Research on pressure-regulating device based on different combination layouts, slopes and sprinkler interval distances

To improve the water application uniformity for sprinkler irrigation on sloping land, a new type of pressure-regulating device was designed. The pressure regulation device was installed between the pipe and the inlet of the sprinkler to regulate the pressure gradient. In this study, PIPENET software was used to simulate the installation of pressure regulation device on the corresponding PY10 sprinklers and analyze the working modes of each sprinkler in the irrigation system. The simulation considered factors such as sprinkler combination layout, ground slope and sprinkler interval distance, with average application rate and uniformity coefficient as evaluation criteria. The results showed that the installation of pressure regulation device reduced the pressure difference between each sprinkler. Under these conditions, irrigation uniformity was improved. The research results indicate that integrating different sprinkler layouts, ground slopes and sprinkler interval distances significantly improved the effectiveness of pressure-regulating device installation in hilly areas. This study provided a reference for addressing poor irrigation uniformity in sloping land in hilly areas.


Introduction
Sloping land is important arable land for the people in hilly areas to survive and develop.Due to issues such as large height differences, rugged terrain and shallow soil layers, sprinkler irrigation uniformity on sloping land is poor [1].
The influence factors of sprinkler uniformity include sprinkler hydraulic performance, slope, sprinkler combination layouts and sprinkler inlet pressure difference.Many scholars had made many in-depth studies on optimization of sprinkler uniformity.Liu et al. [2]developed a method for calculating the combination uniformity of variable irrigation system, and obtained the relationship between sprinkler interval distance and uniformity.Zhao et al. [3]revealed that the radial distribution of precipitation depth was more uniform.When the sprinkler installation height was better than the standard height, there was no significant difference in irrigation uniformity coefficient compared to the standard height.Sun et al. [4]opted for triangular combination layout in hilly area, because when the sprinkler interval distance was greater than 5.5m, triangular combination layout provided the best irrigation uniformity, followed by square combination layout.Hexagonal combination layout had the lowest irrigation uniformity.Zhang et al. [5]conducted comparative tests on pulsation pressure and constant pressure, and found better irrigation uniformity under pulsation pressure.Liu et al. [6]designed the circular and U-shaped spatial flow channels, the hydraulic performance of the sprinkler was improved.Shi et al. [7]performed square combination layout for improve the irrigation uniformity in the spray area by increasing the working pressure.Hui et al. [8]compared sprinklers installed perpendicular to the slope ground and those installed perpendicular to the ground, and the former performed well.Tareq et al. [9]found the law of irrigation uniformity decreases with increasing slope.Gao et al. [10]increased the sprinkler installation height to improve the uniformity of individual sprinkler irrigation,within a certain range of installation height.Fu et al. [11]utilized pulsation pressure to improve sprinkler irrigation uniformity.
This study utilized network analysis to optimize the combination of parameters for sprinkler irrigation, supported by experimental methods.The approach investigated the impact of installing a pressure regulating device on the sprinkler irrigation system.

Structural design and working principle
The structural diagram of the pressure-regulating device was shown in figure 1 The inlet diameter of the pressure regulation device was 32mm, the outlet diameter was 20mm, the height of the auxiliary labyrinth channel was 3mm, the height of the compensating cavity was 4mm, the width of the labyrinth flow channel was 5mm, the thickness of the elastic diaphragm was 3mm, and the Shore hardness was 65mm.
The experimental model was manufactured using 3D printing technology, with a manufacturing accuracy of 0.1mm.In order to reduce the workload of the sprinkler test, PIPENET software was used to calculate the actual working pressures of each sprinkler in the sprinkler system under different operating conditions.The combined water distribution was calculated using the principle of water quantity superposition, in order to obtain the uniformity and average application rate of the sprinkler irrigation system under different working conditions.Figure 2 was performance diagram of pressureregulating device for single sprinkler.Diagram of sprinkler irrigation system.The impact sprinkler (type is PY10) was selected.The main pipe was DN50 PVC pipe, the branch pipe was DN25 PVC pipe, and the riser was DN25 galvanized steel pipe.The roughness coefficient of the PVC pipe was 0.009, and the roughness coefficient of the galvanized steel pipe was 0.15.

Simulation design
The factors of combination layout, ground slope and sprinkler interval distance were considered respectively for simulation.The combination layout included square and triangular, while the ground slope and sprinkler interval distance were set at 6°, 8°, 10°, 12°, and 11m, 12m, 13m and 14m respectively.The pressure at the sprinkler inlet in the irrigation system was simulated.The results within the normal range of the sprinklers working pressure can be verified to obtain the inlet pressure of each sprinkler.

Calculation method of average application rate and excessive intensity of sprinkler irrigation
The sprinkler average application rate refers to the amount of water sprayed by a nozzle per unit area within a given time.It is an important performance indicator in sprinkler design and production.The average application rate also serves as the fundamental basis for sprinkler irrigation system design and operation management.High average application rate can lead to surface water accumulation, runoff, and reduced irrigation water utilization efficiency.Low average application rate can make it take longer to spray in order to meet crop water requirements, and evaporation losses will increase.It is very important to choose the right average application rate.The calculation formula of average application rate is as follows [12]: where: i h -Precipitation depth of each measuring point on the spraying area, mm/h; n -Total measuring points on the spraying area.
Sprinkler irrigation uniformity is an index to measure the uniformity of water distribution in the spraying area.Sprinkler irrigation uniformity is an important parameter to evaluate the performance of sprinkler system.Christian uniformity was selected.The calculation formula of sprinkler irrigation uniformity is as follows [13]: where: h  -Average application rate, mm/h; h -Average deviation of precipitation depth at each measuring point (measuring cylinder), mm/h.

Effect of installing the pressure-regulating device on the performance of the sprinkler system
By adjusting the performance parameters of pumps in the irrigation system, the working pressure of the first sprinkler was set to the maximum working pressure.By adjusting parameters such as ground slope and sprinkler interval distance, the following working conditions of the sprinklers could be achieved.The working condition of sprinkler interval distance of 11m was shown in figure 4, and its ground slope was 6°.After installing the pressure regulation device, the working pressure of the sprinklers on the branch pipe became more stable.The pressure regulation device could effectively dissipate energy and stabilize flow.Installing the pressure regulation device could effectively improve the low uniformity caused by large elevation differences and long transportation distances in hilly areas.The influence of different slopes and sprinkler interval distances on irrigation uniformity was shown in figure 5. From figure 5, it could be observed that at a certain slope, irrigation uniformity generally decreased with an increase in nozzle spacing.At slope of 6°, there was a noticeable change in irrigation uniformity.At slopes of 8°to 12°, the change in irrigation uniformity became relatively gradual with variations in sprinkler interval distance.When there was no pressure regulation device on the sprinklers, the uniformity was higher, reaching up to 80%.When the sprinkler interval distance was 11m and the slope was 6°, the irrigation uniformity mostly stayed within the range of 70% to 80% in other cases.After installing the pressure regulation device, the irrigation uniformity could reach 80% or more.When the nozzle spacing was 12m and the slope was 6°, the irrigation uniformity was relatively high, reaching around 85%.The curve after installing the pressure-regulating device demonstrated a smoother change in uniformity with variations in nozzle spacing when the slope remains constant.The influence of nozzle combination layout on irrigation uniformity when the nozzle spacing was 12m was shown in figure 6.It could be observed from figure 6 that, the irrigation uniformity was better with the pressure regulation device, reaching mostly above 80%.Without installing pressureregulating device, except for a slope of 8°, the triangular combination layout performed better than the square combination layout in terms of uniformity.However, with the installation of pressure-regulating device, the triangular combination layout exhibited significantly better uniformity than the square combination layout.7 and figure 8 respectively.The water quantity was mainly distributed in the bottom part and diffused from the bottom center, while the water quantity in the upper part was less.After installing the pressureregulating device, the water quantity in the upper part increased, and the sprinkler irrigation average application rate increased and the uniformity of sprinkler irrigation improved.The water distribution was mainly concentrated on one side.The water distribution at the edge improved after installing the pressure regulating device, the sprinkler average application rate improved and the uniformity of sprinkler irrigation was not obvious.

Conclusions
Large elevation difference and long-distance transportation in hill areas caused poor irrigation uniformity.To improve the water application uniformity for sprinkler irrigation on sloping land, a new type of pressure-regulating device was designed.
Combined with the pressure regulating performance of the pressure-regulating device, the pipe network of the sprinkler irrigation system was simulated by PIPENET, the working conditions of the sprinkler irrigation system were obtained after the pressure-regulating device was installed.Compared with the sprinkler without the pressure-regulating device, the working pressure difference on the branch pipe was reduced, and the working pressure became more stable.
Based on the uniformity and sprinkler average application rate, the irrigation uniformity could reach 80% or more after installing the pressure regulation device.The uniformity of sprinkler irrigation system under triangular combination layout was higher than square combination layout.

. 1 .Figure 1 .
Figure 1.Structure diagram of pressure-regulating device.The pressure-regulating device mainly consists of an inner shell, outer shell and elastic diaphragm, including auxiliary labyrinth channel, compensating cavity and labyrinth flow channel.The elastic diaphragm and labyrinth channel had energy dissipation and flow stabilization effects, thereby regulating the inlet pressure of the sprinkler.The inlet diameter of the pressure regulation device was 32mm, the outlet diameter was 20mm, the height of the auxiliary labyrinth channel was 3mm, the height of the compensating cavity was 4mm, the width of the labyrinth flow channel was 5mm, the thickness of the elastic diaphragm was 3mm, and the Shore hardness was 65mm.The experimental model was manufactured using 3D printing technology, with a manufacturing accuracy of 0.1mm.In order to reduce the workload of the sprinkler test, PIPENET software was used to calculate the actual working pressures of each sprinkler in the sprinkler system under different operating conditions.The combined water distribution was calculated using the principle of water quantity superposition, in order to obtain the uniformity and average application rate of the sprinkler irrigation system under different working conditions.Figure2was performance diagram of pressureregulating device for single sprinkler.

Figure 2 .Figure 3 .
Figure 2. Performance of pressure-regulating device for single sprinkler.The schematic diagram of the sprinkler system was shown in figure 3(a).The pipe network diagram was shown in figure 3(b), which was simulated and designed for the hilly area.

Figure 4 .
Figure 4.The working condition of sprinkler interval distance of 11m.The working condition of sprinkler interval distance of 11m was shown in figure4, and its ground slope was 6°.After installing the pressure regulation device, the working pressure of the sprinklers on the branch pipe became more stable.The pressure regulation device could effectively dissipate energy and stabilize flow.Installing the pressure regulation device could effectively improve the low uniformity caused by large elevation differences and long transportation distances in hilly areas.

Figure 5 .
Figure 5. Influence of different slopes and sprinkler interval distances on sprinkler uniformity.The influence of different slopes and sprinkler interval distances on irrigation uniformity was shown in figure5.From figure5, it could be observed that at a certain slope, irrigation uniformity generally decreased with an increase in nozzle spacing.At slope of 6°, there was a noticeable change in irrigation uniformity.At slopes of 8°to 12°, the change in irrigation uniformity became relatively gradual with variations in sprinkler interval distance.When there was no pressure regulation device on the sprinklers, the uniformity was higher, reaching up to 80%.When the sprinkler interval distance was 11m and the slope was 6°, the irrigation uniformity mostly stayed within the range of 70% to 80% in other cases.After installing the pressure regulation device, the irrigation uniformity could reach 80% or more.When the nozzle spacing was 12m and the slope was 6°, the irrigation uniformity was relatively high, reaching around 85%.The curve after installing the pressure-regulating device demonstrated a smoother change in uniformity with variations in nozzle spacing when the slope remains constant.

Figure 6 .
Figure 6.Influence of sprinkler combination layout on sprinkler irrigation uniformity.The influence of nozzle combination layout on irrigation uniformity when the nozzle spacing was 12m was shown in figure6.It could be observed from figure6that, the irrigation uniformity was better with the pressure regulation device, reaching mostly above 80%.Without installing pressureregulating device, except for a slope of 8°, the triangular combination layout performed better than the square combination layout in terms of uniformity.However, with the installation of pressure-