Resonant and Near-Resonant Vibrational—Vibrational Energy Transfer between Molecules in Collisions

Rapp, Donald; Englander‐Golden, Paula

doi:10.1063/1.1725158

Cited by 153 publications

(24 citation statements)

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“…Namely, a collinear collision model taking into account a repulsive intermolecular potential is given by the Schwartz, Slawsky, and Herzfeld (SSH) theory [12,13] and its extensions [14][15][16][17][18][19][20]. This theory is capable to simulate single-jump transition probabilities in conditions where these are much smaller than unity.…”

Section: A Basic Trends Of the Modelsmentioning

confidence: 99%

State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

Silva

Guerra

Loureiro

2007

Journal of Thermophysics and Heat Transfer

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This paper presents the application of the forced harmonic oscillator method to the simulation of state-resolved dissociation processes behind high-temperature shock waves typical of atmospheric reentries. Improvements have been brought to the model, considering a more precise method for the calculation of the different vibrational level energies, therefore increasing the accuracy of the predicted transition probabilities between higher vibrational levels close and above the dissociation limit. The model has been validated against data issued from recent experiments, as well as data issued from semiclassical trajectory calculations for collisions between different species. A good overall agreement is achieved against such other data. A database of reaction rates has been constructed with the purpose of simulating shock-heated nitrogen flows. Dissociation processes behind a shock wave have been simulated for different postshock translational temperatures. At lower temperatures, the well-known ladder-climbing phenomenon is the main dissociation channel behind a shock wave, with dissociation occurring for transitions from the vibrational levels close to the dissociation limit. At higher temperatures, transitions between the different vibrational levels of nitrogen become roughly equiprobable, and the overall range of bound vibrational levels contributes to the dissociation. Nomenclature C k ij = transformation matrix C p = specific heat at constant pressure, J=kg=K C v = specific heat at constant volume, J=kg=K E = level energy, Hz E m = Morse potential well, J h = enthalpy, J=kg J s = Bessel function k B = Boltzmann constant, 1:3806505 10 23 J=K kT = thermal reaction rate, cm 3 =s M = Mach number m = mass, kg m= mass parameter, m AB m C =m AB m C or m AB m CD =m AB m CD P = probability r = internuclear distance, m S VT = vibration-translation steric factor, 4=9 S VV = vibration-vibration steric factor, 1=27 T = macroscopic temperature, K T r = rotational temperature, K T tr = translational temperature, K T tr-r = translational-rotational temperature, K T v = vibrational temperature, K t = time, s Vr = intermolecular potential, J V-T = vibration-translation processes V-V-T = vibration-vibration-translation processes v = vibrational level v = velocity, m=s v = averaged collision velocity, m=s Z = gas-kinetic collisional frequency, Hz = repulsive potential parameter, m 1 = heat capacity ration, C p =C v = mass parameter, m A =m A m B "= two-state first-order V-T transition probability, P1 ! 0 = mass parameter, m A m B =m A m B = two-state first-order V-V-T transition probability, 4P1; 0 ! 0; 1 1=2 = generalized two-state first-order V-V-T transition probability = collision cross section, m 2 ! = vibrational transition frequency, Hz ! e = harmonic oscillator energy, Hz ! e x e = first-order anharmonic oscillator energy, Hz Subscripts f = final vibrational quantum number i = initial vibrational quantum number max = maximum vibrational level before dissociation qbound = vibrational level above the dissociation limit tr =...

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Section: A Basic Trends Of the Modelsmentioning

confidence: 99%

State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

Silva

Guerra

Loureiro

2007

Journal of Thermophysics and Heat Transfer

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“…First, most of these models, such as the Schwartz, Slawsky, Herzfeld ͑SSH͒ theory, Rapp-Englander-Golden model, Sharma-Brau theory etc. [24][25][26][27] are based on first-order perturbation theory ͑FOPT͒, and therefore, cannot be applied at highcollision energies, high-quantum numbers, and for multiquantum processes ͓͉iϪ f ͉Ͼ1 in Eqs. ͑1͒ and ͑2͔͒.…”

Section: Three-dimensional Nonperturbative Analytic Model Of Vibratiomentioning

confidence: 99%

Three-dimensional nonperturbative analytic model of vibrational energy transfer in atom–molecule collisions

Adamovich

Rich

1998

The Journal of Chemical Physics

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Articles you may be interested inThree-dimensional analytic probabilities of coupled vibrational-rotational-translational energy transfer for DSMC modeling of nonequilibrium flows Phys. Fluids 26, 046102 (2014); 10.1063/1.4872336The He-LiH potential energy surface revisited. II. Rovibrational energy transfer on a three-dimensional surface A three-dimensional He-NaH potential energy surface for rovibrational energy transfer studies Reactive and inelastic collisions of H atoms with vibrationally excited water moleculesA three-dimensional semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom has been developed. The model is based on analysis of classical trajectories of a free-rotating ͑FR͒ molecule acted upon by a superposition of repulsive exponential atom-to-atom potentials. The energy transfer probabilities have been evaluated using the nonperturbative forced harmonic oscillator ͑FHO͒ model. The model predicts the probabilities for vibrational energy transfer as functions of the total collision energy, orientation of a molecule during a collision, its rotational energy, and impact parameter. The model predictions have been compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential-energy surface. The comparison demonstrates not only remarkably good agreement between the analytic and numerical probabilities across a wide range of collision energies, but also shows that the analytic FHO-FR model correctly reproduces the probability dependence on other collision parameters such as rotation angle, angular momentum angle, rotational energy, impact parameter, and collision reduced mass. The model equally well predicts the cross sections of single-quantum and multiquantum transitions and is applicable up to very high-collision energies and quantum numbers. Most importantly, the resultant analytic expressions for the probabilities do not contain any arbitrary adjustable parameters commonly referred to as ''steric factors.'' The model provides new insight into kinetics of vibrational energy transfer and yields accurate expressions for energy-transfer rates that can be used in kinetic modeling calculations.

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“…Here the rate coefficients are treated in a form proposed by Rapp and Englander-Golden 19 Kft+'i 1 = » 1 (»+ l)^o? sech^alAE^-AE^.il^ii)) (19) The rate of change of population of a vibrational pseudospecies due to radiative transitions is given by…”

Section: Description Of the Mixlas Analysismentioning

confidence: 99%

Coupled Two-Dimensional Computer Analysis of CW Chemical Mixing Lasers

et al. 1975

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The advantages of utilizing chemical reactions to support laser emission have been recognized for several years. However, a central problem identified in a variety of cw chemical mixing lasers is the dominance of gas-dynamics on the character of the flowing active medium, pointing to the need for a theoretical model that couples the effects of fluid mechanics of mixing with the nonequilibrium kinetics and the cascade of vibrational-rotational laser transitions. As one of the efforts to meet this need, a two-dimensional, rate equation model has been developed. A detailed discussion of the computer model is presented, as well as sample calculations for a representative "cold reaction" HF laser. Comparisons are made with experiment where appropriate. Nomenclature C k= mass fraction of species k c p = specific heat at constant pressure D k = laminar diffusion coefficient for species k A£y = activation energy for reaction j E r = rotational-state energy-specific total enthalpy including heats of formation h k = specific enthalpy of species k A/i k = heat of formation for species k AHj = heat of reaction for reaction j k = Boltzmann's constant, chemical rate coefficient, thermal conductivity K =V-TorV-V rate coefficient L = active optical path length Le -Lewis number = (D k + e d )/(/c + K) m -velocity ratio between primary and secondary m -mass flow rate m k -mass of one molecule of species k M -Mach number n -density ratio between primary and secondary n k *= number density of species k n v = number density of emitter molecules in vibrational state v n v>J -number density of emitter molecules in vibrational state v and rotational state J p = pressure p 0 = total pressure •p, -Prandtl number = c p (n + e)/(/c + /c) q = volumetric rate of heat addition to the gas mixture g rad = volumetric rate of radiative energy emission g rot = rotational partition function R = specific gas constant t R v , v +1 = matrix element for the radiative transition v +1 -> v r^r 2 = reflectivities of left and right mirrors i -time T = static temperaturePresented as Paper 74-224 at the AIAA 12th Aerospace Sciences = total temperature u = velocity in x (flow) direction = average relative velocity between molecules v -velocity in z (transverse) direction w k = mass rate of production of species k per unit volume W v = intracavity flux (sum of right and left running fluxes) for the radiative transition v +1 -»t; Xi -dummy symbol for chemical species i x = coordinate in flow direction z = coordinate transverse to flow in optical direction OL P = pressure-broadened half width OD = Doppler-broadened half width oiij, a-j = stoichiometric coefficients for species i in reaction ; e = eddy viscositŷ d = eddy diffusion coefficient r\ = efficiency K = eddy thermal conductivity /z = coefficient of viscosity v = frequency of emitted radiation £ = line shape parameter = oi p (ln2) ll2 /tx D p = gas density a = specific power (f > = line shape factor

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Resonant and Near-Resonant Vibrational—Vibrational Energy Transfer between Molecules in Collisions

Cited by 153 publications

References 5 publications

State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

Three-dimensional nonperturbative analytic model of vibrational energy transfer in atom–molecule collisions

Coupled Two-Dimensional Computer Analysis of CW Chemical Mixing Lasers

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