Centrifugal instabilities in finite containers: a periodic model

1980 ◽  
Vol 99 (3) ◽  
pp. 575-596 ◽  
Author(s):  
P. Hall
Keyword(s):  
Model Problem ◽  
Fluid Velocity ◽  
Normal Component ◽  
Tangential Velocity ◽  
Normal Derivative ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Periodic Model ◽  
Circulatory Flow ◽  
Imperfect Bifurcation

A simplified model problem has recently been suggested by Schaeffer (1980) in order to explain the results obtained by Benjamin (1978) in his investigation of Taylor vortices in short cylinders. In particular Schaeffer reproduces the results obtained by Benjamin for cylinders so short that only two-cell or four-cell flows are possible. The model given by Schaeffer has artificial conditions imposed on the fluid velocity field at the end walls. These conditions depend on a parameter α and reduce to the no-slip condition when α = 1. If α = 0 the conditions require that the normal component of the velocity and the normal derivative of the tangential velocity vanish at the ends. In this case the onset of Taylor vortex-like motion occurs as a bifurcation from purely circumferential flow. If α is now taken to be small and positive, there is no bifurcation and the circulatory flow develops smoothly. We shall use perturbations method for the case of small α. The imperfect bifurcation problem which we obtain predicts some results consistent with those of Benjamin.

High-order asymptotic expansion for the acoustics in viscous gases close to rigid walls

2014 ◽  
Vol 24 (09) ◽  
pp. 1823-1855 ◽  
Author(s):  
Kersten Schmidt ◽  
Anastasia Thöns-Zueva ◽  
Patrick Joly
Keyword(s):  
Asymptotic Expansion ◽  
Normal Component ◽  
Tangential Velocity ◽  
Normal Derivative ◽  
Two Dimensions ◽  
Singularly Perturbed Problem ◽  
Optimal Error Estimates ◽  
Complete Asymptotic Expansion ◽  
Curvature Effects ◽  
Rigid Walls

We derive a complete asymptotic expansion for the singularly perturbed problem of acoustic wave propagation inside gases with small viscosity. This derivation is for the non-resonant case in smooth bounded domains in two dimensions. Close to rigid walls the tangential velocity exhibits a boundary layer of size [Formula: see text] where η is the dynamic viscosity. The asymptotic expansion, which is based on the technique of multiscale expansion is expressed in powers of [Formula: see text] and takes into account curvature effects. The terms of the velocity and pressure expansion are defined independently by partial differential equations, where the normal component of velocities or the normal derivative of the pressure, respectively, are prescribed on the boundary. The asymptotic expansion is rigorously justified with optimal error estimates.

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.

Taylor-vortex instability and annulus-length effects

1976 ◽  
Vol 75 (1) ◽  
pp. 1-15 ◽  
Author(s):  
J. A. Cole
Keyword(s):  
Critical Speed ◽  
Taylor Vortex ◽  
Vortex Instability ◽  
Critical Speeds ◽  
Taylor Vortices ◽  
Torque Measurements ◽  
Concentric Cylinders ◽  
Theoretical Predictions ◽  
Range Of Values ◽  
Visual Observations

Critical speeds for the onset of Taylor vortices and for the later development of wavy vortices have been determined from torque measurements and visual observations on concentric cylinders of radius ratios R1/R2 = 0·894–0·954 for a range of values of the clearance c and length L: c/R1 = 0·0478–0·119 and L/c = 1–107. Effectively zero variation of the Taylor critical speed with annulus length was observed. The speed at the onset of wavy vortices was found to increase considerably as the annulus length was reduced and theoretical predictions are realistic only for L/c values exceeding say 40. The results were similar for all four clearance ratios examined. Preliminary measurements on eccentrically positioned cylinders with c/R1 = 0·119 showed corresponding effects.

Performance of Plain Journal Bearings Operating Under Vortex Flow Conditions

1974 ◽  
Vol 96 (1) ◽  
pp. 145-149 ◽  
Author(s):  
J. Freˆne ◽  
M. Godet
Keyword(s):  
Reynolds Number ◽  
Friction Torque ◽  
Point Of View ◽  
Taylor Vortex ◽  
Experimental Program ◽  
Frictional Torque ◽  
Taylor Vortices ◽  
Attitude Angle ◽  
Relative Eccentricity ◽  
High Reynolds

An experimental program conducted on an original device was undertaken to study the performance of plain bearings operating at sufficiently high Reynolds number to introduce Taylor vortices. Curves of relative eccentricity, attitude angle, and friction torque were obtained versus speed and load. Experimental results conducted for Reynolds number smaller than 1100 indicate that both laminar and Taylor vortex regimes are encountered. The occurrence of the vortices is identified by a break in the slope of the friction torque versus speed curves. The position of the break is in good agreement with the theoretical predictions of Di Prima and Ritchie. From the practical point of view, the data show that for constant viscosity the occurence of Taylor vortices does not alter the curves of eccentricity versus either speed or load but modifies the attitude angle and frictional torque. In turn, the increase in frictional torque, and subsequently of temperature may cause a decrease in viscosity and thus a drop in load carrying capacity for fluids such as oils whose variations of viscosity with temperature is large.

Visual Observations and Torque Measurements in the Taylor Vortex Regime Between Eccentric Rotating Cylinders

1971 ◽  
Vol 93 (1) ◽  
pp. 121-129 ◽  
Author(s):  
P. Castle ◽  
F. R. Mobbs ◽  
P. H. Markho
Keyword(s):  
Outer Cylinder ◽  
Taylor Vortex ◽  
Rotating Cylinders ◽  
Taylor Vortices ◽  
Torque Measurements ◽  
Good Agreement ◽  
Visual Observations

The instability of Taylor vortices in the flow between a stationary outer cylinder and an eccentric rotating inner cylinder has been investigated by visual observations and by torque measurements. It is shown that both a “weak” and “strong” wavy mode of instability can be detected by torque measurements, giving critical Taylor numbers in good agreement with visual observations.

Application of Taylor Vortices in Hemocompatibility Investigations

2003 ◽  
Vol 26 (4) ◽  
pp. 331-338 ◽  
Author(s):  
S. Körfer ◽  
S. Klaus ◽  
K. Mottaghy
Keyword(s):  
Laminar Flow ◽  
Protein Adsorption ◽  
Secondary Flows ◽  
Artificial Organs ◽  
Vortical Flow ◽  
Taylor Vortex ◽  
Vortex Center ◽  
Flow Conditions ◽  
Shear Rates ◽  
Taylor Vortices

Background Artificial organs, implants and extracorporeal circulation affect the physiological flow characteristics of blood as a liquid organ. These artificial systems consist of a wide variety of biomaterials with different geometries and, therefore, with their own flow properties. Secondary flow also occurs in extra – as well as in intracorporeal circulation. Methods In order to investigate the influence of vortical flow conditions a modified Taylor-Couette system was introduced. It consisted of two coaxial cylinders whose surfaces were the target of investigation. The annular gap was filled with donor blood shear and secondary flows were produced by rotating the inner cylinder. Platelet activation and protein adsorption were investigated as markers for thrombogenicity. Results At shear rates high enough to establish stable Taylor vortices (G ≥ 550 s −1) significant differences between vortical Taylor flow and steady laminar flow were detected. At shear rates of G ≥ 550 s −1 laminar flow caused a significantly higher platelet drop and PF4 release when compared to Taylor vortex flow. Also protein adsorption per square unit was significantly higher for laminar flow. Conclusions Based on the present data we conclude that vortical flow patterns lead to an accumulation of platelets and plasma proteins in the vortex center and therefore to a decreased probability of contact between platelets and material surfaces. It can be concluded that a preactivation of the platelets circulating in extracorporeal circuits can be manifested downstream in other geometrical configurations and flow conditions.

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 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.

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.

scholarly journals Spin-up in a tank induced by a rotating bluff body

1999 ◽  
Vol 388 ◽  
pp. 49-68 ◽  
Author(s):  
D. MAYNES ◽  
J. KLEWICKI ◽  
P. McMURTRY
Keyword(s):  
Steady State ◽  
Turbulent Diffusion ◽  
Bluff Body ◽  
Fluid Velocity ◽  
Tangential Velocity ◽  
The Body ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
Acceleration Rate ◽  
Time Required

Spin-up of a turbulent flow in a cylindrical tank caused by a rotating bluff body has been investigated using flow visualization, fluid velocity measurements, and hydrodynamic torque measurements. During the spin-up process three distinct temporal regimes exist. These regimes are: (i) a build-up regime where the torque and the tangential velocity fluctuations in the close proximity of the body remain constant; (ii) a decay regime where these quantities decay with power-law relations; and (iii) a mean flow steady state where these values remain relatively constant. Experiments were conducted in two tanks differing in volume by a factor of 80 and with a large range of bluff body sizes. A non-dimensional time scale, τ, based upon turbulent diffusion is determined and the tangential velocity fluctuations and torque coefficient start to decay at a fixed value of τ. Likewise, steady state is attained at a larger fixed value of τ. This time scaling is physically based upon the time required for momentum to be transferred over the entire tank volume due to turbulent diffusion, and is general for any body size, tank size, rotation rate, and acceleration rate.

Sign in / Sign up

Export Citation Format

Share Document