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No AccessRegular Articles

Lift Equivalence and Cancellation for Airfoil Surge–Pitch–Plunge Oscillations

Published Online:24 Sep 2020https://doi.org/10.2514/1.J059068

Abstract

A NACA 0018 airfoil in freestream velocity is oscillated in longitudinal, transverse, and angle-of-attack directions with respect to the freestream velocity, known as surge, plunge, and pitch. The lift-based equivalence method introduces phase shifts between these three motions to construct in-phase sinusoidal components for maximum lift, waveform construction. Lift cancellation is also determined with the exact negative pitch and plunge motion amplitudes found from the equivalence method to achieve out-of-phase wave destruction. Lift cancellation occurs when a combination of these motions is sought to obtain a constant lift magnitude throughout the oscillation cycle. To achieve both equivalence and cancellation of lift, a prescribed pure pitch amplitude through the Theodorsen theory equates the corresponding equivalent plunge amplitude and pitch–plunge phase shift. These Theodorsen, linear superposition findings of pitch–plunge are leveraged toward the Greenberg theory to determine a closed-form, surge–pitch–plunge solution through the addition of a surge–plunge phase shift and optimal surge amplitude for lift cancellation. The lift cancellation surge–pitch–plunge amplitudes define the equivalence amplitude investigated here and theoretically limit the experiment to combinations of the first lift harmonic of the Greenberg theory. The analytical results are then compared with experimental lift force measurements and dye visualization. The normalized lift differences due to unsteady wake and boundary-layer behavior are examined to explore the extents of the Greenberg theory for these cases of lift-based equivalence and cancellation.

References

  • [1] Maresca C., Favier D. and Rebont J., “Experiments on an Aerofoil at High Angle of Incidence in Longitudinal Oscillations,” Journal of Fluid Mechanics, Vol. 92, No. 4, 1979, pp. 671–690. https://doi.org/10.1017/S0022112079000823 Google Scholar

  • [2] Granlund K., Monnier B., Ol M. V. and Williams D., “Airfoil Longitudinal Gust Response in Separated vs. Attached Flows,” Physics of Fluids, Vol. 26, No. 2, 2014, Paper 027103. https://doi.org/10.1063/1.4864338 CrossrefGoogle Scholar

  • [3] Greenblatt D., Mueller-Vahl H., Strangfeld C., Medina A., Ol M. V. and Granlund K. O., “High Advance-Ratio Airfoil Streamwise Oscillations: Wind Tunnel vs. Water Tunnel,” AIAA Paper 2016-1356, 2016. https://doi.org/10.2514/1.J056408 Google Scholar

  • [4] McGowan G. Z., Granlund K., Ol M. V., Gopalarathnam A. and Edwards J. R., “Investigations of Lift-Based Pitch–Plunge Equivalence for Airfoils at Low Reynolds Numbers,” AIAA Journal, Vol. 49, No. 7, 2011, pp. 1511–1524. https://doi.org/10.2514/1.J050924 LinkGoogle Scholar

  • [5] Baik Y. S., Bernal L. P., Granlund K. and Ol M. V., “Unsteady Force Generation and Vortex Dynamics of Pitching and Plunging Airfoils,” Journal of Fluid Mechanics, Vol. 709, Oct. 2012, pp. 37–68. https://doi.org/10.1017/jfm.2012.318 CrossrefGoogle Scholar

  • [6] Ol M., “Vortical Structures in High Frequency Pitch and Plunge at Low Reynolds Number,” 37th AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2007-4233, June 2007. LinkGoogle Scholar

  • [7] Rival D. and Tropea C., “Characteristics of Pitching and Plunging Airfoils Under Dynamic-Stall Conditions,” Journal of Aircraft, Vol. 47, No. 1, 2010, pp. 80–86. https://doi.org/10.2514/1.42528 LinkGoogle Scholar

  • [8] Sunada S., Kawachi K., Matsumoto A. and Sakaguchi A., “Unsteady Forces on a Two-Dimensional Wing in Plunging and Pitching Motions,” AIAA Journal, Vol. 39, No. 7, 2001, pp. 1230–1239. https://doi.org/10.2514/2.1458 LinkGoogle Scholar

  • [9] Strangfeld C., Rumsey C., Müller-Vahl H., Greenblatt D., Nayeri C. and Paschereit C., “Unsteady Thick Airfoil Aerodynamics: Experiments, Computation, and Theory,” 45th AIAA Fluid Dynamics Conference, AIAA Aviation Forum, AIAA Paper 2015-3071, 2015. https://doi.org/10.2514/1.J056408 LinkGoogle Scholar

  • [10] Favier D., Agnes A., Barbi C. and Maresca C., “Combined Translation/Pitch Motion: A New Airfoil Dynamic Stall Simulation,” Journal of Aircraft, Vol. 25, No. 9, 1988, pp. 805–814. https://doi.org/10.2514/3.45663 LinkGoogle Scholar

  • [11] Dunne R., Schmid P. J. and McKeon B. J., “Analysis of Flow Timescales on a Periodically Pitching/Surging Airfoil,” AIAA Journal, Vol. 54, No. 11, 2016, pp. 3421–3433. https://doi.org/10.2514/1.J054784 LinkGoogle Scholar

  • [12] Choi J., Colonius T. and Williams D., “Surging and Plunging Oscillations of an Airfoil at Low Reynolds Number,” Journal Fluid Mechanics, Vol. 763, Jan. 2015, pp. 237–253. https://doi.org/10.1017/jfm.2014.674 CrossrefGoogle Scholar

  • [13] Leung J. M., Wong J. G., Weymouth G. D. and Rival D. E., “Modeling Transverse Gusts Using Pitching, Plunging, and Surging Airfoil Motions,” AIAA Journal, Vol. 56, No. 8, 2018, pp. 3271–3278. https://doi.org/10.2514/1.J056961 LinkGoogle Scholar

  • [14] Greenberg J. M., “Airfoil in Sinusoidal Motion in a Pulsating Stream,” NACA TN 1326, 1947. Google Scholar

  • [15] Theodorsen T., “General Theory of Aerodynamic Instability and the Mechanism of Flutter,” NACA TR 496, 1935. Google Scholar

  • [16] Wagner H., “Uber die Entstehung des dynamischen Auftriebs von Tragflugeln,” Zeitschrift fur angewandte Mathematik and Mechanik, Bd. 5, Heft 1, Feb. 1925, pp. 17–35. Google Scholar

  • [17] Isaacs R., “Airfoil Theory for Flows of Variable Velocity,” Journal of the Aeronautical Sciences, Vol. 12, No. 1, 1945, pp. 113–117. https://doi.org/10.2514/8.11202 LinkGoogle Scholar

  • [18] Van der Wall B. G. and Leishman J. G., “On the Influence of Time-Varying Flow Velocity on Unsteady Aerodynamics,” Journal of the American Helicopter Society, Vol. 39, No. 4, Oct. 1994, pp. 25–36. https://doi.org/10.4050/JAHS.39.25 CrossrefGoogle Scholar

  • [19] Greenblatt D., “Unsteady Low-Speed Wind Tunnels,” AIAA Journal, Vol. 54, No. 6, 2016, pp. 1817–1830. https://doi.org/10.2514/1.J054590 LinkGoogle Scholar

  • [20] Stewart E., “Design, Analysis, and Validation of a Free Surface Water Tunnel,” M.Sc. Thesis, North Carolina State Univ., Raleigh, NC, Sept. 2017. Google Scholar

  • [21] Mueller T. J., “Low Reynolds Number Aerodynamics,” Proceedings of the Conference, Springer Science & Business Media, Notre Dame, IN, Vol. 54, 1989, pp. 281–292. Google Scholar

  • [22] Visbal M. R., “Numerical Investigation of Deep Dynamic Stall of a Plunging Airfoil,” AIAA Journal, Vol. 49, No. 10, 2011, pp. 2152–2170. https://doi.org/10.2514/1.J050892 LinkGoogle Scholar

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