A variety of modelling methods have been proposed to predict the complex, highly non-linear, interaction between turbulence and chemical reaction in both premixed and non-premixed flames. Among these, PDF methods have the advantages of representing convection and reaction exactly without modelling assumptions, and they have been demonstrated to be an effective approach for calculating turbulent reactive flows.

The PDF calculations performed on TNF workshop target flames (simple jet flames, piloted jet flames, bluff body flames) clearly demonstrate the ability of PDF method to account accurately for strong turbulent combustion interactions such as local extinction and re-ignition. In recent PDF calculations on turbulent lifted flames in a vitiated coflow, the numerical model is found to capture the most interesting feature of this particular lifted flame: the strong sensitivity of liftoff height to coflow temperature. More work is performed on piloted jet flames and bluff body flames to investigate the effect of detailed chemical mechanisms and mixing models.

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Recently, the Lagrangian investigations of local extinction, re-ignition and auto-ignition in piloted jet flame and lifted jet flames are performed. The processes of local extinction, re-ignition and auto-ignition are illustrated by the particle trajectories in composition space.