scholarly journals Non-existence of an Inviscid Fluid Motion between Two Fixed Cylinders

1970 ◽  
Vol 34 (1) ◽  
pp. 83-87
Author(s):  
M Jalal Ahammad
Keyword(s):  
Stream Function ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Inviscid Fluid ◽  
Academy Of Sciences

A problem on the plane inviscid and irrotational fluid motion due to the presence of a linesource and sink in the region between two fixed co-axial circular cylinders is considered in terms ofthe stream function. It has been shown that the solution of the problem is not possible in the light ofthe Eulerian theory of inviscid fluid motion.Key words: Non-existence; Inviscid fluid motion; Fixed cylinderDOI: 10.3329/jbas.v34i1.5494Journal of Bangladesh Academy of Sciences, Vol.34, No.1, 83-87, 2010

scholarly journals A Problem on Viscous Fluid Motion Between two Fixed Cylinders

1970 ◽  
Vol 33 (1) ◽  
pp. 107-115
Author(s):  
SK Ken ◽  
MJ Ahammad
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Unit Length ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Fluid Bed ◽  
Academy Of Sciences ◽  
Viscous Fluid Motion

A problem on the two dimensional slow viscous fluid motion obeying the Stokes equations is solved in terms of the Earnshaw stream function, when a line source and equal line sink are arbitrarily situated in a viscous fluid bed between two fixed co-axial circular cylinders. Fluid mechanical properties of interest, such as drags and torques acting upon the cylinders are calculated. Also we have shown the variation of the forces per unit length on the inner cylinder with its radius keeping outer cylinder fixed, whose radius is assumed to be one. DOI: 10.3329/jbas.v33i1.2955 Journal of Bangladesh Academy of Sciences, Vol. 33, No. 1, 107-115, 2009

scholarly journals Stokes Flow between Two Cylinders

2012 ◽  
Vol 36 (1) ◽  
pp. 123-135
Author(s):  
A Murad ◽  
SK Sen
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
Hydrodynamic Force ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Line Sink ◽  
Academy Of Sciences ◽  
Viscous Fluid Motion

The two-dimensional slow viscous fluid motion between two co-axial circular cylinders showed  the inner cylinder is shear-free and the outer one is rigid. The flow is due to the presence of a line source and a line sink of equal strength on the outer cylinder. The stream function for the flow in the annular region is established. The hydrodynamic force on the inner shear-free cylinder has been  evaluated. Some numerical values for the force have been presented in a table and compared with  corresponding known values where both inner and outer cylinders are rigid. DOI: http://dx.doi.org/10.3329/jbas.v36i1.10928 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 1, 123-135, 2012

scholarly journals A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180642 ◽  
Author(s):  
H. Alemi Ardakani ◽  
T. J. Bridges ◽  
F. Gay-Balmaz ◽  
Y. H. Huang ◽  
C. Tronci
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Variational Principle ◽  
Stream Function ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Fluid Sloshing ◽  
Pressure Boundary Condition ◽  
Vessel Motion

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

scholarly journals The rotation of two circular cylinders in a viscous fluid

1922 ◽  
Vol 101 (709) ◽  
pp. 169-174 ◽  
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Stream Function ◽  
Elastic Stress ◽  
Steady Motion ◽  
Elastic Equilibrium ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Concentric Circles ◽  
Hydrodynamical Problem

In a previous communication we employed the solution of the equation ∇ 4 ψ = 0 in bipolar co-ordinates defined by α + iβ = log x + i ( y + a )/ x + i ( y - a ) (1) to discuss the problem of the elastic equilibrium of a plate bounded by any two non-concentric circles. There is a well-known analogy between plain elastic stress and two-dimensional steady motion of a viscous fluid, for which the stream-function satisfies ∇ 4 ψ = 0. The boundary conditions are, however, different in the two cases, and the hydrodynamical problem has its own special difficulties.

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

2016 ◽  
Vol 8 (5) ◽  
pp. 784-794 ◽  
Author(s):  
Vatsala Mathur ◽  
Kavita Khandelwal
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Newtonian Fluid ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Circular Cylinders ◽  
Generalized Solutions ◽  
Special Cases ◽  
Graphical Illustration

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Taylor dispersion in concentrated suspensions of rotating cylinders

1986 ◽  
Vol 164 ◽  
pp. 185-215 ◽  
Author(s):  
A. Nadim ◽  
R. G. Cox ◽  
H. Brenner
Keyword(s):  
Fluid Motion ◽  
Convective Motion ◽  
Taylor Dispersion ◽  
Transport Processes ◽  
Circular Cylinders ◽  
Matched Asymptotic Expansion ◽  
Concentrated Suspensions ◽  
Scale Invariant ◽  
Mass Transfer Processes ◽  
Diffusion Phenomena

Laminar heat- or mass-transfer processes are theoretically investigated for two-dimensional spatially periodic suspensions of circular cylinders, each member of which rotates steadily about its own axis under the influence of an external couple. The novelty of the ensuing convective-diffusion phenomena derives from the absence of convective motion at the suspension lengthscale (the ‘macroscale’), despite its presence at the interstitial or particle lengthscale (the ‘microscale’). The latter fluid motion consists of a cellular vortex-like flow characterized by closed streamlines. These periodically closed streamlines give rise to a situation in which there exists no net flow at the macroscale. The resulting macroscale transport of heat or mass thus proceeds purely by conduction, the rate being characterized by a tensor diffusivity — dependent upon the angular velocity of the cylinders. Matched-asymptotic-expansion methods together with generalized Taylor dispersion theory are used to calculate this macroscale conductivity in the dual limit of large rotary Péclet numbers and small gap widths between adjacent cylinders. This prototype study illustrates the fact that the usual separation of transport processes into distinct convective and conductive contributions is not generally a scale-invariant concept; that is, microscale convec-tional contributions to the transport of heat or mass are not generally representable by corresponding macroscale convectipnal contributions to the transport. Possible applications of the analysis exist in the area of enhanced conduction rates in ferrofluids or other dipolar fluids rotating relative to a fixed external field (or conversely).

scholarly journals Numerical Study on the Charge Transport in a Space between Concentric Circular Cylinders

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Y. K. Suh ◽  
K. H. Baek
Keyword(s):  
Charge Transport ◽  
Charge Distribution ◽  
Numerical Study ◽  
Fluid Motion ◽  
Reaction Rates ◽  
Essential Elements ◽  
Circular Cylinders ◽  
Double Layers ◽  
Total Charge ◽  
Numerical Solution Methods

Electrification is one of the key factors to be considered in the design of power transformers utilizing dielectric liquid as a coolant. Compared with enormous quantity of experimental and analytical studies on electrification, numerical simulations are very few. This paper describes essential elements of numerical solution methods for the charge transport equations in a space between concentric cylinders. It is found that maintaining the conservation property of the convective terms in the governing equations is of the uttermost importance for numerical accuracy, in particular at low reaction rates. Parametric study on the charge transport on the axial plane of the annular space with a predetermined velocity shows that when the convection effect is weak the solutions tend to a one-dimensional nature, where diffusion is simply balanced by conduction. As the convection effect is increased the contours of charge distribution approach the fluid streamlines. Thus, when the conduction effect is weak, charge distribution tends to be uniform and the role of the convection effect becomes insignificant. At an increased conduction effect, on the other hand, the fluid motion transports the charge within the electric double layers toward the top and bottom boundaries leading to an increased amount of total charge in the domain.

On the disturbance of the steady flow of an inviscid liquid between parallel planes

1934 ◽  
Vol 234 (732) ◽  
pp. 43-78 ◽  
Keyword(s):  
Mathematical Proof ◽  
Fluid Motion ◽  
Steady Motion ◽  
Circular Cylinders ◽  
General Validity ◽  
Inviscid Liquid ◽  
Characteristic Value ◽  
Characteristic Values ◽  
The Stability ◽  
Liquid Flows

1—In a number of papers dealing with the stability of fluid motion, RAYLEIGH employed a certain method, which we may refer to as the “characteristic-value” method. For some problems this method gives results in agreement with observation. For example, it establishes that a heterogeneous inviscid liquid at rest under gravity is stable if the density decreases steadily as we pass upward; it establishes that an inviscid liquid rotating between concentric circular cylinders is stable if, and only if, the square of the circulation increases steadily as we pass outward. This result was stated by RAYLEIGH, and its validity appears to be confirmed by the experiments of TAYLOR, but a simple < d 2 u 0 /dy 2 retains the same sign throughout the liquid, u 0 being the velocity in the steady motion and y the distance from one of the planes. This result is deduced from the fact that mathematical proof by the characteristic value method was not given. I have recently supplied such a proof, extending the problem to include a heterogeneous liquid. But when the method is applied to some other problems, the situation is not so satisfactory. Among the results to which Rayleigh was led is the following. If an inviscid liquid flows between parallel planes, the motion is stable if the characteristic values of a parameter in a certain differential equation cannot be complex, the implication being that they are therefore real. Rayleigh further claimed that the method established the stability of a uniform shearing motion, for which d 2 u 0 /dy 2 =0. KELVIN and LOVE criticized the method, and a review of the situation in 1907 was given by ORR. In spite of the fact that its general validity remains obscure, the characteristic-value method has been widely employed. It is not the purpose of the present paper to attempt to justify or to discredit the characteristic-value method in general. The paper deals only with the simplest of all stability problems, that of an inviscid liquid flowing between fixed parallel planes. In §2 the method is discussed in some detail and in §3 an argument is developed to show that Rayleigh’s criterion for stability, mentioned above, cannot be legitimately deduced by his method. He proved that complex characteristic values are impossible, and I now prove that real characteristic values are also impossible. The conclusion to be drawn is that the characteristic-value method is not applicable to this case.

scholarly journals The line of action of the resultant pressure in discontinuous fluid motion

1922 ◽  
Vol 102 (716) ◽  
pp. 361-372
Keyword(s):  
Stream Function ◽  
Complex Variable ◽  
Velocity Potential ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Fluid Stream

1. The problem of any barrier in a fluid stream is best attacked by the method due to Levi-Civita, of which useful accounts, with extensions, are given by Cisotti and Brillouin. The resultant pressure for any barrier has been given in terms of the constants defining the barrier; but the calculations required to find the line of action of this pressure have not been carried out. It is our object to supply this deficiency here. The motion is two-dimensional. Let the complex variable z (≡ x + iy ) define position in any plane perpendicular to the generators of the barrier, the x axis being parallel to the direction of the stream at infinity. We define u = ∂ϕ/∂ x = ∂ψ/∂ y , v = ∂ϕ/∂ y = -∂ψ/∂ x , where u , v are the velocity components, and ϕ, ψ are the velocity potential and stream function respectively. Let w ≡ ϕ + iψ and define ζ, Ω, r, θ so that ζ ≡ re θ = dz / dw ; Ω = log ζ ≡ log r + iθ . (1)

On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid

1986 ◽  
Vol 173 ◽  
pp. 289-302 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Euler Equations ◽  
Stream Function ◽  
Wide Class ◽  
Magnetic Relaxation ◽  
Topological Invariant ◽  
Vortex Rings ◽  
Inviscid Fluid ◽  
Arbitrary Signature ◽  
Axisymmetric Solutions ◽  
Uniform Stream

A wide class of solutions of the steady Euler equations, representing localized rotational disturbances imbedded in a uniform stream U0 is inferred by considering the process of magnetic relaxation to analogous magnetostatic equilibria. These solutions, which may be regarded as generalizations of vortex rings, are characterized by their streamline topology, distinct topologies giving rise to distinct solutions.Particular attention is paid to the class of axisymmetric solutions described by Stokes stream function ψ(s, z). It is argued that the appropriate topological ‘invariant’ characterizing the flow is the function Vψ representing the volume inside toroidal surfaces ψ = const, in the region of closed streamlines where ψ > 0. This function is described as the ‘signature’ of the flow, and it is shown that in a certain sense, flows with different signatures are topologically distinct. The approach yields a method by which flows of arbitrary signature V(ψ) may in principle be found, and the corresponding vorticity ωφ = sFψ calculated.

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