Investigation on the Drop Size Distribution of SpraysProduced by a High‐Pressure Swirl Injector. Measurementsand Application of the Maximum Entropy Formalism

This paper reports an investigation on the volume‐based drop size distribution of sprays produced by swirl atomizers dedicated to direct‐injection spark‐ignited engines. Because of the use of high injection pressures to reduce the atomization time, the spatial density of the spray is high and prevents from classical measurements of spray drop size distribution. This problem is overcome by combining an experimental approach to the application of the maximum entropy formalism (M.E.F.). Based on the determination of correction factor series to correct the measurements from multiple light scattering, the experimental procedure allows obtaining some distribution characteristic features. According to a previous study, two of these characteristics are used as information in a M.E.F. procedure to derive the spray volume‐based drop size distribution. This characteristic is of paramount importance for evaluating the large drop population with accuracy. The overall procedure is presented in detail and discussed. It was applied to a series of four swirl atomizers in order to study the influence of the nozzle geometry and of the injection pressure on the injector performances. Conducted under both stationary and transient working conditions, this study allows a more precise understanding of the performances of GDI injectors as far as the spray drop size distributions are concerned.     

Development of a Three-parameter Volume-based Spray Drop Size Distribution through the Application of the Maximum Entropy Formalism

This work is an extension of a previous investigation on the determination of mathematical volume-spray drop size distributions by the application of the maximum entropy formalism. A two-parameter drop size distribution was derived and was found to give reasonable fits with experimental distributions obtained under different experimental conditions. However, as it is discussed, this two-parameter distribution shows critical limitations and cannot be applied in any situations of interest as far as drop size distributions in liquid sprays are concerned. To overcome this problem, a third parameter, equivalent to a drop diameter, is introduced into the procedure. This correction leads to a three-parameter drop size distribution with independent mean, width and symmetry. This function is a generalized gamma distribution and it can cover more practical situations than the previous two-parameter distribution. Furthermore, it is found that, contrary to the two-parameter distribution, the new volume-based drop size distribution shows a corresponding number-based drop size distribution with a physical behavior as the drop diameter decreases. This last result shows the importance of using three parameters to describe spray drop size distributions and that one of these parameters must represent the population of small drops.     

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.     

On the Capability of the Generalized Gamma Function to Represent Spray Drop‐Size Distribution

The three‐parameter, Generalized Gamma function solution of a recent MEF formulation used to derive liquid spray drop‐size distribution, is applied to sprays resulting from three different atomization processes. The objectives of these applications are to determine the sign of the parameters for which this function reports a more reliable fit and to further understand the parameter stability problem reported elsewhere. It is found that the lack of stability of the parameters is related to a characteristic feature of the mathematical function and appears for a series of spray drop‐size distributions with constant shape. For each situation analyzed in the present study, the Generalized Gamma function provides a very good fit with parameters that are either constant or correlated to the working conditions. As far as the sign of the parameters is concerned, the results show that the best formulation is a function of the spray and that it is impossible to know, a priori, which parameter sign will report the best fit. Finally, for one situation, it is found that the Generalized Gamma function allows extrapolation of drop sizes outside the measured values. All of the results converge to conclude that the three‐parameter Generalized Gamma function, which is identical to the well‐known Nukiyama‐Tanasawa distribution, accumulates valuable attributes to represent liquid spray drop‐size distributions.     

Characterisation of the acoustic cavitation cloud by two laser techniques

An experimental investigation of the size and volumetric concentration of acoustic cavitation bubbles is presented. The cavitation bubble cloud is generated at 20 kHz by an immersed horn in a rectangular glass vessel containing bi-distilled water. Two laser techniques, laser diffraction and phase Doppler interferometry, are implemented and compared. These two techniques are based on different measuring principles. The laser diffraction technique analyses the light pattern scattered by the bubbles along a line-of-sight of the experimental vessel (spatial average). The phase Doppler technique is based on the analysis of the light scattered from single bubbles passing through a set of interference fringes formed by the intersection of two laser beams: bubble size and velocity distributions are extracted from a great number of single-bubble events (local and temporal average) but only size distributions are discussed here. Difficulties arising in the application of the laser diffraction technique are discussed: in particular, the fact that the acoustic wave disturbs the light scattering patterns even when there are no cavitation bubbles along the measurement volume. As a consequence, a procedure has been developed to correct the raw data in order to get a significant bubble size distribution. After this data treatment has been applied the results from the two measurement techniques show good agreement. Under the emitter surface, the Sauter mean diameter D(3, 2) is approximately 10 microm by phase Doppler measurement and 7.5 microm by laser diffraction measurement at 179 W. Note that the mean measured diameter is much smaller than the resonance diameter predicted by the linear theory (about 280 microm). The influence of the acoustic power is investigated. Axial and radial profiles of mean bubble diameters and void fraction are also presented.     

Further Development and Application of a Tomographical Data Processing Method for Laser Diffraction Measurements in Sprays

Using a tomographical transformation, a data processing method is developed to extend the Malvern line-of-sight measurements based on laser diffraction theory into pointwise spatial distributions of various spray characteristics including droplet volume and number concentrations as well as all mean diameters of practical interest. The method has been applied to characterize the structures of sprays injected into still ambient air and annular air streams with various liquid and air flow rates. It is found that the various mean droplet diameters may have different tendencies of radial variations, exhibiting their respective importance in characterizing sprays, and that the air flow can significantly modify the spray structure along both the radial and axial directions and may cause the dilution or accumulation of droplets in certain regions.     

Application of the Maximum Entropy Formalism on Sprays Produced by Ultrasonic Atomizers

A recent application of the Maximum Entropy Formalism on liquid atomization problems led to the development of a mathematical volume‐based drop‐size distribution. This function, which depends on three parameters, is a reduction of the four‐parameter generalized Gamma function. The aim of the present work is to investigate the relevance of the three parameters in the characterization of liquid atomization processes. To achieve this, a variety of experimental drop‐size distributions of ultrasonic sprays were analyzed with the mathematical function. Firstly, it is found that the mathematical drop‐size distribution is very suitable to represent the volume‐based drop‐size distribution of ultrasonic sprays. Furthermore, it is seen that when considering the three parameters introduced by the function, one of them is constant for all the situations investigated, and the other two are linked to a non‐dimensional group that includes the main parameters controlling the drop production. These results are very important, since they suggest a possible development of physical models of primary atomization based on the M.E.F., which would allow for the prediction of the spray drop‐size distribution. Thusfar, such a model does not exist.     

超短脉冲激光光束被局域体全息光栅衍射的性质分析

利用二维耦合波理论,分析了超短脉冲激光光束被完全重叠型的局域体全息光栅衍射的时空变化性质,给出了衍射和透射脉冲激光光束沿光栅出射边界的强度时空分布。以LiNbO3晶体为例,数值研究了衍射光脉冲强度沿光栅出射边界的分布和脉冲波形的变化及光栅的总衍射效率受光栅二维尺寸、入射角度、光栅折射率调制度及入射脉冲的脉冲时域半峰全宽等条件的影响而变化的情况。与一维体全息光栅对超短脉冲激光光束衍射的性质,及此光栅对连续光衍射的性质作比较,给出了合理选择光栅参量及入射条件以在光栅出射边界上得到总衍射效率较大且分布较均匀的衍射光脉冲的方法。     

Experimental and Theoretical Study of Sprays Produced by Ultrasonic Atomisers

The atomisation of liquids by means of low-frequency ultrasonic atomisers results from unstable surface waves generated on the free surface of a thin liquid film. These unstable waves are obtained from the tuning of the amplitude and the frequency of an imposed oscillation. The thin liquid film develops as the liquid spreads over the atomising surface of the atomiser. This paper focuses on a systematic experimental analysis of the sprays produced by low-frequency ultrasonic atomisers. The thickness of the liquid film was measured and its effects on the drop diameter were studied together with the effects of both the liquid's physical properties and the ultrasonic atomiser's characteristics. The relationship between the mean drop diameter and the surface wave wavelength was accurately determined and introduced into a mathematical approach based on the maximum entropy formalism to predict the drop size distribution of the spray. Within the range of working conditions tested, the application of this formalism is successful and provides a procedure for the prediction of spray drop size distributions from calculations only.     

Global Rainbow Thermometry for Mean Temperature and Size Measurement of Spray Droplets

Global rainbow thermometry is a new technique for measuring the average size and temperature of spray droplets. For data inversion a global rainbow pattern is employed, which is formed by constructive interference of laser light scattered by an ensemble of spherical droplets. The non‐spherical droplets and liquid ligaments provide a uniform background and hence do not influence the interference pattern from which average size and temperature are derived. This is a large improvement with respect to standard rainbow thermometry, investigated since 1988, which is strongly influenced by particle shape. Moreover, the technique is applicable to smaller droplets than the standard technique because the global pattern is not spoiled by a ripple structure. Data inversion schemes based on inflection points, minima and maxima are discussed with respect to spray dispersion and droplet flux. The temperature derivation from inflection points appears to be independent of spray dispersion. Preliminary measurements in a heated water spray are reported. The mean diameter obtained from the rainbow pattern is smaller than the arithmetic mean diameter measured by phase‐Doppler anemometry. The accuracy of the temperature measurement by global rainbow thermometry is shown to be a few degrees Celsius.     

A digital image analysis technique for quantitative characterisation of high-speed sprays

A digital image analysis technique developed as a particle or droplet sizing tool and capable of measuring non-spherical objects has been examined in terms of its suitability for quantitative measurements in moderately dense sprays and in particular the potential capability for the characterisation of small diameter, high-speed two-phase flows by employing high-intensity pulsed lasers for illumination. In order to evaluate robustness of the image analysis technique (PDIA), measurement certainty and also to assess whether measurement performance is sensitive to the optical set-up, the technique was applied to data obtained from a hollow cone spray via two independent optical configurations which employed firstly a diode laser and secondly an Nd:YAG laser. The calibration response of the two optical set-ups revealed significant differences in terms of the depth-of-field characteristics and thus effective measurement volume dimensions. Despite these differences, a comparison of PDIA spray data revealed excellent agreement between the two datasets for measured diameters in the range 10–90 μm in the number distributions which not only confirmed robustness of the technique but also the potential of PDIA for the measurement of fast, small diameter objects. Subsequent comparisons of the PDIA data were made with PDA data obtained within the same spray in space and time and showed excellent agreement between the two techniques for droplets larger than approximately 25 μm in diameter. Discrepancies between PDIA and PDA were observed in the volume size distributions for the larger droplets measured whose diameters were greater than approximately 40 μm. This discrepancy is due to the ability of PDIA to measure the diameter of non-spherical droplets which were shown to exist in significant numbers at this measurement location within the spray. In contrast, the well-established technique PDA, which relies on the assumption of droplet sphericity clearly does not detect the presence of these larger deformed droplets.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

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.     

Two-dimensional soot distributions in buoyant turbulent fires

Spatially resolved two-dimensional soot volume fractions were measured using laser-induced incandescence in 7.1 cm methane and ethylene turbulent buoyant flames to study the distributions of soot in vertical and horizontal planes, and to provide data for soot model validation. Factors affecting the LII signals were considered including the laser energy profile and the laser attenuation effects. The absolute soot volume fractions were obtained by comparison to existing extinction measurements. The instantaneous soot images were collected to cover the entire flame height. Statistical quantities of soot volume fractions including mean, root mean square, probability density function, and spatial correlation coefficient were calculated at five downstream locations. The results show that instantaneous distributions of soot volume fractions exhibit significant differences compared to the ensemble averages, strong fluctuation around the mean, relatively homogeneous probability density function, and highly anisotropic spatial correlation.     

Implementation of the Laser Diffraction Technique for Acoustic Cavitation Bubble Investigations

Knowledge of the acoustic cavitation cloud would be useful for improving ultrasound reactor design. Among the characterisation techniques, few are adapted to bubble investigations in an intense ultrasound field. Some problems raised by these measurements result from interactions between the acoustic pressure wave and the measuring light wave. This paper reports the implementation of the laser diffraction technique to determine the size and volume concentration of bubbles generated by a dipping horn operating at 20 kHz. Measurements were performed with a Malvern 2600 instrument. The size distribution, deduced from the diffraction pattern scattered by the bubble cloud crossed by a laser beam, is disturbed by the acoustic pressure wave involving deviation of a light beam at low diffusion angles (acousto‐optic effect). A bubble size correction procedure based on the subtraction of the light energy due to the ultrasound wave is described. The size measurements, and thus the correction procedure, were validated by a second laser technique based on a different measuring principle: phase Doppler interferometry. The measurement reliability was further confirmed by an original application of laser diffraction based on measurements performed just after sonication. These three methods lead to a mean bubble size (Sauter mean diameter) of about 10 μm at a high ultrasound power input. Concerning the void fraction, only measurements achieved after sonication and by laser diffraction predict a correct estimation of this parameter.     

A Predictive Model for the Initial Droplet Size and Velocity Distributions in Sprays and Comparison with Experiments

The distribution of sizes and velocities of droplets initially formed in sprays is an important piece of information needed in the spray modelling, because it defines the initial condition of the spray droplets in the predictive calculations of the downstream two‐phase flow fields. A predictive model for the initial droplet size and velocity distributions in sprays is formulated in this study. The present model incorporates both the deterministic and the stochastic aspect of spray formation process. The deterministic aspect takes into account of the unstable wave motion before the liquid bulk breakup through the linear and nonlinear instability analysis, which provides information for the liquid bulk breakup length, the mass‐mean diameter and a prior distribution for the droplet sizes corresponding to the unstable wave growth of various wavelengths. The stochastic aspect deals with the final stage of droplet formation after the liquid bulk breakup by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub‐models are coupled together by the various source terms signifying the liquid‐gas interaction, the mass mean diameter and the prior distribution based on the instability analysis. The initial droplet size and velocity distributions are measured experimentally by phase‐Doppler interferometry for sprays generated by a planar research nozzle and a practical gas turbine airblast nozzle. For the two nozzles, the liquid bulk sheet is formed before its breakup in a coflowing air stream. It is found that the model predictions are in satisfactory agreement with the experimental data for all the cases measured. Hence the present model may be applied to a variety of practical sprays to specify the initial conditions for the spray droplets formed in practical spray systems.     

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.     

Assessment of Pulsed Gasoline Fuel Sprays by Means of Qualitative and Quantitative Laser‐based Diagnostic Methods

The combination of qualitative measuring techniques such as imaging, with quantitative drop sizing techniques like Laser Diffraction and Phase Doppler Analyzer (PDA), has been applied for assessing the sprays formed by injectors for gasoline direct injection (DI) engines. Both, the sizing instruments as well as the imaging, are offering temporal resolution in order to investigate the important features of pulsed DI sprays. Using a combination of the spatially integrating Laser Diffraction instrument with strobe illuminated dual view 2D‐imaging, the overall spray properties have been assessed. Having the 2D information of the global spray shape in two perpendicular directions allows one to immediately correlate the concentration and drop size measurement results of the Laser Diffraction instrument with the global spray appearance. Thus, the changes of the spray pattern can be related with the sizing information as the spray propagates away from the injector. For injector design improvements, however, it is required to achieve a higher spatial resolution and especially to measure closer to the injector exit orifice than the Laser Diffraction allows. By using a Phase Doppler Analyzer, the different phases of the injection event, i.e. opening of the injector, main spray and closing phase of the injector, can be distinguished from each other. However, in sprays, where the spray geometry is changing with time, the PDA can suffer due to its high spatial resolution, yielding results that are difficult to interpret.Assisting the PDA with a simultaneous imaging technique of similar spatial resolution creates a very robust experimental approach. By visualizing the plane perpendicular to the PDA probe volume, i.e. the crossing of the PDA laser beams on the spray image itself, a very precise adjustment of the PDA probe volume with respect to the spray rather than the nozzle can be achieved. This becomes critical when getting to the near orifice area at distances closer than 10mm. The synchronized images also bring additional information to the point measurement provided by the PDA. It becomes easier to choose which particular phase of the spray formation the user wants to characterize. Finally, more confidence in the interpretation of PDA data from locations close to the injector tip is reached.     

Laser Spectrometric Measurement System for Local Express Diagnostics of Flame at Combustion of Liquid Hydrocarbon Fuels

A laboratory laser spectrometric measurement system for investigation of spatial distributions of local temperatures in a flame at combustion of vapors of various liquid hydrocarbon fuels in oxygen or air at atmospheric pressure is presented. The system incorporates a coherent anti-Stokes Raman spectrometer with high spatial resolution for local thermometry of nitrogen-containing gas mixtures in a single laser shot and a continuous operation burner with a laminar diffusion flame. The system test results are presented for measurements of spatial distributions of local temperatures in various flame zones at combustion of vapor—gas n-decane/nitrogen mixtures in air. Its applicability for accomplishing practical tasks in comparative laboratory investigation of characteristics of various fuels and for research on combustion in turbulent flames is discussed.