Numerical investigation of supercritical Taylor-vortex flow for a wide gap

1984 ◽  
Vol 138 ◽  
pp. 21-52 ◽  
Author(s):  
H. Fasel ◽  
O. Booz
Keyword(s):  
Flow Field ◽  
Vortex Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Plane Boundary ◽  
Aspect Ratios ◽  
Taylor Vortex Flow ◽  
Wide Gap

For a wide gap (R1/R2= 0.5) and large aspect ratiosL/d, axisymmetric Taylor-vortex flow has been observed in experiments up to very high supercritical Taylor (or Reynolds) numbers. This axisymmetric Taylor-vortex flow was investigated numerically by solving the Navier–Stokes equations using a very accurate (fourth-order in space) implicit finite-difference method. The high-order accuracy of the numerical method, in combination with large numbers of grid points used in the calculations, yielded accurate and reliable results for large supercritical Taylor numbers of up to 100Tac(or 10Rec). Prior to this study numerical solutions were reported up to only 16Tac. The emphasis of the present paper is placed upon displaying and elaborating the details of the flow field for large supercritical Taylor numbers. The flow field undergoes drastic changes as the Taylor number is increased from just supercritical to 100Tac. Spectral analysis (with respect toz) of the flow variables indicates that the number of harmonics contributing substantially to the total solution increases sharply when the Taylor number is raised. The number of relevant harmonics is already unexpectedly high at moderate supercriticalTa. For larger Taylor numbers, the evolution of a jetlike or shocklike flow structure can be observed. In the axial plane, boundary layers develop along the inner and outer cylinder walls while the flow in the core region of the Taylor cells behaves in an increasingly inviscid manner.

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.

Numerical Solutions of the Navier-Stokes Equations for Axisymmetric Flows

1968 ◽  
Vol 10 (5) ◽  
pp. 389-401 ◽  
Author(s):  
D. R. Strawbridge ◽  
G. T. J. Hooper
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Labyrinth Seal ◽  
Taylor Vortex ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
Flow Through

A numerical method is presented for the solution of the time dependent Navier-Stokes equations for the axisymmetric flow of an incompressible viscous fluid. The method is applied to the problems of Taylor-vortex flow about an enclosed rotating cylinder and between infinite concentric cylinders, and to the analysis of the flow through a labyrinth seal. The torque calculations, which show favourable agreement with experiment, and the resulting flow patterns are presented graphically.

Marginal instability in Taylor–Couette flows at a very high Taylor number

1979 ◽  
Vol 94 (3) ◽  
pp. 453-463 ◽  
Author(s):  
A. Barcilon ◽  
J. Brindley ◽  
M. Lessen ◽  
F. R. Mobbs
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Quantitative Agreement ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Centrifugal Instability ◽  
The One ◽  
Flow Experiments

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where Tc is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T, the turbulent vortex flow structure is similar to the one observed when T – Tc is small and this structure is apparently insensitive to further increases in T. These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Görtler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Görtler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Görtler vortex spacings.

scholarly journals Turbulent Taylor vortex flow

1979 ◽  
Vol 93 (3) ◽  
pp. 515-527 ◽  
Author(s):  
E. L. Koschmieder
Keyword(s):  
Experimental Error ◽  
Initial Conditions ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Narrow Gap ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Critical Wavelength ◽  
Wide Gap ◽  
Gap Width

The wavelength of turbulent Taylor vortices at very high Taylor numbers up to 40000Tc, has been measured in long fluid columns with radius ratios η = 0·896 and η = 0·727. Following slow acceleration procedures the wavelength (in units of the gap width) of turbulent axisymmetric vortices was found to be λ = 3·4 ± 0·1 with the small gap and about λ = 2·4 ± 0·1 with the larger gap, and thus in both cases substantially larger than the critical wavelength of laminar Taylor vortices. In the narrow and wide gap the wavelength was, within experimental error, independent of the Taylor number for T > 100Tc. In the experiments with the narrow gap a clear dependence of the value of the wavelength of the turbulent vortices on initial conditions was found. After sudden starts to Taylor numbers > 700Tc the wavelength of steady axisymmetric turbulent vortices was only 2·4 ± 0·05, being then the same as the wavelength of the vortices after sudden starts in the wide gap, and being, within the experimental error, independent of the Taylor number. In the narrow gap all values of the wavelength between λmax = 3·4 and λmin = 2·4 can be realized as steady states through different acceleration procedures. In the wide gap the dependence of the wavelength on initial conditions is just within the then larger experimental uncertainty of the measurements.

The effects of eccentricity on torque and load in Taylor-vortex flow

1978 ◽  
Vol 87 (2) ◽  
pp. 209-231 ◽  
Author(s):  
P.M. Eagles ◽  
J. T. Stuart ◽  
R. C. Diprima
Keyword(s):  
Vortex Flow ◽  
Nonlinear Effects ◽  
Critical Value ◽  
Taylor Number ◽  
Circular Cylinders ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Small Parameters ◽  
Extended Analysis

This paper extends two earlier papers in which DiPrima & Stuart calculated first (1972b) the critical Taylor number to order ε2, where the eccentricity ε is proportional to the displacement of the axes of the circular cylinders, and second (1975) the torque and load to order ε associated with nonlinear effects of Taylor vortices. In the latter paper, it was shown that to order ε the torque arising from the Taylor vortices is identical with that for the concentric problem, which was first calculated, by a perturbation method, by Davey (1962). This deficiency is remedied in the present paper, where the calculation is taken to order ε2. It is found that, as ε rises, the torque associated with the Taylor vortices falls slightly when we keep constant the percentage elevation of the Taylor number above the ε-dependent critical value. This result is in accordance with experimental observations by Vohr (1967, 1968). In addition, results of calculations of the pressure field developed by the Taylor-vortex flow in association with the eccentric geometry are presented; this is larger than in the concentric case owing to a Reynolds lubrication effect. Also given are the associated components of the load on the inner cylinder, but only for Taylor numbers close to the critical value.One additional observation by Vohr, for cylinders with a mean ratio of the gap to the inner radius of 0·099, was that the maximum Taylor-vortex strength with ε = 0·475 occurred some 50° downstream of the maximum gap for a 20% elevation of the Taylor number above the critical value. Calculations in the two earlier papers (1972b, 1975) gave 90 and 76°, respectively, for that angle. Note that in the 1975 paper a geometrical correction of order ε was included. Here, with an additional modification of order ε due to the flow, this result is improved to 49° by the extended analysis presented, although the ‘small’ parameters are somewhat outside the range for which perturbation theory is expected to be valid.

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.

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