**4. Conclusions**

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 walls.

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 three components of the turbulence energy.

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 experiments. It was obtained that the character of modification of all three normal components of the Reynolds stress taken place at the initial period of the turbulence decay are uniform almost all over the channel cross-sections. The increase of the grid mesh size slows down the rate of the turbulence enhancement which is caused by particles.
