Incompressible Flow over Airfoils - SNUaancl.snu.ac.kr/aancl/lecture/up_file/_1508074408_12th...
Transcript of Incompressible Flow over Airfoils - SNUaancl.snu.ac.kr/aancl/lecture/up_file/_1508074408_12th...
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Incompressible Flow over Airfoils
Road map for Chap. 4
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< 4.1 Introduction >
Incompressible flow over airfoils
Incompressible Flow over Airfoils
Prandtl (20C 초) Airfoil (2D)
Wing (3D)
Body
Airfoil : any section of the wing cut by a plane normal to y-axis
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< 4.2 Airfoil Nomenclature >
NACA (National Advisory Committee for Aeronautics) series
Incompressible Flow over Airfoils
Thickness
Camber
Leading edge
Mean camber line
Trailing edge
Chord lineUpper surface
Lower surface
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< 4.2 Airfoil Nomenclature >
NACA (National Advisory Committee for Aeronautics) series
Incompressible Flow over Airfoils
NACA 4-digit series
* NACA2412
2 : max. camber = 2% of the chord4 : the location of max. camber = 40% of the chord12 : max. thickness = 12% of the chordIf the airfoil is symmetric, it becomes NACA00XX
NACA 5-digit series
* NACA230122 : 2*0.3/2 = 0.3 design CL
30 : 30/2 % = the location of max. camber12 : max. thickness = 12% of the chord
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< 4.2 Airfoil Nomenclature >
NACA (National Advisory Committee for Aeronautics) series
Incompressible Flow over Airfoils
6-digit series laminar flow airfoil
* NACA65-218
6 : series designation5 : min. pressure location = 50% of the chord2 : design CL= 0.218 : max. thickness = 18% of the chord
Other notations
* SC1095
* VR12
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< 4.3 Airfoil Characteristics >
Incompressible Flow over Airfoils
* 1930~40 NASA carried numerous experiments on NACA airfoil characteristics(Measured Cl, Cd, Cm 2-D data)
* In the future, new airfoils should be designed and tested(consideration of aerodynamic, dynamic & acoustic limitation)
* Typical lift characteristics of an airfoilStall
Stall angle (12~18deg)
Zero lift angle
Maximum lift coefficient
: angle of attack
SepatationDynamic stall
How to measure Cl, Cd, Cm?
a0 =
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< 4.3 Airfoil Characteristics >
Incompressible Flow over Airfoils
[Def.] a, angle of attack : the angle between the freestream velocity and the chord
[Note] 1. a0 is not usually a function of Re.2. Cl,max is dependent on Re.
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< 4.3 Airfoil Characteristics >
Typical drag & pitching moment characteristics
Incompressible Flow over Airfoils
* Aerodynamic drag = Pressuredrag
Skin frictiondrag
(form drag)
Profile drag
* AC (Aerodynamic Center)[Def.] The point about which the moment is independent of AOA
Subsonic : AC=c/4Supersonic : AC=c/2
+
Sensitive to Re.
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< 4.4 Vortex Sheet >
Kutta-Joukowski Theorem
Incompressible Flow over Airfoils
* Kutta (German), Joukowski(Russia)
* Incompressible, inviscid flow
L = rvG
* G : positive clockwise
G
LiftG
Vortex filament of strength G
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< 4.4 Vortex Sheet >
Incompressible Flow over Airfoils
* g(s) = the strength of vortex sheet
per unit length along s
* From Biot-Savart Law
* Velocity potential for vortex flow
* Velocity potential at P
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< 4.4 Vortex Sheet >
Incompressible Flow over Airfoils
* Circulation around the dashed path
* If
(Note)
The local strength of the vortex sheet is equal to the difference (jump) in
tangential velocity across the vortex sheet
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< 4.4 Vortex Sheet >
(Note)
“Vortex sheet method” is more than just a mathematical device; it also has
a physical meaning
ex. : Replacing the boundary layer ( ) with a vortex sheet
Incompressible Flow over Airfoils
* “Vortex Sheet” - Application for inviscid, incompressible flow
* Calculate g(s) to form the streamlines with a give airfoil shape
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< 4.5 The Kutta Condition >
Incompressible Flow over Airfoils
* For a circular cylinder,
* For a given a, should have only one solution
?
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< 4.5 The Kutta Condition >
Incompressible Flow over Airfoils
* From the experiments, we know that the velocity at the trailing-edge in
finite. Kutta Condition
* The circulation around the airfoil is the value to ensure that the flow
smoothly leaves the trailing edge.
g(TE)=V1-V2=0
V(TE)=finite
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< 4.6 Kelvin’s Circulation Theorem >
Incompressible Flow over Airfoils
* Assume)
The time rate of change of circulation around a closed curve
consisting of the same fluid elements is zero
1. Inviscid
2. Incompressible
3. No body forces
Ex) Starting vortex
[ at rest ] [ after the start ]