Skip to main content
Log in

Water droplets behavior in sprinkler irrigation: Thermal-fluid dynamical assessment and quantum considerations

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

The present paper is aimed at analyzing the behavior of water droplets traveling in air from the nozzle to the ground according to a traditional numerical and a quantum point of views. Considering a single-droplet system, an analytical model based on the Newtonian kinematics is here described, considering the most relevant parameters involved: droplet initial diameter, droplet initial velocity, water and air temperatures, diffusion coefficient of water in air, air relative humidity, environmental radiation, and presence of wind. The effect of those parameters on water evaporation is, hence, discussed. Differently, when a multi-droplet system in considered, the problem becomes even more complicated due to the difficulty of assessment of interdroplet reciprocal affections and both a Newtonian description and a numeric implementation are definitely hard to obtain. An alternative to traditional approaches to treat the water droplet dynamics is the quantum approach, which is here introduced and pointed out in order to give an as full as possible description of the whole phenomenon. Such an approach offers a more tight description of the microscopic phenomena that influence the evolution of the whole multi-droplet system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Christiansen, J.E., Irrigation by Sprinkling, California Agricultural Experiment Station Bulletin 670, Berkeley, CA: Univ. of California, 1942.

    Google Scholar 

  2. Kinzer, G.D. and Gunn, R., The Evaporation, Temperature and Thermal Relaxation-Time of Freely Falling Water Drops, J. Meteorol., 1951, vol. 8, no. 2, pp. 71–83.

    Article  Google Scholar 

  3. Edling, R.J., Kinetic Energy, Evaporation and Wind Drift of Droplets from Low-Pressure Irrigation Nozzles, Trans. ASAE, 1985, vol. 28, no. 5, pp. 1543–1550.

    Article  Google Scholar 

  4. Kincaid, D.C. and Longley, T.S., A Water Droplet Evaporation and Temperature Model, Trans. ASAE, 1989, vol. 32, no. 2, pp. 457–463.

    Article  Google Scholar 

  5. Keller, J. and Bliesner, R.D., Sprinkler and Trickle Irrigation, New York: Van Nostrand Reinhold, 1990.

    Book  Google Scholar 

  6. Thompson, A.L., Gilley, J.R., and Norman, J.M., A Sprinkler Water Droplet Evaporation and Plant Canopy Model: II. Model Applications, Trans. ASAE, 1993, vol. 36, no. 3, pp. 743–750.

    Article  Google Scholar 

  7. Yazar, A., Evaporation and Drift Losses from Sprinkler Irrigation Systems under Various Operating Conditions, Agric. Water Manag., 1984, vol. 8, pp. 439–449.

    Article  Google Scholar 

  8. Uddin, J., Smith, R., Hancock, N., and Foley J.P., Droplet Evaporation Losses during Sprinkler Irrigation: An Overview, in Irrigation Australia Conference and Exhibition 2010: One Water Many Futures, Sydney, Australia, 2010, pp. 1–10.

    Google Scholar 

  9. Lorenzini, G., Simplified Modeling of Sprinkler Droplet Dynamics, Biosyst. Eng., 2004, vol. 87, no. 1, pp. 1–11.

    Article  Google Scholar 

  10. Lorenzini, G., Water Droplet Dynamics and Evaporation in an Irrigation Spray, Trans. Asabe, 2006, vol. 49, no. 2, pp. 545–549.

    Article  MathSciNet  Google Scholar 

  11. De Wrachien, D. and Lorenzini, G., Modeling Jet Flow and Losses in Sprinkler Irrigation: Overview and Perspective of a New Approach, Biosyst. Eng., 2006, vol. 94, no. 2, pp. 297–309.

    Article  Google Scholar 

  12. Lorenzini, G. and Saro, O., Thermal Fluid Dynamic Modeling of a Water Droplet Evaporating in Air, Int. J. Heat Mass Transfer, 2013, vol. 62(C), pp. 323–335.

    Article  Google Scholar 

  13. Bird, R.B., Steward, W.E., and Lighfoot, E.N., Transport Phenomena, New York: Wiley, 1960.

    Google Scholar 

  14. Park, S.W., Mitchell, J.K., and Bubenzer, G.D., Splash Erosion Modeling: Physical Analysis, Trans. ASAE, 1982, vol. 25, no. 2, pp. 357–361.

    Article  Google Scholar 

  15. Park, S.W., Mitchell, J.K., and Bubenzer, G.D., Rainfall Characteristics and Their Relation to Splash Erosion, Trans. ASAE, 1983, vol. 26, no. 3, pp. 795–804.

    Article  Google Scholar 

  16. Guglielmini, G. and Pisoni, C., Introduzione alla Trasmissione del Calore, Milano: Casa Editrice Ambrosiana, 2001.

    Google Scholar 

  17. Bavi, A., Kashkuli, H.A., Boroomand, S., Naseri, A., and Albaji, M., Evaporation Losses from Sprinkler Irrigation under Various Operating Conditions, J. Appl. Sci., 2009, vol. 9, no. 3, pp. 597–600.

    Article  Google Scholar 

  18. Friso, D. and Bortolini, L., Calculation of Sprinkler Droplet-Size Spectrum from Water Distribution Radial Curve, Int. J. Energy Technol., 2010, vol. 2, no. 24, pp. 1–11.

    Google Scholar 

  19. Kollár, L.E. and Farzaneh, M., Modeling the Evolution of Droplet Size Distribution in Two-Phase Flows, Int. J.Multiphase Flow, 2007, vol. 33, pp. 1255–1270.

    Article  Google Scholar 

  20. Lorenzini, G., Air Temperature Effect on Spray Evaporation in Sprinkler Irrigation, Irrig. Drain., 2002, vol. 51, no. 4, pp. 301–309.

    Article  Google Scholar 

  21. Varghese, S.K. and Gangamma, S., Evaporation of Water Droplets by Radiation: Effect of Absorbing Inclusions, Aerosol Air Qual. Res., 2007, vol. 7, no. 1, pp. 95–105.

    MATH  Google Scholar 

  22. Lorenzini, G., Conti, A., and De Wrachien, D., Computational Fluid Dynamics (CFD) Picture of Water Droplet Evaporation in Air, Irrigat. Drain. Sys. Eng., 2012.

    Google Scholar 

  23. Lopreore, C.L. and Wyatt, R.E., Quantum Wave Packet Dynamics with Trajectories, PRL, 1999, vol. 82, pp. 5190–5193.

    Article  ADS  Google Scholar 

  24. De Wrachien, D. and Lorenzini, G., Quantum Mechanics Applied to the Dynamic Assessment of a Cluster of Water Particles in Sprinkler Irrigation, J. Eng. Therm., 2012, vol. 21, no. 3, pp. 1–5.

    Article  Google Scholar 

  25. De Wrachien, D., Lorenzini, G., and Medici, M., Sprinkler Irrigation Systems: State-of-the-Art of Kinematic Analysis and Quantum Mechanics Applied toWater Jets, Irrig. Drain., 2013, vol. 62, pp. 407–413.

    Article  Google Scholar 

  26. Wyatt, R.E., Quantum Dynamics with Trajectories. Introduction to Quantum Dynamics, New York: Springer, 2005.

    MATH  Google Scholar 

  27. Ghosh, S.K., Quantum Fluid Dynamics within the Framework of Density Functional Theory, in Quantum Trajectories, Chattaraj, Ed., CRC Press, 2011, pp. 183–195.

    Google Scholar 

  28. Holland, P., Quantum Field Dynamics from Trajectories, in Quantum Trajectories, Chattaraj, Ed., CRC Press, 2011, pp. 73–86.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Lorenzini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lorenzini, G., Medici, M., Saro, O. et al. Water droplets behavior in sprinkler irrigation: Thermal-fluid dynamical assessment and quantum considerations. J. Engin. Thermophys. 23, 316–324 (2014). https://doi.org/10.1134/S1810232814040092

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1810232814040092

Keywords

Navigation