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At least 217 records · Page 12

Acid droplet generation in SRM exhaust clouds

A free energy analysis is applied to the co-condensation/evaporation of H2O and HCl vapors on wettable particles in open air in order to model droplet nucleation in solid rocket motor (SRM) exhaust clouds. Formulations are defined for the free energy change, the drop radius, the saturation ratio, the total number of molecules, and the mean molecular radius in solution, as well as the molecular volume and the concentration range. The free energy release in the phase transition for the AL2O3 nuclei in the SRM exhaust is examined as a function of the HCl molefraction and nucleating particle radius, based on Titan III launch exhaust cloud conditions 90 sec after ignition. The most efficient droplet growth is determined to occur at an HCl molefraction of 0.082 and a particle radius of 0.0000013 cm, i.e. a molality of 5.355.

Dingle, A. N.↗

Droplet Growth or Evaporation Does Not Buffer the Variability in Supersaturation in Clean Clouds

Abstract Water vapor supersaturation in clouds is a random variable that drives activation and growth of cloud droplets. The Pi Convection–Cloud Chamber generates a turbulent cloud with a microphysical steady state that can be varied from clean to polluted by adjusting the aerosol injection rate. The supersaturation distribution and its moments, e.g., mean and variance, are investigated for varying cloud microphysical conditions. High-speed and collocated Eulerian measurements of temperature and water vapor concentration are combined to obtain the temporally resolved supersaturation distribution. This allows quantification of the contributions of variances and covariances between water vapor and temperature. Results are consistent with expectations for a convection chamber, with strong correlation between water vapor and temperature; departures from ideal behavior can be explained as resulting from dry regions on the warm boundary, analogous to entrainment. The saturation ratio distribution is measured under conditions that show monotonic increase of liquid water content and decrease of mean droplet diameter with increasing aerosol injection rate. The change in liquid water content is proportional to the change in water vapor concentration between no-cloud and cloudy conditions. Variability in the supersaturation remains even after cloud droplets are formed, and no significant buffering is observed. Results are interpreted in terms of a cloud microphysical Damköhler number (Da), under conditions corresponding to , i.e., the slow-microphysics regime. This implies that clouds with very clean regions, such that is satisfied, will experience supersaturation fluctuations without them being buffered by cloud droplet growth. Significance Statement The saturation ratio (humidity) in clouds controls the growth rate and formation of cloud droplets. When air in a turbulent cloud mixes, the humidity varies in space and time throughout the cloud. This is important because it means cloud droplets experience different growth histories, thereby resulting in broader size distributions. It is often assumed that growth and evaporation of cloud droplets buffers out some of the humidity variations. Measuring these variations has been difficult, especially in the field. The purpose of this study is to measure the saturation ratio distribution in clouds with a range of conditions. We measure the in-cloud saturation ratio using a convection cloud chamber with clean to polluted cloud properties. We found in clouds with low concentrations of droplets that the variations in the saturation ratio are not suppressed.

54 ENVIRONMENTAL SCIENCES↗

Aerosol-Ice Formation Closure Pilot Study (AEROICSTUDY) Field Campaign Report

The aerosol-ice formation closure pilot study (AEROICESTUDY) was a field campaign conducted at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility at the Southern Great Plains (SGP) observatory from October 7 to 28, 2019. The purpose of this campaign was to test a field observational approach for conducting an aerosol-ice formation closure study. In other words, the goal was to predict the number of ice nucleating particles (INPs) from the measurements of physical and chemical aerosol properties and compare those to measured INP number concentrations. This project was motivated by the fact that the aerosol community has widely conducted aerosol radiative closure, aerosol-cloud condensation nuclei (CCN), and CCN-droplet closure studies to test the physical models and parameterizations that cloud-resolving and climate models rely on to perform reliable simulations of the Earth system and energy budget. However, very few closure studies related to INPs have been conducted, and to our knowledge, none using robust, size-resolved, ambient aerosol composition measurements as model inputs.

54 ENVIRONMENTAL SCIENCES↗

Aerosol-Ice Formation Closure Pilot Study (AEROICSTUDY) Field Campaign Report

The aerosol-ice formation closure pilot study (AEROICESTUDY) was a field campaign conducted at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility at the Southern Great Plains (SGP) observatory from October 7 to 28, 2019. The purpose of this campaign was to test a field observational approach for conducting an aerosol-ice formation closure study. In other words, the goal was to predict the number of ice nucleating particles (INPs) from the measurements of physical and chemical aerosol properties and compare those to measured INP number concentrations. This project was motivated by the fact that the aerosol community has widely conducted aerosol radiative closure, aerosol-cloud condensation nuclei (CCN), and CCN-droplet closure studies to test the physical models and parameterizations that cloud-resolving and climate models rely on to perform reliable simulations of the Earth system and energy budget. However, very few closure studies related to INPs have been conducted, and to our knowledge, none using robust, size-resolved, ambient aerosol composition measurements as model inputs.

aerosol-ice formation↗

Aerosol-Ice Formation Closure Pilot Study (AEROICESTUDY) Field Campaign Report

The aerosol-ice formation closure pilot study (AEROICESTUDY) was a field campaign conducted at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility at the Southern Great Plains (SGP) observatory from October 7 to 28, 2019. The purpose of this campaign was to test a field observational approach for conducting an aerosol-ice formation closure study. In other words, the goal was to predict the number of ice nucleating particles (INPs) from the measurements of physical and chemical aerosol properties and compare those to measured INP number concentrations. This project was motivated by the fact that the aerosol community has widely conducted aerosol radiative closure, aerosol-cloud condensation nuclei (CCN), and CCN-droplet closure studies to test the physical models and parameterizations that cloud-resolving and climate models rely on to perform reliable simulations of the Earth system and energy budget. However, very few closure studies related to INPs have been conducted, and to our knowledge, none using robust, size-resolved, ambient aerosol composition measurements as model inputs

AEROICESTUDY↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e.,pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.A spectral-bin microphysical model is very expensive from a from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Besides the initial differences in aerosol concentration, preliminary results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CCN case but has less cloud water mass aloft. Because the spectral-bin model explicitly calculates and allows for the examination of both the mass and number concentration of species in each size categor, a detailed analysis of the instantaneous size spectrum can be obtained for the two cases. It is shown that since the low CCN case produces fewer droplets, larger sized develop due to the greater condensational and collectional growth, leading to a broader size spectrum in comparison to the high CCN case.

Tao, Wei-Kuo↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitable affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distribution parameterized as spectral bin microphysics are needed to explicitly study the effect of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembel (GCE) model. The formulation for the explicit spectral-bim microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), groupel and frozen drops/hall] Each type is described by a special size distribution function containing many categories (i.e., 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep cloud systems in the west Pacific warm pool region and in the mid-latitude using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Besides the initial differences in aerosol concentration, preliminary results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CCN case but has less cloud water mass aloft. Because the spectral-bim model explicitly calculates and allows for the examination of both the mass and number concentration of cpecies in each size category, a detailed analysis of the instantaneous size spectrum can be obtained for the two cases. It is shown that since the low CCN case produces fever droplets, larger size develop due to greater condencational and collectional growth, leading to a broader size spectrum in comparison to the high CCN case.

Tao, Wei-Kuo↗

Wind Tunnel PSD and MVD Characterization Using New 1D2D Optical Array Probes

This work explores characterization of the liquid clouds using a combination of a forward scattering probe and two Optical Array Probes. Current OAP probes provide particle shape, size, and number concentration from two-dimensional shadow images. However, past studies have shown that such images are subject to distortion when outside of the focal plane. This affects the retrieval of particle size distributions, particularly in the Supercooled Large Droplet size range. In this article, the use of a Droplet Measurement Technologies Cloud Droplet Probe and two new OAPs produced by Science Engineering Associates, is examined using wind tunnel data, to assess suitability for use in a wind tunnel calibration in SLD conditions. The new OAP probes exploit a flexible and simple grey scale imaging method to eliminate some present shortcomings of commonly used OAPs, and to reduce correction factors. Spinning disk measurements were used to specify probe depth of field, and average size errors. Composite spectra covering the nominal 2-3200 µm size range were formed by crossing over from the CDP to 1D2D-X at 48 µm, and then to the 1D2D-Y at about 400 µm. A good overlap was found at the crossover points without any artificial scaling. Composite spectra adequately closed the liquid water content distribution, and provided integrated LWCs within about 35% of the hot-wire LWCs used for tunnel calibration. This discrepancy was at least partially attributed to LWC underestimation by the hot-wire at high MVD. A model of probe performance was used to show an example of expected accuracy of ideal probes subject to the same OAP distortions and using the same mitigating procedures and corrections, predicting PSD Median Volume Diameter and integrated LWC errors of less than 10%.

Aircraft Icing↗

The Association Between Cloud Droplet Number over the Summer Southern Ocean and Air Mass History

The cloud properties and governing processes in Southern Ocean marine boundary layer clouds have emerged as a central issue in understanding the Earth's climate sensitivity. While our understanding of Southern Ocean cloud feedbacks have evolved in the most recent climate model intercomparison, the background properties of simulated summertime clouds in the Southern Ocean are not consistent with measurements due to known biases in simulating cloud condensation nuclei concentrations. This paper presents several case studies collected during the Capricorn 2 and Marcus campaigns held aboard Australian research vessels in the Austral Summer of 2018. Combining the surface–observed cases with MODIS data along forward and backward air mass trajectories, we demonstrate the evolution of cloud properties with time. These cases are consistent with multi–year statistics showing that long trajectories of air masses over the Antarctic ice sheet are critical to creating high droplet number clouds in the high latitude summer Southern Ocean. We speculate that secondary aerosol production via the oxidation of biogenically derived aerosol precursor gasses over the high actinic flux region of the high latitude ice sheets is fundamental to maintaining relatively high droplet numbers in Southern Ocean clouds during Summer.

54 ENVIRONMENTAL SCIENCES↗

Comments on 'Do ultrafine cloud condensation nuclei invigorate deep convection?'

Here we elaborated on the deficiencies associated with the theoretical arguments and model simulations in Grawbowski and Morrison (2020; GM20), and showed that the concept of convective invigoration by aerosols can be supported by both accurate theoretical analysis and explicit physics modeling with prognostic aerosols and supersaturation. Above the freezing level, droplet freezing itself does not change mass loading and the latent heat release resulting from freezing leads to an increase in the buoyancy. The derivation in GM20 is erroneous because of omitting the liquid water sink term. They also ignored the effect of enhanced latent heating from the subsequent growth processes (deposition and riming) after freezing. Regarding aerosol effect on condensational growth, the quasi-steady assumption for supersaturation as adopted in GM20 is invalidated especially when droplet number concentration is low and updraft is strong from both theoretical analysis and our bin microphysics modeling results. The quasi-steady assumption makes condensation independent of droplet number and size and therefore reduces the overall aerosol effects on cloud dynamics. Studying aerosol effects on clouds particularly deep convective clouds requires the exact solution of supersaturation. Any assumption imposed to supersaturation such as saturation adjustment and quasi-steady approximation leads to incorrect aerosol effects on diffusional growth. The exact supersaturation equation clearly shows that condensation depends on droplet number and size, and more droplets in the polluted clouds increase condensation (thus lower supersaturation), leading to enhanced buoyancy and updraft speeds.

Convective invigoration, deep convective clouds, a↗

Preferrential Concentration of Particles in Protoplanetary Nebula Turbulence

Preferential concentration in turbulence is a process that causes inertial particles to cluster in regions of high strain (in-between high vorticity regions), with specifics depending on their stopping time or Stokes number. This process is thought to be of importance in various problems including cloud droplet formation and aerosol transport in the atmosphere, sprays, and also in the formation of asteroids and comets in protoplanetary nebulae. In protoplanetary nebulae, the initial accretion of primitive bodies from freely-floating particles remains a problematic subject. Traditional growth-by-sticking models encounter a formidable "meter-size barrier" [1] in turbulent nebulae. One scenario that can lead directly from independent nebula particulates to large objects, avoiding the problematic m-km size range, involves formation of dense clumps of aerodynamically selected, typically mm-size particles in protoplanetary turbulence. There is evidence that at least the ordinary chondrite parent bodies were initially composed entirely of a homogeneous mix of such particles generally known as "chondrules" [2]. Thus, while it is arcane, turbulent preferential concentration acting directly on chondrule size particles are worthy of deeper study. Here, we present the statistical determination of particle multiplier distributions from numerical simulations of particle-laden isotopic turbulence, and a cascade model for modeling turbulent concentration at lengthscales and Reynolds numbers not accessible by numerical simulations. We find that the multiplier distributions are scale dependent at the very largest scales but have scale-invariant properties under a particular variable normalization at smaller scales.

protoplanetary nebulae↗

EPCAPE-PT-LANL Measurements: Cloud Condensation Nuclei Counter

Coastal cities offer a unique environment for studying aerosol-cloud interactions and the effects of urban emissions on cloud properties. As part of the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE), the Partitioning Thrust by Los Alamos National Laboratory (EPCAPE-PT-LANL) was conducted. Our campaign focused on measuring the optical and chemical properties of aerosols and their interactions within marine stratocumulus clouds in La Jolla, California. EPCAPE-PT-LANL enhances the primary goals of EPCAPE through innovative observations of vapor-phase transitions between aerosols and cloud droplets, the impact of black carbon on aerosol-cloud dynamics, and the effects of cloud processing on aerosol optical properties. Instrument: Cloud Condensation Nuclei Counter, single column (Droplet Measurements Technology) Files: data_10sec_CCNc.csv, data_10min_CCNc.csv Header: - SuperSaturation[unitless]: The level of supersaturation, expressed as a unitless percentage, at which cloud condensation nuclei (CCN) activity is measured. - NumberConcentration[/cm3]: Number concentration of particles acting as CCN at the baseline supersaturation level, measured in particles per cubic centimeter. - NumberConcentration_SS2[/cm3]: Number concentration of particles acting as CCN at a supersaturation level of 0.2%, measured in particles per cubic centimeter. - NumberConcentration_SS4[/cm3]: Number concentration of particles acting as CCN at a supersaturation level of 0.4%, measured in particles per cubic centimeter. - QualityControl_Flag[bool]: A boolean flag indicating whether the data point passed quality control checks. - CVI_Flag[bool]: A boolean flag indicating whether the Counterflow Virtual Impactor (CVI) was active (true) or inactive (false) during the measurement.

54 ENVIRONMENTAL SCIENCES↗

Global Importance of Secondary Ice Production

Measured ice crystal number concentrations are often orders of magnitude higher than the number concentrations of ice nucleating particles, indicating the existence of secondary ice production (SIP) in clouds. Here, we present the first study to examine the global importance of SIP through the droplet shattering during freezing of rain, ice-ice collision fragmentation, and rime splintering, using a global climate model. Our results show that SIP happens quite uniformly in the two hemispheres and dominates the ice formation in the moderately cold clouds with temperatures warmer than –15°C. SIP decreases the global annual average liquid water path by –14.6 g m –2 (–22%), increases the ice water path by 8.7 g m –2 (23%), improving the model agreement with observations. SIP changes the global annual average shortwave, longwave, and net cloud forcing by 2.1, –1.0, and 1.1 W m –2 , respectively, highlighting the importance of SIP on cloud properties on the global scale.

54 ENVIRONMENTAL SCIENCES↗

High-Volume Precipitation Spectrometer (HVPS) Instrument Handbook

The high-volume precipitation spectrometer (HVPS) is a U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility instrument for measuring hydrometeors larger than 150 μm. It is an open-path instrument located on the outside of the aircraft, typically below the wing. A laser sheet throws a shadowgraph image of the hydrometeor (cloud droplets or ice crystals) in the sample volume on a photodiode array. As the hydrometeor moves through the sample volume, this optical array records the moving shape and a two-dimensional picture can be recorded. At an air speed of 100 m/s, the sample volume is 310 l/s. The recorded images can be analyzed for size distributions, number concentrations, and further cloud properties detailed below. Hydrometeors in the range of 0.3-19.2 mm can be fully recorded at a 150 μm resolution; larger particles can only be sized along the direction of flight.

54 ENVIRONMENTAL SCIENCES↗

A Model Intercomparison Study of Aerosol‐Cloud‐Turbulence Interactions in a Cloud Chamber: 1. Model Results

This study presents the first model intercomparison of aerosol‐cloud‐turbulence interactions in a controlled cloudy Rayleigh‐Bénard Convection chamber environment, utilizing the Pi Chamber at Michigan Technological University. We analyzed simulated cloud chamber‐averaged statistics of microphysics and thermodynamics in a warm‐phase, cloudy environment under steady‐state conditions at varying aerosol injection rates. Simulation results from seven distinct models (DNS, LES, and a 1D turbulence model) were compared. Our findings demonstrate that while all models qualitatively capture observed trends in droplet number concentration, mean radius, and droplet size distributions at both high and low aerosol injection rates, significant quantitative differences were observed. Notably, droplet number concentrations varied by over two orders of magnitude between models for the same injection rates, indicating sensitivities to the model treatments in droplet activation and removal and wall fluxes. Furthermore, inconsistencies in vertical relative humidity profiles and in achieving steady‐state liquid water content suggest the need for further investigation into the mechanisms driving these variations. Despite these discrepancies, the models generally reproduced consistent power‐law relationships between the microphysical variables. This model intercomparison underscores the importance of controlled cloud chamber experiments for validating and improving cloud microphysical parameterizations. Recommendations for future modeling studies are also highlighted, including constraining wall conditions and processes, investigating droplet/aerosol removal (including sidewall losses), and conducting simplified experiments to isolate specific processes contributing to model divergence and reduce model uncertainties.

54 ENVIRONMENTAL SCIENCES↗

Radar Retrieval Evaluation and Investigation of Dendritic Growth Layer Polarimetric Signatures in a Winter Storm

Abstract This study evaluates ice particle size distribution and aspect ratio φ Multi-Radar Multi-Sensor (MRMS) dual-polarization radar retrievals through a direct comparison with two legs of observational aircraft data obtained during a winter storm case from the Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) campaign. In situ cloud probes, satellite, and MRMS observations illustrate that the often-observed K dp and Z DR enhancement regions in the dendritic growth layer can either indicate a local number concentration increase of dry ice particles or the presence of ice particles mixed with a significant number of supercooled liquid droplets. Relative to in situ measurements, MRMS retrievals on average underestimated mean volume diameters by 50% and overestimated number concentrations by over 100%. IWC retrievals using Z DR and K dp within the dendritic growth layer were minimally biased relative to in situ calculations where retrievals yielded −2% median relative error for the entire aircraft leg. Incorporating φ retrievals decreased both the magnitude and spread of polarimetric retrievals below the dendritic growth layer. While φ radar retrievals suggest that observed dendritic growth layer particles were nonspherical (0.1 ≤ φ ≤ 0.2), in situ projected aspect ratios, idealized numerical simulations, and habit classifications from cloud probe images suggest that the population mean φ was generally much higher. Coordinated aircraft radar reflectivity with in situ observations suggests that the MRMS systematically underestimated reflectivity and could not resolve local peaks in mean volume diameter sizes. These results highlight the need to consider particle assumptions and radar limitations when performing retrievals. significance statement Developing snow is often detectable using weather radars. Meteorologists combine these radar measurements with mathematical equations to study how snow forms in order to determine how much snow will fall. This study evaluates current methods for estimating the total number and mass, sizes, and shapes of snowflakes from radar using images of individual snowflakes taken during two aircraft legs. Radar estimates of snowflake properties were most consistent with aircraft data inside regions with prominent radar signatures. However, radar estimates of snowflake shapes were not consistent with observed shapes estimated from the snowflake images. Although additional research is needed, these results bolster understanding of snow-growth physics and uncertainties between radar measurements and snow production that can improve future snowfall forecasting.

Meteorology & Atmospheric Sciences↗

On the Role of Airborne Ice Nucleating Particles in Primary and Secondary Ice Formation Processes in Convective Midlatitude Clouds

Abstract Formation of ice in mixed-phase clouds may proceed via primary nucleation and secondary ice production (SIP). Primary nucleation involves the presence of ice nucleating particles (INPs), while SIP follows primary nucleation, resulting in ice crystal number concentrations N ice exceeding the number of INPs. The ice formation pathways in young congestus clouds are not well understood nor are the environmental conditions favorable for the onset of SIP. Coincident airborne measurements of INPs and N ice collected during the Secondary Production of Ice in Cumulus Experiment (SPICULE) campaign over the U.S. central Great Plains are reported for young congestus clouds. Number concentrations of INPs and N ice at temperatures between −10° and −20°C were used to categorize whether SIP was active in each analyzed cloud pass. Observational data suggested that fragmentation of freezing droplets (FFDs) was occurring and the most likely SIP mechanism for ice enhancement during the early stages of the sampled clouds, where higher cloud-base temperatures and stronger updrafts produced conditions favorable for the onset of FFD. Simple model simulations of a congestus cloud were used to compare predictions of N ice from newly implemented SIP mechanisms (including FFD) alongside those from the existing Hallett–Mossop (HM) mechanism. Although predicted N ice , when all SIP mechanisms were active, was in good agreement with observations, the dominant SIP mechanism in the model was predicted to be HM. The rate of heterogeneous freezing in raindrops was likely inhibiting realistic FFD rates in the simulated cloud. These discrepancies between the observations and simulations underscore the need for extended laboratory studies to formulate improved model representations of SIP in convective clouds.

Patnaude, Ryan J. [Department of Atmospheric Scien↗

Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays

The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.

Chiu, H. H.↗