Droplet Size Distribution Function Research Articles

Comparison of Cloud Properties between SGLI Aboard GCOM-C Satellite and MODIS Aboard Terra Satellite

This study presents a comprehensive comparison of Level 2.0 cloud properties between a Second-generation Global Imager (SGLI) aboard the GCOM-C satellite and a Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Terra satellite, to better understand the qualities of cloud properties obtained from SGLI/GCOM-C launched on 23 December 2017. The cloud pixels identified as water phase by both satellite sensors are highly consistent to each other by more than 90%, although the consistency is only ~60% for ice phase cloud pixels. A comparison of cloud properties—cloud optical thickness (COT) and cloud particle effective radius (CER)—between these two satellite sensors reveals that water and ice cloud properties can have different degrees of agreement depending on underlying surface. The relative difference (RD) values of 22% (18%) and 37% (24%) for water cloud COT (CER) comparison over ocean and land surfaces and respective values of 35% (42%) and 35% (62%) for comparisons of ice cloud properties, and also other comparison metrics, suggest better agreements for water cloud properties than for ice cloud properties, and for ocean surface than for land surface. Though cloud properties differences between MODIS and SGLI can arise from inherent features of cloud retrieval algorithms, such as differences in ancillary data, surface reflectance, cloud droplet size distribution function, model for ice particle habit, etc., this study further identifies the important roles of cloud thickness and Sun and satellite positions for differences in cloud properties between SGLI and MODIS: the differences in cloud properties are found to increase for thinner clouds, higher solar zenith angle, and higher differences in viewing zenith and azimuth angles between these satellite sensors, and such differences are more distinct for water cloud properties than for ice cloud properties.

An experimental analysis of droplet charging in a wind tunnel

The aim of this paper is to introduce an experimental analysis of droplet charging that occurs due to liquid film atomization on two different surfaces. The atomization of the droplets from the liquid film at high speed is still not satisfactory understood. The phenomena can be found in steam turbines, wind turbines, aeroplanes and other technical applications. The liquid film atomization is associated with the electrostatic charge of the formed droplets. The paper describes the experiment when the coated and non-coated surfaces were tested for an estimation of the droplet size distribution function and the droplet charge. A new wind tunnel was developed for the study of liquid film atomization in similar conditions in steam turbines. The coarse droplets are formed in the steam turbine from the liquid films on the blades and inner casings. The coarse droplets formed on the non-moving blades don´t exactly follow the bulk flow and they collide with the moving blades. These collisions cause erosion and corrosion processes which have an unfavourable effect on the reliability and the efficiency of steam turbines. The tunnel is equipped with the standard instrumentation for the measurement of the flow properties and for the analysis of the size distribution function of the droplets. Two measurements methods were used to attain the size of the droplets, along with their photogrammetry and light scattering. The first tested surface is polished stainless steel and the second is the electrical isolating and hydrophobic coating. The results from the measurement suggest the possibility of the better understanding the erosion processes in steam turbines.

Microscopic phenomena inferred from the rheological analysis of an emulsion

The rheological behavior of an emulsion is determined by microstructural changes caused by external loads. Some of these changes are irreversible due to the occurrence of the destabilization processes. Therefore, a deeper understanding of the system may be acquired by linking rheological characterization results with microscopic events. It is important to understand the rheological consequences of the occurrence of destabilization phenomena such as coalescence and flocculation. An experimental study was performed to verify the destabilization of samples during shear in a rheometer. Coalescence was assessed by measuring changes in the droplet size distribution functions, while the degree of flocculation was determined with the use of consecutive flow curves. Additionally, the occurrence of the non-equilibrium condition was studied. As a case study, the method developed in this paper was applied to a water-in-oil crude emulsion.

Application of the generalised fully Lagrangian approach to simulating polydisperse gas-droplet flows

In this paper, we demonstrate the application of a generalised fully Lagrangian approach to the simulation of polydisperse gas-evaporating droplet flows. The paper focuses on the proposed methodology for modelling the dispersed phase, droplets, in both steady and transient cases. To account for polydispersity, the set of Lagrangian variables is extended to include the droplet size, and the droplet size distribution function is introduced to the droplet parameter set. According to the Lagrangian approach, all the droplet parameters, including the distribution function, are found along the droplet trajectories. An interpolation scheme to convert droplet parameter fields from a Lagrangian to an Eulerian framework for visualising droplet distribution is proposed. The developed methodology was applied to simple 1D and 2D stationary cases for verification, after which it was incorporated into OpenFOAM to simulate steady and periodic flows around a cylinder. In the case of a steady flow, a region devoid of droplets is formed behind the cylinder. From the droplet distribution plots, it was observed that small and medium sized droplets reach a region near to the axis of the symmetry of the flow. In the case of periodic flow, the analysis of droplet distribution is based on instantaneous pictures of the droplet parameters rather than their values along droplet trajectories. In this flow, strongly influenced by vortices, a strong droplet segregation is shown; at various locations one can see a full droplet size spectrum, only small or large droplets, and/or droplets from a narrow size interval. In all cases, the effect of the evaporation is to decrease the maximum value of the droplet distribution function shifted towards smaller-sized droplets.

INTEGRATION OF THE NUMERICAL SOLUTION MODULE OF THE KINETIC EQUATION INTO THE CFD PACKAGE FOR THE VOLUME CONDENSATION PROBLEM OF THE VAPOR-GAS MIXTURE FLOW THROUGH A NOZZLE

Objective. Integrating the numerical solution module of the kinetic equation for the droplet size distribution function in a CFD package. Application of the module to volumetric condensation at the supersonic flow of a vapor-gas mixture through a nozzle in a two-dimensional formulation, comparison of the results with experimental data of third-party authors.Methods. In this paper, the problem of volume condensation in the supersonic flow of a vapor-gas mixture through a nozzle is solved by finite element methods in a two-dimensional formulation using user-defined functions.Results. A module for the numerical solution of the kinetic equation for the droplet size distribution function is presented as a user-defined function integrated into the calculated CFD package.Conclusion. The module application to volumetric condensation for a vapor-gas mixture flow through the nozzle gave a qualitative agreement in all areas and a quantitative agreement in the area of intense condensation with measurement data. The distributions of temperatures, pressures, and the degree of supersaturation are presented both along the central axis and on the plane bounded by the contour of the computational domain. It is shown that the module does not depend on the solver type (stationary or non-stationary).

The Impact of Cesium Vapor Bulk Condensation on the Transport of Aerosols in the Reactor Plant’s Primary Circuit during a Severe Accident at a Nuclear Power Plant with VVER

The article presents the results from numerical modeling of aerosol particles' deposition process during their transportation in the horizontal section of the reactor plant’s primary circuit model for the conditions typical for a severe accident at an NPP equipped with VVER reactors. The effect that the bulk condensation of cesium vapors has on the growth and deposition of aerosols during their transportation is analyzed. The influence of the initial size and concentration of aerosol particles on their growth rate and subsequent deposition is considered. Homogeneous condensation occurring in the absence of heterogeneous condensation nuclei (solid aerosol particles) and also heterogeneous condensation under the conditions in which nuclei of the new phase do not emerge according to the homogeneous mechanism are considered as the limit cases. Data on the average size of the produced droplets and aerosol particles along the channel axis in the condensation zone with the varied value of aerosol particles mass fraction in the flow have been obtained, which corresponded to different ratios of the condensate mass fraction in the form of droplets and liquid layer on the surface of solid aerosol particles. It has been established that the general deposition rate decreases if the flow contains droplets generated as a result of homogeneous bulk condensation and having a size smaller than the size of grown aerosol particles. The article describes the analysis scheme of the modeled section whose geometrical shape was specified based on the horizontal section of the experimental installation in the FALCON-ISP1 series of experiments on the deposition and transport of radionuclide aerosols. The cesium vapor homogeneous-heterogeneous condensation process is modeled by numerically solving—using the method of moments—the kinetic equation for the droplet size distribution function with involvement of the authors’ COND-KINET-1 computer program. The transport and deposition of aerosol particles in the primary circuit channel were modeled using the MAVR-TA computer code developed at the National Research Center Kurchatov Institute.

A Software Package for Simulating Physicochemical Processes and Properties of Working Fluids

A software package consisting of the TETRAN-PRO and the COND-KINET-1 proprietary computer codes, as well as computational methods and models they are based on, is described. The TETRAN-PRO code calculates the composition and thermodynamic properties of a multicomponent reacting system under thermodynamic equilibrium conditions, including products of combustion or pyrolysis of organic and composite fuels. The difference of this code from similar ones is the use of the method of prevailing components, which is most effective as to convergence, computation time, and the range of parameters used. The code includes the necessary database of the original thermodynamic properties for 3000 individual substances. The TETRAN-PRO code’s capabilities are demonstrated by the results from calculation of mercury vapors' conversion in the combustion products of Kuznetsk and Berezovo coals. The COND-KINET-1 calculates the parameters of a condensation aerosol formed during the bulk condensation in a vapor-gas mixture flow. The process is described with a system of moment equations for the droplet size distribution function, which is closed by the equations of momentum and energy. A comprehensive approach, thermodynamic and kinetic, has been formulated to the description of the bulk condensation in multicomponent reacting systems based on the TETRAN-PRO and COND-KINET-1 codes. The approach’s capabilities are demonstrated by the example of numerically simulating the formation of environmentally dangerous submicron particles in burning coals according to the condensation mechanism. Data on the concentration and size distribution of the generated particles are obtained. The predicted data on the fractional composition of particles are compared with the experiment.

Combining level-set method and population balance model to simulate liquid–liquid two-phase flows in pulsed columns

The level-set method and population balance model (PBM) were combined to develop a numerical framework for the simulation of liquid–liquid two-phase flows in a pulsed disc and doughnut column (PDDC). First, breakup behavior in droplet swarms in a local area of the PDDC was elucidated under a low holdup condition using a modified level-set method with multi-levels. The droplet breakup frequency function and the daughter droplet size distribution function were determined via statistical analysis on the breakup behavior in droplet swarms. The determined droplet breakup kernel functions were then plugged into the PBM to simulate liquid–liquid two-phase flows in the full-scale PDDC. The calculated droplet size distribution agreed well with the experimental results. The developed numerical framework provides a strategy to simulate two-phase flows avoiding the use of adjustable parameters which are dependent on experiments.

Time-resolved droplet size and velocity distributions in a dilute region of a high-pressure pulsed diesel spray

The principal objective of the present work is to experimentally investigate the time-resolved spray characteristics. Droplets data in a dilute region of a high-pressure diesel spray were obtained by employing the PDIA (particle/droplet image analysis) method with double pulse laser illumination. Eulerian specification was adopted to describe the transient spray microscopic behavior within a fixed test window at ten representative instants after triggering the injection. The experimental results indicate that the transient spray evolution can be characterized in three distinct stages. During stage I (the latency stage), the spray tip develops and reaches the test location, but no discrete droplets were clearly observed. During stage II, the spray passes through the test window, from which discrete droplets are observed to disperse in the dilute region and the SMD of the droplets increases rapidly. During stage III, bulk spray disappears in the test window and only discrete droplets were observed. The SMD of the droplets is decreased to a “steady-state” value. Based on these sampled and processed data, the droplet size distribution functions were obtained and compared with the Rosin-Rammler and the Nukiyama-Tanasawa function. Finally, the Stokes number and the Weber number of each droplet were determined, and the movement of the droplets were analyzed. The measured time dependent droplet behaviors are believed to provide important data for spray modeling and simulation.

Effect of Channel Geometry and Properties of a Vapor–Gas Mixture on Volume Condensation in a Flow through a Nozzle

A method of direct numerical solution of the kinetic equation for the droplet size distribution function was used for the numerical investigation of volume condensation in a supersonic vapor–gas flow. Distributions of temperature for the gas phase and droplets, degree of supersaturation, pressure, fraction of droplets by weight, the number of droplets per unit mass, and of the nucleation rate along the channel were determined. The influence of nozzle geometry, mixture composition, and temperature dependence of the mixture properties on the investigated process was evaluated. It has been found that the nozzle divergence angle determines the vapor–gas mixture expansion rate: an increase in the divergence angle enhances the temperature decrease rate and the supersaturation degree raise rate. With an increase or decrease in the partial pressure of incondensable gas, the droplet temperature approaches the gas phase temperature or the saturation temperature at the partial gas pressure, respectively. A considerable effect of the temperature dependence of the liquid surface tension and properties on gas phase parameters and the integral characteristics of condensation aerosol was revealed. However, the difference in results obtained with or without considering the temperature dependence of evaporation heat is negligible. The predictions are compared with experimental data of other investigations for two mixtures: a mixture of heavy water vapor with nitrogen (incondensable gas) or n-nonane vapor with nitrogen. The predictions agree quite well qualitatively and quantitatively with the experiment. The comparison of the predictions with numerical results from other publications obtained using the method of moments demonstrates the usefulness of the direct numerical solution method and the method of moments in a wide range of input data.

Simulation of size-dependent aerosol deposition in a realistic model of the upper human airways

An Eulerian internally mixed aerosol model is used for predictions of deposition inside a realistic cast of the human upper airways. The model, formulated in the multi-species and compressible framework, is solved using the sectional discretization of the droplet size distribution function to accurately capture size-dependent aerosol dynamics such as droplet drift, gravitational settling and diffusion. These three mechanisms are implemented in a consistent way in the model, guaranteeing that the total droplet mass as given by the droplet size distribution is always equal to the total droplet mass due to the mass concentration fields. To validate the model, we simulate monodisperse glycerol aerosol deposition inside the lung cast, for which experimental data is available. Provided that an adequate computational mesh is used and an adequate boundary treatment for the inertial deposition velocity, excellent agreement is found with the experimental data. Finally, we study the size-dependent deposition inside the lung cast for a polydisperse aerosol with droplet sizes ranging from the nanometer scale to beyond the micrometer scale. The typical ‘V-shape’ deposition curve is recovered. The aim of this paper is to 1) provide an overview of the Eulerian aerosol dynamics model and method, to 2) validate this method in a relevant complex lung geometry and to 3) explore the capabilities of the method by simulating polydisperse aerosol deposition.

Simulation of the liquid break-up at an AdBlue injector with the volume-of-fluid method followed by off-line coupled Lagrangian particle tracking

Numerical simulation of the liquid break-up and prediction of the droplet size distribution of injection devices is a challenging task. For predicting the disintegration process, interface capturing techniques, e.g. the volume-of-fluid method, are mandatory. The extensive computational effort caused by the high resolution requirements in space and time determine the limitation for many applications. Validations of such simulations with experimental data can be only rarely found in the literature. This study presents a comprehensive numerical and experimental investigation of the break-up process at an industrial low-pressure three-hole injector. The numerical simulations for three different injection pressures are performed with an efficient volume-of-fluid approach. At certain time instants the volume fraction field is scanned for coherent liquid structures, and the ligament size distribution is evaluated. The simulated mean droplet diameters and the droplet size distribution functions show a good agreement with the performed measurements. The high computational effort, caused by the fine mesh resolution, limits the axial extension of the simulated domain, here fifty times the nozzle diameter. In order to extend the simulated spray domain, an off-line coupling approach with a Lagrangian particle method is proposed. Therefore, the detached droplets from the volume-of-fluid simulation are used as initial conditions for the subsequent Lagrangian spray simulation on a coarser computational grid. This presented second step determines the link between liquid disintegration on a micro-scale, and spray simulation on a macro-scale. The aim of this study was to develop a predictive simulation tool for determination of the injector characteristics.

Direct measurement of droplet breakage in a pulsed disc and doughnut column

The lack of experimental data for the droplet breakup has been one of the limitations for the application of population balance model (PBM). In this work, a high‐speed camera was used to directly measure the droplet breakup frequency and daughter size distribution in a pulsed disc and doughnut column. It was found from the captured video that multiple breakup events were more frequently observed than binary breakup. The multiple breakup was treated as an original breakup and several intermediate breakups to characterize the process quantitatively. The effects of pulsation intensity, dispersed phase flow rates, and the spatial locations were investigated in detail. Empirical correlations were finally established for both the breakup frequency function and the daughter droplet size distribution function and fitted well with the experimental data. The correlation equations were then used in a simplified PBM to calculate the droplet number density, which further proved the feasibility of the correlations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4188–4200, 2017

Statistical Model of Polydisperse Fuel Spray in Three Dimensional Space

In this study, we investigate the problem of the effects of droplets dispersion dynamics on ignition of polydisperse spray in turbulent mixing layers using probability density function. Studies of this problem have been found to be instrumental in developing understanding of turbulent combustion including the ignition of turbulent gaseous diffusion flames. The parameters used to describe the distribution of droplet sizes are the moments of the droplet size distribution function which are allowed to vary in the fourth vector (x,y,z,t). In our analysis we applied the Homotopy Analysis Method. This method contains a certain auxiliary parameter which provides a way to control the convergence region and the rate of convergence of the series solutions.

Droplet Breakup in a Square-Sectioned Pulsed Disc and Doughnut Column

In this work, droplet breakup in a square-sectioned pulsed disc and doughnut column (PDDC) was investigated experimentally. Droplet breakup was observed by a high-speed online camera. Three different breakup patterns, tensile breakup, popping breakup, and revolving breakup, were observed. In all these patterns, shear stress was the main factor causing the breakup. Breakup frequency function and daughter droplet size distribution function were studied in different experimental conditions. Computational fluid dynamics simulation was used to study the flow field in the PDDC. Particle image velocimetry measurement was performed to verify the simulation results. The shear stress was calculated based on the simulation. The breakup frequency function and daughter droplet size distribution function were then correlated with the shear stress. The calculated results from the correlation equations were in good agreement with the experimental data. The correlation equations were finally applied in a simplified popula...

Liquid water cloud properties during the Polarimeter Definition Experiment (PODEX)

Abstract We present retrievals of water cloud properties from the measurements made by the Research Scanning Polarimeter (RSP) during the Polarimeter Definition Experiment (PODEX) held between January 14 and February 6, 2013. The RSP was onboard the high-altitude NASA ER-2 aircraft based at NASA Dryden Aircraft Operation Facility in Palmdale, California. The retrieved cloud characteristics include cloud optical thickness, effective radius and variance of cloud droplet size distribution derived using a parameter-fitting technique, as well as the complete droplet size distribution function obtained by means of Rainbow Fourier Transform. Multi-modal size distributions are decomposed into several modes and the respective effective radii and variances are computed. The methodology used to produce the retrieval dataset is illustrated on the examples of a marine stratocumulus deck off California coast and stratus/fog over California's Central Valley. In the latter case the observed bimodal droplet size distributions were attributed to two-layer cloud structure. All retrieval data are available online from NASA GISS website.

Experimental study of the interaction between terahertz radiation from the Novosibirsk free-electron laser and water aerosol

Interactions of high-power terahertz radiation from the Novosibirsk free-electron laser at a wave-length of 130 µm in an atmospheric window with a model aerosol cloud with a known droplet size distribution function has been studied experimentally for the first time. The experimental data are compared with theoretical calculation results obtained from solution of the lidar equation for conditions of the experiment.

On the rupture of a round liquid jet: the primary atomization process

The present study analyzes the process of fragmentation of a liquid volume into a cloud of droplets, a well-known phenomenon usually denoted as primary atomization. The experimental work was performed in a single-orifice pressure-swirl atomizer. For the first time, a transition was observed in the droplet size distribution function (DSDF) that transforms from a Nukiyama–Tanasawa type to a power law dependence described by the function d −x . A non-dimensional group including atomizing pressure was identified as the controlling parameter in the transition, as in other similar fracture processes, for example in solid materials. The value obtained for the critical exponent of a power law function that best fitted the DSDF for the maximum atomizing pressure is a quantitative evidence of the three-dimensional characteristics of this process.

Experimental Investigation of the Dispersion of Liquids by Ejection Atomizers

This paper presents the results of an experimental investigation of the dispersivity of liquid droplets in the spray cone of ejection atomizers. The calculational droplet size distribution function was measured by the method of low angles of the probe laser radiation scattering indicatrix on a pneumohydraulic bench under cold blow conditions. The efficiency of the proposed circuit designs of atomizers has been analyzed.

Interpretation of Multiwavelength-Retrieved Droplet Effective Radii for Warm Water Clouds in Terms of In-Cloud Vertical Inhomogeneity by Using a Spectral Bin Microphysics Cloud Model

Abstract This study examines the impact of in-cloud vertical inhomogeneity on cloud droplet effective radii (CDERs) of water-phase cloud retrieved from 1.6-, 2.1-, and 3.7-μm-band measurements (denoted by r1.6, r2.1, and r3.7, respectively). Discrepancies between r1.6, r2.1, and r3.7 due to in-cloud vertical inhomogeneity are simulated by using a spectral bin microphysics cloud model and one-dimensional (1D) remote sensing simulator under assumptions that cloud properties at the subpixel scale have horizontal homogeneity and 3D radiative transfer effects can be ignored. Two-dimensional weighting functions for the retrieved CDERs with respect to cloud optical depth and droplet size are introduced and estimated by least squares fitting to the relation between the model-simulated droplet size distribution functions and the retrieved CDERs. The results show that the 2D weighting functions can explain CDER discrepancies due to in-cloud vertical inhomogeneity and size spectrum characteristics. The difference between r1.6 and r2.1 is found to primarily depend on the vertical difference in droplet size distribution because the peak widths of their weighting functions differ in terms of cloud optical depth. The difference between r3.7 and r2.1, in contrast, is highly dependent on r2.1 because the magnitude of its weighting function is always greater than that of r3.7 over the entire range of optical depths and droplet sizes, except for the cloud top. The overestimation of retrieved CDER compared with in situ CDER in a typical adiabatic cloud case is also interpreted in terms of in-cloud vertical inhomogeneity based on the 2D weighting functions and simulation results.