**Author details**

**Figure 13.** Effect of particles on the modification of the turbulence kinetic energy: 1 –*M* =4.8mm,*x* / *M* =46; 2 –

The analysis of Figure 13 shows that the increase of the grid mesh size results in the weaker contribution of particles to the turbulence enhancement and dissipation of the kinetic energy taking place over the cross-section for the initial period of the turbulence decay. This can be explained by the higher rate of the particles involvement into the turbulent motion due to the

The RSTM model has been elaborated for the horizontal and vertical turbulent particulate flows in the channels of rectangular and square cross-sections with the smooth and rough

The present RSTM model has been validated for the unladen channel gas flow with the rough wall. It satisfactorily described the experimental data on the averaged gas axial velocity and

Further, the present model was applied to simulate the vertical grid-generated turbulent particulate channel flow. It considered both the enhancement and attenuation of turbulence by means of the additional terms of the transport equations of the normal Reynolds stress components. The model allowed to carry out the calculations covering the long distance of the channel length without using algebraic assumptions for various components of the Reynolds stress. The numerical results showed the effects of the particles and the mesh size of the turbulence generating grids on the turbulence modification that had been observed in

*M* =4.8mm,*x* / *M* =93; 3 –*M* =10mm,*x* / *M* =46; 4 –*M* =10mm,*x* / *M* =93.

three components of the turbulence energy.

**4. Conclusions**

60 Computational and Numerical Simulations

walls.

longer residence time that comes from the larger size of the eddies.

Alexander Kartushinsky1\*, Ylo Rudi1 , Medhat Hussainov1 , Igor Shcheglov1 , Sergei Tisler1 , Igor Krupenski1 and David Stock2

\*Address all correspondence to: aleksander.kartusinski@ttu.ee

1 Research Laboratory of Multiphase Media Physics, Faculty of Science, Tallinn University of Technology, Tallinn, Estonia

2 School of Mechanical and Materials Engineering, Washington State University, Pullman, Washington, USA
