# Pure Electric Sweeper Performance Analysis and Test Verification of Dust Extraction Port
## 2 Numerical Simulation and Experimental Research Methods
### Numerical Simulation
\tag{6}\]  
Reynolds number:  
\[\text{Re}=\dfrac{\rho|u-u_{x}|d_{x}}{\mu} \tag{7}\]  
Gravitational force:  
\[G=m_{x}(1-\
icefrac{{\rho}}{{\rho_{x}}})g \tag{8}\]  
The lifting force is calculated by the following equation [24]:  
\[F_{N}=\dfrac{2 kv_{2}^{\
icefrac{{1}}{{\rho}}}\rho d_{ij}}{\rho pd_{p}(d_{lk}d _{kl})^{\
icefrac{{1}}{{4}}}}(u-u_{x}) \tag{9}\]  
where \(k\) generally taken as 2.594, \(v_{2}\) is the sport viscosity and \(d_{ij}\), \(d_{lk}\), and \(d_{kl}\) are the tensor variables. The particle distribution of the pavement particles in the simulation was adopted from the particle distribution proposed by [PERSON] et al. [8], and the specific distribution and main parameters are shown in Figure 3 and Table 2.  
Figure 3: Interval distribution of sand particles. The particles are in suspension when their own gravity is equal to the force of the air flow. Only when the airflow force is greater than its minimum value will the particle begin to move [25]. The particle movement velocity is the minimum air speed at which the particle starts to levitate, so the minimum velocity (\(u_{1}\)) at which the particle moves is as follows [26]:  
\[u_{1}=B\sqrt{\frac{\rho_{s}-\rho}{\rho}gd} \tag{10}\]  
where \(\rho_{s}\) is the particle density, \(d\) is the particle size, \(g\) is the gravity acceleration and \(B\) is the experience coefficient. Referring to the study by [PERSON] et al. [27], it can be concluded that the maximum start-up velocity for dust particles with a diameter of less than 3 mm is 20 m/s. A jet source is used at the inlet of the dust suction port to release the particles and the boundary condition is set to escape, where the particles enter the interior of the dust suction port uniformly from the dust suction inlet. The boundary condition is reflect at the inside of the suction port and the exit boundary is trap. The particles are trapped at the exit of the exhaust pipe during the simulation, while the tracking of the particles stops. The removal efficiency is expressed by the ratio of the number of particles collected at the outlet (_trap_) to the total number of particles incident (_tracked_) [28]. \[\eta_{1}=trap/tracked \tag{11}\]  
In a realistic working environment, the pressure, velocity and flow rate of the airflow entering the forward surface of the suction port are unknown, so in order to realistically simulate the working environment of the suction port, an external air domain needs to be added outside the port [29]. In conjunction with the study by [PERSON] et al. [30], it is clear that the geometric parameters of the external expansion domain directly affect the accuracy of the simulation. When the geometrical parameters are larger than a threshold value, the effect can be neglected. For different structures of dust extraction ports, the threshold value of the geometric parameter of the external expansion domain should be found and selected as the value of the geometric parameter in the calculation when the computational accuracy and computational efficiency of the simulation results are required to be high. Figure 4 shows the influence of the geometric parameters of the external expansion domain on the accuracy of the calculation. Here the influence of the length L, height H and angle \(\theta\) of the external expansion domain on the air velocity and pressure at the forward air surface and the air velocity at the exit of the exhaust pipe is investigated by varying the length L, height H and angle \(\theta\) to obtain the optimum geometric threshold. The optimum thresholds are 60 mm for the length, 80 mm for the height and 70\({}^{\circ}\) for the angle. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Particle mass flow rate (kg/s) & 0.5 \\ Min diameter (um) & 40 \\ Median diameter (um) & 81 \\ Max diameter (um) & 160 \\ Distribution coefficient & 5.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Discrete phase main parameters.