Interaction of infinite thin elastic cylindrical shell and pulsating spherical inclusion in potential subsonic flow of ideal compressible liquid

In the present paper a method is proposed to investigate behaviour of the axis symmetric system consisting of an infinite thin elastic cylindrical shell, filled by potential flow of ideal compressible liquid and containing pulsating spherical inclusion. This coupled problem is considered in the framework of classical mechanics models: linear potential flow theory and thin elastic shells theory based on the Kirchhoff - Love hypotheses. The approach suggested consists in possibility of rewriting general solution of the corresponding mathematical physics equations from one to the other coordinate system. It enables to satisfy boundary conditions on both the spherical and the cylindrical surfaces and to get an exact analytical solution (as a Fourier series) of the coupled interaction problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a free piston problem for potential ideal fluid flow

Our goal was to model and analyze a stationary and evolutionary potential ideal fluid flow through the junction of two pipes in the gravity field. Inside the ‘vertical’ pipe, there is a heavy piston that can freely move along the pipe. In the stationary case, we are interested in the equilibrium position of the piston in dependence on the geometry of junction, and in the evolutionary case, we study motion of the piston also in dependence on geometry. We formulate corresponding initial and boundary value problems and prove the existence results. The problem is nonlinear because the domain is unknown. Furthermore, we study some qualitative properties of the solutions and compare them with the qualitative properties of a free piston problem for Newtonian fluid flow. All theoretical results are illustrated with numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytic construction of the near field in a transonic flow near a thin axisymmetric body

A solution of the axisymmetric problem of unsteady transonic flow around thin bodies of revolution is proposed in the form of a double series expansion in powers of the distance to the axis of symmetry and its logarithm in a neighborhood of a given point at the symmetry axis. Chains of recurrence equations are obtained for the coefficients of the series. The convergence of the constructed series is proved by the method of special majorants. The theorem of existence and uniqueness of the solution to the boundary-value problem for a nonlinear partial differential equation with a singularity at the symmetry axis is obtained in the asymptotic model of unsteady transonic flow under consideration. Thereby the application of the proposed series is justified to the problems of unsteady transonic flow around thin axisymmetric bodies with a drift of the nonpenetration condition onto the symmetry axis. Hence, these series can be used in numerical-analytical methods and model computations.     

Two dimensional incompressible ideal flow around a thin obstacle tending to a curve

In this work we study the asymptotic behavior of solutions of the incompressible two dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by Iftimie, Lopes Filho and Nussenzveig Lopes, obtained in the context of an obstacle tending to a point, see [D. Iftimie, M.C. Lopes Filho, H.J. Nussenzveig Lopes, Two dimensional incompressible ideal flow around a small obstacle, Comm. Partial Differential Equations 28 (1–2) (2003) 349–379].     

Forced axisymmetric oscillations of a viscoelastic cylindrical shell

The variational problem of forced oscillations of a cylindrical shell is reduced to a system of linear integrodifferential equations for which a periodic solution is constructed.Moscow Institute of Electronic Machinery. Translated from Mekhanika Polimerov, No. 6, pp. 1111–1114, November–December, 1975.     

Non-isothermal fluid flow through a thin pipe with cooling

The stationary flow of a Boussinesquian fluid with temperature-dependent viscosity through a thin straight pipe is considered. The fluid in the pipe is cooled by the exterior medium. The asymptotic approximation of the solution is built and rigorously justified by proving the error estimate in terms of domain thickness. The boundary layers for the temperature at the ends of the pipe are studied.     

Creep of a thermoplastic cylindrical shell under axisymmetric loading

The solution of the problem of creep of an axisymmetrically loaded thermoplastic cylindrical shell is considered. The strains and stresses for the zero-moment zone and with allowance for the edge effect are predicted on the basis of Kachanov's variational method using a computer. An algorithm is constructed for polyethylene and PVC shells at various values of the load. The analysis of the results obtained is illustrated by the calculation data for individual variants of the program.Leningrad Mozhaiskii Military Engineering Academy. Translated from Mekhanika Polimerov, No. 3, pp. 512–518, May–June, 1969.     

On steady irrotational flow of incompressible ideal fluid in a circular domain with free surface

We study irrotational steady flows of an incompressible ideal fluid in a two-dimensional circular domain, with free surface. Stationary solutions have been studied as bifurcation problems assuming the obstacle exactly circular, and in the presence of surface tension. In this paper, disregarding the surface tension, for non circular obstacles, we analize the set of solutions close to bifurcation points letting the Froud number as driving parameter.

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Sunto Si studiano moti irrotazionali stazionari di un fluido ideale incomprimibile in un dominio bidimensionale circolare con superficie libera. Di recente, le soluzioni stazionarie sono considerate come problemi di biforcazione assumendo che l’ostacolo sia un cerchio, supponendo che vi sia una tensione superficiale sulla superficie libera. In questo lavoro trascurando la tensione superficiale e considerando ostacoli non circolari, analizziamo l’insieme delle soluzioni vicino punti di biforcazione al variare del numero di Fround.

     

Steady vortex pairs in two phase shear flow of an ideal fluid

This study proves an existence of a steady vortex pairs in two phase shear flow in plane domain. The method was used is a variational principle in which a functional related to the kinetic energy can be maximised over the set where the vorticity being a rearrangement of a prescribed function.     

A modified least squares FE-method for ideal fluid flow problems

A modified least squares FE-method suitable e.g. for calculating the ideal fluid flow is presented. It turns out to be essentially more efficient than the conventional least squares method.     

Arterial dynamics based on the model of a multilayered shell with fluid flow

The dynamic process in a blood vessel segment of finite length is investigated. The vessel is assumed to be a multilayer cylindrical shell consisting of a large number of alternating layers, each of which possesses anisotropic elastic properties. Geometric nonlinearity is taken into account. The blood is assumed to be an ideal compressible fluid. A numerical solution has been obtained using a computer.     

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.     

Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell

The purpose of this paper is to study bifurcation points of the equation T(v) = L(λ,v) + M(λ,v), (λ,v) ? Λ × D in Banach spaces, where for any fixed λ ? Λ, T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ,0) = 0 for all λ ? Λ. We assume that λ is a characteristic value of the pair (T, L) such that the mapping T – L(λ ,·) is Fredholm with nullity p and index s, p > s ? 0. We shall find some sufficient conditions to show that (λ ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non-linear ordinary differential equations of second order.     

Rotation of an axisymmetric particle in a plane flow

The rotation of an inertialess ellipsoidal particle in a shear flow of a Newtonian fluid has been firstly analyzed by Jeffery [1]. He found that the particle rotates such that the end of its symmetry axis describes a closed periodic orbit. Based on the balance equation of the angular momentum we derived the equation of rotational motion of a cylindrical particle, that is suspended in a plane shear flow field of a viscous fluid, and solved numerically. The rotary inertia is taken into account. The solution is compared with the rotation of a slender particle. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On axisymmetric stokes flow past a torus

A method is presented for determining the exact solution of the Stokes equation for axisymmetric streaming flow past a torus. By solving directly for the velocity and pressure fields rather than introducing a stream function, the problem is reduced to the solution of a second order difference equation for a coefficient sequence. The force acting on the torus is evaluated for a number of values of the parameter defining the torus geometry.

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Zusammenfassung In dieser Arbeit wird eine Methode entwickelt um die exakte Lösung der Stokes' schen Gleichung für einen axisymmetrischen Fluss um einen Torus zu erhalten. Indem man direkt Geschwindgkeits- und Druckverteilung ausrechnet (statt eine Stromfunktion einzuführen) wird das Problem auf die Lösung einer Differenzengleichung zweiter Ordnung für eine Folge von Koeffizienten reduziert. Die am Torus wirksame Kraft wird dann für mehrere Parameterwerte der Torusgeometrie bestimmt.

     

An improved nonlinear Reynolds equation for a thin flow of a viscous incompressible fluid

A scalar nonlinear second-order equation describing a fluid flow between two closely spaced rigid walls is constructed on the basis of an asymptotic analysis of the Navier-Stokes equations. This equation takes into account the convective term and the surface curvature; it improves the Reynolds equation and provides a two-term asymptotics for the solution to the initial problem. Integral and pointwise error estimates are obtained. It is demonstrated that the one-dimensional model cannot be improved further.     

Homotopy Analysis Method for the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall

In this article, a powerful analytical method, called the Homotopy Analysis Method (HAM) is introduced to obtain the exact solutions of heat transfer equation of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall for turbine cooling applications. The HAM is employed to obtain the expressions for velocity and temperature fields. Tables are presented for various parameters on the velocity and temperature fields. These results are compared with the solutions which are obtained by Numerical Methods (NM). Also the convergence of the obtained HAM solution is discussed explicitly. These comparisons show that this analytical method is strongly powerful to solve nonlinear problems arising in heat transfer.