Skip to main content
SpringerLink
Log in

Simulation of Primary Film Atomization Due to Kelvin–Helmholtz Instability

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Liquid film atomization under a high-speed air flow (water was considered as the liquid) due to the Kelvin–Helmholtz instability is studied using the volume of fluid (VOF) method. We develop an approach for modeling the primary breakup and use it to investigate the grid convergence, choose the optimal size of the grid cell, and calculate the primary breakup of the film in the channel. The dependences of the mean break-off angle, the velocity modulus, and the Sauter droplet diameter on the longitudinal coordinate of the channel are obtained. The step-by-step averaging over the ensemble of droplets and over time allows us to get smooth coordinate dependences of the characteristics of the ensemble of the droplet. The value of the most useful parameter for engineering applications, the mean Sauter diameter D32 (equal to the ratio of the mean droplet volume to its mean area) is close to that obtained using a semiempirical formula from the literature, based on the experiment where hot wax is atomized by a high-speed airflow. The dependence of the Sauter mean diameter on the thickness of the liquid layer agrees qualitatively with the experimental dependence. The study of the grid’s convergence showed that the number of the smallest droplets increases rapidly with decreasing cell size. Their contribution to the average characteristics of the droplet’s ensemble, however, remains insignificant; nonetheless, their input to the mean characteristics remains insignificant; thus, there is no reason to decrease the grid cell size to account for small droplets.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Luo, H. and Svendsen, H.F., Theoretical model for drop and bubble breakup in turbulent dispersions, AIChE J., 1996, vol. 42, no. 5, pp. 1225–1233. https://doi.org/10.1002/aic.690420505

    Article  Google Scholar 

  2. Lehr, F., Millies, M., and Mewes, D., Bubble-size distributions and flow fields in bubble columns, AIChE J., 2002, vol. 8, no. 11, pp. 2426–2443. https://doi.org/10.1002/aic.690481103

    Article  Google Scholar 

  3. O’Rourke, P.J. and Amsden, A.A., The TAB method for numerical calculation of spray droplet breakup, SAE Tech. Papers, 1987, p. 872089. https://doi.org/10.4271/87208910.4271/872089

    Google Scholar 

  4. Beale, J.C. and Reitz, R.D., Modeling spray atomization with the Kelvin–Helmholtz/Rayleigh–Taylor hybrid model, Atomiz. Spray, 1999, vol. 9, pp. 623–650.

    Article  Google Scholar 

  5. Ménard, T., Tanguy, S., and Berlemont, A., Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet, Int. J. Multiphase Flow, 2007, vol. 33, no. 5, pp. 510–524. https://doi.org/10.1016/j.ijmultiphaseflow.2006.11.001

    Article  Google Scholar 

  6. Berlemont, A., Bouali, Z., Cousin, J., Desjonqueres, P., Doring, M., Menard, T., and Noel, E., Simulation of liquid/gas interface break-up with a coupled Level Set/VOF/Ghost fluid method, in Proceedings of the 7th International Conference on Computational Fluid Dynamics ICCFD7-2105, Big Island, Hawaii, July 9–13, 2012. https://doi.org/www.iccfd.org/iccfd7/assets/pdf/papers/ICCFD7-2105_paper.pdf.

    Google Scholar 

  7. Desjardins, O., McCaslin, J., Owkes, M., and Brady, P., Direct numerical and large-eddy simulation of primary atomization in complex geometries, Atomiz. Spray, 2013, vol. 23, no. 11, pp. 1001–1048.

    Article  Google Scholar 

  8. Mehravaran, K., Direct simulations of primary atomization in moderate-speed diesel fuel injection, Int. J. Mater. Mech. Manuf., 2013, vol. 1, no. 2, pp. 207–209. https://doi.org/10.7763/IJMMM.2013.V1.44

    Google Scholar 

  9. Ling, Y., Fuster, D., Tryggvason, G., Scardovelli, R., and Zaleski, St., 3D DNS of spray formation in gasassisted atomization, in Proceedings of the 24th International Congress of Theoretical and Applied Mechanics, Montreal, Canada, Aug. 21–26, 2016.

    Google Scholar 

  10. Chaussonnet, G., Riber, E., Vermorel, O., Cuenot, B., Gepperth, S., and Koch, R., Large Eddy Simulation of a prefilming airblast atomizer, in Proceedings of the 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, September 1–4, 2013.

    Google Scholar 

  11. Jeffreys, H., On the formation of water waves by wind, Proc. R. Soc. London, Ser. A, 1925, vol. 107, no. 742, pp. 189–206. https://doi.org/10.1098/rspa.1925.0015

    Article  ADS  MATH  Google Scholar 

  12. Andritsos, N. and Hanratty, T.J., Interfacial instabilities for horizontal gas-liquid flows in pipeline, Int. J. Multiphase Flow, 1987, vol. 13, no. 5, pp. 583–603. https://doi.org/10.1016/0301-9322(87)90037-1

    Article  Google Scholar 

  13. Tian, Ch. and Chen, Y., Numerical simulation of Kelvin–Helmholtz instability: a two-dimensional parametrical study, Astrophys. J., 2016, vol. 824, no. 1. https://doi.org/10.3847/0004-637X/824/1/60

    Google Scholar 

  14. Lee, H.G. and Kim, J., Two-dimensional Kelvin–Helmholtz instabilities of multi-component fluids, Eur. J. Mech. A, 2015, vol. 49, pp. 77–88. https://doi.org/10.1016/j.euromechflu.2014.08.001

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Woodmanse, D.E. and Hanratty, Th.J., Mechanism for the removal of droplets from a liquid surface by a parallel air flow, Chem. Eng. Sci., 1969, vol. 24, no. 2, pp. 299–307. https://doi.org/10.1016/0009-2509(69)80038-2

    Article  Google Scholar 

  16. Raynal, L., Instability on the gas-liquid mixture interface, PhD Thesis, Grenoble: Univ. J. Fourier, 1997.

    Google Scholar 

  17. Jerome, J.J.S., Marty, S., Matas, J., Zaleski, St., and Hoepffner, J., Vortices catapult droplets in atomization, Phys. Fluids, 2013, vol. 25, no. 11. https://doi.org/10.1063/1.4831796

    Book  Google Scholar 

  18. Ebner, J., Gerendás, M., Schäfer, O., and Wittig, S., Droplet entrainment from a shear-driven liquid wall film in inclined ducts: experimental study and correlation comparison, in Proceedings of the ASME Turbo Expo 2001, New Orleans, Louisiana, USA, June 4–7, 2001, Paper No. 2001-GT-0115. https://doi.org/10.1115/2001-GT-0115

    Google Scholar 

  19. Shalanin, V.A., Eulerian methods for modeling flows with free surface, Molod. Uchen., 2016, no. 2 (106), pp. 258–261.

    Google Scholar 

  20. Leonov, A.A., Chudanov, V.V., and Aksenova, A.E., Methods of direct numerical simulation in two-phase media, in Trudy IBRAE RAN (Collection of Articles of IBRAE RAS), Bolshov, L.A., Ed., Moscow: Nauka, 2013, no. 14.

    Google Scholar 

  21. Lyubimov, D.V. and Lyubimova, T.P., About a numerical method for solution of problem with deformable interface, Model. Mekh., 1990, vol. 4, no. 1, pp. 136–140.

    Google Scholar 

  22. Brackbill, J.U., Kothe, D.B., and Zemach, C., A continuum method for modeling surface tension, J. Comput. Phys., 1992, vol. 100, no. 2, pp. 335–354. https://doi.org/10.1016/0021-9991(92)90240-Y

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Senecal, P.K., Schmidt, D.P., Nouar, I., Rutland, C.J., Reitz, R.D., and Corradini, M.L., Modeling highspeed viscous liquid sheet atomization, Int. J. Multiphas. Flow, 1999, vol. 25, nos. 6–7, pp. 1073–1097. https://doi.org/10.1016/S0301-9322%2899%2900057-9

    Article  MATH  Google Scholar 

  24. Dombrowski, N. and Hooper, P.C., The effect of ambient density on drop formation in sprays, Chem. Eng. Sci., 1962, vol. 17, no. 4, pp. 291–305. https://doi.org/10.1016/0009-2509%2862%2985008-8

    Article  Google Scholar 

  25. Dombrowski, N. and Johns, W.R., The aerodynamic instability and disintegration of viscous liquid sheets, Chem. Eng. Sci., 1963, vol. 18, no. 3, pp. 203–214. https://doi.org/10.1016/0009-2509%2863%2985005-8

    Article  Google Scholar 

  26. Strokach, E.A. and Borovik, I.N., Numerical simulation of kerosene dispersion process by the centrifugal atomizer, Vestn. MGTU Baumana, Ser. Mashinostr., 2016, no. 3 (108), pp. 37–54. https://doi.org/10.18698/0236-3941-2016-3-37-54

    Google Scholar 

  27. Mayer, E., Theory of liquid atomization in high velocity gas streams, ARS J., 1961, vol. 31, no. 12, pp. 1783–1785.

    MATH  Google Scholar 

  28. Weiss, M.A. and Worsham, C.H., Atomization in high velocity airstreams, ARS J., 1959, vol. 29, no. 4, pp. 252–259.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Perm State University, Perm, Russia

    M. G. Kazimardanov & T. P. Lubimova

  2. AO ODK-Aviadvigatel, Perm, Russia

    M. G. Kazimardanov, S. V. Mingalev & L. Yu. Gomzikov

  3. Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, Russia

    T. P. Lubimova

Authors
  1. M. G. Kazimardanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. V. Mingalev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. P. Lubimova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. Yu. Gomzikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. G. Kazimardanov.

Additional information

Original Russian Text © M.G. Kazimardanov, S.V. Mingalev, T.P. Lubimova, L.Yu. Gomzikov, 2018, published in Vychislitel’naya Mekhanika Sploshnykh Sred, 2017, Vol. 10, No. 4, pp. 416–425.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kazimardanov, M.G., Mingalev, S.V., Lubimova, T.P. et al. Simulation of Primary Film Atomization Due to Kelvin–Helmholtz Instability. J Appl Mech Tech Phy 59, 1251–1260 (2018). https://doi.org/10.1134/S0021894418070064

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894418070064

Keywords

Search

Navigation