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# Aer 101 chapter 5

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### Aer 101 chapter 5

1. 1. Chapter 5 Airfoils Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
2. 2. <ul><li>Introduction </li></ul><ul><li>In this chapter the following will be studied: </li></ul><ul><li>1- Geometric characteristics of the airfoils. </li></ul><ul><li>2- Aerodynamic characteristics of the airfoils. </li></ul><ul><li>3- Flow similarity ( Dynamic similarity ) </li></ul><ul><li>■ Airfoil Geometric Characteristics </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
3. 3. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
4. 4. 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.
5. 5. <ul><li>4- Chord C : The distance from the leading to trailing edge </li></ul><ul><li>measured along the chord line. </li></ul><ul><li>5- Camber : The maximum distance between the mean </li></ul><ul><li>camber line and the chord line. </li></ul><ul><li>6- Leading edge radius and its shape through the leading </li></ul><ul><li>edge. </li></ul><ul><li>7- The thickness distribution: The distance from the upper </li></ul><ul><li>surface to the lower surface, measured perpendicular </li></ul><ul><li>to chord line </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
6. 6. <ul><li>► Airfoil Families (Series) </li></ul><ul><li># NACA (National Advisory Committee for Aeronautics) or </li></ul><ul><li>NASA (National Aeronautics and Space administration) </li></ul><ul><li>identified different airfoil shapes with a logical numbering </li></ul><ul><li>system. </li></ul><ul><li># Abbott & Von Doenhoff “ Theory of Wing Sections” includes a summary of airfoil data ( geometric and aerodynamic data ) </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
7. 7. <ul><li>■ NACA Airfoil Series </li></ul><ul><li>1- NACA 4-digit series </li></ul><ul><li>2- NACA 5-digit series </li></ul><ul><li>3- NACA 1-series or 16-series </li></ul><ul><li>4- NACA 6- series </li></ul><ul><li>5- NACA 7- series </li></ul><ul><li>6- NACA 8- series </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
8. 8. <ul><li>► NACA Four-Digit Series </li></ul><ul><li>Example: NACA 2412 </li></ul><ul><li>NACA 2 4 12 </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Camber in percentage of chord y c = 0.02 C Position of camber in tenths of chord x c = 0.4 C Maximum thickness (t ) in percentage of chord (t/c) max = 0.12 x c y c C
9. 9. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
10. 10. <ul><li>► NACA Five-Digit Series </li></ul><ul><li>Example: NACA 23012 </li></ul><ul><li>NACA 2 30 12 </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University When multiplied by 3/2 yields the design lift coefficient C l in tenths. C l = 0.3 When divided by 2, gives the position of the camber in percent of chord x c = 0.15 C Maximum thickness (t ) in percentage of chord (t/c) max = 0.12
11. 11. <ul><li>► NACA Six- Series </li></ul><ul><li>Example: NACA 64-212 </li></ul><ul><li>NACA 6 4 - 2 12 </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University 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. 12. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Conventional Airfoil Pressure distribution On upper surface
13. 13. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Laminar Airfoil Pressure distribution On upper surface
14. 14. <ul><li>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. </li></ul><ul><li>Airfoils can be drawn using these Tables. </li></ul><ul><li>From airfoil drawing we can extract its geometric data: </li></ul><ul><li>- camber line </li></ul><ul><li>- maximum camber ratio and its position </li></ul><ul><li>- maximum thickness ratio and its position </li></ul><ul><li>-leading edge radius </li></ul><ul><li>-trailing edge angle </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Assignment 1 : Meaning of numbering system for NACA 1-series, NACA 7-Series, and NACA 8- Series.
15. 15. <ul><li>Tabe for NACA 2410, 2412, 2415 </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
16. 16. <ul><li>■ Center of Pressure and Aerodynamic Center </li></ul><ul><li># Center or pressure : The point of intersection between the chord line and the line of action of the resultant aerodynamic force R. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
17. 17. <ul><li># In addition to lift and drag, the surface pressure and shear stress distribution create a moment M which tends to rotate the wing. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University # Moment on Airfoil
18. 18. <ul><li>Neglect shear stress </li></ul><ul><li>F 1 is the resultant pressure force on the upper surface. </li></ul><ul><li>F 2 is the resultant pressure force on the lower surface. </li></ul><ul><li>Points 1 & 2 are the points of action of F 1 & F 2 . </li></ul><ul><li>R is resultant force of F 1 & F 2 . </li></ul><ul><li>F 1 ≠ F 2 because the pressure distribution on the upper surface differs from the pressure distribution on the lower surface. </li></ul><ul><li>Thus, F 1 & F 2 will create an aerodynamic moment M which will tend to rotate the airfoil. </li></ul><ul><li>The value of M depends on the point about which we choose to take moment. </li></ul><ul><li>For subsonic airfoils it is common to take moments about the quarter-chord point. It is denoted by M c/4 . </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
19. 19. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University M c/4 is function of angle of attack α , i.e. its value depends on α .
20. 20. <ul><li>■ Aerodynamic Center </li></ul><ul><li>≠ Aerodynamic center: The point on the chord line about which moments does not vary with α . </li></ul><ul><li>● The moment about the aerodynamic center (ac) is designated M ac . </li></ul><ul><li>● By definition, M ac = constant </li></ul><ul><li>● For low-speed and subsonic airfoils, ac is generally very close to the quarter-chord point </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
21. 21. <ul><li>■ Lift, Drag, and Moment Coefficients </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University 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
22. 22. <ul><li>Mach number M ∞ = V ∞ /a ∞ . Since V ∞ is listed above, we can designate a ∞ as our index for compressibility. </li></ul><ul><li>6- Size of the aerodynamic surface. For airplane we use the plan form wing area S to indicate size. </li></ul><ul><li>7- Shape of the airfoil. </li></ul><ul><li>● Hence, for a given shape of airfoil, we can write: </li></ul><ul><li>L = f 1 ( α , V ∞ , ρ ∞ , µ ∞ , a ∞ , S ) </li></ul><ul><li>D = f 2 ( α , V ∞ , ρ ∞, µ ∞ , a ∞ , S ) </li></ul><ul><li>M = f 3 ( α , V ∞ , ρ ∞ , µ ∞ , a ∞ , S ) </li></ul><ul><li>● 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 . </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
23. 23. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University 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. 24. <ul><li>● Then by cross plotting that data obtained, we could be able to get a precise functional relation for L, D, and M. </li></ul><ul><li>● This is the hard way which could be very time consuming and costly. </li></ul><ul><li>● Instead, we can use the theory of dimensional analysis . </li></ul><ul><li>● 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. </li></ul><ul><li>● The results of this theory are: </li></ul><ul><li>C L = f 1 ( α ,, M ∞ , Re) </li></ul><ul><li>C D = f 2 ( α ,, M ∞ , Re) </li></ul><ul><li>C M = f 3 ( α ,, M ∞ , Re) </li></ul><ul><li>-where C L = L/ q ∞ S = Lift coefficient </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
25. 25. <ul><li>- C D = D/ q ∞ S = Drag coefficient </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University - C M = M/ q ∞ S C = Moment coefficient and q ∞ = ½ ρ ∞ V 2 ∞ , 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- C L c l , L l 3- C D c d , D d 4- C M c m , M m Dynamic similarity parameters Per unit span
26. 26. <ul><li>■ Airfoil Data </li></ul><ul><li>● A goal of theoretical aerodynamics is to predict values of c l , c d , and c m from the basic equations and concepts of physical science. </li></ul><ul><li>● However, simplifying assumptions are usually necessary to make the mathematics tractable. </li></ul><ul><li>● Therefore, when theoretical results are obtained, they are generally not “exact ”. </li></ul><ul><li>● As a result we have to rely on experimental measurements. </li></ul><ul><li>● c l , c d , and c m were measured by NACA for large number of airfoils in low-speed wind tunnels. </li></ul><ul><li>● At low-speed the effect of M ∞ is cancelled. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
27. 27. <ul><li>● These measurements were carried out on straight, constant-chord wings completely spanned the tunnel test section from one side to the other. </li></ul><ul><li>● In this fashion, the flow essentially “ saw” a wing with no wing tips, and the experimental airfoil data were obtained for “infinite wings” </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
28. 28. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
29. 29. <ul><li>● Results of airfoil measurements include c l , c d , c m,c/4 , and c m,ac . </li></ul><ul><li>● The results are given in the form of graphs as follows: </li></ul><ul><li>- The 1 st page of graph gives data for c l and c m,c/4 versus </li></ul><ul><li>angle of attack for the NACA airfoil. </li></ul><ul><li>- The 2 nd page of graph gives c d and c m,ac versus c l for </li></ul><ul><li>the same airfoil. </li></ul><ul><li>Note : Some results of these airfoil data are given in Appendix D ( “Introduction to Flight”, Anderson ) </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
30. 30. <ul><li>Example: Airfoil data for NACA 2415 </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University c l and c m,c/4 versus α NACA 2415 Mach number is not included
31. 31. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University c d and c m,ac versus c l NACA 2415 Mach number is not included
32. 32. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Mach number is not included
33. 33. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Mach number is not included
34. 34. <ul><li>► Variation of c l with α </li></ul><ul><li>● This variation is shown in the following sketch. </li></ul><ul><li>* c l varies linearly with α over a large range of α . </li></ul><ul><li>* At α = 0 c l ≠ 0 due to the positive camber. </li></ul><ul><li>* c l = 0 at α L=0 ( zero lift direction/zero lift angle of attack) </li></ul><ul><li>* For large values of α ,the linearity breaks down. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
35. 35. <ul><li>* As α is increased beyond a certain value; c l reaches to c lmax and then drops as α is further increased. </li></ul><ul><li>* When c l is rapidly decreasing at high α , the airfoil is stalled. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Flow mechanism associated with stalling Separated flow
36. 36. <ul><li>► Comparison of Lift Curves for Cambered and Symmetric Airfoils </li></ul><ul><li>* For symmetric airfoil the lift curve goes through the origin. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
37. 37. <ul><li>► The Phenomenon of Airfoil Stall </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University 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. 38. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
39. 39. <ul><li>■ Compressibility Correction For Lift & Moment Coefficient </li></ul><ul><li>For 0.3 < M ∞ ≤ 0.7 , the corrections for c l and c m , using < Prandtl-Glauert rule , are given as: </li></ul><ul><li>- c l = c l,0 / √ [1- M ∞ 2 ] </li></ul><ul><li>- c m = c m,0 / √ [1- M ∞ 2 ] </li></ul><ul><li>Where c l,0 is the low-speed value of the lift coefficient, </li></ul><ul><li>c m,0 is the low-speed value of the moment coefficient. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
40. 40. <ul><li>■ Flow Similarity (Dynamic Similarity) </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
41. 41. <ul><li>Consider two different flow fields over two different bodies, as shown in figure. </li></ul><ul><li>By definition , different flows are dynamically similar if: </li></ul><ul><li>1- The bodies and any other solid boundaries are </li></ul><ul><li>geometrically similar for the flow. </li></ul><ul><li>2- The dynamic similarity parameters are the same for </li></ul><ul><li>flows ( i.e.Re and M ∞ are the same for the flows). </li></ul><ul><li># If different flows are dynamically similar, the following results are satisfied: </li></ul><ul><li>1- The streamline patterns are geometrically similar. </li></ul><ul><li>2- The distribution of v/v ∞ , p/p ∞ ,T/T ∞ ,..etc throughout </li></ul><ul><li>the flow field are the same when plotted against </li></ul><ul><li>common non-dimensional coordinates. </li></ul><ul><li>3- The force and moment coefficients are the same (i.e. </li></ul><ul><li>c l , c d , and c m are the same. </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
42. 42. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University v/v ∞ s 1 /d 1 , s 2 /d 2 <ul><li>* Thus we can say that flows over geometrically similar bodies </li></ul><ul><li>at the same Mach and Reynolds numbers are dynamically </li></ul><ul><li>similar. </li></ul><ul><li>Hence, the lift, drag, and moment coefficients will be identical </li></ul><ul><li>for the bodies. </li></ul>
43. 43. <ul><li>► This is the key point in the validity of wind-tunnel testing: </li></ul><ul><li>“ 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” </li></ul><ul><li># This means that: </li></ul><ul><li>[ M ∞1 ] model = [ M ∞2 ] prototype </li></ul><ul><li>[ Re 1 ] model = [ Re 2 ] prototype </li></ul><ul><li>and [ c l1 ] model = [ c l2 ] prototype </li></ul><ul><li>[ c d1 ] model = [ c d2 ] prototype </li></ul><ul><li>[ c m1 ] model = [ c m2 ] prototype </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University