Probability density function modeling of evaporating droplets dispersed inisotropic turbulence

A statistical closure scheme is used to obtain an approximate equation for probability density function to predict the statistical properties of inter est of collisionless evaporating droplets suspended in isothermal isotropic turbulent flows. The resulting Fokker-Planck equation has nonlinear, time- dependent drift and diffusion coefficients that depend on the statistical p roperties of the droplet slip velocity. Approximate analytical expressions for these properties are derived, and the equation is solved numerically af ter implementing the path-integral approach. The time evolution of various statistical properties related to the droplet diameter are then calculated and compared with the data available from the stochastic (Mashayek, F., "St ochastic Simulations of Particle-Laden Isotropic Turbulent Flow," Internati onal Journal of Multiphase Flow, Vol. 25, No. 8, 1999, pp. 1575-1599) and d irect numerical (Mashayek, E, Jaberi, E A., Miller, R. S., and Givi, P., "D ispersion and Polydispersity of Droplets in Stationary Isotropic Turbulence ," International Journal of Multiphase Flow, Vol. 23, No. 2, 1997, pp. 337- 355) simulations.