Unsteady MHD Flow on a Rotating Cone in a Rotating Fluid

Unsteady flow over an infinite permeable rotating cone in a rotating fluid in the presence of an applied magnetic field has been investigated. The unsteadiness is induced by the time-dependent angular velocity of the body, as well as that of the fluid. The partial differential equations governing the flow have been solved numerically by using an implicit finite-difference scheme in combination with the quasi-linearization technique. For large values of the magnetic parameter, analytical solutions have also been obtained for the steady-state case. It is observed that the magnetic field, surface velocity, and suction and injection strongly affect the local skin friction coefficients in the tangential and azimuthal directions. The local skin friction coefficients increase when the angular velocity of the fluid or body increases with time, but these decrease with decreasing angular velocity. The skin friction coefficients in the tangential and azimuthal directions vanish when the angular velocities of fluid and the body are equal but this does not imply separation. When the angular velocity of the fluid is greater than that of the body, the velocity profiles reach their asymptotic values at the edge of the boundary layer in an oscillatory manner, but the magnetic field or suction reduces or suppresses these oscillations.     

Editorial: Recent advances in mechanics of unconventional electronics

正Conventional electronics is planar,hard,and rigid due to the intrinsic brittle nature of inorganic semiconductor materials(e.g.,silicon and gallium arsenide).The modern electronic technology has typically been concerned with large or small but durable and long-lasting electronics.Recently developed materials and mechanics concepts yield unconventional electronics with unique     

Sedimentation of solid discs in viscous medium

Free sedimentation velocities of thin discs have been measured in castor oil and liquid paraffin at constant temperature. Wall and end corrections have been applied to the measured velocities and the corrected values have been compared with those calculated fromOverbeck andGans' equations. Sedimentation velocities have been measured in both edgewise and broadsideon positions. Good agreements have been obtained with the theory in both types of sedimentation. The broadsideon position has been found to be the preferred orientation and all particles deviating even slightly from the edgewise position take the preferred orientation quickly. Results of other investigators have been discussed in the light of the present findings.Based on a dissertation submitted by (1) in partial fulfilment of the requirements for M. Sc. degree of the Dacca University in 1961.     

Vortex shedding behind rings and discs

The wake structure of discs and bluff rings has been investigated experimentally in a wind tunnel. The rings have an inner diameter d_i, and an outer diameter d_o and are classified according to the parameter (d_o + d_i)/(d_o − d_i) = d/w. the ratio of mean diameter to ring width. As d/w → ∞ the flow approaches that around a two dimensional bluff body whereas as d/w tends to unity the body approaches a solid disc. A distinct change in the vortex shedding pattern is found around d/w = 5. Below this critical value velocity fluctuations in the wake have a weak periodic component which is 180° out of phase across a diameter of the body. Above d/w = 5. regular and coherent axisymmetric vortex ring shedding is observed with shedding occurring alternately from the inner and outer circumferences of the bluff body. Flow visualization and conditional averaging of hot-wire data are used to investigate the vortex structure.     

Boundary Regularity of Rotating Vortex Patches

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is C ^∞, provided the patch is close to the bifurcation circle in the Lipschitz norm. The rotating patch is also convex if it is close to the bifurcation circle in the C ² norm. Our proof is based on Burbea’s approach to V-states.     

Bifurcation from Discrete Rotating Waves

Discrete rotating waves are periodic solutions that have discrete spatiotemporal symmetries in addition to their purely spatial symmetries. We present a systematic approach to the study of local bifurcation from discrete rotating waves. The approach centers around the analysis of diffeomorphisms that are equivariant with respect to distinct group actions in the domain and the range. Our results are valid for dynamical systems with finite symmetry group, and more generally, for bifurcations from isolated discrete rotating waves in dynamical systems with compact symmetry group.     

Rotating viscosimeters for process control

Summary Compared to the viscosity measurement under laboratory conditions there are additional demands on the measuring instrument when viscosity-dependent processes are to be monitored, controlled or regulated. Rotational-type viscosimeters with a coaxial cylinder system lend themselves for solving this problem. The various problems of viscosity measurement in production processes make high demands on the universal applicability of the viscosimeters. An instrument-technical solution on the basis of standardized basic modular units is of advantage. An instrument system process viscosimeters for viscosity measurements in receptacles and pipe lines is described.

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Zusammenfassung Gegenüber der Viskositätsmessung unter Laboratoriumsbedingungen ergeben sich zusätzliche Forderungen an das Meßgerät, wenn viskositätsabhängige Produktionsprozesse überwacht, gesteuert oder geregelt werden müssen. Rotationsviskosimeter mit koaxialem Zylindersystem sind zur Lösung dieser Aufgabe geeignet. Die unterschiedlichen Viskositätsmeßprobleme in Produktionsprozessen stellen hohe Anforderungen an die universelle Einsetzbarkeit der Viskosimeter. Vorteilhaft ist eine gerätetechnische Lösung auf der Basis von typisierten Grundbausteinen. Ein Gerätesystem Prozeßviskosimeter für Viskositätsmessungen in Behältern und Rohrleitungen wird beschrieben.

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With 3 figures     

Predicting the draught requirements of concave agricultural discs

The paper presents a rapid method for calculating the draught force generated by a concave disc tool when cutting a Mohr-Coulomb soil. The mean equivalent stress derived by distributing the draught force uniformly over the furrow cross-section is calculated using a set of non-dimensional factors in a two term additive equation. Tables of these factors are provided to cover the analysis of any disc of standard size and curvature operating over a practical range of cutting depths and disc and tilt angle settings. The furrow area can be estimated from published calculation tables (not reproduced here). From a knowledge of these parameters it is possible to calculate the draught force acting on the disc. A number of simplifying assumptions have been made to facilitate the development of an uncomplicated calculating procedure. Consequently the calculated values of draught must be considered as order of magnitude predictions.     

Settling of discs inside a vertical fluid-filled tube

The broadside settling of discs along the centerline of a fluid-filled tube is studied. The Stokes equation is solved by a method of eigenfunction expansions and collocation. Depending on the geometry, the flow field shows different arrangements of recirculating eddies. Due to mutual shielding, the discs settle faster when they are closer together.     

A theory for swaging of discs and lugs

A practical theory for swaging bored holes within plates and cylinders is proposed which can take into account work-hardening in the presence of small plastic strains based upon equivalent stress-strain data. With the appropriate choice of yield function, this theory applies to the swaging of both thin and thick plates under respective plane stress and plane strain conditions. The theory can be adapted further to the autofrettage of open and closed-ended, thick-walled cylinders where similar plane deformations conditions apply. Here swaging refers to the practice in which an oversized plug or sphere is forced into the bore thereby expanding it permanently to leave a residual circumferential compression in the bore material upon removal of the expanding tool. A similar effect results from applying an initial over-pressure to a long thick-walled cylinder in an autofrettage process. Both treatments are employed to enhance the fatigue resistance when the service loading upon the disc or cylinder amounts to a cyclic, circumferential tension within its bore. Strain gauges bonded to the entry face of the plate are used to monitor the circumferential and radial strain distributions both during and after the swaging process. Experimental results presented for swaging of thin and thin annular discs in aluminium alloy show that the measured residual strain distributions concord with the theory for large discs with a 10/1 diameter ratio. The agreement is less satisfactory with the loss in axial symmetry for parallel-sided lugs with a width to hole diameter ratio of 4/1.     

Optimal Design of Rotating Disks in Creep

Abstract

Minimum-weight design of axially-symmetric rotating disks in a state of stationary creep is determined for a prescribed value of the creep velocity at the outer edge of the disk. The constitutive equations used for stationary creep are Norton's law generalized to multiaxial states of stress based on von Mises' criterion and associated flow rule. The resulting nonlinear optimization problem is solved iteratively using a series expansion to approximate the thickness variation of the disk, In each iteration step the nonlinear creep equations are solved for the stresses and a linearized perturbation problem is solved for the stress gradients. The optimization procedure is used to determine the optimal shape of a solid rotating disk carrying a uniform traction at the outer edge, and this result is compared with the corresponding disk of uniform strength. Variations in the optimal shape due to a central hole and due to temperature distributions are illustrated by some examples.     

Rotating electroosmotic flow of an Eyring fluid

A perturbation analysis is presented in this paper for the electroosmotic(EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem.Using the relaxation time as the small ordering parameter,analytical solutions are deduced for the leading-as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman–electric double layer(EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.     

Thermal Vibrational Convection in Rotating Cavities

The average vibrational motion of a nonisothermal fluid in a uniformly rotating cavity is described theoretically. Equations are obtained using the averaging technique in the high-frequency vibration approximation. It is found that the rotation significantly affects both the intensity of the average flows and the structure of the pulsatory velocity field generating resonance amplification of the fluid vibrations ar certain ratios of the rotation frequency and the force field oscillation frequency. This makes rotation an important controlling factor ensuring a strong averaged effect under relatively weak vibrational action. The problem of excitation of vibrational convection in a plane rotating layer is considered on the basis of the equations obtained when the vibration frequency substantially exceeds the rotation frequency.     

Acoustics of Rotating Deformable Saturated Porous Media

We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For Kibel numbers A A(1), the acoustic filtration law resembles a Darcys law, but with a conductivity which depends on the wave frequency and on the angular velocity. The bulk momentum balance shows new inertial terms which account for the convective and Coriolis accelerations. Three dispersive waves are pointed out. An investigation in the inertial flow regime shows that the two pseudo-dilatational waves have a cut-off frequency.     

Numerical Investigation of the Flow Past a Rotating Golf Ball and Its Comparison with a Rotating Smooth Sphere

Large-eddy simulations are conducted for a rotating golf ball and a rotating smooth sphere at a constant rotational speed at the subcritical, critical and supercritical Reynolds numbers. A negative lift force is generated in the critical regime for both models, whereas positive lift forces are generated in the subcritical and supercritical regimes. Detailed analysis on the flow separations on different sides of the models reveals the mechanism of the negative Magnus effect. Further investigation of the unsteady aerodynamics reveals the effect of rotating motion on the development of lateral forces and wake flow structures. It is found that the rotating motion helps to stabilize the resultant lateral forces for both models especially in the supercritical regime.     

Rotating convection in a finite cylinder

This paper is devoted to analyzing numerically experimental observations of azimuthally travelling waves that appear in rotating convection in a circular container at intermediate Prandtl numbers. The instability is a Hopf bifurcation that gives rise to a pattern precessing generally counter to the rotation direction. Two types of modes can be differentiated, the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the center. Results are presented for Prandtl number 6.8 and aspect ratio d/h equal to 2.5 as a function of the rotation rate. For rigid insulating sidewalls, and rigid thermally conducting top and bottom lids, the results agree well with those mesured experimentally.