Nonaxisymmetric Free Convection Flow over a Rotating Disk in a Viscoelastic fluid with Magnetic Field

The non axisymmetric motion produced by a buoyancy-induced secondary flow of a viscoelastic fluid over an infinite rotating disk in a verticalplane with a magnetic field applied normal to the disk has been studied.The governing Navier Stokes equations and the energy equation admit a self similar solution. The system of ordinary differential equations has been solved numerically using Runge-Kutta Gill subroutine.The turning moment for the viscoelastic fluid is found to be less than that of the Newtonian fluid but the turning moment is increased due to the magnetic parameter. The resultant force due to the buoyancy-induced secondary flow increases with the magnetic parameter but reduces as the viscoelastic parameter increases. The quantity of fluid, which is pumped outwards due to the centrifuging action of the disk, for the viscoelastic fluid is more than that of the Newtonian fluid. The buoyancy-induced secondary flow boundary layer is much thicker than the primary boundary layer thickness. The thermal boundary layer due to the primary flow increases with the magnetic parameter decreases as the viscoelastic parameter increases. The heat transfer increases with the viscoelastic parameter but decreases as the magnetic parameter increases. The effect of the viscoelastic parameter is more pronounced on the secondary flow than on the primary flow.     

Uniform Flow Past an Axially Uniform Viscous Vortex

It is believed that the flow past a tornado causes the formation of smaller vortices which produce the “suction spots” observed along the path of destruction. Here we develop a greatly simplified mathematical model to investigate this phenomenon. An axially uniform vortex is developed by visualizing a circular tube with uniform surface suction of fluid possessing circulation at infinity. This vortex is then perturbed by a uniform flow past it. An inner asymptotic expansion of an E^1/3 radial boundary layer is matched to an outer expansion to obtain a solution. The results show that a stagnation point developing into a secondary vortex is formed in a free shear layer at critical flow conditions. However, it is difficult to apply our results quantitatively because of the difficulty in comparing the axially uniform vortex with a real tornado vortex.     

Vortex Interaction in a Ducted Flow

The objective of this study is to describe the structure of pipe flow by considering it as a superposition of many axisymmetric vortex rings. In knowing the unsteady gross feature of pipe flow, the investigation on vortex interactions is important. As a first step to the goal, we investigate the nonlinear interaction among vortex rings whose number is three at most. The interaction among vortex rings of equal circulation is here investigated. Momentum and energy conservation of the present vortex ring system are also discussed to know a better understanding of the perturbed pipe flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady Porous Flow with a Free Surface

Three different numerical methods for solving unsteady two-dimensionalporous flow problems with a free surface are presented. Thevelocity potential is expressed as the solution to a variationalproblem which is solved by a Rayleigh-Ritz expansion, a Kantorovichexpansion and a co-ordinate transformation method. The freesurface equation is solved by a Crank-Nicolson procedure. Thethree methods were tested on the same set of problems and theobtained results are virtually identical.     

Attached primes over noncommutative rings

Attached primes and secondary representations were introduced in 1973 by Macdonald [I.G. Macdonald, Secondary representation of modules over a commutative ring, Sympos. Math. 11 (1973) 23-43] to develop a dual theory to the associated primes and primary decomposition in commutative algebra. This article generalizes Macdonald’s theory to the noncommutative setting.     

Flow near the Apex of a Plane Delta Wing

A series expansion is obtained for the exponent n of the singularityof the solution of Laplace's equation for the flow near theapex of a plane delta wing when the angular sector occupiedby the wing is small. A further term is found in the expansiondue to Legendre when the wing is almost a half-plane, and thevalue of n is determined numerically for a range of intermediatevalues of the apex angle.     

Flow Past a Swept Wing with a Compliant Surface: Stabilizing the Attachment-Line Boundary Layer

Many aquatic species such as dolphins and whales have fins, which can be modeled as swept wings. Some of these fins, such as the dorsal fin of a dolphin, are semi-rigid and therefore can be modeled as a rigid swept wing with a compliant surface. An understanding of the hydrodynamics of the flow past swept compliant surfaces is of great interest for understanding potential drag reduction mechanisms, especially since swept wings are widely used in hydrodynamic and aerodynamic design. In this paper, the flow past a swept wing with a compliant surface is modeled by an attachment-line boundary layer flow, which is an exact similarity solution of the Navier–Stokes equations, flowing past a compliant surface modeled as an elastic plate. The hydrodynamic stability of the coupled problem is studied using a new numerical framework based on exterior algebra. The basic instability of the attachment line boundary layer on a rigid surface is a traveling wave instability that propagates along the attachment line, and numerical results show that the compliance results in a substantial reduction in the instability region. Moreover, the results show that, although the flow-field is three-dimensional, the qualitative nature of the instability suppression is very similar to the qualitative reduction of instability of the two-dimensional Tollmien–Schlichting modes in the classical boundary-layer flow past a compliant surface.     

Turbulent Flow with Embedded Vortical Structures Induced by Vortex Generators in a Cascade

Presented work is the next step after several experimental examinations of vortex generator influence on a flow separation occurring on a model of the NACA 63A421 airfoil with deflected simple flap. In this stage of research the vortices produced by vortex generators (VGs) were studied using Particle Image Velocimetry technique (PIV) and numerical simulations. Vane type VGs with two spacings among VGs pairs in straight channel with turbulent flow were tested. The average velocity flow field, peak of vorticity and circulation decay downstream of VGs were evaluated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Second Order Chemical Reaction on MHD Free Convective Radiating Flow over an Impulsively Started Vertical Plate

An attempt has been made to study laminar convective heat and mass transfer flow of an incompressible, viscous and electrically conducting fluid over an impulsively started vertical plate with conduction-radiation embedded in a porous medium in presence of transverse magnetic field. The influence of both second order chemical reaction and heat generation are taken into account. The governing coupled partial differential equations are solved by Crank-Nicolson method. The effects of important physical parameters on the velocity, temperature and concentration have been analyzed through graphs. The results of the present study agree well with the previous solutions. Applications of the present study are shown in material processing systems and different industries. The important findings of present study are: chemical reaction parameter acts as resistive force to reduce the velocity whereas heat source parameter enhances the velocity.     

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper, we investigate the asymptotic validity of boundary-layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl’s boundary-layer solution to Navier-Stokes solutions with different Reynolds numbers. We show how Prandtl’s solution develops a finite-time separation singularity. On the other hand, the Navier-Stokes solutions are characterized by the presence of two distinct types of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover, we apply the complex singularity-tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.     

A Free Associative Algebra as a Free Module over a Specht Subalgebra

Let k be a field of characteristic 0 and let k<X> be a free associative algebra with finite basis X. Let R=R(k,X) be the universal enveloping algebra of the square of Lie(X), regarded as a subalgebra of k<X> and called the Specht subalgebra of the free algebra. We prove that k<X> is a free (left) R-module, find sufficient conditions for some system of elements in k<X> to be a basis for this module, and obtain an explicit formula that allows us to calculate the R-coefficients of the elements of the free algebra over a special basis of symmetric monomials.     

Flow over a profile in a channel with dynamical effects

The work deals with a numerical solution of 2D inviscid incompressible flow over the profile NACA 0012 in a channel. The finite volume method in a form of cell‐centered scheme at quadrilateral C‐mesh is used. Governing system of equations is the system of Euler equations. Numerical results are partially compared with experimental data. Steady state solutions of the flow as well unsteady flows caused by prescribed oscillation of the profile were computed. The method of artificial compressibility and the time dependent method are used for computation of the steady state solution. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Stability of Attached Shock Waves in Magnetogasdynamic Flow Past a Wedge

The question of the physical significance of the new phenomenaindicated by Cabannes' work on magnetogasdynamic flow past awedge is considered from the point of view of the stabilityof the shock waves. Analytical and heuristic reasons are givensuggesting that downstream-facing shocks are stable if the upstreamflow is supersonic and unstable if it is subsonic, while upstreamfacing shocks are always to be considered unstable.     

On a Hele-Shaw Flow Problem with Free and Solid Boundary Components

The purpose of this work is to study a one phase Hele-Shaw fluid flow occupying a time variable domain \(\Omega (t)\), due to the injection of the fluid with a constant rate at a single point of the initial domain \(\Omega (0)\), and in the presence of a fixed solid body \(\Omega _0\). We show the short time existence and uniqueness of the solution for the corresponding boundary value problem in the three dimensional case and in the absence of surface tension.     

Vortex Generation in a Liquid Metal Duct Flow near a Magnetic Dipole

The generation of vortical structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces which act on the fluid elements. Our model uses the quasi-static approximation applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at smaller flow Reynolds numbers Re as well as the fully time-dependent regimes at higher values with a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes on Re and the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared, the streamwise, spanwise and wall-normal ones. The most efficient generation of turbulence at a fixed distance above the duct occurs for the spanwise orientation in which we can observe the formation of Hartmann layers at the top plate. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

群环上的幂自由模

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The Numerical Solution of a Minimization Problem Associated with a Free Surface Flow

The solution of the differential equation governing the seepageof fluid through a porous dam can be shown to be equivalentto the minimization of a quadratic functional over a fixed rectangularregion. The latter problem is solved using the method of finiteelements, and the results compared with earlier computations.An analysis of the singularity at the separation point is usedto find the position of the separation point.     

Free streamline-boundary layer analysis for separated flow over an airfoil

We propose a model which combines boundary layer computations with a free streamline potential flow for obtaining pressure distributions on an airfoil section in steady flow near stall conditions. The model is conceptually simple and uses elements which can be computed rapidly and efficiently. The solution is essentially analytical and can be used naturally in the larger context of matching asymptotic expansions to get information about three dimensional flows.

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Sommario Si propone un metodo di calcolo della pressione lungo un profile alare in regime di flusso stazionario in prossimitã dello stallo. II metodo combina le equazioni dello strato limite con un modello di flusso a linee di corrente libere e scia separata. I risultati numerici richiedono un minimo dispendio di tempo di calcolo e sono in buon accordo con gli esperimenti e con una soluzione viscosa.

     

On Optimal Control of a Free Surface Flow

We discuss an optimal control approach for a 2D Stokes flow with a free surface. The aim is to optimize the shape of a polymer film by adjusting the ambient pressure in a casting process. The resulting minimization problem is solved by the method of steepest descent. Numerical results will be presented. Furthermore we state the adjoint system for the Lagrangian formalism. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)