径向反应器流体均布设计的研究

本文探讨了径向反应器流体均布设施的合理设计。流体在主流道的动量可以用修正动量方程来描述 dp+2k(γ/g)wdw+(λ γw_2/D_e 2g)dx=0 这里P、γ/g、w、λ、D_e和x分别指流体静压、流体密度、主流道流速、管摩擦系数、主流道当量直径、主流道长度。动量交换系数k已经被测得。分流流道动量交换系数在0.65—0.72之间。集流流道k值稍大于1。分析了主流道的静压分布。在分流流道中,按照摩阻项和动量交换项的相对大小提出了四个流动模型。 条件 模型 λL/（6D_ek）1 动量交换控制 λL/（6D_ek）1 摩阻控制 λL/（4D_ek）<1 动量交换占优势 λL/（4D_ek）>1 摩阻占优势在分流流道中。由于动量交换项和摩阻项对静压有相反的影响,所以静压变化趋势依赖于各种模型。但是,在集流流道中,它们的影响是一致的,而总是使静压趋于下降。为了降低径向反应器中分、合流流道间静压变化的差异,当分流流道受动量交换所控制或动量交换占优势时,采用“Ⅱ”型分布是合理的。相反,如果分流流道受摩阻控制或摩阻占优势时,则“Z”型分布将是合适的。根据各种流动模型,推荐了分流流道与集流流道合适的截面比。分别测定了分、合流测     

Numerical flow simulation of viscoplastic fluids in annuli

This paper describes numerical solutions for the laminar flow of non-Newtonian fluids in vertical annuli using the Herschel-Bulkley model to describe the rheological behaviour of such materials. Numerical solutions have been obtained when there is both axial and tangential flows in either a concentric or eccentric annulus. The tangential flow arises from the rotation of the inner cylinder of the annulus and the axial flow from a constant axial pressure gradient. The flow is analysed by solving the momentum and continuity equation numerically using the finite element method. The dimensionless velocity, deformation and stress profiles with other quantities such as the apparent viscosity and pressure distribution have been calculated for various eccentricities, radius ratios, fluid properties and flow parameters; the results give insights into the flow behaviour in the annuli. It is shown that the inclusion of rotational effects, for a fixed pressure gradient, is likely to increase the axial volumetric flowrate over non-rotating situations in concentric geometries. New results reveal that, in eccentric annuli, the situation is reversed and the flowrate gradually decreases as the rotation rate is increased.     

Finite element modeling of ultra fine particle filtration by a membrane filter

Theoretical work has been carried out to investigate the filtration of ultra fine aerosol particles in a membrane filter. The analysis was done using a finite element method with a Newtonian fluid model for the carrier medium. Both inertial filtration and diffusional filtration were considered. Prior to the main analysis, our numerical scheme was tested with the analytical results for the diffusion of particles in the cylinder and showed good agreement, which confirms the importance of axial diffusion occurring in a short cylinder like a very thin membrane filter. Particle size, porosity, pressure drop, and flow velocity are found to be main variables that determine the filter efficiency. Two important mechanisms of filtration have opposite effects on the efficiency, depending on the variables. Increases in particle size, pressure drop, and flow velocity cause increases in the efficiency for intertial deposition, while decreases in those variables cause increases in the diffusional efficiency. The existence of a minimum value of total filtration efficiency (sum of inertial efficiency and diffusional efficiency) was indicated for intermediate values of the variables. Lower porosity is found to favor inertial deposition more than diffusion. Some other effects of filtration conditions on the total efficiency are also discussed.     

Unsteady flow of a micro-polar fluid between two concentric circular cylinders

This paper examines the flow of a micropolar fluid between concentric cylinders in the case where the outer cylinder is held fixed while the inner cylinder is subjected to an arbitrary time dependent angular velocity. Here integral transforms are effectively used to obtain closed form solutions. The special case of a periodic angular velocity is then considered. The results obtained are compared as far as possible with their classical counterparts and some of the physical quantities have been represented graphically. It has been found that, in comparison to classical fluids, an increased couple is experienced by the inner cylinder.     

周向多入口凹壁面切向射流流动特性分析

为了探究三维凹壁面切向射流周向入口数量对流场的影响,选取Realizable k-ε模型,并使用非平衡壁面函数处理近壁面湍流流动,数值模拟了周向多入口流场的流动特性。流场研究表明,随着入口数量增加,前入口对后入口流动参数的叠加先增强后降低,在入口后周向角度30°～40°,射流区域叠加最强,射流外侧靠近入口处的影响最大。多股射流流场叠加使立式圆筒体内部的流动更加均匀,涡旋结构稳定在轴线附近。周向多入口凹壁面射流相较于单入口在切向速度、湍流动能、静压力最大值等参数上均产生叠加作用,其中三入口与单入口更接近,叠加作用最小。对总流量相同的不同入口结构设备内旋流流动研究表明,离心分离因数、湍流动能和静压力与入口速度相关性较大,叠加特性对旋流流动的增强作用不明显。可通过提高多入口射流速度提高离心分离因数及物料的处理量。     

PERISTALTIC MOTION OF AN OLDROYD-B FLUID WITH INDUCED MAGNETIC FIELD

The problem of peristaltic flow in a channel is solved using the incompressible and magnetohydrodynamic (MHD) Oldroyd-B fluid. The induced magnetic field effects are incorporated in the mathematical modeling. Computations are performed for the small wave number. The obtained mathematical results show that the induced magnetic field effects taken into account in the model substantially affect the flow quantities. It is found that relaxation and retardation times have opposite effects on the flow quantities such as velocity and pressure rise. Moreover, it is observed that induced magnetic field and current density are larger for Oldroyd-B fluid than for the viscous fluid. The salient features of the emerging flow parameters are examined by graphs.     

Modeling of the pressure drop and flow field in a rotating fluidized bed

Rotating fluidized beds (RFB) have found applications as dust filters, dryers, particle coaters, and granulators, and recently as catalytic reactors for the clean up of diesel exhaust. However, successful design and operation of an RFB requires an in-depth understanding of the fundamentals of the fluid dynamics involved. In this study, mechanistic models have been developed to account for the pressure drop relationship with respect to rotating speed, flow rate, properties of the granular particles, and fluidization conditions in the RFB. The models show that the total pressure drop across the bed is quadratically dependent on the rotating speed as well as the flow rate. These quadratic relationships have also been validated experimentally. The pressure drop relationship has further been validated through a full flow field numerical simulation of flow through a rotating bed with a slotted cylindrical distributor but without granular particles in the bed. Using our analytical model together with experimental results from three different types of distributors, a slotted cylinder with a thin metal screen, a perforated cylinder with a thin metal screen, and a sintered metal cylinder, three semi-empirical quadratic equations are obtained to predict the pressure drop across these distributors. A comparison of the distributor pressure drop with that across the fluidized bed (granules only) shows that the pressure drop across the distributor is appreciable and cannot be neglected in RFB applications. The higher the rotating speed, the more significant the pressure drop across the distributor.     

MODELING OF THE PRESSURE DROP AND FLOW FIELD IN A ROTATING FLUIDIZED BED

Rotating fluidized beds (RFB) have found applications as dust filters, dryers, particle coaters, and granulators, and recently as catalytic reactors for the clean up of diesel exhaust. However, successful design and operation of an RFB requires an in-depth understanding of the fundamentals of the fluid dynamics involved. In this study, mechanistic models have been developed to account for the pressure drop relationship with respect to rotating speed, flow rate, properties of the granular particles, and fluidization conditions in the RFB. The models show that the total pressure drop across the bed is quadratically dependent on the rotating speed as well as the flow rate. These quadratic relationships have also been validated experimentally. The pressure drop relationship has further been validated through a full flow field numerical simulation of flow through a rotating bed with a slotted cylindrical distributor but without granular particles in the bed. Using our analytical model together with experimental results from three different types of distributors, a slotted cylinder with a thin metal screen, a perforated cylinder with a thin metal screen, and a sintered metal cylinder, three semi-empirical quadratic equations are obtained to predict the pressure drop across these distributors. A comparison of the distributor pressure drop with that across the fluidized bed (granules only) shows that the pressure drop across the distributor is appreciable and cannot be neglected in RFB applications. The higher the rotating speed, the more significant the pressure drop across the distributor.     

Rotary cylinders: Solid transport prediction by dimensional and rheological analysis

A semi-experimental model for predicting the axial transport of the granular bed in a rotating cylinder is proposed. It is based on dimensional analysis and on the determination of an apparent viscosity characterizing the flow behaviour of the bed. Unknown constants in the model are determined either by analysis or by tuning with experimental data. An example of such tuning is shown to work well. The model is capable of giving, as a function of filling angle and friction angle, the axial velocity that varies along the cylinder axis. This is important for the control of the process taking place inside the cylinder.     

关于非牛顿流体的轴向Couette流动的研究

对于一些二阶流动和麦克斯韦流体,由于圆柱沿着对称轴不断加速而产生的速度场的变化,在一些适应的边值问题的特征函数条件下,可以描述为Fourier-Bessel级数的形式。这样的处理方式可以满足包括偏微分方程和所有外加的初始和边界条件。对于α或者λ→0,他们都将趋向于牛顿流体的情形。本文最后,对应这种通过圆柱的流动的解,几张图给出了对于不同的值和材料常数时的情形。     

Effect of a Magnetic Field on a Micropolar Fluid Flow in the Vicinity of an Axisymmetric Stagnation Point on a Circular Cylinder

The effect of a magnetic field on a micropolar fluid flow in the vicinity of an axisymmetric stagnation point on a circular cylinder is studied numerically. The governing conservation equations of continuity, momentum and angular momentum are partial differential equations which are transformed into a system of ordinary differential equations by using the usual similarity transformations. The resulting system of coupled non‐linear ordinary differential equations is solved numerically by using the shooting method. The numerical results indicate the velocity, angular velocity and pressure distributions for different parameters of the problem including Reynolds number, magnetic parameter and dimensionless material properties, etc. In addition, the effect of the pertinent parameters on the local skin friction coefficient and the couple stress are discussed numerically and illustrated graphically.     

Non-newtonian flow through open channels

A general method is proposed for prediction of the flow rate and maximum velocity in the isothermal, steady, uniform, laminar flow of any incompressible, time-independent non-Newtonian fluid in straight open channels of arbitrary cross section. The method requires only a knowledge of two geometric coefficients and a function of shear stress, used to characterize the behavior of the fluid model. The slip effect at the solid boundary has been taken into consideration. Numerical values of the geometric parameters have been determined for flow through an inclined plane of infinite width, semi-circular, semi-elliptical, rectangular, and 90° and 60° symmetric triangular open channels. Applications have been made to various non-Newtonian fluid models such as the power-law, Bingham, Ellis, Meter and the Reiner-Rivlin general model. Numerical examples are presented. A generalization of the Fanning friction factor — Reynolds number is also presented. The problem of determining the point of transition from laminar to turbulent flow in the general case is examined, as is the problem of prediction of the friction factor in turbulent flow.     

离心萃取器转筒入口半径对筒内流场的影响

目前,对离心萃取器的研究多采用计算流体力学方法,为定性研究;对其转筒区域的流场研究,特别是入口半径对分离效果的影响少有报道.为了解决一问题,本文采用了PIV技术对离心萃取器转筒内部流场进行测试,使用自制转筒,分别在转筒入口半径为7mm、10mm和13mm时,观察筒内距离转筒入口11mm处截面上的流场变化规律.研究发现:以地面为参考系时,流体的转速随着转筒半径的增大而增大,而以转筒为参考系时,在每个分离腔内都能形成涡流;当入口半径为10mm时,截面内切向速度绝对值比入口半径为7mm和13mm的要大,液体更容易流向转筒边壁,分离效果更好,同时其径向速度相对于转筒为正值时,基本处于最大值,说明液体进入转筒入口后能快速被甩至边壁处,更加有利于分离.     

Boundary effects on thermophoresis of aerosol cylinders

An analytical study is presented for the thermophoretic motion of a circular cylindrical particle in a gaseous medium with a transversely imposed temperature gradient near a large plane wall parallel to its axis in the quasisteady limit of negligible Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The presence of the confining wall causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhance the viscous retardation of the moving particle. Through the use of cylindrical bipolar coordinates, the transport equations governing this problem are solved and the wall effects on the thermophoresis of the aerosol cylinder are computed for various cases. The presence of the plane wall can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distance, and the direction of the applied temperature gradient. The direction of the thermophoretic motion of a cylindrical particle near a plane wall is different from that of the prescribed thermal gradient, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the thermophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.     

Heat and mass transfer in non-newtonian fluid flow with power function velocity profiles

Heat and mass transfer in laminar and turbulent non-Newtonian fluids is investigated in this work using the power function velocity profiles. Analytical solutions are presented for cases of mass transfer in laminar non-Newtonian fluid flows, namely for a flat velocity profile (plug flow), for the case of a constant velocity gradient at the solid boundary (Couette flow), and for the velocity distribution within a laminar boundary layer on a flat plate, and these are illustrated by rotating disks and cylinders in laminar Ostwald-de Waele fluids. Further, turbulent mass transfer processes (tubular flow, rotating disk, and rotating cylinder) in non-Newtonian fluids (Ostwald-de Waele fluid and drag-reducing fluid) at low and large Schmidt numbers are also discussed using the solutions of mass transfer in flows with power function velocity profiles. Reasonable agreement is found between the predictions of this work and the available experimental data and correlations.     

Numerical Simulation of the Lock-In Effect of a Fixed-Fixed Tube in Cross Flow

This paper deals with the development of a numerical calculation code that is able to simulate the three-dimensional flow through a heat exchanger tube bundle and therefore allows a coupled calculation of fluid-structure interaction between the flow and the tube bundle. The incompressible flow field is calculated by a Navier-Stokes solver using a first-order power law scheme, a SIMPLEC algorithm to calculate the pressure and velocity correction fields, and a line-by-line Gauss-Seidl tridiagonal algorithm to solve the linearised system of equations. The transient parts of the Navier-Stokes equations are discretised by a second-order forward finite differencing scheme. The turbulence is examined with the aid of a large-eddy turbulence model. The transient fluid forces acting on the tubes are calculated by integration of all local flow pressure values on the surfaces of the tubes. As an example a single fixed-fixed cylinder in a flow channel is considered using the structural calculation part already developed as well as the new flow field and flow forces subroutines. The time series of the tube's motion and the fluid forces acting on the tube are analysed by Fourier's transformation. The lock-in effect occurring when the vortex shedding frequency approaches the first natural frequency of the tube can be excellently demonstrated by varying the inflow velocity over a wide range of Reynolds numbers.     

MODELLING GAS-SOLID FLOW IN A PNEUMATIC-FLASH DRYER

Investigations of aerodynamics of gas-solid flow in a pneumatic-flash dryer in semiindustrial scale have been carried out. Apparatus was composed of three elements with varying cross-sectional area connected together, i.e. expanding cone, decreasing cone and a vertical pipe with constant diameter. A mathematical model of the dryer is based on the continuity equations for both gas and solid phase and on differential equations for momentum balance of the gas-solid mixture and momentum balance of the solid phase. The model has been solved by means of Gear's numerical method. The effect of various empirical correlations for the solid-wall friction factor has been shown. Distributions, resulting from the model, for pressure, gas velocity, panicle velocity, voidage and residence time of panicle along the axis of apparatus have been presented. The results of numerical calculations have been verified on the basis of measurements in pan.     

Longitudinal mixing of granular material flowing through a rotating cylinder Part II. Experimental

Experiments on axial dispersion for continuous flow of, e.g. long grain rice through a laboratory-scale rotating cylinder are reported. The model of piston flow with superimposed longitudinal diffusivity proved to be valid. Axial dispersion coefficients were determined under varying conditions of loading, speed of rotation and number of rotations, linear flow velocity, inclination, types of particle movement, shapes of cylinder entrance and exit end faces. Furthermore, the effect of some variations in the properties of the solid particles has been studied e.g. particle shape, particle size distribution and particle cohesion. Some experiments with a cylinder of larger diameter are reported.

Longitudinal dispersion coefficients could be rather low, e.g. down to 0·04 cm²/sec, much lower than most other types of fluid flow processes and reactors.     

Drag on two coaxial rigid spheres moving along the axis of a cylinder filled with Carreau fluid

The boundary effect on the drag on two identical, rigid spheres moving along the axis of a long cylinder filled with a Carreau fluid for Reynolds number ranges from 0.1 to 40 is investigated. The influences of the key parameters of the problem under consideration, including the separation distance between two spheres, the relaxation time constant and the power-law index of a Carreau fluid, the Reynolds number, and the ratios (radius of sphere/radius of cylinder), on the drag acting on two spheres are investigated. We show that the boundary effect for the present case is more significant than that for the corresponding Newtonian fluid. The presence of the cylinder has the effect of enhancing the convective motion in the rear part of a sphere, thereby forming wakes and a reverse flow field, and this phenomenon is enhanced by the shear-thinning nature of a fluid. If the boundary effect is insignificant, the shear-thinning nature of a fluid has the effect of reducing the deviation of the ln(drag coefficient)-ln(Reynolds number) curve from a Stokes'-law-like relation. On the other hand, if it is significant, this deviation has a local minimum as the shear-thinning nature of a fluid varies.