Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “phase space methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Two-step spin-coating of vacancy-ordered double perovskites enables growth of thin films for electronic devices

Vacancy-ordered double perovskites (VODPs), such as Cs 2 TeX 6 (X = Cl, Br, I), are lead-free alternatives to conventional metal-halide perovskites (MHPs). One limitation of VODPs is the lack of processes to form thin films relevant for physical characterization and electronic devices. A two-step spin-coating method was developed for synthesizing high-quality films of Cs 2 TeBr 6 . Independently depositing CsBr and TeBr 4 enables high precursor concentrations and control over crystallization kinetics. By optimizing the spin-coating parameters, conversion of precursors to phase pure films was observed using structural and surface characterization methods. The growth of mixed-halide systems was investigated using alternative salts including CsCl and CsI. The formation of halide alloys was found to depend on the existence of routes to byproducts. Lastly, single carrier diodes of Cs2TeBr6 were designed following valence band characterization with photoelectron spectroscopy. Temperature-dependent space-charge-limited current measurements revealed that transport occurs by hopping and the hole mobility is 3.2 × 10 −5 cm 2 V −1 s −1 near room temperature. As a result, the insights from the 2-step procedure provide a pathway towards making semiconducting devices from VODPs.

Kuklinski, Owen [University of California, Santa B↗
DOE OSTI2022

A self-consistent hybrid model of kinetic striations in low-current argon discharges

A self-consistent hybrid model of standing and moving striations was developed for low-current DC discharges in noble gases. We introduced the concept of surface diffusion in phase space ( r , u ) (where u denotes the electron kinetic energy) described by a tensor diffusion in the nonlocal Fokker–Planck kinetic equation for electrons in the collisional plasma. Electrons diffuse along surfaces of constant total energy ε = u - eφ ( r ) between energy jumps in inelastic collisions with atoms. Numerical solutions of the 1d1u kinetic equation for electrons were obtained by two methods and coupled to ion transport and Poisson solver. We studied the dynamics of striation formation in Townsend and glow discharges in argon gas at low discharge currents using a two-level excitation-ionization model and a ‘full-chemistry’ model, which includes stepwise and Penning ionization. Standing striations appeared in Townsend and glow discharges at low currents, and moving striations were obtained for the discharge currents exceeding a critical value. These waves originate at the anode and propagate towards the cathode. We have seen two types of moving striations with the two-level and full-chemistry models, which resemble the s and p striations previously observed in the experiments. Simulations indicate that processes in the anode region could control moving striations in the positive column plasma. The developed model helps clarify the nature of standing and moving striations in DC discharges of noble gases at low discharge currents and low gas pressures.

Physics↗
NASA NTRS1974

Shuttle ascent trajectory optimization with function space quasi-Newton techniques

A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.

Edge, E. R.↗
NASA NTRS1980

Normal and shear impact of layered composite with a crack - Dynamic stress intensification

The dynamic response of a layered composite under normal and shear impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. One of the objectives was to develop an analytical method for determining dynamic stress solutions which should lead to a numerical method which utilizes Fourier transform for the space variable and Laplace transform for the time variable. The time-dependent angle loading is separated into two parts: a symmetric and a skew-symmetric with reference to the crack plane. By superposition, the transient boundary conditions consist of applying normal and shear tractions to a crack embedded in a layered composite; one phase of the composite could represent the fiber while the other could be the matrix. Mathematically, these conditions reduce the problem to a system of dual integral equations solved in the transform plane for the transform of the dynamic stress-intensity factor.

Sih, G. C.↗
NASA NTRS2011

Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results

Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.

Petersen, Walter A.↗
NASA NTRS2012

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

Xu, Feng↗
NASA NTRS2017

Metabolomic and Genomic Markers of Atherosclerosis as Related to Oxidative Stress, Inflammation, and Vascular Function in Twin Astronauts

BACKGROUND: Future human space travel will consist primarily of long-duration missions onboard the International Space Station (ISS) or exploration-class missions to Mars, its moons, or nearby asteroids. Astronauts participating in long-duration missions may be at an increased risk of oxidative stress and inflammatory damage due to radiation, psychological stress, altered physical activity, nutritional insufficiency, and hyperoxia during extravehicular activity. By studying one identical twin during his 1-year ISS mission and his ground-based twin, this work extends a current NASA-funded investigation to determine whether these spaceflight factors contribute to an accelerated progression of atherosclerosis. This study of twins affords a unique opportunity to examine spaceflight-related atherosclerosis risk that is independent of the confounding factors associated with different genotypes. PURPOSE: The purpose of this investigation was to determine whether biomarkers of oxidative and inflammatory stress are elevated during and after long-duration spaceflight and determine if a relation exists between levels of these biomarkers and structural and functional indices of atherosclerotic risk measured in the carotid and brachial arteries. These physiological and biochemical data will be extended by using an exploratory approach to investigate the relationship between intermediate phenotypes and risk factors for atherosclerosis and the metabolomic signature from plasma and urine samples. Since metabolites are often the indirect products of gene expression, we simultaneously assessed gene expression and DNA methylation in leukocytes. HYPOTHESIS: We predict that, compared to the ground-based twin, the space-flown twin will experience elevated biomarkers of oxidative stress and inflammatory damage, altered arterial structure and function, accelerated telomere shortening, dysregulation of genes associated with oxidative stress and inflammation, and a metabolic profile shift that is associated with elevated atherosclerosis risk factors. METHODS: In the space-flown twin, a panel of biomarkers of oxidative and inflammatory stress were measured in venous blood samples and in 24-h (in-flight) and 48-h (pre- and post-flight) urine pools collected twice before flight, six times during the mission (~FD15, 75, 180, 240, 300, 335), and early in the post-flight recovery phase (3-5 days after landing). We also measured metabolomic (targeted and untargeted approaches) and genomic markers (DNA methylation, mRNA gene expression, telomere length) in these samples. Arterial structure, assessed from measures of intima-media thickness, also were measured using standard clinical ultrasound at the same time points. Arterial function was assessed using brachial flow-mediated dilation, a well-validated measure used to assess endothelium-dependent vasodilation and a sensitive predictor of atherosclerotic risk, only before and after spaceflight. All of the same measures were obtained in the ground-based twin, but less frequently. DISCUSSION: All data collection has been completed for both the space-flown twin and the ground-based twin. Vascular structure and function measures have been analyzed, blood and urine samples have been batch-processed. Results from these individuals will be compared to each other, to data from other Twin Study investigations, and to the larger complement of subjects participating in the companion study currently ongoing in ISS astronauts.

Lee, Stuart M. C.↗
NASA NTRS2010

On-Orbit Prospective Echocardiography on International Space Station Crew

Introduction A prospective trial of echocardiography was conducted on of six crewmembers onboard the International Space Station. The main objective was to determine the efficacy of remotely guided tele-echocardiography, including just-in-time e-training methods and determine what "space normal" echocardiographic data is. Methods Each crewmember operator (n=6) had 2-hour preflight training. Baseline echocardiographic data were collected 55 to 167days preflight. Similar equipment was used in each 60-minute in-flight session (mean microgravity exposure - 114 days (34 -- 190)). On Orbit ultrasound operators used an e-learning system within 24h of these sessions. Expert assistance was provided using ultrasound video downlink and two-way voice. Testing was repeated 5 to 16 days after landing. Separate ANOVA was used on each echocardiographic variable (n=33). Within each ANOVA, three tests were made: a) effect of mission phase (preflight, in-flight, post flight); b) effect of echo technician (two technicians independently analyzed the data); c) interaction between mission phase and technician. Results Nine rejections of the null hypothesis (mission phase or technician or both had no effect) were discovered and considered for follow up. Of these, six rejections were for significant technician effects, not as a result of space flight. Three rejections of the null hypothesis (Aortic Valve time velocity integral, Mitral E wave Velocity and heart rate) were attributable to space flight, however determined not to be clinically significant. No rejections were due to the interaction between technician and space flight. Conclusion No consistent clinically significant effects of long-duration space flight were seen in echocardiographic variables of the given group of subjects.

Hamilton, Douglas R.↗
DOE OSTI2021

High-Performance/-Precision/-Z(HPPZ) Scintillator Grids via Advanced Electrochemistry. Phase I – Project # 20210572MFR- Mid year review [Slides]

Scintillation grids with improved imaging resolution in time and space, are required for future mission needs at various facilities (pRad user station, LANSCE, DARHT, Scorpius etc). Current technologies use inorganic crystal scintillators, which are positioned within a high-Z scintillator septa. Dense and high-Z materials are optimal for gamma-ray detection making them promising candidates for development of high -performance/-precision/-Z (HPPZ) scintillator grids. The current resolution of standard chemical etching and fabrication processes of high-Z materials is very low, leading to undesired undercutting and ultimately reducing crystal performance efficiency. Goals are to: Perform initial feasibility studies with the aim of producing complex parts for applications with difficult-to-process high-Z material; Use of pulse and pulse-reverse electrochemical methods on additive approaches to produce high-precision Au and Re scintillator grids at a small scale; and, Follow up in Phase II with the delivery of a large-scale scintillator grid of the best material candidate with unprecedented properties for LANL needs determined in Phase I.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Performance evaluation of a wrapped around condenser for heat pump water heater applications

In this report, accurate performance evaluation of a wrapped-around condenser for heat pump water heaters (WHPWH) is critical since the COP of the system depends heavily on thermal stratification and condenser design. An analytical, quasi-steady state heat balance method has been developed to determine the optimal spacing between adjacent channels, tube diameter, tube shape, and total refrigerant charge amount for the condenser. The heat transfer rate is compared among three approaches: the refrigerant thermodynamic model, the condenser-wrap fin model, and the analytical natural convection model on the inside of the tank for the three regions based on the refrigerant phase (e.g., super-heated, saturated, or subcooled). The heat transfer rate was predicted by a combination of slug-plug and annular flow for a D-shaped helical tube. Experimental data were used as boundary conditions for validating the model. The rate of heat transfer based on tube shape and tank wall temperatures was compared by CFD analysis. Parametric analysis indicates a tradeoff between refrigerant mass, pressure drop, tube diameter, and tube length to maximize the heat transfer rate. The model suggests the saturated region length can be extended by 400%, and the condenser pressure drop can be reduced by 23% with an optimal spacing pattern.

42 ENGINEERING↗
DOE OSTI2026

Novel thermal energy storage component: Development, performance, and phase transition diagnosis

Thermal energy storage (TES) using phase change materials (PCMs) is a promising technology for capturing and storing excess thermal energy for later use. However, challenges such as poor heat transfer efficiency and a lack of modular, scalable designs have limited widespread adoption of TES in real-world applications. This study developed and evaluated modular brick-type and blade-type TES prototypes featuring an aluminum housing, an embedded serpentine coil for active or passive thermal exchange, and a cost-effective metal mesh to enhance PCM thermal conductivity. The blade-type TES achieved notable geometric efficiency, with a thickness-to-length ratio of 0.03 and a thickness-to-width ratio of 0.08, enabling highly compact and modular thermal storage suitable for space-constrained applications. The paper presents a detailed evaluation of the TES prototypes’ performance. The comparative analysis indicated that the TES prototypes provide a highly cost-effective, thermally optimized alternative for compact energy storage and load shifting. A novel diagnostic technique was also introduced: using a portable endoscope to capture real-time visualizations of PCM phase transitions inside the TES. This method provides critical insights into internal heat transfer mechanisms, identifies potential issues, and offers valuable support for optimizing the TES design and developing the control algorithm. Overall, the modular brick-type and blade-type TES designs demonstrated in this work provide a scalable, efficient, and economically viable solution for advancing TES across residential, commercial, and industrial sectors. The designs’ compact structure, enhanced thermal performance, and integrated diagnostic capabilities make them strong candidates for future deployment in energy-efficient systems.

Gao, Zhiming [ORNL] (ORCID:0000000271397995)↗
DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Combustion response modeling for composite solid propellants

A computerized mathematical model of the combustion response function of composite solid propellants was developed with particular attention to the contributions of the solid phase heterogeneity. The one-dimensional model treats the solid phase as alternating layers of ammonium perchlorate and binder, with an exothermic melt layer at the surface. Solution of the Fourier heat equation in the solid provides temperature and heat flux distributions with space and time. The problem is solved by conserving the heat flux at the surface from that produced by a suitable model of the gas phase. An approximation of the BDP flame model is utilized to represent the gas phase. By the use of several reasonable assumptions, it is found that a significant portion of the problem can be solved in closed form. A method is presented by which the model can be applied to tetramodal particle size distributions. A computerized steady-state version of the model was completed, which served to validate the various approximations and lay a foundation for the combustion response modeling. The combustion response modeling was completed in a form which does not require an iterative solution, and some preliminary results were acquired.

Source record↗
NASA NTRS1982

Direct observation of interface instability during crystal growth

The general aim of this investigation was to study interface stability and solute segregation phenomena during crystallization of a model system. Emphasis was to be placed on direct observational studies partly because this offered the possibility at a later stage of performing related experiments under substantially convection-free conditions in the space shuttle. The major achievements described in this report are: (1) the development of a new model system for fundamental studies of crystal growth from the melt and the measurement of a range of material parameters necessary for comparison of experiment with theory. (2) The introduction of a new method of measuring segregation coefficient using absorption of a laser beam by the liquid phase. (3) The comparison of segregation in crystals grown by gradient freezing and by pulling from the melt. (4) The introduction into the theory of solute segregation of an interface field term and comparison with experiment. (5) The introduction of the interface field term into the theories of constitutional supercooling and morphological stability and assessment of its importance.

Tiller, W. A.↗
NASA NTRS2010

Use of a Microphone Phased Array to Determine Noise Sources in a Rocket Plume

A 70-element microphone phased array was used to identify noise sources in the plume of a solid rocket motor. An environment chamber was built and other precautions were taken to protect the sensitive condenser microphones from rain, thunderstorms and other environmental elements during prolonged stay in the outdoor test stand. A camera mounted at the center of the array was used to photograph the plume. In the first phase of the study the array was placed in an anechoic chamber for calibration, and validation of the indigenous Matlab(R) based beamform software. It was found that the "advanced" beamform methods, such as CLEAN-SC was partially successful in identifying speaker sources placed closer than the Rayleigh criteria. To participate in the field test all equipments were shipped to NASA Marshal Space Flight Center, where the elements of the array hardware were rebuilt around the test stand. The sensitive amplifiers and the data acquisition hardware were placed in a safe basement, and 100m long cables were used to connect the microphones, Kulites and the camera. The array chamber and the microphones were found to withstand the environmental elements as well as the shaking from the rocket plume generated noise. The beamform map was superimposed on a photo of the rocket plume to readily identify the source distribution. It was found that the plume made an exceptionally long, >30 diameter, noise source over a large frequency range. The shock pattern created spatial modulation of the noise source. Interestingly, the concrete pad of the horizontal test stand was found to be a good acoustic reflector: the beamform map showed two distinct source distributions- the plume and its reflection on the pad. The array was found to be most effective in the frequency range of 2kHz to 10kHz. As expected, the classical beamform method excessively smeared the noise sources at lower frequencies and produced excessive side-lobes at higher frequencies. The "advanced" beamform routine CLEAN-SC created a series of lumped sources which may be unphysical. We believe that the present effort is the first-ever attempt to directly measure noise source distribution in a rocket plume.

Panda, J.↗
NASA NTRS2021

Aqua Factorem: Ultra Low Energy Lunar Water Extraction

We propose a new method we call Aqua Factorem to extract lunar water. It will drastically reduce energy and complexity of lunar mining operations helping to establish this industry. Other methods to extract water from the regolith are based on phase change, pumping energy into the regolith to sublimate the ice into vapor, then capturing the vapor, re-freezing it, and hauling the solid ice to a chemical processor where it is converted again into vapor for purification then electrolysis. This requires transporting high power into the permanently shadowed regions (PSRs) not only to vaporize the ice in situ in the soil but to heat the surrounding soil itself, which is wasted energy. Still other methods are based on strip mining and hauling the resource along with slag (the unwanted silicates, which constitutes about 95% of the mass), to a processing unit that is located outside the PSRs. That may be a simpler architecture but is generally not favored because hauling 49,000 t of regolith over many kilometers yearly to produce the projected demand of 2,450 t of propellant would be terribly difficult and expensive with high risk that the vehicles will get stuck driving with such loads across the unprepared regolith. We propose an alternative to both of these approaches, taking advantage of the processing that the unique lunar geology has already performed. Micrometeoroid bombardment has already broken most solid material in the upper part of the regolith into fine grains. This includes solid material of all compositions, including the ice, which is as hard as granite at PSR temperatures and is therefore essentially another type of rock. These ice grains are intermixed with all the other minerals, so a simple, ultra-low-energy grain-sorting process can extract the ice without phase change. As another benefit it can extract the 1 wt% free metal known to be in lunar soil, again with very little energy. The ice can then be hauled to the chemical processing unit in solid phase and converted into rocket propellant. We estimate the 800 kW power needed for thermal extraction can be reduced to less than 100 watts using the new method. This affects the entire architecture of the mining operation producing extensive economic benefit, which we will quantify in this study. We will study it in the context of a mission to mine propellants commercially for space tugs that boost commercial communication satellites from Geosynchronous Transfer Orbit (GTO) to Geostationary Orbit (GEO) then return to the lunar surface for refueling. This simple architecture requires the minimum number of in-space elements, and notably does not require an in-space propellant depot, so it provides the lowest cost and lowest risk startup for a commercial operation. The study will also test the innovative Aqua Factorem process through laboratory experiments, and this will produce basic insights into the handling of lunar resources.

lunar↗
DOE OSTI2020

Flash Graphene from Plastic Waste

In this work, an approach to upcycling plastic waste (PW) products is presented. The method relies on flash Joule heating (FJH) to convert PW into flash graphene (FG). In addition to FG, the process results in the formation of carbon oligomers, hydrogen, and light hydrocarbons. In order to make high quality graphene, a sequential alternating current (AC) and direct current (DC) flash is used. Here, the FJH process requires no catalyst and works for PW mixtures, which makes the process suitable for handling landfill PW. The energy required to convert PW to FG is ~ 23 kJ/g or ~ $125 in electricity per ton of PW, potentially making this process economically attractive for scale-up. The FG was characterized by Raman spectroscopy and had a I 2D /I G peak ratio up to 6 with a low-intensity D band. Moreover, transmission electron microscopy and X-ray diffraction analysis show that the FG is turbostratic with an interlayer spacing of 3.45 Å. The large interlayer spacing will facilitate its dispersion in liquids and composites. Analysis of FG dispersions in 1% Pluronic aqueous solution shows that concentrations up to 1.2 mg/mL can be achieved. The carbon oligomers that distilled from the process were characterized by Fourier-transform infrared spectroscopy and have chemical structures similar to the starting PW. Initial analysis of gas phase products shows the formation of considerable amounts of hydrogen along with other light hydrocarbons. Since graphene is naturally occurring and it shows a low toxicity profile, this could be an environmentally beneficial method to upcycle PE.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1958

Three-Dimensional Orbits of Earth Satellites, Including Effects of Earth Oblateness and Atmospheric Rotation

The principal purpose of the present paper is to present sets of equations which may be used for calculating complete trajectories of earth satellites from outer space to the ground under the influence of air drag and gravity, including oblateness effects, and to apply these to several examples of entry trajectories starting from a circular orbit. Equations of motion, based on an "instantaneous ellipse" technique, with polar angle as independent variable, were found suitable for automatic computation of orbits in which the trajectory consists of a number of revolutions. This method is suitable as long as the trajectory does not become nearly vertical. In the terminal phase of the trajectories, which are nearly vertical, equations of motion in spherical polar coordinates with time as the independent variable were found to be more suitable. In the first illustrative example the effects of the oblateness component of the earth's gravitational field and of atmospheric rotation were studied for equatorial orbits. The satellites were launched into circular orbits at a height of 120 miles, an altitude sufficiently high that a number of revolutions could be studied. The importance of the oblateness component of the earth's gravitational field is shown by the fact that a satellite launched at circular orbital speed, neglecting oblateness, has a perigee some 67,000 feet lower when oblateness forces are included in the equations of motion than when they are not included. Also, the loss in altitude per revolution is double that of a satellite following an orbit not subject to oblateness. The effect of atmospheric rotation on the loss of altitude per revolution was small. As might be surmised, the regression of the line of nodes as predicted by celestial mechanics is unchanged when drag is included. It is clear that the inclination of the orbital plane to the equator will be relatively unaffected by drag for no atmospheric rotation since the drag lies in the orbital plane in this case. With the inclusion of atmospheric rotation it was found that the inclination of the plane changed about one-millionth of a radian per revolution. Thus the prediction of the position of the orbital plane of an earth satellite is not complicated by the introduction of drag. The line of apsides, which without drag but with oblateness moves slowly in space, tends to move with the satellite when drag is included in the calculations. As a results, the usual linearized solutions based on oblateness alone must be basically altered when drag is included to take into account the rapid movement of the line of apsides. In the second illustrative example the final revolution was calculated to impact for a number of trajectories in an orbital plane inclined at 650 to the equator. Of particular interest is the large effect the oblateness gravitational field and atmospheric rotation can have on the impact point. For a value of CDA/m of unity, and for an initial downward angle at 80 miles altitude of 0.01 radian, such as might be utilized for manned re-entry, oblateness had an influence of about 300 miles in the impact point, and atmospheric rotation had about a 150-mile influence.

Nielsen, Jack N.↗