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At least 559 records · Page 31

Performance, Stability, and Plume Characterization of the HERMeS Thruster with Boron Nitride Silica Composite Discharge Channel

NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5kW Technology Demonstration Unit-3 (TDU-3) has been the subject of extensive technology maturation in preparation for flight system development. Detailed performance, stability, and plume characterization tests of the thruster were performed at NASA GRC's Vacuum Facility 5 (VF-5). The TDU-3 thruster implements a magnetic topology that is identical to TDU-1. The TDU-3 boron nitride silica composite discharge channel material is different than the TDU-1 heritage boron nitride discharge channel material. Performance and stability characterization of the TDU-3 thruster was performed at discharge voltages between 300V and 600V and at discharge currents between 5A and 21.8A. The thruster performance and stability were assessed for varying magnetic field strength, cathode flow fractions between 5% and 9%, varying harness inductance, and for reverse magnet polarity. Performance characterization test results indicate that the TDU-3 thruster performance is in family with the TDU-1 levels. TDU-3's thrust efficiency of 65% and specific impulse of 2,800sec at 600V and 12.5kW exceed performance levels of SOA Hall thrusters. Thruster stability regimes were characterized with respect to the thruster discharge current oscillations (discharge current peak-to-peak and root mean square magnitudes), discharge current waveform power spectral density analysis, and maps of the current-voltage-magnetic field. Stability characterization test results indicate a stability profile similar to TDU-1. Finally, comparison of the TDU-1 and TDU-3 plume profiles found that there were negligible differences in the plasma plume characteristics between the TDU with heritage boron nitride versus the boron nitride silica composite discharge channel.

ion engines↗

Optimization Algorithms as Quantum Performance Benchmarks

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) have the potential to demonstrate significant run-time performance benefits over current state-of-the-art solutions. Using existing methods for characterizing classical optimization algorithms, we analyze solution quality obtained by solving Max-Cut problems using a quantum annealing device and gate-model quantum simulators and devices. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through effective visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. The framework is an enhancement to the existing open-source QED-C Application-Oriented Benchmark suite and can connect to the open-source analysis libraries. The suite can be executed on various quantum simulators and quantum hardware systems.

benchmarking↗

Fast Machine Learning Lidar Surrogate Simulator: Pristine Clear Sky

The simulations of lidar signals and retrievals rely on a range of optic-physical models, such as radiative transfer models, particle scattering and absorption models, along with the output data from atmospheric physical models. Integrating these different models to represent signals of a lidar system is computationally expensive, and performing backward retrievals can be complex and ambiguous. However, with the advantages of Machine Learning, there is a new potential for building effective lidar signal database linked to corresponding atmospheric profiles. For this project, we are developing a fast pre-trained neural network as the lidar surrogate simulator using simulated data for a CALIPSO-like lidar (355 nm, 532nm, and 1064nm), and a CO2 differential absorption lidar (DIAL) near 1571nm. Specifically, we utilize a long short-term memory (LSTM) model to map the relationships between atmospheric profiles (pressure, temperature, air density and CO2 mixing ratio) and lidar signals. This approach allows us to build machine learning based simulators that can reconstruct lidar signals at specific bands from MERRA reanalysis data, and perform retrievals of atmospheric profiles using lidar signals at various wavelengths. As a first step, the results show the potential of this method to establish a foundational model for sensor signals. This model offers the promise of enabling both accurate predictions and rapid retrievals, providing a more efficient approach to signal processing and analysis.

Shan Zeng↗

STAT7 v1.2 User Guide: The STAT7 Code for Statistical Propagation of Uncertainties in Steady-State Thermal Hydraulics Analysis of Plate-Fueled Reactors

The STAT7 software was developed to perform steady-state, single-phase thermal hydraulics analysis of plate-fueled reactors based on statistical propagation of uncertainties. Application of the software is for non-power research and test reactors, including conversion to low-enriched uranium fuel of U.S. High-Performance Research Reactors such as Massachusetts Institute of Technology Research Reactor. Since it can be necessary to repeat analysis during fuel reloading, STAT7 accommodates flexibility in analyzing many realistic aspects of reactor fuel management. STAT7 uses a Monte Carlo approach to model uncertainty in common fuel fabrication parameters and other key reactor operating parameters required for thermal hydraulics analyses of research and test reactors. These safety calculations are ultimately intended to protect against high fuel plate temperatures due to critical heat flux, or onset of flow instability. STAT7 supports water properties based on the IAPWS-IF97 functions (The International Association for the Properties of Water and Steam Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam) in addition to the fit functions. STAT7 predicts axial profiles of fuel, cladding, and coolant temperature along a lateral stripe that runs the full length of the fuel plate from the bottom to the top. STAT7 can simultaneously analyze all of the axial nodes of all of the fuel plates and all of the coolant channels for one latera stripe of a fuel element. Power splits are calculated for each axial node of each plate to determine how much of the power goes out each face of the plate. By running STAT7 multiple times, full core analysis can be performed by analyzing the margin to onset of nucleate boiling and onset of flow instability for each axial node of each stripe of each plate of each fuel element in the core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Analysis of CO Transport from Australia Fires and Its Impact to Ozone, Water Vapor and Clouds Using CrIS Single-Field-of-View Sounder Products and Other Remote Sensing and MERRA-2 Reanalysis Data

Australia’s unprecedented fire disasters at the end of 2019 to early 2020 emitted huge amounts of carbon monoxide (CO) and fire aerosol particles, and the long-range transport of the smoke plumes poses great impact to climate change, such as altering the Antarctic ozone (O3) hole. Spaceborne observations from satellites have been proven successful in monitoring CO from wildfires in the past decade and can be used to examine the associated CO transport. The primary remote sensing data used in this study is the Single Field of View (SFOV) Sounder Atmospheric Product (SiFSAP) derived from the Cross-track Infrared Sounder (CrIS) on SNPP, a new product that will be generated at NASA and released to the public in a few months. SiFSAP has a high spatial resolution of ~14 km and includes atmospheric profiles of temperature, water vapor, CO, O3, as well as cloud products, and as the SiFSAP algorithm performs both day- and night-time retrievals, it provides an additional observation for night-time in comparison to the day-time-only solar polar satellite instruments such as MOPPIT, OMPS, and TROPOMI. Most recent significant improvements in the quality of this product plus its good spatial resolution (better than most global weather and climate models) enable us to conduct process-oriented analysis of CO transport, and the variation of water vapor, O3 and clouds (optical depth, effective radius and cloud height) within and around the fire plumes. The wind fields from MERRA-2 reanalysis will be used to help characterize the transport. Other remote sensing data, such as CO from AIRS, MOPPIT and TROPOMI, O3 from OMPS and TROPOMI, as well as the UV aerosol index from OMI and OMPS, will be used and compared with SiFSAP sounder products. Cross-validation of CO and O3 from these different sensors with the corresponding MERRA-2 products will also be carried out. Along the plume transport path, some enhancement of O3 and correlation between fire aerosol, cloud optical depth and water vapor have been found but need further investigation. Using the transport of fire plumes over the Southern Pacific Ocean as a unique testbed, this study will demonstrate the trace species monitoring capability of current satellite observations, in particular, for CO and O3, and hopefully, it will provide some insight on the impacts on fire emissions on air quality and climate.

Xiaozhen (Shawn) Xiong↗

Metagenome-assembled genomes provide insight into the metabolic potential during early production of Hydraulic Fracturing Test Site 2 in the Delaware Basin

Demand for natural gas continues to climb in the United States, having reached a record monthly high of 104.9 billion cubic feet per day (Bcf/d) in November 2023. Hydraulic fracturing, a technique used to extract natural gas and oil from deep underground reservoirs, involves injecting large volumes of fluid, proppant, and chemical additives into shale units. This is followed by a “shut-in” period, during which the fracture fluid remains pressurized in the well for several weeks. The microbial processes that occur within the reservoir during this shut-in period are not well understood; yet, these reactions may significantly impact the structural integrity and overall recovery of oil and gas from the well. To shed light on this critical phase, we conducted an analysis of both pre-shut-in material alongside production fluid collected throughout the initial production phase at the Hydraulic Fracturing Test Site 2 (HFTS 2) located in the prolific Wolfcamp formation within the Permian Delaware Basin of west Texas, USA. Specifically, we aimed to assess the microbial ecology and functional potential of the microbial community during this crucial time frame. Prior analysis of 16S rRNA sequencing data through the first 35 days of production revealed a strong selection for a Clostridia species corresponding to a significant decrease in microbial diversity. Here, we performed a metagenomic analysis of produced water sampled on Day 33 of production. This analysis yielded three high-quality metagenome-assembled genomes (MAGs), one of which was a Clostridia draft genome closely related to the recently classified Petromonas tenebris. This draft genome likely represents the dominant Clostridia species observed in our 16S rRNA profile. Annotation of the MAGs revealed the presence of genes involved in critical metabolic processes, including thiosulfate reduction, mixed acid fermentation, and biofilm formation. These findings suggest that this microbial community has the potential to contribute to well souring, biocorrosion, and biofouling within the reservoir. Our research provides unique insights into the early stages of production in one of the most prolific unconventional plays in the United States, with important implications for well management and energy recovery.

natural gas↗

Uncertainties in predicting solar panel power output

The problem of calculating solar panel power output at launch and during a space mission is considered. The major sources of uncertainty and error in predicting the post launch electrical performance of the panel are considered. A general discussion of error analysis is given. Examples of uncertainty calculations are included. A general method of calculating the effect on the panel of various degrading environments is presented, with references supplied for specific methods. A technique for sizing a solar panel for a required mission power profile is developed.

Anspaugh, B.↗

Microwave emission from smooth bare fields and soil moisture sampling depth

This paper studies the depth to which soil moisture can be directly estimated with microwave measurements over smooth bare fields. The analyses are based on both theoretical and experimental considerations at the frequencies of 1.4, 5.0, and 10.7 GHz. Radiative transfer calculations of microwave emissivities at these frequencies are performed with a number of moisture profiles measured for two soils. The calculated emissivities are compared with those derived from the Fresnel equation to deduce the microwave sampling depth in soils. The data acquired from the ground-level radiometric measurements during the summers of 1979-1981 are examined and compared with the theoretical analysis. Both theoretical and experimental analyses lead to the conclusion that the microwave samplinhg depth in soils is about one tenth of the wavelength of observation. It is shown that the moisture content at any depth near the surface of a smooth soil can be estimated, in principle, by a combination of a radiometric measurement and a curve generated by the Fresnel equation at an appropriate frequency, provided that the texture of the soil is known.

Wang, James R.↗

Two-dimensional thermal-hydraulics analyses of the Pellet Bed Reactor for Nuclear Thermal Propulsion

Thermal-hydraulics design and analyses of the Pellet Bed Reactor for nuclear thermal propulsion are performed using the nuclear propulsion thermal-hydraulic analysis model to determine the 2D steady-state temperature, pressure, and flow fields in the core and optimize the orificing in the hot-frit to avoid hot spots in the core at full power operation. Results show that by properly adjusting the axial porosity profile in the hot frit, hot spots in the core can be essentially eliminated during full power operation. This important accomplishment is achieved at the expense of slightly larger pressure losses in the core because of flow restriction at the hot frit. However, the overall pressure losses is only about 11 percent of the propellant inlet pressure.

Morley, Nicholas J.↗

Mars Dynamics from Earth-Based Tracking of the Mars Pathfinder Lander

Measurements of Mars' rotational variations can be conducted via Earth-based radio tracking observations of the Mars Pathfinder lander during an extended mission. Two-way range measurements between an Earth tracking station and the lander will enable precise monitoring of the planet's orientation, allowing details of Mars' internal structure and global surface/atmosphere interactions to be determined. An analysis has been performed to investigate the accuracy with which key physical parameters of Mars can be determined using the Earth-based radio tracking measurements. Acquisition of such measurements over one Martian year should enable determination of Mars' polar moment of inertia to 1% or better, providing a strong constraint on radial density profiles (and hence on the iron content of the core and mantle) and on long-term variations of the obliquity, which influences the climate. Variations in Mars length of day and polar motion should also be detectable, and will yield information on the seasonal cycling of carbon dioxide between the atmosphere and the surface.

Folkner, W. M.↗

Coronal Structures in Cool Stars

Many papers have been published that further elucidate the structure of coronas in cool stars as determined from EUVE, HST, FUSE, Chandra, and XMM-Newton observations. In addition we are exploring the effects of coronas on the He I 1083081 transition that is observed in the infrared. Highlights of these are summarized below including publications during this reporting period and presentations. Ground-based magnetic Doppler imaging of cool stars suggests that active stars have active regions located at high latitudes on their surface. We have performed similar imaging in X-ray to locate the sites of enhanced activity using Chandra spectra. Chandra HETG observations of the bright eclipsing contact binary 44i Boo and Chandra LETG observations for the eclipsing binary VW Cep show X-ray line profiles that are Doppler-shifted by orbital motion. After careful analysis of the spectrum of each binary, a composite line-profile is constructed by adding the individual spectral lines. This high signal-to-noise ratio composite line-profile yields orbital velocities for these binaries that are accurate to 30 km/sec and allows their orbital motion to be studied at higher time resolutions. In conjunction with X-ray lightcurves, the phase-binned composite line-profiles constrain coronal structures to be small and located at high latitudes. These observations and techniques show the power of the Doppler Imaging Technique applied to X-ray line emission.

Oliversen, Ronald↗

High-Volume Airborne Fluids Handling Technologies to Fight Wildfires

NASA recently partnered with the U.S. Forest Service (USFS) on a project to examine mission suitability and recommend policies and procedures for the use of very large aerial firefighting aircraft such as the Boeing 747 and DC-10 aerial retardant delivery aircraft. The aircraft under study included a 10Tanker DC-10 and an Evergreen B-747. NASA's Dryden Flight Research Center and Ames Research Center worked with the USFS to help determine the safe flight envelope for these Very Large Air Tanker (VLAT) aircraft for the USFS and the Department of the Interior (DOI). This new generation of supertankers includes aircraft like these that have as much as four times the delivery capacity of the previous generation of aerial firefighting aircraft. Dryden performed operational test and evaluation assessments and reported findings and recommendations on these aircraft in cooperation with Ames. The team developed, implemented, and directed an evaluation test plan for use in flight test and in simulation. Ames provided support using pilot-in-the-loop simulations and coordinated simulator models, flight profiles, and data analysis with Dryden. The test plan was designed to evaluate the suitability of VLAT aircraft as a function of mission environment. Based on this analysis, NASA generated interim flight envelope limitations to enhance safety and operational utility in the fire-retardant delivery mission. These recommended flight limitations were adopted by the USFS. The 10Tanker DC-10 has been in use for several years with the California Department of Forestry and Fire Protection(Cal-Fire), but until NASA took on the challenge of reviewing VLAT capabilities and limitations, the USFS was hesitant to add them to the federal wildfire arsenal. The DC-10 delivery system is based on an externally mounted set of tanks and a bomb-bay style set of clamshell doors that are opened in precisely calibrated ways to deliver the amounts and concentrations of retardant called for by the specific wildfire situation. The system was manufactured by Jordan Air of Central Point, OR, and was installed by Victorville Aerospace in Victorville, CA. It can deliver 12,000 gallons (45.4 kL) of retardant in as little as eight seconds. The aircraft can deliver a partial load of retardant and make multiple drops on the same flight, or the entire load can be rapidly delivered in one pass if required for maximum coverage. The Evergreen 747 uses internal tankage and a pressurized delivery system to enable volume and coverage levels that also meet USFS requirements, but enables computer control of flow for desired precision. This system was designed and built by Adaptive Aerospace of Tehachapi, CA and can deliver about 20,000 gallons (75.7 kL) of retardant in approximately ten seconds. The 747 can also make multiple independent drops, or deliver the entire load at once. NASA found that both of these VLAT aircraft are compatible with the wildfire suppression mission when used to supplement other aerial retardant delivery platforms. The major recommendations for deployment that resulted from this study relate to terrain clearance, the type of terrain in the drop area, availability of qualified lead planes to guide the VLAT approach to the drop area, and low-altitude maneuvering limitations. NASA s analysis suggests that with the appropriate flight procedures, these aircraft will provide a powerful set of tools to fight wildfires.

Dickerson, Mark↗

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earth's magnetosphere as a laboratory to study the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10 (sup -4) pascals (10 (sup -6) torr) and the surrounding temperature achieving -180 degrees Centigrade. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperature versus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDA/FLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 degrees Centigrade of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 degrees Centigrade and the heater power goal is to be within 5 percent of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Correlation↗

Objective Assessment Method for RNAV STAR Adherence

Flight crews and air traffic controllers have reported many safety concerns regarding area navigation standard terminal arrival routes (RNAV STARs). Specifically, optimized profile descents (OPDs). However, our information sources to quantify these issues are limited to subjective reporting and time consuming case-by-case investigations. This work is a preliminary study into the objective performance of instrument procedures and provides a framework to track procedural concepts and assess design specifications. We created a tool and analysis methods for gauging aircraft adherence as it relates to RNAV STARs. This information is vital for comprehensive understanding of how our air traffic behaves. In this study, we mined the performance of 24 major US airports over the preceding three years. Overlaying 4D radar track data onto RNAV STAR routes provided a comparison between aircraft flight paths and the waypoint positions and altitude restrictions. NASA Ames Supercomputing resources were utilized to perform the data mining and processing. We assessed STARs by lateral transition path (full-lateral), vertical restrictions (full-lateral/full-vertical), and skipped waypoints (skips). In addition, we graphed frequencies of aircraft altitudes relative to the altitude restrictions. Full-lateral adherence was always greater than Full-lateral/ full- vertical, as it is a subset, but the difference between the rates was not consistent. Full-lateral/full-vertical adherence medians of the 2016 procedures ranged from 0% in KDEN (Denver) to 21% in KMEM (Memphis). Waypoint skips ranged from 0% to nearly 100% for specific waypoints. Altitudes restrictions were sometimes missed by systematic amounts in 1,000 ft. increments from the restriction, creating multi-modal distributions. Other times, altitude misses looked to be more normally distributed around the restriction. This tool may aid in providing acceptability metrics as well as risk assessment information.

Stewart, Michael↗

SOLAR SAIL PROPULSION SENSITIVITY TO MEMBRANE SHAPE AND OPTICAL PROPERTIES USING THE SOLAR VECTORING EVALUATION TOOL (SVET)

Solar sail propulsive performance is dependent on sail membrane optical properties and on sail membrane shape. Assumptions of an ideal sail (flat, perfect reflector) can result in errors which can affect spacecraft control, trajectory analyses, and overall evaluation of solar sail performance. A MATLAB(R) program has been developed to generate sail shape point cloud files for two square-architecture solar sail designs. Simple parabolic profiles are assumed for sail shape under solar pressure loading. These files are then input into the Solar Vectoring Evaluation Tool (SVET) software to determine the propulsive force vector, center of pressure, and moments about the sail body axes as a function of sail shape and optical properties. Also, the impact of the center-line angle, due to non-perfect optical properties, is addressed since this constrains sail force vector cone angle and is often overlooked when assuming ideal-reflector membranes. Preliminary sensitivity analysis using these tools aids in determining the key geometric and optical parameters that drive solar sail propulsive performance.

Ewing, Anthony↗

Comparison Testing and Analysis of Braided Cords Constructed from Varying Kevlar Fiber Types

Material advancements move quickly, resulting in material obsolescence issues that require parachute engineers to understand how the material properties change with a material upgrade and if there are expected impacts to overall performance of the parachute. The objective of this test was to measure the elongation of different Kevlar types at both the cord-level and at the yarn-level to determine if a change in Kevlar type impacted parachute performance. An Instron machine with a pin-to-pin connection was used to measure load and displacement time histories for various Kevlar cord and yarn samples in a cyclic load profile. Twenty-four cord samples and twenty-four yarn samples were tested; each sample was cycled five times to the relevant maximum load (either to breaking strength or to the 30% peak load expected in flight). In addition to the Instron measurements, a photogrammetric technique was also implemented to measure elongation of the samples using button targets. Modulus test data shows approximately a 10% difference in elongation between Kevlar 29AP and Kevlar 129, and another 10% difference in elongation between Kevlar 29 and Kevlar 29AP. Although this is a measurable change in modulus, the effect on parachute performance is likely small, particularly for non-primary structure elements of relatively small length. This test campaign provides an example of the type of testing and analysis that parachute engineers could do to understand how material upgrades affect performance of their systems.

Parachutes↗

Comparison Testing and Analysis of Braided Cords Constructed from Varying Kevlar Fiber Types

Material advancements move quickly, resulting in material obsolescence issues that require parachute engineers to understand how the material properties change with a material upgrade and if there are expected impacts to overall performance of the parachute. The objective of this test was to measure the elongation of different Kevlar types at both the cord-level and at the yarn-level to determine if a change in Kevlar type impacted parachute performance. An Instron machine with a pin-to-pin connection was used to measure load and displacement time histories for various Kevlar cord and yarn samples in a cyclic load profile. Twenty-four cord samples and twenty-four yarn samples were tested; each sample was cycled five times to the relevant maximum load (either to breaking strength or to the 30% peak load expected in flight). In addition to the Instron measurements, a photogrammetric technique was also implemented to measure elongation of the samples using button targets. Modulus test data shows approximately a 10% difference in elongation between Kevlar 29AP and Kevlar 129, and another 10% difference in elongation between Kevlar 29 and Kevlar 29AP. Although this is a measurable change in modulus, the effect on parachute performance is likely small, particularly for non-primary structure elements of relatively small length. This test campaign provides an example of the type of testing and analysis that parachute engineers could do to understand how material upgrades affect performance of their systems.

Modulus Testing↗

A new methodology to determine kinetic parameters for one- and two-step chemical models

In this paper, a new methodology to determine kinetic parameters for simple chemical models and simple transport properties classically used in DNS of premixed combustion is presented. First, a one-dimensional code is utilized to performed steady unstrained laminar methane-air flame in order to verify intrinsic features of laminar flames such as burning velocity and temperature and concentration profiles. Second, the flame response to steady and unsteady strain in the opposed jet configuration is numerically investigated. It appears that for a well determined set of parameters, one- and two-step mechanisms reproduce the extinction limit of a laminar flame submitted to a steady strain. Computations with the GRI-mech mechanism (177 reactions, 39 species) and multicomponent transport properties are used to validate these simplified models. A sensitivity analysis of the preferential diffusion of heat and reactants when the Lewis number is close to unity indicates that the response of the flame to an oscillating strain is very sensitive to this number. As an application of this methodology, the interaction between a two-dimensional vortex pair and a premixed laminar flame is performed by Direct Numerical Simulation (DNS) using the one- and two-step mechanisms. Comparison with the experimental results of Samaniego et al. (1994) shows a significant improvement in the description of the interaction when the two-step model is used.

Mantel, T.↗