Thermochemical relaxation phenomena in the shock tunnel nozzle and behind a normal shock wave formed in its test section are investigated theoretically in one dimension using a state-to-state description. Test gas is assumed to be air containing hydrogen as an impurity. The state-to-state rate coefficients calculated by the forced harmonic oscillator model of Adamovich, Macheret, Rich, and Treanor ("Vibrational Energy Transfer Rates Using a Forced pages 57-65) are multiplied by correction factors to numerically reproduce the existing experimental data on vibrational relaxation times and dissociation rates. The calculations show that freezing in the nozzle causes the relaxation behind a normal shock wave to be generally different from that in free flight. In a shock tunnel with a nozzle length of 5 meters operating at a reflected-shock pressure of 1000 atmosphere, standard, free-flight conditions are simulated fairly closely in its test section.
Nomenclature
A= nozzle cross-sectional area a i = coefficients in Eq.(1) C = average molecular speed, cm=s c = continuum (free) state E v = energy level of state v, cm 1 , or erg H = enthalpy, erg=g or MJ=kg I = radiation intensity, arbitrary units Kv; v 0 = rate coefficient for v-to-v 0 transition, cm 3 =s k = Boltzmann constant 1:3806 10 16 erg=K M = colliding species m = mass of one atom or molecule, g n = number density, cm 3 p = pressure, dyne=cm 2 or atm T = translational-rotational temperature, K T ve = hypothetical vibrational temperature of a harmonic oscillator having the same vibrational energy as the given vibrational distribution T v1 = vibrational temperature by ratio of v 1 to v 0 state populations u = flow velocity, cm=s u s = shock velocity in a shock tube, cm=s v = vibrational quantum number, or initial state v max = maximum vibrational quantum number v 0 = final state vibrational quantum number X = mol fraction of species X x = distance from throat or shock wave, cm = cross section, cm 2 v = vibrational relaxation time, s Subscripts m = molecule p = peak in radiation 0 = settling chamber * = nozzle throat