Non-dimensional analysis on the momentum equation of the magnetically driven arc

Abstract

Arc behavior under an alternating magnetic field to the arc is theoretically investigated. It is known that the arc profiles are influenced by various operating parameters such as an imposed magnetic flux density, an arc current, a flow rate to the plasma gas and so on. Therefore theoretical analysis on the arc is complicated. In the present work, the authors investigated a new approach to understand the arc behavior driven by the alternating magnetic field. A characteristic time and a characteristic length were defined. Using these characteristic time and length, the fundamental equations which governed the arc behavior were rewritten into the non-dimensional forms. Appropriate choices of these characteristic values made it possible to eliminate the influences of the various operating parameters from the non-dimensional equations. As the result, numerical analyses became very easy. Non-dimensional arc profiles obtained from the non-dimensional differential equations were rearranged into real arc profiles by the simple inverse conversions from the non-dimensional values to the real dimensional ones. Influences of the operating parameters appear again in the arc behavior through the inverse conversion processes.

Keywords

• alternating magnetic field
• electromagnetic force
• transferred arc
• non-dimensional analysis