Flow of a Newtonian fluid in agitators of different configurations

Abstract

The flow of a viscous incompressible fluid in agitators with solid and anchor blades is analyzed. Mathematical formulation for the problem involves Navier-Stokes and continuity equations in the plane approximation. A solution algorithm is developed based on the control volume method and a SIMPLE correction procedure. The differential equations are discretized with unstructured triangular meshes that take into account the geometric features of the flow region. Tests were performed to verify the approximation convergence and to estimate the order of accuracy of the numerical scheme, as well as to verify the original calculation program. Parametric studies were carried out for Reynolds numbers in range of 0.1-100, which is characteristic of the technology of fluid materials processing in industrial mixers. Distributions of the kinematic and dynamic characteristics of the flow were obtained, and the flow patterns, whose specific feature is the presence of circulation zones in paddle agitators of different configurations, were demonstrated. Calculations are done to determine the position of marker particles and the evolution of reference lines, which give a visual representation of the process and demonstrate the presence of areas of uniform and non-uniform mixing. A quantitative mixing quality parameter is introduced to compare agitators of different configurations with each other and to consider the process of mixing over time. The process is evaluated quantitatively by the values of the integral of the dissipative function, which shows the energy consumption, and by the value of the quantitative parameter of the inhomogeneity of the marker particle distribution. The latter allows a more detailed study of the mixing process over the volume over time.