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At least 253 records · Page 14

High-Pressure Gaseous Burner (HPGB) Facility Completed for Quantitative Laser Diagnostics Calibration

A gas-fueled high-pressure combustion facility with optical access, which was developed over the last 2 years, has just been completed. The High Pressure Gaseous Burner (HPGB) rig at the NASA Glenn Research Center can operate at sustained pressures up to 60 atm with a variety of gaseous fuels and liquid jet fuel. The facility is unique as it is the only continuous-flow, hydrogen-capable, 60-atm rig in the world with optical access. It will provide researchers with new insights into flame conditions that simulate the environment inside the ultra-high-pressure-ratio combustion chambers of tomorrow's advanced aircraft engines. The facility provides optical access to the flame zone, enabling the calibration of nonintrusive optical diagnostics to measure chemical species and temperature. The data from the HPGB rig enables the validation of numerical codes that simulate gas turbine combustors, such as the National Combustor Code (NCC). The validation of such numerical codes is often best achieved with nonintrusive optical diagnostic techniques that meet these goals: information-rich (multispecies) and quantitative while providing good spatial and time resolution. Achieving these goals is a challenge for most nonintrusive optical diagnostic techniques. Raman scattering is a technique that meets these challenges. Raman scattering occurs when intense laser light interacts with molecules to radiate light at a shifted wavelength (known as the Raman shift). This shift in wavelength is unique to each chemical species and provides a "fingerprint" of the different species present. The facility will first be used to gather a comprehensive data base of laser Raman spectra at high pressures. These calibration data will then be used to quantify future laser Raman measurements of chemical species concentration and temperature in this facility and other facilities that use Raman scattering.

Nguyen, Quang-Viet↗

High-Pressure Gaseous Burner (HPGB) Facility Became Operational

A gas-fueled high-pressure combustion facility with optical access, developed over the last 3 years, is now collecting research data in a production mode. The High-Pressure Gaseous Burner (HPGB) rig at the NASA Glenn Research Center can operate at sustained pressures up to 60 atm with a variety of gaseous fuels and liquid jet fuel. The facility is unique because it is the only continuous-flow, hydrogen-capable 60-atm rig in the world with optical access. It will provide researchers with new insights into flame conditions that simulate the environment inside the ultra-high-pressure-ratio combustion chambers of tomorrow s advanced aircraft engines. The facility provides optical access to the flame zone through four fused-silica optical windows, enabling the calibration of nonintrusive optical diagnostics to measure chemical species and temperature. The data from the HPGB rig enable the validation of numerical codes that simulate gas turbine combustors.

Nguyen, Quang-Viet↗

Urban Air Mobility Network and Vehicle Type - Modeling and Assessment

This paper describes exploratory modeling of an on-demand urban air mobility (UAM) network and sizing of vehicles to operate within that network. UAM seeks to improve the movement of goods and people around a metropolitan area by utilizing the airspace for transport. Aircraft sizing and overall network performance results are presented that include comparisons of battery-electric and various hybrid-electric vehicles that are fueled with diesel, jet fuel, compressed natural gas, and liquefied natural gas (LNG). Hybrid-electric propulsion systems consisting of internal combustion engine-generators, turbine-generators, and solid oxide fuel cells are explored. Ultimately, the "performance" of the UAM network over a day for each of the different vehicle types, propulsion systems, and stored energy sources is described in four parameters: 1) the average cost per seat-kilometer, which considers the costs of the energy/fuel, vehicle acquisition, insurance, maintenance, pilot, and battery replacement costs, 2) carbon dioxide emission rates associated with vehicle operations, 3) the average passenger wait time, and 4) the average load factor, i.e., the total number of seats filled with paying passengers divided by the total number of available seats. Results indicate that the "dispatch model," which determines when and where aircraft are flown around the UAM network, is critical in determining the overall network performance. This is due to the often-conflicting desires to allow passengers to depart with minimal wait time while still maintaining a high load factor to reduce operating costs. Additionally, regardless of the dispatch model, hybrid-electric aircraft powered by internal combustion engines fueled with diesel or LNG are consistently the lowest cost per seat-kilometer. Battery-electric and future technology LNG/solid oxide fuel cell aircraft produce the lowest emissions (assuming the California grid) with LNG-fueled internal combustion engine-powered hybrids producing only slightly more carbon dioxide.

Assessment↗

Biofuel production from palm oil deoxygenation using nickel-molybdenum on zirconia catalyst using glycerol as a hydrogen donor

The growing demand for renewable energy has generated interest in biofuels as alternatives to fossil fuels. Second-generation biofuels, derived from deoxygenating fats and oils, have garnered a higher level of interest from industry and academia due to their potential for direct replacement of diesel and jet fuels. Palm oil, mostly cultivated in Thailand and composed of C16 and C18 fatty acids, is a primary feedstock sought for biofuel production. Palm oil deoxygenation contains several pathways that may or may not require hydrogen gas. This study aimed to produce biofuels in different fuel ranges, such as gasoline, jet fuel, and diesel, through palm oil deoxygenation using glycerol as a hydrogen source. Glycerol, a low-value byproduct, was used as a hydrogen donor, whereas nickel-molybdenum-supported catalysts were chosen for their high efficiency in deoxygenation and cost-effectiveness. The study investigated the impact of reaction time, temperature, and catalyst activation method on palm oil deoxygenation. Catalyst characterization methods, including XRD, SEM, TEM, XPS, FTIR, TGA, and nitrogen-sorption, were employed to understand the role of catalysts’ activity during palm oil upgrading. Findings indicated that alkane hydrocarbons are the major components in liquid products. The presence of excess hydrogen in post reaction gaseous phase proves the hydrogen donation capability of glycerol. Increased reaction time and temperature facilitated the removal of oxygen from palm oil. Nickel-molybdenum on zirconia activated by sulfidation demonstrated higher stability than by reduction activation.

09 BIOMASS FUELS↗

Toward net-zero sustainable aviation fuel with wet waste–derived volatile fatty acids

Significance To meet the growing demand for sustainable aviation fuels (SAF), conversion pathways are needed that leverage wet waste carbon and meet jet fuel property specifications. Here, we demonstrate SAF production from food waste–derived volatile fatty acids (VFA) by targeting normal paraffins for a near-term path to market and branched isoparaffins to increase the renewable content long term. Combining these distinct paraffin structures was shown to synergistically improve VFA-SAF flash point and viscosity to increase the renewable blend limit to 70%. Life cycle analysis shows the dramatic impact on the carbon footprint if food waste is diverted from landfills to produce VFA-SAF, highlighting the potential to meet jet fuel safety, operability, and environmental goals.

09 BIOMASS FUELS↗

Co-hydrotreatment of Bio-oil and Waste Cooking Oil to Produce Transportation Fuels

This paper reports the co-hydrotreatment of the heavy bio-oil fraction with waste cooking oil (WCO) using NiMo/γ-Al 2 O 3 catalyst, followed by the distillation of resulting deoxygenated oil and the characterization of resulting fuel cuts. The heavy BTG bio-oil fraction was obtained by removing the very reactive light-oxygenated compounds via rotary evaporation, subsequently mixed with 1-butanol. The resulting oil was blended with WCO and subjected to a two-step co-hydrotreatment process. The first step, called “stabilization,” is aimed at saturating highly reactive hydrogen-deficient compounds. The second step, called “deoxygenation,” aimed to remove bio-oil oxygen, primarily as H 2 O. This study examined the impact of varying bio-oil concentrations (0, 10, 20, 30, 40 wt.% of WCO) on the upgraded oil's yield, composition, and fuel properties. The resulting hydrotreated oil was distilled into gasoline-range, kerosene-range, and diesel-range hydrocarbons at <150 °C, 150 to 250 °C, and 250 to 350 °C, respectively. The yield of the hydrotreated oil indicates that as the bio-oil concentration increases, the amounts of coke (0.7 to 2.4 %) and water (2 to 10 wt. %) increase while the organic layer yields decrease (80 to 63 %). The coke yield was comparable to the coke yield obtained when co-processing the pyrolytic lignin fraction. This suggests that coke is formed from both the sugar oligomers and the lignin-derived oligomers. The UV-fluorescence analysis on the hydrotreated oil shows that more polycondensed and conjugated ring compounds formed as the bio-oil concentration is increased. These compounds are precursors of coke. FTIR results showed that most raw materials were converted to biofuels after the hydrotreatment. To achieve less than 1 wt. % of coke yield, blends with up to 20 wt. % pyrolysis oil should be used. An increase in bio-oil concentration leads to a slight increase in gasoline yield and a decrease in kerosene and diesel yields. The identified carbon species found in the fuel cuts include n-paraffin, iso-paraffin, cycloparaffin, and aromatics. Further, the jet fuel cut (kerosene) was characterized by density, surface tension, and viscosity. Our product conforms to the standard specifications for sustainable aviation fuels (Jet A-1). Further research is suggested to fine-tune the operating parameters for achieving reduced coke yield and enhanced kerosene yield.

09 BIOMASS FUELS↗

Hydrogen for the subsonic transport

Relations between air travel and fuel requirements are examined. Alternate fuels considered in connection with problems related to a diminishing supply of petroleum include synthetic jet fuel, methane, and hydrogen. A cruise flight of a subsonic aircraft on a hydrogen-fueled jet engine was demonstrated in 1957. However, more development work is required to provide a sound engineering base for a complete air transportation system using hydrogen as fuel. Aircraft designs for alternate fuels are discussed, giving attention to hydrogen-related technology already available and new developments which are needed.

Korycinski, P. F.↗

Air terminals and liquid hydrogen commercial air transports

An initial appraisal is made of results of two studies of the ground requirements of liquid hydrogen (LH2) air transports. Each hypothesized the use of a 400-passenger 5500 nautical mile range subsonic commercial LH2 transport. Two of the world's busiest commercial airports, Chicago O'Hare International and San Francisco International, were selected for study. The current and predicted wide-body traffic at these airports was assumed to simulate the LH2 transport traffic at these airports in the 1990-1995 time period. Both studies produced conceptual designs for facilities to generate the required quantities of fuel from pipeline gaseous hydrogen and to deliver liquid hydrogen to the airplanes. Although the LH2 and jet fuel facilities were kept apart, both study teams found it practical to converge the fuel supply lines so that with proper safety and operational procedures and specialized LH2 equipment both LH2 and jet fuel transports can use common ramp and gate facilities.

Korycinski, P. F.↗

Fuel Flexible Gas Turbine Combustor Flametube Facility Upgraded

In fiscal year 2003, test cell 23 of the Research Combustion Laboratory (RCL 23) at the NASA Glenn Research Center was upgraded with the addition of gaseous hydrogen as a working propellant and the addition of a 450-psig air-supply system. Test flexibility was further enhanced by upgrades to the facility control systems. RCL 23 can now test with gaseous hydrogen flow rates up to 0.05 lbm/sec and jet fuel flow rates up to 0.62 lbm/sec. Research airflow rates up to 3 lbm/sec are possible with the 450-psig supply system over a range of inlet temperatures. Nonvitiated, heated air is supplied from a shell and tube heat exchanger. The maximum nonvitiated facility air temperature is 1100 F at 1.5 lbm/sec. Research-section exhaust temperatures are limited to 3200 F because of material and cooling capacity limits. A variety of support systems are available depending on the research hardware configuration. Test section ignition can be provided via either a hydrogen air torch system or an electronic spark system. Emissions measurements are obtained with either pneumatically or electromechanically actuated gas sample probes, and the electromechanical system allows for radial measurements at a user-specified axial location for measurement of emissions profiles. Gas analysis data can be obtained for a variety of species, including carbon monoxide (CO), carbon dioxide (CO2), nitrogen oxides (NO and NOx), oxygen (O2), unburnt hydrocarbons, and unburnt hydrogen. Facility control is accomplished with a programmable logic control system. Facility operations have been upgraded to a system based on graphical user interface control screens. A data system is available for real-time acquisition and monitoring of both measurements in engineering units and performance calculations. The upgrades have made RCL 23 a highly flexible facility for research into low emissions gas turbine combustor concepts, and the flame tube configuration inherently allows for a variety of fuel nozzle configurations to be tested in a cost-effective manner. RCL 23 is poised to be a leading facility for developing modern low-emission fuel nozzles for use with jet fuel and alternative fuels.

Little, James E.↗

Airstart performance of a digital electronic engine control system in an F-15 airplane

The airstart performance of the F100 engine equipped with a digital electronic engine control (DEEC) system was evaluated in an F-15 airplane. The DEEC system incorporates closed-loop airstart logic for improved capability. Spooldown and jet fuel starter-assisted airstarts were made over a range of airspeeds and altitudes. All jet fuel starter-assisted airstarts were successful, with airstart time varying from 35 to 60 sec. All spooldown airstarts at airspeeds of 200 knots and higher were successful; airstart times ranged from 45 sec at 250 knots to 135 sec at 200 knots. The effects of altitude on airstart success and time were small. The flight results agreed closely with previous altitude facility test results. The DEEC system provided successful airstarts at airspeeds at least 50 knots lower than the standard F100 engine control system.

Licata, S. J.↗

Fuel Cell/Reformers Technology Development

NASA Glenn Research Center is interested in developing Solid Oxide Fuel Cell for use in aerospace applications. Solid oxide fuel cell requires hydrogen rich feed stream by converting commercial aviation jet fuel in a fuel processing process. The grantee's primary research activities center on designing and constructing a test facility for evaluating injector concepts to provide optimum feeds to fuel processor; collecting and analyzing literature information on fuel processing and desulfurization technologies; establishing industry and academic contacts in related areas; providing technical support to in-house SOFC-based system studies. Fuel processing is a chemical reaction process that requires efficient delivery of reactants to reactor beds for optimum performance, i.e., high conversion efficiency and maximum hydrogen production, and reliable continuous operation. Feed delivery and vaporization quality can be improved by applying NASA's expertise in combustor injector design. A 10 KWe injector rig has been designed, procured, and constructed to provide a tool to employ laser diagnostic capability to evaluate various injector concepts for fuel processing reactor feed delivery application. This injector rig facility is now undergoing mechanical and system check-out with an anticipated actual operation in July 2004. Multiple injector concepts including impinging jet, venturi mixing, discrete jet, will be tested and evaluated with actual fuel mixture compatible with reforming catalyst requirement. Research activities from September 2002 to the closing of this collaborative agreement have been in the following areas: compiling literature information on jet fuel reforming; conducting autothermal reforming catalyst screening; establishing contacts with other government agencies for collaborative research in jet fuel reforming and desulfurization; providing process design basis for the build-up of injector rig facility and individual injector design.

Source record↗

Mach 0.3 Burner Rig Facility at the NASA Glenn Materials Research Laboratory

This Technical Memorandum presents the current capabilities of the state-of-the-art Mach 0.3 Burner Rig Facility. It is used for materials research including oxidation, corrosion, erosion and impact. Consisting of seven computer controlled jet-fueled combustors in individual test cells, these relatively small rigs burn just 2 to 3 gal of jet fuel per hour. The rigs are used as an efficient means of subjecting potential aircraft engine/airframe advanced materials to the high temperatures, high velocities and thermal cycling closely approximating actual operating environments. Materials of various geometries and compositions can be evaluated at temperatures from 700 to 2400 F. Tests are conducted not only on bare superalloys and ceramics, but also to study the behavior and durability of protective coatings applied to those materials.

Fox, Dennis S.↗

2.3.4.104 - Lignin Conversion to Sustainable Aviation Fuel Blendstocks

The Lignin Conversion to Sustainable Aviation Fuel Blendstocks (LigSAF) project focuses on the conversion of lignin-rich streams to deoxygenated aromatic and cycloalkane blendstocks in the jet fuel range. This work is done in close collaboration with the BETO-funded Lignin-First Biorefinery Development project and industrial scale-up partners, and the work is closely guided by analysis to develop cost-effective and sustainable routes to produce lignin-based SAF blendstocks. To date, we have demonstrated the continuous catalytic conversion of a lignin oil from poplar to deoxygenated aromatic products at -85% C-mol yield. This hydrodeoxygenation process uses a stable, earth-abundant catalyst and requires no solvent. We have also established a baseline process model and associated techno-economic analysis and life cycle assessment that together demonstrate the potential to achieve cost parity with fossil carbon-based jet fuel at -70% reduction in greenhouse gas emissions. Current work is focused on expanding the slate of feedstocks for hydrodeoxygenation to include lignin oils from softwoods, agricultural residues, and grasses as well as from hydrolysis lignin substrates from biochemical conversion and pulp-and-paper processes. We are also undertaking catalyst development efforts to tune the reaction selectivity from aromatic compounds to cycloalkanes. Lastly, we are investigating reaction engineering strategies to slurry solids for hydrodeoxygenation reactions.

aromatics↗

Developing Non-Food Grade Brassica Biofuel Feedstock Cultivars with High Yield, Oil Content, and Oil Quality that are Suitable for Low Input Production Dryland Systems (Final Report)

The U.S. uses a substantial amount of fossil fuel as an energy source for a wide range for functions including home heating, agriculture and transportation. In the transportation sector, diesel and jet fuel are consumed at a rapid rate, and alternative liquid energy is being investigated globally and nationally to reduce our dependence on fossil fuel and reduce the impact of our carbon footprint on global climate change. Non-food Brassica crops have the potential of producing high oil yield (over 250 gal acre-1) and have oil quality highly desirable for use as biodiesel or bio jet fuel. Developing oilseed feedstock Brassica cultivars with higher seed and oil yield, with high oil quality and with resistance to pathogens, that can be grown with few chemical inputs will helping break our dependence on fossil fuels and reduce importation of fossil fuels. While some oilseed Brassicas have been grown on a small scale for many years in the Pacific Northwest (PNW), adoption has been limited, and the potential of the crops have not been realized or even fully investigated. This report summarizes the results of a study to develop superior non-food grade winter (B. napus) and spring (B. napus and B. juncea) oilseed cultivars suitable for a range of PNW, and other US environments with high resistance to the biotic and abiotic stresses suitable for high-quality biofuel feedstocks. In conducting this work, genome-wide association selection was used to dissect the genetic architecture of industrial Brassica oilseed germplasm for yield, quality, and resistance to biotic and abiotic stresses. A genome-wide bioinformatics approach was used to identify putative PRR (pattern recognition receptor) - type resistance genes that confer durable resistance to blackleg. A novel transgenic approach was developed to generate resistant non-food oilseed lines using PPR genes Br1033 and Br8486. These genes were inserted into regionally adapted oilseed cultivars.

09 BIOMASS FUELS↗

Turbulent Jet Flames Into a Vitiated Coflow

Examined is the vitiated coflow flame, an experimental condition that decouples the combustion processes of flows found in practical combustors from the associated recirculating fluid mechanics. The configuration consists of a 4.57 mm diameter fuel jet into a coaxial flow of hot combustion products from a lean premixed flame. The 210 mm diameter coflow isolates the jet flame from the cool ambient, providing a hot environment similar to the operating conditions of advanced combustors; this important high temperature element is lacking in the traditional laboratory experiments of jet flames into cool (room) air. A family of flows of increasing complexity is presented: 1) nonreacting flow, 2) all hydrogen flame (fuel jet and premixed coflow), and 3) set of methane flames. This sequence of experiments provides a convenient ordering of validation data for combustion models. Laser Raman-Rayleigh-LIF diagnostics at the Turbulent Diffusion Flame laboratory of Sandia National Laboratories produced instantaneous multiscalar point measurements. These results attest to the attractive features of the vitiated coflow burner and the well-defined boundary conditions provided by the coflow. The coflow is uniform and steady, isolating the jet flame from the laboratory air for a downstream distance ranging from z/d = 50-70. The statistical results show that differential diffusion effects in this highly turbulent flow are negligible. Complementing the comprehensive set of multiscalar measurements is a parametric study of lifted methane flames that was conducted to analyze flame sensitivity to jet and coflow velocity, as well as coflow temperature. The linear relationship found between the lift-off height and the jet velocity is consistent with previous experiments. New linear sensitivities were found correlating the lift-off height to coflow velocity and temperature. A blow-off study revealed that the methane flame blows off at a common coflow temperature (1260 K), regardless of coflow or jet velocity. An explanation for this phenomenon is that entrainment of ambient air at the high lift-off heights prevents autoignition. Analysis of the results suggests that flame stabilization occurs through a combination of flame propagation, autoignition, and localized extinction processes. Proposed is an expanded view of distributed reaction combustion based on analysis of the distributions of probe volume conditions at the stabilization region of the lifted hydrogen and methane flames. Turbulent eddies the size of the flame thickness mix fuel and hot coflow across the flame front, thereby enhancing the reaction zone with autoignition of reactants at elevated temperatures; this is the reverse effect of turbulent flames in ambient air, where intense turbulence in cool mixtures result in localized extinction. Each of the three processes (i.e., flame propagation, autoignition and localized extinction) contributes to flame stabilization in varying degrees, depending on flow conditions.

Holdeman, James D.↗

Fuel Sensitivity of Gas Emissions, Lean Blowout and Combustion Dynamics for a 9-Point LDI Combustor

Fuel sensitivity of gaseous emissions, approach to lean blowout and combustion dynamics are evaluated in this study. Experiments were conducted at the NASA Glenn Research Center's CE-5 flame tube test facility with a 9-point Swirl-Venturi Lean Direct Injection (SV-LDI) combustor. A reference jet fuel (A2) and two test fuels (C1 and C3) from were provided by the National Jet Fuels Combustion Program (NJFCP). C1 is essentially a 2-component iso-paraffin test fuel with a low cetane number of 17, and C3 is a high viscosity test fuel. Approach to lean blowout was monitored in terms of the rapid increase in CO emissions index as equivalence ratio decreased, but testing did not proceed all the way to lean blowout (LBO). Burning C1 was found to produce lower NOx emissions, but C1 flame temperatures were about 25 K higher relative to A2 at near LBO points (where CO emissions increased very rapidly). The NOx emissions of C3 were similar to A2. At low power conditions where fuel injector performance is not optimized for this 9-point LDI combustor, C3 had higher CO emissions than A2 and C1, likely due to C3's higher viscosity relative to A2 and C1. No discernable difference in combustion dynamics was observed between the three fuels tested in the 9-point LDI combustor. While a systematic ignition test campaign was not conducted, it was observed that C1 required a higher equivalence ratio and inlet air temperature for test rig ignition compared to A2 and C3.

Lean Direct Injection↗

Fuel Sensitivity of Gas Emissions, Lean Blowout and Combustion Dynamics for a 9-Point LDI Combustor

Fuel sensitivity of gaseous emissions, approach to lean blowout and combustion dynamics are evaluated in this study. Experiments were conducted at the NASA Glenn Research Center's CE-5 flame tube test facility with a 9-point Swirl-Venturi Lean Direct Injection (SV-LDI) combustor. A reference jet fuel (A2) and two test fuels (C1 and C3) from were provided by the National Jet Fuels Combustion Program (NJFCP). C1 is essentially a 2-component iso-paraffin test fuel with a low cetane number of 17, and C3 is a high viscosity test fuel. Approach to lean blowout was monitored in terms of the rapid increase in CO emissions index as equivalence ratio decreased, but testing did not proceed all the way to lean blowout (LBO). Burning C1 was found to produce lower NOx emissions, but C1 flame temperatures were about 25 K higher relative to A2 at near LBO points (where CO emissions increased very rapidly). The NOx emissions of C3 were similar to A2. At low power conditions where fuel injector performance is not optimized for this 9-point LDI combustor, C3 had higher CO emissions than A2 and C1, likely due to C3's higher viscosity relative to A2 and C1. No discernable difference in combustion dynamics was observed between the three fuels tested in the 9-point LDI combustor. While a systematic ignition test campaign was not conducted, it was observed that C1 required a higher equivalence ratio and inlet air temperature for test rig ignition compared to A2 and C3.

Combustion dynamics↗

Structure of a swirl-stabilized spray flame by imaging, laser Doppler velocimetry, and phase Doppler anemometry

Data are presented which describe the mean structure of a steady, swirl-stabilized, kerosene spray flame in the near-injector region of a research furnace. The data presented include ensemble-averaged results of schlieren, luminosity, and extinction imaging, measurement of the gas phase velocity field by laser Doppler velocimetry, and characterization of the condensed phase velocity by phase Doppler anemometry. The results of these studies define six key regions in the flame: the dense spray region; the rich, two-phase, fuel jet; the main air jet; the internal product recirculation zone; the external product recirculation zone; and the gaseous diffusion flame zone. The first five of these regions form a conical mixing layer which prepares the air and fuel for combustion. The air and fuel jets comprise the central portion of this mixing layer and are bounded on either side by the hot product gases of the internal and external recirculation zones. Entrainment of these product gases into the air/fuel streams provides the energy required to evaporate the fuel spray and initiate combustion. Intermittency of the internal recirculation and spray jet flows accounts for unexpected behavior observed in the aerodynamics of the two phases. The data reported herein are part of the database being accumulated on this spray flame for the purpose of detailed comparison with numerical modeling.

Edwards, C. F.↗