Jet breakup length is an important parameter which reflects the length of sprinkler range. Based on the linear instability theory, the dispersion equation of cylindrical jet was established and the theoretical value of jet breakup length was calculated. The jet breakup length and initial amplitude of surface wave were measured by applying the high-speed photography technology. Meanwhile, the numerical simulation was conducted by combining Level Set-VOF method for describing the jet breakup length to verify the theoretical and experimental results. Within the jet velocity and working pressure range of discussion, the results of comparison showed that the theoretical analysis gave a reasonable explanation to the influence of jet velocity, nozzle diameter and nozzle cone angle on jet breakup length. Comparing the theoretical value of jet breakup length with the experimental and simulated values, the three results accorded one another. The experimental jet breakup lengths were the lowest and the simulation values were the largest, and the relative error was less than 10%, especially the theoretical value was closer to the average value. For choosing the theoretical calculation of jet breakup length, a semi-empirical and semi-theoretical formula of range for the rotating sprinkler was concluded by the curve fitting method and the fitting formula was verified. The results showed the high accuracy of the ranges determined by this formula and the average relative error was less than 2.5%. The new formula was in good agreement with the data of different types of sprinklers comparing with other empirical formulas, and the error was only 5%. Meanwhile, the possibility of using this formula widely to determine the ranges of same series of sprinkler was confirmed. Keywords: sprinkler, irrigation, formula, cylindrical jet, jet breakup length, dispersion equation, high speed photography, Level Set-VOF method DOI: 10.25165/j.ijabe.20181101.2777 Citation: Jiang Y, Li H, Chen C, Xiang Q J. Calculation and verification of formula for the range of sprinklers based on jet breakup length. Int J Agric & Biol Eng, 2018; 11(1): 49–57.

The distribution of water deteriorates when the operating pressure of an impact sprinkler (IS) decreases to some level. The aeration jet method is utilized to form an aeration impact sprinkler (AIS), aiming to improve the uniformity of water distribution under low pressure. Based on the structures of a 20PY₂ impact sprinkler, an IS and AIS with the same sprinkler discharge were studied under operating pressures range between 150 and 250 kPa. A square test zone was formed by the four sprinklers, and the combined irrigation experiment was conducted under windless conditions. The results showed that the water loss ranged from 3% to 9.5% in all 18 test schemes. The coefficient of uniformity (CU) and distribution uniformity (DU) were used to quantify the degree of uniformity. The AIS had an approximately 3%–7% greater CU than the IS, which resulted in the CU reaching the specified value in the IS standard when the sprinkler functioned under low operating pressure. A linear relationship was found between the CU and DU_lq. The uniformity of water distribution clearly changed with the operating pressure (150 kPa, 200 kPa, and 250 kPa) but decreased slightly with the increase in combination spacing (1 R, 1.1 R, and 1.2 R). In addition, the results of field experiment were compared with those of the simulation developed from a single sprinkler indoor experiment based on the water distribution radial curve. The simulated coefficient of uniformity was highly consistent with the experimental data and had an error of <7%. A sprinkler water jet with the aeration method was proven to be a feasible solution to reduce the operating pressure.

In nature, cavitation bubbles typically appear in clusters, engaging in interactions that create a variety of dynamic motion patterns. To better understand the behavior of multiple bubble collapses and the mechanisms of inter-bubble interaction, this study employs molecular dynamics simulation combined with a coarse-grained force field. By focusing on collapse morphology, local density, and pressure, it elucidates how the number and arrangement of bubbles influence the collapse process. The mechanisms behind inter-bubble interactions are also considered. The findings indicate that the collapse speed of unbounded bubbles located in lateral regions is greater than that of the bubbles in the center. Moreover, it is shown that asymmetrical bubble distributions lead to a shorter collapse time overall.

In this study, a self-propelled hard hose traveler is designed based on the traditional hard hose traveler. The traveler demonstrated enhanced field applicability and intelligence level in Europe and central-eastern China. A parametric configuration scheme was attained through the irrigator’s computational modeling and experimental validation. This study proposed a uniform water distribution calculation model for single-sprinkler linear-move irrigation. The deviation rate between calculated and experimental values was 7.3%. The average application depth decreased with increased sprinkler motion speed and path spacing. The uniformity of water distribution (CU value) exhibited an oscillating trend as the path spacing varied. When moving along a specific path, the CU value increased and decreased with the increased sprinkler rotation angle. By combining irrigation and sprinkler motions, the CU value decreased and increased with the increased sprinkler rotation angle. The combined sprinkler and irrigation motions showed a significantly better effect than the specific path irrigation. The highest CU value was 95.0%, with a nozzle diameter of 16.0×6.0 mm2, a sprinkler rotation angle of 180°, and a path spacing of 1.6 R.