Stokes flow of a rotating sphere around the axis of a circular orifice or a circular disk

This paper presents an infinite series solution to the creeping flow equations for the axisymmetric motion of a sphere of arbitrary size rotating in a quiescent fluid around the axis of a circular orifice or a circular disk whose diameters are either larger or smaller than that of the sphere. Numerical tests of the convergence are passed and the comparison with the exact solution and other computational results shows an agreement to five significant figures for the torque coefficients in both cases. The torque coefficients are obtained for the sphere located up to a position tangent to the wall plane containing either the orifice or the disk. It is concluded that the torque coefficients of the sphere and the disk are monotonically increasing with the decrease of the distance from the disk or the orifice plane in both cases.     

On the dynamics of rotating circular cable structures

The combined effect of gravity and a centrifugal field on the dynamics of a heavy cable with negligible bending stiffness is treated. The inextensible length of the cable is preassigned in such a way that the cross-sectional shape of the cable structure is circular if the contiguration rotates about its central axis with a constant speed and no external forces act. Under the additional influence of gravity, complicated nonlinear weight-excited vibrations occur.To understand the variety of vibrational phenomena. The dynamic system is studied by some experiments first. In order to explain the experimental results theoretically, the governing nonlinear boundary value problem is derived next. Subsequently, an appropriate variational formulation for application of a Rayleigh Ritz procedure is suggested. The resulting nonlinear ordinary differential equations approximately deseribe a part of the observed vibrational behaviour.Both the experiments and the calculations demonstrate that, for high speeds, nonlinear weight-excited vibrations about the circular reference configuration occur. On the other hand, for low velocitites, periodie and even chaos-like snap-through phenomena appear.     

Evaluation of elastic compensation using elastic/plastic rotating circular disk problems

A version of elastic compensation is evaluated in the context of stress and deformation analysis of elastic/plastic rotating circular disks of both constant and variable thicknesses undergoing small deflections. An iterative incremental method is combined with finite difference methodology to generate information about the entire quasistatic loading histories of such disks. The evaluation process involves comparison of representative numerical results with corresponding predictions existing in the literature.     

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.     

On vortex shedding behind a circular disk

Abtract  Experiments were performed for individual realizations of the vortex shedding process behind a circular disk at Reynolds numbers of 10³–10⁵, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90° apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential locations 180° apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow. Received: 4 April 19969/Accepted: 29 January 1997     

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     

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.

     

On the flow between a rotating and a porous fixed disk with suction

Numerical self-similar solutions are reported for the laminar, incompressible flow between a rotating disk and a porous, fixed one with suction. Validation of the method is obtained through the numerical integration of the full Navier-Stokes equations applied to a reference radially confined geometry, and also with hot-wire measurements of the tangential velocity component. The flow structure is analysed for different values of the rotational and suction Reynolds numbers. It is shown that suction causes an important angular acceleration of the rotating core, whose velocity may thus considerably exceed that of the rotating disk. The physical reason for this unusual behavior is discussed in detail.     

Stability of open circular cylindrical shells reinforced with longitudinal ribs

We obtain exact and approximate solutions to buckling problems for circular cylindrical open shells hinged at all edges and quasiregularly reinforced with discrete longitudinal ribs. It is shown that analogous solutions to natural-vibration problems for such shells can easily be found Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 83–92, December 2008.     

Elastic-plastic deformation of the rotating solid disk

Summary The plane state of stress in a rotating circular disk of elastic-plastic material with linear strain hardening is studied based on Tresca's yield condition and its associated flow rule. The plastic core consists of two parts with different forms of the yield condition. By specializing the results to perfectly plastic material, the usual statically determinate stress distribution is recovered but, since the plastic strain at the axis becomes infinite, these stresses are not meaningful.

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Die elastisch-plastische deformation der rotierenden vollscheibe

Übersicht Der ebene Spannungszustand in einer rotierenden Kreisscheibe aus elastisch-plastischem Werkstoff mit linearer Verfestigung wird berechnet unter Zugrundelegung der Trescaschen Fließbedingung und der zugehörigen Fließregel. Der plastische Kern setzt sich zusammen aus zwei Teilen, in denen die Mießbedingung verschiedene Formen annimmt. Durch Grenzwertbildung werden die Ergebnisse auf idealplastisches Verhalten spezialisiert; man findet die übliche statisch bestimmte Spannungsverteilung. Da diese aber mit unbeschränkten plastischen Dehnungen an der Scheibenachse verbunden ist, können die Spannungen nicht sinnvoll sein.

     

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Reslts show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds numberRe and rotation parameter α, is built by a kinematic analysis of the steady flow fields. The project supported by the National Natural Science Foundation of China     

Equalizing plane incompressible fluid flow through a rotating circular lattice of thin curved profiles with radial direction at the inlet

The problem of equalizing the two dimensional flow of an incompressible fluid through a plane lattice of radial plates has been solved approximately by Mitrokhin [1]. In the following we present an approximate solution of the same problem for a cascade of thin curved blades which have a radial direction at the entrance. The bases of the proposed solution are the same assumptions as used in [1]. The formulas of Mitrokhin for the cascade of radial plates are a particular case which derives from the formulas obtained for the flow equalization radius and energy losses associated with separated flow.     

Darcy-Forchheimer flow by rotating disk with partial slip

The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method(OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.