A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames

In this paper, the chemical response of different species to turbulent effects is investigated in the context of one-dimensional laminar non-premixed flamelets. Turbulent effects are modeled as abrupt changes in the scalar dissipation rate. One-dimensional unsteady flamelet calculations assuming unity-Lewis number for all species are performed for an ethylene/air configuration. From the time-evolution of the species mass fractions, it is found that transient effects are not substantial for radicals such as OH$\mathrm{OH}$ and H$\mathrm{H}$, and species such as CO,_CO2$\mathrm{CO}\text{,}{\mathrm{CO}}_2$ and _C2H2${\mathrm{C}}_2{\mathrm{H}}_2$, consistent with their small characteristic chemical time scales. The steady state flamelet assumption for these species is well justified and their mass fractions can be pre-tabulated using the steady state flamelet solutions legibly. On the other hand, aromatic species are characterized by relatively slow chemistry, and substantial transient effects are observed for these species. The evolution of their mass fractions and chemical source terms are studied through a reaction flux analysis. Specifically for Polycyclic Aromatic Hydrocarbons (PAH), the chemical production terms are found to be linearly proportional to the mass fraction of smaller aromatic species, and the chemical consumption terms are found to be linearly proportional to their own mass fractions. Based on the unsteady flamelet results, the validity of various existing flamelet-based pre-tabulation methods is examined, and a new linear relaxation model is proposed for PAH. The proposed relaxation model is validated through the unsteady flamelet formulation, and results are compared against full chemistry calculations.