# Design of NO\({}_{2}\) Photoacoustic Detection System Based on Finite Element Simulation
## 2 Experimental Principle
### Basic Structure of Photoacoustic Cell  
The core component of the photoacoustic spectrum detection system is the photoacoustic cell, which is the place where the photoacoustic reaction occurs. The design structure of the photoacoustic cell will have a great influence on the photoacoustic signal. This paper designs and produces a classic cylindrical resonant photoacoustic cell, the core part of which is a cylindrical buffer cavity and a resonator and the composition of which is shown in Figure 1. As shown in Figure 1, the structure of the cylindrical resonant photoacousticcell designed in this paper consists of two parts: 1. the shell unit of the photoacoustic cell, which mainly includes the buffer cavity, incident window, exit window, inlet and outlet hole, etc., 2. the resonator unit, which mainly includes a resonator, a sound hole, a microphone slot, etc. The overall shell is rectangular, and the interior is made of a cylindrical cavity made of duralumin material. The cavity in the middle of the photoacoustic cell is called the resonator, the surface of the resonator is plated with nickel, and the modulation laser and the gas to be measured react in the resonator. A sound opening is arranged in the orthogonal position of the resonator, and a slot is machined above the opening to install a microphone with high sensitivity. The cavities at both ends of the photoacoustic pool are called buffer cavities, and the main function of the buffer cavity is to buffer the gas flowing into the buffer cavity to reduce the acoustic background noise. The air inlet and the air outlet are arranged at the upper part of the buffer cavity. The buffer cavity and the resonator of the photoacoustic cell are the most important components of the photoacoustic cell, and their design size will directly affect the size of the photoacoustic signal. However, the photoacoustic effect contains complex multi-physical field-coupling problems, and it is difficult to determine the specific design size by an analytical calculation method. In this paper, the approximate range of the resonator of the photoacoustic cell is determined by a theoretical analysis and practical requirements, and then, the specific design size is determined by a finite element simulation. The noise in the daily living environment is mostly medium- and low-frequency noise, and its noise frequency is lower than 1000 Hz. In order to avoid interference from external noise, the normal acoustic frequency value of the designed cylindrical resonant photoacoustic cell should be greater than 1200 Hz. According to Equations (5) and (6), we can see the following:  
\[f_{100}=\frac{v}{2(L_{c}+\frac{16}{3\pi}R_{c})}>1200\;\mathrm{Hz} \tag{7}\]  
According to the equation of the state of an ideal gas,  
\[v=\sqrt{\frac{\gamma P_{0}}{\rho_{0}}}=\sqrt{\frac{\gamma R}{M}T_{0}} \tag{8}\]  
where \(\gamma\) represents the specific heat ratio of the gas, \(P_{0}\) represents gas pressure, \(\rho_{0}\) represents gas density, \(M\) represents the molar quantity of the gas, \(R\) represents the gas constant, and \(T_{0}\) represents the thermodynamic temperature. These parameters of N\({}_{2}\) at a normal temperature and pressure are as follows: \(\gamma=1.401\), \(T_{0}=293\;\mathrm{K}\), \(R=8.314\;\mathrm{J/K\cdot mol}\), and \(M=0.028\;\mathrm{kg/mol}\). Combined with Formula (7), it can be seen that the resonance length of the cylindrical resonant photoacoustic cell is less than 130 mm. The resonant-length design of the photoacoustic cell needs to balance processing, noise, and performance problems. Too long  
Figure 1: Structure of cylindrical photoacoustic cell. a length facilitates the introduction of environmental noise at the same time as drilling and polishing, and too short a length is not conducive to the acoustic performance of the photoacoustic cell. In addition, the resonance radius of the photoacoustic pool should also be slightly larger than the spot size of the beam (2 mm), but it cannot be too large, and the cavity radius is too large to affect the resonance effect.