Drop Size Data Research Articles

Stratiform Precipitation Processes in Cyclones Passing over a Coastal Mountain Range

Abstract The Olympic Mountains Experiment (OLYMPEX) documented precipitation and drop size distributions (DSDs) in landfalling midlatitude cyclones with gauges and disdrometers located at various distances from the coast and at different elevations on the windward side of the mountain range. Statistics of the drop size and gauge data for the season and case study analysis of a high-rainfall-producing storm of the atmospheric river type show that DSDs during stratiform raining periods exhibit considerable variability in regions of complex terrain. Seasonal statistics show that different relative proportions of drop sizes are present, depending on synoptic and mesoscale conditions, which vary within a single storm. The most frequent DSD regime contains modest concentrations of both small and large drops with synoptic factors near their climatological norms and moderate precipitation enhancement on the lower windward slopes. The heaviest rains are the most strongly enhanced on the lower slope and have DSDs marked by large concentrations of small to medium drops and varying concentrations of large drops. During the heavy-rain period of the case examined here, the low-level flow was onshore and entirely up terrain, the melting level was ~2.5 km, and stability moist neutral so that large amounts of small raindrops were produced. At the same time, melting ice particles produced at upper levels contributed varying amounts of large drops to the DSD, depending on the subsynoptic variability of the storm structure. When the low-level flow is directed downslope and offshore, small-drop production at low altitudes is reduced or eliminated.

Studies of Drop Behavior and Prediction of Sauter Mean Drop Diameter in Various Rotary Agitated Extraction Columns

Knowledge of droplet behavior is one of the most important criteria for determination of mass transfer kinetics for choosing the type of liquid-liquid extraction columns. Mean drop size data of dispersed phase droplets in continuous phase have been obtained for Various Rotary Agitated Liquid-Liquid Extraction Columns . The effects of operational variables such as mass transfer directions with acetone transfer, rotor speed and dispersed and continuous phase velocities have been investigated. The Satuer mean drop diameter was influenced mainly by mass transfer direction and agitation speed. In this research work, previous experimental works in agitated extraction columns (RDC, ARDC, PRDC, Scheibel, Oldshue-Rushton and Kuhni columns) are reviewed. Calculations with the literature correlations cannot predict experimental data, thus unified correlations considering the physical properties, operating conditions and geometric parameters were provided to predict the mean drop size (d32). The results of the proposed correlation were compared with the experimental data obtained from the literature and the present investigation. This correlation covers several physical systems for various rotary agitated extractors. Findings of this study demonstrated that the proposed correlation leads to an accurate prediction for the Satuer mean drop diameter in rotary extraction columns.

Spray absorption of CO2 into monoethanolamine: Mass transfer coefficients, dropsize, and planar surface area

Spray columns show potential to absorb CO2 into aqueous amine solvents such as monoethanolamine (MEA). Low gas phase pressure drop, less susceptibility to corrosion due to the absence of internals, and greater tolerance to use of precipitating solvents, are some of the favorable attributes associated with spray columns. At present, there is a need for robust spray absorption data with the CO2-MEA system. Experimental dropsize measurements with MEA as the test solvent have never been reported. Measurement of dropsize distributions can help ascertain the surface area available for absorption. In this spray study, absorption rates in terms of overall mass transfer coefficients, drop size data, and planar surface area for the CO2-MEA system, quantified in a 0.2m ID, lab-scale column are presented. The dropsize measurements are made with a Phase Doppler Interferometry (PDI) system. The effects of liquid rate, inlet loading, MEA concentration, and gas–liquid contact height on the performance of a full-cone nozzle are elucidated. Results from the study show an increase in mass transfer coefficients with MEA concentration and liquid rate. The mass transfer data, dropsize data and surface area quantification indicate that the free MEA content dominates spray absorption. The data also indicate the occurrence of a great degree of mass transfer in the region immediate downstream of the nozzle tip. The study provides fundamental insight into spray absorption phenomena and can aid in more robust, application specific design of spray columns.

Geographic Variation of USLE/RUSLE Erosivity and Erodibility Factors

There is a great reliance on the Universal Soil Loss Equation (USLE) and the Revised Universal Soil Loss Equation (RUSLE) to predict long-term rainfall erosion in relation to land management in both the United States and the rest of the world. In the USLE/RUSLE modeling approach, geographic variations in soil loss associated with climate and soil are taken into account through variations in the rainfall-runoff erosivity factor (R) and the soil erodibility factor (K) and equations developed in the United States to predict the values for these factors are often used outside the United States without validation in the area that they are applied. Data on rainfall kinetic energy required to calculate the event erosivity index, EI30, are seldom directly available and consequently, EI30 values are often calculated using rainfall intensity-kinetic energy relationships that may produce erroneous results because the rainforming systems at a location differ to a great extent from those occurring at the location where the drop-size data were obtained. Also, failure to consider runoff as an independent factor in producing rainfall erosion in the USLE/RUSLE leads to spatial variations in K that cannot be determined simply from measured soil properties. Erosivity indices that include runoff as a factor may lead to soil erodibility factors that are better related to measured soil properties but that potential has yet be realized. Meanwhile, models like RUSLE2 take account of the runoff effect on soil loss through temporal variations in K that are empirically related to rainfall and temperature in the United States but the method is untested elsewhere. The modeling approaches adopted USLE/RUSLE and RUSLE2 are extremely useful in determining soil loss for land management purposes despite any real or perceived lack of ability to predict event soil loss accurately.

Liquid Jets in Subsonic Air Crossflow at Elevated Pressure

The breakup, penetration, droplet size, and size distribution of a Jet A-1 fuel in air crossflow has been investigated with focus given to the impact of surrounding air pressure. Data have been collected by particle Doppler phased analyzer (PDPA), Mie-scattering with high speed photography augmented by laser sheet, and Mie-scattering with intensified charge-coupled device (ICCD) camera augmented by nanopulse lamp. Nozzle orifice diameter, do, was 0.508 mm and nozzle orifice length to diameter ratio, lo/do, was 5.5. Air crossflow velocities ranged from 29.57 to 137.15 m/s, air pressures from 2.07 to 9.65 bar, and temperature held constant at 294.26 K. Fuel flow provides a range of fuel/air momentum flux ratio (q) from 5 to 25 and Weber number from 250 to 1000. From the results, adjusted correlation of the mean drop size has been proposed using drop size data measured by PDPA as follows: (D0/D32)=0.267Wea0.44q0.08(ρl/ρa)0.30(μl/μa)-0.16. This correlation agrees well and shows roles of aerodynamic Weber number, Wea, momentum flux ratio, q, and density ratio, ρl/ρa. Change of the breakup regime map with respect to surrounding air pressure has been observed and revealed that the boundary between each breakup modes can be predicted by a transformed correlation obtained from above correlation. In addition, the spray trajectory for the maximum Mie-scattering intensity at each axial location downstream of injector is extracted from averaged Mie-scattering images. From these results, correlations with the relevant parameters including q, x/do, density ratio, viscosity ratio, and Weber number are made over a range of conditions. According to spray trajectory at the maximum Mie-scattering intensity, the effect of surrounding air pressure becomes more important in the farfield. On the other hand, effect of aerodynamic Weber number is more important in the nearfield.

Spatially resolved characteristics of pharmaceutical sprays

AbstractSpatially resolved drop size, velocity, and volume flux data for five different spray coating guns were described in this study. Such spatially resolved measurements show how sprays respond to changes in operating conditions and gun design in ways that less complete measurements can not provide. Data for instance, allow us to recognize the unique drop size distribution of one of the sprays tested, which ultimately was an important factor in determining the dual roles of the shaping air flows: depending on drop size, viscosity, and the magnitude of the shaping air velocity, the shaping air can either pinch or induce secondary atomization to the sprays. When the former outweighs the latter, a dumbbell‐shaped spray develops; a more uniform spray results when the opposite occurs. Volume flux data from the different sprays also suggest that a more robust and consistent tablet coating process can likely be designed by utilizing multiple overlapping round sprays. © 2011 American Institute of Chemical Engineers AIChE J, 2012

Inter-phase mass transfer in turbulent liquid-liquid dispersions: A comparative analysis of models

A comparative evaluation of eight models used to predict the dispersed phase mass transfer coefficient was undertaken using recent drop size and mass transfer data obtained under well known and controlled hydrodynamic conditions encountered in screen-type static mixers. A wide range of experimental conditions were covered ( ɛ = 1.5–117 W/kg, ϕ = 0.1–0.47) thereby allowing for proper assessment of the strength and weaknesses of each model. All models failed to properly predict the experimental results over a wide range of design and operating conditions with the exception of those that contain a system-specific adjustable fitting parameter. Although these models yielded reasonably acceptable order-of-magnitude predictions, they could not accurately account for the variations in the different parameters investigated. This shows that proper understanding of the various factors affecting the dispersed phase mass transfer coefficient is still incomplete and highlights the need for phenomenological models that can account for the various physicochemical and hydrodynamic conditions on the dispersed-phase mass transfer coefficient.

Rotor–stator devices: The role of shear and the stator

High shear rotor–stator mixers are widely used in process industries including the manufacture of many food, cosmetic, pharmaceutical, and health care products. Many of these products involve emulsification where the drop size distribution affects the processing and the product properties. Therefore, an understanding of the mechanisms that breaks the drops is key for any design process. In rotor–stator devices there are two main mechanisms that can break drops, one due to the rotor and one due to the stator. For the inviscid systems studied, this article shows that when a rotor–stator device is used in a recycle loop the effective equilibrium drop size is largely unaffected by the presence of the stator and is mainly dependant on the rotor. The article also goes on to show that the effective equilibrium drop size data can be correlated on the agitator shear rate.

Truncated Gamma Drop Size Distribution Models for Rain Attenuation in Singapore

A model that is less sensitive to errors in the extreme small and large drop diameters, the gamma model with central moments (3, 4 and 6), is proposed to model the rain drop size distribution of Singapore. This is because, the rain rate estimated using measured drop size distribution shows that the contributions of lower drop diameters are small as compared to the central drop diameters. This is expected since the sensitivity of the Joss distrometer degrades for small drop diameters. The lower drop diameters are therefore removed from the drop size data and the gamma model is redesigned for its moments. The effects of the removal of a particular rain drop size diameter on the specific rain attenuation (in dB) and the slant-path rain attenuation calculations with forward scattering coefficients for vertical polarization are analyzed at Ku-band, Ka-band and Q-band frequencies. It is concluded that the sensitivity of the Joss distrometer although affects the rain rate estimation at low rain rates, does not affect the slant path rain attenuation on microwave links. Therefore, the small drop diameters can be ignored completely for slant path rain attenuation calculations in the tropical region of Singapore.

A study of drop breakage in lean dispersions using the inverse-problem method

The inverse-problem approach has been applied to new experimental drop-size data in order to make direct estimations of breakage rates and fragment distributions in lean dispersions of moderately-viscous droplets. Evolving size distributions were measured over extended periods in three vessels of different scale with agitation conditions encompassing a range of average energy dissipation rates from 0.2 to 1.5 W/kg. The silicone oils used as the dispersed phase ranged in viscosity from 50 to 500 mPa s. Measured distributions were first tested for self-similarity which, if confirmed, allows the droplet breakage rates to be determined to within a constant factor. The novelty of the current work is centred upon the use of two dissimilar inversion methods ( Sathyagal et al., 1996, Kostoglou and Karabelas, 2001) to provide both the daughter-drop size distributions and the final breakage rates across the full range of experimental conditions. The objective here was to ensure that the inversion process, which is known to be ill-conditioned, produced consistent results that are independent of the procedure employed. Both methods yielded near-identical results for the breakage kernel function with fragment numbers ranging from as many as six in the early stages of the agitation period to two for the smallest surviving parent drops. The inhomogeneous breakage kernels were found to be well-represented by the generalised functions proposed by Diemer and Olson (2002); the function parameters indicated a breakage process tending towards erosion. Droplet breakage rates showed a significant dependence upon vessel size and energy dissipation rate with the influence of dispersed-phase viscosity being particularly marked. The consistency of the results was tested by solving the population balance equations for pure breakage with the experimental breakage rate and kernel function being used to reconstruct the size distributions at chosen times. These realisations of the evolving distribution were found to be in close agreement with the experimental measurements.

SHAPE SLOPE PARAMETER DISTRIBUTION MODELLING OF ELECTROMAGNETIC SCATTERING BY RAIN DROPS

Gamma model parameters using 2nd, 3rd and 4th moments are calculated from the drop size data of Singapore. The gamma model is simplifled into two parameter model by flnding a relation between the shape and slope parameters, and ⁄. Due to the poor correlation found between and ⁄, the drop size data is flltered based on their rain rates before a good correlation between the two parameters can be found. The -⁄ relations are then fltted for the difierent ranges of rain rate flltering. Scatter plots of and ⁄ are plotted with constant median volume diameter (D0) lines. The -⁄ relations for the difierent rain types for the tropical island of Singapore are proposed and compared with the -⁄ relations from three other countries of difierent climatic zones. T-Matrix calculations are performed to flnd the polarimetric variables at S-band by using the gamma DSD calculated from the Singapore's drop size data. The calculated difierential re∞ectivity and horizontal re∞ectivity are used along with the best -⁄ relations to flnd the gamma model parameters. The retrieved rain rate using polarimetric variables is compared with the distrometer's measured rain rate. Results show a good agreement between the retrieved rain rate and the measured rain rate. Therefore, the proposed shape slope relationship is found to be suitable for rain rate retrieval.

Laser Precipitation Monitor for Measurement of Drop Size and Velocity of Moving Spray-Plate Sprinklers

Sprinkler drop size distribution and associated drop velocities have a major influence on sprinkler performance in regards to kinetic energy transferred to the soil surface. A laser instrument commercially marketed for real-time rainfall measurements as a Laser Precipitation Monitor (LPM) was used to measure drop size and velocity from 10 moving spray-plate type sprinklers. Measured drop size and velocity were used to determine sprinkler drop size distribution and kinetic energy applied to the soil by sprinkler discharge. Drop size distributions measured by the LPM were compared to drop size distributions measured in earlier studies using the traditional flour pellet method. Eight of the ten measured drop size distributions were not significantly different between measurement methods. However, the operating conditions when the two methods did not compare well were outside sprinkler manufacturer specifications. Based on this limited study, the results from the two drop size measurement methods can be vastly different for sprinklers under operating conditions that produce relatively compact streams of water drops; which method is more accurate for this condition remains unknown. Kinetic energy values calculated using measured drop size and velocity data were not significantly different from values determined using flour pellet drop size data and a ballistic model for estimating sprinkler droplet tangential velocity. The laser instrument used in this study provided a relatively easy means to obtain reliable estimates of sprinkler kinetic energy per unit volume of applied water for various moving spray-plate sprinkler types and operating conditions. Measured drop size distribution and computed kinetic energy applied by sprinkler discharge is sufficient for practical field application purposes.

ANALYSIS OF A TWO-FLUID SPRAYER AND ITS USE TO DEVELOP THE NUMBER SIZE DISTRIBUTION MOMENTS SPRAY MODEL, PART II: COMPUTATIONAL ANALYSIS

This study presents the development of a new spray model that captures the full polydisperse nature of spray flow without using drop size classes. In this model, the size information concerning the spray is obtained by calculating three moments of the drop size distribution function from transport equations and one moment from a Gamma distribution function. The method reduces the need to presume a particular distribution function for the drop sizes and the complexity of the solution scheme. Drop size data obtained from the examination of the structures of a free spray using a laser-diffraction-based drop analyzer were used to further develop the new spray model and determine its ability to accurately predict such sprays. Test results include the axial distributions of the radial-averaged drop sizes and the local drop distribution at axial positions, and indicate that the drop size distribution is dependent on the atomizing air pressure of the injector and the position of the drop from the injector nozzle. At higher pressure cases the distributions were observed to be bimodal. These trends are captured by the computational results and compare well with those from another moments spray model.

Effervescent Atomization of Viscoelastic Liquids: Experiment and Modeling

The effervescent atomization of viscoelastic liquids is reported. A total of 23 fluids, formulated from a 60wt% glycerine/40wt% water solvent to which were added varying concentrations (0.001–0.5wt%) of poly(ethylene oxide) polymers whose molecular weights ranged from 12,000 to 900,000, were sprayed through a conventional effervescent atomizer. Mean drop sizes were measured using a forward light scattering instrument. The drop size (D32) data show the expected decrease with an increase in air-liquid ratio by mass (ALR), the expected increase with an increase in polymer concentration, plus an increase with an increase in polymer molecular weight for most cases. However, no significant change in D32 was observed for polymer solutions whose molecular weights ranged from 12,000 to 35,000, suggesting the presence of a critical molecular weight below which spray performance is unaltered. This argues for two different factors controlling drop size: Polymer molecular weight is most influential at the highest polymer concentrations while polymer concentration is most influential at the lowest polymer concentrations. Analysis of the spray formation process was carried out using a ligament formation model previously developed for the effervescent atomization of Newtonian liquids coupled with a linear stability model for the breakup of viscoelastic liquid jets. The jet breakup model assumes that an unrelaxed axial tension exists within the fluid. A comparison of model predictions and experimental data indicates that the model predicts the observed dependencies of mean drop size on ALR, polymer concentration, and polymer molecular weight. Quantitative agreement is within 10–50% of experimental values in all cases. Finally, a shortcoming of the model is noted and a means of avoiding this limitation reported.

Evaluation of drop size distribution from chord length measurements

AbstractThe relationship between the chord length distribution (CLD) obtained by a point sensor and the drop size distribution (DSD) in a liquid‐liquid dispersion is investigated. Based on analysis of the frequency of drop‐cuttings by the sensor, a physical model is built to derive the probability density function of chord lengths for a given DSD, and vice versa. The effect of biased sampling towards larger drops relevant to point sensors, which is often ignored by investigators, is included in this relationship. A new algorithm is introduced to solve the problem of noisy or even negative DSD values by adding smoothing equations while performing the backward conversion. The effects of parameters, such as the number of drop size groups used, the noise level, and the smoothing factor value, on the backward transform are further studied. Both forward and backward transforms are shown to be in good agreement with ideal data when using continuous (e.g., log‐normal, uniform) distributions and with data obtained from Monte‐Carlo simulations. Good agreement is also found between the DSD obtained from chord length measurements and drop size data determined by direct observation. © 2005 American Institute of Chemical Engineers AIChE J, 2006

ELECTROSTATIC EFFECTS ON AGRICULTURAL AIR-ATOMIZED SPRAYS AND DEPOSITION. PART II: A COMPUTATIONAL STUDY

This article reports on a computational investigation of inductively charged sprays used in crop spraying. The charged sprays are produced using an air-atomizing induction-charging nozzle. In complementary research, the spray structures are experimentally characterized based on drop size and velocity data obtained using laser-based techniques, both in the free spray and in the near-target vicinity. The experimental deposition study used spectrophotometry analysis to quantify the drop residue on a grounded target. The study reported on here comprises the computational simulation of free spray and deposition aspects of charged and uncharged sprays, and uses the data obtained in the parallel investigation to determine the ability of the computational model to accurately predict such sprays. Experimental test results demonstrate the dominance of hydrodynamic effects within the charged free sprays, whereas, in the vicinity of a grounded target, the sprays are influenced by the attractive electrostatic force fields created, leading to greater drop depositions on the target than for an uncharged spray. These trends are confirmed by the computational results. However, there are differences of detail. The model generally underpredicts the effects of the electric fields on the spray motion near the target. This is probably due to an incorrect mass flux profile at the injector, leading to too little mass and, hence, charge being predicted in the target vicinity.

Non-aqueous phase liquid drop formation within a water saturated fracture

This work focuses on the mechanisms of non-aqueous phase liquid (NAPL) drop formation within a single fracture fed from a NAPL reservoir by way of a circular orifice, such as a pore. The fracture is assumed to be fully saturated, the relative wettability of the system is assumed water-wet, and the water velocity profile within the fracture is described by a Poiseuille flow. The size of the NAPL drops is investigated for various water flow velocities and NAPL entrance diameters. A force balancing method was used to determine the radii of detached drops. The drop sizes calculated from the model developed here are shown to be in agreement with available experimental drop size data. It is shown that at low Reynolds numbers the buoyancy force is the dominant force acting on the drop during the formation process and at high Reynolds numbers the viscous forces dominate. A simplified expression relating the geometry of the fractured system to the drop radii is developed from the model equations, and it is shown to predict drop radii that match well with both the model simulations and the available experimental data.

On the Separation of Tropical Convective and Stratiform Rains

Abstract This work resolves an apparent conflict between the results of Yuter and Houze and Atlas et al. concerning relations between radar reflectivity factor Z and rainfall rate R derived from essentially the same drop size data observed aloft during the Tropical Ocean and Global Atmosphere program's (TOGA) Coupled Ocean–Atmosphere Response Experiment (COARE). It is shown that the single relation found by Yuter and Houze is founded upon distinct underlying Z–R relations for stratiform and convective rains. This result occurs despite the fact that errors in rain types classified by different methods and the variability of the effective drop sizes within each type tend to obscure the distinction. This newly found agreement between the two distinctly different methods of analysis also suggests the essential equivalence of the classification methods of Steiner et al. (based upon the existence of a maximum in the observed reflectivity field) and of Atlas et al. (based upon the magnitude of the drafts). Howev...

Spray Extraction Columns: Drop Size and Dispersed-Phase Holdup

Mean drop size and dispersed-phase holdup data are generalized for spray extraction columns with loose, close, and turbulized close drop packings. A graphical method is suggested for determining the conjugate holdup values.

Developments in Spray Modeling in Diesel and Direct-Injection Gasoline Engines

Developments in Spray Modeling in Diesel and Direct-Injection Gasoline Engines — In direct- injection engines the fuel spray characteristics influence the combustion efficiency and exhaust emissions. The performance of available spray models for predicting liquid and vapor fuel distributions, and their influence on combustion is reviewed for both diesel and gasoline direct injection engines. A phenomenological nozzle flow model is described for simulating the effects of diesel injector nozzle internal geometry on the fuel injection and spray processes. The flow model provides initial conditions for the liquid jet breakup model that considers wave instabilities due to Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) mechanisms. A linearized instability analysis has also been extended to consider the breakup of liquid sheets for modeling pressure-swirl gasoline injectors. Diesel engine predictions have been compared with extensive data from in-cylinder laser diagnostics carried out in optically accessible heavy-duty, DI Diesel engines over a wide range of operating conditions. The results show that the nozzle flow model used in combination with the KH and RT models gives realistic spray predictions. In particular, the limited liquid fuel penetration length observed experimentally and the flame shape details are captured accurately. The liquid sheet breakup model has also been compared favorably with experimental spray penetration and drop size data for gasoline hollow-cone sprays. This model is currently being applied to study stratified charge combustion in GDI engines.