The effect of variable properties on the helical flow and heat transfer of power law fluids

Summary Laminar flow and forced convection heat transfer of the time independent non–Newtonian fluid obeying power law stress-strain relation have been investigated numerically in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder rotates about the common axis with constant angular velocity and the outer cylinder is at rest. The viscosity of the fluid and thermal conductivity are assumed to vary with the temperature. The outer surface of the annulus is considered to be adiabatic, while the inner surface has a uniform temperature. The tangential and axial momentum equations and energy equation have been solved iteratively by using a finite difference method. For the steady fully developed flow, the velocity distributions, temperature profiles, the volumetric flow rate, torque and the average Nusselt number have been obtained for different values of the radius ratio and model parameters.     

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.     

On some helical flows of Oldroyd-B fluids

Summary In this study the velocity fields and the associated tangential stresses corresponding to some helical flows of Oldroyd-B fluids between two infinite coaxial circular cylinders and within an infinite circular cylinder are determined in forms of series in terms of Bessel functions. At time t = 0 the fluid is at rest and the motion is produced by the combined action of rotating and sliding cylinders. The solutions that have been obtained satisfy the governing differential equations and all imposed initial and boundary conditions. For λ _r = 0, λ = 0 or λ _r = λ = 0 they reduce to the similar solutions for a Maxwell, second grade or Newtonian fluid, respectively. Finally, for comparison, the velocity profiles corresponding to the four models are plotted for different values of t.     

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.     

Analysis of shear bands in a dynamically loaded viscoplastic cylinder containing two rigid inclusions

Summary We study plane strain thermomechanical deformations of a hollow circular cylinder containing two rigid non-heat-conducting ellipsoidal inclusions placed on a radial line symmetrically with respect to the center. These inclusions can be viewed as precipitates or second phase particles in an alloy. The material of the cylinder is presumed to exhibit thermal softening, but strain and strain-rate hardening. The impact load applied on the inner surface of the cylinder is modeled by prescribing a radial velocity and zero tangential tractions at material particles situated on the inner surface. Rigid body motion of the inclusion is considered and no slip condition between the inclusion and the cylinder material is imposed.It is found that shear bands initiate from points adjacent to inclusion tips near the inner surface of the cylinder and propagate toward this surface. At inclusion tips near the outer surface of the cylinder, the maximum principal logarithmic strain and the temperature are high and the effective stress is low, but severe deformations there do not propagate outward.     

Asymptotic analysis of the viscous micro/nano pump at low Reynolds number

The steady viscous parabolic flow past an eccentrically placed rotating cylinder is studied in the asymptotic limit of small Reynolds number. It is assumed that the flow around the rotating cylinder undergoes boundary slip described by the Navier boundary condition. This involves a single parameter to account for the slip, referred to as the slip length ?, and replaces the standard no-slip boundary condition at solid boundaries. The streamlines for ? > 0 are closer to the body than for ? = 0, and it is discovered that the loss of symmetry due to the rotation of the cylinder is significantly reduced by the inclusion of slip. This arises as a result of a balance between the rotation velocity and the slip velocity on that portion of the cylinder which rotates opposite to the free-stream flow. Streamline patterns for nonzero eccentricity partially agree with Navier–Stokes simulations of the viscous pump; the small discrepancy is primarily due to the fact that here wall effects are not explicitly considered. Expressions for the frictional drag and the torque on the cylinder are obtained. The expression for the torque agrees well with the lubrication solution for the flow past a rotating cylinder placed symmetrically in a fully developed channel flow. The results presented here may be used to validate numerical schemes developed to study the viscous pump.     

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.

     

On the steady flow produced in fluid-particle suspension by an infinite rotating disk with surface suction

The steady flow of a fluid-particle suspension over an infinite rotating disk with uniform suction is considered. The equations of motion are reduced to ordinary differential equations by similarity transformations and solved numerically by using a least-squares finite-element method. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically for the suction parameter A = 3.0 in order to illustrate some interesting features of the solutions. It is observed that the radial velocity of the particle attains its maximum on the surface of the disk and the particles slip in the tangential direction on the disk. The magnitudes of the radial velocity components of both the fluid and particle phases are found to decrease rapidly as suction increases.     

Experimental study of density segregation at end walls in a horizontal rotating cylinder saturated with fluid: friction to lubrication transition

What is the effect of interstitial fluid viscosity on granular density segregation in a horizontal rotating cylinder? We conducted experiments in the rolling regime with equal amounts of equal sized high and low density, nearly spherical granular particles saturated with air, water, and water-glycerin mixtures. We held particle density, rotation rate and characteristic length scale constant to highlight differences due purely to the interstitial fluid. Images of the granular flow at an end wall were used to determine radial and axial density segregation rates and patterns. Over a four decade change in viscosity, segregation rates varied by only a factor of two. However, for ratios of lubrication to frictional stresses above one, segregation rates decreased by about 30%, and we observed several notable phenomena in the segregation pattern formation. These were a creeping mode of radial density segregation, a change in shape of the granular bed to kidney shaped from flat, and for cylinders more than half full the typically reported unsheared central portion of the granular bed (often referred to in the literature as a core region) was disrupted by a wavy instability where the rate of disappearance of the core region decreased as the fill level increased.     

Optimum design method for double-layer thick-walled concrete cylinder with different modulus

The stress state of thick-walled cylinder will be improved when it is composed of multi-layer concrete with different Young’s modulus of elasticity. The optimum design method for double-layer concrete cylinders is discussed in this paper. When the modulus of the inner-layer concrete is less than the outer one, the stress concentration on the cylinder inner surface will be relieved and the maximum tangential stress may be transferred from the inner surface of inner-layer to the inner surface of outer-layer, where is in triaxial stress state. The elastic limit bearing capacity of double-layer concrete cylinder will be improved due to the high compressive strength of concrete in triaxial stress state. Compared with the conditional single-layer thick-walled cylinder, the thickness of the double-layer cylinder can be reduced evidently. On the basis of stress solution of double-layer cylinder and by using the mixed penalty function method, the minimum wall thickness required, the best thickness ratio and the modulus ratio of inner layer to outer layer are calculated for cases in which the external load and uniaxial compressive strength are known already. If the thickness and uniaxial compressive strength is given, the best thickness ratio and modulus ratio of inner layer to outer layer can also be proposed by using the mixed penalty function method.     

Isothermal slip flow over curved surfaces

It has long been recognised that the no-slip-boundary condition employed in the Navier-Stokes equations can only be applied when the Knudsen number, Kn?10⁻³. If the Knudsen number is increased beyond this value, rarefaction effects start to influence the flow and the molecular collision frequency per unit area becomes too small to maintain the no-slip-boundary condition. Unfortunately, Maxwell's famous slip equation describing the velocity discontinuity at the wall is often misapplied when analysing flows over curved or rotating boundaries. In the present study, a generalised version of Maxwell's slip equation is used to investigate low Knudsen number isothermal flow over walls with substantial curvature. The generalised slip equation is written in terms of the tangential shear stress to overcome the limitations of the conventional slip-boundary treatment. The study considers a number of fundamental, but challenging, rarefied flow problems and demonstrates that Maxwell's conventional slip equation is unable to capture important flow phenomena over curved or rotating surfaces.     

基于模型试验和数值模拟的柔性串列圆柱体涡激振动研究

采用物理模型试验和CFD数值模拟方法研究了大长径比、低质量比的柔性串列圆柱体涡激振动现象。通过分析串列圆柱振幅、振动频率、受力特性和流场结构等特性,着重研究流速和圆柱间距对下游圆柱涡激振动特性影响。研究发现,上、下游圆柱涡激振动幅值差别较大,并且当流速大于某个值后,两者主导频率也不相同,由此提出分离约化速度U r。流速和间距都会影响上游尾流对下游圆柱的作用,其中流速会影响上游尾涡强度及其发展程度,间距会影响上游尾涡发展空间及其与下游圆柱的接触位置。     

Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.     

Thermophoretic deposition of aerosol particles in laminar mixed-convection flow in a channel with two heated built-in square cylinders

The thermophoretic deposition of aerosol particles in laminar mixed-convection flow in a channel with two heated built-in square cylinders was studied numerically. The objective of this research was to study the effect of free convection and the distance between cylinders, on deposition of particles. Continuity, momentum and energy equations were solved to determine the velocity and temperature profiles in the channel. The particle trajectories were evaluated by solving the Lagrangian equation of motion that included the drag, Brownian diffusion and thermophoresis forces. It was found that the temperature gradient near the channel wall, in mixed flow regime, is higher than the temperature gradient in forced convection regime. Increasing the temperature gradient increased the effect of thermophoresis on deposition of particles. It was observed that the deposition was increased with the Richardson number. The distance between cylinders is a parameter that influences the deposition of particles. Temperature gradient decreases with increasing the cylinders’ distance; on the other hand, the length of the high temperature gradient zone, which is located in the region between the cylinders where the most deposition occurs, will be increased. These two opposite phenomena cause the fact that at a distance which is four times longer than the cylinders’ length, a maximum cumulative deposition fraction occurs. It was eventually concluded that the thermophoresis and the inertial impaction are dominant deposition mechanisms of particles on the channel wall.     

Studying the Dependence of the Aerodynamic Characteristics of Rotating Cylinders on the Rake Angle of Air Flow

The results of experimental studies on estimating the lift force and lift coefficient of a rotating cylinder of constant cross section are presented. The data on the effect of the flow rake angle on the aerodynamic characteristics of rotating cylinders within a range of angles from 0° to 90° are analyzed. It has been established that a decrease in the lift coefficient is observed at flow rake angles above 30°, so the wind engine element shows a positive result within a range of rake angles from–30 ° ≤ α ≤ 30°. The data of these experimental studies can be used for the development of wind engines with blades designed as rotating cylinders with a smooth surface.     

Analytical study of energy-force parameters in the upsetting-torsion of cylindrical semifinished products made of a highly ductile material

The upper-bound method is used to solve a problem concerning the upsetting of a solid circular cylinder made of a linear strain-hardening material. The cylinder is upset with the use of flat rotating dies. Total power consumed in the operation is minimized on the basis of a parameter that characterizes slip between the dies and the ends of the semifinished product. Analytic expressions are obtained to determine the upsetting force and turning moment. It is found that a decrease in the upsetting force increases the friction coefficient on the contact surfaces, the rotational velocity of the dies, and strain in the height direction.Translated from Problemy Prochnosti, No. 6, pp. 68–71, June, 1994.     

Stable crack growth in a surface compression-strengthened hollow cylinder

In this paper the static fatigue problem for a circumferentially cracked hollow cylinder is examined. For this particular configuration, stable crack growth, in the absense of any external forces, is determined for cylinders with axial components of residual stress which are compressive on the inner and outer radial surfaces and tensile in the cylinder wall. An initial surface crack which is deep enough to penetrate the compression strengthened surface region and enters the tensile zone may propagate in a stable manner until either sudden spontaneous failure occurs or the crack arrests. Since a portion of the crack near the cylinder surface will be closed because of the compressive residual stress field, an additional unknown in the problem is the extent of the crack surface contact. This crack surface contact length is determined by iteration on the integral equation which arises in the mathematical derivation for an embedded circumferential crack in a hollow cylinder. As an illustration of stable crack growth for this geometry with a realistic residual stress distribution, numerical results are presented for a hollow, soda-lime glass cylinder, based on crack growth rates in soda-lime glass exposed to water at 25‡ C. Using the fracture toughness and slow crack growth characteristics for soda-lime glass, the conditions for no crack propagation, crack propagation leading to crack arrest, and catastrophic failure are established.     

Numerical and experimental study of a spherical particle flow in a cylindrical tube under vacuum conditions

The paper aims at developing a validated model that can accurately predict the flow of a particulate material. This model will serve as a virtual design tool for the design of a novel passive safety system for nuclear reactors. Therefore an experimental setup consisting of a vertical glass tube is filled with 500±30 μm spherical glass particles. The experiment is then placed in a vacuum and the particles are released by opening a valve. The velocity of the particles is recorded during their fall at three different heights using a non invasive optical tracking technique with an original implementation. The same experiment is then simulated using the Discrete Element Method and results are compared. A good agreement between the simulation and the experiment was found. The sensitivity of the simulation to a change in the contact stiffness, dynamic Coulomb coefficient of friction and tangential contact force model was investigated. The influence of the initial position of the simulated particles on the packing factor was shown to be very important. Finally the experiment proved to be extremely sensitive to a perturbation of the outflow section of the tube, something that was predicted by the simulations.