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.

Ligament Mediated Fragmentation of Viscoelastic Liquids

“…Recent studies [7,[9][10][11] have shown that old paradigms for understanding disintegration of Newtonian liquids, based on either cascade theory [12] (leading to log-normal size distributions) or maximum entropy theories [13] (leading to Poisson size distributions) do not adequately capture all physical aspects of these processes. Villermaux et al [10] show that the atomization process for Newtonian liquids can be precisely described by a fragmentationcoalescence scenario [14].…”

“…However, none of these studies address the role of viscoelasticity on the distribution of droplet sizes. The few attempts in the literature to address the size distributions for polymeric liquids [28,29] base their assumptions on older paradigms [12,13].…”

Eulerian Multiphase Population Balance Model of Atomizing, Swirling Flows

“…The only macroscopic constraint on the choice of n ij arises from the conservation of mass during a single breakage event (14) and is identically satisfied by equation (13). In addition, equation (13) allows the possibility of producing distribution coefficients consistent with Kolmogorov's hypothesis (see, for instance, Gorokhovski and Saveiliev [26] or Apte et al [11]) that breakups of all sized particles produce the same number of particles.…”

Prediction of droplet size distribution in sprays of prefilming air-blast atomizers

“…A new approach is developed by Gorokhovski and Saveliev (2003) and Apte et al (2003) based on the Kolmogorov's scenario of the breakup of particles. Kolmogorov wrote a stochastic theory for the breakup of solid particles that describes the cascade of uncorrelated breakage events.…”