# Design of NO\({}_{2}\) Photoacoustic Detection System Based on Finite Element Simulation
## 3 Design of Photoacoustic System Simulation
### Design Dimensions of the Buffer Cavity  
The buffer cavity is the place where the gas is buffered in a photoacoustic cell, and because it is far from the resonance point, theoretically speaking, the impact on the photoacoustic signal is relatively small. The design of the buffer cavity of the photoacoustic cell can also be intuitively analyzed through the COMSOL simulation platform to determine the specific size of the buffer cavity.  
In the finite element calculation, the maximum sound pressure on the center line of the simulation model was extracted from the calculated results. First, the sweep frequency range was set. Referring to the longitudinal acoustic intrinsic frequency of the photoacoustic cell in Section 2.1, the frequency of the photoacoustic cell was scanned within the frequency range of 1000 Hz to 2500 Hz, and the scanning interval was 5 Hz. Furthermore, the length Lb of the resonator of the photoacoustic cell and the diameter Rb of the resonator, as shown in Table 1, were parameterized. The scanning range of Lb was from 40 mm to 60 mm, with a scanning interval of 10 mm, and the scanning range of Rc was from 10 mm to 30 mm, with a scanning interval of 5 mm, thus obtaining the simulation diagram shown in Figure 9.  
The simulation of different lengths and radii of resonator provides guidance for the design of resonator. As can be seen from Figure 10, under different buffer cavity lengths, there is such a feature that when the radius of the buffer cavity is less than 15 mm, the size of the photoacoustic signal decreases significantly, and the resonance frequency increases slightly. When the radius of the buffer cavity is greater than 15 mm, the size and resonance frequency of the photoacoustic signal are basically unchanged. Therefore, considering the principle of minimizing the design size of the photoacoustic cell, the radius of the buffer cavity of the photoacoustic cell was selected to be 20 mm.  
Figure 9: Simulation results for both variables.  
It can be roughly seen from Figure 10 that a change in buffer cavity length has little influence on the photoacoustic signal. In order to show this feature more clearly, the influence of different buffer cavity lengths under a buffer cavity radius of 20 mm was further studied. As shown in Figure 11, different buffer cavity lengths have little influence on the resonance frequency and photoacoustic signal, so the design of the buffer cavity length mainly considers the buffer effect on the gas and the size of the photoacoustic pool. In this paper, the length of the photoacoustic buffer cavity is 50 mm.  
Figure 11: The effect of length changes.  
Figure 10: Influence of radius changes at different lengths. (**a**) Length, 40 mm; (**b**) length, 50 mm; (**c**) length, 60 mm.  
Based on the above simulation results, three characteristics of the cylindrical photoacoustic cell buffer cavity and resonator design can be summarized: 1. The size of the photoacoustic signal increases with an increase in the length of the resonator L and decreases with an increase in the radius R. 2. When the radius Rb of the buffer cavity is greater than 15 mm, the size and resonance frequency of the photoacoustic signal are basically unchanged; when the radius Rb of the buffer cavity is less than 15 mm, the photoacoustic signal will be weakened. 3. In the proposed buffer cavity length range (40 mm to 60 mm), the design length of the buffer cavity Lb on the photoacoustic signal is very small and can be ignored. Based on the theoretical analysis and simulation results in Section 3, the length of the designed photoacoustic resonator L is 90 mm, and the radius R is 4 mm. The length of the buffer cavity Lb is 50 mm, and the radius Rb is 20 mm.