the exchanges of mass, momentum, and of course energy between the two phases. However, for the sake of simplic-
The paper is concerned with the construction of a numerical method for the computation of the dispersion of a cloud of liquid ity, we do not introduce combustion models in this work droplets by a turbulent gas flow field. The cloud of droplets is modbut only consider vaporization of droplets since our main eled by a semi-fluid system intermediate between a fluid model interest lies in the prediction of the dispersion of the cloud and a kinetic description of the dispersed phase. The semi-fluid of droplets. This study is thus a preliminary step towards model is deduced from the kinetic model by integration with respect to the velocity variables and makes it possible to describe clouds the computation of the full piston in a Diesel engine.
of particles such that the velocity distribution of any family of parti-
In order to model two-phase fluid flows, we might either cles with a given radius and a given temperature found at a given chose an Eulerian model or a Lagrangian one. In the Eulocation of the physical space is a Gaussian function. A numerical lerian approach, each phase is modeled as a single fluid, scheme, consistent with the semi-fluid model and inspired by Peroccupying the whole physical space. Exchange terms are thame's or Deshpande's kinetic schemes, is proposed. The interactions with the gas phase are taken into account thanks to a particle included to account for the exchanges of mass, momentum, in cell method. Numerical experiments illuminate the features of and energy between the two phases. Such models are usuthe method. แฎ 1997 Academic Press ally obtained by averaging the Navier-Stokes equations satisfied by the gas phase around the droplets and the liquid phase inside the droplets. Since the location of the droplets may change from one experiment to another one, the two-phase flow. Note that alternately, using Liouville's 256