Evaluation of a diffuse interface treatment for pressure in phase change simulations using adaptive mesh refinement

  • Bernardo Alan de Freitas DuarteEmail author
  • Millena Martins Villar
  • Ricardo Serfaty
  • Aristeu da Silveira Neto
Technical Paper


Phase change computational simulations using a diffuse interface treatment for pressure were investigated in order to quantify the spurious currents and its consequences on the interface transport in the present paper. In addition, benchmarks were conducted with a sharp interface treatment for pressure. Namely, a Delta function method (Delta) was employed for the diffuse interface treatment and a ghost fluid method (GFM) for the sharp approach. An additional force term in the non-divergent form of the momentum equation is proposed for the first time in the literature, and its impact on interface motion during simulations of bubble growth by intense phase change has been quantified. In addition, the influence of recoil force on interface position was evaluated in simulations of water bubble condensation at near critical pressure. Finally, simulations of a complex industrial application were performed using the diffuse interface treatment, namely a case of film boiling with the development of Rayleigh–Taylor instability. Both interface treatments presented excellent results for the interface evolution in time. Even with the presence of some relevant spurious currents in the Delta method, the bubble evolution in time was accurately predicted. The sharp interface treatment potential was especially evident using a mass density flux of 1.0 kg/(m2 s) or higher. Therefore, a diffuse interface treatment for pressure has been presented as an appropriate strategy for most phase change simulations since the presence of the spurious currents did not disturb the interface position, and its magnitude was low for even moderate phase change intensities. The inclusion of the source term due to the additional force in the non-divergent form of the momentum equation and the recoil force term was irrelevant in the cases tested. Lastly, the film boiling simulation using the diffuse interface treatment revealed the possibility of treating complex 3D cases for industrial applications with this method.


GFM method Delta function method Boiling Spurious currents Recoil force 



The authors gratefully acknowledge financial support from Petrobras, CNPQ, Fapemig and Capes. The authors are also grateful to the mechanical engineering graduate program from the Federal University of Uberlândia (UFU).


  1. 1.
    Haelssig J, Thibault A, Etemad S (2010) Direct numerical simulation of interphase heat and mass transfer in multicomponent vapour-liquid flows. Int J Heat Mass Transf 53:3947. CrossRefzbMATHGoogle Scholar
  2. 2.
    Welch SWJ, Wilson J (2000) A volume of fluid based method for fluid flows with phase change. J Comput Phys 160:662. CrossRefzbMATHGoogle Scholar
  3. 3.
    Juric D, Tryggvason G (1998) Computations of boiling flows. Int J Multiph Flow 24:387. CrossRefzbMATHGoogle Scholar
  4. 4.
    Nikolayev V, Chatain D, Garrabos Y, Beysens D (2016) Experimental evidence of the vapor recoil mechanism in the boiling crisis. Phys Rev Lett 97:253. CrossRefGoogle Scholar
  5. 5.
    Strotos G, Gavaises M, theodorakakos A, Bergeles G (2011) Numerical investigation of the evaporation of two-component droplets. Fuel 90:1492. CrossRefzbMATHGoogle Scholar
  6. 6.
    Tanguy S, Sagan M, Lalanne B, Couderc F, Colin C (2014) Benchmarks and numerical methods for the simulation of boiling flows. J Comput Phys 264:1. CrossRefzbMATHGoogle Scholar
  7. 7.
    Pan Z, Weibel J, Garimella SV (2016) A Saturated-Interface-Volume Phase ChangeModel for Simulating Flow Boiling. Int J Heat Mass Transf 93:945. CrossRefGoogle Scholar
  8. 8.
    Tryggvason G, Lu J (2015) Direct numerical simulations of flows with phase change. Procedia IUTAM 15:2. CrossRefGoogle Scholar
  9. 9.
    Tsui Y, Lin SW, Lai YN, Wu FC (2014) Phase change calculations for film boiling flows. Int J Heat Mass Transf 70:745. CrossRefGoogle Scholar
  10. 10.
    Tanguy S, Menard T, Berlemont A (2007) A level set method for vaporizing two-phase flows. J Comput Phys 221:837MathSciNetCrossRefGoogle Scholar
  11. 11.
    Harvie D, Davidson M, Rudman M (2006) An analysis of parasitic current generation in volume of fluid simulations. Appl Math Model 30:1056. CrossRefzbMATHGoogle Scholar
  12. 12.
    Akhtar M, Kleis S (2013) Boiling flow simulations on adaptive octree grids. Int J Multiphase Flow 53:88. CrossRefGoogle Scholar
  13. 13.
    Francois MM, Cummins SJ, Dendy ED, Kothe DB, Sicilian JM, Williams MW (2006) A balanced-force algorithm for continuous andsharp interfacial surface tension models within a volume tracking framework. J Comput Phys 213:141. CrossRefzbMATHGoogle Scholar
  14. 14.
    Samkhaniani N, Ansari MR (2016) Numerical simulation of bubble condensation using CF-VOF. Progres Nucl Energy 89:120. CrossRefGoogle Scholar
  15. 15.
    Lee MS, Riaz A, Aute V (2017) Direct numerical simulation of incompressible multiphase flow with phase change. J Comput Phys 344:381. MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface-tension. J Comput Phys 100:335. MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Raghupathi PA, Kandlikar SG (2016) Bubble growth and departure trajectory under asymmetric temperature conditions. Int J Heat Mass Transf 95:824. CrossRefGoogle Scholar
  18. 18.
    Ningegowda BM, Premachandran B (2014) A coupled level set and volume of fluid method with multi-directional advection algorithms for two-phase flows with and without phase change. Int J Heat Mass Transf 79:532CrossRefGoogle Scholar
  19. 19.
    Nikolopoulos N, Theodorakakos A, Bergeles G (2007) A numerical investigation of the evaporation process of a liquid droplet impinging onto a hot substrate. Int J Heat Mass Transf 50:303. CrossRefzbMATHGoogle Scholar
  20. 20.
    Deen N, Kuipers J (2013) Direct numerical simulation of wall-to liquid heat transfer in dispersed gas-liquid two-phase flow using a volume of fluid approach. Chem Eng Sci 102:268. CrossRefGoogle Scholar
  21. 21.
    Kim DG, Jeon CH, Park IS (2017) Comparison of numerical phase-change models through Stefan vaporizing problem. Int Commun Heat Mass Transf 87:228. CrossRefGoogle Scholar
  22. 22.
    Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201. CrossRefzbMATHGoogle Scholar
  23. 23.
    Wachem BGM, Schouten JC (2002) Experimental validation of 3-D Lagragian VOF model: bubble shape and rise velocity. AIChE J 48:253. CrossRefGoogle Scholar
  24. 24.
    Liu XD, Fedkiw R, Kang M (2000) A boundary condition capturing method for Poisson’s equation on irregular domains. J Comput Phys 160:151. MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Chorin AJ (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22:745. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Centrella JM, Wilson JR (1984) Planar numerical cosmology. II—the difference equations and numerical tests. Astrophys J Suppl Ser 54:229. CrossRefGoogle Scholar
  27. 27.
    Scriven LE (1959) On the dynamics of phase change. Chem Eng Sci 10:1. CrossRefGoogle Scholar
  28. 28.
    Kamei S, Hirata M (1990) Condensing phenomena of a single vapor bubble into subcooled water. Exp Heat Transf 3:173. CrossRefGoogle Scholar
  29. 29.
    Yang Y, Pan LM, Xu JJ (2014) Effects of microgravity on Marangoni convection and growth characteristic of a single bubble. Acta Astronaut 100:129. CrossRefGoogle Scholar
  30. 30.
    Sharp DH (1984) An overview of Rayleigh–Taylor instability. Physica 12:3. CrossRefzbMATHGoogle Scholar
  31. 31.
    Sidharth GS, Candler GV, Dimotakis P (1991) Baroclinic torque and implications for subgrid-scale modeling. In: 7th AIAA theoretical fluid mechanics conference, pp 1–13.
  32. 32.
    Roberts MS, Jacobs JW (2016) The effects of forced small-wavelength, finite-bandwidth inital perturbations and miscibility on the turbulent Rayleigh–Taylor instability. J Fluid Mech 787:50. MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Tryggvason G (1988) Numerical simulations of the Rayleigh–Taylor instability. J Comput Phys 75:253. CrossRefzbMATHGoogle Scholar
  34. 34.
    Berenson PJ (1961) Film boiling heat transfer from a horizontal surface. J Heat Transf 83:351. CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Bernardo Alan de Freitas Duarte
    • 1
    Email author
  • Millena Martins Villar
    • 1
  • Ricardo Serfaty
    • 2
  • Aristeu da Silveira Neto
    • 1
  1. 1.Federal University of UberlândiaUberlândiaBrazil
  2. 2.CENPESIlha do FundãoBrazil

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