A theoretical study of flame properties as a function of the characteristics of flame gases

Part I General equations are presented for a method of calculating the net rate of production and the fractional mass-flow rate for each species without introducing the kinetic steady-state approximation. Mathematical problems of smoothness and stability which must be surmounted in any method which avoids the kinetic steady-state approximation are discussed in section 3. To facilitate applications, section 4 and Appendix C give the equations in a form and notation which singles out convenient calculational units and has been found to be adapted to the study of one-dimensional time-independent real flames. The checks used to test the validity of the results are summarized. Section 6 shows that the method's major disadvantage lies in the use of a more complex system of equations, while its major advantages are: (a) it reduces the number of differential equations and thereby simplifies the eigenvalue character of the problem; (b) in contrast to the conventional steady-state approximation, it is consistent in a sense which section 2 shows is required in problems of practical interest. Thus it avoids the most serious inadequacy of the conventional kinetic steady-state approximation: the failure to include the fractional mass flow for an intermediate species. Part II Various methods were applied to numerous numerical integrations of the hydrodynamic equations for a one-dimensional time-independent flame with idealized kinetics and transport properties. The method developed in part I proved to be very convenient for sets of parameters which do not lead to too great deviations from the kinetic steady state. Part II is devoted to an analysis of these results to study: (a) how the kinetic model and the kinetic and transport parameters affect the properties of free-radical flames; (b) various assumptions and approximations which have been used in flame theories. The parameter variations were chosen to test the significance of the assumption of unit Lewis numbers and the use of the kinetic steady-state approximation. To clarify the relation between these results and the behaviour of other systems, the significant aspects of the model are summarized and the equations are cast in suitable dimensionless forms which are used in interpreting numberical results. The total mass-flow rate appears in a dimensionless eigenvalue which is shown to be comparatively insensitive to the kinetic and transport parameters for intermediate species and to vary most from flame to flame, with changes in the thermal conductivity and the specific rates of reactions responsible for the major volume rate of heat release. The analysis then considers the following points: (1) Relations are developed between the functional form of the curves for the mole fractions and fractional mass-flow rates of intermediate species and: (a) the processes of kinetics and diffusion; (b) the way typical intermediates enter the kinetic schema. (2) The shifts in the flame profiles with variations in parameters to increase the deviations from the kinetic steady state are interpreted. (3) Interpretations are given for shifts which parameter variations induce in curves for the relative importance of convection, diffusion, and thermal conduction in maintaining energy conservation. (4) For this flame, it appears that the approximation of constant specific enthalpy could be used to calculate the mole fraction of a major component with an error of at most a few per cent even when the Lewis numbers are not unity. (5) The data show that the ignition temperature approximation would introduce two different serious errors. (6) The suggestion that radical recombination might serve as an important means of energy transport does not apply to this flame. (7) The explicit relation is given between the temperature gradient at the flame holder and the discontinuity in mole fractions in the Hirschfelder-Curtiss model. The discontinuity is not of a physically significant size.