Steady-state flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders

A boundary value problem for a quasi-linear equation determining the velocity profile of a flow of a polymer fluid in a pipe formed by two coaxial cylinders is considered. On the basis of methods of approximation without saturation, a computational algorithm of increased accuracy is developed, making it possible to solve the problem in a wide range of parameters, including record-low values of r ₀, the radius of the inner cylinder.     

Constant shear flow past two circular cylinders

Zusammenfassung Es wird die Scherströmung um zwei Kreiszylinder behandelt unter Verwendung orthogonaler krummliniger Bipolar-Koordinaten, wobei die Hauptströmung sowohl normal als auch parallel zu den Zylinderachsen verläuft. Die Kräfte auf die Zylinder werden berechnet, ebenso die Lage der Staupunkte in Abhängigkeit vonN=U/ c.     

On the flow of a viscous incompressible fluid between two coaxial rotating porous cylinders

Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically.     

Couette flow between corrugated cylinders

This note reports some analytic Stokes solutions to the flows outside a rotating corrugated cylinder and between two rotating corrugated cylinders of either epitrochoidal or hypotrochoidal cross-sections. The results are obtained by using conformal mappings and general biharmonic solutions inside and outside of a unit circle.     

Two-dimensional viscous flow between circular cylinders: application to damping devices for seismic isolation

A detailed analysis of the fluid dynamics of the two-dimensional viscous flow between circular cylinders is dealt with in this paper. Analytic solutions are found on the basis of asymptotic expansions with respect to a small parameter defined by the ratio between the difference of the radii and the radius of the internal cylinder. The analysis is related to the study of recently developed devices for seismic isolation of buildings based on modified pile foundation, separated from the soil, in which a viscous fluid is inserted in the void space between the pile and the lining of the surrounding soil. The availability of this analytical solution contributes to obtaining accurate predictions of the force on the pile.     

Non-Newtonian flow between concentric cylinders

The nonlinear rheological effects of Oldroyd 6-constant fluid between concentric cylinders is addressed. Numerical solution of nonlinear differential equation is given. The nonlinear effects on the velocity is shown and discussed. This reveal that characteristics for shear thickening/shear thinning behavior of a fluid is dependent upon the rheological properties.     

Natural convection between horizontal heated concentric circular cylinders

Natural convection between infinitely long, horizontal, heated, concentric circular cylinders is considered. It is assumed that the temperature difference between the cylinders is small and also that the radius of the inner cylinder is small. It is shown that the problem is mainly conduction dominated provided thatR, the ratio of the radius of the outer cylinder to the radius of the inner cylinder, is not too large. The criterion derived for a conduction dominated problem is a relation betweenR and the Grashof number.

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Zusammenfassung Die freie Konvektion zwischen zwei unendlichen, horizontalen, geheizten, konzentrischen Zylindern wird untersucht. Der Temperaturunterschied zwischen den Zylindern sowohl wie der Radius des inneren Zylinders, wird klein angenommen. Es wird gezeigt, dass das Problem vom Wärmedurchgang beherrscht ist, fallsR, das Verhältnis zwischen dem Radius des äusseren und inneren Zylinders, nicht zu gross ist. Das abgeleitete Kriterium für diesen Fall ist eine Beziehung zwischenR und der Grashof-Zahl.

     

Exact solutions for the rotational flow of a generalized Maxwell fluid between two circular cylinders

Unsteady flow of an incompressible generalized Maxwell fluid between two coaxial circular cylinders is studied by means of the Laplace and finite Hankel transforms. The motion of the fluid is produced by the rotation of cylinders around their common axis. The solutions that have been obtained, written in integral and series form in terms of the generalized G_a,b,c(·, t)-functions, are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. They satisfy all imposed initial and boundary conditions and for λ → 0 reduce to the solutions corresponding to the Newtonian fluids performing the same solution. Furthermore, the corresponding solutions for ordinary Maxwell fluids are also obtained for β = 1. Finally, in order to reveal some relevant physical aspects of the obtained results, the diagrams of the velocity field ω(r, t) have been depicted against r and t for different values of the material and fractional parameters.     

Fully developed laminar slip and no-slip flow in rough microtubes

The effect of surface roughness on developed laminar flow in microtubes is investigated. The tube boundary is defined by r=R[1+e sin( lq)]{r=R\left[{1+\varepsilon\, {\rm sin}\left( {\lambda \theta }\right)}\right]}, with R representing the reference radius and e{\varepsilon} and λ the roughness parameters. The momentum equation is solved using Fourier–Galerkin–Tau method with slip at the boundary. A novel semi-analytical method is developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow that are not restricted to small values of el{\varepsilon \lambda } . The analytical solution collapses onto the perturbation solution ofDuan and Muzychka (J. Fluids Eng., 130:031102, 2008) for small enough values of el{\varepsilon \lambda } .     

Fully developed laminar slip and no-slip flow in rough microtubes

The effect of surface roughness on developed laminar flow in microtubes is investigated. The tube boundary is defined by \({r=R\left[{1+\varepsilon\, {\rm sin}\left( {\lambda \theta }\right)}\right]}\), with R representing the reference radius and \({\varepsilon}\) and λ the roughness parameters. The momentum equation is solved using Fourier–Galerkin–Tau method with slip at the boundary. A novel semi-analytical method is developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow that are not restricted to small values of \({\varepsilon \lambda }\) . The analytical solution collapses onto the perturbation solution ofDuan and Muzychka (J. Fluids Eng., 130:031102, 2008) for small enough values of \({\varepsilon \lambda }\) .     

Effects of radial temperature gradient on the stability of flow of a viscous incompressible fluid between two rotating cylinders

Stability of the flow of a viscous incompressible fluid in a narrow gap between two concentric cylinders rotating in opposite directions is studied. Exact values of critical Taylor number for the first and second modes are derived by a numerical procedure and these are compared with the known results. It is observed that the value of the critical Taylor number T_crit decreases with increasing the values of a parameter $\text{N (N =}\text{Ra}\text{T}\text{,}\text{Ra = Rayleigh number, T = Taylor number}\text{)}$, and the rate of decrease in the value of T_crit is more when the two cylinders rotate in the opposite directions.     

Stationary flows of a weakly conducting incompressible polymeric liquid between coaxial cylinders

Under study are the stationary solutions of the mathematical model describing nonisothermal electroconvection of a weakly conducting polymeric liquid in the channel between two coaxial cylinders.     

Stability of viscous flow between rotating cylinders

Zusammenfassung Ein Beweis des Rayleighschen Kriteriums der Stabilität einer zähen Strömung zwischen zwei unendlichen, coaxialen, rotierenden Zylindern, der auf einer einfachen Abänderung des Energieintegrals für die Perturbationsgeschwindigkeit begründet ist, wird dargestellt.     

Linear oscillatory hydromagnetic flow between two coaxial cylinders

Hydromagnetic flow between two coaxial circular cylinders is discussed when the inner cylinder oscillates axially under a radial magnetic field. Exact solution is given for the case of a perfectly conducting fluid. Expressions for velocity, induced magnetic field, current density, electric field, viscous drag and energy transfer are derived and expressed in polar forms so as to facilitate the study of magnitude and phase variations. Current sheets are found to exist on the two boundaries.     

Rotation implementation of a circular cylinder in incompressible flow via staggered grid approach

In this paper, we present a finite difference method for the implementation of the rotation of a circular cylinder in the incompressible flow field by solving the two-dimensional unsteady Navier-Stokes equations. The approach is to use staggered grid method so that the accuracy and order of convergence of the associated algorithms can be maintained. The proposed method is easy to be implemented and is effective. A set of simulations for the flow dynamics is provided to show the computational results.     

Stability analysis of shear-thinning flow between rotating cylinders

Stability of the shear thinning Taylor–Couette flow is carried out and complete bifurcation diagram is drawn. The fluid is assumed to follow the Carreau–Bird model and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed, that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear thinning effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.     

Steady flow of incompressible fluid between two co-rotating disks

This article provides an analytical solution of the Navier–Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of unknown components of velocity and pressure in a radial direction – in contrast to the Briter–Pohlhausen analytical solution, which is supported by simplified Navier–Stokes equations. The obtained infinite system of ordinary differential equations forms recurrent relations from which unknown functions can be calculated successively. The first and second approximations of solution are solved analytically and the third and fourth approximations of solutions are solved numerically. The numerical example demonstrates agreements with results obtained by other authors using different methods.     

Unsteady flow of a dusty gas in cylinders with circular and sectorial cross sections

The problems of flow of a viscous incompressible gas embedded with particles in a circular cylinder and a cylinder whose cross section is a sector of a circle are discussed. The analysis applies to flows with pressure gradients which are arbitrary functions of time. Explicit expressions for the exact velocities of the gas and particles are obtained by using the methods of operational calculus—the finite Hankel transform, the Laplace transform, etc. Numerical results are obtained for developing flow due to a constant pressure gradient.     

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.

     

Rheological and flow modelling of viscoelastic fluids between eccentric cylinders

Viscoelastic fluid flows within eccentric rotating cylinders are simulated using a finite element based commercial software POLYFLOW, and an approach based on the stream-tube method (STM) and domain decomposition.