The diagram shows the flow of a fluid past an airfoil. The gray lines represent the direction of the fluid’s flow. Black regions represent solid obstacles to the flow. In which of the three regions within the dashed lines is the fluid’s flow most turbulent?
In the diagram, we see fluid flowing generally from left to right. And recall that these gray lines illustrate the motion of different layers of the fluid. Now, in this question, we have to make some inferences about the fluid’s motion without using any numbers or mathematics. That’s okay though. Certain properties of fluid motion, such as turbulence, are notoriously difficult to model quantitatively. Still, we can describe it by applying some qualitative knowledge about steady and turbulent flow.
We can begin by recalling that turbulent flow is characterized by a fluid changing in speed and direction more rapidly. The term “steady” means just the opposite, where the fluid is just going with the flow. Fluid lines that are regularly spaced and parallel to one another indicate regions of steady fluid flow, whereas lines that are curved and bunched together illustrate the chaos of turbulence. Out of the boxed-in regions, I, II, and III, we have to identify the one that features the most turbulent fluid flow. We’ll do this by comparing the shapes of the flow lines within those regions.
As the fluid encounters this airfoil, we see that the fluid gets redirected around it. But notice that there are different consequences to the fluid’s motion depending on whether it goes above or below the airfoil. Region II shows fluid the travels below the airfoil. The flow lines here do have some gentle curvature. But overall they’re relatively straight and parallel to each other. So we can say that the fluid in region II has a quite steady flow. But what about the fluid that moves above the airfoil?
The flow lines have some more noticeable curvature on the left-hand side of region I, where the fluid first gets pushed over top of the obstacle. From there, the flow lines do appear to start to smooth over. But then notice that things get pretty chaotic toward the back end of the airfoil. The flow lines change direction once again, which mixes up the fluid. This means turbulence. And here it’s so extreme that a flow line in the diagram forms a closed loop. This means that the fluid here has to point in every direction as it goes around. Not only is it changing direction constantly, but it also drags the surrounding layers of fluid along with it. So it’s slowing down, twisting, and turning all in a very small area. This is by design though, since an airfoil needs different fluid motion above and below it in order to provide lift to something like an airplane.
The fluid eventually does pass over the obstacle. And we can see how it later evens out, resulting in a relatively steady flow over here in region III. The bulk of the turbulence caused by the airfoil is within region I. And since it’s the only region of the three that contains a closed loop, we know that the fluid’s flow is most turbulent in region I.