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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Diffusion-Limited Kinetics in Reactive Systems

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, in this study, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term “the reactive transport effect”. We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid–surface interfaces accounting for diffusion limitations and the reactive transport effect.

Johnson, Matthew Sean↗
DOE OSTI2020

Nano-layer deposition of metal oxides via a condensed water film

Abstract Nanocoatings on solids can be achieved by various processes, including sol-gel and atomic layer deposition. However, challenges remain for achieving uniform nanocoatings on nanoscale substrates at a large scale. Here, we report a versatile and fundamentally different technique, termed condensed layer deposition, for depositing conformal metal oxide nanocoatings on nanoparticles and nanofibers. This approach involves water in liquid hydrocarbons condensing as a nanoscale water film on the substrate surface, enabled by interfacial tension between polar water and nonpolar liquid hydrocarbons. Chemical precursors are then added, which react with the condensed water film to form a metal oxide nanocoating. We demonstrate this for titania, alumina, and niobia on substrates including carbon nanotubes, iron oxide particles and carbon black. Condensed layer deposition can achieve oxide nanocoatings on a variety of substrates with tunable thickness, in one pass, at room temperature.

36 MATERIALS SCIENCE↗
NASA NTRS1999

Experimental Observations on a Low Strain Counter-Flow Diffusion Flame: Flow and Bouyancy Effects

Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra L = (β g 0 L 3 ∆T)/(𝑎v)) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.

J. A. Sutula↗
DOE OSTI2025

Logical approach to tritium vacuum pump selection for fusion applications

Vacuum pumps have been used for tritium processing since the 1940s following the isolation of pure tritium. The largest problem facing tritium vacuum pumps is the tritium radioactive decay. The beta particles, recoil energy, and subsequent radical formations are detrimental to most carbon-based materials. Carbon materials, such as plastics, elastomers, carbon fiber, activated carbon, etc., react with tritium to form methane and in the process strip material from the carbonbased material. Other reactions can be self-catalyzing, as is the case with nitrogen and tritium forming tritiated ammonia at room temperature and pressure. Tritium also readily isotopically exchanges with surface -OH groups, increasing the amount of protium in the gas stream while creating a tritium holdup on the surface. Metals are the preferred material when working with tritium, but tritium will permeate into and through almost all metals at some point. The entrapped tritium can decay inside the metal, creating local helium distortions that can impact the structural properties above and beyond the hydrogen embrittlement issue tritium can cause.

Angelette, Lucas M. [Savannah River National Labor↗
DOE OSTI2021

Aerosol emissions from water-lean solvents for post-combustion CO 2 capture

Advanced water-lean solvents (WLS) for post-combustion CO 2 capture have been gaining interest due to their ability to reduce the parasitic penalty from energy needed for solvent regeneration. Commercial implementation of these novel CO 2 capture technologies hinges on successful control of amine emissions. RTI conducted a parametric study of fundamental and operational variables influence on overall amine aerosol and vapor emissions from our water-lean solvent eCO 2 Sol™ using our 6-kW equivalent bench-scale gas absorption system. The parametric testing used a simulated flue gas with 15 % CO 2 , 2.3–4.2 % H 2 O, and 0–6 ppm sulfite (SO 3 ) to examine the impact of the presence of aerosols to the capture performance and amine emissions from the system. The SO 3 reacts with water in the flue gas to create H 2 SO 4 , which forms liquid aerosol droplets and provide nucleation sites for growth of aerosols. Scanning Mobility Particle Sizer and Aerodynamic Particle Sizer instruments monitored the aerosol particle size distribution. Parametric testing results suggested that the presence of the aerosols in the flue gas could increase the overall amine emissions by 10X compared to the baseline emissions from WLS’s vapor pressure. Principal component analysis (PCA) and projection to latent squares (PLS) developed models to predict the aerosol-based amine emissions from process data. The predictive PLS model had a correlation coefficient (Q 2 ) of 0.92 and could predict the aerosol-based emissions from the NAS process with ±15 % accuracy (average absolute deviation, AAD). The PLS regression model also identified key variables affecting aerosol-based emissions from WLS.

42 ENGINEERING↗
NASA NTRS2012

Large Eddy Simulation (LES) of Particle-Laden Temporal Mixing Layers

High-fidelity models of plume-regolith interaction are difficult to develop because of the widely disparate flow conditions that exist in this process. The gas in the core of a rocket plume can often be modeled as a time-dependent, high-temperature, turbulent, reacting continuum flow. However, due to the vacuum conditions on the lunar surface, the mean molecular path in the outer parts of the plume is too long for the continuum assumption to remain valid. Molecular methods are better suited to model this region of the flow. Finally, granular and multiphase flow models must be employed to describe the dust and debris that are displaced from the surface, as well as how a crater is formed in the regolith. At present, standard commercial CFD (computational fluid dynamics) software is not capable of coupling each of these flow regimes to provide an accurate representation of this flow process, necessitating the development of custom software. This software solves the fluid-flow-governing equations in an Eulerian framework, coupled with the particle transport equations that are solved in a Lagrangian framework. It uses a fourth-order explicit Runge-Kutta scheme for temporal integration, an eighth-order central finite differencing scheme for spatial discretization. The non-linear terms in the governing equations are recast in cubic skew symmetric form to reduce aliasing error. The second derivative viscous terms are computed using eighth-order narrow stencils that provide better diffusion for the highest resolved wave numbers. A fourth-order Lagrange interpolation procedure is used to obtain gas-phase variable values at the particle locations.

Bellan, Josette↗
NASA NTRS2013

Colors of Jupiter's large anticyclones and the interaction of a Tropical Red Oval with the Great Red Spot in 2008

The nature and mechanisms producing the chromophore agents that provide color to the upper clouds and hazes of the atmospheres of the giant planets are largely unknown. In recent times, the changes in red coloration that have occurred in large- and medium-scale Jovian anticyclones have been particularly interesting. In late June and early July 2008, a particularly color-intense red tropical oval interacted with the Great Red Spot (GRS) leading to the destruction of the red tropical oval and cloud dispersion. We present a detailed study of the tropical vortices, usually white but sometimes red, and a characterization of their color spectral signatures and dynamics. From the spectral reflectivity in methane bands we study their vertical cloud structure compared to that of the GRS and BA. Using two spectral indices we found a near-correlation between anticyclones cloud top altitudes and red color. We present detailed observations of the interaction of the red oval with the GRS and model simulations of the phenomena that allow us to constrain the relative vertical extent of the vortices. We conclude that the vertical cloud structure, vertical extent and dynamics of Jovian anticyclones are not the causes of their coloration. We propose that the red chromophore forms when background material (a compound or particles) is entrained by the vortex, transforming into red once inside the vortex due to internal conditions, exposure to ultraviolet radiation or to the mixing of two chemical compounds that react inside the vortex, confined by a potential vorticity ring barrier.

red color↗
DOE OSTI2020

Feasibility of using reactive silicate particles with temperature-responsive coatings to enhance the security of geologic carbon storage

The large-scale deployment of geologic carbon storage will require minimizing the risk of CO 2 leakage. Here we report on a novel strategy to seal leakage pathways by injecting functionalized reactive calcium silicate (CaSiO 3 ) particles. The particles consist of a mineral silicate core within a temperature-sensitive Poly(N,N-dimethylaminoethyl methacrylate) coating that limits contact between the core and the surrounding CO 2 (aq) above a switching temperature making them relatively unreactive deep in the subsurface. If the CO 2 leaks to shallower depths and cooler temperatures, the coatings would extend and enable the silicate core to react with CO 2(aq) to form solid carbonate precipitates that reduce the permeability of the fracture or flow path. A combined laboratory- and simulation-based investigation was conducted to explore key early-stage research questions related to the feasibility of this leakage management strategy. Sand columns were injected with either coated or uncoated CaSiO 3 particles and the permeability was measured before and after exposure to CO 2 . Experiments were conducted at 35 °C and 70 °C, a range that spans the switching temperature for the coatings. Results show that at the cooler temperature the coating effectively enabled reaction and permeability reduction. At higher temperatures, the coated particles limited mineral carbonation and the permeability decrease was minimal compared to columns with uncoated particles. Here, the morphology and location of the precipitates provides insight about permeability evolution. Model simulations of 2D radial particle transport from an injection point provided insight into the effects of particle size, coating properties, and concentrations of particles in several representative rock formations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Characterizing Reactive Transport Behavior in a Three-Dimensional Discrete Fracture Network

While several studies have linked network and in-fracture scale properties to conservative transport behavior in subsurface fractured media, studies on reactive transport cases remain relatively underdeveloped. In this study, we explore the behavior of an irreversible kinetic reaction during the interaction of two solute plumes, one consisting of species A and the other species B. When the plumes converge, these species react kinetically to form a new species C via A+B→kC. This reactive system is studied using a three-dimensional discrete fracture network (DFN) model coupled with reactive Lagrangian particle tracking. We find that the interplay of network topology and chemical properties of the reactive solutes controls reactive transport processes. The network topology drives species A and B together, and the chemical properties dictate whether and how quickly a reaction occurs. Results demonstrate that reactions are most likely to occur in high-velocity fractures that make up the network backbone. The interplay between species’ chemical properties and transport is characterized by a non-dimensional Damköhler (Da) number. We show that the spatial distribution of reactions is sensitive to Da, which subsequently influences late-time tailing behavior in outlet breakthrough time distributions. The results of this study provide initial insights into how an irreversible reaction occurs during transport in a fracture network, using a methodology that can be applied to study reactive transport in a wide range of fractured media environments and contexts.

58 GEOSCIENCES↗
NASA NTRS2012

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows.

Drozda, Tomasz G.↗
NASA NTRS2000

Numerical Simulation of a Chemically Reacting Sorbent Bed for LSS Applications

A detailed numerical model of a chemisorption bed has been developed. The model is based on the constant pressure mass transport equation for gaseous flow through a packed bed, and the equation for diffusion and reaction within a spherical particle. Because there is a wealth of data from the NASA and the Navy bodies of literature, the LiOH-H2O-CO2 system is chosen for application of the model and interpretation of results. Prior models of this system from the life support literature are limited. The current model incorporates many of the features of elaborate models developed for investigation of industrial systems or energy applications (e.g., coal, desulphurization): it distinguishes bulk convection and bed dispersion; mass transport to the particle surface, transport within the particle, and reaction. It uses the nonsteady (not pseudo-steady state) form of the equations. The chemistry is modeled as a multi-step, reversible reaction with evolving solid structure. The resulting system of equations is large. The ODEPACK family of solvers is used to integrate the system. Reaction coefficients are determined by experiment. Typical results of the model are illustrated with mission input parameters. Using the model, an explanation is offered for 1) the varied performance results found after pre-breathing (or after simulated pre-breathe conditions), 2) interrupted use and 3) low temperature use. In addition, options for a reusable canister are explored. The computational resource implications of adding energy equations are discussed briefly, as are applicability to other relevant space and undersea systems.

Luna, Bernadette↗
NASA NTRS1995

Resistance to Rolling in the Adhesive Contact of Two Elastic Spheres

For the stability of agglomerates of micron sized particles it is of considerable importance to study the effects of tangential forces on the contact of two particles. If the particles can slide or roll easily over each other, fractal structures of these agglomerates will not be stable. We use the description of contact forces by Johnson, Kendall and Roberts, along with arguments based on the atomic structure of the surfaces in contact, in order to calculate the resistance to rolling in such a contact. It is shown that the contact reacts elastically to torque forces up to a critical bending angle. Beyond that, irreversible rolling occurs. In the elastic regime, the moment opposing the attempt to roll is proportional to the bending angle and to the pull-off force P(sub c). Young's modulus of the involved materials has hardly any influence on the results. We show that agglomerates of sub-micron sized particles will in general be quite rigid and even long chains of particles cannot be bent easily. For very small particles, the contact will rather break than allow for rolling. We further discuss dynamic properties such as the possibility of vibrations in this degree of freedom and the typical amount of rolling during a collision of two particles.

Dominik, C.↗
NASA NTRS1995

Resistance to Rolling in the Adhesive Contact of Two Elastic Spheres

For the stability of agglomerates of micron sized particles it is of considerable importance to study the effects of tangential forces on the contact of two particles. If the particles can slide or roll easily over each other, fractal structures of these agglomerates will not be stable. We use the description of contact forces by Johnson, Kendall and Roberts, along with arguments based on the atomic structure of the surfaces in contact, in order to calculate the resistance to rolling in such a contact. It is shown that the contact reacts elastically to torque forces up to a critical bending angle. Beyond that, irreversible rolling occurs. In the elastic regime, the moment opposing the attempt to roll is proportional to the bending angle and to the pull-off force P(sub c). Young's modulus of the involved materials has hardly any influence on the results. We show that agglomerates of sub-micron sized particles will in general be quite rigid and even long chains of particles cannot be bent easily. For very small particles, the contact will rather break than allow for rolling. We further discuss dynamic properties such as the possibility of vibrations in this degree of freedom and the typical amount of rolling during a collision of two particles.

Dominik, C.↗
DOE OSTI2020

Verification and Validation of MFiX-PIC

This work is aimed at verification and validation (V&V) of particle-in-cell (PIC) approach in the National Energy Technology Laboratory’s (NETL) Multiphase Flow with Interphase eXchanges (MFiX-PIC) which was officially released in April 2019. Under verification, the results from MFiX-PIC are compared with exact or analytical solutions, while experimental results are used for benchmarking under validation. The test suite consists of the following cases: Terminal velocity. Particle advection in time-varying flow field. Particle settling in a dense medium. Evaporation. Rayleigh-Taylor instability. Minimum fluidization. Mini-circulating fluidized bed. The cases reported in a format consistent with the existing Verification and Validation Manual (Musser et al., 2018) explore a wide range of flow velocities and concentration regimes. Only one case considered in this work verifies the implementation of heat and mass transfer routines in MFiX-PIC, while a few other studies are currently underway to further expand the validation space in reacting flows. This study highlights the need for a rigorous analysis to objectively quantify the effect of model parameters. In addition, there is a scarcity of high-quality experimental data in the literature suitable for validating PIC methodology. Future efforts would include performing experiments which provide results for a valuable database. While designing such experiments, particle count should be significant to have sufficient particles per parcel while maintaining an optimal parcel to cell volume ratio. Also, datasets should have objectively assessed experimental uncertainty whereby confidence interval in those measurements become more explicit.

42 ENGINEERING↗
DOE OSTI2021

A simulation-based parametric study of CLOU chemical looping reactor performance

Chemical looping with oxygen uncoupling (CLOU) is a variant on chemical looping combustion in which the oxygen carrier releases gaseous O 2 in the fuel reactor, making it well-suited for solid fuels, since the released gaseous O 2 readily reacts with solid char. This work presents several computational fluid dynamic (CFD) simulations of copper-based CLOU in a dual fluidized bed system, each with different operating conditions. The modeling predicted that coal particle sizes as large as 1000 μm did not significantly affect performance. Increased oxygen carrier copper loading resulted in an excess of gaseous oxygen in the product gas stream. Decreasing the oxygen carrier bed mass as well as reducing the air reactor fluidizing velocity did not supply enough oxygen to the fuel reactor to complete combustion of the coal. This generated a failure state in which the temperature continued to decrease in the fuel reactor from the lack of combustion, which in turn reduced the O 2 equilibrium partial pressure, further lowering the amount of combustion possible. Sufficient O 2 can be maintained in the fuel reactor by ensuring a high enough air reactor velocity and a large enough supply of oxygen carrier inventory to handle the chosen coal feed rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

SimELIT: A Novel GUI-Based Comprehensive Ion Trajectory Simulation Software for Mass Spectrometry

Ion trajectory simulation in mass spectrometry systems from injection to detection is technically challenging but very important for better understanding the ion dynamics in instrument development. Here, in this work, we present SimELIT (Simulator of Eulerian and Lagrangian Ion Trajectories), a novel ion trajectory simulation platform. SimELIT is built upon a suite of multiphysics solvers compiled into OpenFOAM (an open-source numerical solver library particularly used for computational mechanics), with a simple web-based graphical user interface (GUI) allowing users to define the details of OpenFOAM cases and run simulations. SimELIT is a modular program and can provide extensions of physics (e.g., gas flows, electrodynamic fields) and thus enable ion trajectory simulations from the ion source to detector. The current version (SimELIT) provides two numerical solvers for ion trajectory simulations–(1) a Lagrangian particle tracker in vacuum and (2) a Eulerian ion density solver in background gas in the presence of electric fields. Here, we describe the architecture of SimELIT, including its use of Docker and the React Framework, and demonstrate the computation of ion trajectories of multiple m/z values in a static/linear voltage drop in vacuum (across a 1 m long flight tube). Further, the drift motion of ions under 1 Torr pressure conditions in a static background (N 2 ) gas through a 20 V/cm static electric field is shown. The results produced from SimELIT were compared with SIMION and theoretical estimates. In addition, we report the computation of ion trajectories in electrodynamic fields within a planar FAIMS device operating at atmospheric pressure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Formation, chemical evolution and solidification of the dense liquid phase of calcium (bi)carbonate

Metal carbonates, which are ubiquitous in the near-surface mineral record, are a major product of biomineralizing organisms and serve as important targets for capturing anthropogenic CO 2 emissions. However, pathways of carbonate mineralization typically diverge from classical predictions due to the involvement of disordered precursors, such as the dense liquid phase (DLP), yet little is known about DLP formation or solidification processes. Using in situ methods we report that a highly hydrated bicarbonate DLP forms via liquid–liquid phase separation and transforms into hollow hydrated amorphous CaCO 3 particles. Acidic proteins and polymers extend DLP lifetimes while leaving the pathway and chemistry unchanged. Molecular simulations suggest that the DLP forms via direct condensation of solvated Ca 2+ •(HCO 3 – ) 2 complexes that react due to proximity effects in the confined DLP droplets. Furthermore, our findings provide insight into CaCO 3 nucleation that is mediated by liquid–liquid phase separation, advancing the ability to direct carbonate mineralization and elucidating an often-proposed complex pathway of biomineralization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2016

Development of Hydroxyl Tagging Velocimetry for Low Velocity Flows

Hydroxyl tagging velocimetry (HTV) is a molecular tagging technique that relies on the photo-dissociation of water vapor into OH radicals and their subsequent tracking using laser induced fluorescence. Velocities are then obtained from time-of-flight calculations. At ambient temperature in air, the OH species lifetime is relatively short (<50 μs), making it suited for high speed flows. Lifetime and radicals formation increases with temperature, which allows HTV to also probe low-velocity, high-temperature flows or reacting flows such as flames. The present work aims at extending the domain of applicability of HTV, particularly towards low-speed (<10 m/s) and moderate (<500 K) temperature flows. Results are compared to particle image velocimetry (PIV) measurements recorded in identical conditions. Single shot and averaged velocity profiles are obtained in an air jet at room temperature. By modestly raising the temperature (100-200 degC) the OH production increases, resulting in an improvement of the signal-to-noise ratio (SNR). Use of nitrogen - a non-reactive gas with minimal collisional quenching - extends the OH species lifetime (to over 500 μs), which allows probing of slower flows or, alternately, increases the measurement precision at the expense of spatial resolution. Instantaneous velocity profiles are resolved in a 100degC nitrogen jet (maximum jet-center velocity of 6.5 m/s) with an uncertainty down to 0.10 m/s (1.5%) at 68% confidence level. MTV measurements are compared with particle image velocimetry and show agreement within 2%.

Andre, Matthieu A.↗