The Stewartson layer of a rotating disk of finite radius

It is shown that if a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, an axial layer in the form of a cylindrical shell exists at the edge of the disk. This shell of thickness O(E ^1/3) has length O(E ^–1) in axial direction, where E is the Ekman number. Its most characteristic element is the axial velocity of O(E ^1/6) which is larger than everywhere else in the field. We calculate the velocity components and the pressure in this layer.     

The flow between a rotating disk and a stationary porous disk of finite thickness

The flow of a viscous incompressible fluid between a rotating disk and a stationary disk is studied. The two disks are impermeable. There is a layer of porous medium over the stationary disk. The generalized Darcy law is used to represent the fluid motion in the porous medium and the Navier-Stokes equations in the pure fluid medium. The nonlinear equations representing the motion, together with the boundary conditions and the matching conditions at the interface, constitute a two point boundary value problem. In view of the sensitive nature of the problem to the choice of missing initial conditions required for the forward integration, a shooting method in conjunction with the continuation method is used to produce the numerical solution. The response of the velocity profiles and stresses on the boundaries to the increase in the thickness of the porous layer is studied.     

Nonlinear critical layers in the boundary layer on a rotating disk

The work of Gregory, Stuart and Walker (1955, Proc R Soc Ser A 406:93–106) and Hall (1986, Phil Trans R Soc London Ser A 248:155–199) is extended to include nonlinear effects for the stationary cross-flow vortex. It is shown that amplitude-dependent neutral modes are described by a forced Haberman equation. The corrections to the neutral wavenumbers and waveangles are derived and it is suggested that the nonlinear neutral modes can have wavenumbers decreased by an O(1) amount as compared to linear theory.     

Fluid flow between a rotating disk and a fixed wall

The results of a theoretical investigation of the fluid flow in the gap between a rotating disk and a fixed wall are presented. The variations of the rate of twisting of the fluid and the statistical pressure along the radius are analyzed for the case of centripetal flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 4, pp. 611–617, April, 1974.     

Secondary flows in the gap between a rotating cone and a stationary disk

The flow of an elastic-viscous incompressible liquid (polyethylene melt) in the batching zone of a disk extruder is examined. It is shown experimentally that a state of complex stress exists in the conical gap independent of its angle.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 5, pp. 913–917, November, 1973.     

Computation of the flow between a rotating and a stationary naturally permeable disk

A numerical exploration for the flow between a rotating and a stationary disk made up of porous material having depth equal to the distance between the two disks, is carried out by continuation method. The flow field has been studied by solving Navier-Stokes equations in the free fluid region and using Darcy's equations in the porous region.     

Transitional flow conditions on a rotating disk

Transitional flow conditions on the surface of a freely rotating disk were investigated by cine-recording, acoustic, and visual methods.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 6, pp. 1060–1067, December, 1976.     

Hydrodynamic electrochemistry: design for a high-speed rotating disk electrode

We report a novel gas-driven high-speed rotating disk electrode (HSRDE). The HSRDE when immersed in an aqueous solution rotates at approximately 650 Hz, generating laminar flow resulting in a diffusion layer, under steady-state conditions, of thickness approximately 2 microm. The use of high-pressure gas to drive the rotator offers significant improvement in electrical noise as compared to conventional mechanically driven devices. The electroanalytical utility of the HSRDE was exemplified by the anodic stripping voltammetry of arsenic(III) at a gold working electrode. The charge under the arsenic stripping peak was found to increase by more than 1 order of magnitude under the enhanced mass transport regime at the HSRDE in comparison to that seen under quiescent conditions.     

Characteristics of flow between a rotating and a static disk in the presence of radial flow

An improved method is proposed for the calculation of the flow in the gap between a rotating and a static disk in the presence of radial flow. The algorithm of the solution is realized on a Nairi-2 computer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 2, pp. 234–241, February, 1977.     

Optimization of jet cooling of a rotating disk

The author presents empirical formulas for optimizing a jet system for cooling of a disk rotating in a housing, in terms of the heat transfer coefficient.     

Rheodynamics of a disk rotating in a non-Newtonian liquid

The power approximation to the consistency flow curve of a rotating disk is considered; a criterial relationship for the rheodynamic resistance of the disk is then deduced. Experimental data obtained in solutions of sodium carboxymethyl cellulose (CMC) for C=0–1.5% agree closely with the proposed generalization.     

Calculation of air-film cooling of a rotating disk

An analysis and generalization is made of experimental data on the effectiveness of film-cooling of a rotating disk.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 5, pp. 862–869, November, 1968.     

Laminar film condensation due to a rotating disk

Summary Regular perturbation methods are employed to investigate the problem of laminar film condensation on a rotating disk in a large volume of quiescent vapour for small and large rates of cooling at the disk surface. The flow and thermal fields are represented by the Von Karman similar solution. Exact numerical solutions of the similar equations are obtained for the case of steam-water condensation and compared with those derived analytically.     

Thermoelastic analysis of a functionally graded rotating disk

A semi-analytical thermoelasticity solution for hollow and solid rotating axisymmetric disks made of functionally graded materials is presented. The radial domain is divided into some virtual sub-domains in which the power-law distribution is used for the thermomechanical properties of the constituent components. Imposing the necessary continuity conditions between adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are obtained. Solution of the linear algebraic equations yields the thermoelastic responses for each sub-domain as exponential functions of the radial coordinate. Some results for the stress, strain and displacement components along the radius are presented due to centrifugal force and thermal loading. Results obtained within this solution are compared with those of a finite element analysis in the literature. Based on the results, it is shown that the property gradation correlates with thermomechanical responses of FG disks.     

Rotationally symmetric fluctuating flow about a rotating disk

Superposed mean flow due to fluid performing torsional oscillations at large distances from a rotating disk is analysed. For low frequency of oscillations an analytical-numerical solution is obtained for small values of the amplitude parameter, which agrees fairly well with the available numerical results in the limit of zero frequency. Method of multiple scales is employed to derive a solution for high frequency range and for finite values of the amplitude parameter.     

Calculation of flow of a medium in the gap between a rotating disk and a fixed boundary wall

This paper examines the problem of determining the friction coefficients on the side surface of a rotating disk and a fixed boundary wall for different directions of the flowing medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 3, pp. 435–442, March, 1977.     

Deceleration of a porous rotating disk in a viscous fluid

The flow due to a rotating disk decelerating with an angular velocity inversely proportional to time with either surface suction (or injection) which again varies with time is investigated. The unsteady Navier-Stokes equations are transformed to non-linear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using a globally convergent homotopy method. The flow depends on two non-dimensional parameters, namely an unsteadiness parameter $\text{S}$ and a suction (or injection) parameter $\text{A}$. Some interesting numerical results are presented graphically and discussed.