Thermochemical Relaxation in Shock Tunnels

Abstract

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

State-to-state and simplified models for shock heated reacting air flows

“…[2,3], for the boundary layer near re-entering bodies in Ref. [4], for the flows in shock tubes [5].…”

Experimental and Numerical Investigation of Hypervelocity Carbon Dioxide Flow over Blunt Bodies

“…In a reflected shock tunnel, chemical and vibrational freezing can occur downstream from the nozzle throat, which has been previously documented to alter the test conditions in a complex manner [16][17][18]. In the present work, the hypervelocity expansion tube (HET) is used to provide additional high-enthalpy CO 2 data and comparison with the numerical result.…”

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

“…In the first case, the vibrational distributions before a shock front are traditionally supposed to be thermal equilibrium with the temperature T 0 whereas in the second case we consider the shock wave appearing in the vibrationally excited air mixture. Such conditions may occur in the shock tube test section when the shock wave originates in a flow after its freezing in a nozzle (see for example [29]), in a flow near complex form bodies or in cases of another kinds of vibrational energy pumping before the shock front. In both considered cases the vibrational level populations just behind the shock front are the same as in the free stream because within the shock front they are assumed to be frozen due to substantial difference in relaxation times (see Eq.…”

“…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.…”