[BLANK_AUDIO] Welcome back to Sports and Building Aerodynamics in the week on wind-tunnel testing. In this module, we're going to focus on similarity and flow quality and we start again with a module question. A wind-tunnel test is performed with a building model at scale 1:50 and for a full-scale wind speed of 10 meter per second. The question is, is it possible to match the Reynolds number with that in full scale? A yes, B no. 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 importance of similarity in wind-tunnel testing. You will understand the most relevant dimensionless numbers and their meaning. The difficult issues in matching these dimensionless numbers in the wind tunnel, and some very basic items of flow quality. Usually, wind-tunnel testing in building aerodynamics is performed with scale models and these scale models are used to predict full-scale behavior. And then strictly, the scale model and full-scale reality should be similar. Or, similarity should be achieved, also called similitude. There are different types of similarity. Geometric similarity, first and foremost, means that if you scale building dimensions, you have to do this consistently, and you also have to scale the appropriate length scales in the atmospheric boundary layer. So this type of rescaling is clearly not allowed. Then there is kinematic similarity that applies for the position, velocity and acceleration in the flow field. And then finally there's dynamic similarity concerning forces, acceleration and so on, which actually, intrinsically, also includes geometric and the kinematic similarity. 34 00:01:42,914 --> 00:01:46,710
So, based on the non-dimensional form of
the Navier-Stokes equations that we discussed in the first week of this MOOC, you can actually derive and find dimensionless numbers which should have the same value or similar value in model and in full scale. And let's have a look at some of those numbers. The first one that we also discussed earlier, in this week, but also in the first week, is the Reynolds number, which indicates, or is a measure of the ratio of inertia forces to viscous forces. Then there is the Mach number, as you see indicated here, the speed at a certain point in the flow field divided by the speed of sound. And this is an indication of the inertia force versus the elasticity force. Then there is the Froude number which indicates the inertia force in proportion to the gravity force. And here L is a length scale and g is the gravitational acceleration. And then there's the Grashof number, which indicates the ratio of buoyancy forces to viscous forces. And here you see in this equation the thermal expansion coefficient beta, the gravitational acceleration appearing, and also a temperature difference. 55 00:02:47,830 --> 00:02:49,510
About the importance of dimensionless
numbers. Well, the Froude number, actually, is only important for dynamic tests in which we are going to include the motion of the model. This is very important for structural engineering. But for this MOOC we're not going to do that, so we are not going to focus on the Froude number anymore. So when we apply our sports and building simulations in the wind tunnel, we're going to assume that the model is stationary and that the Reynolds and the Mach number are the important similarity and flow quality numbers. If you can match those to the full-scale values, then we will have a dynamically similar model-scale test. And that then means that the non-dimensional functions that you can derive of the velocity components, the pressure coefficient, density, viscosity, temperature and so on, they will be the same in the model and in full scale. So let's look at a few issues here, a few problematic issues, Reynolds number matching. In practice it's seldom possible to match both Reynolds number and the Mach number and often you can match none of those. The Mach number is actually not so important if you're looking at low-speed applications and sport and building aerodynamics are certainly low-speed applications with Mach numbers well below 0.4. The Reynolds number is often important, and we saw that in the first week. For example, for a flow around a cylinder, circular cylinder where the Reynolds number really can determine where flow separation takes place, and it also has a very large effect on the drag force. But as mentioned before, Reynolds number matching is often not possible in building aerodynamics. Look for example, at this case where we have a full-scale model that we scaled down in the wind tunnel with a factor 50. In the wind-tunnel, we also use air as a medium so the kinematic viscosity remains the same. And this would mean that for a full-scale wind speed of 10 meter per second the reduced-scale wind speed to match the Reynolds number should be 500 meter per second which is well above a Mach number of one. And here it would severely violate Mach number similarity. Even if it would be feasible to establish such a very high wind speed in the tunnel. So the conclusion is: matching of Reynolds number is often not possible. But sometimes this also does not matter that much. In building aerodynamics for example, certainly when we are focusing on buildings with sharp edges, the separation points, as also mentioned earlier are at those sharp edges. And that yields flow fields at small scale that are often much less Reynolds number dependent than you would have for example, with objects with rounded shapes such as the circular cylinder that we have discussed before. If we have buildings with round shapes and the absence of sharp edges where flow separation would would take place, then what is sometimes done in wind tunnels, it's actually roughening the surface of the models. To make sure that the transition from laminar to turbulent boundary layer occurs more closely to what happens in the reality. Often, also we see that the distortion of the flow in building aerodynamics is negligible and Reynolds number independence could well be achieved for Reynolds numbers that are larger than about ten thousand. However, there are some other particular cases in which Reynolds number similarity will be important. For example, and this is a case study that we'll focus on in week four, if you're focusing on natural ventilation, that can take place sometimes through very small openings. Well, scaling down these openings in the wind tunnel might reduce the flow through these very narrow openings from a turbulent to a laminar flow. And then of course you're severely violating Reynolds number independence. And that's why natural ventilation studies in wind tunnels are far from straightforward. Another issue is Grashof number matching. And this also deals with for example ventilation of buildings where thermal effects, buoyancy can be important. And let's for an example look at this stadium. It's a football stadium that has some ventilation openings, and let's try to scale this down in the wind tunnel and see if we can reproduce that flow. Well, let's take a scale of at least 1:50 because the stadium is quite high, there is an internal height of 66 meter. Let's assume outside is 19 degree C, inside 26, so a 7 degree difference that can help the wind in ventilating the stadium. So we'll get the thermal buoyancy there. We can calculate the Grashof number, which in this case because of the large height of the stadium gives a very large number: 3.25 at 10 to the power of 14. And then, ideally, this is the number we should match in the wind tunnel. Let's see if this can be achieved. Well in the wind tunnel we also use air so again kinematic viscosity at full scale and reduced scale is the same. There's a factor of 50 difference in the length scale. In the Grashof number this has a power of three this dimension so it's 125,000. And this means that if you want to compensate for the smaller scale we have to do this with the Grashof number matching by temperature. So this means that we would have to establish a temperature difference that is 125,000 times larger than in reality. So this is 875,000 Kelvin, which is about 150 times hotter than the surface of the sun, which is clearly not feasible. So indeed the conclusion here is that matching Grashof numbers is often not possible, and this also explains why there are not that many thermally-induced ventilation studies being performed in wind tunnels. And this is also a reason why these kind of studies often has to be performed with computational fluid dynamics, or with full-scale measurements. Let's turn back to the module question now. A wind-tunnel test is being performed at the building model scale of 1:50. Well, actually, as mentioned before in this presentation, it's not possible to match this Reynolds number. Finally, another issue, a third issue in similarity, is the stratification of the atmospheric boundary layer. As mentioned also in one of the previous modules, usually wind engineers get a break here because we want to focus on strong winds for many of our applications. Where the ABL is so well-mixed that the effect of temperature gradients on the flow is often negligible. And this is indeed a good approach, a suitable approach for, for example, pedestrian-level wind studies, wind loads on buildings, wind energy and so on. But not necessarily for air pollution. And certainly also not for the urban heat island effect where stratification effects will become very pronounced. But irrespective of this applicability its extremely difficult to model stratification, thermal stratification in wind tunnels. Finally let's give a few comments about flow quality. In aeronautical, climatic, and general-purpose wind tunnels what we usually want to achieve is a smooth, uniform mean wind speed profile that is as smooth as possible. And with a turbulence intensity that is as low as possible. For example in the wind tunnel that we have used for cycling aerodynamics, and which you will learn about in week six, the approach-flow turbulence intensity due to the proper use of honeycombs and screens is only 0.02%, which is extremely low. But in atmospheric boundary layer wind tunnels, we do not want to have this smooth, uniform wind speed profile, we want to have the appropriate wind speed gradient. And we want to have high turbulence, not just any turbulence, a turbulence that fits the turbulence spectra that we find in reality. Concerning flow quality, there is a set of flow indicators that has been developed in the past and you can find more about this in this publication. In this module, we've learned about the importance of similarity in wind-tunnel testing, about the most relevant dimensionless numbers and their meaning, the difficult issues in matching dimensionless numbers such as the Grashof number and the Reynolds number, and some very basic items of flow quality. In the next module, the seventh one, we'll focus on some important aspects of best practice in wind-tunnel testing, in particular as related to wind engineering applications. We'll see what the blockage ratio means and how important it is. We'll look at consistent modeling of length scales, and at some main issues involving Reynolds number scaling again. Thank you for watching, and we hope to see you again next time. [BLANK_AUDIO]
