Experimental and Computational Analysis of Rigid Flapping Wings for Micro Air Vehicles
Abstract
Targeted experiments in parallel with a systematic computational-fluid-dynamics analysis were performed for a micro-air-vehicle-scale rigid flapping wing in forward flight. Two-component time-resolved particle-image-velocimetry measurements were performed in an open-circuit wind tunnel on a wing undergoing pure flap-wing kinematics at a fixed wing-pitch angle. Chordwise velocity fields were obtained at equally spaced spanwise sections along the wing (30 to 90% span) at two instants during the flap cycle (middownstroke and midupstroke) for the reference Reynolds numbers of 15,000. The flowfield measurements were used for the validation of the three-dimensional computational-fluid-dynamics model. The computational-fluid-dynamics analysis used a compressible Reynolds-averaged Navier–Stokes solver to resolve the complex, highly vortical, three-dimensional flow. The objectives of the combined efforts were to understand the unsteady aerodynamic mechanisms and their relation to force production on a rigid wing undergoing an avian-type flapping motion. Overall, the computational-fluid-dynamics results showed good agreement with the experimental data for resolution of the overall highly unsteady and vortical flowfield. A control-volume approach used to calculate the strength of the leading-edge vortex from the particle-image-velocimetry measurements and from the computational-fluid-dynamics-generated flowfields showed comparable results. A hybrid momentum-based method was used to estimate the sectional vertical force coefficient from the particle-image-velocimetry-measured flowfield, which agreed well with the computational-fluid-dynamics force prediction over a range of flapping frequencies and wing-pitch angles. In general, it was observed that the flow over the wing was highly susceptible to changes in induced angle of attack resulting from the flapping motion and variations in reduced frequency, which manifested in the predicted airloads. Based on the computational analysis, the spanwise flow component was not significant, except near the wing tip, and therefore most of the vertical force and propulsive thrust produced could be explained using the magnitude and direction of the sectional lift and drag forces acting on the wing. For the present wing kinematics, most of the upward vertical force was produced during the downstroke and positive propulsive thrust during the upstroke, which shows the need for appropriate temporal and spanwise pitch modulation of the wing along with flapping to produce positive vertical force and propulsive thrust during the entire flap cycle.
References
[1] , “Aerodynamic Characteristics of Wings at Low Reynolds Number,” Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, edited by Mueller T. J., Vol. 195,
Progress in Astronautics and Aeronautics , AIAA, Reston, VA, 2001, pp. 341–398, Chap. 1.[2] , “Aerodynamics of Small Vehicles,” Annual Review of Fluid Mechanics, Vol. 35, No. 1, 2003, pp. 89–111. doi:https://doi.org/10.1146/annurev.fluid.35.101101.161102 ARVFA3 0066-4189
[3] , “Unsteady Aerodynamics for Micro Air Vehicles,” Final Report of Task Group AVT-149, NATO Research and Technology Organization, TR-AC/323 (AVT-149) TP/332, Brussels, 2010.
[4] , Aerodynamics of Low Reynolds Number Flyers, Cambridge Univ. Press, New York, 2008, pp. 29–35, 45–49, 144–148.
[5] , Principles of Helicopter Aerodynamics, 2nd ed., Cambridge Univ. Press, Cambridge, England, U.K., 2006, pp. 334–337.
[6] , “Flapping Wings and Aerodynamic Lift: The Role of Leading-Edge Vortices,” Journal of Aircraft, Vol. 45, No. 12, 2007, pp. 2817–2819. doi:https://doi.org/10.2514/1.33205 JAIRAM 0021-8669
[7] , “Comparative Scaling of Flapping and Fixed Wing Flyers,” AIAA Journal, Vol. 44, No. 1, Jan. 2006, pp. 24–33. doi:https://doi.org/10.2514/1.4035 AIAJAH 0001-1452
[8] , “Challenges Facing Future Micro-Air-Vehicle Development,” Journal of Aircraft, Vol. 43, No. 2, March–April 2006, pp. 290–305. doi:https://doi.org/10.2514/1.4922 JAIRAM 0021-8669
[9] , “Phase-Locked Particle Image Velocimetry Measurements of a Flapping Wing,” Journal of Aircraft, Vol. 43, No. 6, Nov.–Dec. 2006, pp. 1867–1875. doi:https://doi.org/10.2514/1.21347 JAIRAM 0021-8669
[10] , “Yaw Dynamics Identification of an Insect-Inspired Flapping Wing Micro Air Vehicle,” AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2014-1468, Jan. 2014.
[11] , “Delfly Freeflight—Autonomous Flight of the Delfly in the Wind Tunnel Using Low-Cost Sensors,” M.S. Thesis, Delft Univ. of Technology, Delft, The Netherlands, June 2012.
[12] , “Development of the Nano Hummingbird: A Tailless Flapping Wing Micro Air Vehicle,” 50th AIAA Aerospace Sciences Meeting, AIAA Paper 2012-0588, Jan. 2012.
[13] , “Comparison of Hovering Efficiency of Rotating Wing and Flapping Wing Micro Air Vehicles,” Journal of the American Helicopter Society, Vol. 55, No. 2, April 2010, p. 25001. doi:https://doi.org/10.4050/JAHS.55.025001 JHESAK 0002-8711
[14] , “Insects Versus Birds: The Great Divide,” 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2006-0035, Jan. 2006.
[15] , “Flapping Flight and Power in Birds and Insects,” Swimming and Flying in Nature, edited by Wu T. Y. T., Brokaw C. J. and Brennen C., Vol. 2, Plenum, London, 1975, pp. 729–762.
[16] , “The Fluid Dynamics of Insect Flight,” Annual Review of Fluid Mechanics, Vol. 13, No. 1, 1981, pp. 329–350. doi:https://doi.org/10.1146/annurev.fl.13.010181.001553 ARVFA3 0066-4189
[17] , “The Mechanics of Flight in the Hawkmoth Manduca Sexta, 2. Aerodynamic Consequences of Kinematic and Morphological Variation,” Journal of Experimental Biology, Vol. 200, Pt. 21, 1997, pp. 2723–2745. JEBIAM 0022-0949
[18] , “Force and Flowfield Measurements on a Rigid Wing Undergoing Hover-Capable Flapping and Pitching Kinematics in Air at MAV-Scale Reynolds Numbers,” 54th AIAA ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2013-1706, April 2013.
[19] , “Evolution and Breakdown of a Leading Edge Vortex on a Rotating Wing,” 51st AIAA Aerospace Sciences Meeting, AIAA Paper 2013-0843, Jan. 2013.
[20] , “The Vortex Wake of a “Hovering” Model Hawkmoth,” Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, Vol. 352, No. 1351, 1997, pp. 317–328. doi:https://doi.org/10.1098/rstb.1997.0023 PTRBAE 0962-8436
[21] , “The Three-Dimensional Leading-Edge Vortex of a ‘Hovering’ Model Hawkmoth,” Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, Vol. 352, No. 1351, 1997, pp. 329–340. doi:https://doi.org/10.1098/rstb.1997.0024 PTRBAE 0962-8436
[22] , “Lift and Drag Characteristics of Rotary and Flapping Wings,” Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, edited by Mueller T. J., Vol. 195,
Progress in Astronautics and Aeronautics , AIAA, Reston, VA, 2001, Chap. 12.[23] , “Wing Rotation and the Aerodynamic Basis of Insect Flight,” Science, Vol. 284, No. 5422, June 1999, pp. 1954–1960. doi:https://doi.org/10.1126/science.284.5422.1954 SCIEAS 0036-8075
[24] , “Spanwise Flow and the Attachment of the Leading-Edge Vortex on Insect Wings,” Nature, Vol. 412, No. 6848, Aug. 2001, pp. 729–733. doi:https://doi.org/10.1038/35089071
[25] , “The Influence of Wing Wake Interactions on the Production of Aerodynamic Forces in Flapping Fight,” Journal of Experimental Biology, Vol. 206, No. 13, July 2003, pp. 2257–2272. doi:https://doi.org/10.1242/jeb.00381 JEBIAM 0022-0949
[26] , “Force Production and Flow Structure of the Leading Edge Vortex on Flapping Wings at High and Low Reynolds Numbers,” Journal of Experimental Biology, Vol. 207, No. 7, 2004, pp. 1063–1072. doi:https://doi.org/10.1242/jeb.00848 JEBIAM 0022-0949
[27] , “Flow Visualization of Micro Air Vehicle Scaled Insect-Based Flapping Wings,” Journal of Aircraft, Vol. 42, No. 2, March–April 2005, pp. 385–390. doi:https://doi.org/10.2514/1.6055 JAIRAM 0021-8669
[28] , “Rotational Accelerations Stabilize Leading Edge Vortices on Revolving Fly Wings,” Journal of Experimental Biology, Vol. 212, No. 16, April 2009, pp. 2705–2719. doi:https://doi.org/10.1242/jeb.022269 JEBIAM 0022-0949
[29] , “Force Production Mechanisms of a Flapping MAV Wing,” American Helicopter Society Aeromechanics Specialist’s Conference, Vols. 1–2, American Helicopter Soc. International, Alexandria, VA, 2008, p. 782, http://toc.proceedings.com/02630webtoc.pdf.
[30] , “Investigation of Aerodynamics of Flapping Wings for Micro Air Vehicle Applications,” Ph.D. Thesis, Univ. of Maryland, College Park, MD, May 2013.
[31] , “Flying and Swimming Animals Cruise at a Strouhal Number Tuned for High Power Efficiency,” Nature, Vol. 425, No. 6959, Oct. 2003, pp. 707–711. doi:https://doi.org/10.1038/nature02000
[32] , “A Computational Fluid Dynamic Study of Hawkmoth Hovering,” Journal of Experimental Biology, Vol. 201, No. 4, Feb. 1998, pp. 461–477. JEBIAM 0022-0949
[33] , “Unsteady Aerodynamic Force Generation by a Model Fruit Fly Wing in Flapping Motion,” Journal of Experimental Biology, Vol. 205, No. 1, 2002, pp. 55–70. JEBIAM 0022-0949
[34] , “Unsteady Two-Dimensional Theory of a Flapping Wing,” Physical Review E: Statistical Physics, Plasma, Fluids, and Related Interdisciplinary Topics, Vol. 66, No. 5, Jan. 2002, Paper 051907. doi:https://doi.org/10.1103/PhysRevE.66.051907
[35] , “Computational Investigation of Flapping-Wing Flight,” 37th AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2007-4209, June 2007.
[36] , “Simulation of Flow About Flapping Airfoils Using Finite Element Incompressible Flow Solver,” AIAA Journal, Vol. 39, No. 2, Feb. 2001, pp. 253–260. doi:https://doi.org/10.2514/2.1320 AIAJAH 0001-1452
[37] , “Experimental Studies to Understand the Hover and Forward Flight Performance of a MAV-Scale Flapping Wing Concept,” Journal of the American Helicopter Society, Vol. 57, No. 2, April 2012, Paper 022002. JHESAK 0002-8711
[38] , Computational Investigation of Micro-Scale Coaxial Rotor Aerodynamics in Hover, Ph.D. Dissertation, Dept. of Aerospace Engineering, Univ. of Maryland, College Park, MD, Jan. 2009.
[39] , “A Diagonal Form of an Implicit Approximate Factorization Algorithm,” Journal of Computational Physics, Vol. 39, No. 2, Feb. 1981, pp. 347–363. doi:https://doi.org/10.1016/0021-9991(81)90156-X JCTPAH 0021-9991
[40] , “Towards the Ultimate Conservative Difference Scheme 5. A Second-Order Sequel to Godunov’s Method,” Journal of Computational Physics, Vol. 135, No. 2, June 1997, pp. 229–248. doi:https://doi.org/10.1006/jcph.1997.5704 JCTPAH 0021-9991
[41] , “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,” Journal of Computational Physics, Vol. 135, No. 2, June 1997, pp. 250–258. doi:https://doi.org/10.1006/jcph.1997.5705 JCTPAH 0021-9991
[42] , “Upwind Schemes, Multigrid and Defect Correction for the Steady Navier–Stokes Equations,” Proceedings of the 11th International Conference on Numerical Methods in Fluid Dynamics, Vol. 323,
Lecture Notes in Physics , Springer–Verlag, Berlin, 1989, pp. 344–348. doi:https://doi.org/10.1007/3-540-51048-6_52[43] , “A Preconditioned Dual-Time, Diagonalized ADI Scheme for Unsteady Computations,” 13th Computational Fluid Dynamics Conference, AIAA Paper 1997-2101, July 1997.
[44] , “Implementation of Preconditioned Dual-Time Procedures in OVERFLOW,” 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2003-0072, Jan. 2003.
[45] , “A One-Equation Turbulence Model for Aerodynamic Flows,” 30th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 1992-0439, Jan. 1992.
[46] , “On Overset Grids Connectivity and Automated Vortex Tracking in Rotorcraft CFD,” Ph.D. Dissertation, Dept. of Aerospace Engineering, Univ. of Maryland, College Park, MD, Jan. 2008.
[47] , Springer Handbook of Experimental Fluid Mechanics, Springer–Verlag, Berlin, 2007, pp. 295–296.
[48] , “The Effect of a Discrete Window Offset on the Accuracy of Cross-Correlation Analysis of Digital PIV Recordings,” Experiments in Fluids, Vol. 23, No. 1, 1997, pp. 20–28. doi:https://doi.org/10.1007/s003480050082 EXFLDU 0723-4864
[49] , “Iterative Image Deformation Methods in PIV,” Measurement Science and Technology, Vol. 13, No. 1, Jan. 2002, pp. 1–19. doi:https://doi.org/10.1088/0957-0233/13/1/201 MSTCEP 0957-0233
[50] , “On Errors of Digital Particle Image Velocimetry” Measurement Science and Technology, Vol. 8, No. 12, 1997, pp. 1427–1440. doi:https://doi.org/10.1088/0957-0233/8/12/007 MSTCEP 0957-0233
[51] , Particle Image Velocimetry: A Practical Guide, Springer–Verlag, Berlin, 1998, pp. 117–134.
[52] , “Combining PIV, POD and Vortex Identification Algorithms for the Study of Unsteady Turbulent Swirling Flows,” Measurement Science and Technology, Vol. 12, No. 9, Aug. 2001, pp. 1422–1429. doi:https://doi.org/10.1088/0957-0233/12/9/307 MSTCEP 0957-0233
[53] , Fundamentals of Aerodynamics, McGraw–Hill, New York, 2007, pp. 162–164.
[54] , “Invariants of the Velocity-Gradient, Rate-of-Strain, and Rate-of-Rotation Tensors Across the Turbulent/Nonturbulent Interface in Jets,” Physics of Fluids, Vol. 20, No. 5, May 2008, Paper 055101. doi:https://doi.org/10.1063/1.2912513