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Intermediate Fluid Mechanics [ME563 Course Notes]

Intermediate Fluid Mechanics [ME563 Course Notes] - ME 563...

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ME 563 - Intermediate Fluid Dynamics - Su Lecture 0 - Visual fluids examples Fluid dynamics is a unique subject because it’s very visual. The book “An Album of Fluid Mo- tion” by Milton van Dyke (on reserve at Wendt) is a collection of fascinating images from fluids experiments. You really can’t say you understand fluids if you only think of it in terms of equations. Figure 1 is a top view of a triangular wing immersed in a flow of water (moving from left to right in the image). Colored fluid, appearing as white, is introduced near the leading edge. The wing Figure 1: Turbulent transition in flow over a wing. is inclined at a 20 angle of attack. Initially the fluid pattern is very smooth, then the filaments of colored fluid make a very abrupt transition to turbulence. The abruptness of the turbulent transition is interesting for many reasons, not least of which is that it’s not really predicted by the equations of fluid flow. Another interesting property of fluid flows is that the organization of it is very persistent. The upper left photo in Fig. 2 is of the wake of a circular cylinder in a water flow. The cylinder is at the left edge of the photo. The mean flow is very slow – about one cylinder diameter per second. The Reynolds number is 105. The alternating pattern of eddies (vortices) is called the ‘K`arm` an vortex street.’ Intuitively, it kind of makes sense that a slow, laminar flow would be very organized. The upper right photo in Fig. 2, showing the wake of a plate at a 45 angle of attack, is taken at a flow that is, relatively, about 40 times faster (Reynolds number 4300). The flow in this case is turbulent, but even so, the alternating pattern of eddies is visible above the randomness. To drive home this point further, the lower photo in the figure is of the wake of a tanker inclined at roughly 45 to the mean current. The pattern assumed by the oil slick is amazingly similar to that in the upper right photo, even though the Reynolds number of the ship wake is on the order of 10 7 . The sheer range of length scales that are interesting in fluids problems is pretty remarkable too. Active research ranges from flow in microchannels (blood flow in capillaries, for example) all the way up to cosmic systems like nebulae. The upper left photo in Fig. 3 shows the Kelvin-Helmholtz instability, which arises in the interface between flow streams at different velocities. The photo shows a rectangular tube (the 18 inch ruler in the image shows the scale), with pure water moving left-to-right on top and colored salt water moving right-to-left below. The upper image on the right is of clouds near Denver. On the leeward (sheltered) side of mountain ranges, you will often have layers of high winds above relatively slow air. When clouds sit near the interfaces, these Kelvin- Helmholtz structures result. Needless to say, the cloud structures are much bigger than those seen in the lab, but the math is the same. (The cloud image is taken from “Hydrodynamic Stability” by Drazin and Reid, also on reserve.) 1

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Figure 2: Persistence of flow organization, for Reynolds numbers spanning five orders of magnitude.
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