Subsonic Wingsan introduction

and review

W.H. MasonConfiguration Aerodynamics Class

Topics

•  Subsonic Wing Calculation Method Review•  Aero of High Aspect Ratio Wings•  Slender Wings

VLM Methods – a way to get insight

•  Linear, inviscid aerodynamics – strictly subsonic

•  Ignores thickness – bc’s applied on the mean plane•  VLM is essentially a 3D thin airfoil theory

•  Finds ΔCp, not the upper/lower surface pressures

•  Very handy and accurate as seen below

•  Really good for understanding interacting surface ideas

Choices: VLMpc, Tornado, AVL, JKayVLM, XFLR5, VSPaero

First, review a great tool to understand wing aero

The classic method

Usually employs aflat wake to downstreaminfinity – a linear problem

• Each panel is modeled using a horseshoe vortex of as yet unknown strength (has bound and trailing vortex “legs”)• The Biot-Savart Law is used to compute the induced velocity at a control point due to the contributions from each horseshoe vortex•  Summing up the contributions from each horseshoe vortex and satisfying the boundary conditions leads to a linear system of algebraic equations for the unknown vortex strengths

Need to include the contributions from both sides of the wing!

To complete the method

•  The classical VLM method puts the bound vortex on the ¼ chord of the panel, and the control point is placed at the ¾ chord point

•  The boundary condition satisfies the angle of attack, the camber slope, and the wing twist. They are simply added up so that you can pick how to divide up the contributions. This is basically a bookkeeping problem.

•  Solving the linear system for the horseshoe vortex strengths is an analysis problem.

•  Using the same system, but specifying the vortex strengths you can find the required camber and twist, a design problem

•  Many variations have been used, lots of Refs in the text.

VLM Models and Tips

Convergence with number of “panels”

F/A-18

0

2

4

0 40 80 120 160 200 240Total number of panels

Vortex Lattice Method

(5) (9)( ) Number of chordwise panels

Δ Neutralpoint,

percent c

Panel Models

F-15 3-Surface VLM Model

Three-Surface F-15 Longitudinal Derivatives

Canard Height Effect

F-15 horizontal tail effectiveness

F-15 aileron effectiveness

Warren-12 Test Case

Note: CM about wing apex,Reference chord is 1.0

The key:Define it for others!

The reference trap wing

Source: Stinton, Design of the Airplane

Comment: Reference Area(s)

For More On Calculation Methods

http://www.cambridge.org/us/academic/subjects/engineering/aerospace-engineering/applied-computational-aerodynamics-modern-engineering-approach

Aerodynamics of High Aspect Ratio Wings

• Planforms

• Spanloads

• Pitching moment and pitchup

• Aerodynamic Center

• Isobars/Twist

• Camber

• 2D-3D connection

• Canard and Ground Effects

Typical Planform Characteristics ofTransport Aircraft

Clearly the A380 pays a price to satisfy the 80 meter gate box limit

6

7

8

9

10

11

12

1950 1960 1970 1980 1990 2000 2010

Aspect Ratio Trends - Commercial Transports

AR

Ist flight date

B787

A380B707-120

DC-8-10

B747-200B

B707-320C

L-1011

A300

DC-10-30

A310

B767

B747-400MD-11

A330

B777-200

A340-500

A330-300B777-300ER

Forward, Unswept and Aft Swept Planforms, AR = 2.8

Related Spanloads and Section Lift Coefficients

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.0 0.2 0.4 0.6 0.8 1.0y/(b/2)

Spanload,

Warren 12 planform, sweep changed

aft swept wing

unswept wing

forward swept wing

ccl / ca

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.0 0.2 0.4 0.6 0.8 1.0y/(b/2)

Section CL

Warren 12 planform, sweep changed

aft swept wing

unswept wing

forward swept wing

For an untwisted planar wing

Forward, Unswept and Aft Swept Planforms, AR = 8

Related Spanloads and Section Lift Coefficients

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0

Spanload,

y/(b/2)

Aspect ratio 8 wings

aft swept wing

unswept wingforward swept wing

ccl / ca

0.00

0.50

1.00

1.50

0.0 0.2 0.4 0.6 0.8 1.0

Section CL

Aspect ratio 8 planforms

aft swept wing

unswept wing

forward swept wing

y/(b/2)

For an untwisted planar wing

Example: VLM Pitching Moment agrees well with data until wing pitchup

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Cm

CL

AR = 10, Λc/4 = 35°, λ = 0.5data from NACA RM A50K27

Re = 10 million

x ref = c/4

VLMpc calculation

A confusion factor with modern wingsThe LE and TE are scheduled with Mach and AlphaFrom AIAA F-16 Case Study

Note – the curves don’t go to 0.25 at 0 deg sweep!

0.20

0.25

0.30

0.35

0.40

0.45

-40 -30 -20 -10 0.0 10 20 30 40

Aerodynamic Center Variation with Sweep

aero ctr,% mac

C/4 sweep, deg.

Vortex Lattice AnalysisNS = 25, NC = 8 (200 panels)

AR = 10,taper = 0.5

AR = 6,taper = 1/3

Low Aspect Ratio Wing Neutral Point (ac)For a rectangular wing it moves forward!

From Schlichting and Truckenbrodt,Aerodynamics of the Airplane

AR

Discovered while making pre-test estimates

Inboard Wing built/tested at VT

0.25

0.05

1 5 73

Isobars on untwisted/uncambered swept wing- needs aero design!

Note: this is actually a transonic case, M = 0.93, α = 2°from AFFDL-TR-77-122, February 1978.

These funny NACA report numbers denote series classified at the time, “L” stands for Langley, reports starting with “A” denote Ames

Without twist and camber: don’t get full effect of sweep

Now: DesignTypical Twist Distributions

- to improve isobars/spanloads -

-1.00.01.02.03.04.05.06.07.0

0 0.2 0.4 0.6 0.8 1

θ,deg.

y/(b/2)

-1.00.01.02.03.04.05.06.0

0 0.2 0.4 0.6 0.8 1

θ,deg.

y/(b/2)

Aft Swept Wing Forward Swept Wing

from LAMDES on the software website

A LAMDES artifact

Design Typical Camber Variation

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

(z-zle)/c

x/c

η = 0.925η = 0.475

η = 0.075

Cambers from the LAMDES code on the software website

Relating 2D and 3D

The airfoil problem is converted to 2D (normal), solved (designed), and put in the wing 3D

c2D = cs cosΛM 2D = M∞ cosΛ

t / c)2D = t / c)s / cosΛcL2D = cLn / cos

2 Λ

Now Canards Canard-Wing Interaction

canard wake extends to indinitywing wake not shown

A A

Canard wakestreams overwing

-2.0-1.5-1.0-0.50.00.51.01.5

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

w

Downwash from canard across wingat Section A-A

Upwash outboardof canard tips

Look at example from WT testingWing tested at NASA Langley, NASA TN D-7910 by Blair GlossSeveral combinations tested, we illustrate the outlined wing and canard

Note: all the test results are tabulated in the NASA TN

Canard Effects on Lift and Moment

NASA TN D-7910 by Blair Gloss

-0.50

0.00

0.50

1.00

1.50

-10 0 10 20 30 40 50

Canard Effect on LIft- minimal at low alpha -

CL

Alpha - deg.

Wing Alone

Wing - Canard

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

-10 0 10 20 30 40 50

Canard Effect on Pitching Moment- large effect on moment -

CM

Alpha - deg

Wing Alone

Wing - Canard

Example for Minimum Induced Drag Calculations

Sample case in John Lamar’s NASA TN with LAMDES

Canard Wing Induced Drag

0.0200

0.0250

0.0300

0.0350

0.0400

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

CDi

Δx/cForward Aft

Canard lift must benegative to trim

M = 0.3, CL = 0.5

Canard heightabove wing ,

0.1

0.2

z/b

0.3

Computations from LamDes

Advantage of verticalseparation clearly evident

Static Margin

Stable Unstable

Advantage of relaxedstatic stability evident

Note: The sample case may not be a good design, the canard is too big.

Typical Required Twist Distribution

-1.00.01.02.03.04.05.06.0

0.0 0.2 0.4 0.6 0.8 1.0

θ,

y/(b/2)

in presenceof canard

withoutcanard

canard tipvortex effect

deg.

-2.00.02.04.06.08.0

0.0 0.2 0.4 0.6 0.8 1.0

θ

y/(b/2)

withoutcanard

in presenceof canard

canard tipvortex effect

Aft Swept Wing Forward Swept Wing

Actual twist values are heavily dependent on the canard load!

Some Variations: Tip treatment

from Feifel, in NASA SP-405, 1976

A Whitcomb “winglet”

The “Raked Wingtip” used on the Boeing 767-400

from Kroo, Ann. Rev. of Fluid Mech., 2001

Rounding the intersection leads to a “blended winglet”

Note “Yehudi”

Ground Effects from VLM

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

CLα

h/c

AR4

2

1

Solid lines: computed using JKayVLMDashed lines: from Kalman, Rodden and GiesingSymbols: Experimental data

hU∞

c

c/4

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

CMα

h/c

Solid lines: computed using JKayVLMDashed lines: from Kalman, Rodden and Giesing

AR124

But ground effect can be complicatedA G650 crashed in New Mexico, April 2, 2011 – both pilots diedWhy? CLmax IGE can be less than CLmax OGE with flaps down

Data showed adverse flap effects for CLmax, NACA TN 705, 1939

IGE: In Ground Effect

OGE: Out of Ground Effect

A completely new category Slender Wings

See NASA CP 2416

Consider Two Entirely Different

Wing Concepts

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.0 2.0 4.0 6.0 8.0 10

Wings Transition from Slender Wing Theoryto High Aspect Ratio Wings with Airfoils

CLα-radians

Aspect Ratio

Slender WingTheory

2D lift curve slope

Finite Wing Lift Curve SlopeVariation with Aspect Ratio

Polhamus NACA TN 1862 (1949)also in Nicolai

Think of high aspect ratio wings as havingairfoils.Slender wings don’thave “airfoils” per say,Instead, think of spanwise sections.

High aspect ratio wings approach the 2π slopeThe slender wing slope is (π/2)AR

Laser Light Sheet Leading Edge Vortex Flow

Aviation Week & Space Technology, July 29, 1985

Light Sheet is a great way to see the LE vortex

Northrop IR & D example of flow over a delta wing configuration.

Exhibited at the 36th Paris air show.

Drawback?It’s “draggy” lift

Vortex Lift

https://www.youtube.com/watch?v=5_jt4x_TpOIThanks to James Stewart you can see a video of the flowfield:

The Polhamus LE Suction Analogy

Edward C. Polhamus,NASA TN D-3767

Another View of the Suction Analogy

R.M. Kulfan, Wing Geometry Effects on Leading Edge Vortices, AIAA 79-1872

Results of the Polhamus Suction Analogy

0.00

0.500

1.00

1.50

2.00

0.0° 10.0° 20.0° 30.0° 40.0°

CL

α

AR = 1.5 (Λ = 69.4°)

VortexLift

PotentialLift

Experimental data fromBartlett and Vidal

Prediction from PolhamusLeading Edge Suction Analogy

Reduce Drag with a Vortex Flap?The Concept

The reality?

Flight International, 16 March 1985

This concept was briefly popular, but it proved too hard to achieve.

Strakes are also low aspect ratio slender wings. Because they don’t stall, even low tail designs can have

a nose-down moment problem

F-16

ForebodyStrakes

Note: Eventually the horizontal tail size was increased 25%

Note: you can apply the LE Suction Analogy to the strake in VLMpc

This is a Hybrid Wing Concept

The Concorde Exploited Both Ground Effects and Vortex Lift to be Even Somewhat Practical

From Poisson-Quinton, Sustained Supersonic Cruise Aircraft Experience

VortexBurst

And VLM works for Hypersonic Class Concepts

Jimmy Pittman and James Dillon, “Vortex Lattice Prediction of Subsonic Aerodynamics of Hypersonic Vehicle Concepts,” Journal of Aircraft, October 1977, pp. 1017-1018.

To Conclude

This just gives you the very basics- no end to planform concepts, invent one yourself!