Calculation of the flow of an ideal fluid past a wing of finite thickness

The problem of irrotational flow past a wing of finite thickness and finite span can be reduced by Green's formula to the solution of a system of Fredholm equations of the second kind on the surface of the wing [1]. The wake vortex sheet is represented by a free vortex surface. Besides panel methods (see, for example, [2]) there are also methods of approximate solution of this problem based on a preliminary discretization of the solution along the span of the wing in which the two-dimensional integral equations are reduced to a system of one-dimensional integral equations [1], for which numerical methods of solution have already been developed [3–6]. At the same time, a discretization is also realized for the wake vortex sheet along the span of the wing. In the present paper, this idea of numerical solution of the problem of irrotational flow past a wing of finite span is realized on the basis of an approximation of the unknown functions which is piecewise linear along the span. The wake vortex sheet is represented by vortex filaments [7] in the nonlinear problem. In the linear problem, the sheet is represented both by vortex filaments and by a vortex surface. Examples are given of an aerodynamic calculation for sweptback wings of finite thickness with a constriction, and the results of the calculation are also compared with experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 124–131, October–December, 1981.     

Effets d'entrée en écoulements pulsés non-newtoniens

Sommaire Le présent travail concerne l'étude des champs de vitesse dans la région d'entrée dans un écoulement pulsé, newtonien et pseudoplastique en conduites cylindriques circulaires. Trois méthodes d'étude ont été utilisées: une méthode analytique, une méthode aux différences finies et une méthode expérimentale basée sur la vélocimétrie à laser. Les résultats obtenus à l'aide de ces méthodes sont confrontés entre eux. Les influences des paramètres rhéologiques et hydrodynamiques sur ces écoulements sont également analysées.

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Summary The purpose of this work is the study of the entrance effects for pulsating flow of inelastic non-newtonian fluids in cylindrical tubes. Founding upon classic methods relating to steady flows, we consider this problem as development of hydrodynamic boundary layer. The evolutions of velocity profiles have been obtained on the one hand by laser velocimetry on aqueous solutions of high polymers and, on the other hand, by numerical resolution of non-linear equations relating to such flows. The relative influences of rheological and hydrodynamical parameters have been analysed and compared.

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Zusammenfassung Die vorliegende Veröffentlichung befaßt sich mit der Einlaufströmung in zylindrische Rohre für den Fall pulsierender Strömungen newtonscher und unelastischer nicht-newtonscher Flüssigkeiten. Dabei werden drei Untersuchungsmethoden verwendet: eine analytische Methode, eine numerische Methode auf der Basis der Finiten Differenzen und eine experimentelle Methode unter Einsatz eines Laser-Doppler-Anemometers. Die mit Hilfe dieser Methoden gewonnenen Ergebnisse werden miteinander verglichen und der Einfluß der verschiedenen rheologischen und hydrodynamischen Parameter auf die Strömungsform wird analysiert.

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Avec 9 figures et 3 tableaux     

On the elastodynamics of stiffened plates

Summary A method of determining the response of a stiffened elastic plate to a dynamic excitation is presented here. Green's function for such a combined system has been systematically derived based on the eigenfunctions of the system obtained through the application of Galerkin's method. With that Green's function a wide range of dynamic forcing functions can be considered.

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Zur elastodynamik versteifter platten

Übersicht Vorgestellt wird eine Methode zur Ermittlung der Antwort versteifter Platten auf dynamische Erregungen. Mit Hilfe der Eigenfunktionen des Systems, die durch Anwendung der Galerkin-Methode gewonnen werden, wird die Greensche Funktion solcher kombinierten Tragwerke systematisch hergeleitet. Damit kann ein weiter Bereich dynamischer Anregungsfunktionen behandelt werden.

     

Difference between the longitudinal Frenkel-Biot waves in water-and gas-saturated porous media

The problem of the propagation of longitudinal Biot waves in a porous medium saturated with a weakly compressible liquid (water) or a gas is considered theoretically. The frequency dependence of the phase velocities and damping coefficients is investigated numerically. It is shown that for a certain relationship between the parameters of the porous medium and the saturating fluid there is a “critical” frequency at which the properties of longitudinal waves of both kinds are identical. An analytical expression for this “critical” frequency is obtained. It is shown that for a gas-saturated porous medium, at a certain frequency, in both longitudinal waves the relative gas-matrix motion changes type. Assuming that the saturating-gas behavior corresponds to an adiabatic equation of state, an estimate is obtained for the threshold pore pressure necessary for the restructuring of the relative motion. The wave associated with matrix deformation is shown to have a high damping coefficient in a porous medium saturated with a weakly compressible liquid (water in the case considered) but to be only weakly damped in a gas-saturated porous medium.     

Numerical modeling of the single-phase Stefan problem in a layer with transparent and semitransparent boundaries

Numerical modeling of the single-phase Stefan problem in a semitransparent layer with transparent, nonabsorbing, and partially radiation-absorbing boundaries is performed. It is shown that at low temperatures of the medium, convection is a determining factor on the boundary of the irradiated sample, and at high temperatures, radiation is predominant. The absence of absorption on the boundaries of the layer leads to acceleration of the heating of the plate and considerable deceleration of melting processes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 84–91, May–June, 2006.     

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical simulations that there are obvious jumping phenomena in the resonant response–frequency curves. It is indicated from the phase portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear vibrations of the string-beam coupled system under certain conditions. An erratum to this article is available at .     

Variational solutions for some steady and non-steady laminar viscous flows with stagnation points

Recently, Lebon and Lambermont proposed a general variational principle for fluid mechanics. In this paper, the criterion is applied to steady and non-steady stagnation flows; the plane and the axisymmetrical cases are considered. By using Glansdorff-Prigogine self consistent method, approximate analytic solutions are derived. It is shown that the steady solution is rather quickly reached. For this latter case, the present solutions are compared with previous ones obtained by direct integration of the Navier-Stokes equations.