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First published online September 16, 2005
Journal of Experimental Biology 208, 3785-3804 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01852

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A computational study of the aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight

Ji Kang Wang and Mao Sun^*

Ministry-of-Education Key Laboratory of Fluid Mechanics, Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, People's Republic of China

View larger version (29K): [in a new window]   Fig. 1. Sketches of the model wings, the flapping motion and the reference frames. FW and HW denote fore- and hindwings, respectively. O,X,Y,Z is an inertial frame, with the X and Y axes in the horizontal plane. ß, stroke plane angle; V, incoming flow velocity.

View larger version (107K): [in a new window]   Fig. 2. Some portions of the moving overset grids.

View larger version (22K): [in a new window]   Fig. 3. Time courses of (A) total vertical force coefficient (CV) and (B) total thrust coefficient (CT) in one cycle at various d (hovering, J=0). d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (17K): [in a new window]   Fig. 4. Time courses of vertical force coefficients of forewing (CV,f) and hindwing (CV,h) at hovering (J=0). (A) d=180°, (B) d=90°, (C) d=60°, (D) d=0°. d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (27K): [in a new window]   Fig. 5. Time courses of (A) total vertical force coefficient (CV) and (B) total thrust coefficient (CT) in one cycle at various d (forward flight, J=0.3). d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (30K): [in a new window]   Fig. 6. Time courses of (A,C,E,G) total vertical force coefficient (CV) and (B,D,F,H) total thrust coefficient (CT) in one cycle at various d and J. d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (26K): [in a new window]   Fig. 7. Time courses of vertical force, lift and drag coefficients for the hindwing (A) and the forewing (B) in one cycle at d=180° and J=0.3. CV,h, Cl,h and Cd,h, vertical force, lift and drag coefficients of the hindwing, respectively; CV,f, Cl,f and Cd,f, vertical force, lift and drag coefficients of the forewing, respectively; d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (25K): [in a new window]   Fig. 8. Time courses of vertical force, lift and drag coefficients for the hindwing (A) and the forewing (B) in one cycle at d=180° and J=0.6. CV,h, Cl,h and Cd,h, vertical force, lift and drag coefficients of the hindwing, respectively; CV,f, Cl,f and Cd,f, vertical force, lift and drag coefficients of the forewing, respectively; d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (38K): [in a new window]   Fig. 9. Plot of spanwise component of vorticity at half-wing length at various times in a stroke cycle for the forewing (A) and the hindwing (B) at d=180°, J=0 (d=52° and u=8°). Solid and broken lines indicate positive and negative vorticity, respectively; the magnitude of non-dimensional vorticity at the outer contour is 1 and the contour internal is 3. d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively; , non-dimensional time.

View larger version (36K): [in a new window]   Fig. 10. Plot of spanwise component of vorticity at half-wing length at various time in a stroke cycle for the forewing (A) and the hindwing (B), at d=180°, J=0.3 (d=36° and u=22°). Solid and broken lines indicate positive and negative vorticity, respectively; the magnitude of non-dimensional vorticity at the outer contour is 1 and the contour internal is 3. d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively; , non-dimensional time.

View larger version (36K): [in a new window]   Fig. 11. Plot of spanwise component of vorticity at half-wing length at various time in a stroke cycle for the forewing (A) and the hindwing (B), at d=180°, J=0.6 (d=32° and u=51°). Solid and broken lines indicate positive and negative vorticity, respectively; the magnitude of non-dimensional vorticity at the outer contour is 1 and the contour internal is 3. d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively; , non-dimensional time.

View larger version (42K): [in a new window]   Fig. 12. Plot of spanwise component of vorticity at half-wing length at various time in a stroke cycle for the forewing (A) and the hindwing (B), at d=60°, J=0.0 (d=48° and u=5.5°). Solid and broken lines indicate positive and negative vorticity, respectively; the magnitude of non-dimensional vorticity at the outer contour is 1 and the contour internal is 3. d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively; , non-dimensional time.

View larger version (41K): [in a new window]   Fig. 13. Plot of spanwise component of vorticity at half-wing length at various time in a stroke cycle for the forewing (A) and the hindwing (B), at d=60°, J=0.3 (d=32° and u=21.8°). Solid and broken lines indicate positive and negative vorticity, respectively; the magnitude of non-dimensional vorticity at the outer contour is 1 and the contour internal is 3. d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively; , non-dimensional time.

View larger version (41K): [in a new window]   Fig. 14. Plot of spanwise component of vorticity at half-wing length at various time in a stroke cycle for the forewing (A) and the hindwing (B), at d=60°, J=0.6 (d=31° and =50°). Solid and broken lines indicate positive and negative vorticity, respectively; the magnitude of non-dimensional vorticity at the outer contour is 1 and the contour internal is 3. d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively; , non-dimensional time.

View larger version (54K): [in a new window]   Fig. 15. Sectional streamline plots at half-wing length at the mid-downstroke and mid-upstroke of the forewing (A) and the hindwing (B) at various J (d=180°). d, difference in phase angle between the hindwing and forewing; J, advance ratio; d and u, geometric angles of attack in the down- and upstrokes, respectively.

View larger version (20K): [in a new window]   Fig. 16. Time courses of vertical force coefficients of forewing (CV,f), single forewing (CV,sf), hindwing (CV,h) and single hindwing (CV,sh) and thrust coefficients of the forewing (CT,f), single forewing (CT,sf), hindwing (CT,h) and single hindwing (CT,sh) in one cycle: (A,B) d=180°, J=0; (C,D) d=180°, J=0.3; (E,F) d=180°, J=0.6. d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (19K): [in a new window]   Fig. 17. Time courses of vertical force coefficients of forewing (CV,f), single forewing (CV,sf), hindwing (CV,h) and single hindwing (CV,sh) and thrust coefficients of the forewing (CT,f), single forewing (CT,sf), hindwing (CT,h) and single hindwing (CT,sh) in one cycle; (A,B) d=90°, J=0; (C,D) d=90°, J=0.3; (E,F) d=90°, J=0.6. d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (19K): [in a new window]   Fig. 18. Time courses of vertical force coefficients of forewing (CV,f), single forewing (CV,sf), hindwing (CV,h) and single hindwing (CV,sh) and thrust coefficients of the forewing (CT,f), single forewing (CT,sf), hindwing (CT,h) and single hindwing (CT,sh) in one cycle; (A,B) d=60°, J=0; (C,D) d=60°, J=0.3; (E,F) d=60°, J=0.6. d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (18K): [in a new window]   Fig. 19. Time courses of vertical force coefficients of forewing (CV,f), single forewing (CV,sf), hindwing (CV,h) and single hindwing (CV,sh) and thrust coefficients of the forewing (CT,f), single forewing (CT,sf), hindwing (CT,h) and single hindwing (CT,sh) in one cycle; (A,B) d=0°, J=0; (C,D) d=0°, J=0.3; (E,F) d=0°, J=0.6. d, difference in phase angle between the hindwing and forewing; J, advance ratio; , non-dimensional time.

View larger version (16K): [in a new window]   Fig. 20. Diagram used for computing the mean relative velocity of the section at r2 from the wing root. ß, stroke plane angle; r2, radius of the second moment of wing area; U, velocity due to flapping.

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