[BLANK_AUDIO] Welcome back to Sports and Building Aerodynamics in the week on basic aspects of fluid flow. In this second module on flow properties we start again with the module question. What you see here are two drawings of streamlines obtained by a computational fluid dynamics simulation of the viscous, subsonic, compressible flow around an airfoil at a Reynolds number of 100,000, a Mach number of 0.5, and at a zero angle of attack. Which statement is correct? A, both flows are laminar flows. B, flow one is laminar, flow two is turbulent. Or C, flow one is turbulent and flow two is laminar. Or D, both flows are turbulent flows. Please hang on to your answer and we'll come back to this later in this module. At the end of this module you will understand the difference between laminar and turbulent flow. You'll understand how the simple train analogy explains the concept of turbulent viscosity. You will recognize the main features of turbulent flow, and you will understand the two very different definitions of turbulence intensity. Let's start with laminar versus turbulent flow. Well most flows encountered in engineering practice, and certainly also in sports and building aerodynamics, are turbulent. So this indeed holds for sports applications like cycling, but also the 100 meter sprint, for example, that we'll also address in this MOOC. And then, it holds for building aerodynamics. [BLANK_AUDIO] Concerning the difference between laminar and turbulent flow, there's an important experiment performed by Osborne Reynolds and published in 1883, with the title: An Experimental Investigation of the Circumstances which Determine whether the Motion of Water shall be Direct or Sinuous and of the Law of Resistance in Parallel Channels. This is actually a drawing of Osborne Reynolds together with his experimental setup where it's actually a container with water where he released dye into the water. And when he did that at rather small flow rates, low flow rates, the flow of the dye actually did not significantly effect the flow of the water and there was no mixing of the dye with the water, and that you see in the top drawing, so that was called a laminar flow. And then when he would increase the flow rate, well actually mixing started to occur, and with increasing flow rate, the mixing became more intense and more pronounced. And then this is turbulent flow as indicated in the second drawing of the tube. This is another illustration that shows the same experiment where you see the near-laminar flow and the turbulent flow, or maybe actually better the transitional flow from laminar to turbulent. So you see the dye actually generating or reproducing vortical structures in this flow. There are many different definitions of turbulence. This is one from the Encyclopaedia Britannica, that says: it's a type of fluid flow in which the fluid undergoes irregular fluctuations or mixing, in contrast to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow, the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction. I think this is a definition that many of us will recognize, and with which we actually indeed associate the difference between laminar and turbulent flow. This is another definition, also by Encyclopaedia Britannica saying: in fluid mechanics a flow condition in which local speed and pressures change unpredictably as an average flow is maintained. Common examples are wind and water swirling around obstructions, or fast flow (Reynolds number larger than 2,100) of any sort. Eddies, vortices, and a reduction in drag are characteristics of turbulence. And actually this definition is not completely correct, because the Reynolds number of 2,100, that applies for flow in tubes and not for all or many other flows. This is another definition here by Lewis Fry Richardson, saying: big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls, and so on to viscosity. Actually indicating the turbulence cascade, where larger vortical structures break up into smaller ones until finally they are so small that they are actually removed by viscosity and turned into heat. This is another interesting definition by Horace Lamb: I'm and old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is turbulent motion of fluids. And about the former, I am rather optimistic. A later quote is one by Marcel Lesieur saying that: turbulence is a dangerous topic which is at the origin of serious fights in scientific meetings since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what is exactly the problem to be solved. Yet another short quote is that by Peter Bradshaw saying: turbulence was the invention of the devil on the seventh day of creation, when the good Lord wasn't looking. A more extensive quote, also by Peter Bradshaw, is that: perhaps the biggest fallacy about turbulence is that it can be reliably described statistically by a system of equations which is far easier to solve than the full time-dependent, three-dimensional Navier-Stokes equations. And this is indeed very correct. Often we will need to go to the full time-dependent, three-dimensional Navier-Stokes equations to accurately describe fluid flow, at least in turbulence cases. So can we make a definition of laminar and turbulent flow based on the Reynolds number, which is defined as follows. So it is the ratio of inertia forces to viscous forces. So in the nominator we have the product of characteristic velocity and the characteristic length scale of the flow, and in the denominator there is the kinematic viscosity. But the question is, what is the characteristic velocity, and the characteristic length scale for a complex flow. There are many definitions that can be made on this, many different choices, and depending on these choices you will get completely different Reynolds numbers. In addition, it's also the case that the transition from laminar to turbulent flow does not always occur at the same Reynolds number. Small geometrical details can be responsible for this transition, but can also delay it. An often used definition, actually, is the following, saying that laminar flow is the flow in laminae. This derives from Latin, the Latin lamina means layer. So it's a smooth flow, where actually the only exchange of mass but also momentum then between the different fluid layers is the exchange of molecules. In a turbulent flow then, well you would have a chaotic flow, where fluid parcels, not molecules anymore, but big groups of molecules, are being exchanged between the different fluid layers. And this is schematically indicated here. The first aspect, actually, that is something that we related to molecular viscosity using a simple train analogy. Actually, if you have turbulent flow and you exchange not only molecules, but groups of molecules, parcels, then this momentum exchange between the different layers will be much more pronounced. You could say that this also gives rise to a sort of viscosity. This is called the turbulent viscosity. So is the definition easy between laminar and turbulent flow? Well to illustrate that or to focus on that, let's look again at our module question. Where we have the streamlines by a CFD simulation around an airfoil at Reynolds number of 100,000, Mach number 0.5, zero angle of attack. Well, maybe unexpectedly, the right answer is B. Flow one is the laminar flow and flow two is the turbulent flow. So what is actually going on here? Well, actually this is called a numerical experiment, performed with CFD. And the very interesting thing with CFD is that as opposed to nature you can actually switch between laminar and turbulent flow almost at the click of a button. So then, figure one is the result, actually a snapshot, of a laminar separated and unsteady flow, because indeed laminar flows can be unsteady, and this is just an image of the streamlines at a given moment in time, while in figure two you have a turbulent attached and steady flow. [BLANK_AUDIO] So, what is the conclusion about the difference between laminar and turbulent flow? Well, the conclusion maybe is that there is no generally accepted definition of turbulence, and that the best way to define it might be to summarize its properties. That is that turbulent flows are highly unsteady, so they appear to be random. They are three dimensional even if the nominal flow and mean flow is two dimensional. They have a large amount of vorticity embedded in them, the conserved quantities are stirred, so it's mixed and this means turbulent diffusion. This is a dissipative process so transforming kinetic energy to internal energy. You have coherent structures present in the turbulent flow, and the fluctuations in the flow occur at a broad range of length and time scales, so a large range of eddies or vortical structures are present. In turbulent flow we can also apply the so-called Reynolds decomposition, which is also named after Osborne Reynolds. Assume this measurement, for example, of a flow, where we have in blue, and with small letter u indicated the instantaneous speed at a given point. We can take the time average, then we get the red curve and indicated with the capital letter U. And when we subtract the red curve from the blue curve then we get the green curve, which actually indicates the turbulent fluctuations. If then you need to communicate these turbulent fluctuations to an audience, well then it's useful to actually convert those fluctuations into one particular value. First what you see here on the left side is then actually the Reynolds decomposition, so you split up the instantaneous speed in the mean speed and the fluctuating part. And then of the fluctuating part, you can actually determine the so-called rms value, root mean square. So you take the root of the mean of the square of the turbulent fluctuations. This is indicated with sigma and with subscript u for determining fluctuations in the x direction. In the same way, you can define them in the other two directions, again always in the same point. So you can do that for any point in the flow, and then you get these definitions of the standard deviation of turbulent fluctuations, or the rms values. And when you divide those by the mean speed that you find at this point, in this case in the flow direction then you get what is called the turbulence intensity in the three directions. However, for a complex, three-dimensional flow, sometimes also turbulence intensity is defined not by dividing by the mean speed U in flow direction, but by the mean speed in each of the three coordinate directions. And this actually is a very different definition of the one that we had on the previous slide. And unfortunately, sometimes in scientific publications, it's not mentioned what definition of turbulence intensity was used, and just the value is indicated. And then it can be very difficult to determine actually what the real value was of these turbulent fluctuations. Some additional comments on laminar versus turbulent flows. Well, laminar flows can be steady, as indicated here on the left side, but it can also be transient. Turbulent flows are actually always transient, but they can be stationary. This means that, if, in your mean approach-flow conditions are constant, so, invariable over a shift of time, then you have a statistically stationary flow. In this module, we've learned about the difference between laminar and turbulent flow. We've seen how a simple train analogy also explains the concept of turbulent viscosity. We've looked at the main features of turbulent flow and at the two very different definitions of turbulence intensity. In the next module we're going to focus on some basic aspects, concepts of fluid statics, kinematics and dynamics, and on the difference between the Navier-Stokes equations, the Euler equations and the Bernoulli equation. Thank you very much for watching, and we hope to see you again in the next module. [BLANK_AUDIO]