1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Aerodynamic forces and vortical structures in flapping butterfly's forward flight
Rent:
Rent this article for
USD
10.1063/1.4790882
/content/aip/journal/pof2/25/2/10.1063/1.4790882
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/2/10.1063/1.4790882

Figures

Image of FIG. 1.
FIG. 1.

Definitions of coordinates and the Euler angles. The positive directions of the thoracic and joint angles θ, θ, β, η, and θ are expressed by the round arrows. (a) First, the coordinate of the left wing corresponds to that of the thorax on the right side. (d) After the three rotations (1: about the axis by β + π, 2: about the axis by −η, 3: about the axis by −θ) the coordinate corresponds to . (e) The coordinate of the thorax corresponds to that of the abdomen after the rotation about the axis by −θ (4). The positive directions of the Euler angles of the rotations ϕ are determined by the right-hand rule.

Image of FIG. 2.
FIG. 2.

Observed joint angles of the abdomen and the wings of a tethered butterfly. The abdominal pitching angle, the approximate flapping angle, the approximate lead-lag angle, the approximate feathering angle are denoted by θ, β, η, and θ, respectively.

Image of FIG. 3.
FIG. 3.

Observed thoracic coordinates during a free flight. The means of the vertical and horizontal coordinates during the flapping period are set to 0. The pitching angle is scaled by the right-hand axis.

Image of FIG. 4.
FIG. 4.

Upward and streamwise forces and longitudinal torque acting on the thorax of the tethered butterflies in the numerical simulation and the experiment. (a) Upward force, (b) streamwise force, and (c) longitudinal torque. The aerodynamic forces and pitching moment in the simulation are also drawn as the lift, drag, and pitching moment, respectively.

Image of FIG. 5.
FIG. 5.

Smoke structures in the tethered experiment. The smoke is released on the vertical segment of = 4 /5 on the inflow boundary. (a) Topview and (b) sideview.

Image of FIG. 6.
FIG. 6.

Passive tracers in the tethered simulation. (a) Topview and (b) sideview.

Image of FIG. 7.
FIG. 7.

Lift, drag, and pitching moment due to aerodynamic force in the prescribed simulation. The pitching moment is scaled by the right-hand axis.

Image of FIG. 8.
FIG. 8.

Upward and streamwise forces and longitudinal torque due to extra control applied to the thorax in the prescribed simulation. The longitudinal torque are scaled by the right-hand axis.

Image of FIG. 9.
FIG. 9.

Torques applied to the joints of the abdomen and of the left wing τ, τ and τ in the prescribed simulation.

Image of FIG. 10.
FIG. 10.

Power due to aerodynamic force , extra control , and joint control forces in the prescribed simulation. The power due to the joint control is the sum of those due to the abdominal and wing joints, i.e., = + + .

Image of FIG. 11.
FIG. 11.

Vortical structures visualized by the -criterion, i.e., the second invariant of velocity gradient tensor in the prescribed simulation. The isosurface of = 1 × 10 s is drawn. (a) Topview and (b) sideview.

Image of FIG. 12.
FIG. 12.

Schematic illustration of the three-dimensional vortical structures. The directions of the coherent vortices are expressed by the arrows.

Image of FIG. 13.
FIG. 13.

Near-field structures viewed from above and behind in the prescribed simulation. The forces and the isosurface of = 2.5 × 10 s are drawn. The streamlines starting from two segments are drawn at = /4. The spanwise vorticities ω on the right wing and the streamwise vorticities ω in the downstream are also drawn on the corresponding cross-section at = /4. (a) Forces and -criterion at = /4, (b) streamlines and vorticities at = /4, (c) forces and -criterion at = 5/8, and (d) forces and -criterion at = 7/8. The magnitudes and the direction of the forces are, respectively, expressed by density (density of blue) and by the displacement from the wing. The forces and the streamlines are shown on the left side while the isosurface of and the vorticities are shown on the right side.

Image of FIG. 14.
FIG. 14.

Lift, drag, and pitching moment due to aerodynamic force during the first free-flight flapping period.

Image of FIG. 15.
FIG. 15.

Thoracic coordinates during the first free-flight flapping period.

Image of FIG. 16.
FIG. 16.

Lift, drag and pitching moment due to aerodynamic force during the three free-flight flapping periods with the smaller abdominal mass 3 /4.

Image of FIG. 17.
FIG. 17.

Thoracic coordinates during the three free-flight flapping periods with the smaller abdominal mass 3 /4.

Image of FIG. 18.
FIG. 18.

Upward and streamwise forces and longitudinal torque in four tests for computational validation.

Tables

Generic image for table
Table I.

Physical properties of butterflies (chestnut tiger).

Generic image for table
Table II.

Numerical conditions of three simulations.

Loading

Article metrics loading...

/content/aip/journal/pof2/25/2/10.1063/1.4790882
2013-02-21
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Aerodynamic forces and vortical structures in flapping butterfly's forward flight
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/2/10.1063/1.4790882
10.1063/1.4790882
SEARCH_EXPAND_ITEM