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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Calculation of kinetic rate constants from thermodynamic data

A new scheme for relating the absolute value for the kinetic rate constant k to the thermodynamic constant Kp is developed for gases. In this report the forward and reverse rate constants are individually related to the thermodynamic data. The kinetic rate constants computed from thermodynamics compare well with the current kinetic rate constants. This method is self consistent and does not have extensive rules. It is first demonstrated and calibrated by computing the HBr reaction from H2 and Br2. This method then is used on other reactions.

Marek, C. John↗
NASA NTRS1994

Oxidation Kinetics of Chemically Vapor-Deposited Silicon Carbide in Wet Oxygen

The oxidation kinetics of chemically vapor-deposited SiC in dry oxygen and wet oxygen (P(sub H2O) = 0.1 atm) at temperatures between 1200 C and 1400 C were monitored using thermogravimetric analysis. It was found that in a clean environment, 10% water vapor enhanced the oxidation kinetics of SiC only very slightly compared to rates found in dry oxygen. Oxidation kinetics were examined in terms of the Deal and Grove model for oxidation of silicon. It was found that in an environment containing even small amounts of impurities, such as high-purity Al2O3 reaction tubes containing 200 ppm Na, water vapor enhanced the transport of these impurities to the oxidation sample. Oxidation rates increased under these conditions presumably because of the formation of less protective sodium alumino-silicate scales.

Opila, Elizabeth J.↗
NASA NTRS1997

Kinetics and Thermochemistry of the Cl((sup 2)P(sub J)) + C2Cl4 Association Reaction

A laser flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the Cl(sup 2)P(sub j) + C2Cl4 association reaction as a function of temperature (231-390 K) and pressure (3-700 Torr) in nitrogen buffer gas. The reaction is found to be in the falloff regime between third and second order over the range of conditions investigated, although the second-order limit is approached at the highest pressures and lowest temperatures. At temperatures below 300 K, the association reaction is found to be irreversible on the experimental time scale of approximately 20 m-s. The kinetic data at T is less than 300 K have been employed to obtain falloff parameters in a convenient format for atmospheric modeling. At temperatures above 330 K, reversible addition is observed, thus allowing equilibrium constants for C2Cl5 formation and dissociation to be determined. Second- and third-law analyses of the equilibrium data lead to the following thermochemical parameters for the association reaction: Delta-H(298) = -18.1 +/- 1.3 kcal/mol, Delta-H(0) = -17.6 +/- 1.3 kcal/mol, and Delta-S(298) = -27.7 +/- 3.0 cal/mol.K. In conjunction with the well-known heats of formation of Cl((sup 2)P(sub j)) and C2Cl4 the above Delta-H values lead to the following heats of formation for C2Cl5, at 298 and 0 K: Delta-H(f,298) = 8.0 +/- 1.3 kcal/mol and Delta-H(f,0) = 8.1 +/- 1.5 kcal/mol. The kinetic and thermochemical parameters reported above are compared with other reported values, and the significance of reported association rate coefficients for understanding tropospheric chlorine chemistry is discussed.

Nicovich, J. M.↗
NASA NTRS1997

Temperature-Dependent Kinetics Studies of the Reactions Br((sup 2)P(sub 3/2)) + CH3SCH3 reversible reaction CH3SCH2 + HBr. Heat of Formation of the CH3SCH2 Radical

Time-resolved resonance fluorescence detection of Br((sup 2)P(sub 3/2)) atom disappearance or appearance 266 nm laser flash photolysis of CF2Br2/CH3SCH3/H2/N2 and Cl2CO/CH2SCH3/HBr/H2/N2 mixtures has been employed to study the kinetics of the reactions Br((sup 2)P(sub 3/2)) + CH3SCH3 reversible reaction HBr + CH3SCH2 (1,-1) as a function of temperature over the range 386-604 K. Arrhenius expressions in units of cu cm/molecule which describe the results are k3= (9.0 +/- 2.9) x 10 (exp -11) exp[(-2386 +/- 151)/T]; errors are 2 sigma and represent precision only. To our knowledge, these are the first kinetic data reported for each of the two reactions studied. Second and third law analyses of the equilibrium data for reactions 1 and -1 have been employed to obtain the following enthalpies of reaction in units of kcal/mol: Delta-H(298) = 6.11 +/- 1.37 and Delta-H(0) = 5.37 +/- 1.38. Combining the above enthalpies of reaction with the well-known heats of formation of Br, HBr, CH3SCH3 gives the following heats of formation of the CH3SCH2 radical in units of kcal/mol: Delta-H(sub(f,298)) = 32.7 +/- 1.4 and Delta-H(sub (f,0)) = 35.3 +/- 1.4; errors are 2 sigma and represent estimates of absolute accuracy. The C-H bond dissociation energy in CH3SCH3 obtained from our data, 93.7 +/- 1.4 kcal/mol at 298 K and 92.0 +/- 1.4 kcal at 0 k, agrees well with a recent molecular beam photofragmentaion study but is 3 kcal/mol lower than the value obtained from an iodination kinetics study.

Jefferson, A.↗
NASA NTRS1997

Temperature-Dependent Kinetics Studies of the Reactions Br((sup 2)P3/2) + H2S yields SH + HBr and Br((sup 2)P3/2) + CH3SH yields CH3S + HBr. Heats of Formation of SH and CH3S Radicals

Time resolved resonance fluorescence detection of Br(sup 2)P3/2) atom disappearance or appearance following 266-nm laser flash photolysis of CF2Br2/H2S/H2/N2, CF2Br2/CH3SH/H2/N2, Cl2CO/H2S/HBr/N2, and CH3SSCH3/HBr/H2/N2 mixtures has been employed to study the kinetics of the reactions Br((sup 2)P3/2) + H2S = SH + HBr (1,-1) and Br((sup2)P3/2) + CH3SH = CH3S + HBr (2, -2) as a function of temperature over the range 273-431K. Arrhenius expressions in units of 10(exp -12) cu cm/molecule/s which describe the results are k1 = (14.2 +/- 3.4) exp[(-2752 +/- 90)/T],(k-1) = (4.40 +/- 0.92) exp[(-971 +/- 73)/T],k(2) = (9.24 +/- 1.15) exp[(-386 +/- 41)/T], and k(-2) = (1.46 +/-0.21) exp[(-399 +/-41)/T; errors are 2 sigma and represent precision only. By examining Br((sup 2)P3/2) equilibrium kinetics following 355nm laser flash photolysis of Br2/CH3SH/H2/N2 mixtures, a 298 K rate coefficient of (1.7 +/- 0.5) x 10(exp -10) cu cm/molecule/s has been obtained for the reaction CH3S + Br2 yields CH3SBr + Br. To our knowledge, these are the first kinetic data reported for each of the reactions studied. Measured rate coefficients, along with known rate coefficients for similar radical + H2S, CH3SH, HBr,Br2 reactions are considered in terms of possible correlations of reactivity with reaction thermochemistry and with IP - EA, the difference between the ionization potential of the electron donor and the electron affinity of the electron acceptor. Both thermochemical and charge-transfer effects appear to be important in controlling observed reactivities. Second and third law analyses of the equilibrium data for reactions 1 and 2 have been employed to obtain the following enthalpies of reaction in units of kcal/mol: for reaction 1, Delta-H(298) = 3.64 +/- 0.43 and Delta-H(0) = 3.26 +/-0.45; for reaction 2, Delta-H(298) = -0.14 +/- 0.28 and Delta-H(0) = -0.65 +/- 0.36. Combining the above enthalpies of reaction with the well-known heats of formation of Br, HBr, H2S, and CH3SH gives the following heats of formation for the RS radicals in units of kcal/mol: Delta-H(sub f)(sub 0)(SH) = 34.07 +/- 0.72, Delta-H(sub f)(sub 298)(SH) = 34.18 +/- 0.68, Delta-H(sub f)(sub 0)(CH3S) = 31.44 +/- 0.54, Delta-H(sub f)(sub 298)(CH3S) = 29.78 +/- 0.44; errors are 2 sigma and represent estimates of absolute accuracy. The SH heat of formation determined from our data agrees well with literature values but has reduced error limits compared to other available values. The CH3S heat of formation determined from our date is near the low end of the range of previous estimates and is 3-4 kcal/mol lower than values derived from recent molecular beam photofragmentation studies.

Nicovich, J. M.↗
NASA NTRS1998

Gas-Kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics

A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.

Xu, Kun↗
NASA NTRS1998

Protein Crystallization: Specific Phenomena and General Insights on Crystallization Kinetics

Experimental and simulation studies of the nucleation and growth kinetics of proteins have revealed phenomena that are specific for macromolecular crystallization, and others that provide a more detailed understanding of solution crystallization in general. The more specific phenomena, which include metastable liquid-liquid phase separations and gelation prior to solid nucleation, are due to the small ratio of the intermolecular interaction-range to the size of molecules involved. The apparently more generally applicable mechanisms include the cascade-like formation of macrosteps, as an intrinsic morphological instability that roots in the coupled bulk transport and nonlinear interface kinetics in systems with mixed growth rate control. Analyses of this nonlinear response provide (a) criteria for the choice of bulk transport conditions to minimize structural defect formation, and (b) indications that the "slow" protein crystallization kinetics stems from the mutual retardation of growth steps.

Rosenberger, F.↗
NASA NTRS1999

Calcium Kinetics During Space Flight

Bone loss is one of the most detrimental effects of space flight, threatening to limit the duration of human space missions. The ability to understand and counteract this loss will be critical for crew health and safety during and after extended-duration missions. The hypotheses to be tested in this project are that space flight alters calcium homeostasis and bone mineral metabolism, and that calcium homeostasis and bone mineral metabolism will return to baseline within days to weeks of return to Earth. These hypotheses will be evidenced by elevated rates of bone mineral resorption and decreased bone mineral deposition, decreased absorption of dietary calcium, altered calcitropic endocrine profiles, elevated excretion of calcium in urine and feces, and elevated excretion of markers of bone resorption. The second hypothesis will be evidenced by return of indices of calcium homeostasis and bone metabolism to preflight levels within days to weeks of return to Earth. Studies will be conducted on International Space Station astronauts before, during, and after extended-duration flights. Measurements of calcium kinetics, bone mass, and endocrine/biochemical markers of bone and calcium homeostasis will be conducted. Kinetic studies utilizing dual isotope tracer kinetic studies and mathematical modeling techniques will allow for determination of bone calcium deposition, bone calcium resorption, dietary calcium absorption and calcium excretion (both urinary and endogenous fecal excretion). These studies will build upon preliminary work conducted on the Russian Mir space station. The results from this project will be critical for clarifying how microgravity affects bone and calcium homeostasis, and will provide an important control point for assessment of countermeasure efficacy. These results are expected to aid in developing countermeasures for bone loss, both for space crews and for individuals on Earth who have metabolic bone diseases.

Smith, Scott M.↗
NASA NTRS2000

LSENS, The NASA Lewis Kinetics and Sensitivity Analysis Code

A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS (the NASA Lewis kinetics and sensitivity analysis code), are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include: static system; steady, one-dimensional, inviscid flow; incident-shock initiated reaction in a shock tube; and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method (LSODE, the Livermore Solver for Ordinary Differential Equations), which works efficiently for the extremes of very fast and very slow reactions, is used to solve the "stiff" ordinary differential equation systems that arise in chemical kinetics. For static reactions, the code uses the decoupled direct method to calculate sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters. Solution methods for the equilibrium and post-shock conditions and for perfectly stirred reactor problems are either adapted from or based on the procedures built into the NASA code CEA (Chemical Equilibrium and Applications).

Radhakrishnan, K.↗
NASA NTRS2001

Effects of Gas-Phase Radiation and Detailed Kinetics on the Burning and Extinction of a Solid Fuel

This is the first attempt to analyze both radiation and detailed kinetics on the burning and extinction of a solid fuel in a stagnation-point diffusion flame. We present a detailed and comparatively accurate computational model of a solid fuel flame along with a quantitative study of the kinetics mechanism, radiation interactions, and the extinction limits of the flame. A detailed kinetics model for the burning of solid trioxane (a trimer of formaldehyde) is coupled with a narrowband radiation model, with carbon dioxide, carbon monoxide, and water vapor as the gas-phase participating media. The solution of the solid trioxane diffusion flame over the flammable regime is presented in some detail, as this is the first solution of a heterogeneous trioxane flame. We identify high-temperature and low-temperature reaction paths for the heterogeneous trioxane flame. We then compare the adiabatic solution to solutions that include Surface radiation only and gas-phase and surface radiation using a black surface model. The analysis includes discussion of detailed flame chemistry over the flammable regime and, in particular, at the low stretch extinction limit. We emphasize the low stretch regime of the radiatively participating flame, since this is the region representative of microgravity flames. When only surface radiation is included, two extinction limits exist (the blow-off limit, and the low stretch radiative limit), and the burning rate and maximum flame temperatures are lower, as expected. With the inclusion of surface and gas-phase radiation, results show that, while flame temperatures are lower, the burning rate of the trioxane diffusion flame may actually increase at low stretch rate due to radiative feedback from the flame to the surface.

Rhatigan, Jennifer L.↗
NASA NTRS2001

Kinetic Inductance Photodetectors Based on Nonequilibrium Response in Superconducting Thin-Film Structures

While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitivity at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of approximately 1 ms at 1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as approximately 10(exp -19) W/Hz(exp 1/2) at He4 temperatures.

Sergeev, A. V.↗
NASA NTRS2002

A Lighter-Than-Air System Enhanced with Kinetic Lift

A hybrid airship system is proposed in which the buoyant lift is enhanced with kinetic lift. The airship would consist of twin hulls in which the buoyant gas is contained. The twin hulls would be connected in parallel by a wing having an airfoil contour. In forward flight, the wing would provide kinetic lift that would add to the buoyant lift. The added lift would permit a greater payload/altitude combination than that which could be supported by the buoyant lift alone. The buoyant lift is a function of the volume of gas and the flight altitude. The kinetic lift is a function of the airfoil section, wing area, and the speed and altitude of flight. Accordingly there are a number of factors that can be manipulated to arrive at a particular design. Particular designs could vary from small, lightweight systems to very large, heavy-load systems. It will be the purpose of this paper to examine the sensitivity of such a design to the several variables. In addition, possible uses made achievable by such a hybrid system will be suggested.

Spearman, M. Leroy↗
NASA NTRS2002

Transport and Growth Kinetics in Microgravity Protein Crystal Growth

The dynamic coupling between mass transport and incorporation of growth units into the surface of a crystal growing from solution in microgravity is used to derive quantitative information on the crystal growth kinetics. To this end, new procedures for experiment preparation, interferometric data processing and model fitting have been developed. The use of experimental data from the bulk diffusive maw transport together with a model for steady state stagnant crystal growth allows the detailed quantitative understanding of the kinetics of both the concentration depletion zone around the crystal and the growth of the crystal interface. The protein crystal used in the experiment is shown to be growing in the mixed kinetic regime (0.2 x 10(exp -6) centimeters per second less than beta R/D less than 0.9 x 10(exp -6) centimeters per second).

Otalora, F.↗
NASA NTRS2003

Kinetic Fractionation of Stable Isotopes in Carbonates on Mars: Terrestrial Analogs

An ancient Martian hydrosphere consisting of an alkali-rich ocean would likely produce solid carbonate minerals through the processes of evaporation and/or freezing. We postulate that both (or either) of these kinetically-driven processes would produce carbonate minerals whose stable isotopic compositions are highly fractionated (enriched) with respect to the source carbon. Various scenarios have been proposed for carbonate formation on Mars, including high temperature formation, hydrothermal alteration, precipitation from evaporating brines, and cryogenic formation. 13C and 18O -fractionated carbonates have previously been shown to form kinetically under some of these conditions, ie.: 1) alteration by hydrothermal processes, 2) low temperature precipitation (sedimentary) from evaporating bicarbonate (brine) solutions, and 3) precipitation during the process of cryogenic freezing of bicarbonate-rich fluids. Here we examine several terrestrial field settings within the context of kinetically controlled carbonate precipitation where stable isotope enrichments have been observed.

Socki, Richard A.↗
NASA NTRS2001

Relative effectiveness of kinetic analysis vs single point readings for classifying environmental samples based on community-level physiological profiles (CLPP)

The relative effectiveness of average-well-color-development-normalized single-point absorbance readings (AWCD) vs the kinetic parameters mu(m), lambda, A, and integral (AREA) of the modified Gompertz equation fit to the color development curve resulting from reduction of a redox sensitive dye from microbial respiration of 95 separate sole carbon sources in microplate wells was compared for a dilution series of rhizosphere samples from hydroponically grown wheat and potato ranging in inoculum densities of 1 x 10(4)-4 x 10(6) cells ml-1. Patterns generated with each parameter were analyzed using principal component analysis (PCA) and discriminant function analysis (DFA) to test relative resolving power. Samples of equivalent cell density (undiluted samples) were correctly classified by rhizosphere type for all parameters based on DFA analysis of the first five PC scores. Analysis of undiluted and 1:4 diluted samples resulted in misclassification of at least two of the wheat samples for all parameters except the AWCD normalized (0.50 abs. units) data, and analysis of undiluted, 1:4, and 1:16 diluted samples resulted in misclassification for all parameter types. Ordination of samples along the first principal component (PC) was correlated to inoculum density in analyses performed on all of the kinetic parameters, but no such influence was seen for AWCD-derived results. The carbon sources responsible for classification differed among the variable types with the exception of AREA and A, which were strongly correlated. These results indicate that the use of kinetic parameters for pattern analysis in CLPP may provide some additional information, but only if the influence of inoculum density is carefully considered. c2001 Elsevier Science Ltd. All rights reserved.

NASA Center KSC↗
NASA NTRS2004

Computation Molecular Kinetics Model of HZE Induced Cell Cycle Arrest

Cell culture models play an important role in understanding the biological effectiveness of space radiation. High energy and charge (HZE) ions produce prolonged cell cycle arrests at the G1/S and G2/M transition points in the cell cycle. A detailed description of these phenomena is needed to integrate knowledge of the expression of DNA damage in surviving cells, including the determination of relative effectiveness factors between different types of radiation that produce differential types of DNA damage and arrest durations. We have developed a hierarchical kinetics model that tracks the distribution of cells in various cell phase compartments (early G1, late G1, S, G2, and M), however with transition rates that are controlled by rate-limiting steps in the kinetics of cyclin-cdk's interactions with their families of transcription factors and inhibitor molecules. The coupling of damaged DNA molecules to the downstream cyclin-cdk inhibitors is achieved through a description of the DNA-PK and ATM signaling pathways. For HZE irradiations we describe preliminary results, which introduce simulation of the stochastic nature of the number of direct particle traversals per cell in the modulation of cyclin-cdk and cell cycle population kinetics. Comparison of the model to data for fibroblast cells irradiated photons or HZE ions are described.

Cucinotta, Francis A.↗
NASA NTRS2008

Errors in Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) Kinetic Temperature Caused by Non-Local Thermodynamic Equilibrium Model Parameters

The vast set of near global and continuous atmospheric measurements made by the SABER instrument since 2002, including daytime and nighttime kinetic temperature (T(sub k)) from 20 to 105 km, is available to the scientific community. The temperature is retrieved from SABER measurements of the atmospheric 15 micron CO2 limb emission. This emission separates from local thermodynamic equilibrium (LTE) conditions in the rarefied mesosphere and thermosphere, making it necessary to consider the CO2 vibrational state non-LTE populations in the retrieval algorithm above 70 km. Those populations depend on kinetic parameters describing the rate at which energy exchange between atmospheric molecules take place, but some of these collisional rates are not well known. We consider current uncertainties in the rates of quenching of CO2 (v2 ) by N2 , O2 and O, and the CO2 (v2 ) vibrational-vibrational exchange to estimate their impact on SABER T(sub k) for different atmospheric conditions. The T(sub k) is more sensitive to the uncertainty in the latter two and their effects depend on altitude. The T(sub k) combined systematic error due to non-LTE kinetic parameters does not exceed +/- 1.5 K below 95 km and +/- 4-5 K at 100 km for most latitudes and seasons (except for polar summer) if the Tk profile does not have pronounced vertical structure. The error is +/- 3 K at 80 km, +/- 6 K at 84 km and +/- 18 K at 100 km under the less favourable polar summer conditions. For strong temperature inversion layers, the errors reach +/- 3 K at 82 km and +/- 8 K at 90 km. This particularly affects tide amplitude estimates, with errors of up to +/- 3 K.

Garcia-Comas, Maya↗
NASA NTRS2011

A Model of Reduced Kinetics for Alkane Oxidation Using Constituents and Species for N-Heptane

The reduction of elementary or skeletal oxidation kinetics to a subgroup of tractable reactions for inclusion in turbulent combustion codes has been the subject of numerous studies. The skeletal mechanism is obtained from the elementary mechanism by removing from it reactions that are considered negligible for the intent of the specific study considered. As of now, there are many chemical reduction methodologies. A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described and applied to n-heptane. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the LLNL (Lawrence Livermore National Laboratory) skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation (LES) in which functional forms are used to replace the small scales eliminated through filtering of the governing equations; in LES, these small scales are unimportant as far as the overwhelming part of dynamic energy is concerned. Here, the scales thought unimportant for recovering the thermodynamic energy are removed. The concept is tested by using tabular information from the LLNL skeletal mechanism in conjunction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is over-predicted, a fact traced to neglecting a detailed description of the processes leading to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into this conceptual reduction in addition to the modeling the evolution of the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole fractions of the quasisteady light species. The model is compact in that there are only nine species-related progress variables. Results are presented showing the performance of the model for predicting the temperature and species evolution. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure, and initial temperature.

Harstad, Kenneth G.↗