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Numerical modeling of D-mappings was studied and applied to solving nonlinear stiff systems. These mappings were locally linearized for convergence analysis, and some applications were made to chemical kinetics. The technique avoids using multistep implicit codes that require inversion of Jacobian matrices, but depends on the Jacobians for its convergence analysis.
The Computational Singular Perturbation CSP methods is employed (1) in the modeling of a homogeneous isothermal reacting system and (2) in the numerical simulation of the chemical reactions in a hypersonic flowfield. Reduced and simplified mechanisms are constructed. The solutions obtained on the basis of these approximate mechanisms are shown to be in very good agreement with the exact solution based on the full mechanism. Physically meaningful approximations are derived. It is demonstrated that the deduction of these approximations from CSP is independent of the complexity of the problem and requires no intuition or experience in chemical kinetics.
Quantitative values were computed which show the effects of the presence of small amounts of oxygen, hydrogen, and hydroxyl radicals on the finite-rate chemical kinetics of premixed hydrogen-air mixtures undergoing isobaric autoignition and combustion. The free radicals were considered to be initially present in hydrogen-air mixtures at equivalence ratios of 0.2, 0.6, 1.0, and 1.2. Initial mixture temperatures were 1100 K, 1200 K, and 1500 K, and pressures were 0.5, 1.0, 2.0, and 4.0 atm. Of the radicals investigated, atomic oxygen was found to be the most effective for reducing induction time, defined as the time to 5 percent of the total combustion temperature rise. The reaction time, the time between 5 percent and 95 percent of the temperature rise, is not decreased by the presence of free radicals in the initial hydrogen-air mixture. Fuel additives which yield free radicals might be used to effect a compact supersonic combustor design for efficient operation in an otherwise reaction-limited combustion regime.
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.
A simple function with two undetermined parameters has been used in place of the Thomson-Gibbs relation to relate the activation energy of the vaporization reaction to cluster size. The parameters are iterated to assume optimum values in numerical computation so experimental data may be correlated. Calculations show this approach closely predicts and correlates available data for water, benzene, and ethanol. The nucleation formulism is redeveloped with an emphasis on the chemical kinetic view. Surface tension of the liquid and free energy of droplet formation are not used in its derivation.
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Turbulent boundary layer effects on chemical and kinetic measurements of gas mixture composition from nonuniform shock tube flow
Physical and chemical conditions in the coma of a bright 'new' comet are related to the composition of the nucleus. Chemical and photolytic processes are described and correlated to distance in the coma above the nucleus and to heliocentric distance of the comet. Two classes for the composition of comets are considered based on their place of origin: in the environs of the giant planets or in a companion fragment of the presolar nebula. Comparison of model results with coma observations leads to some restrictions about the nucleus composition. It is expected that these restrictions become more stringent as coma models are developed further and as observations become more detailed. Composition based on an origin of comets in the presolar nebula yields abundances of C2, C3, and CN that are in agreement with observations.
Master equation derived and applied to problems of internal vibrational relaxation and intramolecular rearrangement reactions
Although the combustion of hydrocarbons is our primary source of energy today, the chemical reactions, or pathway, by which even the simplest hydro-carbon reacts with atmospheric oxygen to form CO2 and water may not always be known. Furthermore, even when the reaction pathway is known, the reaction rates are always under discussion. The shock tube has been an important and unique tool for building a data base of reaction rates important in the combustion of hydrocarbon fuels. The ability of a shock wave to bring the gas sample to reaction conditions rapidly and homogeneously makes shock-tube studies of reaction kinetics extremely attractive. In addition to the control and uniformity of reaction conditions achieved with shock-wave methods, shock compression can produce gas temperatures far in excess of those in conventional reactors. Argon can be heated to well over 10 000 K, and temperatures around 5000 K are easily obtained with conventional shock-tube techniques. Experiments have proven the validity of shock-wave theory; thus, reaction temperatures and pressures can be calculated from a measurement of the incident shock velocity. A description is given of the chemical shock tube and auxiliary equipment and of two examples of kinetic experiments conducted in a shock tube.
NASA JPL has been creating a code in FORTRAN called KINETICS to model the chemistry of planetary atmospheres. Recently there has been an effort to introduce Message Passing Interface (MPI) into the code so as to cut down the run time of the program. There has been some implementation of MPI into KINETICS; however, the code could still be more efficient than it currently is. One way to increase efficiency is to send only certain variables to all the processes when an MPI subroutine is called and to gather only certain variables when the subroutine is finished. Therefore, all the variables that are used in three of the main subroutines needed to be investigated. Because of the sheer amount of code that there is to comb through this task was given as a ten-week project. I have been able to create flowcharts outlining the subroutines, common blocks, and functions used within the three main subroutines. From these flowcharts I created tables outlining the variables used in each block and important information about each. All this information will be used to determine how to run MPI in KINETICS in the most efficient way possible.
An anaytical study of hydrogen air kinetics was performed. Calculations were made over a range of pressure from 0.2 to 4.0 atm, temperatures from 850 to 2000 K, and mixture equivalence ratios from 0.2 to 2.0. The finite rate chemistry model included 60 reactions in 20 species of the H2-O2-N2 system. The calculations also included an assessment of how small amounts of the chemicals H2O, NOx, H2O2, and O3 in the initial mixture affect ignition and reaction times, and how the variation of the third body efficiency of H2O relative of N2 in certain key reactions may affect reaction time. The results indicate that for mixture equivalence ratios between 0.5 and 1.7, ignition times are nearly constant; however, the presence of H2O and NO can have significant effects on ignition times, depending on the mixture temperature. Reaction time is dominantly influenced by pressure but is nearly independent of initial temperature, equivalence ratio, and the addition of chemicals. Effects of kinetics on reaction at supersonic combustor conditions are discussed.
Random photochemical reaction rates are employed in a 1D photochemical model to examine uncertainties in tropospheric concentrations and thereby determine critical kinetic processes and significant correlations. Monte Carlo computations are used to simulate different chemical environments and their related imprecisions. The most critical processes are the primary photodissociation of O3 (which initiates ozone destruction) and NO2 (which initiates ozone formation), and the OH/methane reaction is significant. Several correlations and anticorrelations between species are discussed, and the ozone/transient OH correlation is examined in detail. One important result of the modeling is that estimates of global OH are generally about 25 percent uncertain, limiting the precision of photochemical models. Techniques for reducing the imprecision are discussed which emphasize the use of species and radical species measurements.
The present work aims to derive a set of thermomechanical relaxation rate parameters and chemical reaction rate coefficients relevant to future interplanetary missions. It also attempts to assess the impact of thermochemical nonequilibrium phenomena on radiative heating rates for the stagnation point of the Martian entry vehicle.
Following the recent discussions by O'Brien (1971) and Donaldson and Hilst (1972) of the effects of inhomogeneous mixing and turbulent diffusion on simple chemical reaction rates, the present report provides a more extensive analysis of when inhomogeneous mixing has a significant effect on chemical reaction rates. The analysis is then extended to the development of an approximate chemical sub-model which provides much improved predictions of chemical reaction rates over a wide range of inhomogeneities and pathological distributions of the concentrations of the reacting chemical species. In particular, the development of an approximate representation of the third-order correlations of the joint concentration fluctuations permits closure of the chemical sub-model at the level of the second-order moments of these fluctuations and the mean concentrations.
The differential equations governing the transient response of a one-dimensional ablative thermal protection system are presented for thermal nonequilibrium between the pyrolysis gases and the char layer and with finite rate chemical reactions occurring. The system consists of three layers (the char layer, the uncharred layer, and an optical insulation layer) with concentrated heat sinks at the back surface and between the second and third layers. The equations are solved numerically by using a modified implicit finite difference scheme to obtain solutions for the thickness of the charred and uncharred layers, surface recession and pyrolysis rates, solid temperatures, porosity profiles, and profiles of pyrolysis-gas temperature, pressure, composition, and flow rate. Good agreement is obtained between numerical results and exact solutions for a number of simplified cases. The complete numerical analysis is used to obtain solutions for an ablative system subjected to a constant heating environment. Effects of thermal, chemical, and mass transfer processes are shown.
This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.