Unsteady incompressible fluid flow past a cascade of thin curved plates

A large number of papers have been devoted to the study of unsteady flow past airfoil cascades. The majority of authors solve the problem for slightly curved profiles oscillating at low angles of attack.Among other work, we note that of Söhngen [1] on the flow past a dense cascade of plates oscillating synchronously and in phase in a potential fluid flow at a high angle of attack. Samoilovich [2] studied the flow past a cascade of plates of arbitrary shape oscillating with an arbitrary phase shift between neighboring plates. He presents the solution for the case of variable circulation in the quasisteady formulation. Stepanov [3] studied the same question with a linear approach to the flow behind the cascade. Musatov [4] examined the problem of the flow past a cascade of plates oscillating with an arbitrary phase shift between neighboring plates in a fluid flow, again at a high angle of attack, and considered the variation of the relative position of the plates durilng the oscillation process.The present paper considers the flow of a perfect incompressible fluid past a cascade of thin curved oscillating plates with account for the relative displacements of the plates during oscillation. To determine the intensity of the bound vortices per unit length, a linear integral equation is obtained. This represents a generalization of the Birnbaum equation to the case considered (see [5]). Equations are presented for calculating the unsteady aerodynamic forces and moments acting on the plates. As an example, the aerodynamic forces and moments are calculated for the quasistationary formulation of the problem.     

Modeling of transverse self-oscillations of a circular cylinder in an incompressible fluid flow in a plane channel with circulation

Experimentally observed self-oscillations of a cylinder in a plane channel whose width is slightly greater than the cylinder diameter under the impact of the incoming fluid flow are modeled. Within the model of a nonseparated potential flow around the cylinder, the coefficients of added mass of the cylinder are calculated with the help of the generalized method of images. When the cylinder touches the channel wall, the circulation sign changes, and its value is determined by the boundary element method and the no-slip condition for the fluid at the contact point. The Joukowski force and the drag force proportional to the square of velocity are taken into account in the equations of motion of cylinder.     

Simulation of the motion of thin rotating jets of a viscous incompressible fluid

A regular procedure is proposed for deriving approximate equations of motion of straight thin rotating jets of a viscous incompressible fluid, and similarity parameters of such flows are established. The problem of the stability of free steady motion of a finite jet is considered in the framework of a model that takes into account in the zeroth approximation the effects of viscosity, the rotation of the jet, and capillarity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 51–59, March–April, 1984.     

Exact solutions for the incompressible viscous fluid of a porous rotating disk flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions with suction and injection through the surface included. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the exact velocity equations obtained. Making use of this solution, analytical formulas corresponding to the permeable wall shear stresses are extracted.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. As a result, exact formulas are obtained for the temperature field which take different forms depending on whether suction or injection is imposed on the wall. The impacts of several quantities are investigated on the resulting temperature field. In accordance with the Fourier‘s heat law, a constant heat transfer from the porous disk to the fluid takes place. Although the influence of dissipation varies, suction enhances the heat transfer rate as opposed to the injection.     

Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating disk flow

The main interest of the present investigation is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion due to a disk rotating with a constant angular speed. For an external uniform magnetic field applied perpendicular to the plane of the disk, the governing equations allow an exact solution to develop taking into account of the rotational non-axisymmetric stationary conducting flow.Making use of the analytic solution, exact formulas for the angular velocity components as well as for the wall shear stresses are extracted. It is proved analytically that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. According to Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though decreases for small magnetic fields because of the dominance of Joule heating, it eventually increases for growing magnetic field parameters.     

Fluid flow in a rotating cylindrical container with a rotating disk at the fluid surface

Fluid flow in a rotating cylindrical container of radius R_w and height H with a co-axially rotating disk of radius R_d at the fluid surface is numerically investigated. The container and the disk rotate with angular velocities Ω_w and Ω_d, respectively. We solve the axisymmetric Navier-Stokes equations using a finite-volume method. The effects of the relative directions and magnitudes of the disk and container rotations are studied. The calculations are carried out with various ratios of Ω_w and Ω_d for H/R_w = 2 and R_d/R_w = 0.7. Streamlines and velocity vectors in the meridional plane and azimuthal velocities are obtained. The flow fields in the meridional plane are discussed with relation to azimuthal velocities in the interior of the container. The numerical results are also compared with experimental data.     

On flow and stability of a Newtonian fluid past a rotating plane

An exact solution is given for the steady flow of a Newtonian fluid occupying the halfspace past the plane z=0 uniformly rotating about a fixed normal axis (Oz). This solution is obtained in a velocity field of the form considered by Berker [2] and can be deduced as a limiting case, as h+, of the solution to the problem relative to the strip 0zh imposing at z=h either the adherence boundary conditions or the free surface conditions. Furthermore, the stability of this flow, subject to periodic disturbances of finite amplitude, is studied using the energy method and the result is compared with those corresponding to stability of flows in the strip 0zh.

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Sommario In questa nota si mostra che-oltre alla calssica soluzione di von Karman [1] — esiste, per opportuni valori del gradiente di pressione all'infinito, una soluzione esatta per il moto stazionario di un fluido Newtoniano posto nel semispazio limitato dal piano z=0 uniformemente rotante attorno ad un asse ad esso perpendicolare (Oz). Tale soluzione, ottenuta sulla scia del lavoro di Berker [2], si può dedurre anche come limite, per h+, della soluzione del problema relativo alla striscia 0zh quando sul piano z=h si assegnano o le condizioni di aderenza o le condizioni di frontiera libera. Si studia poi la stabilità di tale moto rispetto a perturbazioni spazialmente periodiche di ampiezza finita col metodo dell'energia e si confronta il risultato ottenuto con quelli relativi alla stabilità dei moti nella striscia 0zh.

     

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung’s (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain–energy density function. The fluid is described through a Navier–Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response.     

Steady flow of a viscous incompressible fluid between two co-axial circular cylinders with suction and injection

In the present paper an attempt has been made to study the steady flow of a viscous incompressible fluid between two co-axial circular cylinders with small outward and inward normal suction on the outer and inner cylinders respectively with the assumption that the pressure is uniform over a cross-section. The expressions for axial velocity, the volume of fluid flowing per unit time across a cross-section and components of stress at any point of the fluid are derived.

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Stationäre Strömung einer zähen, inkompressiblen Flüssigkeit zwischen zwei koaxialen Kreiszylindern bei Absaugen und Ausblasung

Zusammenfassung Es wird die stationäre Strömung eines zähen, inkompressiblen Fluids zwischen zwei koaxialen Kreiszylindern mit geringer Absaugung oder Ausblasung sowohl am Innen- wie am Außenzylinder unter der Annahme gleichförmiger Druckverteilung über jeden Querschnitt untersucht. Die Beziehungen für die Axialgeschwindigkeit, der Fluidstrom über jeden Querschnitt und die Spannungskomponenten in jedem Punkt des Fluidfeldes werden hergeleitet.

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Nomenclature density of the fluid - x axial coordinate - y radial coordinate - azimuthal coordinate - u axial velocity - v radial velocity - w azimuthal velocity - p pressure - coefficient of viscosity - kinematic viscosity - a radius of the inner cylinder - b radius of the outer cylinder - v₀ suction velocity on the inner cylinder - v₀ suction velocity on the outer cylinder =suction parameter for the inner cylinder =suction parameter for the outer cylinder =dimensionlessy coordinates Q=discharge per unit time     

Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein: in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature. In the first set of simulations the cylinder is forced to transversely oscillate at a fixed amplitude, while the oscillation frequency has been varied around the Strouhal value. Both geometries exhibit in-phase vortex shedding, with the vortex cores bent according to the body's curvature, although the wake topology is markedly different. In particular, the configuration that was found to suppress the vortex shedding in absence of forced motion exhibits now a primary instability in the near wake. A second set of simulations has been performed imposing an oscillatory roll to the curved cylinder, which is forced to rotate transversely around the axis of its bottom section. This case shows entirely different wake features from the previous one: the vortex shedding appears to be out-of-phase along the body's span, with straight cores that tend to twist after being shed and manifest a secondary spanwise instability. Further, the damping effect stemming from the transverse planar motion of the part of the cylinder parallel to the flow is no longer present, leading to a positive energy transfer from the fluid to the structure.     

Steady laminar flow of viscoelastic fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of viscoelastic fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows in three kinds of pipes whose center-lines are specified by

as the examples of once, twice, and periodically curved pipes, respectively, are discussed in comparison with purely viscous flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small. In addition, the reason why the secondary flow of a viscoelastic fluid in a curved pipe of circular cross-section is stronger than that of a purely viscous fluid is explained. In the present paper, the White—Metzner model is employed as the constitutive equation.     

RETRACTED ARTICLE: Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating disk flow

The main interest of the present paper is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion due to a disk rotating with a constant angular speed. In place of the traditional von Karman’s axisymmetric evolution of the flow, the rotational non-axisymmetric stationary conducting flow is taken into consideration here. As a consequence, for an external uniform magnetic field applied perpendicular to the plane of the disk, the governing equations allow an exact solution to develop, which is influenced by a fixed point on the disk and also is bounded everywhere in the normal direction to the wall.     

Steady laminar flow of a power-law fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of power-law fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows, in three kinds of pipes whose center-lines are specified by

as examples of once, twice, and periodically-curved pipes, respectively, are discussed in comparison with Newtonian flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small.     

Effect of curvature on dual solutions of flow through a curved circular tube

Dual solutions, i.e., two-vortex and four-vortex solutions, of the flow through a curved circular tube are numerically obtained by the spectral method for 0 ⩽ δ ⩽ 0.8 and 500 ⩽ Dn ⩽ 10000, where δ is the non-dimensional curvature of the tube and Dn the Dean number. It is found that the critical Dean number above which the four-vortex solution exists takes the lowest value 956 at δ = 0 and increases with δ. In terms of the Reynolds number of the flow, however, the critical Reynolds number decreases from infinity as δ increases from zero, takes the minimum value of about 250 at δ ≈ 0.52, and then increases again.     

On thin film flow of a third-grade fluid down an inclined plane

An exact solution for the thin film flow of a third-grade fluid on an inclined plane is presented. This is a corrected version of the solution obtained by Hayat et al. (Chaos Solitons Fractals 38:1336–1341, 2008). An alternative parametric form for the solution is also derived. The variation of the dimensionless velocity and average velocity is given for a wide range of parameter values. An asymptotic solution for large parameter values is obtained giving rise to a boundary-layer structure at the free surface.     

Steady circulatory flow about a rotating circular cylinder with uniformly distributed suction at the surface

An exact solution for steady circulatory flow about an infinite porous circular cylinder rotating with a given angular velocity in an incompressible non-Newtonian second-order fluid that is also rotating so that a given circulation is maintained at infinity, is investigated. Using the Coleman-Noll model for the fluid, it is found that when circulation, velocity, vorticity and pressure are affected by non-Newtonian effects due to second-order terms in the constitutive equation of the fluid even at the first-order approximation or the series solution used, torque is independent of these effects even when the second-order approximation is considered.