Lift and Airfoils in 2D at Subsonic Speeds
In a way, lift is the most visible of the aerodynamic forces. We see heavier-than-air animals and machines flying through the air every day, and something has to be holding them up there. Of course, we can predict the existence of aerodynamic lift mathematically by solving equations of motion for the flow around the lifting object. The accuracy of such predictions depends on the level of fidelity of the equations we choose to solve and varies with the type of lifting-surface shape and with the flow situation. Some types of lifting flow are easier to predict accurately than others. In principle, however, if we had the computing power available to carry out a direct numerical simulation (DNS) solution of the Navier-Stokes (NS) equations for the flow, we would be able to predict any lifting flow, 2D or 3D, with high accuracy. So in one sense, the physics of lift is perfectly understood: Lift happens because the flow obeys the NS equations with a no-slip condition on solid surfaces.
On the other hand, physical explanations of lift, without math, pose a more difficult problem. Practically everyone, the nontechnical person included, has heard at least one nonmathematical explanation of how an airfoil produces lift when air flows past it. Such explanations fall into several general categories, with many variations. Unfortunately, most of them are either incomplete or wrong in one way or another. And some give up at one point or another and ...