Kinetic Modeling and Monte-Carlo Simulations of Droplet Coalescence in a Turbulent Gas Flow

Two-phase gas-droplet flows are involved in a lot of industrial applications, especially in the combustion field (Diesel engine, turbomachinery, rocket engine,…). Among all the characteristics of the spray, the droplet size distribution generally has a major influence on the global performances of the system and must be accurately taken into account in a numerical simulation code. This is a difficult task because the carrier gas flow is very often turbulent. Hence, droplets located in the vicinity of the same point may have different velocities and coalesce, leading at the end to a strong modification of the initial droplet size distribution. The first part of our contribution will be devoted to the presentation of a new kinetic model for droplet coalescence in turbulent gas flows. This model is an extension, to the case of sprays, of the ideas introduced by Simonin, Deutsch and Lavie´ville in [1]. The key ingredient is the use of the “joint density function”, fgp (t, x, r, v, u), representing the density of droplets at time t, located at point x, with radius r and velocity v and “viewing” an instantaneous turbulent gas velocity u. The great advantage of using fgp (t, x, r, v, u) instead of the usual density function fp (t, x, r, v) is the possibility to close the collision operator, in the governing kinetic equation, with less restrictive assumptions on the velocity correlations of two colliding droplets. The link between this model and the usual one (relying on the so-called “chaos assumption”) will be discussed. In the second part of our contribution, we shall present a new Monte-Carlo algorithm derived from our kinetic model. Numerical simulation results, for some academic test cases (homogeneous isotropic turbulence), will be shown and compared to the results obtained with a classical algorithm for droplet collision, based on the chaos assumption (see for example [2] or [3]). The figure 1 below shows a comparison between the temporal evolution of the mass mean radius computed by a classical collision model (neglecting the influence of gas and droplet velocity correlation) and by the “joint-pdf” based model. In the first case, the growth rate of the droplet, due to coalescence phenomena, is overestimated. Moreover, figure 2 shows that the droplet kinetic energy, induced by the turbulent gas motion, decays rapidly with the chaos assumption based model, as already noticed by Lavie´ville et al [1] in the case of solid particle collisions.