Laminar flow in an annulus between two concentric rotating porous spheres

Summary An analysis is presented for the steady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric porous spheres with injection/suction at their boundaries. The inner sphere rotates with constant angular velocity about its own fixed axis, while the outer sphere is stationary. A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique. The solution obtained is in the form of a power series expansion in terms of the rotational Reynolds number Re, and an injection/suction Reynolds number Re _w , and is valid for small values of these parameters. Results for the velocity distributions, streamlines, and viscous torques for various values of the flow parameters Re, Re _w , and radius ratios are presented. Viscous torques at the inner and outer spheres are compared with those obtained from the numerical solution of the Navier-Stokes equations, in order to find the range of Re and Re _w for which this solution is accurate.     

Nonlinear stability of motion of viscous liquid between concentric rotating cylinders

The nonlinear stage of the growth of perturbations in the hypercritical region is investigated in the case of a viscous liquid motion in the gap between two rotating cylinders by using the balance method for perturbation energy.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 4, pp. 719–727, October, 1977.     

Micropolar fluid flow between two eccentric coaxially rotating spheres

Summary The steady flow of an incompressible micropolar fluid between two rotating eccentric spheres is investigated. The solution is obtained by perturbation techniques by expanding the spin and velocity fields in power series of the eccentricity and the Reynolds number. The effects of the coupling number, the length ratio, the eccentricity and the relative rotational speeds of the spheres on the flow behaviour are investigated.     

On the slow steady motion of a viscous fluid due to two rotating tori

Summary An approximate solution, correct to order three in a small parameter, is established for the velocity field induced in a viscous fluid by the slow rotation of two tori. The tori possess a common axis and have concentric circular sections. The small parameter is the ratio of the radius of the outer circular section to the distance of the section centre from the axis of rotation. The torque acting on each toroidal surface is also obtained.With 3 Figures     

Circulation motion of a viscous incompressible stream in an extruder channel

An extruder in the form of a rectangular channel completely filled with an incompressible liquid is considered. The upper wall moves at an arbitrary angle to the channel axis. Equations for the circulation velocity and the flow lines in a channel cross section are obtained and studied numerically.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 4, pp. 626–629, April, 1974.     

Unsteady flow of a viscous incompressible liquid between two cylinders

A study has been made of the unsteady motion of a viscous incompressible liquid between two cylinders, the outer one being of arbitrary, slightly non-circular shape, while the inner one is circular and rotates about the origin. Results have been obtained which account for certain phenomena occurring in high-speed rotary hydraulic bearings.     

Numerical investigation of the tangential twist of an incompressible viscous fluid jet

The problem of the formation of eddy flow of tangential twist is examined. The fluid flow mode is laminar. The flow parameters are found by the numerical solution of the complete system of Navier-Stokes equations.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 6, pp. 1047–1054, June, 1976.     

Perturbed motion of a viscous fluid layer on the surface of a rotating cylinder

We investigate the plane flow of a viscous fluid layer plane flow on the surface of a cylinder rotating with a constant angular velocity with account for inertia forces and the acceleration of gravity.Lomonosov Moscow State University, Moscow; Bauman Moscow State Technical University; Belarusian State University, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 689–694, June, 1994.     

Oscillatory flow of a micropolar fluid generated by the rotary oscillations of two concentric spheres

In this paper we examine the flow of an incompressible micropolar fluid between two concentric spheres, generated by their rotary oscillations about a common diameter. The spheres are assumed to be oscillating with the same amplitude but with different angular speeds. The speeds of oscillation are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian assumption. The analytical expressions for velocity and microrotation components are determined in terms of modified Bessel functions of first and second kind. The couples experienced by the inner and outer spheres are calculated and are expressed in terms of two real parameters K and K^′ whose variation is studied numerically. The variations of K and K^′ with respect to micropolarity parameter and frequency parameter are displayed graphically.     

The unsteady hydrodynamic force during the collision of two spheres in a viscous fluid

The time-dependent Stokes equations were solved in the vicinity of two spheres colliding in a viscous fluid with viscosity ν to determine the rate of change of the hydrodynamic forces during large accelerations associated with Hertzian mechanical contact of small duration \({\tau_{\rm c}}\). It was assumed that the gap clearance remains finite during contact and is approximately equal to the height σ of surface micro-asperities. The initial condition corresponds to the steady-state axisymmetric solution of Cooley and O’Neill (Mathematika 16:37–49, 1969), and the initial value problem for the time-dependent Stokes streamfunction was solved using Laplace transform methods. Assuming that σ is small compared to the sphere radius a, we used singular perturbation expansions and tangent-sphere coordinates to obtain an asymptotic solution for the viscous flow in the gap and around the moving sphere. The solution provides the dependence of the resistance, added mass and history forces on σ, the sphere velocity and acceleration, and the ratio of the sphere diameters. We found that the relative importance of viscous and mechanical forces during contact depends on a new Stokes number \({St_{\rm c}=\sigma^2/\nu \tau_{\rm c}}\). Integration of Newton’s equation for the motion of the sphere during mechanical contact showed that there is a critical \({St_{\rm c}=O(\sigma/a)}\) for which there is no rebound at the end of contact.     

Analysis of the flow of an irregular viscous fluid between two revolving cylinders

We propose a mathematical model for the flow of an irregular viscous fluid between two revolving cylinders in a bipolar coordinate system. We present an analytic solution of the system of equations obtained, and we also obtain formulas for determining velocity fields, temperature fields, and energy characteristics.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 2, pp. 256–262, February, 1976.     

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.     

粘滞固体滑移界面层的超声测量

超声纵波与横波分别垂直入射到固体间的Stokes流体滑移界面层时,其反射系数与界面层的特性(包括粘滞系数、体积弹性模量、厚度)或入射波的频率有关.通过对纵横波两种波型各自在粘滞流体界面层的反射特性的讨论,结合两种粘滞性不同的流体界面层试验测量结果,说明了使用纵横波测量滑移界面层粘滞性的不同特点.     

Heat transfer in flow of an incompressible viscous liquid between disks

Using approximate equations of motion, an investigation has been made of the development of steady laminai radial flow of a viscous incompressible liquid in the gap between parallel disks. In the region of hydrodynamically stable flow the heat transfer problem is solved for a given constant heat flux at the wall.     

Hydrodynamics and heat exchange in viscous incompressible liquid flow between disks rotating in a cylindrical casing

The article provides the results of a numerical investigation of convective heat exchange in a closed system consisting of two coaxial disks rotating at the same angular velocity within an immobile cylindrical casing.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 1, pp. 23–29, January, 1985.     

Effects of transpiration on free convection in an annulus between concentric porous spheres

An analysis is presented to study the effects of transpiration on free convection in an annulus between concentric porous spheres. A regular perturbation technique is applied to solve the steady-state Navier-Stokes equations of motion and the energy equation, whereby the stream-function and temperature are expanded in the form of power series in terms of the Rayleigh number Ra, and injection/suction Reynolds number Re. The analytical solution is valid for small values of Ra and Re, and all values of the Prandtl number Pr. A finite-difference solution of the governing steady-state equations of motion and energy is also provided. The range of validity of the analytical solution is determined by comparison with the numerical solution. Plots of the flow patterns, velocity distributions, temperature profiles, local and overall heat transfer rates are presented for Pr = 0.7 and different values of Re, Ra, and the radius ratio . Results are shown over a range of values of Ra and Re such that the effects of mixed convection in the annulus can be clearly observed.     

Steady and unsteady finite element analysis of incompressible viscous fluid

Finite element procedures and related illustrative numerical examples for incompressible viscous fluid motion are discussed in this paper. The steady flow problem is solved by the Newton–Raphson method and the perturbation method. By numerical examples, it can be shown that the combined use of the Newton–Raphson method and perturbation method is suitable. For the analysis of unsteady flow, the perturbation method is employed. Assuming that the basic flow is known, unsteady flow is calculated by accumulating the solution of the linearized equation in which the boundary values are varied by small amounts. Steady flows of temperature dependent free convection are also discretized and analyzed by the same procedure as the conventional finite element Galerkin method. For shape functions, quadratic polynomials are used for velocity and temperature, and linear polynomials for pressure. It is to be noted that the selections of shape functions and solution method are the keys to the analysis of highly non-linear fluid flow problems such as those discussed in this paper.