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Experimental and Computational Study on Flapping Wings with Bio-Inspired Hover Kinematics

Published Online:https://doi.org/10.2514/1.J052644

In this paper, force and particle-image-velocimetry vorticity measurements of biologically inspired hover kinematics are compared to corresponding results of an unsteady aerodynamic vortex model and a Navier–Stokes (NS) solver. The Reynolds number and the reduced frequency are 4.8×103 and 0.38, respectively. Three kinematics derived from the measured hovering kinematics of an Agrius convolvuli are considered: 1) without elevation angle, 2) elevation angle accounted in the pitch angle, and 3) pure sinusoidal pitch–plunge neglecting higher harmonics. The Navier–Stokes computations show good qualitative agreement with experiments with consistent underprediction. The time-averaged thrust coefficients obtained using Navier–Stokes computations are 82 to 87% of the corresponding force measurements. The standard deviation of time history of thrust coefficients, also normalized by the measured time-averaged values, is 13 to 20%. The underprediction is possibly due to blockage effects in the experiments, also reflected in lower values of the vorticity compared to particle-image-velocimetry measurements. The unsteady aerodynamic vortex model captures some of the peaks in a qualitative manner. The relative difference in the time-averaged forces and standard deviation are 8 to 18% and 66 to 93%, respectively. The differences in prediction of time histories are not reflected in the estimation of time-averaged forces due to cancellation effects, wherein the forces are underpredicted in the first half of the stroke and overpredicted in the second half. The discrepancies are attributed to the simplifying assumptions in the unsteady aerodynamic vortex model, which overpredicts the vorticity in the leading-edge vortex and results in significant differences in the wing–wake interaction process.

References

  • [1] Willmott A. P. and Ellingtion C. P., “The Mechanics of Flight in the Hawkmoth Manduca Sexta,” Journal of Experimental Biology, Vol. 200, No. 21, 1997, pp. 2705–2722. JEBIAM 0022-0949 Google Scholar

  • [2] Miller L. A. and Peskin C. S., “A Computational Fluid Dynamics of ‘Clap and Fling’ in the Smallest Insects,” Journal of Experimental Biology, Vol. 208, No. 2, 2005, pp. 195–212. doi:https://doi.org/10.1242/jeb.01376 JEBIAM 0022-0949 CrossrefGoogle Scholar

  • [3] Shyy W., Lian Y., Tang J., Viieru D. and Liu H., Aerodynamics of Low Reynolds Number Flyers, Cambridge Univ. Press, Cambridge, England, U.K., 2008, pp. 1–158. CrossrefGoogle Scholar

  • [4] Trizila P., Kang C., Aono H., Shyy W. and Visbal M., “Low-Reynolds-Number Aerodynamics of a Flapping Rigid Flat Plate,” AIAA Journal, Vol. 49, No. 4, 2011, pp. 806–823. doi:https://doi.org/10.2514/1.J050827 AIAJAH 0001-1452 LinkGoogle Scholar

  • [5] Ol M., Bernal L. P., Kang C. and Shyy W., “Shallow and Deep Dynamic Stall for Flapping Low Reynolds Number Airfoils,” Experiments in Fluids, Vol. 46, No. 5, 2009, pp. 883–901. doi:https://doi.org/10.1007/s00348-009-0660-3 EXFLDU 0723-4864 CrossrefGoogle Scholar

  • [6] Kang C., Aono H., Baik Y., Bernal L. and Shyy W., “Fluid Dynamics of Pitching and Plunging Flat Plate at Intermediate Reynolds Numbers,” AIAA Journal, Vol. 51, No. 2, 2013, pp. 315–329. doi:https://doi.org/10.2514/1.J051593 AIAJAH 0001-1452 LinkGoogle Scholar

  • [7] Gogulapati A. and Friedmann P. P., “Approximate Aerodynamic and Aeroelastic Modeling of Flapping Wings in Forward Flight,” AIAA Journal, Vol. 52, No. 1, 2014, pp. 212–218. doi:https://doi.org/10.2514/1.J052596 LinkGoogle Scholar

  • [8] Vandenheede R. B. R., Bernal L. P., Morrison C. L. and Humbert S., “Force Generation of Bio-inspired Hover Kinematics,” 50th AIAA Aerospace Sciences Meeting, AIAA Paper  2012-0708, Jan. 2012. LinkGoogle Scholar

  • [9] Shyy W., Aono H., Chimakurthi S., Trizila P., Kang C., Cesnik C. and Liu H., “Recent Progress in Flapping Wing Aerodynamics and Aeroelasticity,” Progress in Aerospace Sciences, Vol. 46, No. 7, 2010, pp. 284–327. doi:https://doi.org/10.1016/j.paerosci.2010.01.001 PAESD6 0376-0421 CrossrefGoogle Scholar

  • [10] Ramananarivo S., Godoy-Diana R. and Thiria B., “Rather Than Resonance, Flapping Wing Flyers may Play on Aerodynamics to Improve Performance,” Proceedings of the National Academy of Sciences, Vol. 108, No. 15, 2011, pp. 5964–5969. doi:https://doi.org/10.1073/pnas.1017910108 Google Scholar

  • [11] Kang C., Aono H., Cesnik C. and Shyy W., “Effects of Flexibility on the Aerodynamic Performance of Flapping Wings,” Journal of Fluid Mechanics, Vol. 689, Dec. 2011, pp. 32–74. doi:https://doi.org/10.1017/jfm.2011.428 JFLSA7 0022-1120 CrossrefGoogle Scholar

  • [12] Liu H., Ellington C. P., Kawachi K., van den Berg C. and Wellmott A. P., “A Computational Fluid Dynamic Study of Hawkmoth Hovering,” Journal of Experimental Biology, Vol. 201, No. 4, 1998, pp. 461–477. JEBIAM 0022-0949 CrossrefGoogle Scholar

  • [13] Ansari S. A., Zbikowski R. and Knowles K., “Non-Linear Unsteady Aerodynamic Model for Insect-Like Flapping Wing in Hover. Part 1: Methodology and Analysis,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 220, No. 2, 2006, pp. 61–83. doi:https://doi.org/10.1243/09544100JAERO49 CrossrefGoogle Scholar

  • [14] Ansari S. A., Zbikowski R. and Knowles K., “Non-Linear Unsteady Aerodynamic Model for Insect-Like Flapping Wing in Hover. Part 2: Implementation and Validation,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 220, No. 2, 2006, pp. 169–186. doi:https://doi.org/10.1243/09544100JAERO50 CrossrefGoogle Scholar

  • [15] Gogulapati A., Friedmann P. P., Kheng E. and Shyy W., “Approximate Aeroelastic Modeling of Flapping Wings in Hover,” AIAA Journal, Vol. 51, No. 3, 2013, pp. 567–583. doi:https://doi.org/10.2514/1.J051801 LinkGoogle Scholar

  • [16] Balay S., Gropp W. D., McInnes L. C. and Smith B. F., “Efficient Management of Parallelism in Object Oriented Numerical Software Libraries,” Modern Software Tools in Scientific Computing, Birkhauser Boston, Cambridge, MA, 1997, pp. 163–202. CrossrefGoogle Scholar

  • [17] Balay S., PETSc Users Manual, Argonne National Lab., Lemont, IL, 2010. Google Scholar

  • [18] Balay S., Brown J., Buschelman K., Gropp W. D., Kaushik D., Knepley M. G., McInnes L. C., Smith B. F. and Zhang H., “PETSc Web Page,” 2011, http://www.mcs.anl.gov/petsc [retrieved 1 March 2011]. Google Scholar

  • [19] Flagout R. and Yang U., “Hypre: A Library of High Performance Preconditioners,” Proceedings of Computational Science—ICCS 2002, edited by Sloot P., Hoekstra A., Tan C. and Dongarra J., Springer–Verlag, Berlin, 2002, pp. 632–641. CrossrefGoogle Scholar

  • [20] Luke E. A. and George T., “Loci: A Rule-based Framework for Parallel Multi-Disciplinary Simulation Synthesis,” Journal of Functional Programming, Vol. 15, No. 3, 2005, pp. 477–502. doi:https://doi.org/10.1017/S0956796805005514 JFPRES 0956-7968 CrossrefGoogle Scholar

  • [21] Thomas P. and Lombard C., “Geometric Conservation Law and Application to Flow Computations on Moving Grids,” AIAA Journal, Vol. 10, No. 10, 1979, pp. 1030–1037. doi:https://doi.org/10.2514/3.61273 AIAJAH 0001-1452 LinkGoogle Scholar

  • [22] Kamakoti R. and Shyy W., “Evaluation of Geometric Conservation Law Using Pressure-Based Fluid Solver and Moving Grid Technique,” International Journal of Heat and Fluid Flow, Vol. 14, No. 7, 2004, pp. 851–865. doi:https://doi.org/10.1108/09615530410546254 IJHFD2 0142-727X CrossrefGoogle Scholar

  • [23] Vandenheede R. B. R., “Force Generation of Bio-Inspired Hover Kinematics: An Experimental Campaign,” M.S. Thesis, Delft Univ. of Technology, Delft, The Netherlands, June 2012. LinkGoogle Scholar

  • [24] Shyy W. and Liu H., “Flapping Wings and Aerodynamic Lift: The Role of Leading-Edge Vortices,” AIAA Journal, Vol. 45, No. 12, 2007, pp. 2817–2819. doi:https://doi.org/10.2514/1.33205 AIAJAH 0001-1452 LinkGoogle Scholar

  • [25] Dickinson M. H., Lehmann F.-O. and Sane S. P., “Wing Rotation and the Aerodynamic Basis of Insect Flight,” Science, Vol. 284, No. 5422, 1999, pp. 1954–1960. doi:https://doi.org/10.1126/science.284.5422.1954 SCIEAS 0036-8075 CrossrefGoogle Scholar