Rates of thermal relaxation in direct simulation Monte Carlo methods

Haas, Brian L.; Hash, David; Bird, G. A.; Lumpkin, Forrest E.; Hassan, H. A.

doi:10.1063/1.868221

Cited by 118 publications

(79 citation statements)

References 19 publications

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“…Rotational and vibrational energy exchange was performed using the BorgnakkeLarsen method. 10 Following Haas et al, 19 multiple relaxation events were prohibited. The methodology for selecting relaxing particles was that of Gimelshein et al 20 For simplicity, constant relaxation probabilities of 0.30 and 0.01 for rotation and vibration, respectively, were used.…”

Section: Strong Shock In Dissociating Nitrogenmentioning

confidence: 99%

A macroscopic chemistry method for the direct simulation of gas flows

Lilley

Macrossan

2004

Physics of Fluids

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In most chemistry methods developed for the direct simulation Monte Carlo ͑DSMC͒ technique, chemical reactions are computed as an integral part of the collision simulation routine. In the macroscopic chemistry method developed here, the simulation of collisions and reactions are decoupled in that reactions are computed independently, after the collision routine. The number of reaction events to perform in each cell is calculated using the macroscopic reaction rates k Ϯ and equilibrium constant K*, with local macroscopic flow conditions. The macroscopic method is developed for the symmetrical diatomic dissociating gas. For each dissociation event, a single diatomic simulator particle is selected with a probability based on its internal energy, and is replaced by two atomic particles. For each recombination event, two atomic particles are selected at random, and are replaced by a single diatomic particle. The dissociation energy is accounted for by adjusting the translational thermal energies of all particles in the cell. The macroscopic method gives density profiles in agreement with experimental data for the chemical relaxation region downstream of a strong shock in nitrogen. In the nonequilibrium region within the shock, and along the stagnation streamline of a blunt cylinder in rarefied flow, the macroscopic method gives results in excellent agreement with those obtained using the most common conventional DSMC chemistry method in which reactions are calculated during the collision routine. The number of particles per computational cell has a minimal effect on the results provided by the macroscopic method. Unlike most DSMC chemistry methods, the macroscopic method is not limited to simple forms of k Ϯ and K*. Any forms may be used, and these may be any function of the macroscopic conditions. This is demonstrated by using a two-temperature rate model, and a form of K* with a number density dependence. With the two-temperature model, the macroscopic method gives densities in the post-shock chemical relaxation region that also agree with the experimental data. For a form of K* with a number density dependence, the macroscopic method can accurately reproduce chemical recombination behavior. In a primarily dissociative flow, the number density dependence of K* has very little effect on the flow. The macroscopic method requires slightly less computing time than the most common DSMC chemistry method.

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Section: Strong Shock In Dissociating Nitrogenmentioning

confidence: 99%

A macroscopic chemistry method for the direct simulation of gas flows

Lilley

Macrossan

2004

Physics of Fluids

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“…In Ref. 30, relaxation probabilities for both the particle selection and pair selection are discussed in detail. In the baseline DSMC calculations to be discussed here, the Z V cont of Millikan and White 31 is used.…”

Section: Review Of Energy Exchange Models For Hypersonic Flowsmentioning

confidence: 99%

“…21 Table VI summarizes the values of Z R ϱ , T R * , and v for N 2 , O 2 , and NO that are used in the DSMC calculations. In addition, the temperature-dependent collision numbers of Haas et al 30 were used. Figure 5 shows a comparison of the collision numbers predicted by the original MW ͑Refs.…”

Section: B Investigation Of Energy Exchange Modelsmentioning

confidence: 99%

Development of kinetic-based energy exchange models for noncontinuum, ionized hypersonic flows

2008

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Ultrahigh Mach number re-entry vehicles create sufficiently energetic flow conditions with substantial ionization occurring in the noncontinuum flow regime. To model these noncontinuum, ionized, and thermochemically nonequilibrium flows, a direct simulation Monte Carlo (DSMC) approach is investigated. Energy exchange models that have been developed for Navier–Stokes computational fluid dynamics computations are examined and revised for application to the DSMC method. Since the electron–heavy particle collision rate is approximately two orders of magnitude higher than that between heavy particles, a new model is developed for electron scattering collision processes and electron-vibrational energy exchange based on the electron-molecule shape resonance phenomena. It is found that the flow electron and vibrational temperatures are sensitive to the electron-vibrational relaxation model because the relaxation time changes by orders of magnitude. The DSMC calculations of the bow-shock region of a blunt body were found to predict the correct flow features for free stream Knudsen numbers spanning the near-free molecular to the continuum limit. The range of degree of ionization was found to vary from the highest altitude to the lowest from 1% to 11%.

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“…The number density remains constant in time @n=@t ¼ 0. The relaxation rates of the kinetic model equations have been compared numerically with the corresponding ones of the DSMC method and it has been found that good agreement is observed by setting [34,14].…”

Section: Appendix a Relaxation Rates In A Homogenous Gasmentioning

confidence: 89%

Effect of vibrational degrees of freedom on the heat transfer in polyatomic gases confined between parallel plates

Tantos

Ghiroldi

Valougeorgis

et al. 2016

International Journal of Heat and Mass Transfer

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Conductive stationary heat transfer through rarefied nonpolar polyatomic gases, confined between parallel plates maintained at different temperatures, is investigated. It is assumed that gas molecules possess both rotational and vibrational degrees of freedom, described by the classical rigid rotator and quantum harmonic oscillator models, respectively. The flow structure is computed by the Holway kinetic model and the Direct Simulation Monte Carlo method. In both approaches the total collision frequency is computed according to the Inverse Power Law intermolecular potential. Inelastic collisions in DSMC simulations are based on the quantum version of the Borgnakke–Larsen collision model. Results are presented for N2, O2, CO2, CH4 and SF6 representing diatomic as well as linear and nonlinear polyatomic molecules with 1 up to 15 vibrational modes. The translational, rotational, vibrational and total temperatures and heat fluxes are computed in a wide range of the rarefaction parameter and for various ratios of the hot over the cold plate temperatures. Very good agreement, between the Holway and DSMC results is observed as well as with experiments. The effect of the vibrational degrees of freedom is demonstrated. In diatomic gases the vibrational heat flux varies from 5% up to 25% of the total one. Corresponding results in polyatomic gases with a higher number of vibrational modes show that even at low reference temperatures the contribution of the vibrational heat flux may be considerably higher. For example in the case of SF6 at 300 K and 500 K the vibrational heat flux is about 67% and 76% respectively of the total heat flux. Furthermore, it is numerically proved that the computed solutions are in agreement with the Chapman–Enskog approximation in a central strip of the computational domain even at moderately large values of the rarefaction parameter, as found in previous investigations. This property has been used to compute the gas thermal conductivity predicted by the adopted models

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Rates of thermal relaxation in direct simulation Monte Carlo methods

Cited by 118 publications

References 19 publications

A macroscopic chemistry method for the direct simulation of gas flows

A macroscopic chemistry method for the direct simulation of gas flows

Development of kinetic-based energy exchange models for noncontinuum, ionized hypersonic flows

Effect of vibrational degrees of freedom on the heat transfer in polyatomic gases confined between parallel plates

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