《空气动力学》（双语版）Chapter 4 Incompressible Flow Over Airfoils

Chapter 4 Incompressible Flow Over Airfoils Of the many problems now engaging attention, the following are considered of immediate importance and will be considered by the committee as rapidly as funds can be secured for the purpose. . The evolution of the more efficient wing sections of practical form, embodying suitable dimension for an economical structure, with moderate travel of the center-of-pressure and still affording a large range of angle-of- attack combined with efficient action From the first annual report of the NACA 1915

Chapter 4 Incompressible Flow Over Airfoils Of the many problems now engaging attention, the following are considered of immediate importance and will be considered by the committee as rapidly as funds can be secured for the purpose…. The evolution of the more efficient wing sections of practical form, embodying suitable dimension for an economical structure, with moderate travel of the center-of-pressure and still affording a large range of angle-of- attack combined with efficient action. From the first annual report of the NACA, 1915

4 1 Introduction ELudiwig Prandtl and his colleagues at Gottingen,Germany, showed that the aerodynamic consideration of wings could be split into two parts (1)the study of the section of a wingan airfoil And(2) the modification of such airfoil properties to account for the complete, finite wing

4.1 Introduction Ludiwig Prandtl and his colleagues at Göttingen, Germany, showed that the aerodynamic consideration of wings could be split into two parts. (1) the study of the section of a wing—an airfoil. And (2) the modification of such airfoil properties to account for the complete, finite wing

Definition of airfoil Airfoil section

Definition of airfoil

oThe purpose of this chapter Present theoretical methods for the calculation of airfoil aerodynamic properties. Y Road map of this chapter

The purpose of this chapter: Present theoretical methods for the calculation of airfoil aerodynamic properties. Road map of this chapter

4.2 Airfoil nomenclature Leading edge Thickness Mean cam ber line Cam ber Chord line chord- Trailing edge Leading edge:前缘 trailing edge:后缘 Chord line:弦线 chord length:弦长 7 hickness:厚度 camber 弯度 Mean chamber line:中弧线

4.2 Airfoil nomenclature Leading edge: 前缘 trailing edge: 后缘 Chord line: 弦线 chord length: 弦长 Thickness: 厚度 camber: 弯度 Mean chamber line: 中弧线

ONACA four digit"series airfoil NACA2412 The first digit: maximum camber in hundredths The second digit: the location of maximum camber along the chord from leading edge in tenth of the chord The last two digits: maximum thickness in hundredth of the chord NACA0012: symmetrical airfoil

NACA “four digit” series airfoil NACA2412: The first digit: maximum camber in hundredths; The second digit: the location of maximum camber along the chord from leading edge in tenth of the chord; The last two digits: maximum thickness in hundredth of the chord. NACA0012: symmetrical airfoil

4.3 Airfoil characteristics(experiment) Stall due t fow se paration CL max 0 lift slo =0

4.3 Airfoil characteristics(experiment)

◆ Special definitions C lift coefficient a angle of attack ao lift slope Lmax Maximum lift coefficient al-o zero-lift attack angle stall Consequence of the flow separation It is impossible for we to calculate c ma with inviscid flow approximation!!

Special definitions l c  a0 l,max c  L0 stall lift coefficient angle of attack lift slope Maximum lift coefficient zero-lift attack angle Consequence of the flow separation It is impossible for we to calculate with inviscid flow approximation!! l,max c

o Experiment results for NACA2412 NACA 2412 airfoil L=0 2. q1.(457) C12.0 1.6 C1ma×1.6 1.2 Lift coefficient 0.8 0.4 0 0 stall 16 -0.4 Eq.(4.64)--0.1 Moment 0.8 coefficient -0.2 0.3 oRe=3.l×10 回Re=8.9X10 0.4 8081624 a, degrees

Experiment results for NACA2412 0  L0  2.1 cl,max 1.6 0  stall 16

Source of drag 0.024 0.020 profile drag 0.016 口 0.012 Aerodynamic center 0.008 8a自 Drag coefficient 0.004 0 0 m ac -0.05 coefficient 0.1 ⊙Re=3.×10 0.15 日Re=89Xl0 12-8-40481216

Source of drag profile drag Aerodynamic center m ac c