scholarly journals Travelling azimuthal waves on Taylor vortices of the flow between two concentric spheres with the inner sphere rotating. 1st Report. States and modulation of travelling waves.

1986 ◽  
Vol 52 (480) ◽  
pp. 2787-2793
Author(s):  
Koichi NAKABAYASHI ◽  
Yoichi TSUCHIDA
Keyword(s):  
Travelling Waves ◽  
Taylor Vortices ◽  
Concentric Spheres ◽  
Inner Sphere ◽  
Azimuthal Waves

Taylor vortices between two concentric rotating spheres

1982 ◽  
Vol 119 ◽  
pp. 1-25 ◽  
Author(s):  
Fritz Bartels
Keyword(s):  
Reynolds Number ◽  
Finite Difference ◽  
Flow Field ◽  
Critical Reynolds Number ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Finite Difference Methods ◽  
Taylor Vortices ◽  
Concentric Spheres ◽  
Inner Sphere

The laminar viscous flow in the gap between two concentric spheres is investigated for a rotating inner sphere. The solution is obtained by solving the Navier-Stokes equations by means of finite-difference techniques, where the equations are restricted to axially symmetric flows. The flow field is hydrodynamically unstable above a critical Reynolds number. This investigation indicates that the critical Reynolds number beyond which Taylor vortices appear is slightly higher in a spherical gap than for the flow between concentric cylinders. The formation of Taylor vortices could be observed only for small gap widths s ≤ 0·17. The final state of the flow field depends on the initial conditions and the acceleration of the inner sphere. Steady and unsteady flow modes are predicted for various Reynolds numbers and gap widths. The results are in agreement with experiment if certain accuracy conditions of the finite-difference methods are satisfied. It is seen that the equatorial symmetry is of great importance for the development of the Taylor vortices in the gap.

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.

Forced Convection in Concentric-Sphere Heat Exchangers

1968 ◽  
Vol 90 (1) ◽  
pp. 125-129 ◽  
Author(s):  
H. A. Rundell ◽  
E. G. Ward ◽  
J. E. Cox
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Empirical Relation ◽  
Outer Sphere ◽  
Coolant Fluid ◽  
Transfer Rates ◽  
Concentric Spheres ◽  
Temperature Heat ◽  
Inner Sphere ◽  
Visualization Techniques

The first experimental investigation of forced convection of a fluid through the annulus formed by two concentric spheres was performed. The fluid enters and leaves the annulus through diametrically opposed openings in the outer sphere. The inner sphere serves as a constant-temperature heat source. Four sphere-size combinations were tested. The flow patterns in the annulus were established by flow visualization techniques; characteristic photographic results are presented. Energy considerations include heat transfer rates, inner-sphere surface temperatures, and temperature traverses of the coolant fluid. An empirical relation correlates the heat transfer data.

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.

Effects of wall compliance on the linear stability of Taylor–Couette flow

2009 ◽  
Vol 630 ◽  
pp. 331-365
Author(s):  
ANAÏS GUAUS ◽  
CHRISTOPHE AIRIAU ◽  
ALESSANDRO BOTTARO ◽  
AZEDDINE KOURTA
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Spring Stiffness ◽  
Narrow Gap ◽  
Taylor Vortices ◽  
Concentric Cylinders ◽  
Wall Compliance ◽  
Rigid Frames ◽  
The Stability ◽  
Azimuthal Waves

The stability of the laminar flow in the narrow gap between infinitely long concentric cylinders, the inner of which rotates, is examined for the case of compliant bounding walls, modelled as thin cylindrical shells supported by rigid frames through arrays of springs and dampers. Sufficiently soft walls have a destabilizing influence on the axisymmetric Taylor vortices produced by the centrifugal force, although the effect is limited to modes with large axial wavelengths. Due to the walls flexibility, hydroelastic modes are generated. Complex modal exchanges are observed, as function of the wall properties and the Reynolds number. For axisymmetric modes an asymptotic analysis is conducted in the limit of small axial wavenumber, to show the correspondence between such exchanges and singularities in the analytical solutions. While the axisymmetric modes dominate the spectrum when the walls are rigid or very mildly compliant, a critical non-zero azimuthal wavenumber exists for which the hydroelastic modes become more unstable. Shorter azimuthal waves are favoured by increasing spring stiffness.

scholarly journals Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Deepak Kumar Srivastava
Keyword(s):  
Angular Velocity ◽  
Outer Sphere ◽  
Present Situation ◽  
Dissipated Energy ◽  
Slow Rotation ◽  
Azimuthal Component ◽  
Concentric Spheres ◽  
Special Cases ◽  
Inner Sphere ◽  
Angular Velocities

The problem of concentric pervious spheres carrying a fluid source at their centre and rotating slowly with different uniform angular velocities , about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists, and the couple, rate of dissipated energy is found analytically in the present situation. The expression of couple on inner sphere rotating slowly with uniform angular velocity , while outer sphere also rotates slowly with uniform angular velocity , is evaluated. The special cases, like (i) inner sphere is fixed (i.e., ), while outer sphere rotates with uniform angular velocity , (ii) outer sphere is fixed (i.e., ), while inner sphere rotates with uniform angular velocity , and (iii) inner sphere rotates with uniform angular velocity , while outer sphere rotates at infinity with angular velocity , have been deduced.

Flow regimes in a circular Couette system with independently rotating cylinders

1986 ◽  
Vol 164 ◽  
pp. 155-183 ◽  
Author(s):  
C. David Andereck ◽  
S. S. Liu ◽  
Harry L. Swinney
Keyword(s):  
Large Scale ◽  
Travelling Waves ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Spectral Studies ◽  
Rotating Cylinders ◽  
Taylor Vortices ◽  
Aspect Ratios ◽  
Numerical Studies ◽  
Flow States

Our flow-visualization and spectral studies of flow between concentric independently rotating cylinders have revealed a surprisingly large variety of different flow states. (The system studied has radius ratio 0.883, aspect ratios ranging from 20 to 48, and the end boundaries were attached to the outer cylinder.) Different states were distinguished by their symmetry under rotation and reflection, by their azimuthal and axial wavenumbers, and by the rotation frequencies of the azimuthal travelling waves. Transitions between states were determined as functions of the inner- and outer-cylinder Reynolds numbers, Ri and Ro, respectively. The transitions were located by fixing Ro and slowly increasing Ri. Observed states include Taylor vortices, wavy vortices, modulated wavy vortices, vortices with wavy outflow boundaries, vortices with wavy inflow boundaries, vortices with flat boundaries and internal waves (twists), laminar spirals, interpenetrating spirals, waves on interpenetrating spirals, spiral turbulence, a flow with intermittent turbulent spots, turbulent Taylor vortices, a turbulent flow with no large-scale features, and various combinations of these flows. Some of these flow states have not been previously described, and even for those states that were previously described the present work provides the first coherent characterization of the states and the transitions between them. These flow states are all stable to small perturbations, and the transition boundaries between the states are reproducible. These observations can serve as a challenge and test for future analytic and numerical studies, and the map of the transitions provides several possible codimension-2 bifurcations that warrant further study.

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