Problems of predicting turbulent burning rates

Different approaches to the modelling of turbulent combustion first are reviewed briefly. A unified, stretched flamelet approach then is presented. With Reynolds stress modelling and a generalized probability density function (PDF) of strain rate, it enables a source term, in the form of a probability of burning function, P_b, to be expressed as a function of Markstein numbers and the Karlovitz stretch factor. When P_b is combined with some turbulent flame fractal considerations, an expression is obtained for the turbulent burning velocity. When it is combined with the profile of the unstretched laminar flame volumetric heat release rate plotted against the reaction progress variable and the PDF of the latter, an expression is obtained for the mean volumetric turbulent heat release rate. Through these relationships experimental values of turbulent burning velocity might be used to evaluate P_b and hence the CFD source term, the mean volumetric heat release rate.

Different theoretical expressions for the turbulent burning velocity, including the present one, are compared with experimental measurements. The differences between these are discussed and this is followed by a review of CFD applications of these flamelet concepts to premixed and non-premixed combustion. The various assumptions made in the course of the analyses are scrutinized in the light of recent direct numerical simulations of turbulent flames and the applications to the flames of laser diagnostics. Remaining problem areas include a sufficiently general combination of strain rate and flame curvature PDFs to give a single PDF of flame stretch rate, the nature of flame quenching under positive and negative stretch rates, flame responses to changing stretch rates and the effects of flame instabilities.