A calculation method of droplet equivalent indicators of sprinkler irrigation based on energy-weighting

Droplet velocity and particle size determine droplet kinetic energy and have a major impact on soil erosion, crop leaf strike and farm microclimate. The equivalent droplet velocity and diameter describe the average characteristics of the droplet and are important parameters for measuring the spray quality of the nozzle and the degree of droplet fragmentation. Traditional droplet testing methods can only measure number and particle size, so the equivalent method previously used cannot calculate the average droplet characteristics in terms of droplet energy. With the widespread use of optical instruments in sprinkler tests, droplet velocities can also be measured and the corresponding methods for calculating droplet equivalent indicators should be improved and developed. This study proposed an energy weighted method for calculating droplet equivalent indicators. Based on droplet data sprayed by five types of sprinkler nozzles, the characteristics, and differences between the calculation results of the energy weighted method and other types of methods were compared. The regression relationship between energy weighted equivalent indicators and other types of indicators was established. The results show that: 1) The energy weighted equivalent droplet diameter is the largest, followed by the equivalent method related to droplet volume, and the smallest is the equivalent method related to droplet number. The overall trend in droplet equivalent diameter related to energy and volume along the radial direction is relatively similar, but there are significant differences at the proximal end of the spray. This is because although a larger proportion of smaller droplets occupy the near end of the spray water, there are also a certain number of large droplets which, after being ejected from the nozzle outlet, fall steeply to the ground without being sufficiently broken up. Large droplets carry a greater kinetic energy and contribute more to the energy at the measurement point, so the energy weighted droplet equivalent diameter is more biased in favour of these large droplets. 2) The droplet equivalent velocity and equivalent diameter calculated by the energy weighted equivalent method can characterise droplets with a high energy contribution. The histogram of the distribution of the number of droplet velocities shows that droplets with velocities less than 6 m/s occupy a large proportion of the droplets. The IWOB nozzle, for example, has a number weighted equivalent velocity of 3.93 m/s, corresponding to a droplet number accumulation frequency of 29.7%, but an energy accumulation frequency of only 4.5%. The energy weighted equivalent droplet velocity is 4.55 m/s. The number of droplets less than this velocity carries about 43.8% of the energy and the number of droplets greater than this velocity is about 21.4%. This velocity is between the maximum velocity and the number-weighted equivalent droplet velocity and may represent the velocity characteristics of a large droplet carrying more energy. 3) There was a good exponential regression between the droplet terminal velocity calculated by the empirical formula and the energy weighted equivalent droplet velocity, and there was a good exponential regression between the equivalent droplet diameter related to volume and the energy weighted equivalent droplet diameter, with correlation coefficients greater than 0.80. 4) The energy weighted equivalent droplet kinetic energy provides a better estimate of the kinetic energy of precipitation per unit time and area, with a coefficient of determination of 0.84 for the logarithmic regression relationship. The results of the study may provide ideas for reflecting the average characteristics of droplets from an energy perspective.