DETAILED KINETIC MODELING OF SOOT FORMATION DURING SHOCK-TUBE PYROLYSIS OF C₆H₆: DIRECT COMPARISON WITH THE RESULTS OF TIME-RESOLVED LASER-INDUCED INCANDESCENCE (LII) AND CW-LASER EXTINCTION MEASUREMENTS

Abstract

The results of calculations of the main parameters of the soot formation process (τ, k _f, SY, and r _m) carried out with the use of the detailed kinetic model of soot formation are compared with the experimental measurements of these parameters by the continuous-wave (CW)-laser extinction technique and by the time-resolved laser-induced incandescence (LII) method during C₆H₆ pyrolysis behind reflected shock waves. The detailed kinetic model of soot formation that is developed incorporates the gas-phase mechanisms of acetylene pyrolysis and the mechanisms of formation of polyaromatic hydrocarbons, polyyne molecules, and pure carbon clusters. It combines the H abstraction/C₂H₂ addition and polyyne pathways of the soot formation process. The formation, growth, and coagulation of soot precursors and soot particles are described within the framework of the discrete Galerkin technique based on an error-controlled expansion of the size distribution function of heterogeneous species into the orthogonal polynomials of a discrete variable (in particular, the number of monomers in the heterogeneous particle) that makes it possible to preserve a discrete character of any elementary transformations of heterogeneous particles and to describe them as elementary chemical reactions for the heterogeneous particles of all sizes. The comparison of the calculations with the experimental measurements of the induction time τ, observable rate of soot particle growth, k _f, and soot yield SY by the CW-laser extinction method in the pyrolysis of benzene/argon mixtures in shock-tube experiments clearly demonstrates that the coincidence is quantitatively good for all the main parameters of soot formation. A particular difference between the values of the mean soot particle radius r _m experimentally measured by the time-resolved LII technique and calculated with the help of the detailed kinetic model is observed at the low and high temperatures. The results presented demonstrate the current level of the predictive capabilities of the detailed kinetic model of soot formation and the reliability of the time-resolved LII technique for the quantitative determination of the soot particle sizes.

Keywords:

• soot formation
• shock-tube pyrolysis
• detailed kinetic modeling
• HACA and polyyne pathways of soot formation
• laser-induced incandescence
• CW-laser extinction measurements

This work was supported by the Deutsche Forschungsgemeinschaft and by the Russian Foundation for Basic Research, Project Nos. 01-03-32034, 02-03-04002, and 02-03-04005.

Notes

^aRate coefficients are presented in the form k = A T ^b exp(−E _a/RT).

^bIndex n denotes the number of carbon atoms, which are incorporated into the particle in each act of interaction with carbon-containing gas-phase species.

^cNotation PR[1] means the concentration of the precursors of soot particles formed by the HACA pathway containing n carbon atoms (n = 28–32) without active sites on their surface, P[1] is the concentration of the precursors with active sites on their surface (n = 24–32).

^dRate coefficient is chosen to be similar to the rate coefficient of soot particle inception proposed by Appel et al. (2000).

^eThis reaction was added into the kinetic scheme of soot precursor formation because it considerably improves the coincidence of the results of calculations and experimental measurements even if a rather low value of the rate coefficient is chosen for this reaction.

^fNotation P[N] means the concentration of soot particles with active sites on their surface after N acts of interaction with various carbon-containing gas-phase species. The number of carbon atoms in such a particle is determined by index n.

^gRate coefficient is chosen to be similar to the rate coefficient of soot particle growth proposed by Appel et al. (2000).

^hNotation PR[N] means the concentration of soot particles without active sites on their surface. (Index N corresponds to the number of interactions of active soot particles P[N] with various carbon-containing gas-phase species.) The number of carbon atoms in such a particle is determined by index n.

ⁱRate coefficient is chosen to be similar to the rate coefficient of transformation of soot particles proposed by Appel et al. (2000).

^jNotation S[N] means the concentration of soot particles with active sites on their surface formed via the polyyne pathway of soot formation and via the transformation of the P[N] particles into S[N] particles.

^kThe rate coefficient is chosen to be similar to the rate coefficient of transformation of the precursors of pure carbon particles into soot-like particles proposed in the work of Agafonov et al. (2002).

^lThe rate coefficient of coagulation is chosen to be the same as those proposed by Agafonov et al. (2002).

^mNotation C[1] means the concentration of the precursors of soot particles formed by the polyyne pathway containing n carbon atoms (n = 16–22) with active sites on their surface.

ⁿThe rate coefficients were taken from the work of Krestinin, (1994, 1998).

^oNotation C[N] means the concentration of the precursors of soot particles formed by the polyyne pathway with active sites on their surface after N acts of interaction with various carbon-containing gas-phase species.

^pThe rate coefficients were constructed to be similar to the rate coefficients of interactions of the corresponding gas-phase species with large molecules.

^qThe rate coefficient is chosen to be equal to the rate coefficient of coagulation.