Advertisement

OpenFOAM® pp 235-247 | Cite as

Implementation of a Flexible and Modular Multiphase Framework for the Analysis of Surface-Tension-Driven Flows Based on a Hybrid LS-VOF Approach

  • Paolo CapobianchiEmail author
  • Marcello Lappa
  • Mónica S. N. Oliveira
Chapter

Abstract

The mathematical modelling and numerical simulation of multiphase flows are both demanding and highly complex. In typical problems with industrial relevance, the fluids are often in non-isothermal conditions, and interfacial phenomena are a relevant part of the problem. A number of effects resulting from the presence of temperature differences must be adequately taken into account to make the results of numerical simulations consistent and realistic. Moreover, in general, gradients of surface tension at the interface separating two liquids are a source of numerical issues that can delay (and in some circumstances even prevent) the convergence of the solution algorithm. Here, we propose a fundamental and concerted approach for the simulation of the typical dynamics resulting from the presence of a dispersed phase in an external matrix under non-isothermal conditions based on the modular computer-aided design, modelling and simulation capabilities of the OpenFOAM® environment. The resulting framework is tested against the migration of a droplet induced by thermocapillary effects in the absence of gravity. The simulations are fully three-dimensional and based on an adaptive mesh refinement (AMR) strategy. We describe in detail the countermeasures taken to circumvent the problematic issues associated with the simulation of this kind of flow.

References

  1. 1.
    Albadawi A., Donoghue D. B., Robinson A. J., Murray D. B., Delauré Y. M. C., (2013), Influence of surface tension implementation in volume of fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment, International Journal of Multiphase Flow, 53, 11–28.CrossRefGoogle Scholar
  2. 2.
    Balasubramaniam R. and Subramanian R. S, (2000), The migration of a drop in a uniform temperature gradient at large Marangoni numbers, Physics of Fluids, 12(4): 733–743.zbMATHCrossRefGoogle Scholar
  3. 3.
    Balasubramaniam R., Lacy C.E., Wozniak G., Subramanian R.S., (1996), Thermocapillary migration of bubbles and drops at moderate values of the Marangoni number in reduced gravity, Physics of Fluids, 8(4): 872–880.CrossRefGoogle Scholar
  4. 4.
    Berberović, van Hinsberg N. P., Jarkirlić S., Roisman L. V., Tropea C., (2009), Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution, Phyical. Review E, 79, 036306.Google Scholar
  5. 5.
    Brackbill J.U., Kothe D.B., Zemach C., (1992), A Continuum Method for Modeling Surface Tension, Journal of Computational Physics, 100 (2): 335–354.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Brady P. T., Hermann M., Lopez J. M., (2011), Confined thermocapillary motion of a three-dimensional deformable drop, Physics of Fluids, 23, 022101.CrossRefGoogle Scholar
  7. 7.
    Brunet P., Baudoin M., Bou Matar O., Zoueshtiagh F., (2010), Droplet displacement an doscillation induced by ultrasonic surface acoustic waves: A quantitative study, Physical Review E 81, 036315.Google Scholar
  8. 8.
    Fletcher C. A. J., Compuational techniques for fluid-dynamics (Springer Verlag, Berlin, 1991).Google Scholar
  9. 9.
    Hadland P.H., Balasubramaniam R., Wozniak G., Subramanian R.S., (1999), Thermocapillary migration of bubbles and drops at moderate to large Marangoni number and moderate Reynolds number in reduced gravity, Experiments in Fluids, 26: 240–248.CrossRefGoogle Scholar
  10. 10.
    Haj-Hariri H., Shi Q., Borhan A., (1997), Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers, Physics of Fluids 9 (4):845–855.CrossRefGoogle Scholar
  11. 11.
    Harper J.F. and Moore D.W., (1968), The motion of a spherical liquid drop at high Reynolds number, Journal of Fluid Mechanics, 32(2): 367–391.zbMATHCrossRefGoogle Scholar
  12. 12.
    Lappa M., (2004), Fluids, Materials and Microgravity: Numerical Techniques and Insights into the Physics, 538 pages, Elsevier Science (2004, Oxford, England).Google Scholar
  13. 13.
    Lappa M., (2005a) Assessment of VOF Strategies for the analysis of Marangoni Migration, Collisional Coagulation of Droplets and Thermal wake effects in Metal Alloys under Microgravity conditions, Computers, Materials & Continua, 2(1), 51–64.Google Scholar
  14. 14.
    Lappa M., (2005b), Coalescence and non-coalescence phenomena in multi-material problems and dispersed multiphase flows: Part 2, a critical review of CFD approaches, Fluid Dynamics & Materials Processing, 1(3): 213–234.Google Scholar
  15. 15.
    Ma X., Balasubramanian R., Subramanian R. S., (1999), Numerical simulation of thermocapillary drop motion with internal circulation, Numerical Heat Transfer, 35, 291–309.CrossRefGoogle Scholar
  16. 16.
    Nguyen N., Ng K. M., Huang X., (2006), Manipulation of ferrofluid droplet using planar coils, Applied Physics Letters 89, 052509.CrossRefGoogle Scholar
  17. 17.
    OpenFOAM® User Guide, 2008.Google Scholar
  18. 18.
    Subramanian R. S and Balasubramaniam R., (2001), The motion of bubbles an drops in reduced gravity, Cambridge University Press.Google Scholar
  19. 19.
    Sussman, M. and Fatemi, E., (1999): An efficient, interface-Preserving Level Set Redistancing Algorithm and its application to Interfacial Incompressible Fluid Flow. SIAM Journal of. Scientific Computing, 20, 1165–1191.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Sussman, M., Puckett, E., (2000), A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. Journal of Computational Physics, vol. 162, pp. 301–337.MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Tryggvason G., Bunner B., Esmaeeli A., Juric D., Al-Rawahi N., Tauber W., Han J., Nas S., and Jan Y.-J., (2001), A Front Tracking Method for the Computations of Multiphase Flow, Journal of Computational Physics, 169: 708–759.MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Tryggvason G., Scardovelli R., Zaleski S., (2011), Direct numerical simulations of gas-liquid multiphase flows, Cambridge University Press.Google Scholar
  23. 23.
    Wozniak G., (1991), On the thermocapillary motion of droplets under reduced gravity, Journal of Colloid and Interface Science, 141(1): 245–254.CrossRefGoogle Scholar
  24. 24.
    Yamamoto T., Okano Y., Dost S., (2016), Validation of the S-CLSVOF method with the density-scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows, International Journal of Numerical Methods in Fluids.Google Scholar
  25. 25.
    Yin Z., Chang L., Hu W., Li Q., and Wang H., (2012), Numerical simulations on thermocapillary migrations of nondeformable droplets with large Marangoni numbers, Physics of Fluids, 24, 092101.CrossRefGoogle Scholar
  26. 26.
    Young N.O., Goldstein J.S., Block M.J., (1959), The motion of bubbles in a vertical temperature gradient, Journal of Fluid Mechanics, 6, 350–360.zbMATHCrossRefGoogle Scholar
  27. 27.
    Zhao J., Zhang L., Li Z., Qin W., (2011), Topological structure evolvement of flow and temperature fields in deformable drop marangoni migration in microgravity, International Journal of Heat and Mass Transfer, 54, 4655–4663.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Paolo Capobianchi
    • 1
    Email author
  • Marcello Lappa
    • 1
  • Mónica S. N. Oliveira
    • 1
  1. 1.James Weir Fluids Laboratory, Department of Mechanical and Aerospace EngineeringUniversity of StrathclydeGlasgowUK

Personalised recommendations