Centrifugal instabilities of circumferential flows in finite cylinders: nonlinear theory

1980 ◽  
Vol 372 (1750) ◽  
pp. 317-356 ◽  
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Perturbation Expansion ◽  
Direct Consequence ◽  
Finite Amplitude ◽  
Taylor Vortex ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
Axisymmetric Disturbances ◽  
Finite Cylinders

In an earlier paper, Blennerhassett & Hall (1979) investigated the linear stability of the flow between concentric cylinders of finite length. The inner cylinder was taken to rotate, while the outer cylinder was fixed. Furthermore, the end walls rotated such that the flow was purely circumferential. In this paper the finite amplitude development of the unstable disturbances to the flow is considered. It is found that the usual perturbation expansion of nonlinear stability theory must be modified if the cylinders are not infinitely long. The bifurcation to a Taylor vortex flow in finite cylinders is shown to be two-sided. The latter effect is shown to be a direct consequence of the finiteness of the cylinders and by taking the cylinders to be very long, we recover the results obtained previously for the infinite problem. The interaction of the two most dangerous modes of linear theory is also investigated. For certain values of the length of the cylinders the initial finite amplitude Taylor vortex flow is shown to become unstable to another class of axisymmetric disturbances. The effect of perturbing the end conditions towards the no-slip conditions appropriate to most experimental configurations is also discussed. Some discussion of the instability problem in very long cylinders with fixed ends is given.

Experimental Study on the Effects of Surface Roughness on the Behaviors of Hydrodynamic Instabilities of Couette-Taylor Flow

2017 ◽  
Author(s):  
Mostafa Monfared ◽  
Lamia Gaied ◽  
Emna Berrich ◽  
Ebrahim Shirani ◽  
Maxence Bigerelle ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Vortex Flow ◽  
Outer Cylinder ◽  
Wire Mesh ◽  
Taylor Vortex ◽  
Hydrodynamic Instabilities ◽  
Taylor Flow ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
Effect Of Surface

Couette-Taylor flow is a type of fluid flow that occurs in the annulus between differentially concentric cylinders, when the outer cylinder is fixed and the inner cylinder rotates and the rotation rate exceeds a critical value. In this research we have studied the effect of surface roughness on the hydrodynamic structures of Couette-Taylor Flow. The PIV technique has been applied for flow visualization. At first, for a smooth surface, the different flow patterns include Couette flow, Taylor vortex flow, wavy vortex flow, modulated wavy vortex flow and turbulent flow. They are investigated numerically and experimentally. The transition Taylor number for every flow regime is also taken into consideration. The results showed that the numerical results correspond quite well to the experimental data. Then, the different surface conditions for inner cylinder which are studied are: a smooth one, a sandpaper-type P180, a canvas plastic with different wire-mesh roughness. They are used to study the effects of surface roughness on the flow structures and critical Taylor numbers. The experimental results showed that the roughness causes a delay in the appearance of the first instabilities.

Numerical Study of Effects of Initial Flow Field on Taylor Vortex Flow

2007 ◽  
Author(s):  
H. Furukawa ◽  
M. Hanaki ◽  
T. Watanabe
Keyword(s):  
Flow Field ◽  
Vortex Flow ◽  
Numerical Study ◽  
Outer Cylinder ◽  
Visual Observation ◽  
Taylor Vortex ◽  
Initial Flow ◽  
Taylor Vortex Flow ◽  
The Difference ◽  
Mode Formation

In concentrically rotating double cylinders consisting of a stationary outer cylinder and a rotating inner cylinder, Taylor vortex flow appears. Taylor vortex flow occurs in journal bearings, various fluid machineries, containers for chemical reaction, and other rotating components. Therefore, the analysis of the flow structure of Taylor vortex flow is highly effective for its control. The main parameters that determine the modes of Taylor vortex flow of a finite length are the aspect ratio Γ, Reynolds number Re. Γ is defined as the ratio of the cylinder length to the gap length between cylinders, and Re is determined on the basis of the angular speed of the inner cylinder. Γ was set to be 3.2, 4.8 and 6.8, and Re to be values in the range from 100 to 1000 at intervals of 100. Thus far, a large number of studies on Taylor vortex flow have been carried out; however, the effects of the differences in initial conditions have not yet been sufficiently clarified. In this study, we changed the initial flow field between the inner and outer cylinders in a numerical analysis, and examined the resulting changes in the mode formation and bifurcation processes. In this study, the initial speed distribution factor α was defined to be a function of the initial flow field and set to be 1.0, 0.999, 0.9 and 0.8 for the calculation. As a result, a difference was observed in the final mode depending on the difference in α for each Γ. From this finding, non-uniqueness, which is a major characteristic of Taylor vortex flow, was confirmed. However, no regularities regarding the difference in mode formation were found and the tendency of the mode formation process was not specified. Moreover, the processes of developing the vortex resulting in different final modes were monitored over time by visual observation. Similar flow behaviors were initially observed after the start of the calculation. Then, a bifurcation point, at which the flow changed to a mode depending on α, was observed, and finally the flow became steady. In addition, there was also a difference in the time taken for the flow to reach the steady state. These findings are based on only visual observation. Accordingly, a more detailed analysis at each lattice point and a comparison of physical quantities, such as kinetic energy and enstrophy, will be our future tasks.

Numerical Simulation of Taylor Vortex Flow by GDQ Method

2000 ◽  
Author(s):  
L. Wang ◽  
C. Shu ◽  
Y. T. Chew
Keyword(s):  
Vortex Flow ◽  
Stokes Equations ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Computational Effort ◽  
Numerical Results ◽  
Numerical Code ◽  
Taylor Vortex ◽  
Specific Flow ◽  
Taylor Vortex Flow

Abstract In this study, the GDQ method was used to simulate a specific flow regime, Taylor vortex flow, of the motion of fluids between two concentric cylinders with rotating inner cylinder and stationary outer cylinder. An approach combining the SIMPLE strategy and GDQ discretization based on non-staggered mesh was proposed to solve the time-dependent, three-dimensional incompressible Navier-Stokes equations in primitive variable form. The numerical solution obtained has the accuracy of second-order in temporal discretization and high-order in spatial discretization. Also, this numerical code may allow the direct numerical simulations for the various regimes of Couette-Taylor flow problem. The performance of this approach was studied through a test case of Taylor vortex flow. The reported numerical results were compared with those from others. For this approach, accurate numerical results can be obtained by using fewer grid points compared with low-order methods. As a consequence, the computational effort can be greatly reduced.

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.

The Effect of Taylor Vortex Flow on the Development Length in Concentric Annuli

1979 ◽  
Vol 21 (2) ◽  
pp. 59-64 ◽  
Author(s):  
D. A. Simmers ◽  
J. E. R. Coney
Keyword(s):  
Reynolds Number ◽  
Vortex Flow ◽  
Outer Cylinder ◽  
Outer Wall ◽  
Taylor Vortex ◽  
Rotational Flow ◽  
Development Length ◽  
Full Development ◽  
Annular Gap ◽  
Taylor Vortex Flow

Results are presented of an investigation into a developing, combined axial and rotational flow in an annular gap formed by a stationary outer cylinder and a rotatable inner cylinder for an annulus radius ratio of 0–8 and an axial Reynolds number of 1200. These results show that, in the Taylor vortex flow régime, the development length decreases with the parameter Re2a/Ta and that the greatest development length in an annular gap, for a given axial Reynolds number, occurs when the Taylor number is near to its critical value. Consideration of isothermal heat transfer through the outer wall of the annular gap suggests that, in the development of the flow, the Nusselt number rises to a high value before falling to a constant value, at full development.

The Effect of Taylor Vortex Flow on the Radial Forces in an Annulus Having Variable Eccentricity and Axial Flow

1978 ◽  
Vol 100 (2) ◽  
pp. 210-214 ◽  
Author(s):  
J. E. R. Coney ◽  
J. Atkinson
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Radial Force ◽  
Taylor Vortex ◽  
Eccentric Annulus ◽  
Taylor Vortex Flow ◽  
Radial Forces ◽  
Force Variation

Results are presented in dimensionless form as obtained in an experimental study of the resultant radial force variation in an eccentric annulus formed by a stationary outer cylinder and a rotating inner cylinder, through which an axial flow of oil may be pumped. Two eccentricity ratios, 0.5 and 0.9, and three axial Reynolds numbers for the flow of the fluid in the annulus, 0, 25, and 50, are considered. It is shown that the onset of Taylor vortex flow has a marked effect on the magnitude and direction of the resultant radial force. The resultant forces and attitude angles are compared with those derived from Sommerfeld’s journal bearing theory. Comparisons are also made between critical Taylor numbers for the present investigation and those available in the literature.

On wavy instabilities of the Taylor-vortex flow between corotating cylinders

1988 ◽  
Vol 188 ◽  
pp. 585-598 ◽  
Author(s):  
Masato Nagata
Keyword(s):  
Vortex Flow ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Taylor Vortex ◽  
Axisymmetric Solution ◽  
Boundary Flow ◽  
Taylor Vortex Flow ◽  
Average Rotation ◽  
The One ◽  
Outflow Boundary

At least four wavy instabilities are found numerically by analysing the linear stability of Taylor-vortex flow (TVF) in the limit of a small gap between two concentric cylinders which rotate differentially in the same direction. Two of the wavy instabilities, including the one leading to conventional wavy vortex (WVF), have the same axial wavelength as TVF at the onset of instability, while the other two are characterized by subharmonic modes with axial wavelengths twice as long as those of TVF. The two subharmonic instabilities appear to correspond to the wavy-inflow-boundary flow (WIB) and the wavy-outflow-boundary flow (WOB) observed in the experiment of Andereck, Liu & Swinney (1986). The phase velocities, measured in the rotating frame of reference, of all the wavy instabilities are non-zero at the onset except that the phase velocity of WVF vanishes in the region where the average rotation rate Ω of the cylinders is small. By using this simple bifurcation property of WVF for small Ω, time-independent finite-amplitude non-axisymmetric solution branches bifurcating from TVF are followed numerically. The most interesting findings are that some of the solution branches cross the line Ω = 0, producing three-dimensional nonlinear solutions in plane Couette flow.

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

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.

scholarly journals On the finite Dean problem: linear theory

1988 ◽  
Vol 30 (2) ◽  
pp. 157-178
Author(s):  
B. J. Kachoyan ◽  
P. J. Blennerhassett
Keyword(s):  
Outer Cylinder ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Mean Flow ◽  
Dean Flow ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
End Conditions ◽  
Pressure Driven Flow

AbstractThe Dean problem of pressure-driven flow between finite-length concentric cylinders is considered. The outer cylinder is at rest and the small-gap approximation is used. In a similar procedure to that of Blennerhassett and Hall [8] in the context of Taylor vortices, special end conditions are imposed in which the ends of the cylinder move with the mean flow, allowing the use of a perturbation analysis from a known basic flow. Difficulties specific to Dean flow (and more generally to non-Taylor-vortex flow) require the use of a parameter α which measures the relative strengths of the velocities due to rotation and the pressure gradient, to trace the solution from Taylor to Dean flow. Asymptotic expansions are derived for axial wavenumbers at a given Taylor number. The calculation of critical Taylor number for a given cylinder height is then carried out. Corresponding stream-function contours clearly show features not evident in infinite flow.

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