Modeling Dissociation-Vibration Coupling with the Macroscopic Chemistry Method

Lilley, Charles R.; Macrossan, Michael N.

doi:10.1063/1.1941668

Cited by 4 publications

(4 citation statements)

References 11 publications

(24 reference statements)

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“…One of the advantages of this approach is that the large quantity of reaction rate data that is commonly used in Computational Fluid Dynamics simulations may be applied directly in DSMC simulations. In addition, multitemperature reaction rate data such as the two-temperature model of Park 2 can also be used directly, 3 as can reaction rates that depend on the fluid density. 4 Lilley and Macrossan 1 have applied MCM to investigate dissociation and recombination reactions in a symmetrical diatomic gas.…”

Section: Introductionmentioning

confidence: 99%

Multiple reactions and trace species in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

2007

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The Macroscopic Chemistry Method is a technique for modeling chemical reactions in the Direct Simulation Monte Carlo ͑DSMC͒ method. The approach differs from conventional DSMC chemistry methods in that the change in the number of each species over a time step is calculated from the overall macroscopic cell parameters, rather than on a collision pair basis. The Macroscopic Chemistry Method ͑MCM͒ can be applied in flows where the collision rate is highly nonequilibrium and has previously been applied to model dissociation-recombination reactions of a symmetrical diatomic gas. Here we propose a procedure for applying MCM to a multiple species reaction set that includes exchange reactions, as well as a method by which trace species can be modeled without the need for variable weighting factors. The procedure is tested in constant volume reservoir relaxation simulations of a high-temperature gas and quasi-one-dimensional expansion of a high-speed, high-temperature gas. Initial compositions are chosen to resemble Earth and Martian atmosphere reacting systems. For the reservoir relaxation simulations, comparisons of the species mole fractions and overall temperature predicted by MCM are made with numerical integration of the reaction rate equations. For the one-dimensional expansion, results using the trace species algorithm are compared with a simulation without the trace species algorithm but with a much larger number of simulator particles. The reaction set consists of 54 chemical reactions ͑40 dissociation and 14 exchange reactions͒ among 8 species. The trace species algorithm exactly reproduces the temperature history predicted by numerical integration for the reservoir simulation. Without the trace species algorithm, the errors in the mole fractions are proportional to the inverse of the number of simulator particles used. For both the reservoir and expansion flow simulations, the trace species algorithm gives an improvement in accuracy equivalent to using 100 times the number of simulator particles.

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Section: Introductionmentioning

confidence: 99%

Multiple reactions and trace species in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

2007

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“…In previous applications of MCM [7][8][9][10] the reaction rates have been calculated (1) from the kinetic temperature in an Arrhenius rate equation, (2) from the density-dependent reaction rates given by Gupta et al 11 , and (3) from the two-temperature model of Park 12 . In the first two examples, the reaction rate was taken as the value expected for conditions of thermal equilibrium.…”

Section: Modelling Of Chemical Reactions In Dsmcmentioning

confidence: 99%

Nonequilibrium reaction rates in the macroscopic chemistry method for direct simulation Monte Carlo calculations

2007

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The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity.For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions.Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates 'intra-modal' non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

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“…In MCM, chemical reactions are computed by solving the chemical kinetic equations at the end of each time-step using macroscopic information obtained from all the simulator particles in a cell, not just those selected for collisions. The macroscopic method has been used with a variety of temperature and multi-temperature dependent reaction rates [2,5], and with reaction rates which depend on the local density as well as temperature [2].…”

Section: Introductionmentioning

confidence: 99%

“…The Macroscopic Chemistry Method has been extensively tested for steady flows [3][4][5][6], though it has not been applied to unsteady flows. Important insight may be gained into the fluid dynamics of a particular problem by observing the transient fluid motion.…”

Section: Introductionmentioning

confidence: 99%

Simulation of unsteady flows by the DSMC macroscopic chemistry method

Goldsworthy¹,

Macrossan²,

Abdel–jawad³

2009

Journal of Computational Physics

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In the Direct Simulation Monte Carlo (DSMC) method, a combination of statistical and deterministic procedures applied to a finite number of 'simulator' particles are used to model rarefied gas-kinetic processes. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reactions are decoupled from the specific particle pairs selected for collisions. Information from all of the particles within a cell, not just those selected for collisions, is used to determine a reaction rate coefficient for that cell. Unlike particle-based methods, MCM can be used with any viscosity or nonreacting collision models and any non-reacting energy exchange models. It can be used to implement any reaction rate formulations, whether these be from experimental or theoretical studies. MCM has been previously validated for steady flow DSMC simulations. Here we show how MCM can be used to model chemical kinetics in DSMC simulations of unsteady flow. Results are compared with a collision-based chemistry procedure for two binary reactions in a 1-D unsteady shock-expansion tube simulation. Close agreement is demonstrated between the two methods for instantaneous, ensemble-averaged profiles of temperature, density and species mole fractions, as well as for the accumulated number of net reactions per cell.

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Modeling Dissociation-Vibration Coupling with the Macroscopic Chemistry Method

Cited by 4 publications

References 11 publications

Multiple reactions and trace species in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

Multiple reactions and trace species in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

Nonequilibrium reaction rates in the macroscopic chemistry method for direct simulation Monte Carlo calculations

Simulation of unsteady flows by the DSMC macroscopic chemistry method

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