Welcome back to Sports and Building Aerodynamics, in the week on basic aspects of fluid flow. This is the third module on boundary layers. And we start again with the module question. A ball with a smooth surface is launched into the air, at a flow Reynolds number of about 400,000. When the same size of ball, with a rougher surface, is launched at the same flow Reynolds number, this rougher ball will, A, fly less far than the smooth ball, B, equally far as the smooth ball, or C, farther than the smooth ball. Please hang on to your answer, and we come back to this question later on in this module. At the end of this module you will understand the effect of flow separation on aerodynamic drag. You will understand how boundary layers and boundary layer separation influence form drag and skin friction drag. And you will understand an interesting counter-intuitive aspect about aerodynamic drag. So what are the consequences of flow separation? Well for a bluff body, due to flow separation what you will find is that often the form drag is much larger than the skin friction drag. For a streamlined body however, often you will find that the skin friction is substantially larger than the form drag. And the limit case there was a semi-infinite flat plate that is parallel to the oncoming flow direction. For a cyclist, for example, which is a bluff body in time-trial position, computer simulations indicate that 93% of the aerodynamic drag is form drag and only 7% is skin friction drag. Let's focus again on the flow around a circular cylinder. This is the case for a so-called irrotational flow or you could also say flow with in this case zero viscosity. And then if you focus on the pressure distribution around the circumference of the cylinder, you see the overpressures indicated at the upstream and downstream side and on the sides you see the underpressure. And this was unrealistic; we call that the paradox of d'Alembert because indeed if you integrate the pressure over the circumference you will get a net zero force. So this is not realistic. However, if you include the boundary layer concept and let's say we have a Reynolds number that will keep the boundary layer laminar, and then you can get this profile of the pressure coefficient as a function of the angle. And you can also draw that in a similar way as we did for the non-viscous flow. And then you will see that there is actually quite a large part of the circumference where the pressure is negative. That means negative compared to the reference pressure. And then indeed if you integrate this pressure over the surface, you will get a resulting force, a drag force in the downstream direction. If you then look at the turbulent flow or the turbulent boundary layer, well then you see that there is actually, as we mentioned also in a previous module, a much better pressure recovery in the turbulent case. So you will not have this profile of the pressure, but you will get this one with actually a lower absolute value of the pressure in the wake. But on the sides you will get a larger underpressure. But then if you integrate again these pressures over the surface, you will find that the resulting drag force is less than with the laminar boundary layer. This can also be shown as a function of drag coefficient. So what you see here is the drag coefficient as a function of the Reynolds number. And you see that, as the Reynolds number increases as long as the flow stays laminar, then you get a rather gradual decrease of this drag coefficient. But at the moment where the flow, where the boundary layer transitions from laminar to turbulent, you get a sudden drop. And the sudden drop is quite substantial. So there are two reasons for that drop. First of all, it is the narrower wake, because the separation occurs later. For example at the angle of 125 degrees and not 82 degrees, which means that your turbulent wake is narrower. And this indeed yields lower drag force. But another point is that apart from being narrower, this wake also has a better pressure recovery. And that was shown in this figure. So, even though the skin friction is higher in a turbulent boundary layer but for bluff bodies this does not matter that much because there, form drag is often much larger than skin friction drag. So this means that if you have the turbulent boundary layer that the overall drag force will be substantially lower. than in the laminar boundary layer case. So, let's look then at, at the flow not around a circular cylinder but around a sphere, and we again assume that it is a non-rotating sphere so a translating sphere and the behavior here is actually very similar to that of a circular cylinder. Transition to turbulence occurs at a bit higher Reynolds number: 500,000. And as with the circular cylinder, with higher Reynolds numbers, the separation point moves a little bit upstream. Here there is no vortex street, but there is, a kind of ring-like vortex that starts oscillating, and then shuts off, breaks off at higher Reynolds numbers. And this is the drag coefficient as a function of the Reynolds number for a sphere. Where also here we see the sudden drop where and the boundary layer transitions from laminar to turbulent. Let's turn back to the module question, where we have a smooth ball, or a ball with a smooth surface that we launch into the air at a Reynolds number of about 400,000. And then we do the same, for the same type of ball, but with a rougher surface. And then, the question was, which statement here is correct. And this is statement C. The ball with a rough surface will fly substantially farther than the smooth ball, because of the lower form drag due to the presence of the turbulent and not the laminar boundary layer. So that brings us to a counter-intuitive aspect on aerodynamic drag and boundary layers. And that is that rougher surfaces can have a lower drag. And the reason is that for a range of Reynolds numbers, roughening the surface will decrease the form drag. And the reason for that is that if you roughen the surface you will have the transition of a laminar to a turbulent boundary layer, that remains attached to the surface longer. So there is two aspects then. First of all, you have a narrower wake. And second, in this narrower wake you have a much better pressure recovery. And both of these effects can reduce the form drag, and for bluff bodies thus also the total aerodynamic drag. And this is also the reason why golf balls have dimples so the surface is rougher. and the boundary layer stays attached longer, with a narrower wake, and better pressure recovery, and the ball will fly farther. But then you might wonder why did bicycle time-trial helmets have dimples in the past and have they now disappeared, or almost completely disappeared? And there might be different reasons for that. First of all, if you calculate the Reynolds number around this kind of helmet, it's already quite large. And this could mean that the boundary layer is turbulent anyway. And that adding the dimples would not really help. On the other hand, it might even increase the resistance by increasing the skin friction. Also the surface of a helmet is also only a very small fraction of the total surface of a cyclist and a bicycle. In golf balls, for example, it is the total surface of the body. Here it's only a small fraction. And finally, as mentioned before, the helmet itself is more streamlined than the cyclist. This means that the skin friction drag will be relatively more important than it is for the cyclist's body. So the dimples might even have a small negative effect. In this module, we've learned about the effect of flow separation on aerodynamic drag. We've seen how boundary layers and boundary layer separation influence form drag and skin friction drag. And we focused also on an interesting counter-intuitive aspect about aerodynamic drag. In the next module, which is the final module in this week, we'll focus on some basic aspects about the atmospheric boundary layer. The concept of neutral stratification, and we'll look at the typical profiles of mean wind speed and turbulence intensity in this neutral atmospheric boundary layer. We'll also see how the aerodynamic roughness length can be practically estimated. Thank you for watching and we hope to see again in the next module.
