FEM analysis of cylindrical resonant photoacoustic cells

Abstract

Using a mathematical model on photoacoustics that includes both temperature and pressure effects explicitly, we analyze the behaviour of resonances of a cylindrical photoacoustic cell consisting of two buffer volumes and a resonator. We excite the cell at a certain frequency and find the ratio of resonator versus buffer diameter needed to obtain resonance. The results show that the resonance ratio depends on the absolute cell size. Also the amplitude of the acoustic signal measured in the middle of the resonator does not necessarily decrease when the total cell volume is increased. If the resonator diameter is sufficiently small, decreasing its diameter will increase the acoustic signal, although the total cell volume has to be increased to obtain resonance. This gives the advantage of being able to obtain a comparably large signal and at the same time use large buffer diameters to suppress window absorption signals. Finally we also compare the quality of the above-mentioned model and the lossy Helmholtz equation. We find that there is a shift in resonance ratio and the signal damping differs slightly. Albeit these differences are not large, and in many cases negligible, the model can be easily coupled with a solid absorption model in order to investigate the importance of thermal and pressure coupling between two acoustic media subject to heat absorption.