Criterion similarity equation for determining the drops diameter of artificial rain

Development and implementation of water-saving technologies into irrigation agriculture aimed at increasing the efficiency of irrigation water use, is one of the priorities for achieving guaranteed and stable yields of agricultural crops. Study of parameters of artificial rain is one of the key moments in design of irrigation equipment. Research of the rain formation process is necessary in order to avoid negative effect on soil cover and vegetation, and also to increase efficiency of artificial irrigation, also reducing the power consumption. At the same time, one of the key characteristics is the diameter of drops created by rain-forming devices, which directly affects the other main characteristics of artificial rain and depends on the physical and mechanical properties of water, parameters of working fluid flow and geometric parameters of rain- forming devices. Based on the theoretical studies, a criterion similarity equation was obtained, allowing to calculate the drop diameter using parameters characterizing the process of artificial rain formation, to predict the size of drops when designing sprinkling equipment. The parameters having greatest effect on drop diameter are determined. It was revealed that, in accordance with the criterion equation obtained, the process of formation of artificial rain drops can be characterized by a geometric similarity criterion, as well as by Ohnezorge and Froude number. Calculations on the proposed formulas are well correlated with the results of other authors’ experiments. The studies conducted further allow to significantly improve the accuracy of determining the diameter of drops for various types of sprinkling nozzles, match design parameters and operating fluid flow parameters for the specified conditions.

1. Isaev A. P. Hydraulics of irrigation sprinklers. Moscow, Mashinostroenie Publ., 1973. 215 p. (in Russian).

2. Belyaev V. V., Lebedev B. M. Irrigation sprinklers. Design, calculation, operation and testing. Moscow, Mashgiz Publ., 1957. 232 p. (in Russian).

3. Lebedev B. M. Irrigation sprinklers: theory and design. 2nd ed. Moscow, Mashinostroenie Publ., 1977. 246 p. (in Russian).

4. Guber K. V. Irrigation sprinklers and their use. Moscow, Rossel’khozizdat Publ., 1975. 70 p. (in Russian).

5. Fokin B. P., Nosov A. K. Modern problems of the use of multitower sprinkling machines. Stavropol, 2011. 80 p. (in Russian).

6. Bautista-Capetillo C. F., Salvador R., Burguete J., Montero J., Tarjuelo J. M., Zapata N., Gonzalez J., Playan E. Com-paring methodologies for the characterization of water drops emitted by an irrigation sprinkler. Transactions of the ASABE, 2009, vol. 52, no. 5, pp. 1493-1504. https://doi.org/10.13031/2013.29140

7. DeBoer D. W. Drop and energy characteristics of a rotating spray-plate sprinkler. Journal of Irrigation and Drainage Engineering, 2002, vol. 128, no. 3, pp. 137-146. https://doi.org/10.1061/(asce)0733-9437(2002)128:3(137)

8. Kincaid D. C., Solomon K. H., Oliphant J. C. Drop size distributions for irrigation sprinklers. Transactions of the ASAE, 1996, vol. 39, no. 3, pp. 839-845. https://doi.org/10.13031/2013.27568

9. Shakhrai D. S., Basarevskii A. N. Analysis of artificial rain characteristics in the process of designing irrigation sprinklers. Peredovye tekhnologii i tekhnicheskoe obespechenie sel’skokhozyaistvennogo proizvodstva: materialy Mezhdu- narodnoi nauchno-prakticheskoi konferentsii, Minsk, 30-31 marta 2017 g. [Advanced technologies and technical support for agricultural production: materials of the International scientific and practical conference, Minsk, March 30-31, 2017]. Minsk, 2017, pp. 384-387 (in Russian).

10. Obumakhov D. L., Shkura V. N., Churaev A. A. Allowable technological parameters of artificial rain at sprinkler ir-rigation of agricultural lands. Nauchnyi zhurnal Rossiiskogo NIIproblem melioratsii = Scientific Journal of Russian Scientific Research Institute of Land Improvement Problems, 2016, no. 1 (21), pp. 60-74 (in Russian).

11. Li J., Kawano H., Yu K. Droplet size distributions from different shaped sprinkler nozzles. Transactions of the ASAE, 1994, vol. 37, no. 6, pp. 1871-1878. https://doi.org/10.13031/2013.28278

12. Ouazaa S., Burguete J., Paniagua M. P., Salvador R., Zapata N. Simulating water distribution patterns for fixed spray plate sprinkler using the ballistic theory. Spanish Journal of Agricultural Research, 2014, vol. 12, no. 3, pp. 850-863. https:// doi.org/10.5424/sjar/2014123-5507

13. Sanchez Burillo G., Delirhasannia R., Playan E., Paniagua P., Latorre B., Burguete J. Initial drop velocity in a fixed spray plate sprinkler. Journal of Irrigation and Drainage Engineering, 2013, vol. 139, no. 7, pp. 521-531. https://doi.org/10.1061/ (asce)ir.1943-4774.0000573

14. Dashkov V. N., Kapustin N. F., Basarevskii A. N. Substantiation of the efficiency criteria of application of artificial overhead irrigation. Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya agrarnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Agrarian series, 2006, no. 4, pp. 100-106 (in Russian).

15. Prandtl L. Fuhrer durch die Stromungslehre. 2 Aufl. Braunschweig, Friedr. Vieweg & Sohn, 1944. 384 S. (Russ. ed.: Prandtl’ L. Gidroaeromekhanika. Moscow, Izdatel’stvo inostrannoi literatury Publ., 1949. 520 p.).

16. N. Ashgriz (ed.). Handbook of atomization and sprays: theory and applications. New York, Springer, 2011. 935 p. Doi: https://doi.org/10.1007/978-1-4419-7264-4

17. Kravtsov A. M., Shakhrai D. S., Popko S. S. Sprinkler nozzle with adjustable hydraulic parameters. Agropanorama [Agropanorama], 2017, no. 5, pp. 9-15 (in Russian).

18. Shekikhachev Yu. A., Shomakhov L. A., Pazova T. Kh., Balkarov R. A., Aloev V. Z., Shekikhacheva L. Z., Medov- nik A. N., Tverdokhlebov S. A. Substantiation of the parameters of artificial rain. Nauchnyi zhurnal KubGAU = Scientific Journal of KubSAU, 2014, no. 99 (05), pp. 650-659 (in Russian).

19. Oertel H. (ed.). Prandtl’s essentials of fluid mechanics. 2nd ed. Applied Mathematical Sciences. Vol. 158. New York, Springer-Verlag, 2004. 723 p. https://doi.org/10.1007/b97538

20. Kirpichev M. V., Mikheev M. A. (ed.). Similarity theory. Moscow, Publishing house of the USSR Academy of Sciences, 1953. 95 p. (in Russian).

21. Nogid L. M., Fedosov M. F. (ed.). Theory of similarity and dimension. Leningrad, Sudpromgiz Publ., 1959. 95 p. (in Russian).

22. Ohnesorge W. von. Formation of drops by nozzles and the breakup of liquid jets. Zeitschrift fur Angewandte Mathe- matik und Mechanik = Journal of Applied Mathematics and Mechanics, 1936, vol. 16, no. 6, pp. 355-358 (in German). https:// doi.org/10.1002/zamm.19360160611

23. Rublev V., Loginov V. Calculation of motion trajectory of liquid drop in a gas stream taking into account its deforma-tion. Sistemi obrobki informatsii = Information Processing Systems, 2007, no. 1 (59), pp. 128-129 (in Russian).

24. Gusein-zade S. Kh., Pereverzentsev L. A., Kovalenko V. I., Lutskii V. G. Multiple sprinkler systems. Moscow, Kolos Publ., 1984. 191 p. (in Russian).