Welcome back to Sports & Building Aerodynamics, in the week on building aerodynamics. In this module we're going to focus on wind-driven rain. We start again with a module question. What you see in these photographs is the Royal Festival Hall in London. On the left side, you see it after completion. On the right side you see what happened to this building, to this building facade after some time. The question is, what is the main reason for this facade disfigurement by wind-driven rain? Is that A) Leaching of facade material by wind-driven rain. B) Too high salt concentrations in the facade material. C) Incorrect detailing of the window sills. Or D) None of the above. Please hang on to your answer, and we'll come back to this later on. At the end of this module you will understand some important characteristics of rain, and wind-driven rain. You will understand the importance of wind-driven rain. The parameters determining wind-driven rain and also the complexity of this process. So let's start with a few definitions. Rain can be defined as particles of liquid water that are formed within a cloud and fall towards the ground. That's the definition by the International Cloud Atlas. It can also be defined, this is the definition of the American Meteorological Society, by precipitation composed of liquid water drops with a diameter larger than 0.5 mm. And precipitation actually that is composed of smaller drops is referred to as drizzle. Then rain intensity is the volume of rainfall that reaches a certain area during a certain period of time, and it is expressed in millimeter per hour or in liter per square meter per hour. Be careful here, you cannot express rain intensity as millimeter per square meter per hour. This is sometimes mentioned even in scientific articles, but this makes no sense as you can see in the unit analysis below. This is a very popular raindrop shape, but actually, this is not a real raindrop shape, this is the shape that is sometimes used in cartoons; the actual raindrop shape is quite different. These are photographs of raindrops falling in stagnant air, and what you can see indicated with a number is their equivalent diameter in micrometer. So we see that small droplets are spheres, but that larger droplets actually tend to be more like oblate spheroids. So this is quite an important difference, certainly compared to the teardrop shape that is used in cartoons and other animations. When a raindrop is falling from the cloud it will accelerate, but at some point the drag force and the gravity force will become equal to each other. That's when the acceleration drops to zero and when the so-called terminal velocity has been reached. The terminal velocity can then be calculated by equating these two forces and if you measure terminal velocities, or if we calculate them you get this curve. What you can see here is the terminal velocity of fall of a raindrop as a function of its diameter. And what is remarkable from this curve is that for raindrops larger than about four millimeters that actually the terminal velocity does not increase substantially when increasing the volume. The reason for that is that due to the shape of the raindrop, the oblate spheroid, actually the drag force increases relatively compared to the gravity. And that's the reason why drops of four millimeter and six millimeter have more or less the same terminal velocity. Then raindrops not only have a very large range of shapes but also a large range of sizes. And here you see the probability density function of raindrop size as a function of raindrop diameter, you see that for different rainfall intensities. So this curve indicates that when you have a low rainfall intensity, for example 0.1 millimeter per hour, that you have a lot of drops situated in the range between zero and two millimeter diameter. For higher rainfall intensities, for example, the dotted curve of 10 millimeter per hour, you see that you have a much larger fraction of large drops. There are different empirical and semi-empirical formulae that describe raindrop spectra. This is one example, the raindrop spectrum by Best, but many others have been devised and are being used. Wind-driven rain then is a combination of wind and rain. So, it's wind actually that carries, or gives the raindrops a horizontal velocity component. It carries them along and it can drive them against the windward facade of buildings. So, what you see here are trajectories of raindrops falling from the sky and ending on the building facade or on the ground surrounding the building. Let's look at a few definitions for wind-driven rain. We define first the rain intensity vector. This vector is defined for every raindrop diameter. Its size is equal to the fraction of the rainfall intensity for that specific diameter and its direction is the direction from which the rain is coming. We can then split this up into a horizontal component, this is the wind-driven rain intensity, so this is the flux through a vertical plane, and you can split it up into the vertical component; this is the regular rainfall intensity, as measured by meteorological stations and this is the flux through a horizontal plane. Wind-driven rain is important because a lot of problems in terms of building facade pathology are associated with wind-driven rain. For example, rain penetration, frost damage, salt efflorescence, structural cracking due to thermal and moisture gradients. But also surface facade soiling that has become so characteristic for so many of our buildings, and sometimes so characteristic that our eye doesn't even notice it any more. But clearly this kind of facade disfigurement is unwanted. This is also the photograph shown before, the Royal Festival Hall after completion and after some time. And what happened here is actually the combination of atmospheric dry and wet deposition on the facade combined with wind-driven rain, and run-off of the rain over the facade. Wind-driven rain has quite some influencing parameters, that also causes wind-driven rain to be quite complex. Building geometry of course plays a role, but also the surroundings, the environment and topography, the position on the building facade, wind speed, because the higher the wind speed, the higher the wind-driven rain intensity, wind direction of course, rainfall intensity, and the raindrop size distribution are also important parameters. And wind-driven rain is complex, because each of these parameters is quite complex. The wind-flow pattern around buildings as discussed before is quite complex, and this of course translates to wind-driven rain intensities on the facade. Then you have a large range of droplet shapes and sizes, and then you have a very high temporal variability of wind and rain. And what you see here is actually measurement data of wind speed, wind direction and rainfall intensity, all ten minute values for a certain period of time. You see the wind direction indicated by this curve and on the right axis. Here you see the wind direction fluctuating around 225 degrees, which is southwest. Then you see the wind speed fluctuating between zero and eight meters per second, and you also see rainfall intensity fluctuating between about zero and eight millimeters per hour. So a high temporal variability, which also translates in a vary high temporal variability of wind-driven rain. Let's go back to the module question then. What is the main reason for this facade disfigurement by wind-driven rain? Well actually, maybe to your surprise it is the incorrect detailing of window sills. Let me briefly explain that. Well actually, a window sill should have a shape maybe a little bit like this, with a very small, but very important detail. This is a so-called drip, and the reason of the drip is that it allows actually the rain water to stay away from the facade. So what you have if rain runs down a glass pane then on the sill, then by surface tension actually it could remain attached to the surface and then reach the wall below the sill. However because of the drip, indeed the rain will drip and be kept away from the facade. This is quite important, but when this small detail is neglected, this is what can happen. And even though this detail was already used by the Greeks and the Romans in ancient times, you see that nowadays there are still designers that just forget it in their facade design. So what happened here is that due to dirt deposition on the facade, which is quite uniform, the facade gets darker and darker. Then wind-driven rain intensities are highest at the top of the facade, so there they rinse away the dirt, so this is called white washing. But then on the windows you have also rain on the glass pane that runs down. The horizontal, or the nearly horizontal, surface of the sill collects much more dirt than vertical surfaces. So this very dirty rain water then runs down along the facade. There's no drip, so it reaches the facade again. The water is absorbed and the dirt stays behind, and that's why you see these dirt stains below the window sills. When you go further down there you will see that actually the water that runs down the glass pane and down the sill is actually quite dirty, but it's still less dirty than the facade surface, that actually does not receive that much wind-driven rain. So there actually there is a relative effect of white washing, and this way you get this very let's say unintended checker-board pattern of facade surface soiling. In this module, we've learned about some important characteristics of rain and wind-driven rain. On the importance of wind-driven rain, the parameters that determine wind-driven rain and the complexity of this process. In the next module we'll continue with wind-driven rain, and we're going to see how assessment of wind-driven rain can be performed. And we'll also have a look at wetting patterns on building facades. Thank you very much for watching, and we hope to see you again in the next module.
