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. Analogous to electromagnetic and fluid mechanics inductions, vortices are described by the same relationship: the Biot-Savart law. When vortex threads form a vortex track due to fluid mechanics, they induce, analogous to electrical coils on an iron core, a core flow that can be faster than the wind that generates it. In this publication, the velocity field induced in a cylinder using the axially symmetric system of vortex rings and screw vortices and the hydrodynamic flow function in the ideal incompressible fluid are calculated. Also similar problem for mathematical modelling of the heat generation in fluids with alternating current using vortexes is considered. In 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 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, (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.