Investigation of the Corona Discharge Problem Based on Different Computational Approaches of Dimensional Analysis

Although corona discharge is notorious for its detrimental effects, it is also used in many beneficial practical applications. Despite the existence of a variety of sophisticated theoretical and experimental methods for investigating corona discharge, we explore yet a much simpler method that relies on the use of Dimensional Analysis (DA). The DA method does not demand profound knowledge of the underlying phenomenon or its governing equations, as it only needs the correct identification of the variables influencing the phenomenon, and the specification of their physical dimensions. The classical and well-known Gauss-Jordan elimination method is compared with other matrix-oriented computational approaches in analyzing the pertinent dimensional system. This method relies upon solution-preserving elementary row operations, i.e., operations that one can use on a matrix without spoiling the solution set for an associated matrix equation. A distinct advantage of this method is that it does not pre-suppose a particular value of the matrix rank but tackles the task of determining this rank while proceeding towards its ultimate result. Moreover, this method can also be used to find the inverse of a regular (invertible) matrix or to determine the solution (if any) of a system of linear equations. As a bonus, novel results of numerical investigations of bases, regimes, and dimensionless products are extensively presented in this paper. A remarkable observation made herein is that the set of variables pertinent for a particular phenomenon cannot be arbitrarily partitioned into basis (input) variables and regime (output or isolated) variables. The paper running example deals with expressing a specific variable, viz. ozone generation rate per unit length of wire (r0) through dimensionless products in terms of a set of determining or influencing variables.