Water–sediment separation efficiency prediction of gill-piece separation device

As the key piece of equipment of a micro-irrigation system, the filter can prevent clogging of the emitter and ensure normal operation of the micro-irrigation system. A gill-piece separation device is used for the removal of viscous sediment, which helps to reduce the sediment concentration and decrease the burden on the filter. In this study, using the water–sediment separation efficiency as an evaluation index, a uniform orthogonal experiment was conducted to study the flow rate, sediment concentration, and gill-piece spacing using a physical model. Based on the experimental results of the physical model, multiple linear regression and projection pursuit regression were used for analysis. The results showed that the order of the factors affecting the water–sediment separation efficiency was as follows: flow rate at muddy water inlet> gill-piece spacing> sediment concentration. The correlation coefficients of the water–sediment separation efficiency models established using multiple linear regression and projection pursuit regression were 0.93 and 0.98, respectively. Both models could predict the water–sediment separation efficiency and determine the optimal working conditions of the gill-piece separation device.


INTRODUCTION
China is one of many countries with a severe sediment problem. In sediment-laden rivers, cascade treatment methods are mainly used to achieve efficient water diversion and sand removal. Common first-level sediment treatment engineering measures are sluice-type, bend-type, bottomstockade-type, and layered water diversion projects. However, the treated water flow often cannot meet the requirements on sediment concentration or particle size. Therefore, secondary sediment treatment engineering measures must be built on the intake gate or downstream channel to further treat the sediment, such as a vortex tube sediment extractor, sand funnel, and circular-ring desilting and sediment ejection basin (Zhang ). To prevent the clogging of emitters in micro-irrigation systems with surface water as the water source, a settling basin is usually set up to allow the sediment to settle, and then a single or combined filter is installed to further purify the water. Next, the treated purified water is transported to the emitter via a pipeline system to meet the water requirements for crop growth.
Extensive studies have been carried out on filters, which have yielded fruitful results. Sand filters exhibit the best fil- In Northwest China and North China, the sediment in most rivers has high concentrations and small particle sizes, which increases the difficulty of sediment treatment.
As the key equipment of a micro-irrigation system, the filter can remove most of the impurities in the water. However, when the filter is used to treat muddy water with a high sediment concentration, problems such as easy clogging and frequent flushing occur. Although increasing the area of the settling basin in front of the filter can reduce the sediment concentration, it will increase the system investment and occupy more floor area, and it cannot effectively process viscous fine sediment. Studies have shown that the sediment concentration and particle size are the main factors that cause the clogging of emitters. When the particle size is less than 0.1 mm, the sediment concentration has a significant impact on clogging. When the sediment concentration is greater than 1.25 kg/m 3 , the risk of clogging will increase (Niu et al. ). Therefore, determining how to effectively purify fine sediment with a high sediment concentration is very important for delaying the clogging of emitters and ensuring the safe operation of micro-irrigation systems. To meet the demands of agricultural water, high turbidity water must be purified, and the addition of flocculants plays an important role. However, inorganic salt and organic polymer flocculants have problems such as requiring large dosages, being harmful to the human body, and creating environmental pollution. Separating fine sediment, reducing the sediment concentration in water resources, and improving the separation efficiency have been the subjects of sediment studies. Qiu improved the traditional inclinedplate settling basin and developed a new water-sediment separation device called the gill-piece separation device.
The gill-piece separation device could accelerate the sedimentation of sediment particles, with sedimentation velocities that were 1.9-3.7 times faster than those under static conditions. A series of subsequent studies was carried out on the gill-piece separation device under static water conditions. In terms of structural optimization, Zhu et al.
(, a, b) carried out sediment deposition experiments on different sandy water flows and studied the effects of the gill-piece type, inclination, and spacing on the efficiency of the water-sediment separation. The results showed that the gill-piece in the gill-piece separation device should be arranged in a single row of gill-pieces, and the optimal arrangement for the gill-piece inclination angle was α ¼ 60 and β ¼ 45 . The gill-piece spacing had a great influence on the efficiency of the water-sediment separation. The smaller the gill-piece spacing was, the higher the separation efficiency became. Yan et al. pieces was far greater than that on the lower surface of the gill-pieces. The larger the sediment particle size was, the higher the water-sediment separation efficiency became.
The smaller the sediment concentration was, the higher the water-sediment separation efficiency became. These studies laid a foundation for the practical application and structural optimization of gill-piece separation devices.
Many studies have been carried out on the gill-piece separation device using physical experiments and numerical simulations. However, the relationships between the water-sediment separation efficiency of the gill-piece separation device and the key structural (gill-piece spacing) and operating (sediment concentration and inlet flow) parameters have not yet been established. In this study, based on previous study results, a uniform orthogonal experiment was designed. The results were analyzed using multiple linear regression and projection pursuit regression (PPR) to obtain the order of the factors that affected the watersediment separation efficiency of gill-piece separation devices and to construct a water-sediment separation efficiency prediction model.

Device
The experiments were conducted in the hydraulic engineering laboratory of the College of Hydraulic and Civil Engineering of Xinjiang Agricultural University. The gillpiece separation device was a new water-sediment separation device, which is mainly used for the treatment of viscous fine sediment. It was composed of gill-pieces and a gill-duct. The gill-piece separation device used in this experiment was made of polymethyl methacrylate with a uniform texture and no bubbles. The circulation system is shown in Figure 1. It was composed of a water tank, mixing pump, water pump, gill-piece separation device, and gate valve, and it was provided with a clean water outlet, sediment outlet, and diversion port. Before the experiment, the prepared water and sediment were added into the water tank and fully mixed using the mixing pump. The pump was turned on to pump the well-mixed sandy water into the gill-piece separation device for the water-sediment separation experiments. After settling due to the gill-piece separation device, the sediment particles were discharged into the water tank from the bottom sediment outlet, and the clean water flowed from the upper overflow port back to the water tank. The water and sediment in the water tank were then remixed evenly, and the experiment entered the next cycle. The structure of the gill-piece separation device is shown in Figure 2. The device had a length a of 200 mm, width b of 100 mm, and height h of 1,000 mm.
The gill-piece spacing was d. The gill-pieces were fixed on the two side walls in the length direction of the ordinary tube at an inclination angle of α ¼ 60 , forming an inclination angle of β ¼ 45 with the two side walls in the width direction. A clean water ascending channel was set between the gill-piece and the ordinary tube, with a width e of 10 mm, and the sediment descending channel had a width f of 10 mm. The diameter of the sediment outlet at the bottom of the gill-piece separation device was 2.5 mm.
There were sandy water inlet and clean water outlet channels with diameters of 20 mm on both sides in the width direction, and the clean water outlet was 950 mm away from the bottom of the gill-piece separation device.

Working principle of gill-piece separation device
The experiments were carried out under static and dynamic water conditions. The static water conditions were as fol-

Sediment
The gill-piece separation device was mainly used for the treatment of viscous fine sediment. In this experiment, the natural loess from Xishan Mountain, Urumqi City, Xinjiang Uygur Autonomous Region was selected as the experimental sediment, and the sediment density was ρ s ¼ 2,650 kg/m 3 .
The particle size distribution was as follows: 100% of the particles were smaller than 0.075 mm, 80.4% were smaller than 0.048 mm, 47.8% were smaller than 0.023 mm, 26.0% were smaller than 0.01 mm, 13.5% were smaller than 0.005 mm, and 6.6% were smaller than 0.0015 mm. The median diameter D 50 was 0.025 mm. Figure 4 shows the particle size distribution.

Steps
Before the experiment, the viscous sediment and water were mixed evenly in various proportions to prepare sediment-  was selected for this experiment, as shown in Table 1. The experiments were designed mainly to investigate the influence of the flow rate of muddy water at the inlet, the sediment concentration, and the gill-piece spacing on the water-sediment separation efficiency of gill-piece separation device.

Flow rate measurements
The flow rate was determined by measuring the volume.
Glass beakers were used to take water samples with certain volumes at the clean water outlet and the desilting outlet.
The corresponding time T was recorded with a stopwatch.
The water sample volume V was measured using a graduated cylinder. Sampling was performed three times at each position, and average value was taken as the volume of the water sample. The corresponding flow rate could be calculated using the following equations: where Q is the flow rate (m 3 /h), V is the volume of the water sample (m 3 ), T is the sampling time (h), Q c is the flow rate at the clean water outlet (m 3 /h), Q d is the flow rate at the desilting outlet (m 3 /h), and Q m is the flow rate at the muddy water inlet (m 3 /h). The flow rate Q m at the muddy water inlet could be calculated by substituting the flow rate Q c at the outlet of the clean water and the flow rate Q d at the desilting outlet into Equation (2).

Measurement of sediment concentration
The principle of the replacement method was used to measure the sediment concentration quickly and accurately. The volume of the conical flask was calculated using Equation (3), where the sample was weighed using an electronic balance with an accuracy of 0.01 g, and the sediment concentration of the sample was calculated using Equation (4): where S m is the sediment concentration of the muddy water

Experimental index
The water-sediment separation efficiency was used to evaluate the filtration performance of the gill-piece separation device. The water-sediment separation efficiency refers to the ratio of the difference between the sediment concentration at the inlet of the muddy water and that at the outlet of the clean water to the sediment concentration of the muddy water. The equation is: where η is the water-sediment separation efficiency (%), S m is the sediment concentration at the inlet of the muddy water (kg/m 3 ), and S c is the sediment concentration at the outlet of the clean water (kg/m 3 ).

Uniform orthogonal experiment results
In the uniform orthogonal experiment, the water-sediment separation efficiency was the index, and the results are shown in Table 2  Order 1 3 2 Figure 5 | Normal P-P plot of regression standardized residuals.
The regression model was statistically significant. R 2 ¼ 0.874, suggesting that the fit was good. Table 3 shows that among the independent variables, the flow rate at the muddy water inlet, sediment concentration, and gill-piece spacing had a significant impact on the water-sediment separation efficiency (P < 0.1). According to the standardized coefficient of the regression model, the level of influence of each factor on the water-sediment separation efficiency was in the following order: flow rate at muddy water inlet > gill-piece spacing > sediment concentration, which was consistent with the results of the range analysis.
According to the results of the SPSS regression analysis, the obtained prediction model of the water-sediment separation efficiency was as follows: where η is the water-sediment separation efficiency (%), Q is the flow rate (m 3 /h), S is the sediment concentration (kg/m 3 ), and d is the gill-piece spacing (cm).
According to Equation (6), when the minimum flow rate was 0.3 m 3 /h, the minimum sediment concentration was 2 kg/m 3 , and the maximum gill-piece spacing was 11 cm.
The water-sediment separation efficiency of the gill-piece separation device reached a maximum of 45.06%, which was consistent with the results of the range analysis.
The water-sediment separation efficiency predicted using Equation (6) was compared with the measured value, as shown in Figure 6. Under the same conditions, the predicted water-sediment separation efficiency was close to the measured value. The mean relative error between the measured value and the predicted value was 8.44%, and the R was 0.93. Therefore, this model could be used to predict the water-sediment separation efficiency of gill-piece separation device.
where f i is the i th ridge function, Ef i ¼ 0, Ef i 2 ¼ 1, and P p n¼1 α 2 in ¼ 1. The solution steps have been published previously (Jiang et al. ).
The PPR was used to analyze the experimental data of nine groups of physical gill-piece separation device models.
The model projection parameters were: N m ¼ 9, p ¼ 3, Q ¼ 1, for, while Span is the smooth coefficient, whose value depends on the accuracy of the experimental data and determines the sensitivity of the model. The range of Span is 0 < Span < 1.
The smaller the value, the more sensitive the model is.
In the process of establishing the water-sediment separation efficiency model using PPR, the calculated contribution weight coefficient β and projection direction The weight coefficients of the influence of the flow rate at the muddy water inlet, sediment concentration, and gillpiece spacing on the water-sediment separation efficiency of the gill-piece separation device are shown in Table 4.
The flow rate at the muddy water inlet had the greatest effect on the water-sediment separation efficiency, followed by the gill-piece spacing, and the sediment concentration had the least effect, which is consistent with the conclusions of the range analysis.   factors on the regression model. PPR can make full use of the information and real dependencies of the data itself and solve the optimization problem by exploring the internal structure of the data, giving it a higher degree of fitting.
It was found that, although the gill-piece separation device could treat the viscous sediment, its water-sediment separation efficiency was not high. To further improve the water-sediment separation capacity of the gill-piece separation device, the structural optimization requires further study. In previous studies, the water inlets were all arranged on the side of the device, and the size of the device was relatively small. Therefore, further improvement measures can be performed. The size of the gill-piece separation device could be increased to increase its sediment treatment capacity. The position of the water inlet could be changed, e.g., the water inlet could be moved to the bottom. The material or the structural form of the gill-pieces could be changed to increase the speed and efficiency of sediment treatment. Considering the influence of drainage solid flux may make the efficiency prediction more accurate. We will study this factor in further.

CONCLUSION
In this study, the effects of the flow rate at the muddy water inlet, sediment concentration, and gill-piece spacing on the water-sediment separation efficiency were investigated using a uniform orthogonal experimental design. The order of influence of each factor on the water-sediment separation efficiency was as follows: flow rate at muddy water inlet > gill-piece spacing > sediment concentration. Multiple linear regression and the PPR method were used to establish a prediction model of the water-sediment separation efficiency. The models established using the above two methods could well predict the water-sediment separation efficiency of the gill-piece separation device. The prediction results of the PPR model were more accurate than those of the multiple linear regression, and its R reached 0.98. The established PPR model was used to predict the optimal working conditions. When the gill-piece spacing was 11 cm, the sediment concentration was 2 kg/m 3 , and the flow rate at the muddy water inlet was 0.3 m 3 /h, the water-sediment separation efficiency reached the maximum value. The models in this study were both established under a sediment concentration of 2-12 kg/m 3 , a flow rate of 0.3-1.1 m 3 /h, and a gill-piece spacing of 5-11 cm. Whether these models are applicable under other conditions should be studied in the future.