Perfectly conducting elliptic flow past an insulator

Résumé Pour illustrer les effets d'un champ magnétique sur un écoulement plan stationnaire d'un fluide non visqueux idéal, parfait conducteur d'électricité, on envisage les cas particuliers où le champ magnétique a une composante différente de zéro. On utilise l'analyse linéaire pour étudier les faibles perturbations d'un écoulement initialement uniforme.Nous considérons le mouvement, uniforme a l'infini amont, en présence d'une paroi rectiligne à laquelle fait suite une paroi courbe (faible perturbation) et un profil mince.

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This research was supported by the National Science Foundation under Grant GP-8719.     

Molecular modellingof flow past an inclined flat plate

Molecular flow past an inclined plate is simulated on a scientific personal computer. Wake flow and turbulent effects are described and discussed for various fluid speeds.     

Near critical laminar flow past an expansion ramp

Steady two-dimensional laminar flows past an expansion ramp are known to exist up to a critical ramp angle in the limit c as the Reynolds number tends to infinity. The theory of viscous-inviscid interaction combined with a local bifurcation analysis is used to study the evolution of three-dimensional unsteady perturbations if for both sub- and supercritical conditions. Special emphasis is placed on the effects of controlling devices and the phenomenon of bubble bursting. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotating flow past an elliptic-cylindrical bump of large aspect ratio

Summary Very slow flow of a rapidly rotating fluid past a right cylindrical obstacle of heightd on one of two co-rotating parallel planes, separated by a distanceh, is studied. The elliptic boundaryvalue problem for the geostrophic flow is formulated quite generally, and solutions are given for an infinitely-long ridge and an elliptic cylinder. A modified Ekman number,E _*v/d ², where is the inverse aspect ratio of the cylinder, characterizes the latter solution. ForE _*<1, the fluid flows around a stagnant Taylor column over the elliptic cylinder; forE _*1, the fluid flows over the cylinder as though it were an infinitely-long ridge;E _*=O(1) shows part of the fluid flowing over, and part around, the cylinder. The drag increases from orderE ^–1/4 to orderE ^–1 asE _* increases from small to large values.

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Zusammenfassung In dieser Arbeit wird die sehr langsame Strömung in einem rasch rotierenden Fluid untersucht um einen zylindrischen Körper, dessen Höhed die viel kleiner ist als die Distanzh der zwei unendlich ausgedehnten mitrotierenden parallelen Platten, welche das Fluid begrenzen; der Körper sitzt auf der unteren Platte. Eine allgemeine Formulierung des elliptischen Randwertproblems wurde für die geostrophische Strömung angegeben. Lösungen wurden für ein unendlich langes Wehr und einen elliptischen Zylinder gefunden. Eine modifizierte Ekman-Zahl,E _*=v/d ² E, in welcher das reziproke Verhältnis von Länge zu Durchmesser darstellt, charakterisiert die Lösung für den elliptischen Zylinder. WennE _*1, umgeht die Flüssigkeit die stagnierende Taylorsäule, die auf dem elliptischen Zylinder ruht; wennE _*1, geht die Flüssigkeit über den Zylinder, als ob er ein unendlich langes Wehr wäre; wennE _*=0(1), geht ein Teil der Flüssigkeit über den Zylinder und ein anderer um ihn herum. Der Reibungswiderstand erhöht sich von 0(E ^–1/4) zu 0(E ^–1), wennE _* von kleinen zu grossen Werten ansteigt.

     

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.     

The flow of an electrically conducting fluid at a rear stagnation point

Summary We consider the impulsively generated magnetohydrodynamic flow at a rear stagnation point. The work of Leibovich is carried further by formulating the inner viscous problem and providing analytical solutions and complete numerical solutions for the entire range of the interaction parameter. It is shown that the present results are consistent with previously obtained numerical solutions to the steady equations of both similarity and non-similarity form.

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Résumé Nous considérons l'écoulement magneto-hydrodynamique impulsivement engendré à un point de stagnation arrière. On porte plus loin l'étude de Leibovich par la formulation du problème visqueux intérieur et en fournissant des solutions analytiques et numériques complètes correspondantes au champ entier du paramètre d'interaction. On montre que les résultats actuels sont en accord avec les solutions numériques, et de similitude et de non-similitude, déjà connues des équations stationnaires.

     

Flow of a conducting dusty gas past a flat plate

An exact solution is derived by Laplace-transform technique for the problem of the flow of a conducting dusty gas occupying a semi-infinite space in the presence of a transverse magnet field. It is assumed that the flow is independent of the distance parallel to the plate and that the mass concentration of dust is small. Formulas are derived in terms of a constant external impulsive velocity field for the velocity profiles of both the dust and the conducting gas only for values of Hartmann number greater than or equal to unity. For these values of the Hartmann number the skin friction is also obtained.     

Visco-elastic flow past a spheroid

Summary The creeping flow of an Oldroyd visco-elastic liquid past a spheroid whose shape varies slightly from that of a sphere is examined. An explicit expression is obtained for the stream function characterizing the flow. As a particular case the flow past an oblate spheroidal particle is investigated. Two special known cases are then deduced.     

Hypersonic flow past a sphere

The effects of dissociation or ionization of air on the analytical solution for hypersonic flow past a sphere are considered here, under certain assumptions. It has been assumed that the shock wave is in the shape of a sphere, that the density ratio across the shock is constant, that the flow behind the shock is at constant density and that dissociation or ionization only occurs behind the shock wave. Thus the effects of the compressibility of the air, variation of density ratio along the shock, and the department of the shock shape from being circular are not taken into account. Here the velocity, pressure, temperature, pressure coefficient and vorticity, etc., at any point between the shock and the surface of the sphere in the presence of dissociation or ionization are obtained. In addition, shock detachment distance, drag coefficient, stagnation point velocity gradient and sonic points on the shock and the surface have also been obtained. The results have been compared with the corresponding results obtained in the case when dissociation or ionization does not occur behind the shock.     

Nonuniform supersonic flow past wedges

Summary The problem of steady, inviscid, nonuniform, supersonic flow past pointed wedges with attached shock waves is considered. The solution is obtained by the one-strip approximation of the method of integral relations. The results agree well with experimental data.

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Résumé Le problème de l'écoulement supersonique non-uniforme non-visqueux stationnaire autour d'un dièdre est considéré dans le cas des ondes de choc attachées. La solution est obtenue par la première approximation de la méthode des relations intégrales. Le rapport entre les résultats théoriques et expérimentaux est bon.

     

Steady supersonic flow past an almost straight wedge with large vertex angle

This paper studies the problem on the steady supersonic flow at the constant speed past an almost straight wedge with a piecewise smooth boundary. It is well known that if each vertex angle of the straight wedge is less than an extreme angle determined by the shock polar, the shock wave is attached to the tip of the wedge and constant states on both side of the shock are supersonic. This paper is devoted to generalizing this result. Under the hypotheses that each vertex angle is less than the extreme angle and the total variation of tangent angle along each edge is sufficiently small, a sequence of approximate solutions constructed by a modified Glimm scheme is proved to be convergent to a global weak solution of the steady problem. A sequence of the corresponding approximate leading shock fronts issuing from the tip is shown to be convergent to the leading shock front of the obtained solution. The regularity of the leading shock front is established and the asymptotic behaviour of the obtained solution at infinity is also studied.     

Subsonic triple deck flow past a flat plate with an elastic stretch

The steady laminar subsonic flow past a flat plate having a stretch of an elastic membrane, the pressure on the other side of which is adjustable, is studied within the framework of the triple deck theory. The resulting lower deck problem is supplemented with a membrane equation relating the pressure difference across the membrane to its curvature. By pressurizing or depressurizing the membrane, it assumes the form of a hump or a dent that alters the flow characteristics. Numerical solutions obtained, in either case, give plausible account of the interaction between the membrane and the flow.     

Lie group analysis of radiation natural convection flow past an inclined surface

Radiation effects on natural convection heat transfer past an inclined semi-infinite surface is investigated using Lie group analysis. Symmetries found reduce the partial differential equations governing the fluid motion to a system of ordinary differential equations with appropriate boundary conditions. Numerical solution obtained using the fourth order Runge–Kutta scheme with shooting method shows that the thickness of the thermal boundary layer decreases and velocity increases with increasing Grashof number. Also it is observed that increasing the value of the radiation parameter increases both the temperature and velocity of the fluid.     

Magnetohydrodynamic flow past a circular cylinder

This paper deals with the slow-flow problem of an incompressible, viscous, electrically conducting fluid past a circular cylinder in an aligned magnetic field. The solutions for the velocity and magnetic fields are sought by the method of matched asymptotic expansions under the assumptions:R, R _mM1, such thatR=O(R _m). The influence ofR andR _m on this solution is studied toO(R/(logM)²) andO(R/logM), respectively.

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Zusammenfassung Die Arbeit behandelt das Problem des langsamen Fliessens einer nicht zusammendrückbaren zähen elektrisch leitenden Flüssigkeit, die um einen Kreiszylinder mit parallel zur Strömung gerichtetem Magnetfeld strömt. Die Lösungen für die Geschwindigkeit und das Magnetfeld werden gefunden durch die Methode der angepassten asymptotischen Entwicklungen unter den VoraussetzungenR, R _mM1, so dassR=O(R _m). Der Einfluss vonR undR _m auf diese Lösungen wird fürO(R/(logM)²) bzw.O(R _m /logM) untersucht.

     

Supersonic flow past a semi-infinite plane

Zusammenfassung Die Bewegungs- und Energiegleichungen für Überschallströmung an einer halb-unendlichen Ebene werden analytisch gelöst.Die Ergebnisse sind in guter Übereinstimmung mit Croccos numerischer Lösung.     

Simulation of the flow past a circular cylinder using an unsteady panel method

In the present work, an in-house UnSteady Double Wake Model (USDWM) is developed for simulating general flow problems behind bodies. The model is presented and used to simulate flows past a circular cylinder at subcritical, supercritical, and transcritical flows. The flow model is a two-dimensional panel method which uses the unsteady double wake technique to model flow separation and its dynamics. In the present work the separation location is obtained from experimental data and fixed in time. The highly unsteady flow field behind the cylinder is analyzed in detail. The results are compared with experiments and Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations and show good agreement in terms of the vortex shedding characteristics, drag, and pressure coefficients for the different flow regimes.     

Micropolar flow past a stretching sheet

Summary This paper studies the flow of an incompressible, constant density micropolar fluid past a stretching sheet. The governing boundary layer equations of the flow are solved numerically using a globally convergent homotopy method in conjunction with a least change secant update quasi-Newton algorithm. The flow pattern depends on three non-dimensional parameters. Some interesting results are illustrated graphically and discussed.

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Résumé Nous étudions l'écoulement d'un fluid micropolaire et incompressible, de densité constante, le long d'une surface qui l'étend. Les équations de la couche limite qui régissent l'écoulement sont résolues numériquement. On utilise un algorithme quasi-Newtonien de type least change secant update avec une méthode homotopique /`a convergence globale. Certains résultats intéressants sont discutés et illustrés graphiquement.

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This work performed at Sandia National Laboratories supported by the U. S. Department of Energy under contract number DE-AC04-76DP00789.     

Non-Newtonian flow past a stretching plate

In this paper we have considered the study of boundary layer flow past a stretching plate in visco-elastic fluid (Walters' liquid B Model).The solution of boundary layer equation of motion past a stretching plate is obtained by using similarity parameter method. The influence of visco-elastic parameterk ₀ ^* on the flow velocity is investigated.

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Zusammenfassung Die Arbeit behandelt die Grenzschichtströmung um eine gespannte Platte in einer viskoelastischen Flüssigkeit (Walters Flüssigkeitsmodell B).Die Lösung der Grenzschicht-Bewegungsgleichung für eine gespannte Platte wird durch die Ähnlichkeits-Parametermethode erzielt. Der Einfluß des viskoelastischen Parametersk ₀ ^* auf die Strömungsgeschwindigkeit wird untersucht.

     

Accelerated slip flow past a cylinder

This study deals with boundary layer flow along the entire length of a stationary semi-infinite cylinder under a steady, accelerated free-stream. Considering flow at reduced dimensions, the no-slip boundary condition is replaced with a Navier boundary condition. Asymptotic series solutions are obtained for the shear stress coefficient in terms of the Bingham number that corresponds to prescribed values of both the slip coefficient and the index of acceleration. By investigating motion at small and large axial distances, the series solutions are presented. For flow in the intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the shear stress along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.