Drag on a circular cylinder oscillating in an elastico-viscous fluid

Résumé On calcule la force agissant sur un cylindre soumis à de petites oscillations latérales dans une masse infinie de fluide élastique et visqueux. On trouve que l'élasticité dans le liquide a pour effet de réduire à la fois la masse virtuelle du cylindre et la grandeur de la force d'amortissement agissant sur le cylindre.     

The damping force on a body oscillating in an elastico-viscous fluid

Résumé On calcule la force d'amortissement agissant sur un corps de forme arbitraire auquel on fait subir de petites oscillations latérales dans une expansion infinie de liquide élastique et visqueux. On montre que l'élasticité a pour effet de réduire la résistance à des fréquences hautes et de l'augmenter à des fréquences basses.     

Numerical investigation of laminar fluid flow in an oscillating sphere

The paper deals with the numerical simulation of three dimensional oscillating fluid flow of filled and partial filled hollow spheres. We use a program based on finite volume method developed by the DLR. Our main interest is on the secondary flow in the middle plane. Results are presented for Newtonian fluids in dependence of different boundary conditions which are compared with analytical and experimental investigations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A boundary-layer in an elastico-viscous fluid

Zusammenfassung Die Prandtlsche Grenzschichttheorie wird verallgemeinert, so dass sie die Nollschen «einfachen Flüssigkeiten» erfasst. Es wird bewiesen, dass bei Flüssigkeiten mit geringem «Erinnerungsvermögen» die in der Grenzschicht vorhandenen Spannungen denjenigen ähnlich sind, welche bei einer einfachen Schubbeanspruchung vorkommen.     

Some exact solutions of an elastico-viscous fluid

The exact solutions for the unsteady flow of an elastico-viscous fluid caused by general periodic oscillations are obtained. Further, the plate is assumed to be rigid as well as porous executing periodic rotary oscillations. The velocity field and shear stress are established.     

Unsteady flow of an elastico-viscous fluid past a circular cylinder

Résumé Une solution numérique est obtenue pour l'écoulement initial d'un fluid élastique et visqueux autour d'un cylindre circulaire, à nombres de Reynolds 40 et 100. On emploi la méthode d'integration numérique de l'équation de tourbillon.     

Stability of the flow of an elastico-viscous fluid

Summary The eigenvalues of the generalized Orr-Sommerfeld equation for an elasticoviscous fluid are found for a constant velocity profile. The result shows that the effect of elasticity is to stabilize the flow.It is also shown that the second-order equation of state is not a suitable model for a fluid when the stability of that fluid is to be analysed.

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Zusammenfassung Die Eigenwerte der allgemeinen Orr-Sommerfeld-Gleichung für eine elastisch-viskose Flüssigkeit werden für ein Profil mit konstanter Geschwindigkeit angegeben. Das Ergebnis beweist, daß der Einfluß der Elastizität eine Stabilisierung der Strömung bewirkt.Es wird auch gezeigt, daß die Zustandsgleichung zweiter Ordnung kein geeignetes Modell für eine Flüssigkeit ist, deren Stabilität analysiert werden soll.

     

Drag on an elliptic cylinder in a fluid particle suspension

An elliptic cylinder is performing oscillations parallel to either of the principal axes of the cross-sectional ellipse in a fluid particle suspension. The stream function governing the flow and the velocity components are determined in terms of Mathieu functions. The drag on the cylinder is evaluated and expressed in terms of two parametersK andK. The effects of the variation of the frequency parameter, eccentricity parameter and relaxation time parameter on the drag parametersK, K is studied numerically.     

Unsteady motion of a spheroid in an elastico-viscous liquid

In this paper we have considered the unsteady motion of a spheroid moving from rest in viscoelastic fluid. The paper has been divided into two sections. In Section A a general formula as well as approximate formula for the drag has been calculated. In Section B the expression for the velocity of the spheroid started from rest under the action of constant force has been investigated.     

Unsteady motion of a spheroid in an elastico-viscous liquid

In this paper we have considered the unsteady motion of a spheroid moving from rest in viscoelastic fluid. The paper has been divided into two sections. In Section A a general formula as well as approximate formula for the drag has been calculated. In Section B the expression for the velocity of the spheroid started from rest under the action of constant force has been investigated.

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Zusammenfassung In dieser Arbeit wird die nicht-stationäre Bewegung eines Spheroids von der Ruhe in einem viskoelastischen Fluid betrachtet. Die Arbeit ist in zwei Abschnitte geteilt. Im ersten Teil werden allgemeine Formeln sowie Näherungen für den Widerstand entwickelt. Im zweiten Abschnitt werden Ausdrücke für die Geschwindigkeit eines Speroids hergeleitet, welches von der Ruhe aus unter dem Einfluss einer konstanten Kraft sich bewegt.

     

Laminar flow of an elastico-viscous fluid between two parallel walls with heat transfer

Zusammenfassung Für eine laminar zwischen zwei parallelen Wänden strömende viskoelastische Flüssigkeit mit Stoffgleichung nachNoll wird der Wärmeübergang zwischen den Wänden für konstante bzw. linear veränderliche Wandtemperatur berechnet.     

A study of an arbitrary Stokes flow past a fluid coated sphere in a fluid of a different viscosity

A general method to discuss the problem of an arbitrary Stokes flow (both axisymmetric and non-axisymmetric flows) of a viscous, incompressible fluid past a sphere with a thin coating of a fluid of a different viscosity is considered. We derive the expressions for the drag and torque experienced by the fluid coated sphere and also discuss the conditions for the reduction of the drag on the fluid coated sphere. In fact, we show that the drag reduces compared to the drag on a rigid sphere of the same radius when the unperturbed velocity is either harmonic or purely biharmonic, i.e., of the form ${r^2\vec{\textbf{v}}}$ , where ${\vec{\textbf{v}}}$ is a harmonic function. Previously Johnson (J Fluid Mech 110:217–238, 1981), who considered a uniform flow showed that the drag on the fluid coated sphere reduces compared to the drag on the uncoated sphere when the ratio of the surrounding fluid viscosity to the fluid-film viscosity is greater than 4. We show that this result is true when the undisturbed velocity is harmonic or purely biharmonic, uniform flow being a special case of the former. However, we illustrate by an example that the drag may increase in a general Stokes flow even if this ratio is greater than 4. Moreover, when the unperturbed velocity is harmonic or purely biharmonic, and the ratio of the surrounding fluid viscosity to the fluid-film viscosity is greater than 4 for a fixed value of the viscosity of the ambient fluid, we determine the thickness of the coating for which the drag is minimum.     

Slow rotation of a sphere in a slightly viscoelastic fluid contained in an infinite cylinder

Zusammenfassung In den letzten Jahren haben viskoelastische Strömungen an Bedeutung gewonnen. Wegen des nichtlinearen Charakters dieser Probleme ist es notwendig, vereinfachende Verfahren zu verwenden.Langlois undRivlin haben eine Anzahl solcher Aufgaben mit besonderen mathematischen Verfahren gelöst. In der klassischen Dynamik viskoser Flüssigkeiten ist das Problem der langsamen Bewegung einer Kugel in einem unendlichen Kreiszylinder durchBrenner undSonshine behandelt worden. In der vorliegenden Arbeit wird die Aufgabe verallgemeinert und die durch eine rotierende Kugel erzeugte Strömung einer schwach viskoelastischen Flüssigkeit in einem unendlichen Kreiszylinder untersucht. Die Bewegung wird so langsam vorausgesetzt, dass Trägheitsglieder vernachlässigbar sind. Das Geschwindigkeits- und das Druckfeld werden analytisch untersucht; ferner wird ein anschauliches Beispiel durchgerechnet und die Strömung im Bilde dargestellt.     

Starting solutions for oscillating motions of an Oldroyd-B fluid over a plane wall

In this paper, we establish the starting solutions for oscillating motions of an Oldroyd-B fluid between two side walls perpendicular to a plane wall. The expressions for the velocity field and the associated tangential stress at the bottom wall are obtained, presented under integral and series form. These satisfy all imposed initial and boundary conditions. The obtained solutions are graphically analyzed for the variations of interesting flow parameters. In the absence of side walls, all solutions that have been obtained reduce to those corresponding to the motion over an infinite plate. Moreover, the obtained solutions can be specialized to give similar solutions for Maxwell, second grade and Newtonian fluids performing the same motions.     

Scattering of an acoustic pulse by a rigid sphere on a sedimentary (fluid) bottom

We study the problem of scattering of acoustic pulses on a rigid sphere located near the interface of two media in one of which (the bottom) sound absorption is taken into account. To find the amplitudes of the echo-signal in the distal field we apply the Fourier transform with respect to time and the method of T-matrices. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 137–141.     

On hydromagnetic rotating flow of an Oldroyd-B fluid near an oscillating plate

An initial value investigation is made of the motion of an incompressible, viscoelastic, conducting Oldroyd-B fluid bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with a constant angular velocity about an axis normal to the plate. The flow is generated from rest in the rotating viscoelastic system due to harmonic oscillations of a given frequency superimposed on the plate in presence of a transverse magnetic field. The exact solutions for the velocity field and the wall shear stress are obtained. The results are examined quantitatively for a particular case of an impulsively moved plate and the effects of various flow parameters on them are discussed. Many known results are found to emerge as limiting cases of the present analysis.     

Slow motion of a micropolar fluid through a porous sphere bounded by a solid sphere

The paper examines the slow motion of a micropolar fluid produced by the relative motion of a solid sphere to an inside porous sphere. The result extends the Cunningham’s problem to micropolar fluid when the inner sphere is porous with prescribed radial suction/injection velocity at the surface of the sphere. The result can also be taken as an extension of the work of Ramkissoon and Majumdar when the fluid is bounded at a radiusr=b (b>a) but the solid sphere is replaced by a porous sphere. The force experienced by the inner sphere has been calculated and particular cases of interest have been deduced.     

On the solution of some boundary-value problems arising in elastico-viscous fluid mechanics

Résumé En mécanique des fluides visquex et élastiques, on rencontre souvent des équations différentielles du troisième ordre avec seulement deux conditions aux limites. On voit que la méthode ordinairement employée est approximative, n'est pas uniformément valable et donne des résultats faux. On donne également une autre méthode de résolution.