Chapter 5

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					     Chapter 5

        Airfoils


1      Prof. Galal Bahgat Salem
    Aerospace Dept. Cairo University
• 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




2                      Prof. Galal Bahgat Salem
                    Aerospace Dept. Cairo University
3      Prof. Galal Bahgat Salem
    Aerospace Dept. Cairo University
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.


4                     Prof. Galal Bahgat Salem
                   Aerospace Dept. Cairo University
    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




5                         Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University
►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 )




6                      Prof. Galal Bahgat Salem
                    Aerospace Dept. Cairo University
■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




7                    Prof. Galal Bahgat Salem
                  Aerospace Dept. Cairo University
►NACA Four-Digit Series
 Example:   NACA 2412

                     NACA 2 4             12

                                                             Maximum thickness (t )
        Camber in              Position of camber            in percentage of chord
    percentage of chord        in tenths of chord                (t/c)max = 0.12
        yc = 0.02 C                 xc = 0.4 C




                          xc         yc
                                          C

8                            Prof. Galal Bahgat Salem
                          Aerospace Dept. Cairo University
9      Prof. Galal Bahgat Salem
    Aerospace Dept. Cairo University
►NACA Five-Digit Series
 Example:    NACA 23012

                         NACA 2               30         12

     When multiplied by 3/2         When divided by 2, gives
      yields the design lift                                        Maximum thickness
                                      the position of the
     coefficient Cl in tenths.                                      (t ) in percentage of
                                     camber in percent of
             Cl = 0.3                                               chord (t/c)max = 0.12
                                      chord xc = 0.15 C




10                                  Prof. Galal Bahgat Salem
                                 Aerospace Dept. Cairo University
 ►NACA Six- Series
  Example:    NACA 64-212

                    NACA 6 4 - 2                      12


     Series       Location of minimum                        Maximum thickness (t )
  designation 6   pressure in tenths of                      in percentage of chord
                     chord (0.4 C)                                (t/c)max = 0.12
                                      Design lift
                                     coefficient in
                                     tenths (0.2)


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

 11                          Prof. Galal Bahgat Salem
                          Aerospace Dept. Cairo University
              Pressure distribution
              On upper surface




     Conventional Airfoil
12        Prof. Galal Bahgat Salem
       Aerospace Dept. Cairo University
       Pressure distribution
       On upper surface




      Laminar Airfoil

13      Prof. Galal Bahgat Salem
     Aerospace Dept. Cairo University
• 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.


14                        Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University
• Tabe for NACA 2410, 2412, 2415




15              Prof. Galal Bahgat Salem
             Aerospace Dept. Cairo University
■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.


16                     Prof. Galal Bahgat Salem
                    Aerospace Dept. Cairo University
# 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




17                          Prof. Galal Bahgat Salem
                         Aerospace Dept. Cairo University
• 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 .

18                     Prof. Galal Bahgat Salem
                    Aerospace Dept. Cairo University
     Mc/4 is function of angle of attack α, i.e. its value depends
     on α .

19                         Prof. Galal Bahgat Salem
                        Aerospace Dept. Cairo University
■ 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


20                    Prof. Galal Bahgat Salem
                   Aerospace Dept. Cairo University
■Lift, Drag, and Moment Coefficients




     For an airplane in flight, L, D, and M depend on:
     1- Angle of attack α
     2- Free-stream velocity V∞
     3- Free-stream density ρ∞ , that is, altitude
     4- Viscosity coefficient µ∞
     5- Compressibility of the airflow which is governed by
21                       Prof. Galal Bahgat Salem
                      Aerospace Dept. Cairo University
   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 .

22                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
     L       (V∞, ρ∞, µ∞ , a∞, S)             (α, ρ∞, µ∞ , a∞, S)       (α, V∞, µ∞ , a∞, S)
                                        L
                 = const                          = const L                  = const
                  1                               2                            3


                                    α                          V∞                      ρ∞
           (α, V∞, ρ∞, a∞, S)
                                            (α, V∞, ρ∞, µ∞, S)
                                                                        (α, V∞, ρ∞, µ∞, a∞)
              = const                          = const
      L                                 L                           L       = const
                 4                                      5                       6

                            µ∞                                                         S
                                                               a∞

     Therefore, 6 experiments are required for each dependent variable.

23                             Prof. Galal Bahgat Salem
                            Aerospace Dept. Cairo University
● 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

24                        Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University
      - CD = D/ q∞S = Drag coefficient
      - CM= M/ q∞S C = Moment coefficient

             and q∞ = ½ ρ∞ V2∞ , C = Airfoil chord
                                                          Dynamic
      - Re = ρ∞ V∞ C/μ∞ = Reynolds number                 similarity
      - M∞ = V∞ / a∞ = Mach number                        parameters
     ►Note :
         1- For airfoil ( 2D flow )               S=Cx1
         2- CL                                   cl , L     l    Per
         3- CD                                   cd , D    d     unit
         4- CM                                   cm , M    m     span


25                        Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University
                   ■ 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.
26                  Prof. Galal Bahgat Salem
                 Aerospace Dept. Cairo University
●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”




27                     Prof. Galal Bahgat Salem
                    Aerospace Dept. Cairo University
28      Prof. Galal Bahgat Salem
     Aerospace Dept. Cairo University
● 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 )




29                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
Example: Airfoil data for NACA 2415




     cl and cm,c/4
     versus α
     NACA 2415




Mach number is not
included


30                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
cd and cm,ac
versus cl
NACA 2415




Mach number is not
included


31                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
 Mach number is not
 included




32                       Prof. Galal Bahgat Salem
                      Aerospace Dept. Cairo University
Mach number is not
included




33                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
►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.




34                        Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University
 * 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.
                                         Separated flow




     Flow mechanism
     associated with
     stalling




35                        Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University
 ►Comparison of Lift Curves for Cambered and            Symmetric Airfoils
* For symmetric airfoil the lift curve goes through the origin.




36                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
►The Phenomenon of Airfoil Stall

*It is of critical importance
     in airplane design.
*It is caused by flow                        Separated 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.

37                              Prof. Galal Bahgat Salem
                             Aerospace Dept. Cairo University
38      Prof. Galal Bahgat Salem
     Aerospace Dept. Cairo University
■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.




39                          Prof. Galal Bahgat Salem
                         Aerospace Dept. Cairo University
■ Flow Similarity (Dynamic Similarity)




40                     Prof. Galal Bahgat Salem
                    Aerospace Dept. Cairo University
• 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.
41                      Prof. Galal Bahgat Salem
                     Aerospace Dept. Cairo University
                 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.


 42                        Prof. Galal Bahgat Salem
                        Aerospace Dept. Cairo University
►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


43                        Prof. Galal Bahgat Salem
                       Aerospace Dept. Cairo University

				
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