Tailoring wing structures for reduced drag penalty in off-design

flight conditions

Melih Papila Raphael T. HaftkaSabanci University, Turkey University of Florida

SPONSOR: NASA Langley Research Center

William H. MasonVirgina Tech.

Rafael AlvesInstituto Tecnologico de Aeronautica, Brasil

2

Motivation

Airplanes are prone to frequent deviations from cruise design condition during service life.

The wing of an airplane is not optimal with respect to induced drag at all flight conditions as the structural deformation and the effective twist change

The drag penalty for flight at off-design conditions can translate to thousands of gallons of jet fuel over the lifetime of an airplane.

3

Motivation-Analytical proof

Given a rigid wing planform

Assume minimum induced drag for two different lift coefficients (elliptic circulation or spanload) associated with two different angles of attack. )1()( )2()(

)1(LC

)2(LC

sin)1()1( A sin)2()2( A

)2()1(

Constant angle of incidence (no twist)

)2()1(

Elliptic circulation

Elliptic circulation

Constant angle of incidence, along the span (no twist) and elliptical circulation is only possible if the wing also has an elliptic chord distribution Elliptic circulation

Difference

4

Objectives

Demonstrate the effect of fixed geometric wing twist on induced drag due to change in flight conditions

Compare with a wing of variable twist as the flight condition changes

5

Outline

Motivation and objectives Example wing problem Approach Analysis models Results

for near elliptic distribution for straight-line wrapped surfaces

Concluding remarks and future work

6

Example: Airbus A380-like swept wing

Wing span, b (m) 79.8

Sweep at ¼ chord, 4/1 , (°) 34.7

Aspect ratio, AR 7.5

Root chord, rc (m) 16.3

Tip chord, tc (m) 4.9

Taper ratio, 0.3

Root geometric twist (°) 0

Flies at Mach 0.85

http://www.promotex.ca/articles/cawthon/2004/images/2004-02-01-2.jpg

y

x

cr

ctb/2

Λ1/4

7

Approach

Two cruise conditions at Mach 0.85 distinguished by two lift coefficients

Two optimal wings (minimum induced drag) associated with the cruise conditions Design condition – Optimal wing(1)

Off-design condition – Optimal wing(2)

Compare to Optimal wing(1) flying at off-design condition at different angle of attack

)1(LC

)2(LC

8

Approach Induced drag penalty for the

design condition optimal wing operating at the off-design condition

ARe

CC LDi

2

Compare drag coefficients and span

efficiencies

flight path

Optimal wing(1) incidence (design))1(LC

flight path

Non- optimal incidence (off-

design)

Adjust angle of attack

)2(LC

flight path

Optimal wing(2)

incidence (off-design)

)2()2( ,iD

Ce

)2(LC

min

)2()2(max ,

iDCe

9

Cruise scenarios

Two Cruise conditions at Mach 0.85(1) Design condition(2) Off-design condition

Scenario I Scenario II Lift coefficient,

)2(LC / )1(

LC

0.7

(0.42 / 0.6)

0.7

(0.42 / 0.6) Altitude (ft)

)2(h / )1(h

35,000 / 43,000

43,000 / 43,000

Cruise weight (kg), )2(W / )1(W

1

0.7

Aircraft on short hops for which the lower

flight altitudes may be required

Lower payload (fewer passengers)

10

Simplifications

Weight change during flight due to fuel consumption ignored

Assume level flight (ascent and descent ignored)

11

Analysis for induced drag penalty

Effect of fixed geometric wing twist on induced drag at different flight conditions reflected by span efficiency factor e.

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2

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Analysis for induced drag penalty

Aerodynamic model

MSC.NASTRAN static aeroelasticity solver for spanload (Doublet-Lattice subsonic lifting surface) 8x50 model, aerodynamic

pressure coefficients at the center of each box

)(

)()( 1

)(

j

N

iji

ijp

jl c

xcc

chord

av

jljjspan c

ccc

)()()(

Given spanload, LIDRAG (FORTRAN code from Virginia Tech) computes span efficiency e and total lift coefficient CL

Local lift-coefficient

Spanload

13

Rib Shear web

Spar Shear web

Skin panel

Rib caps

Spar caps

Analysis for induced drag penaltyStructural model

MSC.NASTRAN structural model Leading and trailing edge spars Fifteen equally spaced ribs

Upper and lower skins are assumed identical

Each bay has uniform thickness for structural optimization: 14 skin panel thicknesses variables.

Structural optimization: minimize weight under stress constraints (a load factor of 2.5 on the dynamic pressure and a safety factor of 1.5 on the stress allowable)

Young’s modulus, E (GPa) 70 Poison’s ratio, 0.33

Allowable stress, all (MPa) 489

Density, (kg/m3) 2769

Aluminum

140

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1eta

op

tim

al t

ot.

an

gle

of

inc

ide

nc

e (

de

gre

e)

des ign condition

off-des ign condition

Near elliptic distribution

Recall the goal: assess performance of optimal geometric wing twist at off-design condition.

Optimal total angle of incidence via Aerodynamic Analyses, LAMDES.

Total angle of incidence

flight path

)(tot

15

Induced drag penalty- Rigid wing

Near elliptic distribution

Design condition (1)

Optimal wing Off-design condition (2)

Optimal wing Off-design condition (2)

Non-optimal wing

Lift coefficient, LC )1(LC = 0.6

)2(LC = 0.42

)2(LC = 0.42

Span efficiency, e )1(maxe = 0.99736 )2(

maxe = 0.99738 )2(e = 0.99884

Induced drag

coefficient, iD

C

0.01539

0.00751

0.00749

Induced drag penalty

)2(max

)2()2(max

e

ee = -0.004

Attributed to LAMDES not finding true optimum or true elliptic spanload, but near optimal.

How the structural deformation will affect results?

ARe

CC LDi

2

16

Induced drag penalty- Elastic wing

Near elliptic distribution

Design (1)

Optimal wing Off-design (2)

Optimal wing Off-design (2)

Non-optimal wing Scenario I

Off-design (2) Non-optimal wing

Scenario II Lift coefficient,

LC

)1(

LC = 0.60

)2(

LC = 0.42

)2(

LC = 0.42

)2(

LC = 0.42

Span efficiency, e )1(

maxe = 0.99736

)2(

maxe = 0.99884

)2(e = 0.98912

)2(e = 0.97922

Induced drag

coefficient, iD

C

0.01539

0.00749

0.00758

0.00766

Induced drag penalty,

)2(max

)2()2(max

e

ee

0.01

0.02

~2 drag count (0.0002)

ARe

CC LDi

2

17

Induced drag penalty- Elastic wing Near elliptic distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

eta

span

load

optimal

Scenario II

Scenario I

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1eta

ang

le o

f in

cid

ence

optimal

Scenario II

Scenario I

Spanload Total angle of incidence

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Induced drag penalty- Rigid wing

Straight-line wrapped surfaces

Design condition (1)

Optimal wing Off-design condition (2)

Non-optimal wing Off-design condition (2)

Optimal wing Lift coefficient,

LC

)1(LC = 0.6 )2(

LC = 0.42 )2(LC = 0.42

Altitude,

h

)1(h = 43000 ft )2(h = 35000 ft )2(h = 35000 ft

Span efficiency, e )1(maxe = 0.99722 )2(e = 0.98937 )2(

maxe = 0.99755

Induced drag

coefficient, iD

C

0.015321 0.007567 0.007505

Induced drag penalty )2(

max

)2()2(max

e

ee = 0.008

ARe

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2

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Induced drag penalty- Elastic wing Straight-line wrapped

surfaces

Design (1)

Optimal wing Off-design (2)

Optimal wing Off-design (2)

Non-optimal wing Scenario I

Off-design (2) Non-optimal wing

Scenario II Lift coefficient,

LC

)1(

LC = 0.60

)2(

LC = 0.42

)2(

LC = 0.42

)2(

LC = 0.42

Span efficiency, e )1(

maxe = 0.99722

)2(

maxe = 0.99755

)2(e = 0.99728

)2(e = 0.99359

Induced drag

coefficient, iD

C

0.015321

0.00750

0.00751

0.00757

Induced drag penalty,

)2(max

)2()2(max

e

ee

0.0003

0.004

Penalty was 0.8 for rigid wing, Insensitive to structural deformation

ARe

CC LDi

2

20

Induced Drag Penalty- Elastic WingStraight-line wrapped surfaces

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

eta

span

load

optimal

Scenario II

Scenario I

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1eta

ang

le o

f in

cid

ence

optimal

Scenario II

Scenario I

Spanload Total angle of incidence

21

Cost penalty – Scenario INear elliptic distribution

Consider induced drag about 25% of total drag, then 0.25x0.01= 0.25% penalty on total drag

16.65 liter/km, then loss 16.65x0.0025= 0.04 liter/km

Max range 15000, cruise about 5000 km loss 200 liter/flight

Assume 300 flights/year, half flown at a lower altitude than the design altitude

30000 liter/year fuel loss

22

Two types of total angle of incidence distributions investigated at off-design condition at a lower lift coefficient than design lift coefficient.

For near elliptic spanload (near optimal wing with respect to induced drag) such changes resulted in about a two drag-count increase which may be sufficient to suggest tailoring the structure as the flight condition changes

The straight-line wrapped surfaces was found more effective at the off-design conditions if the wing was not tailored because it was insensitive to the structural deformation and the penalty level was lower.

Concluding Remarks

23

Work in progress

Study complete flight envelope, ascend, cruise and descend Optimize the wing structure so that the deformation provides near

optimal wing twist associated with the changing flight condition. Composite wing skin and treat fiber orientation(s) as design

variable