tran sonic air foils
TRANSCRIPT
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Lesson 26Review: Transonic flowfields are inherently nonlinear Advances in both experimental and computational methods
were required and achieved
Today: Discussion of transonic airfoil characteristics and design goals
Primarily associated with
Richard Whitcomb, Feb 21, 1921 Oct. 13, 2009
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Subsonic Linear Theory, Even with the
Compressibility Correction,
Cant Predict Transonic Flow!From Desta Alemayhu
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A real example
Illustrates tricks used to get calculations to agree with test data
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REVIEW: Obtaining CFD solutions
Grid generation Flow solver
Typically solving 100,000s (or millions in 3D)of simultaneous nonlinearalgebraic equations
An iterative procedure is required, and its noteven guaranteed to converge!
Requires more attention and skill than lineartheory methods
Flow visualization to examine the results
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Airfoils
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
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Angle of attack effects: NACA 0012-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
0.00 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
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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 curvatureall 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, CL
= 0.665
Note strong shock
Note that flow acceleratescontinuously into the shock
Note the low aft loading associatedwith absence of aft camber.
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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
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What the supercritical concept achieved
From NASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990
Section drag at CN
= 0.65 Force limit for onset of upper-surface boundary layer separation
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And the Pitching Moment
From NASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990
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How Supercritical Foils are Different
From NASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990
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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, CL
= 1.04
Note weak shockNote that the pressuredistribution is "filled out",providing much more lifteven though shock is weaker
Note the high aft loadingassociated with aft camber.
"Noisy" pressure distribution is associatedwith "noisy" ordinates, typical of NASAsupercritical ordinate values
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Whitcombs 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
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Airfoils 31 and 33
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Off Design
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Foils 31 and 33 Drag
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NASA Airfoils Developed Using the Guidelines
fromNASA Supercritical Airfoils, by Charles D. Harris, NASA TP 2969, March 1990
Filled symbols denote
airfoils that were tested
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NASA Airfoil Catalog
Note: watch out for coordinates tabulated in NASA TP 2969!
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Frank Lynchs Pro/Con Chart
for supercritical airfoils
F.T. Lynch, Commercial TransportsAerodynamic Design for Cruise Performance
Efficiency, in Transonic Aerodynamics, ed. by D. Nixon, AIAA, 1982.
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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
+C
L
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
This is an approximation until CFD or WT results arrive!
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Airfoil Limits
Shevell and NASA Projections Comparedto 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 0.18
t/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
CL
0.4
0.7
1.0NASA projection
Korn equation estimate, A
= .95
In W.H. Mason, Analytic Models for Technology Integration in
Aircraft Design, AIAA Paper 90-3262, September 1990.
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For the curious: the airfoil used on the X-29
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Just when we thought
airfoil design was
finished
See Henne, Innovationwith Computational
Aerodynamics: The
Divergent Trailing Edge
Airfoil, inApplied
Computational
Aerodynamics, P.A.
Henne, ed., AIAA
Progress in Aero Series,
1990
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Used on the MD-11
resisted in Seattle!
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Take a Look at
the PressureDistribution
Comparison of the
DLBA 243 and the
DLBA 186 Calculated
Pressure Distributionat M = 0.74
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To Conclude:
You now know the basis for
transonic airfoils