State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

Abstract

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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