Mass transfer between the attached wake of a bluff body and the free stream

The rate of fluid exchange between the attached recirculating wake and the free stream has been measured for spheres and circular discs set normal to the flow. The body Reynolds number was varied from 50 to 200. The results are presented in terms of mass transfer coefficient, the height of a transfer unit and the dimensionless mean residence time. The last of these parameters appears to correlate wake shedding phenomena over a very wide range of Reynolds number. A simple model is proposed for the prediction of mass transfer coefficient from wake geometry data.     

Particle deposition in the wake of charged spheres

Earlier work in this laboratory, wherein aerosols were collected from gas streams moving around charged water droplets, indicated the likelihood of high rates of deposition on the aft side of the droplet where flow conditions are not adequately represented by potential flow theory. Further tests were made with metal spheres and the aerosol deposition pattern observed with scanning electron microscopy. Results from these test confirm that the developed wake has a definite influence on the collection pattern as well as the overall collection efficiency. Generally, minima were observed aft of the separation point at an angle at which the vortices flow tangentially to the sphere. Maxima appeared forward of the separation and advanced toward the forward stagnation point as the Reynolds number increased and overall collection efficiency declined. At higher levels of field intensity the deposition profile appeared flat as one scanned around the sphere, with a peak at the rear stagnation point. Very little information is available concerning deposition in the wake of moving droplets. This seems particularly important for scrubbers and spray towers where particles are collected by droplets moving at high Reynolds numbers where wakes and eddies are quite common.     

Effect of blockage on drag and heat transfer from a single sphere and an in-line array of three spheres

The effect of blockage ratio on the steady flow and heat transfer characteristics of incompressible fluid over a sphere and an in-line array of three spheres placed at the axis of a tube has been investigated numerically. The Navier-Stokes and thermal energy equations have been solved numerically using FLUENT for the following ranges of parameters: for a single sphere, 2 ≤ β ≤ 10; 1 ≤ Re ≤ 100; for the three-sphere system, for two values of sphere-to-sphere distance, namely s = 2 and 4. All computations were carried out for two values of the Prandtl number, i.e., 0.74 and 7, corresponding to the flow of air and water respectively. Extensive results on streamline patterns, wake characteristics (angle of separation and recirculation length), drag coefficient and Nusselt number are presented to elucidate the interplay between the blockage and the Reynolds number and their influence on drag and Nusselt number.     

Wall effects in flow past a circular cylinder in a plane channel: a numerical study

This paper describes a numerical study on the steady flow of an incompressible Newtonian fluid past a circular cylinder confined in a plane rectangular channel. Using FLUENT (version 6), two-dimensional steady state computations were carried out for an uniform inlet velocity and for different values of the Reynolds numbers in the range between 0.1 and 200 and blockage ratios (ratio of the channel width to the cylinder diameter) in the range between 1.54 and 20. The flow parameters such as drag coefficient, length of the recirculation zone, and the angle of separation are presented as functions of the Reynolds number and blockage ratio. The total drag coefficient (C_D) was found to decrease with an increase in the blockage ratio (λ) for a fixed value of the Reynolds number (Re) and to decrease with increasing Reynolds number for a fixed value of λ. Similarly, for a fixed value of λ, both the angle of separation and the length of the recirculation zone increase with the increasing Reynolds number.     

圆盘摩擦损失降阻新方法的实验研究

采用在封闭空腔间隙流场内插入一自由旋转圆盘的方法降低圆盘摩擦损失。在圆盘旋转雷诺数为２×１０５～９．５×１０５条件下，对空腔轴向间距比Ｓ／Ｄ２为０．０７８３～０．１０８７、插入盘的无量纲轴向位置Ｌ／Ｓ及其半径不同情况分别进行实验研究。结果表明，采用插入盘方法可以降低圆盘摩擦损失；插入盘半径减小使圆盘摩擦损失增大；随着轴向间距、圆盘旋转雷诺数增大，降阻效果增强；插入盘位于不同轴向位置对降阻效果有不同影响。最后，对减阻的机理进行初步分析。     

Wake characteristics of three-phase fluidized beds

Wake volumes in three-phase fluidized beds hae been computed from phase holdup and bubble rising velocity data over a wide range of experimental conditions. The ratio of the wake to gas holdup k? increased with liquid velocity and decreased with gas velocity and surface tension. A correlation relating k? to these variables was derived. Both a stable wake and vortex shedding appeared to contribute to the measured wake volume.     

MOTION OF AND MASS TRANSFER FROM AN ASSEMBLAGE OF SOLID SPHERES MOVING IN A NON-NEWTONIAN FLUID AT HIGH REYNOLDS NUMBERS

An approximate solution for the motion of an assemblage of solid spheres moving in a power-law fluid in the high Reynolds number region is obtained using a combination of Happel's free-surface cell model and the boundary layer theory. It is theoretically predicted that the drag coefficient will decrease with the increase of the shear-thinning anomaly. The results of the present analysis are in reasonably good agreement with the available experimental data for fixed and fluidized beds. The influence of the non-Newtonian behavior on the mass transfer rate from an assemblage of solid spheres is also discussed.     

Thermal expansion behavior of composites based on axisymmetric ellipsoidal particles

A new model for calculating the coefficients of thermal expansion, CTE, in all three coordinate directions is developed for composites containing aligned, axisymmetric elliptical particles, i.e., characterized by a single aspect ratio, that in the limit approximate the shapes of spheres, fibers and discs. This model is based on Elshelby's method but employs a somewhat different formulation than used in prior papers; a main advantage of the current approach is that it can be readily extended to composites based on ellipsoidal particles with no axes of symmetry, i.e., all three major axes are different, as recently demonstrated for modulus. CTE predictions for the simple case of axisymmetric particles are illustrated by calculations for glass particles in the shape of spheres, fibers and discs in an epoxy resin and are compared to those from the popular Chow theory. For spherical-shaped particles, the CTEs in all directions are the same and decrease modestly as the volume fraction of filler particles increases. As the particle aspect ratio increases from unity, the thermal expansion becomes anisotropic. The coefficient of longitudinal linear thermal expansion always decreases with increasing aspect ratio and filler loading due to the mechanical constraint of the filler. For aligned axisymmetric particles, the coefficients of linear thermal expansion are always the same in two directions. The values in the transverse direction may be higher or lower than that of the matrix depending on the values of aspect ratio and filler loading; these regions are mapped out for this particular set of matrix and filler properties. The two-dimensional constraints on matrix expansion caused by discs versus the one-dimensional effects of fibers cause quantitative differences in behavior for the two shapes.     

MOTION OF AND MASS TRANSFER FROM AN ASSEMBLAGE OF SOLID SPHERES MOVING IN A NON-NEWTONIAN FLUID AT HIGH REYNOLDS NUMBERS

An approximate solution for the motion of an assemblage of solid spheres moving in a power-law fluid in the high Reynolds number region is obtained using a combination of Happel's free-surface cell model and the boundary layer theory. It is theoretically predicted that the drag coefficient will decrease with the increase of the shear-thinning anomaly. The results of the present analysis are in reasonably good agreement with the available experimental data for fixed and fluidized beds. The influence of the non-Newtonian behavior on the mass transfer rate from an assemblage of solid spheres is also discussed.     

Drag on two co-axial rigid spheres moving normal to a plane: Newtonian and Carreau fluids

The boundary effect and the presence of a nearby entity on the drag of a rigid entity is investigated by considering the movement of two identical, rigid, coaxial spheres normal to a plane in both a Newtonian and a Carreau fluid at a low to medium large Reynolds number. The parameters key to the phenomenon under consideration, including the nature of the fluid, the separation distance between two spheres, the distance between the near sphere and the plane, and the Reynolds number, on the drag coefficient are discussed. We show that the influence of a boundary on the drag coefficient is more important than that of the nature of a fluid and that of the separation distance between two spheres. The variation of the drag coefficient as a function of Reynolds number for a Carreau fluid is similar to that for a Newtonian fluid. Due to the shear-thinning nature of the former the drag coefficient in the former is smaller than that in the latter. The influence of the index parameter of a Carreau fluid becomes appreciable only if the Carreau number is sufficiently large. Correlations between the drag coefficient and the key parameters of a system are developed for the case when the Reynolds number is smaller than l.     

Motion and coalescence of a pair of bubbles rising side by side

Bouncing and coalescence of a pair of slightly deformed bubbles rising side by side in a quiescent liquid are experimentally studied. The trajectories and shapes of the bubbles are investigated in detail by using a high-speed video camera. The wakes of bubbles are visualized by using a photochromic dye that is colored with UV light irradiation. We observe that the patterns of the trajectories of rising bubbles are strongly dependent on the Reynolds number. When the Reynolds number is over the critical region, two bubbles approach each other and then collide. After the collision, two types of motions are observed—coalescence and bouncing. We investigate the critical Reynolds number and Weber number over which the bubbles bounce. In the definitions of these numbers, we use vertical velocity, instead of horizontal one, as the characteristic velocity. We clarify that the critical Weber number is around 2 regardless of the Morton number. The critical Reynolds number decreases with an increase in the Morton number. Moreover, the visualization of the wake of bubbles enables us to observe the vortex separation from the rear surface of the bubbles on collision. We find that the vortex separation from the rear of bouncing bubbles causes a decrease in the rising velocity and an increase in the horizontal speed after their collision. We also observe that the behavior of repeatedly bouncing bubbles is significantly influenced by the wake instability of a single bubble rather than by the bubble-bubble interaction. By applying an existing model for spherical bubble-bubble interaction, we clarify that the revised model accurately describes the trajectory of a pair of slightly deformed bubbles using the restitution coefficient and velocity fluctuation from the experimental results.     

Effect of power-law index on critical parameters for power-law flow across an unconfined circular cylinder

The conditions for the formation of a wake and for the onset of wake instability for the flow of power-law fluids over an unconfined circular cylinder are investigated numerically by solving the continuity and momentum equations using FLUENT (version 6.2). The effect of power-law index on the critical Reynolds numbers, Strouhal number and drag coefficient has been presented over a wide range of power-law index (0.3?n?1.8) thereby establishing the limits of the flow without separation and the steady symmetric flow regimes, respectively. While both the shear-thinning (n<1) and the shear-thickening (n>1) seem to lower the value of the critical Reynolds number denoting the onset of wake instability as compared to that for Newtonian fluids, the effect is seen to be more prominent for shear-thickening fluids than that for shear-thinning fluids. The corresponding values of the critical Strouhal number (St_c) and drag coefficient have also been presented for the critical values of the Reynolds number. Included here are also a series of streamline plots showing the onset of asymmetry and of the time-dependent flow regime.     

Transient three-dimensional heat transfer from rotating spheres with surface blowing

Transient heat transfer and thermal patterns around a rotating spherical particle with surface blowing are studied numerically for Reynolds numbers in the range 10?Re?300 and non-dimensional angular velocities up to Ω=1. This range of Reynolds number includes three distinct wake regimes: steady and axisymmetrical, steady but non-symmetrical, and unsteady with vortex shedding. The Navier-Stokes and energy equations for an incompressible viscous flow are solved numerically by a finite-volume method in a three-dimensional and time-accurate manner. The transient aspects of the thermal wakes associated with the aforementioned wake regimes have been explored. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that an unsteady three-dimensional flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects, and thus, the temperature distributions around the particle are significantly affected. Despite the fact that particle rotation brings about major changes locally, the surface-averaged heat transfer rates are not influenced appreciably even at high rotational speeds; consequently, it is shown that the total heat transfer rates associated with rotating spheres with surface blowing can be calculated from heat transfer correlations developed for flow over evaporating droplets.     

HIGH TEMPERATURE INCIPIENT FLUIDIZATION IN MONO AND POLYDISPERSE SYSTEMS

Tests have been made on the behaviour of fluidized beds at high temperature (15-950^°C). Bed materials used were silica sand of different sizes.

Bed voidage at minimum fluidization conditions was found to be dependent on temperature rise and on increase in Reynolds number. Plots of bed voidage function, bed voidage and Ar versus Re_mf show a change in the behaviour at Reynolds numbers between approximately 0.75-2. This is explained in terms of a variation in the fluid flow pattern inside the bed: at very low Re_mf creeping flow exists, but at higher values of Reynolds number, separation of boundary layer takes place and a wake appears at the rear of the particle, creating a low pressure zone. This contributes to attractive forces between particles at the minimum fluidization conditions, decreasing the value of ε_mf. If Re_mf increases, the separation point moves towards the rear of the particle and the wake shrinks; attractive forces decrease, and ε_mf increases.

Data on u_mf, both for monodisperse systems and binary mixtures, are compared with predictions from different equations.     

HYDRODYNAMIC INTERACTION OF TWO SPHERICAL BUBBLES RISING IN-LINE: A SEMI-ANALYTICAL APPROACH

A model is proposed to relate the flow structure in the wake behind a leading bubble with the hydrodynamic force acting on the trailing bubble rising in-line. The model is valid at separation distances between bubbles (s) within the same order of magnitude as their diameters (d_B) (2.5 ≤ s/d_B ≤ 14.5) and moderate-to-large particle Reynolds numbers (50 ≤ Re₁ ≤ 300). An equation for the axial velocity profile in the wake of a spherical bubble was proposed in the form of an analytical approximation, but incorporating a theoretically reasoned artificial origin, which was fitted to numerical data. This equation, once substituted in a general hydrodynamic force model, resulted in a predictive equation explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. Moreover, the force experienced by the leading bubble due to the trailing bubble presence was obtained, and the theoretical equilibrium distances between the bubbles were calculated; good agreement with known behavior was achieved.     

Dynamic simulation of flow-induced fiber fracture

A dynamic simulation method has been developed of the fracture process of a fiber in a flow field using the particle simulation method proposed i a previous paper. The fiber is modeled with bonded spheres as a fiber model. The flexibility of the fiber model is altered by changing three parameters of the stretching, bending, and twisting constants between adjacent spheres. The stress induced in each bond of the fiber model as a result of deformation is formulated using displacement of the bodn distanc, bond angle, and torsion angle fr each pair of spheres. After deformation, the fiber model fractures at the bond at which the stress surpasses the strength of the fiber. The motion of the fiber model in a flow field is determined by solving the translational and rotational motion equations for individual spheres under the hydrodynamic force and torque exerted on them. The correctness of the method and formulation was verified by comparing the simulated deflection curve of a cantilever beam (with a concentrated load at the end) with the theoretical curve. Good agreement was found in both the deflection and slope of the beam. The fracture process of a fiber after bending deformation in a two-dimensional siimple shear flow was simulated under assumptions of an infinitely dilute system, no hydrodynamic interaction, and a low Reynolds number of a particle. The calculated critical conditions of the flow field for fiber fracture were compared with Forgacs and Mason's theoretical ones. Simulated values of the fracture condition of the fluid shear stress related to the Young's modulus of a fiber agree with theoretical ones over an aspect ratio of 15.     

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.     

The vertical force of bulk solids on objects in bins

The vertical force exerted on discs, spheres and horizontal square bars in test bins was measured during gravity flow of bulk solids. Approximate methods for estimating the vertical force on such objects were developed from the equation which expressed the stress in a conical mass flow hopper. With three adjustable parameters, good agreement was obtained between experimental and computed results for discs, provided the disc diameter was more that five times as large as the particle diameter. Identical parameters for a given material were found to be applicable in analyses for spheres and horizontal square bars.     

Numerical simulation of mixing process in T-shaped and DT-shaped micromixers

Recently, numerous studies have been done on the micro- and nano-scale equipment because of their importance and wide range of application. Micromixers are among the equipment in which two or more fluids are mixed and have applications in the processes, such as chemical synthesis. In this research, a numerical investigation using finite volume approach is done on mixing two incompressible fluids in 3D mixers with T- and double-T-(DT) shaped geometries in the range of Reynolds numbers 75–400. One of the important parameters for the quantitative analysis of the mixing performance of micromixers is the mixing index. So, the effects of different geometries, Reynolds number and channel length on this parameter are studied. The results show that, at different Reynolds numbers, the mixing index of fluids in the DT-shaped channel with 90° is less than the corresponding one in T-shaped mixers because changing the flow regime occurs at higher Reynolds numbers in the DT-shaped channels. The amount of mixing index increases by decreasing the angle of branches in the DT-shaped channel. It is observed that the mixing index of fluids increases along the channel, which tends to a constant value far away from the inlet.     

Wall factor for acceleration and terminal velocity of falling spheres at high reynolds numbers

The wall factor for spheres in the acceleration and terminal velocity ranges was determined experimentally for very high Reynolds numbers (13 500 < Re < 70 000). Experiments were performed with 12, 15, 18, 21, 25 and 31.75 mm spheres, falling in water inside cylinders 3.4, 4.9, 7, 10, 14 and 19 cm in diameter. A published empirical equation was found to yield good results for the terminal velocity wall factor in the range of studied Reynolds numbers.