*2.3. Test Method*

The water flow distribution and droplet kinetic energy distribution experiments were performed in an indoor no-wind sprinkler irrigation hall with a diameter of 44 m. The PY15 impact sprinkler installation height was 1.4 m. Full-round spraying took place under the working pressure levels of 100 kPa, 150 kPa, 200 kPa, 250 kPa, and 300 kPa. Since there was no wind in the sprinkler hall, the instruments were placed along a linear path (ray). The data collected on this ray could be used to represent the data over the entire rotation. As it can be seen in Figures 5 and 6, rain gauges (opening diameter 85 mm) were placed in the radial direction of the jet at 1.0 m intervals. In order to ensure that the collected water would not overflow, the rain gauge was designed as a cylinder with a wedge-shaped opening edge without any defects. The test started after 10 min to ensure stable operation, and lasted for 1 h to determine the water application rate at each point. In addition, after the nozzle operated stably for 10 min, the 2DVD was moved by a distance of 2.0 m, and the diameter and velocity at each point were measured successively. The test duration at each point was at least 5 min. This is to ensure that the number of water droplets collected at each test location is higher than 5000, which is enough to provide appropriate water droplet statistics. In order to reduce the random and edge effect measurement errors caused by droplet splashing, the 3σ criterion of the normal distribution law of random errors is adopted to statistically test the particle number corresponding to the velocity value in each diameter range [29]. According to the relationship between droplet diameter and droplet falling speed, the diameter range was determined, so as to identify and eliminate the gross error, and then, the spray water drop strike kinetic energy was calculated.

**Figure 5.** Schematic layout of the experimental system.

**Figure 6.** The test site.

#### *2.4. Data Processing*

2.4.1. Coefficient of Variation

The coefficient of variation (*CV*) is the ratio of the standard deviation of the water depth in each rainfall gauge to the arithmetic mean deviation [30]. The worse the uniformity of the radial water application profile of the sprinkler, the greater the measured *CV*. The relationship of the coefficient of variation *CV* is given as follows:

$$CV = \frac{SD}{MN} \times 100\% \,\tag{1}$$

where *CV* is the coefficient of variation (%), *SD* is the standard deviation of the water depth received by all rain gauges (mm), and *MN* is the arithmetic mean of the water in all rain drums.

#### 2.4.2. Kinetic Energy of Droplets per Unit Volume

The kinetic energy of droplets per unit volume refers to the ratio of the sum of the kinetic energy of individual droplets at different measuring points to the total volume [31]; the relationship is as follows:

$$E\_{ks} = \frac{\sum\_{j=1}^{m} E\_{sd\_j}}{1000 \sum\_{j=1}^{m} \frac{1}{6} \pi \bullet m\_j \bullet d\_j^3} \,\tag{2}$$

$$E\_{sd} = \frac{\sum\_{i=1}^{n} \frac{1}{12} \pi \bullet \rho\_{\omega} \bullet d\_i^3 \bullet m\_{di} \bullet V\_{di}^2}{\sum\_{i=1}^{n} m\_{di}},\tag{3}$$

where *d* is the droplet diameter (mm), *Eks* is the kinetic energy of water droplets per unit volume (J/L), *Esdj* is the kinetic energy of a single water droplet with diameter *d* (J/L), *mj* is the number of particles corresponding to the velocity of water droplets with diameter *d*, and *j* is the water droplet diameter class.

### 2.4.3. Kinetic Energy Intensity

The kinetic energy intensity represents the magnitude of the kinetic energy at the measured point per unit time. It can be determined by the water droplet diameter, droplet velocity, and water application rate [31], and the relationship is as follows:

$$K = \frac{\sum\_{j=1}^{m} E\_{sd\_j}}{1000 \sum\_{j=1}^{m} \frac{1}{6} \pi \bullet d\_j^3} \times \frac{h\_j}{3600^\prime} \tag{4}$$

where *K* is the spray kinetic energy intensity at the distance j from the nozzle (W/m2), and *hj* is the water application rate at different distances from the nozzle (mm/h).

For an overlapping sprinkler irrigation system, the uniformity coefficient of kinetic energy intensity distribution can be calculated by the Christensen average, which can reflect the distribution of rainfall energy in a sprinkler irrigation system. Therefore, the uniform coefficient of kinetic energy intensity distribution can comprehensively evaluate the advantages and disadvantages of different systems in terms of potential runoff. The equation is:

$$\text{CUI}\_K = \left( 1 - \frac{\sum\_{k=1}^{N} (K\_k - \overline{K})}{\sum\_{k=1}^{N} K\_k} \right) \times 100\%,\tag{5}$$

where *CUk* is the uniformity coefficient of the kinetic energy intensity (%), *N* is the total number of measuring points, and *K* is the average kinetic energy intensity (W/m2).

#### **3. Results and Analysis**

#### *3.1. Water Discrete Degree Analysis*

In order to study the difference in hydraulic performance between the non-circular nozzle and circular nozzle under low pressure and the performance of the non-circular nozzle under medium pressure, the test pressure of the circular nozzle was set to 100~200 kpa

and that of the non-circular nozzle was set to 100~300 kpa. Table 3 shows the *CV* for nozzles with different shapes under different working pressure levels. According to Table 3, under the same working pressure, the *CV* of the circular nozzle was the largest, while that of the diamond nozzle was the smallest. It indicated that the water distribution of the diamond nozzle was the most uniform, while that of the round nozzle was the least uniform. The *CV* of the C2 nozzle decreased with pressure; the *CV* of the D2 and E1 nozzles increased at first and then decreased, reaching a maximum at 150 kPa, decreasing at 250 kPa, and increasing at 300 kPa. Within the pressure range of 100–200 kPa, the *CV*s of both the D2 and E1 nozzles were far smaller than that of the C2 nozzle, indicating that the water distribution of the non-circular nozzles at low pressure was more uniform than that of the circular nozzles.

**Table 3.** Coefficient of variation for nozzles with different shapes under different working pressure levels.


Table 4 displays the *CV* for diamond nozzles with different *L/Ds*. According to Table 4, the *CV* of the D2 nozzle (*L/D* = 1.32) was the lowest, indicating that the water distribution under this *L/D* was the most uniform. The *CV* of the D1 and D3 nozzles exhibited a decreasing trend. Their maximum value appeared at 100 kPa, far exceeding that of the D2 nozzle, and the water distribution was uneven. Therefore, the diamond nozzle should be designed with an *L/D* of 1.32. Table 5 presents the *CV* for elliptical nozzles with different *L/Ds*. According to Table 5, the *CV* followed the E2 > E3 > E1 sequence, and the E1 nozzle with the smallest *L/D* had the best water distribution uniformity.

**Table 4.** Coefficient of variation for diamond nozzles with different *L/Ds*.


**Table 5.** Coefficient of variation for elliptical nozzles with different *L/Ds*.


According to Tables 3–5, the maximum *CV* appeared at the low pressures of 100 kPa and 150 kPa, indicating that, at low pressure, the water distribution is more uneven. When the pressure reached 300 kPa, the *CV*s of all nozzles had little differences. Under low pressure, the water distribution of the non-circular nozzles (i.e., diamond and elliptical) was more uniform than that of the circular nozzle. In order to further verify the uniformity of the low-pressure water distribution of the non-circular nozzles, the radial water distribution of a single nozzle under different working pressures was investigated.

#### *3.2. Radial Water Application Profiles*

Figure 7 shows the radial water distribution curves of three nozzles (C2, D2, and E1) with an outlet diameter of 5 mm. It can be observed that the water distribution of the different nozzles was concentrated at the middle and distal end of the wetted radius, and the water application rate dropped rapidly to 0 after the peak application rate was reached. Moreover, with the increase of working pressure, the wetted radius increased, the peak application rate value decreased, and the distance from the nozzle corresponding to the peak application rate value increased. In general, the lower the working pressure, the more uneven the water distribution. Under the same working pressure, the wetted radius of the elliptical nozzle was the shortest, while that of the circular nozzle was the longest. The peak application rate was obtained in the following order: diamond < elliptical < circular. According to Figure 7 and Table 3 above, under the same working pressure, the water distribution of the diamond nozzle was the most uniform, while that of the circular nozzle was the least uniform.

**Figure 7.** Radial water distribution of different nozzles under different working pressures. (C2 refers to the circular nozzle with a diameter of 5 mm; D2 refers to the diamond nozzle with an aspect ratio of 1.32; E2 refers to the elliptic nozzle with an aspect ratio of 2).

Figure 8 shows the radial water distribution of diamond nozzles D1, D2, and D3 with different outlet diameters and *L/Ds* in the order of D1 > D2 > D3 under different working pressure levels. It can be observed that the wetted radius increased with decreasing *L/D*. Furthermore, the water application rate at the measuring point 2 m away from the sprinkler increased gradually with decreasing *L/D*. The amount of water was mainly concentrated at 8~12 m. The radial distribution of the water application rate exhibited an overall trend of increasing first and then decreasing. After the peak value was reached, it quickly decayed to

0. The higher the working pressure, the stronger the phenomenon that the water application rate decreased with increasing *L/D*.

**Figure 8.** Radial water distribution of diamond nozzles with different outlet diameters under different working pressure levels. (D1, D2, and D3 refer to the diamond nozzles with aspect ratios of 1.54, 1.32, and 1.11, respectively).

Figure 9 shows the radial water distribution of equal flow elliptical nozzles (E1, E2, and E3) with different aspect ratios under different pressure levels. Combined with Table 5, it can be found that the E1 nozzle with the smallest *L/D* had the most uniform water distribution, while the E3 nozzle with the largest *L/D* and a slit-like shape had the largest

peak water application rate and the smallest wetted radius. In general, the smaller the aspect ratio, the closer its shape to a circle, the smaller the peak application rate value, and the more uniform the water distribution. The sprinkler water application rate of the E3 nozzle with the largest *L/D* was much higher than that of the other two nozzles before reaching the peak application rate, and it declined faster, soon after reaching the peak application rate. The wetted radius decreased with increasing *L/D* and decreasing working pressure. At 150~300 kPa, the distances from the initial position of the E1, E2, and E3 nozzles when they reached the peak application rate were 9 m, 10 m, and 8 m, respectively. This is because when the *L/D* was too large, the nozzle shape tended to be a "slit" and the wetted radius decreased.

**Figure 9.** Radial water distribution of elliptical nozzles with different aspect ratios under different working pressure levels. (E1, E2, and E3 refer to the elliptic nozzles with aspect ratios of 1.43, 2, and 2.58, respectively).

### *3.3. Water Distribution Uniformity Coefficient for Combined Sprinkler Irrigation*

After having determined the water distribution of the different single sprinkler heads, the main reasons affecting the uniformity of combined sprinklers are the combination mode of sprinkler heads and the combination spacing. The MATLAB software was employed to simulate and calculate the combination uniformity (*CU*) coefficients of each non-circular nozzle under different spacing in a rectangular combination arrangement at low pressure (100~200 kPa), and verify the effect of non-circular nozzles on *CU*. To avoid missing areas of water application, the combination spacing was selected as 1.0 R, 1.1 R, 1.2 R, and 1.3 R, where R is the effective spraying radius of the wetted radius of the sprinkler. The *CU* coefficients of the different nozzles under different working pressures and combination spacing are listed in Table 6.

**Table 6.** Combination uniformity coefficients of each nozzle under different pressures and combination spacing.


It can be seen in Table 6 that, for the same nozzle, the *CU* coefficient increased with increasing working pressure and decreased with increasing combination spacing. Among the three different-shaped nozzles, the best combination spacing for the C2 nozzle was 1.0 R, and the *CU* coefficient was the highest (65.26%) when the working pressure was 200 kPa and the combination spacing was 1.0 R. The highest uniformity coefficient (72.28%) was presented by the D2 nozzle, under a working pressure of 200 kPa and combination spacing of 1.1 R. The highest uniformity coefficient (68.72%) of the elliptical nozzle combination was presented by the E3 nozzle, under a working pressure of 200 kPa and a combination spacing of 1.1 R. The C2 nozzle could achieve 65% uniformity at 200 kPa and 1.0 R, while the non-circular nozzles could meet the requirements at 100 kPa, indicating that the combined sprinkler irrigation with non-circular nozzles is more uniform under low pressure. The three-dimensional (3D) distribution diagrams when the *CU* coefficient of each nozzle combination was the best are presented in Figure 10.

**Figure 10.** 3D water distribution under combined sprinkler irrigation. (C2 refers to the circular nozzle with a diameter of 5 mm; D2 refers to the diamond nozzle with an aspect ratio of 1.32; E3 refers to the elliptic nozzle with an aspect ratio of 2.58).

#### *3.4. Kinetic Energy Intensity Distribution of Single Nozzles*

Figure 11 displays the kinetic energy intensity distribution of each nozzle under different working pressure levels using B-spline curves. According to Figure 11a, the maximum kinetic energy intensity of the C2 nozzle at 100 kPa, 150 kPa, and 200 kPa was at a distance of 11 m, 12 m, and 12 m, respectively. According to Figure 11b, the maximum kinetic energy intensity of the D2 nozzle at 100 kPa, 150 kPa, 200 kPa, 250 kPa, and 300 kPa was in all cases found at a distance of 10 m. According to Figure 11c, the maximum kinetic energy intensity of the E1 nozzle at 100 kPa, 150 kPa, 200 kPa, 250 kPa, and 300 kPa was at a distance of 8 m, 10 m, 10 m, 10 m, and 10 m, respectively.

**Figure 11.** Kinetic energy intensity of the different single nozzles as a function of the distance from the nozzle under different working pressure levels. (C2 refers to the circular nozzle with a diameter of 5 mm; D1, D2, and D3 refer to the diamond nozzles with aspect ratios of 1.54, 1.32, and 1.11, respectively; E1, E2, and E3 refer to the elliptic nozzles with aspect ratios of 1.43, 2, and 2.58, respectively).

Based on Figure 11a–c, it can be seen that, within 0–8 m, the slope of the radial profile of the diamond nozzle was the largest, and that of the circular nozzle was the smallest. That is, the further the nozzle shape from a circle, the larger the radial increase of the kinetic energy intensity. In Figure 11c–e, it can be observed that, with the increase of the *L/D*, the peak value of kinetic energy intensity increased, and the distance from the nozzle position to the peak value position under each pressure was shorter. Within 0–6 m, the E3 nozzle (largest *L/D*) was closest to a straight line, and the slope of the radial profile was the largest, while the E1 nozzle (smallest *L/D*) had the smallest slope of the radial profile. This indicated that the larger the L/D, the greater the radial increase of the kinetic energy intensity. According to Figure 11b,f,g, the larger the outlet diameter, the higher the peak value of the kinetic energy intensity. Under each working pressure, the slopes of the kinetic energy intensity curves of the nozzles with an outlet diameter of 5 mm were the closest before and after reaching the peak value.

In the kinetic energy intensity curves of each nozzle plotted by B-splines, it can be observed that the peak value of the kinetic energy intensity corresponded to a distance from the nozzle position that increased with increasing working pressure, which ranged between 100 and 200 kPa. The distribution trend of the kinetic energy intensity of each nozzle along the radial direction under each working pressure was the same. It increased first and then decreased with increasing distance from the nozzle position, and then decreased rapidly to 0 after reaching the peak value of kinetic energy intensity. At 100 kPa and 150 kPa, the kinetic energy near the end of the wetted radius increased sharply, resulting in a high impact intensity on the soil surface structure, which can cause soil compaction and surface runoff.
