Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Deep swirling flow down a plughole with air entrainment

Experiments have been carried out to determine the water depth required to entrain a given amount of air with a given circulating water flow discharging through a vertical pipe set in the flat bottom of a vessel. The circulation angle, , between the radial direction and the velocity vector far from discharge pipe was set at 0°, 10°, 30° or 60°.

It is shown that results are not dependent upon the diameter of the offtake pipe, if that is sufficiently small, and results are then expressed either as a dimensionless water depth vs a dimensionless ratio of the flow rates of the two phases or as a dimensionless flow rate of one phase vs the dimensionless flow rate of the other phase. An approximate theory describes trends in the data and is mostly in good quantitative agreement.

The results are used to examine the work of others on the entrainment of air or steam by water flowing along the bottom of a horizontal pipe into a small bottom offtake and the similar entrainment of water by air or steam flowing into a small top offtake. These systems occur in certain PWR loss of coolant accidents.     

Inertial-microfluidic radial migration in solid/liquid two-phase flow through a microcapillary: Particle equilibrium position

Although equilibrium of spherical particles under radial migration has been extensively investigated, mostly in macroscale flows with characteristic lengths on the order of centimeters, it is not fully characterized at relatively small Reynolds numbers, 1 ≤ Re ≤ 100. This paper experimentally studies “inertial microfluidic” radial migration of spherical particles in circular Poiseuille flow through a microcapillary. Microparticle tracking experiments are performed to obtain the spatial distribution of the particles by adopting a depth-resolved measurement technique. Through the analysis of the radial distribution of particles, inertial microfluidic circular Poiseuille flow is shown to induce a strong radial migration of particles at substantially small Re, which is quite in contrast to the pipe flows at large Re previously reported. This particle migration phenomenon is so prominent that particle equilibrium positions are formed even at small Re. However, it turns out that there exists a certain critical Re below which particle equilibrium position is almost fixed, but above which it seems to drift toward the channel wall.     

Steady laminar flow through thin curved pipes

Let R, τ denote, respectively, the radius of curvature and radius of torsion of the pipe (centre-line) and let a be a typical cross-sectional diameter.

The major part of the present paper addresses the case of flows through pipes of constant cross-section; (Re)²(a/R), Re(a/τ), (a/R) and (a/τ) all being small. Re is the Reynolds number for the flow. It is found that, even without further specifications of the details of the pipe, many important results can be obtained about the secondary flow which occurs and the pressure losses resulting from it. For example, it is shown that an important feature of such flows is valid for any corss-sectional shape; this was not obvious from previous works which treated only special cases having significant symmetries. Also, a new method for calculating the modified axial pressure gradient is presented which reduces dramatically the amount of work required therefor.

The remainder of the paper presents some results for similar flows through pipes of varying cross-section.     

Heavy particle dispersion from a point source in turbulent pipe flow

Dispersion of heavy particles from a point source in high-Reynolds pipe flow was studied using large-eddy simulation, LES. A stochastic Langevin type Lagrangian model developed by Berrouk et al. was used to account for heavy particle transport by the sub-grid scale motion. In both the LES and in an experiment by Arnason, the larger particles dispersed more than the small ones. The change in diffusivity with particle size is interpreted in terms of the effect of inertia and cross-trajectory effects and qualitatively compared with the analysis of heavy particle dispersion in isotropic turbulence by Wang and Stock. Particle inertia has a much larger influence on the dispersion than the crossing-trajectories effects.     

Probability of rebound and eject of sand particles in wind-blown sand movement

When incident particles impact into a sand bed in wind-blown sand movement, rebound of the incident particles and eject of the sand particles by the incident particles affect directly the development of wind sand flux. In order to obtain rebound and eject lift-off probability of the sand particles, we apply the particle-bed stochastic collision model presented in our pervious works to derive analytic solutions of velocities of the incident and impacted particles in the post-collision bed. In order to describe randomness inherent in the real particle-bed collision, we take the incident angle, the impact position and the direction of resultant action of sand particles in sand bed on the impacted sand particle as random variables, and calculate the rebound and eject velocities, angles and coefficients (ratio of rebound and eject velocity to incident velocity). Numerical results are found in accordance with current experimental results. The rebound and eject lift-off probabilities versus the incident and creeping velocities are predicted. The project was supported by the National Natural Science Foundation of China (10532040, 10601022). The English text was polished by Yunming Chen.     

Stochastic homogenization of reinforced polymer with very small carbon inclusions

In this study, we wish to determine a homogenized model of a material reinforced by spherical inclusion that is randomly distributed in space. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional. In this study, we want to determine a homogenized model of a material reinforced by a spherical inclusion distributed randomly in space. The peculiarity here is that these particles are of very small size, this generating an energy due to the strong contrast of microstructure. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. The random distribution is taken into account during the transition of scales, so as to preserve the statistical information, and that in spite of the passage to the limit. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional.     

Effect of velocity and pipeline configuration on dispersion in turbulent hydrocarbon-water flow using laser image processing

Drop size distribution and concentration profile data for hydrocarbon-water mixtures are obtained in a 8.2 cm dia pipe at a range of velocities for a straight horizontal pipe, horizontal and vertical flow after one bend and vertical flow after three bends. The laser image processing technique employed in this project is proven reliable.

The maximum drop size (d₉₉), is more dependent on the number of upstream interactive bends than on the velocity. The drop size distributions follow a Rosin-Rammler power law. The values of Rosin-Rammler exponents, based on this work, are on average 2.1 for all the configurations studied.

The concentration profiles as a function of velocity for straight horizontal flow are obtained and show the transition from stratified to adequately dispersed flow at about 2.3 m/s velocity. The concentration profiles for horizontal or vertical flow after one bend show dispersed flow in some cases; however, in other cases swirling makes representative sampling more difficult.

Vertical downflow after three interactive bends breaks the droplets to a finer size, and concentration profiles obtained in this location are more uniform than the other configurations studied. Representative sampling can be accomplished in this location even at 0.7–1.0 m/s velocity, in a 8.2 cm pipe.     

Particle motion and turbulence in dense two-phase flows

Measurements of particle mean and r.m.s. velocity were obtained by laser-Doppler anemometry in a descending solid-liquid turbulent flow in a vertical pipe with volumetric concentrations of suspended spherical particles of 270 μm mean diameter in the range 0.1–14%. Similar measurements were obtained in the flow downstream of an axisymmetric baffle of 50% area blockage placed in the pipe with volumetric concentrations of 310 μm particles up to 8% and of 665 μm particles up to 2%. In order to enable measurements in high particle concentrations without blockage of the laser beams the refractive index of the particles was matched to that of the carrier fluid.

The results show that the particle mean velocity profiles become more uniform and the particle r.m.s. velocity decreases with increasing concentration in both flow cases. The particle mean velocity in the pipe flow also decreases with concentration and the relative velocity, the difference between the particle velocity and the fluid velocity in single-phase flow, decreases with increasing Reynolds number. The length of the recirculation region downstream of the baffle was shorter than in single-phase flow by 11 and 24% for particle concentrations of 4 and 8%, respectively. The particle mean velocities were hardly affected by size for concentrations up fo 2%, but the r.m.s. velocities were lower with the larger particles.     

Stochastic methods in dispersion theory

In this study we show how methods from the theory of stochastic processes can be applied to problems in dispersion theory.First, we show that Taylor dispersion with adsorbing boundaries is easily transformed into a new Taylor dispersion problem without adsorbing boundaries. The transformed problem can then be solved using any of the traditional methods used for Taylor dispersion.Secondly, we consider the dispersion of particles in a channel (between parallel plates) with one partially adsorbing surface and one perfectly reflecting boundary. We determine the exact law of the position of adsorption for an arbitrary channel flow in terms of an infinite series of iterated integrals of the flow field, which is assumed to be a function of the cross-channel coordinate only. We also consider the case of shear flow over an adsorbing plane, by taking the limit where one of the boundaries is taken to infinity     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity, residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient, the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But, the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter, respectively. In addition, the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity,residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient,the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But,the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter,respectively.In addition,the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

非牛顿流体固粒悬浮流的若干问题

非牛顿流体固粒悬浮流具有广泛的应用背景,其特殊的流动属性使其成为一些新兴技术领域的核心突破点.同时,该流动又比较复杂,即便是在低固粒浓度的情况下,非牛顿流体特性也会对整个系统的微结构产生重要的影响,从而进一步影响固粒的运动.本文给出了非牛顿流体方程、固粒运动方程和非牛顿流体固粒悬浮流的特征参数,分析了这些参数的作用;阐述了单个固粒在管道中的径向移动、多固粒的相互作用和聚集、多固粒形成的链状结构以及非圆球固粒运动等方面的研究成果、结果分析以及尚未解决的问题,并对以上问题进行了总结和展望,给出了需要深入研究的具体问题和内容,旨在为进一步的研究提供参考和依据.     

非球形固体颗粒对弯管内壁的磨损机制

为研究弯管内固体颗粒在液相夹带条件下的运动特性及颗粒对弯管内壁的磨损,采用计算流体动力学与离散元耦合的方法,建立数值模型,考虑固液两相之间的作用,对弯管内的固液两相流动进行数值模拟;通过软件的应用程序编程接口嵌入自编译磨损模型;借助试验结果,验证数值模型的有效性.结果表明,所建立的数值模拟方案可以准确地模拟颗粒在管内的运动特征并能够预测弯管内壁的磨损位置以及磨损程度.弯管内的二次流对颗粒运动有重要影响,弯管外侧壁面中心线附近的磨损较严重,磨损的形式以小角度划擦切削为主.弯管磨损主要与颗粒对壁面的碰撞速度、碰撞角度及碰撞频率有关.运动中的颗粒与壁面发生多次碰撞,碰撞角度逐渐减小.随着颗粒球形度的增大,在相同碰撞条件下引起的磨损量变小,但是会降低颗粒的随流性.颗粒形状影响颗粒在流场中的运动速度以及颗粒与壁面的碰撞.随着颗粒球形度增大,严重磨损区域向弯管进口方向移动,壁面平均磨损量先减小后增大;当输送颗粒的球形度为0.91时,壁面磨损量最小.     

Electromagnetic propagation in periodic porous structures

A variational technique is employed to compute approximate propagation constants for electromagnetic waves in a dielectric structure which is periodic in the X−Y plane and translationally invariant in the Z-direction. The fundamental cell, in the periodic structure, is composed of a pore and the surrounding host media. The pore is a circle of radius R₀ filled with a dielectric ε₁ and the host dielectric characterized by ε₂. The size of the cell is characterized by the length A which is R₀.

Two limiting cases are considered. In the first, the pore size is assumed to be much smaller than the wavelength; this limit is motivated by microwave heating of porous material. The approximate propagation constants are explicitly computed for this case and are shown to depend upon the two dielectric constants, the relative areas of the two regions in the cell, and on a modal number. They are not given by a simple mixture formula.

In the second limit, the pore size is taken to be of the same order as the wavelength; this limit is motivated by the propagation of light in a holey fiber. In this case our argument directly yields the dispersion relationship recently derived by Ferrando et al. [Opt. Lett. 24 (1999) 276], using intuitive and physical reasoning. Thus, our method puts theirs into a mathematical framework from which other approximations might be deduced.     

Spectrum of density fluctuations in a particlefluid system—II. Polydisperse spheres

This paper presents an extension of the analysis shown in Part I to a polydisperse particle-fluid system. The density autocorrelation is shown to be a function of two quantities, a generalized Overlap function for which an analytical expression is derived, and the radial distribution function (RDF). In Fourier transform space, the density spectrum again appears to be a strong function of the mean particle size, and secondarily the mean particle separation distance. One unusual result is previously observed oscillations in the density spectrum of a monodisperse system of particles are severely dampened or even eliminated in the polydisperse case, depending on the width of the particle size distribution. Apparently contributions from different particle correlations interfere with each other, thereby reducing the coherent oscillations seen in the monodisperse particle-fluid system. Furthermore at large wavenumbers, the spectrum decays with a −2 power-law, independent of the shape of the particle size distribution. This behavior can be traced to the Overlap function which controls the behavior of the spectrum beyond the first peak. Remarkably the −2 power-law spectrum is determined by the shape of the particles (i.e. spheres) rather than their spatial distribution (RDF).

The effect of an asymptotically large pressure gradient on the correlation of several important higher-order moments is revisited for the polydisperse system. The relatively simple relationships developed for the monodisperse system are lost in the polydisperse case because particles of different sizes will be influenced differently by an applied pressure gradient. The result is moments that are of different order in velocity can no longer be related to each other (as they were in the monodisperse system), even in this idealized flow. A more comprehensive understanding of this phenomenon can only be achieved through direct numerical simulation or experiment.     

Effect of drag reducing polymer on air–water annular flow in an inclined pipe

Drag reduction (DR) for air and water flowing in an inclined 0.0127 m diameter pipe was investigated experimentally. The fluids had an annular configuration and the pipe is inclined upward. The injection of drag reducing polymer (DRP) solution produced drag reductions as high as 71% with concentration of 100 ppm in the pipeline. A maximum drag reduction that is accompanied (in most cases) by a change to a stratified or annular-stratified pattern. The drag reduction is sensitive to the gas and liquid superficial velocities and the pipe inclination. Maximum drag reduction was achieved in the case of pipe inclination of 1.28° at the lowest superficial gas velocity and the highest superficial liquid velocity. For the first time in literature, the drag reduction variations with the square root of the superficial velocities ration for flows with the same final flow patterns have self-similar behaviors.     

Determination of Nanoparticle Macrotransport Coefficients from Pore Scale Processes

Nanoparticle transport in porous media is modeled using a hierarchical set of differential equations corresponding to pore scale and macroscale. At the pore scale, movement and interaction of a single particle with a solid matrix is modeled using the advection–dispersion–sorption equation. A single nanoparticle entering the space encounters viscous, diffusion and surface forces. Surface forces (electrostatic and van der Waals forces) between nanoparticles and mineral grains appear as sorption propensity on solid matrix boundary condition. These local events are then transformed into a macroscale continuum by imposing periodic boundary conditions for contiguous unit cells representing porous media and using a scheme of moment analysis. At the macroscale, propagation and retention of particles are characterized by three position-independent coefficients: mean nanoparticle velocity vector \({\bar{\mathbf{U}}}^*\), macroscopic dispersion coefficient \({\bar{\mathbf{D}}}^*\), and mean nanoparticle retention rate constant \({\bar{K}}^*\). The modeling results are validated with a set of nanoparticle transport tests in porous microchips. We also present simulations of realistic porous media, where an actual image of sandstone samples is processed into binary tones. The representative unit cells are constructed from the resulting binary image by searching for areas within the sample with maximum similarities to the whole sample in terms of porosity and specific surface area, which are found to show strong correlations with the resulting \({\bar{\mathbf{U}}}^*\) and \({\bar{K}}^*\), respectively.     

Particle Clustering in Isotropic Turbulent Flow

A kinetic statistical model for describing the dispersion and clustering of heavy particles in homogeneous isotropic turbulence is presented. The model developed is used for calculating the relative velocities and the radial distribution function of a pair of particles in a steady suspension. The results obtained are compared with the known data obtained by direct numerical simulation.     

A Multiscale Theory of Swelling Porous Media: II. Dual Porosity Models for Consolidation of Clays Incorporating Physicochemical Effects

A three-scale theory of swelling clay soils is developed which incorporates physico-chemical effects and delayed adsorbed water flow during secondary consolidation. Following earlier work, at the microscale the clay platelets and adsorbed water (water between the platelets) are considered as distinct nonoverlaying continua. At the intermediate (meso) scale the clay platelets and the adsorbed water are homogenized in the spirit of hybrid mixture theory, so that, at the mesoscale they may be thought of as two overlaying continua, each having a well defined mass density. Within this framework the swelling pressure is defined thermodynamically and it is shown to govern the effect of physico-chemical forces in a modified Terzaghi's effective stress principle. A homogenization procedure is used to upscale the mesoscale mixture of clay particles and bulk water (water next to the swelling mesoscale particles) to the macroscale. The resultant model is of dual porosity type where the clay particles act as sources/sinks of water to the macroscale bulk phase flow. The dual porosity model can be reduced to a single porosity model with long term memory by using Green's functions. The resultant theory provides a rational basis for some viscoelastic models of secondary consolidation.