The vortex formation in a horizontal finite cylinder by alternating electric current¹

This work is partly financially supported by the project No 01.0130 of Latvian Science Council.

Abstract

We have investigated and calculated the distribution of electromagnetic fields and forces induced by a three‐ phase axially‐symmetric system of electric current with six electrodes in a cylinder of a finite length [1, 3]. In this paper the alternating current is fed to each of nine discrete circular conductors‐electrodes, which are placed on the internal wall of the cylinder. This new mathematical model describes a real device [7], which transforms electric energy into heat.

The viscous incompressible flow of weakly electroconductive liquid‐electrolyte is obtained by the finite‐difference method, using the monotonous vector finite difference schemes. The average axially‐symmetric motion of electrolyte and vortex distribution in a cylinder has been considered. The dependence of electromagnetic forces and velocity distribution at the inlet of the cylinder is investigated in the case of:

1. the vortex formation from the Lorentz force inside the cylinder by the electrode

2. the vortex‐breakdown from the swirl velocity at the inlet of the cylinder.

Straipsnyje yra nagrinejamas skysto elektrolito judejimas baigtiniame cilindre, veikiamas kintančio elektromagnetinio lauko. Panaudojant savo anksčiau sukurta metoda suvidurkintu laike elektromagnetiniu jegu reikšmiu gavimui, autoriai formuluoja stacionaru Navier‐Stokso uždavini klampiam nespudžiam elektrolito tekejimui aprašyti. Sukurto matematinio modelio skaitiniam sprendimui yra pasiūloma originali monotonine baigtiniu skirtumu schema. Yra pateikiami skaitiniu eksperimentu rezultatai su 9 žiediniais laidininkais‐elektrolitais, tolygiai paskirstytais vidiniame cilindro paviršiuje. Autoriai analizuoja gaunamus cilindre srautus priklausomai nuo elektromagnetiniu jegu pasiskirstymo (skirtingos elektrodu pajungimo schemos) ir sukurinio greičio cilindro iejime. Labiausiai autorius domina salygos, kada cilindro viduje susidaro sūkuriai.

Key words:

• electroconductive liquid
• vortex formation
• electric current

Notes

This work is partly financially supported by the project No 01.0130 of Latvian Science Council.