Mathematical modeling of velocity field induced by the vortex

Abstract

In new technological applications, it is important to use vortex distributions in the area for obtaining large velocity fields. This paper, it was calculated the distribution of the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of the finite number of vortex threads: 1) circular vortex lines in a finite cylinder, positioned on its inner, 2) spiral vortex threads, positioned on the inner surface of the finite cylinder or cone, and 3) linear vortex lines in the plane channel, positioned on its boundary. An original method was used to calculate the components of the velocity vectors. Such kind of procedure allows calculating the velocity fields inside the domain depending on the arrangement, the intensity, and the radii of vortex lines. In this paper, we have developed a mathematical model for the process in the element of Hurricane Energy Transformer. This element is a central figure in the so-called RKA (ReaktionsKraftAnlage) used on the cars’ roofs.