**Acknowledgements**

**Figure 18.** Profiles of the turbulence modulation for 750 μm coal particles in the pipes *D*=30.5, 45.75 and 61 mm,

The turbulence modulation is shown in Figures 17 and 18 for the considered particles sizes in two marginal cases: *δ*=250 and 750 *μ*m. It is evident that the increase of the particle size leads to decrease of the attenuation rate of turbulence. The effect of the inter-particle collisions (Figure 18) results in the enhancement of turbulence by particles in vicinity of the flow axis and its damping, that occurs in the region locating between the flow axis and the pipe wall.

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

**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.

of solid particles under the conditions of the upward turbulent pipe flow:

*m* \* =10, Re=4.4×10<sup>4</sup>

**4. Conclusions**

.

36 Computational and Numerical Simulations

The work was done within the frame of the target financing under the Project SF0140070s08 (Estonia) and supported by the ETF grant Project ETF9343 (Estonia). The authors are grateful for the technical support of Computational Biology Initiative High Performance Computing Center of University of Texas at San Antonio (USA) and Texas Advanced Computing Center in Austin (USA). This study is related to the activity of the European network action COST MP1106 "Smart and green interfaces - from single bubbles and drops to industrial, environ‐ mental and biomedical applications".
