Numerical calculation and optimization of photoacoustic cell for photoacoustic spectrometer

Abstract

Photoacoustic spectroscopy (PAS) offers intrinsic attractive features in the detection of trace gases, including ultra-compact size and background-free absolute absorption measurement. The photoacoustic (PA) cell is a key component in the PAS system, which determines the performance of the PAS sensor. In this paper, a cylindrical resonant photoacoustic cell is taken as a research target. Based on the fundamental theory of acoustics and absorption spectrum, a mathematical model of acoustic field excitation in the PA cell is established. The acoustic resonance frequency, quality factor and cell constant of the PA cell are used as three key parameters to describe its performance. By employing advanced computer numerical calculation and finite element simulation technology, we establish a simulation model and impose the excitation load and boundary conditions on the model according to the actual working conditions. Then we calculate and simulate the acoustic modal of the PA cell, and the first eight acoustic modal values of the cavity and the visual vibration model of the acoustic pressure are obtained. With considering the acoustic loss, the thermo-acoustic coupling multi-physical field simulation of photoacoustic cell is carried out. Comparing with analytical calculation and experiment results, the reliability and feasibility of using numerical simulation method to calculate the relevant parameters of photoacoustic cell are demonstrated. In order to obtain a better structure of photoacoustic cell, an optimization algorithm combining response surface proxy model with multi-objective genetic algorithm is proposed. We try to change the shapes of both ends of the resonator in the original photoacoustic cell into the shape of the bell mouth. Take into account the case that the longitudinal acoustic normalization frequency of the PA cell is larger than 1000 Hz, Pareto optimal solution set with the maximum quality factor <i>Q</i> and cell constant <i>C</i>_cell of the PA cell is obtained. The results show that the maximum error between the predicted and simulated values of the proxy model of the PA cell <i>Q</i> and <i>C</i>_cell is only 1.3%. Comparing with the original PA cell, the <i>Q</i> factor and the <i>C</i>_cell of the optimized PA cell are increased by 48.9% and 34.4%, respectively. The performance of the optimized photoacoustic cell is obviously improved. The proposed algorithm of photoacoustic numerical simulation combined with multi-objective optimization design can provide helpful reference for designing the PA cell in PAS sensor development.