Modelling axial dispersion of granular material in inclined rotating cylinders with bulk flow

The axial dispersion of approximately monosized particles in rolling mode in rotating cylinders with bulk flow is examined using a Monte Carlo model and discrete element method (DEM) simulations. The Monte Carlo model predicts that the mean square displacement relative to the mean axial displacement of the bed undergoes oscillations in time. The nature of these oscillations depends on the fill level of the cylinder and the extent of particle mixing during avalanches. When the cylinder is half full the Monte Carlo model predicts undamped oscillations, whereas a filling fraction of 0.26 produces oscillations whose amplitude decreases with time. If mixing during avalanches is assumed to be perfect then the oscillations occur about a linear increase with time. In contrast, if it is assumed that the particles do not mix during avalanching, the oscillations occur about an increase with time which has a gradient which increases with time. There is good qualitative agreement between the Monte Carlo model with perfect mixing and the DEM when the filling fraction is 0.26. For a filling fraction of 0.5 the DEM data show oscillations about a faster than linear increase with time.

     

The vibration of rotating elastic membrane cylinders

Using membrane theory we first investigate the finite deformation of a right circular cylinder of compressible hyperelastic material rotating about its axis. A necessary and sufficient condition for axial shortening to accompany rotation is given. Secondly we consider small amplitude vibrations propogating on such a finitely deformed cylindrical membrane. The same equations are shown to govern both the compressible and incompressible cases. For axi-symmetric vibrations analytical results are obtained and are used to show that neither pure torsional nor pure longitudinal vibrations can propagate in a rotating cylinder. Numerical results are given for a variety of different forms of vibration for a particular realistic material model.     

Axial particle diffusion in rotating cylinders

We study the interface dynamics of a binary particle mixture in a rotating cylinder numerically. By considering only the particle motion in axial direction, it is shown that the initial dynamics can be well described by a one-dimensional diffusion process. This allows us to calculate a macroscopic diffusion constant and we study its dependence on the inter-particle friction coefficient, the rotation speed of the cylinder and the density ratio of the two components. It is found that radial segregation reduces the drift velocity of the interface. We then perform a microscopic calculation of the diffusion coefficient and investigate its dependence on the position along the cylinder axis and the density ratio of the two particle components. The latter dependence can be explained by looking at the different hydrostatic pressures of the two particle components at the interface. We find that the microscopically calculated diffusion coefficient agrees well with the value from the macroscopic definition when it is measured in the middle of the cylinder.     

Vortex nucleation in deformed rotating cylinders

Superfluid states in a rotating elliptic cylinder are studied with semiclassical hydrodynamics. Two distinct approaches are used to obtain the critical angular velocity for the appearance of a vortex: (1) Equilibrium thermodynamics predicts that ω _c1 increases monotonically with deformation at fixed cross-sectional area. (2) Predictions based on a critical slip speedv _c at the walls depend on the detailed form ofv _c ; the resulting ω _c need not vary monotonically with deformation. The analogous situation in a rectangular cylinder is also discussed.     

The appearance of vortices in the flow of helium II between rotating cylinders

We argue that the appearance of quantized vortices in laminar Taylor-Couette flow of helium II is a problem for which free energy minimization should give valid results even in the presence of dissipation. We (approximately) reduce the problem to an equivalent problem in solid-body rotation, for which the solution for the low-lying states has been obtained by Fetter. We then use approximations to the solution for solid-body rotation to predict the appearance of vortices for the general Taylor-Couette problem. These results compare moderately well with the existing data, which now seem relatively incomplete.     

Radial segregation of ternary granular mixtures in rotating cylinders

We carry out an experimental study of the equilibrium segregation of ternary granular mixtures in a rotating cylinder. In all the experiments, 50% of the volume of the cylinder is filled with the granular mixture and the rotational speed used ensures operation in the rolling regime of flow. Mixtures of spherical particles differing only in size and of spherical particles differing in size and density are considered, using steel balls and glass beads of different sizes. Volume fractions of the components (f{\phi}) are measured by sampling at different radial positions (r) to yield the radial volume fraction profiles (f(r){\phi(r)}). Results for mixtures differing only in size of the components indicate that the segregation process is nearly independent of the sizes of the large and middle size particles for the same size of small particles. In the case of mixtures with different size and density components, the segregation patterns depend on the direction of the resultant driving force. In many of the mixtures considered, the pattern of segregation can be qualitatively predicted by considering binary interactions between the components. However, in some mixtures, ternary interactions are found to determine the pattern obtained.     

Stability of power law fluid flow between rotating cylinders

The centrifugal instability of power law fluid flow when the fluid fills the gap between two rotating concentric cylinders of infinite length is addressed. The instability of the circular Couette flow is determined via linear stability analysis. In the narrow gap case, the critical Taylor number is determined analytically, while in the general gap case, a finite-difference numerical method is employed. The results are shown to be in agreement with existing theoretical and experimental findings. The super-critical flow is investigated by means of a weakly non-linear analysis method. The Taylor-vortex flow (the secondary stable flow) is obtained. The instability of this flow is determined as we present the critical Taylor number when the Taylor vortices begin to exhibit a waviness in the azimuth     

Friction and heat transfer in the gap between two rotating coaxial cylinders

An attempt is made at a theoretical analysis of the friction and heat transfer in the gap between two coaxial cylinders rotating in one direction. The interaction of a fluid with the channel walls is divided into two stages: 1) formation of roller, annular fluid flows in the gap; and 2) friction and heat transfer with forced flow past the walls.     

Natural convection in an annulus between two rotating vertical cylinders

Summary A numerical study is conducted to understand the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two concentric vertical cylinders which rotate about their axis with different angular velocities. The inner and outer side walls are maintained isothermally at temperature _c and _h , respectively, while the horizontal top and bottom walls are adiabatic. The vorticity-stream function form of the Navier-Stokes equations and the energy equation have been solved by modified Alternating Direction Implicit method and Successive Line Over Relaxation method. Numerical results are obtained for a wide range of the Grashof number, Gr, nondimensional rotational speeds _i , _o of inner and outer cylinders and for different values of the Prandtl number Pr. The effects of the aspect ratio,A, on the heat transfer and flow patterns are obtained forA=1 and 2. The numerical results show that when the outer cylinder alone is rotating and the Grashof number is moderate, the outward bound flow is confined to a thin region along the bottom surface while the return flow covers a major portion of the cavity. For a given inner or outer cylinder rotation the temperature field is almost independent of the flow in the annulus for fluids with low Prandtl number, while it depends strongly for high Prandtl number fluids. At a high Grashof number, with moderate rotational speeds, the dominant flow in the annulus is driven by thermal convection, and hence an increase in the heat transfer rate occurs. In the case of unit aspect ratio, the flow pattern is unicellular for the rotation of the cylinders in the same direction, and when they rotate in the opposite direction two or more counter rotating cells separated by a stagnation surface are formed. The rate of heat transfer at the hot cylinder is suppressed when its speed of rotation is higher than that of the cooler cylinder. The computed heat transfer and flow patterns are compared with the available results of a nonrotating cylindrical annulus, and good agreement is found.     

Hydromagnetic flow between rotating eccentric cylinders with suction at the porous walls

The effect of a radial magnetic field on the flow of a viscous, incompressible fluid between two eccentric rotating cylinders with suction at both the cylinders, for very small clearance ratio is investigated. The expressions for the stream function and pressure are obtained using perturbation analysis. Conclusions are drawn from the streamlines and pressure plots which are shown graphically for various values of flow parameters.     

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.     

Structure parameters governing fracture toughness of engineering materials

Conclusions 1. Of the two concepts of brittle fracture of engineering materials based on the decohesion and coalescence fracture mechanisms, respectively, the first reflects the threshold fracture toughness for materials of perfect structure, the second — the minimal fracture toughness of the material of a real structure. Since the coalescence fracture mechanism is observed with most engineering materials and requires higher fracture energy and the decohesion mechanism is a part of the coalescence mechanism, it is necessary to investigate both of them in order to study the nature of the fracture process and to optimize the material structure. 2. The model parameters on which the coalescence fracture mechanism is based, namely, characteristic distance X_c and microcleavage stress _f ^* , are directly related to the material minimal fracture toughness and are defined by the weakest elements of its microstructure. 3. Rigorous physical interpretation of the characteristic distance and microcleavage stress requires statistical (dimensional and orientation) consideration, yet modeling of the fracture process in mean values of the above parameters seems to be useful. 4. Fracture toughness dependences on the temperature and loading rate both for a number of ceramic materials and for steels in the brittle-to-ductile transition region have much in common. For this reason, it is possible to use some fracture models, and, in particular, the K_µ-model, to analyze fracture of ceramic materials and to optimize their structure. 5. The main ways of enhancing fracture toughness of engineering materials are associated not only with the plasticization of the latter but also with the creation of such structures that would contribute to an increase of their minimal fracture toughness values. This can be achieved by increasing each of the two fundamental parameters of the material fracture micromechanism: characteristic distance and cleavage stress.Institute of Strength Problems, Ukraine Academy of Sciences, Kiev. Université de Metz. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 3, pp. 113–123, May–June, 1993.     

Experimental investigation of axial dispersion in a horizontal rotating cylinder

This work reports experimental measurements of the dispersion of particles during rotation in a horizontal cylinder. The axial dispersion of a pulse of approximately monodisperse black glass ballotini into a bed of clear glass ballotini of the same size is analysed. This is done using a sectioning technique, where the concentration is determined throughout the cylinder for a given rotation time and speed. The concentration profile is fitted to an appropriate solution of Fick’s second law to determine the dispersion coefficient. The dispersion coefficient is compared for various drum rotation rates and glass ballotini sizes. The cylinder was filled to 35 % by volume and rotated at a range of speeds between 5 and 20 rpm. The particle sizes vary from 1.14 to 3.15 mm. The dispersion coefficient was found to be dependent on both particle size and rotation speed. As the rotation speed, \(\omega \), was increased the dispersion coefficient increased proportionally to \(\omega ^{0.8}\). As the particle diameter, \(d_p\), was increased the dispersion coefficient increased proportionally to \(d_p^{1.84}\). These results are compared with previous experimental and simulation data, in particular the simulations of Third et al. (Powder Technol 203:510, 2010). Strong agreement was found between the simulations of Third et al. and the experimental results.

     

Current-induced instabilities of hydromagnetic flow in a small gap between rotating conducting cylinders

Summary.  In considering the stability of an electrically conducting fluid between rotating perfectly conducting cylinders with a current-induced pressure gradient acting in the azimuthal direction and with an applied axial magnetic field, the assumption of small-gap approximation is made and the governing equations with respect to both axisymmetric and non-axisymmetric disturbances are solved by a direct numerical procedure. A parametric study covering wide ranges of Q, the Hartmann number which represents the strength of the axial magnetic field, and β, a parameter characterizing the ratio of current-induced and rotation velocities, is conducted for the situation where the outer cylinder is stationary and the inner cylinder is rotating. It is found that the stability characteristics are thoroughly different from those of the case of weakly conducting walls. The variation of the onset mode is shown in the (β, Q)-plane, and the transition of the corresponding neutral curves is discussed in detail. Results for the critical Taylor number and wavenumber pertaining to the critical disturbances are presented. The critical values of radial current density required for the onset of instability are also determined. Received May 8, 2002; revised November 11, 2002 Published online: May 8, 2003 The financial support for this work from National Science Council of Taiwan, ROC, through Grant No. NSC 89-2212-E-132-006 is gratefully acknowledged.     

Tangential velocity profiles of granular material within horizontal rotating cylinders modelled using the DEM

Flow regimes of granular materials in horizontal rotating cylinders are industrially important since they have a strong influence on the rates of heat and mass transfer within these systems. The tangential velocity profile, which describes how the average particle velocity in the direction parallel to the surface of the bed varies along a radius perpendicular to the surface of the bed, has been examined for many experimental and simulated systems. This paper is concerned with tangential velocity profiles within rotating cylinders simulated using the discrete element method. For high fill levels good agreement is found between the simulated velocity profiles and the equation proposed by Nakagawa et al. (Exp Fluids 16:54–60, 1993) based on magnetic resonance measurements. At lower fill levels slip is observed between the cylinder wall and the particles in contact with it and also between the outer layer of particles and the bulk of the bed. It is demonstrated that this slip occurs when the particles in contact with the wall are able to rotate and that it may be prevented either by using non-spherical particles or by attaching “lifters” to the cylinder wall.     

Influence of temperature field on stability of fluid motion between rotating cylinders

The Rayleigh method is used to obtain relations giving the influence of the amount and direction of heat flow on the stability of a fluid between rotating cylinders.     

On the stability of secondary Taylor flow between rotating cylinders with a wide gap

In a general formulation, the problem of the stability of small perturbations in a homogeneous viscous fluid between rotating cylinders with a wide gap is investigated numerically.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 1, pp. 99–106, July, 1973.     

二维旋转直柱光子晶体的频率带隙结构分析

设计了一种二维方形旋转正四边形直柱光子晶体,利用平面波展开方法计算了其光子频率带结构,发现在低频和高频区域,该类光子晶体的光子频率禁带明显增大.计算了空气中Al材料的旋转四边形直柱光子晶体的带结构和态密度,当填充比等于0.5时存在绝对带隙,旋转角度为45°时绝对带隙最大,旋转角度为0时,光子频率禁带位于高频区域.利用FDTD方法检验了计算结果,并分析了旋转角度为45°时,正四边形直柱光子晶体的波导特性以及TM模的电场分布.