# Design of NO\({}_{2}\) Photoacoustic Detection System Based on Finite Element Simulation
## 3 Design of Photoacoustic System Simulation  
### System Modeling and Modal Analysis  
The simulation platform used was the COMSOL multi-physics simulation platform. COMSOL6.3 is a global and powerful simulation software, which includes a variety of physical fields such as structural mechanics, acoustics, electromagnetism, and fluid flow. It provides a simulation under a single physical field and flexible coupling of multiple physical fields for analyses. According to the structure and specific size of the photoacoustic cell, shown in Figure 1, a finite element analysis (FEM) was used to simulate and calculate the photoacoustic system. First of all, we optimized the physical model of the photoacoustic pool to a certain extent, ignoring the falling hole, the outlet hole, and the opening of the sound hole, and only retained the main part of the photoacoustic pool. Figure 3 shows a system grid model established by the COMSOL simulation platform. Some parameters were further set to facilitate the subsequent parameter scanning. The specific parameter settings are shown in Table 1. The expression of the design parameters of the photoacoustic cell given here was determined by research and analysis after the parameter scanning.  
In the selection of a physical field, a frequency domain analysis of thermos-viscous acoustics was carried out. The division of the physical grid is an important factor affecting the simulation effect. The model was set to the user control grid, the free tetrahedral grid type, and was calibrated to the general physics, with a maximum cell size of 3.4 mm and a minimum cell size of 0.05 mm.  
An acoustic modal simulation was carried out on the built finite element model. Figure 4 shows the first 6 acoustic modes. In this figure, the colors from red to blue  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Expression** & **Description** \\ \hline L & 90 mm & Cavity length \\ R & 4 mm & Cavity radius \\ Lb & 50 mm & Buffer cavity length \\ Rb & 20 mm & Buffer cavity radius \\ \hline \hline \end{tabular}
\end{table}
Table 1: Photoacoustic cell parameters.  
Figure 3: Grid model of photoacoustic cell.  
Figure 2: Schematic of experimental setup.  
represent the relative strength of the sound pressure, and the sound pressure of the part close to blue is zero. From Figure 4, we can observe the following points: 1. With an increase in mode order, the acoustic modes of the photoacoustic cell become more and more complex. 2. When designing the position of the acoustic sensor, try to choose the position with strong sound pressure. 3. When designing the inlet and outlet, try to choose a position with low sound. Figure 5a shows the pressure change in the photoacoustic cell under the second-order mode, and Figure 5b shows the pressure change on the center line of the photoacoustic cell under the second-order mode.  
The photoacoustic cell designed in this paper works in the second-order mode, and the sound pressure distribution in this mode is characterized by the sound pressure decreasing gradually from the middle of the photoacoustic cell to both ends. According to the distribution characteristics of the sound pressure, the microphone was installed in the center of the resonator, and the inlet and outlet were installed in the buffer cavity. The acoustic mode in this state is called the \"operating longitudinal acoustic normal mode\", and the operating frequency in this mode is called intrinsic frequency or normal frequency.  
Figure 4: Acoustic mode simulation of photoacoustic cell. (**a**) First pattern (207 Hz); (**b**) second pattern (1769 Hz); (**c**) third pattern (3118 Hz); (**d**) fourth pattern (3424 Hz); (**e**) fifth pattern (3567 Hz); (**f**) sixth pattern (4893 Hz).  
Figure 5: Eigenfrequency finite element simulation. (**a**) Acoustic simulation results (1769 Hz); (**b**) acoustic pressure of the scanning length.  
Through a simulation of its acoustic mode, the working mode of the system and the design position of the microphone were provided with guidance.