Nonlinear and Time-Dependent Aerodynamics:

Implications for Testing and Flight Mechanics Analysis

Jerry E. JenkinsVoluntary Emeritus Corps

AFRL Wright-Patterson AFB, OH

The Delta Wing Model

Free-to-Roll Tests

• Instantaneous motion state insufficient

• Bypasses stable trim points

( , )

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing

AIAA-97-0742

• Free-to-Roll tests perplexing results– Aerodynamic responses at moderate angles of attack

• Not determined by instantaneous motion state • Highly dependent on motion history

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing

AIAA-97-0742

• Free-to-Roll tests perplexing results– Aerodynamic responses at moderate angles of attack

• Often not determined by instantaneous motion state • Highly dependent on motion history

• Viscous effects superimposed on potential flow– L. E. Vortex system structure – Vortex breakdown dynamics

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing

AIAA-97-0742

Flow Structure

• The steady-state flow-field can become unstable– At some flight conditions (Critical States)

– Bifurcations in static force and moment characteristics

0.020

0.010

Ro

llin

g-M

om

ent

Co

effi

cien

t

5

Critical StateRegion I

= 30 o

Side-slip Angle - deg4

Region II

Critical State

0.025

0.015

0.005

0.000

Critical State

10 15 20

3 5 6 7 8 9

Region III Region IV

Critical State

Roll Angle - deg

Critical States

Flow Structure & Bifurcations

Left Wing

25

20

15

10

5

0

-5

Leeward

W indward

Critical S tates

Ro

ll A

ng

le -

de

g.

?

Concentrated Vortex - Secondary and Tertiary Attached

Concentrated Vortex - Secondary Attached Tertiary Lifts O ff

Concentrated Vortex - Secondary & Tertiary L ift O ff

Breakdown over P lanformBurst Point M oves Tow ard T.E . w ith Increasing Roll Angle

Region I

Region II

25

20

15

10

5

0

-5

Leeward

W indward

Critical S tates

Ro

ll A

ng

le -

de

g.

?

Concentrated Vortex - Secondary and Tertiary Attached

Concentrated Vortex - Secondary Attached Tertiary Lifts O ff

Concentrated Vortex - Secondary & Tertiary L ift O ff

Breakdown over P lanformBurst Point M oves Tow ard T.E . w ith Increasing Roll Angle

Region I

Region II

Flow Structure & Bifurcations

Right Wing

25

20

15

10

5

0

-5

W indw ard

Leew ard

C ritical S tates

Ro

ll A

ng

le -

de

g.

?

R everse Flow - S ingle Lift-O ff of Sw irling Flow Forw ardSeperation at T.E ., Reattachm ent Point N ear W ingtip

R everse Flow - S ingle Lift-O ff Point for Sw irling FlowB reakdow n Near Apex

B reakdow n over P lanformB urst Point M oves Tow ard Apex w ith Increasing Roll Angle

R egion I

R egion II

25

20

15

10

5

0

-5

W indw ard

Leew ard

C ritical S tates

Ro

ll A

ng

le -

de

g.

?

R everse Flow - S ingle Lift-O ff of Sw irling Flow Forw ardSeperation at T.E ., Reattachm ent Point N ear W ingtip

R everse Flow - S ingle Lift-O ff Point for Sw irling FlowB reakdow n Near Apex

B reakdow n over P lanformB urst Point M oves Tow ard Apex w ith Increasing Roll Angle

R egion I

R egion II

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing

AIAA-97-0742

Flow Structure

• The steady-state flow-field can become unstable– At some flight conditions (Critical States)

– Bifurcations in static force and moment characteristics

• Must transition to a new stable state when perturbed– Can require a considerable amount of time

– Static tests give us no clue as to how long

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing

AIAA-97-0742

Flow Dynamics

• Flow processes acting on at least three time scales– Transitions between equilibrium states – Potential flow phenomena – Vortex breakdown movement in response to the motion

Ramp Across a Critical State65o Delta Wing

Critical StateEncounter

Critical StateEncounter

Attached and Vortical Flow Contributions

Ramp and Hold

Potential Flow

0.020

0.010

0.000

-0.010

Rol

ling-

Mom

ent C

oeff

icie

nt

Roll Angle - deg-10 -5 0 5 10

Critical StateCritical State

Region I

Region II

Critical State

= 30 o

Side-slip Angle - deg

-5 -4 -3 -2 -1 0 1 2 3 4 5

Can isolate CS transients including motion history

No Critical State Encounter No Critical State Encounter

Critical State EncounterCritical State Encounter

( )Deg.

( )Deg. ( )Deg.

( )Deg.

static static

staticstatic

f = 7.7 Hz

f = 7.7 Hzf = 7.7 Hz

f = 7.7 Hz

f = 1.1 Hzf = 1.1 Hz

f = 1.1 Hzf = 1.1 Hz

Rolli

ng M

omen

t Co

effic

ient

- Cl

Rolli

ng M

omen

t Co

effic

ient

- Cl

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

-6 -4 -2 0 42 6 -6 -4 -2 0 42 6

-3 -1 1 3 75 9 -3 -1 1 3 75 9

No Critical State Encounter No Critical State Encounter

Critical State EncounterCritical State Encounter

( )Deg.

( )Deg. ( )Deg.

( )Deg.

static static

staticstatic

f = 7.7 Hz

f = 7.7 Hzf = 7.7 Hz

f = 7.7 Hz

f = 1.1 Hzf = 1.1 Hz

f = 1.1 Hzf = 1.1 Hz

Rolli

ng M

omen

t Co

effic

ient

- Cl

Rolli

ng M

omen

t Co

effic

ient

- Cl

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

-6 -4 -2 0 42 6 -6 -4 -2 0 42 6

-3 -1 1 3 75 9 -3 -1 1 3 75 9

Harmonic Motion With and Without Critical State Encounters

Rolling Moment Pitching Moment

k = 0.02 & 0.14

Harmonic Motion With and Without Critical State Encounters

Rolling Moment Pitching Moment

k = 0.02 & 0.14

No Critical State Encounter No Critical State Encounter

Critical State EncounterCritical State Encounter

( )Deg.

( )Deg. ( )Deg.

( )Deg.

static static

staticstatic

f = 7.7 Hz

f = 7.7 Hzf = 7.7 Hz

f = 7.7 Hz

f = 1.1 Hzf = 1.1 Hz

f = 1.1 Hzf = 1.1 Hz

Rolli

ng M

omen

t Co

effic

ient

- Cl

Rolli

ng M

omen

t Co

effic

ient

- Cl

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

-6 -4 -2 0 42 6 -6 -4 -2 0 42 6

-3 -1 1 3 75 9 -3 -1 1 3 75 9

No Critical State Encounter No Critical State Encounter

Critical State EncounterCritical State Encounter

( )Deg.

( )Deg. ( )Deg.

( )Deg.

static static

staticstatic

f = 7.7 Hz

f = 7.7 Hzf = 7.7 Hz

f = 7.7 Hz

f = 1.1 Hzf = 1.1 Hz

f = 1.1 Hzf = 1.1 Hz

Rolli

ng M

omen

t Co

effic

ient

- Cl

Rolli

ng M

omen

t Co

effic

ient

- Cl

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

Pitc

hing

Mom

ent C

oeffi

cien

t -

Cm

-6 -4 -2 0 42 6 -6 -4 -2 0 42 6

-3 -1 1 3 75 9 -3 -1 1 3 75 9

Static Nonlinearities - AIAA 2004-5275

Region 1 2 3

4

Region 5

Multiple Time Scales in Linear RegionAIAA 2004-5275

• Slow responses cannot keep up with rapid motions

Broadband Input

• Allwine, et. al., “Nonlinear Modeling of Unsteady Aerodynamics at High Angle of Attack,” AIAA 2004-5275

Multiple Time Scales (F-16XL)AIAA 2001-4016

• Variation of in-phase & out-of-phase components

Lift-Curve slope

Lift due to pitch rate

Reduced freq.

Schroeder sweep

• Murphy, P.C., and Klein, V., “Estimation of Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Testing,”

AIAA 2001-4016

Langley Fighter Model

Roll-Damping “Derivative”AIAA-2004-5273

Nonlinear & Unsteady Aero Characteristics: Summary

• Free-to-Roll tests difficult to explain results– Aerodynamic responses at moderate angles of attack

• Often not determined by instantaneous motion state • Highly dependent on motion history

• Traced to leading edge vortex system dynamics– Vortex system structure – Vortex breakdown phenomenon

• Response characteristics not unique to delta wings– Static discontinuities, i.e. flow-field instabilities– Multiple time scales

Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint

• Unsteady Aero prescribed motion

• Flight Mechanics motion is unknown a priori – Stability and Control– Flight Control System Design

Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint

• Unsteady Aero prescribed motion

• Flight Mechanics motion is unknown a priori – Stability and Control– Flight Control System Design

• Small-amplitude dynamic data inadequate– Stability “derivatives” – Exhibit frequency and amplitude dependence – Powerless to describe the aerodynamics

Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint

• Unsteady Aero prescribed motion

• Flight Mechanics motion is unknown a priori – Stability and Control– Flight Control System Design

• Small-amplitude dynamic data inadequate– Stability “derivatives” – Exhibit frequency and amplitude dependence – Powerless to describe the aerodynamics

• Need math models for aerodynamics– Applicable to arbitrary motions– Functions of the translational and rotational DOF

Nonlinear & Unsteady Aero Characteristics:AIAA-97-0742

AIAA-2001-4016AIAA-2004-5273

• Results were for single DOF motions in wind tunnel

• Understanding requires that we – acknowledge the existence of multiple time scales – Consider the individual effects of translation and rotation – Include lags present in both responses

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached?

• Assumptions:– Square-Cube Law holds

Vehicle Inertia Variation with Mass

3sm f 5and yy sI f

Vehicle Weight Variation with Wing Area

32W S

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached?

• Assumptions:– Square-Cube Law holds

– Want to fly in similar CL range

• Conclusions:

32

s

s

e s

Wf

S

U f

R f

Wing- Loading

Flight Speed

Reynolds Number

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached?

• Assumptions:– Square-Cube Law holds

– Want to fly in similar CL range

– Hold non-dimensional derivatives constant

• i.e. ignore Re effects

• Conclusions:

sp

sp

1

2

sf

c

U

Short - period frequency (damping ratio unchanged)

Reduced frequency unchanged

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached?

• Consequences:– Magnitude of atmospheric disturbances do not scale

• Relative angular disturbances,

– Responses to disturbances up to not attenuated• Control system rates must increase

– Sensor sampling rates– Servo response times

– Aerodynamic effects• Convective time lags unaltered• Separated, vortex dominated flows ( low )

sp

1

sf

eR

Static Test Recommendations

• Closely spaced static data– Critical state detection

• Examine all components of the force and moment– Critical States are flow field events

• Make sweeps should in both directions – Hysteresis detection– Another indication of critical states

Dynamic Test Recommendations• Structure dynamic tests based on static test results

Dynamic Test Recommendations• Structure dynamic tests based on static test results

• Filtering (except anti-aliasing) should not be used– Ensemble averaging recommended

Dynamic Test Recommendations• Structure dynamic tests based on static test results

• Filtering (except anti-aliasing) should not be used– Ensemble averaging recommended

• Record the complete response– potential nonlinear effects -- Linearize off line

Dynamic Test Recommendations• Structure dynamic tests based on static test results

• Filtering (except anti-aliasing) should not be used– Ensemble averaging recommended

• Record the complete response– potential nonlinear effects -- Linearize off line

• Cover wide range reduced frequencies – Try to saturate the viscous effects – Extract both "static" and dynamic stability derivatives– Frequency dependence multiple time scales

Linear Aero Model from Broadband Data AIAA 2004-5275

• Linear system ID works quite well

Dynamic Test Recommendations• Structure dynamic tests based on static test results

• Filtering (except anti-aliasing) should not be used– Ensemble averaging recommended

• Record the complete response– potential nonlinear effects -- Linearize off line

• Cover wide range reduced frequencies – Try to saturate the viscous effects – Extract both "static" and dynamic stability derivatives– Frequency dependence multiple time scales

• Ramp and hold motions invaluable– Isolate critical state transients– Provide quantitative measures for response times– Examine history effects. – Consider other types of "motion and hold" experiments

Ramp-Between-Harmonics

Nonlinear Model Constructed from SSM’s AIAA 2004-5275

Nonlinear Model Constructed from SSM’s AIAA 2004-5275

Nonlinear Model Constructed from SSM’s AIAA 2004-5275