Modeling of the Deformation Dynamics of Single and Twin Fluid Droplets Exposed to Aerodynamic Loads

  • Lars Wieth
  • Samuel Braun
  • Geoffroy Chaussonnet
  • Thilo F. Dauch
  • Marc Keller
  • Corina Höfler
  • Rainer Koch
  • Hans-Jörg Bauer
Conference paper

Abstract

Droplet deformation and breakup plays a significant role in liquid fuel atomization processes. The droplet behavior needs to be understood in detail, in order to derive simplified models for predicting the different processes in combustion chambers. Therefore, the behavior of single droplets at low aerodynamic loads was investigated using the Lagrangian, mesh-free Smoothed Particle Hydrodynamics (SPH) method. The simulations to be presented in this paper are focused on the deformation dynamics of pure liquid droplets and fuel droplets with water added to the inside of the droplet. The simulations have been run at two different relative velocities. As SPH is relatively new to Computational Fluid Dynamics (CFD), the pure liquid droplet simulations are used to verify the SPH code by empirical correlations available in literature. Furthermore, an enhanced characteristic deformation time is proposed, leading to a good description of the temporal initial deformation behavior for all investigated test cases. In the further course, the deformation behavior of two fluid droplets are compared to the corresponding single fluid droplet simulations. The results show an influence of the added water on the deformation history. However, it is found that, the droplet behavior can be characterized by the pure fuel Weber number.

Notes

Acknowledgements

The financial support of the German Federal Ministry of Economics and Technology and Siemens AG within the cooperative research project ‘Entwicklung von Verbrennungstechnologien im CEC für klimaschonende Energieerzeugung (03ET7011E)’ is gratefully acknowledged.

This work was performed on the computational resource ForHLR Phase I, funded by the Ministry of Science, Research and the Arts Baden-Württemberg and DFG (“Deutsche Forschungsgemeinschaft”).

References

  1. 1.
    Adami, S., Hu, X.Y., Adams, N.A.: A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation. J. Comput. Phys. 229, 5011–5021 (2010)CrossRefMATHGoogle Scholar
  2. 2.
    Bartz, F.-O., Schmehl, R., Koch, R., Bauer, H.-J.: An extension of dynamic droplet deformation model to secondary atomization. In: 23rd Annual Conference on Liquid Atomization and Spray Systems, Brno (2010)Google Scholar
  3. 3.
    Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  4. 4.
    Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Braun, S., Krug, M., Wieth, L., Höfler, C., Koch, R., Bauer, H.-J.: Simulation of primary atomization: assessment of the smoothed particle hydrodynamics (SPH) method. In: 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan (2015)Google Scholar
  6. 6.
    Braun, S., Wieth, L., Koch, R., Bauer, H.-J.: A framework for permeable boundary conditions in SPH: inlet, outlet, periodicity. In: 10th International SPHERIC Workshop, Parma (2015)Google Scholar
  7. 7.
    Colagrossi, A., Landrini, M.: Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191, 448–475 (2003)CrossRefMATHGoogle Scholar
  8. 8.
    Dryer, F.L.: Water addition to practical combustion systems – concepts and applications. Symp. Int. Combust. 16 (1), 279–295 (1977)CrossRefGoogle Scholar
  9. 9.
    Forschungshochleistungsrechner ForHLR Phase I http://www.bwhpc-c5.de/wiki/index.php/ForHLR_Phase_I_Hardware_and_Architecture. Cited 04 Apr 2016
  10. 10.
    Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics theory and application to non-spherical stars. Mon. Not. R. Aston. Soc. 181, 375–389 (1977)CrossRefMATHGoogle Scholar
  11. 11.
    Guildenbecher, D.R., López-Rivera, C., Sojka, P.E.: Secondary atomization. Exp. Fluids 46, 371–402 (2009)CrossRefGoogle Scholar
  12. 12.
    Hinze, J.O.: Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289–295 (1955)CrossRefGoogle Scholar
  13. 13.
    Höfler, C., Braun, S., Koch, R., Bauer, H.-J.: Modeling spray formation in gas turbines – a new meshless approach. J. Eng. Gas. Turb. Power 135, 011503-1–011503-8 (2013)Google Scholar
  14. 14.
    Hsiang, L.-P., Faeth, G.M.: Near-limit drop deformation and secondary breakup. Int. J. Multiph. Flow. 18 (5), 635–652 (1992)CrossRefMATHGoogle Scholar
  15. 15.
    Hu, X.Y., Adams, N.A.: Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows. Phys. Fluids 18, 101702 (2006)CrossRefGoogle Scholar
  16. 16.
    Hu, X.Y., Adams, N.A.: An incompressible multi-phase SPH method. J. Comput. Phys. 227, 264–278 (2007)CrossRefMATHGoogle Scholar
  17. 17.
    Khare, P., Ma, D., Chen, X., Yang, D.: Breakup of liquid droplets. In: 12th Triennial International Conference on Liquid Atomization and Spray Systems, Heidelberg (2012)Google Scholar
  18. 18.
    Lechner, C., Seume, J.: Stationäre Gasturbinen. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Liu, M.B., Liu, G.R.: Smoothed particle hydrodynamics (SPH) an overview and recent developments. Arch. Comput. Method E 17, 25–76 (2010)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024 (1977)CrossRefGoogle Scholar
  21. 21.
    Monaghan, J.J.: Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30, 543–574 (1992)CrossRefGoogle Scholar
  22. 22.
    Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110, 399–406 (1994)CrossRefMATHGoogle Scholar
  23. 23.
    Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136, 214–226 (1997)CrossRefMATHGoogle Scholar
  24. 24.
    O’Rourke, P.J., Amsden, A.A.: The TAB method for numerical calculation of spray droplet breakup. In: International Fuels and Lubricants Meeting and Exposition, Toronto (1987)Google Scholar
  25. 25.
    Quan, S., Schmidt, D.P.: Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow. Phys. Fluids 18, 102103 (2006)CrossRefGoogle Scholar
  26. 26.
    Ranger, A.A., Nicholls, J.A.: Aerodynamic shattering of liquid drops. AIAA J. 7 (2), 285–289 (1969)CrossRefGoogle Scholar
  27. 27.
    Schmehl, R.: Advanced modeling of droplet deformation and breakup for CFD analysis of mixture preparation. In: 18th Annual Conference on Liquid Atomization and Spray Systems, Zaragoza (2002)Google Scholar
  28. 28.
    Schmehl, R., Maier, G., Wittig, S.: CFD analysis of fuel atomization, secondary droplet breakup and spray dispersion in the premix duct of a LPP combustor. In: 8th International Conference on Liquid Atomization and Spray Systems, Pasadena (2000)Google Scholar
  29. 29.
    Wieth, L., Braun, S., Koch, R., Bauer, H.-J.: Modeling of liquid-wall interaction using the meshless Smoothed Particle Hydrodynamics (SPH) method. In: 26th European Conference on Liquid Atomization and Spray Systems, Bremen (2014)Google Scholar
  30. 30.
    Zaleski, S., Li, J., Succi, S.: Two-dimensional Navier-Stokes simulation of deformation and breakup of liquid patches. Phys. Rev. Lett. 75 (2), 244–247 (1995)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Lars Wieth
    • 1
  • Samuel Braun
    • 1
  • Geoffroy Chaussonnet
    • 1
  • Thilo F. Dauch
    • 1
  • Marc Keller
    • 1
  • Corina Höfler
    • 1
  • Rainer Koch
    • 1
  • Hans-Jörg Bauer
    • 1
  1. 1.Institut für Thermische StrömungsmaschinenKarlsruhe Institut für TechnologieKarlsruheGermany

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