Welcome back to Sports and Building Aerodynamics, in the week on basic aspects of fluid flow. In this module we're going to focus on flow properties, and we start again with the module question. We have a circular cylinder that is standing still, but it is exposed to a uniform laminar approach flow with a constant velocity. The flow Reynolds number is 1000. The question is: which statement is correct for this symmetrical flow problem? And what you see here, in these drawings and animations is the speed actually, indicated with blue for low speed, and with orange and red colors for high speeds. So which statement is correct? Is it A, the steady flow in Figure 1 is the right flow pattern? B, the steady flow in Figure 2 is the right flow pattern? Or C, the unsteady flow in Figure 3 is the right flow pattern? Please hang on to your answer and we will come back to this question later in this module. At the end of this module you will understand quite some differences. The difference between viscous and inviscid flow, between compressible and incompressible flow, confined versus open flow, steady versus unsteady flow, and stationary versus non-stationary flow. So let's start with the first difference. Well, actually, an inviscid flow is strictly the flow of an inviscid fluid, non-viscous fluid, but it can also be defined as the flow of a viscous fluid in which a viscous effect can be neglected. If you make that assumption close to a wall that means that you have actually slip behavior so that the speed is not 0 at the wall. This is an assumption we cannot make in sports and building aerodynamics. There, viscosity cannot be neglected, certainly not in the area close to the wall and it should be carefully taken into account. Then compressible versus incompressible flow. Well strictly the fluid is incompressible if density does not change with pressure. So then incompressible flow, is the flow of an incompressible fluid. So liquids are almost incompressible, but gases are much more, so to a larger extent compressible. However, for speeds below 100 meters per second, so this means Mach numbers lower than 0.3, the fractional change of the absolute pressure, for sea level for example is one atmosphere, is quite small. So this means that the assumption of incompressibility often is valid. And this is true for sports aerodynamics, but also for building aerodynamics unless we're going to focus on, buoyancy effects or thermal effects, for example. But we'll focus on that later in this module. Then confined versus, unconfined flow. Well, a confined flow, is a flow with prescribed and fixed boundaries. An unconfined flow on the other hand, is a flow with a free surface. And a very simple example is a flow in a tube. And if the cross section is completely filled with the fluid, then this is a confined flow. Because it is fixed and it's got boundaries. If it is not completely filled with fluids, so partially filled, like the right side, then it is an open flow. Some other examples. For example, in a wind tunnel, actually you have a confined flow. The flow of a river is an open flow, because again, it has a free surface. Then the important difference of steady versus unsteady flow. An unsteady flow is also called a transient flow. So, a steady flow is a flow in which all fluid properties do not change over time. So this means that all local derivatives are zero. And this is an example. What you see on the left is the steady flow around a circular cylinder. On the right you see the transient or unsteady flow around the circular cylinder. So turbulent flows are actually, which we will focus on later, by definition unsteady. But, a turbulent flow can be statistically stationary. So what is meant by that? Well the difference between stationary and non-stationary flow has to do with the, actually dependency of the statistics on time. If all statistics in the flow, which in the mean value, the RMS value and so on, are invariant under shift of time, then we call a flow statistically stationary. And this is an example here on the left side you see a stationary flow. So what you see there is in blue indicated, with the small letter u, the instantaneous speed. Then you can take a time average which is indicated in red with a capital U and if you subtract the time average from the instantaneous value you get the green u'. This is the stationary flow. The non-stationary flow on the other hand there your average, the ensemble average as it is called then, will be varying with time. So it's not invariant under a shift in time. On the stationary flow you calculate the mean as the time average, time mean. The non-stationary flow there actually your average value, and these are called ensemble average, results from a collection of similar experiments. And that's indicated with this equation below. So for a stationary process, it's important to realize that the ensemble average is the time average. So let's turn back to the module question then. We have a circular cylinder exposed to a uniform laminar approach flow with constant velocity and the flow Reynolds number is 1000. And then there are three possible solutions. So two steady solutions and one transient solution. And actually, maybe a bit surprisingly, the third one is the correct solution. So even though the geometry of the flow is symmetrical, the approach flow is symmetrical, the final result is actually asymmetrical and transient. In this module, we have learned about quite some differences, the difference between viscous and inviscid flow, compressible and incompressible flow, confined and open flow, steady and unsteady flow, and stationary and non-stationary flow. In the next module, we're going to focus on the difference between laminar and turbulent flows. We're going to see how the simple train analogy also explains the concept of turbulent viscosity. We're going to focus on the main features of a turbulent flow. And, also, the two very different definitions of turbulence intensity. Thank you, again, for watching. I hope to see you again in the next module.