Simultaneous Measurement of Droplet Size and Three-Components of Velocity in Spray

The combination of the optical diagnostics and image processing technique has produced various methods of practical measurement in engineering. The measurement of size and velocity of droplets in fuel spray is one typical example. In general, the spray is a complicated and three-dimensional two-phase flow; therefore multi-dimensional field measurement of the spray field is indispensable. In the present paper, a technique of simultaneous measurement of droplet size and three-components of velocity is proposed and applied to spray issuing from the swirl nozzle as a practical application. The focused image of glare points is captured by a stereoscopic arrangement, and droplet size and the three-components of velocity are evaluated from the doublet image. Fundamental optical arrangements to capture the image of the glare points with a stereo view are established, and the feasibility and the accuracy of the technique are confirmed. © 2004 The Optical Society of Japan     

Rainbow Interferometry with Wire Diffraction for Simultaneous Measurement of Droplet Temperature,Size and Velocity

A rainbow measurement technique is presented which measures simultaneously the size, temperature and velocity of individual droplets in a spray. The technique is based on rainbow interferometry in combination with diffraction by a wire placed in the spatial filter of the scattered-light detector. A photomultiplier detects the wire diffraction pattern superimposed on the rainbow interference pattern created by a droplet scattering laser light. The velocity is determined from the equivalent geometric wire shadow. The necessary sphericity validation is performed by comparing the Airy and the ripple droplet diameters, resulting from the respective interference structures. The temperature is recovered from the position of the wire diffraction pattern relative to the main rainbow maximum. The technique was applied to a water spray at ambient temperature. The results showed the importance of nonsphericity detection.     

Droplet Size Distribution and Sphericity Measurements of Low‐Density Sprays Through Image Analysis

An image analysis technique has been developed in order to determine the drop size distributions of sprays produced by low‐velocity plain cylindrical jets. The particle sizing method is based on incoherent backlight images. Each drop is analyzed individually in the image. The two‐dimensional image resulting from the projection of the three‐dimensional object shape (the drop) on a screen (the video sensor surface) is modeled. The model, based on the point spread function formulation, has been developed to derive a relation between contrast and relative width of individual drops. This relation is used to extend the domain of validity of drop size in terms of size range, out of focus and image resolution. The shape parameter is determined for each drop image through morphological analysis. Spherical and non‐spherical droplets are then sorted on the basis of this parameter. Non‐spherical drops are regarded as non‐fully atomized liquid bulks or coalesced drops. Finally, the droplet size distribution of true spherical droplets is established for a low‐velocity plain cylindrical liquid jet.     

Effects of Fractal Size Distributions on Velocity Distributions and Correlations of a Polydisperse Granular Gas

By the Monte Carlo method, the effect of dispersion of disc size distribution on the velocity distributions and correlations of a polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersion can be described by a fractal dimension D, and the smooth hard discs are engaged in a two- dimensional horizontal rectangular box, colliding inelastically with each other and driven by a homogeneous heat bath. In the steady state, the tails of the velocity distribution functions rise more significantly above a Gaussian as D increases, but the non-Gaussian velocity distribution functions do not demonstrate any apparent universal form for any value of D. The spatial velocity correlations are apparently stronger with the increase of D. The perpendicular correlations are about half the parallel correlations, and the two correlations are a power-law decay function of dimensionless distance and are of a long range. Moreover, the parallel velocity correlations of postcollisional state at contact are more than twice as large as the precollisional correlations, and both of them show almost linear behaviour of the fractal dimension D.     

A Droplet Within the Spherical Model

Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffuse, as opposed to sharp, and find the corresponding density profiles (droplet shapes). The spatial location of a droplet is not fixed in translation-invariant models, hence, their natural states are described by mixed phases. To obtain pure macroscopic states (which describe localized droplets) one can use generalized quasi-averages. Conventional quasi-averaging deforms droplets and, hence, can not be used for this purpose. On the contrary, application of the generalized method of quasi-averages to the spherical model yields density profiles which do not depend on the magnitude of the applied external field.     

Increased Resolution of Size Distributions with the Coulter Counter

The limiting resolution of Coulter size measurements, the size within which two separate populations can be distinguished, is discussed in relation to the standard aperture. Electronic pulse editing, by comparing pulse height to width, enables small particles to be resolved from baseline instrument noise, but can give incomplete resolution of ultra-narrow distributions from artefactually produced peaks using the standard aperture. Improvements in the minimum measurable size and in sizing resolution of narrow size ranges are also shown to be possible by improving the signal quality from the Coulter aperture. A novel mathematical approach is described for the derivation of true size spectra for narrow particle size distributions by deconvolution of the composite spectra resulting from the effect of the inhomogeneous electric field in the Coulter aperture. Simple empirical equations are used derived from the location and amplitude of the spurious peaks observed in such composites relative to the genuine peaks. The method is applied to three “industrial” materials (wide size range samples) to determine the likelihood that such size ranges are affected by the spurious or artefactual peaks. A fresh blood sample deconvoluted by this method is shown to be apparently composed of more than one population of cells.     

A Nanometer Aerosol Size Analyzer (nASA) for Rapid Measurement of High-concentration Size Distributions

We have developed a fast-response nanometer aerosol size analyzer (nASA) that is capable of scanning 30 size channels between 3 and 100 nm in a total time of 3 s. The analyzer includes a bipolar charger (Po²¹⁰), an extended-length nanometer differential mobility analyzer (Nano-DMA), and an electrometer (TSI 3068). This combination of components provides particle size spectra at a scan rate of 0.1 s per channel free of uncertainties caused by response-time-induced smearing. The nASA thus offers a fast response for aerosol size distribution measurements in high-concentration conditions and also eliminates the need for applying a de-smearing algorithm to resulting data. In addition, because of its thermodynamically stable means of particle detection, the nASA is useful for applications requiring measurements over a broad range of sample pressures and temperatures. Indeed, experimental transfer functions determined for the extended-length Nano-DMA using the tandem differential mobility analyzer (TDMA) technique indicate the nASA provides good size resolution at pressures as low as 200 Torr. Also, as was demonstrated in tests to characterize the soot emissions from the J85-GE engine of a T-38 aircraft, the broad dynamic concentration range of the nASA makes it particularly suitable for studies of combustion or particle formation processes. Further details of the nASA performance as well as results from calibrations, laboratory tests and field applications are presented below.     

水平管油水分散流液滴粒径及其分布规律研究

油水两相分散流是油水混输管道常见的流型之一,液滴是油水分散流的主要特征,液滴在油水两相管路中受到湍流惯性力、剪切力、界面张力、黏性力等多种力的作用而发生聚结和破裂,从而形成不同的液滴粒径及其分布。本研究采用高速摄像和显微照相两种方法研究了水平管中油水分散流的液滴粒径随混合流量、温度和含油率等参数的变化规律,并利用三种概率分布函数研究了液滴粒径的分布特性。研究结果表明:分散相液滴的Sauter平均直径随混合流量的增加而逐渐减小、随温度升高而逐渐增大、随含油率的增大而增大;液滴粒径的分布规律与Log-Normal和Frechet概率分布函数符合较好。     

Quasi-Self-Preserving Log-Normal Size Distributions in the Transition Regime

A log-normal model, based on the extended SIMPLER-algorithm utilizing the Modal Aerosol Dynamics Modelling Technique, and a sectional model are compared for Brownian coagulation in the transition regime. The models are in good agreement with respect to the calculated particle size distribution moments. Applying the log-normal model a simple coagulation model consisting of a closed set of five equations is developed that does not require the solution of ordinary diferential equations.     

Necking in Extrusion Film Casting: Numerical Predictions of the Maxwell Model and Comparison with Experiments

The role of viscoelasticity in determining the extent of necking of a web of molten polymer extruded in an isothermal steady state extrusion film casting (EFC) process is considered. Following a brief review of experimental and theoretical efforts on this problem, analytical and numerical solutions to a well-established model for extrusion film casting using the Maxwell constitutive equation is presented. The extent of film necking was found to either increase or decrease with draw ratio (DR) depending on the Deborah number (De). The locus of points on the draw ratio-Deborah number diagram at which the draw ratio dependence of the necking width inverts was calculated and compared with the locus that separates the unattainable regime from the experimentally accessible regime. Predicted trends were found to be in qualitative agreement with experimental data for various polyethylene grades.     

Error Estimates in the Sampling From Particle Size Distributions

It is often necessary to estimate the properties of particle size distributions from limited samples taken from large populations. When the distributions are broad, and higher order moments required, as in the case of volume based particle size distributions, the inferred parameters d_3,50 (volume median diameter) and GSD (geometric standard deviation) can have high intrinsic errors not immediately obvious to the measuring scientist. We show that there is a critical number of particles, N_crit, which must be counted or else the error may blow up catastrophically. N_crit is very sensitive to the width of the distribution, and is approximately proportional to GSD¹¹ We develop formulae to estimate the random sampling error inherent in measured values of the d_3,50 and GSD for the log-normal distribution; compare the predictions to a typical experimental particle size measurement; and then generalize to the median of any arbitrary moment, d_{r, 50}.     

Critical Region for Droplet Formation in the Two-Dimensional Ising Model

We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L ² , inverse temperature > _c and overall magnetization conditioned to take the value m L ² –2m v _L , where _c ^–1 is the critical temperature, m =m () is the spontaneous magnetization and v _L is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v _L ^3/2 L ^–2 tends to a definite limit. Specifically, we identify a dimensionless parameter , proportional to this limit, a non-trivial critical value _c and a function such that the following holds: For < _c , there are no droplets beyond log L scale, while for > _c , there is a single, Wulff-shaped droplet containing a fraction _c =2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, and are related via a universal equation that apparently is independent of the details of the system.     

A Double Gaussian Beam Method for the Determination of Particle Size,Direction and Velocity

This paper describes a technique aimed at measuring particle size by light scattering from gaussian laser beams. The uncertainties in illumination due to the beam shape are avoided by determination of the direction and velocity. The method, which we arbitrarily called the Two Beam System (TBS), uses a simple birefringent prism to separate the incident laser beam into two orthogonally polarised overlapping parallel beams. The relative delay and amplitudes of the intensities scattered out of the orthogonal polarisations are indicative of the particle direction and velocity. Having obtained the direction of travel of the particle, its size is then obtained from the scattered intensity using Mie theory.     

On the Regression Model for Generalized Normal Distributions

The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generalized normal regression model that assumes a non-normal response. In this paper, we propose regression models based on generalizations of the normal distribution. The proposed regression models can be used effectively in modeling data with a highly skewed response. Furthermore, we study in some details the structural properties of the proposed generalizations of the normal distribution. The maximum likelihood method is used for estimating the parameters of the proposed method. The performance of the maximum likelihood estimators in estimating the distributional parameters is assessed through a small simulation study. Applications to two real datasets are given to illustrate the flexibility and the usefulness of the proposed distributions and their regression models.     

Limiting Distributions for a Polynuclear Growth Model with External Sources

The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by Prähofer and Spohn. Depending on the strength of the sources, the limiting distribution functions are either the Tracy–Widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.     

Description of Two-dimensional Distributions of Particle Size and Particle Velocity of a flowing discontinuous phase by means of special mathematical functions

As potential approximation functions for measured two-dimensional distributions, the two-dimensional normal distribution and the two-dimensional log-normal distribution are presented, in addition to mixed forms in which one of the two variables is linearly and the other logarithmically normally distributed. For all four distribution functions, regression curves are calculated, with x being understood as independent and y as dependent variable. The general concept is applied to the specific case of a two-dimensional distribution of particle size x and particle velocity y. In this context, a number of particularities result from the fact that a distinction has to be made between concentration-dependent and flux-dependent measurement.     

Optimization of the Initial Interface Configuration for In-Situ Neutron Reflectometry Experiments

Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques - The possibilities of optimizing the initial structure of the solid-liquid interface for in-situ neutron reflectometry...     

Infrared Extinction of Artificial Aerosols and the Effects of Size Distributions

The artificial aerosol is widely used in the modern battlefield to protect potential targets and to conceal movement of personnel and materiel. In this paper we investigated into the infrared extinction characteristics of the aerosol. The emphasis was placed upon the effects of the particle size distribution in an attempt to achieve optimal design. The particulates were assumed spherical in shape and Mie's theory is employed in the calculation of their extinction cross sections. Both spectral and average extinction coefficients per unit mass were computed for a certain kind of agent with the grain size distribution function being lognormal, which is considered suitable for artificial particles. Parametric studies are performed to examine the influence of the mean and the standard deviation . This study will afford indications for the optimal design of infrared obscurants.