Sphere rotating in a viscous fluid inside a cylindrical tube

Summary We consider the viscous liquid in Poiseuillian flow in an infinite circular cylinder of radiusR ₀ and a sphere of radiusa which is allowed to rotate with uniform angular velocity about the axis. Using the method of reflections, the effect of the inertia terms on the velocity field and on the force and torque on the body are calculated for small values ofa/R ₀.With 3 Figures     

Stability of the flow of a rotating liquid film along the inside surface of a cylindrical tube

Under consideration is the problem of formation of Taylor vortices in a rotating film of a viscous incompressible fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 6, pp. 1061–1065, June, 1980.     

Diffusion driven rotating flow in a cylindrical container

Summary The diffusion driven flow of a viscous incompressible fluid in a closed circular cylindrical container with a rotating cylindrical boundary and stationary end disks is numerically and experimentally studied. The numerical solutions are obtained using an upwind finite difference scheme and are validated by comparison with the experimental results and with earlier reported computational results obtained by using different numerical schemes. Further numerical results are obtained for an extended range of Reynolds number and aspect ratio of the cylinder.     

On the laminar boundary-layer flow over rotating spheroids

We study the laminar boundary-layer flow over a general spheroid rotating in otherwise still fluid. In particular, we distinguish between prolate and oblate spheroids and use an appropriate spheroidal coordinate system in each case. An eccentricity parameter e is used to distinguish particular bodies within the oblate or prolate families and the laminar-flow equations are established for each family with e as a parameter. In each case, setting e = 0 reduces the equations to those already established in the literature for the rotating sphere. We begin by solving the laminar-flow equations at each latitude using a series-solution approximation. A comparison is then made to solutions obtained from an accurate numerical method. The two solutions are found to agree well for a large range of latitudes and eccentricities, and at these locations the series solution is to be preferred due to its simplicity and ease of computation. A discussion of the resulting flows is given with particular emphasis on the implications for their hydrodynamic stability. Their stability characteristics are expected to be very similar to those over the rotating sphere as already studied in the literature.     

Flow induced by an asymmetrically placed disk rotating coaxially inside a cylindrical casing

Summary In this paper, the flow due to a rotating disk non-symmetrically placed with respect to the height of the enclosing stationary cylinder is analyzed numerically. The full Navier-Stokes equations expressed in terms of stream function and vorticity are solved by successive over-relaxation for different disk radii, its distance from the bottom casing and rotational Reynolds numbers. It is observed that the flow pattern is strongly influenced by the size and the position of the disk. When the disk is very close to the top casing and small in radius, there are two regions of different scales and the vortices in the region of small scale are trapped between the disk and the top casing. Further, the variation of the moment coefficient is determined for different positions and sizes of the rotating disk. The calculations shows that the frictional torque increases rapidly, when the disk approaches the top casing. This finding is of importance for the design of vertical rotating disk reactors applied in chemical vapor deposition.     

Nonlinear effects on rotating disk flow in a cylindrical casing

Summary The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration. The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.     

Measurement of liquid entrainment from a horizontal cylindrical vessel by a flow of air

An empirical formula has been derived for the time needed for removal of a liquid from a horizontal cylindrical chamber by an air flow.     

On the purely analytic computation of laminar boundary layer flow over a rotating cone

The fundamental purpose of the present research is to obtain analytical expressions for the solution of the steady laminar flow of an incompressible viscous Newtonian fluid over a rotating cone. Using a proper similarity transformation akin to the classical one of Von Karman the nonlinear equations of motion are reduced to a boundary value problem whose solution is then derived in terms of a series of exponentially-decaying functions for the full range of cone half-angle ? characterizing the conical flow structure. The exact numerical method is found to improve as the cone half-angle is decreased. The effects of the cone half-angle on the physically significant relevant parameters, such as the wall shears, the torque and the vertical suction are clarified. Purely explicit analytical expressions for the solution of governing equations to support the numerically evaluated solutions are also obtained via the homotopy analysis method.     

The transfer of heat from a rotating disk to a liquid in a regime of laminar flow

We present the results from an experimental study of the transfer of heat from a disk for a substantial temperature difference between the liquid and the disk, and for a change in the viscosity of the liquid over a wide range.     

Simulation of laminar flow inside ducts of irregular geometry using integral transforms

 The Generalized Integral Transform Technique is employed in the hybrid numerical-analytical solution of the steady two-dimensional Navier–Stokes equations, defined within arbitrarily shaped domains, for incompressible laminar channel flow. The formalism is illustrated for the classical test-case of laminar flow in a gradual expansion duct. Numerical results with automatic global accuracy control are obtained for suggested values of Reynolds numbers in the literature, and critically compared against previously reported benchmark solutions for the same problem. The relative merits of the proposed approach are then pointed out. Received 24 May 1999     

Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

 The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied. Received 16 March 2000     

Numerical solution of laminar flow generated in an annulus by rotating screens

Summary The governing equation and the appropriate boundary condition describing stationary laminar flow in a curved channel and in an annulus with one (upper) and two (upper and lower) rotating screens, were solved numerically by finite-difference method. In the curved channel multiple solutions were obtained in accordance with the predictions of previous theoretical and experimental investigations. In contrast to that, no multiple solutions were found for the flow in an annulus, neither with two nor with one rotating screen. The numerically computed axial velocity distributions in annulus were compared to the corresponding experimental profiles measured in a turbulent flow of a homogeneous fluid created in annulus by one or two rotating screens. The qualitative agreement between the results was unexpectedly good.     

Numerical study of disk driven rotating MHD flow of a liquid metal in a cylindrical enclosure

Summary A numerical study of the steady laminar MHD flow driven by a rotating disk at the top of a cylinder filled with a liquid metal is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. The effect of an axial magnetic field on the flow is investigated for an aspect ratioH/R equal to 1. The magnetic Reynolds number is assumed to be small whereas the interaction parameter,N, is large compared to unity. This allows to derive asymptotic results for the flow solution which are found in good agreement with the numerical calculations. The effect of the top, botton and vertical walls conductivity on the flow is studied. Various combinations of these conductivities are considered. The results obtained showed that one can control the primary flow through a good choice of the electrical conductivity of both the disk and cylinder walls.Notation B Magnetic field - H Height of the cylinder - Ha Hartmann number - jz Axial electric current - N Interaction parameter - P Dimensionless pressure - R Radius of the cylinder - Re Reynolds number - R _m Magnetic Reynolds number - r Dimensionless radius - V _r Dimensionless radial velocity - V _z Dimensionless axial velocity - V Dimensionless azimuthal velocity - Z Dimensionless height Greek symbols Density of the fluid - v Kinematic viscosity - Dynamic viscosity - Electrical conductivity - Angular velocity - Dimensionless electric potential - Thickness of the Ekman layer - Laplacian operator - r Increment of the grid in the radial direction - Z Increment of the grid in the axial direction     

Hydrodynamic study of a rotating MHD flow in a cylindrical cavity by ultrasound Doppler shift method

An experimental study of a steady laminar magnetohydrodynamic (MHD) flow driven by a rotating disk at the top of a cylindrical cavity filled with water or mercury is presented. The velocity distributions were analysed using the ultrasound velocity (UVP) measuring technique. The uniform and constant applied magnetic field is directed along the axis of the cavity. The measurements were compared with results obtained from a numerical model based on a finite volume computational fluid dynamics (CFD) model. The effects of the magnetic field, the fluid and wall electrical conductivities, and the wall thickness are investigated through the conductance ratio k which characterises the influence of the wall on the closure of the electric current distribution. The other relevant parameters are the Hartmann number M, and the Reynolds number Re. The study was performed essentially for different values of Re ? 30,000 and M ? 260. There were close agreement between numerical results, the present ultrasonic measurements and other reported experimental and numerical works. The experiments have revealed something that has not been predicted numerically, the sidewall layer is unstable for special conditions of Hartmann and Reynolds numbers.     

Heat transfer inside a rotating rectangular cavity

The qualitative liquid-flow pattern is considered for a rotating rectangular cavity in the case of heat transfer in a direction parallel to the axis of rotation; calculational relations describing the heat transfer are obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 1, pp. 89–93, January, 1978.     

Decay of electrified rotating capillary jets

A study was made of the effect of electrification and rotation of the nonmono-disperse decay of capillary jets. The study was conducted within the framework of the complete system of equations of hydrodynamics by the Bubnov-Galerkin method.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 2, pp. 231–237, February, 1991.     

Two-dimensional flow of viscous fluid between cylindrical rollers rotating in opposite directions

A method of calculating the hydrodynamic parameters of two-dimensional flow of a viscous fluid through a channel formed by rotating cylinders is described.     

Calculation of a laminar boundary layer on a rotating porous disk

Averaging of noninertial terms over the boundary-layer section in the equations of motion is used to study the effect of suction and injection on the hydrodynamic flow near a rotating disk.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 6, pp. 1022–1026, December, 1985.