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Unsteady Aerodynamic Forces: Experiments, Simulations, and Models Steve Brunton & Clancy Rowley FAA/JUP Quarterly Meeting April 6, 2011 Wednesday, March 28, 2012
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Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

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Page 1: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Unsteady Aerodynamic Forces: Experiments, Simulations, and Models

Steve Brunton & Clancy RowleyFAA/JUP Quarterly Meeting

April 6, 2011Wednesday, March 28, 2012

Page 2: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

FLYIT Simulators, Inc.

Motivation

Predator (General Atomics)

Applications of Unsteady Models

Conventional UAVs (performance/robustness)

Micro air vehicles (MAVs)

Flow control, flight dynamic control

Autopilots / Flight simulators

Gust disturbance mitigation

Need for State-Space Models

Need models suitable for control

Combining with flight models

Daedalus Dakota

Wednesday, March 28, 2012

Page 3: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Flight Dynamic Control

flight dynamics

aerodynamics

coupled model

estimatorcontroller

reference trajectory,wind disturbances

deviation from desired path, or state

position,aerodynamic state

thrust, elevator, aileron, blowing/suction

Wednesday, March 28, 2012

Page 4: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Stall velocity and size

RQ-1 Predator (27 m/s stall)

Daedalus Dakota (18m/s stall)

Puma AE(10 m/s stall)

Smaller, lower stall velocity

Vstall =�

(CLmaxS)−1 W

S

W

L

CL

V

Wing surface area

Aircraft weight

Lift force

Lift coefficient

Velocity of aircraft

Wednesday, March 28, 2012

Page 5: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift vs. Angle of Attack

0 10 20 30 40 50 60 70 80 900.4

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Angle of Attack, (deg)

Lift

Coe

ffici

ent,

C L

Average Lift pre SheddingAverage Lift post SheddingMin/Max of Limit Cycle

Need model that captures lift due to moving airfoil!

Wednesday, March 28, 2012

Page 6: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift vs. Angle of Attack

0 10 20 30 40 50 60 70 80 900.4

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Angle of Attack, (deg)

Lift

Coe

ffici

ent,

C L

Average Lift pre SheddingAverage Lift post SheddingMin/Max of Limit CycleSinusoidal (f=.1,A=3)

Need model that captures lift due to moving airfoil!

Wednesday, March 28, 2012

Page 7: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift vs. Angle of Attack

0 10 20 30 40 50 60 70 80 900.4

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Angle of Attack, (deg)

Lift

Coe

ffici

ent,

C L

Average Lift pre SheddingAverage Lift post SheddingMin/Max of Limit CycleSinusoidal (f=.1,A=3)Canonical (a=11,A=10)

Need model that captures lift due to moving airfoil!

Wednesday, March 28, 2012

Page 8: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift

Drag

Re = 300

2D Model Problem

α = 32◦

Added-Mass

Periodic Vortex SheddingTransient

Wednesday, March 28, 2012

Page 9: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift

Drag

Re = 300

2D Model Problem

α = 32◦

Added-Mass

Periodic Vortex SheddingTransient

Wednesday, March 28, 2012

Page 10: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Reduced Order Indicial Response

+ CL

G(s)

!"#$%&$'(#)*+,+#))()+-#$$

.#$'+)*/#-%0$

CL!̈

CL!̇

s

CL!

s2

Brunton and Rowley, in preparation.

Model Summary

ODE model ideal for control design

Based on experiment, simulation or theory

Linearized about α = 0

Recovers stability derivatives associated with quasi-steady and added-mass

CLα , CLα̇ , CLα̈

quasi-steady and added-mass

Reduced-order model

input

fast dynamics

d

dt

xαα̇

=

Ar 0 00 0 10 0 0

xαα̇

+

Br

01

α̈

CL =�Cr CLα CLα̇

xαα̇

+ CLα̈ α̈

CL(t) = CSL(t)α(0) +

� t

0CS

L(t− τ)α̇(τ)dτ

Wednesday, March 28, 2012

Page 11: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift vs. Angle of Attack

0 10 20 30 40 50 60 70 80 900.4

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Angle of Attack, (deg)

Lift

Coe

ffici

ent,

C L

Average Lift pre SheddingAverage Lift post SheddingMin/Max of Limit Cycle

Models linearized at α = 0◦+ CL

G(s)

!"#$%&$'(#)*+,+#))()+-#$$

.#$'+)*/#-%0$

CL!̈

CL!̇

s

CL!

s2

Wednesday, March 28, 2012

Page 12: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

10 2 10 1 100 101 102

40

20

0

20

40

60

Mag

nitu

de (d

B)

10 2 10 1 100 101 102200

150

100

50

0

Frequency (rad U/c)

Phas

e (d

eg)

Indicial ResponseROM, r=3Wagner/TheodorsenDNSROM, r=3 (MIMO)

Bode Plot - Pitch (QC)

Frequency response

Reduced order model with ERA r=3 accurately reproduces Indicial Response

Indicial Response and ROM agree better with DNS than Theodorsen’s model.

output is lift coefficient CL

input is ( is angle of attack)α̈ α

Brunton and Rowley, in preparation.

Pitching at quarter chord

Asymptotes are correct for Indicial Response because it is based on experiment

Model for pitch/plunge dynamics [ERA, r=3 (MIMO)] works as well, for the same order model

Quarter-Chord Pitching

Wednesday, March 28, 2012

Page 13: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Lift vs. Angle of Attack

0 10 20 30 40 50 60 70 80 900.4

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Angle of Attack, (deg)

Lift

Coe

ffici

ent,

C L

Average Lift pre SheddingAverage Lift post SheddingMin/Max of Limit Cycle

Models linearized at α = 0◦+ CL

G(s)

!"#$%&$'(#)*+,+#))()+-#$$

.#$'+)*/#-%0$

CL!̈

CL!̇

s

CL!

s2

Wednesday, March 28, 2012

Page 14: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

10−2 10−1 100 101 102−40

−20

0

20

40

60Frequency Response Linearized at various !

Mag

nitu

de (d

B)

ERA, !=0DNS, !=0ERA, !=10DNS, !=10ERA, !=20DNS, !=20

10−2 10−1 100 101 102−200

−150

−100

−50

0

Frequency

Phas

e

Bode Plot of Model (-) vs Data (x)

Direct numerical simulation confirms that local linearized models are accurate for small amplitude sinusoidal maneuvers

Brunton and Rowley, AIAA ASM 2011Wednesday, March 28, 2012

Page 15: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

PLANTuk u(t) yky(t)

u

�u

Time

A

T

0

0

(Indicial) Step Response

Previously, models are based on aerodynamic step response

Idea: Have pilot fly aircraft around for 5-10 minutes, back out the Markov parameters, and construct ERA model.

Wednesday, March 28, 2012

Page 16: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

CL(t)

!

Random Input Maneuver

Idea: Have pilot fly aircraft around for 5-10 minutes, back out the Markov parameters, and construct ERA model.

Wednesday, March 28, 2012

Page 17: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Wind Tunnel Setup

NACA 0006 Airfoil (24.6 cm chord)

Push rods and sting

Test section

Servo tubes

Wednesday, March 28, 2012

Page 18: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Experimental Information

Free Stream Velocity: 4.00 m/s

Chord Length: 0.246 m

Reynolds Number: 65,000

1.0 Convection time = .06 seconds

Force measurement: ATI Nano25 force transducer

Velocity measurement: Pitot tube, Validyne DP-103 pressure transducer

NACA 0006 Airfoil

Pitch point x/c = .11 (11% chord)

Pushrod position measurement: linear potentiometer

Pushrod actuation: Copley servo tubes

Andrew Fejer Unsteady Flow Wind Tunnel(.6m x .6m x 3.5m test section)

Acknowledgments: Professor David Williams

Seth Buntain and Vien Quatch

Wednesday, March 28, 2012

Page 19: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

0 500 1000 1500 2000 2500 3000 3500 40002

1.5

1

0.5

0

0.5

1

1.5

Convective Time

Phase Averaged Data

940 950 960 970 980 990

1

0.5

0

0.5

1

0 10 20 30 40 50 60 70 80

!0.4

!0.2

0

0.2

0.4

0.6

0.8

1

1.2

Convective Time

Norm

al F

orc

e (

N)

Step!Up, Step!Down, 5 degrees

Phase averaged over 200 cycles

Wednesday, March 28, 2012

Page 20: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

0 10 20 30 40 50 60 70 80 90!10

!8

!6

!4

!2

0

2

4

6

8

10

Convective Times (s=tU/c)

Angle

(degre

es)

Commanded Angle

Measured Angle

Wing Maneuver

Wednesday, March 28, 2012

Page 21: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

What are we modeling?

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured Force

ROM, r=3

Model using command acceleration

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured Force

ROM, r=3

Model using measured acceleration

Wednesday, March 28, 2012

Page 22: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

What are we modeling?

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured Force

ROM, r=3

Model using command acceleration

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured Force

ROM, r=3

Model using measured acceleration

!cmnd !pot CLAerodynamicsActuator

our model

Simulink!pos

Wednesday, March 28, 2012

Page 23: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured ForceROM, r=3

Four Test Maneuvers

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Angle

(degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured ForceROM, r=3

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured Force

ROM, r=3

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Angle

(degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Measured ForceROM, r=3

Maneuver 1 Maneuver 2

Maneuver 3 Maneuver 4

Wednesday, March 28, 2012

Page 24: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

10!2

10!1

100

101

102

103

!60

!40

!20

0

20

40

60M

agnitu

de (

dB

)

10!2

10!1

100

101

102

103

!150

!100

!50

0

Frequency (rad/s ! c/U)

Phase

(degre

es)

maneuver 1

maneuver 2

maneuver 3

maneuver 4

Bode Plots for AoA=0

Model using measured acceleration

Idea: lets combine all maneuvers into one large system ID maneuver!

Wednesday, March 28, 2012

Page 25: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

−40−20

020406080

Mag

nitu

de (d

B)

10−2 10−1 100 101 102−180−135−90−45

045

Phas

e (d

eg)

Bode Diagram

Frequency (rad/sec)

0 50 100 150 200 250 300 350 400 450−10

0

10An

gle

(deg

rees

)

0 50 100 150 200 250 300 350 400 450

−2

−1

0

1

2

3

Convective time

Nor

mal

For

ce (N

)

Measured ForceROM, r=3

Bode Plot for AoA=0

Resonant peak

Added-mass “bump”

Wednesday, March 28, 2012

Page 26: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

CL!

CL!̇

CL!̈{{

Hi from OKIDHi ! !CL!

Hi ! !CL! ! CL!̇

Impulse response in α̈

0 5 10 15

0

0.05

0.1

0.15

0.2

Mar

kov

para

met

er

Convective time

Model using ALL data

0 50 100 150 200 250 300 350 400 450−10

0

10An

gle

(deg

rees

)

0 50 100 150 200 250 300 350 400 450

−2

−1

0

1

2

3

Convective time

Nor

mal

For

ce (N

)

Measured ForceROM, r=3

Theory Experimental

Wednesday, March 28, 2012

Page 27: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

0 10 20 30 40 50 60 70 80

!0.4

!0.2

0

0.2

0.4

0.6

0.8

1

1.2

Convective Time

Norm

al F

orc

e (

N)

Step!Up, Step!Down, 5 degrees

30Hz Mechanical Oscillation

Wednesday, March 28, 2012

Page 28: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Angle

(degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Experiment 4

Model 1

Model 2

Model 3

Model 4

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Angle

(degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Experiment 3

Model 1

Model 2

Model 3

Model 4

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Experiment 2

Model 1

Model 2

Model 3

Model 4

0 10 20 30 40 50 60 70 80 90 100!10

0

10

Ang

le (

degre

es)

0 10 20 30 40 50 60 70 80 90 100

!2

!1

0

1

2

3

Convective time

Norm

al F

orc

e (

N)

Experiment 1

Model 1

Model 2

Model 3

Model 4

Models agree with data

Wednesday, March 28, 2012

Page 29: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

0 10 20 30 40 50 60 70 80 90

−2

0

2

Verti

cal P

ositi

on (i

nche

s)

0 10 20 30 40 50 60 70 80 90

−2

−1

0

1

2

3

Convective time

Nor

mal

For

ce (N

)

Measured ForceROM, r=3

Model for Plunging

−20

0

20

40

60

Mag

nitu

de (d

B)

10−2 10−1 100 101 1020

45

90

135

180

Phas

e (d

eg)

Bode Diagram

Frequency (rad/sec)

Wednesday, March 28, 2012

Page 30: Unsteady Aerodynamic Forces: Experiments, Simulations, …faculty.washington.edu/sbrunton/talks/JUP_2011_04_06_Princeton.pdfUnsteady Aerodynamic Forces: Experiments, Simulations, and

Conclusions

Reduced order model based on indicial response at non-zero angle of attack

- Based on eigensystem realization algorithm (ERA)- Models appear to capture dynamics up to Hopf bifurcation

Observer/Kalman Filter Identification with more realistic input/output data

- Efficient computation of reduced-order models- Ideal for simulation or experimental data

Brunton and Rowley, AIAA ASM 2009-2011

OL, Altman, Eldredge, Garmann, and Lian, 2010

Leishman, 2006.

Wagner, 1925.

Theodorsen, 1935.

Confirmation with experimental data- Tested modeling procedure in Dave Williams’ wind tunnel experiment- Flexible procedure works with various geometry, Reynolds number

Juang, Phan, Horta, Longman, 1991.

Juang and Pappa, 1985.

Ma, Ahuja, Rowley, 2010.

Wednesday, March 28, 2012