Welcome back to Sports & Building Aerodynamics in the week on building aerodynamics. In this module, we're going to continue our focus on wind-driven rain, and we start again with a module question, this time a question in two parts. Consider these four buildings and the wind direction is as indicated and let's assume that the four buildings are exposed to the same wind and rain conditions. Every building will receive the highest wind-driven rain intensity at its top corner, which is indicated with number 1. But the question is, which of these four buildings receives the highest wind-driven rain intensity at this position? Is that the first building, which is a low-rise cubic building, the second one, which is a wide building slab, the third one, which is a high and wide building slab, or the fourth one, which is a tower building? The second question is an open question, not multiple choice this time. If the rain impinges on a windward surface of a facade which can be an impervious surface that does not absorb rain water. Then the rain will run down along the facade and it will also accumulate on its way down. And then you could imagine that at the bottom of the facade of a high-rise building, you get very large runoff streams. So theoretically, it should be possible to take a shower at the bottom of a high-rise building. The question is, why does this not happen in reality? 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 how assessment of wind-driven rain is performed, and you will understand wetting patterns on building facades. So to assess wind-driven rain, there are mainly three methods, measurements, semi-empirical formulae and numerical simulation with Computational Fluid Dynamics. An overview of these methods is given in this article and I will provide a brief summary here. Actually, the measurement principle of wind-driven rain is extremely simple, but actually measuring it accurately, it appears to be very difficult. What you see here in this graph is on the left side a traditional rain gauge, with a horizontal aperture. So this measures the horizontal rainfall intensity and if you want to have a wind-driven rain gauge, then you make a vertical aperture as shown on the right, and then indeed you catch the wind-driven rain, you collect it in a reservoir and it can be measured. And this is an example of a practical implementation of a wind-driven rain gauge. You see the collection tray, in this case in PVC, attached to the building facade, then a tube that should deviate the rain water into the collector and then indeed the collector can be weighted, and then you get the amount of wind-driven rain, so this appears to be very simple. However, when raindrops impinge on such a surface, first of all, they stick to the surface, and then do not run down until there are a sufficient amount of raindrops. And then these raindrops will start evaporating, even during a rain event. Then they flow into the tube, also there they start evaporating and then they remain in the reservoir. And also from that reservoir they will be evaporating and certainly when the sun will start heating up the water in this reservoir. So, it is not as easy as one would imagine. There are some particular advantages and disadvantages then. The advantage is that the real complexity can be taken into account, but of course you're subjected to uncontrollable meteorological conditions. The measurement errors are a very big concern. Measurements are only valid for the building where you did the measurements and for the particular meteorological conditions, and often measurements are only made at a few discrete positions. A special case of measurements which I need to mention here are wind-tunnel measurements of wind-driven rain. And there are not that many groups in the world that have performed this, and the first to our knowledge were Inculet and Surry at the Boundary Layer Wind Tunnel Laboratory at the University of Western Ontario. And this was really a very nice, very interesting study, where spray nozzles were installed in a boundary layer wind tunnel, where the raindrop spectra were scaled very carefully, where the building facades were mounted with water-sensitive paper that actually turns from a yellow color to blue when the raindrops hit it, and actually then the wind-driven rain intensity was determined by very carefully counting, and sizing the stains on this facade. Of course, also here there are advantages and disadvantages. In a wind tunnel you can control your measurement conditions. You can measure at all positions across a building facade, but you need to scale raindrop spectra, which is not easy, although it was done in an excellent way here, and the measurements are very labour intensive because you have to size each of these stains. Then there are semi-empirical formulae. Actually, all existing semi-empirical formulae are based on the rather old equation by Hoppestad and by Lacy, which is indicated here. That relates the wind-driven rain intensity to the wind speed, U, the horizontal rainfall intensity, Rh, and the angle between the wind direction and the normal to the wall. And there is a proportionality factor here, which is the factor alpha, the wind-driven rain coefficient. But this equation is very simple and earlier we mentioned that wind-driven rain is quite complex because you have the complex wind-flow pattern around the building, different raindrop shapes and sizes, and actually, this means that all this complexity has to be put into this single wind-driven rain coefficient. Of course, it is impossible for this wind-driven rain coefficient to satisfy all these requirements. Nevertheless, some very valuable attempts have been made in the European Standard that later also became an International Standard on wind-driven rain assessment. Where this coefficient alpha is determined as a function of different influencing parameters of wind-driven rain. Nevertheless, there are some important disadvantages, of course there are also advantages. It's a simple formula, it's easy to use, so it's also suitable for standardization. But you can only obtain rough estimates, and sometimes the errors are a factor two to five compared with measurements. Wind-driven rain coefficients are actually only available for a limited number of configurations, and verification and validation is actually lacking. And that's a reason to turn to numerical simulation with Computational Fluid Dynamics. This approach then has five steps. The first four steps were actually made by Choi and later on we extended this approach with a fifth step. So first you start calculating the steady-state wind-flow pattern around the building. Then you inject raindrops of different sizes in this wind-flow pattern, of course you take into account the correct raindrop drag coefficient, terminal velocity of fall. Then you can calculate the specific catch ratio, which is for a given raindrop diameter, the ratio between the wind-driven rain intensity on the facade, and the horizontal rainfall intensity. When you integrate those values over the raindrop spectrum, you can determine the catch ratio. This is the ratio of the wind-driven rain intensity divided by the horizontal rainfall intensity. And finally this can be combined with meteorological data records to determine the wind-driven rain intensity on building facades for real rain events. Also here advantages and disadvantages, you can control the boundary conditions very well, you can get whole-flow field data, so wind-driven rain intensities over the entire building facade. But you need solution verification and validation, which are time-consuming but they are very much needed. So let me briefly show you an example. This is the VLIET test building at the University of Leuven in Belgium where you see a module with a sloped roof, a module with a flat roof and in between actually there is a module, also with a flat roof, but without roof overhang. The validation study is actually reported in more detail in this article, and I will provide a brief summary here. Here you see the meteorological tower that we installed southwest of this building with three cup anemometers and at the top an ultrasonic anemometer to measure the oncoming wind speed profile. Then there is a rain gauge, measuring horizontal rainfall intensity, and this rain gauge is placed behind a semi-circular turf wall, to limit the wind error, so in accordance to the guidelines from the World Meteorological Organization. Then there are rain gauges, wind-driven rain gauges on the facades. And you can see here that we deviate the rainwater with a tube through the facade to the inside of the building, where we have these kind of tubes where the water column is measured by a pressure sensor. So here you see the different gauges indicated by black rectangles on the surface. You also see the meteorological tower on the left in this figure and here you see the numbers of the wind-driven rain gauges. Important here is that you also see how roof overhang varies along the length of the building. And you indeed see that in the middle we have 0 roof overhang, and this will prove to be quite important. This is what you see if you stand with your back against the building, the southwest facade and if you look in the southwest direction. It's fairly open terrain, although there is a row of high trees also indicated here. Then we start the CFD simulations. We need to do validation, and in this case by sub-configuration validation for a cube, for which wind-tunnel experiments were available in literature. Then we performed the CFD simulations for the VLIET test building itself. Also based on a grid-sensitivity analysis. The 3D steady RANS approach was used with the realizable k-epsilon model, sand-grain based roughness modifications in the wall functions and the second-order discretization schemes. And then these are raindrop trajectories that we can calculate in this wind-flow pattern. You see a perspective view, a front view, and a top view. In this case of raindrop trajectories of one millimeter raindrops, in a wind field that has a wind speed of ten meters per second at ten meters height. And you clearly see how the raindrops approach the building and then are deviated around the corners together with the corner streams around this building. When you have larger raindrops, 5 mm for example, you see that because of the higher inertia these drops are much less influenced by the wind-flow pattern. Then we can calculate the catch ratio and then actually also calculate the catch ratio for an entire rain event. So what you see here are ten-minute values of wind direction, wind speed, and rainfall intensity. The wind direction is more or less 225 degrees, this is perpendicular to our southwest facade. The wind speed ranges between let's say zero and eight meters per second. And the rainfall intensities are mainly concentrated at the end of this event. And based on the CFD simulations, we can calculate the cumulative amount of wind-driven rain, for example, at position 13. So you see measured values indicated with dots and simulation values indicated with a solid line. And here we get quite a good agreement on this position. Then we can also look at the catch ratio across the entire facade at the end of the rain event. That's what you see here. So the black areas are the areas that are sheltered from rain by the roof overhang; so a zero catch ratio. But you see very high values where there's no roof overhang; about almost 50%. This means that 50% of all the rain, falling on a horizontal plane, is also falling on this building facade. Here you see also local maxima at the corner and also here at the corner of this building. Of course, it's interesting then to compare our CFD simulations with measurements. And let's first look at this side of the facade and the agreement is definitely not perfect, but it is also not too bad. Here we also have some deviations, but again the overall agreement is satisfactory. Also here. But here it is not, here we get very large differences. So what's going on here? Well actually, this was our computational domain. This is the position of the measurement mast, and what we did not include in our model were the trees and the trees slowed down the wind speed, and less wind speed means less wind-driven rain. And that's the reason why in the measurements we have much less wind-driven rain then in our simulations, where this row of trees is not present. But well, leaving this out of the evaluation, we can say that actually, the CFD simulations quite accurately described the spatial distribution of wind-driven rain over the facade. When we have confidence in this model, we can use it to calculate wind-driven rain intensities on different types of buildings. And these are the buildings from the module question, where we're going to look at catch ratios across the facade. This is the low-rise cubic building, you see the windward facade and the catch ratios over that. This is for a rainfall intensity of one millimeter per hour, and a wind speed of ten meters per second at ten meters height. And at the top corner we get a catch ratio of 1.72. This means that 172% of the rainfall on a horizontal plane is falling on this corner. This is really a lot. It is also due of course, to the fact that the wind speed is high and the rainfall intensity is low, which means many small droplets. Let's go then to the other building and even though this building is higher, you see that the maximum value of the catch ratio decreases. Let's go to an even higher building, and it decreases even further and then the tower building, you see it increases again. So these are at least to say counter-intuitive results because one could follow the following argumentation. Wind speed increases with height, so the higher the building, the higher the wind speed near the top of the building, and also the more wind-driven rain it should receive. But this is clearly not what is happening here. So, what else is going on? Well, what we have here actually is again similar to what we saw with the V-shaped buildings, this is called the subsonic upstream disturbance that acts here. And this is schematically indicated here, this is the vertical cross-section of the buildings. And the larger and the wider the building, the more it will slow down the wind speed in front of it. This means that the raindrops will get a lower horizontal velocity component. And actually the driving force reduces, so there will be less wind-driven rain on the facade. This can also be shown here, these are contours of wind speed ratio. So wind speed divided by wind speed at ten meters height in the vertical center plane of the building. So wind is from left to right. And if you look at the line indicated with 1 here, this is an indication, well the elevation of this line is an indication of the disturbance of the wind flow, which is clearly largest for this building; the wide and high building slab. Not for the tower building because that building is very slender even though it is higher. And if you look then at raindrop trajectories indeed here you see also that for the low-rise cubic building, they are almost not disturbed by the upstream effect of the building. But for, the third building, this is clearly the case to the largest extent. So coming back to the module question, which is the building that receives the highest wind-driven rain intensity? Well maybe a surprising result is that actually this is the low-rise cubic building. And then the other question. Why are we not able to take a shower at the bottom of high-rise buildings? Well, actually the reason is, as you can see here from the catch ratio on this high-rise building, that the catch ratio is actually only high near the top corner of the building, near the top edge of the building. If you have a roof overhang there, it's even much lower that as indicated here. This means that when the rain starts running down from this position, it will wet the lower positions, and it will also stick to the facade and start evaporating. In addition, there are facade details that can project the rain droplets away from the facade. And this actually, a combination of these factors is the reason why you cannot take showers at the bottom of high-rise buildings. In this module we've learned about how the assessment of wind-driven rain is performed and about the wetting patterns on building facades. In the next module, we're going to focus on advantages and disadvantages of wind energy harvesting in the built environment. And we're going to look at some common misconceptions about wind energy in the built environment. Thank you very much for watching. I hope to see you again in the next module.
