a review of research on unsteady airfoil behavior

8/2/2019 A Review of Research on Unsteady Airfoil Behavior

1/16

A REVIEW OF RESEARCH ON

UNSTEADY AIRFOIL BEHAVIOR

Term project for MAE 551

Airfoil Theory

Kiran Ramesh


2/16

Importance of Unsteady

Aerodyncamics The first attempts at flight focused on flapping wings.

The concept of separating lift and thrust generation led to fixed-wing

aircrafts.

While these have been successful for human-carrying flight, they are

unsuitable for flight at low reynolds numbers .

Ref 1


3/16

Low reynolds number flight has evoked a great deal of interest lately for

the development of micro air vehicles and to understand the mechanisms

of bird and insect flight.

Lockheed Martin

Micro Star

Problems faced by conventional aircraft at low Re regimes : Laminar separation bubbles

Difficulty in causing the flow to transition from laminar to turbulent

Inefficiency caused by inability to include large propellers, etc.


4/16

Advantages offered by flapping wings

Flapping flight results in angle of attack being changed constantly

Downwash caused by the vortices generated helps keep B.L attached.

High maneuverability - Since stall is prevented by effect of downwash,

high angles of attack are possible.


5/16

Flapping motion produces lift as well as thrust.

Eg. For a plunging motion, the net freestream velocity seen by the airfoil is as

shown below. The resultant force has lift and thrust components.

Though net lift over the plunging cycle would be zero, thrust would be a

positive value.

Though large aircrafts can use propellers for thrust, this would greatly improve

the performance for small aircrafts.

Fig from http://aa.nps.edu/programs/aero/propulsion/http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


6/16

Research in Unsteady Aerodynamics

Study in unsteady aerodynamics has primarily been motivated by research

in aeroelasticity to reduce/eliminate undesirable effects such as flutter

and gusts.

Theoretical models like theodorsens theory, indicial response etc. provide

a foundation on which unsteady aerodynamics modeling can be based.

The assumptions made in these theories however, are clearly violated at

low Re flows.

Computational modeling based on the Navier-Stokes equations, while

taking the low-Re effects into account is extremely expensive and is not

suitable for design purposes. Strip theory, vortex lattice methods, blade

element theory are some techniques used to create simpler models

Data collected from birds and insects are useful in understanding some of

the complexities involved.
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


7/16

Characteristics of an Unsteady Problem

Reduced Frequency Degree of unsteadiness

quasi-steady

unsteadydominated by unsteady effects

Reduced Time Relative Distance travelled by the airfoil through the flowin terms of airfoil semi-chords during a time t

Used in transient problems where relative freestream velocity cannot betaken to be a constant.
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


8/16

Quasi-Steady Thin airfoil Theory

Unsteady terms in governing equations are neglected.

Plunging/Pitching motion of the airfoil is taken into account by altering the

effective angle of attack and incorporating the effect of pitch rate.

Inviscid Solution

Does not take effect of shed wake into account

Does not take apparent mass into account
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


9/16

Theodorsens Theory

The airfoil and wake are represented by a sheet in the same plane.

The downwash on the airfoil surface caused by the wake is solved subject

to Kutta condition and conservation of circulation.

Apparent mass Effect
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


10/16

Theodorsens function affects the circulatory part of the lift in accordancewith the reduced frequency of the problem.

Inviscid solution, valid only for small perturbations.

Only applicable to harmonically oscillated airfoil.

Attached flow is assumed
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


11/16

Wagners Indicial Response

Can be used to solve for arbitrary changes in angle of attack.

Time-domain solution.

k is an ambiguous parameter. Reduced time takes nonsteady value of velocityinto account.

Lift starts at 50% and asymptotically approaches steady value due to shedvortex
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


12/16

Response to arbitrary loads are obtained through superposition of indicial

responses using the duhamel integral.

Circulatory part of lift coefficient for an arbitrary motion is given by,

Apparent mass contribution is proportional to instantaneous motion.

The above integral can be solved numerically using a recurrence method

or by integrating for simple forcing functions.
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


13/16

Challenges in unsteady aerodynamic

modelling Computational(Navier-Stokes Solvers) and Experimental approaches give

information about a particular scenario. However, this is not useful for

design purposes, theoretical models are required.

Though plenty of flapping flight data of birds and insects has beencollected and analyzed by biologists, zoologists these are usually quasi-

steady models developed for particular scenarios (Not generic)

Emulating bird flight has not been very successful because apart from then

numerous factors that complicate the aerodynamics, birds also extensivelyuse aerodynamic-structural interaction(aeroelasticity) to improve

efficiency.
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


14/16

Scope of Research

The thrust in research on unsteady low-re flows is currently being providedby the challenge of developing micro air vehicles

Ucal Berkeley MicroBat DelFly (TU Delft)
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


15/16

Theodorsen and Wagner theories are the stepping stones upon which

more generic theoretical models for unsteady flows are being developed.

Viscous effects which are important at low reynolds numbers have to beaccounted for.

Corrections have to be made to justify the assumptions made in these

theories(Such as co-planar wake, flat plate..)

If we are to try and emulate the flight of birds, these theories must be

extended to a flexible airfoil.

Since unsteady flows are among the least explored areas in aerodynamics,

it provides a rich field of research Hovering, perching, gust response etc.
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1


16/16

QUESTIONS ?

References :1. Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, edited by T. J.

Mueller

2. Leishman, J. G., Principles of Helicopter Aerodynamics, Vol. 12 of Cambridge Aerospace

Series, Cambridge Univ. Press, Cambridge, England, UK, 2000.

3. Katz, J. and Plotkin, A., Low-Speed Aerodynamics, Vol. 13 of Cambridge Aerospace Series,

Cambridge Univ. Press, Cambridge, England, UK, 2nd ed.
http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1http://aa.nps.edu/jones-cgi/animation.cgi?pwd=research/unsteady/panel_methods/anim1

a review of research on unsteady airfoil behavior

Documents