Abstract
In a tandem wing configuration, the hindwing often operates in the wake of the forewing and, hence, its performance is affected by the vortices shed by the forewing. Changes in the phase angle between the flapping motions of the fore and the hind wings, as well as the spacing between them, can affect the resulting vortex/wing and vortex/vortex interactions. This study uses 2D numerical simulations to investigate how these changes affect the leading dege vortexes (LEV) generated by the hindwing and the resulting effect on the lift and thrust coefficients as well as the efficiencies. The tandem wing configuration was simulated using an incompressible Navier-Stokes solver at a chord-based Reynolds number of 5 000. A harmonic single frequency sinusoidal oscillation consisting of a combined pitch and plunge motion was used for the flapping wing kinematics at a Strouhal number of 0.3. Four different spacings ranging from 0.1 chords to 1 chord were tested at three different phase angles, 0°, 90° and 180°. It was found that changes in the spacing and phase angle affected the timing of the interaction between the vortex shed from the forewing and the hindwing. Such an interaction affects the LEV formation on the hindwing and results in changes in aerodynamic force production and efficiencies of the hindwing. It is also observed that changing the phase angle has a similar effect as changing the spacing. The results further show that at different spacings the peak force generation occurs at different phase angles, as do the peak efficiencies.
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Abbreviations
- A :
-
Planform area with unit depth
- C L :
-
Lift coefficient
- C P :
-
Power coefficient
- C R :
-
Resultant coefficient
- C T :
-
Thrust coefficient
- f :
-
Flapping frequency
- h 0 :
-
Plunging amplitude
- h(t):
-
Plunging displacement
- L :
-
Instantaneous lift force
- M :
-
Instantaneous pitching moment
- p :
-
Pressure
- t :
-
Time
- T :
-
Flapping period
- u :
-
Flow velocity
- k :
-
Reduced frequency
- St :
-
Strouhal number
- V :
-
Instantaneous plunge velocity
- αave :
-
Average angle of attack
- α0 :
-
Pitching amplitude
- α(t):
-
Pitching angle
- ηL :
-
Lift efficiency
- ηP :
-
Propulsive efficiency
- ν :
-
Kinematic viscosity
- ρ :
-
Fluid density
- φ α :
-
Pitching phase lag
- φ h :
-
Plunging phase lag
- Ψ :
-
Phase angle
- ω :
-
Instantaneous rotational velocity
References
May, M. L.: Dragonfly flight: Power requirements at high speed and acceleration. The Journal of Experimental Biology 158, 325–342 (1991)
Reavis, M. A., Luttges, M. W.: Aerodynamic forces produced by a dragonfly. AIAA Journal 88–0330, 1–13 (1988)
Schmidt, W.: Der Wellpropeller, ein Neuer Antrieb fuer Wasser-, Land-, und Luftfahrzeuge. Zeitschrift fur Flugwissenschaften 13, 427–479 (1965)
Bosch, H.: Interfering airfoils in two-dimensional unsteady incompressible flow. AGARD-CP-277 (1977)
Tuncer, I. H., Platzer, M. F.: Thrust generation due to airfoil flapping. AIAA Journal 34, 324–331 (1996)
Alexander, D. E.: Unusual phase relationships between forewings and hindwings in flying dragonflies. Journal of Experimental Biology 109, 379–383 (1984)
Ruppell, G.: Kinematic analysis of symmetrical flight maneuvers of Odonata. The Journal of Experimental Biology 144, 13–42 (1989)
Azuma, A., Watanabe, T.: Flight performance of a dragonfly. The Journal of Experimental Biology 137, 221–252 (1988)
Thomas, A. L. R., Taylor, G. K., Srygley, R. B., et al.: Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady flight-generating mechanisms, controlled primarily via angle of attack. The Journal of Experimental Biology 207, 4299–4323 (2004)
Lan, C. E.: The unsteady quasi-vortex-lattice method with application to animal propulsion. Journal of Fluid Mechanics 93, 747–765 (1979)
Usherwood, J. R., Lehmann, F. O.: Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl. J. R. Soc Interface 5, 1303–1307 (2008)
Maybury, W., Lehmann, F. O.: The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings. The Journal of Experimental Biology 207, 4707–4726 (2004)
Yamamoto, M., Isogai, K.: Measurement of unsteady fluid dynamic forces for a mechanical dragonfly model. AIAA Journal 43, 2475–2480 (2005)
Wang, Z., Russell, D.: Effect of forewing and hindwing interactions on aerodynamic forces and power in hovering dragonfly flight. Physical Review Letters 99, 1–4 (2007)
Lan, S. L., Sun, M.: Aerodynamic force and flow structures of two airfoils in flapping motions. Acta Mechanica Sinica 17, 310–331 (2001)
Sun, M., Lan, S. L.: A computational study of the aerodynamic forces and power requirements of dragonfly (Aeschna juncea) hovering. The Journal of Experimental Biology 207, 1887–1901 (2004)
Isogai, K., Fijishiro, S., Saitoh, T., et al.: Unsteady threedimensional viscous flow simulation of a dragonfly hovering. AIAA Journal 42, 2053–2059 (2004)
Warkentin, J., DeLaurier, J.: Experimental aerodynamic study of tandem flapping membrane wings. Journal of Aircraft 44, 1653–1651 (2007)
Saharon, D., Luttges, M.: Three-dimensional flow produced by a pitching-plunging model dragonfly wing. In: Proc. of the 25th AIAA Aerospace Sciences Meeting, AIAA Paper 87-0121 (1987)
Saharon, D., Luttges, M.: Visualization of unsteady separated flow produced by mechanically driven dragonfly wing kinematics model. In: Proceeding of the 26th Aerospace Sciences Meeting, AIAA Paper 88-0569 (1988)
Saharon, D., Luttges, M.: Dragonfly unsteady aerodynamic: The role of the wing phase relations in controlling the produced flows. In: Proc. of the 27th AIAA Aerospace Sciences Meeting, AIAA Paper 89-0832 (1989)
Akhtar, I., Mittal, R., Lauder G., et al.: Hydrodynamics of a biologically inspired tandem flapping foil configuration. Theoretical and Computational Fluid Dynamics 21, 155–170 (2007)
Huang, H., Sun, M.: Dragonfly forewing-hindwing interaction at various flight speeds and wing phasings. AIAA Journal 45, 508–511 (2007)
Wang, J., Sun, M.: A computationalmodel of the aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight. The Journal of Experimental Biology 208, 3785–3804 (2005)
Broering, T., Lian, Y., Henshaw, W.: Numerical investigation of energy extraction in a tandem flapping wing configuration. AIAA J. 50, 2295–2307 (2012)
Rival, D., Hass, G., Tropea, C.: Recovery of energy from leading- and trailing-edge vortices in tandem-airfoil configurations. Journal of Aircraft 48, 203–211 (2011)
Lim, K. B., Tay, W. B.: Numerical analysis of the s1020 airfoils in tandem under different flapping configurations. Acta Mech. Sin. 26, 191–207 (2010)
Taylor, G. K., Nudds, R. L., Thomas, A. L. R., et al.: Flying and swimming animals cruise at a strouhal number tuned for high power efficiency. Nature 425, 707–711 (2003)
Henshaw, W. D., Petersson, N. A.: A split-step scheme for the incompressible Navier-Stokes equations. In: Numerical Simulation of Incompressible Flows, World Scientific, River Edge, USA 108–125 (2003)
Balay, S., Gropp, W. D., Mcinnes, L. C., et al.: The portable extensible toolkit for scientific computation, Tech. Rep. http://www.mcs.anl.gov/petsc/petsc.html, Argonne National Laboratory (1999)
Young, J.: Numerical simulation of the unsteady aerodynamic flapping airfoils. [Ph.D. Thesis], The University of New South Wales/Australian Defence Force Academy (2005)
Young, J., Lai, J., Germain, C.: Simulation and parameter variation of flapping-wing motion based on dragonfly hovering. AIAA Journal 46, 918–924 (2008)
Lian, Y., Shyy, W.: Aerodynamics of low reynolds number plunging airfoil under gusty environment, In: Proc. of the 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2007-71 (2007)
Ol, M.: Unsteady aerodynamics for micro air vehicles. NATO RTO AVT-149 Report (2010)
Henshaw, W. D., Schwendeman, D. W.: Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow. Journal of Computational Physics 216, 744–779 (2006)
Wakeling, J. M., Ellington, C. P.: Dragonfly flight: II: Velocity, acceleration, and kinematics of flapping flight. The Journal of Experimental Biology 200, 557–582 (1997)
Jones, K. D., Lund, T., Platzer, M. F., et al.: Experimental and computational investigation of flapping wing propulsion formicro air vehicles. Progress in Astronautics and Aeronautics 195, 307–339 (2001)
Ramamurti, R., Sandberg, W.: Simulation of flow about flapping airfoils using finite element incompressible flow solver. AIAA Journal 39, 253–260 (2001)
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Broering, T.M., Lian, YS. The effect of phase angle and wing spacing on tandem flapping wings. Acta Mech Sin 28, 1557–1571 (2012). https://doi.org/10.1007/s10409-012-0210-8
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DOI: https://doi.org/10.1007/s10409-012-0210-8