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Article

Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve

by 1,2, 2,*, 1,*, 3 and 2
1
School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
2
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100048, China
3
Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, Beijing 100081, China
*
Authors to whom correspondence should be addressed.
Water 2023, 15(2), 287; https://doi.org/10.3390/w15020287
Received: 22 November 2022 / Revised: 5 January 2023 / Accepted: 8 January 2023 / Published: 10 January 2023
(This article belongs to the Special Issue Fertigation in Agriculture: Challenges and Solutions)

Abstract

:
Automatic flushing valve (AFV) can improve the anti-clogging ability of the drip fertigation system. The minimum inlet pressure (Hamin) required for automatic closing and the maximum flushing duration (FDmax) are two important performance indexes of AFV. The existing AFV products have the problem of larger Hamin and smaller FDmax, which result higher investment and operating cost, and poor flushing efficiency. Based on the mechanical analysis of the AFV elastic diaphragm and the derivation of the FD, elastic diaphragm hardness (E), ascending channel offset distance (D), and drain hole width (W) were selected as the experimental factors, and nine AFVs were designed by L9(33) orthogonal test method to investigate the influence of elastic diaphragm hardness and structural parameters on the hydraulic performance of AFVs. The hydraulic performance test results showed that the Hamin of the nine AFVs ranged from 0.026 to 0.082 MPa and FDmax ranged from 36.3 to 95.7 s. Hamin was positively correlated with E and D and negatively correlated with W. FDmax was negatively correlated with E and W and tended to increase and then decrease with D. All elastic diaphragm hardness and structural parameters had a significant effect on Hamin, and E and W had a significant effect on FDmax. Based on the range analysis, two new combinations of AFV elastic diaphragm hardness and structural parameters with minimum Hamin (E = 40 HA, D = 0 mm, W = 2 mm) and maximum FDmax (E = 40 HA, D = 2 mm, W = 1.68 mm) were determined, and the corresponding Hamin was 0.022 MPa, 63.3% lower than that of the existing product, and FDmax was 116.4 s, 71.2% higher than that of the existing product. In this study, two ternary nonlinear mathematical regression models of Hamin and FDmax with elastic diaphragm hardness and structural parameters was constructed. The simulation accuracy of the models is good and can be used to quickly predict the optimal combination of AFV parameters to satisfy the actual engineering-required Hamin and FDmax.

1. Introduction

Drip fertilization can improve the uniformity of water and fertilizer distribution in crop root zone [1], improve the current status of water and fertilizer resources utilization in dryland agriculture, and promote the improvement of crop yield and quality. In recent years, drip fertilization has developed rapidly in China [2,3,4]. By the end of 2020, the application area of fertigation technology in China exceeded 10 million ha. When fertilizer enters the dripline with irrigation water, the precipitation process of suspended particles of sediment and other suspended impurities in the water is susceptible to fertilizer in the pipe network, the mechanism of emitter clogging is more complex, and the probability of clogging may be higher [5]. Ca2+, Mg2+, K+ and SO42- in fertilizers form large sediment particle agglomerates with sulfate and other precipitates, which accelerate the formation of clogging silt in the flow channel [5,6,7,8], which in turn reduces the turbulence of water flow and makes sediment particles prone to siltation in the dripline and flow channels [9,10].
Regular acid-chlorine treatment is one of the most commonly used blockage control methods for drip fertigation systems [11,12,13]. Magnetized water can inhibit the formation of scale [14], and a suitable intensity of magnetization can improve the anti-clogging performance of drip fertigation systems [15]. In addition, techniques such as micro- and nanobubble sterilization and electrochemical removal have also been used to purify water and remove clogging substances attached to the inner wall surface of the dripline [16,17]. These anti-clogging methods for drip fertigation systems are mainly controlled by inhibiting the production of clogging materials, promoting the decomposition of existing clogging materials, or promoting the separation of precipitates from the pipe wall.
Dripline flushing technology, which accelerates the speed of water flow in the pipe network to improve the hydraulic shear force and strip sediment on the pipe wall while providing a discharge path for clogging suspended matter and further reducing the chances of clogging material into the emitter flow channel, is a simple, convenient and effective method for emitter anti-clogging performance [17,18,19,20]. At present, most of the flushing operations adopt the method of manually opening and closing the end of the driplines [21]. However, most projects can only be flushed once at the beginning or end of the irrigation season due to its cumbersome flushing operation and large consumption of manpower and material resources. It often fails to achieve the desired flushing effect [22]. The automatic flushing valve (AFV) is installed at the end of one or more driplines to automatically open and flush the pipes when the drip irrigation system is activated, and then automatically close after the designed length of time (FD) [23,24]. When the inlet pressure (Ha) is 0.06–0.1 MPa, the FD of both AFVs produced by Naandanjain (NaanDanJain Irrigation, Ltd., Post Naan, Israel) and Netafim (Netafim Ltd., Tel Aviv, Israel) is less than 10 s, which is much less than the FD requirement of 3–6 min proposed by scholars [11,13,25,26,27,28]. Zhao developed an AFV with a FD of 53 s by improving the delay channel structure [29], Mo et al. increased the water storage volume by adding an exhaust device to the upper cavity of the AFV, and the FD could be increased to 68 s [24]. After 400 h of continuous operation with a water source of 1 kg/m³ sand content, the average relative flow rate of the emitter on a 12 m long dripline with an AFV was 16.6% higher than that without an AFV [29]; the average relative flow rate of the emitter on a 48 m long dripline with an AFV was increased by 4.0% compared to that without an AFV [30]. The installation of an AFV can substantially improve the dripline blockage resistance, but the effect decreases with increasing dripline length. The FD of the existing AFV may still be short for the common dripline length of 60~80 m in actual projects, which cannot meet the flushing demand. In addition, there has been a lack of in-depth research on the intrinsic mechanisms to improve the FD by optimizing the AFV elastic diaphragm hardness and structural parameters.
As the AFV needs to rely on the gradual accumulation of water pressure in the upper cavity to push the elastic diaphragm downwards expansion movement to achieve the delayed automatic closing function, the minimum value of the inlet pressure required for automatic closing is Hamin. When the drip irrigation system is equipped with AFVs, the water supply pressure of the pump not only needs to meet the design pressure value (e.g., 0.1 MPa) of the emitter farthest from the pump but also the Hamin of the AFV farthest from the pump. In addition, the increased water velocity in the pipeline during flushing can substantially increase the head loss along the pipeline network, which in turn increases the pump water supply pressure demand. Then, reducing Hamin can reduce the pump input cost and operation cost of an automatic flushing drip irrigation system and promote the application of automatic flushing technology, but no research related to Hamin of the AFV has been reported.
Based on this, the mechanical parameters of elastic diaphragm and structural parameters affecting the hydraulic performance of the AFV were screened through force analysis of the elastic diaphragm, and different AFVs composed of different elastic diaphragm hardness (E), ascending channel offset distance (D) and width of drain hole (W) were set up with the help of orthogonal tests, and the tests were processed. The effects of elastic diaphragm hardness and structural parameters on Hamin and FDmax were studied, and the mechanism of structural parameter optimization on the hydraulic performance of AFV was investigated. The mathematical model of quantitative characterization of Hamin and FDmax with the change of elastic diaphragm hardness and structural parameters was constructed. This provides a theoretical basis for AFV update iteration and technical support for alleviating the problem of drip irrigation water and fertilizer integration clogging.

2. Materials and Methods

2.1. The Working Principle of the Automatic Flushing Valve

Automatic flushing valve (AFV) is mainly consisting of valve body, elastic diaphragm, valve cover and threaded ring. The raised edge of the elastic diaphragm is fixed between the valve body and the valve cover by the threaded ring. When the pump starts, the AFV starts flushing, and the water flow from the end of the dripline enters the AFV inlet and then divides into two paths of movement (as shown by the blue arrow in Figure 1a): firstly, a small portion of the water flow enters the delay channel through the ascending channel and moves counterclockwise for one turn before entering the upper cavity; secondly, a large amount of water flow carries the suspended clogging matter from the pipes and is discharged from the drain hole through the outlet.
As the amount of water in the upper cavity gradually increases, the elastic diaphragm gradually moves downwards under the resultant force in the vertical direction (Fy) (Equation (4)). Fy is composed of the upper cavity water pressure (F1y) (Equation (1)), the lower cavity water pressure (F2y) (Equation (2)), and the elastic force of the elastic diaphragm (F3y) (Equation (3)). Since the Fy is greater than zero, the Ha (inlet pressure at the beginning of flushing for the AFV to automatically close) can be calculated in Equation (5).
F 1 y = ( H a - h f 1 - h f 2 ) × S x
F 2 y = ( H a - h f 1 ) × ( S x - S d r a i n x )
F 3 y = a × E + b
F y = F 1 y F 2 y F 3 y > 0
H a > h f 1 + h f 2 × S x + a × E S d r a i n x
where F1y is the downwards vertical force (N) exerted by water in the upper cavity on the elastic diaphragm. F2y is the vertical upwards force of water in the lower cavity on the elastic diaphragm (N). F3y is the vertical elastic force of the elastic diaphragm (N); E is the hardness of the elastic diaphragm (HA); Fy is the vertical downwards resultant force of the elastic diaphragm (N); a and b are the primary term coefficient and constant term, respectively, a > 0 [31]; Ha is the AFV inlet pressure (MPa); hf1 is the water loss generated in the water inlet (MPa) in Figure 1b; hf2 is the water loss generated in the ascending channel in Figure 1b and delay channel (MPa) in Figure 1a; Sx is the projection area of the elastic diaphragm on the horizontal plane (m2); and Sdrain x is the projection area of the drain hole on the horizontal plane (m2).
The time used from the beginning to the end of the AFV is the flushing duration (FD, s), which is the quotient of the water storage volume (Cw, mL) and the average flow rate of water entering the upper cavity from the end of the delay channel (q, mL/s) (Equation (6)). According to the result from Mo et al. [24], Cw is approximately equal to the volume added by the downwards movement of the elastic diaphragm (Cb, mL) based on the initial volume of the upper cavity (Ca, mL).
FD = C w / q C b / q

2.2. Analysis of Parameters Affecting the Hydraulic Performance of AFVs

Ha and FD are the key design parameters for automatic flushing drip irrigation system (AFDS). From Equation (5), it can be seen that Ha increases with the decrease in Sdrainx and the increase in E. Furthermore, this can be achieved by setting different drain hole widths (W) and elastic diaphragm materials. From Equation (6), FD can increase with the increase in Cb and decrease in q. When Ha is the same, Cb may be influenced by E. In addition, this paper intends to increase hf2 by setting a different ascending channel offset distance (D) to reduce the delay channel inlet pressure and thus reduce q.

2.2.1. Experimental Design

Referring to the research results of Zhao et al. and Mo et al. [23,24], E is set to a total of three levels, 40, 55, and 60 HA, D is set to a total of three levels, 0, 2, and 4 mm (Figure 2a–c), and W is set to a total of three levels, 1, 1.68, and 2 mm (Figure 2d–f). The experiment is designed using orthogonal experimental Table L9 (33), and the experimental design is shown in Table 1. The elastic diaphragm hardness test is carried out using a Shore durometer on the “A” scale. The range of Shore durometer (Yueqing Handpi Instrument Co., Ltd., Zhejiang, China) is 0–100 HA with an accuracy of 0.5 grade.

2.2.2. Experimental Method and Measurement Index

The AFV hydraulic performance experiment was conducted at the China National Water Conservation Irrigation Engineering Research Center (Beijing, China) with a local tap water source, and the water temperature was maintained at (23 ± 2) °C [32,33]. The 3D model of the AFV used for the experiment was designed with UG NX 10.0 software (Siemens PLM Software, Germany) and processed with 3D printing technology (accuracy of 0.1 mm) using DSM IMAGE8000 photosensitive resin (Royal DSM Group, Netherlands). Before experiment, three AFVs with the same specifications were installed at the end of the PE pipe (Figure 3), the ball valve was closed, and the three buckets were placed directly under each of the three AFVs. The centrifugal pump (CDLF4 10, South Pump Industry Co., Ltd., Zhejiang, China) was started, and the pressure gauge was set (range 0~0.25 MPa, accuracy 0.4 grade, Yangquan Instrument Co., Ltd., Shanxi, China) through the valve to read H. At the same time, the three ball valves were quickly opened, the AFVs began to work, and the timer started. At this time, the pressure gauge readings from H quickly decreased to Ha, and the AFVs discharged water into the bucket. When the AFV was closed and no water flowed out, the timing stopped, the timer time was the FD. At this point, the pressure gauge reading returned to H. Each experiment was repeated three times. During the experiment, the minimum Ha to control the AFV automatic closure was Hamin, and the corresponding flushing duration was FDmax.

2.3. Data Analysis

All statistical analyses and the function describing the relationship of hydraulic performance with the mechanical parameters of elastic diaphragm and structural parameters were performed by SPSS 26.0 statistical software (SPSS, Inc., Chicago, IL, USA). The construction of mathematical models was also completed by SPSS 26.0 statistical software. The consistency between the experimental results and the prediction results of the mathematical model was evaluated by the root mean square error (RMSE) and the normalized root mean square error (nRMSE). (Equations (7) and (8)) [34,35,36].
RMSE = i = 1 n ( S i - E i ) 2 n
nRMSE = i = 1 n ( S i - E i ) 2 n E ave × 100 %
where Si and Ei were the simulated and measured values, respectively; i was the number of the measured value, n was the total number of measured values; and Eave was the average of all measured values. The model evaluation criteria were as follows: nRMSE ≤ 10%, excellent agreement between the simulated and measured rates; 10% < nRMSE < 20%, good; 20% ≤ nRMSE ≤ 30%, fair; and nRMSE > 30%, poor.

3. Results and Analysis

3.1. Hydraulic Performance Experimental Results

The range of Hamin and FDmax for nine AFVs is 0.026~0.082 MPa and 36.3~95.7 s (Table 2), respectively. Figure 4 shows that FDmax and Hamin are negatively correlated; E1D1W1 has the smallest Hamin, 0.026 MPa, and the largest FDmax, 95.7 s.

3.2. Analysis of the Hydraulic Performance Range of AFVs

Through range analysis, we can obtain the influence of the change in the level of the experimental factor on the index to determine the optimal level of the factor and obtain the primary and secondary order of the factors affecting the hydraulic performance of the AFV. As shown in Table 3, Hamin1, Hamin2, and Hamin3 and FDmax1, FDmax2, and FDmax3 are the average values of Hamin and FDmax, respectively, when each experimental factor is taken at the 1, 2 and 3 levels, such that Hamin1 = (0.026 + 0.031 + 0.041)/3= 0.033 MPa, where 0.026, 0.031 and 0.041 MPa are the Hamin values at E = 40 HA (Table 2), respectively. R is the range of the corresponding factor; a larger R indicates that the experimental factor in the design range of the change leads to greater changes in the value of the experimental index and a greater degree of influence of the factor on the hydraulic performance of the AFV. The range analysis results show that the main order of the effect of each experimental factor on Hamin and FDmax is D, E, and W, and E, W, and D, respectively.
The trend diagram of factors and experimental indexes with the experimental factors as horizontal coordinates and the experimental indexes as vertical coordinates is shown in Figure 5. Hamin is positively correlated with E and D and negatively correlated with W. FDmax is negatively correlated with E and W and shows a trend of increasing and then decreasing with D. When E is reduced from 60 HA to 40 HA, the reduction of Hamin is 42.1% and the increase of FDmax is 91.4%; when D is reduced from 4 mm to 0 mm, the reduction of Hamin is 47.6% and the increase of FDmax is 3.5%; and when W is increased from 1 mm to 2 mm, the reduction of Hamin is 16.3%, at which time FDmax decreases by 18.7%.
The optimal factor combination is E1D1W3 when the smaller Hamin is the optimal principle and E1D2W1 when the larger FDmax is the optimal principle, and these two AFVs are not in Table 2.

3.3. Variance Analysis of the Hydraulic Performance of the Automatic Flushing Valve

To further explore whether the influence of experimental factors on hydraulic performance is statistically significant, this study conducts variance analysis at significance levels of 0.05 and 0.1. As shown in Table 4, E, D and W have significant effects on Hamin. E and W have a significant effect on FDmax, while D has no significant effect on FDmax.

3.4. Construction and Verification of a Mathematical Regression Model for Hydraulic Performance of AFV

The suitable flushing duration per unit length of dripline (T = FD/m, where m is the number of driplines controlled by one AFV; FD is the time taken from the beginning to the end of flushing by the AFV (s); and T is the flushing duration per unit length of dripline (s/m).) is determined by the water quality conditions, fertilizer type, water and fertilizer system, blockage formation characteristics and other factors together. The pump water supply pressure in AFDS is influenced by the size and parameters of the pipe network system, Hamin, m, etc. The smaller Hamin is, the less pressure is required for the pump of the drip irrigation system, and the lower the system investment and freight cost. When the T is certain, the m increases with increasing FD; thus, the number of AFVs required for the system decreases, and the investment is reduced. Therefore, it is necessary to determine the appropriate Hamin and FDmax according to the actual project requirements and then determine the AFV elastic diaphragm hardness and structural parameters. In this study, the multivariate nonlinear regression models of Hamin and FDmax with E, D, and W are constructed with the help of SPSS 26.0 statistical software, and the coefficients of determination (R2) of Hamin and FDmax regression models are 0.953 and 0.829, respectively, which means well fitted.
Within the range of factors and level parameters in Table 1, this paper additionally processes 15 different specifications of AFVs for hydraulic performance experimentation, and the measured results and the predicted results from Equations (9) and (10) are shown in Table 5 and Figure 6. The relative errors between the measured and predicted values of Hamin and FDmax are −12.2% to 19.0% and −18.4% to 18.3%, respectively, with a small root mean square error (RMSE) of 0.003 MPa and 10.2 s, respectively, and the normalized root mean square error (nRMSE) is 8.0% and 14.5%, respectively, both less than 20%. The range analysis results show that the combination with the smallest Hamin result is E1D1W3 and the combination with the largest FDmax is E1D2W1. As shown in Table 5, the measured Hamin of E1D1W3 is 0.022 MPa, and the measured FDmax of E1D2W1 is 116.4 s, which are lower and larger than the values in Table 2, respectively. The regression Equations (9) and (10) can be used to predict the combination of AFV elastic diaphragm hardness and structural parameters corresponding to Hamin and FDmax required for the actual project and can shorten the development time.
H amin = 0.002 D 2 0.009 × W 2 + 0.001 × E + 0.005 × D + 0.025 × W + 0.004 × E × D × W 0.031
FD max = 0.037 × E 2 2.244 × D 2 11.625 × W 2 + 1.493 × E 0.389 × D + 13.556 × W + 0.114 × E × D × W + 95.205

4. Discussion

Both Zhao et al. and Mo et al. focused on the increase in FDmax for the AFV without considering the decrease in Hamin [23,24]. Compared with the conventional drip irrigation system without AFVs, the AFV in the flushing process, the water flow in the pipe network system increases significantly, resulting in a significant increase in the head loss (hf) between the pump and the AFVs inlet. To meet the Hamin of the farthest AFV from the pump, the pump water supply pressure of AFDS (H) should be greater than (Hamin + hf). It is necessary to reduce the Hamin and then reduce the pump input and operating costs.
From the mechanical analysis of the AFV elastic diaphragm and the experiment results, it can be seen that Hamin decreases with the decrease in hf1, hf2, Sx and E and decreases with the increase in Sdrainx. When E decreases from 60 HA to 40 HA, Hamin decreases by 42.1% on average; D decreases from 4 mm to 0 mm leading to the decrease of hf2, and thus Hamin decreases by 47.6% on average; W increases from 1 mm to 2 mm leading to an increase in Sdrainx and an average decrease in Hamin of 16.3%; and the effects of Hamin by E, D and W all reach significance levels.
Increasing T promotes the discharge of fine-grained sediments from drip irrigation pipes [27], and in addition, increasing FD increases m when T is certain (see Section 3.4), which in turn reduces the number of AFVs and reduces the investment in AFDS. Assuming that the air in the upper cavity of the AFV cannot be discharged and that the compression factor of air is close to 1, the FD is mainly influenced by Cb and q (Equation (7)). When Ha is the same, the AFV flushing is over, and the elastic diaphragm is in close contact with the outlet and the expansion of the elastic diaphragm on the horizontal plane increases as E decreases, which in turn increases Cb (Figure 1d); therefore, when E decreases from 60 HA to 40 HA, FDmax increases significantly by 91.2% on average. When W decreases from 2 mm to 1 mm, FDmax increases by 22.9% on average, probably because the elastic diaphragm moves downwards under the action of Fy (Figure 1c,d), and Fy decreases with the increase of F2y (Equation (4)); therefore, when the AFV is guaranteed to close automatically, increasing F2y within a certain range can slow down the process of downwards movement of the elastic diaphragm and increase the FD. F2y increases as W decreases (Equation (2)), F2y increases as the force Fy on the elastic diaphragm decreases, and the AFV automatically closes the longer the flushing duration is needed; therefore, FDmax increases as W decreases. hf2 increases as D increases. When Ha is the same, q decreases as D increases, resulting in FD increases as D increases. When D increases from 1 mm to 2 mm, FDmax increases by 13.8%; however, when D increases from 2 mm to 4 mm, hf2 increases, and Hamin increases from 0.040 MPa to 0.063 MPa before the AFV can close automatically (Table 3), and the increase in q causes the FD to decrease.
In this study, two combinations of AFV elastic diaphragm hardness and structural parameters are obtained in the extreme difference analysis with the objectives of Hamin and FDmax: E1D1W3 and E1D2W1, respectively. The measured Hamin of the E1D1W3 AFV is 0.022 MPa, which is 15.4% lower than the lowest value of Hamin in Table 2 and 63.3% lower than the existing AFV [29]. The measured FDmax of E1D2W1 is 116.4 s, which is 21.6% higher than the maximum value of FDmax in Table 2 and 71.2% higher than the existing AFV [24].
In actual projects, the appropriate Hamin needs to be determined according to the scale of the pipe network system and parameters such as length and diameter of pipes at all levels, and the appropriate FDmax needs to be determined by considering the system investment and operation cost. The appropriate FDmax also needs to be determined by considering the water quality conditions of water sources, fertilizer types, clog formation characteristics, system investment, and other factors through a large number of experiments [13,25,26,28]. The quantitative regression model of Hamin, FDmax and AFV elastic diaphragm hardness and structural parameters constructed in this study has a good prediction accuracy [34,35,36], which can help manufacturers to produce AFVs for practical engineering needs at low cost and quickly by providing a theoretical basis and prediction guidance. In future research, it is necessary to construct a hydraulic calculation model of AFDS to study the dynamic balance relationship of water supply pressure and flow rate required by pumps and Hamin under different engineering conditions.

5. Conclusions

Using orthogonal experimental design and hydraulic performance experimental methods, the influencing rule and optimization mechanisms of elastic diaphragm hardness and structural parameters of E, D and W on Hamin and FDmax were examined, and the main conclusions were drawn as follows:
  • The physical relationship model between Hamin and FDmax and the elastic diaphragm hardness and structural parameters and the measured results of hydraulic performance show that Hamin increases with increasing E and D and decreases with increasing W, FDmax decreases with increasing E and W, and E, D and W have a significant effect on Hamin. E and W have significant effects on FDmax (p < 0.05);
  • Based on range analysis, the minimum Hamin is 0.022 MPa, which is lower than the Hamin of the existing AFV by 63.3%. And the maximum FDmax is 116.4 s, which is higher than that of the existing AFV by 71.2%.
  • The ternary nonlinear regression equation of hydraulic performance and elastic diaphragm hardness and structural parameters of the AFV has a good prediction accuracy, which can quickly give the structural parameter combination of the AFV required by the actual project and shorten the research and development time.

Author Contributions

Conceptualization, Y.M.; methodology, H.G. and Y.M.; software, H.G.; validation, Y.M., F.W. and S.G.; formal analysis, H.G., Y.M. and J.W.; investigation, H.G. and Y.M.; writing—original draft preparation, H.G.; writing—review and editing, Y.M. and F.W.; funding acquisition, Y.M. All authors have read and agreed to the published version of the manuscript.

Funding

The work was supported the Research and Development Support Program of China Institute of Water Resources and Hydropower Research (ID0145B042021), the Inner Mongolia Autonomous Region Key Research and Transformation of Achievements Program (2022YFHH0030), and the Agricultural Science and Technology Innovation Program (No 2021-2025).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

AFVAutomatic flushing valve
HaThe inlet pressure, (MPa)
HaminThe minimum inlet pressure, (MPa)
FDThe flushing duration, (s)
FDmaxThe maximum flushing duration, (s)
EElastic diaphragm hardness, (HA)
DAscending channel offset distance, (mm)
WDrain hole width, (mm)
AFDSAutomatic flushing drip irrigation system
F1yThe downwards vertical force exerted by water in the upper cavity on the elastic diaphragm, (N)
F2yThe vertical upwards force of water in the lower cavity on the elastic diaphragm, (N)
F3yThe vertical elastic force of the elastic diaphragm, (N)
FyThe vertical downwards resultant force of the elastic diaphragm, (N)
hf1The water loss generated in the water inlet, (MPa)
hf2The water loss generated in the ascending channel and delay channel, (MPa)
SxThe projection area of the elastic diaphragm on the horizontal plane, (m2)
Sdrain xThe projection area of the drain hole on the horizontal plane, (m2)
CwThe water storage volume of the AFV body, (mL)
CaThe initial volume of the upper cavity, (mL)
CbThe volume added by the downwards movement of the elastic diaphragm, (mL)
CairThe volume of air in the upper cavity, (mL)
qThe average flow rate of water entering the upper cavity from the end of the delay channel, (mL/s)
mThe number of driplines controlled by one AFV
TThe flushing duration per unit length of dripline, (s/m)
HThe pump water supply pressure of AFDS, (MPa)
RMSERoot mean square error
nRMSEThe normalized root mean square error
hfThe head loss between the pump and the AFVs inlet, (MPa)

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Figure 1. Schematic diagram of the automatic flushing valve (AFV) structure. 1. Valve body; 2. Elastic diaphragm; 3. Valve cover; 4. Threaded ring; 5. Raised edge of the elastic diaphragm; 6. Water inlet; 7. Ascending channel; 8. Delay channel; 9. Upper cavity; 10. Outlet; 11. Drain hole; and 12. Lower cavity. Note: Ca is the initial volume of the upper cavity, mL; Cb is the volume added by the downwards movement of the elastic diaphragm, mL; F1y is the downwards vertical force exerted by water in the upper cavity on the elastic diaphragm, N; F2y is the vertical upwards force of water in the lower cavity on the elastic diaphragm, N; F3y is the vertical elastic force of the elastic diaphragm, N; and the blue arrow is the direction of water movement.
Figure 1. Schematic diagram of the automatic flushing valve (AFV) structure. 1. Valve body; 2. Elastic diaphragm; 3. Valve cover; 4. Threaded ring; 5. Raised edge of the elastic diaphragm; 6. Water inlet; 7. Ascending channel; 8. Delay channel; 9. Upper cavity; 10. Outlet; 11. Drain hole; and 12. Lower cavity. Note: Ca is the initial volume of the upper cavity, mL; Cb is the volume added by the downwards movement of the elastic diaphragm, mL; F1y is the downwards vertical force exerted by water in the upper cavity on the elastic diaphragm, N; F2y is the vertical upwards force of water in the lower cavity on the elastic diaphragm, N; F3y is the vertical elastic force of the elastic diaphragm, N; and the blue arrow is the direction of water movement.
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Figure 2. Schematic diagram of the variation in different ascending channel offset distances (D) (D1, D2 and D3) and different drain hole widths (W) (W1, W2 and W3) of the AFV.
Figure 2. Schematic diagram of the variation in different ascending channel offset distances (D) (D1, D2 and D3) and different drain hole widths (W) (W1, W2 and W3) of the AFV.
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Figure 3. Schematic diagram of the hydraulic experimental platform of the AFV. 1. Automatic flushing valve; 2. PE pipe; 3. ball valve; 4. bucket; 5. centrifugal pump; and 6. pressure gauge.
Figure 3. Schematic diagram of the hydraulic experimental platform of the AFV. 1. Automatic flushing valve; 2. PE pipe; 3. ball valve; 4. bucket; 5. centrifugal pump; and 6. pressure gauge.
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Figure 4. Automatic flushing valve minimum closing pressure (Hamin) (a) and maximum flushing duration (FDmax) (b), three-dimensional distribution of experimental results. Note: The diameter of the sphere or circle is proportional to the value of Hamin (a) or FDmax (b); the red sphere represents Hamin; the magenta sphere represents FDmax; the blue, yellow and green circles represent the projections of Hamin (a) or FDmax (b) on the three faces of D-W, E-D and E-W, respectively.
Figure 4. Automatic flushing valve minimum closing pressure (Hamin) (a) and maximum flushing duration (FDmax) (b), three-dimensional distribution of experimental results. Note: The diameter of the sphere or circle is proportional to the value of Hamin (a) or FDmax (b); the red sphere represents Hamin; the magenta sphere represents FDmax; the blue, yellow and green circles represent the projections of Hamin (a) or FDmax (b) on the three faces of D-W, E-D and E-W, respectively.
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Figure 5. Effect of different factor levels on the minimum closing pressure (Hamin) (a) and maximum flushing duration (FDmax) (b) of the automatic flushing valve (AFV).
Figure 5. Effect of different factor levels on the minimum closing pressure (Hamin) (a) and maximum flushing duration (FDmax) (b) of the automatic flushing valve (AFV).
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Figure 6. Comparison of measured and predicted values by the regression model for the automatic flushing valve.
Figure 6. Comparison of measured and predicted values by the regression model for the automatic flushing valve.
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Table 1. Experimental design.
Table 1. Experimental design.
OrderTreatmentsExperimental Factors
E (HA)D (mm)W (mm)
1E1D1W14001.00
2E1D2W24021.68
3E1D3W34042.00
4E2D1W35502.00
5E2D2W15521.00
6E2D3W25541.68
7E3D1W26001.68
8E3D2W36022.00
9E3D3W16041.00
Table 2. Hydraulic performance experimental results for the AFVs.
Table 2. Hydraulic performance experimental results for the AFVs.
TreatmentsHamin (MPa)FDmax (s)
E1D1W10.02695.7
E1D2W20.03183.3
E1D3W30.04187.3
E2D1W30.03338.7
E2D2W10.04082.7
E2D3W20.06558.7
E3D1W20.04054.3
E3D2W30.04848.7
E3D3W10.08236.3
Table 3. Minimum closing pressure (Hamin) and maximum flushing duration (FDmax) range analysis of the automatic flushing valve.
Table 3. Minimum closing pressure (Hamin) and maximum flushing duration (FDmax) range analysis of the automatic flushing valve.
Experimental IndexesExperimental Factors
E (HA)D (mm)W (mm)
HaminHamin10.0330.0330.049
Hamin20.0460.0400.045
Hamin30.0570.0630.041
R0.0240.0300.008
FDmaxFDmax188.862.971.6
FDmax260.071.665.4
FDmax346.460.858.2
R42.410.813.4
Note: Subscripts 1~3 are 3 levels, same below.
Table 4. Variance analysis of the influence of experimental factors on minimum closing pressure (Hamin) and maximum flushing duration (FDmax).
Table 4. Variance analysis of the influence of experimental factors on minimum closing pressure (Hamin) and maximum flushing duration (FDmax).
Experimental IndexesEDW
Hamin78.236 **131.082 **10.180 **
FDmax33.773 **2.3573.219 *
Note: * and ** represent p < 0.1 and p < 0.05, respectively.
Table 5. Model Validation.
Table 5. Model Validation.
TreatmentsE
(HA)
D (mm)W (mm)HaminFDmax
Predicted Value
(MPa)
Measured Value (MPa)Relative Error
(%)
Predicted Value
(s)
Measured Value
(s)
Relative Error
(%)
E1D1W24001.680.0240.026−9.386.473.018.3
E1D1W34002.000.0210.022−2.777.094.3−18.4
E1D2W14021.000.0330.02819.097.7116.4−16.1
E1D3W24041.680.0510.0479.379.690.3−11.9
E2D1W15501.000.0360.036−0.468.680.4−14.6
E2D1W25501.680.0370.0363.356.658.7−3.5
E2D2W25521.680.0430.0407.368.073.3−7.3
E2D2W35522.000.0380.039−1.962.655.313.3
E2D3W35542.000.0580.0539.160.065.5−8.4
E3D1W16001.000.0400.046−12.255.062.7−12.2
E3D1W36002.000.0400.0391.433.733.9−0.4
E3D2W16021.000.0510.0479.559.067.8−13.1
E3D2W26021.680.0470.0447.856.367.6−16.7
E3D3W26041.680.0700.0656.951.658.0−11.0
E3D3W36042.000.0620.0612.251.057.8−11.8
RMSE 0.003 MPa10.2 s
nRMSE (%) 8.014.5
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Gao, H.; Mo, Y.; Wu, F.; Wang, J.; Gong, S. Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve. Water 2023, 15, 287. https://doi.org/10.3390/w15020287

AMA Style

Gao H, Mo Y, Wu F, Wang J, Gong S. Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve. Water. 2023; 15(2):287. https://doi.org/10.3390/w15020287

Chicago/Turabian Style

Gao, Hao, Yan Mo, Feng Wu, Jiandong Wang, and Shihong Gong. 2023. "Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve" Water 15, no. 2: 287. https://doi.org/10.3390/w15020287

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