《空气动力学》（双语版）Chapter 5 Incompressible Flow Finite Wings

Chapter 5 Incompressible Flow Finite Wings

Chapter 5 Incompressible Flow Finite Wings

5.1 Introduction o The properties of airfoils are the same as the properties of a wing with infinite span. However, all real airplanes have wings of finite span eIn the present chapter, we will apply our knowledge of airfoil properties to the analysis for finite wings o As We have mentioned in the previous chapter, the analysis for the aerodynamics of wings is separated in two steps. Now, we are going on the second step in Prandtl's philosophy of wing theory

5.1 Introduction The properties of airfoils are the same as the properties of a wing with infinite span. However, all real airplanes have wings of finite span. In the present chapter, we will apply our knowledge of airfoil properties to the analysis for finite wings. As we have mentioned in the previous chapter, the analysis for the aerodynamics of wings is separated in two steps. Now, we are going on the second step in Prandtl’s philosophy of wing theory

Streamline over the top surface Streamline over the bottom surface Top vie (planform) Wing area=S Wing span b

Ft Low pressure ront vIew High pressure

Question: why are the aerodynamic characteristics of a wing any different from the properties of its section? Airfoil can be respected as two-dimensional body, but any finite wing is a three-dimensional body ATtention should be paid for the flow pattern near the wing tips. And try to understand the reason for such a flow phenomena X For general cases, there is a spanwise velocity component on both top and bottom surface of the wing, but their direction are different XX A trailing vortex is created at each wing tip. These wing-tip vortices downstream of the wing induce a small downward velocity in the neighborhood of the wing itself

Question : why are the aerodynamic characteristics of a wing any different from the properties of its section? Airfoil can be respected as two-dimensional body, but any finite wing is a three-dimensional body. ※Attention should be paid for the flow pattern near the wing tips. And try to understand the reason for such a flow phenomena. ※ For general cases, there is a spanwise velocity component on both top and bottom surface of the wing, but their direction are different. ※ A trailing vortex is created at each wing tip. These wing-tip vortices downstream of the wing induce a small downward velocity in the neighborhood of the wing itself

XX The two vortices tend to drag the surrounding air with them, and this secondary movment induces a small component is called downwash(下洗) X The downwash velocity combines with the freestream velocity to produce a loca/relative wind which is canted downward in the vicinity of each airfoil section of the wing X definition of induced angle of attack

※ The two vortices tend to drag the surrounding air with them, and this secondary movment induces a small component is called downwash(下洗）. ※ The downwash velocity combines with the freestream velocity to produce a local relative wind which is canted downward in the vicinity of each airfoil section of the wing. ※ definition of induced angle of attack

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XX TWo important effects due to the downwash 1 the angle of attack actually seen(or feel) by the local section is the angle between the chord line and the local relative wind. This angle is defined by a a cc =a-al 2 The local lift vector is in the direction perpendicular to the local relative wind. As a subsequence there is a drag created by the presence of downwash

※ Two important effects due to the downwash. 1 the angle of attack actually seen(or feel) by the local section is the angle between the chord line and the local relative wind. This angle is defined by aeff  eff = −i 2 The local lift vector is in the direction perpendicular to the local relative wind. As a subsequence, there is a drag created by the presence of downwash

Geometric angle of attack induced angle of attack feff effective angle of attack Chord line Local airfoil section of finite wing rela e Ind