The formation of OH in the shock wave induced combustion of H2 and O2 has been measured by oscillographically recording the absorption of ultraviolet OH line radiation. The main features of the reaction course are: (1) an induction period whose length, ti, varies inversely with [O2], (2) an increase in the product [O2] ti as ti becomes short compared to the vibrational relaxation time of O2, and (3) at the end of the induction period, a sigmoid rise of [OH] to a maximum, followed by a slow decrease. ti has been studied over the ranges: 1100°≤T≤2600°K, 1.3×10—5≤[O2]≤8.0×10—4 mole/1, 0.25≤[H2]/[O2]≤5., 0.004≤[O2]/[Ar]≤0.20, and 5≤ti≤500 μsec. Agreement between incident and reflected shock experiments has been demonstrated. According to the branching chain mechanism known from explosion limit studies, ti is governed by the rate of H+O2→ lim k1OH+O according to: 2 k1[O2]ti=2.303 n, where n is the number of decades by which [OH] increases between initiation and the end of the induction period. The values of [O2]ti, which is nearly proportional to 1/k1, are summarized by: log10([O2]ti) (mole 1—1 sec)= —10.647+(3966±625)/T. The value k1=1.4×109 deduced at 1650°K from this work is combined with data near 800°K to give: k1=3×1011 exp(—17.5±3. kcal/RT) (mole/1)—1 sec.—1. The relation of these results to detonation experiments is discussed.

Kinetic Studies of Hydroxyl Radicals in Shock Waves. II. Induction Times in the Hydrogen-Oxygen Reaction

Self‐sustaining and overdriven detonations in 2H2 + O2 + 2CO have been studied in a shock tube at initial pressures from 0.01 to 1.4 atm. Measurements have included pressure, density obtained interferometrically, and luminosity whose intensity is shown to be proportional to [CO][O]. Strongly overdriven waves are one dimensional and are followed by the calculated equilibrium state. Self‐sustaining detonations are followed by a state in which the pressure and density are lower than calculated according to the usual C‐J hypothesis, and in which the flow is supersonic with respect to the wave front. Furthermore, the flow in and behind the reaction zone invariably appears to be turbulent. In an examination of the implications of this turbulence, a Chapman‐Jouguet detonation is considered to be one with the minimum velocity of propagation which will satisfy the conservation relations for turbulent flow at the rear of reaction zone. It is shown that this minimum (C‐J) velocity is slightly greater than that calculated assuming turbulence is not present, and that the final state attained following the decay of turbulence can lie either on the ``strong'' or ``weak'' detonation branch of the Hugoniot curve. Intermediate states, including the conventionally calculated C‐J state, in general do not represent stable solutions. The self‐sustaining detonation, which must correspond to the weak detonation solution, appears as a special case of a C‐J detonation.

Turbulent Structure of Gaseous Detonation

The measured velocity of gaseous detonation waves is less than that predicted by the Chapman‐Jouguet plane wave theory. The velocity deficit (difference between theoretical and measured velocities) has been found earlier to vary inversely with the tube diameter and initial pressure. A quantitative explanation of this effect is advanced by determining the growth of the viscous boundary layer on the tube wall and its effect upon the flow in the reaction zone of the detonation front. It is proposed that the boundary layer displacement effect within the reaction zone produces a uniform flow divergence throughout the detonation front. The velocity deficit due to this two‐dimensional flow is determined, using measured values of reaction zone thickness. The agreement of the velocity deficit with measured values is within a factor of two for the five hydrogen‐oxygen‐inert gas mixtures and one acetylene‐oxygen mixture for which sufficient data are available.

Two‐Dimensional Gaseous Detonations: Velocity Deficit

An electron beam densitometer has been used to investigate the behavior of a conventional 1⅛‐in. i.d. shock tube operating at initial pressures of the order of 1 mm Hg. These experiments show that such a shock tube does not perform as predicted by simple theory. Most of the experiments were performed in argon with shock Mach numbers ranging between 1.2 and 7.0. The most striking observation was that for a given shock velocity, Ms = 1.6, the distance between the shock wave and contact surface as observed at the densitometer was proportional to initial pressure and independent of expansion chamber length over a tenfold range of tube length. At an initial pressure of 0.5 mm Hg the time interval between the arrival of the shock and the contact surface varied between 600 μsec at Ms = 1.2 and 20 μsec at Ms = 7.0. The diaphragm pressure ratio (Ar ‐ Ar) required to produce a shock of velocity Ms = 1.6 varied from 200 at an initial pressure of 0.25 mm Hg to 20 at an initial pressure of 50 mm Hg. For a given diaphragm pressure ratio the shock velocity decreased with distance in a highly nonlinear manner. The density behind the shock wave was observed to increase significantly before the arrival of the contact surface under all conditions. This surprising shock‐tube behavior is believed to be related to severe laminar boundary layer development behind the shock wave at low initial pressures.

Shock‐Tube Performance at Low Initial Pressure

Detonations in hydrocarbon fuel blends

Detonation velocities have been measured in mixtures of cyanogen and oxygen at several pressures and in tubes of several diameters, with a reproducibility of the order of 0.1 percent. Thermodynamic calculations of detonation velocities were carried out for several assumed heats of dissociation of nitrogen and of carbon monoxide and for several experimental conditions. Methods are described for the extrapolation of experimental velocities to the limit of an infinite plane wave in ideal gases. The comparison of these extrapolations with thermodynamic calculations gives best agreement for DN2=9.76 ev and DCO=11.11 ev, the difference of experimental and calculated velocities averaging to 0.08 percent, with a standard deviation of 0.3 percent, which agrees with the predicted standard deviation. Several lower dissociation energies, which have been recommended on the basis of spectroscopic studies and of appearance potentials, give such poor agreement with these experimental data that they constitute very strong...

Gaseous Detonations. III. Dissociation Energies of Nitrogen and Carbon Monoxide

A simple system is described for determining the velocity of detonation or strong shock waves, with temperatures above 3000°K, by using the conductivity behind the wave. Wave contact is made by two 36‐mil wires set 0.1 inch apart in a Teflon plug mounted in the experimental tube. When a wave passes, signals are produced across a 30‐K resistor in series with these wires and a 0.001 μf capacitor charged to 300 v. Any number of circuits may be paralleled across a single signal resistor if a diode is added to each circuit to prevent signal deterioration. The arrival time of a wave at a pin can be determined with an accuracy of almost 10−8 sec from an oscilloscope record of the signals. The principal advantages of this system are excellent space resolution and very simple basic circuitry. An amplifier is described which can be used with an individual pin circuit to fire a thyratron and extend the range of applicability of this system to waves with temperatures as low as 1000°K.

Precision Measurement of Detonation and Strong Shock Velocity in Gases

Density ratios across shock waves in a 0.85 Kr+0.15 C2N2 mixture at an initial pressure of 50 mm Hg and room temperature, have been determined with an x‐ray densitometer as a function of shock velocity. The heat required to dissociate cyanogen into two CN radicals D(C2N2) has been determined to be 145±6 kcal/mole by comparing the experimental data with curves of density ratio vs shock velocity calculated as a function of D(C2N2). Dissociation energies of 174±3 kcal/mole for CN and 129±3 kcal/mole for HCN forming H and CN, and a heat of formation of 109±3 kcal/mole for CN, were obtained by the application of Hess's law to the appropriate chemical reactions using this value of D(C2N2) and the currently accepted values for the dissociation energy of nitrogen (225 kcal/mole) and the heat of sublimation of graphite (170 kcal/mole). The value of D(HCN) was confirmed by analogous density‐velocity measurements on shock waves in a 0.85 Kr+0.15 HCN mixture. A rate constant for the recombination of CN to form C2N2 at 2900°K was deduced from the variation of density with time behind the shock. The value obtained was of the order of 1×109 (mole/liter)—2 sec—1.

Dissociation Energy of Cyanogen and Related Quantities by X‐Ray Densitometry of Shock Waves

Precision Flash X‐Ray Determination of Density Ratio in Gaseous Detonations

Detonation velocities were accurately measured in acetylene‐oxygen mixtures ranging in composition from 7 to 90 percent acetylene at 1 atmos total pressure. The velocities rise very sharply with concentration to 50 percent acetylene, then drop equally sharply to about 70 percent and from then on rise slightly to 90 percent. The thermodynamic calculations of velocities, in which no adjustable parameters were used, are in perfect agreement with experimental data in the range of 25 to 50 percent acetylene. The velocity at 7 percent, near the detonability limit, is distinctly higher than the calculated value. The calculated velocities from 50 to 90 percent acetylene lie on a smooth curve, showing no break near 70 percent acetylene as do the experimental data. They are higher than the experimental velocities, except at 85 to 90 percent acetylene, where the two curves join again. The disagreement in the intermediate composition range persists when the velocities are recalculated assuming a low heat of sublimation of carbon. A hypothesis is advanced that no solid carbon is formed in detonation waves of mixtures containing up to 70 percent acetylene, because of delays in the nucleation process. The velocities calculated with the assumptions of gaseous equilibria and of the formation of supersaturated carbon vapor, are in acceptable agreement with observations.

Herbert T. Knight

Papers

Gaseous Detonations. III. Dissociation Energies of Nitrogen and Carbon Monoxide

Precision Measurement of Detonation and Strong Shock Velocity in Gases

Dissociation Energy of Cyanogen and Related Quantities by X‐Ray Densitometry of Shock Waves

Precision Flash X‐Ray Determination of Density Ratio in Gaseous Detonations

Gaseous Detonations. IV. The Acetylene‐Oxygen Mixtures