Flow between a porous rotating disk and a plane

It is shown that when a viscous incompressible fluid is sucked through a stationary porous disk spontaneous rotation of the fluid sets in at a certain Reynolds number. This is consistent with the results of a specially designed experiment. Another unusual result is the existence of multicell regimes, corresponding to suction, when the force acting on the porous, rapidly rotating disk is a lift force and, moreover, anomalously large. Charts of the possible steady-state flow regimes, stable and unstable, have been constructed. In the case of fairly intense suction and rotation a stable self-oscillating regime is observed. In the limit of vanishingly small viscosity unusual boundary layer properties associated with suction are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 53–65, November–December, 1989.     

On unsteady forced flow against a rotating disk

Summary The solution of unsteady forced flow against an unsteadily rotating disk is obtained when the outer flow and the angular velocity of the disk are expressed in powers series of t. The solution is established by expanding the velocity components and the pressure in powers of small time. The extension of the obtained solutions is possible by using Zeytounian's technique. Finally, an analysis is made for the problem of the time-dependent flow due to an infinite rotating disk started accelerated from rest.

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Sommario La soluzione del flusso forzato contro un disco rotante in regime non permanente è ottenuta quando il flusso esterno e la velocità angolare del disco sono espresse in una serie di potenze t. La soluzione è formulata esponendo la componente della velocità e la pressione in potenze di tempo piccolo. L'estensione delle soluzioni ottenute è possibile usando la tecnica di Zeytounian. Infine si fa l'analisi del flusso dipendente dal tempo dovuto a un disco rotante infinito accelerato dalla quiete.

     

Magnetohydrodynamic flow past a porous rotating disk in a circular magnetic field

This paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non-dimensional parameters. There is excellent agreement with previous work and asymptotic formulae.     

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.     

Oscillatory flow due to eccentrically rotating porous disk and a fluid at infinity

An analytical solution of the unsteady Navier–Stokes equations is obtained for the flow due to non-coaxial rotations of an oscillating porous disk and a fluid at infinity, rotating about an axis parallel to the axes of rotation of the disk through a fixed point. The velocity distributions and the shear stresses at the disk are obtained for three different cases when the frequency parameter is greater than, equal to or less than the rotation parameter. The flow has a boundary layer structure even in the case of blowing at the disk.     

Oscillatory flow due to eccentrically rotating porous disk and a fluid at infinity embedded in a porous medium

An oscillatory flow due to non-coaxial rotations of an oscillating porous disk and a fluid at infinity rotating about an axis parallel to the axis of rotation of the disk through a fixed point has been investigated. An analytical solution of the unsteady Navier-Stokes equations is obtained for three cases when the frequency parameter is less than, equal to or greater than the rotation parameter. The influences of the physical parameters acting on the flow are explained with the help of the figures. It is found that the depth of the penetration or the wave length of the layers decreases with an increase in porosity parameter.     

Transient flow near a rotating disk

Summary The solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient. The primary tangential velocity exhibits a single overshoot of its steady value while the growth of the secondary flows is monotonic. The overshoot is seen to be a direct consequence of the lag in the development of the secondary flows. An analytical solution is obtained for a related linearized problem: The angular velocity of an infinite disk, initially rotating with an infinite environment, is perturbed. The oscillatory decays to the steady state, which occur in both unbounded and bounded linearized analyses, are discussed in relation to the overshoot in the impulsively started disk problem.     

Spiral and circular waves in the flow between a rotating and a stationary disk

 Circular and spiral waves are observed in the flow between a rotating and a stationary disk. These waves are generated by instabilities of the stationary disk boundary layer. This experimental work is devoted to their study by means of flow visualization and measurements of the associated velocity fields. In particular, instantaneous velocity profiles are measured by ultrasonic Doppler anemometry. The spatio-temporal characteristics of the waves are studied with the help of Fourier transforms of these velocity signals. Received: 21 April 1997/Accepted: 2 February 1998     

Numerical study of the flow and heat transfer in a Reiner-Rivlin fluid on a rotating porous disk

An unsteady flow and heat transfer to an infinite porous disk rotating in a Reiner—Rivlin non-Newtonian fluid are considered. The effect of the non-Newtonian fluid characteristics and injection (suction) through the disk surface on velocity and temperature distributions and heat transfer is considered. Numerical solutions are obtained over the entire range of the governing parameters.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 85–95, January–February, 2005.     

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.     

Rotationally symmetric flow over a rotating disk

The rotationally symmetric flow over a rotating disk in an incompressible viscous fluid is analyzed by a new method when the fluid at infinity is in a state of rigid rotation (in the same or in the opposite sense) about the same axis as that of the disk. Asymptotic expansions for the velocity field over the entire flow field are obtained for the general class of one-parameter rotationally symmetric flows. This method is further extended to the case when a uniform suction or injection is assumed at the rotating disk. Fluid motion induced by oscillatory suction of small amplitude at the rotating disk is also discussed.An initial-value analysis reveals that resonance is possible only when the angular velocity of the rotating fluid is greater than that of the rotating disk.     

Laminar source flow between parallel porous disks with equal suction and injection

An analysis is presented for laminar source flow between parallel stationary porous disks with suction at one of the disks and equal injection at the other. The solution is in the form of an infinite series expansion about the solution at infinite radius, and is valid for all suction and injection rates. Expressions for the velocity, pressure, and shear stress are presented and the effect of the cross flow is discussed.Nomenclature a distance between disks - A, B, ..., J functions of R _w only - F static pressure - p dimensionless static pressure, p(a ²/ ²) - Q volumetric flow rate of the source - r radial coordinate - r dimensionless radial coordinate, r/a - R radial coordinate of a point in the flow region - R dimensionless radial coordinate of a point in the flow region, R - Re source Reynolds number, Q/2a - R _w wall Reynolds number, Va/ - reduced Reynolds number, Re/r ² - critical Reynolds number - velocity component in radial direction - u dimensionless velocity component in radial direction, a/ - average radial velocity, Q/2a - u dimensionless average radial velocity, Re/r - ratio of radial velocity to average radial velocity, u/u - velocity component in axial direction - v dimensionless velocity component in axial direction, v - V magnitude of suction or injection velocity - z axial coordinate - z dimensionless axial coordinate, z a - viscosity - density - kinematic viscosity, / - shear stress at lower disk - shear stress at upper disk - ₀ dimensionless shear stress at lower disk, - ₁ dimensionless shear stress at upper disk, - dimensionless stream function     

An analytical and experimental investigation of flow characteristics generated by rotating porous disk

This paper is concerned with investigations of the gas flow around and in the cell-porous rotating disk. A simple 1D model of gas flow is presented. Usually the cell-porous materials are applied in heat exchangers and stationary filters. On the other hand, peculiarities of the flow revealed under theoretical analysis and some experimental observations demonstrate that rotating porous disks may also be effectively exploited in the shear-force machines for the gas transport purposes.