Abstract
This study proposes a three-dimensional spray calculation model for a rotary sprinkler to evaluate the characteristics of water droplets under different rotation speeds. The water droplet trajectories are calculated using ballistic trajectory equations, and the secondary breakup of droplets is computed based on the WAVE breakup model. A water superposition model is proposed to calculate the water application rate within the spraying wetted area, and the accuracy of the model is verified through experiments at a rotation speed of 2 rpm. The characteristics of the sprayed droplets are analyzed and compared for five different rotation speeds. The results show that the relationship between droplet velocity and diameter follows an exponential function, while the droplet diameter and distance from the sprinkler follow a logarithmic function. As the rotation speed increases, the diameter of droplets decreases, the velocity and the peak value of specific power increase, and the area of the radially wet region expands. At the pressures of 200 and 300 kPa, the model has average standard deviations of 0.46 and 0.35, respectively, for predicting the water application rate. The prediction errors of the irrigation peak are 8.69% and 2.78%, respectively, confirming the good accuracy of the model. The results of this research can support the water-saving irrigation industry and provide an effective theoretical basis for the arrangement and application of sprinklers in sprinkler irrigation systems.
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The datasets generated during the current study are available from the author on reasonable request.
References
Aghajani H, Dembele S, Wen JX (2014) Analysis of a semi-empirical sprinkler spray model. Fire Saf J 64:1–11. https://doi.org/10.1016/j.firesaf.2014.01.004
Ashgriz N, Poo JY (1990) Coalescence and separation in binary collisions of liquid drops. J Fluid Mech 221:183–204
Bailey AG, Balachandran W, Williams TJ (1983) The Rosin–Rammler size distribution for liquid droplet ensembles. J Aerosol Sci 14:39–46
Bautista-Capetillo C, Zavala M, Playán E (2012) Kinetic energy in sprinkler irrigation: different sources of drop diameter and velocity. Irrig Sci 30:29–41. https://doi.org/10.1007/s00271-010-0259-8
Carrión P, Tarjuelo JM, Montero J (2001) SIRIAS: a simulation model for sprinkler irrigation. I. Description of model. Irrig Sci 20:73–84. https://doi.org/10.1007/s002710000031
Christiansen JE (1942) Irrigation by sprinkling. University of California Berkeley, California 4:89–93
de Lima JLMP, Torfs PJJF, Singh VP (2002) A mathematical model for evaluating the effect of wind on downward-spraying rainfall simulators. Catena (Amst) 46:221–241
Deboer DW (2002) Drop and energy characteristics of a rotating spray-plate sprinkler. J Irrig Drain Eng 128:137–146. https://doi.org/10.1061/ASCE0733-94372002128:3137
Friso D, Bortolini L (2012) Influence of the trajectory angle and nozzle height from the ground on water distribution radial curve of a sprinkler. J Agric Eng 43:4. https://doi.org/10.4081/jae.2012.e4
Fukui Y, Nakanishi K, Okamura S (1980) Computer evaluation of sprinkler irrigation uniformity. Irrig Sci 2:23–32
Hua L, Li H, Jiang Y (2022) A spraying model of non-atomizing sprinkler based on jet fragmentation. J Appl Fluid Mech 15:1491–1501. https://doi.org/10.47176/jafm.15.05.1039
Issaka Z, Li H, Yue J et al (2018) Water-smart sprinkler irrigation, prerequisite to climate change adaptation: a review. J Water Clim Change 9:383–398
Issaka Z, Li H, Jiang Y et al (2019) Comparison of rotation and water distribution uniformity using dispersion devices for impact and rotary sprinklers. Irrig Drain 68:881–892. https://doi.org/10.1002/ird.2375
Jones DP, Watkins AP (2012) Droplet size and velocity distributions for spray modelling. J Comput Phys 231:676–692. https://doi.org/10.1016/j.jcp.2011.09.030
Karimi N, Dehghan D, Moloudi S et al (2022) Investigating the effect of some factors of sprinkler building irrigation system and its management on uniformity coefficient in sprinkler irrigation. J Water Soil Conserv. https://doi.org/10.1002/ird.2784
Kincaid DC (1996) Spradrop kinetic energy from irrigation sprinklers. Trans ASAE 39:847–853
King BA, Bjorneberg DL (2012) Droplet kinetic energy of moving spray-plate center-pivot irrigation sprinklers. Trans ASABE 55:505–512
Li Y, Li H, Liu J, Chen C (2014) Effects of rotational speed of sprinkler on hydraulic performance. J Irrig Drain 33:171–174
Li J, Kawano H (1996) Sprinkler rotation nonuniformity and water distribution. Trans Am Soc Agric Eng 39:2027–2031. https://doi.org/10.13031/2013.27705
Li H, Issaka Z, Jiang Y, et al (2019) Overview of emerging technologies in sprinkler irrigation to optimize crop production. Int J Agric Biol Eng 12:1–9. https://doi.org/10.25165/j.ijabe.20191203.4310
Liu AB, Mather D, Reitz RD (1993) Modeling the effects of drop drag and breakup on fuel sprays. In: SAE technical papers. SAE International
Liu JP, Zhu XY, Yuan SQ, Liu XF (2018) Droplet motion model and simulation of a complete fluidic sprinkler. Trans ASABE 61:1297–1306. https://doi.org/10.13031/trans.12639
Pereira LS (1999) Higher performance through combined improvements in irrigation methods and scheduling: a discussion. Agric Water Manag 40:153–169
Playán E, Zapata N, Faci JM et al (2006) Assessing sprinkler irrigation uniformity using a ballistic simulation model. Agric Water Manag 84:89–100
Reitz RD (1987) Modeling atomization processes in high-pressure vaporizing sprays. Atomisation Spray Technol 3:309–337
Robles O, Latorre B, Zapata N, Burguete J (2019) Self-calibrated ballistic model for sprinkler irrigation with a field experiments data base. Agric Water Manage. https://doi.org/10.1016/j.agwat.2019.105711
Sanchez I, Faci JM, Zapata N (2011) The effects of pressure, nozzle diameter and meteorological conditions on the performance of agricultural impact sprinklers. Agric Water Manage 102:13–24. https://doi.org/10.1016/j.agwat.2011.10.002
Vories ED, Asce SM, von Bernuth RD, Mickelson RH (1987) Simulating sprinkler performance in wind. J Irrig Drain Eng 113:119–130
Wiersma J (1955) Effect of wind variation on water distribution from rotating sprinklers. Agric Exp Station Tech Bull 27. http://openprairie.sdstate.edu/agexperimentsta_tb/27
Zardari M, Tomas S, Molle B, Courault D (2022) Empirical modeling of aerosol transport from sprinkler irrigation. Irrig Sci. https://doi.org/10.1007/s00271-022-00822-x
Zhang Y, Zhu D, Zhang L, Gong X (2015) Water distribution model of fixed spray plate sprinkler based on ballistic trajectory equation. Trans Chin Soc Agric Mach 46:55–61
Zhang R, Liu Y, Zhu D et al (2023) Modelling the spray range of rotating nozzles based on modified ballistic trajectory equation parameters. Irrig Drain. https://doi.org/10.1002/ird.2784
Funding
This research was founded by the National Natural Science Foundation of China, grant numbers No.51939005, No.52009137; the Graduate Research and Innovation Projects of Jiangsu Province, grant number KYCX21_3345. This work also appreciates the foundation of the China Scholarship Council.
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Simulation work and original draft preparation, LH; manuscript revision, LB; funding acquisition and writing review, HL and YJ.
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Hua, L., Li, H., Bortolini, L. et al. A model for predicting effects of rotation variation on water distribution of rotary sprinkler. Irrig Sci (2023). https://doi.org/10.1007/s00271-023-00896-1
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DOI: https://doi.org/10.1007/s00271-023-00896-1