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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.

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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Preliminary modeling of triply periodic minimal surface (TPMS) structures using RELAP5-3D

With the United States Department of Energy (DOE)’s goal of quadrupling the nation’s nuclear energy supply by 2050, and with the Advanced Fuels Campaign pushing for new types of advanced reactor fuels and geometries, the need has arisen for new nuclear fuel designs. One such design is to swap out current nuclear fuel geometries in exchange for another type of geometry, called a Triply Periodic Minimal Surface (TPMS). TPMSs are self-supporting, infinitely repeating lattices—attributes that lend themselves well to additive manufacturing. These surfaces also possess enhanced heat transfer properties thanks to their internal area changes and large surface-area-to-volume ratios. Their drawback, however, is an increased pressure drop. Given the small amount of correlations and data (Reynolds numbers in the 2,000–8,000 range), and the minimal amount of experience so far obtained by modeling TPMS structures using 1D systems codes such as the Reactor Excursion and Leak Analysis Program (RELAP5-3D), further research into this topic was needed. Using data from the University of Wisconsin - Madison (UW), curve fits were created for both a Heat Transfer Coefficient (HTC) correlation and a Darcy friction factor empirical coefficient correlation. The curves’ coefficients and multipliers were then output and utilized in RELAP5-3D models of two upcoming experiments—Flow Loop for INFLUX Pressure drop (FLIP) and Microreactor Agile Non-nuclear Experimental Test (MAGNET)—aimed at increasing the available data for Reynolds numbers to the 16,000–36,000 range for TPMS structures. The models were run under the conditions utilized by a Computational Fluid Dynamics (CFD) analysis performed by another group at Idaho National Laboratory. Only CFD pressure drop values were obtained from the FLIP test, and those values showed that the RELAP5-3D models had a lower rate of pressure increase in comparison to the CFD values. In addition, there seemed to be a vertical shift upward in the pressure drop for both models whenever the TPMS porosity decreased, and the RELAP5-3D models showed a higher vertical shift in comparison to the CFD values. The MAGNET results did not correspond to any CFD or experimental results against which they could be compared, so they were instead compared against the proposed CFD input conditions. These values were then compared with each other to make sure the model seemed to be performing as expected, paving the way for future tests that can be run for the purpose of further analyses and comparisons. The pressure drop increased with temperature and mass flow rate independently. The temperature change would decrease with increasing mass flow rate and temperature, which was just as we expected based on the fact that the lower viscosity and decreased density would result in higher friction and churning losses. The last metric that was assessed was the enthalpy flow change, which increased with increasing mass flow rate and decreasing temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Development of Ionic Liquid-Additized, GF-5/6 Compatible Low-Viscosity Oils for Automotive Engine and Rear Axle Lubrication for 4% Improved Fuel Economy

This joint project among ORNL, GM, and DRO successfully developed ionic liquid-additized low viscosity lubricants, SAE 0W-12 and 70W-80, for both IC engine and rear axle lubrication, respectively, and demonstrated combined vehicle fuel economy improvement (FEI). Phosphonium-alkylphosphate ILs have been found to be the most effective among the candidates in protecting surface damage from both sliding wear and rolling contact fatigue, and optimal IL concentrations have been determined. The IL’s impact on three-way catalyst seems to be significantly less adverse than the conventional ZDDP. Oil formulations were optimized for both energy efficiency and wear protection. Tribological bench testing of the IL-additized low-viscosity oils showed at least 40% lower boundary friction, more than 60% lower elastohydrodynamic friction, and greater than 50% less wear compared with commercial baselines. IL-additized lubricants have demonstrated FEI by 9.9% in engine dynamometer tests under extreme conditions and 6.9% increased power output in gear rig tests. Prototype IL-additized engine oil and rear axle fluid exhibited combined FEI of 1.39% and 3.24% benchmarked against the state-of-the-art baselines in vehicle testing of fresh oils under the Federal Test Procedure (FTP) city cycle and Highway Fuel Economy Driving Schedule (HWFET), respectively. Used oil analysis suggested that the IL-additized low-viscosity oils produced less wear than the commercial baselines. The gained fundamental understanding and demonstrated FEI in this work pave the way for future development and implementation of the ionic liquid technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Surface Acoustic Wave Sensors for Refrigerant Leak Detection: Compact, Inexpensive, Selective and Sensitive Sensors

Pacific Northwest National Laboratory (PNNL), in collaboration with Parker and Hannifin, is developing a compact, inexpensive, and highly sensitive and selective surface acoustic wave sensor coated with fluorophillic sorbent for detecting fluorocarbon leaks from HVAC systems. Having a highly effective sorbent sensitive to fluorocarbon refrigerant vapors provides a means to develop a sensing device for leak detection. Surface acoustic wave (SAW) sensors with a gas sensing film deposited between the delay lines or on the interdigital transducer have been used to detect gas and vapor molecules in harsh environments with high sensitivity. As part of this project, PNNL screened several sorbent materials that are shown to be selective towards fluorocarbon refrigerant (R32) molecule. The identified sorbent materials were synthesized, characterized, and tested towards R32 using various spectroscopic technique. Next, the sorbent material was coated on a SAW sensor as a thin film using vapor deposition and drop coating methods. The coated thin film was further characterized and tested towards the detection of pure R32 and R32 in ambient air at room temperature to demonstrate the SAW response towards R32 in presence of other competing gases and vapors in air.

42 ENGINEERING↗
DOE OSTI2025

Surface and bulk two-level-system losses in lithium niobate acoustic resonators

Lithium niobate (LN) is a promising material for building acoustic resonators used in quantum applications, but its performance is limited by poorly understood material defects called two-level systems (TLSs). Here, in this work, we fabricate high-performance acoustic resonators from LN with quality factors up to 6 ×10 7 and use them to separate bulk and surface contributions to TLS loss. By comparing these bulk acoustic wave (BAW) resonators with previous surface-acoustic-wave and phononic-crystal studies, we show that devices with high surface-participation ratios are limited by surface TLSs, while our BAW devices reveal an intrinsic bulk TLS limit. Through systematic surface treatments and microscopy, we demonstrate that BAW resonator performance remains unchanged despite surface modifications, confirming operation in a bulk-limited regime. Here, our work establishes quantitative bounds on both surface and bulk TLS losses in LN within the context of the material growth and fabrication approaches we have pursued, and it provides guidance for future device engineering and materials development.

acoustic wave phenomena↗
DOE OSTI2020

Enhancement of Photoemission on p-Type GaAs Using Surface Acoustic Waves

We demonstrate that photoemission properties of p-type GaAs can be altered by surface acoustic waves (SAWs) generated on the GaAs surface due to dynamical piezoelectric fields of SAWs. Multiphysics simulations indicate that charge-carrier recombination is greatly reduced, and electron effective lifetime in p-doped GaAs may increase by a factor of 10× to 20×. It implies a significant increase, by a factor of 2× to 3×, of quantum efficiency (QE) for GaAs photoemission applications, like GaAs photocathodes. Conditions of different SAW wavelengths, swept SAW intensities, and varied incident photon energies were investigated. Essential steps in SAW device fabrication on a GaAs substrate are demonstrated, including deposition of an additional layer of ZnO for piezoelectric effect enhancement, measurements of current–voltage (I–V) characteristics of the SAW device, and ability to survive high-temperature annealing. Results obtained and reported in this study provide the potential and basis for future studies on building SAW-enhanced photocathodes, as well as other GaAs photoelectric applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

First-principles study of the topological surface states of α-Sn(111)

α-Sn is on the boundary of a couple of distinct topological phases. It will transform into a topological insulator under a suitable strain. However, a clear picture of its topological surface states (TSSs) is still lacking. Furthermore we perform first-principles calculations on the electronic structure of α-Sn(111) surface to identify its TSSs and reveal their properties. The results show that the presence of valence band reorganizes the TSSs in the inverted sp gap into two Dirac cones. The lower one is in the valence band continuum; the upper one resides in the gap between the valence and conduction bands. We also demonstrate the transformation of the surface states by switching on or off of strain and/or spin-orbit coupling. Without spin-orbit coupling, only the TSSs associated with the lower Dirac cone survive, and they are spin unpolarized. The results are useful for understanding and engineering the topological properties of α-Sn.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Preliminary Modeling of Triply Periodic Minimal Surface (TPMS) Structures with RELAP5-3D

This poster goes over preliminary work performed on modeling triply periodic minimal surfaces (TPMS) with RELAP5-3D. The poster starts off with the need for advanced nuclear fuel designs for future reactors, and how TPMS are being researched for this purpose. There is then a focus on what a TPMS is and then moves onto the motivation for why this geometry is being modeled and looked into. The methodology is then shown for how data from different experiments will be used for pre-test predictions and eventual creation of empirical coefficients and multipliers to be used in models. Then there is a show of how data would be compared between the experimental tests, CFD, and RELAP5-3D values. The results from the simulations and comparisons are then presented to show how the CFD and RELAP5-3D compare to each other currently, with no experimental data to compare to for one test model. Results from the second test model are also presented to show that there is stability in the solving of that model.

42 - ENGINEERING↗
DOE OSTI2021

Selective Biosorption of Valuable Rare Earth Elements Among Co-Occurring Lanthanides

To meet the increasing demand for rare earth elements (REEs) essential for low carbon-intensity energy technologies, new methods are needed for selective REE extraction from unconventional resources. Only a few REEs have significant economic value, but isolation of target rare earths from co-occurring lanthanides is challenging due to their similar chemical behavior. We present a novel approach to enhance separation of specific REEs from lanthanide mixtures. Escherichia coli cells engineered with lanthanide binding tags (LBTs) were immobilized in nonadsorbing, permeable polyethylene glycol diacrylate beads and packed into continuous flow, fixed-bed columns. Breakthrough of 15 rare earths in the +3 oxidation state resulted in notable differences in adsorption selectivity, with greatest separation between europium (Eu) and lanthanum (La) due to competitive displacement. REE adsorption onto fixed-bed columns was predicted by coupling a surface complexation model to a calibrated one-dimensional dual porosity transport model that accounts for interbead advective and intrabead diffusive transport. A tradeoff between high-abundance, low-affinity native carboxyl sites and low-abundance, high-affinity engineered LBT sites dictates process recovery efficiency and selectivity. Key chemical and operational parameters are identified to maximize selective extraction of high-value lanthanides, achieving a threefold enhancement of Eu recovery relative to La in a mixed REE solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Integrated TBC/EBC for SiC Fiber Reinforced SiC Matrix Composites for Next Generation Gas Turbines (Final Report)

In this ambitious project, a significant challenge preventing widespread use of ceramic matrix composites in hot section components of gas power generating turbines was addressed. Hot section components made from SiC fiber reinforced SiC matrix composites (SiC/SiC composites), have the potential to achieve a combined cycle energy efficiency of above 65%. To achieve this efficiency, the temperature of the combustion gases on the turbine component surface is expected to reach as high as ~1700ºC (3100ºF). However, SiC/SiC composites suffer from volatilization at high temperature under high velocity steam environment – typical in a turbine hot chamber. This integrated collaborative project, between two research groups at Clemson University and a team of engineers and scientists at GE Gas Power, focused on design, fabrication and evaluation of a new graded environmental barrier coating. Using the excellent compositional tailorability of polymer derived ceramics (PDCs), we developed an integrated EBC/BC that smoothly transitions from bottom SiC/SiC bond interface to hermetic sesquioxide (Y 2 O 3 ) top surface. This smooth compositional transition avoided the sharp CTE mismatch at interfaces to greatly reduce the thermal stress. The developed EBC is compatible with and bonds well with the bond coat that GE uses. The top hermetic oxide surface ensures low oxygen transportation and volatilization rates under the high velocity steam environment. The graded microstructure with increasing sesquioxide concentration also decreases the amount of Si and C elements near the top hermetic sesquioxide layer. Coatings made using a process suitable for manufacturing – atmospheric plasma spraying was demonstrated. The microstructure of coatings made using this process were fully characterized. Finally, the performance of these coatings was investigated under the most demanding conditions for this application. Specifically, high temperature, high velocity steam exposure; thermal shock test; and thermal cycling tests. The graded coatings performed exceptionally well in all these tests. Specific suggestions for future development in this area have also been identified. In addition to the excellent technical progress, this project helped initiate a robust collaboration between the research groups at Clemson and GE Gas Power. It also provided a high-quality learning and mentoring opportunity for the three post-doctoral research associates and two UG students at Clemson University who worked on this project. All proposed tasks, sub-tasks were completed, and all milestones achieved.

03 NATURAL GAS↗
DOE OSTI2022

Topology optimization for the design of porous electrodes

Porous electrodes are an integral part of many electrochemical devices since they have high porosity to maximize electrochemical transport and high surface area to maximize activity. Traditional porous electrode materials are typically homogeneous, stochastic collections of small-scale particles and offer few opportunities to engineer higher performance. Fortunately, recent breakthroughs in advanced and additive manufacturing are yielding new methods to structure and pattern porous electrodes across length scales. These architected electrodes are emerging as a promising new technology to continue to drive improvement; however, it is still unclear which structures to employ and few tools are available to guide their design. Here we address this gap by applying topology optimization to the design of porous electrodes. We demonstrate our framework on two applications: a porous electrode driving a steady Faradaic reaction and a transiently operated electrode in a supercapacitor. We present computationally designed electrodes that minimize energy losses in a half-cell. For low-conductivity materials, the optimization algorithm creates electrode designs with a hierarchy of length scales. Further, the designed electrodes are found to outperform undesigned, homogeneous electrodes. Finally, we present three-dimensional porous electrode designs. We thus establish a topology optimization framework for designing porous electrodes.

25 ENERGY STORAGE↗
DOE OSTI2023

Scalable in situ non-destructive evaluation of additively manufactured components using process monitoring, sensor fusion, and machine learning

Laser Powder Bed Fusion (L-PBF) Additive Manufacturing (AM) is among the metal 3D printing technologies most broadly adopted by the manufacturing industry. However, the current industry qualification paradigm for critical-application L-PBF parts relies heavily on expensive non-destructive inspection techniques, which significantly limits the use-cases of L-PBF. In situ monitoring of the process promises a less expensive alternative to ex situ testing, but existing sensor technologies and data analysis techniques struggle to detect sub-surface flaws (e.g., porosity and cracking) on production-scale L-PBF printers. In this work, an in situ NDE (INDE) system was engineered to detect subsurface flaws detected in X-Ray Computed Tomography (XCT) directly from process monitoring data. A multilayer, multimodal data input allowed the INDE system to detect numerous subsurface flaws in the size range of 200–1000µm using a novel human-in-the-loop annotation procedure. Furthermore, a framework was established for generating probability-of-detection (POD) and probability-of-false-alarm (PFA) curves compliant with NDE standards by systematically comparing instances of detected subsurface flaws to post-build XCT data. Here, we also introduce for the first time in the AM in situ sensing literature the a 90/95 – the flaw size corresponding to a 90% detection rate on the lower 95% confidence interval of the POD curve. The INDE system successfully demonstrated POD capabilities commensurate with traditional NDE methods. Traditional ML performance metrics were also shown to be inadequate for assessing the ability of the INDE system’s flaw detection performance. It is the hope of the authors that future studies will adopt the POD and PFA approach outlined here to provide better insight into the utility of process monitoring for AM.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. Here, in this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

42 ENGINEERING↗
DOE OSTI2020

Hypervelocity impact flash expansion geometry under various spacecraft surface electrical conditions

A more congested space environment due to increasing space activities introduces new threats to spacecraft operators. Among these threats include hypervelocity impacts from microparticles (< 1 µg) in the form of meteoroids and space debris. These microparticles travel at speeds between 11.2 and 72.8 km/s with respect to the Earth and can impact spacecraft forming a small (~1 µm) and dense (~ 10 26 m -3 ) plasma. This plasma can generate a strong optical emission (impact flash) and a radio frequency (RF) emission. These emissions can lead to spacecraft electrical anomalies when the impacted spacecraft surface (target) carries high electrical potential due to various space weather effects. To understand the microparticle hypervelocity impact plasma and its associated threat to spacecraft electronics, we studied the hypervelocity impact flash expansion geometry under various spacecraft surface electrical conditions. Three high-speed broadband photomultiplier tubes (PMT) are used to capture the temporal evolution of the impact flash and the temporal evolution of the angular distribution of the impact flash expansion geometry in a 3 MV electrostatic dust accelerator during a ground-based experiment. Overall, results indicate that the impact surface electrical condition has a statistically significant influence on the impact flash geometry, and a strong similarity between the impact plasma and flash expansion geometry. Thus, this paper provides new experimental support for the impact flash origin from and connection with the impact plasma, and serves as the first impact flash expansion geometry characterization under various impact surface electrical conditions in a collisionless environment (< 10 -5 Torr).

42 ENGINEERING↗
DOE OSTI2024

Corrosion testing needs and considerations for additively manufactured materials in nuclear reactors

Additive manufacturing (AM) technologies have developed rapidly in recent years, creating new opportunities and challenges for the nuclear industry; however, adoption requires that their corrosion performance be evaluated. Here, we discuss known reactor-specific corrosion issues for multiple reactor types and engineering concerns such as regulations and standards. A review of corrosion studies conducted on select AM alloys informs a discussion on key bulk and surface factors likely to impact corrosion behaviors. Recommendations to assess corrosion performance for AM materials are provided, including management of the unique nature of as-built AM surfaces and the inherent process variability that occurs for AM components.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Separation characteristics of cations and natural organic matter in electrodialysis

Natural organic matter (NOM) in water can cause the formation of disinfection byproducts (DBPs) when NOM reacts with a disinfectant such as chlorine. Nanofiltration (NF) and reverse osmosis (RO) are effective treatment methods to remove NOM. However, the simultaneous presence of both NOM and divalent cations such as Ca 2+ can enhance fouling in NF and RO. Therefore, an appropriate pretreatment to remove such cations before NF or RO would delay fouling and perhaps improve water recovery and NOM removal efficiency. Electrodialysis (ED) is potentially an excellent pretreatment method because it separates inorganic ions well using ion exchange membranes (IEMs) but does not separate NOM well because of its size and consequent low diffusivity. This research focused on ion and NOM separation with ED using three different types of commercially available IEM pairs, two different commercially available NOM sources, and six different influents at 500 mg/L total dissolved solids in the presence or absence of both hardness (Ca 2+ and Mg 2+ ) and NOM. The target waters of interest in this research were drinking water supplies that require little or no desalination but substantial removal of NOM; after NOM separation in NF or RO, some or all of the ED concentrate can be added to the NF/RO permeate to create the finished water prior to disinfection. The results indicate that ED can effectively separate alkaline earth metal ions without separation of NOM. Cation exchange membranes with high exchange capacity, high selectivity for divalent cations are desirable, and both anion and cation exchange membranes should have low affinity for organic adsorption. As a result, the process would work particularly well for NOM with relatively low hydrophobicity, since NOM adsorption to most surfaces increases with hydrophobicity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Determining Catalytically Relevant Surfaces through Coverage-Dependent Lattice Gas Models: Carbon Adsorption on Fe(100)

Here, we have quantified the C–C lateral interactions on Fe(100) using a density functional theory (DFT)-parameterized lattice gas cluster expansion (LG CE) model trained using 265 unique configurations spanning a C coverage from 0 to 1 monolayer (ML). Our LG CE model shows high predictive accuracy with a leave-multiple-out cross-validation score of 10.2 and 16.6 meV/site for systems with and without the top two layers of Fe atoms fixed, respectively. Electronic ground-state structures identified from the lattice gas model (including the structures at 0 and 1 monolayers) were further used to generate ab initio phase diagrams under a range of temperatures and pressures. At low temperatures (<400 K), we found that the 1.0 monolayer structure is dominant, whereas at higher temperatures (>500 K), the 0.88 ML structure is most likely to form on the Fe surface. Interestingly, our model identified a c (2 × 2) ordered structure at 1/2 ML, which correlates well with previous DFT studies for carbon adsorption on iron surfaces and matches with the experimentally observed low-energy electron diffraction structure. Overall, the DFT-parameterized energies for the C/Fe system including effects of coverage and configurational space can further help in developing multiscale models for various heterogeneous reactions involving C–C and C–Fe interactions.

08 HYDROGEN↗
DOE OSTI2020

Effects of Tethered Polymers on Dynamics of Nanoparticles in Unentangled Polymer Melts

Polymer-tethered nanoparticles (NPs) are commonly added to a polymer matrix to improve the material properties. Critical to the fabrication and processing of such composites is the mobility of the tethered NPs. Here, we study the motion of tethered NPs in unentangled polymer melts using molecular dynamics simulations, which offer a precise control of the grafted chain length N g and the number z of grafted chains per particle. As Ng increases, there is a crossover from particle-dominated to tethered-chain-dominated terminal diffusion of NPs with the same z. The mean squared displacement of loosely tethered NPs in the case of tethered-chain-dominated terminal diffusion exhibits two subdiffusive regimes at intermediate time scales for small z. The first one at shorter time scales arises from the dynamical coupling of the particle and matrix chains, while the one at longer time scales is due to the participation of the particle in the dynamics of the tethered chains. The friction of loosely grafted chains in unentangled melts scales linearly with the total number of monomers in the chains, as the friction of individual monomers is additive in the absence of hydrodynamic coupling. As more chains are grafted to a particle, hydrodynamic interactions between grafted chains emerge. As a result, there is a nondraining layer of hydrodynamically coupled chain segments surrounding the bare particle. Outside the nondraining layer is a free-draining layer of grafted chain segments with no hydrodynamic coupling. The boundary of the two layers is the stick surface where the shear stress due to the relative melt flow is balanced by the friction between the grafted and melt chains in the interpenetration layer. The stick surface is located further away from the bare surface of the particle with higher grafting density.

42 ENGINEERING↗
DOE OSTI2025

Aldehyde cool-flame chemistry explains a missing source of organic acids

Combustion emission is a significant source of organic acids, impacting atmospheric chemistry and climate. Their formation mechanisms, however, remain poorly understood, leading to underestimation in kinetic models. We investigate the cool-flame oxidation of key combustion intermediates—C 1 –C 4 aldehydes and benzaldehyde. Using in-situ synchrotron vacuum ultraviolet photoionization mass spectrometry, we observe the direct conversion of aldehydes to organic acids, a process enhanced by HO 2 radicals. Quantum chemistry calculations reveal that the reaction of RC(O)O 2 with HO 2 on the singlet potential energy surface contributes to organic acids. Incorporating this pathway into a kinetic model significantly improves organic acid prediction. Despite the high-temperature nature of engine combustion, significant spatial and temporal inhomogeneities (e.g., near-wall regions and crevice volumes) lead to localized cool-flame conditions, facilitating organic acid formation and emission. Elucidating the acid formation under cool-flame conditions provides a critical mechanism for accurately modelling anthropogenic organic acid emissions and developing mitigation strategies.

SVUV-PIMS↗