## Abstract

The composite flux method described by Dixon-Lewis, Goldsworthy & Greenberg (1.975 *a*)for the computation of detailed temperature and composition profiles in suitable flames has been applied to the simulation of the properties of a number of fuel-rich and fuel-lean hydrogen-oxygen-nitrogen flame systems. The reaction mechanism proposed by Day, Dixon-Lewis & Thompson (1972), extended to include all the reverse reactions, has been used in the simulation, together with assumed sets of reaction rate and transport parameters. The computed profiles have then been compared with published measurements in flames, covering a wide range of experimental conditions, in order to arrive iteratively at an optimum, self-consistent set of rate parameters which also takes full account of the available elementary reaction rate data from sources other than flames. The flame properties considered in this part of the investigation were (*a*) radical recombination profiles in both fuel-rich and fuel-lean flames, and (*b*) the burning velocities and properties of the main reaction zones of several low temperature, slow burning, fuel-rich flames. Three sets of rate parameters which satisfy all the constraints, and which differ only in detail, are given as sets 1, 2 and 3 in table 4 of the paper. Measurements by Kaskan (1958 *b*) of radical recombination in the hydrogen-lean systems have used the (0, 0) band ultraviolet absorption of the hydroxyl radical in order to measure its concentration. The interpretation of the measurements so as also to be consistent with the remaining flame measurements by other methods additionally allows a determination of the oscillator strength associated with the transition. A band oscillator strengths *f*_{00}— 9.5 x 10^{-4} was found. Following the establishment of the reaction rate parameters, one set of these (table 9) was used to calculate the expected properties of the whole composition range of hydrogen-air premixed flames. In these cases, as well as in the calculations already summarized, either partial equilibrium or kinetic quasi-steady state assumptions must be used in conjunction with the composite flux method. Partial equilibrium assumptions on the reactions

may be employed to relate the concentrations of H, OH, O and O_{2} in calculations where only the concentration profiles in the recombination regions of the flames are required. In the calculation of complete flame properties, quasi-steady state assumptions must be used to relate the concentrations either of O, OH and HO_{2} with that of H (rich flame formulation), or of H, O and HO_{2} with that of OH (lean flame formulation). Subsequent investigation showed that the quasi-steady state assumptions were not completely valid for oxygen atoms everywhere in the flames. Nevertheless, further calculations on several flames by the completely different approach of implicit finite difference solution of the time-dependent flame equations, which does not involve any quasi-steady state assumptions, led to results essentially identical with the original computations. The departures from the quasi-steady state do not therefore significantly affect the flame properties computed by the composite flux method. The general pattern of flame structure which emerges from the complete flame calculations is one in which radicals are produced by chain branching reactions in the hotter regions of the flames, while the major heat releasing reactions occur at lower temperatures. Ahead of the heat release zone there is only a very small preheat zone where heating occurs purely by thermal conduction. This behaviour is different from that of flame models which assume a large preheat zone coupled with a single global exothermic reaction of high activation energy. Comparison of the results of calculations which employed respectively the partial equilibrium and quasi-steady state assumptions showed that the former were valid in the ‘recombination zones’ of the flames for predicting the concentrations of those species which are present in significant amounts. Except in lower temperature flames, for example the 15% hydrogen-air flame and to some extent the 70% hydrogen-air flame, the ‘recombination zones’ extend almost back from the hot boundaries of the flames to the maxima in the hydrogen atom mole fraction profiles. On continuing the flame integrations back from the recombination zones into the main reaction zones, the quasi-steady state overall radical concentrations, represented by *X*_{H} + 2*X*_{O} + *X*_{OH}, where *X* is mole fraction, fall below those calculated with the partial equilibrium assumptions. On the other hand, the distribution of the radical pool between H, O and OH is such that in fuel-rich flames the comparatively small quasi-steady state oxygen atom concentration, and to a lesser extent also the hydroxyl radical concentration, appreciably overshoot their partial equilibrium values. This is referred to as *kinetic overshoot*. It is observable only in sufficiently fuel-rich flames, and for example, there is no observable hydroxyl radical kinetic overshoot in hydrogen-air flames containing less than about 50 % hydrogen, and no similar oxygen atom overshoot in those with less than 30 % hydrogen. A fundamental feature of the flame model used is that it assumes a state of thermal equilibrium to exist at each point in the flames, so that the properties of the gas at each point can be represented by a single temperature. This assumption may not be valid in faster flames, because of the finite velocities of relaxation of thermal disequilibrium between the various degrees of freedom in the system. Properly carried out, a comparison of the computed burning velocities of the hydrogen—air flames with experimental observation should throw light on the possible effect of such slow relaxation on the flame properties. However, an attempt at such a comparison initially raised several questions about the interpretation of burning velocity measurements. These are fully discussed. The hydrogen—air flame having the maximum burning velocity is that containing 41 % hydrogen. At this composition it is concluded that the true burning velocity lies in the range (285 ± 10) cms^{-1}, and hence is not more than 4 or 5 % above the computed value. Finally, the effect on the computed flame properties of (*a*) changes in the diffusion coefficient and (*b*) neglect of thermal diffusion of hydrogen atoms was investigated. Other conditions being equal in fuel-rich hydrogen-air flames near stoichiometric, the neglect of thermal diffusion caused an increase of 5-6% in the computed burning velocity.

## Footnotes

This text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR.

- Received May 10, 1978.

- Scanned images copyright © 2017, Royal Society