Simulation and visualization of formation of vortex ring, its propagation and transportation of passive scalar

Authors

DOI:

https://doi.org/10.26089/NumMet.v22r311

Keywords:

computational fluid dynamics, vortex dynamics, vortex ring, vorticity, finite Lyapunov exponent method

Abstract

Numerical simulation of gas-dynamic processes accompanying the formation and propagation of vortex rings obtained using a piston generator is considered. The influence of the characteristics of the vortex ring on the transfer of the passive particles is discussed. Unsteady Navier--Stokes equations are used for numerical calculations, and finite volume method is applied to their discretization. The results of numerical simulation make it possible to obtain the geometric and dynamic characteristics of the vortex ring, which correspond to the self-similar theory of the vortex ring and experimental data. In addition to traditional approaches to visualization of vortex flows based on the construction of contours of various flow quantities, invariants of the velocity gradient tensor and the method of Lyapunov exponents over a finite time interval are used to visualize vortex structures.

Author Biographies

K.N. Volkov

D.F. Ustinov Baltic State Technical University «Voenmekh»,
Faculty of Rocket and Space Engineering
• Leading Researcher

V.N. Emelyanov

I.E. Kapranov

AO TsKB Rubin
• PhD., Scientist

References

  1. M. A. Lavrent’ev and B. V. Shabat, Hydrodynamics Problems and Their Mathematical Models (Nauka, Moscow, 1973) [in Russian].
  2. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Univ. Press, Cambridge, 2012; Mir, Moscow, 1973).
  3. A. H. M. Eisenga, Dynamics of a Vortex Ring in a Rotating Fluid (Technische Universiteit Eindhoven, Eindhoven, 1997).
  4. P. G. Saffman, Vortex Dynamics (Cambridge Univ. Press, Cambridge, 1992; Nauch. Mir, Moscow, 2000).
  5. Y. Xiang, S. Qin, and H. Liu, “Patterns for Efficient Propulsion during the Energy Evolution of Vortex Rings,” Eur. J. Mech. B Fluids 71, 47-58 (2018).
  6. L. Qin, Y. Xiang, H. Lin, and H. Liu, “Formation and Dynamics of Compressible Vortex Rings Generated by a Shock Tube,” Exp. Fluids 61 (2020). doi 10.1007/s00348-020-2920-1.
  7. K. Shariff and A. Leonard, “Vortex Rings,” Annu. Rev. Fluid Mech. 24, 235-279 (1992).
  8. V. V. Meleshko, A. A. Gourjii, and T. S. Krasnopolskaya, “Vortex Rings: History and State of the Art,” J. Math. Sci. 187 (6), 772-808 (2012).
  9. P. McGavin and D. I. Pontin, “Vortex Line Topology during Vortex Tube Reconnection,” Phys. Rev. Fluids 3 (2018). doi 10.1103/PhysRevFluids.3.054701.
  10. D. G. Akhmetov and O. P. Kisarov, “Hydrodynamic Structure of a Vortex Ring,” Zh. Prikl. Mekh. Tekh. Fiz. 7 (4), 120-124 (1966) [J. Appl. Mech. Tech. Phys. 7 (4), 87-90 (1966)].
  11. J. P. Sullivan, S. E. Widnall, and S. Ezekiel, “Study of Vortex Rings Using a Laser Doppler Velocimeter,” AIAA J. 11 (10), 1384-1389 (1973).
  12. D. G. Akhmetov, “Formation and Basic Parameters of Vortex Rings,” Zh. Prikl. Mekh. Tekh. Fiz. 42 (5), 70-83 (2001) [J. Appl. Mech. Tech. Phys. 42 (5), 794-805 (2001)].
  13. D. G. Akhmetov, “Model of Vortex Ring Formation,” Zh. Prikl. Mekh. Tekh. Fiz. 49 (6), 25-36 (2008) [J. Appl. Mech. Tech. Phys. 49 (6), 909-918 (2008)].
  14. A. Weigand and M. Gharib, “On the Evolution of Laminar Vortex Rings,” Exp. Fluids 22 (1997). doi 10.1007/s003480050071.
  15. Z. Sun, B. Pointz, and C. Bruecker, “Transition of a Vortex Ring Visualized by 3D Scanning TomoPIV,” in Proc. 18th Int. Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, Lisbon, Portugal, July 4-7, 2016 ,
    https://openaccess.city.ac.uk/id/eprint/15664/
  16. T. Maxworthy, “Some Experimental Studies of Vortex Rings,” J. Fluid Mech. 81 (3), 465-495 (1977).
  17. V. F. Kop’ev and S. A. Chernyshev, “Vortex Ring Oscillations, the Development of Turbulence in Vortex Rings and Generation of Sound,” Usp. Fiz. Nauk 170 (7), 713-742 (2000) [Phys. Usp. 43 (7), 663-690 (2000)].
  18. K. Shariff, A. Leonard, and J. H. Ferziger, “Dynamical Systems Analysis of Fluid Transport in Time-Periodic Vortex Ring Flows,” Phys. Fluids 18 (2006). doi 10.1063/1.2189867.
  19. M. Cheng, J. Lou, and T. T. Lim, “Evolution of an Elliptic Vortex Ring in a Viscous Fluid,” Phys. Fluids 28 (2016). doi 10.1063/1.4944059.
  20. M. Bergdorf, P. Koumoutsakos, and A. Leonard, “Direct Numerical Simulations of Vortex Rings at {rm Re}_{Gamma}=7500,” J. Fluid Mech. 581, 495-505 (2007).
  21. P. J. Archer, T. G. Thomas, and G. N. Coleman, “Direct Numerical Simulation of Vortex Ring Evolution from the Laminar to the Early Turbulent Regime,” J. Fluid Mech. 598, 201-226 (2008).
  22. J. R. Mansfield, O. M. Knio, and C. Meneveau, “Dynamic LES of Colliding Vortex Rings Using a 3D Vortex Method,” J. Comput. Phys. 152 (1), 305-345 (1999).
  23. K. Lindsay and R. Krasny, “A Particle Method and Adaptive Treecode for Vortex Sheet Motion in Three-Dimensional Flow,” J. Comput. Phys. 172 (2), 879-907 (2001).
  24. K. Kontis, R. An, and J. A. Edwards, “Compressible Vortex-Ring Interaction Studies with a Number of Generic Body Configurations,” AIAA J. 44 (12), 2962-2978 (2006).
  25. H. Zare-Behtash, K. Kontis, N. Gongora-Orozco, and K. Takayama, “Compressible Vortex Loops: Effect of Nozzle Geometry,” Int. J. Heat Fluid Fl. 30 (3), 561-576 (2009).
  26. V. V. Nikulin and M. S. Kotel’nikova, “Numerical Investigation of an Interaction between a Surface and a Vortex Ring Moving Normally to It,” Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 15 (4), 79-84 (2015).
  27. A. I. Stroutchayev, “Carry of a Passive Impurity by a Vortex Ring at Interaction with an Obstacle,” in Physics of Aerodisperse Systems (Odessa Univ., Odessa, 2002), Issue 39, pp. 195-205.
  28. V. V. Selivanov and D. P. Levin, “Possibilities of Using Acoustic Means of Non-Lethal Action in Law Enforcement Operations,” Vestn. Bauman Mosk. Gos. Tekh. Univ., Ser. Mech. Eng. No. 2, 102-114 (2009).
  29. V. V. Selivanov and D. P. Levin, Non-Lethal Weapon (Bauman Gos. Tekh. Univ., Moscow, 2017) [in Russian].
  30. K. Volkov, “Multigrid and Preconditioning Techniques in CFD Applications,” in CFD Techniques and Thermo-Mechanics Applications (Springer, Cham, 2018), pp. 83-149.
  31. K. N. Volkov, V. N. Emelyanov, I. V. Teterina, and M. S. Yakovchuk, “Methods and Concepts of Vortex Flow Visualization in the Problems of Computational Fluid Dynamics,” Vychisl. Metody Programm. 17 (1), 81-100 (2016).
  32. M. A. Green, C. W. Rowley, and G. Haller, “Detection of Lagrangian Coherent Structures in Three-Dimensional Turbulence,” J. Fluid Mech. 572, 111-120 (2007).

Published

14-09-2021

How to Cite

Волков К.Н., Емельянов В.Н., Капранов И.Е. Simulation and Visualization of Formation of Vortex Ring, Its Propagation and Transportation of Passive Scalar // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2021. 22. 182-199. doi 10.26089/NumMet.v22r311

Issue

Section

Methods and algorithms of computational mathematics and their applications

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