Mathematical Modeling the Processes of Supersonic Cold Gas Dynamic Spraying of Nanoparticles on Substrates

The work is devoted to the development of multiscale approaches for modeling the processes of supersonic cold gas dynamic spraying of nanoparticles on the substrates. Modeling of gas dynamic spraying processes involves solving two practical problems: a) controlled transportation of nanoclusters to the spraying place in the general gas flow; b) analysis of the interaction of nanoclusters with the substrate surface in its boundary layer. A combination of these problems is considered, which is implemented on the basis of a multiscale calculation of a two-phase flow of a gaseous medium with the inclusion of finely dispersed solid metal particles. The work proposes a new multiscale computing technology that combines macroscopic, microscopic and mesoscopic descriptions of the physical processes under study at the model level. Within its framework, two two-scale approaches are used, taking into account, respectively, macro- and micro- and macroand mesolevels of spatial detail. The macroscopic components of the final mathematical model are based onmodified quasigasdynamic equations for analyzing the flow of a two-phase multicomponent gaseous medium, as well as Maxwell's equations near the substrate surface for calculating the effect of electromagnetic fields on the solid phase. Newton's dynamics equations are used to describe processes on micro- and mesoscopic scales. In the first case, these are the equations of molecular dynamics, written taking into account the pressure forces in the gas phase andmechanical stresses in the solid phase. In the second case, these are the equations of particle dynamics, taking into account mainly the Lorentz force. For the numerical implementation of the macroscopic components of the model, the grid method of finite volumes is used; for the micromodel, the Verlet scheme is used; for the mesomodel, a symmetric scheme is used that approximates the equations of Newton's electrodynamics. The aims of the work were a physically substantiated formulation of all model components and preliminary calculations of the motion of a nickel nanocluster accelerated by a supersonic nitrogen flow near a nickel substrate.