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Near wake vortex dynamics of a hovering hawkmoth

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Abstract

Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wing-based micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventually break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time-varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.

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Abbreviations

a 0 :

acceleration (or deceleration) of the insect wing

c m :

mean wing chord length (reference length)

C x , C y , C z :

dimensionless force coefficients

C D :

dimensionless coefficient of horizontal (drag or thrust) force

C L :

dimensionless coefficient of vertical (lift) force

C S :

dimensionless coefficient of sideslip force

dt :

time increment

f :

flapping wing frequency

F aero :

aerodynamic force

\({{\pmb F}^{*}_{\rm aero}}\) :

dimensionless aerodynamic force

\({{\pmb F}^{*}_{{\rm aero},i}}\) :

dimensionless aerodynamic force of the cell (i)

i :

cell index

k = 2π f/ (2U ref):

reduced frequency

M m :

mass of flight muscle

n :

unit outward normal vector

O:

origin of earth-fixed Cartesian coordinates

O′:

origin of wingbase-fixed Cartesian coordinates

p :

pressure

\({P^{*}_{\rm aero}}\) :

dimensionless aerodynamic power

P aero :

muscle-mass-specific aerodynamic power

q :

flux vector with respect to pseudo-compressibility

q*:

communication vector in overlapping zones of the two grids

\({{\pmb r}_i^{*}}\) :

dimensionless positional vector of the cell (i)

R :

wing length

Re :

Reynolds number

S(t):

surface area of the control volume

S w :

planform area of a wing

t :

dimensionless time

T :

dimensionless period of one flapping cycle

\({{\pmb T}_{{\rm aero}}^\ast}\) :

dimensionless aerodynamic torques

T aero :

aerodynamic torques

u, v, w :

x, y, and z velocity components in the Cartesian coordinate system

U ref :

reference velocity at the wing tip

V(t):

volume of the control volume

V f :

velocity of the insect body

\({{\pmb v}^{\ast}_{i}}\) :

dimensionless velocity of the cell (i)

x, y, z :

wingbase-fixed Cartesian coordinates

X, Y, Z :

earth-fixed Cartesian coordinates

α :

feathering angle (or angle of attack of the wing)

β :

stroke plane angle

γ :

pseudo-compressibility coefficient

χ :

body angle

\({\Phi}\) :

wingbeat amplitude

θ :

elevation angle

\({\Phi}\) :

positional angle (or flapping angle)

\({\phi _{\rm cn}}\) , \({\phi _{\rm sn}}\) , θ cn, θ sn, α cn, α sn :

Fourier coefficients kinematic data of the flapping wing

ρ :

air density

τ :

pseudo time

ν :

kinematic viscosity of air

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Authors and Affiliations

  1. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Hikaru Aono & Wei Shyy

  2. Graduate School of Engineering, Chiba University, Chiba, 263-8522, Japan

    Hao Liu

Authors
  1. Hikaru Aono
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  2. Wei Shyy
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  3. Hao Liu
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Correspondence to Hikaru Aono.

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Aono, H., Shyy, W. & Liu, H. Near wake vortex dynamics of a hovering hawkmoth. Acta Mech Sin 25, 23–36 (2009). https://doi.org/10.1007/s10409-008-0210-x

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  • DOI: https://doi.org/10.1007/s10409-008-0210-x

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