Flamelet modelling of non-premixed turbulent combustion with local extinction and re-ignition

Extinction and re-ignition in non-premixed turbulent combustion is investigated. A flamelet formulation accounting for transport along mixture fraction iso-surfaces is developed. A new transport term appears in the flamelet equations, which is modelled by a stochastic mixing approach. The timescale appearing in this model is obtained from the assumption that transport at constant mixture fraction is only caused by changes of the local scalar dissipation rate. The space coordinates appearing in this term can then be replaced by the mixture fraction and the scalar dissipation rate. The dissipation rate of the scalar dissipation rate appears as a diffusion coefficient in the new term. This is a new parameter of the problem and is called the re-ignition parameter. The resulting equations are simplified and stochastic differential equations for the scalar dissipation rate and the re-ignition parameter are formulated. The system of equations is solved using Monte Carlo calculations. The results show that the newly appearing transport term acts by modifying the S-shaped curve such that the lower turning point appears at higher scalar dissipation rate. In an a priori study, predictions using this model are compared with data from a direct numerical simulation of non-premixed combustion in isotropic turbulence simulating extinction and re-ignition.