Current-density approximation for efficient computation of the electrostatic field in wire-plate precipitators

In this paper, numerical computation of ionic space charge and electric field produced by corona discharge in an electrostatic precipitator is addressed. The problem is defined by a reduced set of the Maxwell equations. The efficiency of numerical iterative computations is significantly improved by deriving an initial field as close as possible to the final solution from an approximation of the current-density field J. Different techniques to approximate J are proposed. A first analytic approximation (J) over tilde is derived, which verifies by construction the boundary conditions of the problem and, in particular, gives the correct average value at the plate. A second approximation is also considered, which contains a free parameter that can be computed by an optimization procedure based on the known value of the potential at the wire. Finally, Karhunen-Loeve (KL) decomposition is used and the current-density field is expressed as the sum of (J) over tilde and of a linear combination of few KL basis functions. The coefficients can be determined again by an optimization algorithm. Starting from these approximated J fields, a procedure is proposed to obtain, at negligible computational cost, an estimate of the complete electrostatic field. It is shown that this estimate is in all cases much closer to the exact solution than guesses typically employed in the literature. Hence, when it is used as initialization for standard numerical solvers, this significantly improves the efficiency of the numerical algorithm. In particular, the initialization based on the second approximation gives a significant efficiency gain without any noticeable additional cost.