Остання редакція: 2019-04-20

#### Анотація

In the simulation of the motion of solids in the gas stream, two basic methods of the Lagrange and Euler are usually used [1-3]. The Lagrange method can reliably describe the motion of single particles, provided that they are elastic coincident with the wall of the nozzle, which is valid only for powdered material of a coarse fraction (more than 100 microns). In the case of fine particles (up to 10 microns) and fine particles (up to 100 microns) of the powder composition fraction, elastic coagulation of the particles does not play an important role. Therefore, the environment with such particles in the framework of this method can be considered as solid. Therefore, following these facts, in order to simulate the motion of the dispersed phase in the gas stream in this paper, the main theoretical aspects of the disperse phase calculation by the Euler method were considered. The advantage of this method is that the difference in concentrations of the disperse phase between the two points determines the diffusion flow generated by the turbulent ripples of the continuous medium, the motion of which is also described within the framework of the Euler methodology. To calculate the turbulence of two phases, a standard (k-ε) Launder-Soplding model is used, which has proved itself well in the simulation of currents with small gradients of turbulent fluctuations and has a high accuracy of the results. The motion of the dispersed phase is calculated according to the Euler method by integrating the velocity in a step.

With further integration, the particle velocity is calculated at the beginning of the step. At the end of the step, the new particle velocity is calculated by analytical method. Properties of the solid phase are taken at the beginning of the time interval. The moment of movement of individual particles of the disperse phase will depend on the velocity of the particles at the beginning of the time interval. When calculating all the acting forces, such variables of the solid phase as density, viscosity and velocity should also be taken into account when moving the dispersed phase. In accordance with the above calculations, the velocity of the motion of the solid phase affects the velocity of movement of particles of the dispersed phase and vice versa there is a reverse effect of the velocity of movement of particles of the dispersed phase on the velocity of the continuous phase, that is, there is a connection between the two phases. We assume that a separate particle of the dispersed phase moves within the stream of the continuous phase. The forces acting on the particle of the dispersed phase, which influence its acceleration, depend on the difference between the velocity of the particle and the solid phase, as there is a displacement of the solid phase stream over the disperse phase.

The calculation of the instantaneous velocity of the equation depends on the flow regime, that is, there may be medium or strong turbulence of the gas jet stream. The path of each particle of a dispersed phase enters a discrete domain that has a unique character, therefore, to track the motion of a particle in a turbulent stream, instantaneous velocity is decomposed into two components, stable and unstable. Therefore, it should be noted that two identical particles of a dispersed phase that started moving from one point of the discrete domain, but at different times can move in different trajectories, because their instantaneous speeds may be different. This is the main criterion for the distribution of disperse phase particles in a turbulent flow. The model for the distribution of particles of the dispersed phase in a turbulent flow assumes that the particle always moves in only one vortex. Each vortex has an unstable component of the velocity, period of existence, and length. When a particle enters the vortex, an unstable velocity component for this vortex is added to a stable component of the continuous phase velocity, thus giving an instantaneous value of the velocity of the solid phase.

**Conclusion**. According to preliminary calculations, it should be noted that each component of the unstable velocity of the particle dispersion phase in the gas stream may have different values for each vortex.

#### Посилання

1. V.L. Naidek Distribution of dispersed particles in a two-phase gas-laser flow [Text] / V.L. Naidek, VP Likhoshva, E.A. Reintal, F.I. Kirchu and others. -Metal and Casting of Ukraine, 2009.-No.11-12, p.4-7.

2. Kondrashev P.V. Modeling of gas dynamics of a powder jet during the implementation of the technology "RAPID PROTOTYPING" [Text] / P.V. Kondrashev.-East-European Journal of Advanced Technologies, 5/7 (65), 2013.-p. 4-10.