A Two-Phase LES Compressible Model for Plasma-Liquid Jet Interaction

  • Céline Caruyer
  • Stéphane Vincent
  • Erick Meillot
  • Jean-Paul Caltagirone
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 110)


The numerical simulation of the interaction between a plasma flow and a liquid jet is important for understanding and predicting the physical parameters involved in plasma spraying processes. This work proposes an original model for dealing with three-dimensional and unsteady turbulent interactions between a plasma flow and a liquid water jet. A compressible model, based on augmented Lagrangian, Large Eddy Simulation (LES) turbulence modeling and Volume of Fluid (VOF) approaches, capable of managing incompressible two-phase flows as well as turbulent compressible motions is presented.


Large Eddy Simulation Weber Number Smagorinsky Model Compressible Model Large Eddy Simulation Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basu, S., Jordan, E.H., Cetegen, B.K.: Fluid mechanics and heat transfer of liquid precursor droplets injected into high-temperature plasmas. J. Therm. Spray Tech. 17, 60–72 (2008)CrossRefGoogle Scholar
  2. 2.
    Caiden, R., Fedkiw, R.P., Anderson, C.: A numerical method for two phase flow consisting of separate compressible and incompressible regions. J. Comput. Phys. 166, 1–27 (2001)zbMATHCrossRefGoogle Scholar
  3. 3.
    Caltagirone, J.P., Vincent, S., Caruyer, C.: A multiphase compressible model for the simulation of multiphase flows. Physics of Fluids (under submission)Google Scholar
  4. 4.
    David, E.: Modélisation des écoulements compressibles et hypersoniques. PhD thesis, Institut National Polytechnique de Grenoble (1993)Google Scholar
  5. 5.
    Fincke, J.R., Crawford, D.M., Snyder, S.C., Swank, W.D., Haggard, D.C., Williamson, R.L.: Entrainment in high-velocity, high-temperature plasma jets. Part I: experimental results. Int. J. Heat Transfer 46, 4201–4213 (2003)CrossRefGoogle Scholar
  6. 6.
    Gustafsson, I.: On first and second order symmetric factorization methods for the solution of elliptic difference equations. Chalmers, University of Technology 1 (1978)Google Scholar
  7. 7.
    Kataoka, I.: Local instant formulation of two-phase flow. Int. J. Multiph. Flow 12, 745–758 (1986)zbMATHCrossRefGoogle Scholar
  8. 8.
    Liu, Z., Reitz, R.D.: An analysis of the distorsion and breakup mechanisms of high speed liquid drops. Int. J. Multiphase Flow 23, 631–650 (1997)zbMATHCrossRefGoogle Scholar
  9. 9.
    Marchand, C., Vardelle, A., Mariaux, G., Lefort, P.: Modelling of the plasma spray process with liquid feedstock injection. Surf. Coat. Technol. 202, 4458–4464 (2008)CrossRefGoogle Scholar
  10. 10.
    Marchand, C., Vardelle, A., Mariaux, G., Lefort, P.: Modelling of the plasma spray process with liquid feedstock injection. Surf. Coat. Technol. 202, 4458–4464 (2008)CrossRefGoogle Scholar
  11. 11.
    Mariaux, G., Vardelle, A.: 3-D time-dependent modelling of the plasma spray process. part I: flow modelling. Int. J. Therm. Sci. 44, 357–366 (2005)CrossRefGoogle Scholar
  12. 12.
    Meillot, E., Guenadou, D.: Thermal plasma flow modeling: A simple model for gas heating and acceleration. Plasma Chem. Plasma Process. 24, 217–238 (2004)CrossRefGoogle Scholar
  13. 13.
    Meillot, E., Guenadou, D., Bourgeois, C.: Three-dimension and transient D.C. plasma flow modeling. Plasma Chem. Plasma Process. 28, 69–84 (2007)CrossRefGoogle Scholar
  14. 14.
    Nourgaliev, R.R., Dinh, T.N., Theofanous, T.G.: Adaptive characteristics-based matching for compressible multifluid dynamics. J. Comput. Phys. 213, 500–529 (2006)zbMATHCrossRefGoogle Scholar
  15. 15.
    Nourgaliev, R.R., Theofanous, T.G.: High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set. J. Comput. Phys. 224, 836–866 (2007)zbMATHCrossRefGoogle Scholar
  16. 16.
    Sagaut, P.: Large eddy simulation for incompressible flows - An introduction. Springer, Heidelberg (1998)Google Scholar
  17. 17.
    Scardovelli, R., Zaleski, S.: Direct numerical simulation of free-surface and interfacial flow. Ann. Rev. Fluid Mech. 31, 567–603 (1999)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Smagorinsky, J.: General circulation experiments with the primitive equations. I: The basic experiments. Month. Weath. Rev. 91(3), 99–165 (1963)CrossRefGoogle Scholar
  19. 19.
    Trelles, J.P., Pfender, E., Heberlein, J.: Multiscale finite element modeling of arc dynamics in a d.c. plasma torch. Plasma Chem. Plasma Process. 26, 557–575 (2006)CrossRefGoogle Scholar
  20. 20.
    Vincent, S., Balmigere, G., Caruyer, C., Meillot, E., Caltagirone, J.: Contribution to the modeling of the interaction between a plasma flow and a liquid jet. Surf. Coat. Technol. (2008), doi:10.1016/j.surfcoat.2008.11.009Google Scholar
  21. 21.
    Vincent, S., Caltagirone, J.P.: Efficient solving method for unsteady incompressible flow problems. Int. J. Num. Meth. Fluids 30, 795–811 (1999)zbMATHCrossRefGoogle Scholar
  22. 22.
    Vincent, S., Caltagirone, J.P., Lubin, P., Randrianarivelo, T.N.: An adaptative augmented lagrangian method for three-dimensional multimaterial flows. Comput. Fluids 33, 1273–1289 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Vincent, S., Larocque, J., Lacanette, D., Toutan, A., Lubin, P., Sagaut, P.: Numerical simulation of phase separation and a priori two-phase les filtering. Comput. Fluids 37, 898–906 (2008)zbMATHCrossRefGoogle Scholar
  24. 24.
    Van Der Vorst, H.A.: A fast and smoothly converging variant of bi-cg for the solution of non-symmetric linear systems. J. Sci. Stat. Comput. 44, 631–644 (1992)CrossRefGoogle Scholar
  25. 25.
    Williamson, R.L., Fincke, J.R., Crawford, D.M., Snyder, S.C., Swank, W.D., Haggard, D.C.: Entrainment in high-velocity, high-temperature plasma jets. Part II: computational results and comparison to experiment. Int. J. Heat Transfer 46, 4215–4228 (2003)CrossRefGoogle Scholar
  26. 26.
    Yabe, T., Yuan, P.Y.: Unified numerical procedure for compressible and incompressible flow. J. of The Physical Society of Japan 60, 2105–2108 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Céline Caruyer
    • 1
  • Stéphane Vincent
    • 2
  • Erick Meillot
    • 1
  • Jean-Paul Caltagirone
    • 2
  1. 1.CEA-DAM Le RipaultMontsFrance
  2. 2.Tranferts Ecoulements Fluides Energétique (TREFLE)UMR CNRS 8508, ENSCPB

Personalised recommendations