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Chinese Journal of Mechanical Engineering
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Turned trochoidal disturbance on a liquid jet surface

Chinese Journal of Mechanical Engineering volume 27, pages 846–852 (2014)Cite this article

An Erratum to this article was published on 12 December 2014

Abstract

This paper shows that a turned trochoidal function disturbance may lead to peripheral drops production. The resulting model is used to describe that a turned trochoidal disturbance leads to peripheral drops production on the liquid jet surface without the necessity for superimposed disturbances. The trochoid is a non-unique parametric function. Only non-unique parametric functions disturbances may lead to peripheral drops production. The trochoidal function disturbance is decomposed to Fourier series. Every Fourier element receives an amplification factor in accordance to the Rayleigh inviscid jet model. Peripheral drops are received on the jet surface. The paper shows that all trochoidal disturbance functions, prolate cycloid, cycloid and curtate cycloid have a capability of peripheral drops producing. A limited capability of peripheral drops production is introduced for the trochoidal curtate cycloid. Produced drops size are reduced for increasing the jet velocity and wave number. Smaller drops are also received by transition from the prolate cycloid to curtate cycloid disturbance.

References

  1. LORD RAYLEIGH. On the instability of jets[J]. Proc. London Math. Soc., 1878, 10: 4–13.

    MathSciNet  MATH  Google Scholar 

  2. ZIMMELS Y, SADIK S. Formation of sprays from liquid jets by a superimposed sequence of nonaxial disturbances[J]. Appl. Phys. Lett., 2001, 79: 4601.

    Article  Google Scholar 

  3. DRAZIN P G, REID W H. Hydrodynamic stability[M]. Cambridge: Cambridge University Press, 2004.

    Book  MATH  Google Scholar 

  4. GERSTNER F. Theory of the waves including a therefrom derived theory of the dike profiles[J]. Ann. Phys., 1809, 2: 412–455.

    Article  Google Scholar 

  5. WEBER JAN ERIK H. Do we observe Gerstner waves in wave tank experiments?[J]. Wave Motion, 2011, 48: 301–309.

    Article  MathSciNet  MATH  Google Scholar 

  6. INOGAMOV N A. A cylindrical analog of trochoidal Gerstner waves[J]. Fluid Dynamics, 1985, 20(5): 791–796.

    Article  MathSciNet  MATH  Google Scholar 

  7. ADRIAN CONSTANTIN, WALTER A STRAUSS. Trochoidal solution to the incompressible two-dimensional Euler equations[J]. J. Math., 2010, 12: 181–201.

    MathSciNet  MATH  Google Scholar 

  8. DARLES E, CRESPIN B, GHAZANFARPOUR D. Accelerating and enhancing rendering of realistic ocean scenes[C/CD]//Proceedings of WSCG’2007, Plzen, Czech Republic, January-February, 2007.

    Google Scholar 

  9. DARLES E, CRESPIN B, GHAZANFARPOUR D, et al. A survey of ocean simulation and rendering techniques in computer graphics[J]. Computer Graphics Forum, 2011, 30(1): 43–60.

    Article  Google Scholar 

  10. WU P K, MIRANDA R F, FAETH G M. Effects of initial flow on primary breakup of Nonturbulent and turbulent round liquid jets[J]. Atomization and Sprays, 1995, 5: 175–196.

    Article  Google Scholar 

  11. POMEAU YVES, EMMANUEL VILLERMAUX. Two hundred years of capillarity research[J]. Physics Today, 2006 (3): 39–44.

    Google Scholar 

  12. WEBER JAN ERIK H. Do we observe Gerstner waves in wave tank experiments?[J]. Wave Motion, 2011, 48: 301–309.

    Article  MathSciNet  MATH  Google Scholar 

  13. QIAN LIJUAN, LIN JIANZHONG. Modeling on effervescent atomization: A review[J]. Physics, Mechanics & Astronomy, 2011, 54(12): 2109–2129.

    Article  MathSciNet  Google Scholar 

  14. DESJARDINS O, PITSCH H. Detailed numerical investigation of turbulent atomization of liquid jets[J]. Atomization and Sprays, 2010, 20(4): 311–336.

    Article  Google Scholar 

  15. SHINGO J, UMEMURA A. Surface instability and primary characteristics of straight liquid jet sprays[J]. International Journal of Multiphase Flow, 2011, 37: 1294–1304.

    Article  Google Scholar 

  16. OLIVIER DESJARDINS, JEREMI O MCCASLIN, MARK OWKES, et al. Direct numerical and large-eddy simulation of primary atomization in complex geometries[J]. Atomization and Sprays, 2013, 23(11): 1001–1048.

    Article  Google Scholar 

  17. WIM VAN HOEVE, STEPHAN GEKLE, JACCO H. SNOEIJER, et al. Breakup of diminutive Rayleigh jets[J]. Physics of Fluids, 2010, 22: 122003.

    Article  Google Scholar 

  18. MEHRABIAN HADI, JAMES J FENG. Capillary breakup of a liquid torus[J]. J. Fluid Mech., 2013, 717: 281–292.

    Article  MATH  Google Scholar 

  19. AWASTHI M K, ASTHANA R, AGRAWAL G S. Viscous potential flow analysis of Kelvin-Helmholtz instability of cylindrical interface with axial electric field[J]. Int. J. of Appl. Math. and Mech., 2012, 8(13): 1–12.

    Google Scholar 

  20. ESSAM A IBRAHIM, KENNY R JEREMI, NATHAN B WALKER. Atomization of shear coaxial liquid jets[J]. Applied Physics Research, 2010, 2(1): 3–18.

    Google Scholar 

  21. VILLE ANTON VUORINEN, HARRI HILLAMO, OSSI KAARIO, et al. Effect of droplet size and atomization on spray formation: a priory study using large-eddy simulation[J]. Flow Turbulent Combust, 2011, 86: 533–561.

    Article  MATH  Google Scholar 

  22. YANG LI-JUN, TONG MING-XI, FU QING-FEI. Linear stability analysis of a three-dimensional viscoelastic liquid jet surrounded by a swirling air stream[J]. Journal of Non-Newtonian Fluid Mechanics, 2013, 191: 1–13.

    Article  Google Scholar 

  23. RUO AN-CHENG, CHEN KUAN-HUNG, CHANG MIN-HSING, et al. Instability of a charged non-Newtonian liquid jet[J]. Physical Review E, 2012, 85: 016306.

    Article  Google Scholar 

  24. ZHAKIN A I, BELOV P A. The study of charged jets: the correlation between the theory and the experiments[J]. Surface Engineering and Applied Electrochemistry, 2013, 49(49): 290–295.

    Article  Google Scholar 

  25. ZHAKIN A I, BELOV P A. Experimental study of the outflow of charged drops and jets[J]. Surface Engineering and Applied Electrochemistry, 2013, 49(3): 205–214.

    Article  Google Scholar 

  26. ZHAKIN A I, BELOV P A, KUZ’KO A E. Experimental investigation of charged liquid jet efflux from a capillary[J]. Technical Physics Letters, 2013, 39(3): 299–301.

    Article  Google Scholar 

  27. GRIGOR’EVE A I, SHIRYAEVA S O, PETRUSHOV N A. On the stability of capillary waves on the surface of a charged jet moving relative to the environment[J]. Technical Physics, 2011, 56(2): 171–177.

    Article  Google Scholar 

  28. RUO AN-CHENG, CHANG MIN-HSING, CHEN FALIN. Electrohydrodynamic instability of a charged liquid jet in the presence of an axial magnetic field[J]. Physics of Fluids, 2010, 22: 044102.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, ORT Braude College, Karmiel, 21982, Israel

    Shalom Sadik

  2. Division of Environmental, Water and Agricultural Engineering, Faculty of Civil and Environmental Engineering, Technion-IIT, Haifa, 32000, Israel

    Felix Kirzhner

  3. Biotechnology Engineering, ORT Braude College, Karmiel, 21982, Israel

    Denis Kramarenko

Authors
  1. Shalom Sadik
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  2. Felix Kirzhner
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  3. Denis Kramarenko
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Corresponding author

Correspondence to Shalom Sadik.

Additional information

SADIK Shalom, born in 1952, is currently a staff member at Department of Mechanical Engineering, Ort Braude College, Israel. He teaches the courses Mechanics of Fluids and Heat Transfer. After long years working outside academy as leading new technologies projects he turned to the academic direction and completed his PhD thesis in the Technion at 2001. Thesis subject: Mechanisms of Nonaxial Disturbances in Evolution Processes of Jets into Sprays. Related to the thesis dissertation he published three quality papers. The first paper was published in Applied Physics Letters: Formation of Sprays from Liquid Jets by a Superimposed Sequence of Nonaxial Disturbances. His research interests include fluid mechanics and heat transfer.

KIRZHNER Felix, born in 1949, is currently senior researcher at Civil and Environmental Engineering Dept., in the Technion, Haifa, Israel. He has published more than 70 papers and 3 books. His research interests include rook mechanics, particles behavior, waste water treatment technologies.

KRAMARENKO Denis, born in 1986, is currently a research assistant at MIT, HST-Harvard-MIT Division of Health Sciences and Technology.

An erratum for this article can be found at http://dx.doi.org/10.3901/CJME.2014.1210.303

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Sadik, S., Kirzhner, F. & Kramarenko, D. Turned trochoidal disturbance on a liquid jet surface. Chin. J. Mech. Eng. 27, 846–852 (2014). https://doi.org/10.3901/CJME.2014.0527.102

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  • DOI: https://doi.org/10.3901/CJME.2014.0527.102

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