Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Drop size distribution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24

Numerical modeling for dilute and dense sprays

We have successfully implemented a numerical model for spray-combustion calculations. In this model, the governing gas-phase equations in Eulerian coordinate are solved by a time-marching multiple pressure correction procedure based on the operator-splitting technique. The droplet-phase equations in Lagrangian coordinate are solved by a stochastic discrete particle technique. In order to simplify the calculation procedure for the circulating droplets, the effective conductivity model is utilized. The k-epsilon models are utilized to characterize the time and length scales of the gas phase in conjunction with turbulent modulation by droplets and droplet dispersion by turbulence. This method entails random sampling of instantaneous gas flow properties and the stochastic process requires a large number of computational parcels to produce the satisfactory dispersion distributions even for rather dilute sprays. Two major improvements in spray combustion modelings were made. Firstly, we have developed a probability density function approach in multidimensional space to represent a specific computational particle. Secondly, we incorporate the Taylor Analogy Breakup (TAB) model for handling the dense spray effects. This breakup model is based on the reasonable assumption that atomization and drop breakup are indistinguishable processes within a dense spray near the nozzle exit. Accordingly, atomization is prescribed by injecting drops which have a characteristic size equal to the nozzle exit diameter. Example problems include the nearly homogeneous and inhomogeneous turbulent particle dispersion, and the non-evaporating, evaporating, and burning dense sprays. Comparison with experimental data will be discussed in detail.

Chen, C. P.↗

Silica-Aerogel Composites Opacified with La(0.7)Sr(0.3)MnO3

As part of an effort to develop improved lightweight thermal-insulation tiles to withstand temperatures up to 1,000 C, silica aerogel/fused-quartz-fiber composite materials containing La0.7Sr0.3MnO3 particles as opacifiers have been investigated as potentially offering thermal conductivities lower than those of the otherwise equivalent silica-aerogel composite materials not containing La(0.7)Sr(0.3)MnO3 particles. The basic idea of incorporating opacifying particles into silica-aerogels composite to reduce infrared radiative contributions to thermal conductivities at high temperatures is not new: it has been reported in a number of previous NASA Tech Briefs articles. What is new here is the selection of La(0.7)Sr(0.3)MnO3 particles as candidate opacifiers that, in comparison with some prior opacifiers (carbon black and metal nanoparticles), are more thermally stable. The preparation of a composite material of the present type includes synthesis of the silica-aerogel component in a sol-gel process. The La(0.7)Sr(0.3)MnO3 particles, made previously in a separate process, are mixed into the sol, which is then cast onto fused-quartz-fiber batting. Then the aerogel-casting solution is poured into the mold, where it permeates the silica fiber felt. After the sol has gelled, the casting is aged and then subjected to supercritical drying to convert the gel to the final aerogel form. The separate process for making the La(0.7)Sr(0.3)MnO3 particles begins with the slow addition of corresponding proportions of La(CH3COOH)3, Mn(CH3COOH)3, and Sr(NO3)2 to a solution of H2O2 in H2O. The solution is then peptized by drop-wise addition of NH4OH to obtain a sol. Next, the sol is dried in an oven at a temperature of 120 C to obtain a glassy solid. The solid is calcined at 700 C to convert it to La(0.7)Sr(0.3)MnO3. Then La(0.7)Sr(0.3)MnO3 particles are made by ball-milling the calcined solid. The effectiveness of La(0.7)Sr(0.3)MnO3 particles as opacifiers and thermal-conductivity reducers depends on the statistical distribution of particle sizes as well as the relative proportions of La(0.7)Sr(0.3)MnO3 and aerogel. For experiments performed thus far, samples of aerogel/fiber composites were formulated to have, variously, silica target density of 0.07 or 0.14 g/cu cm and to contain 30 percent of La(0.7)Sr(0.3)MnO3 in average particle size of 0.3 or 3 microns. The thermal conductivities of the samples containing the 3 micron La(0.7)Sr(0.3)MnO3 particles were found to be lower than those of the samples containing the 0.3 micron La(0.7)Sr(0.3)MnO3 particles. The optimum particle size is believed to be between 1 and 5 microns.

Rhine, Wendell↗

Xplo-SA9T: Optimization of Sorbent Technology With Existing and New Amine Variants for Carbon Dioxide Removal and Humidity Control

Scrubbing of the spacesuit air stream to control humidity and regulate carbon dioxide (CO 2 ) relies on amine-loaded resins, colloquially known as sorbents. The efficacy of Rapid Cycle Amine technology relies on the propensity of nitrogens toward adsorption of CO 2 while simultaneously offering regenerative properties under vacuum or positive pressure. The commonly utilized sorbent, SA9T, was recreated and evaluated further to increase stability and serve as a benchmark comparison for newly synthesized amine sorbent technologies. Ongoing storage studies with eight different environments will allow the development of applicable storage protocols and provide insight into possible ammonia generation pathways. Attempts to alleviate the known issues with SA9T included the alteration of the primary amine (tetraethylenepentamine), the choice of resin, and the particle size distribution. In-house CO 2 breakthrough experiments were conducted using a specialized apparatus that can simulate spacesuit conditions, offering high-quality triplicate capacity analysis affording direct comparison to known adsorbents in the literature. Thermo-Desorption Gas Chromatography Mass Spectrometry studies on the synthesized materials revealed any reagent or solvent offgassing while Nuclear Magnetic Resonance spectroscopy tracked the stability of the bound amine. Scanning Electron Microscope images of sieved materials provided a more accurate size interpretation facilitating synthetic design and pressure drop elimination. All efficient sorbents were synthesized to a commercial batch scale subsequent to evaluation including Xplo-SA9T.

John R Tidwell↗

Gas and drop behavior in reacting and non-reacting air-blast atomizer sprays

A detailed study of the two-phase flow produced by a gas-turbine air-blast atomizer is performed with the goal of identifying the interaction between the two phases for both nonreacting and reacting conditions. A two-component phase Doppler interferometry is utilized to characterize three flowfields produced by the atomizer: (1) the single-phase flow, (2) the two-phase nonreacting spray, and (3) the two-phase reacting spray. Measurements of the mean and fluctuating axial and azimuthal velocities for each phase are obtained. In addition, the droplet size distribution, volume flux, and concentration are measured. The results reveal the strong influence of the dispersed phase on the gas, and the influence of reaction on both the gas and the droplet field. The presence of the spray significantly alters the inlet condition of the atomizer. With this alteration quantified, it is possible to deduce that the inertia associated with the dispersed phase damps the fluctuating velocities of the gas. Reaction reduces the volume flux of the droplets, broadens the local volume distribution of the droplets in the region of the reaction zone, increases the axial velocities and radial spread of the gas, and increases the anisotropy in the region of the reaction zone.

Mcdonell, Vincent G.↗

Modeling the formation of ion clusters by applying classical nucleation theory

Experiments have been conducted to study the clustering of atmospheric trace gases around ion cores (Castleman and Tang, 1972; Searcy and Fenn, 1974; Castleman, 1978). The classical liquid-drop model is used to investigate this ion-induced formation mechanism. Results obtained from models of the distribution of Pb(+)-(H2O)n and H(+)-(H2O)n type clusters under various conditions are compared with experimental results. The distribution of water-ion clusters in the atmosphere as a function of altitude is calculated. In situ measurements of the water-ion cluster distributions in the upper atmosphere are then compared with present predictions. It is concluded that the classical nucleation theory can be used to predict rough estimates for ion cluster sizes under many conditions.

Yue, G. K.↗

High Ice Water Content at Low Radar Reflectivity near Deep Convection: Part II. Evaluation of Microphysical Pathways in Updraft Parcel Simulations

The aeronautics industry has established that a threat to aircraft is posed by atmospheric conditions of substantial ice water content (IWC) where equivalent radar reflectivity (Ze) does not exceed 20-30 dBZ and supercooled water is not present; these conditions are encountered almost exclusively in the vicinity of deep convection. Part 1 (Fridlind et al., 2015) of this two-part study presents in situ measurements of such conditions sampled by Airbus in three tropical regions, commonly near 11 km and -43 C, and concludes that the measured ice particle size distributions are broadly consistent with past literature with profiling radar measurements of Z(sub e) and mean Doppler velocity obtained within monsoonal deep convection in one of the regions sampled. In all three regions, the Airbus measurements generally indicate variable IWC that often exceeds 2 gm (exp -3) with relatively uniform mass median area-equivalent diameter (MMD(sub eq) of 200-300 micrometers. Here we use a parcel model with size-resolved microphysics to investigate microphysical pathways that could lead to such conditions. Our simulations indicate that homogeneous freezing of water drops produces a much smaller ice MMD(sub eq) than observed, and occurs only in the absence of hydrometeor gravitational collection for the conditions considered. Development of a mass mode of ice aloft that overlaps with the measurements requires a substantial source of small ice particles at temperatures of about -10 C or warmer, which subsequently grow from water vapor. One conceivable source in our simulation framework is Hallett-Mossop ice production; another is abundant concentrations of heterogeneous ice freezing nuclei acting together with copious shattering of water drops upon freezing. Regardless of the production mechanism, the dominant mass modal diameter of vapor-grown ice is reduced as the ice-multiplication source strength increases and as competition for water vapor increases. Both mass and modal diameter are reduced by entrainment and by increasing aerosol concentrations. Weaker updrafts lead to greater mass and larger modal diameters of vapor-grown ice, the opposite of expectations regarding lofting of larger ice particles in stronger updrafts. While stronger updrafts do loft more dense ice particles produced primarily by raindrop freezing, we find that weaker updrafts allow the warm rain process to reduce competition for diffusional growth of the less dense ice expected to persist in convective outflow.

Reflectivity↗

Performance of Small Pore Microchannel Plates

Small pore size microchannel plates (MCP's) are needed to satisfy the requirements for future high resolution small and large format detectors for astronomy. MCP's with pore sizes in the range 5 micron to 8 micron are now being manufactured, but they are of limited availability and are of small size. We have obtained sets of Galileo 8 micron and 6.5 micron MCP's, and Philips 6 micron and 7 micron pore MCP's, and compared them to our larger pore MCP Z stacks. We have tested back to back MCP stacks of four of these MCP's and achieved gains greater than 2 x 1O(exp 7) with pulse height distributions of less than 40% FWHM, and background rates of less than 0.3 events sec(exp -1) cm(exp -2). Local counting rates up to approx. 100 events/pore/sec have been attained with little drop of the MCP gain. The bare MCP quantum efficiencies are somewhat lower than those expected, however. Flat field images are characterized by an absence of MCP fixed pattern noise.

Siegmund, O. H. W.↗

Computational and Experimental Study of Energetic Materials in a Counterflow Microgravity Environment

Counterflow diffusion flames are studied for various fuels flowing against decomposition products from solid ammonium perchlorate (AP) pellets in order to obtain fundamental understanding of composite propellant flame structure and chemistry. We illustrate this approach through a combined experimental and numerical study of a fuel mixture consisting of C2H4 CO + H2, and C2H2 + C2H4 flowing against solid AP. For these particular AP-fuel systems, the resulting flame zone simulates the various flame structures that are ex+ to exist between reaction products from Ap crystals and a hydrocarbon binder. As in all our experimental studies, quantitative species and temperature profiles have been measured between the fuel exit and AP surface. Species measured included CN, NH, NO, OH, N2, CO2, CO, H2, CO, HCl, and H2O. Temperature was measured using a thermocouple at the exit, spontaneous Raman scattering measurements throughout the flame, OH rotational population distributions, and NO vibrational population distributions. The burning rate of AP was also measured as a function of strain rate, given by the separation distance between the AP surface and the gaseous hydrocarbon fuel tube exit plane. This distance was nominally set at 5 mm, although studies have been performed for variations in separation distance. The measured 12 scalars are compared with predictions from a detailed gas-phase kinetics model consisting of 86 species and 531 reactions. Model predictions are found to be in good agreement with experiment and illustrate the type of kinetic features that may be expected to occur in propellants when AP particle size distributions are varied. Furthermore, the results constitute the continued development of a necessary database and validation of a comprehensive model for studying more complex AP-solid fuel systems in microgravity. Exploratory studies have also been performed with liquid and solid fuels at normal gravity. Because of melting (and hence dripping) and deep thermal wave penetration into the liquid, these experiments were found feasible, but not used for obtaining quantitative data. Microgravity experiments are needed to eliminate the dripping and boiling phenomena of these systems at normal gravity. Microgravity tests in the NASA Glenn 2.2 second drop tower were performed (1) to demonstrate the feasibility of performing propellant experiments using the NASA Glenn microgravity facilities, (2) to develop the operational procedures for safe handing of the energetic materials and disposal of their toxic combustion by-products and (3) to obtain initial measurements of the AP burning rate and flame structure under microgravity conditions. Experiments were conducted on the CH4/AP system previously studied at normal gravity using a modified design of the counterflow burner and a NASA Glenn Pig Rig, i.e., one of the existing drop rigs for general-purpose usage. In these experiments, the AP burning rate was measured directly with a linear variable differential transducer (LVDT) and video imaging of the flame structure was recorded ignition was achieved by hot wires stretched across the AP surfaces. Initial drop tower combustion data show that with the same burner separation distance and flow conditions of the normal gravity experiments, the AP burning rate is approximately a factor of two lower. This difference is likely a result of radiation effects, but further tests with longer test times need to be conducted to verify that steady state conditions were achieved under microgravity conditions.

Takahashi, Fumiaki↗

Analysis of TRMM Microphysical Measurements: Tropical Rainfall Measuring Mission (TRMM)

SPEC Incorporated participated in three of the four TRMM field campaigns (TEFLUN-A, TEFLUN-B and KWAJEX), installing and operating a cloud particle imager (CPI) and a high volume precipitation spectrometer (HVPS) on the SPEC Learjet in TEFLUN-A, the University of North Dakota Citation in TEFLUN-B and KWAJEX, and a CPI on the NASA DC-8 in KWAJEX. This report presents and discusses new software tools and algorithms that were developed to analyze microphysical data collected during these field campaigns, as well as scientific interpretations of the data themselves. Software algorithms were developed to improve the analysis of microphysical measurements collected by the TRMM aircraft during the field campaigns. Particular attention was paid to developing and/or improving algorithms used to compute particle size distributions and ice water content. Software was also developed in support of production of the TRMM Common Microphysical Product (CMP) data files. CMP data files for TEFLUN-A field campaign were produced and submitted to the DAAC. Typical microphysical properties of convective and stratiform regions from TEFLUN-A and KWAJEX clouds were produced. In general, it was found that in the upper cloud region near -20 to -25 C, stratiform clouds contain very high (greater than 1 per cubic centimeter) concentrations of small ice particles, which are suspected to be a residual from homogeneous freezing and sedimentation of small drops in a convective updraft. In the upper cloud region near -20 to -25 C, convective clouds contain aggregates, which are not found lower in the cloud. Stratiform clouds contain aggregates at all levels, with the majority in the lowest levels. Convective cloud regions contain much higher LWC and drop concentrations than stratiform regions at all levels, and higher LWC in the middle and upper regions. Stratiform clouds contain higher IWC than convective clouds only at the lowest level. Irregular shaped ice particles are found in very high concentrations throughout both convective and stratiform cloud regions. A striking difference in particle shape in cirrus formed in situ, cirrus formed from maritime anvils and cirrus formed from continental anvils. Over 50% of the mass of in situ cirrus ice particles is composed of bullet rosettes, while bullet rosettes are virtually non-existent in maritime and tropical anvils. Tropical anvils are composed of mostly singular, plates, capped columns, and blocky irregular shapes, while continental anvils have a much higher percentage of aggregates, some of which are chains of small spheroidal particles that appear to result from homogeneous freezing of drops. A correlation between high electric fields in continental anvils and the formation of aggregates is hypothesized.

Source record↗

Passive imaging based multi-cue hazard detection spacecraft safe landing

Accurate assessment of potentially damaging ground hazards during the spacecraft EDL (Entry, Descent and Landing) phase is crucial to insure a high probability of safe landing. A lander that encounters a large rock, falls off a cliff, or tips over on a steep slope can sustain mission ending damage. Guided entry is expected to shrink landing ellipses from 100-300 km to -10 km radius for the second generation landers as early as 2009. Regardless of size and location, however, landing ellipses will almost always contain hazards such as craters, discontinuities, steep slopes, and large rocks. It is estimated that an MSL (Mars Science Laboratory)-sized lander should detect and avoid 16- 150m diameter craters, vertical drops similar to the edges of 16m or 3.75m diameter crater, for high and low altitude HAD (Hazard Detection and Avoidance) respectively. It should also be able to detect slopes 20' or steeper, and rocks 0.75m or taller. In this paper we will present a passive imaging based, multi-cue hazard detection and avoidance (HDA) system suitable for Martian and other lander missions. This is the first passively imaged HDA system that seamlessly integrates multiple algorithm-crater detection, slope estimation, rock detection and texture analysis, and multicues- crater morphology, rock distribution, to detect these hazards in real time.

hazard detection↗

Prediction of Performance Variation Caused by Manufacturing Tolerances and Defects in Gas Diffusion Electrodes of Phosphoric Acid (PA)–Doped Polybenzimidazole (PBI)-Based High-Temperature Proton Exchange Membrane Fuel Cells

The automated process of coating catalyst layers on gas diffusion electrodes (GDEs) for high-temperature proton exchange membrane fuel cells results inherently into a number of defects. These defects consist of agglomerates in which the platinum sites cannot be accessed by phosphoric acid and which are the consequence of an inconsistent coating, uncoated regions, scratches, knots, blemishes, folds, or attached fine particles—all ranging from μm to mm size. These electrochemically inactive spots cause a reduction of the effective catalyst area per unit volume (cm2/cm3) and determine a drop in fuel cell performance. A computational fluid dynamics (CFD) model is presented that predicts performance variation caused by manufacturing tolerances and defects of the GDE and which enables the creation of a six-sigma product specification for Advent phosphoric acid (PA)-doped polybenzimidazole (PBI)-based membrane electrode assemblies (MEAs). The model was used to predict the total volume of defects that would cause a 10% drop in performance. It was found that a 10% performance drop at the nominal operating regime would be caused by uniformly distributed defects totaling 39% of the catalyst layer volume (~0.5 defects/μm2). The study provides an upper bound for the estimation of the impact of the defect location on performance drop. It was found that the impact on the local current density is higher when the defect is located closer to the interface with the membrane. The local current density decays less than 2% in the presence of an isolated defect, regardless of its location along the active area of the catalyst layer.

Gurau, Vladimir (ORCID:0000000327429061)↗

The Impact of Stripped Cores on the Frequency of Earth-size Planets in the Habitable Zone

The frequency of Earth-size planets in the habitable zone(HZ)of Sun-like stars, hereafter, is a key parameter to evaluate the yield of nearby Earth analogs that can be detected and characterized by future missions. Yet, this value is poorly constrained as there are no reliable exoplanet candidates in the HZ of Sun-like stars in the Kepler field. Here, we show that extrapolations relying on the population of small(<1.8R), short-period(<25 days)planets bias to large values. As the radius distribution at short orbital periods is strongly affected by atmospheric loss, we reevaluate using exoplanets at larger separations. We find that drops considerably, to values of only5% - 10%. Observations of young(<100 Myr)clusters can probe short-period sub-Neptunes that still retain most of their envelope mass. As such, they can be used to quantify the contamination of sub-Neptunes to the population of Kepler short-period small planets and aid in more reliable estimates of.

Pascucci, Ilaria↗

NASA Tech Briefs, December 2012

The topics include: Pattern Generator for Bench Test of Digital Boards; 670-GHz Down- and Up-Converting HEMT-Based Mixers; Lidar Electro-Optic Beam Switch with a Liquid Crystal Variable Retarder; Feedback Augmented Sub-Ranging (FASR) Quantizer; Real-Time Distributed Embedded Oscillator Operating Frequency Monitoring; Software Modules for the Proximity-1 Space Link Interleaved Time Synchronization (PITS) Protocol; Description and User Instructions for the Quaternion to Orbit v3 Software; AdapChem; Mars Relay Lander and Orbiter Overflight Profile Estimation; Extended Testability Analysis Tool; Interactive 3D Mars Visualization; Rapid Diagnostics of Onboard Sequences; MER Telemetry Processor; pyam: Python Implementation of YaM; Process for Patterning Indium for Bump Bonding; Archway for Radiation and Micrometeorite Occurrence Resistance; 4D Light Field Imaging System Using Programmable Aperture; Device and Container for Reheating and Sterilization; Radio Frequency Plasma Discharge Lamps for Use as Stable Calibration Light Sources; Membrane Shell Reflector Segment Antenna; High-Speed Transport of Fluid Drops and Solid Particles via Surface Acoustic Waves; Compact Autonomous Hemispheric Vision System; A Distributive, Non-Destructive, Real-Time Approach to Snowpack Monitoring; Wideband Single-Crystal Transducer for Bone Characterization; Numerical Simulation of Rocket Exhaust Interaction With Lunar Soil; Motion Imagery and Robotics Application (MIRA): Standards-Based Robotics; Particle Filtering for Model-Based Anomaly Detection in Sensor Networks; Ka-band Digitally Beamformed Airborne Radar Using SweepSAR Technique; Composite With In Situ Plenums; Multi-Beam Approach for Accelerating Alignment and Calibration of HyspIRI-Like Imaging Spectrometers; JWST Lifting System; Next-Generation Tumbleweed Rover; Pneumatic System for Concentration of Micrometer-Size Lunar Soil.

Source record↗

Shedding light on U.S. small and midsize data centers: Exploring insights from the CBECS survey

As demand for digital services accelerates, the energy and environmental footprint of data centers faces increasing scrutiny. While hyperscale cloud facilities have driven efficiency gains, small and midsize U.S. data centers remain a critical yet underexamined segment with significant untapped potential for energy savings. This study leverages data from the Commercial Buildings Energy Consumption Survey (CBECS) to analyze trends in server stocks, computing customers, cooling system adoption and efficiency, and geospatial distribution from 2012 to 2018. Findings reveal a sharp decline in small and midsize data centers, from 1.764 million to 1.398 million, with server counts dropping from 5.177 million to 4.262 million—aligning with the broader shift toward cloud computing. More than 40 % of servers in small data centers and 55 % in midsize data centers are housed in office buildings, and over half of all servers are concentrated in climate zones 5A (cold), 3A (mixed-humid), and 4A (mixed-humid), with the highest densities in metropolitan hubs. While direct expansion units remain the dominant cooling system, a clear transition toward more energy-efficient solutions, particularly air economizers, is evident. By integrating server and cooling system distributions, we estimate Power Usage Effectiveness (PUE) and Water Usage Effectiveness (WUE) for U.S. data centers by size and year. Results show that midsize data centers are more energy-efficient but more water-intensive due to the widespread use of water-cooled chillers. These findings highlight the trade-offs in cooling system selection and provide a critical foundation for policies aimed at enhancing efficiency in an evolving data center landscape.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Strange quark matter as dark matter: 40 yr later, a reappraisal

ABSTRACT Forty years ago Witten suggested that dark matter could be composed of macroscopic clusters of strange quark matter. This idea was very popular for several years, but it dropped out of fashion once lattice quantum chromodynamics calculations indicated that the confinement/deconfinement transition, at small baryonic chemical potential, is not first order, which seemed to be a crucial requirement in order to produce large clusters of quarks. Here, we revisit the conditions under which strangelets can be produced in the Early Universe. We discuss the impact of an instability in the hadronic phase separating a low density, positive-strange-charge phase from a high-density phase with a negative strange charge. This second phase can rapidly stabilize by forming colour-superconducting gaps. The strangelets then undergo partial evaporation. In this way, we obtain distributions of their sizes in agreement with the observational constraints and we discuss the many astrophysical and cosmological implications of these objects. Finally, we examine the most promising techniques to detect this type of strangelets. We also show that strangelets can exist with masses $\lesssim $1017 g, while primordial black holes are ruled out in that mass range, allowing us to distinguish between these two dark matter candidates.

Clemente, Francesco Di (ORCID:0000000282573819)↗

Data-driven nonlocal model for fragmentation in the crushing of solids

A technique is proposed for reproducing particle size distributions in three-dimensional simulations of the crushing and comminution of solid materials. The method is designed to produce realistic distributions over a wide range of loading conditions, especially for small fragments. In contrast to most existing methods, the new model does not explicitly treat the small-scale process of fracture. Instead, it uses measured fragment distributions from laboratory tests as the basic material property that is incorporated into the algorithm, providing a data-driven approach. The algorithm is implemented within a nonlocal peridynamic solver, which simulates the underlying continuum mechanics and contact interactions between fragments after they are formed. Finally, the technique is illustrated in reproducing fragmentation data from drop weight testing on sandstone samples.

58 GEOSCIENCES↗

A New Look into the Effect of Large Drops on Radiative Transfer Process

Recent studies indicate that a cloudy atmosphere absorbs more solar radiation than any current 1D or 3D radiation model can predict. The excess absorption is not large, perhaps 10-15 W/sq m or less, but any such systematic bias is of concern since radiative transfer models are assumed to be sufficiently accurate for remote sensing applications and climate modeling. The most natural explanation would be that models do not capture real 3D cloud structure and, as a consequence, their photon path lengths are too short. However, extensive calculations, using increasingly realistic 3D cloud structures, failed to produce photon paths long enough to explain the excess absorption. Other possible explanations have also been unsuccessful so, at this point, conventional models seem to offer no solution to this puzzle. The weakest link in conventional models is the way a size distribution of cloud particles is mathematically handled. Basically, real particles are replaced with a single average particle. This "ensemble assumption" assumes that all particle sizes are well represented in any given elementary volume. But the concentration of larger particles can be so low that this assumption is significantly violated. We show how a different mathematical route, using the concept of a cumulative distribution, avoids the ensemble assumption. The cumulative distribution has jumps, or steps, corresponding to the rarer sizes. These jumps result in an additional term, a kind of Green's function, in the solution of the radiative transfer equation. Solving the cloud radiative transfer equation with the measured particle distributions, described in a cumulative rather than an ensemble fashion, may lead to increased cloud absorption of the magnitude observed.

Marshak, Alexander↗