Aerodynamics of Flapping Flight

Aerodynamics of Flapping Flight

Kiran RameshApplied Aerodynamics Lab - NCSU

Kiran RameshApplied Aerodynamics Lab - NCSU

Early Attempts at FlightAimed to mimic birds.

Used flapping wings (Ornithopters)

Shown beside - Flapping flyers developed around the early 20th century (Source : Wikipedia)

E.P.Frost’s 1902 Ornithopter

Otto Lilienthal’s kleiner Schlagflügelapparat(1894)

Reasons for Failure

Flapping wings - Couldn’t sustain sufficient lift and thrust.

Fixed-wing aircraft - Independent lift and thrust generation

Forces on an aircraftSource : NASA

Learning from NatureLarge Birds

Large aspect ratio wings

Predominantly glide

Small Birds and Insects

Small aspect ratio wings

Flap more vigorously with decreasing size Source: natures-desktop-hd.com

Micro Air VehiclesReynolds number between 10,000 and 10,0000

Wingspan < 15cm

Capabilities:

Handling gusts

Maneuverability

Landing, perching, hovering

Existing MAVsWasp

(Aerovironment) Micro Star

(Lockheed Martin)

Hummingbird (Aerovironment)

Delfly(TU Delft)

Microrobotic Fly (Harvard)

Advantages of Flapping

Downwash by TE vortices helps keep boundary-layer attached

This prevents stall, high AoA and maneuverability are possible

Lift + Thrust can be generated

Typical unsteady flows

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Plunging motionSmall amplitude

Small LEV formation

Pitching motionLarge amplitude

Massively Separated flow

Challenges in using flapping flyers

Unsteady aerodynamics not well understood

Apparent-mass effects

Complicated wake structure

Leading edge vortices / Massive separation

Thin-Airfoil Theory

Solves the problem of airfoil at an angle of attack

Airfoil is approximated as a camberline

Vorticity distribution taken to be a Fourier series

aerospaceweb.org

www.desktop.aero/appliedaero

SolutionU - Freestream velocity, - chordwise location

Fourier Series:

Boundary Conditions:

Kutta Condition

No normal flow through airfoil

Solution for symmetric airfoil :

γ(θ ) = 2U A01+ cosθ

sinθ+ An sinnθ∑⎛

⎝⎜⎞⎠⎟

θ

A0 =αCl =2πA0

Unsteady Thin-Airfoil Theory

Built upon Katz and Plotkin’s method.

Airfoil is free to move arbitrarily in pitch and plunge

Trailing edge vortex shed at every time-step

Fourier Series:

Same boundary conditions

Downwash on airfoil:

Velocity induced by wake:

γ(θ , t) = 2U(t) A0 (t)1+ cosθ

sinθ+ An (t)sinnθn=1

∞

∑⎛⎝⎜

⎞⎠⎟

W (x, t)=

∂η∂x

U cosα + &hsinα( )−U sinα − &α(x−ac) + &hcosα −wi

wi = −Γwk

2π∑ x−xk

(x−xk)2 + (z−zk)

2 cosα +Γwk

2π∑ z−zk

(x−xk)2 + (z−zk)

2 sinα

Iteration to find the strength of shed vortex

Fourier Coefficients:

Airfoil’s Bound Vorticity:

Kelvin’s condition: Total vorticity in Field =0

An (t)=1π

W(x,t)U(t)

cosnθ dθ0

π

∫

Γ(t) =U(t)cπ A0 (t) +A1(t)

2⎛⎝⎜

⎞⎠⎟

Γ(t) + Γ k = 0∑

Solution obtained using iteration (Such that Kelvin’s condition is satisfied)

Forces - Normal, Suction

J Exp BiolDecember 2003vol. 206 no. 23 4191-4208

CN =2π cosα +

&hU

sinα⎛

⎝⎜⎞

⎠⎟A0 +

A1

2⎛⎝⎜

⎞⎠⎟+

cU 2

3U4

&A0 +U4

&A1 +U8

&A2⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

CS =2πA02

Results0-45-0 Pitch Ramp Hold motion

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Lift Coefficient Comparison

Predicting LEV formation

Leading Edge Separation - Caused by adverse pressure gradient at the leading edge

Velocity at the leading edge is directly related to the suction peak

Leading Edge Suction Parameter

We define LESP as - Nondimensional velocity at the leading edge.

For a thin airfoil:

LESP is derived as:

Hypothesis - For a given airfoil and Reynolds number, LE separation occurs at the same LESP

VLE (t)=12

limx−>LE

γ(x,t) x

LESP(t)=A0 (t)

Example

Modeling LEVs using LESP

Discrete vortices shed from leading edge when LESP > LESPcrit

Positions of vortices determined in accordance with velocity at LE

Strengths of LEV’s calculated such that the LESP is brought back to LESPcrit

0-45-0 Pitch Ramp Hold

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0-25-0 Pitch Ramp Hold

0-90 Pitch-up motion

Sinusoidal Plunging motion

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Applications

Other applications of this research include:

Rotorcraft aerodynamics

Wind turbines

Investigating possibility of larger aircraft employing flapping wings

Questions?

Project Collaborators:

Jianghua Ke and Dr.Jack Edwards, NCSU (CFD)

Dr.Michael Ol and Dr.Kenneth Granlund, AFRL (EXP)

Thank you MAE GSA!