Welcome back to Sports & Building Aerodynamics, in the week on cycling aerodynamics. In this module, on CFD simulations for a single cyclist, we start again with the module question. CFD simulations of the aerodynamic drag of cyclists are validated with wind-tunnel measurements on a real cyclist. What is the typical accuracy of such simulations, if they are performed according to best practice guidelines? Is that A) Better than 5%. B) About 10%. C) About 20%. or D) Worse than 25%. So 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 how high-resolution CFD simulations of cycling aerodynamics are performed. You will understand the accuracy of CFD simulations of aerodynamic drag. You will understand the flow field around a cyclist, and the pressure field on a cyclist body. This is still part of the research project on optimization of power output and aerodynamic drag. And this is the part where we're going to validate the CFD simulations in order to demonstrate their potential accuracy. More information about these CFD simulations, all the computational details, can be found in this article. And we focus again on three positions on the bicycle, the upright position, the dropped position, and the time-trial position. The geometry of the cyclist was obtained by 3D laser scanning, using exactly the same data files as were obtained for the rapid prototyping of the model cyclist that you saw before. So this is the model geometry for the upright position, and here you see the model geometry for the time-trial position. Then this model was placed into a computational domain, with a blockage ratio that is exactly the same as in the wind tunnel, because we want to reproduce the wind tunnel conditions as much as possible. Then a high-resolution high-quality grid was made. It's a hybrid grid you see, and it has 7.7 million cells. We applied grid-convergence analysis to be sure that we have a grid-independent solution. The average cell size in the wake resulting from that grid-convergence analysis is three centimeters. So we have y-star values on the surface of the cyclist below three, which means that indeed we are resolving the laminar sublayer, which is very important because we want to accurately be able to simulate the boundary layer on the cyclist surface, but also flow separation of this boundary layer. So the minimum cell size at the surface of the cyclist is only 30 micrometers. And this is really needed in order to be able to resolve the laminar sublayer at the cyclist body. Here you have a more detailed view of the computational grid. And you see that the cell sizes close to the surface of the cyclist are indeed very, very small, indeed yielding this y-star value below three. Then boundary conditions of course need to be applied here. We applied a wind speed of 10 meters per second, and the turbulence intensity from the wind tunnel of 0.02%. 10 meters per second is a bit lower than in the wind-tunnel test. But we did that here on purpose, because we wanted to limit the grid resolution in the boundary layer. And even with 10 meters per second, you already have to use only 30 micrometer cells. We know from week one that the thickness of the boundary layer actually is inversely proportional to the Reynolds numbers. So the higher the wind speed in the simulation, the thinner this boundary layer will become and the smaller the cells we need to use. We checked the Reynolds number independence here and at 10 meters per second for the full-scale cyclist this was satisfied, so that's why we use this lower speed. Then some other boundary conditions. The cyclist body is a smooth no-slip wall. The side walls were modeled as slip walls, just in order to avoid the high grid resolution that we otherwise would have needed to apply at the solid walls, at the no-slip walls. And at the outlet there we set the reference static pressure. Then some other important computational settings and parameters. As a solver we used the Ansys/Fluent CFD code. First, we chose the 3D steady RANS equations as the approximate form, and combined that with the standard k-epsilon turbulence model for the higher Reynolds number part and close to the surface of the cyclist we applied low-Reynolds number modeling with the one-equation Wolfshtein model. And second-order discredization schemes. The SIMPLE algorithm for pressure-velocity coupling and second-order pressure interpolation. Then we also applied Large Eddy Simulation, together with the dynamic Smagorinsky sub-grid scale model. And here you see some other settings. I will not read them in detail but you see that we have a times step of about four multiplied with ten to the minus four seconds. And that yields a Courant-Friedrichs-Levy number below one in the majority of the domain, which is important, and even about 0.2 in the wake. And we need about 1.4 flow-through times to obtain stationary values of the drag and the surface pressures. Let's look at some results then. First, visualization of some results. Here you see in a vertical plane, cutting midway through the cyclist, you see the wind speed, where high speeds are indicated in the orange and red. And the low speeds you see them in the wake and also below the helmet, because this is not really an aerodynamic position of the head. So you see also below the helmet, actually, a low-velocity region. Also there a pronounced wake that will indeed increase the aerodynamic drag. Here we might do a first qualitative comparison between the wind-tunnel tests and the CFD simulations that we obtained. Where, in the CFD simulations indeed you see this vortex shedding, so the flapping of the flow. And that's also something that was quite clear from the wind-tunnel tests. This is a top view of the cyclist in upright position. You see that the wake is actually a little bit bent away from the center plane. And that's because one leg of the cyclist there, because this is a position without pedaling, one leg is a bit in front of the other. But what is clear here is that there is indeed a quite wide wake behind the cyclist, and that this is also a very unsteady wake. This is the time-trial position. A bit a similar image except for the fact that now the wake is not as tall, not as high as it was before. You also see now that the helmet is in a more aerodynamic position and that the low-velocity region behind this helmet is much more limited. So this is a position that definitely gives less aerodynamic drag. And you can also look at this from the top. And even you can see that compared with the upright position, even the width of the wake here in this aerodynamic position is less, is more narrow. Let's then look at a more quantitative validation study. Here you see results that we obtained for the upright position for the drag area of the cyclist, with the RANS approach and with the LES approach. And in the final column, the fourth column, you see the percentage difference with the wind-tunnel measurements. And this is 13% which is not too bad. Then looking at the dropped position, it is 7% for the RANS simulations, 3% deviation for LES, which is considered a very good agreement. And then for the time-trial position, it's 12% with RANS, and 6% with LES. Then we can look in more detail at the pressures. Because we had the 30 pressure plates on the body of the cyclist. This is the result for the RANS simulations. What you see in this graph is on the horizontal axis we put the pressure coefficients that we measured in the wind tunnel and on the vertical axis we put the pressure coefficients that we obtained with CFD. And if we have an exact match, that would mean that the points that you see in this graph would be on this red line. You see that some of them, or many of them are very close, but you also see that some of them are quite far off. This can be done for RANS. This can also be done for LES. Then you see that for LES, overall, the points move closer to the one-to-one line. This is for the upright position, we can have a similar result for the time-trial position. Where indeed, we see that many of the points are very close to the one-to-one line, but there are indeed some outliers. And when you look at those positions, those numbers, those are exactly the points that are on the side, of the body of the cyclist. So the pressure in front of the cyclist and at the back of the cyclist is predicted quite well. The points at the sides of the torso and the legs and the arms, there we get some discrepancies. The reason is that these are very difficult points to predict. That is where flow separation takes place, and these are flow separation points that also change position over time and are therefore very difficult to predict with Computational Fluid Dynamics. Let's then analyze the flow field a little bit more in detail. These are pictures of pressure coefficients in a vertical plane cutting through the cyclist. So this is static pressure made dimensionless and I have to mention that we cut the color bar here, so the actual pressure coefficients are higher and lower than those indicated here. But the color bar was cut to give a better visualization of the pressure field. You clearly see the overpressure in front of the cyclist and the underpressure behind him. And it's indeed overpressure in front of the cyclist that pushes him back and underpressure behind him that sucks him back, and you could look at it this way. And this then yields the total drag force. And this is for the upright position. You get similar results for the dropped position and for the time-trial position. Then another results we can analyze is the pressure field on the body of the cyclist. So, this is again static pressure, but then visualized on the cyclist and also here the color bars have been cut. You see that the lowest pressure, as mentioned also before, does not occur on the back of the cyclist, but on the sides of the torso, arms and legs, and even on the sides of the helmet, not on the back of the helmet. And this is also something that we noticed previously from the measurements. You can also get a similar image then for the dropped position and for the time-trial position. The number that you see indicated here at the back indicates the pressure coefficient, the minimum pressure coefficient at the back of the cyclist. And you see that by assuming, by taking a more aerodynamic position, that it's not only the pressure in front of the cyclist that will decrease, and it's not only the frontal area of the cyclist that will decrease and that will yield a lower drag force. No, it's also the pressure at the back of the cyclist, maybe a bit surprisingly, that decreases quite substantially. More information on the next validation study, that's for the dummy cyclist, can be found in this article. So I will briefly run through those simulations as well. So this is the 1:2 scale model. We focused here on the upright position only. For the computational domain we took the wind-tunnel dimensions, that you can see indicated here. We made two different grids here because we also wanted to evaluate the accuracy of wall functions. So this is the low-Reynolds number grid, then also another grid was made, with coarser cells. A more feasible grid, easier to construct. So this is the wall function grid, and then we applied Richardson extrapolation to determine the discretization error. This was 3%, which is considered to be certainly low enough, so certainly acceptable. And then we continued applying boundary conditions. Here we had to apply a higher speed because it's a lower cyclist or a smaller cyclist model. So for Reynolds number independence we had to go to the 20 meters per second, and this is also indicated here. This is the graph that we also saw earlier with the measurements. We can use the 3D steady RANS equations with a wide variety of turbulence models, and with both low-Reynolds number modeling and with wall functions. These are the other computational details. Then also Large-Eddy Simulation was applied, again with the dynamic Smagorinsky sub-grid scale model. With similar time-stepping features and run-through times as before. And then let's have a look at some results. Here, we only present results for the drag area. And what you can see here is that surprisingly, the relatively simple standard k-epsilon model provides a very good agreement with the measurements. And this is also the case for the SST k-omega model. And that even, in this case at least, Large Eddy Simulation gives a slightly higher deviation. We can also look again at this kind of graphs where we plot the wind-tunnel results versus the CFD results. And then here you see that indeed many of the points are very close to the one-to-one line, but there are also some clear discrepancies. Interestingly, here we see that the correlation coefficient for LES is higher than for the standard k-epsilon model, even though when we integrate those pressures over the surface of the cyclist, for the total drag force the standard k-epsilon model is a bit better. So that's the conclusion here from this graph. Let's turn back to the module question now. What about their accuracy. What, if you validate with measurements of a real cyclist, so not the dummy cyclist that is sitting still. But the real cyclist that is also moving, that has also clothing that has wrinkles, which you cannot reproduce in CFD. What is then the typical accuracy of such simulations? And the answer here is that it's about 10%. In this module, we've learned about how high-resolution CFD simulations of cycling aerodynamics are performed. We've learned about the accuracy of CFD simulations of aerodynamic drag. We've seen some issues about the flow field around the cyclist. And we've also looked at the pressure field on a cyclist body. In the next module, we're going to focus on CFD simulations for two cyclists, two drafting cyclists. Thank you very much for watching and we hope to see you again in the next module.
