Results of simulation
Analysis of the initial model simulation
Figures 12 and 13 respectively depict the airflow velocity distribution cloud diagram and velocity vector diagram of the suction hood width direction neutral surface.
Vector diagram of air velocity distribution. Note: I represents the stage before the airflow enters the suction hood; II represents the stage of airflow entering the suction hood; III represents the stage after the airflow enters the suction hood.
As shown in Figs. 12 and 13, the airflow generated by the fan mainly affects the movement of the film and impurity materials on the sieve disc directly below the suction hood. Before entering the suction hood (I), the airflow is distributed along the edge of the sieve disc, forming a low-velocity region. In this region, the velocity is greater than the suspension velocity of the residual film but less than that of the cotton straw and soil, so that the films tend to enter the suction hood. When the airflow enters the suction hood along the edge of the disc (II), an accelerated region is formed. This is due to the decrease in the airflow movement space formed by the sieve disc and suction hood, forming a ‘throat tube’, which contributes to the rapid stratification and separation of the materials. In this region, the residual films quickly concentrate on the upper layer of the film and impurity materials and enter the suction hood. After the airflow enters the suction hood (III), two micro-velocity regions are formed at 1/3 of the two edges of the suction hood near the bottom. This is because the airflow through the ‘throat tube’ still has an accelerating trend, converging towards the middle of the suction hood. The airflow in the middle area of the suction hood accelerates upward. This is because the hood has a wide lower and narrow upper structure, resulting in a continuous decrease in the airflow movement space and increasing acceleration of the airflow. From bottom to top, an airflow belt with a velocity level higher than the level is formed, which promotes the residual films to pass through the hood quickly without blockage.
To further analyze the variation law of the airflow velocity on the sieve surface under the double action, the distribution of airflow velocity measurement points was established as shown in Fig. 14. Furthermore, Fig. 14a shows 11 measurement point columns such as A ~ A’ established in the length direction of the sieve surface, and Fig. 14b illustrates the distribution of 29 measurement points in the width direction of each measurement point column. Thus, a total of 319 measurement points is taken.
Distribution of airflow velocity measurement points in the airflow-disc sieve double action area. (a) Measuring points along the length of the disc sieve. A ~ A′ represent Column 1 ~ Column 11 in sequence. (b) Measuring points along the width of the disc sieve. (I) represents Column 1 (also Column 11); (II) represents Column 2 (also Column 10); (III) represents Column 3 (also Column 9); (IV) represents Column 4 (also Column 8); (V) represents Column 5 (also Column 7); (VI) represents Column 6.
Through the CFD-Post module, the airflow velocity at each measuring point is extracted when the wind pressure is -100 Pa, and the change trend of airflow velocity is obtained, as shown in Fig. 15. The change law of airflow velocity at symmetrical positions on both sides of the middle line (column 6) is consistent, which is manifested as the periodic fluctuation of airflow velocity from columns 2 to 10, and the overall change law is approximately ‘jagged’. Among them, the airflow velocity near the edge of the suction hood (columns 2 and 10 as one group, columns 3 and 9 as another group) shows a periodic fluctuation that first attenuates and then increases in the width direction of the disc sieve, and the velocity trend near the center (columns 4 ~ 8) is the opposite. This is because the adjacent discs on the same shaft are arranged at a phase angle of 60°, and the adjacent discs on the adjacent shaft are staggered at a phase angle of 30°, thus, different airflow motion spaces are formed in the cross-section of each column of the measuring points (Fig. 14b). The corresponding airflow motion space changes periodically, and the airflow velocity also fluctuates periodically. The law is that the airflow velocity near the sieve disc is small, and the velocity far from the disc is large. This is due to the negative pressure field formed by the fan and suction hood. Under negative pressure, the airflow in the external flow field passes through the sieve discs and enters the suction hood from the bottom of the disc sieve. When the airflow bypasses the disc, the streamline turns inward (Fig. 16), and there is a reverse pressure gradient. The kinetic energy of air is converted into pressure energy, and the velocity decreases. After passing through the discs, the velocity increases under the action of the fan and the suction hood. Therefore, the airflow velocity near the discs is in the decreasing stage, and the velocity far from the discs is in the continuous acceleration stage, which makes the transverse airflow of the sieve surface always fluctuate. The airflow velocity difference aggravates the disturbance of the migration trajectory of the material on the sieve surface, which is beneficial to the movement of the residual films in the lower layer to the upper layer, and then realizes separation under airflow attraction. The airflow velocity of the sieve surface (columns 1 and 11) away from the suction hood is basically stable, and the average velocity is 0.95 m/s. This is because there is no obstacle near the measuring point, which has no effect on the airflow motion space.
Trend of airflow velocity on the sieve surface of the initial model.
Airflow distribution around the measurement points. Pn refers to the measuring point near the sieve disc; Pf refers to the measuring point far from the sieve disc.
Analysis of the effect of wind pressure on airflow velocity
Figure 17 presents the trends of the airflow velocity on the sieve surface under different wind pressure conditions. Figure 17a, b, c and d represent the variation trends at the air inlet under − 50 Pa, -75 Pa, -125 Pa, and − 150 Pa wind pressure, the overall trends being basically the same. With the increase in wind pressure, the airflow velocity increases, but the growth rate gradually decreases, indicating that the wind pressure has a significant effect on the airflow velocity. When the negative wind pressure increases from 50 to 150 Pa, the growth rate of the airflow velocity near the discs decreases from 22.67 to 9.61%, and that of the velocity far from the discs decreases from 27.80 to 11.58%. This shows that when the negative wind pressure continues to increase to a critical value, the airflow velocity tends to be stable. During the separation process, the airflow velocity on the sieve surface needs to be between the suspension velocity of the residual film and that of impurities such as cotton straw and soil. The maximum airflow velocity cannot exceed the suspension velocities of cotton straw and soil, and the minimum airflow velocity cannot be smaller than the suspension velocity of the residual film. In the previous experiments, the suspension velocity range of the residual film was 1.04 ~ 3.20 m/s, the suspension velocity range of the cotton straw was 6.70 ~ 8.59 m/s, and the suspension velocity range of the soil was 6.40 ~ 15.80 m/s. When the wind pressure is -125 Pa, the maximum velocity far from the discs is 3.57 m/s, and the minimum is 1.57 m/s, which are higher than the suspension velocity of the residual film, which can make the residual films at the measuring point on the far screen surface separate from the cotton stalks and stones under the action of airflow. When the wind pressure is -125 Pa, the airflow velocity far from the discs has covered the range of the residual film suspension velocity, and the utilization rate of the airflow is high, which meets the airflow demand during the separation process. Under this condition, the airflow velocity of the connection port between the suction hood and pipeline is 13.67 m/s.
Trend of airflow velocity on screen surface under different wind pressure conditions, plotted by Origin 2018 software (https://www.originlab.com/). (a) Wind pressure is -50 Pa; (b) wind pressure is -75 Pa; (c) wind pressure is -125 Pa; (d) wind pressure is -150 Pa.
When the fan rotational velocity is 1160 r/min, the average value of the airflow velocity of the connection port between the suction hood and pipeline is 13.15 m/s, and the error with the airflow velocity value under the wind pressure of -125 Pa in the simulation test is 3.80% (less than 5%), which provides a basis for the setting of the fan rotational velocity in the film and impurity materials separation experiment.
Results of separation experiment
Regression analysis of experiment results
Table 3 showcases the Box-Behnken experimental design and results, unveiling how fan rotational velocity A, disc rotational velocity B, feeding quantity C influence impurity removal rate Y1 and film leakage rate Y2. According to Table 3, Design-Expert 13 data analysis software was used for multiple regression fitting analysis. A variance analysis was conducted on the experimental results and regression models, and the results are shown in Table 4. Coded regression models with the impurity removal rate Y1 and the film leakage rate Y2 as response functions and the influencing factors as independent variables were obtained, as shown in Eq. (26).
$$\left\{ {\begin{array}{*{20}l} {Y_{1} = 95.10 – 0.9387A + 0.43B – 1.01C + 2.16AB – 0.225AC} \hfill \\ { – 0.0675BC – 0.4780A^{2} – 0.3405B^{2} – 0.3680C^{2} } \hfill \\ {Y_{2} = 37.94 – 7.23A + 5.29B – 1.08C – 5.34AB + 3.17AC} \hfill \\ { + 0.885BC – 5.90A^{2} – 3.16B^{2} + 6.77C^{2} } \hfill \\ \end{array} } \right.$$
(26)
The P-values of the impurity removal rate (Y1) and film leakage rate (Y2) are all less than 0.01, indicating that the established regression models of Y1 and Y2 are highly significant. The P-values of the lack-of-fit terms are all greater than 0.05, indicating that the models have a high degree of fit. The coefficients of determination R2 of the models are 0.903 and 0.920, respectively, indicating that the models can explain more than 90% of the variability of the experimental data, and are suitable for the prediction of the impurity removal rate and film leakage rate of the separation device.
By analyzing the P-value of each factor, the effect of the factor on the impurity removal rate Y1 is in the order of feeding quantity C, fan rotational velocity A, disc rotational velocity B in descending order, and the effect on the film leakage rate Y2 is in the order of fan rotational velocity A, disc rotational velocity B, feeding quantity C in descending order.
Sensitivity analysis
To further analyze the response of the device’s separation performance to parameter deviations, a parameter sensitivity analysis was conducted based on the Box-Behnken experiment. According to Table 3, the mean and range of the corresponding impurity removal rate and film leakage rate under different levels of each factor can be obtained. Under different levels of fan rotational velocity A, the mean values of the impurity removal rate are 95.20%, 94.78% and 93.33% respectively, with a range of 1.87%. The mean values of the film leakage rate are 41.08%, 39.54% and 26.62% respectively, with a range of 14.46%. Under different levels of disc rotational velocity B, the mean values of the impurity removal rate are 93.90%, 94.72% and 94.76% respectively, with a range of 0.86%. The mean values of the film leakage rate are 29.92%, 38.32% and 40.51% respectively, with a range of 10.59%. Under different levels of feeding quantity C, the mean values of the impurity removal rate are 95.33%, 94.73% and 93.31% respectively, with a range of 2.02%. The mean values of the film leakage rate are 41.25%, 33.91% and 39.10% respectively, with a range of 7.34%. Thus, C causes the largest range of the impurity removal rate, while B causes the smallest range. This indicates that the change of C has the greatest influence on the impurity removal rate, followed by A, and B has the least influence. A causes the largest range of the film leakage rate, while C causes the smallest range. This shows that A has the greatest influence on the film leakage rate, followed by B, and C has the least influence. This is consistent with the results of the factor significance analysis of variance given in Table 4.
The sensitivity coefficient µ is introduced for parameter sensitivity analysis27. Equation (27) gives the calculation method for the coefficient.
$$\mu = \left| {\frac{x}{\Delta x} \times \frac{f(x + \Delta x) – f(x)}{{f(x)}}} \right|$$
(27)
where, x is the initial input value of the parameter; Δx is the input variable value of the parameter; f(x) is the calculated output result corresponding to the initial input value; f(x + Δx) is the calculated output result corresponding to the variable value. The larger µ is, the greater the influence of the parameter on the analysis index, and vice versa.
According to Eq. (27), the mean values of the sensitivity coefficients of the impurity removal rate under different levels of A, B and C are 0.02, 0.01 and 0.02, respectively; the mean values of the sensitivity coefficients of the film leakage rate are 0.32, 0.43 and 0.26, respectively. Therefore, the sensitivity of A, B and C to the impurity removal rate, from high to low, is A = C > B. However, the overall sensitivity levels of the three parameters to the impurity removal rate are relatively low. The sensitivity of A, B and C to the film leakage rate, from high to low, is B > A > C. This is different from the above-mentioned analysis of variance and range analysis. The main reason is that the sensitivity coefficient analysis is based on the relative change ratio between parameters and results, which can effectively explain the relative influence degree. In contrast, the analysis of variance decomposes the total variation and comprehensively considers the influence of factors and their interactions on the results. The range analysis judges the importance of factors by comparing the ranges of test results under different levels of each factor, only considering the difference between the maximum and minimum values. Therefore, the results of the sensitivity coefficient analysis are also reasonable. As can be seen from the above analysis, the parameter changes have a relatively low sensitivity to the impurity removal rate and a relatively high sensitivity to the film leakage rate. That is, as the parameters change, the impurity removal rate varies within a small range, while the film leakage rate varies within a large range. Therefore, when considering the weight of the response targets of the impurity removal rate and the film leakage rate during the operation and optimization phases of the separation device, the priority and weight of the film leakage rate indicator can be moderately increased to ensure the stable and efficient operation of the device.
Response surface analysis
Figure 18 shows that the interaction of fan rotational velocity A and disc rotational velocity B influences the effect of the impurity removal rate Y1, when the feeding quantity C is fixed at the central level (C = 154 kg/h). When A is at a lower level, Y1 exhibits a decreasing trend with the increase of B. When A is at a higher level, Y1 shows a gradual increase with the increase of B. When B is at a lower level, Y1 exhibits a decreasing trend with the increase of A. When B is at a higher level, Y1 shows a gradually increasing trend with the increase of A.
Figure 19 shows that the interaction of the fan rotational velocity A and disc rotational velocity B affects the film leakage rate Y2, when the feeding quantity C is fixed at the central level (C = 154 kg/h). When A is at a lower level, Y2 shows an increasing tendency with the increase of B. When A is at a higher level, Y2 shows a tendency to increase firstly and then decrease with the increase of B. When B is at a lower level, Y2 tends to increase and then decrease with the increase of A. When B is at a higher level, Y2 tends to decrease with the increase of A.
The surface plot of impurity removal rate response, generated by Origin 2018 software. It shows the interactive effects of fan rotational velocity A and disc rotational velocity B on impurity removal rate Y1.
The surface plot of film leakage rate response, generated by Origin 2018 software. It shows the interactive effects of fan rotational velocity A and disc rotational velocity B on the film leakage rate Y2.
Reason analysis: When the disc rotational velocity B (B = 26 r/min) is at a lower level, the film and impurity materials maintain a low-velocity migration. The vertical displacement after the collision with the disc is small, and there is basically no gap between the material layers. According to Eq. (17), when the materials move along the sieve disc, the velocity difference between the residual films and the straw-soil mixture is small, the relative motion trend is weak, and separation is difficult. Owing to the coverage of the straw-soil mixture, the effect of airflow on residual films is weakened. The residual films pressed underneath are transported with the movement of the cotton straw and soil to the cotton and soil impurity collection boxes. Consequently, the impurity removal rate Y1 decreases, and the film leakage rate Y2 increases. As the fan rotational velocity A increases from 1120 to 1450 r/min, the wind force continues to strengthen. In this case, the surface layer of broken straw and soil particles with a small mass overcome gravity and are transported to the residual film collection box under the action of airflow. The force component of gravity of the straw-soil mixture in the normal direction is partially offset by the wind force, the pressure on the residual films is reduced, and the bonding strength between the residual film layers is reduced. The broken films (the maximum outside dimensions in the range of 0 ~ 100 mm) are drilled from the gap of the residual film layers, and migrated to the residual film collection box under the action of air flow. As a result, the impurity removal rate Y1 continues to decrease, and the film leakage rate Y2 gradually decreases.
When the disc rotational velocity B (B = 54 r/min) is at a higher level, the film and impurity materials maintain rapid transport. The vertical displacement after the collision is large, and the gaps are generated between the material layers. When moving along the sieve surface, the velocity difference between the residual films and the straw-soil mixture is large, the relative motion trend is obvious, and it is easy to separate. In the process of movement, the broken films drill out from the gap between the material layers, and move to the residual film collection box under the action of air flow. As the fan rotational velocity A increases from 870 to 1450 r/min, the wind force continues to increase, and the pressure of the straw-soil mixture on the residual films decreases. In this case, the acceleration and motion velocity of the residual films in the vertical direction gradually increase, and the films are rapidly transported to the residual film collection box. As a result, the impurity removal rate Y1 gradually decreases, and the film leakage rate Y2 gradually decreases.
When the fan rotational velocity A (A = 870 r/min) is at a lower level, the wind force is small. With the disc rotational velocity B increasing from 26 to 54 r/min, the transport velocity of the film and impurity materials increases. The velocity difference between the residual films and the straw-soil mixture also increases, and the separation tendency is enhanced. Due to the insufficient airflow intensity and the short time of full contact with the airflow, when the residual films are separated from the straw-soil mixture, there are fewer residual films that can be transported to the residual film collection box. After migrating through the suction hood, the residual films are mixed with the straw-soil mixture. As a result, the impurity removal rate Y1 gradually decreases, and the film leakage rate Y2 gradually increases.
When the fan rotational velocity A (A = 1450 r/min) is at a higher level, the wind force is large. With the disc rotational velocity B increasing from 26 to 39 r/min, the transport velocity of the film and impurity materials gradually increases. The vertical displacement after the collision gradually increases, and the gaps between the material layers gradually become more. When moving along the sieve surface, the separation trend of the residual films from the straw-soil mixture increases, the pressure of the straw-soil mixture on the residual films gradually weakens, and the amount of residual film migrating to the residual film collection box increases. During the movement, the broken films drill out from the gap between the material layers, and maintain a slower migration velocity. In this case, the broken films leak directly from the sieve disc gap before reaching the double action area. As a result, both the impurity removal rate Y1 and the film leakage rate Y2 gradually increase. With the disc rotational velocity B increasing from 39 to 54 r/min, the separation trend of the residual films from the straw-soil mixture continues to increase, and the amount of residual film migrating to the residual film collection box continues to increase. During the movement process, the broken films drill out from the gap, and maintain a faster migration velocity. In this case, the broken films quickly move to the double action area, and are transported to the residual film collection box under the action of the airflow. As a result, the impurity removal rate increases, while the film leakage rate decreases.
Parameter optimization
The impurity removal rate is related to the purity and quality of the separated residual films, while the film leakage rate is related to processing costs, production continuity and environmental impact. From the perspective of actual production, the main purpose of designing this separation device is to provide key pretreatment technical equipment for the resource utilization of waste residual films. By doing so, it can reduce the environmental pollution caused by plastic films and improve the efficiency of resource utilization. When this separation device is used to process the film-impurity mixture, it can yield relatively clean residual films. This, in turn, raises the added value of the residual films and boosts economic benefits. Therefore, it is necessary to ensure the highest impurity removal rate first, and secondly, to keep the film leakage rate at a relatively low level, to improve the resource utilization rate of residual films. Taking the maximum impurity removal rate Y1 and the minimum film leakage rate Y2 as the optimization objectives, the optimization module in the Design-Expert 13 data analysis software is used to optimize the target. The objective function and constraint conditions are as listed in Eq. (28) below.
$$\left\{ {\begin{array}{*{20}l} {{\text{max }}Y_{1} (A,B,C)} \hfill \\ {{\text{min }}Y_{2} (A,B,C)} \hfill \\ {870r/\min \le A \le 1450r/\min } \hfill \\ {{26}r/\min \le B \le 54r/\min } \hfill \\ {110kg/h \le C \le 198kg/h} \hfill \\ \end{array} } \right.$$
(28)
The optimal parameter combination for the device is obtained as follows: fan rotational velocity is 1450 r/min, disc rotational velocity is 54 r/min, and feeding quantity is 130 kg/h. The theoretical values of the separation performance index after optimization are: the impurity removal rate Y1 is 96.51%, and the film leakage rate Y2 is 21.92%. Table 5 depicts the optimization results for maximizing impurity removal rate Y1 and minimizing film leakage rate Y2.
As shown in Table 5, a physical verification test was carried out, and the results show that the average impurity removal rate is 91.90%, the average film leakage rate is 27.22%, and the error between the physical test value and the predicted value is 4.61% and 5.30%, respectively. The reasons for the errors may be the non-uniformity of the film-impurity materials. For example, the caking and uneven distribution of residual films and impurities may lead to insufficient representativeness of each sample taken. Another possible cause is the human-related factors in the test operation process. For instance, the uniformity of film-impurity material feeding and the timing of equipment start-up and shutdown can interfere with the test results. Although there are errors between the predicted values and the actual test results, the errors are small. It still indicates that the parameter optimization has relatively high reliability, and the constructed response model has good predictability. Subsequently, regarding the sample selection issue, more scientific sampling methods, such as multi-point sampling and stratified sampling followed by uniform mixing before measurement, will be adopted to ensure the representativeness of the samples. For the test operation issue, detailed operation specifications and procedures will be formulated, and the operators will be trained to reduce errors caused by human factors. Meanwhile, in the process of test data processing, reasonable statistical methods and error analysis models, such as taking the average of multiple measurements and conducting uncertainty analysis, will be used to improve the accuracy and reliability of the test results.
