Prof. Galal Bahgat Salem Aerospace Dept. Cairo University 1 Chapter 5 Airfoils

Prof. Galal Bahgat Salem Aerospace Dept. Cairo University

1

Chapter 5

Airfoils


2

• Introduction In this chapter the following will be studied:

1- Geometric characteristics of the airfoils.

2- Aerodynamic characteristics of the airfoils.

3- Flow similarity ( Dynamic similarity )

■ Airfoil Geometric Characteristics


3


4

Airfoil geometric characteristics include:1- Mean camber line : The locus of points halfway between the upper and lower surfaces as measured perpendicular to the mean camber line.2- Leading & trailing edges: The most forward and rearward points of the mean camber line.3- Chord line: The straight line connecting the leading and trailing edges.


5

4- Chord C : The distance from the leading to trailing edge

measured along the chord line.

5- Camber : The maximum distance between the mean

camber line and the chord line.

6- Leading edge radius and its shape through the leading

edge.

7- The thickness distribution: The distance from the upper

surface to the lower surface, measured perpendicular

to chord line


6

►Airfoil Families (Series)

# NACA (National Advisory Committee for Aeronautics) or

NASA (National Aeronautics and Space administration)

identified different airfoil shapes with a logical numbering

system.

# Abbott & Von Doenhoff “ Theory of Wing Sections” includes a summary of airfoil data ( geometric and aerodynamic data )


7

■NACA Airfoil Series

1- NACA 4-digit series

2- NACA 5-digit series

3- NACA 1-series or 16-series

4- NACA 6- series

5- NACA 7- series

6- NACA 8- series


8

►NACA Four-Digit Series

Example: NACA 2412

NACA 2 4 12

Camber in percentage of chord

yc = 0.02 C

Position of camber in tenths of chord

xc = 0.4 C

Maximum thickness (t ) in percentage of chord

(t/c)max = 0.12

xc yc

C


9


10

►NACA Five-Digit Series

Example: NACA 23012

NACA 2 30 12

When multiplied by 3/2

yields the design lift coefficient Cl in tenths.

Cl = 0.3

When divided by 2, gives the position of the

camber in percent of chord xc = 0.15 C

Maximum thickness (t ) in percentage of chord (t/c)max = 0.12


11

►NACA Six- Series

Example: NACA 64-212

NACA 6 4 - 2 12

Series designation 6

Location of minimum pressure in tenths of

chord (0.4 C)

Design lift coefficient in tenths (0.2)

Maximum thickness (t ) in percentage of chord

(t/c)max = 0.12

►Note that this is the series of laminar airfoils . Comparison of conventional and laminar flow airfoils is shown in the following Figure.


12

Conventional Airfoil

Pressure distributionOn upper surface


13

Laminar Airfoil

Pressure distributionOn upper surface


14

• The Handbook “Theory of Wing Sections” gives the shape of airfoils in terms of upper and lower surfaces station and ordinate as given in the following Tables.

• Airfoils can be drawn using these Tables.• From airfoil drawing we can extract its geometric data:

- camber line

- maximum camber ratio and its position

- maximum thickness ratio and its position

-leading edge radius

-trailing edge angle

Assignment 1 : Meaning of numbering system for NACA 1-series, NACA 7-Series, and NACA 8- Series.


15

• Tabe for NACA 2410, 2412, 2415


16

■Center of Pressure and Aerodynamic Center

# Center or pressure : The point of intersection between the chord line and the line of action of the resultant aerodynamic force R.


17

# In addition to lift and drag, the surface pressure and shear stress distribution create a moment M which tends to rotate the wing.

# Moment on Airfoil


18

• Neglect shear stress

• F1 is the resultant pressure force on the upper surface.

• F2 is the resultant pressure force on the lower surface.

• Points 1 & 2 are the points of action of F1 & F2 .

• R is resultant force of F1 & F2 .

• F1 ≠ F2 because the pressure distribution on the upper surface differs from the pressure distribution on the lower surface.

• Thus, F1 & F2 will create an aerodynamic moment M which will tend to rotate the airfoil.

• The value of M depends on the point about which we choose to take moment.

• For subsonic airfoils it is common to take moments about the quarter-chord point. It is denoted by Mc/4 .


19

Mc/4 is function of angle of attack α, i.e. its value depends on α .


20

■ Aerodynamic Center

≠ Aerodynamic center: The point on the chord line about which moments does not vary with α.

●The moment about the aerodynamic center (ac) is designated Mac .

● By definition, Mac = constant ● For low-speed and subsonic airfoils, ac is generally very

close to the quarter-chord point


21

■Lift, Drag, and Moment Coefficients

For an airplane in flight, L, D, and M depend on:1- Angle of attack α2- Free-stream velocity V∞

3- Free-stream density ρ∞ , that is, altitude4- Viscosity coefficient µ∞

5- Compressibility of the airflow which is governed by


22

Mach number M∞ = V∞/a∞. Since V∞ is listed above, we can designate a∞ as our index for compressibility.

6- Size of the aerodynamic surface. For airplane we use the plan form wing area S to indicate size.

7- Shape of the airfoil.

● Hence, for a given shape of airfoil, we can write:

L = f1( α, V∞, ρ∞, µ∞ , a∞, S )

D = f2( α, V∞, ρ∞, µ∞ , a∞, S )

M = f3( α, V∞, ρ∞, µ∞ , a∞, S )

●The variation of L with (α, V∞, ρ∞, µ∞ , a∞, S) taking one at a time with the others constant could be obtained by experiment in a wind tunnel .


23

L

α

)V∞, ρ∞, µ∞ , a∞, S(

= const

1

L

V∞

2 3

ρ∞

4 5 6

L

L L L

µ∞ a∞S

Therefore, 6 experiments are required for each dependent variable.

)α, ρ∞, µ∞ , a∞, S( )α, V∞, µ∞ , a∞, S(

= const = const

)α, V∞, ρ∞, a∞, S(

= const)α, V∞, ρ∞, µ∞, S(

= const)α, V∞, ρ∞, µ∞, a∞(

= const


24

● Then by cross plotting that data obtained, we could be able to get a precise functional relation for L, D, and M.

● This is the hard way which could be very time consuming and costly.

●Instead, we can use the theory of dimensional analysis.●This theory can reduce time, effort, and cost by grouping

α, V∞, ρ∞, µ∞ , a∞, S , and L or D or M into a fewer number of non-dimensional parameters.

●The results of this theory are:

CL= f1 (α,, M∞, Re)

CD = f2 (α,, M∞, Re)

CM = f3 (α,, M∞, Re)

-where CL = L/ q∞S = Lift coefficient


25

- CD = D/ q∞S = Drag coefficient

- CM= M/ q∞S C = Moment coefficient

and q∞ = ½ ρ∞ V2∞ , C = Airfoil chord

- Re = ρ∞ V∞ C/μ∞ = Reynolds number

- M∞ = V∞ / a∞ = Mach number

►Note : 1- For airfoil ( 2D flow ) S = C x 1 2- CL cl , L l 3- CD cd , D d 4- CM cm , M m

Dynamic similarity parameters

Per unit span


26

■ Airfoil Data● A goal of theoretical aerodynamics is to predict

values of cl, cd, and cm from the basic equations and concepts of physical science.

● However, simplifying assumptions are usually necessary to make the mathematics tractable.

● Therefore, when theoretical results are obtained, they are generally not “exact”.

● As a result we have to rely on experimental measurements.

● cl, cd, and cm were measured by NACA for large number of airfoils in low-speed wind tunnels.

● At low-speed the effect of M∞ is cancelled.


27

●These measurements were carried out on straight, constant-chord wings completely spanned the tunnel test section from one side to the other.

● In this fashion, the flow essentially “ saw” a wing with no wing tips, and the experimental airfoil data were obtained for “infinite wings”


28


29

● Results of airfoil measurements include cl, cd, cm,c/4, and cm,ac.

● The results are given in the form of graphs as follows:

- The 1st page of graph gives data for cl and cm,c/4 versus

angle of attack for the NACA airfoil.

- The 2nd page of graph gives cd and cm,ac versus cl for

the same airfoil.

Note: Some results of these airfoil data are given in Appendix D ( “Introduction to Flight”, Anderson )


30

Example: Airfoil data for NACA 2415

cl and cm,c/4 versus αNACA 2415

Mach number is not included


31

cd and cm,ac versus cl

NACA 2415



32



33



34

►Variation of cl with α

● This variation is shown in the following sketch.

* cl varies linearly with α over a large range of α.

* At α = 0 cl ≠ 0 due to the positive camber.

* cl = 0 at αL=0 ( zero lift direction/zero lift angle of attack)

* For large values of α,the linearity breaks down.


35

* As α is increased beyond a certain value; cl reaches to clmax and then drops as α is further increased.

* When cl is rapidly decreasing at high α , the airfoil is stalled.

Flow mechanism associated with stalling

Separated flow


36

►Comparison of Lift Curves for Cambered and Symmetric Airfoils

* For symmetric airfoil the lift curve goes through the origin.


37

►The Phenomenon of Airfoil Stall

Separated flow

*It is of critical importance

in airplane design.

*It is caused by flow

separation on the upper

surface of the airfoil due to

high adverse pressure

gradient.

*When separation occurs,

the lift decreases

drastically, and the drag

increases suddenly.


38


39

■Compressibility Correction For Lift & Moment Coefficient

For 0.3 < M∞ ≤ 0.7 , the corrections for cl and cm , using <Prandtl-Glauert rule , are given as:

- cl = cl,0 / √ [1- M∞2]

- cm = cm,0 / √ [1- M∞2]

Where cl,0 is the low-speed value of the lift coefficient,

cm,0 is the low-speed value of the moment coefficient.


40

■ Flow Similarity (Dynamic Similarity)


41

• Consider two different flow fields over two different bodies, as shown in figure.

• By definition, different flows are dynamically similar if: 1- The bodies and any other solid boundaries are geometrically similar for the flow. 2- The dynamic similarity parameters are the same for

flows ( i.e.Re and M∞ are the same for the flows).# If different flows are dynamically similar, the following

results are satisfied: 1- The streamline patterns are geometrically similar.

2- The distribution of v/v∞ , p/p ∞,T/T ∞ ,..etc throughout the flow field are the same when plotted against common non-dimensional coordinates. 3- The force and moment coefficients are the same (i.e.

cl, cd, and cm are the same.


42

v/v∞

s1/d1 , s2/d2

* Thus we can say that flows over geometrically similar bodies at the same Mach and Reynolds numbers are dynamically similar.• Hence, the lift, drag, and moment coefficients will be identical for the bodies.


43

►This is the key point in the validity of wind-tunnel testing:

“ If a scale model of a flight vehicle is tested in a wind tunnel, the measured lift, drag, and moment coefficients will be the same as for free flight as long as the Mach and Reynolds numbers of the wind-tunnel test-section flow are the same as for the free-flight case”

# This means that:

[ M∞1 ]model = [ M∞2 ]prototype

[ Re1 ]model = [ Re2 ]prototype

and [ cl1 ]model = [ cl2 ]prototype

[ cd1]model = [ cd2 ]prototype

[ cm1 ]model = [ cm2 ]prototype

Documents

Prof. Galal Bahgat Salem Aerospace Dept. Cairo University 1 Chapter 5 Airfoils