## 5 Results and Discussion
### Hydrodynamic Modes for Weighing Solid Particles on a Shelf  
The special nature of the gas flow distribution determines the conditions for the emergence of various hydrodynamic modes of interaction between solid particles in the material and the ascending gas flow. It enables widely to influence the heat treatment efficiency (for example, cooling and drying) of granular and grained materials in devices with inclined perforated shelves. At low gas flow velocities, the material continuously fed into the device with a flow rate of 6 kg/(m\({}^{2}\)-s) moves along the surface of the inclined shelf in the form of a rapidly \"jumping\" layer since the particles at the outlet of the supply pipe have sufficient inertia force. The porosity of such a layer reaches 0.8-0.85, and the concentration of material particles in it is 20-30 kg/m\({}^{3}\) (0.15-0.2 m\({}^{3}\)/m\({}^{3}\)). Particles of the material after moving along the inclined shelf surface with a velocity of 0.2-0.3 m/s are inhibited at the device wall in the outloading space and are accumulated on the wall surface (Figure 7a). Figure 6: The influence of the constructive parameters of the shelf on the uneven profile of gas flow velocities. Degree of the shelf perforation \(\psi\): 1–3—respectively, 5%, 15%, 30%. The tilt angle of the shelf—\(\gamma=25^{\circ}\). Gas flow velocity in the free cross-section—1.65 m/s. Figure 7: Photographic image of hydrodynamic modes: (**a**) “gravitationally falling layer” mode; (**b**) “transitional” mode; (**c**) “weighted layer” mode; (**d**) “piston” mode. The accumulated particles layer is blown by the ascending gas flow. Moreover, the layer mass due to the arrival of new portions of solid particles of material gradually increases. At a certain point in time, it exceeds the aerodynamic force of the ascending air flow, after which some of the particles are fallen down the device through the outloading space. In this nature of the motion of the material particles, both on the inclined shelf surface and the outloading space, the aerodynamic forces of the ascending flow do not provide sufficient resistance to the motion of the solid particles. The main part of the material moves in the form of a thin layer through the outloading space mainly by gravitational forces. Therefore, this nature of the motion of the solid particles in the material was called the \"gravitationally falling layer\" mode. By increasing the gas flow velocity, its impact on the material layer grows. It begins to weigh particles both on the shelf contact surface and near the surface of the device wall in the outloading space (Figure 7b). In this case, the porosity of the material layer moving along the surface of the inclined shelf decreases to 0.7-0.75, and the concentration of solid particles of the material increases accordingly to 80-150 kg/m\({}^{3}\) (0.25-0.3 m\({}^{3}\)/m\({}^{3}\)). This mode was called \"transitional\". If a certain velocity of the gas flow is reached, its effect on the material particles increases so much that their share in the upper part of the layer, breaks away from the wall surface. As a result of the breakaway of solid particles in the material, their concentration in this zone increases, the particles do not have time to get carried away by the gas flow to the upper part of the device and, losing their velocity, \"fall\" down onto the inclined shelf surface. Thus, a continuously circulating vortex layer of solid material particles is formed above the surface of the inclined shelf. Having reached a certain period, the formed circulating vortex layer of solid particles has a stationary state in its hydrodynamic structure and is characterized by a constant concentration of solid particles in the layer equal to 160-280 kg/m\({}^{3}\) (0.32-0.35 m\({}^{3}\)/m\({}^{3}\)). The porosity of such a layer is 0.65-0.68, which corresponds to the porosity of fluidized systems.