also in the ultimate regime. This very large-scale flow pattern, which is most pronounced at the axial location of the vortex centre, is similar to the well-known wavy Taylor vortex flow, which has comparable wave speeds, but much larger azimuthal wavenumbers.

Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave

1984 ◽  
Vol 146 ◽  
pp. 65-113 ◽  
Author(s):  
Philip S. Marcus
Keyword(s):  
Couette Flow ◽  
Vortex Flow ◽  
Travelling Waves ◽  
Maximum Amplitude ◽  
Travelling Wave ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Taylor Couette ◽  
Taylor Couette Flow

We use a numerical method that was described in Part 1 (Marcus 1984a) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equilibria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque, wave speed, energy dissipation rate, enstrophy, and energy and enstrophy spectra. We also plot several 2-dimensional projections of the velocity field. Using the results of the numerical calculations, we conjecture that the travelling waves are a secondary instability caused by the strong radial motion in the outflow boundaries of the Taylor vortices and are not shear instabilities associated with inflection points of the azimuthal flow. We demonstrate numerically that, at the critical Reynolds number where Taylor-vortex flow becomes unstable to wavy-vortex flow, the speed of the travelling wave is equal to the azimuthal angular velocity of the fluid at the centre of the Taylor vortices. For Reynolds numbers larger than the critical value, the travelling waves have their maximum amplitude at the comoving surface, where the comoving surface is defined to be the surface of fluid that has the same azimuthal velocity as the velocity of the travelling wave. We propose a model that explains the numerically discovered fact that both Taylor-vortex flow and the one-travelling-wave flow have exponential energy spectra such that In [E(k)] ∝ k1, where k is the Fourier harmonic number in the axial direction.

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.

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

2019 ◽  
Vol 870 ◽  
pp. 901-940 ◽  
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.

Development and Effects of Super-Critical Taylor-Vortex Flow in a Lightly Loaded Journal Bearing

1974 ◽  
Vol 96 (1) ◽  
pp. 28-35 ◽  
Author(s):  
R. C. DiPrima ◽  
J. T. Stuart
Keyword(s):  
Vortex Flow ◽  
Axial Direction ◽  
Basic Flow ◽  
Circular Cylinders ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Secondary Motion ◽  
The Stability ◽  
Unified Description

At sufficiently high operating speeds in lightly loaded journal bearings the basic laminar flow will be unstable. The instability leads to a new steady secondary motion of ring vortices around the cylinders with a regular periodicity in the axial direction and a strength that depends on the azimuthial position (Taylor vortices). Very recently published work on the basic flow and the stability of the basic flow between eccentric circular cylinders with the inner cylinder rotating is summarized so as to provide a unified description. A procedure for calculating the Taylor-vortex flow is developed, a comparison with observed properties of the flow field is made, and formulas for the load and torque are given.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

Destabilization of the Taylor Vortex Flow by a Radial Temperature Gradient

2006 ◽  
Author(s):  
Vale´rie Lepiller ◽  
Jong-Yeon Hwang ◽  
Arnaud Prigent ◽  
Kyung-Soo Yang ◽  
Innocent Mutabazi
Keyword(s):  
Temperature Gradient ◽  
Vortex Flow ◽  
Taylor Vortex ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Taylor Vortices ◽  
Numerical Studies ◽  
Taylor Vortex Flow ◽  
Spatio Temporal ◽  
Small Inclination

Both experimental and numerical studies have shown that the Taylor vortices are destabilized by a weak radial temperature gradient and transit to spiral vortices with a small inclination. For a large radial temperature gradient, from Taylor vortices emerges a disordered pattern with some windows of spiral vortices. Spatio-temporal characteristics of resulting pattern are presented.

scholarly journals Steady supercritical Taylor vortex flow

1973 ◽  
Vol 58 (3) ◽  
pp. 547-560 ◽  
Author(s):  
J. E. Burkhalter ◽  
E. L. Koschmieder
Keyword(s):  
Vortex Flow ◽  
Finite Cylinder ◽  
Taylor Vortex ◽  
End Effects ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Critical Wavelength ◽  
Very High ◽  
Long Cylinder

Experiments studying steady supercritical Taylor vortex flow have been made using pairs of long cylinders with two different radius ratios, three fluids of different viscosities and three different end boundaries for the fluid column. The emphasis in these experiments is on the determination of the wavelength of the Taylor vortices and the size of the end rings. The wavelength which one measures in a finite cylinder differs from the wavelengths found theoretically for infinitely long cylinders. Provided that the end effects were properly taken into account, the wavelength of singly periodic Taylor vortices in aninfinitely long cylinder was found to remain constant between T/Tc = 1 and T/Tc, ≈ 80 in experiments with radius ratios η = 0·505 and η = 0·727. Further studies of Taylor vortex flow at very high Taylor numbers, where the vortices are either doubly periodic or truly turbulent, showed that the wavelength increases under these conditions. However, the observed wavelengths were no longer unique but distributed statistically around a wavelength larger than the critical wavelength.

On vortex air motions above an axisymmetric source of mass, momentum and heat

1995 ◽  
Vol 290 ◽  
pp. 299-317
Author(s):  
Y. A. Berezin ◽  
K. Hutter
Keyword(s):  
Large Scale ◽  
Nonlinear Differential Equations ◽  
Azimuthal Velocity ◽  
Small Scale ◽  
Ambient Atmosphere ◽  
Plume Dispersion ◽  
Governing Equations ◽  
Balance Equations ◽  
Velocity Pressure ◽  
Polytropic Atmosphere

We study axisymmetric plume dispersion from a steady source of mass, momentum and/or heat that is subjected to either a time-dependent large-scale external vortex or small-scale turbulent axisymmetric helicity. On the basis of the turbulent boundary layer and Boussinesq assumptions and by assuming similarity profiles with Gaussian distribution in the radial direction the balance equations of mass, momentum, and energy reduce to a system of nonlinear differential equations for amplitude functions of axial velocity, pressure and density differences as well as azimuthal velocity. The system of equations is closed with Taylor's entrainment assumption.The plume radius and the typical radius of the large-scale external vortex are also determined. For a simple density structure of the ambient atmosphere (i.e. adiabatic conditions) analytical results can be obtained, but for more complicated cases, i.e. a layered polytropic atmosphere, the governing equations are examined numerically; computations are reasonably simple and efficient.

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

2014 ◽  
Vol 748 ◽  
pp. 756-767 ◽  
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.

Experimental Study on Oscillatory Couette-Taylor Flows Behaviour

2013 ◽  
Author(s):  
Emna Berrich ◽  
Fethi Aloui ◽  
Jack Legrand
Keyword(s):  
Mass Transfer ◽  
Angular Velocity ◽  
Time Evolution ◽  
Vortex Flow ◽  
Outer Cylinder ◽  
Taylor Vortex ◽  
Shear Rates ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Wall Shear

In the simplest and original case of study of the Taylor–Couette TC problems, the fluid is contained between a fixed outer cylinder and a concentric inner cylinder which rotates at constant angular velocity. Much of the works done has been concerned on steady rotating cylinder(s) i.e. rotating cylinders with constant velocity and the various transitions that take place as the cylinder(s) velocity (ies) is (are) steadily increased. On this work, we concentrated our attention in the case in which the inner cylinder velocity is not constant, but oscillates harmonically (in time) clockwise and counter-clockwise while the outer cylinder is maintained fixed. Our aim is to attempt to answer the question if the modulation makes the flow more or less stable with respect to the vortices apparition than in the steady case. If the modulation amplitude is large enough to destabilise the circular Couette flow, two classes of axisymmetric Taylor vortex flow are possible: reversing Taylor Vortex Flow (RTVF) and Non-Reversing Taylor Vortex Flow (NRTVF) (Youd et al., 2003; Lopez and Marques, 2002). Our work presents an experimental investigation of the effect of oscillatory Couette-Taylor flow, i.e. both the oscillation frequency and amplitude on the apparition of RTVF and NRTVF by analysing the instantaneous and local mass transfer and wall shear rates evolutions, i.e. the impact of vortices at wall. The vortices may manifest themselves by the presence of time-oscillations of mass transfer and wall shear rates, this generally corresponds to an instability apparition even for steady rotating cylinder. On laminar CT flow, the time-evolution of wall shear rate is linear. It may be presented as a linear function of the angular velocity, i.e. the evolution is steady even if the angular velocity is not steady. At a “critical” frequency and amplitude, the laminar CT flow is disturbed and Taylor vortices appear. Comparing to a steady velocity case, oscillatory flow accelerate the instability apparition, i.e. the critical Taylor number corresponds to the transition is smaller than that of the steady case. For high oscillation amplitudes of the inner cylinder rotation, the mass transfer time-evolution has a sinusoidal evolution with non equal oscillation amplitudes. If the oscillation amplitude is large enough, it can destabilize the laminar Couette flow, Taylor vortices appears. The vortices direction can be deduced from the sign of the instantaneous wall shear rate time evolution.

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