Objective In a trace gas detection system based on photoacoustic spectroscopy technology, the photoacoustic cell is a key performance component of the system. More and more high-performance photoacoustic cells have been designed, and many of them have a variety of specially-shaped photoacoustic cells. However, heterogeneous photoacoustic cells with high design properties represented by topology optimization often mean greater processing costs, while traditional photoacoustic cells are often limited by shape optimization parameters and low design freedom. Therefore, research on the photoacoustic cell must be thorough and in-depth. In this paper, a curved beam waist photoacoustic cell with a hyperbolic generatrix is proposed and designed. This scheme introduces innovative generatrix eccentricity parameter, realizes three-dimensional optimization, and effectively fills the gap between traditional photoacoustic cells and highly-designed specially-shaped photoacoustic cells.
Methods Based on the finite element method, we use COMSOL software to construct a two-dimensional model of a curved beam waist photoacoustic cell with a generatrix eccentricity of 7.14. To ensure the accuracy of the solution, this paper considers the influence of thermal viscosity loss on the simulation model. The first eight acoustic modal values of the structure and the visual mode shape are analyzed with respect to thermal viscosity loss. On this basis, the amplitude-frequency response curve of the photoacoustic cell was analyzed and the quality factor Q was calculated via Lorentz fitting, and the rationality of the microphone placement position was verified. To study the designability of the photoacoustic cell, we optimized the parameters of the photoacoustic cell. When eccentricity trended toward infinity, the effects of the length of the resonant cavity of the curved beam waist photoacoustic cell and the eccentricity of the generatrix on the resonance frequency and the sound pressure amplitude were analyzed in detail. To alleviate the design distress caused by too few parameters, generatrix eccentricity was introduced as the third optimization parameter, and its influences on the resonance frequency and sound pressure amplitude were analyzed in detail. Finally, further study of the influence of the variation of generatrix eccentricity on the resonance peak of the photoacoustic cell was analyzed.
Results and discusssions Simulation results show that the quality factor of the photoacoustic cell in the preliminary design is as high as 83.3, indicating that the photoacoustic cell is a high-quality photoacoustic cell. Analyzing the optimized photoacoustic cell parameters, it was found that the length of the resonant cavity is more sensitive to the resonant frequency, while the semiminor axis length of the generatrix is more sensitive to the sound pressure amplitude. Further analysis of the simulation results shows that when the semiminor axis length of the generatrix is large, it is very limited to adjust the sound pressure amplitude by changing the length of the resonant cavity, while adjusting the semiminor axis length of the generatrix hardly changes the resonance frequency. Therefore, only relying on these two parameters to optimize the design will be limiting and provide challenges meeting the design requirements of special photoacoustic cells. After the introduction of the generatrix eccentricity parameter, by changing and adjusting the generatrix eccentricity, the resonance frequency can be adjusted within a certain range without affecting the sound pressure amplitude. In the evolution graph of the frequency domain response curve with the eccentricity of the generatrix, it can be seen that two resonance peaks are excited when the eccentricity trends toward infinity, and four resonance peaks are excited when the eccentricity of the generatrix is five. Among the four resonance peaks with an eccentricity of 5, the first and second resonance peaks are stronger, and the quality factors reach 75.9 and 128.9, respectively.
Conclusions The quality factor Q of the designed photoacoustic cell is higher than 50, so this kind of curved beam waist photoacoustic cell can be designed with a higher quality factor, which can effectively improve the sensitivity of the trace gas detection system. After adding the optimized parameter of generatrix eccentricity, three-dimensional optimization was realized, which has a higher degree of designability than traditional cylindrical photoacoustic cells. The amplitude-frequency response characteristics of the photoacoustic cell show that a small eccentricity can excite multiple resonance peaks, and a resonance peak with a high quality factor can be obtained by adjusting the generatrix eccentricity. This shows that multi-peak resonance can be achieved by adjusting the eccentricity of the generatrix, so that the same photoacoustic cell has two or more effective working frequencies, which greatly improves the designability of the photoacoustic cell. This curved beam waist photoacoustic cell design has important theoretical and engineering application value for the multi-scene adaptability of novel photoacoustic trace gas detection technology.
