Influence of blending cycloalkanes on the energy content, density, and viscosity of Jet-A
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Concern for emission reduction has motivated the development of new cost-effective alternative sustainable aviation fuels (SAFs). Drop-in SAFs with blends of the certified and the alternative fuels are beneficial because they do not require engine modifications for use in current aviation engines. Combustion characteristics are of particular concern when comparing a new fuel with Jet-A. Lean blow-off and flame stabilization have been identified to be governed by the fuel propensity to autoignition, i.e. derived cetane number. However, fundamental investigation is required to identify the impact of derived cetane number on the combustion mode of flame stabilization in a realistic combustor. The combustion mode has also a direct impact on turbulent combustion modeling closures. DNS simulations are performed in the low-Mach solver of the Pele Suite called PeleLMeX. Lagrangian multi-phase modeling is used to capture the liquid spray injection of Jet-A (reference fuel) and C1 as a representative of a low cetane number SAF. Adaptive Mesh Refinement (AMR) is used to enable a more efficient simulation of a more realistic domain size and embedded boundary treatment is used to model a bluff-body geometry. Local extinction and edge flame propagation were observed for both fuels. The edge flame propagation mode was quantified in terms of a Damkohler number defined as the ratio between progress variable reaction rate and its diffusive flux. Initial analysis suggests that a mixed mode combustion occurs for the edge flame propagation, with flame propagation assisted by ignition and autoignition co-existing for both Jet-A and C1 flames. The analysis of the extinction region shows a larger progress variable for Jet-A which can further increase the local displacement speed and present a faster reignition of the stoichiometric mixture fraction.
For safety purposes, reliable reignition of aircraft engines in the event of flame blow-out is a critical requirement. Typically, an external ignition source in the form of a spark is used to achieve a stable flame in the combustor. However, such forced turbulent ignition may not always successfully relight the combustor, mainly because the state of the combustor cannot be precisely determined. Uncertainty in the turbulent flow inside the combustor, inflow conditions, and spark discharge characteristics can lead to variability in sparking outcomes even for nominally identical operating conditions. Prior studies have shown that of all the uncertain parameters, turbulence is often dominant and can drastically alter ignition behavior. For instance, even when different fuels have similar ignition delay times, their ignition behavior in practical systems can be completely different. In practical operating conditions, it is challenging to understand why ignition fails and how much variation in outcomes can be expected. The focus of this work is to understand relight variability induced by turbulence for two different aircraft fuels, namely Jet-A and a variant named C1. A detailed, previously developed simulation approach is used to generate a large number of successful and failed ignition events. Using this data, the cause of misfire is evaluated based on a discriminant analysis that delineates the difference between turbulent initial conditions that lead to ignition or failure. From the discriminant analysis, a compressed sensing algorithm is then applied to help pinpoint the locations of relevant turbulent features. Findings from the discriminant analysis are confirmed with the time history of near kernel properties. Next, a clustering strategy is used to identify ignition and misfire modes. With this approach, it was determined that the cause of ignition failure is different for the two fuels. While it was found that Jet-A is influenced by fuel entrainment, C1 was found to be more sensitive to small scale turbulence features. Finally, a larger variability is found in the ignition modes of C1, which can be subject to extreme events induced by kernel breakdown.
Here, this work outlines an optimized process for converting 2,3-butanediol (BDO) into sustainable aviation fuel (SAF) and C4 chemicals. BDO is reactively separated from fermentation broth by forming dioxolanes, which are converted to isobutyraldehyde, methyl ethyl ketone (MEK), and 1,3-butadiene. These intermediates are reduced and dehydrated over Cu/ZSM-5 to form alkenes, which can be oligomerized and hydrotreated to jet-range alkanes. Previous BDO-dioxolane-alkene processes are limited by the requirement for a continuous aldehyde source for dioxolane formation. Brønsted acidic zeolites catalyze dioxolane deacetalization to form isobutyraldehyde and MEK in a >2:1 molar ratio, providing an internal, recyclable aldehyde source. Dioxolane formation optimization was performed to achieve >95% dioxolane yields over Amberlyst-15 and minimize isobutyraldehyde recycle. The overall BDO-dioxolane-fuel process yields an alkane mixture that enables at least a 50% v/v blend with Jet-A. Techno-economic analyses and life cycle assessments for this BDO-dioxolane-fuel process yield scenarios with <$2.50 per gallon gas equivalent and >58% reduction in CO2 emissions.
With a view towards renewable feedstock while decreasing the CO2 footprint associated with jet travel, biofuels are receiving increasing interest. Presented here is an overview of non-volatile particulate matter (nvPM) emissions, i.e. “soot” as gauged by varied TEM analyses for a J-85 turbojet fueled with Jet-A as well as with blends of Jet-A using Camelina biofuel. A unifying explanation is provided encompassing fuels and spanning length scales across three orders of magnitude. The variation of primary particle size, aggregate size and nanostructure are analyzed as a function of biofuel blend across range of engine thrust levels. The postulate is based on where fuels start along the soot formation pathway. Increasing biofuel content lowers aromatic concentration while placing increasing dependence upon fuel pyrolysis reactions to form the requisite concentration of aromatics for particle inception and growth. The required “kinetic” time for pyrolysis reactions to produce benzene and multi-ring PAHs allows increased fuel-air mixing by turbulence, diluting the fuel-rich soot-forming regions, effectively lowering their equivalence ratio. With a lower precursor concentration, particle inception is slowed, the resulting concentration of primary particles is lowered and smaller aggregates. The lower equivalence ratio also results in smaller primary particles given the lower concentration of growth species.
This paper investigates options to produce low carbon and renewable aviation fuel through existing commercial first generation biorefineries, which could be strategic given the rapid growth of the electric vehicle market for personal mobility. We evaluate the environmental impact of retrofitting a first generation biorefinery to produce aviation fuel through chemical process simulation. The analysis investigates the potential for reducing greenhouse gas (GHG) emissions and displacing fossil fuel (petroleum-based jet kerosene) in the aviation fuel industry through using corn feedstocks in dry grind biorefineries to convert sugars to 1,4-dimethylcyclooctane (DMCO), which qualifies as renewable jet-A fuel blend and is infrastructure compatible. Further, the average life cycle GHG emissions for a baseline case and a scenario with carbon capture and storage (CCS) of fermentative CO 2 are 36 and 5g CO 2 e/MJ DMCO, respectively. Investment in CCS at the biorefinery and adoption of crop best management practices on farms are essential for mitigating the risks of induced land use change GHG emissions for existing corn biorefineries. DMCO as a low-carbon aviation fuel could be a strategic fuel product for retrofitting existing corn dry grind facilities. For aviation fuel supply, corn dry grind facilities could displace about 12% of jet fuel demand in the near term, which would meet sustainable aviation fuel policy targets. We conclude that corn-to-DMCO shows promise for near-term low-carbon fuel markets in the aviation industry and as a bridge to developing biomass-based jet fuel in the future.
Waste terpenes from wood drying are typically processed using a Regenerative Thermal Oxidizer (RTO) and converted to CO2 which is then released to the atmosphere. A novel alternative to this approach is to capture these terpenes using Fluidized Bed Concentrator (FBC) technology developed by CaptisAire which provides a useful waste carbon feedstock for subsequent upgrading. We have developed a catalytic approach where these waste terpenes (comprised of pinenes, limonene, and camphene), are converted to aromatic, and cycloalkane hydrocarbons suitable for use as a Sustainable Aviation Fuel (SAF) blendstock without the need for additional hydrogen. This provides a renewable source for aviation fuel aromatics and increases the potential blend content of renewably sourced alkanes from Hydroprocessed Esters and Fatty Acids (HEFA) and Alcohol to Jet (ATJ) processes. Terpenes were converted in a batch reactor at 260 °C and 120 psi N2 using a combination of Pd/C and H-BEA zeolite. Experimental results infer the role of the zeolite Brønsted acid to facilitate isomerization of pinenes and camphene to limonene, which then undergoes subsequent dehydro-aromatization to p-cymene using Pd/C. Hydrogen release from the dehydro-aromatization process, enables inert conversion of monoterpenes to cycloalkanes without additional hydrogen. Monoterpenes conversion to C10 aromatics (60%) and C10 cycloalkanes (40%) in an inert environment, provides a viable route for SAF blendstock sourced directly from captured waste terpenes. Transition to commercial off-the-shelf catalysts, facilitates scale-up of the terpene conversion process and improves commercial viability. We subsequently created hydrocarbon blends using HEFA or ATJ and converted terpenes, providing a 100% SAF blend with potential to replace traditional Jet-A.
Terpenes are a diverse group of molecules that are synthesized by plants and microorganisms through combining units of isoprene (2-methyl-1,3-butadiene). They typically contain rings and methyl branches, which gives them high energy densities and low freezing points and makes them appealing candidates for sustainable transportation biofuels. Between the original biosynthesis and upgrading options such as hydrogenation, they have a large degree of freedom of structures, e.g., different carbon skeletons, positions of double bonds, and functional groups. Therefore, structure-property data is needed to downselect potential fuel candidates. Here, we measured the sooting tendencies of 17 C10 monoterpenes and 7 of their hydrogenated analogues. The hydrogenated compounds were custom synthesized, so the quantities were too small for conventional smoke point measurements. Thus, the sooting tendencies were quantified with yield sooting index (YSI), which is based on the soot yield in a fuel-doped non-premixed methane flame. Derived smoke points (DSPs) were estimated from a correlation between YSI and smoke point for other hydrocarbons. The YSI of terpenes and their derivatives varies widely from 85.6 to 248.5. The YSI follows the trend: terpenes > dihydroterpenes > tetrahydroterpenes. The DSPs of all the tetrahydroterpenes and some dihydroterpenes are higher than that of a Jet-A fuel sample, suggesting that they offer soot reduction benefits. Further, the YSIs depend strongly on molecular structure; for example, α-pinene and β-pinene have identical carbon skeletons and differ only in the position of one carbon-carbon double bond, but the YSI of α-pinene is 34% higher than that of β-pinene. Detailed decomposition analysis via density functional theory (DFT) suggests that compared with β-pinene, α-pinene requires fewer steps to form the first aromatic ring and the process is more thermodynamically favorable. The YSI difference between the pinenes is mainly affected by the identity of the products from the dominant decomposition pathways.
Combustion emissions from aviation contribute to the formation of condensation trail (contrail) that can lead to the formation of anthropogenic cirrus clouds. Ice particles that form contrails are observed to have a linear correlation with soot particle number density. Synthetic aviation fuels (SAFs) offer a promising route to mitigate the production of soot particles while also increasing energy security. Although studies have focused on combustion and spray behavior, the detailed investigation of soot formation processes for different jet fuels and their impact on models for computational fluid dynamics (CFD) applications is not well understood. Moreover, experimental measurements of soot for canonical flames using Synthetic aviation fuels (SAF) for model validation remain scarce. To address this, we use employed the Lawrence Livermore National Laboratory (LLNL) detailed soot model based on the discrete sectional method. Additionally, we develop two reduced chemical mechanisms for Jet-A and Alcohol-to-Jet (C1) that are suitable for turbulent flame simulations and couple them with the Hybrid Method of Moments (HMOM). The detailed and reduced model frameworks are validated against experimental measurements of soot volume fraction (ƒ ν ) from a counterflow burner experiment previously reported in the literature. Given the good agreement between modeling results and experimental measurements for the (1) spatial distribution of ƒ ν and (2) the non-linear variation of peak ƒ ν with strain rate, we further investigate the modeled sub-processes (nucleation, condensation, surface growth, and oxidation) using the LLNL model to analyze the assumptions in the reduced model framework. Furthermore, the results indicate a significant contribution from resonant radicals to the surface growth of soot particles, which are not accounted for in the current implementation of HMOM and could help reconcile soot predictions by the reduced model with observations.
Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.
Abstract There are many challenges of commissioning a hydrogen combustor into future gas turbine engines; especially regarding achieving emissions goals. Previously, Escudero et al. and Tran et al. conducted a study to adapt the liquid fuel Lean Direct Injection (LDI) concept from Jet-A to gaseous natural gas-hydrogen blends and pure hydrogen [1], [2]. Experimental data was collected at atmospheric conditions using a Box Behnken design of experiments. The design of experiments suggested that biasing the air split in favor of the inner air circuit and increasing the swirl strength of this inner air passage resulted in improved NOx emissions, while the inverse was true for stability, which was quantified by studying the lean blowoff point (LBO) [1], [2]. The trends revealed by the original experiment [1], [2] provided a design direction for further iterations of the experimental hardware. The study presented herein describes the further investigation of such LDI injectors through experimental methods and computational fluid dynamic (CFD) simulations at atmospheric conditions, which were used to identify potential flow behaviors driving enhanced emissions performance. Further evaluation of select injectors from both studies was then conducted at elevated pressures up to 6 atmospheres. The results from both experiments are presented in this study, which include flame observations, emissions measurements, and operational challenges. NOx emissions results are reported on a volume basis in ppmvd corrected to 15% O2 and corrected for fuel. A predictive model for relating NOx emissions to test conditions at atmospheric conditions show high significance to adiabatic flame temperature while little to no significance to fuel composition for the best performing configurations. The results illustrate the connection between atmospheric testing and testing elevated pressures. The design direction indicated by the initial tests and CFD results in promising configurations for implementation into a Multi-point LDI array.
X-ray phase contrast imaging is conducted at 90,517 Hz on a fuel spray to characterize the breakup of the bulk fuel into ligaments and individual droplets in a single-sector, swirl-stabilized combustor under reacting conditions. Phase contrast imaging is used to qualitatively assess spray breakup for two fuels: Jet-A, which represents a normal viscosity fuel, and a blend of JP-5 (64%) and farnesane (36% by volume), which represents a high-viscosity fuel, at three fuel-flow rates and two air inlet temperatures. Time-series images of the fuels show that atomization occurs much more rapidly at higher fuel pressure with thinner ligaments being rapidly shredded. The high-viscosity fuel is qualitatively observed to have markedly longer, thicker ligaments and larger droplet diameters after the primary breakup than the normal viscosity fuel. Using an image processing and droplet quantification strategy, the mean droplet velocity magnitudes were found to decrease with decreasing fuel pressure and fuel-flow rate. The increase in preheat temperature from 323 to 370 K results in an increase in the mean droplet velocity magnitude and a decrease in numerical average and Sauter mean diameter, indicating improved atomization. The high-viscosity fuel was found to have larger average droplet diameters at each condition than the normal viscosity fuel. The increased preheat is found to enhance the combustion efficiency, which is hypothesized to couple with the improved atomization due to the higher combustion temperatures. This indicates the importance of examining spray atomization and breakup under realistic combusting conditions for relevant fuels as the heat release directly couples with the atomization process.
In the past, clean combustion systems were characterized by high system development costs due to growing complexity and escalating manufacturing costs from conventional manufacturing processes. As a result, high efficiency concepts are difficult to design and more difficult to be cost-effectively manufactured. In recent years, with the introduction of additive manufacturing (AM) technologies, the rapid prototyping and mass production processes of clean combustion systems are promising to be significantly simplified with significant reduction in terms of engine manufacturing cost and engine energy cost. Compared with conventional manufacturing built parts, the AM process enabled a simpler design to be adopted for the nozzle, reducing the number of required braze and weld joints from twenty-five to just five. The resulting nozzle was 25% lighter and five times more durable and contributed to a 15% reduction in fuel burn in comparison with the previous model produced. Applying these improvements to a fleet of 5,000 turbofan engines at 150 kN thrust would result in fuel cost savings of $ \$ $6B annually (at $ \$ $5/gallon Jet-A fuel price, 700 gallon/hour fuel consumption rate, and 2,300 operational hours per year), and reduce CO2 emissions by more than 25 million tons per year. These advances support core Department of Energy (DOE) missions in energy efficiency, improving productivity, and environmental sustainability. Maximizing the benefit of these new capabilities will require high prediction capability of high speed turbulent flow with wall modeled Large Eddy Simulation (LES). GE Aviation maintains that advanced simulation technology and supercomputing is required in order to provide the appropriate boundary conditions to realize the maximum potential of AM and Ceramic Matrix Composite to reduce cooling flow, a first order penalty on the Brayton cycle. The algorithm developed using the ANSYS/Fluent software would provide the foundation for entirely new avenues of research and development with potential multi-billion dollar impact to the US economy, and significant reduction in carbon based emissions across the aerospace and power generation industries. The formulation of this iWLES (integral wall model for LES) is generic and allows to capture the changes in flow dynamics that have a significant impact on the wall bounded flow characteristics, such as swirler effective area, bulk swirl number, local pressure distribution, exit velocity profile, and turbulence kinetic energy profile. A periodic channel flow with rough flat plate is simulated using LES (Wall-Adapting Local Eddy-viscosity) model to verify the implementation of iWLES in the Fluent User Defined Function (UDF). As the flow fields are highly sensitive due to surface roughness of the wall bounded flows in the combustion systems, there is significant potential to conduct further LES studies focusing on the turbulence boundary layer interaction. Accurately capturing near wall physics will elucidate the impact of rough surfaces on combustor flow and aero-thermal interactions.
In the past, clean combustion systems were characterized by high system development costs due to growing complexity and escalating manufacturing costs from conventional manufacturing processes. As a result, high efficiency concepts are difficult to design and more difficult to be cost-effectively manufactured. In recent years, with the introduction of additive manufacturing (AM) technologies, the rapid prototyping and mass production processes of clean combustion systems are promising to be significantly simplified with significant reduction in terms of engine manufacturing cost and engine energy cost. Compared with conventional manufacturing built parts, the AM process enabled a simpler design to be adopted for the nozzle, reducing the number of required braze and weld joints from twenty-five to just five. The resulting nozzle was 25% lighter and five times more durable and contributed to a 15% reduction in fuel burn in comparison with the previous model produced. Applying these improvements to a fleet of 5,000 turbofan engines at 150 kN thrust would result in fuel cost savings of $6B annually (at $5/gallon Jet-A fuel price, 700 gallon/hour fuel consumption rate, and 2,300 operational hours per year),and reduce CO2 emissions by more than 25 million tons per year. These advances support core Department of Energy (DOE)missions in energy efficiency, improving productivity, and environmental sustainability. Maximizing the benefit of these new capabilities will require high prediction capability of high speed turbulent flow with wall modeled Large Eddy Simulation (LES). GE Aviation maintains that advanced simulation technology and supercomputing is required in order to provide the appropriate boundary conditions to realize the maximum potential of AM and Ceramic Matrix Composite to reduce cooling flow, a first order penalty on the Brayton cycle. The algorithm developed using the ANSYS/Fluent software would provide the foundation for entirely new avenues of research and development with potential multi-billion dollar impact to the US economy, and significant reduction in carbon based emissions across the aerospace and power generation industries. The formulation of this iWLES (integral wall model for LES) is generic and allows to capture the changes in flow dynamics that have a significant impact on the wall bounded flow characteristics, such as swirler effective area, bulk swirl number, local pressure distribution, exit velocity profile, and turbulence kinetic energy profile. A periodic channel flow with rough flat plate is simulated using LES (Wall-Adapting Local Eddy-viscosity) model to verify the implementation of iWLES in the Fluent User Defined Function (UDF). As the flow fields are highly sensitive due to surface roughness of the wall bounded flows in the combustion systems, there is significant potential to conduct further LES studies focusing on the turbulence boundary layer interaction. Accurately capturing near wall physics will elucidate the impact of rough surfaces on combustor flow and aero-thermal interactions.
In 2018 13.7 EJ of fuel were consumed by the global commercial aviation industry. Worldwide, demand will increase into the foreseeable future. Developing Sustainable Aviation Fuels (SAFs), with decreased CO 2 and soot emissions, will be pivotal to the on-going mitigation efforts against global warming. Minimizing aromatics in aviation fuel is desirable because of the high propensity of aromatics to produce soot during combustion. Because aromatics cause o-rings to swell, they are important for maintaining engine seals, and must be present in at least 8 vol% under ASTM-D7566. Recently, cycloalkanes have been shown to exhibit some o-ring swelling behavior, possibly making them an attractive substitute to decrease the aromatic content of aviation fuel. Cycloalkanes must meet specifications for a number of other physical properties to be compatible with jet fuel, and these properties can vary greatly with the cycloalkane chemical structure, making their selection difficult. Building a database of structure-property relationships (SPR) for cycloalkanes greatly facilitates their furthered inclusion into aviation fuels. The work presented in this paper develops SPRs by building a data set that includes physical properties important to the aviation industry. The physical properties considered are energy density, specific energy, melting point, density, flashpoint, the Hansen solubility parameter, and the yield sooting index (YSI). Further, our data set includes cycloalkanes drawn from the following structural groups: fused cycloalkanes, n-alkylcycloalkanes, branched cycloalkanes, multiple substituted cycloalkanes, and cycloalkanes with different ring sizes. In addition, a select number of cycloalkanes are blended into Jet-A fuel (POSF-10325) at 10 and 30 wt%. Comparison of neat and blended physical properties are presented. One major finding is that ring expanded systems, those with more than six carbons, have excellent potential for inclusion in SAFs. Our data also indicate that polysubstituted cycloalkanes have higher YSI values.
The increased accessibility of commercial aviation to the general population has in-creased the conventional jet fuel consumption, thereby causing increased CO2 emissions. One of the strategies to reduce the environmental impact is to use sustainable aviation fuels (SAFs). SAFs are jet fuels obtained from renewable resources such as biomass and waste streams such as plastics/municipal solid wastes. Even though the use of SAFs has been gaining importance over the last two decades, only a few numerical studies on their usage have been reported so far. In this study, two SAFs namely, Alcohol to Jet (ATJ) and Hydrotreated Esters and Fatty Acids (HEFA), are chosen and their use in a simple, Lead Direct Injection (LDI) combustor is studied. The focus of this study is limited to the thermo-chemical properties of the fuels and their impact on fuel distribution and evaporation. Hence, only non-reactive simulations are performed. A high accuracy, adaptive mesh refinement based low-Mach solver, PeleLMeX, is used for performing the simulations. The time-averaged flow results indicate faster evaporation of HEFA when compared to ATJ and Jet-A. The difference in fuel evaporation rates is attributed to the differences in fuel viscosity and surface tension properties and the concomitant variations in the fuel droplet size distributions.
The increased accessibility of commercial aviation to the general population has in-creased the conventional jet fuel consumption, thereby causing increased CO2emissions. One of the strategies to reduce the environmental impact is to use sustainable aviation fuels (SAFs). SAFs are jet fuels obtained from renewable resources such as biomass and waste streams such as plastics/municipal solid wastes. Even though the use of SAFs has been gaining importance over the last two decades, only a few numerical studies on their usage have been reported so far. In this study, two SAFs namely, alcohol to jet (ATJ) and hydrotreated esters and fatty acids (HEFA), are chosen and their use in a simple, lead direct injection (LDI) combustor is studied. The focus of this study is limited to the thermo-chemical properties of the fuels and their impact on fuel distribution and evaporation. Hence, only non-reactive simulations are performed. A high accuracy, adaptive mesh refinement based low-Mach solver, PeleLMeX, is used for performing the simulations. The time-averaged flow results indicate faster evaporation of HEFA when compared to ATJ and Jet-A. The difference in fuel evaporation rates is attributed to the differences in fuel viscosity and surface tension properties and the concomitant variations in the fuel droplet size distributions.