Two-dimensional model of material flow in a screw channel with a fixed cover

Features of the viscous-plastic material flow through the screw channel are studied. A promising direction in this case is the transport models determined by the hydrodynamics of the phase transition. The author also analyzed the effect of dimensions on the flow rate of a viscous-plastic material. The material situated in the channel of the rotating auger and bounded by the fixed body will start to move in a translational motion along the channel due to the shear deformation that appears in it, this is where a forced flow appears. The main parameters that determine the volume flow rate are the depth and width of the channel, the diameter of the screw and the frequency of its rotation. A necessary condition for the existence of this flow is the persistence of shear stress in the material, which is possible only if the material has a certain viscosity. The condition of the return flow is the excessive pressure created by the resistance of the head. We assume the case when in these conditions the auger does not move. Then, under the action of pressure from the side of the head, the material will flow from it along the screw channel – in the opposite direction. The volume flow rate of the counter-flow also depends on the depth of the channel, on the diameter and length of the screw, on the viscosity of the material and on the pressure in the head. In practice, however, there is never a countercurrent in the auger channel, and the head pressure exerts a kind of limitation on the direct flow, which is theoretically viewed as a countercurrent, and the productivity of the screw supercharger is the total flow of the two flows. To account for the geometry of the channel, the author developed a mathematical model of the velocity head in a rectangular channel. The resulting equation makes it possible to determine the shear stress in terms of the shear rate of the material. Taking into account the symmetry and linearity of the velocity distribution in the channel with respect to its midpoint, an equation is obtained for the distribution of the shear rate along the height. The dependence, obtained as a result of the analytical solution of the two-dimensional Poisson equation, makes it possible to simplify considerably the calculation of the discharge-pressure characteristics of the extruder part of the screw presses for pressing vegetable oils with respect to the required screw rotation speed.