Order-of-magnitude scaling of the cathode region in an axisymmetric transferred electric arc

A new technique of order-of-magnitude scaling (OMS) has been applied to the mathematical modeling of the cathode region of a long gas tungsten are (GT A). The estimations obtained are combined with numerical calculations; thus , important features of both techniques are considered simultaneously: the high precision of numerical modeling and the generality and simplicity of a lgebraic expressions. Power-law expressions for the estimations of characte ristic unknowns such as maximum pressure in the cathode spot and maximum pl asma velocity are obtained and are consistent with previous analytical or a symptotic work. Dimensional analysis is used to identify dimensionless grou ps governing the system, and asymptotic considerations are used to identify two dimensionless groups (the Reynolds number and the dimensionless are le ngth) as the most significant ones governing momentum transfer in the catho de region. The estimations obtained are calibrated with functions that depe nd only on these two most significant dimensionless groups. It is suggested that the numerical results for different cases can be reduced to a single general map.