W. C. Gardiner

Shock‐Tube Study of the Hydrogen—Oxygen Reaction. II. Role of Exchange Initiation

An extended analytical solution to the rate equations for the branching‐chain reactions of the H2–O2 reaction under shock‐tube conditions is presented. Together with an experimental determination of the detection threshold for OH of the Bi (3067) line‐absorption method used in earlier experiments, this solution allows quantitative comparison of calculated and experimental ignition delays. It is shown that calculation and experiment can be brought into agreement with slight modification of chain‐reaction rate coefficients deduced from the results of other studies of the H2–O2 reaction. The essential role of the rate of chain initiation by a path other than diatom dissociation in determining the ignition delays is brought to light. Rate‐coefficient expressions for the chain reactions are suggested and supported.

Transition from Branching‐Chain Kinetics to Partial Equilibrium in the Combustion of Lean Hydrogen‐Oxygen Mixtures in Shock Waves

Concentration profiles of the OH radical in the shock‐initiated combustion of lean hydrogen‐oxygen‐argon mixtures at low pressures (∼0.3 atm) and temperatures (∼1400°K) are found to exhibit pronounced spikes prior to attainment of partial equilibrium. It is shown that this effect is not encompassed within the accepted mechanism for the H2–O2 reaction. Possible reconciliations are presented and discussed.

Rate constant of OH + H2 = H2O + H from 1350 to 1600 K

Transient OH maxima were observed in the shock‐initiated combustion of rich (H2:O2:Ar = 10:1:89) hydrogen‐oxygen‐argon mixtures. Computer simulations of the reaction profiles were used to compare an assumed mechanism and set of rate constants with the experimental results. The expression k3 = 5.2×1013 exp(−27 kJ/RT) cm3 mol−1 · s−1 was derived for the reaction OH + H2 = H2O + H over the temperature range 1350–1600 K. The expression k3 = 107.50T1.77 exp(−12.7 kJ/RT) cm3 mol−1 · s−1 was derived combining our results with those of previous investigations spanning the temperature range 300–1800 K.

Elementary reaction rates from post-induction-period profiles in shock-initiated combustion

Elementary reaction rates were measured by following the reaction profiles in the transition zone between the exponential growth and recombination zones in the shock-initiated combustion of H2:O2:Ar=10:1:89, H2:O2:Ar=1:10:89, H2:O2:CO:Ar=1:5:3:91, and H2:O2:CO2:Ar=5:1:4:90 mixtures in the temperature range 1200°–2500°K. Rate-constant expressions for the reactions O H + H 2 = ⋅ H 2 O + H , O H + O H = H 2 O + O , O H + C O = C O 2 + H , were found to be 5.2×1013 exp (−6.5 kcal/RT) 5.5×1013 exp (−7.0 kcal/RT), and 4.0×1012×exp (−8.0 kcal/RT) cm3/mole/sec, respectively. None of these expressions extrapolate linearly on an Arrhenius graph to the room-temperature data. Possible interpretations of nonlinear Arrhenius graphs are discussed.

Rate constant of OH + OH = H2O + O from 1500 to 2000 K

It was shown several years ago that concentration profiles of the OH radical in the shock‐initiated combustion of lean ([H2]/[O2] = 0.1) hydrogen‐oxygen‐argon mixtures at low pressures (≃ 30 kPa) and high temperatures (1200–2000 K) exhibit transient maxima prior to attainment of partial equilibrium. At that time, the maxima could not be accounted for quantitatively in terms of the accepted mechanism of the H2–O2 reaction. The profiles have been reanalyzed utilizing more sophisticated computational techniques and increased knowledge of the reaction mechanism. The occurrence of maxima at temperatures above 1500 K was found to depend upon the ratio of the rate constants of the elementary reactions O+H2→OH+H and OH+OH→H2O+O. Using the rate constant expression 1.6×1014 exp(−56.6 kJ/R T) cm3 mol−1 s−1 for the former reaction, the rate constant expression for the latter was found to be 5.5×1013 exp(−29 kJ/R T) cm3 mol−1 s−1. This latter expression does not extrapolate linearly on an Arrhenius plot to the availab...

Cross sections for reorientation and rotational relaxation of oxygen

Experimental measurements of the collisional EPR linewidths of molecular oxygen are reported for 17 X‐band transitions at resonance magnetic fields up to 0.7 T. In addition to the expected gradual decrease of linewidth with rotational quantum number, a dependence upon orientation quantum number is also observed. The EPR linewidths are comparable to the higher values among the microwave results previously reported for the 60 GHz transitions and substantially larger than the corresponding Raman data.

Chemical Kinetics of the Shock‐Initiated Combustion of Hydrogen at High Pressure and Low Temperatures

The ignition mechanism of the hydrogen–oxygen explosion at temperatures near 1000°K and pressures greater than 1 atm was investigated theoretically using the complete analytic solution to the kinetic equations of an abbreviated, linearized mechanism and numerical integration of the full conventional mechanism for these conditions. It was found that the analytic solution of the simplified mechanism is capable of only a qualitative description of the second limit effect observed in reflected shock experiments on ignition delays, and cannot be forced to yield quantitative agreement. The numerical integration can be forced to give quantitative agreement, but only at the cost of accepting rate‐constant expressions which do not allow quantitative description of the simpler ignition phenomena at higher temperatures and lower pressures. An exception to these conclusions is the use of analytic expressions for interpretation of branching rates early in the induction zone, which appears to be valid within wide limits.

Shock‐Tube Study of OH (2Σ — 2Π) Luminescence

OH (2Σ — 2Π) emission was studied in 1500‐2800°K incident shock waves through low‐pressure H2‐O2‐Ar mixtures with 100‐fold variation in H2/O2 ratio. The transition from chemiluminescent to thermal excitation was found to occur near 2000‐2200°K for these conditions. Intensities measured during the exponential growth period and in the partial equilibrium state following combustion were correlated with possible elementary reactions producing OH(2Σ).

Thermochemical properties of atoms and molecules in specific quantum states

Procedures are described for computing thermochemical properties in the ideal gas state for atoms and molecules in specific quantum states, and in thermal or nonthermal distributions over specific groups of quantum states. Formulas are given to generate values in the JANAF‐compatible format. Applications to electronic states of atoms, vibrational and vibration–rotational states of diatomic molecules, and vibrational states of polyatomic molecules are given as illustrations. It is shown that the choice of procedure for obtaining partition functions has only a minor effect upon the accuracy of the results, the major factors being the energy of the specified state(s) and the accuracy to which the heat of formation of the species itself is known. Procedures are developed for describing systems in which species in specified quantum states are considered together with the same species in a Boltzmann internal distribution, and for expressing the thermochemical properties of state‐selected species as polynomials ...

Collisional linewidths of the EPR spectrum of molecular oxygen

Pressure broadening of the X‐band EPR spectrum of molecular oxygen was studied in an apparatus designed to minimize systemtic and random errors in the collisional linewidth. Results are reported for 16 lines with rotational quantum number N ranging from 1 to 11. No explicit M dependence of linewidth at the 1% accuracy level was found except that the N = 1, J = 1 line with initial M value of 0, which is at a substantially higher field than the other N = 1 lines, was found to be significantly broader than the other N = 1 lines. Otherwise, a slight but definite decrease of width with increasing field was found, presumably due to magnetic alignment of O2. Over the 0.5 to 2.3 Torr pressure range studied there was a remarkable variation of width with pressure, implying a small negative linewidth at zero pressure, for which we were unable to find a satisfactory explanation in theory or systematic measurement errors.