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On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings

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Abstract

Insect wings are subjected to fluid, inertia and gravitational forces during flapping flight. Owing to their limited rigidity, they bent under the influence of these forces. Numerical study by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007) showed that a flexible wing is able to generate almost as much lift as a rigid wing during flapping. In this paper, we take a closer look at the relationship between wing flexibility (or stiffness) and aerodynamic force generation in flapping hovering flight. The experimental study was conducted in two stages. The first stage consisted of detailed force measurement and flow visualization of a rigid hawkmoth-like wing undergoing hovering hawkmoth flapping motion and simple harmonic flapping motion, with the aim of establishing a benchmark database for the second stage, which involved hawkmoth-like wing of different flexibility performing the same flapping motions. Hawkmoth motion was conducted at Re = 7,254 and reduced frequency of 0.26, while simple harmonic flapping motion at Re = 7,800 and 11,700, and reduced frequency of 0.25. Results show that aerodynamic force generation on the rigid wing is governed primarily by the combined effect of wing acceleration and leading edge vortex generated on the upper surface of the wing, while the remnants of the wake vortices generated from the previous stroke play only a minor role. Our results from the flexible wing study, while generally supportive of the finding by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007), also reveal the existence of a critical stiffness constant, below which lift coefficient deteriorates significantly. This finding suggests that although using flexible wing in micro air vehicle application may be beneficial in term of lightweight, too much flexibility can lead to deterioration in flapping performance in terms of aerodynamic force generation. The results further show that wings with stiffness constant above the critical value can deliver mean lift coefficient almost the same as a rigid wing when executing hawkmoth motion, but lower than the rigid wing when performing a simple harmonic motion. In all cases studied (7,800 ≤ Re ≤ 11,700), the Reynolds number does not alter the force generation significantly.

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Abbreviations

A ϕ :

The angle the wing swept over one complete stroke

B :

Buoyancy (N)

C :

Chord length (m)

C D :

Drag coefficient

C L :

Lift coefficient

C H :

Horizontal force coefficient

C V :

Vertical force coefficient

EI:

Overall spanwise flexural stiffness (N m2)

F :

Force (N)

F C :

Chordwise force acting on the wing (N)

F D :

Drag force (N)

\( \bar{F}_{\text{D}} \) :

Time-averaged drag force (N)

F L :

Lift force (N)

\( \bar{F}_{\text{L}} \) :

Time-averaged lift force (N)

F N :

Normal force acting on the wing (N)

\( \bar{F}_{\text{V}} \) :

Time-averaged vertical force (N)

k :

Wing stiffness (N/m)

k c :

Reduced frequency

k R :

Wing relative stiffness

n :

Flapping frequency (s−1)

R :

Wing span measured from wing tip to center of rotation (m)

Re :

Reynolds number

R tip :

Wing span measured from wing tip to wing base (m)

\( \hat{r}_{2} \) :

Dimensionless second moment of wing area

S :

Surface area of wing (m2)

T :

Flapping period (s)

U rev :

Reference velocity (m/s)

t :

Time (s)

t*:

Nondimensional time = t/T

Φ:

Sweeping amplitude (°)

α:

Angle of attack (°)

\( \dot{\alpha } \) :

Angular velocities of rotating (°/s)

β:

Rotational amplitude (°)

δ:

Average stroke plane angle (°)

ε:

Wing displacement in the stiffness test (m)

ϕ:

Sweeping angle (°)

ϕ0 :

Sweeping angle offset (°)

\( \dot{\phi } \) :

Angular velocities of sweeping (°/s)

ν:

Kinematic viscosity (s/m2)

γ:

Average wing deflection angle (°)

θ:

Elevation angle (°)

\( \dot{\theta } \) :

Angular velocities of elevation (°/s)

ρ:

Density (kg/m3)

i :

Initial value

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Authors and Affiliations

  1. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Block EA, 07-08, Singapore, 117576, Singapore

    K. B. Lua, K. C. Lai, T. T. Lim & K. S. Yeo

Authors
  1. K. B. Lua
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  2. K. C. Lai
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  3. T. T. Lim
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  4. K. S. Yeo
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Correspondence to K. B. Lua.

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Lua, K.B., Lai, K.C., Lim, T.T. et al. On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings. Exp Fluids 49, 1263–1291 (2010). https://doi.org/10.1007/s00348-010-0873-5

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  • DOI: https://doi.org/10.1007/s00348-010-0873-5

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