New approach to the droplet break-up modelling in diesel and rocket spray computation

A novel stochastic model of droplets breakup is proposed and implemented into computation of liquid sprays. The evolution equation for the distribution function of radius of the braking drops is written to be an invariant under the group of scaling transformations. Due to this symmetry, it turns out that it is possible to obtain an asymptotic solution and to reduce the evolution equation to the Fokker-Planck type in the long-time limit. The asymptotic solution is a log-normal distribution. This asymptotic solution goes to the power distribution in a broad range of radius. The fractal dimension of the power distribution appears to be consistent with the irregular fragmentary nature of the atomization process. The kinetic equation for the complete distribution function F (x,v.r,l) of liquid particles in the phase space of droplet position, velocity and radius is written. On the basis of this equation, the stochastic computing of droplet breakup is achieved using analytical solution of the Fokker-Planck equation in the space of radius. Performed computations are related to diesel and rocket sprays.