Skip to main content
SpringerLink
Log in

Lattice Boltzmann study of three-dimensional immiscible Rayleigh—Taylor instability in turbulent mixing stage

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

In this paper, we numerically studied the late-time evolutional mechanism of three-dimensional (3D) single-mode immiscible Rayleigh—Taylor instability (RTI) by using an improved lattice Boltzmann multiphase method implemented on graphics processing units. The influences of extensive dimensionless Reynolds numbers and Atwood numbers on phase interfacial dynamics, spike and bubble growth were investigated in details. The longtime numerical experiments indicate that the development of 3D singlemode RTI with a high Reynolds number can be summarized into four different stages: linear growth stage, saturated velocity growth stage, reacceleration stage and turbulent mixing stage. A series of complex interfacial structures with large topological changes can be observed at the turbulent mixing stage, which always preserve the symmetries with respect to the middle axis for a low Atwood number, and the lines of symmetry within spike and bubble are broken as the Atwood number is increased. Five statistical methods for computing the spike and bubble growth rates were then analyzed to reveal the growth law of 3D single-mode RTI in turbulent mixing stage. It is found that the spike late-time growth rate shows an overall increase with the Atwood number, while the bubble growth rate experiences a slight decrease with the Atwood number at first and then basically maintains a steady value of around 0.1. When the Reynolds number decreases, the later stages cannot be reached gradually and the evolution of phase interface presents a laminar flow state.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Burrows, Supernova explosions in the universe, Nature 403(6771), 727 (2000)

    Article  ADS  Google Scholar 

  2. M. Chertkov, Phenomenology of Rayleigh—Taylor turbulence, Phys. Rev. Lett. 91(11), 115001 (2003)

    Article  ADS  Google Scholar 

  3. R. Betti and O. A. Hurricane, Inertial-confinement fusion with lasers, Nat. Phys. 12(5), 435 (2016)

    Article  Google Scholar 

  4. L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. Lond. Math. Soc. 14, 170 (1883)

    MathSciNet  MATH  Google Scholar 

  5. G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their plane, Proc. R. Soc. Lond. A 201(1065), 192 (1950)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Y. Zhou, Richtmyer—Meshkov instability induced flow, turbulence, and mixing (I), Phys. Rep. 720–722, 1 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  7. Y. Zhou, Rayleigh—Taylor and Richtmyer—Meshkov instability induced flow, turbulence, and mixing (II), Phys. Rep. 723–725, 1 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  8. G. Boffetta and A. Mazzino, Incompressible Rayleigh—Taylor turbulence, Annu. Rev. Fluid Mech. 49(1), 119 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. D. Livescu, Turbulence with large thermal and compositional density variations, Annu. Rev. Fluid Mech. 52(1), 309 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. H. Liang, X. L. Hu, X. F. Huang, and J. R. Xu, Direct numerical simulations of multi-mode immiscible Rayleigh—Taylor instability with high Reynolds numbers, Phys. Fluids 31(11), 112104 (2019)

    Article  ADS  Google Scholar 

  11. H. S. Tavares, L. Biferale, M. Sbragaglia, and A. A. Mailybaev, Immiscible Rayleigh—Taylor turbulence using mesoscopic lattice Boltzmann algorithms, Phys. Rev. Fluids 6(5), 054606 (2021)

    Article  ADS  Google Scholar 

  12. P. Ramaprabhu, G. Dimonte, P. Woodward, C. Fryer, G. Rockefeller, K. Muthuraman, P. H. Lin, and J. Jayaraj, The late-time dynamics of the single-mode Rayleigh—Taylor instability, Phys. Fluids 24(7), 074107 (2012)

    Article  ADS  Google Scholar 

  13. T. Wei and D. Livescu, Late-time quadratic growth in single-mode Rayleigh—Taylor instability, Phys. Rev. E 86(4), 046405 (2012)

    Article  ADS  Google Scholar 

  14. D. J. Lewis, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes (II), Proc. R. Soc. Lond. A 202(1068), 81 (1950)

    Article  ADS  Google Scholar 

  15. R. Bellman and R. H. Pennington, Effects of surface tension and viscosity on Taylor instability, Q. Appl. Math. 12(2), 151 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  16. R. Menikoff, R. C. Mjolsness, D. H. Sharp, and C. Zemach, Unstable normal mode for Rayleigh—Taylor instability in viscous fluids, Phys. Fluids 20(12), 2000 (1977)

    Article  ADS  MATH  Google Scholar 

  17. D. Layzer, On the instability of superposed fluids in a gravitational field, Astrophys. J. 122, 1 (1955)

    Article  ADS  MathSciNet  Google Scholar 

  18. V. N. Goncharov, Analytical model of nonlinear, singlemode, classical Rayleigh—Taylor instability at arbitrary Atwood numbers, Phys. Rev. Lett. 88(13), 134502 (2002)

    Article  ADS  Google Scholar 

  19. S. I. Sohn, Effects of surface tension and viscosity on the growth rates of Rayleigh—Taylor and Richtmyer—Meshkov instabilities, Phys. Rev. E 80(5), 055302 (2009)

    Article  ADS  Google Scholar 

  20. R. Betti and J. Sanz, Bubble acceleration in the ablative Rayleigh—Taylor instability, Phys. Rev. Lett. 97(20), 205002 (2006)

    Article  ADS  Google Scholar 

  21. J. T. Waddell, C. E. Niederhaus, and J. W. Jacobs, Experimental study of Rayleigh—Taylor instability: Low Atwood number liquid systems with single-mode initial perturbations, Phys. Fluids 13(5), 1263 (2001)

    Article  ADS  MATH  Google Scholar 

  22. J. Glimm, X. L. Li, and A. D. Lin, Nonuniform approach to terminal velocity for single mode Rayleigh—Taylor instability, Acta Math. Appl. Sin. 18(1), 1 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. P. Ramaprabhu, G. Dimonte, Y. N. Young, A. C. Calder, and B. Fryxell, Limits of the potential flow approach to the single-mode Rayleigh—Taylor problem, Phys. Rev. E 74(6), 066308 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  24. J. P. Wilkinson, and J. W. Jacobs, Experimental study of the single-mode three-dimensional Rayleigh—Taylor instability, Phys. Fluids 19(12), 124102 (2007)

    Article  ADS  MATH  Google Scholar 

  25. X. Bian, H. Aluie, D. X. Zhao, H. S. Zhang, and D. Livescu, Revisiting the late-time growth of single-mode Rayleigh—Taylor instability and the role of vorticity, Physica D 403, 132250 (2020)

    Article  MathSciNet  Google Scholar 

  26. H. Liang, Z. H. Xia, and H. W. Huang, Late-time description of immiscible Rayleigh—Taylor instability: A lattice Boltzmann study, Phys. Fluids 33(8), 082103 (2021)

    Article  ADS  Google Scholar 

  27. X. L. Hu, H. Liang, and H. L. Wang, Lattice Boltzmann method simulations of the immiscible Rayleigh—Taylor instability with high Reynolds numbers, Wuli Xuebao 69(4), 044701 (2020)

    Google Scholar 

  28. H. Liang, Q. X. Li, B. C. Shi, and Z. H. Chai, Lattice Boltzmann simulation of three-dimensional Rayleigh—Taylor instability, Phys. Rev. E 93(3), 033113 (2016)

    Article  ADS  Google Scholar 

  29. Z. X. Hu, Y. S. Zhang, B. L. Tian, Z. W. He, and L. Li, Effect of viscosity on two-dimensional single-mode Rayleigh—Taylor instability during and after the reacceleration stage, Phys. Fluids 31(10), 104108 (2019)

    Article  ADS  Google Scholar 

  30. A. Xu, G. Zhang, Y. Gan, F. Chen, and X. Yu, Lattice Boltzmann modeling and simulation of compressible flows, Front. Phys. 7(5), 582 (2012)

    Article  ADS  Google Scholar 

  31. B. Yan, A. Xu, G. Zhang, Y. Ying, and H. Li, Lattice Boltzmann model for combustion and detonation, Front. Phys. 8(1), 94 (2013)

    Article  ADS  Google Scholar 

  32. F. Chen, A. Xu, and G. Zhang, Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh—Taylor instability, Front. Phys. 11(6), 114703 (2016)

    Article  ADS  Google Scholar 

  33. L. Chen, H. L. Lai, C. D. Lin, and D. M. Li, Specific heat ratio effects of compressible Rayleigh—Taylor instability studied by discrete Boltzmann method, Front. Phys. 16(5), 52500 (2021)

    Article  ADS  Google Scholar 

  34. F. Chen, A. Xu, Y. Zhang, Y. Gan, B. Liu, and S. Wang, Effects of the initial perturbations on the Rayleigh—Taylor—Kelvin—Helmholtz instability system, Front. Phys. 17(3), 33505 (2022)

    Article  ADS  Google Scholar 

  35. Z. L. Guo and C. Shu, Lattice Boltzmann Method and Its Applications in Engineering, World Scientific, Singapore, 2013

    Book  MATH  Google Scholar 

  36. H. Liu, Q. Kang, C. R. Leonardi, S. Schmieschek, A. Narvaez, B. D. Jones, J. R. Williams, A. J. Valocchi, and J. Harting, Multiphase lattice Boltzmann simulations for porous media applications, Computat. Geosci. 20(4), 777 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  37. H. Liang, B. C. Shi, and Z. H. Chai, Lattice Boltzmann modeling of three-phase incompressible flows, Phys. Rev. E 93(1), 013308 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  38. D. Jacqmin, Calculation of two-phase Navier—Stokes flows using phase-field modeling, J. Comput. Phys. 155(1), 96 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. H. Liang, B. C. Shi, Z. L. Guo, and Z. H. Chai, Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows, Phys. Rev. E 89(5), 053320 (2014)

    Article  ADS  Google Scholar 

  40. H. Liang, B. C. Shi, and Z. H. Chai, An efficient phase-field-based multiple-relaxation-time lattice Boltzmann model for three-dimensional multiphase flows, Comput. Math. Appl. 73(7), 1524 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  41. D. d’Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, and L. S. Luo, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philos. Trans.- Royal Soc., Math. Phys. Eng. Sci. 360(1792), 437 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. S. I. Abarzhi, A. Gorobets, and K. R. Sreenivasan, Rayleigh—Taylor turbulent mixing of immiscible, miscible and stratified fluids, Phys. Fluids 17(8), 081705 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. K. R. Sreenivasan, On the scaling of the turbulence energy dissipation rate, Phys. Fluids 27(5), 1048 (1984)

    Article  ADS  Google Scholar 

  44. J. R. Ristorcelli and T. T. Clark, Rayleigh—Taylor turbulence: Self-similar analysis and direct numerical simulations, J. Fluid Mech. 507, 213 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. A. W. Cook, W. Cabot, and P. L. Miller, The mixing transition in Rayleigh—Taylor instability, J. Fluid Mech. 511, 333 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. W. H. Cabot and A. W. Cook, Reynolds number effects on Rayleigh—Taylor instability with possible implications for type Ia supernovae, Nat. Phys. 2(8), 562 (2006)

    Article  Google Scholar 

  47. T. T. Clark, A numerical study of the statistics of a two-dimensional Rayleigh—Taylor mixing layer, Phys. Fluids 15(8), 2413 (2003)

    Article  ADS  MATH  Google Scholar 

  48. D. H. Olson and J. W. Jacobs, Experimental study of Rayleigh—Taylor instability with a complex initial perturbation, Phys. Fluids 21(3), 034103 (2009)

    Article  ADS  MATH  Google Scholar 

  49. B. Akula and D. Ranjan, Dynamics of buoyancy-driven flows at moderately high Atwood numbers, J. Fluid Mech. 795, 313 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 11972142 and 51976128).

Author information

Authors and Affiliations

  1. Department of Physics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Bin Liu & Hong Liang

  2. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Chunhua Zhang

  3. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Qin Lou

Authors
  1. Bin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunhua Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qin Lou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hong Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong Liang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, B., Zhang, C., Lou, Q. et al. Lattice Boltzmann study of three-dimensional immiscible Rayleigh—Taylor instability in turbulent mixing stage. Front. Phys. 17, 53506 (2022). https://doi.org/10.1007/s11467-022-1164-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-022-1164-3

Keywords

Search

Navigation