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- 1. Chapter 5 Airfoils Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. <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. <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. <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. <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. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. <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. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Conventional Airfoil Pressure distribution On upper surface
- 13. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Laminar Airfoil Pressure distribution On upper surface
- 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. <ul><li>Tabe for NACA 2410, 2412, 2415 </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. <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. <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. 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. <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. <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. <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. 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. <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. <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. <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. <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. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. <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. 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. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Mach number is not included
- 33. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University Mach number is not included
- 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. <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. <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. <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. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. <ul><li>■ Flow Similarity (Dynamic Similarity) </li></ul>Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
- 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. 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. <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

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