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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Multidimensional Modeling of Mixture Formation in a Hydrogen-Fueled Heavy-Duty Optical Engine With Direct Injection

Hydrogen (H 2 ), as a carbon-free fuel, is considered as one of the most promising solutions to reduce the carbon footprint of hard-to-decarbonize energy and transportation sectors. As such, hydrogen-fueled internal combustion engines (H 2 ICEs) have recently been receiving increasing attention, particularly in applications such as on-road/off-road heavy-duty transport and combined heat and power. The direct injection (DI) of gaseous hydrogen into the combustion chamber offers great potential for achieving high power density and high engine efficiency, while mitigating the risk of backfire and reducing pre-ignition. However, the numerical simulation of H 2 DI system remains a formidable challenge associated with the high computational cost of reproducing compressible supersonic flow and shocks in narrow injector passages and in near-nozzle regions. In general, there is a lack of well-established and validated practices for the modeling of high-pressure H 2 DI in large-bore engines. Here, to this end, this study focuses on computational fluid dynamics (CFD) modeling of the mixture formation process in a heavy-duty optical engine employing a medium-pressure H 2 DI system. Both large eddy simulations (LES) and Reynolds Averaged Navier–Stokes (RANS) simulations are performed and evaluated against optical data. Gaseous hydrogen is injected into the combustion chamber via a centrally located outward opening hollow-cone injector at a pressure of 40 bar. Simulations are carried out for two injection timings, namely, −120 and −60 °CA. The numerical predictions for H 2 distribution in different horizontal and vertical planes during the compression stroke are systematically compared against optical data obtained through planar laser-induced fluorescence (PLIF) measurements. Overall, the LES approach using the Dynamic Structure model is found to have good predictive capabilities for the early jet penetration in terms of length and shape, as well as the later H 2 distributions. However, the unsteady RANS approach with the renormalization group $k - ϵ$ model, which is widely used by industry to model heavy-duty ICEs, significantly underpredicts the H 2 mixing, even at similar mesh resolution to that used in LES. These results indicate that there is a need for the improvement of mixing submodels within the RANS approach when applied to H 2 DI simulations.

LES↗
DOE OSTI2026

Evaluating hydrogen permeation through medium-density and high-density polyethylene pipes to enable a hydrogen-compatible infrastructure

As the United States and the global community pursue energy abundance and resilience, hydrogen is becoming a critical energy carrier. The future of hydrogen transport depends on one thing: verifying that today’s pipelines are hydrogen ready. This study investigates the permeation behavior of medium-density polyethylene (MDPE) and high-density polyethylene (HDPE) pipelines under pure hydrogen gas environment at various pressures and temperatures. Using thermal desorption analysis (TDA) and direct pipe permeability measurements, hydrogen loss rates are quantified, revealing minimal permeation losses (< 10.5 g/km/day) under realistic operating conditions. Effects of temperature and pressure with Standard Dimension Ratios (SDR), were evaluated to determine their influence on permeation rates of MDPE and HDPE pipelines. In addition, ex-situ density and degree of crystallinity (DOC) of MDPE and HDPEs after hydrogen exposure were also investigated to understand pressure-dependency of polymer properties. The findings provide essential data for assessing polymer-based pipeline materials for safe and reliable hydrogen transport.

08 HYDROGEN↗
DOE OSTI2025

Simulation insights into wetting properties of hydrogen-brine-clay for hydrogen geo-storage

Hydrogen geo-storage is attracting substantial interdisciplinary interest as a cost-effective and sustainable option for medium- and long-term storage. Hydrogen can be stored underground in diverse formations, including aquifers, salt caverns, and depleted oil and gas reservoirs. The wetting dynamics of the hydrogen-brine-rock system are critical for assessing both structural and residual storage capacities, and ensuring containment safety. Through molecular dynamics simulations, we explore how varying concentrations of cushion gases (CO 2 or CH 4 ) influence the wetting properties of hydrogen-brine-clay systems under geological conditions (15 MPa and 333 K). We employed models of talc and the hydroxylated basal face of kaolinite (kaoOH) as clay substrates. Our findings reveal that the effect of cushion gases on hydrogen-brine-clay wettability is strongly dependent on the clay-brine interactions. Notably, CO 2 and CH 4 reduce the water wettability of talc in hydrogen-brine-talc systems, while exerting no influence on the wettability of hydrogen-brine-kaoOH systems. Detailed analysis of free energy of cavity formation near clay surfaces, clay-brine interfacial tensions, and the Willard-Chandler surface for gas-brine interfaces elucidate the molecular mechanisms underlying wettability changes. Our simulations identify empirical correlations between wetting properties and the average free energy required to perturb a flat interface when clay-brine interactions are less dominant. Here, our thorough thermodynamic analysis of rock-fluid and fluid-fluid interactions, aligning with key experimental observations, underscores the utility of simulated interfacial properties in refining contact angle measurements and predicting experimentally relevant properties. These insights significantly enhance the assessment of gas geo-storage potential. Prospectively, the approaches and findings obtained from this study could form a basis for more advanced multiscale simulations that consider a range of geological and operational variables, potentially guiding the development and improvement of geo-storage systems in general, with a particular focus on hydrogen storage.

25 ENERGY STORAGE↗
DOE OSTI2025

Development of a Digital Twin for Hydrogen Dispersion and Safety Assessment in an Electrolyzer Based Hydrogen Production Facility

Digital twin models are virtual representations of physical systems that use real-time data to simulate and optimize performance. This study presents the development and initial implementation of a digital twin (DT) for the electrolyzer-based hydrogen production facility at NREL's Advanced Research on Integrated Energy Systems (ARIES), focused on enhancing safety and optimizing sensor placement through physics-based simulations and metadata integration. The DT incorporates detailed facility-specific information, including component layout, leak locations, and controlled release parameters, to model hydrogen dispersion under varying environmental conditions. Using steady-state computational fluid dynamics (CFD) simulations informed by real meteorological data, such as wind speed, direction, and vertical wind profiles, the DT enables visualization of hydrogen plume behavior and spatial concentration distributions. Comparative analysis between high and low wind speed scenarios illustrates the significant influence of wind dynamics on plume shape and extent, with horizontal momentum dominating dispersion at higher speeds, while buoyancy effects become more prominent under low wind conditions. These simulations generate a rich dataset embedded within the DT, allowing users to assess potential leak outcomes and identify optimal sensor locations based on concentration thresholds. The model supports scenario-based analysis to guide safety strategies and equipment deployment for open-area hydrogen infrastructure. The digital twin thus serves as a dynamic platform for virtual prototyping, providing predictive insight into hydrogen behavior and enhancing risk-informed decision-making. This initial phase establishes a validated foundation for future integration of transient, uncontrolled leak scenarios and real-time sensor feedback, positioning the DT as a critical tool for safety design, operational planning, and adaptive monitoring in hydrogen systems. Overall, the approach demonstrates the value of combining environmental data with digital simulations to inform safer and more efficient deployment of hydrogen technologies.

08 HYDROGEN↗
DOE OSTI2026

Development of a Digital Twin for Hydrogen Dispersion and Safety Assessment in an Electrolyzer-Based Hydrogen Production Facility: Preprint

Digital twin models are virtual representations of physical systems that use real-time data to simulate and optimize performance. This study presents the development and initial implementation of a digital twin (DT) for the electrolyzer-based hydrogen production facility at the National Renewable Energy Laboratory (NREL)'s Advanced Research on Integrated Energy Systems (ARIES), focused on enhancing safety and optimizing sensor placement through physics-based simulations and metadata integration. The DT incorporates detailed facility-specific information, including component layout, leak locations, and controlled release parameters, to model hydrogen dispersion under varying environmental conditions. Using steady-state computational fluid dynamics (CFD) simulations informed by real meteorological data, such as wind speed, direction, and vertical wind profiles, the DT enables visualization of hydrogen plume behavior and spatial concentration distributions. Comparative analysis between high and low wind speed scenarios illustrates the significant influence of wind dynamics on plume shape and extent, with horizontal momentum dominating dispersion at higher speeds, while buoyancy effects become more prominent under low wind conditions. These simulations generate a rich dataset embedded within the DT, allowing users to assess potential leak outcomes and identify optimal sensor locations based on concentration thresholds. The model supports scenario-based analysis to guide safety strategies and equipment deployment for open-area hydrogen infrastructure. The digital twin thus serves as a dynamic platform for virtual prototyping, providing predictive insight into hydrogen behavior and enhancing risk-informed decision-making. This initial phase establishes a validated foundation for future integration of transient, uncontrolled leak scenarios and real-time sensor feedback, positioning the DT as a critical tool for safety design, operational planning, and adaptive monitoring in hydrogen systems. Overall, the approach demonstrates the value of combining environmental data with digital simulations to inform safer and more efficient deployment of hydrogen technologies.

08 HYDROGEN↗
DOE OSTI2025

Importance of hydrogen oxidation reaction current in quantifying hydrogen crossover in PEM water electrolyzers at high differential pressure

Understanding hydrogen permeation in proton exchange membrane water electrolyzers (PEMWEs) operating at high differential pressures (>25 bar) is critical towards developing effective gas recombination strategies that enable safe operation and high efficiency. Developing this understanding relies on accurate quantification of hydrogen crossover rates in water electrolyzers operating under such conditions. In this work, we show that PEMWEs operating at high differential pressures exhibit noticeable hydrogen oxidation reaction (HOR) currents. As the HOR consumes part of the permeated hydrogen at the anode, neglecting HOR currents leads to severe underestimation of the hydrogen crossover rate. We implemented a new method combining hydrogen oxidation current with online gas chromatography measurements to accurately quantify hydrogen crossover rates as a function of operating current density in PEMWEs operating at high differential pressures (10–30 bar g ).

25 ENERGY STORAGE↗
DOE OSTI2025

Physical model and experimental validation of a high temperature proton exchange membrane electrochemical hydrogen pump cell for efficient single-stage extraction of low concentration hydrogen gas

There is interest in valorization of existing natural gas infrastructure to facilitate the co-transportation of hydrogen via blending of hydrogen gas initially at limited concentrations of 1–20 vol% H2 and to subsequently extract hydrogen at fuel cell quality standards (SAE J2719/ISO14687-2). High temperature proton exchange membrane electrochemical hydrogen pump (HT-PEM EHP) based on phosphoric acid doped polybenzimidazole (PA-PBI) exhibits good performance at elevated temperatures (>120 °C), which provides desirable tolerance to non-methane natural gas constituents that are problematic for lower temperature based EHP. To better understand the suitability of the HT-PEM EHP for such gas separation processes, a two-dimensional model of EHP based on PA-PBI was developed. The model is validated for several relevant operating conditions and across cells with differing amounts of phosphoric acid content in the electrodes. Operando micro x-ray computed tomography (CT) imaging of an HT-PEM EHP was used to further validate physical parameters and assumptions of the model. The impacts of pressure, relative humidity of the anode feed, and concentration of feed gases on separation performance are investigated. This study shows that a specific energy of separation of 5.1 kWh/kg H2 at a hydrogen recovery factor (HRF) of 50 vol% can be achieved in a single stage with the EHP, producing fuel cell quality hydrogen purity of 99.99 vol% H2 from a 2 vol% H2/CH4 feed blend, while pressurizing the product H2 at a pressure ratio of 1.3 relative to feed pressure.

Stansberry, John M↗
DOE OSTI2025

Overcoming Barriers in Electrochemical Toluene Hydrogenation for Efficient Hydrogen Storage by Pt 3 Au Alloy Catalysts

Hydrogen storage and transportation are essential for the hydrogen economy, and liquid organic hydrogen carriers (LOHCs), such as a toluene/methylcyclohexane (TOL/MCH) system, offer significant advantages in terms of safety and efficiency. However, the electrochemical reduction of TOL to MCH (TER) faces challenges from competing with the hydrogen evolution reaction (HER) and catalyst instability. Here, in this study, Pt 3 Au is introduced as a highly effective catalyst for TER. Through density functional theory screening, we identified distinctive properties of Pt 3 Au, including enhanced binding to the TER intermediates and effective HER suppression. Experimental validation confirmed these computational predictions, with Pt 3 Au achieving the highest reported Faradaic efficiency (98%) in proton exchange membrane systems. Moreover, long-term testing demonstrated that Pt 3 Au maintained Faradaic efficiencies of >90% over 9 h, highlighting its robustness and operational stability. By integrating computational modeling and experimental evaluation, this work addresses key limitations in LOHC catalysis. Pt 3 Au establishes a benchmark for selective and stable TER performance, paving the way for advanced hydrogen storage technologies. These findings emphasize the critical role of rational catalyst design in overcoming the challenges associated with scalable and efficient hydrogen storage solutions.

LOHC↗
NASA NTRS1978

Hydrogen Embrittlement and Its Control in Hydrogen-Fueled Engine Systems

The nature of hydrogen embrittlement by high pressure gaseous hydrogen is described and methods of designing SSME gaseous hydrogen systems, including techniques of hydrogen embrittlement prevention, are discussed. The effects of gaseous hydrogen environments are emphasized. Results of extensive investigations of gaseous hydrogen environments on metals conducted under the SSME program are presented.

Chandler, W. T.↗
NASA NTRS1982

Evaluation of dopants in hydrogen to reduce hydrogen permeation in candidate Stirling engine heater head tube alloys at 760 deg and 820 deg

Alloy tubes filled with hydrogen doped with various amounts of carbon monoxide, carbon dioxide, ethane, ethylene, methane, ammonia, or water were heated in a diesel fuel-fired Stirling engine simulator materials test rig for 100 hours at 21 MPa and 760 or 820 C to determine the effectiveness of the dopants in reducing hydrogen permeation through the hot tube walls. Ultra high purity (UHP) hydrogen was used for comparison. The tube alloys were N-155, A-286, Incoloy 800, Nitronic 40, 19-9DL, 316 stainless steel, Inconel 718, and HS-188. Carbon dioxide and carbon monoxide in the concentration range 0.2 to 5 vol % were most effective in reducing hydrogen permeation through the hot tube walls for all alloys. Ethane, ethylene, methane, ammonia, and water at the concentrations investigated were not effective in reducing the permeation below that achieved with UHP hydrogen. One series of tests were conducted with UHP hydrogen in carburized tubes. Carburization of the tubes prior to exposure reduced permeation to values similar to those for carbon monoxide; however, carbon dioxide was the most effective dopant.

Misencik, J. A.↗
NASA NTRS1992

Influence of hydrogen oxidation kinetics on hydrogen environment embrittlement

Results are presented from experiments performed to determine the roles of hydrogen absorption and hydrogen electron transfer on the susceptibility of Fe- and Ni-base alloys to ambient-temperature hydroen embrittlement. An apparent independence is noted between hydrogen environment embrittlement and internal hydrogen embrittlement. The experiments were performed on Inconel 718, Incoloy 903, and A286. The electrochemical results obtained indicate that Inconel 718 either adsorbs hydrogen more rapidly and/or the electrochemical oxidation of the adsorbed hydrogen occurred more rapidly than in the other two materials.

Walter, R. J.↗
NASA NTRS2008

Hydrogen Research for Spaceport and Space-Based Applications: Hydrogen Sensors and Systems

The activities presented are a broad based approach to advancing key hydrogen related technologies in areas such as fuel cells, hydrogen production, and distributed sensors for hydrogen-leak detection, laser instrumentation for hydrogen-leak detection, and cryogenic transport and storage. Presented are the results from research projects, education and outreach activities, system and trade studies. The work will aid in advancing the state-of-the-art for several critical technologies related to the implementation of a hydrogen infrastructure. Activities conducted are relevant to a number of propulsion and power systems for terrestrial, aeronautics and aerospace applications. Sensor systems research was focused on hydrogen leak detection and smart sensors with adaptive feedback control for fuel cells. The goal was to integrate multifunction smart sensors, low-power high-efficiency wireless circuits, energy harvesting devices, and power management circuits in one module. Activities were focused on testing and demonstrating sensors in a realistic environment while also bringing them closer to production and commercial viability for eventual use in the actual operating environment.

Anderson, Tim↗
DOE OSTI2025

CO 2 Hydrogenation on Pd(111): The Role of Subsurface Hydrogen and Surface Defects

Palladium-based catalysts are often used in carbon dioxide (CO 2 ) hydrogenation reactions with different possible reaction pathways producing methanol, methane, formic acid, or carbon monoxide. We used ambient pressure X-ray photoelectron spectroscopy (AP-XPS) to understand the surface reaction mechanism of CO 2 hydrogenation on Pd(111). AP-XPS results show that the order in which the reactants are introduced yields different initial surface species. In a CO 2 and H 2 mixture, carbonaceous species (CH x , C*, PdC x ) are formed upon heating Pd(111) at 400 K and above. In addition, a Pd(111) sample pre-exposed to an elevated pressure of H 2 followed by evacuation to ultrahigh vacuum (UHV) can store enough hydrogen atoms in the subsurface and bulk to provide a hydrogen source for the CO 2 hydrogenation reaction to occur when exposed to CO 2 gas alone. In conclusion, the formation of carbonaceous species likely occurs through the decomposition of a transient CH x O intermediate facilitated by low-coordinated sites and surface defects.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Electrochemical Cycling of Liquid Organic Hydrogen Carriers as a Sustainable Approach for Hydrogen Storage and Transportation

Hydrogen (H 2 ), as a high-energy-density molecule, offers a clean solution to carry energy. However, the high diffusivity and low volumetric density of H 2 pose a challenge for long-term storage and transportation. Liquid organic hydrogen carriers (LOHCs) have been suggested as a strategic way to store and transport hydrogen in stable molecules. More so, electrochemical LOHC cycling renders an opportunity to utilize renewable energy for hydrogen storage and transportation toward the goal of eliminating carbon emissions. In this Perspective, examples of electrochemical reactions of organic molecules and their suitability for LOHC couples are examined. A comparative carbon footprint assessment of electrochemical LOHC cycling processes against thermochemical and hybrid LOHC cycling processes was performed. The electrochemical LOHC cycling process had the lowest relative carbon footprint only when highly concentrated LOHCs were used as the feed or when purification of the LOHC product was not required. The carbon footprint in electrochemical cycling of diluted LOHC was primarily contributed to by the LOHC distillation separation process. A sensitivity analysis showed the carbon footprint LOHC concentration dependence during the electrochemical cycling process. Moreover, the electrolyte composition significantly affects the carbon footprint during electrochemical LOHC cycling. Energy utilization, water usage, and toxicity for electrochemical LOHC cycling are discussed to provide an overview for better economic and environmental practices. There are significant opportunities in the electrochemical cycling of LOHCs if appropriate conditions such as high concentrations of reactant, reversible redox cycling ability, high Faradaic efficiencies, and catalyst stabilities are achieved.

25 ENERGY STORAGE↗
DOE OSTI2024

Evaluation of Common Thermoplastic Polymers in High-Pressure Cycling Hydrogen Under Ambient and Cold Environments as Applicable to the Hydrogen Infrastructure

Thermoplastic polymers are required to perform unfailingly under stringent conditions of changing pressures (35 MPa to 70 MPa) and temperatures (-40°C to +85°C) in storage and fueling operations. Although diffusivity in glassy polymers appear to be an order of magnitude lower than elastomers, polymer microstructural attributes such as degree of crystallinity and presence of polar and non-polar groups on the main chain with and without branching can play a substantial role in influencing their behaviors in hydrogen environments. In the work described here, the effect of high-pressure hydrogen cycling on PEEK, PTFE, PA11, HDPE, POM (and different commercial grades of these polymers) under ambient and cold (-40°C) conditions is addressed. Ex-situ characterization for polymer changes included density measurements for impact of hydrogen retention, hardness changes using nanoindentation, storage modulus and glass transition changes using dynamic mechanical and thermal analysis (DMTA), degree of crystallization with Differential Scanning Calorimetry (DSC) and tensile testing following ASTM D412. In other evaluations, solid-state nuclear magnetic resonance (NMR), attenuated total reflectance Fourier transform infra-red spectroscopy (ATRFTIR), X-ray diffraction (XRD), and X-ray CT results are presented. The overall impact of these evaluations is to establish a technical basis for the behaviors of common thermoplastics in cycling hydrogen environments under ambient and cold temperatures while establishing the relationship between polymer structure-based properties and hydrogen transport effects.

Menon, Nalini C.↗
NASA NTRS1996

The alpha Centauri Line of Sight: D/H Ratio, Physical Properties of Local Interstellar Gas, and Measurement of Heated Hydrogen (The 'Hydrogen Wall') Near the Heliopause

We analyze high-resolution spectra of the nearby (1.34 pc) stars alpha Cen A (G2 V) and alpha Cen B (K1 V), which were obtained with the Goddard High Resolution Spectrograph on the Hubble Space Telescope. The observations consist of echelle spectra of the Mg II 2800 A and Fe II 2599 A resonance lines and the Lyman-alpha lines of hydrogen and deuterium. The interstellar gas has a velocity (v = - 18.0 +/- 0.2 km/s) consistent with the local flow vector proposed for this line of sight by Lailement & Berlin (1992). The temperature and nonthermal velocity inferred from the Fe II, Mg II, and D I line profiles are T = 5400 +/- 500 K and xi = 1.20 +/- 0.25 km/s, respectively. However, single-component fits to the H I Lyman-alpha lines yield a Doppler parameter (b(sub HI) = 11.80 km/s) that implies a significantly warmer temperature of 8350 K, and the velocity of the H I absorption (v = - 15.8 +/- 0.2 km/s) is redshifted by about 2.2 km/s with respect to the Fe II, Mg II, and D I lines. The one-component model of the interstellar gas suggests natural logarithm N base HI = 18.03 +/- 0.01 and D/H = (5.7 +/- 0.2) x 10(exp -6) . These parameters lead to a good fit to the observed spectra, but this model does not explain the higher temperature and redshift of H I relative to the other interstellar lines. The most sensible way to resolve the discrepancy between H(I) and the other lines is to add a second absorption component to the H(I) lines. This second component is hotter (T approx. equals 30,000 K), is redshifted relative to the primary component by 2-4 km/s, and has a column density too low to be detected in the Fe(II), Mg(II), and D(I) lines. We propose that the gas responsible for this component is located near the heliopause, consisting of the heated H I gas from the interstellar medium that is compressed by the solar wind. This so-called 'hydrogen wall' is predicted by recent multifluid gasdynamical models of the interstellar gas and solar wind interaction. Our data provide the first measurements of the temperature and column density of H(I) in the hydrogen wall. After considering the effects that a corresponding hydrogen wall around alpha Cen would have on our analysis, our best estimates for the parameters of the solar hydrogen wall are natural log N(sup (2))(H(I)) = 14.74 +/- 0.24, b(sup (2))(H(I)) = 21.9 +/- 1.7 km/s (corresponding to T = 29,000 +/- 5000 K), and v(sup (2))(H(I)) greater than -16km/s. Unfortunately, the existence of this heated H(I) reduces our ability to compute the H(I) column density of the interstellar medium accurately because, with slight alterations to our assumed stellar Lyman-alpha profiles, we discovered that acceptable two-component fits also exist with natural log N(H(I))approx. 17.6. We, therefore, quote large error bars for the H I column density along the alpha Cen line of sight, natural log N(H(I)) = 17.80 +/- 0.30. For this range in N(H(I)), n(H(I)) = 0.15 /cu.cm (+/- a factor of 2) and D/H = (0.5-1.9) x 10(exp -5). This is the first direct measurement of the H(I) density in a local cloud and allows us to predict the distance from the Sun to the edge of the local cloud along various lines of sight. This range in D/H is consistent with the value D/H = 1.6 x 10(exp -5) previously derived for the Capella and Procyon lines of sight. We cannot tell whether D/H ratio varies or is constant in the local interstellar medium, but we do find that the D(I)/Mg(II) ratio for the alpha Cen line of sight is about 4 times smaller than for the Capella and Procyon lines of sight. Therefore, either D/H or the Mg depletion varies significantly over distance scales of only a few parsecs.

Linsky, Jeffrey L.↗
NASA NTRS1999

A Clue to the Extent of Convective Mixing Inside Massive Stars: The Surface Hydrogen Abundances of Luminous Blue Variables and Hydrogen-Poor Wolf-Rayet Stars

Interior layers of stars that have been exposed by surface mass loss reveal aspects of their chemical and convective histories that are otherwise inaccessible to observation. It must be significant that the surface hydrogen abundances of luminous blue variables (LBVs) show a remarkable uniformity, specifically X(sub surf) = 0.3 - 0.4, while those of hydrogen-poor Wolf-Rayet (WN) stars fall, almost without exception, below these values, ranging down to X(sub surf) = 0. According to our stellar model calculations, most LBVs are post-red-supergiant objects in a late blue phase of dynamical instability, and most hydrogen-poor WN stars are their immediate descendants. If this is so, stellar models constructed with the Schwarzschild (temperature-gradient) criterion for convection account well for the observed hydrogen abundances, whereas models built with the Ledoux (density-gradient) criterion fail. At the brightest luminosities, the observed hydrogen abundances of LBVs are too large to be explained by any of our highly evolved stellar models, but these LBVs may occupy transient blue loops that exist during an earlier phase of dynamical instability when the star first becomes a yellow supergiant. Independent evidence concerning the criterion for convection, which is based mostly on traditional color distributions of less massive supergiants on the Hertzsprung-Russell diagram, tends to favor the Ledoux criterion. It is quite possible that the true criterion for convection changes over from something like the Ledoux criterion to something like the Schwarzschild criterion as the stellar mass increases.

Stothers, Richard B.↗