On visualization of the anisotropy of the dispersion of velocities of polydisperse dust in a gas-dust medium

A large number of publications have been devoted to studying the features of the flow in two-phase flows in a gas-dispersed flow with inertial dust particles (shock waves, jets, turbulence, regular structures such as plasma crystals). In recent years, the study of the behavior of various fractions of impurity particles in polydisperse dust mixtures, expressed in the spatial separation of their distributions, has been of increasing interest. Spatial variations of individual components of the dust mixture make it possible to diagnose the state of the carrier gas phase in those cases when the carrier phase is very rarefied and cannot be observed directly (interstellar gas).
This work is a continuation of the authors' work [14], in which an original algorithm was proposed based on the use of three-dimensional color space resources, which allows visualizing spatial distributions of concentrations of up to three fractions of a polydisperse mixture of dust particles simultaneously, as well as an entropy measure that allows visualizing the degree of polydispersity in a heterogeneous gas-and-dust environment. However, the structural features of the impurity phase (caustics, areas of segregation of dust particles by their size, mass, etc.) are not necessarily spatially combined with its dynamic features (collisionless shock waves, flow turning points, stagnation points, accumulation points).
In this paper, we propose a method for visualizing the dynamic features of a polydisperse collisionless mixture of particles in a two-phase gas-dust medium by constructing spatial distribution maps of the particle velocity dispersion anisotropy regions. Strong anisotropy of the velocity dispersion corresponds to the region in which an intense multi-stream flow occurs.
Dust is considered as a mixture of several fractions, each of which contains particles of the same type, while the particle sizes in different fractions are different. For each dust fraction, a field is constructed of the spatial distributions of the eccentricities of the velocity dispersion ellipses. To visualize the degrees of anisotropy of the velocity dispersion of two fractions of a polydisperse dust mixture at once, a specially selected entropy measure is proposed. The results of two-dimensional demonstration calculations of a turbulent gas-dust medium and the anisotropy map in the distribution of the velocity dispersion of an impurity dust component are presented.