The stability of a viscous fluid between rotating cylinders with an axial flow

1960 ◽  
Vol 9 (4) ◽  
pp. 621-631 ◽  
Author(s):  
R. C. Diprima
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Axial Flow ◽  
Taylor Number ◽  
Small Reynolds Number ◽  
Rotating Cylinders ◽  
The Stability

The stability of a viscous fluid between two concentric rotating cylinders with an axial flow is investigated. It is assumed that the cylinders are rotating in the same direction and that the spacing between the cylinders is small. The critical Taylor number is computed for small Reynolds number associated with the axial flow. It is found that the critical Taylor number increases with increasing Reynolds number.

Stability of spiral flow between concentric circular cylinders at low axial Reynolds number

1965 ◽  
Vol 21 (4) ◽  
pp. 635-640 ◽  
Author(s):  
Subhendu K. Datta
Keyword(s):  
Reynolds Number ◽  
Perturbation Theory ◽  
Viscous Liquid ◽  
Axial Flow ◽  
Circular Cylinders ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
The Stability

The stability of a viscous liquid between two concentric rotating cylinders with an axial flow has been investigated. Attention has been confined to the case when the cylinders are rotating in the same direction, the gap between the cylinders is small and the axial flow is small. A perturbation theory valid in the limit when the axial Reynolds number R → 0 has been developed and corrections have been obtained for Chandrasekhar's earlier results.

The stability of a viscous fluid between rotating cylinders with an axial flow

1964 ◽  
Vol 19 (4) ◽  
pp. 528-538 ◽  
Author(s):  
E. R. Krueger ◽  
R. C. Di Prima
Keyword(s):  
Viscous Fluid ◽  
Viscous Flow ◽  
Axial Flow ◽  
Rotating Cylinders ◽  
Counter Rotation ◽  
Theoretical Investigations ◽  
The Stability

The stability of viscous flow between rotating cylinders with an axial flow has been investigated theoretically by Goldstein (1937), Chandrasekhar (1960, 1962), and Di Prima (1960); and experimentally by Cornish (1933), Fage (1938), Kaye & Elgar (1957), Donnelly & Fultz (1960) and Snyder (1962a). As was pointed out by Di Prima (1960) there were a number of discrepancies in the early work of the 1930's which were clarified in part by the papers of the 1960's. In turn, there appear to be certain small detailed differences in the more recent papers. In part it is these differences with which the present paper is concerned. In addition, the results of the previous theoretical investigations which are limited to the case in which the cylinders rotate in the same direction, are extended to the case of counter rotation.

The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids

1966 ◽  
Vol 24 (2) ◽  
pp. 321-334 ◽  
Author(s):  
D. W. Beard ◽  
M. H. Davies ◽  
K. Walters
Keyword(s):  
Viscous Flow ◽  
Couette Flow ◽  
Taylor Number ◽  
Linear Perturbation ◽  
Rotating Cylinders ◽  
Initial Value ◽  
Viscous Liquids ◽  
Maxwell Fluids ◽  
Newtonian Liquids ◽  
The Stability

Consideration is given to the possibility of overstability in the Couette flow of viscous and elastico-viscous liquids. The relevant linear perturbation equations are solved numerically using an initial-value technique. It is shown that over-stability is not possible in the case of Newtonian liquids for the cases considered. In contrast, overstability is to be expected in the case of moderately-elastic Maxwell liquids. The Taylor number associated with the overstable mode decreases steadily as the amount of elasticity in the liquid increases, and it is concluded that highly elastic Maxwell liquids can be very unstable indeed.

On Kelvin–Stuart vortices in a viscous fluid

2008 ◽  
Vol 366 (1876) ◽  
pp. 2717-2728 ◽  
Author(s):  
L.E Fraenkel
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Small Time ◽  
Navier Stokes ◽  
Initial Condition ◽  
Small Reynolds Number ◽  
The One ◽  
Stuart Vortices ◽  
Reversed Time

When one contemplates the one-parameter family of steady inviscid shear flows discovered by J. T. Stuart in 1967, an obvious thought is that these flows resemble a row of vortices diffusing in a viscous fluid, with the parameter playing the role of a reversed time. In this paper, we ask how close this resemblance is. Accordingly, the paper begins to explore Navier–Stokes solutions having as initial condition the classical, irrotational flow due to a row of point vortices. However, since we seek explicit answers, such exploration seems possible only in two relatively easy cases: that of small time and arbitrary Reynolds number and that of small Reynolds number and arbitrary time.

The stability of elastico-viscous flow between rotating cylinders. Part 2

1964 ◽  
Vol 19 (4) ◽  
pp. 557-560 ◽  
Author(s):  
R. H. Thomas ◽  
K. Walters
Keyword(s):  
Viscous Flow ◽  
Stability Problem ◽  
Narrow Channel ◽  
Taylor Number ◽  
Wave Number ◽  
Rotating Cylinders ◽  
Orthogonal Functions ◽  
Determinantal Equation ◽  
Coaxial Cylinders ◽  
The Stability

Further consideration is given to the stability of the flow of an idealized elasticoviscous liquid contained in the narrow channel between two rotating coaxial cylinders. The work of Part 1 (Thomas & Walters 1964) is extended to include highly elastic liquids. To facilitate this, use is made of the orthogonal functions used by Reid (1958) in his discussion of the associated Dean-type stability problem. It is shown that the critical Taylor number Tc decreases steadily as the amount of elasticity in the liquid increases, until a transition is reached after which the roots of the determinantal equation which determines the Taylor number T as a function of the wave-number ε become complex. It is concluded that the principle of exchange of stabilities may not hold for highly elastic liquids.

scholarly journals Flow characteristics analysis of a two-phase suspension between rotating porous cylinders with radial and axial flows

2018 ◽  
Vol 22 (4) ◽  
pp. 1857-1864
Author(s):  
Yu-Chuan Zhu ◽  
Qing-He Xiao ◽  
Ming-Xin Gao ◽  
Qian Liu ◽  
Zhanhong Wan
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Radial Flow ◽  
Outer Cylinder ◽  
Flow Characteristics ◽  
Axial Flow ◽  
Taylor Number ◽  
Two Phase ◽  
Characteristics Analysis ◽  
Correlation Parameters

The flow characteristics problem of the two-phase suspension in the design of filters is presented, and the hydrodynamic stability is carried out to study the flow characteristics of a two-phase suspension between a rotating porous inner cylinder and a concentric, stationary, porous outer cylinder when radial flow and axial flow are present. Linear stability analysis results in an eigenvalue problem that is solved numerically by Wan?s method. The results reveal that the critical Taylor number for the onset of instability is altered by other parameters. For given correlation parameters, increasing the axial Reynolds number increases the critical Taylor number for transition very slightly, the critical Taylor number decreases as the axial Reynolds number becomes negative.

Heat Transfer Enhancement of Reactor Utilizing Taylor-Poiseuille Flow

2014 ◽  
Author(s):  
Li Ye ◽  
Huajun Peng ◽  
Bo Zhou ◽  
Mo Yang ◽  
Zheng Li ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Regime ◽  
Poiseuille Flow ◽  
Axial Flow ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Taylor Number ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

Numerical studies have been conducted to determine the heat transfer performances in a Taylor-Poiseuille flow regime. The flow is confined between two different heated, concentric cylinders. The inner cylinder is allowed to rotate while the outer one remains fixed, an axial flow is added. The influences of rotation Taylor number and axial Reynolds number on heat transfer coefficients are investigated. Results show that temperature in the flow regime presents a remarkable sinusoidal periodicity as the result of the axial arrangement of Taylor vortices, so does the local heat transfer coefficients. Heat transfer efficiency gets strengthened with increasing Taylor number, while damped with increasing Reynolds number. The accuracy of the simulation is validated by compared to the existing linear stability analysis.

The effect of surfactant on the stability of a fluid filament embedded in a viscous fluid

1999 ◽  
Vol 382 ◽  
pp. 331-349 ◽  
Author(s):  
S. HANSEN ◽  
G. W. M. PETERS ◽  
H. E. H. MEIJER
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Viscous Fluid ◽  
High Elasticity ◽  
Fluid Filament ◽  
The Stability ◽  
Elasticity Number

The effect of surfactant on the breakup of a viscous filament, initially at rest, surrounded by another viscous fluid is studied using linear stability analysis. The role of the surfactant is characterized by the elasticity number – a high elasticity number implies that surfactant is important. As expected, the surfactant slows the growth rate of disturbances. The influence of surfactant on the dominant wavenumber is less trivial. In the Stokes regime, the dominant wavenumber for most viscosity ratios increases with the elasticity number; for filament to matrix viscosity ratios ranging from about 0.03 to 0.4, the dominant wavenumber decreases when the elasticity number increases. Interestingly, a surfactant does not affect the stability of a filament when the surface tension (or Reynolds) number is very large.

On the linear stability of spiral flow between rotating cylinders

1982 ◽  
Vol 382 (1782) ◽  
pp. 83-102 ◽  
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Stability Boundary ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
Compound Matrix Method ◽  
Compound Matrix ◽  
High Reynolds ◽  
The Stability ◽  
Axisymmetric Disturbances

A numerical study is made of the effects of both axisymmetric and non-axisymmetric disturbances on the stability of spiral flow between rotating cylinders. If we let Ω 1 and Ω 2 be the angular speeds of the inner and outer cylinders, and R 1 and R 2 be their respective radii, then for fixed values of η = R 1 / R 2 and μ = Ω 2 / Ω 1 , the onset of instability depends on both the Taylor number T and the axial Reynolds number R . Here R is based on the gap width between the cylinders and the average axial velocity of the basic flow, while T is based on the average angular speeds of the cylinders. Using the compound matrix method, we have computed the complete stability boundary in the R , T -plane for axisymmetric disturbances with η = 0.95 and μ = 0. We find that, for sufficiently high Reynolds numbers, there are two distinct axisymmetric modes corresponding to the usual shear and rotational instabilities. We have also obtained the stability boundaries for non-axisymmetric disturbances for R ≼ 6000 for η = 0.95 and 0.77 with μ = 0. These last results are found to be in substantial agreement with the experimental observations of Snyder (1962, 1965), Nagib (1972) and Mavec (1973) in the low and moderate axial Reynolds number régimes.

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