An Improved Method to Determine Particle Dispersion Width for Efficient Modeling of Turbulent Two‐Phase Flows

An improved approach is presented for the hybrid Eulerian‐Lagrangian modeling of turbulent two‐phase flows. The hybrid model consists of a nonlinear k–ε model for the fluid flow and an efficient Lagrangian trajectory model for the particulate flow. The improved approach avoids an empirical correlation required to determine the dispersion width for the existing Stochastic‐Probabilistic Efficiency Enhanced Dispersion (SPEED) model. The improved SPEED model is validated using experimental data for a poly‐dispersed water spray interacting with a turbulent annular air jet behind a bluff‐body. Numerical results for the number‐mean and Sauter‐mean droplet diameters, as well as mean and fluctuating droplet velocities are compared with the experimental data and with the predictions of other dispersion models. It is demonstrated that higher computational efficiency and smoother profiles of Sauter‐mean diameter can be obtained with the improved stochastic‐probabilistic model than with the eddy‐interaction model.     

Experimental Study on Particle Size Distribution and Concentration Using Transmission Fluctuation Spectrometry with the Autocorrelation Technique

Based on the statistical characteristics of the transmission fluctuations in the particle suspension, transmission fluctuation spectrometry with autocorrelation (TFS‐AC) is described theoretically, with the assumptions of geometric ray propagation and completely absorbent particles in the suspension. The experiments presented here are realized in a focused Gaussian beam with the TFS‐AC technique. The acquisition of transmission fluctuation signals is achieved by using a high‐resolution digital oscilloscope. The transition function of TFS‐AC is obtained by varying the autocorrelation time. With a modified iterative Chahine inversion algorithm, solving a linear equation retrieves information on the particle size distribution and particle concentration. Some experimental results on spherical and non‐spherical particles are presented and discussed. The experiments cover a particle size range from 1μm to 1000 μm and a particle concentration of up to 12 %.     

Similarities and Differences Between Two‐Particle and Three‐Particle Interference

We illustrate various methods for implementing experiments that split particles into three beams, using “tritters”, or use three coherent particles (GHZ states), in order to illustrate our belief that any experiment that can be done using two particles is more interesting with three partricles.     

In‐Situ Measurement of Local Particle Flux Densities in a Complex Two‐Phase Flow

An optical measuring technique is presented allowing the exact in‐situ measurement of local particle flux densities in a confined channel flow by counting single particles penetrating an optically well defined measuring volume. This enables a precise flux determination up to the direct vicinity of planar walls. The measurement set‐up and its calibration as well as the whole test facility are described in detail. This measurement technique is used to study the particle transport in electrostatic precipitators. Exemplarily, results of particle flux profiles as well as precipitation, as gained from balances of parts of the precipitator channel, are presented. Furthermore, the possibility to determine particle velocity fluctuations is demonstrated.     

Comparative Test of Methods to Determine Particle Size and Particle Size Distribution in the Submicron Range

Among the most important characteristic properties of disperse systems such as latices, pigments, ceramic materials or drug formulations are the particle size and the particle size distribution. To measure these quantities, several methods and measuring instruments based on different physical principles are available. These include turbidimetry, dynamic and static light scattering, electron microscopy with image analysis, ultra- and disc centrifugation, light diffraction and the electrical sensing zone method. All these measuring techniques are doubtless necessary because of the large product variety and the broad particle size range. However, some problems arise if different techniques are used and the results are compared uncritically without considering to the application range and the resolution of the methods. An extensive comparative test was therefore carried out using seven latices in the submicron range with defined monomodal, bimodal and hexamodal particle size distributions. The most important methods of determining average particle size values and particle size distributions were tested and compared. Of the methods to determine only average particle sizes, turbidimetry is the most efficient, followed by dynamic light scattering with cumulants evaluation. Static light scattering only yields accurate results for small particles with narrow particle size distributions. Of the methods to determine particle size distributions, ultracentrifugation and, somewhat less, disc centrifugation and electron microscopy with image analysis are the most efficient. Dynamic light scattering only yields reliable results in the case of small particles with narrow distribution curves. Light diffraction and the electrical sensing zone method are less suitable for the submicron range.     

Determination of Particle Size Distribution by Par-Tec® 100: Modeling and Experimental Results

Some particle size analyzers, such as the Par-Tec® 100 (Laser Sensor Technology, Redmond, WA, USA), measure the so-called cord length distribution (CLD) as the laser beam emitted from the sensor randomly crosses two edges of a particle (a cord length). The objectives of this study were to develop a model that can predict the response of the Par-Tec® 100 in measuring the CLD of a suspension for spherical and ellipsoidal particles and to infer the actual particle size distribution (PSD) using the measured CLD output. The model showed that the measured CLD is reasonably accurate for the spherical particles. However, this measurement progressively deteriorates as the shape of particles changes from spherical to ellipsoidal with large ratios of major to minor diameters. Experimental results obtained with spherical particles having a normal and a non-normal PSD indicated that the Par-Tec® 100 measurements deteriorate as the PSD deviates from a normal distribution. The information obtained from these experiments also showed that the model can reasonably predict the Par-Tec® response. Use of the inferred PSD rather than the measured CLD made a major improvement in estimating the actual PSD. Mean particle size analysis revealed that the Par-Tec® 100 volume-weighted mean particle size is closest to the unweighted mean particle size measured by sieve analysis.     

Measurements on Particle Size Distribution and Concentration by Transmission Fluctuation Spectrometry with Temporal Correlation

Transmission fluctuation spectrometry with temporal correlation (TFS‐TC) is a new method for particle analysis. When a narrow light beam irradiates on a particle dispersion flow, the variation of the number of particles in the small measuring zone will cause the transmitted light to fluctuate, which includes the complete information on both particle size distribution (PSD) and particle concentration. The method may be used for real‐time, inline/online applications due to its simplicity of measuring principle and experimental setup. Until recently, the theory has been limited to low particle concentrations. In this work, an experimental study of the TFS‐TC measurement is presented for a very wide range of the particle concentrations. By introducing an empirical correction including the high concentration effects and considering the effect from rheological conditions in the inversion algorithm, the particle size distribution and particle concentration are reconstructed, resulting in the coverage of a broad range of particle size and concentration.     

Absorption and Scattering of Light by Highly Concentrated Two‐phase Flows

The spray cone emerging during an extended metal atomization process (called spray forming) has been investigated in order to quantify the influence of highly concentrated multiphase flows on phase‐Doppler‐anemometry (PDA) measurements. Using this non‐intrusive, optical measurement technique not only the local particle size and velocity distributions of the spray can be obtained but also additional information about the mass flux in the multiphase flow. Since standard phase‐Doppler systems can be easily applied to low concentrated particle systems (spherical particles with smooth surfaces and an optical transparent continuous phase taken for granted) the application of this measurement technique to highly concentrated multiphase flows is more complex. Both the laser light propagating from the PDA device to the probe volume and the scattered one going backward to the PDA receiving system are disturbed by passing the highly concentrated multiphase flow. The resulting significant loss in signal quality especially concerns the measurement of the smaller particles of the spray because of their reduced silhouette (in comparison with the bigger ones). Thus, the detection of the smallest particles becomes partially impossible leading to measurement of a distorted diameter distribution of the entire particle collective. In this study the distortions of the measured distributions dependent on the particle number concentration as well as on the path length of the laser light are discussed.     

A Modeling Study on Particle Dispersion in Wall-Bounded Turbulent Flows

Three physical mechanisms which may affect dispersion of particle's motion in wall-bounded turbulent flows, including the effects of turbulence, wall roughness in particle-wall collisions, and inter-particle collisions, are numerically investigated in this study. Parametric studies with different wall roughness extents and with different mass loading ratios of particles are performed in fully developed channel flows with the Eulerian-Lagrangian approach. A low-Reynolds-number $k-\epsilon$ turbulence model is applied for the solution of the carrier-flow field, while the deterministic Lagrangian method together with binary-collision hard-sphere model is applied for the solution of particle motion. It is shown that the mechanism of inter-particle collisions should be taken into account in the modeling except for the flows laden with sufficiently low mass loading ratios of particles. Influences of wall roughness on particle dispersion due to particle-wall collisions are found to be considerable in the bounded particle-laden flow. Since the investigated particles are associated with large Stokes numbers, i.e., larger than $\mathcal{O}(1)$, in the test problem, the effects of turbulence on particle dispersion are much less considerable, as expected, in comparison with another two physical mechanisms investigated in the study.     

非独立模式算法下粒径分布反演及分类的研究

在光全散射法颗粒粒径测量中,提出一种非独立模式算法下粒径分布反演及分类的方法。对被测颗粒系分别按照不同的粒径分布函数同时进行反演,并依据反演误差大小判断被测颗粒系符合哪种分布函数。仿真实验结果表明,在非独立模式下,完全可以利用已知的不同分布函数的反演误差作为分类依据,从而更准确地确定被测颗粒系的粒径分布。采用的遗传反演算法能够在3个可见光波长下得到较准确的粒径分布,反演结果稳定可靠,最大限度地减少了多个波长的使用,从而对光源有更大的选择余地。对透射消光测量结果加入5%随机噪声时,单峰分布颗粒系的反演误差小于5%,多峰分布颗粒系的反演误差小于10%。整个算法运行时间小于2 s。该方法具有原理简单,计算速度快等优点,能够满足颗粒粒径在线测量的要求。     

A New Formulation of the Maximum Entropy Formalism to Model Liquid Spray Drop‐Size Distribution

Considering the differences and disagreements involving the previous application of the Maximum Entropy Formalism to modeling the drop‐size distribution of liquid sprays, a new formulation is suggested. The constraints introduced in this formulation are based on characteristic features common to any liquid atomization process, i. e., the production of large and small drops is always limited. These limitations are a consequence of the action of both destabilizing and stabilizing forces such as aerodynamic and surface tension forces, respectively. The solution resulting from this approach, which makes use of statistical mechanics, is a three‐parameter Generalized Gamma Distribution, which can treat any type of distribution. It is shown that this solution is identical to a Nukiyama‐Tanasawa distribution that should no longer be regarded as an empirical distribution. Although this new formulation clearly answers the question concerning the amount of information required to describe a spray drop‐size distribution, it raises the problem of the mathematical form to be given to this information, and is discussed here.     

On‐line Determination of Particle Size Distributions in Flowing Dispersions

Emulsions are of great importance to industry. They are involved in many engineering operations, including chemical reactions, extraction, emulsification and suspension polymerization, etc. However, an important problem for these processes is how to control the size distribution of the dispersed phase. Indeed, off‐line analysis of the emulsion may generate uncertainties due to sampling and dilution of the product, which are likely to change the dispersion state and physico‐chemical properties. In this work, an on‐line optical method is proposed to characterize dispersed media in real flowing conditions. This method is based on the time‐analysis of back‐scattered light fluctuations. The present paper deals with the development of this method and its application to dispersions of alumina in water. The results obtained with the on‐line optical method are compared with those acquired by classical laser light scattering and microscopy.     

Identification of Regions with Inhomogeneous Particle Behavior in Dilute Gas‐solid Flows

The behavior of the particulate phase in a highly turbulent gas flow has been investigated in a vertical channel. Variations of the flow configuration (1. Flow past a cylinder, 2. flow past a wall‐mounted obstacle and 3. flow around a horizontally injected jet) have been subject to both experiments and numerical simulations. The velocity vector field of the solid phase has been measured by digital particle image velocimetry (DPIV). The measurements have been focused on particle‐obstacle collisions and crossflow in the vicinity of the jet nozzle using the lately developed twinpeak detection method. By application of this method regions of highly inhomogeneous particle behavior could be detected mainly upstream of the flow perturbation. Numerical results have been obtained by an Eulerian‐Lagrangian method on boundary‐fitted grids. Particle‐particle interactions as well as interphase exchange of momentum have been taken into account. The simulation results showed to be well in accordance with the experimental results.     

Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X‐Ray Scattering Curves

A method for recovering the size distribution of spherical particles from small angle scattering data by using a Monte Carlo interference function fitting algorithm is presented. The method is based on the direct simulation of the small angle scattering data upon the assumption of non‐interacting hard sphere ensembles (“dilute” solution approximation). The algorithm for retrieving the particle size distribution does not require any additional parameters apart from the input of the scattering data. The fitting strategy necessarily implies positive particle size distributions, while preserving the advantage of the indirect transformation method for data desmearing. Furthermore, the present approach does not use any regularisation procedures of the best fit solution and favours smooth particle size distributions. The Monte Carlo procedure has been tested against several simulated cases with various types of mono‐ and bi‐modal size distributions and different noise levels. In the special case of non‐interacting spheres, the Monte Carlo fitting algorithm had the same retrieving ability as the well assessed indirect transformation, structure interference and maximum entropy methods. Finally, the algorithm was applied to retrieve the distribution of spherical nanopowders produced by gas‐to‐particle conversion both as free powder and as reinforcing second‐phase agent in polymer nanocomposites.     

Estimation of Particle‐Size Distribution and Classifier Selectivity

A new, practical, and informative technique is presented for the efficient calculation of classifier efficiencies. Kernel density estimation, a well‐developed statistical tool, is applied to particle‐size datasets from classifier flow streams. It is demonstrated that this construction of particle‐size densities is more accurate and appropriate than histograms. The resulting classifier efficiency curves then display the key features of the classifier efficiency without propagating the noise inherent in most particle‐sizing techniques, and without the constraint of any selectivity curve parametrization.     

风沙流中颗粒相浓度和粒度的瞬态同步测量

本文基于激光衍射技术提出了一种新的浓度测量的改进方法。该方法可以同时获得测量颗粒的浓度和粒径分布。基于这一测量方法,通过对大型风洞风沙两相流系统中不同风速,高度条件下颗粒浓度和粒径测量,获得了跃移颗粒的空间结构信息。结果显示,颗粒浓度随来流风速线性增加,且在近床面区域内来流风速对颗粒粒径具有选择性。     

Dust in Plasma I. Particle Size and Ion‐Neutral Collision Effects

A fully kinetic self‐consistent model of an absorbing particle immersed in stationary isotropic weakly collisional plasma has been developed. The combined effects of particle size and ion‐neutral charge exchange collisions have been investigated for intermediate regimes, where no analytic theories are available. It is shown that collisional effects related to the ion orbital destruction (presence of extrema in ion flux collected on the particle surface and in particle potential and charge) are important for small particles, while they are totally absent for large particles. The potential distribution around the particle is quite well represented by a Yukawa form, but with an effective screening length that shows different dependences from the gas pressure for small and large particle size. Analytical fitting formulas of particle charge and potential and screening length depending on the particle radius parameter and on the Knudsen number have been obtained (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)