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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
NASA NTRS2019

Considerations for Femtosecond Laser Electronic Excitation Tagging in High-Speed Flows

Femtosecond laser electronic excitation tagging (FLEET) is an unseeded method for molecular tagging which offers valuable opportunities for measurement of high-speed (transonic, supersonic or hypersonic) flows. The unique nature of high-speed testing demands certain performance from FLEET such as satisfactory signal-to-noise ratio (SNR) at depressed static conditions (i.e., low temperatures, pressures and densities), wide dynamic range for velocity determination (especially single-shot), and measurements with acceptable accuracy and precision. This dissertation strives to evaluate FLEET in those regards and provide strategies to maximize the method's capabilities. A zero-dimensional kinetics model in nitrogen explains FLEET signal changes with pressure/density and/or temperature in terms of plasma-chemical reactions. Poorly known rate coefficients are tuned by comparing model output to measurements, with temporal agreement up to several hundred nanoseconds. Modeling reveals that initial signal peaks at reduced density because of slowed temporal evolution (and decay) of excited populations. Low temperatures enhance signal by enlarging cluster ion populations which contribute to excited species via electron-ion dissociative recombination. A purpose-built free jet facility provides experimental validation of the kinetics model and assesses FLEET velocimetry in low temperature and pressure/density conditions. Signal, lifetime, accuracy and precision results are obtained from unheated subsonic through Mach 4.0 operation of the facility, with best results noted. FLEET measurements of a sweeping jet (SWJ) actuator in compressible operation showcase its advantages in a highly unsteady jet containing subsonic through supersonic velocities. FLEET velocimetry is performed in the device's internal and external flow fields, with the latter compared to hot-wire anemometry. Internal measurements reveal the absence of shockwaves theorized to occur at high pressure ratios. Simultaneous qualitative measurements of compressible jet mixing are shown as a proof-of-concept. Overall, the work demonstrates that previous understanding of SWJ incompressible operation readily extends into the compressible realm. Practical aspects of performing FLEET velocimetry are detailed, along with strategies for improving measurement quality. Determination of a fundamental precision in nitrogen and air is attempted. Experiments show that increasing time delay and/or SNR improves velocimetry precision. A comparison of five camera systems indicates sensors with larger pixels capture higher SNR data and produce more precise results.

FLEET↗
DOE OSTI2026

New Perspectives on Vibrational Energy Transfer in Energetic Materials: Insights from Pressure-Tuned Ultrafast Spectroscopy

Understanding the manner in which vibrational energy flows between molecular and lattice vibrations is of great interest in physical chemistry due to its central role in reactivity and energy dissipation in molecular materials. Here, in this feature article, we highlight our recent efforts employing ultrafast broadband infrared spectroscopy toward understanding the interplay between molecular and lattice vibrations in energetic materials, motivated by the open questions surrounding the role of vibrational energy transfer (VET) in reaction initiation in these materials. Our work addresses the ongoing debate on the participation of doorway modes in VET. We further present new results from high-pressure ultrafast experiments on RDX, a hydrogen-bonded material, and BNFF, a hydrogen-free material, to explore how intermolecular interaction strength governs VET pathways and time scales. Collectively, our findings reveal that vibrational dynamics in these systems occurs across three distinct time regimes, with VET being incomplete out to hundreds of picoseconds, suggesting the importance of considering nonstatistical reactions in the modeling of these materials. These time scales vary as intermolecular interaction strength is indirectly modified by application of static pressure, indicating dramatic changes to the vibrational structure of these materials under shock-relevant conditions. Our results thus shed light on how intermolecular interactions shape vibrational energy redistribution in molecular materials, and highlight the need for further theoretical and experimental investigation.

Carlson, Daniel Ryan [Sandia National Laboratories↗
DOE OSTI2026

GaN Core-shell Nanofin Vertical Transistor (CoNVerT): A New Direction for Power Electronics (Final Scientific/Technical Report)

A novel power transistor architecture, the GaN c ore-shell n anofin ver tical transistor (CoNVerT) to address fundamental challenges in realizing the ultimate limit of GaN power transistor performance was explored experimentally. This technology promises ultra-high-efficiency high voltage/high power applications (e.g. DC/DC converters, motor control, fast charging, actuation), as well as to operate in harsh environments. The device exploits a vertical superjunction structure based on an experimentally-validated core-shell nanofin growth process in which lateral p-n heterojunctions are formed in a single growth step, while still maintaining vertical current flow for compact die size and low cost. The concept leverages the best properties of GaN for mid-range voltage applications: high mobility, high breakdown voltage, and native heterojunction enhancement-mode operation. Due to the crystallographic nature of the nanofin growth by molecular beam epitaxy, the sidewall heterojunctions occur on non-polar planes, resulting in ultra-smooth interfaces for high mobility, no sidewall etch damage and related surface/interface states, and elimination of piezoelectric effects that can limit reliability in conventional structures. This also facilitates superjunction formation for maximum device performance, and the selective-area growth of the nanofin results in dislocation-free growth, even on low-cost Si (111) substrate. In this program, core-shell nanofins were grown by molecular beam epitaxy, test structures to evaluate the doping, resistivity, and other electrical properties were fabricated, and the material and test structures were characterized in detail. The work identified clear potential (e.g., the doping was well controlled as required for superjunction concepts), but also additional areas that require additional effort to resolve (some unexpected crystal defects were encountered that require additional engineering to overcome). Simulation studies of the proposed concept validate that the fundamental approach is very promising, but additional effort in experimental realization is needed.

42 ENGINEERING↗
NASA NTRS1989

Manufactured soils for plant growth at a lunar base

Advantages and disadvantages of synthetic soils are discussed. It is pointed out that synthetic soils may provide the proper physical and chemical properties necessary to maximize plant growth, such as a toxic-free composition and cation exchange capacities. The importance of nutrient retention, aeration, moisture retention, and mechanical support as qualities for synthetic soils are stressed. Zeoponics, or the cultivation of plants in zeolite substrates that both contain essential plant-growth cations on their exchange sites and have minor amounts of mineral phases and/or anion-exchange resins that supply essential plant growth ions, is discussed. It is suggested that synthetic zeolites at lunar bases could provide adsorption media for separation of various gases, act as catalysts and as molecular sieves, and serve as cation exchangers in sewage-effluent treatment, radioactive-waste disposal, and pollution control. A flow chart of a potential zeoponics system illustrates this process.

Ming, Douglas W.↗
NASA NTRS2012

Rayleigh Scattering Density Measurements, Cluster Theory, and Nucleation Calculations at Mach 10

In an exploratory investigation, quantitative unclustered laser Rayleigh scattering measurements of density were performed in the air in the NASA Langley Research Center's 31 in. Mach 10 wind tunnel. A review of 20 previous years of data in supersonic and Mach 6 hypersonic flows is presented where clustered signals typically overwhelmed molecular signals. A review of nucleation theory and accompanying nucleation calculations are also provided to interpret the current observed lack of clustering. Data were acquired at a fixed stagnation temperature near 990Kat five stagnation pressures spanning 2.41 to 10.0 MPa (350 to 1454 psi) using a pulsed argon fluoride excimer laser and double-intensified charge-coupled device camera. Data averaged over 371 images and 210 pixels along a 36.7mmline measured freestream densities that agree with computed isentropic-expansion densities to less than 2% and less than 6% at the highest and lowest densities, respectively. Cluster-free Mach 10 results are compared with previous clustered Mach 6 and condensation-free Mach 14 results. Evidence is presented indicating vibrationally excited oxygen and nitrogen molecules are absorbed as the clusters form, release their excess energy, and inhibit or possibly reverse the clustering process. Implications for delaying clustering and condensation onset in hypersonic and hypervelocity facilities are discussed.

Balla, R. Jeffrey↗
DOE OSTI2021

Discovery of Energy Storage Molecular Materials Using Quantum Chemistry-Guided Multiobjective Bayesian Optimization

Redox flow batteries (RFBs) are a promising technology for stationary energy storage applications due to their flexible design, scalability, and low cost. In RFBs, energy is carried in flowable redoxactive materials (redoxmers) which are stored externally and pumped to the cell during operation. Further improvements in the energy density of RFBs necessitates redoxmer designs with wider redox potential windows and higher solubility. Additionally, designing redoxmers with a fluorescence-enabled self-reporting functionality allows monitoring of the state of health of RFBs. To accelerate the discovery of redoxmers with desired properties, state-of-the- art machine learning ( ML) methods, such as multiobjective Bayesian optimization (MBO), are useful. Here, we first employed density functional theory calculations to generate a database of reduction potentials, solvation free energies, and absorption wavelengths for 1400 redoxmer molecules based on a 2,1,3-benzothiadiazole (BzNSN) core structure. From the computed properties, we identified 22 Pareto-optimal molecules that represent best trade-off among all of the desired properties. We further utilized these data to develop and benchmark an MBO approach to identify candidates quickly and efficiently with multiple targeted properties. With MBO, optimal candidates from the 1400-molecule data set can be identified at least 15 times more efficiently compared to the brute force or random selection approach. Importantly, we utilized this approach for discovering promising redoxmers from an unseen database of 1 million BzNSN-based molecules, where we discovered 16 new Pareto-optimal molecules with significant improvements in properties over the initial 1400 molecules. Furthermore, we anticipate that this active learning technique is general and can be utilized for the discovery of any class of functional materials that satisfies multiple desired property criteria.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Techniques for estimating Space Station aerodynamic characteristics

A method was devised and calculations were performed to determine the effects of reflected molecules on the aerodynamic force and moment coefficients for a body in free molecule flow. A procedure was developed for determining the velocity and temperature distributions of molecules reflected from a surface of arbitrary momentum and energy accommodation. A system of equations, based on momentum and energy balances for the surface, incident, and reflected molecules, was solved by a numerical optimization technique. The minimization of a 'cost' function, developed from the set of equations, resulted in the determination of the defining properties of the flow reflected from the arbitrary surface. The properties used to define both the incident and reflected flows were: average temperature of the molecules in the flow, angle of the flow with respect to a vector normal to the surface, and the molecular speed ratio. The properties of the reflected flow were used to calculate the contribution of multiply reflected molecules to the force and moments on a test body in the flow. The test configuration consisted of two flat plates joined along one edge at a right angle to each other. When force and moment coefficients of this 90 deg concave wedge were compared to results that did not include multiple reflections, it was found that multiple reflections could nearly double lift and drag coefficients, with nearly a 50 percent increase in pitching moment for cases with specular or nearly specular accommodation. The cases of diffuse or nearly diffuse accommodation often had minor reductions in axial and normal forces when multiple reflections were included. There were several cases of intermediate accommodation where the addition of multiple reflection effects more than tripled the lift coefficient over the convex technique.

Thomas, Richard E.↗
DOE OSTI2022

Microfluidic liquid sheets as large-area targets for high repetition XFELs

The high intensity of X-ray free electron lasers (XFELs) can damage solution-phase samples on every scale, ranging from the molecular or electronic structure of a sample to the macroscopic structure of a liquid microjet. By using a large surface area liquid sheet microjet as a sample target instead of a standard cylindrical microjet, the incident X-ray spot size can be increased such that the incident intensity falls below the damage threshold. This capability is becoming particularly important for high repetition rate XFELs, where destroying a target with each pulse would require prohibitively large volumes of sample. We present here a study of microfluidic liquid sheet dimensions as a function of liquid flow rate. Sheet lengths, widths and thickness gradients are shown for three styles of nozzles fabricated from isotropically etched glass. In-vacuum operation and sample recirculation using these nozzles is demonstrated. The effects of intense XFEL pulses on the structure of a liquid sheet are also briefly examined.

47 OTHER INSTRUMENTATION↗
NASA NTRS2008

Simplified Modeling of Oxidation of Hydrocarbons

A method of simplified computational modeling of oxidation of hydrocarbons is undergoing development. This is one of several developments needed to enable accurate computational simulation of turbulent, chemically reacting flows. At present, accurate computational simulation of such flows is difficult or impossible in most cases because (1) the numbers of grid points needed for adequate spatial resolution of turbulent flows in realistically complex geometries are beyond the capabilities of typical supercomputers now in use and (2) the combustion of typical hydrocarbons proceeds through decomposition into hundreds of molecular species interacting through thousands of reactions. Hence, the combination of detailed reaction- rate models with the fundamental flow equations yields flow models that are computationally prohibitive. Hence, further, a reduction of at least an order of magnitude in the dimension of reaction kinetics is one of the prerequisites for feasibility of computational simulation of turbulent, chemically reacting flows. In the present method of simplified modeling, all molecular species involved in the oxidation of hydrocarbons are classified as either light or heavy; heavy molecules are those having 3 or more carbon atoms. The light molecules are not subject to meaningful decomposition, and the heavy molecules are considered to decompose into only 13 specified constituent radicals, a few of which are listed in the table. One constructs a reduced-order model, suitable for use in estimating the release of heat and the evolution of temperature in combustion, from a base comprising the 13 constituent radicals plus a total of 26 other species that include the light molecules and related light free radicals. Then rather than following all possible species through their reaction coordinates, one follows only the reduced set of reaction coordinates of the base. The behavior of the base was examined in test computational simulations of the combustion of heptane in a stirred reactor at various initial pressures ranging from 0.1 to 6 MPa. Most of the simulations were performed for stoichiometric mixtures; some were performed for fuel/oxygen mole ratios of 1/2 and 2.

Bellan, Josette↗
NASA NTRS1993

Marangoni effect induced convection in material processing under microgravity (M-18)

On the ground the upper layer of the liquid in a vessel heated from below becomes hotter than the lower layer. This well-known phenomenon results from buoyancy-induced convection. Though this means that the buoyancy-induced convection is not dominant under microgravity conditions in space, another convection called Marangoni convection may possibly occur. This convection results from an intermolecular force which acts on a free surface, that is surface tension. Since it is stronger at lower temperatures, the liquid surface near the heated wall is pulled to the cooled side as shown. This surface movement causes the inner convection. Marangoni convection, however, may be negligible on the Earth, for the molecular force is generally smaller than buoyancy. Various tests on material processing were recently conducted in space and some high quality crystals free from buoyancy convection were obtained. But, at the same time, others proved to be less uniform than expected in the components' distribution. This nonuniformity seems to be mainly caused by Marangoni convection. It is, therefore, very important to know how to control the convection by studying its characteristics, but the problem is that on the ground it is impossible to carry out the experiment without gravity. That is what a space experiment aboard the space shuttle is planned as the First Material Processing Tests (FMPT) of Japan. The experiment on Marangoni flow visualization is being performed in order to investigate the characteristics of convection in uni-dimensional melt growth under microgravity conditions.

Enya, S.↗
DOE OSTI2025

dynamics of organic-mineral interactions at the metal oxide-solution interface as studied via binding energetics (Final report)

This project focused on addressing longstanding fundamental and experimental uncertainties on how dissolved organic substances (DOS) interact with metal oxide surface under environmentally relevant conditions. By leveraging a custom-built real-time, in-tandem flow adsorption microcalorimetry-UV-Vis/fluorescence spectroscopy platform, we characterized the binding energetics, kinetics and mechanistic pathways driving DOS-metal oxide interactions at temporal resolution on the order of 1-5 seconds. We studied a diverse suite of model organic compounds/substances – including monocarboxylates (e.g. acetate and benzoate), di-carboxylates (oxalate and succinate), amino acids, amino-based nanparticles and natural organic matter – interacting at the mineral-water interface of structurally- and/or chemically distinct metal oxides (including SiO2, boehmite, ferrihydrite, and γ-Al2O3). Our results indicated that DOS-metal oxide interactions are governed by multi-step reaction pathways, often switching between distinct, resolvable enthalpy- and entropy-driven non-electrostatic or electrostatic configurations. To quantify these interactions, we developed and implemented an analytical workflow that integrates peak deconvolution and Monte-Carlo based error propagation to determine site-specific thermodynamic and kinetic parameters for individual binding/debinding events. In addition to resolving apparent first-order rate constants of each event, we were able to quantify associated apparent equilibrium constants as well as free energy, enthalpy and entropy contribution to the activation and subsequent progression of the binding/debinding process across compounds, compound class and metal oxide surfaces. The kinetic-thermodynamic data produced in this study captured how the interplay between oxide surface reactivity and DOS molecular structure jointly drives binding-debinding dynamics. Notably, that at pH below PZC of the oxide surface, neutral species were heavily involved in monocarboxylate binding, while anionic species drove dicarboxylate binding. Also, that among amino acids 1) positional isomers show distinctive binding characteristics to each other while enantiomers show no significant differences in binding characteristics, 2) molecules that bind via outer-sphere complexation show a larger entropic shift between binding and debinding with no impact on oxide surface while 3) inner-sphere interactions increased anion exchange capacity of the oxide surface. The new insights and data from this work has great potential for improving predictive modeling of carbon dynamics and specifically organic-mineral interactions in environmental and industrial systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Molecular fluctuations inhibit intermittency in compressible turbulence

In the standard picture of fully developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients. Microscopically, however, constituent fluid molecules are in constant thermal (Brownian) motion, but the role of molecular fluctuations in large-scale turbulence is largely unknown, and with rare exceptions, it has historically been considered irrelevant at scales larger than the molecular mean free path. Recent theoretical and computational investigations have shown that molecular fluctuations can impact energy cascade at Kolmogorov length scales. Here, we show that molecular fluctuations not only modify energy spectrum at wavelengths larger than the Kolmogorov length in compressible turbulence, but also significantly inhibit spatio-temporal intermittency across the entire dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly Gaussian statistics in the dissipation range. These results demonstrate that the compressible Navier–Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range. Our findings have significant consequences for turbulence modelling in applications such as astrophysics, reactive flows and hypersonic aerodynamics, where dissipation-range turbulence is approximated by closure models.

compressible turbulence↗
DOE OSTI2023

Direct Synthesis of Ammonia from Nitrate on Amorphous Graphene with Near 100% Efficiency

Abstract Ammonia is an indispensable commodity in the agricultural and pharmaceutical industries. Direct nitrate‐to‐ammonia electroreduction is a decentralized route yet challenged by competing side reactions. Most catalysts are metal‐based, and metal‐free catalysts with high nitrate‐to‐ammonia conversion activity are rarely reported. Herein, it is shown that amorphous graphene synthesized by laser induction and comprising strained and disordered pentagons, hexagons, and heptagons can electrocatalyze the eight‐electron reduction of NO 3 − to NH 3 with a Faradaic efficiency of ≈100% and an ammonia production rate of 2859 µg cm −2 h −1 at −0.93 V versus reversible hydrogen electrode. X‐ray pair‐distribution function analysis and electron microscopy reveal the unique molecular features of amorphous graphene that facilitate NO 3 − reduction. In situ Fourier transform infrared spectroscopy and theoretical calculations establish the critical role of these features in stabilizing the reaction intermediates via structural relaxation. The enhanced catalytic activity enables the implementation of flow electrolysis for the on‐demand synthesis and release of ammonia with >70% selectivity, resulting in significantly increased yields and survival rates when applied to plant cultivation. The results of this study show significant promise for remediating nitrate‐polluted water and completing the NO x cycle.

Huang, Libei↗
NASA NTRS2004

High Temperature VARTM with LaRC Polyimides

Recent work at NASA Langley Research Center (LaRC) has concentrated on developing new polyimide resin systems for advanced aerospace applications that can be processed without the use of an autoclave. Polyimide composites are very attractive for applications that require a high strength to weight ratio and thermal stability. Vacuum assisted resin transfer molding (VARTM) has shown potential to reduce the manufacturing cost of composite structures. In VARTM, the fibrous preform is infiltrated on a rigid tool surface contained beneath a flexible vacuum bag. Both resin injection and fiber compaction are achieved under pressures of 101.3 KPa or less. Recent studies have demonstrated the feasibility of the VARTM process for fabrication of void free structures utilizing epoxy resin systems with fiber volume fractions approaching 60%. In this work, the VARTM process has been extended to the fabrication of composite panels from polyimide systems developed at the Langley Research Center. This work has focused on processing LARC(trademark) PETI-8 (Langley Research Center Phenylethynyl Terminated Imide- 8), an aromatic polyimide based on 3,3',4,4' -biphenyltetracarboxylic dianhydride, a 50:50 molar ratio of 3,4'-oxydianiline and 1,3-bis(3-aminophenoxy)benzene, with 4-phenylethynylphthalic anhydride as the endcapping agent. Various molecular weight versions were investigated to determine their feasibility of being processed by VARTM at elevated temperatures. An injection temperature of approximately 280 C was required to achieve the necessary viscosity (<5 Poise) for flow at VARTM pressures. Laminate quality and initial mechanical properties are presented for LARC(trademark) PETI-8 and 6k IM7 uniweave fabric.

Cano, Roberto J.↗
NASA NTRS2001

Rayleigh Scattering Diagnostic for Dynamic Measurement of Velocity and Temperature

A new technique for measuring dynamic gas velocity and temperature is described. The technique is based on molecular Rayleigh scattering of laser light, so no seeding of the flow is necessary. The Rayleigh scattered light is filtered with a fixed cavity, planar mirror Fabry-Perot interferometer. A minimum number of photodetectors were used in order to allow the high data acquisition rate needed for dynamic measurements. One photomultiplier tube (PMT) was used to measure the total Rayleigh scattering, which is proportional to the gas density. Two additional PMTs were used to detect light that passes through two apertures in a mask located in the interferometer fringe plane. An uncertainty analysis was used to select the optimum aperture parameters and to predict the measurement uncertainty due to photon shot-noise. Results of an experiment to measure the velocity of a subsonic free jet are presented.

Seasholtz, Richard G.↗
NASA NTRS2001

Rayleigh Scattering Diagnostic for Dynamic Measurement of Velocity Fluctuations in High Speed Jets

A flow diagnostic technique based on the molecular Rayleigh scattering of laser light is used to obtain dynamic density and velocity data in a high speed flow. The technique is based on analyzing the Rayleigh scattered light with a Fabry-Perot interferometer used in the static, imaging mode. An analysis is presented that established a lower bound for measurement uncertainty of about 20 m/sec for individual velocity measurements obtained in a 100 microsecond time interval. Software and hardware interfaces were developed to allow computer control of all aspects of the experiment and data acquisition. The signals from three photomultiplier tubes were simultaneously recorded using photon counting at a 10 kHz sampling rate and 10 second recording periods. Density and velocity data, including distribution functions and power spectra, taken in a Mach 0.8 free jet, are presented.

Seasholtz, Richard G.↗
DOE OSTI2024

Unlocking the Sun's Secrets: Laboratory Insights into the Sun's Outer Atmosphere

The Sun’s corona, its outermost and hottest atmospheric layer, emits brightly in the extreme ultraviolet (EUV) and X-rays. This emission comes from atoms that have been highly ionized by the high temperature, forming a plasma of atomic ions and free electrons. By studying this light, scientists learn about the complex and dynamic drivers of solar activity. Many past, current, and future solar observatories focus on measuring EUV spectra from the Fe IX ion, as this ion provides powerful diagnostics for solar physics. Using Fe IX spectra, solar physicists can measure the plasma temperature, density, elemental abundances, and flow velocities in the corona. However, atomic data uncertainties concerning spectral line identification and plasma density diagnostics are a major problem for the accurate interpretation of these spectra.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2004

Measurement of Initial Conditions at Nozzle Exit of High Speed Jets

The time averaged and unsteady density fields close to the nozzle exit (0.1 less than or = x/D less than or = 2, x: downstream distance, D: jet diameter) of unheated free jets at Mach numbers of 0.95, 1.4, and 1.8 were measured using a molecular Rayleigh scattering based technique. The initial thickness of shear layer and its linear growth rate were determined from time-averaged density survey and a modeling process, which utilized the Crocco-Busemann equation to relate density profiles to velocity profiles. The model also corrected for the smearing effect caused by a relatively long probe length in the measured density data. The calculated shear layer thickness was further verified from a limited hot-wire measurement. Density fluctuations spectra, measured using a two-Photomultiplier-tube technique, were used to determine evolution of turbulent fluctuations in various Strouhal frequency bands. For this purpose spectra were obtained from a large number of points inside the flow; and at every axial station spectral data from all radial positions were integrated. The radially-integrated fluctuation data show an exponential growth with downstream distance and an eventual saturation in all Strouhal frequency bands. The initial level of density fluctuations was calculated by extrapolation to nozzle exit.

Panda, J.↗