Assumed PDF Modeling of Turbulent Spray Combustion

The present study is a new step in the attempt to extend an approach used in the modeling of gaseous turbulent combustion to spray turbulent combustion. Our attention is focused on the new random fluctuations created by the presence of the spray. The ideas developed here are based on the discussion presented by Borghi (1995). A local study of the equations allows us to find a closure for the new correlation term induced by spray evaporation in the equation for the variance of the mixture fraction. This was done without new assumptions, just by using the stochastic approach already developed in the KIVA II code to describe spray vaporization. We also show the importance of a new variable, Z,, which describes the initial state of an evaporated fluid particle. An equation for the PDF of this variable and for its mean value is also written in closed form. For the moment, its contribution to the mixture fraction PDF is taken into account through its average value. Finally we have tested our model with an experiment where one set of experimental conditions is close to the infinitely fast chemistry and another set of conditions demonstrates the effect of finite chemical kinetics. We have found a qualitative agreement between the measured data and our computational results. Further development should be done, for instance coupling this model with an atomization model to avoid any assumption about the first stages of the evaporation and combustion process.