Dynamics of bi-dispersed settling suspension of non-colloidal particles in rotating cylinder

Non-neutrally buoyant suspension of bi-dispersed non-colloidal particles in viscous fluid rotating in a horizontal cylinder displays in-homogeneities in particle distribution with alternate bands of high and low particle concentrations along the symmetric axis of the cylinder. Experiments were carried out to characterize the axial segregation in bi-dispersed suspension at various filling fraction and rotation speed of cylinder. The mixture of same particles in absence of any suspending fluid did not show any segregation. However, in case of particles suspended in water it was observed that the rate of segregation increases with increase in filling fraction. Once the particles get segregated along the full length of the cylinder, these bands start to migrate along the tube axis finally merging to give wider bands. For a given filling fraction the rate of segregation increases with the angular speed of the rotating cylinder. When the tube is partially filled the particle segregation is observed at higher angular speed, whereas in fully filled case the segregation starts at much lower rotation speed for the same concentration of particles. The segregation pattern changes as the rotation speed is increased. At higher speed the centrifugal force dominates over gravitational and viscous drag forces and this result into completely different segregation patterns. We have also analyzed the evolution of concentration profile from the image analysis of the particles.     

Viscous vortex core generation

Summary The unsteady flow of a viscous incompressible fluid between two porous co-axial circular cylinders is analysed when the outer cylinder is impulsively set into rotation. When there is radial inflow, vorticity is transferred from an unsteady boundary layer initially over the outer cylinder to a steady boundary layer over the inner cylinder.With 1 Figure     

Electro-magnetic collapse of thick-walled cylinders to investigate spontaneous shear localization

We present an electro-magnetic (EM) setup in order to collapse thick-walled cylinders, for the investigation of spontaneous formation of multiple adiabatic shear bands. The EM setup is based on a pulsed current generator using a capacitor bank system. The cylindrical specimen is part of an assembly of coaxial cylinders, where the inner and outer cylinders, each attached to an opposite pole, are short-circuited. Upon capacitor discharge, a high current flows through the cylinders, in opposite directions, creating repulsive magnetic forces between them. The outer cylinder is driven outwards and the inner cylinder is driven inwards - in a collapsing manner. This work presents the design procedure of the specimens’ geometry using numerical simulations, and some preliminary experimental results for SS304L steel specimens. The spatial distribution of the multiple adiabatic shear bands in these specimens is in good agreement with that reported in the literature for explosively driven experiments with the same material. Our numerical simulations of the collapsing cylinder show good agreement with the experimental results for both global behavior and shear band distribution.     

Stability of nonisothermal flow of a viscous liquid in an annular channel

In nonisothermal flow of a viscous liquid in an annular channel between coaxial cylinders where the outer cylinder has finite dimensions and is stationary, and the inner cylinder infinitely moves along the axis, the central position of the latter is unstable. When superimposing a thermal field, principally it is possible to create as large a force as required which holds the inner cylinder exactly on center.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 1, pp. 32–37, July, 1992.     

Influence of particles on the transition to turbulence in pipe flow

We investigate by experiment the influence of suspended solids upon the transition to turbulence in pipe flow. The particles are monodisperse and neutrally buoyant with the liquid. The role of the particles on the transition depends upon both the volume fraction, phi, and particle size. Below a critical particle diameter, particles alter the transition to larger critical Reynolds numbers for all phi. In contrast to this, larger particles move the transition to smaller Reynolds numbers for small phi, but they delay the transition at larger concentration.     

Axisymmetric vibration of infinite piezoelectric cylinders using one-dimensional finite elements

A general finite-element analysis for infinite piezoelectric cylinders has been formulated. The classical three-dimensional elasticity equations of motion are used. The dependence on theta, z, and time are included by assuming appropriate trigonometric functions, and the three-dimensional problem is reduced to a one-dimensional finite element with four degrees of freedom per node. The tabulated results are limited to cylinders with stress-free, shorted electrode (phi=0) boundary conditions at the outside surface of the cylinder. However, solutions for a variety of boundary conditions are possible. Solutions for the piezoelectric cylinder compare favorably with the existing literature. The motion of piezoelectric cylinders with thin coatings is analyzed by modeling the cylinder and thin coating as a layered cylinder.     

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.     

Hydrodynamic stability of viscous flow between curved porous channel with radial flow

A linear stability analysis has been presented for the flow between long concentric stationary porous cylinders driven by constant azimuthal pressure gradient, when a radial flow through the permeable walls of the cylinders is present. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius is varied from −100 to 30. The linearized stability equations form an eigenvalue problem which are solved using a numerical technique based on classical Runge-Kutta scheme combined with a shooting method, termed as unit disturbance method. It is observed that radially outward flow and strong inward flow have a stabilizing effect, while weak inward flow has a destabilizing effect on the stability. Profiles of the relative amplitude of the perturbed radial velocities show that radially outward flow shifts the vortices toward the outer cylinder, while radially inward flow shifts the vortices toward the inner cylinder.     

The shape of a liquid surface in a uniformly rotating cylinder in the presence of surface tension

The free-surface shape of a liquid in a uniformly rotating cylinder in the presence of surface tension is determined before and after the onset of dewetting at the bottom of the cylinder. Two scenarios of liquid withdrawal from the bottom are considered, with and without deposition of thin film behind the liquid. The governing non-linear differential equations for the axisymmetric liquid shapes are solved numerically by an iterative procedure similar to that used to determine the equilibrium shape of a liquid drop deposited on a solid substrate. The numerical results presented are for cylinders with comparable radii to the capillary length of liquid in the gravitational or reduced gravitational fields. The capillary effects are particularly pronounced for hydrophobic surfaces, which oppose the rotation-induced lifting of the liquid and intensify dewetting at the bottom surface of the cylinder. The free-surface shape is then analyzed under zero gravity conditions. A closed-form solution is obtained in the rotation range before the onset of dewetting, while an iterative scheme is applied to determine the liquid shape after the onset of dewetting. A variety of shapes, corresponding to different contact angles and speeds of rotation, are calculated and discussed.     

Vertical Taylor–Couette flow with free surface at small aspect ratio

The free surface flow between two concentric cylinders with vertical axes is investigated using numerical and experimental approaches. The bottom end wall of the cylinders and the outer cylinder are stationary and fixed, and the inner cylinder is allowed to rotate. In such a case, an odd number of Taylor vortices is usually formed (normal mode). However, we found that anomalous modes with outer flow near the bottom end wall or inner flow at the free surface appear in some conditions. Further, we determined bifurcation diagrams between the normal three-cell mode and normal one-cell mode and between the normal five-cell mode and the normal three-cell mode.     

串列双方柱干扰效应流动机理研究

为了研究建筑群体周围的流场结构,减小工程设计中由于干扰效应造成的损失,利用粒子图像测速(PIV)结合数值模拟,研究在较大雷诺数及不同间隙工况下,双方柱流场受干扰时的流动特性及流场空间结构。分析升阻力系数、涡脱频率、斯特劳哈尔数等流场特征参数,探究不同间隙对串列双方柱的影响。当Re=3.42×104时,存在临界间隙比G=4使串列双方柱流场结构发生突变,试验观察到流场中出现双稳态现象;当G<4时,下风向方柱平均阻力系数为负值,小于单方柱情况下的阻力,屏蔽效应明显,上风向方柱后方涡脱落被抑制,平均阻力系数出现了明显的降幅,最大降幅约达10%;当G>4时,上下方柱均有涡旋脱落。该结果对于工程应用具有参考意义。     

Weakly nonlinear stability analysis of thin viscoelastic film flowing down on the outer surface of a rotating vertical cylinder

The paper presents both of the linear and nonlinear stability theories for characterization of viscoelastic film flows down on the outer surface of a rotating infinite vertical cylinder. After showing the insufficiency of the linear model in characterizing certain flow behaviors, a generalized nonlinear kinematic model is then derived to represent the physical system. The model is solved by the long wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, an elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that by increasing the rotation speed, Ω, and decreasing the radius of cylinder, R, the film flow will generally make the flow system less stable. In this study, the interaction of the rotation and the radius of cylinder are taken into account. Generally, Reynolds number is divided into three regions, which are Re<3, 3<Re<8 and 8<Re, for discussion corresponding to the pre-selected Rossby number (Ro=0.1) and viscoelastic parameter (k=0.05).     

On the generation of water waves by cylindrical porous wave maker

Summary By the direct application of Havelock's expansion theorem and exploitation of various properties of Bessel functions, the problem of generation of cylindrical surface waves, in the case of water of infinite depth, in the presence of an impermeable circular cylinder surrounded by a co-axial permeable cylinder immersed vertically in the fluid region, is investigated. The wave motion is generated due to the simple harmonic motion in the radial direction of the (i) inner impermeable cylinder and (ii) co-axial permeable cylinder, when one of the two cylinders is kept fixed. As an application, the problem of scattering of water waves is analyzed when both the cylinders are kept fixed.     

Effects of scale and inertia on granular banding segregation

We report that the formation of much reported axial segregation bands in rotating cylinders loaded with different sized particles depends critically on scale and inertia. Specifically, when the ratio, , of the diameter of the cylinder to the average diameter of the particles is large, axial bands invariably appear, when is small, bands never appear, and between these extremes lies a reversible state where the presence or absence of bands depends on container rotation speed. Our results indicate that banding is associated with a Rayleigh-like instability of a granular core of fine particles, and that this instability is controlled by the inertia of the larger species – and consequently on scale.KeywordsGranular, Segregation, Mixing, Banding, ScalePACS number(s): 05.40.+j, 46.10.+z, 83.10.Hh.     

DEM modeling of shear bands in crushable and irregularly shaped granular materials

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.     

Nonlinear stability analysis of thin Newtonian film flowing down on the inner surface of a rotating vertical cylinder

Summary The paper presents both of the linear and nonlinear stability theories for characterization of Newtonian film flows down on the inner surface of a rotating in.nite vertical cylinder. After showing the insufficiency of the linear model in characterizing certain flow behaviors, a generalized nonlinear kinematic model is then derived to represent the physical system. The model is solved by the long wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, an elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that by increasing the rotation speed, X, and the radius of cylinder, R, the film flow will make the flow system more stable.     

轴线间距对圆柱体低速并联入水空泡演化影响试验研究

为分析圆柱体并联入水过程中入水空泡间相互干扰对于空泡演化特性影响规律,采用基于高速摄像的方法,开展两圆柱体同步并联入水试验研究。通过圆柱体单独入水和双圆柱体并联入水试验对比,分析了圆柱体同步并联入水空泡演化特性与单独入水空泡演化特性的差异,揭示了同步并联入水双空泡演化机理,并进一步给出了入水空泡随轴线间距的变化特性。试验结果表明:并联入水过程中,双空泡形态在空间上呈现出了较好的镜面对称特征;对于深闭合入水空泡,随着两圆柱体轴线间距的增大,空泡在两圆柱体轴线内侧区域的发展程度逐渐提升,且水深较浅处的发展程度提升幅度大于较深处;对于表面闭合入水空泡,随着两圆柱体轴线间距增大,内测区域空泡逐渐趋于饱满,云化现象也逐渐减弱。     

高雷诺数下错列双圆柱气动干扰的机理研究

为了进一步澄清小间距错列双圆柱的气动干扰机理,该文采用大涡模拟方法,在高雷诺数下（Re=1.4×105）,研究了间距为2倍圆柱直径的错列双圆柱的气动性能和流场特性随风攻角的变化规律,分析了两个圆柱气动力系数相关性,探讨了下游圆柱气动力与流场结构的内在联系,对下游圆柱平均升力的流场机理提出了新的解释。研究表明,大涡模拟得到的结果与风洞试验值吻合良好;下游圆柱的气动性能、流场结构和两个圆柱气动力相关性均会随风攻角发生剧烈变化;风攻角在0°~10°时,下游圆柱受平均负阻力作用,其原因分别为两圆柱间的回流区和间隙流;风攻角在10°附近时,下游圆柱受很大平均升力作用,风压停滞点偏移、两圆柱间高速间隙流、下游圆柱间隙侧剪切层的提前分离和再附是平均升力出现的三个因素。     

Holographic scattering in SiO2 nanoparticle-dispersed photopolymer films

We describe an experimental study of holographic (coherent) scattering due to parasitic noise gratings recorded in SiO2 nanoparticle-dispersed photopolymer films. Dependences of film thickness and nanoparticle concentration on holographic scattering losses are evaluated. It is shown that the geometric feature of the holographic scattering pattern in the two-beam recording setup can be explained by the Ewald sphere construction. It is found that holographic scattering becomes noticeable when a film with nanoparticle concentrations higher than 10 vol.% is thicker than 100 microm. The significance of holographic scattering in the characterization of a volume grating recorded in a thick (>100 microm) nanoparticle-dispersed photopolymer film is also discussed.