Nonperturbative analytic theory of V-T and V-V rates in diatomic gases, including multi-quantum transitions

Abstract

The paper addresses the ahalysis, validation, and application of analytic, nonperturbative, semiclassical vibration-translation (V-T) and vibration-vibrationtranslation (V-V-T) rate models f o r atom-diatom and diatom-diatom vibrational molecular energy t r a n s f e r collisions. These "forced harmonic oscillator" (FHO) rate models are corrected and validated by comparison with recent experiments, and with threedimensional semiclassical trajectory calculations f o r N -N 0 -0 and N2-02. which are considered t o be the most reliable theoretical d a t a available. A remarkably good overall agreement i s shown, f o r both the temperature and quantum number dependence of single-quantum and double-quantum V-V-T transitions in the temperature range 2005T58000 K and f o r vibrational quantum numbers 0 9~5 4 0 . I t is demonstrated t h a t the multi-quantum. vibrational energy t r a n s f e r processes occur via a sequential FHO mechanism, as a series 2 2' 2 2'' L e c t u r e r , Dept. of Mechanical Engineering, OSU, Member AIAA 'Associate Research Scientist, Princeton University, Senior Member AIAA 3Professor, Dept. of Mechanical Engineering, OSU, Associate Fellow AIAA 4President, CTSA, Inc., Fellow AIAA Copyright@, 1995 by I.V. Adamovich, '3.0. Macheret, J.W. Rich, and C.E. Treanor Published by t h e American Institute of Aeronautics and Astronautics, Inc. with permission J -I Downloaded by UNIVERSITY OF NEW SOUTH WALES on August 2, 2015 | http://arc.aiaa.org | of virtual single-quantum steps during one collision.An important exception, asymmetric multi-quantum V-V exchange at low temperatures, t h a t occurs via a direct first-order mechanism, is discussed. Analytic thermally averaged FHO V-T and V-V rates are suggested. The FHO model gives new insight into vibrational kinetics and may be easily incorporated into kinetic modeling calculations under conditions when f i r s torder theories are not applicable. 1. I n t r o d u c t i o n Vibrational energy transfer in collisions of diatomic molecules plays a fundamental role in molecular lasers, gas discharges. plasma chemical reactors, highenthalpy gas dynamic flows, and in upper atmosphere chemistry. In these environments, i t creates and maintains strongly nonequilibrium molecular vibrational energy distributions (VDF), which induce nonequilibrium chemical reactions, electronic excitation, dissociation and ionization of diatomics (e.g. see [l-411. The rates of these high energy threshold processes a r e determined by the populations of the high vibrational levels of molecules. These populations are often controlled by vibrationtranslation (V-T) processes,and vibration-vibration-translation (V-V-TI processes, I /involving highly vibrationally excited molecules. In Eqs. (1,2) AB, CD and M represent diatomic molecules and an atom, respectively, and i i f l and f 2 are vibrational quantum numbers. 1' 2' There exists a n extensive literature on the experimental and theoretical study of V-T and V-V-T energy transfer (e.g. see [5-101 and references therein). However, experim...

State-to-state description of reacting air flows behind shock waves

“…Among frequently used models for vibrational energy transitions we can mention the formulas of the Schwartz, Slawsky and Herzfeld theory [35] (usually called SSH-theory) generalized by Gordiets for anharmonic oscillators [36], as well as semi-classical model of the forced harmonic oscillator (FHO) elaborated by Adamovich et al [19] and the correction factor introduced by Park [29] to FHO model to reproduce experimental data. Quasi-classical trajectory calculations for vibrational energy transitions and dissociation in (N 2 , N) and (O 2 , O) systems are carried out in [43][44][45].…”

“…In this case gas dynamic equations in the Euler or Navier-Stokes approximations are coupled to the equations for vibrational level populations of different chemical species and atomic concentrations. This approach received much attention during two last decades for numerical simulations of different flows of air components such as near re-entering bodies [16,17], behind shock waves [18][19][20], in nozzles [21][22][23][24][25], in a boundary layer [26,27] and in a shock layer near re-entering bodies [28], in a shock tunnel nozzle and behind a shock wave in its test section [29]. However, in the majority of papers only two-component mixtures are considered in the state-to-state flow simulations taking into account vibration-dissociation coupling.…”

On the Relation between Population Kinetics and State-to-State Rate Coefficients for Vibrational Energy Transfer

“…The explicit form for the function ( , 0 , ) reads [23]: (8) with the initial and final values given by…”

“…The form of the kinetic relaxation equations and the general properties of their solution are well documented (see e.g. the texts [8][9][10][11]). While a variety of approximations for setting up the relaxation equations is available, a closer look at the simplest of these equations appears worthwhile, in particular when analytical solutions are possible.…”

Analytical models for state-specific diatomic dissociation rate coefficients

“…For inelastic 1000 K transitions of diatomic molecules, analytical models have been proposed for temperature dependent rate coefficients based on the forced harmonic oscillator model [8] and on derivatives of the first-order distorted wave theory of Schwartz, Slawsky, and Herzfeld (SSH), e.g. [9].…”