A new scalar fluctuation model to predict mixing in evaporating two-phase flows

A scalar fluctuation model for two phase flows is proposed for RANS (Reynolds Average Navier Stokes) simulations. It is a two equation model based on the variance v of the gaseous fuel mass fraction and on the scalar dissipation χ. For each quantity a transport equation is solved. The models developed by Mantel and Borghi 11] and Newman et al. 9] are used to close the transport equation of χ for gaseous flows. These models (and an algebraic closure for χ) are compared to (Direct Numerical Simulation) DNS results obtained by Eswaran and Pope 12] in the case of mixing in a gaseous homogeneous stationary turbulence. To get a correct agreement between the RANS models and the DNS results, we had to adjust some constants in these models. It is shown that with the algebraic model it is not possible to correctly reproduce the trends observed in the DNS. Then, the closure proposed by Demoulin and Borghi 13] for the spray source term in the variance equation is adopted. The modelling of the spray source term in the scalar dissipation equation represents the main theoretical work of this paper. Comparisons between experiments and computations are performed in order to validate the complete model. These comparisons are performed on a Gasoline Direct Injection optical access engine. To make comparisons between computations and experiments possible, it is necessary to filter the computed variance. This procedure allows to account for the filtering performed by the pixels of the CCD camera used in the experiments. The two- equation models of Newman et al. and Mantel and Borghi used with the variance and scalar dissipation source terms proposed in this paper predict a high turbulence to mixing time ratio r=τ_tτ_m=χυ?k during the evaporation of droplets. This high mixing rate allows the model of Newman et al. to correctly reproduce fluctuation levels in the spark zone as well as the intense fluctuation in the spray region, while the model of Mantel and Borghi tends to over-estimate fluctuation levels. On the contrary, the algebraic closure imposes a fixed ratio r of the order of 2, which leads to a very high over-prediction of fluctuation levels. These results show that a two-equation model with appropriate spray source terms is needed for correctly modeling the mixing in two-phase flows.