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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Method and system for monitoring and displaying engine performance parameters

The invention is a method and system for monitoring and directly displaying the actual thrust produced by a jet aircraft engine under determined operating conditions and the available thrust and predicted (commanded) thrust of a functional model of an ideal engine under the same determined operating conditions. A first set of actual value output signals representative of a plurality of actual performance parameters of the engine under the determined operating conditions is generated and compared with a second set of predicted value output signals representative of the predicted value of corresponding performance parameters of a functional model of the engine under the determined operating conditions to produce a third set of difference value output signals within a range of normal, caution, or warning limit values. A thrust indicator displays when any one of the actual value output signals is in the warning range while shaping function means shape each of the respective difference output signals as each approaches the limit of the respective normal, caution, and warning range limits.

Abbott, Terence S.↗
NASA NTRS1990

NOVA: A new multi-level logic simulator

A new logic simulator that was developed at the NASA Space Engineering Research Center for VLSI Design was described. The simulator is multi-level, being able to simulate from the switch level through the functional model level. NOVA is currently in the Beta test phase and was used to simulate chips designed for the NASA Space Station and the Explorer missions. A new algorithm was devised to simulate bi-directional pass transistors and a preliminary version of the algorithm is presented. The usage of functional models in NOVA is also described and performance figures are presented.

Miles, L.↗
NASA NTRS1986

Further development of an improved altimeter wind speed algorithm

A previous altimeter wind speed retrieval algorithm was developed on the basis of wind speeds in the limited range from about 4 to 14 m/s. In this paper, a new approach which gives a wind speed model function applicable over the range 0 to 21 m/s is used. The method is based on comparing 50 km along-track averages of the altimeter normalized radar cross section measurements with neighboring off-nadir scatterometer wind speed measurements. The scatterometer winds are constructed from 100 km binned measurements of radar cross section and are located approximately 200 km from the satellite subtrack. The new model function agrees very well with earlier versions up to wind speeds of 14 m/s, but differs significantly at higher wind speeds. The relevance of these results to the Geosat altimeter launched in March 1985 is discussed.

Chelton, Dudley B.↗
NASA NTRS1971

Vacuum distillation: vapor filtered-catalytic oxidation water reclamation system utilizing radioisotopes

The development of a functional model water reclamation system is discussed. The system produces potable water by distillation from the urine and respiration-perspiration condensate at the normal rate generated by four men. Basic processes employed are vacuum distillation, vapor filtration, vapor phase catalytic oxidation, and condensation. The system is designed to use four 75-watt isotope heaters for distillation thermal input, and one 45-watt isotope for the catalytic oxidation unit. The system is capable of collecting and storing urine, and provides for stabilizing the urine by chemical pretreatment. The functional model system is designed for operation in a weightless condition with liquid-vapor phase separators for the evaporator still, and centrifugal separators for urine collection and vapor condensation. The system provides for storing and dispensing reclaimed potable water. The system operates in a batch mode for 40 days, with urine residues accumulating in the evaporator. The evaporator still and residue are removed to storage and replaced with a fresh still for the next 40-day period.

Honegger, R. J.↗
NASA NTRS1991

Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Povinelli, Louis A.↗
NASA NTRS2006

Marshall Space Flight Center Propulsion Systems Department (PSD) KM Initiative

NASA Marshall Space Flight Center s Propulsion Systems Department (PSD) is four months into a fifteen month Knowledge Management (KM) initiative to support enhanced engineering decision making and analyses, faster resolution of anomalies (near-term) and effective, efficient knowledge infused engineering processes, reduced knowledge attrition, and reduced anomaly occurrences (long-term). The near-term objective of this initiative is developing a KM Pilot project, within the context of a 3-5 year KM strategy, to introduce and evaluate the use of KM within PSD. An internal NASA/MSFC PSD KM team was established early in project formulation to maintain a practitioner, user-centric focus throughout the conceptual development, planning and deployment of KM technologies and capabilities with in the PSD. The PSD internal team is supported by the University of Alabama's Aging Infrastructure Systems Center Of Excellence (AISCE), Intergraph Corporation, and The Knowledge Institute. The principle product of the initial four month effort has been strategic planning of PSD KM implementation by first determining the "as is" state of KM capabilities and developing, planning and documenting the roadmap to achieve the desired "to be" state. Activities undertaken to support the planning phase have included data gathering; cultural surveys, group work-sessions, interviews, documentation review, and independent research. Assessments and analyses have been performed including industry benchmarking, related local and Agency initiatives, specific tools and techniques used and strategies for leveraging existing resources, people and technology to achieve common KM goals. Key findings captured in the PSD KM Strategic Plan include the system vision, purpose, stakeholders, prioritized strategic objectives mapped to the top ten practitioner needs and analysis of current resource usage. Opportunities identified from research, analyses, cultural/KM surveys and practitioner interviews include: executive and senior management sponsorship, KM awareness, promotion and training, cultural change management, process improvement, leveraging existing resources and new innovative technologies to align with other NASA KM initiatives (convergence: the big picture). To enable results based incremental implementation and future growth of the KM initiative, key performance measures have been identified including stakeholder value, system utility, learning and growth (knowledge capture, sharing, reduced anomaly recurrence), cultural change, process improvement and return-on-investment. The next steps for the initial implementation spiral (focused on SSME Turbomachinery) have been identified, largely based on the organization and compilation of summary level engineering process models, data capture matrices, functional models and conceptual-level systems architecture. Key elements include detailed KM requirements definition, KM technology architecture assessment, evaluation and selection, deployable KM Pilot design, development, implementation and evaluation, and justifying full implementation (estimated Return-on-Investment). Features identified for the notional system architecture include the knowledge presentation layer (and its components), knowledge network layer (and its components), knowledge storage layer (and its components), User Interface and capabilities. This paper provides a snapshot of the progress to date, the near term planning for deploying the KM pilot project and a forward look at results based growth of KM capabilities with-in the MSFC PSD.

Caraccioli, Paul↗
NASA NTRS2006

Marshall Space Flight Center Propulsion Systems Department (PSD) Knowledge Management (KM) Initiative

NASA Marshall Space Flight Center's Propulsion Systems Department (PSD) is four months into a fifteen month Knowledge Management (KM) initiative to support enhanced engineering decision making and analyses, faster resolution of anomalies (near-term) and effective, efficient knowledge infused engineering processes, reduced knowledge attrition, and reduced anomaly occurrences (long-term). The near-term objective of this initiative is developing a KM Pilot project, within the context of a 3-5 year KM strategy, to introduce and evaluate the use of KM within PSD. An internal NASA/MSFC PSD KM team was established early in project formulation to maintain a practitioner, user-centric focus throughout the conceptual development, planning and deployment of KM technologies and capabilities within the PSD. The PSD internal team is supported by the University of Alabama's Aging Infrastructure Systems Center of Excellence (AISCE), lntergraph Corporation, and The Knowledge Institute. The principle product of the initial four month effort has been strategic planning of PSD KNI implementation by first determining the "as is" state of KM capabilities and developing, planning and documenting the roadmap to achieve the desired "to be" state. Activities undertaken to suppo~th e planning phase have included data gathering; cultural surveys, group work-sessions, interviews, documentation review, and independent research. Assessments and analyses have beon pedormed including industry benchmarking, related local and Agency initiatives, specific tools and techniques used and strategies for leveraging existing resources, people and technology to achieve common KM goals. Key findings captured in the PSD KM Strategic Plan include the system vision, purpose, stakeholders, prioritized strategic objectives mapped to the top ten practitioner needs and analysis of current resource usage. Opportunities identified from research, analyses, cultural1KM surveys and practitioner interviews include: executive and senior management sponsorship, KM awareness, promotion and training, cultural change management, process improvement, leveraging existing resources and new innovative technologies to align with other NASA KM initiatives (convergence: the big picture). To enable results based incremental implementation and future growth of the KM initiative, key performance measures have been identified including stakeholder value, system utility, learning and growth (knowledge capture, sharing, reduced anomaly recurrence), cultural change, process improvement and return-on-investment. The next steps for the initial implementation spiral (focused on SSME Turbomachinery) have been identified, largely based on the organization and compilation of summary level engineering process models, data capture matrices, functional models and conceptual-level svstems architecture. Key elements include detailed KM requirements definition, KM technology architecture assessment, - evaluation and selection, deployable KM Pilot design, development, implementation and evaluation, and justifying full implementation (estimated Return-on-Investment). Features identified for the notional system architecture include the knowledge presentation layer (and its components), knowledge network layer (and its components), knowledge storage layer (and its components), User Interface and capabilities. This paper provides a snapshot of the progress to date, the near term planning for deploying the KM pilot project and a forward look at results based growth of KM capabilities with-in the MSFC PSD.

Caraccioli, Paul↗
NASA NTRS1984

Facular Limb-darkening Functions for Irradiance Modeling

The limb darkening function of faculae is an important factor in estimating facular contributions to solar irradiance variations. The existing photometric data is reviewed and a synthetic limb darkening function for faculae was generated which was compared with the limb darkening functions currently in use for irradiance modeling. The excess facular flux ranges from 0.017 to 0.0349 of the solar photospheric flux for the various representations. The present limitation appears to be the lack of comprehensive photometric data. The representations are especially varied near the limb, where photometry is most difficult. Synoptic data on calcium plage areas is used as a substitute for facular areas in modeling. Based upon the existing data, the present best value for the effect of faculae on the solar constant is given by delta s/s = 3.9 x 10(-8) A (sub plage prime) for an active region near disk center, where A (sub plage) is the calcium plage area in millionths of a solar hemisphere.

Hirayama, T.↗
NASA NTRS1972

System identification computational considerations.

System identification methods may be accurately characterized as inverse computational problems. Three approaches to the computational problem are considered. Equation error methods are based on regression analysis techniques. Attention is given to the maximum conditional likelihood estimate and the maximum unconditional likelihood (Bayesian) estimate. Gradient dependent algorithms for solving the minimization problems are discussed, taking into account Gaussian methods, quadratic model methods, and the homogeneous function model method of Jacobson and Oksman. Some advanced methods are also examined.

Bowles, R. L.↗
NASA NTRS1994

Center for modeling of turbulence and transition: Research briefs, 1993

This research brief contains the progress reports of the research staff of the Center for Modeling of Turbulence and Transition (CMOTT) from June 1992 to July 1993. It is also an annual report to the Institute for Computational Mechanics in Propulsion located at Ohio Aerospace Institute and NASA Lewis Research Center. The main objectives of the research activities at CMOTT are to develop, validate, and implement turbulence and transition models for flows of interest in propulsion systems. Currently, our research covers eddy viscosity one- and two-equation models, Reynolds-stress algebraic equation models, Reynolds-stress transport equation models, nonequilibrium multiple-scale models, bypass transition models, joint scalar probability density function models, and Renormalization Group Theory and Direct Interaction Approximation methods. Some numerical simulations (LES and DNS) have also been carried out to support the development of turbulence modeling. Last year was CMOTT's third year in operation. During this period, in addition to the above mentioned research, CMOTT has also hosted the following programs: an eighteen-hour short course on 'Turbulence--Fundamentals and Computational Modeling (Part I)' given by CMOTT at the NASA Lewis Research Center; a productive summer visitor research program that has generated many encouraging results; collaborative programs with industry customers to help improve their turbulent flow calculations for propulsion system designs; a biweekly CMOTT seminar series with speakers from within and without the NASA Lewis Research Center including foreign speakers. In addition, CMOTT members have been actively involved in the national and international turbulence research activities. The current CMOTT roster and organization are listed in Appendix A. Listed in Appendix B are the abstracts of the biweekly CMOTT seminar. Appendix C lists the papers contributed by CMOTT members.

Liou, William W.↗
NASA NTRS1984

Statistical Time Series Models of Pilot Control with Applications to Instrument Discrimination

A general description of the methodology used in obtaining the transfer function models and verification of model fidelity, frequency domain plots of the modeled transfer functions, numerical results obtained from an analysis of poles and zeroes obtained from z plane to s-plane conversions of the transfer functions, and the results of a study on the sequential introduction of other variables, both exogenous and endogenous into the loop are contained.

Altschul, R. E.↗
NASA NTRSDate not supplied

Integrated Bosch Process System Models for In-Situ Oxygen and Carbon Production

In-Situ Resource Utilization (ISRU) technology is a vital component to NASA’s mission of a sustainable presence on the Moon and Mars. Local resources can be leveraged to reduce resupply frequency and mass. Elements of the Bosch process, combined with the carbothermal reduction process, can produce oxygen on the lunar surface with minimal consumables. The Bosch process can also produce oxygen on the Martian surface by using the CO 2 -rich environment. Between both systems, adsorption pump, solar thermal energy, carbon formation reactor, and water recovery subsystems are modeled and integrated to create a functional model in MATLAB software. The model is used to simulate performance of the system and reduce mass, power, and volume requirements. This integrated system model provides a tool to scale ISRU technologies for oxygen and carbon production. The MATLAB model is created by developing a system of independent subsystem models that are solved for their quasi-steady state values which can be integrated with respect to time to determine the change in current states. A flexible time stepping method is used to ensure a high level of accuracy during periods of rapid change while still making use of a simple explicit integration method. The flexible time step is calculated for each independent subsystem and the minimum value from those is used as the overall time step. A flexible time step is calculated by dividing a resolution value, or the maximum change per time step, by the variables current rate of change. The maximum value from all points in space is used for subsystem models that contain multiple values. The process is done for every variable that is being monitored in each subsystem and the global minimum is used as that iteration’s timestep. Several assumptions used in the MATLAB model for fluid flow dynamics, such as 1-D gas flow through the sorption pump, are supported by modeling in Ansys Fluent software. The Lunar oxygen production system is outlined in Fig. 1. The carbothermal reduction subsystem uses solar energy to heat a mixture of lunar regolith and carbon powder to produce carbon monoxide. To begin, the carbon monoxide feeds to the modified Bosch subsystem along with hydrogen gas. The reactants then enter the carbon formation reactor where water and carbon powder are produced. Solar thermal energy is used to add energy to the reactor, but waste heat from the carbothermal process is another potential heat source. The water is collected and electrolyzed to produce hydrogen which reenters the Bosch subsystem, and the oxygen is stored for downstream use. The carbon powder is collected and feeds back into the carbothermal subsystem. The Martian oxygen production system uses the full Bosch process and is outlined in Fig 2. A CO 2 adsorption pump thermally cycles to scrub and pressurize CO 2 from the environment. Along with an initial supply of hydrogen, the reactants enter the Reverse Water Gas Shift Reactor (RWGSR) which produces carbon monoxide and water. Carbon monoxide and unreacted hydrogen enter the carbon formation reactor to produce water and carbon powder. The water is collected from both reactors and electrolyzed to reintroduce hydrogen and store oxygen for propellant production or life support. Carbon is removed from the carbon formation reactor and stored. The adsorption pump utilizes rapid cycle temperature swings within a stack of zeolite coated surfaces. The subsystem model solves 1-D quasi-steady conservation laws of the quasi-steady form, shown in Eq. 1, for the gas stream and heat exchange liquid to predict performance parameters such as breakthrough capacity and optimum cycle time. The source term S is used to capture interactions between the fluid flows and the sorbent. A quasi-steady-state scheme is used where no time derivatives appear in the governing equations, except for those in the source terms. This results in an autonomous system, where ∂F/∂x = ƒ(F). The fluxes F are provided at the inlet, and an explicit method is used to solve for the spatial distribution of F. The heat and mass flows to the sorbent are then extracted from the source terms. These flows are numerically integrated to produce a 1-D solution for the system’s state as a function of both time and space. The body of the adsorption pump is separated into two semi-independent models: the heat exchanger fluid flow and gas flow through the zeolite coated surfaces. Both models are solved using the above-described method to find a 1-D solution as a function of space and interact only once a timestep is taken. The interaction point is the sorbent through which all heat transfer between the two models must occur. Sorbent mass adsorption is calculated using the Lagergren model, shown in Eq. 2, where the transfer coefficient, λ D , is found by solving a system of nondimensionalized equations derived by using the heat and mass transfer analogy for transport phenomena. Using Grade 544 Type 13X zeolite as the sorbent material, the equilibrium concentration, θ eq , is calculated using the k-site Langmuir isotherm and fit parameters. Additionally, the enthalpy of adsorption used in the model is computed by interpolation of available data [1]. The subsystem model was validated using the Rapid Cycle Temperature Swing Adsorption (RC-TSA) pump. The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC). The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC).

In situ Resource Utilization↗
NASA NTRS1993

Fusing modeling techniques to support domain analysis for reuse opportunities identification

Functional modeling techniques or object-oriented graphical representations, which are more useful to someone trying to understand the general design or high level requirements of a system? For a recent domain analysis effort, the answer was a fusion of popular modeling techniques of both types. By using both functional and object-oriented techniques, the analysts involved were able to lean on their experience in function oriented software development, while taking advantage of the descriptive power available in object oriented models. In addition, a base of familiar modeling methods permitted the group of mostly new domain analysts to learn the details of the domain analysis process while producing a quality product. This paper describes the background of this project and then provides a high level definition of domain analysis. The majority of this paper focuses on the modeling method developed and utilized during this analysis effort.

Hall, Susan Main↗
NASA NTRS1965

Human Tracking Performance in Uncoupled and Coupled Two-Axis Systems

This report presents tile results of an experimental and analytical study of human performance in uncoupled and coupled control systems. Human pilot performance in single and two-axis systems was mathematically modeled by linear second-order describing functions. Model parameters were determined using model matching techniques. Analysis of the models showed that the amplitude ratio and phase lead of the describing function increased with training indicating an increase in open loop bandwidth. The phase margin also decreased with training. Increasing the plant lag time constant resulted in an increase in the model lead time constant and a decrease in the zero frequency gain. No significant difference was found to exist in the normalized tracking error per axis between the two-axis tasks and the single-axis tasks. However tile model lead time constant was significantly greater in two-axis tracking. Manual tracking of two-axis systems with cross-coupling was studied experimentally and analytically. Approximate methods for modeling two-axis performance were developed and checked using a precise spectral analysis approach. Coupled and uncoupled, symmetrical and asymmetrical two-axis performance was compared. The results show that modeling of cross-coupled systems is feasible and that trained subjects are capable of decoupling the axes of some systems. A methodology study compared the identification performance of continuous, iterative, and extrapolation model matching techniques. An iterative technique employing sensitivity equations for the generation of influence coefficients was found to be the best technique due to its excellent identification accuracy and ease of implementation. Convergence in iterative techniques can be improved substantially by equalizing the parameter adjustment rates and limiting the maximum correction per iteration.

Todosiev, E. P.↗
NASA NTRS1991

Relation between the quasi-periodic oscillations and the low-frequency noise of GX 5-1 in the horizontal branch

Ginga observations of quasi-periodic oscillations (QPOs) and the low-frequency noise (LFN) from GX 5-1 in its horizontal-branch spectral state are presented. Power spectral fits were attempted using model functions based on simple oscillating shot models. A clear second-harmonic peak of QPO was detected. Variations in the powers of QPO and LFN on timescales of 8-256 s were also studied. These variations were significant for all of the timescales studied, and were uncorrelated with each other on timescales shorter than a few tens of seconds, and correlated on longer timescales. From simulations based on a simple shot model, it was found that the variation amplitude and the lack of correlation on short timescales are not inconsistent with the oscillating shot models. A more complex model is necessary to fully explain the observed properties.

Mitsuda, Kazuhisa↗
NASA NTRS2014

Aerosol Remote Sensing in Polar Regions

Multi-year sets of ground-based sun-photometer measurements conducted at 12 Arctic sites and 9 Antarctic sites were examined to determine daily mean values of aerosol optical thickness tau(lambda) at visible and near-infrared wavelengths, from which best-fit values of Ångström's exponent alpha were calculated. Analyzing these data, the monthly mean values of tau(0.50 micrometers) and alpha and the relative frequency histograms of the daily mean values of both parameters were determined for winter-spring and summer-autumn in the Arctic and for austral summer in Antarctica. The Arctic and Antarctic covariance plots of the seasonal median values of alpha versus tau(0.50 micrometers) showed: (i) a considerable increase in tau(0.50 micrometers) for the Arctic aerosol from summer to winter-spring, without marked changes in alpha; and (ii) a marked increase in tau(0.50 micrometer) passing from the Antarctic Plateau to coastal sites, whereas alpha decreased considerably due to the larger fraction of sea-salt aerosol. Good agreement was found when comparing ground-based sun-photometer measurements of tau(lambda) and alpha at Arctic and Antarctic coastal sites with Microtops measurements conducted during numerous AERONET/MAN cruises from 2006 to 2013 in three Arctic Ocean sectors and in coastal and off-shore regions of the Southern Atlantic, Pacific, and Indian Oceans, and the Antarctic Peninsula. Lidar measurements were also examined to characterize vertical profiles of the aerosol backscattering coefficient measured throughout the year at Ny-Ålesund. Satellite-based MODIS, MISR, and AATSR retrievals of tau(lambda) over large parts of the oceanic polar regions during spring and summer were in close agreement with ship-borne and coastal ground-based sun-photometer measurements. An overview of the chemical composition of mode particles is also presented, based on in-situ measurements at Arctic and Antarctic sites. Fourteen log-normal aerosol number size-distributions were defined to represent the average features of nuclei, accumulation and coarse mode particles for Arctic haze, summer background aerosol, Asian dust and boreal forest fire smoke, and for various background austral summer aerosol types at coastal and high-altitude Antarctic sites. The main columnar aerosol optical characteristics were determined for all 14 particle modes, based on in-situ measurements of the scattering and absorption coefficients. Diurnally averaged direct aerosol-induced radiative forcing and efficiency were calculated for a set of multimodal aerosol extinction models, using various Bidirectional Reflectance Distribution Function models over vegetation-covered, oceanic and snow-covered surfaces. These gave a reliable measure of the pronounced effects of aerosols on the radiation balance of the surface-atmosphere system over polar regions.

Sun-photometer measurements↗
NASA NTRS2003

Oxidation of Carbon Fibers in a Cracked Ceramic Matrix Composite Modeled as a Function of Temperature

The oxidation model simulates the oxidation of the reinforcing carbon fibers within a ceramic matrix composite material containing as-fabricated microcracks. The physics-based oxidation model uses theoretically and experimentally determined variables as input for the model. The model simulates the ingress of oxygen through microcracks into a two-dimensional plane within the composite material. Model input includes temperature, oxygen concentration, the reaction rate constant, the diffusion coefficient, and the crack opening width as a function of the mechanical and thermal loads. The model is run in an iterative process for a two-dimensional grid system in which oxygen diffuses through the porous and cracked regions of the material and reacts with carbon in short time steps. The model allows the local oxygen concentrations and carbon volumes from the edge to the interior of the composite to be determined over time. Oxidation damage predicted by the model was compared with that observed from microstructural analysis of experimentally tested composite material to validate the model for two temperatures of interest. When the model is run for low-temperature conditions, the kinetics are reaction controlled. Carbon and oxygen reactions occur relatively slowly. Therefore, oxygen can bypass the carbon near the outer edge and diffuse into the interior so that it saturates the entire composite at relatively high concentrations. The kinetics are limited by the reaction rate between carbon and oxygen. This results in an interior that has high local concentrations of oxygen and a similar amount of consumed carbon throughout the cross section. When the model is run for high-temperature conditions, the kinetics are diffusion controlled. Carbon and oxygen reactions occur very quickly. The carbon consumes oxygen as soon as it is supplied. The kinetics are limited by the relatively slow rate at which oxygen is supplied in comparison to the relatively fast rate at which carbon and oxygen reactions occur. This results in a sharp gradient in oxygen concentration from the edge where it is supplied to the nearest source of carbon, which is where the oxygen is quickly consumed. A moving reaction front is seen in which the outlaying carbon is consumed before the next inner layer of carbon begins to react.

Halbig, Michael C.↗