leading edge vortices in insect flight

LEADING EDGE VORTICES

IN INSECT FLIGHT

Introduction

Vortices that are formed on the leading edge of a

flapping insect wing.

Structure, evolution, stability and decay of such

vortices.

Why do we need to study them? Of what

consequence is insect flight to us?

Flight goes small, really small

Micro Air Vehicles

Unconventional methods

We have now a need for Micro Air Vehicles

(MAVs), that have a wing span of less than 15cm

and weigh less than 80g.

Conventional fixed wing configurations are just not

efficient enough at the low Re that these MAVs

operate at.

We need to look elsewhere.

Flapping Wings that we see in creatures of all

sizes!

The best biological analogs for MAVs- Insects

Biological Inspirations

Insect Flight-An Overview

• Insects are capable of unique flight patterns.

• Sustained hovering, slow flight and precise maneuvering.

• Complicated unsteady, three dimensional flow patterns.

• Difficult to analyze with the conventional laws of aerodynamics.

• They don‟t have streamlined wings.

• They have very high angles of attack, much higher than threshold values for stall.

Source: [2]

What lets them fly?

The source of lift in insects has now been identified as

the Leading Edge Vortex(LEV).

The high angles of attack causes flow separation at the

leading edge of the wing and generates a vortex.

This vortex creates the low pressure at the top of the

wing that generates the lift.

How stable is this vortex? How does it evolve? What is

the mechanism that supports it?

The Three Dimensional Leading Edge Vortex of

a „Hovering‟ model Hawkmoth

Coen Van Den Berg And Charles.

P. Ellington (1997)

Objectives

A 3-D flow visualization experiment using a scaled

up model of the hawkmoth wing- “The Flapper”.

Examined the LEV, its generation, evolution and

decay.

Examined the presence of an axial flow of the

vortex, that caused it to be spiral in shape with an

intrinsic helix angle.

Source: [1]

The Flapper

•Scaling factor – 9.6

•Forewing and hind wing that

can twist independently.

•Four degrees of freedom-

•Positional angle ϕ,

•Elevation angle θ,

•Angle of attack of the leading

section αle, and angle of attack

of the trailing section αt.

Image source: The three-dimensional leading-edge vortex of

a `hovering' model hawkmoth, Coen Van Den Berg and

Charles P. Ellington, Phil. Trans. R. Soc. Lond. B (1997) 352,

329±340.

Source: [1]

The experiment

Smoke (vaporized oil) is released from a smoke

rake built into the leading edge of the wing.

Flow cross sections were recorded at four

positional angles ϕ= (50, 30, 0 and -36) o.

For each angle, five span wise positions along the

wing were monitored: 0.25R, 0.50R, 0.63R, 0.75R

and 0.87R.

Source: [1]

Pictorial Representation of Flapper Action

Vortex size and position parameters

Image source: The three-dimensional leading-edge vortex of a `hovering' model hawkmoth, Coen

Van Den Berg and Charles P. Ellington, Phil. Trans. R. Soc. Lond. B (1997) 352, 329±340.

At different positional angles and different

spanwise positions along the wing

Results

General Observations

A clear LEV is seen with a strong axial flow

component.

During the first half of the stroke, ie., between

ϕ=510 and ϕ=00, the LEV was quite stable over the

major portion of the wingspan.

The LEV grew unstable near the tip of the wing

where it meets a large tip vortex.

A similar smaller LEV is present during the

upstroke as well.

No LEV observed at φ=50o

Source: [1]

Image source: The three-dimensional leading-edge vortex of a `hovering' model hawkmoth, Coen

Van Den Berg and Charles P. Ellington, Phil. Trans. R. Soc. Lond. B (1997) 352, 329±340.

At φ=30o

• Clear LEV present with axial flow component from base to tip.

• LEV moved away from the wing surface and chord wise back.

• Height of vortex increased from 1 cm at 0.5R to 3.5cm at 0.63R.

• Vortex was oval at 0.25R (w/h=1.4) and became circular (w/h=1) as it

moved towards the tip.

Image source: The three-dimensional leading-edge vortex of a `hovering' model hawkmoth, Coen Van Den Berg and Charles

P. Ellington, Phil. Trans. R. Soc. Lond. B (1997) 352, 329±340.

Source: [1]

At φ=0o

•The LEV had grown considerably by this time.

•At 0.25R its size was 1.5cm and at 0.75R it had grown to 7 cm.

•The shape of the LEV again showed the same progression from oval to circular.

•Between 0.25R and 0.63R, the LEV remained close to the surface.

•Separation started at that point and at 0.75R and 0.87R, the vortex moved away

rapidly.



Source: [1]

At φ=-36o

•Compared to the LEV at ϕ=0o, the vortex height had decreased by 10-20%

between 0.25R and 0.63R.

•The same change in shape from oval to circular was also visible.

•At 0.75R, the LEV had separated and moved towards the trailing edge and a new

vortex had formed close to the leading edge.



Source: [1]

Flow of the LEV from wing base to wing tip

provides stability

Axial Flow Velocity

Axial flow velocity(Va) variation

Mean value of Va= 31.8 cms-1

Large span-wise variation.

Increased evenly from 0.25R (21.9 cms-1) to 0.50R

(44.2 cms-1).

Pretty much the same between 0.50R and R with a

slight decrease related to vortex breakdown and

separation.

Source: [1]

Significance of Axial Flow

Axial flow adds an extra flow characteristic that

stabilizes the LEV.

Delays the separation of the LEV due to the

influence of the flow surrounding the wing.

First time that the axial velocity was detected as

this was the first 3D experiment.

Compare to Maxworthy(1979), Spedding and

Maxworthy(1986).

Source: [1]

How much lift does the LEV produce?

Circulation and Lift

Circulation of the LEV(C)

C=π.d.Vθ

„d‟ is the average of the vortex height and width.

As helix angle is 45o, we have Va=|Vθ|.

Hence Circulation is calculated for different span-

wise positions.

Source: [1]

Variation of Circulation

Quadrupled between 0.25R and 0.50R

Remained constant or decreased further down,

owing to vortex separation.

Increased at all span wise positions from φ=30o to

0o.

At φ=-36o, the circulation collapsed at 0.75R owing

to vortex separation.

Source: [1]

Circulation Vs. Spanwise Position



Lift

Sectional lift per unit span calculated using the

value for circulation of LEV, „C‟, gives the lift

contribution of the LEV.

Lift increased by a factor of eight from 0.25R to

0.50R and then stabilized.

Lift similar from φ=0o to φ=30o.

Lift much reduced at φ=-36o.

Source: [1]

Span-wise variation of Lift



Contribution of LEV lift

Oriented perpendicular to the wing surface.

Provides two-thirds of the lift required to lift the

hawkmoth.

This is only the lower limit of the lift!

Added to this, there will be boundary layer

circulation that provides the rest of the lift required

to make the insect hover.

Source: [1]

Rotational lift mechanisms or Dynamic Stall?

Mechanism of LEV Production

Mechanism of LEV Production

LEV generated during pronation and recaptured at the start of the downstroke.

Circulation of vortex will be pre established at the start of the downstroke.

Circulation at any spanwise position is proportional to the square of local chord at that point.

LEV generated during downstroke itself.

Circulation will start to grow at the beginning of the downstroke.

Circulation is proportional to the product of the distance from the wing base and the local chord at the point.

Rotational Lift Mechanism Dynamic Stall

Source: [1]

Conclusion

LEV provides two thirds of the required lift for the hawkmoth.

LEV stability is considerably improved by the axial flow component.

Even a marginal increase in LEV stability should greatly augment the lift coefficient.

An effective strategy for man made MAVs can be to increase LEV stability by increasing this axial flow component by utilizing span-wise blowing or suction.

References

1. The three-dimensional leading-edge vortex of a `hovering' model hawkmoth, Coen Van Den Berg and

Charles P. Ellington, Phil. Trans. R. Soc. Lond. B (1997) 352, 329±340.

2. Fixed and flapping wing aerodynamics for micro air vehicle applications, Progress in Astronautics and

Aeronautics, Volume 195, Edited by Thomas J.Mueller

3. Title slide image source: http://www.moorhen.me.uk/iodsubject/moths_02.htm:

20080616_d30_20010624_0943_696 elephant hawk-moth in flight with honeysuckle (web

crop)(r+mbid@576).jpg

4. Slide 9 image source: www.wikipedia.org-Manduca sexta adult female taken by Shawn Hanrahan at the

Texas A&M University Insect Collection in College Station, Texas.

5. Slide 10 image source: http://www.redorbit.com/images/pic/29827/hawk-moth-manduca-sexta-image-1/

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