OUTLINE FOR Chapter 4

Transcription

1 16/8/3 OUTLINE FOR Chapter AIRFOIL NOMENCLATURE The leaing ege circle: (usually raius =. chor length c) The trailing ege: The chor line: Straight line connecting the center of leaing ege circle an the trailing eges. The leaing ege: The chor length c: the length between the leaing ege an the trailing ege. The thickness t: the istance between upper an lower surfaces, measure normal to the chor line. The mean camber line: the locus of points halfway between the upper an lower surfaces, measure normal to the chor line. camber: the maximum istance between the mean camber line an the chor line. The istances of the points of maximum thickness an maximum camber aft of the leaing ege. AERODYNAMICS (W3-1-) 1

2 16/8/3 NACA AIRFOIL NOMENCLATURE NACA four-igit series: ( Example: NACA 1 (% camber at % chor, with 1% thickness) => maximum camber =.c => maximum camber locate at.c from the leaing ege. 1 => maximum thickness =.1c. NACA five-igit series: ( Example: NACA 31 => Maximum camber =.c an *3/=3 => lift coefficient C l =.3 3 => 3/=15 => Maximum camber =.c locate at.15c from the leaing ege. 1 => Maximum thickness =.1c. NACA 6- series: Example: NACA => series esignation 5 => the minimum pressure occurs at.5c for the basic symmetric thickness istribution at zero lift => the esign lift coefficient. 18 => Maximum thickness =.18c Interactive NACA Airfoil Shape

3 16/8/3 NACA Four-Digit Series: NACA NACA NACA1 NACA NACA81 NACA1 NACA881 NACA VARIATION OF PRESSURE DISTRIBUTION OVER AN AIRFOIL WITH ANGLE OF ATTACK Invisci flow C f = 3

4 16/8/3 THE LIFT CURVE Max lift coefficient Lift ecrease, Drag increase C l = a ( - L= ) a = zero-lift Angle of attack Lift Coefficient for NACA1 C l C lmax=1.88 Lift slope ~ Stall angle ~ 1 o Zero-lift angle of attack L= = Angle of attack

5 16/8/3 DARG FOR SUBSONIC -D AIRFOIL D f : skin friction rag, C f =D f /(1/V S) D p : prssure arg (D f >> D p in small angle of attack) Profile rag coefficient C = (D f + D p ) /(1/V S) AERODYNAMICS (W3-1-6) Drag Coefficient C for NACA1 C Skin friction rag Pressure rag Angle of Attack (α) AERODYNAMICS (W ) 5

6 16/8/3 Moment Coefficient C m,le an C m,c/ for NACA1 Angle of Attack (α) NACA 1 AIRFOIL CHARACTERISTICS Moment coefficient about the c/ Aeroynamic Center: Moment coefficient about the aeroynamic center For low spee airfoil, aeroynamic center is always at or near the quarter-chor point, i.e. c/ from leaing ege. 6

7 16/8/3 OUTLINE FOR Chapter THEORETICAL SOLUTION FOR LOW SPEED FLOW OVER AIRFOIL (I) - THE PHILOSOPHY Source/Sink istribute along the chor line Thickness effect Angle of attack effect Thin airfoil theory Camber effect Thick Cambere wing at an angle of attack 7

8 16/8/3 THE VORTEX SHEET The Vortex Sheet recall Vortex Flow = s THE KUTTA CONDITION (I) Just like flow over cyliner, has infinite number of vali theoretical solutions on a flow over airfoil with angle of attack, but from experiments there is a one physical solution for a given airfoil at a given angle of attack. We nee an aitional conition to fix. Kutta conition: For a given airfoil at a given angle of attack, the value of aroun the airfoil is such that the flow leaves the trailing ege smoothly. 8

9 16/8/3 THE KUTTA CONDITION (II) Finite trailing ege angle Cusp trailing ege angle 9

10 16/8/3 The following equations are unconitional satisfie (no assumptions). V ns V l ( V ) na n A Uniform velocity Irrotational flow Application in D Airfoil Lift Calculation upstream V U V S near airfoil c A A far ownstream Uniform velocity Irrotational flow i i U V Downwash velocity W 19 OUTLINE FOR Chapter 1

11 16/8/3 CLASSICAL THIN AIRFOIL THEORY (I) Calculate (s) such that the camber line becomes a streamline of the flow an such that the Kutta conition is satisfie at trailing ege, i.e., THE THIN AIRFOIL THEORY (II) Calculate (x) such that the camber line becomes a streamline of the flow an such that the Kutta conition is satisfie at trailing ege, i.e., 11

12 16/8/3 THE THIN AIRFOIL THEORY (III) Funamental equation for thin airfoil theory Solve integral equation ( ) to satisfy (1) the camber line is a streamline an () Kutta conition (c )= bounary conitions. THE SYMMETRIC AIRFOIL - A FLAT PLATE WITH ANGLE OF ATTACK V - No camber, camber line = chor line z/x= since x is a fixe point, it correspons to a particular point of θ, namely θ o. Mathematical theory of integral equations which satisfy Kutta conition ( ) = by using L Hospital rule 1

13 16/8/3 LIFT AND LIFT COEFFICIENT OF FLOW OVER A FLAT PLATE WITH ANGLE OF ATTACK α MOMENT AND MOMENT COEFFICIENT OF FLOW OVER A FLAT PLATE WITH ANGLE OF ATTACK L V V ( ) (1 cos ) V q ' M LE V c (1 cos ) For a thin, symmetric airfoil, the aeroynamic center is locate at the c/ location. 13

14 16/8/3 EXPERIMENTAL V.S. THEORETICAL C l AND C m,c/ OF NACA1 SYMMETRIC AIRFOIL Conclusion: AERODYNAMICS (W3-3-8) OUTLINE FOR LECTURE 1 AERODYNAMICS (W-1-1) 1

15 16/8/3 THE CAMBERED AIRFOIL WITH ANGLE OF ATTACK (I) solution form Fourier cosine series expansion of the function z/x AERODYNAMICS (W-1-) THE CAMBERED AIRFOIL WITH ANGLE OF ATTACK (II) AERODYNAMICS (W-1-3) 15

16 16/8/3 LIFT AND LIFT COEFFICIENT OF A CAMBERED AIRFOIL AERODYNAMICS (W-1-) Zero-Lift Angle of Attack AERODYNAMICS (W ) 16

17 16/8/3 MOMENT AND MOMENT COEFFICIENT OF A CAMBERED AIRFOIL ' V c M LE [ A (1 cos ) An (1 cos )sin n sin ] n1 (1 cos ) sin n sin (n 1) (n 1) 1 sin n cos sin sin sin (n ) n (n ) SUMMARY 17

18 16/8/3 18 Solution:.86 ].8) ( ) 1.995cos.3736cos (.68 [ x z A.95 ] ).8cos ( ) 1.995cos.3736cos (.68cos [ cos x z A ] ).8cos ( ) 1.995cos.3736cos (.68cos [ cos 1) (cos cos x z x z x z x z A Mathmatica 8 Tutor:

19 16/8/3 A.86 A 1.95 A.79 c l ( A A1 ) cm (a) zero-lift angle of attack: c / ( A A1 ) X cp c [1 c l ( A A1 ) [(.86).95] o L.191ra 1. 9 (b) lift coefficient at = o : c l ( A A1 ) [(.86).95] (c) moment coefficient about the quarter chor: cm c ( A A1 ) (.79.95).17 / () center of pressure at = o : X cp c 1 [1 (.95.79)] ( A 1 A )] Cl 19