Dynamics of spherical metallic particles in cylinder electrostatic separators/purifiers

This paper presents a theoretical analysis of the dynamics of spherical metallic particles in electrostatic separators/purifiers (ESPs). The particle equations of motion are numerically solved in two dimensions using a computational algorithm. The ESPs consist of a pair of conductor cylinder electrodes. The upper cylinder is energized by HVdc, while the lower one is grounded and fixed horizontally on a revolvable axis. Some phenomena and aspects of separation process are explained and depicted including lifting off, impact, "motion collapse" and "sudden bouncing". The results reveal that the several phenomena depend on initial position, radius and density of the particle, curvature of the cylinder electrodes, distance between the electrodes and amplitude of the applied voltage. Optimization of the parameters is presented in order to get better separation/purification processes.     

On the settling of a bidisperse suspension with particles having different sizes and densities

The settling of a bidisperse suspension with small particles having different sizes and densities can be described by an initial value problem for a system of two non-linear, first-order conservation laws. Solutions to this problem are in general discontinuous and exhibit kinematic shocks that separate areas of different composition. The solution requires the construction of so-called elementary curves in phase space, which are determined from eigenvector fields of the Jacobian of the flux function. Differences in solution behavior to the previously analyzed equal-density case are due to an umbilic point, which appears for different densities only. The initial value problem is eventually solved by the front tracking method, which generates a series of Riemann problems. It turns out that the solution of the problem predicts a fairly complex process of sediment formation, and that the stationary solution can consist of non-constant smooth transitions. This observation is of interest for manufacturing of functionally graded materials.     

Continual energy balance equations and entropy of a suspension of rotating spherical particles

Averaged equations of the kinetic energy balance of particle rotational motion and entropy are obtained on the basis of statistical methods developed in [1, 2].Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 4, pp. 605–613, April, 1984.     

The elastic rotating cylinder

A fully relativistic formulation is presented for an infinitely long, elastic cylinder of constant density, rotating uniformly about its axis. The problem is reduced to a non-linear differential equation in the displacement which is linearised to obtain classical and special relativistic solutions. These are compared with a typical general relativistic numerical solution.     

Source-sink flow in a rotating cylinder

Summary This paper describes the axisymmetric source-sink flow in a rapidly rotating cylinder. Relative fluid motion is induced by the presence of a sink in the bottom corner and a ring source located somewhere in the fluid, at some distance from the solid boundaries. In order to neglect nonlinear effects the volumetric flow rates are assumed to be small, i.e. O(E ^1/2), with E the Ekman number of the flow. The transport from the source to the sink is carried by Ekman layers at the end caps, and a Stewartson layer at the sidewall. At the ring source a free Stewartson layer arises, in which the injected fluid is transported towards the Ekman layers. This Stewartson layer consists of layers of thicknesses E ^1/4 and E ^1/3, which both contribute to the vertical O(E ^1/2) transport. The ring source is enveloped by a ring-shaped region of cross-sectional dimensions O(E ^1/2 × E ^1/2), in which the injected fluid is rearranged before erupting into the E ^1/3 layer. As E ^1/2 E ^1/3, this region appears as an isolated singularity in the E ^1/3 layer; in fact it consists of a combination of an upward and a downward directed source, the strengths of which can be determined by transport arguments. The paper presents an analysis of the E ^1/3-layer structure on the basis of a linear theory; it also describes how the analysis can be extended to the situation in which fluid is injected through an array of sources at different heights.     

Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

On compressible flow in a rotating cylinder

Summary Axisymmetric steady flow of a perfect gas in a rotating cylinder is studied by applying a linearised analysis to a small perturbation about isothermal rigid body rotation. Motivated by present day gas centrifuges, special attention is focussed on the effect of a length-to-radius ratio which increases from unit magnitude to infinity and on the effect of a strong radial density gradient associated with the isothermal rigid body rotation. The Ekman number E _*based on the small radial density scale and the density at the cylinder wall is taken to be small. It appears that the flow outside Ekman boundary layers at the end caps consists of three types. These correspond to 1 L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} L _*, E _* ^–1 andE _* ^–1 L _* where L _*is the ratio of the cylinder-length to the radial density scale. For 1 L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} an inviscid flow in a region of limited thickness near the cylinder wall is found. Due to the strong decrease of the density, radial diffusion is not confined to Stewartson boundary layers at the wall (typical for incompressible flow) but extends in the core. This finds expression in two layers in the centre of the cylinder, parallel to the rotation axis, having a structure similar to both Stewartson layers and adjusting the inviscid flow near the wall to a flow dominated by radial diffusion near the rotation axis. For L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} and L _* E _* ^–1 both Stewartson layers become successively of the same thickness as the density scale. At the same time the corresponding layers in the core go to the wall and join. As a result, for L _* E _* ^–1 radial diffusive processes are significant in the entire cylinder, a situation also known from studies of flows in semi-infinite gas centrifuges.     

Temperature distribution in a rotating hollow cylinder

The temperature distribution in a hollow cylinder rotating with a given angular velocity is found for steady-state boundary conditions of the first kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 4, pp. 705–711, October, 1979.     

旋转压电复合圆柱的弹性分析

针对由各向同性弹性核和压电层组成的两层复合圆柱的旋转问题,给出了弹性力学解。先从压电层的静电平衡方程出发,得到含一个待定常数的电位移形式解,并由此分别给出弹性核和压电层的位移通解,然后利用力学和电学边界条件以及界面处的连续条件确定出所有各层中引入的待定常数,最终得到原问题的解。数值结果表明：当压电层的内外表面均接地时,压电层中的径向应力幅值随弹性核材料的杨氏模量增大而增大,而环向应力则正好相反。弹性核材料的泊松比及外加在压电层内外表面上的电势对旋转两层复合圆柱内的应力响应均有显著的影响。     

Dynamics of quantized vortices in rotating superfluid

Dynamics of interactive quantized vortices in rotating superfluid is studied theoretically. This work considers the basic system where superfluid is contained in a cylindrical vessel that rotates about its axis at an angular velocity. Although two-dimensional equilibrium patterns of vortex arrays are understood fairly well at present, there has been only a little amount of information on the dynamical aspects. Thus this work studies some typical dynamical problems, i.e., formation of vortex array and spin-down process. We describe also three-dimensional analysis which is much more troublesome than two-dimensional one.     

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.

     

高速旋转弹章动测试方法研究

旋转弹章动参数是兵器科研生产中的重要参数,现阶段普遍采用雷达测试法对弹丸章动参数进行分析提取,对实验设备要求高,测量难度大。该文提出一种基于姿态变换理论的高速旋转弹章动参数测试的新方法,该方法利用三轴磁传感器与存储测试技术,将三轴磁传感器输出的信号进行解算,得出旋转弹的两个姿态角。通过姿态变换理论,找出偏航角、俯仰角和章动角之间的关系,从而建立章动参数的数学模型,计算出旋转弹的章动角。通过实弹测试实验表明:根据姿态变换理论可以计算出章动角为0.85°,旋转弹的章动周期为36.6 ms,对数据进行分析处理,计算结果误差在0.01%以内。该测试方法简单方便,对今后研究弹丸章动运动具有一定的参考价值。     

Laser-induced diamagnetism in suspension of onion-like carbon particles

It is experimentally established that the bleached fraction of a suspension of onion-like carbon (OLC) particles in N,N-dimethylformamide (DMF), which is clarified under the action of high-power pulsed laser radiation at λ = 1064 nm, is pushed out from inhomogeneous magnetic field. By changing the spatial arrangement of a permanent magnet relative to the point of laser action on the suspension, it is possible to control the direction of motion of the bleached fraction. The observed behavior can be explained by laserstimulated chemical reactions between OLC and DMF, which lead to the formation of a new substance with pronounced diamagnetic properties.     

Note on the motion of surface films in a rotating cylinder

Summary The motion of an insoluble and incompressible surface film at the gas-liquid interface of a fluid system in a finite revolving cylinder is dealt with experimentally. It is shown that the film motion induced by the side-walls affects the film motion at the plane gas-liquid interface considerably. Measurements show a difference of 20 to 30% for small speeds of rotation.With 5 Figures     

Effects of end wall friction in rotating cylinder granular flow experiments

Dry granular flows in half-filled horizontal rotating cylinders were studied by NMR to ascertain end wall effects. We measured the velocity and density profiles in planes perpendicular to the axis of the drums for three cases: (1) Near the end wall of a long ``3D' cylinder, (2) Near the middle of the long cylinder and, (3) For the whole of a short ``2D' cylinder. The velocity near the free surface is fastest for the short cylinder and slowest near the end wall of the long cylinder. We believe that these differences are due to friction between the beads and the end walls, speeding up the flow for the 2D drum and reducing the near-wall speed for the 3D drum.     

Two-dimensional viscous flow of a suspension due to particle settling in a vertical vessel

Summary This paper investigates the influence of the viscosity of the suspension together with wall friction on sedimentation in vessels with vertical walls. The settling process is described by four basic equations, i.e. two continuity and two momentum equations. Assuming a very dilute suspension, an asymptotic expansion for small particle concentration is carried out. To first order, the well-known one-dimensional solution is recovered. The motion of the liquid, however, is a second-order effect governed by the biharmonic equation. In order to find a solution satisfying the boundary conditions, harmonic expansions are used. Thus the problem is reduced to a system of linear algebraic equations. Solutions for the two-dimensional flow of the liquid and the motion of the particles are given, and the influence on the shape of the interface between the suspension and the clear liquid is discussed.With 7 Figures     

Heat transfer from a rotating cylinder under forced convection

An analytic solution is obtained for the heat-transfer coefficient from a rotating cylinder with inflow of coolant for various Reynolds numbers.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 414–420, September, 1981.