Experiments on the stability of spiral flow at low axial Reynolds numbers

1962 ◽  
Vol 265 (1321) ◽  
pp. 198-214 ◽  
Keyword(s):  
Perturbation Theory ◽  
Viscous Flow ◽  
Hydrodynamic Stability ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
The Stability

The hydrodynamic stability of viscous flow between rotating cylinders with superposed axial flow has been studied experimentally. The experiments were confined to the case where the outer cylinder is at rest and the gap between cylinders is small. Particular attention has been given to small rates of axial flow. The results compare satisfactorily with Chandrasekhar’s perturbation theory valid under these conditions.

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 spiral flow between rotating cylinders

1962 ◽  
Vol 265 (1321) ◽  
pp. 188-197 ◽  
Keyword(s):  
Reynolds Number ◽  
Perturbation Theory ◽  
Pressure Gradient ◽  
Viscous Flow ◽  
Axial Flow ◽  
Spiral Flow ◽  
Axial Pressure ◽  
Axial Pressure Gradient ◽  
The Mean ◽  
The Stability

The stability of viscous flow under an axial pressure gradient between two co-axial cylinders rotating in the same direction is considered. The critical Taylor number (T c) for the onset of instability is then a function of the Reynolds number (R) of the mean axial flow. A perturbation theory valid in the limit P-> 0 is developed and the formula T c (B) = T c (0) + 26.5P 2 (R-> 0) is established.

An Experimental Investigation of the Stability of Spiral Vortex Flow

1979 ◽  
Vol 21 (6) ◽  
pp. 397-402 ◽  
Author(s):  
M. M. Sorour ◽  
J. E. R. Coney
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Vortex Cell ◽  
Annular Gap ◽  
Spiral Vortex ◽  
Axial Pressure Gradient ◽  
The Stability

The hydrodynamic stability of the flow in an annular gap, formed by a stationary outer cylinder and a rotatable inner cylinder, through which an axial flow of air can be imposed, is studied experimentally. Two annulus radius ratios of 0.8 and 0.955 are considered, representing wide- and narrow-gap conditions, respectively. It is shown that, when a large, axial pressure gradient is superimposed on the tangential flow induced by the rotation of the inner cylinder, the characteristics of the flow at criticality change significantly from those at zero and low axial flows, the axial length and width of the resultant spiral vortex departing greatly from the known dimensions of a Taylor vortex cell at zero axial flow. Also, the drift velocity of the spiral vortex is found to vary with the axial flow. Axial Reynolds numbers, Rea, of up to 700 are considered.

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 viscous flow between rotating cylinders

1958 ◽  
Vol 246 (1246) ◽  
pp. 301-311 ◽  
Keyword(s):  
Viscous Flow ◽  
Hydrodynamic Stability ◽  
Numerical Results ◽  
Rotating Cylinders ◽  
Characteristic Value ◽  
The Stability

A method of solving the exact characteristic value problem to which a study of the hydrodynamic stability of viscous flow between rotating cylinders leads one, is described. In illustration of the method, detailed numerical results are obtained for the case when the ratio of the radii of the two cylinders is one-half.

Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow

1977 ◽  
Vol 81 (4) ◽  
pp. 641-655 ◽  
Author(s):  
K. C. Chung ◽  
K. N. Astill
Keyword(s):  
Amplification Factor ◽  
Hydrodynamic Instability ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Spiral Flow ◽  
Small Perturbations ◽  
Coaxial Cylinders ◽  
Counter Rotation ◽  
Concentric Cylinders ◽  
The Stability

A linear stability analysis is presented for flow between concentric cylinders when a fully developed axial flow is present. Small perturbations are assumed to be nonaxisymmetric. This leads to an eigenvalue problem with four eigenvalues: the critical Taylor number, an amplification factor and two wavenumbers. The presence of the tangential wavenumber permits prediction of the stability of spiral flow. This made it possible to model the flow more accurately and to extend the range of calculations to higher axial Reynolds numbers than had previously been attainable. Calculations were carried out for radius ratios from 0·95 to 0·1, Reynolds numbers as large as 300 and cases with co-rotation and counter-rotation of the cylinders.

scholarly journals Fluid friction between rotating cylinders I—Torque measurements

1936 ◽  
Vol 157 (892) ◽  
pp. 546-564 ◽  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Centrifugal Force ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Stream Line ◽  
Rotating Cylinders ◽  
Torque Measurements ◽  
Critical Reynolds Numbers ◽  
The Stability

The stability of fluid contained between concentric rotating cylinders has been investigated and it has been shown that, when only the inner cylinder rotates, the flow becomes unstable when a certain Reynolds number of the flow is exceeded. When the outer cylinder only is rotated, the flow is stable so far as disturbances of the type produced in the former case are concerned, but provided the Reynolds number of the flow exceeds a certain value, turbulence sets in. The object of the present experiments was partly to measure the torque reaction between two cylinders in the two cases in order to find the effect of centrifugal force on the turbulence, and partly to find the critical Reynolds numbers for the transition from stream-line to turbulent flow. The apparatus is shown diagrammatically in fig. 1.

The stability of viscous flow between rotating concentric cylinders with an axial flow

1979 ◽  
Vol 366 (1727) ◽  
pp. 555-573 ◽  
Keyword(s):  
Reynolds Number ◽  
Viscous Flow ◽  
Axial Velocity ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Average Value ◽  
Concentric Cylinders ◽  
Axial Pressure Gradient ◽  
Second Mode ◽  
The Stability

The stability of viscous flow between concentric cylinders with the inner cylinder rotating and with an axial flow due to an axial pressure gradient is considered. The analysis is motivated, in part, by recent papers by Hasoon & Martin (1977) and Chung & Astill (1977). Results are given for radius ratios ɳ = R 1 / R 2 = 1 (the small-gap limit), 0.95, and 0.9, and for values of the axial Reynolds number R up to 100. Here R 1 and R 2 are the radii of the inner and outer cylinders, respectively. For the small-gap problem, the results are compared with those obtained by approximating the angular velocity and/or the axial velocity by average values. Two of the conclusions of the paper are that the small-gap problem is a valid approximation to the ɳ ≠ 1 problem for ɳ near 1, and that the approximation of the axial velocity by its average value leads to qualitatively and quantitatively incorrect results. In addition, we find that for axial Reynolds numbers of about ninety a second mode of instability arises and there is a discontinuity in the axial wavenumber of the critical disturbance as a function of the Reynolds number.

Experiments on the stability of viscous flow between rotating cylinders II. Visual observations

1960 ◽  
Vol 258 (1292) ◽  
pp. 101-123 ◽  
Keyword(s):  
Experimental Data ◽  
Viscous Flow ◽  
Hydrodynamic Stability ◽  
Experimental Error ◽  
Asymptotic Form ◽  
Theoretical Calculations ◽  
Rotating Cylinders ◽  
Stability Relation ◽  
The Stability ◽  
Visual Observations

Measurements of the hydrodynamic stability of viscous flow between rotating cylinders have been made with an apparatus similar to that used by Taylor in his original experiments. The ratio of the radii of the cylinders was 1:2. The results confirm Chandrasekhar’s theoretical calculations within experimental error. The asymptotic form of the stability relation when the cylinders rotate in opposite directions is derived and found to agree with experimental data at hand.

The stability of viscous flow between rotating cylinders in the presence of a magnetic field. II

1961 ◽  
Vol 262 (1311) ◽  
pp. 443-454 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Rotating Cylinders ◽  
Counter Rotation ◽  
Angular Velocities ◽  
The Stability

The theory developed in an earlier paper (Chandrasekhar 1953) is extended to allow for counter-rotation of the two cylinders. Explicit results are given for the case when the two cylinders rotate in opposite directions with equal angular velocities.

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