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Numerical Investigation on Evolution of Tip Vortices Generated by Low-Aspect Ratio Rectangular Wings at High Angle of Attack

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Abstract

The onset and evolution of tip vortices generated by the vertical tip of a straight half wing, with a NACA 0012 airfoil section, were studied at a Reynolds number of 1 × 105 by a steady-state calculation at high angles of attack, namely, 10°, 18°, and 42°, where the maximum lift, deep stall, and second peak of the lift coefficient occur, respectively, with three different aspect ratios: 2, 3, and 4. It was found that the counter-rotating vortex wrap initiated within the short wake period at higher angles than the deep stall and affected the contraction of the core trail, as well as resulting in the calculated swirl velocity component exhibiting a significant deviation from the conventional model fit. It was noted that the swirl strength of tip vortices increased continuously, even up to the deep stall phase, where the lift started to decrease immediately after the first peak. Wake contraction was found to follow an exponential decay in the earlier wake region. Compared to both the infinite wing and the elliptical wing, the finite square wing seems to have an offset in the lift coefficient, which could represent the tip loss.

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References

  1. Critzos CC, Heyson HH, Boswinkle RW Jr (1955) Aerodynamic characteristics of NACA0012 airfoil section at angle of attack from 0 to 180 degrees. NACA TN3361

  2. Sheldahl RE, Klimas PC (1981) Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis aerodynamic analysis of vertical axis wind turbines, SAND-80-2114. Sandia National Laboratories Energy Report. https://doi.org/10.2172/6548367

  3. Spera DA (2008) Models of lift and drag coefficients of stalled and unstalled airfoils in wind turbines and wind tunnels, NASA/CR-2008-215434

  4. Lind AH, Lefebvre JN, Jones AR (2014) Time-averaged aerodynamics of sharp and blunt trailing-edge static airfoils in reverse flow. AIAA 52(12):2751–2764. https://doi.org/10.2514/1.j052967

    Article  Google Scholar 

  5. Park BH, Han YO (2018) Steady aerodynamic and flow behaviors of two-dimensional NACA0012 airfoil in one revolution angle of attack. IJASS 19(1):pp. https://doi.org/10.1007/s42405-018-0010-x

    Article  Google Scholar 

  6. Prandtl L (1921) Applications of modern hydrodynamics to aeronautics, NACA Report No. 116

  7. Corsiglia VR, Schwind RG, Chigier NA (1973) Rapid scanning, three-dimensional hot-wire anemometer surveys of wing-tip vortices. J Aircr 10(12):752–757. https://doi.org/10.2514/6.1973-681

    Article  Google Scholar 

  8. Dacles-Mariani J, Zilliac GG, Chow JS, Bradshaw P (1995) Numerical/experimental study of a wingtip vortex in the near field. AIAA J 33(9):1561–1568. https://doi.org/10.2514/3.12826

    Article  Google Scholar 

  9. Ghias R, Mittal R, Dong H, Lund T (2005) Study of tip-vortex formation using large-eddy simulation, In: 43rd AIAA aerospace sciences meeting and exhibit, p 1280. https://doi.org/10.2514/6.2005-1280

  10. Spalart PR, Allmaras SR (1992) A one-equation turbulence model for aerodynamic flows. In: 30th aerospace sciences meeting and exhibit, p 439. https://doi.org/10.2514/6.1992-439

  11. ANSYS Fluent Theory Guide (2013) release15.0, ANSYS Inc

  12. Ahsan M (2014) Numerical analysis of friction factor for a fully developed turbulent flow using k–ε turbulence model with enhanced wall treatment. Beni-Suef Univ J Basic Appl Sci 3(4):269–277. https://doi.org/10.1016/j.bjbas.2014.12.001

    Article  Google Scholar 

  13. Polhamus EC (1969) A concept of the vortex lift of the vortex lift of sharp edge delta wings based on a leading edge suction analogy, NASA Technical note, NASA-TN-D-3767

  14. Hsiao CT, Pauley LL (1998) Numerical study of the steady-state tip vortex flow over a finite-span hydrofoil. J Fluids Eng 120:345–353. https://doi.org/10.1115/1.2820654

    Article  Google Scholar 

  15. Spentzos A, Barakos GN, Badcock KJ, Richards BE, Wernert P, Schreck S, Raffel M (2005) Investigation of three-dimensional dynamic stall using computational fluid dynamics. AIAA J 43(5):1023–1033. https://doi.org/10.2514/1.8830

    Article  Google Scholar 

  16. Tairo K, Colonius T (2009) Three-dimensional flows around low-aspect ratio flat plate wings at low Reynolds numbers. JFM 623:187–207. https://doi.org/10.1017/s0022112008005314

    Article  MATH  Google Scholar 

  17. Anande GK, Sukumar PP, Selig MS (2015) Measured aerodynamic characteristics of wings at low Reynolds numbers. Aerosp Sci Technol 42:392–406. https://doi.org/10.1016/j.ast.2014.11.016

    Article  Google Scholar 

  18. Gerz T, Holzäpfel F, Darracq D (2002) Commercial aircraft wake vortices. Prog Aerosp Sci 38(3):181–208. https://doi.org/10.1016/s0376-0421(02)00004-0

    Article  Google Scholar 

  19. Han YO, Leishman G (2004) Investigation of helicopter rotor blade tip vortex alleviation using a slotted tip. AIAA J 42(3):524–535. https://doi.org/10.2514/1.3254

    Article  Google Scholar 

  20. You JY, Kwon OJ, Han YO (2009) Viscous flow simulation of rotor blades with tip slots in hover. J Am Helicopter Soc 54(1):012006–1–012006-9. https://doi.org/10.4050/jahs.54.012006

    Article  Google Scholar 

  21. Lamb H (1932) Hydrodynamics. Cambridge University Press, New York, pp 592–593, 668–669

  22. Vatistas GH, Kozel V, Mih WC (1991) Simpler model for concentrated vortices. Exp Fluids 24(11):73–76. https://doi.org/10.1007/bf00198434

    Article  Google Scholar 

  23. Milne-Thompson LM (1968) Theoretical hydrodynamics, 5th edn. Macmillan & Co., Ltd., London, p 355

    Book  Google Scholar 

  24. Vatistas GH (2006) Simple model for turbulent tip vortices. J Aircr 43(5):1577–1579. https://doi.org/10.2514/1.22477

    Article  Google Scholar 

  25. Devenport WJ, Rife MC, Liapis SI, Follin GJ (1996) The structure and development of a wing tip vortex. J Fluid Mech 312:67–106. https://doi.org/10.1017/s0022112096001929

    Article  MathSciNet  Google Scholar 

  26. Birch D, Lee T, Mokhtarian F, Kafyeke F (1992) Rollup and near-field behavior of a tip vortex. J Aircr 40(3):603–607. https://doi.org/10.2514/2.3137

    Article  Google Scholar 

  27. Bailey SCC, Tavoularis S, Lee BHK (2006) Effects of free-stream turbulence on wing-tip vortex formation and near field. J Aircr 43(5):1282–1291. https://doi.org/10.2514/1.19433

    Article  Google Scholar 

  28. Chang JW, Park SO (2000) Measurements in the tip vortex roll-up region of an oscillating wing. AIAA J 38(6):1092–1095. https://doi.org/10.2514/2.1072

    Article  Google Scholar 

  29. Tung C, Pucci SL, Caradonna FX, Morse HA (1981) The structure of trailing vortices generated by model rotor blades, NASA Technical Memorandum

  30. Han YO, Leishman G, Coyne AJ (1997) Measurements of the velocity and turbulence structure of a rotor tip vortex. AIAA J 35(3):477–485. https://doi.org/10.2514/3.13529

    Article  Google Scholar 

  31. Landgrebe AJ (1972) The wake geometry of a hovering helicopter rotor and its influence on rotor performance. J Helicopter Soc 17(4):2–15. https://doi.org/10.4050/jahs.17.3

    Google Scholar 

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Acknowledgements

This work was supported by the 2014 year Yeungnam University Research Grant.

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Correspondence to Yong Oun Han.

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Lee, J.H., Han, Y.O. Numerical Investigation on Evolution of Tip Vortices Generated by Low-Aspect Ratio Rectangular Wings at High Angle of Attack. Int. J. Aeronaut. Space Sci. 20, 44–56 (2019). https://doi.org/10.1007/s42405-018-0101-8

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