Hypersonic Aerodynamics 0100 - Introduction to Hypersonic Aerodynamics
W.H. Mason Configuration Aerodynamics...
Transcript of W.H. Mason Configuration Aerodynamics...
Subsonic Airfoils
W.H. MasonConfiguration Aerodynamics Class
Typical Subsonic Methods: Panel Methods• For subsonic inviscid flow, the flowfield can be found by
solving an integral equation for the potential on the surface• This is done assuming a distribution of singularities along
the surface, and finding the “strengths” of the singularities• The airfoil is represented by a series of (typically) straight
line segments between “nodes”, and the nonpenetrationboundary condition is typically satisfied at control points
• Some version of a Kutta condition is required to close thesystem of equations.
1234
N + 1NN - 1
node
panel
Comparison of Panel Method Pressure Distributionwith Exact Conformal Transformation Results
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
PANELExact Conformal Mapping
Cp
x/c
Convergence with increasing numbers of panels
0.950
0.955
0.960
0.965
0.970
0.975
0.980
0 20 40 60 80 100 120
CL
No. of Panels
NACA 0012 Airfoil, α = 8°
A better way to examine convergence: Lift
0.9500.9550.9600.9650.9700.9750.980
0 0.01 0.02 0.03 0.04 0.05 0.06
CL
1/n
NACA 0012 Airfoil, α = 8°
Convergence with Panels: Moment
-0.250
-0.248
-0.246
-0.244
-0.242
-0.240
0 0.01 0.02 0.03 0.04 0.05 0.06
Cm
1/n
NACA 0012 Airfoil, α = 8°
Convergence with Panels: Drag
0.0000.0020.0040.0060.0080.0100.012
0 0.01 0.02 0.03 0.04 0.05 0.06
CD
1/n
NACA 0012 Airfoil, α = 8°
Pressures: 20 and 60 panels-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.000.0 0.2 0.4 0.6 0.8 1.0
20 panels60 panels
CP
x/c
NACA 0012 airfoil, α = 8°
Pressures: 60 and 100 panels-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.000.0 0.2 0.4 0.6 0.8 1.0
60 panels100 panels
CP
x/c
NACA 0012 airfoil, α = 8°
Comparison with WT Data: Lift- recall: panel methods are inviscid! -
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
-5.0° 0.0° 5.0° 10.0° 15.0° 20.0° 25.0°
CL, NACA 0012 - PANEL
CL, NACA 0012 - exp. data
CL, NACA 4412 - PANEL
CL, NACA 4412 - exp. data
CL
α
NACA 0012
NACA 4412
Comparison with Data: Pitching Moment- about the quarter chord -
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
-0.00
0.05
0.10
-5.0 0.0 5.0 10.0 15.0 20.0 25.0
Cm, NACA 0012 - PANELCm, NACA 4412 - PANELCm, NACA 0012 - exp. dataCm, NACA 4412 - exp. data
Cm
α
c/4
NACA 0012
NACA 4412
For Completeness: Drag DataEffect of Camber
-0.50
0.00
0.50
1.00
1.50
2.00
0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018
CL
CD
Re = 6 million
NACA 4412
NACA 0012
data from Abbott and von Doehhoff
Comparison with WT Pressure Distribution-1.2
-0.8
-0.4
-0.0
0.4
0.8
1.20.0 0.2 0.4 0.6 0.8 1.0 1.2
α = 1.875°M = .191Re = 720,000transition free
Cp
x/c
NACA 4412 airfoil
Predictions from PANEL
data from NACA R-646
XFOIL: the code for subsonic airfoils
• Panel Methods: Inviscid!• Couple with a BL analysis to include
viscous effects• The single element viscous subsonic airfoil
analysis method of choice: XFOIL– by Prof. Mark Drela at MIT
• Link available from my software site
Airfoil pressures: What to look for-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
CP
x/c
NACA 0012 airfoil, α = 4°
Trailing edge pressure recovery
Expansion/recovery around leading edge(minimum pressure or max velocity, first appearance of sonic flow)
upper surface pressure recovery(adverse pressure gradient)
lower surface
Leading edge stagnation point
Rapidly accelerating flow,favorable pressure gradient
Effect of Angle of Attack-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
α = 0°α = 4α = 8CP
x/c
NACA 0012 airfoilInviscid calculation from PANEL
Comparison of NACA 4-Digit Airfoils0006, 0012, 0018
-0.30
-0.20
-0.10
-0.00
0.10
0.20
0.30-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0006 (max t/c = 6%)NACA 0012 (max t/c = 12%)NACA 0018 (max t/c = 18%)
y/c
x/c
Thickness Effects on Airfoil PressuresZero Lift Case
-1.00
-0.50
0.00
0.50
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0006, α = 0°NACA 0012, α = 0°NACA 0018, α = 0°
CP
x/c
Inviscid calculation from PANEL
Thickness Effects on Airfoil Pressures, CL = 0.48-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0006, α = 4°
NACA 0012, α = 4°
NACA 0018, α = 4°
CP
x/c
Inviscid calculation from PANEL
Comparison of NACA 4-Digit Airfoilsthe 0012 and 4412
-0.30
-0.20
-0.10
-0.00
0.10
0.20
0.30
-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0012 (max t/c = 12%)NACA 4412 foil (max t/c = 12%)
y/c
x/c
Highly Cambered Airfoil Pressure Distribution- NACA 4412 -
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 4412, α = 0°NACA 4412, α = 4°
CP
x/c
Note: For a comparison of cambered and uncambered presuure distributions at the same lift, see Fig. 18.
Inviscid calculation from PANEL
Camber Effects on Airfoil Pressures, CL = 0.48-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0012, α = 4°
NACA 4412, α = 0°
CP
x/c
Inviscid calculation from PANEL
Camber Effects on Airfoil Pressures, CL = 0.96-4.00
-3.00
-2.00
-1.00
0.00
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0012, α = 8°NACA 4412, α = 4°
CP
x/c
Inviscid calculations from PANEL
Camber Effects on Airfoil Pressures, CL = 1.43-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
NACA 0012, α = 12°NACA 4412, α = 8°
CP
x/c
Inviscid calculations from PANEL
NACA 6712 Airfoil- Heavy Aft Camber Geometry -
-0.05
0.05
0.15
-0.1 0.1 0.3 0.5 0.7 0.9 1.1
y/c
x/c
NACA 6712 Airfoil- Heavy Aft Camber, Pressure Distribution -
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00-0.1 0.1 0.3 0.5 0.7 0.9 1.1
α = -.6 (CL = 1.0)
CP
x/c
NACA 6712
Inviscid calculations from PANEL
Whitcomb GA(W)-1 Airfoil
-0.10-0.050.000.050.100.15
0.0 0.2 0.4 0.6 0.8 1.0
y/c
x/c-1.00
-0.50
0.00
0.50
1.000.0 0.2 0.4 0.6 0.8 1.0
Cp
x/c
GA(W)-1
α = 0°
Inviscid calculations from PANEL
Liebeck’s Hi-Lift Airfoil: Geometry and Lift- note shape of pressure recovery -
From R.T. Jones, Wing Theory
Liebeck’s Hi-Lift Airfoil: Drag
From Bertin,Aerodynamics for Engineers
Camberline Design: DesCam
0.00
0.02
0.04
0.06
0.08
0.10
0.12
-0.50
0.00
0.50
1.00
1.50
2.00
0.0 0.2 0.4 0.6 0.8 1.0
(Z-Z0)/C - DesCamZ/C - from Abbott & vonDoenhoff
Z/CΔCP
X/C
Design ChordLoading
Airfoil Selection
Issues:• Cruise CL, and CLmax, don’t forget Cm0
-large LE radius?-Near parallel trailing edge closure
• Profile Drag: Laminar flow? • Thickness for low weight and internal volume• Tails: often symmetric, 6 series foils picked
To Conclude
You have the tools to do single element airfoil design