# Aerodynamic Window Sealing of a Large-Aperture Channel for High-Power Laser Transmission
## 2 Theory Model  
The high-power laser emission system carries air purification equipment, which filters out most of the water and dust particles in the air to obtain a dry and clean gas with a very low heat absorption coefficient. The purge gas can be considered a viscous fluid with constant density, and the flow field in the channel is considered an incompressible field. The incompressible viscous gas hydrodynamic equations for the numerical analysis of the fluid in a large-aperture channel are expressed as [21]:  
\[\
abla.\overrightarrow{v}=0 \tag{1}\]  
\[\frac{\partial\overrightarrow{v}}{\partial t}+\left(\overrightarrow{v}. \
abla\right)\overrightarrow{v}=\overrightarrow{F}-\frac{1}{\rho}\
abla p +\frac{\mu}{\rho}\
abla^{2}\overrightarrow{v} \tag{2}\]where \(\overset{\rightarrow}{v}\) indicates the velocity vector, \(\overset{\rightarrow}{F}\) denotes the external force per unit volume, and \(\mu\) indicates the dynamic viscosity.  
The motion of the discrete phase of the dust particles is solved by the equation of balance of forces, which are expressed as [22]:  
\[\frac{du_{p}}{dt}=F_{D}\Big{(}u_{f}-u_{p}\Big{)}+\frac{g\big{(}\rho_{p}-\rho \big{)}}{\rho_{p}}+F_{p} \tag{3}\]  
\[F_{D}=\frac{18\mu}{\rho_{p}d_{p}^{2}}\frac{C_{D}\text{Re}}{24} \tag{4}\]  
\[\text{Re}=\frac{\rho d_{p}\Big{|}u_{p}-u_{f}\Big{|}}{\mu} \tag{5}\]  
\[C_{D}=0.22+\frac{24}{\text{Re}}\Big{[}1+0.15\text{Re}^{0.6}\Big{]} \tag{6}\]  
where \(u_{f}\) denotes the fluid speed, \(u_{p}\) corresponds to the particle speed, \(\rho_{p}\) symbolizes the particle density, \(d_{p}\) indicates the particle diameter, \(C_{D}\) denotes the traction coefficient, and \(F_{p}\) refers to the other force on the dust particle.  
It is assumed that ambient air comprises ambient gas and dust particles. The high-power laser transmitted in the channel is a collimating Gauss light beam with a waist radius of 50 mm. To avoid the influence of the channel on the beam, a large-aperture channel with an outer diameter of 160 mm and an inner diameter of 154 mm was selected. Three blowing schemes modeled to achieve large-aperture channel sealing using the incompressibility of the purge gas are presented in Figure 1. Figure 1a illustrates that the channels are connected using a dynamic sealing structure, and that the mirrors are installed at the corners of the channels so that the laser can freely change the beam direction by transmitting in the rotating channels. Moreover, the air purification equipment output volume flow of purge gas is certain, and the gas has three transmission paths. First, via the axial blowing directly into the large-aperture channel; second, via the guide tube radial blowing to the large-aperture channel port; third, via simultaneous axial blowing and radial blowing. Figure 1b,c show the structure and location of the radial blowing scheme outlet. If radial blowing is required to seal the large-aperture channel, the width of the airflow must be greater than 160 mm. To leave a margin for airflow width, we chose to use nine guide tubes with an outer diameter of 20 mm. At the same time, the cuboid pipe of \(180\times 180\times 20\) mm in size was connected to the outlet of the guide tube so that the gas flowed out from the other side of the cuboid pipe more evenly.  
Figure 1: _Cont._