A flame index for the lagrangian probability density function method

To separate the nonpremixed and premixed modes in partially premixed flame simulations with the transported PDF method, a flame index is proposed based on the subgrid mixing rate between Lagrangian particles. The mixing rate on local equivalence ratio and progress variable is compared to measure the combustion mode. With a renormalized progress variable, the proposed flame index is 0 for equilibrium solution of the nonpremixed flame, and 1 for the premixed flame with homogeneous cold flow. The index is validated on a series of constructed turbulent combustion subgrid particles and the partially stirred reactors with different mixing models. Tests demonstrate that the flame index for PDF method works well for nonpremixed flames with variant scalar dissipation rate. Furthermore, the index shows a consistent trend at different parameters. Results also confirms that the localness of the EMST model make it predict the physical process well.