Issue 
Mechanics & Industry
Volume 21, Number 6, 2020



Article Number  618  
Number of page(s)  15  
DOI  https://doi.org/10.1051/meca/2020093  
Published online  15 December 2020 
Regular Article
Enhancement of particle collection efficiency considering the structural interplay: particle motion characteristics analysis
^{1}
Panjin Institute of Industrial Technology, Liaoning Key Laboratory of Chemical Additive Synthesis and Separation, Dalian University of Technology, Panjin 124221, PR China
^{2}
State Key Laboratory of Fluorine Containing Functiona, Shandong Huaxia Shenzhou New Material Co. Ltd., Zibo 255000, PR China
^{3}
School of Mechanical & Automotive Engineering, Qingdao University of Technology, Qingdao 266071, PR China
^{*} email: zhangxilong@qut.edu.cn
Received:
13
August
2020
Accepted:
25
November
2020
The vacuumblowing cleaning system, utilizing positive and negative pressure mixeddelivery theory, has been adopted for the road sweeper vehicle. To enhance the solid particle separation performance and to evaluate the motion characteristics of inhaled particles under different structural parameters, the gassolid flow in the vacuumblowing cleaning system was investigated by using computational fluid dynamics (CFD) technology. The influence of the main structural parameters on the grade dust collection efficiency and average detention time of the inhaled particles was determined, such as suctioninlet diameter, suctioninlet inclination angle, and front baffle inclination angle. And the interplay between them was also investigated. In addition, a dust collection efficiency model was built, based on uniform design (UD) and multiple regression analysis (MRA), and subsequently verified via experiments. The results revealed that the structural parameters have significant influence on the dust collection performance. The suctioninlet diameter, front baffle inclination angle, and suctioninlet inclination angle exerted the highest, secondhighest, and lowest influence, respectively. Furthermore, the interaction among structural parameters also influenced the collection performance. The highest, secondhighest, and lowest levels of influence were determined for the inlet diameter/baffle inclination angle, inlet inclination angle/baffle inclination angle, and inlet diameter/inlet inclination interactions, respectively. The highest dust collection efficiency (i.e., 96.10%) and a short average detention time of particles in the chamber were realized under the following conditions: suctioninlet diameter and inclination angle: 200 mm and 110°, respectively, and front baffle inclination angle: 105°.
Key words: Road sweeper vehicle / vacuumblowing cleaning system / CFD / particle motion characteristics / uniform design / multiple regression analysis
© AFM, EDP Sciences 2020
1 Introduction
In recent years, particulate pollution has become increasingly severe, and has attracted considerable attention [1]. Road dust and sediment give rise to urban particulate pollution. Rapid and efficient removal of these small particles has become essential for building environmentally friendly cities [2,3]. The health of the citizens is also impacted by the road particulate matter. According to related medical research reports, the road particulate matter may lead to the death of premature infants [4], respiratory tract infections [5,6], and deprementia [7,8] or other adultaffecting diseases [9–11].
A road sweeper vehicle is a sanitation device, that is, a new highefficiency cleaning device integrating road cleaning, garbage collection, and transportation [12–14]. This device is considered the most efficient for the cleaning of dust, sediment, and rainwater, thereby yielding significant laborforce savings with consideration of the cleaning efficiency. However, Vaze [15] has expressed doubts about the efficiency of the road sweeper, because only some of the particles will be collected, and small particles will be released into the air. As the core of the dust suction system of a road sweeper, the dust collection system directly affects the dust collection efficiency of the sweeper and haze governance in cities. Chen et al. [16] improved the shape of the dust collection system, through a traditional prototype testing method, by placing wing panels parallel to the ground at the front and back of the sweeper. The duration of airflow action on the ground particles increased, owing to this placement.
Trial production prototype can test the manufacturing feasibility of product design. But it costs money and time. With the development of computer technology, computational fluid dynamics (CFD) technology has been employed, as a design guide, in the field of sanitation equipment. Xu et al. [17,18] applied CFD method for the firsttime ever to the design of a road sweeper. The authors proposed that the dust suction power can be improved by changing the shape of the horizontal section comprising the dust collection system. Using a parameter design method, Yang et al. [19] assessed the width, diameter, and inclination angle of the dust collection system, and determined the optimal combination of structural parameters. Structural design needs theoretical guidance. From the perspective of fluid mechanics, Zeng [20] analyzed (via simulations) and performed structural development of the flow field associated with the dust collection system of a highway sweeper. The results revealed that the optimized structure will prevent gas escape and, in turn, secondary pollution. Zhang et al. [21] found that the structural parameters of the external expansion area affect the accuracy of simulation computations, and the rational selection of parameters for the expansion area is particularly important for the calculation result and calculation accuracy.
The aforementioned studies are all based on the analysis of single gasphase flow, thereby providing theoretical support for the structural design and simulation computation of a dust collection system. However, the presence of a solid phase under real conditions is ignored. Using a gassolid twophase liquid computing method, Wu [22] determined the running speed and system pressure drop of a dust collection system, and proposed an optimum operationcondition range. Changing the operational conditions is a good way to enhance the solid particle separation performance, because there is no structural interference. But the performance gains are limited. Wu [26] combined the computing method with the motion trail of particles, and optimized the angle and pressure drop of the back baffle. The results revealed that the optimal dust collection efficiency is achieved at an angle and pressure drop of 135° and 2400 Pa, respectively.
The principle of operation determines the structural characteristics. The above investigation and research are concentrated upon the effect of traditional vacuum cleaning system. The traditional vacuum type only utilizes the negative pressure delivery theory. We have proposed a novel structure which utilizes both negative and positive pressure mixeddelivery theory [23], and we call this novel structure the vacuumblowing cleaning system. The particle behavior is more complicated in the mixedpressure field. To enhance the solid particle separation performance and to evaluate the motion characteristics of inhaled particles accurately, the interplay between geometrical parameters is the key to demonstrate the influence and mechanism clearly [24,25]. Therefore, the interplay between structural parameters should not be neglected for the dust collection efficiency of prediction and optimization.
In this work, the structural parameters required for the modeling of a vacuumblowing cleaning system are investigated from the viewpoint of their influence on the dust collection efficiency. Specifically, the motion characteristics of inhaled particulates are evaluated using a computing method where a gassolid twophase liquid is considered. The total dust collection efficiency, grade dust collection efficiency, and average retention time are subsequently computed. Moreover, the optimal structure is determined based on uniform experiments and regression analysis considering the structural interplay, and the rationality of the numerical simulation is verified via experiments.
2 Physical model and computation domain
Physical model of the sweeper vehicle is shown in Figure 1a. For successful inhalation of ground particles during operation, a certain ground clearance (generally 10–15 mm) must be maintained between the vacuumblowing cleaning system and the ground. For the simulation performed in this work, the ground clearance is set to 10 mm. Figure 1b shows the operational principle of the vacuumblowing cleaning system. Suctioninlet 1 is connected to a centrifugal fan, where the negative pressure generated allows clearanceinduced suction against the surrounding air. Moreover, the incoming air from Blowinginlet 4 blows the particulate matter toward Suctioninlet 1. Under the action of the applied blowing force, the negative pressure generated by Suctioninlet can suck the particles up easily with lower pressure. In our previous published papers, we have clarified the mechanism of the reverse blowing flow rate that acted on the Blowinginlet, and we also calculated the optimized results [23]. So the Blowinginlet helps enhance the cleaning efficiency and reduces the consumption of energy for centrifugal fan. Finally, the flowing air carries particles into the cleaning trunk, thereby resulting in particle elimination.
The airinlet gap area of the vacuumblowing cleaning system is small, and measurement and calculation of the air inflow velocity, incoming air flow, and pressure in the surrounding gap are difficult. Moreover, the gap is an interface between the inner flow field and outer space, where the air flow is complex. The difficulty in setting entrance boundary conditions can be overcome by designating the gap surrounding the dust collection system as an expansion area [17–22,26] (see Fig. 2), and the structural parameters of expansion area are designed based on Reference [21]. Specifically, to simulate actual conditions, the four entrances of the expansion area are set to standard atmosphere pressure. The main structural parameters of the flow channel are shown in Table 1.
Fig. 1 Physical model. (a) Sweeper vehicle. (b) Vacuumblowing cleaning system. 
Fig. 2 CFD computation domain of the vacuumblowing cleaning system. 
Structural parameters.
3 Meshing and numerical methodology
3.1 Algorithm selection and model parameter setting
To improve the computational accuracy, the finite volume method was employed for equation discretization, and a standard k−ε turbulence model was applied [17–21,26]. The turbulence model is used to solve the flow in the core of turbulence. But to the nearwall treatment, the wall function is a semiempirical description, and it is also a complement to the turbulence model. For our research, scalable wall functions was adopted [27]. Furthermore, an incompressible steadystate solution method was adopted for the internal part, and a secondorder upwind difference scheme was chosen to discretize the governing equations. The pressurevelocity coupling and SIMPLE solution algorithm were selected in order to predict incompressible flow [28]. Boundary conditions were set as follows: for the flow field calculation, the suctioninlet vent, blowinginlet, expansion area, and other boundary conditions were set as the pressure outlet, velocity inlet, pressure inlet, and wall surface, respectively. The average value of the pressure outlet was −2300 Pa according to the measurement at the suctioninlet. The average value of the velocity inlet was 22.9 m/s, because the reverse blowing flow rate and the blowinginlet diameter were 1871 m^{3}/h and 170 mm, respectively. The expansion areas connected the atmosphere, so the value of the pressure inlet was 0. The wall surface at the bottom of the dust collection system was nonslipping stationary wall. The other wall surfaces were moving wall, and the value of them was 5 km/h, which simulated the driving status.
The discrete phase model (DPM) was used for describing the particle characteristics [26,29]. For turbulent fluctuations in the flow, the turbulent dispersion with stochastic tracking, discrete random walk model, and steady particle tracking were utilized, respectively. For particle treatment, the particles in this study were treated as spherical. The simulation calculation of the dust collection efficiency under actual working conditions, such as the diameter, density, etc., was performed in combination with the particle properties test results [30]. The particles were static and uniform spatial distribution on the floor [22,26,29]. For injection definition, the injection surface of particles was defined at the bottom surface of the front expansion area considering the sanitation device driving forward. Sand was the main particulate matter on the pavement [22]. Therefore, the particle properties of sand were adopted for simulation [31]. The DEM collision model was used to simulate the friction of particles through UDF (User Define Function). For particlewall interaction, the wall boundary conditions were set as the “reflect” condition and the collision was assumed inelastic. The particles could be exported at the Suctioninlet 1 (Fig. 1), so this surface was set as the “escape” condition.
ANSYS Fluent 14.5 was selected as a solver for the flow field calculation. Table 2 is list of details for the parameter settings that applied to the simulation calculation.
Parameter setting for simulation calculation.
3.2 Grid discretization and fundamental assumption
The structure of the vacuumblowing cleaning system is complex and, hence, a structured grid partition is employed after the entire structure is divided into several subareas. Meanwhile, a relatively dense grid is chosen around the wall surface, to seize the velocity gradient at the boundary layer. The dense grid meets the exponential growth rule. The y+ is usually used for turbulence problems. The y+ is a nondimensional distance to the wall, and it can be described as following:$$y+=\frac{{u}_{*}y}{v}$$(1)Where u_{*} is the friction velocity, y is the distance to the nearest wall, and v is the local kinematic viscosity.
We find that the grid y+ of the boundary layer is 3 in our published paper [23]. It is suitable for the simulated calculation of vacuumblowing cleaning system. Hence we adopt the grid of y+ = 3. The grid model is shown in Figure 3.
The grid was divided by ANSYS ICEM 14.5. Figure 4 shows the independence analysis results of the structured grid. According to the figure, the simulation flow value at the suctioninlet vent increases gradually with increasing number of grid points, whereas the relative error decreases gradually. The simulation flow value at the vent and relative error converge (in general) for grid numbers over 160,000. The model considers ideal conditions for the simulation analysis, and neglects the flow loss resulting from the air leak. Therefore, the simulation analysis value is slightly larger than the actual experimental value. The number of grid points is set to 162,874, based on the computation structure accuracy and computer processing power. This number of points yields (in general) a stable flow at the suctioninlet vent, and a small relative error (i.e., 3.12%) between the simulation data and the experimental results.
To simplify the working process of dust collection during mobile operation of the vacuumblowing cleaning system, the simulation model is simplified as follows: (i) The cleaning operation occurs without heat exchange between the air in the vacuumblowing cleaning system and external air; (ii) The airflow in the dust collection system is incompressible and undergoes stablestate flow, and boundary conditions remain unchanged with the time;(iii) The expansion area is designated as the region surrounding the vacuumblowing cleaning system, and the inlet pressure is set to standard atmospheric pressure; (iv) The vacuumblowing cleaning system moves at a constant speed during operation, and dust particles are static unless being inhaled via the front inlet surface.
Fig. 3 Grid model and partial enlargement. 
Fig. 4 Grid independence analysis. 
4 Analysis of structure influence parameters
4.1 Suctioninlet diameter
Considering the dimensional impact of the vacuumblowing cleaning system in the assembly of a road sweeper, the length, width, and height of the dust collection system have been changed only slightly. Of the four inlet surfaces comprising the dust collection system, the front inlet surface has the greatest impact on and is positively correlated with the dust collection efficiency [22]. The energy loss and dust collection performance are assessed by calculating the average velocity of the front inlet surface (AVFIS), average velocity of the suctioninlet vent (AVSIV), and average pressure of the inlet surface (APIS) [19,32]. Suppose α is 70° and β is 120°, respectively. The impact of the suctioninlet diameter on the average velocity of the front inlet surface, average velocity of the suctioninlet vent, and average pressure of the suctioninlet entrance is shown in Figure 5.
The average velocity of the front inlet surface increases continuously with increasing suctioninlet diameter. In addition, the average velocity of the suctioninlet vent and the average pressure of the suctioninlet entrance decrease with increasing diameter. This results from the fact that the pressure at the inlet vent is constant, entrance area increases with increasing diameter, and dust collection power increases continuously. Therefore, the average velocity of the front inlet surface and entrance increases, but the incremental flow value at the vent is less than the increase amplitude of the crosssectional area; thus, the average velocity of the vent decreases. The increase in the suctioninlet diameter leads to a reduction in both the distance between the inlet and the front baffle and the linear loss of the inlet. The entrance is significantly impacted by the pressure of the vent and, hence, the pressure of the entrance gradually approaches the pressure of the vent. Consequently, the average pressure of the suctioninlet entrance decreases.
The total dust collection efficiency is the ratio of the quality of collected dust particles to the particles that enters the device. While the grade dust collection efficiency is the dust collection efficiency for different particle diameter. The number of particles can be monitored by software postprocessing at different sections in the vacuumblowing cleaning system. As the device goes forward, so the particles come into the device through the front ground. The bottom surface of the front expansion area, as an injection surface, injects the particles. The particles can escape through the suctioninlet surface. Through this method, we can calculated the number and get the total and grade dust collection efficiency [33].
The grade dust collection efficiency is an important indicator for assessing the vacuumblowing cleaning system performance associated with the collection of differentsized particles. The grade dust collection efficiency and pressure distribution for different suctioninlet diameters are shown in Figure 6. As the figure shows, for a given inlet diameter, the efficiency decreases with increasing particle size. The largest reduction in the efficiency (i.e., from 99.7% to 93.9%) occurs at an inlet diameter of 160 mm. For a given particle size, the efficiency increases with increasing inlet diameter, with the most significant increase (i.e., 3.2%) occurring at a particle size of 152 µm. These results indicate that changes in the suctioninlet diameter have a significant influence on the grade dust collection efficiency of the dust collection system. In the case of the inlet with a constant negative pressure, the inlet diameter is positively correlated with the dust collection power, which enhances the collection of particulate matter. The flow mobility increases with decreasing particle size. Compared with the mobility, the grade dust collection efficiency is less affected by changes in the diameter.
The average particleretention time is defined as how long does the particle come in and out of the device. What's more, the average particleretention time is employed to evaluate the particle dynamic characteristics, and it can be obtained by monitoring of particle trajectories [34]. However, different structure has different retention time. There has no critical value of the retention time after which particles cannot be collected [22,23]. In order to realize the synchronous transportation of differentsized particles in the industrial process, it is necessary to match the mean residence time of differentsized particles with the transportation completion time [35,36]. Therefore, the average particleretention time represents another important indicator for assessing whether particles in the dust collection system can be smoothly delivered to garbage. The retention time of particle is more uniform is better, and the shortest average retention time possible is desired. In view of this, different model requires the calculation of the average particleretention time [37].
Figure 7 shows the average retention time of differentsized particles associated with three suctioninlet diameters (i.e., 160, 180, and 200 mm). For the same suctioninlet diameter, the average retention time increases with increasing particle diameter. However, for the same particle diameter, it decreases with increasing inlet diameter. This indicates that, for different grain sizes, the running time of particles in the dust collection system varies. The average retention time of small particles is lower than that of large particles. Therefore, small particles are more easily collected than large particles. The average retention time associated with the 200mm inlet changes more slowly than the time associated with the 160mm inlet. The increase in the suctioninlet diameter yields significant improvement in a certain phase of the particlecollection performance. As previously shown in Figure 7, an infinite increase in the suctioninlet diameter yields negligible contribution to the dust collection efficiency and the positive diameterefficiency correlation is destroyed. Thus, a dynamic equilibrium period is realized and, hence, increasing the inlet diameter only yields no improvement in the dust collection efficiency.
Fig. 5 Impact of the suctioninlet diameter on the velocity and pressure. 
Fig. 6 Grade dust collection efficiency and pressure distribution for different suctioninlet diameters. (a) Grade dust collection efficiency. (b) Pressure distribution at the plane of x = 500 mm. 
Fig. 7 Average retention time of differentsized particles at the suctioninlet. 
4.2 Inclination angle of suctioninlet
Suppose D1 is 190 mm and α is 70°, respectively. The dependence of the velocity and pressure on the inclination angle β of the suctioninlet is shown in Figure 8. As the figure shows, when β increases, the average velocity of the front inlet surface increases initially and then decreases, whereas the pressure of the suctioninlet decreases initially and then increases. However, the average velocity of the inlet vent changes only slightly. These results from the fact that, for β smaller than 105°, the internal air flows smoothly, energy loss is small, dust collection power improves, average velocity of the front inlet surface increases, and the static pressure of the entrance decreases. For β larger than 105°, the local resistance in the inner chamber increases, thereby resulting in increased energy loss and, hence, a decrease in the average velocity of the front inlet surface. However, the sectional area of the entrance increases with increasing β. The entrance is only slightly affected by the pressure of the vent and, therefore, the pressure at the entrance of the suctioninlet increases. For inclination angles ranging from 90° to 130°, the velocity of the suctioninlet vent remains constant, owing to the: constant vent pressure, and the approximately equal resistances resulting from the increase in the sectionalarea entrance, increase in the dust collection power, and roughness of the airflow.
The grade dust collection efficiency and pressure distribution for different inclination angles (90°, 115°, and 130°) of the suctioninlet are shown in Figure 9. As the figure shows, for a fixed particle size and increasing inclination angle, the efficiency increases initially and then decreases. The largest decrease in efficiency (i.e., 2.3%) occurs at a particle size of 152 µm and an inclination angle of 90°. For the same inclination angle, the efficiency decreases with increasing particle diameter, especially for an angle of 90°, where the largest drop (from 99.7% to 94.1%) occurs. The change in the inclination angle of the suctioninlet has a significant impact on the dust collection efficiency, with excessively large or small angles yielding low efficiency. A suitable inclination angle contributes to the smoothness of air flow, energy loss reduction, and realization of optimal dust collection efficiency.
The average retention time of particles determined for three different inclination angles (90°, 115°, and 130°) of the suctioninlet is shown in Figure 10. For a given inclination angle, the average retention time increases with increasing particle diameter. For particles of different sizes, the running time of particles inside the dust collection system varies, and the retention time is positively correlated with the particle size. Values of 0.1641, 0.1660 and 0.1711 s are obtained for Δt (i.e., the difference in the average retention time) corresponding to inclination angles of 90°, 115° and 130°, respectively. Therefore, the increase in the inclination angle of the suctioninlet has only a slight impact on the average particleretention time. Furthermore, compared with the variation in particle diameter, the increase in the suctioninlet inclination angle exerts less influence on the retention time.
Fig. 8 Dependence of the velocity and pressure on the inclination angle β of the suctioninlet. 
Fig. 9 Grade dust collection efficiency and pressure distribution for different inclination angles of the suctioninlet diameters. (a) Grade dust collection efficiency. Pressure distribution at the plane of x=500 mm. 
Fig. 10 Average retention time of particles determined for different inclination angles of the suctioninlet. 
4.3 Inclination angle of front baffle
Suppose D1 is 190 mm and β is 115°, respectively. The dependence of the velocity and pressure on the inclination angle α of the front baffle is shown in Figure 11. As the figure shows, when α increases, the average velocity of the front inlet surface increases initially and then decreases, whereas the opposite trend is observed for the average pressure. However, the average velocity of the inlet changes only slightly. This results from the fact that, for inclination angles smaller than 100°, when the angle increases, the internal air flows smoothly, energy loss is small, dust collection power improves, average velocity of the front inlet surface increases, and static pressure of the entrance decreases. If the inclination angle α is larger than 100°, the increase in the local resistance (owing to the reduction in the volume of the inner chamber) has significant impact on the flow field. This results in a velocity drop of the front inlet surface. The external impact on the inner pressure increases significantly, and the average pressure of the suctioninlet entrance increases. The velocity of the inlet vent remains almost unchanged for α values ranging from 50° to 120°, owing to an increase in the local resistance in the inner chamber. Consequently, the energy loss increases with decreasing volume of the chamber, but the smoothness of the air flow offsets the energy loss resulting from the small space.
The grade dust collection efficiency and pressure distribution for different inclination angles (60°, 90°, and 115°) of the front baffle are shown in Figure 12. The dust collection efficiency calculated for different inclination angles of the front baffle are shown in Figure 12. As the figure shows, for a given particle diameter, the efficiency decreases when the inclination angle decreases from 115° to 60° (for example, a particle size of 152 µm corresponds to a 4.5% decrease). Similarly, for the same inclination angle, the efficiency decreases with increasing particle diameter. The most significant drop (from 99.7% to 93.0%) occurs for diameters ranging from 45 to 152 µm, and a given inclination angle of 60°. This results from the fact that, similar to the suctioninlet inclination angle, a suitable baffle inclination angle contributes to the smoothness of air flow and improvement of the dust collection efficiency.
The average retention time of the particles is determined for three different inclination angles (i.e., 60°, 90°, and 115°) of the front baffle (see Fig. 13). As the figure shows, for a given inclination angle, the average retention time increases with increasing size of the particles. This results from the fact that the top cover of the dust collection system must be connected to the vehicle body. The cover size remains unchanged, and the increase in the inclination angle of the baffle leads to an increase in the width of the vacuumblowing cleaning system and the volume of the chamber. Therefore, the average retention time of particles in the vacuumblowing cleaning system increases slightly.
Fig. 11 Dependence of the velocity and pressure on the inclination angle α of the front baffle. 
Fig. 12 Grade dust collection efficiency and pressure distribution for different inclination angles of the front baffle. (a) Grade dust collection efficiency. (b) Pressure distribution at the plane of x = 500 mm. 
Fig. 13 Average retention time of particles corresponding to three different inclination angles of the front baffle. 
5 Enhancement of particle collection efficiency considering the structural interplay
5.1 Experiment design and multiple regression model building
The suctioninlet diameter, suctioninlet inclination angle, and front baffle inclination angle are evaluated. This evaluation is combined with uniform design and multiple regression analysis, where the criteria of a U_{12}(4^{3}) uniform design table are employed (see Tab. 3 for the calculation results) [38].
Considering the interaction among parameters and the quadratic component of the single factor, a ternary quadratic linear regression equation is adopted for modeling [38–40], as shown in equation (2).$$y={b}_{0}+{\displaystyle \sum _{i=1}^{n}}{b}_{i}{x}_{i}+{\displaystyle \sum _{i=1}^{n}}{b}_{ii}{{x}_{i}}^{2}+{\displaystyle \sum _{i<j}}{b}_{ij}{x}_{i}{x}_{j}$$(2)Where, n: number of factors, y: predicted value, x_{i}: influence factor, b_{0}: constant, b_{ii}: quadratic coefficient, and b_{ij}: interaction term coefficient.
Equation (2) is formulated via stepwise regression of the quadratic polynomials. The resulting ternary quadratic regression equation describing the front inlet surface average velocity of the vacuumblowing cleaning system relative to the diameter of the suctioninlet, inclination angle of the inlet, and inclination angle of the front baffle is:$$\begin{array}{l}y=1787.824019.8143{x}_{1}+4.9474{x}_{2}5.7579{x}_{3}+0.0492{x}_{1}^{2}0.0356{x}_{2}^{2}0.0135{x}_{3}^{2}\\ \text{\hspace{1em}}0.0009{x}_{1}{x}_{2}+0.0272{x}_{1}{x}_{3}+0.0306{x}_{2}{x}_{3}\end{array}$$(3)
Factor level table of structural parameters and experimental results.
5.2 Significance test of regression equation
The multiple linear regression equation composed of structural parameters describing the vacuumblowing cleaning system is formulated. This equation is then subjected to a significance test (in this case, an F test) that considers the linear relation between the dependent variable y and the three independent variables [41]. Table 5 shows the variance analysis of the structuralparameter linear regression equation that describes the vacuumblowing cleaning system. Based on the table of F values (i.e., Tab. 4), F_{0.05 (9,2)} = 19.38 < 49.38, which is indicative of a significant linear relation between the average velocity of the front inlet surface of the vacuumblowing cleaning system and (i) suctioninlet diameter, (ii) inclination angle of the suctioninlet and (iii) inclination angle of the front baffle. In other words, the ternary quadratic regression is significant.
Variance analysis of linear regression equation composed of structural parameters describing the vacuumblowing cleaning system.
5.3 Identifying interaction effects between the main structural parameters
The significance of the regression equation is determined. Using the determined values, the significance of the linear relation between each factor x and the dependent variable y (see Eq. (2)) is ascertained via the ttest method [39] (see Tab. 5 for the corresponding results). The t_{bi} (i = 1,2…9) is partial regression coefficient.
Based on the table of t values (see Tab. 6), t_{0.05(2)} =4.303. Valid results are obtained for $\left{t}_{{b}_{6}}\right<{t}_{0.05\left(2\right)}$ only, indicating that the partial regression coefficient b_{7} has negligible impact on the regression equation and should therefore be eliminated. Considering the correlation among independent variables, insignificant independent variables should be eliminated in a stepwise manner [40,42]. The final regression equation describing the average velocity of the front inlet surface, diameter of the suctioninlet, inclination angle of the suctioninlet, and inclination angle of the front baffle is given as follows:$$\begin{array}{l}y=1799.966619.9410{x}_{1}+5.0444{x}_{2}5.8940{x}_{3}+0.0492{x}_{1}^{2}0.0367{x}_{2}^{2}\\ \text{}0.0128{x}_{3}^{2}+0.0275{x}_{1}{x}_{3}+0.0303{x}_{2}{x}_{3}\end{array}$$(4)
t Statistics.
Standardization of regression analysis coefficients.
5.4 Structuralparameter optimization and numerical verification
The parameter degree of influence is determined via standardization of the regression coefficients comprising equation (3) (see Tab. 6 for the standardized regression coefficients). With respect to the degree of influence on the test index (i.e., the average velocity of the front inlet surface), the order of the terms comprising the regression equation can be determined from the absolute values of the standardized regression coefficients. These coefficients can be written in descending order of this influence, that is, x_{1} > x_{1}^{2} > x_{3} > x_{2}^{2} > x_{1}x_{3} > x_{2} > x_{2}x_{3} > x_{3}^{2}. The maximum of the regression equation is determined (in combination with MATLAB2014), and is realized for the following structuralparameter combination: suctioninlet diameter x_{1} = 201.0 mm, suctioninlet inclination angle x_{2} = 110.7°, and front baffle inclination angle x_{3} = 106.2°.
A comparison of 12 testresult sets reveals poor matching of the parameters and, hence, the feasibility of the structuralparameter sets is determined via tests that consider these parameters. Considering actual engineering dimensions and machining precision, the following set of structural parameters is designated: inlet diameter x_{1} = 200.0 mm, inclination angle of suctioninlet x_{2} = 110°, and inclination angle of front baffle x_{3} = 105°. These parameters are used in the structuralparameter matching for the vacuumblowing cleaning system, and the calculation model is reverified. The dust collection efficiency values determined before and after optimization are then compared (see Tab. 7).
The total dust collection efficiency can be determined from:$${\eta}_{T}={\displaystyle {\displaystyle \sum}_{n=1}^{\infty}}\left({\eta}_{d}\u2022{f}_{d}\right)$$(5)
Where, η_{T}– total dust collection efficiency, f_{d}– proportion of mass fraction corresponding to different grain sizes, and η_{d}– grade dust collection efficiency.
The total dust collection efficiency of the vacuumblowing cleaning system before and after optimization is 89.92% and 96.10% (i.e., 6.18% higher), respectively. Figure 14 shows the motion trail and retention time of particles in the vacuumblowing cleaning system with the optimized structure. The trail of particles in the figure shows that (i) the leakage of dust in the right front of the driving direction is effectively controlled, and (ii) owing to reverse blow at the left of the vacuumblowing cleaning system, all particles are blown to the region near the suctioninlet at the right and are inhaled under a negative pressure effect. At the same time, the optimized results show that retention time of particle is more uniform is better. In order to realize the synchronous transportation of differentsized particles in the industrial process, it is necessary to match the mean residence time of differentsized particles with the transportation completion time [35,36]. In this way, we can avoid the phenomena of particles back mixing and enhance the dust collection efficiency.
Comparison of the grade dust collection efficiency η_{g} before and after optimization.
Fig. 14 Motion trail and retention time of particles in the dust collection system before and after structure optimization. (a) Before optimization. (b) After optimization. 
6 Experimental verification
The model machine of the vacuumblowing cleaning system need rework because of structural improvements. Considering the impact on traffic and the potential safety hazard, a school is taken as the test site (see Fig. 15), which is designed as a road surface uniformly covered with dust particles. To avoid the complexity of testing that installed on the sweeper vehicle, the vacuumblowing cleaning system is tested by adding centrifugal and axial flow fan. The centrifugal fan is used to provide negative pressure, which connects to the suctioninlet. The axial flow fan is used to provide positive pressure, which connects to the blowinginlet and produces the reverse blowing flow rate. The type of the centrifugal fan is 926NO.3.3A (Liaoning Jinfeng Blower Co., Ltd, China). The value of the pressure can be easily controlled by frequency converter, and the regulated value is −2300Pa. Similarly, the value of the reverse blowing flow rate is adjusted to 1871 m^{3}/h. The experiment is started, after the fans are stable. The movement of the vacuumblowing cleaning system is powered by a forklift.
The experimental verification is divided into two parts. One is a contrastive analysis of velocity, and the other is a contrastive analysis of dust collection efficiency. For velocity analysis, the two measure points are tested at the same time (see Fig. 15c). The location distribution of the first measure point A is at the x = 200 mm and y = 325 mm. The second measure point B is at the x = 700 mm and y = 325 mm. The two measuring points are all 20 mm higher than the ground surface. The KasdaKV621 hotwire anemometers (Tianjin Kasda Instruments Co.,Ltd, China) were adopted for measuring speed, and they were fixed by the flange. The data acquisition instrument WS5921/U60232, Beijing Wavespectrum Science & Technology Co., Ltd, was also used. A computer with a Vib‘SYS program was used together with the data acquisition instrument.
The road surface uniformly covered with dust particles, and the distribution density was 0.15 kg/m^{2}. We got the dust particles of the experiment from tertiary highway on the basis of the Reference [22]. Though the particles trajectory within the mechanical equipment were not be tracked, we could use velocity calibration and dust quality weighing method for experimental verification. The forklift moved at a speed of 6 km/h, and the contrastive analysis of experimental and simulation data is shown in Figure 16. The value of Measure point A is larger than Measure point B. The Measure point B is far from the suctioninlet, so it has low vacuum degree. The experimental data were a little lower than simulation one. The reasons are as follows. Firstly, the different sizes and properties adopt different dust particle models, which leads to different calculation results of the particle trajectories. The different particle trajectories also results in a statistics error for large quantity of particles in suctioninlet. Secondly, the simulation is carried out in an ideal environment, so it has not the leakage of air. In reality, the equipment can not be completely sealed and without leakage, there must be pressure loss. These factors are the main reasons, which leads to the simulation data is higher than experimental one. The comparison of experimental and simulation data at the velocity of 6 km/h preliminarily indicates that the CFD simulation method is authentic.
For dust collection efficiency analysis, using the method of mass calculation, the dust collection efficiency of the vacuumblowing cleaning system is defined as the ratio of the quality of ground particles before and after dust collection [22,26]. Although the process of collecting and weighing particles is inevitably affected by human error, the obtained results are significant. The dust collection efficiency measurement results and CFD simulation results are compared in Figure 17.
In each case, the dust collection efficiency decreases with increasing speed of the vehicle. The increase in the running speed of the vacuumblowing cleaning system leads to an increase in the speed of the vacuumblowing cleaning system relative to that of the particles. This is detrimental to dust collection and leads to a decrease in the dust collection efficiency. The relative error associated with the efficiency is determined from equation (6). The maximum allowable dust collection performance error of the dust collection system is 10% [22,26,29,43]. This requirement is satisfied by values of 12.31%, 1.01%, and 6.53% for the maximum relative error, minimum relative error, and average relative error, respectively. Therefore, CFDbased simulation of the vacuumblowing cleaning system is feasible.
The relative error is determined from:$$\mathrm{\Delta}p=\left\frac{{p}_{s}{p}_{t}}{{p}_{t}}\right\times 100\%$$(6)Where, △p, p_{s}, and p_{t} are the relative error, simulated value, and measured value, respectively.
Fig. 15 Prototype and site test. (a) Trialmanufacture. (b) Model machine. (c) Site test. 
Fig. 16 Contrastive analysis of experimental and simulation data, v_{t} = 6 km/h. (a) Measure point A. (b) Measure point B. 
Fig. 17 Comparison of dust collection efficiency associated with different running speeds. 
7 Conclusion
Preliminary theoretical calculations of the structure and vacuumblowing cleaning system have been performed and the size interference of the vacuumblowing cleaning system in the assembly of the road sweeper is considered. The suctioninlet diameter, suctioninlet inclination angle, and front baffle inclination angle of the vacuumblowing cleaning system are selected as the main influence factors, and each factor is evaluated via singlefactor effect analysis. The influence of these three structural parameters on the dust collection performance of the vacuumblowing cleaning system is determined through a uniform optimization design and multiple regression analysis method. In addition, a regression equation considering interaction between the factors is formulated, and the average velocity of the front inlet surface comprising the vacuumblowing cleaning system is taken as the optimization objective. The results of this study are summarized as follows:

The suctioninlet diameter, suctioninlet inclination angle, and front baffle inclination angle influence the dust collection performance of the vacuumblowing cleaning system. Singlefactor effect analysis shows that the dust collection performance increases with increasing suctioninlet diameter. Furthermore, the dust collection efficiency increases initially and then decreases when the inclination angle of the inlet or front baffle increases.

The factors may be written in descending order of their influence on the dust collection efficiency of the vacuumblowing cleaning system, that is, x_{1} (suctioninlet diameter) >x_{3} (inclination angle of front baffle) >x_{2} (inclination angle of suctioninlet).

The interaction between the suctioninlet diameter and the front baffle inclination angle exerts the most influence on the dust collection efficiency of the vacuumblowing cleaning system. The interaction between the inclination angle of the suctioninlet and the inclination angle of the front baffle exerts the secondmost significant influence. However, the interaction between the suctioninlet diameter and its inclination angle exerts only a weak influence.

The maximum grade dust collection efficiency is realized under the following conditions: suctioninlet diameter: 200 mm, suctioninlet inclination angle: 110°, and front baffle inclination angle: 105°. The total dust collection efficiency of the vacuumblowing cleaning system before and after optimization is 89.92% and 96.10% (i.e., 6.18% higher), respectively. Experimental verification revealed an average relative error of 6.53%.
Acknowledgments
This research was supported by the China Postdoctoral Science Foundation(2020M672084, 2018M631167); Liaoning Key Laboratory of Chemical Additive Synthesis and Separation Open Foundation (ZJKF2005). National Natural Science Foundation of China (21706023, 51806114, 51874187). Yingkou Science and Technology Bureau of Creation and Innovation for Company and Doctor.
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Cite this article as: Y. Xi, Y.l. Zhang, X.l. Zhang, Y. Dai, Enhancement of particle collection efficiency considering the structural interplay: particle motion characteristics analysis, Mechanics & Industry 21, 618 (2020)
All Tables
Variance analysis of linear regression equation composed of structural parameters describing the vacuumblowing cleaning system.
Comparison of the grade dust collection efficiency η_{g} before and after optimization.
All Figures
Fig. 1 Physical model. (a) Sweeper vehicle. (b) Vacuumblowing cleaning system. 

In the text 
Fig. 2 CFD computation domain of the vacuumblowing cleaning system. 

In the text 
Fig. 3 Grid model and partial enlargement. 

In the text 
Fig. 4 Grid independence analysis. 

In the text 
Fig. 5 Impact of the suctioninlet diameter on the velocity and pressure. 

In the text 
Fig. 6 Grade dust collection efficiency and pressure distribution for different suctioninlet diameters. (a) Grade dust collection efficiency. (b) Pressure distribution at the plane of x = 500 mm. 

In the text 
Fig. 7 Average retention time of differentsized particles at the suctioninlet. 

In the text 
Fig. 8 Dependence of the velocity and pressure on the inclination angle β of the suctioninlet. 

In the text 
Fig. 9 Grade dust collection efficiency and pressure distribution for different inclination angles of the suctioninlet diameters. (a) Grade dust collection efficiency. Pressure distribution at the plane of x=500 mm. 

In the text 
Fig. 10 Average retention time of particles determined for different inclination angles of the suctioninlet. 

In the text 
Fig. 11 Dependence of the velocity and pressure on the inclination angle α of the front baffle. 

In the text 
Fig. 12 Grade dust collection efficiency and pressure distribution for different inclination angles of the front baffle. (a) Grade dust collection efficiency. (b) Pressure distribution at the plane of x = 500 mm. 

In the text 
Fig. 13 Average retention time of particles corresponding to three different inclination angles of the front baffle. 

In the text 
Fig. 14 Motion trail and retention time of particles in the dust collection system before and after structure optimization. (a) Before optimization. (b) After optimization. 

In the text 
Fig. 15 Prototype and site test. (a) Trialmanufacture. (b) Model machine. (c) Site test. 

In the text 
Fig. 16 Contrastive analysis of experimental and simulation data, v_{t} = 6 km/h. (a) Measure point A. (b) Measure point B. 

In the text 
Fig. 17 Comparison of dust collection efficiency associated with different running speeds. 

In the text 
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