Skip to main content
SpringerLink
Log in

Investigation of coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles. Five scenarios are considered, each with varying initial separations S/L (where L demotes the side length of the square) ranging from 0.125 to 1.0. Squares are filled with SF6 gas, and are enclosed by N2 gas. The simulations of shock-induced multi-species flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin solver. The simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two squares. When the separation is large, the squares experience a weaker coupling effect and evolve independently. While, as the separation reduces, the coupling effect manifests earlier in the interaction and becomes more substantial. As a result, this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis, leading to the emergence of multiple jets such as the twisted downward, upward, and coupled jets. A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity production. Notably, a significant quantity of vorticity is produced along the squares interface for smaller separation. Further, these coupling effects result in various interface features (upstream/downstream movement, and height/width evolution), and temporal variations of various spatially integrated fields. Finally, the analysis of the flow structure also considers the interaction between two more flow parameters, the Mach and Atwood numbers, in order to evaluate the coupling effects.

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

References

  1. R. D. Richtmyer, Comm. Pure Appl. Math. 13, 297 (1960).

    Article  MathSciNet  Google Scholar 

  2. E. E. Meshkov, Fluid Dyn 4, 101 (1969).

    Article  ADS  Google Scholar 

  3. M. Mohaghar, J. Carter, G. Pathikonda, and D. Ranjan, J. Fluid Mech. 871, 595 (2019).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  4. M. Groom, and B. Thornber, J. Fluid Mech. 908, A31 (2021), arXiv: 2304.13453.

    Article  ADS  CAS  Google Scholar 

  5. N. Peng, Y. Yang, J. Wu, and Z. Xiao, J. Fluid Mech. 911, A56 (2021).

    Article  ADS  CAS  Google Scholar 

  6. J. D. Lindl, R. L. McCrory, and E. M. Campbell, Phys. Today 45, 32 (1992).

    Article  CAS  Google Scholar 

  7. R. Betti, and O. A. Hurricane, Nat. Phys. 12, 435 (2016).

    Article  CAS  Google Scholar 

  8. J. Yang, T. Kubota, and E. E. Zukoski, AIAA J. 31, 854 (1993).

    Article  ADS  CAS  Google Scholar 

  9. W. D. Arnett, J. N. Bahcall, R. P. Kirshner, and S. E. Woosley, Annu. Rev. Astron. Astrophys. 27, 629 (1989).

    Article  ADS  CAS  Google Scholar 

  10. M. Brouillette, Annu. Rev. Fluid Mech. 34, 445 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  11. Y. Zhou, Phys. Rep. 720–722, 1 (2017).

    ADS  Google Scholar 

  12. Y. Zhou, Phys. Rep. 723–725, 1 (2017).

    ADS  Google Scholar 

  13. G. H. Markstein, Symposium (Int.) Combust. 6, 387 (1957).

    Article  Google Scholar 

  14. J. F. Haas, and B. Sturtevant, J. Fluid Mech. 181, 41 (1987).

    Article  ADS  Google Scholar 

  15. J. W. Jacobs, J. Fluid Mech. 234, 629 (1992).

    Article  ADS  CAS  Google Scholar 

  16. J. W. Jacobs, Phys. Fluids A-Fluid Dyn. 5, 2239 (1993).

    Article  ADS  CAS  Google Scholar 

  17. G. Layes, G. Jourdan, and L. Houas, Phys. Rev. Lett. 91, 174502 (2003).

    Article  ADS  PubMed  Google Scholar 

  18. G. Layes, G. Jourdan, and L. Houas, Phys. Fluids 17, 028103 (2005).

    Article  ADS  Google Scholar 

  19. D. Ranjan, J. H. J. Niederhaus, J. G. Oakley, M. H. Anderson, R. Bonazza, and J. A. Greenough, Phys. Fluids 20, 036101 (2008).

    Article  ADS  Google Scholar 

  20. Z. Zhai, T. Si, X. Luo, and J. Yang, Phys. Fluids 23, 084104 (2011).

    Article  ADS  Google Scholar 

  21. T. Si, Z. Zhai, and X. Luo, Laser Part. Beams 32, 343 (2014).

    Article  ADS  CAS  Google Scholar 

  22. X. Wang, D. Yang, J. Wu, and X. Luo, Phys. Fluids 27, 064104 (2015).

    Article  ADS  Google Scholar 

  23. J. Ding, Y. Liang, M. Chen, Z. Zhai, T. Si, and X. Luo, Phys. Fluids 30, 106109 (2018).

    Article  ADS  Google Scholar 

  24. J. J. Quirk, and S. Karni, J. Fluid Mech. 318, 129 (1996).

    Article  ADS  CAS  Google Scholar 

  25. J. Giordano, and Y. Burtschell, Phys. Fluids 18, 036102 (2006).

    Article  ADS  Google Scholar 

  26. A. Bagabir, and D. Drikakis, Shock Waves 11, 209 (2001).

    Article  ADS  Google Scholar 

  27. J. H. J. Niederhaus, J. A. Greenough, J. G. Oakley, D. Ranjan, M. H. Anderson, and R. Bonazza, J. Fluid Mech. 594, 85 (2008).

    Article  ADS  Google Scholar 

  28. Y. Zhu, Z. Yang, Z. Pan, P. Zhang, and J. Pan, Comput. Fluids 177, 78 (2018).

    Article  MathSciNet  CAS  Google Scholar 

  29. Z. Wang, B. Yu, H. Chen, B. Zhang, and H. Liu, Phys. Fluids 30, 126103 (2018).

    Article  ADS  Google Scholar 

  30. A. Kundu, and S. De, Comput. Fluids 193, 104289 (2019).

    Article  MathSciNet  CAS  Google Scholar 

  31. S. Singh, and M. Battiato, Phys. Rev. Fluids 6, 044001 (2021).

    Article  ADS  Google Scholar 

  32. S. Singh, M. Battiato, and R. S. Myong, Phys. Fluids 33, 066103 (2021).

    Article  ADS  CAS  Google Scholar 

  33. J. Ray, R. Samtaney, and N. J. Zabusky, Phys. Fluids 12, 707 (2000).

    Article  ADS  CAS  Google Scholar 

  34. J. S. Bai, L. Y. Zou, T. Wang, K. Liu, W. B. Huang, J. H. Liu, P. Li, D. W. Tan, and C. L. Liu, Phys. Rev. E 82, 056318 (2010).

    Article  ADS  Google Scholar 

  35. P. Y. Georgievskiy, V. A. Levin, and O. G. Sutyrin, Shock Waves 25, 357 (2015).

    Article  ADS  Google Scholar 

  36. L. Zou, S. Liao, C. Liu, Y. Wang, and Z. Zhai, Phys. Fluids 28, 036101 (2016).

    Article  ADS  Google Scholar 

  37. J. Chen, F. Qu, X. Wu, Z. Wang, and J. Bai, Phys. Fluids 33, 043301 (2021).

    Article  ADS  CAS  Google Scholar 

  38. K. R. Bates, N. Nikiforakis, and D. Holder, Phys. Fluids 19, 036101 (2007).

    Article  ADS  Google Scholar 

  39. Z. Zhai, M. Wang, T. Si, and X. Luo, J. Fluid Mech. 757, 800 (2014).

    Article  ADS  Google Scholar 

  40. X. Luo, M. Wang, T. Si, and Z. Zhai, J. Fluid Mech. 773, 366 (2015).

    Article  ADS  CAS  Google Scholar 

  41. D. Igra, and O. Igra, Phys. Fluids 30, 056104 (2018).

    Article  ADS  Google Scholar 

  42. D. Igra, and O. Igra, J. Fluid Mech. 889, 1 (2020).

    Article  MathSciNet  Google Scholar 

  43. S. Singh, Phys. Fluids 32, 126112 (2020).

    Article  ADS  CAS  Google Scholar 

  44. S. Singh, Phys. Rev. Fluids 6, 104001 (2021), arXiv: 2108.12558.

    Article  ADS  Google Scholar 

  45. S. Singh, and M. Battiato, Phys. D-Nonlinear Phenom. 453, 133844 (2023).

    Article  Google Scholar 

  46. S. Singh, Int. J. Heat Mass Transfer 179, 121708 (2021).

    Article  CAS  Google Scholar 

  47. S. Singh, and M. Battiato, Comput. Fluids 242, 105502 (2022).

    Article  CAS  Google Scholar 

  48. S. Singh, and M. Torrilhon, Phys. Fluids 35, 012117 (2023).

    Article  ADS  CAS  Google Scholar 

  49. S. Singh, Eur. J. Mech.-B Fluids 101, 131 (2023).

    Article  ADS  MathSciNet  Google Scholar 

  50. C. D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, Philos. Trans. R. Soc. London. Ser. A-Math. Phys. Eng. Sci. 357, 269 (1999).

    Article  ADS  CAS  Google Scholar 

  51. C. Tomkins, K. Prestridge, P. Rightley, P. Vorobieff, and R. Benjamin, J Vis 5, 273 (2002).

    Article  CAS  Google Scholar 

  52. C. Tomkins, K. Prestridge, P. Rightley, M. Marr-Lyon, P. Vorobieff, and R. Benjamin, Phys. Fluids 15, 986 (2003).

    Article  ADS  CAS  Google Scholar 

  53. S. Kumar, G. Orlicz, C. Tomkins, C. Goodenough, K. Prestridge, P. Vorobieff, and R. Benjamin, Phys. Fluids 17, 082107 (2005).

    Article  ADS  Google Scholar 

  54. S. Kumar, P. Vorobieff, G. Orlicz, A. Palekar, C. Tomkins, C. Good-enough, M. Marr-Lyon, K. P. Prestridge, and R. F. Benjamin, Phys. D-Nonlinear Phenom. 235, 21 (2007).

    Article  ADS  Google Scholar 

  55. L. Zou, W. Huang, C. Liu, J. Yu, and X. Luo, J. Fluids Eng. 136, 091205 (2014).

    Article  Google Scholar 

  56. Z. Zhai, J. Ou, and J. Ding, Phys. Fluids 31, 096104 (2019).

    Article  ADS  Google Scholar 

  57. S. Singh, Development of A 3D Discontinuous Galerkin Method for the Second-Order Boltzmann-Curtiss Based Hydrodynamic Models of Diatomic and Polyatomic Gases, Dissertation for the Doctoral Degree (Gyeongsang National University, Gyeongsang, 2018).

    Google Scholar 

  58. E. Johnsen, and T. Colonius, J. Comput. Phys. 219, 715 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  59. S. Gottlieb, and C. W. Shu, Math. Comp. 67, 73 (2006).

    Article  ADS  Google Scholar 

  60. S. Singh, A. Karchani, T. Chourushi, and R. S. Myong, J. Comput. Phys. 457, 111052 (2022).

    Article  Google Scholar 

  61. L. Krivodonova, J. Comput. Phys. 226, 879 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  62. A. Marquina, and P. Mulet, J. Comput. Phys. 185, 120 (2003).

    Article  ADS  MathSciNet  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied and Computational Mathematics, RWTH Aachen University, Aachen, 52056, Germany

    Satyvir Singh

  2. Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 244712, India

    Satyvir Singh

  3. Mathematics Department, University College in Darb, Jazan University, Abu As Sadad, 89653, Saudi Arabia

    Dhouha Taib Jalleli

Authors
  1. Satyvir Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dhouha Taib Jalleli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Satyvir Singh.

Additional information

Satyvir Singh acknowledges the funding through the German Research Foundation within the research unit DFG-FOR5409.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, S., Jalleli, D.T. Investigation of coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles. Sci. China Phys. Mech. Astron. 67, 214711 (2024). https://doi.org/10.1007/s11433-023-2218-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-023-2218-2

Search

Navigation