A flamelet-based relaxation model for polycyclic aromatic hydrocarbons in turbulent flames

In this paper, the response of different species to turbulent unsteadiness is investigated utilizing the 1D unsteady laminar diffusion flamelet model. Turbulent effects are modeled solely through a abrupt change in the scalar dissipation rate. Steady-state flamelets are perturbed by the modeled turbulent effects. One-dimensional flamelet calculations assuming unity-Lewis number for all species are performed. Based on the numerical results, relations between the chemical source terms and species mass fractions are examined for various representative species. It is found that the smallest turbulent time scale remains much larger than that of the gaseous phase chemistry for some small species. The steadystate flamelet assumption for these species is well justified and their mass fractions can be pre-tabulated using the flamelet library legibly. On the other hand, PAH chemistry is relatively slow, and these PAH species cannot react instantaneously to the abrupt change in the local scalar dissipation rate. Based on the above considerations, a relaxation model is proposed for the chemical source terms of light species, species of moderate molecular weights, and heavy hydrocarbons. These source terms can be decomposed into a positive production term and a negative consumption term. The production term is observed to be constant for a given mixture fraction value, whereas the consumption term is found to be linearly dependent on the local species concentration. The dependence of the consumption term on the species mass fraction is found to be determined only by the scalar dissipation rate after its abrupt change. This observation suggests that the relaxation model can be fully pre-tabulated using the results of steady state flamelets. Based on the relaxation results, the validity of different chemistry tabulation models is assessed.