A numerical model of parallel disc capacitor probe used in nondestructive dielectric permittivity evaluation by algebraic topological method

Abstract

Non-destructive evaluation methods for characterizing solid and liquid dielectric material deploy Parallel Disc Capacitor (PDC) as sensing probes. In this work, the authors demonstrate a non-conventional numerical technique known as the Algebraic Topological Method (ATM) to build a numerical model of the PDC probe and validate it using the experiment as well as the Finite Element Model (FEM). The PDC probe under study is made with two metallic (SS 304) discs of diameter 75 mm and thickness 1.5 mm, soldered with SS terminals of length 40 mm and diameter 1.5 mm, and they are separated by the dielectric material under test. The capacitance of PDC with Air, Teflon, Perspex, and Nylon as dielectric material was measured using an LCR meter, and dielectric constants were calculated as per ASTM D150 standard. The dielectric constant values were incorporated into PDC numerical models developed using ATM and FEM. To account for leaking fields, the PDC models were embedded within an air domain measuring 100 mm in diameter and 50 mm in height. The 3D Maxwellian capacitance was then extracted by computing the stored energy within these dielectric regions and compared with results from measurements and FEM simulations. The findings demonstrate that ATM effectively computed electrostatic potential, electric fields—including fringing fields—stored energy, and 3D capacitance of the PDC model, showing good agreement with FEM and experimental results.