Analyses of Kolmogorov’s model of breakup and its application into Lagrangian computation of liquid sprays under air-blast atomization

Abstract

This paper considers the breakup of liquid drops at the large Weber number within the framework of Kolmogorov’s scenario of breakup. The population balances equation for droplet radius distribution is written to be an invariant under the group of scaling transformations. It is shown that due to this symmetry, the long-time limit solution of this equation is a power function. When the standard deviation of droplet radius strongly increases and, consequently, the characteristic length scale disappears, the power asymptotic solution can be viewed as a further evolution of Kolmogorov’s log-normal distribution. This new universality appears to be consistent with the experimental observation of fractal properties of droplets produced by air-blast breakup. The scaling properties of Kolmogorov’s model at later times are also demonstrated in the case where the breakup frequency is a power function of instantaneous radius. The model completes the Liouville equation for distribution function of liquid particles in the phase space of droplet position, velocity, and radius. The numerical scheme is proposed for stochastic modeling of droplets production. Lagrangian simulation of the spray under air-blast atomization is performed using KIVA II code, which is a frequently used code for computation of turbulent flows with sprays. The qualitative agreement of simulation with measurements is demonstrated.