# Optimization of Screen-Hole-Clearing Devices for Mechanized Residual Film-Impurity Separation
## 2 Materials and Methods
### Working Parameters of the Blocking Clearing Device  
#### 2.3.1 Nozzle Spraying Device  
Nozzle Jet Airflow Coverage Area  
As displayed in Figure 2, the airflow occurred from the circular section (with radius R) nozzle spray, with point M as the pole; \(\angle\)AMO was the diffusion angle \(\zeta\); and the exit velocity in the section with uniform distribution was \(v_{0}\). The jet axis MO was regarded as the \(x\)-axis. The nozzle jet and the surrounding media had a constant mass and momentum exchange. This induced a flow in the surrounding media, and the mass flow rate of the jet and the cross-sectional area of the jet along the \(x\) direction increased, thereby forming a cone-like flow field involving diffusion in the surrounding media, as depicted by the cone CAMDF in Figure 2. The jet was continuously substituted in the surrounding media, enabling boundary expansion, and the velocity of the main body of the jet decreased gradually. The part of the jet with velocity \(v_{0}\) was the core of the jet, represented by the cone AOD displayed in Figure 2. The section BOE was the transition section, and the section on the axis of the airflow velocity had a velocity \(v_{0}\). The section between the exit section and the transition section was the jet start section, and the section beyond the transition section was the jet body section [13; 14; 15; 16]. When the radius of any circular section is \(R\) and the nozzle radius is \(r_{0}\), the radius of the jet along the shooting range according to the change law is as follows:  
\[\left\{ \begin{array}{l}\tan\zeta=\frac{\text{BO}}{\text{MO}}=\phi\zeta\\ \frac{R}{r_{0}}=\frac{l_{0}+s}{l_{0}}=1+\frac{s}{r_{0}/\tan\zeta}\end{array}  \right., \tag{1}\]  
where \(\phi\) is the nozzle shape coefficient; circular nozzle, \(\phi\) = 3.4; \(\zeta\) is the turbulence coefficient; and the diffusion angle is 60\({}^{\circ}\). According to the relational formula, the calculated value of the turbulence coefficient was 0.509. Combining the two equations in Equation (1) yields:  
\[R=r_{0}+1.731s. \tag{2}\]  
Figure 2: Nozzle jet airflow diffusion state analysis. Note: \(l\) indicates the distance from the pole to any circular section, m; \(l_{0}\) indicates the vertical distance from the pole to the nozzle section, m; \(s\) denotes the distance from the nozzle to any circular section, m; \(s_{0}\) denotes the length of the starting section, m.  
In the nozzle jet stream formed by the jet cone, the momentum at each cross-section was equal (in Figure 3), and the flow rate on the exit section and the relationship between the flow rate on any section was  
\[\pi\rho r_{0}^{2}v_{0}^{2}=\int_{0}^{R}2\pi\rho v_{\mathrm{y}}{}^{2}ydy, \tag{3}\]  
where \(\rho\) is the fluid density, kg/m\({}^{3}\); \(v_{0}\) is the speed of the nozzle exit section, m/s; and \(v_{y}\) is the speed at point \(y\), m/s. Dividing both sides by \(x\) obtained the following:  
\[\left\{ \begin{array}{l}\left(\frac{r_{0}}{R}\right)^{2}\left(\frac{v_{0}}{v _{\mathrm{m}}}\right)^{2}=2\int_{0}^{1}\left(\frac{v}{v_{\mathrm{m}}}\right)^ {2}\frac{y}{R}d\left(\frac{y}{R}\right)\\ B\mathrm{n}=\int_{0}^{1}\left(\frac{v}{v_{\mathrm{m}}}\right)^{n}\eta d\eta \end{array} \right., \tag{4}\]  
where \(v_{m}\) is the axial velocity of the section, m/s; and \(\eta\) is \(\frac{y}{R}\). According to the range of variation in \(\frac{y}{R}\) and \(\frac{v}{v_{\mathrm{m}}}\), B\({}_{2}\) was assumed to be 0.0464, and the velocity of the jet along the shooting range according to the law of change was  
\[\frac{v_{\mathrm{m}}}{v_{0}}=\frac{1.897}{0.578+\frac{s}{r_{0}}}, \tag{5}\]  
where the velocity of airflow at other locations in the same circular section was expressed as the mass-averaged flow velocity, \(v_{2}\); \(v_{2}\) = 0.47 \(v_{\mathrm{m}}\). Reasonable Range of Distance from the Nozzle to the Screen Surface  
When the screen hole faced the nozzle, the trommel screen rotation process resulted in the formation of a screen hole between the two nozzles for the jet airflow.