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Lunar and Planetary Science XXXVI, Part 1

Contents include the following: Observations with Near Infrared Spectrometer for Hayabusa Mission in the Cruising Phase. First Results of Quadrantid Meteor Spectrum. Compositional Investigation of Binary Near-Earth Asteroid 66063 (1998 RO1): A Potentially Undifferentiated Assemblage. Impact-induced Hydrothermal Activity on Early Mars. HRTEM and EFTEM Studies of Phyllosilicate-Organic Matter Associations in Matrix and Dark Inclusions in the EET92042 CR2 Carbonaceous Chondrite. Volumetric Analysis of Martian Rampart Craters. High Pressure Melting of H-Chondrite: A Match for the Martian Basalt Source Mantle. MERView: A New Computer Program for Easy Display of MER-acquired M ssbauer Data. Distribution, Exchange, and Topographic Control of Subsurface Ice on Mars. Shock-induced Damage Beneath Normal and Oblique Impact Craters. Amphitrites Patera Studied from the Mars Express HRSC Data. Oxygen Isotope Microanalysis of Enveloping Compound Chondrules in CV3 and LL3 Chondrites. Gamma-Ray Irradiation in the Early Solar System and the Conundrum of the Lu-176 Decay Constant. Magnesium Isotope Mapping of Silica-rich Grains Having. Extreme Oxygen Isotope Anomalies Extreme Oxygen Isotopic Anomalies from Irradiation in the Early Solar System, Re-Examining the Role of Chondrules in Producing the Elemental Fractionations in Chondrites. Meteorite Data on the Solar Modulation of Galactic Cosmic Rays and an Inference on the Solar Activity Influence on Climate of the Earth. Volatiles Enrichments and Composition of Jupiter. Thinking Like a Wildcatter Prospecting for Methane in Arabia Terra, Mars. Size Distribution of Genesis Solar Wind Array Collector Fragments. Initial Subdivision of Genesis Early Science Polished Aluminum Collector. Presolar Graphite and Its Noble Gases. Young Pb-Isotopic Ages of Chondrules in CB Carbonaceous Chondrites. Fe Isotopic Composition of Martian Meteorites. Petrology and Geochemistry of Nakhlite MIL 03346: A New Martian Meteorite from Antarctica.

Source record↗

Lamb Wave Stiffness Characterization of Composites Undergoing Thermal-Mechanical Aging

The introduction of new, advanced composite materials into aviation systems requires a thorough understanding of the long term effects of combined thermal and mechanical loading upon those materials. Analytical methods investigating the effects of intense thermal heating combined with mechanical loading have been investigated. The damage mechanisms and fatigue lives were dependent on test parameters as well as stress levels. Castelli, et al. identified matrix dominated failure modes for out-of-phase cycling and fiber dominated damage modes for in-phase cycling. In recent years, ultrasonic methods have been developed that can measure the mechanical stiffness of composites. To help evaluate the effect of aging, a suitably designed Lamb wave measurement system is being used to obtain bending and out-of-plane stiffness coefficients of composite laminates undergoing thermal-mechanical loading. The system works by exciting an antisymmetric Lamb wave and calculating the velocity at each frequency from the known transducer separation and the measured time-of-flight. The same peak in the waveforms received at various distances is used to measure the time difference between the signals. The velocity measurements are accurate and repeatable to within 1% resulting in reconstructed stiffness values repeatable to within 4%. Given the material density and plate thickness, the bending and out-of-plane shear stiffnesses are calculated from a reconstruction of the dispersion curve. A mechanical scanner is used to move the sensors over the surface to map the time-of-flight, velocity, or stiffnesses of the entire specimen. Access to only one side of the material is required and no immersion or couplants are required because the sensors are dry coupled to the surface of the plate. In this study, the elastic stiffnesses D(sub 11), D(sub 22), A(sub 44), and A(sub 55) as well as time-of-flight measurements for composite samples that have undergone combined thermal and mechanical aging for a duration of 10,000 hours are reported.

Seale, Michael D.↗

Mapping the Structure of Heterogeneous Materials

Image-processing microdensitometer/Fourier analyzer yields statistics of subcomponent distribution. Nondestructive method for studying structure heterogeneous materials uses energy-dispersive X-ray analysis in scanning electron microscope. Scanning microdensitometer/Fourier analyzer (SMFA) is applied to SEM images to obtain statistics about sample structure. Method originally developed for studying effect on combustion of fine structure of composite solid propellants.

Strand, L. D.↗

Characterization of C/Enhanced SiC Composite During Creep-Rupture Tests Using an Ultrasonic Guided Wave Scan System

An ultrasonic guided wave scan system was used to nondestructively monitor damage over time and position in a C/enhanced SiC sample that was creep tested to failure at 1200 C in air at a stress of 69 MPa (10 ksi). The use of the guided wave scan system for mapping evolving oxidation profiles (via porosity gradients resulting from oxidation) along the sample length and predicting failure location was explored. The creep-rupture tests were interrupted for ultrasonic evaluation every two hours until failure at approx. 17.5 cumulative hours.

Roth, Don J.↗

Geologic and mineral and water resources investigations in western Colorado using ERTS-1 data

The author has identified the following significant results. Topography was found to be the most important factor defining folds on ERTS-1 imagery of northwestern Colorado; tonal variations caused by rock reflectance and vegetation type and density are the next most important factors. Photo-linears mapped on ERTS-1 imagery of central Colorado correlate well with ground-measured joint and fracture trends. In addition, photo-linears have been successfully used to determine the location and distribution of metallic mineral deposits in the Colorado Mineral Belt. True color composites are best for general geologic analysis and false color composites prepared with positive/negative masks are useful for enhancing local geologic phenomena. During geologic analysis of any given area, ERTS-1 imagery from several different dates should be studied.

Knepper, D. H., Jr.↗

Tartarus Colles: A sampling of the Martian highlands

Several of the most fundamental issues about the geology of Mars can be addressed using information on composition and structure of the plateau plains ('highlands') that cover approximately half the planet. The units that compose the highlands are interpreted as a mixture of volcanic, fluvial, lacustrine, and impact ejecta deposits. A more precise inventory of differing of igneous and sedimentary lithologies in highland rock units would not only lead to a better understanding of how the plateau plains formed, but would also clarify the nature of the surface environment during the first 800 m.y. of martian history. Structural features including bedforms, joints, and small faults that are unresolved from orbit record a history of the emplacement and deformation of the highlands. In addition, weathering products present in this very ancient terrain represent a mineralogic record of past climate and of the pathways by which bedrock is altered chemically. Their similarity or dissimilarity to bright soils observed spectroscopically and in situ at the Viking Lander sites will be evidence for the relative roles of regional sources and global eolian transport in producing the widespread cover of 'dust.' Unfortunately, these issues are difficult to address in the plateau plains proper, because bedrock is covered by mobile sand and weathering products, which dominate both surface composition and remotely measurable spectral properties. However, the 'Tartarus Colles' site, located at 11.41 deg N, 197.69 deg W at an elevation of -1 km, provides an excellent opportunity to address the highland geology within the mission constraints of Mars Pathfinder. The site is mapped as unit HNu, and consists of knobby remnants of deeply eroded highlands. It contains rolling hills, but lacks steep escarpments and massifs common in most highland remnants, and is free of large channels that would have removed colluvium from eroded upper portions of the stratigraphic column. These characteristics indicate that variety of bedrock types from throughout the Noachian-Hesperian stratigraphic column may remain at the site.

Murchie, Scott↗

Thermographic Analysis of Composite Cobonds on the X-33

The methods utilized to perform an infrared thermography inspection of the bondline of structural reinforcing caps on X-33 liquid hydrogen (LH2) tank during the manufacture are described in this presentation. A total of thirty-six caps were bonded to the tank using a wet cobond process with vacuum bagging and low temperature curing. The thermal map of each bondline was acquired through the vacuum bag by applying heat to the cap and then viewing it during cool down. Poorly bonded regions, or voids, were characterized by localized hot spots in the thermal image. These regions were marked on the tank by referring to a live thermal image, then hand massaged in an attempt to remove the entrapped air. The cap was then reinspected and, if it was determined that the entrapped air could not be removed, the cap was removed and the adhesive cleaned away before it cured. Measures were then taken to better match the surface of the cap to the tank and the process repeated. After the bondline had cured sufficiently to allow vacuum bag removal, a "flash heating" thermographic Investigation was performed to verify that the cap had bonded properly to the tank. Any regions that had opened up after the preliminary inspection were marked and filled by drilling small holes in the cap and injecting resin. A final inspection was then performed to ensure the quality of the bondline.

Russell, Samual S.↗

Planetary Nebulae with Supporting IR Data

We present new HST/WFPC2 imagery for the planetary nebula (PN) NGC 6818. Observations were made in line filters F437N, F487N, F502N, and F656N plus continuum filter F547M. The primary goal was to develop a high spatial resolution (approx. 0.1 in.) map of the intrinsic line ratio [O III] 4363/5007 and thereby evaluate the electron temperature (T(sub e)) and the mean-square T(sub e) variation (t(sup 2) across the PN. In this process we developed an extinction map from the F487N (H(beta)) and F656N (H(alpha)) images by comparing the observed line ratios in each pixel to the theoretical ratio and computing a c(H(beta)) map which was used to correct the observed 4363/5007 ratios for reddening. We also adjust for the continuum contribution to the line filter data. We present color-coded pictures of the reddening (c(H(beta))) map, the [O III] T(sub e) map, as well as our determinations of t(sup 2). The T(sub e) map shows a decline from approx. 14000 K in the inner regions to approx. 11000 K at the outer edge. Such a radial T(sub e) gradient is expected for a high-excitation nebula with a prominent He(++) zone such as NGC 6818. A composite of images taken in 3 filters (F656N, red; F487N, blue; and F502N, [O III] 5007, green) shows a roughly spherical outer envelope as well as a brighter vase-shaped interior "bubble". There is a prominent orifice to the North and a smaller one to the South, along the major axis, possibly caused by a blow-out from a fast wind. This nebula has an appearance remarkably similar to that of the PN NGC 3918 previously imaged with HST by H. Bond. We note from the continuum images (F547M) two stars in the nebular field that are fainter than the prominent central star; these are roughly 2-4 sec. N and NE of the central star. Further study is needed to establish whether or not there may be a physical association of either star with the central star.

Harrington, J. Patrick↗

Rotation Rate of Saturn's Magnetosphere using CAPS Plasma Measurements

We present the present status of an investigation of the rotation rate of Saturn's magnetosphere using a 3D velocity moment technique being developed at Goddard which is similar to the 2D version used by Sittler et al. for SOI and similar to that used by Thomsen et al.. This technique allows one to nearly cover the full energy range of the Cassini Plasma Spectrometer (CAPS) IMS from 1 V . E/Q < 50 kV. Since our technique maps the observations into a local inertial frame, it does work during roll maneuvers. We make comparisons with the bi-Maxwellian fitting technique developed by Wilson et al. and the similar velocity moment technique by Thomsen et al. . We concentrate our analysis when ion composition data is available, which is used to weight the non-compositional data, referred to as singles data, to separate H+, H2+ and water group ions (W+) from each other. The chosen periods have high enough telemetry rates (4 kbps or higher) so that coincidence ion data, similar to that used by Sittler et al. for SOI is available. The ion data set is especially valuable for measuring flow velocities for protons, which are more difficult to derive using singles data within the inner magnetosphere, where the signal is dominated by heavy ions (i.e., proton peak merges with W+ peak as low energy shoulder). Our technique uses a flux function, which is zero in the proper plasma flow frame, to estimate fluid parameter uncertainties. The comparisons investigate the experimental errors and potential for systematic errors in the analyses, including ours. The rolls provide the best data set when it comes to getting 4PI coverage of the plasma but are more susceptible to time aliasing effects. In the future we will then make comparisons with magnetic field observations, Saturn ionosphere conductivities as presently known and the field aligned currents necessary for the planet to enforce corotation of the rotating plasma.

Sittler, E.↗

How Cities Breathe: Ground-Referenced, Airborne Hyperspectral Imaging Precursor Measurements To Space-Based Monitoring

Methane's (CH4) large global warming potential (Shindell et al., 2012) and likely increasing future emissions due to global warming feedbacks emphasize its importance to anthropogenic greenhouse warming (IPCC, 2007). Furthermore, CH4 regulation has far greater near-term climate change mitigation potential versus carbon dioxide CO2, the other major anthropogenic Greenhouse Gas (GHG) (Shindell et al., 2009). Uncertainties in CH4 budgets arise from the poor state of knowledge of CH4 sources - in part from a lack of sufficiently accurate assessments of the temporal and spatial emissions and controlling factors of highly variable anthropogenic and natural CH4 surface fluxes (IPCC, 2007) and the lack of global-scale (satellite) data at sufficiently high spatial resolution to resolve sources. Many important methane (and other trace gases) sources arise from urban and mega-urban landscapes where anthropogenic activities are centered - most of humanity lives in urban areas. Studying these complex landscape tapestries is challenged by a wide and varied range of activities at small spatial scale, and difficulty in obtaining up-to-date landuse data in the developed world - a key desire of policy makers towards development of effective regulations. In the developing world, challenges are multiplied with additional political access challenges. As high spatial resolution satellite and airborne data has become available, activity mapping applications have blossomed - i.e., Google maps; however, tap a minute fraction of remote sensing capabilities due to limited (three band) spectral information. Next generation approaches that incorporate high spatial resolution hyperspectral and ultraspectral data will allow detangling of the highly heterogeneous usage megacity patterns by providing diagnostic identification of chemical composition from solids (refs) to gases (refs). To properly enable these next generation technologies for megacity include atmospheric radiative transfer modeling the complex and often aerosol laden, humid, urban microclimates, atmospheric transport and profile monitoring, spatial resolution, temporal cycles (diurnal and seasonal which involve interactions with the surrounding environment diurnal and seasonal cycles) and representative measurement approaches given traffic realities. Promising approaches incorporate contemporaneous airborne remote sensing and in situ measurements, nocturnal surface surveys, with ground station measurement

Leifer, Ira↗

VIPER: Mission Design & Development

The NASA Artemis Program plans to return humans to the Moon to stay. Extended human stays on the Moon will require substantial resources to sustain human presence over the long-term, requiring continuous supplies delivered from the Earth. However, if some of the resources were indigenously available, substantial logistical complexity and costs could be saved by “living off the land”, wherever possible. The LCROSS, LRO and other missions have confirmed the presence of resources such as volatiles in polar regions, so the next step is to understand the scientific nature and physical distribution of those candidate resources. Those local volatiles could be processed into propellants and human life-supporting needs, reducing risk of maintaining a permanent human presence on the Moon. The Volatiles Investigating Polar Exploration Resource (VIPER) is a surface mobility scientific platform, designed to spend ~100 days mapping and surveying four different Ice Stability Regions to understand the scientific nature and distribution of water and other volatiles. VIPER will also provide scientific mineralogical context of the lunar regolith, such as the presence of silicon and light metals in lunar regolith, providing a composite picture of resource availability and sustainment. This paper will discuss the latest development progress by the VIPER team, following our initial introduction to this mission at IAC2021. The VIPER team has passed both its NASA Preliminary Design Review (PDR) and Critical Design Reviews (CDR), and is now looking to performing significant testing of engineering units representing the design, prior to the team turning its attention to building the flight hardware. VIPER is managed within NASA’s Science Mission Directorate (SMD), utilizing the Commercial Lunar Payload Services (CLPS) delivery model with partner, Astrobotic, Inc.

Daniel Andrews↗

VIPER: Systems Integration Status

NASA’s Artemis Program plans to return humans to the Moon for an extended stay. To do so will require substantial resources to sustain that continued human presence, including continuous supplies delivered from the Earth. Given the expense and complexity of resource deliveries from Earth, if some resources were indigenously available, substantial logistical savings could be available by “living off the land”, wherever possible. The LCROSS[1] , LRO and other missions have confirmed the presence of resources such as water-ice and other volatiles in lunar polar regions, so the next step is to understand the scientific nature and physical distribution of those candidate resources. Those local volatiles could be processed into propellants and human life-supporting needs, reducing risk of maintaining a permanent human presence on the Moon. The Volatiles Investigating Polar Exploration Resource (VIPER) is a surface mobility scientific platform, designed to spend ~100 days mapping and surveying four different Ice Stability Regions to understand the scientific nature and distribution of water and other volatiles. VIPER will also provide scientific mineralogical context of the lunar regolith, such as the presence of silicon and light metals in lunar regolith, providing a composite picture of resource availability and sustainment. This paper will discuss the latest systems-level integration activities by the VIPER team, following our initial introduction to this mission at IAC2021[2] . The VIPER team successfully passed its Systems Integration Review (SIR) in late-2022, and in early 2023, began system-level surface segment (rover) flight hardware assembly. VIPER is managed within NASA’s Science Mission Directorate (SMD), utilizing the Commercial Lunar Payload Services (CLPS) lunar delivery model with partner, Astrobotic, Inc.

VIPER↗

XRF Characterization of MMOD Impact Damage

Introduction The Hypervelocity Impact Technology (HVIT) Group at the NASA Johnson Space Center (JSC) has performed over 150 post flight MMOD inspections on returned space-ex-posed hardware and collected over 1,600 samples. Determination of the impactor source typically requires an analysis of the projectile residue in the damage feature. At this time, about 20% of the samples have been processed. Types of Samples Samples in the HVIT group collection can be classified into two types. Indirect (non-destructive) samples are produced when a pliable material (e.g., adhesive tape or dental mold) is inserted into an impact feature. With this type of sampling technique, crater material and (hopefully) projectile residue material is embedded in the sample media and can detected using further chemical characterizing techniques. Direct (destructive) sampling involves the in-tact extraction of material from the spacecraft and is done in a manner that the entire impact feature can be excised intact. This technique provides the greatest chance of successfully determining impactor source due to the entirety of the projectile remnants being present within the collected sample. Updated Projectile Residue Detection Techniques Previous assessments of projectile provenance have involved the use of samples that are first mounted in epoxy, sectioned to expose the crater interior, imaged with a scanning electron microscope (SEM), then any observed impactor residue was then analyzed using an energy dispersive spectrometer (EDS). This technique, while proven, may be supplemented with other types of elemental analysis techniques that can observe major element chemistry, in order to improve throughput of sample analysis. The Astromaterials Research and Exploration Science (ARES) Division at JSC, for example, operates a Bruker M4 Tornado micro-X-Ray fluorescence (XRF) spectrometer, capable of creating elemental maps of areas around these small impact features in a couple of hours, with a spot size <20 μm. The potential advantage with this technique lies in sample preparation, as no polishing or conductive coatings are needed. Early trials attempted to deter-mine impactor composition by collecting spectra from intact samples by aiming the X-Rays directly into the impact feature, but the signal:noise ratio was too low for confident material identification. Sample preparation for XRF then relies on sectioning the samples parallel to the impactor trajectory in order to expose the largest area of subsurface damage possible, thus maximizing the signal from any small impactor remnants. Complementary to the use of XRF for sample analysis, ARES also houses a Nikon XTH 320 micro-X-Ray computed tomography (XCT). This instrument can be used to create 3D visualizations of impact damage for the determination of crater volumes and dimensions, as well as for the determination of the best place to section each sample for the subsequent XRF analysis.

J L Hyde↗

VIPER Rover: Flight Build and Environmental Test Status

The NASA Artemis Program plans to return humans to the Moon to stay. Extended human stays on the Moon will require substantial resources to sustain human presence, requiring continuous supplies delivered from the Earth. However, if some of the resources were indigenously available, Earth logistical requirements could be substantially reduced by “living off the land” with in-situ lunar resources. Local volatiles could be processed into propellants and human life-supporting needs, reducing risk of maintaining a permanent human presence on the Moon. LCROSS, LRO and other missions have confirmed the presence of lunar volatiles resources in polar regions, so the next step is to understand the physical distribution of those resources, as well as the scientific basis for how water got there, and why it is still there. The Volatiles Investigating Polar Exploration Resource (VIPER) is a surface mobility scientific platform, designed to spend ~100 days mapping and surveying four different Ice Stability Regions to understand the scientific nature and distribution of water and other volatiles. VIPER will also provide scientific mineralogical context of the lunar regolith, such as the presence of silicon and light metals in lunar regolith, providing a composite picture of resource availability and sustainment. This paper will discuss VIPER’s completion of the flight rover build, as well as current progress in environmental testing, preparedness for mission operations, and overall readying for launch integration with our CLPS partner. VIPER is managed within NASA’s Science Mission Directorate (SMD), utilizing the Commercial Lunar Payload Services (CLPS) lunar delivery model.

VIPER↗

Viper Rover: Flight Build and Environmental Test Status

The NASA Artemis Program plans to return humans to the Moon to stay. Extended human stays on the Moon will require substantial resources to sustain human presence, requiring continuous supplies delivered from the Earth. However, if some of the resources were indigenously available, Earth logistical requirements could be substantially reduced by “living off the land” with in-situ lunar resources. Local volatiles could be processed into propellants and human life-supporting needs, reducing risk of maintaining a permanent human presence on the Moon. LCROSS, LRO and other missions have confirmed the presence of lunar volatiles resources in polar regions, so the next step is to understand the physical distribution of those resources, as well as the scientific basis for how water got there, and why it is still there. The Volatiles Investigating Polar Exploration Resource (VIPER) is a surface mobility scientific platform, designed to spend ~100 days mapping and surveying four different Ice Stability Regions to understand the scientific nature and distribution of water and other volatiles. VIPER will also provide scientific mineralogical context of the lunar regolith, such as the presence of silicon and light metals in lunar regolith, providing a composite picture of resource availability and sustainment. This paper will discuss VIPER’s completion of the flight rover build, as well as current progress in environmental testing, preparedness for mission operations, and overall readying for launch integration with our CLPS partner. VIPER is managed within NASA’s Science Mission Directorate (SMD), utilizing the Commercial Lunar Payload Services (CLPS) lunar delivery model.

rover↗

VIPER Rover Flight Build and Environmental Test Status

The NASA Artemis Program plans to return humans to the Moon to stay. Extended human stays on the Moon will require substantial resources to sustain human presence, requiring continuous supplies delivered from the Earth. However, if some of the resources were indigenously available, Earth logistical requirements could be substantially reduced by “living off the land” with in-situ lunar resources. Local volatiles could be processed into propellants and human life-supporting needs, reducing risk of maintaining a permanent human presence on the Moon. LCROSS, LRO and other missions have confirmed the presence of lunar volatiles resources in polar regions, so the next step is to understand the physical distribution of those resources, as well as the scientific basis for how water got there, and why it is still there. The Volatiles Investigating Polar Exploration Resource (VIPER) is a surface mobility scientific platform, designed to spend ~100 days mapping and surveying four different Ice Stability Regions to understand the scientific nature and distribution of water and other volatiles. VIPER will also provide scientific mineralogical context of the lunar regolith, such as the presence of silicon and light metals in lunar regolith, providing a composite picture of resource availability and sustainment. This paper will discuss VIPER’s completion of the flight rover build, as well as current progress in environmental testing, preparedness for mission operations, and overall readying for launch integration with our CLPS partner. VIPER is managed within NASA’s Science Mission Directorate (SMD), utilizing the Commercial Lunar Payload Services (CLPS) lunar delivery model.

rover↗

Mapping target signatures via partial unmixing of AVIRIS data

A complete spectral unmixing of a complicated AVIRIS scene may not always be possible or even desired. High quality data of spectrally complex areas are very high dimensional and are consequently difficult to fully unravel. Partial unmixing provides a method of solving only that fraction of the data inversion problem that directly relates to the specific goals of the investigation. Many applications of imaging spectrometry can be cast in the form of the following question: 'Are my target signatures present in the scene, and if so, how much of each target material is present in each pixel?' This is a partial unmixing problem. The number of unmixing endmembers is one greater than the number of spectrally defined target materials. The one additional endmember can be thought of as the composite of all the other scene materials, or 'everything else'. Several workers have proposed partial unmixing schemes for imaging spectrometry data, but each has significant limitations for operational application. The low probability detection methods described by Farrand and Harsanyi and the foreground-background method of Smith et al are both examples of such partial unmixing strategies. The new method presented here builds on these innovative analysis concepts, combining their different positive attributes while attempting to circumvent their limitations. This new method partially unmixes AVIRIS data, mapping apparent target abundances, in the presence of an arbitrary and unknown spectrally mixed background. It permits the target materials to be present in abundances that drive significant portions of the scene covariance. Furthermore it does not require a priori knowledge of the background material spectral signatures. The challenge is to find the proper projection of the data that hides the background variance while simultaneously maximizing the variance amongst the targets.

Boardman, Joseph W.↗

A Model for the Oxidation of C/SiC Composite Structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

Sullivan, Roy M.↗