### Numerical Simulation of Partially Premixed Combustion Using a Flame Surface Density Approach

#### Abstract

Partially premixed combustion is characterized by a variable equivalence ratio of the mixture in space and time, and where there are both lean and rich mixture zones. Thus the reaction evolves along with a turbulent mixture process, which modiﬁes the composition of reactants and products. In this situation a so-called triple ﬂame could be encountered, in which a rich and a lean premixed ﬂame front as well as a diffusion ﬂame are present. The diffusion ﬂame develops behind the premixed ﬂame front due to turbulent mixing in the hot combustion products. This kind of combustion could be found in Direct Injection Spark Ignition (DISI) engines when they are operated in the stratiﬁed charge mode. The model considered in this work assumes a simpliﬁed one-step irreversible chemical reaction in which fuel and oxidant react together instoichiometric proportions giving products with the composition corresponding to a complete combustion. A transport equation is solved for the oxidant and fuel, from which the amount of products and the combustion progress are computed, while the turbulence is modeled with RANS (Reynolds-Average Navier-Stokes). The reaction rate is assumed in the model as proportional to the product of the Flame Surface Density (FSD) by the local laminar ﬂame speed. Aside from the state and composition of the mixture, the local laminar ﬂame speed is afected by the turbulent mixing process. This mixing process is taken into account by means of the classical β-PDF (Probability Density Function), which is a function of the mixture fraction and its variance. A transport equation is solved for both, the mixture fraction and its variance, and the FSD is computed through a transport equation where several models are available for the source terms. The model is implemented in the open-source toolkit OpenFOAM (R). Computational results are obtained for partially premixed combustions inside constant-volume vessels with several initial conﬁgurations, which are compared with numerical results available in the literature.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**