Об аппроксимации скорости асимметричного потока в межтарелочном пространстве сепаратора

Abstract

We consider the motion of non-Newtonian behavior in the inter-disk space of the liquid separator. The shared medium is supplied from the periphery of the disks and moves to the center of the machine. Under the influence of centrifugal force the particles of the dispersed phase are precipitated to the bottom surface of the top disk to form a thin layer of precipitate, which moves toward the periphery of the disk. The equations of motion are solved by the equal-discharge-increments method. In this case, the flow field is introduced surfaces of equal costs for the continuous phase, which are determined by the conditions of constant flow velocity of the medium between them. To determine the locations of input surfaces, the recurrent type differential equations are recorded. The equations of motion, recorded on the flow lines, are simplified and take the form of ordinary differential equations in the longitudinal coordinate. The term, takes into account the effect of viscous friction in the equation of motion, contains the partial derivatives of the transverse coordinate. For their computation, a grid solution can be represented as a series expansion in the complete system of basis functions, satisfying the boundary condition. The presence of moving sediment layer and the centrifugal force influence causes the asymmetry of the flow in the dispersion medium in the inter-disk space. In this work the basic functions that take into account the asymmetry of the flow were constructed. In order to determine the type of basis functions, the Poiseuille flow in a conical slit with a moving wall was considered. An algebraic equation for calculating the extremum point of the function of speed made up. It is shown, that for the power fluid in the areas of increasing and decreasing functions, there are different solutions. The studies proposed a system of basis functions for the approximation of the grid solutions. It is shown, that the proposed features provide continuity of the viscous stress tensor in the whole flow area.