Understanding Aerodynamics: Arguing from the Real Physics

8

Lift and Wings in 3D at Subsonic Speeds

In this chapter, we extend the discussion of lift from 2D to 3D take up the topics of the flow around a 3D wing, the lift distribution on a 3D wing, the induced drag, wingtip devices, and the manifestations of lift in the extended flowfield. Finally, we'll delve into some of the interesting issues that arise when wings are swept.

8.1 The Flowfield around a 3D Wing

The flow around a 3D wing must differ in some basic ways from the flow around a 2D airfoil, simply because of the finite span and the resulting flow gradients in the spanwise direction. In this section, we'll first describe the general features of 3D wing flowfields, and then we'll look at how they can be explained. The classical approach (starting with the early work of Prandtl and others, see historical sketch by Giacomelli and Pistolisi, in Durand, 1967a) looks at the distribution of bound vorticity and the vorticity in the wake and deduces the velocity field everywhere else using the Biot-Savart law. Though this yields correct results if the correct vorticity distribution is used, it is not a real physical explanation in the cause-and-effect sense, as we argued in Sections 3.3.9 and 7.2. So we'll also seek an explanation based on the local balance of force and acceleration, that is, the interaction of the pressure and velocity fields. We constructed explanations of this type for the generic flow around an obstacle in Section 5.1 and the flow around a 2D lifting airfoil in ...