Transcript Document 7199367

ME403 Chapter 2
2D Airfoil Aerodynamics
Lift is mainly provided by
the wing with an airfoil
cross-section shape
Airfoil Geometry
An airfoil is the 2D crosssection shape of the wing,
which creates significant lift
but minimal drag because of
this aerodynamic shape
Historical Airfoils
Historical Airfoils
Typical Streamlines
Angle of Attack


V
chor
d lin
e
Pressure Distribution
99500
99550
Upper Surface Pressure
Surface Pressue, P, N/sq m
99600
99650
99700
99750
99800
99850
Lower Surface Pressure
Net Normal Force
99900
c
n   ( Pl  Pu )dx
99950
0
100000
0
0.2
0.4
0.6
Chordwise Distance, x, m
0.8
1
Pressure Coefficient Distribution
p  p
cp  1
2
 V
2
In the uniform free-stream:
c p
At the stagnation point
(at which velocity V=0):
p  p
1
0
2
 V
2
1
 V
p0  p 
2
c p0  1
1
1
2
2
  V
 V
2
2
2
Positive Cp means the pressure is higher than the freestream (atmospheric) pressure, and negative Cp means
suction relative to free-stream pressure. The maximum,
which occurs at the stagnation point, is always 1.
Viscous Boundary Layer
Velocity profile creates skin friction (shear) drag on surface
Edge of boundary layer
V
1
Transition
2
3
Separation
4
Flat Plate Skin Friction Drag Coefficient
Curve fit formula for
turbulent boundary
layer (Re > 500,000):
Evolution of
Airfoil Design
Delaying transition
point from Laminar to
Turbulent boundary
layer reduces skin
friction drag
Boundary Layer Flow Separation
When flow separation occurs,
there is also pressure drag.
Pressure (Form) Drag due to Flow Separation
100% Pressure Drag
Total Profile Drag
= Skin Friction Drag
+ Form Drag
Resultant Aerodynamic Force
Lift

V
Total Aerodynamic Force
(Sum of Pressure and Shear)
Airfoil
Drag
Lift & Drag Coefficients
L
l
cl  1
1
2
2
V cb 2 V c
2
D
d
cd  1
1
2
2
V cb 2 V c
2
lift
normal force

drag

V
Chord
Line
chordwise
force
Center of Pressure
The resultant aerodynamic force acts at the Center of
Pressure (c.p.), about which the moment is zero.
Open-Circuit Wind Tunnel
Wind Tunnel Tests
Force transducer behind model senses lift, drag and pitching moment directly.
Motor-controlled mechanism adjusts the model’s angle of attack.
Closed-Circuit Wind Tunnel
Wing Section Models
Model for measuring lift,
drag and pitching moment
Model for measuring surface
pressure distribution
NACA 0006 Data
at Re = 3,180,000
There is a maximum
Lift-to-Drag ratio (L/D).
Location of Center of
Pressure (c.p.) varies
with 
NACA 2312 Data
at Re = 3,120,000
Lift decreases and
drag increases
sharply beyond the
stall (max. Cl) point,
due to boundary
layer separation.
NACA Airfoils and Test Data
4-Digit Series
5-Digit Series
6 Series
http://naca.larc.nasa.gov/reports/1945/naca-report-824/
Stalled Airfoil
Reynolds Number Effect
Aerodynamic Center
Since the c.p. varies with , it is more desirable to use a fixed Aerodynamic
Center (a.c.) as the point of action of the lift and drag. The pitching moment
about this point can be calculated, and is found insensitive to . For most
airfoils, the a.c. locates at around quarter chord (x=c/4).
Pitching Moment
Coefficient:
m
cm  1
2 2

V
c
2
Typical Non-Cambered Airfoil
Lift Curve & Drag Polar
NACA 0006
Typical Cambered Airfoil
NACA 2412
Lift Curve & Drag Polar
Typical Airfoil Aerodynamic Characteristics
at Re = 6 million
NACA 0006
NACA 2412
Zero-Lift Angle of Attack (deg.)
0
-2
Stall Angle of Attack (deg.)
9
16
Maximum Lift Coefficient
0.9
1.7
Lift Curve Slope (/deg.)
0.1
0.108
0
-0.05 to -0.02
0.005
0.006
0.7/0.0076 = 92.1
1.0/0.0088 = 113
Moment Coefficient (before stall)
Minimum Drag Coefficient
Max. Lift-to-Drag Ratio (L/D)
Computation Fluid Dynamics Simulation
CFD Simulation: Near stall
CFD Simulation: Fully Stalled
Airfoil Generator at http://www.ae.su.oz.au/aero/info/index.html
Airfoil Analysis Code at http://www.ae.su.oz.au/aero/info/index.html