Numerical computation of electric fields in presence of curvilinear interface between conductive and non-conductive media

Abstract

Purpose. To elaborate a method of electric field numerical calculation in systems with curved boundaries between conductive and non-conductive media at final volume method usage and application of the rectangular grids. Methodology. At electric field calculation in quasi-stationary approximation, potential of the whole conductive object (rod) is constant. At final difference scheme writing, presence of the curved part of the boundary between conducting and non-conducting media has been taking into account as follows. It was supposed that curved section complements the closed loop on which integration of the solvable equation is done instead of a straight section which extends within a conducting medium. Usage of this approach allows taking into account square of the curved sections of the boundary and distance between surface of non conductive medium and nearest nodes of the computational grid. Results. Dependence of the maximum electric field intensity on the height and radius of curvature peaks rods has been got with the help of calculations. As a result, a polynomial approximation for the analytical expression of the external electric field intensity, upon which application to the conductive object of a certain height and radius of curvature of its top, corona discharges will develop.

Описаны принципы учета криволинейных границ раздела при использовании метода конечных объемов для расчета усиления электрического поля на вершинах проводящих стержней. С помощью проведенных расчетов получена зависимость максимальной напряженности электрического поля от высоты и радиуса скругления вершин стержней. В результате аппроксимации данной зависимости полиномом записано аналитическое выражение для напряженности внешнего электрического поля, при приложении которого к проводящему объекту определенной высоты и радиуса скругления вершины на нем развивается коронный разряд.