Numerical and asymptotic analysis of systematically reduced reaction schemes for hydrocarbon flames

Abstract

We intend to close the gap between the numerical description of hydrocarbon flames using a large number of elementary reactions and the asymptotic description using very few reaction steps. To proceed in this direction we first reduce the hydrocarbon chemistry to the smallest number of steps that still provides a realistic flame structure. For the example of methane oxidation these are the four reaction steps

$$CH_4 + 2H + H_2 O = CO + 4H_2$$

((I))

$$CO + H_2 O = CO_2 + H_2$$

((II))

$$2H + M = H_2 + M$$

((III))

$$O_2 + 3H_2 = 2H + 2H_2 O$$

((IV))

Their rates are algebraicly complicated expressions that contain kinetic data from 9 elementary reactions. If standard values for these data are used, the flame velocity of a stoichiometric methane-air flame is calculated as 45.6 cm/sec . The reaction rates maybe simplified to include only data from the five most important reactions

$$\begin{gathered}CH_4 + H \to CH_3 + H_2 \hfill \\CH_4 + OH \to CH_3 + H_2 O \hfill \\CO + OH \rightleftarrows CO_2 + H \hfill \\O_2 + H + M \to HO_2 + M \hfill \\O_2 + H \rightleftarrows OH + O \hfill \\\end{gathered}$$

where the rate expression of the fourth of these reactions is modified. This model is proposed for the asymptotic analysis of the flame structure.

In the simplified model, reactions I, II and IV have a large activation energy while reaction III has zero activation energy. To develop an understanding of the flame structure that results from the four step model, first the structure of a steady plane premixed flame with one-step and two-step kinetics is discussed. Then the basic structure for the four step kinetics is derived.