Two regimes of liquid film flow on a rotating cylinder

A steady flow of a thin film of a viscous incompressible liquid on a rotating cylinder (the cylinder axis is perpendicular to the direction of the force of gravity) is considered. Capillary effects are taken into account on the free surface. Thin-layer equations derived by Pukhnachov, which depend on the Galileo number and capillary number, are solved. If the first parameter equals zero, the force of gravity also equals zero. If the second parameter equals zero, the surface-tension coefficient also equals zero. The values of these parameters that ensure the solution existence and the number of solutions are determined by the method of collocations. One more solution corresponding to the drop-shaped free surface is found numerically. Variations of flow parameters caused by variations of the Galileo number and capillary number are considered. Branching of the solutions is examined numerically. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 68–78, January–February, 2007.     

Numerical simulation of a flow around an impulsively started radially deforming circular cylinder

The development of a two‐dimensional viscous incompressible flow generated by a deformable circular cylinder impulsively started into rectilinear motion is studied numerically for the Reynolds numbers equal to 550 and 3000. The vorticity transport equation is solved by a second‐order finite difference method in both directions of the domains. The Poisson equation for the streamfunction is solved by a Fourier–Galerkin method in the direction of the flow that is assumed to remain symmetrical and a second‐order finite difference for the radial direction. The advance in time is achieved by a second‐order Adams–Bashforth scheme. The computed results are compared qualitatively with experimental and numerical results done before in the particular non‐deformable case. The comparison is found to be satisfactory. The influence of the deformation of the cylinder on the flow structure and the drag coefficient is then analyzed. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical modeling of a viscous incompressible unsteady separated flow past a rotating cylinder

For studying unsteady flow past a rotating circular cylinder the Navier-Stokes equations are used. The numerical algorithm is based on an artificial-compressibility method, an implicit three-layer second-order scheme with subiterations with respect to time, a third-order scheme with splitting of the flux vectors for the convective terms, and a central-difference scheme for integrating the viscous terms. The calculated velocity profiles, the vorticity fields, the Strouhal numbers, the distribution of the pressure and friction coefficients over the cylinder surface, and the coefficients of the drag and lift forces for the laminar flow regime are analyzed.     

Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two‐dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating‐to‐translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)–vorticity (ω) formulation of the Navier–Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite‐analytic, separation of variable approach. This approach allows one to attenuate the artificial far‐field boundary, and also yields a global conditioning on the wall vorticity in response to the no‐slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non‐oscillatory)‐like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second‐order Runge–Kutta method. Present computations fall into two categories. One with Re=10³ and α≤3; the other with Re=10⁴ and α≤2. Comparisons with other numerical or physical experiments are included. Copyright © 2000 John Wiley & Sons, Ltd.     

Mathematical modeling of motion of a fluid partially filling a rotating cylinder with radially aligned edges

A boundary-value problem of unsteady vortex motion of a viscous incompressible fluid with a free surface in a cavity rotating with a variable angular velocity and shaped as a straight circular cylinder with equidistant radial ribs is solved in a two-dimensional formulation by finite-difference methods. The drag coefficient of the rib is obtained as a function of its depth relative to the free surface.     

Three-dimensional gas flow in a rotating cylinder with a retarding cover

The study of rotating flows is of interest due to both the development of the centrifugal method of separation of gas and isotope mixtures and the possibility of astrophysical applications. An analytical nonlinear model for calculating the hydrodynamic characteristics of the viscous incompressible fluid flow in a rotating cylinder in the presence of a retarding cover is presented. The cases of stationary and rotating covers are considered. The analysis is performed on the basis of the system of hydrodynamic Navier-Stokes equations. The flow domain is divided up into the main flow and end boundary layers at the cylinder bottom and at the rotating cover. In its turn, the main flow is divided up into an inviscid quasi-rigid core and a lateral layer within which almost the entire upward circulatory flow is concentrated. The equations of the boundary layers at the end surfaces are analyzed by the approximate Slezkin-Targ method. The solutions in the boundary and lateral layers are “stitched” together with the velocity distribution in the main flow core. The unknown angular velocity ω ₁ and radial boundary R ₁ of the core are determined from the balance of the moments of the friction forces acting on the main rotating flow and the continuity condition for the circulatory flow. The experimental and calculated data are compared.     

Experimental investigation of the flow around a radially vibrating circular cylinder

This work aims to develop a process for controlling a cylinder wake, especially the von Karman vortex street, in such way so as to drastically reduce the drag coefficient. A new technique for influencing the cylinder wake is proposed in the present experimental study. The flow around a circular cylinder is perturbed by temporarily changing the cylinder diameter. Experiments have been performed for Reynolds numbers in the range Re=9,500 to Re=31,500. Three values of the controlling frequencies are considered: fs₁=0.41, fs₂=0.54 and fs₃=0.73, in addition to the stationary case corresponding to a non-deformable cylinder, fs₀=0. The visualisation flow shows that the pulsing motion of the cylinder walls greatly influences both the near and far wake dynamics. A decrease of the drag is expected.

Liquid metal flow in a finite-length cylinder with a rotating magnetic field

A liquid metal flow induced by a rotating magnetic field in a cylindrical container of finite height was investigated experimentally. It was demonstrated that the flow in a rotating magnetic field is similar to geophysical flows: the fluid rotates uniformly with depth and the Ekman layer exists at the container bottom. Near the vertical wall the flow is depicted in the form of a confined jet whose thickness determines the instability onset in a rotating magnetic field. It was shown that the critical Reynolds number can be found by using the jet velocity u ₀ for Re _cr =u ² ₀/ u/ r. The effect of frequency of a magnetic field on the fluid flow was also studied. An approximate theoretical model is presented for describing the fluid flow in a uniform rotating magnetic field.List of Symbols U _r , U , U _z radial, azimuthal and vertical velocity components, respectively - B _r , U , B _z radial, azimuthal and vertical magnetic induction components - A vector potential of magnetic field - j induced electric current density - electrical conductivity of fluid - electrical potential - kinematic viscosity - tf electromagnetic volume force - angular velocity of fluid rotation - R container radius - H container height - aspect ratio - E Ekman number - Re _cr critical Reynolds number - r, z radial and axial coordinates     

Turbulent flow around a rotating cylinder in a quiescent fluid

 Hot-wire measurements have been carried out in the turbulent flow around a rotating circular cylinder in still air for Reynolds numbers Re=∣U _w ∣D/ν=1.5×10⁴ to 10⁵. The experimental results confirm the analysis derived by asymptotic theory for high Reynolds numbers. Two different ways of deriving the friction law from the experiments (via shear stress and via velocity distribution) resulted practically in the same law. It is shown, that in spite of the curvature of the streamlines the universal logarithmic velocity distribution is still valid near the wall. Received: 8 August 1996/Accepted: 24 April 1998     

Laminar flow of power-law fluids past a rotating cylinder

In this work, the continuity and momentum equations have been solved numerically to investigate the flow of power-law fluids over a rotating cylinder. In particular, consideration has been given to the prediction of drag and lift coefficients as functions of the pertinent governing dimensionless parameters, namely, power-law index (1 ≥ n ≥ 0.2), dimensionless rotational velocity (0 ≤ α ≤ 6) and the Reynolds number (0.1 ≤ Re ≤ 40). Over the range of Reynolds number, the flow is known to be steady. Detailed streamline and vorticity contours adjacent to the rotating cylinder and surface pressure profiles provide further insights into the nature of flow. Finally, the paper is concluded by comparing the present numerical results with the scant experimental data on velocity profiles in the vicinity of a rotating cylinder available in the literature. The correspondence is seen to be excellent for Newtonian and inelastic fluids.     

Advective flow in a rotating liquid film

This paper presents a new exact solution of the Navier–Stokes equations in the Boussinesq approximation that describes thermocapillary advective flow in a slowly rotating horizontal layer of incompressible fluid with free boundaries. Such flow occurs in the case of linear temperature distribution over horizontal coordinates or in the case of heat flux distribution at the layer boundaries. The influence of the Taylor, Marangoni, Grashof, and Biot numbers on the flow and temperature velocity profiles is studied.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.