Mathematical Modeling of Drip Emitter Discharge of Trapezoidal Labyrinth Channel
Authors: N. Philipova
The influence of the geometric parameters of trapezoidal labyrinth channel on the emitter discharge is investigated in this work. The impact of the dentate angle, the dentate spacing, and the dentate height are studied among the geometric parameters of the labyrinth channel. Numerical simulations of the water flow movement are performed according to central cubic composite design using Commercial codes GAMBIT and FLUENT. Inlet pressure of the dripper is set up to be 1 bar. The objective of this paper is to derive a mathematical model of the emitter discharge depending on the dentate angle, the dentate spacing, the dentate height of the labyrinth channel. As a result, the obtained mathematical model is a second-order polynomial reporting 2-way interactions among the geometric parameters. The dentate spacing has the most important and positive influence on the emitter discharge, followed by the simultaneous impact of the dentate spacing and the dentate height. The dentate angle in the observed interval has no significant effect on the emitter discharge. The obtained model can be used as a basis for a future emitter design.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316175Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 609
 Intergovermental Panel on Climate Change. Synthesis Report, 2014, Denmark Available at: http://www.ipcc.ch/pdf/assessment-report/ar5/syr/SYR_AR5_FINAL_full_wcover.pdf.
 Y. Li, P. Yang, S. Ren, “Hydraulic characterization of tortuous flow in path drip irrigation emitter”, J. of Hydrodynamics, Ser. B, vol. 18, no 4, 2006, pp. 449-457.
 J. Zhang, W. Zhao, Y. Tang, Z. Wei, B. Lu, “Numerical investigations of the clogging mechanism in labyrinth channel of the emitter”, Int. J. for Num. Meth. in Eng., vol. 70, 2007, pp.1598-1612.
 J. Zhang, W. Zhao, Z. Wei, Y. Tang, B. Lu, “Numerical and experimental study on hydraulic performance of emitters with arc labyrinth channel”, Computers and Electronics in Agriculture, vol. 56, 2007, pp.120-129.
 D. Yan, P. Yang, S. Ren, Y. Li, ”Numerical study on flow property in dentate path of drip emitters”, New Zealand J. of Agr. Research, vol. 50, 2007, pp. 705-712.
 N. Philipova, N. Nikolov, G. Pichurov, D. Markov, “A mathematical model of emitter discharge depending on geometric parameters of drip emitter labyrinth channel” ,Proc of the 11th National Congress on Theoretical and Applied Mechanics, 2-5 Sept. 2009, Borovets, Bulgaria (CD-ROM), pp. 1-6.
 N. Philipova, N. Nikolov, E. Stoimenova, G. Pichurov, D. Markov, “Mathematical Modeling Drip Emitter Discharge of Triangle Labyrinth Channel”, Comptesrendusdel’Academiebulgare des Scinces, vol. 64, no 1, 2011. Pp.133-140.
 N. Philipova, N. Nikolov, E. Stoimenova, G. Pichurov, D. Markov, “A regression equation of drip emitter discharge depending on the geometric parameters of rectangular labyrinth channel”, Comptesrendusdel’Academiebulgare des Scinces, vol. 64, no 11, 2011, pp. 1607-1614.
 G. Li, J. Wang, M. Alam, Y. Zhao, “Influence ongeometric parameters of labyrinth flow path of drip emitters on hydraulic and anti-clogging performance”, Transactions of ASABE, vol.49, no 3, 2006, pp. 637- 643.
 Mohammed Ali, “Anticlogging Drip Irrigation Emtters Design Inovation”, European International Journal of Science and Technology, vol.2, no 8, 2013, pp. 154-164.
 Z. Wei, “Application of RP and Manufacturing to water-saving emitters”, in Advanced Application of Rapid Prototyping Technology in Modern Engineering, Available at: http://www.intechopen.com/books/advanced-applications-of-rapid- prototyping-technology-in-modern-engineering/application-of-rp-and-manufacturing-to-water -saving-emitter.
 Zhao, W., Zhang, J, Tang, Y., Wei, Z., Lu, B., IFIO International Federation for Information Processing, Vol.294, Computer and Computing Technologies in Agriculture II, vol. 2, 2009, eds D. Li, Z. Chunjiang, Boston: Springer, pp.881-890
 K. Hanjalic, B. Launder, “A Reynolds stress model of turbulence and its application to thin shear flows”, J. Fluid Mech., vol.52, no 4, 1972, pp. 609-638.
 B. Launder, G. Reece, W. Rodi, “Progress in the development of a Reynolds- stress turbulence closure”, J. Fluid Mech., vol. 68, no 3, 1975, pp. 537-566.
 H. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Willey, New York, 1995.
 Fluent 6.3 User’s Guide, Available at:https://www.sharcnet.ca/Software/Fluent6/html/ug/main_pre.htm.
 StatSoft Electronic Statistics Textbook, 2010, Available at http://www.statsoft.com/textbook.