scholarly journals Stability of a viscous liquid contained between two rotating cylinders

1923 ◽  
Vol 102 (718) ◽  
pp. 541-542 ◽  
Keyword(s):  
Viscous Fluid ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Outer Cylinder ◽  
Steady Motion ◽  
Annular Space ◽  
Rotating Cylinders ◽  
High Speeds ◽  
Approximate Form ◽  
The Stability

Part I .—The stability for symmetrical disturbances of a viscous fluid in steady motion between concentric rotating cylinders is investigated mathematically. It is shown that at slow speeds the motion is always stable, but that at high speeds the motion is only stable when the ratio of the speed of the outer cylinder to that of the inner one exceeds a certain value. When the ratio is less than this or when it is negative the motion becomes unstable at high speeds. The “criterion” for stability is found, and in cases suitable for experimental verification an approximate form for the “criterion” is developed which is useful for numerical computation. The type of instability which may be expected to appear when the speed of the cylinders is slowly increased is shown to consist of symmetrical ring-shaped vortices spaced at regular intervals along the length of the cylinders. These vortices rotate alternately in opposite directions. Their dimensions are calculated and it is shown that they are contained in partitions of rectangular cross-section. In the case when the instability arises while both cylinders are rotating in the same direction, these rectangles are squares, so that the vortices are spaced at distances apart equal to the thickness of the annular space between the two cylinders. In the case when the cylinders rotate in opposite directions the spacing, or distance between the centres of neighbouring vortices, is smaller than this; and at the same time two systems of vortices develop—an inner system which is similar to the system which appears when the two cylinders rotate in the same direction, and an outer system, which is much less vigorous and rotates in the opposite direction to the adjacent members of the inner system.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

Rectangular Cross Section Beams Calculation on the Stability of a Flat Bending Shape Taking into Account the Initial Imperfections

2019 ◽  
Vol 974 ◽  
pp. 551-555 ◽  
Author(s):  
I.M. Zotov ◽  
Anastasia P. Lapina ◽  
Anton S. Chepurnenko ◽  
B.M. Yazyev
Keyword(s):  
Cross Section ◽  
Basic Equation ◽  
Applied Load ◽  
Rectangular Cross Section ◽  
Twist Angle ◽  
Stability Loss ◽  
Lateral Buckling ◽  
Initial Imperfections ◽  
Beam Stability ◽  
The Stability

The article presents the derivation of the resolving equation for the calculation of lateral buckling of rectangular beams. When deriving the basic equation, the initial imperfections of the beam are taken into account, which are specified in the form of the eccentricity of the applied load, the initial deflection in the plane of least stiffness and the initial twist angle. The influence of initial imperfections on the process of beam stability loss is investigated.

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.

scholarly journals Calculation of wooden beams on the stability of a flat bending shape enhancement

2018 ◽  
Vol 196 ◽  
pp. 01003 ◽  
Author(s):  
Anton Chepurnenko ◽  
Vera Ulianskaya ◽  
Serdar Yazyev ◽  
Ivan Zotov
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Stability Problem ◽  
Secular Equation ◽  
Rectangular Cross Section ◽  
Center Of Gravity ◽  
Critical Force ◽  
Distributed Load ◽  
Matlab Package ◽  
The Stability

Flat bending stability problem of constant rectangular cross section wooden beam, loaded by a distributed load is considered. Differential equation is provided for the cases when load is located not in the center of gravity. The solution of the equation is performed numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the Matlab package. A relationship between the value of the critical force and the position of the load application point is obtained. A linear approximating function is selected for this dependence.

The Effect of Thermal Diffusion on Flow Stability Between Two Rotating Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 318-322 ◽  
Author(s):  
Chin-Hsiu Li
Keyword(s):  
Temperature Gradient ◽  
Prandtl Number ◽  
Outer Cylinder ◽  
Variable Density ◽  
Radial Temperature Gradient ◽  
Rotating Cylinders ◽  
Radial Temperature ◽  
Stabilizing Effect ◽  
The Stability ◽  
Very High

The influence of variable density on the stability of the flow between two rotating cylinders is re-examined. The instability is shown to set in as an oscillatory secondary flow which was overlooked by previous investigators. Results indicate that the radial temperature gradient destabilizes the flow if the outer cylinder is hotter than the inner one, and the destabilizing effect is enhanced if the Prandtl number is high. For the case where the inner cylinder is hotter than the outer one, the stabilizing effect due to the temperature gradient is shown to be weak for any Prandtl number. This modifies previous results which predicted a very high stabilizing effect due to the temperature gradient. The bifurcating structure of the stability curve is shown.

Recommendations for Designing Wooden Arches on Metal-toothed Plates

2021 ◽  
Author(s):  
Bohdan Demchyna ◽  
◽  
Yaroslav Shydlovskyi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Laboratory Testing ◽  
Horizontal Plane ◽  
Thrust Force ◽  
Rectangular Cross Section ◽  
Rectangular Section ◽  
Pilot Studies ◽  
Different Types ◽  
The Stability

This paper presents the findings of the pilot studies and recommendations for designing of two-hinged wooden arches. The prototype models of wooden arches with the span of 6mand the rise of 1m were designed. The models had a rectangular cross-section of 180x40mm and a T-section of 180x40mm with a plywood plate with the thickness of 6 mm and the width of 500mm. The main objective of the T-section was to ensure the stability of the arch. Each arch was composed of six segments –boards joined by clamping plates. The bowstring truss including two inclined tie bars enables carrying asymmetric loads and provides in-plane stability of the arch. A methodology for laboratory testing of the prototype models of wooden arches subjected to different types of loads was developed. Two prototypes of wooden arches were tested with rectangular cross-sections and two T-section ones subjected to the loading across the span, and two prototypes subjected to the half-span loading. In total, eight arches were tested. Deflections of arches, cross-section deformations and arch thrust force were recorded. The arches were tested until failure. The results of testing revealed insufficient stability of the arches with rectangular cross-section in the horizontal plane. For the arches with T-section the whole arch rib was damaged, the in-plane stability was ensured by the T-section. The collapsing force of the T-section arch was about 1.3 times greater than the collapsing force of the rectangular section arches.

scholarly journals 1. Stability of Fluid Motion.—Rectilineal Motion of Viscous Fluid between two Parallel Planes

1888 ◽  
Vol 14 ◽  
pp. 359-368 ◽  
Author(s):  
W. Thomson
Keyword(s):  
Viscous Fluid ◽  
Fluid Motion ◽  
Steady Motion ◽  
Philosophical Magazine ◽  
University Of Cambridge ◽  
The Stability ◽  
The University

Since the communication of the first of this series of articles to the Eoyal Society of Edinburgh in April, and its publication in the Philosophical Magazine in May and June, the stability or instability of the steady motion of a viscous fluid has been proposed as subject for the Adams Prize of the University of Cambridge for 1888.

scholarly journals XX. The potential of an anchor ring.-Part II

1893 ◽  
Vol 184 ◽  
pp. 1041-1106 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Steady Motion ◽  
Vortex Rings ◽  
Laplace’S Equation ◽  
Single Vortex ◽  
Laplace's Equation ◽  
The Stability ◽  
Work Done

This paper is a continuation of that at pp. 43-95 suprd , on “The Potential of an Anchor Bing.” In that paper the potential of an anchor ring was found at all external points; in this/its value is determined at internal points. The annular form of rotating gravitating fluid was also discussed in that paper; here the stability of such a ring is considered. In addition, the potential of a ring whose cross-section is elliptic, being of interest in connection with Saturn, is obtained. The similarity of the methods employed, as well as of the analysis, has led me to give in this paper also a determination of the steady motion of a single vortex-ring in an infinite fluid, and of several fine vortex rings on the same axis. In Section I. solutions of Laplace’s equation applicable to space inside an anchor ring are obtained. These results are applied to obtain the potential of a solid ring at internal points, and also of a distribution of matter on the surface of the ring. The work done in collecting the ring from infinity is obtained.

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.

scholarly journals XVII. The complete system of the periods of a hollow vortex ring

1895 ◽  
Vol 186 ◽  
pp. 603-619 ◽  
Keyword(s):  
Kinetic Theory ◽  
Vortex Ring ◽  
Cross Section ◽  
Steady Motion ◽  
Dynamical Theory ◽  
Vortex Theory ◽  
Wide Range ◽  
The Cross ◽  
Hollow Vortex ◽  
The Stability

According to the vortex theory of matter, atoms consist of vortex rings in an infinite perfect liquid, the æther. These rings may be either hollow or filled with otating liquid. The cross section of the hollow or rotating core is in the simplest ase small and the ring is circular. Such vortices have been investigated. It has been hown that they can exist, and that they are stable for certain types of deformation, in this paper the stability of the hollow vortex ring is investigated further, with a view to proving that it is stable for all small deformations of its surface. An attempt also made to make the vortex theory of matter agree with the kinetic theory of ases as regards the relation between the velocity and the energy of an atom. On he latter theory the energy of an atom varies as the square of its velocity, while on he former theory the energy decreases as the velocity increases. As the two theories liffer on a fundamental point, while the consequences of the kinetic theory agree over wide range with experiment, those of the vortex theory are likely to be in discrepancy therewith. However, no account has been taken of the electric change which an atom must hold if electrolysis is to be explained. This electrification will evidently alter the relation between the energy and the velocity. The nature of the change thus produced is here discussed for the case of a hollow vortex, the surface of which behaves as a conductor of electricity, a representation which is dynamically realised by the theory of a rotationally-elastic fluid æther developed in Mr. Larmor’s paper, “A Dynamical Theory of the Electric and Luminiferous Medium.” The small oscillations also are worked out with a view to the discussion of the stability of an electrified vortex. 2. The velocity of translation of the vortex in its steady motion is constant and perpendicular to its plane. By impressing on the whole liquid a velocity equal and opposite to this, the hollow is reduced to rest. Since the cross section of the hollow is small, any small length of it may be regarded as cylindrical. A cylindrical vortex must, by reason of symmetry, have its cross section a circle, so that the cross section of the hollow of the annular vortex is approximately circular, and the hollow itself approximately a tore.

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