Subsonic Airfoils 1g5b3l
This document was ed by and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this report form. Report r6l17
Overview 4q3b3c
& View Subsonic Airfoils as PDF for free.
More details 26j3b
- Words: 1,183
- Pages: 32
Subsonic Airfoils
W.H. Mason Configuration Aerodynamics Class
Typical Subsonic Methods: 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 nonpenetration boundary condition is typically satisfied at control points • Some version of a Kutta condition is required to close the system of equations. node N -1
N N+1
4
3
2
1
Comparison of Method Pressure Distribution with Exact Conformal Transformation Results -2.50 -2.00
Exact Conformal Mapping
-1.50 -1.00
-0.50 0.00 0.50 1.00 -0.2
0.0
0.2
0.4
0.6
x/c
0.8
1.0
1.2
Convergence with increasing numbers of s 0.980
NACA 0012 Airfoil, α = 8°
0.975 CL
0.970 0.965 0.960 0.955 0.950 0
20
40
60 80 No. of s
100
120
A better way to examine convergence: Lift
CL
0.980 0.975 0.970 0.965 0.960 0.955 0.950 0
NACA 0012 Airfoil, α = 8°
0.01
0.02
0.03 0.04 1/n
0.05
0.06
Convergence with s: Moment -0.240
NACA 0012 Airfoil, α = 8°
-0.242 -0.244
Cm -0.246 -0.248 -0.250 0
0.01
0.02
0.03
1/n
0.04
0.05
0.06
Convergence with s: Drag 0.012 0.010
NACA 0012 Airfoil, α = 8°
0.008 CD 0.006 0.004 0.002 0.000 0
0.01
0.02
0.03 0.04 1/n
0.05
0.06
Pressures: 20 and 60 s -5.00 NACA 0012 airfoil, α = 8°
-4.00
20 s 60 s
-3.00 -2.00 -1.00 0.00 1.00 0.0
0.2
0.4
x/c
0.6
0.8
1.0
Pressures: 60 and 100 s -5.00 NACA 0012 airfoil, α = 8°
-4.00
60 s 100 s
-3.00 -2.00
-1.00 0.00 1.00 0.0
0.2
0.4
x/c
0.6
0.8
1.0
Comparison with WT Data: Lift - recall: methods are inviscid! 2.50
2.00 NACA 4412 1.50
CL 1.00
NACA 0012
0.50 CL, NACA 0012 - CL, NACA 0012 - exp. data
0.00
CL, NACA 4412 - CL, NACA 4412 - exp. data
-0.50 -5.0°
0.0°
5.0°
10.0°
α
15.0°
20.0°
25.0°
Comparison with Data: Pitching Moment - about the quarter chord 0.10 NACA 0012
0.05 -0.00
Cm
-0.05 c/4 -0.10 -0.15 NACA 4412
-0.20
Cm, NACA 0012 - Cm, NACA 4412 - Cm, NACA 0012 - exp. data Cm, NACA 4412 - exp. data
-0.25 -0.30
-5.0
0.0
5.0
10.0
α
15.0
20.0
25.0
For Completeness: Drag Data Effect of Camber 2.00 Re = 6 million 1.50
1.00
CL 0.50
NACA 4412 NACA 0012
0.00 data from Abbott and von Doehhoff -0.50 0.004
0.006
0.008
0.010
0.012
CD
0.014
0.016
0.018
Comparison with WT Pressure Distribution -1.2 data from NACA R-646 -0.8 -0.4 -0.0 Predictions from
0.4
α = 1.875° M = .191 Re = 720,000 transition free
0.8 1.2
0.0
0.2
NACA 4412 airfoil 0.4
x/c
0.6
0.8
1.0
1.2
XFOIL: the code for subsonic airfoils
• 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 Expansion/recovery around leading edge (minimum pressure or max velocity, first appearance of sonic flow)
-1.50
Rapidly accelerating flow, favorable pressure gradient
-1.00
upper surface pressure recovery (adverse pressure gradient)
-0.50 lower surface 0.00
Trailing edge pressure recovery Leading edge stagnation point
0.50
NACA 0012 airfoil, α = 4° 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Effect of Angle of Attack -5.00 NACA 0012 airfoil Inviscid calculation from -4.00 α = 0°
-3.00
α=4
α=8
-2.00
-1.00
0.00
1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Comparison of NACA 4-Digit Airfoils 0006, 0012, 0018 -0.30
NACA 0006 (max t/c = 6%) NACA 0012 (max t/c = 12%) NACA 0018 (max t/c = 18%)
-0.20 -0.10 y/c -0.00 0.10 0.20 0.30 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Thickness Effects on Airfoil Pressures Zero Lift Case -1.00 Inviscid calculation from -0.50 0.00
0.50
1.00 -0.1
NACA 0006, α = 0° NACA 0012, α = 0° NACA 0018, α = 0° 0.1
0.3
0.5 x/c
0.7
0.9
1.1
Thickness Effects on Airfoil Pressures, CL = 0.48 -3.00 Inviscid calculation from -2.50
NACA 0006, α = 4° NACA 0012, α = 4°
-2.00
NACA 0018, α = 4° -1.50 -1.00 -0.50 0.00 0.50 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Comparison of NACA 4-Digit Airfoils the 0012 and 4412 0.30 0.20 0.10 y/c -0.00 -0.10 NACA 0012 (max t/c = 12%) NACA 4412 foil (max t/c = 12%)
-0.20 -0.30 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Highly Cambered Airfoil Pressure Distribution - NACA 4412 -2.00 Inviscid calculation from -1.50
NACA 4412, α = 0° NACA 4412, α = 4°
-1.00 -0.50
0.00
0.50 Note: For a comparison of cambered and uncambered presuure distributions at the same lift, see Fig. 18. 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Camber Effects on Airfoil Pressures, CL = 0.48 -2.00 Inviscid calculation from -1.50
NACA 0012, α = 4° NACA 4412, α = 0°
-1.00
-0.50 0.00
0.50
1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Camber Effects on Airfoil Pressures, CL = 0.96 -4.00 Inviscid calculations from NACA 0012, α = 8° NACA 4412, α = 4°
-3.00
-2.00 -1.00
0.00
1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Camber Effects on Airfoil Pressures, CL = 1.43 -6.00 Inviscid calculations from -5.00
NACA 0012, α = 12° NACA 4412, α = 8°
-4.00 -3.00
-2.00 -1.00 0.00 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
NACA 6712 Airfoil - Heavy Aft Camber Geometry 0.15 y/c 0.05 -0.05 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
NACA 6712 Airfoil - Heavy Aft Camber, Pressure Distribution -2.00 Inviscid calculations from -1.50
α = -.6 (CL = 1.0)
-1.00 -0.50 0.00 0.50 NACA 6712 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Whitcomb GA(W)-1 Airfoil 0.15 0.10 0.05 y/c 0.00 -0.05 -0.10 -1.00
0.0
0.2
0.4
0.6 0.8 Inviscid calculations from x/c
1.0
-0.50 0.00
0.50
GA(W)-1 α = 0°
1.00 0.0
0.2
0.4
x/c
0.6
0.8
1.0
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 (Z-Z0)/C - DesCam Z/C - from Abbott & vonDoenhoff
0.12
Design Chord Loading
0.10 0.08 Z/C
2.00 1.50 Δ 1.00
0.06 0.50
0.04
0.00
0.02 0.00 0.0
0.2
0.4
0.6 X/C
0.8
-0.50 1.0
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
W.H. Mason Configuration Aerodynamics Class
Typical Subsonic Methods: 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 nonpenetration boundary condition is typically satisfied at control points • Some version of a Kutta condition is required to close the system of equations. node N -1
N N+1
4
3
2
1
Comparison of Method Pressure Distribution with Exact Conformal Transformation Results -2.50 -2.00
Exact Conformal Mapping
-1.50 -1.00
-0.50 0.00 0.50 1.00 -0.2
0.0
0.2
0.4
0.6
x/c
0.8
1.0
1.2
Convergence with increasing numbers of s 0.980
NACA 0012 Airfoil, α = 8°
0.975 CL
0.970 0.965 0.960 0.955 0.950 0
20
40
60 80 No. of s
100
120
A better way to examine convergence: Lift
CL
0.980 0.975 0.970 0.965 0.960 0.955 0.950 0
NACA 0012 Airfoil, α = 8°
0.01
0.02
0.03 0.04 1/n
0.05
0.06
Convergence with s: Moment -0.240
NACA 0012 Airfoil, α = 8°
-0.242 -0.244
Cm -0.246 -0.248 -0.250 0
0.01
0.02
0.03
1/n
0.04
0.05
0.06
Convergence with s: Drag 0.012 0.010
NACA 0012 Airfoil, α = 8°
0.008 CD 0.006 0.004 0.002 0.000 0
0.01
0.02
0.03 0.04 1/n
0.05
0.06
Pressures: 20 and 60 s -5.00 NACA 0012 airfoil, α = 8°
-4.00
20 s 60 s
-3.00 -2.00 -1.00 0.00 1.00 0.0
0.2
0.4
x/c
0.6
0.8
1.0
Pressures: 60 and 100 s -5.00 NACA 0012 airfoil, α = 8°
-4.00
60 s 100 s
-3.00 -2.00
-1.00 0.00 1.00 0.0
0.2
0.4
x/c
0.6
0.8
1.0
Comparison with WT Data: Lift - recall: methods are inviscid! 2.50
2.00 NACA 4412 1.50
CL 1.00
NACA 0012
0.50 CL, NACA 0012 - CL, NACA 0012 - exp. data
0.00
CL, NACA 4412 - CL, NACA 4412 - exp. data
-0.50 -5.0°
0.0°
5.0°
10.0°
α
15.0°
20.0°
25.0°
Comparison with Data: Pitching Moment - about the quarter chord 0.10 NACA 0012
0.05 -0.00
Cm
-0.05 c/4 -0.10 -0.15 NACA 4412
-0.20
Cm, NACA 0012 - Cm, NACA 4412 - Cm, NACA 0012 - exp. data Cm, NACA 4412 - exp. data
-0.25 -0.30
-5.0
0.0
5.0
10.0
α
15.0
20.0
25.0
For Completeness: Drag Data Effect of Camber 2.00 Re = 6 million 1.50
1.00
CL 0.50
NACA 4412 NACA 0012
0.00 data from Abbott and von Doehhoff -0.50 0.004
0.006
0.008
0.010
0.012
CD
0.014
0.016
0.018
Comparison with WT Pressure Distribution -1.2 data from NACA R-646 -0.8 -0.4 -0.0 Predictions from
0.4
α = 1.875° M = .191 Re = 720,000 transition free
0.8 1.2
0.0
0.2
NACA 4412 airfoil 0.4
x/c
0.6
0.8
1.0
1.2
XFOIL: the code for subsonic airfoils
• 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 Expansion/recovery around leading edge (minimum pressure or max velocity, first appearance of sonic flow)
-1.50
Rapidly accelerating flow, favorable pressure gradient
-1.00
upper surface pressure recovery (adverse pressure gradient)
-0.50 lower surface 0.00
Trailing edge pressure recovery Leading edge stagnation point
0.50
NACA 0012 airfoil, α = 4° 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Effect of Angle of Attack -5.00 NACA 0012 airfoil Inviscid calculation from -4.00 α = 0°
-3.00
α=4
α=8
-2.00
-1.00
0.00
1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Comparison of NACA 4-Digit Airfoils 0006, 0012, 0018 -0.30
NACA 0006 (max t/c = 6%) NACA 0012 (max t/c = 12%) NACA 0018 (max t/c = 18%)
-0.20 -0.10 y/c -0.00 0.10 0.20 0.30 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Thickness Effects on Airfoil Pressures Zero Lift Case -1.00 Inviscid calculation from -0.50 0.00
0.50
1.00 -0.1
NACA 0006, α = 0° NACA 0012, α = 0° NACA 0018, α = 0° 0.1
0.3
0.5 x/c
0.7
0.9
1.1
Thickness Effects on Airfoil Pressures, CL = 0.48 -3.00 Inviscid calculation from -2.50
NACA 0006, α = 4° NACA 0012, α = 4°
-2.00
NACA 0018, α = 4° -1.50 -1.00 -0.50 0.00 0.50 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Comparison of NACA 4-Digit Airfoils the 0012 and 4412 0.30 0.20 0.10 y/c -0.00 -0.10 NACA 0012 (max t/c = 12%) NACA 4412 foil (max t/c = 12%)
-0.20 -0.30 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Highly Cambered Airfoil Pressure Distribution - NACA 4412 -2.00 Inviscid calculation from -1.50
NACA 4412, α = 0° NACA 4412, α = 4°
-1.00 -0.50
0.00
0.50 Note: For a comparison of cambered and uncambered presuure distributions at the same lift, see Fig. 18. 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Camber Effects on Airfoil Pressures, CL = 0.48 -2.00 Inviscid calculation from -1.50
NACA 0012, α = 4° NACA 4412, α = 0°
-1.00
-0.50 0.00
0.50
1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Camber Effects on Airfoil Pressures, CL = 0.96 -4.00 Inviscid calculations from NACA 0012, α = 8° NACA 4412, α = 4°
-3.00
-2.00 -1.00
0.00
1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Camber Effects on Airfoil Pressures, CL = 1.43 -6.00 Inviscid calculations from -5.00
NACA 0012, α = 12° NACA 4412, α = 8°
-4.00 -3.00
-2.00 -1.00 0.00 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
NACA 6712 Airfoil - Heavy Aft Camber Geometry 0.15 y/c 0.05 -0.05 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
NACA 6712 Airfoil - Heavy Aft Camber, Pressure Distribution -2.00 Inviscid calculations from -1.50
α = -.6 (CL = 1.0)
-1.00 -0.50 0.00 0.50 NACA 6712 1.00 -0.1
0.1
0.3
0.5 x/c
0.7
0.9
1.1
Whitcomb GA(W)-1 Airfoil 0.15 0.10 0.05 y/c 0.00 -0.05 -0.10 -1.00
0.0
0.2
0.4
0.6 0.8 Inviscid calculations from x/c
1.0
-0.50 0.00
0.50
GA(W)-1 α = 0°
1.00 0.0
0.2
0.4
x/c
0.6
0.8
1.0
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 (Z-Z0)/C - DesCam Z/C - from Abbott & vonDoenhoff
0.12
Design Chord Loading
0.10 0.08 Z/C
2.00 1.50 Δ 1.00
0.06 0.50
0.04
0.00
0.02 0.00 0.0
0.2
0.4
0.6 X/C
0.8
-0.50 1.0
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
Related Documents 171j1w
Subsonic Airfoils 1g5b3l
December 2019 13
Incompressible Flow Over Airfoils 6av55
March 2021 0
Subsonic And Supersonic Air Intakes a322y
November 2019 36
(ebook Aero) - Synthesis Of Subsonic Airplane Design - Torenbeek 734d2o
November 2019 69
Study And Analysis Of Subsonic Wind Tunnel-ppt1234 4053y
April 2021 0