Mathematical expression for drop size distribution in sprays
Logarithmic normal and Chi-square distribution functions evaluated for determining drop size distribution in liquid sprays
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Logarithmic normal and Chi-square distribution functions evaluated for determining drop size distribution in liquid sprays
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There are several leading theories on the processes that led to the formation of chondrites, e.g., sorting by mass, by X-winds, turbulent concentration, and by photophoresis. The juxtaposition of refractory inclusions (CAIs) and less refractory chondrules is central to these theories and there is much to be learned from their relative size distributions. There have been a number of studies into size distributions of particles in chondrites but only on relatively small scales primarily for chondrules, and rarely for both Calcium Aluminum-rich Inclusions (CAIs) and chondrules in the same sample. We have implemented macro-scale (25 cm diameter sample) and high-resolution microscale sampling of the Allende CV3 chondrite to create a complete data set of size frequencies for CAIs and chondrules.
Measurements are presented for the spectral optical thickness of El Chichon's stratospheric aerosol layer, obtained during an airborne latitudinal survey in April and May of 1983. Columnar aerosol size distributions of the stratosphere are derived by inverting the aerosol optical thickness measurements as a function of wavelength and from spectral aerosol depth measurements obtained during an airborne survey in October and November 1982. Spectral optical thickness data and the derived size distributions from both airborne missions show latitidunal regions with similar characteristics. Airborne solar radiometer measurements are shown to be useful in studies of the latitudinal variations of optical and related particle size characteristics of the stratospheric aerosol layer.
Effect of selected fluid parameters on spatial drop size distribution - fluorescent method for studying microscopic properties of fluid spray
Particle size distribution effects on incident radiation from clouds calculated by Monte Carlo method
Particle size distribution influence on reflected and transmitted light from clouds calculated by Monte Carlo technique
A fast technique, based on approximation to atmospheric radiative transfer in the solar aureole, is presented for the retrieval of aerosol size distribution from multispectral measurements of both scattered sky radiance and extinction by aerosol media. In this approximation, it is assumed that for a relatively clear day, the sky radiance is due to single scattering by molecules and aerosols, and to multiple scattering by molecules alone. The accuracy of this approximation is discussed in connection with the inversion of scattered radiation data. Results for aerosol size distributions retrieved from multispectral solar extinction measurements by the nonlinear least squares method are discussed, and the retrievals are found to be accurate when checked against ground truth measurements.
Analysis of lunar particle size distribution data indicates that the surface material is composed of two populations. One population is caused by comminution from the impact of the larger-sized meteorites, while the other population is caused by the melting of fine material by the impact of smaller-sized meteorites. The results are referred to Mars, and it is shown that the Martian atmosphere would vaporize the smaller incoming meteorites and retard the incoming meteorites of intermediate and large size, causing comminution and stirring of the particulate layer. The combination of comminution and stirring would result in fine material being sorted out by the prevailing circulation of the Martian atmosphere and the material being transported to regions where it could be deposited. As a result, the Martian surface in regions of prevailing upward circulation is probably covered by either a rubble layer or by desert pavement; regions of prevailing downward circulation are probably covered by sand dunes.
This paper revisits the problem of finding a parametric form for the rain drop size distribution (DSD) which 1) is an appropriate model for tropical rainfall, and 2) involves statistically independent parameters. Using TOGA/COARE data, we derive a parametrization which meets these criteria. This new parametrization is an improvement on the one that was derived in [3] using TRMM ground truth data from Darwin, Australia. The new COARE data allows us to verify that the spatial variability fo the two
Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.
Radiometric brightess temperatures below about 12 GHz provide accurate estimates of path attenuation through precipitation and cloud water. Multiple brightness temperature measurements at X-band frequencies can be used to estimate rainfall rate and parameters of the drop size distribution once correction for cloud water attenuation is made. Employing a stratiform storm model, calculations of the brightness temperatures at 9.5, 10 and 12 GHz are used to simulate estimates of path-averaged median mass diameter, number concentration and rainfall rate. The results indicate that reasonably accurate estimates of rainfall rate and information on the drop size distribution can be derived over ocean under low to moderate wind speed conditions.
As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.
Shergottites are mafic to ultramafic igneous rocks that represent a majority of known martian meteorites. They are subdivided into gabbroic, poikilitic, basaltic, and olivine-phyric categories based on differences in mineralogy and textures. Their geologic contexts are unknown so analyses of crystal sizes and preferred orientations have commonly been used to infer where shergottites solidified. Such environments range from subsurface cumulates to shallow intrusives to extrusive lava flows, which all have contrasting implications for interactions with crustal material, cooling histories, and potential in situ exposure at the surface. In this study, we present a novel three-dimensional (3D) approach to better understand the solidification environments of these samples and improve our knowledge of shergottites’ geologic contexts. Shape preferred orientations of most phases and crystal size distributions of late-forming minerals were measured in 3D using X-ray computed tomography (CT) on eight shergottites representing the gabbroic, poikilitic, basaltic, and olivine-phyric categories. Our analyses show that highly anisotropic, rod-like pyroxene crystals are strongly foliated in the gabbroic samples but have a weaker foliation and a mild lineation in the basaltic sample, indicating a directional flow component in the latter. Star volume distribution analyses revealed that most phases (maskelynite, pyroxene, olivine, and oxides/sulfides) preserve a foliated texture with variable strengths, and that the phases within individual samples are strongly to moderately aligned with respect to one another. In combination with relative cooling rates during the final stages of crystallization determined from interstitial oxide/sulfide crystal size distribution analyses, these results indicate that the olivine-phyric samples were emplaced as shallow intrusives (e.g., dikes/sills) and that the gabbroic, poikilitic, and basaltic samples were emplaced in deeper subsurface environments.
Powerlaws have long been used to describe the spectral dependence of aerosol extinction, and the wavelength exponent of the aerosol extinction powerlaw is commonly referred to as the Angstrom exponent. The Angstrom exponent is often used as a qualitative indicator of aerosol particle size, with values greater than two indicating small particles associated with combustion byproducts, and values less than one indicating large particles like sea salt and dust. In this study, we investigate the relationship between the Angstrom exponent and the mode parameters of bimodal aerosol size distributions using Mie theory calculations and Aerosol Robotic Network (AERONET) retrievals. We find that Angstrom exponents based upon seven wavelengths (0.34, 0.38, 0.44, 0.5, 0.67, 0.87, and 1.02 micrometers) are sensitive to the volume fraction of aerosols with radii less then 0.6 micrometers, but not to the fine mode effective radius. The Angstrom exponent is also known to vary with wavelength, which is commonly referred to as curvature; we show how the spectral curvature can provide additional information about aerosol size distributions for intermediate values of the Angstrom exponent. Curvature also has a significant effect on the conclusions that can be drawn about two-wavelength Angstrom exponents; long wavelengths (0.67, 0.87 micrometers) are sensitive to fine mode volume fraction of aerosols but not fine mode effective radius, while short wavelengths (0.38, 0.44 micrometers) are sensitive to the fine mode effective radius but not the fine mode volume fraction.
We have developed a fast-response Nanometer Aerosol Size Analyzer (nASA) that is capable of scanning 30 size channels between 3 and 100 nm in a total time of 3 seconds. The analyzer includes a bipolar charger (P0210), an extended-length Nanometer Differential Mobility Analyzer (Nano-DMA), and an electrometer (TSI 3068). This combination of components provides particle size spectra at a scan rate of 0.1 second per channel free of uncertainties caused by response-time-induced smearing. The nASA thus offers a fast response for aerosol size distribution measurements in high-concentration conditions and also eliminates the need for applying a de-smearing algorithm to resulting data. In addition, because of its thermodynamically stable means of particle detection, the nASA is useful for applications requiring measurements over a broad range of sample pressures and temperatures. Indeed, experimental transfer functions determined for the extended-length Nano-DMA using the Tandem Differential Mobility Analyzer (TDMA) technique indicate the nASA provides good size resolution at pressures as low as 200 Torr. Also, as was demonstrated in tests to characterize the soot emissions from the J85-GE engine of a T38 aircraft, the broad dynamic concentration range of the nASA makes it particularly suitable for studies of combustion or particle formation processes. Further details of the nASA performance as well as results from calibrations, laboratory tests and field applications are presented.
The Experiment to Characterize Aircraft Volatile Aerosols and Trace Species Emissions (EXCAVATE) took place at NASA Langley Research Center during January 2002. This ground based study was conducted to examine the role of fuel sulfur content on particulate emissions. Size distributions as a function of engine operating conditions were measured in the exhaust plume of a B-757 at four downstream axial locations (1 m, 10 m, 25 m and 35 m). The engine was run on JP-5 with three different sulfur concentrations, 810 ppm, 1050 ppm, 1820 ppm; and was operated over a range of power settings from idle to near-full power. Zalabsky differential-mobility analyzers DMAS), Met One condensation-nuclei counters (CNCs), and a TSI 3022 condensation-particle counter (CPC) were used to measure the size distributions. The total number-count (particle concentration), number-based Emissions Index (EInumber) and mass-based Emissions Index (E1-J increased with fuel sulfur-content and engine pressure ratio (EPR). Count Mean Diameter (Ch4D) also increased with EPR yet remained fairly constant with fuel sulfur-content for a fixed location in the exhaust plume. Also the mode and CMD both increased with distance in the plume.
A model incorporating limited interaction between the incident energy and particles in the ring is considered which appears to be consistent with the multiple scattering process in Saturn's rings. The model allows for the small physical thickness of the rings and can be used to relate Voyager 1 observations of 3.6- and 13-cm wavelength microwave scatter from the rings to the ring particle size distribution function for particles with radii ranging from 0.001 to 20 m. This limited-scatter model yields solutions for particle size distribution functions for eight regions in the rings, which exhibit approximately inverse-cubic power-law behavior.