Some Transonic Aerodynamics

W.H. Mason

Configuration Aerodynamics Class

Transonic Aerodynamics History

• Pre WWII Prop speeds limited airplane speed– Props did encounter transonic losses

• WWII Fighters started to encounter transonic effects

– Dive speeds revealed loss of control/Mach “tuck”

• Invention of the Jet engine revolutionized airplane design

• Supersonic flow occurred over the wing at cruise

• Aerodynamics couldn’t be predicted, so was mysterious!

– Wind tunnels didn’t produce good data

– Flow was inherently nonlinear, and there were no methods

The P-38, and X-1 reveal transonic control problems/solutions

Airfoil Example: Transonic Characteristics

• From classical 6 series results

Subsonic design pressures

Lift

From NACA TN 1396, by Donald Graham, Aug. 1947

Drag

From NACA TN 1396, by Donald Graham, Aug. 1947

Pitching Moment: a major problem!

From NACA TN 1396, by Donald Graham, Aug. 1947

What’s going on?The flow development illustration

From Aerodynamics for Naval Aviators by Hurt

Addressing the WT Problem

• The tunnels would choke, shocks reflected from walls!

• Initial solutions:

– Bumps on the tunnel floor

– Test on an airplane wing in flight

– Rocket and free-fall tests

• At Langley (1946-1948):

– Make the tunnel walls porous: slots

– John Stack and co-workers: the Collier Trophy

• Later at AEDC, Tullahoma, TN:

– Walls with holes!

Wall interference is still an issue - corrections and uncertainty

Slotted Tunnel

Grumman blow-down pilot of Langley tunnel

Porous Wall

The AEDC 4T, Tullahoma, TN

Solving the Theoretical Computational Problem

• Despite lots of effort: no practical theory

• Numerical methods: from about 1970

– Practical inviscid methods about 1971-1980 till today

• Transonic Small Disturbance Theory (inviscid)

– TSFOIL2 - available on our software site

– Inviscid -viscous interaction methods

• So called “Full Potential Theory” (inviscid)

• Euler Equations (inviscid)

• Reynolds Averaged Navier-Stokes (RANS) viscous

Computational Transonics: the birth of CFD

• Earll Murman and Julian Cole simply try aninnovative and entirely new approach– Use the Transonic Small Disturbance Equation

• Model problem assumes flow is primarily in the x-direction• Nonlinearity allows math type to change locally

1 M 2+1( )M 2

x

>0 locally subsonic, elliptic PDE<0 locally supersonic, hyperbolic PDE

xx + yy = 0

The Murman-Cole Idea

• Replace the PDE with finite difference formulas for the derivatives - a so-called finite difference representation of the PDE

• Make a grid of the flowfield: at each grid point, write down the algebraicequation representation of the PDE

• Solve the resulting system of simultaneous nonlinear algebraic equations usingan iterative process (SOR, SLOR, etc.)

• The new part!– At each grid point, test to see if the flow is locally subsonic or supersonic

– If locally subsonic, represent the xx with a central difference

– Is locally supersonic, represent xx with an “upwind” difference

• The result– The numerical model represents the essential physics of the flow

– If there are shocks, they emerge during the solution (are captured)

– Agrees with experimental data somewhat (and possibly fortuitously)

A few more details

For a few more details, read Chapter 8, Introduction to CFD, on myApplied Computational Aerodynamics web page:http://www.aoe.vt.edu/~mason/Mason_f/CAtxtTop.html

y or "j"

x or "i"

Assume:

x = y = const.x = i xy = j x

i,j i+1,j

i,j-1

i-1,j

i,j+1

i-2,j

xx =i+1, j 2 i, j + i 1, j

x( )2 +O x( )

2

xx =i, j 2 i 1, j + i 2, j

x( )2 +O x( )

For subsonic flow:

For supersonic flow:

Using thisnotationfor the grid:

Flow Direction

One convergence check in CFD

10-4

10-3

10-2

10-1

100

101

102

103

0 100 200 300 400 500 600

• 5% Thick Biconvex Airfoil• 74 x 24 grid• SOR =1.80• AF 2 factor: 1.333

MaximumResidual

Iteration

SOR

AF2

• “Residual” is the sum of the terms in the PDE: should be zero• Note log scale for residual• Two iterative methods compared• This is for a specific grid, also need to check with grid refinement

CFD Grids

Michael Henry, “Two-Dimensional Shock Sensitivity Analysis forTransonic Airfoils with Leading-Edge and Trailing-Edge DeviceDeflections" MS Thesis, Virginia Tech, August 2001, W.H. Mason, Adviser

Most of the work applying CFD is grid generation

Today• CFD has been developed way past this snapshot

• For steady solutions we iterate in time, until a steady statevalue is obtained

– the problem is always hyperbolic in time!

• Key issues you need to understand– Implementing boundary conditions– Solution stability– Discretization error– Types of grids and related issues– Turbulence models

A possible reference, Computational Fluid Mechanics andHeat Transfer, 2nd Ed., by Tannehill, Anderson and PletcherTaylor and Francis, 1997.

Can now use computational simulations asa numerical wind tunnel

• Especially in 2D, many codes include grid generation, and canbe used to investigate airfoil characteristics and modifications

– Remember adding “bumps” to the subsonic airfoil?

• TSFOIL2 is an available and free transonic code, the nextchart illustrates its accuracy

• FLO36 was the ultimate full potential code

– By Antony Jameson, a key contributor to CFD for manyyears, and should have been mentioned earlier.

• MSES is the key Euler/Interacting BL code– By Prof. Drela, also author of XFOIL and AVL

Comparison of inviscid flow model predictions- Airfoils -

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.00.0 0.2 0.4 0.6 0.8 1.0

Cp-upper (TSFOIL2)Cp-lower (TSFOIL2)CP (FLO36)Cp (MSES)Cp crit

Cp

X/C

NACA 0012 airfoil, M = 0.75, = 2°

Euler Eqn. Sol'n.

Full potential eqn. sol'n

Transonic small disturnbancetheory eqn. sol'n.

Cp critical

REVIEW: Obtaining CFD solutions

• Grid generation

• Flow solver– Typically solving 100,000s (or millions in 3D)

of simultaneous nonlinear algebraic equations

– An iterative procedure is required, and it’s noteven guaranteed to converge!

– Requires more attention and skill than lineartheory methods

• Flow visualization to examine the results

Mach number effects: NACA 0012

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.50.0 0.2 0.4 0.6 0.8 1.0

CP(M=0.50)CP(M=0.70)CP(M=0.75)

Cp

X/C

NACA 0012 airfoil, FLO36 solution, = 2°

M=0.50

M=0.70M=0.75

Angle of attack effects: NACA 0012

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.500.00 0.20 0.40 0.60 0.80 1.00

CP( = 0°)

CP( = 1°)

CP( = 2°)

Cp

x/c

FLO36NACA 0012 airfoil, M = 0.75

“Traditional” NACA 6-series airfoil

-0.10

0.00

0.10

0.20

0.00 0.20 0.40 0.60 0.80 1.00

y/c

x/c

Note small leading edge radius

Note continuous curvature all along the upper surface

Note low amount of aft camber

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.500.00 0.20 0.40 0.60 0.80 1.00

Cp

x/c

FLO36 prediction (inviscid)M = 0.72, = 0°, C

L= 0.665

Note strong shock

Note that flow accelerates continuously into the shock

Note the low aft loading associated with absence of aft camber.

A new airfoil concept - from Whitcomb

Progression of the Supercritical airfoil shapeNASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990

1964

1966

1968

What the supercritical concept achieved

From NASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990

Section drag at CN = 0.65Force limit for onset of upper-surface boundary layer separation

And the Pitching Moment

How Supercritical Foils are Different

From NASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990

“Supercritical” Airfoils

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.00 0.20 0.40 0.60 0.80 1.00

y/c

x/c

Note low curvatureall along the upper surface

Note large leading edge radius

Note large amount of aft camber

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.500.00 0.20 0.40 0.60 0.80 1.00

x/c

Cp

FLO36 prediction (inviscid)M = 0.73, = 0°, C

L= 1.04

Note weak shockNote that the pressuredistribution is "filled out", providing much more lift even though shock is weaker

Note the high aft loading associated with aft camber.

"Noisy" pressure distribution is associated with "noisy" ordinates, typical of NASA supercritical ordinate values

Whitcomb’s Four Design Guidelines

• An off-design criteria: a well behaved sonicplateau at M = 0.025 below the design M

• Gradient of pressure recovery gradual enough toavoid separation– in part: a thick TE, say 0.7% on a 10/11% thick foil

• Airfoil has aft camber so that design angle ofattack is about zero, upper surface not sloped aft

• Gradually decreasing velocity in the supercriticalregion, resulting in a weak shock

Read “NASA Supercritical Airfoils,” by Charles D. Harris,NASA TP 2969, March 1990, for the complete story

Example: Airfoils 31 and 33

The following charts are from the 1978 NASA Airfoil Conference,w/Mason’s notes scribbled as Whitcomb spoke (rapidly)

Airfoils 31 and 33

Off Design

Foils 31 and 33 Drag

NASA Airfoils Developed Using the Guidelines

NASA Airfoil Catalog

Note: watch out for coordinates tabulated in NASA TP 2969!

Frank Lynch’s Pro/Con Chartfor supercritical airfoils

Airfoil Limits: the Korn Eqn.

• We have a “rule of thumb” to let us estimate whatperformance we can achieve before drag divergence

– By Dave Korn at NYU in the 70s

MDD +CL

10+

t

c= A

A = 0.87 for conventional airfoils (6 series)

A = 0.95 for supercritical airfoils

Note: the equation is sensitive to A

Airfoil LimitsShevell and NASA Projections Compared

to the Korn Equation

0.65

0.70

0.75

0.80

0.85

0.90

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18t/c

MDD

Shevell advanced transonicairfoil estimate

Korn equation, A = .95

Korn equation, A = .87

Shevell estimate,mid 70's transportairfoil performance

0.65

0.70

0.75

0.80

0.85

0.90

0.02 0.06 0.10 0.14 0.18t/c

MDD C

L0.4

0.7

1.0NASA projectionKorn equation estimate,

A = .95

In W.H. Mason, “Analytic Models for Technology Integration inAircraft Design,” AIAA Paper 90-3262, September 1990.

For the curious: the airfoil used on the X-29

Just when we thoughtairfoil design was

“finished”

Used on the MD-11resisted in Seattle!

Take a Look atthe PressureDistribution

Comparison of theDLBA243 and theDLBA 186 CalculatedPressure Distributionat M = 0.74

Wings

The original DC-8 reflectionplane model, in the VT WT Lab

An advanced Douglas transportWT Model, also in the VT WT Lab

The original model carved by George Shairer

picture taken by Mason at the Museum of Flight, Seattle, WA

Picture of B-52 made in Dayton Hotel over a weekend by Boeing engineers

The problemof transonic

wingdesign

The Standard Transonic Test Case:the ONERA M6 Wing

A standard way to lookat your results

The wing is symmetrical withno twist: note the unsweep ofthe shock and the build up ofthe pressure peak at the tip

y/(b/2)= 0.655 y/(b/2)= 0.800

W.H. Mason, D.A. MacKenzie, M.A. Stern, W.F Ballhaus Jr., and J. Frick, “Automated Procedure for Computing theThree-Dimensional Transonic Flow Over Wing-Body Combinations, including Viscous Effects,” AFFDL-TR-77-122,February 1978.

Comparison: computations to data for the ONERA M6

Ways to use Advanced AerodynamicsFrank Lynch’s Wing Chart

Korn Eqn and Simple Sweep Theory- a sort of Poor Man’s method (no CFD) -

Mdd =A

cos

t / c( )

cos2cl

10cos3

CD = 20 M - Mcrit4

Mcrit = Mdd - 0.1801/3

Extend Korn to swept wings using simple sweep theory

so that we find Mcrit:

CDM= 0.1 CD

M= 0.1 = 80 M - Mcrit

3where using: ,

and then use Lock’s approximation:

Transonic Drag Rise Estimate: B747

747-100 test data taken from Mair and Birdsall, Aircraft Performance, Cambridge University Press, 1992, pp. 255-257

0.00

0.02

0.04

0.06

0.08

0.10

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Prediction, CL = 0.4Prediction, CL = 0.5Prediction, CL = 0.6Flight Test, CL = 0.4Flight Test, CL = 0.5Flight Test, CL = 0.6

CD

Mach number

So how do you design the wing?

• Set the spanload in an MDO trade

• Linear theory gives a good first guess for the twistdistribution

• Design the airfoils in 2D to start, and place in wing

• Finally, full 3D nonlinear analysis and design

• Special attention to root and tip mods to maintain isobarsweep

• Well known requirements, relearned by Jameson

– Viscous effects are important

– You must also model the fuselage

– Need to address off design: buffet onset and overspeed

Antony Jameson, “Re-Engineering the Design Process through Computation” AIAA Paper 97-0641, January 1997

Jameson Wing Design for the MD-12

Off Design Characteristics of the Jameson Wing

Antony Jameson, “Re-Engineering the Design Process through Computation” AIAA Paper 97-0641, January 1997

Transonic Transport Wing DesignKey Lessons learned at Boeing

• You can increase the root thickness w/o a drag penalty

• Nacelle/pylon wing interference can be done with CFDwith almost no penalty

Fighter Wings: A more complicated story

From Richard G. Bradley,“Practical AerodynamicProblems-MilitaryAircraft” in TransonicAerodynamics, AIAA 1982

From Larry Niedling, “The F-15 Wing Development Program”, AIAA Paper 80-3044

Design Points for the F-15

Example of attached flow fighter design

y/(b/2) = 0.436

y/(b/2) = 0.900

y/(b/2) = 0.618

y/(b/2) = 0.764

Grumman proposedHiMAT, M = 0.90

W.H. Mason, D.A. MacKenzie,M.A. Stern, and J.K. Johnson,“A Numerical ThreeDimensional Viscous TransonicWing-Body Analysis andDesign Tool,” AIAA Paper 78-101, Jan.1978.

Fighter Wings: Vortex Flow effects

E

Lift Coefficient

Attached flow concept

Vortex flow concept

Advantage forattached flow

Advantage forvortex flow

To Conclude

• We’ve given a broad overview– Stressed the fundamental physics and issues

• Thousands of papers written on– Computational analysis methods

– Design and optimization methods

– Applications and Design Concepts

• You are prepared to start contributing