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Dissociation of diatomic gases

The Landau-Zener theory of reactive cross sections has been applied to diatomic molecules dissociating from a ladder of rotational and vibrational states. Although the preexponential factor of the Arrhenius rate expression is shown to be a complex function of the dimensionless activation energy, the average over all states in the ladder is well represented by a single factor that varies about as T exp (-n), where the coefficient n is the order of unity. This relation agrees very well with experimental data for dissociation of O2 and N2, for example. The results validate previous empirical assignment of a single preexponential factor in the Arrhenius expression and justify the extrapolation of the expression well beyond the range of data. The theory is then used to calculate the effect of vibrational nonequilibrium on dissociation rate. For Morse oscillators the results are about the same as for harmonic oscillators, and the dissociation from a ladder of equilibrium rotational and nonequilibrium vibrational states is close to an analytic approximation provided by Hammerling, Kivel, and Teare for harmonic oscillators all dissociating from the ground rotational state.

Hansen, C. F.↗

Model free simulations of a high speed reacting mixing layer

The effects of compressibility, chemical reaction exothermicity and non-equilibrium chemical modeling in a combusting plane mixing layer were investigated by means of two-dimensional model free numerical simulations. It was shown that increased compressibility generally had a stabilizing effect, resulting in reduced mixing and chemical reaction conversion rate. The appearance of 'eddy shocklets' in the flow was observed at high convective Mach numbers. Reaction exothermicity was found to enhance mixing at the initial stages of the layer's growth, but had a stabilizing effect at later times. Calculations were performed for a constant rate chemical rate kinetics model and an Arrhenius type kinetics prototype. The Arrhenius model was found to cause a greater temperature increase due to reaction than the constant kinetics model. This had the same stabilizing effect as increasing the exothermicity of the reaction. Localized flame quenching was also observed when the Zeldovich number was relatively large.

Steinberger, Craig J.↗

On reaction kinetics and atmospheric lifetimes of CF3CFHCF3 and CF3CH2Br

The rate constants for the reaction of the OH radical with CF3CFHCF3 and with CF3CH2Br have been measured as a function of temperature using the discharge flow technique with laser induced fluorescence detection of the OH radicals. The temperature dependent rate coefficients are well described by a simple Arrhenius expression, k(T) = A exp(E/(RT)). For the reaction of OH with CF3CFHCF3 we find A = 3.7 x 10 exp -13 cu cm/molecules/s and E/R = 1615 K; for the reaction of OH with CF3CH2Br we report A = 1.4 x 10 exp -12 cu cm/molecule/s and E/R = 1350 K. These Arrhenius parameters imply rate coefficients at 277 K of 1.09 x 10 exp -15 cu cm/molecule/s for CF3CFHCF3 and 1.06 x 10 exp -14 cu cm/molecule/s for CF3CH2Br. We find atmospheric lifetimes for CF3CFHCH3 and CF3CH2Br of 42 years and 4.1 years, respectively. We also estimate the steady state ozone depletion potential (ODP) of the brominated species relative to CFCl3 as about 0.84 using a semiempirical model.

Nelson, D. D., Jr.↗

Vibrational nonequilibrium effects on diatomic dissociation rates

The collision-induced dissociation rate of diatomic molecules from a ladder of rotational and anharmonic vibrational states is developed, and the correction for vibrational nonequilibrium is considered. The result is similar to an analytic correction derived by Hammerling et al. (1959) for harmonic oscillators. An empirical correction algorithm suggested by Park (1987, 1990) gives similar results when vibrational temperature is comparable to kinetic temperature but underestimates the dissociation rate when vibrational temperature is small compared with the kinetic temperature. This algorithm uses an effective temperature in the experimentally determined Arrhenius expression for the rate coefficient, which is a weighted average of the vibrational and kinetic temperature, whereas theory indicates that kinetic temperature should appear only in the exponential term of the Arrhenius expression. Nevertheless, an effective temperature can always be found that will numerically duplicate the proper rate coefficient at any given condition, but a constant weighting factor cannot be expected to provide this. However, the algorithm can he adjusted to give reasonable results over a range of conditions if the geometric weighting factor is taken to be a simple linear function of the ratio of vibrational to kinetic temperature in the gas.

Hansen, C. F.↗

Thermal history effects on electrical relaxation and conductivity for potassium silicate glass with low alkali concentrations

Electrical response measurements from 10 Hz to 100 kHz between 120 and 540 C were made on potassium-silicate glasses with alkali oxide contents of 2, 3, 5 and 10 mol percent. Low alkali content glasses were chosen in order to try to reduce the Coulombic interactions between alkali ions to the point that frozen structural effects from the glass could be observed. Conductivity and electrical relaxation responses for both annealed and quenched glasses of the same composition were compared. Lower DC conductivity (sigma(sub DC)) activation energies were measured for the quenched compared to the annealed glasses. The two glasses with the lowest alkali contents exhibited a non-Arrhenius concave up curvature in the log(sigma(sub DC)) against 1/T plots, which decreased upon quenching. A sharp decrease in sigma(sub DC) was observed for glasses containing K2O concentrations of 5 mol percent or less. The log modulus loss peak (M'') maximum frequency plots against 1/T all showed Arrhenius behavior for both annealed and quenched samples. The activation energies for these plots closely agreed with the sigma(sub DC) activation energies. A sharp increase in activation energy was observed for both series as the potassium oxide concentration decreased. Changes in the electrical response are attributed to structural effects due to different alkali concentrations. Differences between the annealed and quenched response are linked to a change in the distribution of activation energies (DAE).

Angel, Paul W.↗

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

A new release rate equation to model the phase change of water to steam in composite materials was derived from the theory of molecular diffusion and equilibrium moisture concentration. The new model is dependent on internal pressure, the microstructure of the voids and channels in the composite materials, and the diffusion properties of the matrix material. Hence, it is more fundamental and accurate than the empirical Arrhenius rate equation currently in use. The model was mathematically formalized and integrated into the thermostructural analysis code CHAR. Parametric studies on variation of several parameters have been done. Comparisons to Arrhenius and straight-line models show that the new model produces physically realistic results under all conditions.

Mcmanus, Hugh L.↗

High temperature kinetic study of the reactions H + O2 = OH + O and O + H2 = OH + H in H2/O2 system by shock tube-laser absorption spectroscopy

The reactions: (1) H + O2 = OH + O; and (2) O + H2 = OH + H are the most important elementary reactions in gas phase combustion. They are the main chain-branching reaction in the oxidation of H2 and hydrocarbon fuels. In this study, rate coefficients of the reactions and have been measured over a wide range of composition, pressure, density and temperature behind the reflected shock waves. The experiments were performed using the shock tube - laser absorption spectroscopic technique to monitor OH radicals formed in the shock-heated H2/O2/Ar mixtures. The OH radicals were detected using the P(1)(5) line of (0,0) band of the A(exp 2) Sigma(+) from X(exp 2) Pi transition of OH at 310.023 nm (air). The data were analyzed with the aid of computer modeling. In the experiments great care was exercised to obtain high time resolution, linearity and signal-to-noise. The results are well represented by the Arrhenius expressions. The rate coefficient expression for reaction (1) obtained in this study is k(1) = (7.13 +/- 0.31) x 10(exp 13) exp(-6957+/- 30 K/T) cu cm/mol/s (1050 K less than or equal to T less than or equal to 2500 K) and a consensus expression for k(1) from a critical review of the most recent evaluations of k(1) (including our own) is k(1) = 7.82 x 10(exp 13) exp(-7105 K/T) cu cm/mol/s (960 K less than or equal to T less than or equal to 5300 K). The rate coefficient expression of k(2) is given by k(2) = (1.88 +/- 0.07) x 10(exp 14) exp(-6897 +/- 53 K/T) cu cm/mol/s (1424 K less than or equal to T less than or equal to 2427 K). For k(1), the temperature dependent A-factor and the correlation between the values of k(1) and the inverse reactant densities were not found. In the temperature range of this study, non-Arrhenius expression of k(2) which shows the upward curvature was not supported.

Ryu, Si-Ok↗

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗

Mobility of Electron in DNA Crystals by Laser Radiation

The mobility of electrons in laser radiated DNA is closed to the energy transfer and energy migration of a biological molecule. Arrhenius has studied the conductivity of the electrons in a biological molecule. But his result is far from the experimental result and meanwhile the relation between some parameters in his theory and the micro-quantities in DNA is not very clear. In this paper, we propose a new phonon model of electron mobility in DNA and use Lippman-Schwinger equation and S-matrix theory to study the mobility of electrons in DNA crystal. The result is relatively close to the experiment result and some parameters in Arrhenius theory are explained in our work.

Zhang, Kaixi↗

Kinetics of the Reactions of IO Radicals with NO and NO2

A laser flash photolysis-long path absorption technique has been employed to study the kinetics of the reactions of IO radicals with NO and NO2 as a function of temperature and pressure. The IO and NO rate coefficient is independent of pressure over the range 40-200 Torr of N2, and its temperature dependence over the range 242-359 K is adequately described by the Arrhenius expression k(sub 1) = (6.9 +/- 1.7) x 10(exp -12) exp[(328 +/- 71)/T] cu cm/(molecule.s) (errors are 2 sigma, precision only). These Arrhenius parameters are similar to those determined previously for the ClO + NO and BrO + NO reactions. The IO and NO2 association reaction is found to be in the falloff regime over the temperature and pressure ranges investigated (254-354 K and 40-750 Torr of N2). Assuming F(sub c) = 0.4 independent of temperature, a physically reasonable set of falloff parameters which adequately describe the data are k(sub 0) = 7.7 x 10(exp -31)(T/300)(exp -5.0) cm(exp 6)/(molecule(exp 2).s) and k(sub infinity) = 1.55 x 10(exp -11)cu cm/(molecule.s) independent of temperature. The IO + NO2 rate coefficients determined in this study are about a factor of 2 faster than those reported in the only previous study of this reaction.

Daykin, E. P.↗

Numerical Simulation of Combustion and Extinction of a Solid Cylinder in Low-Speed Cross Flow

The combustion and extinction behavior of a diffusion flame around a solid fuel cylinder (PMMA) in low-speed forced flow in zero gravity was studied numerically using a quasi-steady gas phase model. This model includes two-dimensional continuity, full Navier Stokes' momentum, energy, and species equations with a one-step overall chemical reaction and second-order finite-rate Arrhenius kinetics. Surface radiation and Arrhenius pyrolysis kinetics are included on the solid fuel surface description and a parameter Phi, representing the percentage of gas-phase conductive heat flux going into the solid, is introduced into the interfacial energy balance boundary condition to complete the description for the quasi-steady gas-phase system. The model was solved numerically using a body-fitted coordinate transformation and the SIMPLE algorithm. The effects of varying freestream velocity and Phi were studied. These parameters have a significant effect on the flame structure and extinction limits. Two flame modes were identified: envelope flame and wake flame. Two kinds of flammability limits were found: quenching at low-flow speeds due to radiative loss and blow-off at high flow speeds due to insufficient gas residence time. A flammability map was constructed showing the existence of maximum Phi above which the solid is not flammable at any freestream velocity.

Tien, J. S.↗

Development and Application of Tools to Characterize the Oxidative Degradation of AP/HTPB/Al Propellants in a Propellant Reliability Study

The oxidative thermal aging of a crosslinked hydroxyl-terminated polybutadiene (HTPB)/isophorone diisocyanate (IPDI) polyurethane rubber was studied at temperatures between 25 C and 125 C. Changes in tensile elongation, mechanical hardening, polymer network properties, density, O2 permeation, and molecular chain dynamics were investigated as a function of age. The techniques used include solvent swelling, detailed modulus profiling, and NMR relaxation measurements. The Arrhenius methodology, which normally assumes a linear extrapolation of high temperature aging data, is critically evaluated by using extensive data superposition and highly sensitive oxygen consumption measurements. Significant curvature in the Arrhenius diagram of these oxidation rates is observed to be similar to previous results found for other rubber materials that have been evaluated by this technique. Preliminary gel/network properties suggest that crosslinking is the dominant process at higher temperatures. The effect on the oxidation rate of the binder when other constituents found in propellants are present, such as ammonium perchlorate, plasticizer and aluminum powder, is presented.

Celina, Mathew↗

Accelerated Aging of Lead-Free Propellant

Following higher than expected 2-NDPA depletion rates in a lead-free doublebase formulation (RPD-422), an accelerated aging study was conducted to verify the depletion rates. A test plan was prepared to compare the aging characteristics of lead-free propellant and NOSIH-AA2. The study was also designed to determine which lead-free ballistic modifiers accelerated 2-NDPA depletion. The increased depletion rate occurred in propellants containing monobasic copper salicylate. Four lead-free propellants were then formulated to improved aging characteristics over previous lead-free propellant formulations. The new formulations reduced or replaced the monobasic copper salicylate. The new formulations had improved aging characteristics. Their burn rates, however, were unacceptable for use in a 2.75 inch rocket. To compare aging characteristics, stabilizer depletion rates of RPD-422, AA2, M28, and RLC 470/6A were measured or taken from the literature. The data were fit to a kinetic model. The model contained first and zero order terms which allowed the stabilizer concentration to go to zero. In the model, only the concentration of the primary stabilizer was considered. Derivatives beyond the first nitrated or nitroso derivative of 2-NPDA were not considered. The rate constants were fit to the Arrhenius equation and extrapolated to lower temperatures. The time to complete stabilizer depletion was estimated using the kinetic model. The four propellants were compared and the RPD-422 depleted faster at 45 C than both A22 and M28. These types of predictions depend on the validity of the model and on confidence in the Arrhenius relationship holding at lower temperatures. At 45 C, the zero order portion of the model dominates the depletion rate.

Furrow, Keith W.↗

Homogenization Issues in the Combustion of Heterogeneous Solid Propellants

We examine random packs of discs or spheres, models for ammonium-perchlorate-in-binder propellants, and discuss their average properties. An analytical strategy is described for calculating the mean or effective heat conduction coefficient in terms of the heat conduction coefficients of the individual components, and the results are verified by comparison with those of direct numerical simulations (dns) for both 2-D (disc) and 3-D (sphere) packs across which a temperature difference is applied. Similarly, when the surface regression speed of each component is related to the surface temperature via a simple Arrhenius law, an analytical strategy is developed for calculating an effective Arrhenius law for the combination, and these results are verified using dns in which a uniform heat flux is applied to the pack surface, causing it to regress. These results are needed for homogenization strategies necessary for fully integrated 2-D or 3-D simulations of heterogeneous propellant combustion.

Chen, M.↗

Apparent I-Xe Cooling Rates of Chondrules Compared with Silicates from the Colomera Iron Meteorite

In I-Xe dating, a regular pattern of increasing Xe-129/128Xe-128 ratio with increasing extraction temperature is often observed. If one makes the crude assumption that the temperatures at which the Xe is extracted in the laboratory is approximately the same as the temperature at which those sites closed 4.6 Ga ago, a (zeroth order) model cooling rate can be found. In order to test and refine this model we can apply the cooling theory of Dodson to those extraction steps approaching the I-Xe isochrons. Using an Arrhenius plot for these temperature fractions, and assuming that an only single phase is involved, the effective diffusion parameters can be estimated (frequency factor and activation energy). From the apparent (zeroth order) cooling rate, the closure temperature can be estimated from the Dodson equation. This model closure temperature can then be compared with the actual laboratory temperature at which the isochron begins. The ratio of the closure temperature and the temperature corresponding to the start of the isochron provides the ratio of the two temperature scales, incorporation and extraction. The actual cooling rate is then given by the apparent (zeroth order) cooling rate times the temperature scale factor. Figure 1 shows Arrhenius plots for I-Xe data

Hohenberg, C. M.↗

Service Life Extension of the Propulsion System of Long-Term Manned Orbital Stations

One of the critical non-replaceable systems of a long-term manned orbital station is the propulsion system. Since the propulsion system operates beginning with the launch of station elements into orbit, its service life determines the service life of the station overall. Weighing almost a million pounds, the International Space Station (ISS) is about four times as large as the Russian space station Mir and about five times as large as the U.S. Skylab. Constructed over a span of more than a decade with the help of over 100 space flights, elements and modules of the ISS provide more research space than any spacecraft ever built. Originally envisaged for a service life of fifteen years, this Earth orbiting laboratory has been in orbit since 1998. Some elements that have been launched later in the assembly sequence were not yet built when the first elements were placed in orbit. Hence, some of the early modules that were launched at the inception of the program were already nearing the end of their design life when the ISS was finally ready and operational. To maximize the return on global investments on ISS, it is essential for the valuable research on ISS to continue as long as the station can be sustained safely in orbit. This paper describes the work performed to extend the service life of the ISS propulsion system. A system comprises of many components with varying failure rates. Reliability of a system is the probability that it will perform its intended function under encountered operating conditions, for a specified period of time. As we are interested in finding out how reliable a system would be in the future, reliability expressed as a function of time provides valuable insight. In a hypothetical bathtub shaped failure rate curve, the failure rate, defined as the number of failures per unit time that a currently healthy component will suffer in a given future time interval, decreases during infant-mortality period, stays nearly constant during the service life and increases at the end when the design service life ends and wear-out phase begins. However, the component failure rates do not remain constant over the entire cycle life. The failure rate depends on various factors such as design complexity, current age of the component, operating conditions, severity of environmental stress factors, etc. Development, qualification and acceptance test processes provide rigorous screening of components to weed out imperfections that might otherwise cause infant mortality failures. If sufficient samples are tested to failure, the failure time versus failure quantity can be analyzed statistically to develop a failure probability distribution function (PDF), a statistical model of the probability of failure versus time. Driven by cost and schedule constraints however, spacecraft components are generally not tested in large numbers. Uncertainties in failure rate and remaining life estimates increase when fewer units are tested. To account for this, spacecraft operators prefer to limit useful operations to a period shorter than the maximum demonstrated service life of the weakest component. Running each component to its failure to determine the maximum possible service life of a system can become overly expensive and impractical. Spacecraft operators therefore, specify the required service life and an acceptable factor of safety (FOS). The designers use these requirements to limit the life test duration. Midway through the design life, when benefits justify additional investments, supplementary life test may be performed to demonstrate the capability to safely extend the service life of the system. An innovative approach is required to evaluate the entire system, without having to go through an elaborate test program of propulsion system elements. Evaluating every component through a brute force test program would be a cost prohibitive and time consuming endeavor. ISS propulsion system components were designed and built decades ago. There are no representative ground test articles for some of the components. A 'test everything' approach would require manufacturing new test articles. The paper outlines some of the techniques used for selective testing, by way of cherry picking candidate components based on failure mode effects analysis, system level impacts, hazard analysis, etc. The type of testing required for extending the service life depends on the design and criticality of the component, failure modes and failure mechanisms, life cycle margin provided by the original certification, operational and environmental stresses encountered, etc. When specific failure mechanism being considered and the underlying relationship of that mode to the stresses provided in the test can be correlated by supporting analysis, time and effort required for conducting life extension testing can be significantly reduced. Exposure to corrosive propellants over long periods of time, for instance, lead to specific failure mechanisms in several components used in the propulsion system. Using Arrhenius model, which is tied to chemically dependent failure mechanisms such as corrosion or chemical reactions, it is possible to subject carefully selected test articles to accelerated life test. Arrhenius model reflects the proportional relationship between time to failure of a component and the exponential of the inverse of absolute temperature acting on the component. The acceleration factor is used to perform tests at higher stresses that allow direct correlation between the times to failure at a high test temperature to the temperatures to be expected in actual use. As long as the temperatures are such that new failure mechanisms are not introduced, this becomes a very useful method for testing to failure a relatively small sample of items for a much shorter amount of time. In this article, based on the example of the propulsion system of the first ISS module Zarya, theoretical approaches and practical activities of extending the service life of the propulsion system are reviewed with the goal of determining the maximum duration of its safe operation.

Kamath, Ulhas↗

Phosphate microaggregates in Archean sediments

Light microscopy conducted on samples of Archean sediments reveals phosphate microaggregates which are suggestive of a biotic origin (Arrhenius et al., 1993). These aggregates, typically 15 micrometers wide and 50 micrometers long, are thought to be the mineral remains of colonies of microorganisms that lived during the late Archean Eon (greater than or equal to 2.5 Ga). Confocal microscopy was used to study the structures of these microaggregates in three dimensions. Samples used in this study are from the lowermost section of drill core taken from the Dales Gorge Member of the Brockman Iron-Formation (Hamersley Basin) in Western Australia. These sediments are well-preserved and escaped extensive metamorphism typically experienced by older rocks of this type. Two types of samples were prepared for study under the microscope: thin sections (30 micrometers) for transmitted light microscopy to study the general rock texture and to locate the grains of interest, and thick sections (3mm) for confocal microscopy to determine the 3-D structure of the aggregates in situ. The samples have been carefully polished so that they may be directly placed on the oil-immersion lens without the use of a cover slip. No chemical treatments of the surfaces have been performed. The aggregates often form clusters, although isolated aggregates have also been found. The clusters tend to distribute along microbands in the rocks. Electron microprobe analyses show that the phosphate grains and their inclusions, besides calcium and phosphorus, contain no major elements heavier than sodium. The proportions of calcium to phosphorus, the absence of stoichiometric amounts of other cations such as magnesium and iron, as well as optical properties suggest apatite as the mineral form.

Mojzsis, S.↗