Stability of a viscous fluid between rotating cylinders with axial flow and pressure gradient round the cylinders

1973 ◽  
Vol 16 (5) ◽  
pp. 577 ◽  
Author(s):  
L. Elliott
Keyword(s):  
Viscous Fluid ◽  
Pressure Gradient ◽  
Axial Flow ◽  
Rotating Cylinders

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 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.

scholarly journals Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field

2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Mhd Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent Viscosity

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.

Effect of Transverse Curvature on Turbulent-Boundary-Layer Characteristics

1958 ◽  
Vol 2 (04) ◽  
pp. 33-51
Author(s):  
Yun-Sheng Yu
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Shearing Stress ◽  
Transverse Curvature ◽  
Similarity Laws

Tests made on the turbulent boundary layer on a circular cylinder in axial flow at zero pressure gradient are described. From the measurements, similarity laws of the velocity profile are formulated, and various boundary-layer characteristics are evaluated and compared with the flatplate results. It is found that the effect of transverse curvature is to increase the surface shearing stress and to decrease the boundary-layer thickness, and that the latter variation is more pronounced than the former.

scholarly journals Simulation of steady-state cuttings transport through a horizontal annulus channel

2019 ◽  
Vol 196 ◽  
pp. 00011 ◽  
Author(s):  
Yaroslav Ignatenko ◽  
Andrey Gavrilov ◽  
Oleg Bocharov ◽  
Roland May
Keyword(s):  
Steady State ◽  
Pressure Gradient ◽  
Yield Stress ◽  
Cross Section ◽  
Drilling Fluid ◽  
Drill Pipe ◽  
Axial Flow ◽  
Cuttings Transport ◽  
Rigid Spheres ◽  
Pipe Rotation

The current study is devoted to simulating cuttings transport by drilling fluid through a horizontal section of borehole with an annular cross section. Drill pipe rotates in fixed eccentric position. Steady-state flow is considered. Cuttings are rigid spheres with equal diameters. The carrying fluid is drilling mud with Herschel-Bulkley rheology. Suspension rheology depends on local shear rate and particles concentration. Continuous mixture model with algebraic equation for particles slipping velocity is used. Two hydrodynamic regimes are considered: axial flow without drill pipe rotation and with drill pipe rotation. In the case of axial flow was shown that increasing of power index n and consistency factor k increases pressure gradient and decreases cuttings concentration. Increasing of yield stress leads to increasing of pressure gradient and cuttings concentration. Cuttings concentration achieves constant value for high yield stress and not depends on it. Rotation of the drill pipe significantly changes the flow structure: pressure loss occurs and particles concentration decreases in the cross section. Two basic regimes of rotational flow are observed: domination of primary vortex around drill pipe and domination secondary vorticity structures. Transition between regimes leads to significant changes of flow integral parameters.

scholarly journals Stability of lubricated viscous gravity currents. Part 1. Internal and frontal analyses and stabilisation by horizontal shear

2019 ◽  
Vol 871 ◽  
pp. 970-1006 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Viscous Fluid ◽  
Pressure Gradient ◽  
Dynamic Pressure ◽  
Jump Discontinuity ◽  
Local Analysis ◽  
Instability Criterion ◽  
Shear Stresses ◽  
Horizontal Shear ◽  
Dynamical Regimes ◽  
Inner Region

A novel viscous fingering instability, involving a less viscous fluid intruding underneath a current of more viscous fluid, was recently observed in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655). We examine the origin of the instability by asking whether the instability is an internal instability, arising from internal dynamics, or a frontal instability, arising from viscous intrusion. We find it is the latter and characterise the instability criterion in terms of viscosity difference or, equivalently, the jump in hydrostatic pressure gradient at the intrusion front. The mechanism of this instability is similar to, but contrasts with, the Saffman–Taylor instability, which occurs as a result of a jump in dynamic pressure gradient across the intrusion front. We focus on the limit in which the two viscous fluids are of equal density, in which a frontal singularity, arising at the intrusion, or lubrication, front, becomes a jump discontinuity, and perform a local analysis in an inner region near the lubrication front, which we match asymptotically to the far field. We also investigate the large-wavenumber stabilisation by transverse shear stresses in two dynamical regimes: a regime in which the wavelength of the perturbations is much smaller than the thickness of both layers of fluid, in which case the flow of the perturbations is resisted dominantly by horizontal shear stresses; and an intermediate regime, in which both vertical and horizontal shear stresses are important.

Instability of the flow between rotating cylinders: the wide-gap problem

1964 ◽  
Vol 20 (1) ◽  
pp. 35-46 ◽  
Author(s):  
E. M. Sparrow ◽  
W. D. Munro ◽  
V. K. Jonsson
Keyword(s):  
Viscous Fluid ◽  
Closed Form ◽  
Solution Method ◽  
Analytical Investigation ◽  
Radius Ratio ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Coaxial Cylinders ◽  
Wave Numbers ◽  
Wide Gap

An analytical investigation is carried out to determine the conditions for instability in a viscous fluid contained between rotating coaxial cylinders of arbitrary radius ratio. A solution method is outlined and then applied to cylinders having radius ratios ranging from 0·95 to 0·1. Consideration is given to both cases wherein the cylinders are rotating in the same direction and in opposite directions. Results are reported for the Taylor numbers and wave-numbers which mark the onset of instability. The present results are also employed to delineate the range of applicability of the closed-form instability predictions of Taylor and of Meksyn, which were derived for narrow-gap conditions.

scholarly journals On the two-dimensional steady flow of a viscous fluid behind a solid body.-II

1933 ◽  
Vol 142 (847) ◽  
pp. 563-573 ◽  
Keyword(s):  
Experimental Study ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Steady Flow ◽  
Solid Body ◽  
Asymptotic Approximation ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Prandtl Equations ◽  
Sufficient Distance

One reason for carrying out the calculations of the previous paper was to provide material for an experimental study of the transition to turbulence in the wake behind a plate parallel to the stream. A second reason was to compare the results with certain results due to Filon, who has calculated both the List and second approximations to the velocity at a considerable distance from a fixed cylindrical obstacle in an unlimited stream whose velocity at infinity is constant.* He also uses the notions of the Oseen approximation; that is to say, he assumes that the departures from the undisturbed velocity are small, and neglects terms quadratic in these departures for the first approximations, etc .; but he does not assume that v is small and does not use the Prandtl equations. Thus the formulæ of paper 1, paragraph 2, should be limiting forms, for small v, of Filon's formulæ for a symmetrical wake. This is verified in paragraph 2 below; and the calculations in paper 1, paragraph 2, other than the attempt at a third approximation, may be regarded as a simplified form of Filon's calculations. The direct simplification of Filon's results gives the formulæ 2 (31) (p. 569), for the velocity at a sufficient distance downstream in any symmetrical wake provided that the motion is steady, whether v is small or not. these formulæ differ only in the last terms from the formulæ 2 (27) on p. 553 of paper 1, obtained from the Prandtl equations, and these terms are negligible, compared with the others, when v is small, (For the meaning of the symbols, see paragraph 1.3 of paper 1.) Thus the first asymptotic approximation is exactly the same here as in the previous paper ; in the second approximation the more accurate results of this paper contain extra terms, which it is shown on p. 567 arise entirely from the previous neglect of the pressure gradient in the direction of the stream.

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