Spiral capacitor calculation using FEniCS

TL;DR

This paper demonstrates how to model and optimize a spiral capacitor water level sensor using FEniCS by reducing a 3D problem to 2D, applying boundary conditions, and calculating capacitance to find optimal design parameters.

Contribution

It introduces a method to model spiral capacitors with FEniCS, including coordinate transformation, boundary condition setup, and capacitance calculation, with an optimization of sensor sensitivity.

Findings

Optimal spiral frequency and stripe width maximize sensor sensitivity.

FEniCS code effectively solves the Laplace equation for this geometry.

Numerical experiments identify the best design parameters.

Abstract

The paper shows how to optimize a water level sensor consisting of a cylinder with spiraling metal stripes on the side, using a powerful Python library FEniCS. It is shown how to reduce a 3D Laplace equation to a 2D, using a spiraling coordinate system; how to specify the correct boundary conditions for an open region; how to convert the partial differential equation to a variational form for FEniCS; and how to calculate the capacitance. Then the FEniCS code is shown that solves the Laplace equation and calculates the capacitance. The further numeric experiments show that there is an optimal combination of the spiral frequency and the width of the stripes that maximizes the sensitivity of the sensor. The Python code is given to calculate the optimum.