State-to-state rate constants and rotational relaxation time in nitrogen

Sharafutdinov, R. G.; Belikov, A. E.; Strekalov, M.L.; Storozhev, A.V.

doi:10.1016/0301-0104(96)00030-4

Cited by 24 publications

(10 citation statements)

References 14 publications

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“…10 Rotational distributions in free jets, measured by different laser spectroscopic techniques, have also been used to obtain these state-to-state rate constants in systems like CO-He, 11 HF-He, 12 CO-Ar, 13 CS 2 -Ar, 14 or N 2 -N 2 . 15 However, in these works, some kind of empirical scaling law was imposed to relate the different state-to-state rate constants. So far, the most straightforward experimental method to determine state-to-state collisional rate constants is based in populating selected rotational levels by stimulated Raman-pumping, 16 but this technique provides information only about rotational states within the vϭ1 vibrational state, and is difficult to apply below room temperature.…”

Section: Introductionmentioning

confidence: 99%

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3<T<20 K)

Maté

Thibault

Ramos

et al. 2003

The Journal of Chemical Physics

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We present an experimental determination of state-to-state rotational-translational ͑RT͒ rate constants of N 2 :He collisions in the vibrational ground state as a function of temperature in the range 3ϽTϽ20 K. Raman spectroscopy in supersonic expansions of N 2 /He mixtures is used to determine the primary data that, together with the N 2 :N 2 state-to-state RT rates previously determined ͓Ramos et al., Phys. Rev. A 66, 022702 ͑2002͔͒, are needed to solve the master equation according to a procedure that does not impose any particular scaling law. We also report first principle calculations of the N 2 :He state-to-state RT rate constants performed using the full three-dimensional potential energy surface of Reid et al. ͓J. Chem. Phys. 107, 2329 ͑1997͔͒, in the 3ϽTϽ300 K temperature range. The coupled-channel method, and the coupled-states approximation, were applied in the low ͑0-610 cm Ϫ1) and in the high ͑610-1500 cm Ϫ1) energy limits, respectively. A good agreement between theoretical and experimental results is found in the temperature range where comparison is possible.

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Section: Introductionmentioning

confidence: 99%

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3<T<20 K)

Maté

Thibault

Ramos

et al. 2003

The Journal of Chemical Physics

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“…Ultimate progress in the field will certainly require more detailed calculations and thorough measurements of the local jet parameters with good spatial resolution. 20,21 Theoretical values of the cross sections for N 2 rotationally inelastic collisions based on a direct solution of the threedimensional (3D) equations of motion with a realistic intermolecular potential have been obtained using the method of quasiclassical trajectories (QCT), [22][23][24][25] but are restricted to date to temperatures above 100 K. For lower temperatures, theoretical estimates have been worked out with semiempirical models developed mostly from higher-temperature data (see refs [26][27][28][29] and references therein). Given the existing difficulties for the application of rigorous theoretical treatments, one must resort in general to very simple models involving drastic approximations in order to derive relaxation data from the measurements.…”

Section: Introductionmentioning

confidence: 99%

Low-Temperature Rotational Relaxation of N₂ Studied with Resonance-Enhanced Multiphoton Ionization

et al. 1999

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The rotational relaxation of molecular nitrogen has been investigated down to temperatures of about 5 K with a combination of resonance-enhanced multiphoton ionization and supersonic beam time-of-flight techniques. The average rotational relaxation cross section obtained shows a maximum value of 50−60 Å2 at 20−30 K. For lower temperatures this cross section decreases and reaches a value smaller than 30 Å2 at T ≈ 5 K. For temperatures above 30 K, the cross section decreases slowly as the temperature grows and converges approximately to the determinations from other non-jet techniques and theoretical estimates available for T > 80 K. The results are compared to previous measurements from other groups using different methods, and general good agreement is found. However, we observe a significant discrepancy with some of the data from electron-beam-induced fluorescence that yield much larger cross sections for temperatures lower than 30 K.

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“…24 In theory, these MD results could be used to form a state-resolved model for translational-rotational energy exchange in nitrogen (examples of such models can be found in Refs. [26][27][28], or alternatively to determine complete post-collision state probability density functions to be used with a cross-section based model such as the Dynamic Molecular Collision (DMC) model. 29 However, the premise of the current article is that such physically complex (and computationally expensive) models are not required to accurately describe translational-rotational energy transfer.…”

Section: Introductionmentioning

confidence: 99%

A Nonequilibrium-Direction-Dependent Rotational Energy Model for use in Continuum and Stochastic Molecular Simulation

Zhang

Valentini²,

Schwartzentruber³

2013

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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A new rotational energy exchange model for direct simulation Monte Carlo (DSMC) and multi-temperature Navier-Stokes methods is presented. The DSMC model is based only on collision-quantities and reduces to a rotational collision number in the continuum limit, applicable for use with the Jeans relaxation equation. The model is formulated based on recent Molecular Dynamics (MD) simulations of rotational relaxation in nitrogen (Valentini et al, Phys. Fluids 24, 106101 (2012)) and accounts for the dependence of the relaxation rate on the direction to the equilibrium state. This enables a single parameterization of the model to accurately simulate rotational relaxation in both compressing and expanding flows, unlike the widely used Parker model. The DSMC model is simple to implement, numerically efficient, and accurately reproduces a range of pure MD solutions including isothermal relaxations, normal shock waves, and expansions. This demonstrates that the complexity of a state-resolved model is not required for translational-rotational relaxation. A general form for the energy distribution function that should be sampled for post-collision states (using the Borgnakke-Larsen approach) is presented. This general formulation ensures detailed balance and equipartition of energy at equilibrium for any collision-quantity based DSMC model and also explains the behavior of prior rotational models in the literature. The model formulation is also general to the inelastic collision selection procedure used, which is shown to be a crucial aspect in implementing a DSMC collision model. Finally, the increased accuracy of a collision-quantity based model compared to a cell-averaged model is demonstrated by comparing rotational energy distribution functions within a shock wave against a pure MD solution.Nomenclature ∆t DSMC simulation time step ∆x DSMC simulation cell size Γ(·) Gamma function ε r (t) average rotational energy at time t ε * r (t) instantaneous equilibrium rotational energy at time t λ molecular mean free path µ dynamic viscosity ω VHS collision model viscosity parameter ρ density τ c molecular mean collision time τ r characteristic rotational relaxation timẽ p rot intermediate rotational inelastic collision probability ε c total collision energy of a collision pair ε r molecular/particle rotational energy ε r molecular/particle rotational energy after collision ε t molecular/particle translational energy ε t molecular/particle translational energy after collision ζ r rotational degrees of freedom ζ t translational degrees of freedom a Parker model rotational collision number parameter b Parker model rotational collision number parameter C connection factor to link p rot andp rot in DSMC simulation d ref VHS collision model reference diameter k B Boltzmann constant n NDD model rotational collision number parameter p pressure p rot DSMC rotational inelastic collision probability T * NDD model/Parker model rotational collision number parameter T r (t) rotational temperature at time t T t (t) translational temperature at ...

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State-to-state rate constants and rotational relaxation time in nitrogen

Cited by 24 publications

References 14 publications

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3<T<20 K)

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3<T<20 K)

Low-Temperature Rotational Relaxation of N₂ Studied with Resonance-Enhanced Multiphoton Ionization

A Nonequilibrium-Direction-Dependent Rotational Energy Model for use in Continuum and Stochastic Molecular Simulation

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State-to-state rate constants and rotational relaxation time in nitrogen

Cited by 24 publications

References 14 publications

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3&lt;T&lt;20 K)

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3&lt;T&lt;20 K)

Low-Temperature Rotational Relaxation of N2 Studied with Resonance-Enhanced Multiphoton Ionization

A Nonequilibrium-Direction-Dependent Rotational Energy Model for use in Continuum and Stochastic Molecular Simulation

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Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3<T<20 K)

Experimental and theoretical determination of rotational-translational state-to-state rate constants for N2:He collisions at low temperature (3<T<20 K)

Low-Temperature Rotational Relaxation of N₂ Studied with Resonance-Enhanced Multiphoton Ionization