July 6, 2019

There is an intriguing phenomenon when you closely examine the science behind airfoils. Why does the air above the airfoil flow much faster than the air below ? How come the two never meet? The answer is right there in the pressure gradient. Before explaining the reason, we will first describe how the pressure gradient is developed.

A detailed webpage version of the video is given below.

In the first part of the airfoil article, we learned that the flow gets curved as shown due to the Coanda effect. You can explain the pressure distribution by keeping in mind that in a curved flow pressure is higher at the outside, this is illustrated in Fig:1.

There are 3 main flow curvatures in this flow. The biggest is at the top of the airfoil. Far away from the airfoil, the pressure is atmospheric. So, due to this high curvature, pressure will decrease as we move toward the airfoil (Fig:2).

The second curvature is at the bottom of the airfoil, near the tail. This is also curved downward. So here, if we move toward the airfoil, the pressure should increase(Fig:3).

The last flow curvature is also at the bottom of the airfoil, close to the leading edge. This is a very small curvature. This curvature, however, is curved slightly upward. This means that the pressure should decrease in this region as we move toward the airfoil. Due to the very small curvature, there will be a very small drop in pressure as shown in(Fig:4).

We know that faraway from the upstream and downstream, the pressure is atmospheric. At the leading edge of the airfoil, a high-pressure region is generated as the flow directly hits this portion, this is illustrated in Fig:5. So, we can easily construct a pressure distribution as shown. The CFD results conform exactly to our logical conclusions.

Now back to the initial question. To facilitate the analysis, we can neglect this very small drop in pressure (Fig:6A). You can see that at the top, the pressure decreases almost to the midpoint before it increases. At the bottom, the pressure keeps on increasing until it reaches the tail. Only after that it decrease (Fig:6B).

Pause for a moment now, and consider 2 fluid particles starting at the same speed but in different pressure gradients. The top particle is surrounded by a decreasing pressure condition, while the bottom particle sits in an increasing pressure condition as shown in Fig:8A. For the top particle, pressure on the right side is less than at the left side. So, there will be a net force in the same direction of velocity and the particle will speed up. However, the reverse is true for the bottom particle. Here the net force is against velocity direction, so it will decelerate. In short in a decreasing pressure field the fluid particle will accelerate and in an increasing pressure field the fluid particle will decelerate, as shown in Fig:8B

This is exactly what happens in an airfoil also The bottom particle will keep on decelerating . The top particle will accelerate up to the midpoint as shown in(Fig:8A) This means that the speed of the top particle will be higher at any point in time, and the two particles will never meet (Fig:8B).

The bottom particle also experiences a pressure-decreasing scenario as shown in Fig:10. However, it is almost after the trailing edge, and it happens suddenly. Such a sudden drop in pressure will not considerably increase the particle speed.

In short, for this particular problem, the pressure distribution makes the particles flow at different speeds, but the reverse argument does not hold. The different speeds of the particles are not what make the pressure distribution, this is illustrated in Fig:11. Because for the 2nd textbook argument, there is no logical explanation for what causes this speed difference. These two arguments are not 2 different ways of looking at the same thing.