# Optimization of Screen-Hole-Clearing Devices for Mechanized Residual Film-Impurity Separation
## 2 Materials and Methods
### Working Parameters of the Blocking Clearing Device
#### 2.3.2 Calculation of the Fan Wind Speed Range  
The force state of the residual film-impurity mixture blocked at the sieve hole is illustrated in Figure 5.  
Figure 4: Distance from the nozzle to the screen surface and its relationship with the jet radius. (**a**) Local velocity cloud chart. (**b**) Schematic of airflow diffusion. Note: \(L_{1}\) is the minimum distance from the nozzle to a particular screen hole, mm; \(L_{2}\) is the diameter of the screen hole, mm; \(L_{3}\) is the distance from the nozzle to the screen surface, mm. The screen hole was located between the two nozzles, and the airflow resistance effect of the two nozzles on the residual film-impurity mixture was accounted for in the calculation of the fan wind speed range; the airflow resistance was twice the \(F_{\mathrm{t2}}\) component force. The residual film-impurity mixture underwent uniform rotation because of a blockage in the tremmel sieve. Various force components in the vertical direction resulted in a centripetal force. \(F_{N}\) = 0 N when the film-hybrid mixture was separated from the tremmel sieve moment. The relationships representing the residual film-mixture force equilibrium were as follows:  
\[\left\{ \begin{array}{l}2F_{\mathrm{t2}}\sin\delta+mg-F_{\mathrm{t1}}\sin \gamma=m\omega^{2}r\\ F_{\mathrm{t1}}=\frac{1}{2}CA\rho_{\mathrm{s}}v_{\mathrm{1}}\\ F_{\mathrm{t2}}=\frac{1}{2}CA\rho_{\mathrm{s}}v_{\mathrm{2}}\end{array} \right., \tag{8}\]  
where \(m\) is the mass of the membrane mixture, kg; \(g\) is the acceleration of gravity, regarded as 9.81 m/s\({}^{2}\); \(\omega\) is the rotational angular velocity of the tremmel sieve, rad/s; \(r\) is the radius of the tremmel sieve, m; \(C\) is the material resistance coefficient, regarded as 0.44; \(A\) is the material windward area, m\({}^{2}\); \(\rho_{\mathrm{s}}\) is the density of the material, kg/m\({}^{3}\); \(v_{\mathrm{1}}\) is the velocity of the airflow inside the tremmel sieve for clearing, according to the previous study, regarded as \(v_{\mathrm{1}}\) = 8.5 m/s, and the horizontal angle \(\gamma\) = 8\({}^{\circ}\); \(v_{\mathrm{2}}\) is the nozzle jet blockage clearing the airflow at the screen hole speed; and the horizontal angle is \(\delta\), where \(\alpha\leq\delta\leq\beta\), m/s [17]. The force of the nozzle jet airflow on the residual film-impurity mixture in the vertical direction is the sum of the resistance of the jet airflow and the weight of the residual film-impurity mixture. For the clearing of the plug, this force should be greater than the force of the internal flow field of the tremmel screen on the residual film-impurity mixture in the vertical direction. The resistance of the clearing airflow and the centripetal force required for the residual film-impurity mixture should follow the circumferential motion of the tremmel screen. The relationship between the equations was as follows:  
\[2F_{\mathrm{t2}}\sin\delta+mg\geq F_{\mathrm{t1}}\sin\gamma+m\omega^{2}r. \tag{9}\]  
Substituting Equation (8) into Equation (9), the relationship for the airflow velocity \(v_{\mathrm{2}}\) was obtained as follows:  
\[v_{\mathrm{2}}\geq\left.\left(v_{\mathrm{1}}\sin\gamma+\frac{2m\omega^{2}r}{ CA\rho_{\mathrm{s}}}-\frac{2 mg}{CA\rho_{\mathrm{s}}}\right)\right/2\sin\delta \tag{10}\]  
The test revealed that the average mass of the residual film-impurity mixture was 1.03 \(\times\) 10\({}^{-3}\) kg, the average density was 162.5 kg/m\({}^{3}\), the average windward area of the residual film-impurity mixture was 5.57 \(\times\) 10\({}^{-3}\) m\({}^{2}\), the angular velocity of the tremmel sieve was 13\(\pi\)/15 rad/s, and the radius of the tremmel sieve was 0.5 m [18]. According to the relationship between \(L_{\mathrm{1}}\), \(L_{\mathrm{2}}\), and \(L_{\mathrm{3}}\) in Figure 4, 0.44 \(\leq\) sin\(\delta\)\(\leq\) 0.59, so \(v_{\mathrm{2}}\)\(\geq\) 1.308 m/s. Figure 5: Schematic of the force of the residual film plugging process.