Welcome back to Sports and Building Aerodynamics. In the week on basic aspects of fluid flow. This is the second module about boundary layers and we start again with a module question. What you see here are two movies of separated flow around a circular cylinder at a certain but not yet communicated Reynolds number. The question is, which statement is correct. Both flows are laminar. Both flows are turbulent. Flow 1 is laminar and flow 2 is turbulent. Or vice versa flow 1 is turbulent and flow 2 is laminar. Please hang on to your answer and we'll come back to this question later in this module. At the end of this module you will understand the concept of flow separation. You will understand how flow separation is influenced by the type of body, bluff versus streamlined. How it is influenced by the type of boundary layer, laminar versus turbulent. You'll also understand how the flow around a circular cylinder changes as a function of the Reynolds number. Finally, you will understand two interesting counter-intuitive aspects on boundary layers and flow separation. First, let's start with flow separation. In the previous module, we focused on the flow over a flat plate where actually the approaching flow direction was parallel to the plates. And we had a zero pressure gradient there in the external flow. However, if you have a non-zero pressure gradient for example over a curved surface. Then positive and negative pressure gradients can occur and this will influence the boundary layer profile as illustrated in this drawing here. So indeed at some point with the negative pressure gradient, you can get a decelerating flow, where the boundary layer thickness will increase rapidly and you will get a point of inflection indicated here, also in the drawing with the red dot. There is also the point S where flow separation will occur. Because downstream of this point you can get a reverse direction and a backward flow. And so the separation point is defined as a point where the shear stress is 0. And where the flow actually detaches or separates from the surface. Flow separation depends on quite some parameters the most important of which are the adverse pressure gradient, the geometry of the flow, and whether the boundary layer is laminar or turbulent. What you see here is the flow actually around a so called bluff body. So, a non-streamlined body. In these cases, you will get a steep pressure gradient and that will lead to fast separation. And also to a often complex wake behind the body. If you want to have a weak pressure gradient, well what you need to do then is to have a trailing section actually that has a streamlined shape, as shown here. And a weak pressure gradient can delay flow separation. Sometimes even to that extent that separation only takes place at the trailing edge. What you have with buildings with sharp edges, which are bluff bodies with sharp edges, is that separation always takes place at these sharp edges. In cycling aerodynamics, for example, the cyclist does not have sharp edges, apart maybe from some aspects of the bicycle and the helmet. But the cyclist itself has rounded edges. Nevertheless, it's a non-streamlined body, it's a bluff body. And also here flow separation will take place somewhere on the surface of this cyclist. With streamlined bodies on the other hand it can be different. Separation can be absent indeed as mentioned before until the point of the training edge where the flow of course has to detach. What you see here is what we also showed in one of the previous modules, the flow around an airfoil in the wind tunnel. And you see that as the angle of attack increases that suddenly the body is not streamlined anymore. And that you get flow separation and indeed the complex wake. But for low angles of attack, you have almost no flow separation here. If you want to resist flow separation, then the difference between laminar and turbulent boundary layers is important. Because turbulent boundary layers can much easier withstand adverse pressure gradients so we can delay flow separation. And this is important and we'll show that later has a very important effect on the aerodynamic drag. And the reason why this is, is that actually the velocity profile as shown in this graph is fuller, it has more energy. So this quite different from the lamniar boundary layer. For example now, let's look at the flow around a circular cylinder at different Reynolds numbers. On the left side you see the laminar flow for a laminar boundary layer. And this boundary layer will separate already at an angle of 82 degrees. While in the turbulent boundary layer the separation point actually is further downstream so separation is delayed. Because indeed the turbulent boundary layer attaches better to the surface. Of course at some point, in this case 125 degrees the flow will separate. It is still a bluff body. So this is quite an important difference, the separation point, as indicated here with the circles. And this is actually the visualization of this flow in an animation, and the flow in both cases is very unsteady, very transient. But you see that on the left side a laminar flow on average, because separation point also might vary a little bit as a function of time. But on average it is 82 degrees, while on the right side, in the turbulent boundary layer, is 125, on average again. [BLANK_AUDIO] Let's focus now on the flow around a circular cylinder, which is fixed so not rotating, and also not translating, in a uniform low velocity approach flow. So it is a laminar approach flow. Let's look then at different Reynolds numbers. If you have a very low Reynolds number. For example, between one and between four, then you see the fluid speed contours as indicated here. With the high values indicated in orange or red color and the low values indicated in blue. So what you see here is a symmetrical flow pattern for the symmetrical problem. It does not have very pronounced transient behavior. There is no clear separation even, that can be distinguished here. But this changes when we move to the higher Reynolds numbers. This is Reynolds number between 4 and 40, where you will see that you get two standing vortices actually downstream. Those are actually quite stable. The flow in this wake is fully laminar. These vortices actually also act as a bit like rollers over which the rest of the flow will occur. And as the Reynolds number increases, these vortices get more elongated as you can see in the figure on the right side. Then let's increase the Reynolds number even further between 80 and 200. Then, what we get is a so called vortex street, that interacts with the pair of attached vortices. You will get, actually, this vortex shedding. And, this will generate on the cylinder an oscillating lift force. With a specific frequency that can be obtained from the Strouhal number. Which is about 0.21 for the circular cylinder. And this value actually holds for quite a large range of Reynolds numbers. What is important also here is that the vortices in this wake are laminar, and they remain laminar to a very large distance downstream. So let's increase the Reynolds number even further then between 200 and 5,000. What you see here on the left side is the fluid speed contours for a Reynolds number of 1,000, and on the right side you see the vorticity indicated for the same Reynolds number. Here we have the vortex street that is also present, but it now becomes unstable and irregular. And the flow in the vortices themselves also becomes chaotic, however the vortex shedding still occurs at the Strouhal number of 0.21. Okay, increasing the Reynolds number even further, but we remain below 300,000, then we get this flow pattern. The boundary layer is laminar, so the separation occurs at the angle of 82 degrees as discussed before. But the wake however can be fully turbulent. So, separation indeed at this rather fixed point, so more upstream at the cylinder and the pressure in the wake is nearly constant. and lower than the upstream pressure. And the drag coefficient is also about constant and about 1.2. And then if we increase the Reynolds number even further, so above 300,000, but we remain below three million, then we get the turbulent boundary layer. So the boundary layer indeed will become unstable. At some point it transitions to turbulence. Then this turbulent boundary layer will stick better to the surface and separates only at 125 degrees from this forward stagnation point. In this case, the pressure in the wake will be higher than with a laminar boundary layer. This will again be a very important aspect for aerodynamic drag. And actually the drag coefficient itself suddenly reduces to the value of 0.33. Some important comments here. The different Reynolds numbers that are mentioned here are actually for a smooth surface. And the roughness of the surface will really influence or can influence these values to a large extent. Also the intensity of fluctuations in the free stream can do that. So, all the images and animations shown before in this module were for a smooth cylinder with a low level of fluctuations in the free stream. So you could say, a laminar approach flow. At much higher Reynolds numbers even than discussed before, so larger than 3 million. Well then this separation point actually will move a bit upstream, again with increasing Reynolds number. And then I would like to focus on two counter-intuitive aspects, that are also mentioned by Kundu and Cohen in their book. The first one is that small causes can have large effects. Consider for example, a body, in this case, a ball with a diameter d and an approach flow speed U infinity. And let's consider a flow that first has a zero viscosity. So this is an inviscid fluid, inviscid flow, is the theoretical case, then a low viscosity and then changes to high viscosity. Then you can draw these speed profiles so as a function of distance from the wall. Where you first have the uniform profile for the inviscid flow. And then the highly turbulent flow with a very steep velocity gradient close to the wall. And then the velocity gradient decreases as the flow becomes laminar. In the first case, you have no boundary layer. So this is again the theoretical case indeed. Then you have a steep boundary layer. Then we have a weak slope. However in the first case, then this means we have a zero skin friction. Then if we have the highly turbulent flow, we have a high skin friction, and then again we have a lower skin friction. So this is a non-monotonic trend, that is quite remarkable. And you also see this very large difference in flow patterns when you focus on the contours, those contours of speed around a circular cylinder. For the inviscid case and the laminar case, they actually are very similar. And this is for laminar case at very low Reynolds numbers, I have to mention. But then in between you get the sometimes very complex and unsteady flow around the circular cylinder. There is again a clear, non-monotonic trend in the flow behavior. The second counter-intuitive aspect is that symmetric problems can have asymmetric solutions. And this is also something we briefly addressed in module 4. And indeed we saw in several ranges of Reynolds numbers...3 we found for the cases which all have a symmetric geometry and symmetric boundary conditions, we found this unsteady behavior. So this also means that in CFD simulations, numerical simulations, if you force symmetry it's possible that you will not get a realistic solution. Let's turn back to the module question then. Two movies of separated flow around a circular cylinder at a certain Reynolds number, and which statement is correct? Well, I can show you the Reynolds numbers now. For the left animation it's 1,000. For the right animation it's 100,000. And the right answer here is answer C. First flow is laminar albeit very unsteady, and the second flow is turbulent. In this module, we've learned about the concept of flow separation. We've seen how flow separation is influenced by the type of body which can be a bluff body versus steamlined body. And how it was also influenced by the type of boundary layer, laminar versus turbulent. We've also seen how the flow around the circular cylinder changes as a function of Reynolds number and that this flow can be quite complex. Finally, we have looked at two interesting counter-intuitive aspects on boundary layers and flow separation. The next module will focus on the effect of flow separation on aerodynamic drag. We're going to see how boundary layers and boundary layer separation influence the form drag and the skin friction drag. And we will look at another counter-intuitive aspect on aerodynamic drag. Thank you again for watching and I hope to see you again in the next module.
