Calculation and verification of formula for the range of sprinklers based on jet breakup length
Keywords:
sprinkler, irrigation, formula, cylindrical jet, jet breakup length, dispersion equation, high speed photography, Level Set-VOF methodAbstract
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.References
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[20] Davanlou A, Lee J D, Basu S. Effect of viscosity an surface tension on breakup and coalescence of bicomponent sprays. Chemical Engineering Science, 2015; 131: 243–255.
[21] Jin Z X, Dong Y H, Zhou Z W. Numerical simulation of Rayleigh breakup in low-velocity liquid jet. Journal of Shanghai University, 2008; 14(2): 161–167. (in Chinese)
[22] Pan Y, Suga K. Capturing the pinch-off of the liquid jets by the level set method. Journal of Fluids Engineering, 2003; 125: 922–930.
[23] Tian X S, Zhou H, Liu H F. Three-dimensional large eddy simulation of
round liquid jet primary breakup in coaxial gas flow using the VOF method. Fuel Processing Technology, 2015; 131: 396–402.
[24] Ménard T, Tanguy S, Berlemont A. Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet. International Journal of Multiphase Flow, 2007; 33: 510–524.
[25] Shinjo J, Umemura A. Simulation of liquid jet primary breakup: Dynamics of ligament and droplet formation. International Journal of Multiphase Flow, 2010; 36: 513–532.
[26] Thakre S, Manickam L, Ma W M. A numerical simulation of jet breakup in melt coolant interactions. Annals of Nuclear Energy, 2015; 80: 467–475.
[27] Shi S X, Du Q, Qin J R. Temporal mode and spatial mode in the study of liquid jet breakup. Transactions of CSICE, 1999; 17(3): 205–210.
[28] Blaisot J B, Adeline, S. Determination of the growth rate of instability of low velocity free falling jets. Experiments in Fluids, 2000; 29: 247–256.
[29] GB/T 19795.2-2005, Rotating Sprinkler. 2005; pp.1–4.
[30] Bezdek J C, Solomon K H. Upper limit log normal distribution for drop size data. Journal of Irrigation and Drainage Engineering, 1983; 109(1): 72–89.
[31] Chang W H, Chen L F, Wang L X. On spray range of water flow in sprinkler irrigation. Transactions of CSAM, 1991; 22(4): 46–52. (in Chinese)
[32] Tang Y, Zhu X Y, Zheng Y. Simulated experiment of the turbo-type whirling sprinkler for achieving variable rate irrigation. China Rural Water and Hydropower, 2009; 8: 4–7.
[33] Feng C D. Calculation of spray range. Drainage & Irrigation Machinery, 1986; 5(4): 35–38. (in Chinese)
[34] Gan Z M, Yang S H. The formula and experimental research on the range of the whirl sprinkler. Transactions of CSAM, 1998; 29(4): 145–149. (in Chinese)
[2] Han S, Evans R G, Kroeger M W. Sprinkler distribution patterns in windy conditions. Transactions of the ASAE, 1994; 37(5): 1481–1489.
[3] Seginer I, Kantz D, Nir D. The distortion by wind of the distribution patterns of single sprinklers. Agricultural Water Management, 1991; 19: 341–359.
[4] Turn M R, Healey J J, Sazhin S S. Stability analysis and breakup length calculations for steady planar liquid jets. Journal of Fluid Mechanics, 2011; 668: 384–411.
[5] Uchiyama Y, Abe Y, Kaneko A. Experimental study on influence of interfacial behavior on jet surface fragmentation. Proceedings of the 17th International Conference on Nuclear Engineering, 2009; 4: 433–442.
[6] Taveb R, Sakib M N, Ali M. Both experimental and numerical investigation on breakup length of cylindrical falling jet. Process Engineering, 2013; 56: 462–467.
[7] Jiang Y, Li H, Xiang Q J. Experiment on breakup process of low-pressure jets with different nozzle parameters and pressures. Transactions of CSAM, 2015; 46(3):78–82.
[8] Reitz D B. Mechanism of atomization of a liquid jet. Physics of Fluids A, 1982; 25: 1730–1742.
[9] Hou J, Cao J M, Li G H. Derivation on linear stability theory of zero order dispersion relation in liquid jets. Journal of Chang’an University, 2011; 31(4): 94–97.
[10] Du Q, Guo J, Meng Y L. The instability analysis of gas rotations on the breakup of an annular liquid jet. Transactions of CSICE, 2007; 25(3): 217–222.
[11] Park H, Yoon S S, Heister S D. On the nonlinear stability of a swirling liquid jet. International Journal of Multiphase Flow, 2006; 32(9): 1100–1109.
[12] Ibrahim A A, Jog M A. Nonlinear breakup of a coaxial liquid jet in a swirling gas stream. Physics of Fluids, 2006; 18(11): 1141–1501.
[13] Wang X Y, Wang J F, Zhi L Z. Theory and experiment on jet breakup length of charged liquid. Transactions of CSAM, 2013; 44(2): 93–96. (in Chinese)
[14] Wan Y X, Huang Y, Zhu Y. Experiment on the breakup process of free round liquid jet. Journal of Aerospace Power, 2008; 23(2): 208–214. (in Chinese)
[15] Zhu Y, Wan Y X, Huang Y. Study on the breakup lengths of free round liquid jets. Journal of Aerospace Power, 2007; 22(8): 1258–1263. (in Chinese)
[16] Morozumi Y, Fukai J. Growth and structure of surface disturbances of a round liquid jet in a coaxial airflow. Fluid Dynamics Research, 2004; 34: 217–231.
[17] Sallam K A, Dai Z, Faeth G M. Liquid breakup at the surface of turbulent round liquid jets in still gases. International Journal of Multiphase Flow, 2002; 28: 427–449.
[18] Wang F J, Fang T G. Liquid jet breakup for non-circular orifices under low pressures. International Journal of Multiphase Flow, 2015; 72: 248–262.
[19] Negeed E S R, Hidaka S, Kohno M. Experimental and analytical investigation of liquid sheet breakup characteristics. International Journal of Heat and Fluid Flow, 2011; 32(1): 95–106.
[20] Davanlou A, Lee J D, Basu S. Effect of viscosity an surface tension on breakup and coalescence of bicomponent sprays. Chemical Engineering Science, 2015; 131: 243–255.
[21] Jin Z X, Dong Y H, Zhou Z W. Numerical simulation of Rayleigh breakup in low-velocity liquid jet. Journal of Shanghai University, 2008; 14(2): 161–167. (in Chinese)
[22] Pan Y, Suga K. Capturing the pinch-off of the liquid jets by the level set method. Journal of Fluids Engineering, 2003; 125: 922–930.
[23] Tian X S, Zhou H, Liu H F. Three-dimensional large eddy simulation of
round liquid jet primary breakup in coaxial gas flow using the VOF method. Fuel Processing Technology, 2015; 131: 396–402.
[24] Ménard T, Tanguy S, Berlemont A. Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet. International Journal of Multiphase Flow, 2007; 33: 510–524.
[25] Shinjo J, Umemura A. Simulation of liquid jet primary breakup: Dynamics of ligament and droplet formation. International Journal of Multiphase Flow, 2010; 36: 513–532.
[26] Thakre S, Manickam L, Ma W M. A numerical simulation of jet breakup in melt coolant interactions. Annals of Nuclear Energy, 2015; 80: 467–475.
[27] Shi S X, Du Q, Qin J R. Temporal mode and spatial mode in the study of liquid jet breakup. Transactions of CSICE, 1999; 17(3): 205–210.
[28] Blaisot J B, Adeline, S. Determination of the growth rate of instability of low velocity free falling jets. Experiments in Fluids, 2000; 29: 247–256.
[29] GB/T 19795.2-2005, Rotating Sprinkler. 2005; pp.1–4.
[30] Bezdek J C, Solomon K H. Upper limit log normal distribution for drop size data. Journal of Irrigation and Drainage Engineering, 1983; 109(1): 72–89.
[31] Chang W H, Chen L F, Wang L X. On spray range of water flow in sprinkler irrigation. Transactions of CSAM, 1991; 22(4): 46–52. (in Chinese)
[32] Tang Y, Zhu X Y, Zheng Y. Simulated experiment of the turbo-type whirling sprinkler for achieving variable rate irrigation. China Rural Water and Hydropower, 2009; 8: 4–7.
[33] Feng C D. Calculation of spray range. Drainage & Irrigation Machinery, 1986; 5(4): 35–38. (in Chinese)
[34] Gan Z M, Yang S H. The formula and experimental research on the range of the whirl sprinkler. Transactions of CSAM, 1998; 29(4): 145–149. (in Chinese)
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Published
2018-01-31
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Jiang, Y., Li, H., Chen, C., & Xiang, Q. (2018). Calculation and verification of formula for the range of sprinklers based on jet breakup length. International Journal of Agricultural and Biological Engineering, 11(1), 49–57. Retrieved from https://ijabe.migration.pkpps03.publicknowledgeproject.org/index.php/ijabe/article/view/2777
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