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SUMMARYModelling turbulent ames with an acceptable accuracy remains an open problem. In order to progress in our understanding of turbulent combustion, direct numerical simulations have been extensively employed during the last decade. These direct simulations generally rely on a fully compressible formulation, leading to extremely small time-steps associated with the propagation of acoustic waves. But, for many practical applications, acoustic phenomena are not essential. Using an incompressible approach while taking into account a dilatation term should then be much more e cient in terms of computing time. In this article we want to investigate this point by comparing results of direct simulations relying either on the compressible equations or on the low-Mach number formulation. We employ in both cases detailed models to describe chemistry and transport, in order to obtain an accurate description of the reaction zones. Two test-cases are considered for the evaluation of the low-Mach number approximation. We ÿrst compute the evolution of homogeneous isotropic turbulence decaying with time, without chemical reactions. In the second case a turbulent premixed ozone ame is investigated. For both conÿgurations the computing time associated with the low-Mach number simulation is at least an order of magnitude shorter, while keeping a similar accuracy for the ame properties. This demonstrates that the low-Mach number formulation is extremely e cient and suitable to investigate the detailed structure of turbulent ames when acoustic phenomena are not of primary interest.

The paper presents an original work in which a hybrid turbulent combustion model, based upon a stochastic evaluation of the Joint Scalar Probability Density Function (PDF), is used in conjunction with a skeletal soot model and a detailed kinetic mechanism for fuel oxidation. First, the Probabilistic Eulerian Lagrangian turbulent combustion model, which is theoretically able to describe chemical reactions occurring in a turbulent flow for a wide range of Damkohler numbers, is presented and justified. Then, the chemistry model which accounts for soot formation and oxidation is exposed and validated in rich ethylenepremixed laminarflames. This modelling approach coupling turbulence and chemistry is eventually applied to predict soot levels in a turbulent jet diffusion flame of ethylene burning in still air, Results are in good agreement with experimental data and the peak value of soot volume fraction on the centreline is fairly well described even though an accurate radiative heat transfer model is still necessary to be more predictive on mean temperature levels.

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