Boundary-value solutions of the one-dimensional laminar flame propagation equations

Abstract

The classic flame problem has been treated as a boundary-value problem using powerful new techniques for difficult multi-variable equations. Efficient solution methods and general computer programs for arbitrary chemical species and reactions have been developed. Although simplified transport equations were used, the approach in readily extended to any level of complexity justified by the transport and kinetic data available. The flame systems have been studied initially: O 3 O 2, H 3 Br 3 + and H 2 O 3. Solution have been obtained for the ozone decomposition flame at concentrations including 100% O 3. The calculated values of the flame velocity were about twice the experimental ones, in contrast to previous good agreement in early computations by other workers. The solution techniques are now well established so that the kinetic and transport data as well as the basis of the comparison with the experimental data must be suspect. Results on the H 2 Br 2 flame indicate that the steady-state approximation in flames is largely inapplicable, and in any case, is of little help in a general approach. Solution profiles for H 2 O 3 indicate that HO 2 and H 2O 2 are kinetically important species under many conditions in H 2 O 2 flames. In all the above flames, reasonable solutions have been found with a single parameter (eigenvalue), the flame velocity. The techniques which have been developed should make feasible inter-relations of overall flame structure data and elementary kinetic steps heretofore impossible. The feasibility of complex multi-reaction kinetics in more complicated flow situations involving boundary value problems, such as boundary layers and imperfectly stirred reactors, is also indicated by the present work.