Numerical prediction of multireactive turbulent flows by a Eulerian-Lagrangian method

In most practical cases of flows in turbomachine combustion chambers, many chemical reactions take place, involving several reactive species; the probability density function (p.d.f.) of mass fractions and temperature then depends on several random variables. The Eulerian balance equation for the p.d.f. is then very complicated and it is often impossible to solve it numerically. However, using both classical Eulerian balance equations for mean-values and standard deviation, and Lagrangian models, allows to find a quite realistic approximation of the p.d.f. projection in the phase space (mass fractions and temperature). This projection consists of just a few curves, even in the case of a multidimensional p.d.f. a simple integration along these curves then provides the different mean values of the flow field. For example using this method for a premixed air-methane flame allows one to compute all the mean characteristic values, at each point of the flame, particularly the mass fractions of methane and CO, and the temperature.