APPLICATION OF STREAMFUNCTION VORTICITY APPROACH IN DESIGN OF AN AXISYMMETRICAL RADIAL INFLOW GEOMETRY WITH FREE LIQUID SURFACE

This paper is concerned with the evaluation of flow patterns in steady-state, incompressible, axisymmetric flows using the streamfunction-vorticity approach. To extend the significance of the method in engineering applications, potential usefulness dealing with flow domains containing curvilinear and nonrectangular oriented boundaries is demonstrated. Using upwind-noncentred approximations for the convective terms in the vorticity transport equation the solutions are stable for Reynolds numbers in the order of 1000. The solution method provides quick information about flow patterns in the plane. The method is applied to the evaluation of flow fields in funnel geometries with an upward directed feeding stream and a free liquid surface. The flow in such devices is of interest, among others, in construction of flotation equipment. The magnitude of the circulation region was realized to influence the performance of the apparatus. Design suggestions to reduce the amount of circulation and the influence of the Reynolds number variation on the flow pattern are discussed. The results of numerical calculations show reasonable agreement with measured data obtained by hot-film anemometry.