Now we will look at the flow visualization experiment conducted to observe the eddy phenomenon of Poseokjeong. We made a section model of Poseokjeong channel using 3D printing. We placed the model inside a water tank, and used dye solution to visualize the movement of current. This is the water tank used in the experiment. We placed the 3D-printed section model of Poseokjeong inside the water tank, and conducted the visualization experiment with the Reynolds number of 7500. And the process of the experiment is shown on the slide. We put the dye solution at this inner part and also at this outer part of the section model for visualization. Characteristic observations were that at the inner part, flow separation of the water occurs at the vertex here and forms a big recirculation area. On the other hand, at the outer part here, a section of slowed flow is created. When we observe these characteristics over time, we can see, thanks to the dye solution, that flow separation occurs here, and the separated fluid creates large recirculation. And the main flow continues like this. Meanwhile on the opposite side, a slow flow of fluid is formed. Let's look at a video clip of this. You can see here a flow separation occurring. And afterwards, it recirculated in this way. And here, an area of large recirculation is formed. When we enlarge this part, we can see the recirculation more clearly. As you can see, it flows along the shear layer, and the flow recirculates very slowly. Therefore, the cup that floated along this current gets stuck in the eddy and rotates. On the other hand if we look at this opposite side, as I have said before, because the water flow is very slow, the area where an eddy forms is extremely narrow. Therefore, it would be difficult for a cup to rotate here. So unless one quickly grabs a cup as it floats along, it will just float by on the current. After this experiment, we studied this phenomenon further with numerical analysis. Generally, such complicated fluid movements should be calculated with partial differential equations. However, partial differential equations are not easy to work with. Because it's hard to find an exact solution, we use the finite element method (FEM) and obtain an approximate solution. This is how we do it. Let's say we have a physical phenomenon like this. We divide this into many grids. And afterwards, we convert the partial differential equation to an ordinary differential equation. Then we can obtain an approximate solution. The finite element method has been used for a long time. It's widely used in fluid mechanics, heat transfer, and structural analysis. In fact, within fluid mechanics, the finite element method is applied in studying internal flow, external flow, fluid-structure interaction, hydraulic shock absorber internal flow, or turbine or such flow analysis. This is the FEM study conducted by Professor Shim, Eun Bo of Kangwon National University. He made a grid model of Poseokjeong from the inlet to the outlet. And factors in surface grid such as viscosity, Reynolds number, surface tension, and surface roughness are all considered in the analysis. The result of the analysis shows that, as we saw earlier in the experiment, eddies formed at places where the channel sharply curved or changed in width. The color red indicates high flow speed and green low flow speed. We can see here shortly after the inlet the speed rapidly increases. And then, the speed slowly decreases, and at places where the width changes a lot or the channel sharply turns, we can notice that eddies form. This is the overall diagram but if we see sections, here when the channel curves sharply, the speed increase as the cross-section area of the channel changes, and a strong eddy is formed here. And here as well, we can see that this happens near the inlet too. On the contrary, near the end where it's slower, the speed of flow decreases. The formation of eddies still occurs at places like this, but the vorticity is much smaller. The basic principle of vortex formation arises from velocity gradient. For example, in case of a shear flow that's fast at the top and slow at the bottom, a vortex forms like this. Rotation occurs, and due to velocity gradient, vorticity distribution forms like this. After all, as fluid flows, the speed either increases or decrease according to the change in the width of a channel, and when the channel suddenly widens, flow separation occurs and a velocity gradient is formed resulting in an eddy like this. We can observe these in nature and inside our body as well. In a case of angiostenosis where blood vessels get blocked, in the back of the constricted part, the line of flow shows that large eddies are formed. When we express this in equivorticity lines, we can see that at the crest, where constriction occurs, the value is very high. Let's look at different inlet flows. In case of a Poisseuile flow, which is the straight inlet flow, large vortices form. However, swirling inlet flows decreases the size of vortices. Because the channel at Poseokjeong is 3 dimensional, not 2 dimensional, there are sections where swirling flow is formed and also sections where water flows straight. And we know that depending on the type of in-flow at a specific section, the size and intensity of the eddy can vary. The flow pattern at Poseokjeong can be also observed in nature. This is a strait in Norway. When water runs north from south, we see here that vortices form here, like these. However, when the water runs in the opposite direction, vortices form in different locations. In the northbound current, they are formed at these two places, but in the opposite current, they are formed here and also here. These patterns are caused by the change in the width of the channel and subsequent change in the flow speed which in turn causes flow separation and creates recirculation areas. These phenomena that we can see in Poseokjeong are also found in nature. Another example is found in the sand of shallow coastal water where vortices grind off the bottom as they move. When we look at the shape left on the bottom by the movement of vortices, we can see that it looks similar to the Poseokjeong channel. From this, we can assume that the Silla people observed vortices in nature and applied it when constructing Poseokjeong. This shows how wise our ancestors were.
