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Research on the Mechanism of Resistance Generation in Disc Acceleration Based on Lagrangian Method

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Proceedings of the International Conference on Aerospace System Science and Engineering 2020 (ICASSE 2020)

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Abstract

During flapping wing flight or fish swimming, a large-scale vortex structure is in general generated by each stroke motion of the wing or the trail, and contributes most of the lift and thrust. As a fundamental model to characterize the wake structures of flapping flight and fish swimming, the disc vortex ring (DVR) generated by the impulsive motion of a disc contains numerous unsteady aerodynamic mechanisms. In this paper, an experimental set-up was designed to produce DVRs with different acceleration, particle image velocimetry (PIV) technique was used to measure the growth and evolution process of wake vortices, and force sensor was used to measure the instantaneous change in drag directly. PIV results show that a DVR is formed in the wake during the disc starting, and the circulation growth of DVR satisfies the Logistic growth model. Using the Lagrangian coherent structure (LCS) to analyze the formation of DVR shows that, under the interaction of the add-mass effects of disc and DVR, the vortex flow shows a significant Lagrangian drift, which contributes a significant increase of the drag. Besides, the results of the drag measurement show that the formation process of the vortex ring consists of three phases, including a peak and a valley. Based on the vorticity-moment theorem, the evolution of drag is explained in terms of the dynamics of DVR and the added-mass effects. Moreover, the findings of this paper provide a new Lagrangian perspective for understanding the mechanism of lift and thrust during flapping wing flight and fish swimming.

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References

  1. Afanasyev YD (2006) Formation of vortex dipoles. Phys Fluids 18:037103

    Article  MathSciNet  Google Scholar 

  2. Akhmetov DG (2009) Vortex rings. Springer

    Google Scholar 

  3. Altshuler DL, Pan MPH, Lozano J (2009) Wake patterns of the wings and tail of hovering hummingbirds. Exp Fluids 46:835–846

    Google Scholar 

  4. Baik YS, Bernal LP, Granlund K, Ol MV (2012) Unsteady force generation an vortex dynamics of pitching and plunging aerofoils. J Fluid Mech 709:37–68

    Google Scholar 

  5. Benjamin T (1976) The alliance of practical and analytical insights into the non-linear problems of fluid mechanics. In: Applications of methods of functional analysis to problems in mechanics, vol 503, pp 8–28

    Google Scholar 

  6. Costello JH, Colin SP, Dabiri JO (2008) Medusan morphospace: phylogenetic constraints, biomechanical solutions, and ecological consequences. Invertebr Biol 127:265–290

    Article  Google Scholar 

  7. Dabiri JO (2006) Note on the induced Lagrangian drift and added-mass of a vortex. J Fluid Mech 547:105–113

    Article  MathSciNet  Google Scholar 

  8. Dabiri JO (2009) Optimal vortex formation as a unifying principle in biological propulsion. Annu Rev Fluid Mech 41:17–33

    Article  MathSciNet  Google Scholar 

  9. Dabiri JO (2010) A wake-based correlate of swimming performance and foraging behaviour in seven co-occurring jellyfish species. J Exp Biol 213:1217–1225

    Article  Google Scholar 

  10. Dabiri JO, Colin SP, Costello JH, Gharib M (2005) Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses. J Exp Biol 208:1257–1265

    Article  Google Scholar 

  11. Dabiri JO, Gharib M (2005) Starting flow through nozzle with temporally variable exit diameter. J Fluid Mech 538:111–136

    Article  Google Scholar 

  12. David MJ, Mathur M, Govardhan RN, Arakeri JH (2018) The kinematic genesis of vortex formation due to finite rotation of a plate in still fluid. J Fluid Mech 839:489–524

    Article  Google Scholar 

  13. Dickinson MH (1996) Unsteady mechanism of force generation in aquatic and aerial locomotion. Am Zool 36:537–554

    Article  Google Scholar 

  14. Didden N (1979) On the formation of vortex rings: rolling-up and production of circulation. J Appl Mech Phys 530:101–116

    Google Scholar 

  15. Fernando JN, Rival DE (2016a) On vortex evolution in the wake of axisymmetric and non-axisymmetric low-aspect-ratio accelerating plates. Phys Fluids 28:017102

    Google Scholar 

  16. Fernando JN, Rival DE (2016b) Reynolds-number scaling of vortex pinch-off on low aspect-ratio propulsors. J Fluid Mech 799R3:1–12

    Google Scholar 

  17. Gao L, Yu SCM (2010) A model for the pinch-off process of the leading vortex ring in a starting jet. J Fluid Mech 656:205–222

    Article  Google Scholar 

  18. Gao L, Yu SCM (2012) Development of the trailing shear layer in a starting jet during pinch-off. J Fluid Mech 700:382–405

    Article  Google Scholar 

  19. Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140

    Article  MathSciNet  Google Scholar 

  20. Haller G, Beron-Vera FJ (2013) Coherent Lagrangian vortices: the black holes of turbulence. J Fluid Mech 731(R4):1–4

    MathSciNet  MATH  Google Scholar 

  21. Jeon D, Gharib M (2004) On the relationship between the vortex formation process an cylinder wake vortex patterns. J Fluid Mech 519:161–181

    Article  Google Scholar 

  22. Kelvin L (1880) Vortex statics. Phil Mag 10:97–109

    Article  Google Scholar 

  23. Krueger PS (2005) An over-pressure correction to the slug model for vortex ring circulation. J Fluid Mech 545:427–443

    Article  Google Scholar 

  24. Krueger PS, Gharib M (2003) The significance of vortex ring formation to the impulse and thrust of a starting jet. Phys Fluids 15:1271–1281

    Article  MathSciNet  Google Scholar 

  25. Lawson JM, Dawson JR (2013) The formation of turbulent vortex rings by synthetic jets. Phys Fluids 25:105113

    Article  Google Scholar 

  26. Linden PF, Turner JS (2001) The formation of ‘optimal’ vortex rings, and the efficiency of propulsion device. J Fluid Mech 427:61–72

    Article  Google Scholar 

  27. McPhaden CJ, Rival DE (2018) Unsteady force estimation using a Lagrangian drift-volume approach. Exp Fluids 59:64

    Article  Google Scholar 

  28. Milano M, Gharib M (2005) Uncovering the physics of flat plates with artificial evolution. J Fluid Mech 534:403–409

    Article  Google Scholar 

  29. Muijres FT, Johansson LC, Barfield R, Wolf M, Spedding GR, Heenstrom A (2008) Leading-edge vortex improves lift in slow-flying bats. Science 319:1250–1253

    Article  Google Scholar 

  30. Onu K, Huhn F, Haller G (2015) LCS tool: a computational platform for Lagrangian coherent structures. Chaos 7:26–36

    Google Scholar 

  31. O’Farrell C, Dabiri JO (2010) A Lagrangian approach to identifying vortex pinch-off. Chaos 20:017513–017521

    Article  Google Scholar 

  32. Pedrizzetti G (2010) Vortex formation out of two-dimensional orifices. J Fluid Mech 665:198–216

    Article  MathSciNet  Google Scholar 

  33. Peng JF, Dabiri JO (2008) An overview of a Lagrangian method for analysis of animal wake dynamics. J Exp Biol 211:280–287

    Article  Google Scholar 

  34. Qin SY, Liu H, Xiang Y (2018) On the formation modes in vortex interaction for multiple co-axial co-rotating vortex rings. Phys Fluids 30:011901

    Article  Google Scholar 

  35. Rayner JMV (1979) A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal. J Fluid Mech 91:697–730

    Article  Google Scholar 

  36. Rival D, Prangemeier T, Tropea C (2009) The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight. Exp Fluid 46:823–833

    Article  Google Scholar 

  37. Saffman PG (1992) Vortex dynamics. Cambridge University Press

    Google Scholar 

  38. Sallet DW (1975) Impulsive motion of a circular disk which causes a vortex ring. Phys Fluids 18:109–111

    Article  Google Scholar 

  39. Shariff K (1992) Vortex rings. Annu Rev Fluid Mech 24:235–279

    Article  MathSciNet  Google Scholar 

  40. Shenoy AR, Kleinstreuer C (2008) Flow over a thin circular disk at low to moderate Reynolds numbers. J Fluid Mech 605:253–262

    Article  Google Scholar 

  41. Shusser M, Gharib M (2000) Energy and velocity of a forming vortex ring. Phys Fluids 12:618–712

    Article  MathSciNet  Google Scholar 

  42. Shusser M, Rosenfeld M, Dabiri JO, Gharib M (2006) Effect of time-dependent piston velocity program on vortex ring formation in a piston/cylinder arrangement. Phys Fluids 18:033601–033611

    Article  Google Scholar 

  43. Taylor GI (1953) Formation of a vortex ring by giving an impulse to a circular disc and then dissolving it away. J Appl Phys 24:104–105

    Article  MathSciNet  Google Scholar 

  44. Wang XX, Wu ZN (2010) Stroke-averaged lift forces due to vortex rings and their mutual interactions for a flapping flight model. J Fluid Mech 654:453–472

    Article  MathSciNet  Google Scholar 

  45. Wang XX, Wu ZN (2012) Lift force reduction due to body image of vortex for a hovering flight model. J Fluid Mech 709:648–658

    Article  MathSciNet  Google Scholar 

  46. Wu JC (1981) Theory for aerodynamic force and moment in viscous flows. AIAA J 19:432–441

    Article  Google Scholar 

  47. Xiang Y, Lin HY, Zhang B, Liu H (2018a) Quantitative analysis of vortex added-mass and impulse generation during vortex ring formation based on elliptic Lagrangian coherent structures. Exp Therm Fluid Sci 94:295–303

    Google Scholar 

  48. Xiang Y, Qin SY, Liu H (2018b) Patterns for efficient propulsion during the energy evolution of vortex rings. Eur J Mech B Fluids 71:47–58

    Google Scholar 

  49. Yang AL, Jia LB, Yin XZ (2012) Formation process of the vortex ring generated by an impulsively starting circular disc. J Fluid Mech 713:65–85

    Article  Google Scholar 

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Acknowledgements

Financial support from the State Key Development Program of Basic Research of China (2014CB744802) is gratefully acknowledged. Besides, this work was also supported by NSFC Project (91441205).

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Correspondence to Fuxin Wang .

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Lin, S., Wang, F., Li, Z., Xiang, Y. (2021). Research on the Mechanism of Resistance Generation in Disc Acceleration Based on Lagrangian Method. In: Jing, Z., Zhan, X. (eds) Proceedings of the International Conference on Aerospace System Science and Engineering 2020. ICASSE 2020. Lecture Notes in Electrical Engineering, vol 680. Springer, Singapore. https://doi.org/10.1007/978-981-33-6060-0_11

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  • DOI: https://doi.org/10.1007/978-981-33-6060-0_11

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