A large number of data points for the vibrational relaxation time (pτv in atm sec) of simple systems have been logarithmically plotted vs (T°K)—⅓. It appears that each system is well represented by a straight line, and that most of these straight lines when extended to higher temperatures intersect near the point [pτv=10—8 atm sec, (T°K)—⅓=0.03]. Systems with a small reduced mass μ are exceptions to such a simple convergence, and in an improved scheme, the location of the convergence point is dependent on the reduced mass. Such a presentation has lead to an empirical equation correlating available measurements of vibrational relaxation times: log10(pτv)=(5.0×10−4)μ12θ43[T−13−0.015μ14]−8.00, where θ is the characteristic temperature of the oscillator in K deg. This equation reproduces the measured times within 50% for systems as diverse as N2, I2, and O2–H2. In the worst case thus far, O2–Ar near 1000°K, it is off by a factor of 5.

Systematics of Vibrational Relaxation

A number of chemical-kinetic problems related to phenomena occurring behind a shock wave surrounding an object flying in the earth atmosphere are discussed, including the nonequilibrium thermochemical relaxation phenomena occurring behind a shock wave surrounding the flying object, problems related to aerobraking maneuver, the radiation phenomena for shock velocities of up to 12 km/sec, and the determination of rate coefficients for ionization reactions and associated electron-impact ionization reactions. Results of experiments are presented in form of graphs and tables, giving data on the reaction rate coefficients for air, the ionization distances, thermodynamic properties behind a shock wave, radiative heat flux calculations, Damkoehler numbers for the ablation-product layer, together with conclusions.

Review of chemical-kinetic problems of future NASA missions, II: Mars entries

Plasma-assisted ignition and combustion

A two-temperatur e chemical-kinet ic model for air is assessed by comparing theoretical results with existing experimental data obtained in shock tubes, ballistic ranges, and flight experiments. In the model, one temperature (T) is assumed to characterize the heavy-particle translational and molecular rotational energies, and another temperature (Tv) the molecular vibrational, electron translational, and electronic excitation energies. The theoretical results for nonequilibrium flow in shock tubes are obtained using the computer code STRAP (shock-tube radiation program) and for flow along the stagnation streamline in the shock layer over spherical bodies using the newly developed code SPRAP (stagnation-point radiation program). Substantial agreement is shown between the theoretical and experimental results for relaxation times and radiative heat fluxes. At very high temperatures, the spectral calculations need further improvement. The present agreement provides strong evidence that the two-temperature model characterizes principal features of nonequilibriu m airflow. New theoretical results using the model are presented for the radiative heat fluxes at the stagnation point of 6 m radius sphere, representing an aeroassisted orbital transfer vehicle, over a range of freestream conditions. Assumptions, approximations, and limitations of the model are discussed. Nomenclature = average molecular speed ^/$kT/nm, cm s ~ ! = pre-exponential factor in reaction rate coefficient, cm3mole~ 1 s~ * - average vibrational energy per particle, erg = average vibrational energy per particle under equilibrium, erg = reaction energy, erg

Assessment of two-temperature kinetic model for ionizing air

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

The vibrational energy exchange N2(v=1)+CO(v=0)=N2(v=0)+CO(v=1) should be fast, due to near resonance of the energy levels. We have studied the rate of this exchange relative to the rate of energy transfer from translational to vibrational degrees of freedom in a shock‐heated mixture of 1% CO—99% N2. Vibrational relaxation of the CO is observed by its infrared emission near 2000 cm—1. The density change behind the incident shock is simultaneously observed with an interferometer and gives a measurement of the N2 relaxation time. In the 3200°—4200°K range both methods are applicable; they yield identical relaxation times within the data scatter of ±20%. In contrast, at 3600°K, the vibrational relaxation time of pure N2 is four times that of pure CO. The exchange reaction thus appears fast enough to make the vibrational temperatures of the N2 and CO equal during the vibrational relaxation of the mixture. In the 1900° to 5400°K range, our study gives vibrational relaxation times in seconds for pure N2 (p=1 at...

Vibrational Energy Exchange between N2 and CO. The Vibrational Relaxation of Nitrogen

The vibrational relaxation of oxygen has been studied by shock‐tube interferometry from 600° to 2600°K with the result that at 1 atm pressure the relaxation time τv in seconds is found to be τv=1.49×10—10 exp (133T—½). The presence of up to 2% CO has no observable effect on this time. The previous experimental work of Blackman was probably influenced by impurities at the lower temperatures but the present results are in accord with his at the higher temperatures. Comparison is made with various theoretical calculations and the primary temperature dependence of T—½ is confirmed. It is further noted that Schwartz's Method A of matching the exponential interaction is in better accord with observations than Method B.

Vibrational Relaxation of Oxygen

The vibrational relaxation time of oxygen in several mixtures of O2+He and O2+Ar has been determined by shock‐tube interferometry Using the previously determined data for O2–O2 collisions, the vibrational relaxation time for O2–He and O2–Ar collisions has been found The latter is in agreement with Camac's determination and extends to somewhat lower temperatures For oxygen infinitely dilute in helium, the vibrational relaxation time in atm·sec is given by pτv=53×10—9 exp(60T—½) from 400° to 1600°K

Oxygen Vibrational Relaxation in O2–He and O2–Ar Mixtures

The vibrational relaxation of oxygen containing from ¼% to 2% of CH4, C2H2, and C2H4 has been studied by shock‐tube interferometry. From about 450° to 1300°K the vibrational relaxation zone is not affected by chemical reaction, and the observed oxygen relaxation in mixtures containing only small amounts of hydrocarbon may be accounted for by using the standard formula for a binary mixture and assuming the relaxation time in seconds of oxygen dilute in 1 atm of the hydrocarbon to be given by log10τO2–CH4 = 18T—⅓−8.7, log10τO2–C2H2 = 7.5T—⅓−7.3, and log10τO2–C2H4 = −6.92. For higher temperatures, the exothermic reaction may result in a nonlaminar flow behind an aplanar shock, and the relaxation zone then cannot be resolved interferometrically. For still higher temperatures the relaxation zone is again laminar, but the vibrational excitation of O2 is accelerated by concurrent chemical reactions in the induction zone. From the observation at lower temperatures that τO2–CH4<τCH4 and τO2–C2H4<τC2H4 one is led t...

Donald R. White

Papers

Systematics of Vibrational Relaxation

Vibrational Energy Exchange between N2 and CO. The Vibrational Relaxation of Nitrogen

Vibrational Relaxation of Oxygen

Oxygen Vibrational Relaxation in O2–He and O2–Ar Mixtures

Vibrational Relaxation of Oxygen by Methane, Acetylene, and Ethylene