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

Goldsworthy, Mark; Macrossan, Michael N.; Abdel–jawad, Madhat

doi:10.1063/1.2742747

Cited by 6 publications

(10 citation statements)

References 12 publications

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“…In MCM, the thermal equilibrium reaction rates evaluated from the given rate coefficients, in this case those in Eqs. (5) and (6), are multiplied by two 'rate correction factors' Z ψ and F ψ as described by Goldsworthy et al [3]; this accounts for the deviation between the actual non-equilibrium distribution function and the thermal equilibrium distribution function as derived from the cell temperature.…”

Section: Chemical Rate Equations For the Model Gasmentioning

confidence: 99%

“…These difficulties may be overcome if chemical reactions are decoupled from the non-reacting collision procedures. A decoupled chemistry procedure known as the Macroscopic Chemistry Method (MCM) was proposed by Lilley and Macrossan [2] and refined by Goldsworthy et al [3] [4]. In this method, chemical reactions are computed by solving the chemical kinetic equations at the end of each time-step, using information obtained from all the simulator particles in a cell, not just those that are selected for collisions.…”

Section: Introductionmentioning

confidence: 99%

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Transient Macroscopic Chemistry in the DSMC Method

Goldsworthy¹,

Macrossan²,

Abdel–jawad³

2008

AIP Conference Proceedings

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Abstract. In the Direct Simulation Monte Carlo method, a combination of statistical and deterministic procedures applied to a finite number of 'simulator' particles are used to model rarefied gas-kinetic processes. Traditionally, chemical reactions are modelled using information from specific colliding particle pairs. In the Macroscopic Chemistry Method (MCM), the reactions are decoupled from the specific particle pairs selected for collisions. Information from all of the particles within a cell is used to determine a reaction rate coefficient for that cell. MCM has previously been applied to 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 and during the unsteady development of 2-D flow through a cavity. For the shock tube simulation, close agreement is demonstrated between the two methods for instantaneous, ensemble-averaged profiles of temperature and species mole fractions. For the cavity flow, a high degree of thermal non-equilibrium is present and non-equilibrium reaction rate correction factors are employed in MCM. Very close agreement is demonstrated for ensemble-averaged mole fraction contours predicted by the particle and macroscopic methods at three different flow-times. A comparison of the accumulated number of net reactions per cell shows that both methods compute identical numbers of reaction events. For the 2-D flow, MCM required similar CPU and memory resources to the particle chemistry method. The Macroscopic Chemistry Method is applicable to any general DSMC code using any viscosity or non-reacting collision models and any non-reacting energy exchange models. MCM can be used to implement any reaction rate formulations, whether these be from experimental or theoretical studies.

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Section: Chemical Rate Equations For the Model Gasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transient Macroscopic Chemistry in the DSMC Method

Goldsworthy¹,

Macrossan²,

Abdel–jawad³

2008

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

show abstract

“…To overcome these difficulties the Macroscopic Chemistry Method (MCM) was proposed by Lilley and Macrossan [2] and refined by Goldsworthy et al [3,4]. In this method, the rates of chemical reactions are largely decoupled from the collision procedures; any collision models such as the Lennard-Jones or Morse potentials can be used.…”

Section: Introductionmentioning

confidence: 99%

“…We have previously shown [3] that, because MCM assumes only that the steric factor is the same for equilibrium and non-equilibrium conditions, it produces plausible non-equilibrium reaction rates. On the other hand, when TCE is applied in highly non-equilibrium conditions, the reaction rates arise from a variation in the steric factor which has no basis in theory or experiment but is dictated purely for reasons of mathematical tractability.…”

Section: Introductionmentioning

confidence: 99%

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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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Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method

Prasanth¹,

Kakkassery²

2008

Fluid Dyn. Res.

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The direct simulation Monte Carlo (DSMC) method is a technique for the numerical simulation of the rarefied gas flows by employing simulated molecules in simulated physical spaces. In the procedures involved in DSMC, the accuracy of the simulation of intermolecular collisions depends on the collision model adopted in the collision routine. The simplest molecular model is the hard-sphere model. In order to improve the accuracy of the simulations, more and more refined collision models were introduced for the use in DSMC. Thus, the variable hard-sphere, the variable soft-sphere, the generalised hard-sphere, the generalised soft-sphere and the variable sphere models were put forward by various researchers. And, all these models have met with varying degrees of success. Meanwhile, the Borgnakke-Larsen model, statistical inelastic cross-section models for both continuous and discrete internal energy and the dynamic molecular collision model were proposed for the treatment of polyatomic molecules in which transfer of energy among translational, rotational and vibrational degrees of freedom is possible. This paper gives a brief introduction to the intermolecular potentials based on which the molecular models have been constructed. Then the various models are introduced in the chronological sequence; finally concluding with a brief summary of the progress that has been made so far in this area.

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

Cited by 6 publications

References 12 publications

Transient Macroscopic Chemistry in the DSMC Method

Transient Macroscopic Chemistry in the DSMC Method

Simulation of unsteady flows by the DSMC macroscopic chemistry method

Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method

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