Evolution Of Droplet Size Distribution Research Articles

Evolution of Droplet Size Distributions During the Transition of an Ultraclean Stratocumulus Cloud System to Open Cell Structure: An LES Investigation Using Lagrangian Microphysics

AbstractA state‐of‐the‐art Lagrangian microphysics scheme is used in a large‐eddy simulation to investigate the stratocumulus transition from closed to open cell structure. Processes controlling precipitation development, which is a key to the transition, are analyzed by leveraging unique benefits of Lagrangian microphysics, particularly the ability to track computational drops in the flow. Sufficient time is needed for coalescence growth of cloud drops to drizzle within the updraft‐downdraft cycle of large eddies. This favors broad drop size distributions (DSDs) and drizzle growth in downdrafts, where drops are typically much older than in updrafts. During the closed cell stage, mean cloud drop radius is too small, and the DSDs are too narrow, so that the timescale for coalescence is much longer than the large eddy turnover time and drizzle growth is limited. The closed‐to‐open cell transition occurs when these timescales become comparable and the precipitation flux increases sharply.

Experimental study on the evolution of droplet size distribution during the fog life cycle

Abstract. The evolution of the droplet size distribution (DSD) during the fog life cycle remains poorly understood and progress is required to reduce the uncertainty of fog forecasts. To gain insights into the physical processes driving the microphysical properties, intensive field campaigns were conducted during the winters of 2010–2013 at the Instrumented Site for Atmospheric Remote Sensing Research (SIRTA) in a semi-urban environment southwest of Paris city center to monitor the simultaneous variations in droplet microphysical properties and their potential interactions at the different evolutionary stages of the fog events. Liquid water content (LWC), fog droplet number concentration (Nd) and effective diameter (Deff) show large variations among the 42 fog events observed during the campaign and for individual events. Our findings indicate that the variability of these parameters results from the interaction between microphysical, dynamical and radiative processes. During the formation and development phases, activation of aerosols into fog droplets and condensational growth were the dominant processes. When vertical development of radiation fog occurred under the influence of increasing wind speed and subsequent turbulent motion, additional condensational growth of fog droplets was observed. The DSDs with single mode (around 11 µm) and double mode (around 11 and 22 µm) were observed during the field campaign. During the development phase of fog with two droplet size modes, a mass transfer occurred from the smaller droplets into the larger ones through collision–coalescence or Ostwald ripening processes. During the mature phase, evaporation due to surface warming induced by infrared radiation emitted by fog was the dominant process. Additional droplet removal through sedimentation is observed during this phase for fog with two droplet size modes. Because of differences in the physical processes involved, the relationship between LWC and Nd is largely driven by the DSD. Although a positive relationship is found in most of the events due to continuous activation of aerosol into fog droplets, LWC varies at a constant Nd in fog with large Deff (>17 µm) due to additional collision–coalescence and Ostwald ripening processes. This work illustrates the need to accurately estimate the supersaturation for simulating the continuous activation of aerosols into droplets during the fog life cycle and to include advanced parameterizations of relevant microphysical processes such as collision–coalescence and Ostwald ripening processes, among others, in numerical models.

Observed and Bin Model Simulated Evolution of Drop Size Distributions in High‐Based Cumulus Congestus Over the United Arab Emirates

AbstractThis study examines microphysical processes in developing high‐based cumulus congestus over the United Arab Emirates using aircraft observations and a large‐eddy‐simulation model with bin microphysics. A notable feature of this case is the lack of mm‐sized drops despite having a liquid cloud layer km deep, contrasting with copious large drops observed in maritime tropical cumulus congestus having a similar vertical extent. Modeled drop size distributions are similar to observations at various temperatures between 9.5 and −12°C, including the lack of mm‐sized drops. Cloud dilution leads to low‐to‐moderate liquid water contents (∼0.5–1.5 g m−3) in most of the cloud core, several times smaller than adiabatic values. Dilution is enhanced in the inflowing branch of the toroidal circulations associated with individual cloud thermals, which are favored regions for secondary droplet activation (activation above cloud base). Secondary activation in general contributes substantially to the droplet population. Turning it off leads to a sharp decrease in droplet concentration and increase in mean size aloft, but does little to increase rain drop production. Warm rain generation (or lack thereof) in this case is therefore determined more by the sub‐cloud aerosol and the cloud base droplet size distribution (DSD) than DSD evolution aloft from secondary droplet activation. Decreasing the aerosol concentration by a factor of 10 greatly increases production of large drops via collision‐coalescence. Thus, despite its high base (low temperatures) and substantial dilution, the simulated cloud is thermodynamically and dynamically capable of rapidly producing copious mm‐sized drops from collision‐coalescence under pristine aerosol conditions.

Optimization of carbon dioxide dissolution in an injection tubing for geologic sequestration in aquifers

Dissolution of liquefied carbon dioxide in a turbulent tubing flow for geologic sequestration in aquifers is simulated. The problem is solved by a two-fluid approach in a three dimensional formulation. For accurate calculation of the droplet dissolution rate, an evolution of droplet size distribution along a tubing is modelled by the population balance equation accounting for droplet breakup, coalescence and interphase mass transfer. The dissolution rate in a horizontal tubing is rather slow due to gravity-induced droplet stratification. The dissolution process in a horizontal tubing is compared with that in a coiled tubing wound on a horizontal reel. In a coiled tubing flow, droplet stratification significantly decreases due to the gravity force causing periodical motion of droplets across the tubing. At relatively high flow velocities, CO2 droplets are well-dispersed even across a horizontal tubing. Droplet dissolution is rather fast in this case, and a notable difference in the dissolution rates in straight and coiled tubing is not observed. An effect of the flow rate on the dissolution process at different tubing diameters is illustrated. Thus, numerical studies show that a coiled tubing can be efficiently used for intensification of liquefied carbon dioxide dissolution for relatively low and moderate flow rates. • Dissolution of CO 2 droplets in a tubing flow in 3-D formulation is modelled. • Dissolution rate in horizontal tubing flow is low due to droplet stratification. • Using coiled tubing wound on a reel strongly enhances dissolution rate. • 3-D simulations allow optimal selection of coiled tubing parameters.

Development of Coalescence and Capture Kernels for the Electrocoalescence Process Based on Batch Experiments

An experimental and theoretical study was performed to analyze the evolution of droplet size distribution and phase separation in water-in-oil emulsions under the effect of the electric field in a batch vessel. The effects of electrostatic time, initial water content, and electrical potential on the efficiency of separation were studied in the experiments. Moreover, a mathematical model based on population, mass and momentum balance equations for disperse, oil and free phases was developed to interpret the experimental data. A coalescence kernel was proposed to predict the aggregation of droplets. Furthermore, a capture term was added to the balance equations to address the creation of free water. The parameters of the coalescence and capture models were estimated using the experimental data. The estimation of the parameters was done using parallel execution of the particle swarm optimization algorithm. The results of the simulation showed a decent performance of the model in predicting the profiles of dr...

Spray dynamics simulations for pulsatile injection at different ambient pressure and temperature conditions

A numerical study on the transient characteristics of a pulsatile, iso-octane spray issuing from a pressure-swirl atomizer is presented. The effects of system pressure and temperature, as well as the initial fuel temperature on spray dispersion and evaporation, are highlighted. The computations were carried out using ANSYS FLUENT-15.0, assuming the spray dispersion to be axisymmetric. Gas phase turbulence is simulated using the renormalized group k- ε model, while the discrete phase model is used for tracking fuel droplets. The linear instability sheet atomization model is adopted for the primary breakup of the liquid sheet, and the Taylor Analogy Breakup and Wave Breakup models are adopted for the secondary breakup, depending upon the operating conditions. The drag force on the droplet is evaluated, after incorporating the effects of evaporation and neighbouring droplets, along with droplet shape distortion. The significance of droplet collision on the evolution of droplet size distribution is examined. The local mean drop sizes and spray penetration length are in agreement with the experimental results of the literature. The predicted results indicate that the spray is narrower and penetrates less at higher ambient pressure. In this respect, the additional force on droplets due to local static pressure gradient is examined in detail. The effect of ambient conditions on the spray evaporation process is studied based on the spatio-temporal evolution of the equivalence ratio of the mixture of fuel vapour and air.

Olive oil droplet coalescence during malaxation

Coalescence of olive oil droplets during malaxation is a crucial phenomenon since it is responsible for the effective oil separation in the following processing steps. Yet it has been scarcely examined. The aim of this work was to study in detail the evolution of droplet size distribution during malaxation in actual processing conditions. For that reason experiments took place in an industrial scale olive oil extraction plant. The effect of malaxation time and the effect of water dilution on the droplet size distribution were examined. The results depict the progressive olive oil droplet coalescence and show a clear effect of water dilution on the rate of coalescence. The higher coalescence rate in the diluted paste was attributed to the decrease in viscosity. Finally it was shown that separation of the diluted paste in a two-phase decanter resulted into smaller droplet sizes (and therefore lower oil content) remaining in the paste.

Theoretical Analysis of the Entrainment–Mixing Process at Cloud Boundaries. Part I: Droplet Size Distributions and Humidity within the Interface Zone

Abstract The problem of a complex entrainment–mixing process is analyzed by solving a diffusion–evaporation equation for an open region in the vicinity of the cloud–dry air interface. Upon normalization the problem is reduced to a one-parametric one, the governing parameter being the potential evaporation parameter R proportional to the ratio of saturation deficit in the dry air to the available liquid water content in the cloud air. As distinct from previous multiple studies analyzing mixing within closed adiabatic volumes, we consider a principally nonstationary problem that never leads to a homogeneous equilibrium state. It is shown that at R < −1 the cloud edge shifts toward the cloud; that is, the cloud dissipates due to mixing with dry air, and the cloud volume decreases. If R > −1, the cloud edge shifts outside; that is, the mixing leads to an increase in the cloud volume. The time evolution of droplet size distribution and its moments, as well as the relative humidity within the expanding cloud–dry air interface, are calculated and analyzed. It is shown that the values of the mean volume radii rapidly decrease within the interface zone in the direction away from the cloud, indicating significant changes in the cloud edge microstructure. Scattering diagrams plotted for the cloud edge agree well with high-frequency in situ measurements, corroborating the reliability of the proposed approach. It is shown that the humidity front moves toward dry air faster than the front of liquid water content. As a result, the mixing leads to formation of a humid air shell around the cloud. The widths of the interface zone and humid shell are evaluated.

Theoretical analysis of mixing in liquid clouds – Part IV: DSD evolution and mixing diagrams

Abstract. Evolution of droplet size distribution (DSD) due to mixing between cloudy and dry volumes is investigated for different values of the cloud fraction and for different initial DSD shapes. The analysis is performed using a diffusion–evaporation model which describes time-dependent processes of turbulent diffusion and droplet evaporation within a mixing volume. Time evolution of the DSD characteristics such as droplet concentration, LWC and mean volume radii is analyzed. The mixing diagrams are plotted for the final mixing stages. It is shown that the difference between the mixing diagrams for homogeneous and inhomogeneous mixing is insignificant and decreases with an increase in the DSD width. The dependencies of the normalized cube of the mean volume radius on the cloud fraction were compared with those on normalized droplet concentration and found to be quite different. If the normalized droplet concentration is used, mixing diagrams do not show any significant dependence on relative humidity in the dry volume. The main conclusion of the study is that traditional mixing diagrams cannot serve as a reliable tool for analysis of mixing type.

Modeling droplet dispersion in a vertical turbulent tubing flow

Usually, during oil production, water and oil flow simultaneously in the wellbore. When water holdup in the borehole is small, water droplets may be dispersed into bulk oil making water breakthrough detection a challenging task. In this paper, a comprehensive engineering model of droplet dispersion is presented.Dispersion of droplets in a long vertical turbulent tubing flow is modeled by an Advection-Diffusion-Population Balance equation. The Prandtl Mixing-Length model of turbulence is used to describe the velocity profile across a tubing. The turbulence energy dissipation rate distribution across a pipe is calculated by an analytical equation. The fixed pivot method is employed for calculation of the population balance term of the governing equation. Droplet fragmentation is modeled using a recently developed droplet breakup model (Eskin et al., 2017). It is assumed that volume concentration of a dispersed phase does not exceed 10%. A computational code developed allows tracking evolution of droplet size distribution along a tubing. Model performance is illustrated by computations of the water in oil dispersion process. Effects of oil/water interfacial tension, well production rate and oil viscosity on dispersion are demonstrated.

Investigation of droplet breakup in liquid–liquid dispersions by CFD–PBM simulations: The influence of the surfactant type

Abstract The accurate prediction of the droplet size distribution (DSD) in liquid–liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population balance model. When a surfactant is included in liquid–liquid dispersions, the droplet breakup behavior will change as an effect of the reduction of the interfacial tension. Moreover, also the dynamic interfacial tension may be different with respect to the static, due to the fact that the surfactant may be easily desorbed from the droplet surface, generating additional disruptive stresses. In this work, the performance of five breakup kernels from the literature is assessed, to investigate their ability to predict the time evolution of the DSD and of the mean Sauter diameter, when different surfactants are employed. Simulations are performed with the Quadrature Method of Moments for the solution of the population balance model coupled with the two-fluid model implemented in the compressibleTwoPhaseEulerFoam solver of the open-source computational fluid dynamics (CFD) code OpenFOAM v. 2.2.x. The time evolution of the mean Sauter diameter predicted by these kernels is validated against experimental data for six test cases referring to a stirred tank with different types of surfactants (Tween 20 and PVA 88%) at different concentrations operating under different stirrer rates. Our results show that for the dispersion containing Tween 20 additional stress is generated, the multifractal breakup kernel properly predicts the DSD evolution, whereas two other kernels predict too fast breakup of droplets covered by adsorbed PVA. Kernels derived originally for bubbles completely fail.

Oil slicks on water surface: Breakup, coalescence, and droplet formation under breaking waves

The ability to calculate the oil droplet size distribution (DSD) and its dynamic behavior in the water column is important in oil spill modeling. Breaking waves disperse oil from a surface slick into the water column as droplets of varying sizes. Oil droplets undergo further breakup and coalescence in the water column due to the turbulence. Available models simulate oil DSD based on empirical/equilibrium equations. However, the oil DSD evolution due to subsequent droplet breakup and coalescence in the water column can be best represented by a dynamic population model. This paper develops a phenomenological model to calculate the oil DSD in wave breaking conditions and ocean turbulence and is based on droplet breakup and coalescence. Its results are compared with data from laboratory experiments that include different oil types, different weathering times, and different breaking wave heights. The model comparisons showed a good agreement with experimental data.

Numerical simulation of water spray in natural draft dry cooling towers with a new nozzle representation approach

Pre-cooling of inlet air with water spray is proposed for performance enhancement of natural draft dry cooling towers (NDDCTs) during high ambient temperature periods. Previous experiments showed promising results on cooling enhancement using spray cooling. In this study, a numerical Eulerian–Lagrangian 3-D model is used to simulate evaporating water sprays produced by real nozzles. A new adaptable method of hollow-cone spray representation in Eulerian–Lagrangian numerical models was developed to reproduce the real nozzle behaviour using experimentally measured initial spray characteristics and taking into account radial evolution of droplet size distribution and air/droplets momentum exchange. Experimental measurements from a wind tunnel test rig simulating NDDCTs inlet flow conditions have been performed for validation. Overall, a good agreement was obtained between numerical predictions and experimental measurements for the streamwise development of droplet size and velocity, and outlet air dry bulb temperature. An average deviation below 5.3% was achieved for all compared parameters. Moreover, the validated CFD model has provided insight into the experimental observations of local droplet velocity increase and higher air cooling in the lower region.

Effective rates of coalescence in oil–water dispersions under constant shear

We report destabilization of highly stable oil–water emulsion under shear. Prior studies on shear induced coalescence are restricted to lower volume fraction (up to 20%) of dispersed phase. In this contribution, the effect of shear induced coalescence in a larger range of volume fractions of dispersed phase, and shear rates, is presented. The experimental ranges have practical relevance in the context of industrial coalescers which exploit low shear to coalesce oil–water emulsions. For our work, a synthetic emulsion mimicking the properties of medium-heavy crude is subjected to simple shear. In summary, the studies reveal the effect of shear rate, volume fraction of dispersed phase and viscosity ratio on the evolving drop size distributions of oil phase. For low shear rates and volume fractions, the evolving drop size distributions show a bimodal distribution, while a multimodal nature of drop size population was observed for higher dispersed phase volume fraction (40%), something which has never been reported thus far. Finally, a population balance model employing diameter based coalescence kernel is used to rationalize the time evolution of droplet size distributions.

An algorithm for the numerical solution of the multivariate master equation for stochastic coalescence

Abstract. In cloud modeling studies, the time evolution of droplet size distributions due to collision–coalescence events is usually modeled with the Smoluchowski coagulation equation, also known as the kinetic collection equation (KCE). However, the KCE is a deterministic equation with no stochastic fluctuations or correlations. Therefore, the full stochastic description of cloud droplet growth in a coalescing system must be obtained from the solution of the multivariate master equation, which models the evolution of the state vector for the number of droplets of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain types of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels, multivariate initial conditions and small system sizes is introduced. The performance of the method was seen by comparing the numerically calculated particle mass spectrum with analytical solutions of the master equation obtained for the constant and sum kernels. Correlation coefficients were calculated for the turbulent hydrodynamic kernel, and true stochastic averages were compared with numerical solutions of the kinetic collection equation for that case. The results for collection kernels depending on droplet mass demonstrates that the magnitudes of correlations are significant and must be taken into account when modeling the evolution of a finite volume coalescing system.

Supersaturation and diffusional droplet growth in liquid clouds: Polydisperse spectra

AbstractEvolution of droplet size distribution (DSD) due to the water vapor diffusion in a vertically moving adiabatic parcels is investigated. Analytical expressions for height dependences of the main DSD parameters and DSD moments are obtained. The asymptotic behavior of the DSD parameters at large heights above cloud base is determined. It is shown that during diffusion growth, the width and the relative dispersion of the DSD decrease with height as z− 1/3 and z− 2/3, respectively. The paper presents examples of DSD evolution in cases DSD forms on aerosols with a three‐mode lognormal distribution. The aerosol distribution parameters used in the study correspond to four aerosol types: “Marine,” “Clean continental,” “Background,” and extremely polluted “Urban.” The vertical profiles of DSD parameters are compared with the asymptotic profiles. It is shown that in case of polydisperse DSD evolution, the vertical profile of supersaturation within several hundred meters above the cloud base can be approximated by a supersaturation profile corresponding to the “equivalent” monodisperse DSD. The initial radius of this equivalent DSD is equal to the mean radius of polydisperse DSD (haze size distribution) at cloud base, which is estimated using the Kohler theory. This result of the relation between the polydisperse and monodisperse solutions is universal. A new equation for estimation of supersaturation maximum for polydisperse case is obtained. The obtained analytical expressions and numerical results are useful for understanding the mechanisms of DSD formation in clouds and for parameterization of warm microphysical processes in cloud models.

The development of polyurethane modified bitumen emulsions for cold mix applications

Bitumen emulsions stand for an alternative paving practice to the traditional hot-mix asphalts. In addition, modified bitumen emulsions show a better performance than unmodified ones. This work studies the feasibility of obtaining polyurethane modified bitumen emulsions, in which an isocyanate-functionalized polyol constitutes the bitumen modifier (in varying concentration from 1 to 4 wt%). Storage stability and high in-service performance are evaluated by means of evolution of droplet size distribution (DSD) and rheology tests, respectively. Regarding the emulsion stability, the key factor seems to be the bitumen modifier concentration used to prepare the modified emulsions. Thus, for a selected 50 wt% bitumen fraction, there is a limit concentration (between 1 and 2 wt%) above which the emulsion becomes unstable under storage. Hence, this result limits the modifier content that can be used in the emulsion and the final level of modification achieved if compared to the original non-modified emulsion. On the other hand, the rheological characterization conducted on the emulsion residues at 60 °C has shown an improved resistance to deformation. In terms of applicability, polyurethane modified bitumens allows for the obtaining of modified emulsions which can be prepared at much lower temperatures than those derived from other polymers.

Droplet breakage and coalescence models for the flow of water-in-oil emulsions through a valve-like element

An experimental and theoretical study was carried out regarding the evolution of droplet size distributions for the flow of water in oil emulsions through a valve-like element that simulates a mixing valve. The water droplets had diameters in the 0.1–100μm range, which includes droplets that are either smaller or larger than the Kolmogorov length scale for the experimental conditions. Droplet breakage and coalescence models that can be used for this size range were proposed. A simplified population balance model was developed to interpret the experimental data and solved by the method of classes. The model parameters were estimated by the orthogonal distance regression method. The simplifying assumption of the model was verified by global optimization using a parallel implementation of the particle swarm optimization method. The agreement between simulated and experimental droplet volume size distributions was good. The predictions of the DeBroukere mean diameter, d43, were unbiased with mean errors of 8%.

Evolution of droplet size distribution and composition in miniemulsions

ABSTRACTA fundamental understanding of the formation, degradation and polymerization of miniemulsions has been hindered by difficulties in quantifying their monomer droplet size distribution (DSD). In this work, particle sizing techniques including capillary hydrodynamic fractionation, acoustic attenuation spectroscopy, surfactant titration, and microscopy were adapted to characterize miniemulsion DSDs. The key ingredient in miniemulsions is the costabilizer, a low water solubility compound that limits monomer diffusion from the smaller to larger droplets (Ostwald ripening). The DSD evolution of styrene miniemulsions employing hexadecane (HD) as costabilizer was characterized. With less costabilizer, droplets were initially smaller, but increased in average size with time, and their DSDs broadened. These changes were slowed with addition of extra surfactant after homogenization. After several days, the average droplet size increased to about 150 nm regardless of the amount of HD or surfactant used. The HD content of separated portions of centrifuged miniemulsions was measured and showed significant Ostwald ripening within minutes after preparation. The further evolution of the DSD is attributed primarily to droplet coalescence. Less composition change occurred with either higher HD content or post‐homogenization surfactant addition, both of which led to minimization of free energy, increasing stability. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014, 52, 1529–1544

Transient characteristics of initial droplet size distribution and effect of pressure on evolution of transient condensation on low thermal conductivity surface

The droplet size distribution evolution in the initial dropwise condensation process from formation of primary droplets to fully developed stage has been investigated by utilizing high speed camera and microscope. Focus was put on the transient characteristics of droplet size distribution in this duration, it has been revealed that the primary droplets just formed on the condensing surface satisfied Lognormal distribution, with coalescing among them (without departing from condensing surface), bimodal size distribution formed, finally the classical exponential size distribution showed on the condensing surface when the condensation became steady state. At the same time, the effect of steam pressure on the evolution of transient dropwise condensation on low thermal conductivity surface has been analyzed. All the investigations included in the present paper are for the first droplets cycle of dropwise condensation.