**4. Conclusions**

2D RANS numerical method fitted with the appropriate closure equations was applied for the computational investigation of the upward turbulent particulate pipe flow at the distance of 100 calibers from the pipe entrance. The axial velocity lag, turbulent kinetic energy of gas and particles mass concentration, effected by the gravity, viscous drag, the particle-turbulence, particle-particle, particle-wall interactions as well as the Saffman and Magnus lift forces, were examined for various particle sizes and flow mass loadings at the same flow Reynolds number.

The obtained numerical results allow to draw the following conclusions pertaining to behavior of solid particles under the conditions of the upward turbulent pipe flow:

**1.** It is obvious that if the motion of particles is exposed only by the viscous and gravitational forces (without the direct effect of turbulence, lift forces and coupling), the absolute magnitude of the axial velocity lag approaches to the particles terminal velocity. However, simultaneous accounting of all force factors, effecting on the fine particles, results in substantial exceeding of their axial velocity lag as compared with their terminal velocity, that is due to intensification of influence of turbulence on a motion of the fine particles.

