**1. Introduction**

Sprinkler irrigation is an effective irrigation method used for reducing water use in agriculture. Sprinkler irrigation systems are generally composed of a water source, a water pump and power equipment, a water delivery pipeline system, and sprinklers. The sprinklers are key pieces of equipment for the implementation of sprinkler irrigation. Their performance not only directly affects the spraying quality, but is also related to the economy of the entire sprinkler irrigation system. Among them, sprinklers with noncircular nozzles can achieve a low-pressure uniform spray, and have the advantage of improving the atomization quality. Therefore, non-circular nozzles have been widely used in agricultural sprinkler irrigation fields [1,2].

**Citation:** Wang, Z.; Jiang, Y.; Liu, J.; Li, H.; Li, H. Experimental Study on Water Distribution and Droplet Kinetic Energy Intensity from Non-Circular Nozzles with Different Aspect Ratios. *Agriculture* **2022**, *12*, 2133. https://doi.org/10.3390/ agriculture12122133

Academic Editors: Vadim Bolshev, Vladimir Panchenko and Alexey Sibirev

Received: 6 October 2022 Accepted: 9 December 2022 Published: 12 December 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Sprinkler hydraulic performance mainly depends on the wetted radius, flow rate, water application rate, uniformity, and droplet diameter [3–6]. Among them, the water application rate and uniformity of the radial water application profile of a sprinkler are important indicators for assessing the uniformity of irrigation property and water distribution, as well as important parameters for evaluating the advantages and disadvantages of sprinkler irrigation systems [7–9]. Bubenzer and Jones [10] reported that the damage degree of water droplets sprayed onto silty soil is a power function relationship between the kinetic energy of water droplets and the sprinkler water application rate. Mohammed and Kohl [11] investigated the distribution trend of the kinetic energy per unit volume of a full-jet nozzle under multiple pressure levels, and revealed that the kinetic energy per unit volume of water droplets along the radial direction increases with decreasing pressure. Christiansen [12] proposed an equation for calculating the uniformity coefficient. El-Wahed et al. [13] surveyed the effects of sprinkler spacing, sprinkler height, and working pressure of a central pivot irrigation system on parameters such as the uniformity coefficient, low value distribution uniformity, and variation coefficient, and determined the best operation condition scheme to reduce the operation costs.

In addition, the droplet diameter, droplet velocity, and droplet kinetic energy of sprinkler irrigation are also important indicators for evaluating the hydraulic performance of a sprinkler, and have an important impact on sprinkler irrigation system quality [14–16]. Xu et al. [17] investigated droplet diameter distribution and developed a normal distribution model, square-root-normal distribution model, logarithmic normal distribution model, and upper limit logarithmic normal distribution model of droplet diameter. Gong et al. [18] used a 2D video disdrometer (2DVD) to study the distribution range of a NelsonD3000 nozzle under different pressure levels, the changing trend of drop diameter, as well as the relationship between drop velocity, angle, and drop diameter. Their results demonstrated that the water droplet diameter and range conformed to the exponential function relationship, and the velocity of water droplets increased logarithmically with the increase of water droplet diameter. Lorenzini [19] investigated the trends of droplet velocity and evaporation under different working pressure levels during sprinkler irrigation. Their results indicated that the air temperature has a significant effect on droplet evaporation, while the air friction should not be mistakenly ignored when calculating droplet evaporation. Ouazaa et al. [20] analyzed the velocity and kinetic energy of droplets using a ballistic model. The results revealed that, under the working pressures of 138 kPa and 69 kPa, the kinetic energy dissipation decreased with increasing nozzle diameter. Yan et al. [4] also analyzed droplet velocity and kinetic energy by using a ballistic model, and reported that the runoff rate, bulk density of soil surface crust, and sediment yield were generally directly proportional to the droplet kinetic energy flux density (DE f) values, while the initiation of runoff, infiltration rate, and infiltration depth prior to runoff were inversely proportional to DE f. Zhu et al. [21] researched single droplet kinetic energy, droplet kinetic energy per unit volume, kinetic energy intensity distribution trend, and the kinetic energy intensity uniformity coefficient under different combination spacings of a full-jet nozzle. The results showed that the relationship between the kinetic energy distribution of a single water droplet and the water droplet diameter in the full-jet nozzle fit well with the developed model and exhibited a power function relationship. Li and Ma [22] investigated the droplet kinetic energy distribution at different measurement points of square and circular nozzles using the flour method and the droplet equation of motion, and analyzed the relationship between nozzle shape and droplet kinetic energy. Moreover, a regression equation able to estimate the total kinetic energy of water droplets from medium-pressure nozzles based on the median diameter was obtained.

The shape of conventional sprinkler nozzles is circular. The newly introduced noncircular nozzles have the advantages of improved water distribution and spraying uniformity, as well as better hydraulic performance under low pressure compared with circular nozzles [23,24]. Wei et al. [25] conducted experiments on the hydraulic performance of non-circular and circular nozzles, produced contour maps of water distribution for a single

sprinkler, and obtained the corresponding range values based on water distribution. Chen et al. [2] investigated the effect of the shape coefficient of four different-shaped non-circular nozzles, i.e., diamond, semicircle + triangle, semicircle + rectangle, and star, on droplet diameter, and concluded that the droplet diameter in the end decreases with the increasing shape coefficient. Li et al. [26] experimentally analyzed and discussed the effects of noncircular nozzle shape and pressure on the shape change of a low-pressure jet, as well as the effects of nozzle outlet shape, working pressure, and inlet angle on the shape change of the jet. Zhou et al. [27] designed a variety of non-circular nozzles with the same area, experimentally investigated the uniformity of radial water application profile of the sprinkler, and found that the combined uniformity coefficient of the non-circular nozzles was significantly higher than that of circular nozzles. Jiang et al. [28] used high-speed photography to study the fracture and flow characteristics of non-circular nozzles, and revealed that, under the same working pressure, the triangular jet had the shortest fracture length and jet diffusion angle. Due to the different jet patterns produced by non-circular nozzles, their hydraulic performance is improved under low pressure. While the wetted radius of non-circular nozzles is reduced compared with that of circular nozzles, uniformity of the radial water application profile of the sprinkler is higher and the water droplet distribution is more uniform under low working pressure.

According to the above literature review, it can be understood that, due to their special geometric structure, non-circular nozzles have various jet shapes, which can reduce working pressure and improve their hydraulic performance. A quantitative study on the droplet distribution characteristics of non-circular nozzles under different working pressure levels will provide theoretical support for the application of non-circular nozzles. Nevertheless, there are only a few existing studies concerning the radio water distribution and water droplet kinetic energy distribution characteristics of non-circular nozzles with different aspect ratios (*L/D*: long axis/minor axis). Furthermore, no study has focused on the direct effect relationship between *L/D*, radio water distribution, and water drop kinetic energy. Consequently, in this paper, taking the non-circular nozzle as the research object, three types of nozzles with different shapes are designed, and the radial water distribution and kinetic energy intensity of non-circular nozzles with different aspect ratios under different working conditions are calculated. A 2DVD is used to test the water diameter and velocity of the non-circular nozzles. The distribution trend of the water drop kinetic energy is calculated, and the relationship between *L/D*, water distribution, and water drop kinetic energy is explored. In addition, the influence rule of water distribution and water drop distribution characteristics on nozzle hydraulic performance is determined, and a theoretical basis for further improving the spraying performance and studying the hydraulic characteristics of the nozzle outflow field is provided.

#### **2. Materials and Methods**

### *2.1. Non-Circular Nozzle Design*

As shown in Figure 1, a common circular nozzle structure was taken as reference. d0 is its outlet diameter, which was set as 4 mm, 5 mm, and 6 mm. Since the outlet section shape and outlet diameter of non-circular nozzles have an impact on the hydraulic performance of the sprinkler, the non-circular nozzles with elliptical and diamond shapes were designed to have the same flow rate. The non-circular nozzles with different aspect ratios are displayed in Figure 2, and the detailed structural parameters are given in Table 1.

**Figure 1.** Schematic diagram (cross-section) of a circular nozzle structure with dimensions (mm).

**Figure 2.** Schematic diagram (right view) of the investigated non-circular nozzles with dimensions (mm).

**Table 1.** Geometric parameters of the circular and non-circular nozzles (mm).


In this paper, a PY15 impact sprinkler produced by Jinlong Spray Irrigation Co., China, was used for the experiments. The PY15 nozzle is a rotary impact nozzle with an inlet

diameter of 15 mm, working pressure of 200~400 kpa, nozzle diameter of 4~6 mm, and a jet elevation angle of 23◦. Each nozzle was manufactured by a wire-cut electric discharge machining (EDM) process and was made of aluminum (Figure 3). Considering the error problem, flow error tests were performed after processing. It was found that the flow error of the nozzles with the same inlet cone angle and outlet diameter was less than 4% under the same pressure level (Table 2). Thus, it was considered that all nozzles followed the same flow principle.

**Figure 3.** Photograph of the sprinkler and nozzles used in experiments.



#### *2.2. Experimental Equipment*

A 2DVD system manufactured by Joanneum Research Co., Graz, Styria, Austria, was employed to measure the size, shape, direction, aggregation state, and falling velocity of single droplets. The 2DVD system comprised two subsystems. The imaging system is composed of two background illumination sources, two line-scan cameras, and other components (Figure 4). The number of pixels of the camera was 512. The test area was 10,000 mm2 (100 × 100 mm). The particle diameter measurement range was 0.2–8.0 mm and the vertical particle velocity range was 0–10.0 m/s. The data analysis and display system consisted of the View\_HYD software (v8.010) designed by Joanneum Research Co., Graz, Styria, Austria, which was used to display the data generated by the 2DVD, record the measured droplet volumes, and calculate the rainfall velocity.

**Figure 4.** 2DVD system used to measure the characteristics of rainfall drops.
