Calculation and verification of formula for the range of sprinklers based on jet breakup length

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.