Table of Contents
Journal of Fluids
Volume 2013, Article ID 532016, 11 pages
http://dx.doi.org/10.1155/2013/532016
Research Article

Numerical and Experimental Analysis of the Growth of Gravitational Interfacial Instability Generated by Two Viscous Fluids of Different Densities

Department of Mechanical Engineering, Jadavpur University, Kolkata 700 032, West Bengal, India

Received 30 April 2013; Revised 20 August 2013; Accepted 4 September 2013

Academic Editor: Andrew W. Cook

Copyright © 2013 Snehamoy Majumder et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. H. Sharp, “An overview of Rayleigh-Taylor instability,” Physica D, vol. 12, no. 1–3, pp. 3–18, 1984. View at Google Scholar · View at Scopus
  2. K. I. Read, “Experimental investigation of turbulent mixing by Rayleigh-Taylor instability,” Physica D, vol. 12, no. 1–3, pp. 45–58, 1984. View at Google Scholar · View at Scopus
  3. D. L. Youngs, “Numerical simulation of turbulent mixing by Rayleigh-Taylor instability,” Physica D, vol. 12, no. 1–3, pp. 32–44, 1984. View at Google Scholar · View at Scopus
  4. S. B. Dalziel, “Rayleigh-Taylor instability: experiments with image analysis,” Dynamics of Atmospheres and Oceans, vol. 20, no. 1-2, pp. 127–153, 1993. View at Google Scholar · View at Scopus
  5. S. I. Voropayev, Y. D. Afanasyev, and G. J. F. van Heijst, “Experiments on the evolution of gravitational instability of an overturned, initially stably stratified fluid,” Physics of Fluids A, vol. 5, no. 10, pp. 2461–2466, 1993. View at Google Scholar · View at Scopus
  6. C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” Journal of Computational Physics, vol. 39, no. 1, pp. 201–225, 1981. View at Google Scholar · View at Scopus
  7. J. A. Sethian, “Curvature and the evolution of fronts,” Communications in Mathematical Physics, vol. 101, no. 4, pp. 487–499, 1985. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations,” Journal of Computational Physics, vol. 79, no. 1, pp. 12–49, 1988. View at Google Scholar · View at Scopus
  9. B. Merriman, J. K. Bence, and S. J. Osher, “Motion of multiple junctions: a level set approach,” Journal of Computational Physics, vol. 112, no. 2, pp. 334–363, 1994. View at Publisher · View at Google Scholar · View at Scopus
  10. J. Zhu and J. Sethian, “Projection methods coupled to level set interface techniques,” Journal of Computational Physics, vol. 102, no. 1, pp. 128–138, 1992. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Unverdi and G. Tryggvasan, “A front-tracking method for viscous, incompressible, multifluid flows,” Journal of Computational Physics, vol. 100, no. 1, pp. 25–37, 1992. View at Publisher · View at Google Scholar · View at Scopus
  12. D. L. Chopp and J. A. Sethian, “Flow under curvature: singularity formation, minimal surfaces, and geodesics,” Journal of Experimental Mathematics, vol. 24, pp. 235–255, 1993. View at Google Scholar
  13. M. Sussman, P. Smereka, and S. Osher, “A level set approach for computing solutions to incompressible two-phase flow,” Journal of Computational Physics, vol. 114, no. 1, pp. 146–159, 1994. View at Publisher · View at Google Scholar · View at Scopus
  14. Y. C. Chang, T. Y. Hou, B. Merriman, and S. Osher, “A level set formulation of Eulerian interface capturing methods for incompressible fluid flows,” Journal of Computational Physics, vol. 124, no. 2, pp. 449–464, 1996. View at Publisher · View at Google Scholar · View at Scopus
  15. J. A. Sethian, “Theory, algorithms, and applications of level set methods for propagating interfaces,” Acta Numerica, vol. 5, pp. 309–395, 1996. View at Publisher · View at Google Scholar
  16. J. A. Sethian, “Adaptive fast marching and level set methods for propagating interfaces,” Acta Mathematica Universitatis Comenianae, vol. 67, no. 1, pp. 3–15, 1998. View at Google Scholar
  17. J. A. Sethian, Fast Marching Methods and Level Set Methods for Propagating Interfaces, The Computational Fluid Dynamics Lecture Series, Von Karman Institute, 1998.
  18. C. Kaliakatos and S. Tsangaris, “Motion of deformable drops in pipes and channels using Navier-Stokes equations,” International Journal of Numerical Methods in Fluids, vol. 34, no. 7, pp. 609–626, 2000. View at Google Scholar
  19. G. Son and N. Hur, “A coupled level set and volume-of-fluid method for the buoyancy-driven motion of fluid particles,” Numerical Heat Transfer B, vol. 42, no. 6, pp. 523–542, 2002. View at Publisher · View at Google Scholar · View at Scopus
  20. J. A. Sethian and P. Smereka, “Level set methods for fluid interfaces,” Annual Review of Fluid Mechanics, vol. 35, pp. 341–372, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Majumder and S. Chakraborty, “New physically based approach of mass conservation correction in level set formulation for incompressible two-phase flows,” Journal of Fluids Engineering, vol. 127, no. 3, pp. 554–563, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Carlès, Z. Huang, G. Carbone, and C. Rosenblatt, “Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: a magnetic levitation investigation and theoretical model,” Physical Review Letters, vol. 96, no. 10, Article ID 104501, 4 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. S. Y. Wang, K. M. Lim, B. C. Khoo, and M. Y. Wang, “An extended level set method for shape and topology optimization,” Journal of Computational Physics, vol. 221, no. 1, pp. 395–421, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. D. L. Sun and W. Q. Tao, “A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows,” International Journal of Heat and Mass Transfer, vol. 53, no. 4, pp. 645–655, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Sussman and E. G. Puckett, “A coupled level set and volume of fluid method for computing 3D and axisymmetric incompressible two-phase flows,” Journal of Computational Physics, vol. 162, no. 2, pp. 301–337, 2000. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Sussman, “A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles,” Journal of Computational Physics, vol. 187, no. 1, pp. 110–136, 2003. View at Publisher · View at Google Scholar · View at Scopus
  27. G. Son, “Efficient implementation of a coupled level-set and volume-of-fluid method for three-dimensional incompressible two-phase flows,” Numerical Heat Transfer B, vol. 43, no. 6, pp. 549–565, 2003. View at Google Scholar · View at Scopus
  28. L. Wang, J. Li, and Z. Xie, “Large-eddy-simulation of 3-dimensional Rayleigh-Taylor instability in incompressible fluids,” Science in China, Series A, vol. 45, no. 1, pp. 95–106, 2002. View at Google Scholar · View at Scopus
  29. D. L. Youngs, “Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability,” Physics of Fluids A, vol. 3, no. 5, pp. 1312–1320, 1991. View at Google Scholar · View at Scopus
  30. C. L. Gardner, J. Glimm, O. McBryan, R. Menikoff, D. H. Sharp, and Q. Zhang, “The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces,” Physics of Fluids, vol. 31, no. 3, pp. 447–465, 1988. View at Publisher · View at Google Scholar
  31. J. Glimm, X. L. Li, R. Menikoff, D. H. Sharp, and Q. Zhang, “A numerical study of bubble interactions in Rayleigh-Taylor instability for compressible fluids,” Physics of Fluids A, vol. 2, no. 11, pp. 2046–2054, 1990. View at Google Scholar · View at Scopus
  32. X. L. Li, B. X. Jin, and J. Glimm, “Numerical study for the three-dimensional Rayleigh-Taylor: instability through the TVD/AC scheme and parallel computation,” Journal of Computational Physics, vol. 126, no. 2, pp. 343–355, 1996. View at Publisher · View at Google Scholar · View at Scopus
  33. Y. Chen, J. Glimm, D. H. Sharp, and Q. Zhang, “A two-phase flow model of the Rayleigh-Taylor mixina zone,” Physics of Fluids, vol. 8, no. 3, pp. 816–825, 1996. View at Google Scholar · View at Scopus
  34. Y. Chen, J. Glimm, D. Saltz, D. H. Sharp, and Q. Zhang, “A two-phase flow formulation for the Rayleigh-Taylor mixing zone and its renormalization group solution,” in Proceedings of the Fifth International Workshop on Compressible Turbulent Mixing, World Scientific, Singapore, 1996. View at Google Scholar
  35. A. W. Cook and P. E. Dimotakis, “Transition stages of Rayleigh-Taylor instability between miscible fluids,” Journal of Fluid Mechanics, vol. 443, pp. 69–99, 2001. View at Publisher · View at Google Scholar · View at Scopus
  36. A. W. Cook and Y. Zhou, “Energy transfer in Rayleigh-Taylor instability,” Physical Review E, vol. 66, no. 2, Article ID 026312, 12 pages, 2002. View at Publisher · View at Google Scholar · View at Scopus
  37. A. W. Cook, W. Cabot, and P. L. Miller, “The mixing transition in Rayleigh-Taylor instability,” Journal of Fluid Mechanics, vol. 511, pp. 333–362, 2004. View at Publisher · View at Google Scholar · View at Scopus
  38. S. V. Patankar, Nuemrical Heat Transfer and Fluid Flow, McGraw-Hill, New York, NY, USA, 1981.