# CFD turbulence modelling mean pressures vs peak pressures

I have been experimenting with using Autodesk CFD to investigate facade/ cladding pressures on a (rectangular) building, comparing results with cladding/ facades pressures pressures from design codes and wind tunnel results.

I understand the complexities and difficulties in what I am doing generally and am really exploring at the moment.

From my introductory understanding of CFD from uni and reading around in the literature I understand that the pressures the various turbulence model produce are 'mean' pressures. Papers etc. are always very explicit in referring to 'mean' whenever talking about velocities/ pressures using these techniques. In cladding design one is interested in peak pressures - this is what the design codes and wind tunnel testing give you to design with.

I wonder whether anyone might be able to provide insight, or might have a good reference for further reading, on the possible relationship between peaks and means in these theories? I am not too strong on statistics but is it something that can be derived? It feels like it ought to be.

• What are your boundary conditions? When using RANS-based models, the flow is decomposed into mean (time averaged) and fluctuating components (turbulence means that at a given point, there will be some deviation from the mean). But I suspect these instantaneous changes are insignificant in the context of architectural structures. If peak pressure correlates with peak wind load, set those peak conditions as your BCs, and examine the resulting pressure profile on your facade. Jul 6, 2015 at 5:50
• Maybe you just mix up the terms? In a turbulence model, the 'mean' refers to a very local averaging (with respect to time space, time, or assembles). Thus, a simulation will provide you with a pressure in space and time that approximates the actual pressure up to the turbulent fluctuations (which are typically small).
– Jan
Jul 6, 2015 at 10:36

First, you can model turbulence using averages; e.g.: RANS.

As you will see, higher order moments appear and you need to find a way to close your equations.

Now that's about mean flows since you want to find solution for the mean values of your variables.

Second, you can derive a stochastic form of the Navier Stokes Equation and solve the probability density function (pdf).

If you have some background on Ito Calculus and a great place to start would be The Kolmogorov-Obukhov Theory of Turbulence

Let's say that you compute averages using RANS (in statistics you will see they call them moments, and the mean is just an example of a first order moment).

Doing this leaves out some information of the system. In reality we have a fluctuating variable, but we only predict the mean. The mean gives you very little information about the system.

Now we can improve our prediction by predicting the variance, which gives you more information about variations about the mean. If you go further, you can predict the probability density function (pdf), and the values of the mean, the variance, and high order moments just fall on your lap.

Stochastic methods give you almost all the information you need, but there is a catch. You must have some basic assumptions; for example you could say that your pdf follows a gaussian distribution, which is not necessarily correct.

• Thanks. I googled the Kolmogorov-Obukhov Theory - looks interesting (and well beyond my mathematical ability unfortunately!). Am I right it's more an alternative approach to RANS models which seems to be what most the commercial CFD packages offer in different forms. Was really more after something that could be added on top of RANS that takes a stab at quantifying the fluctuating components with some sort of 'probability of exceedance' function which is the kind of language structural engineers talk in. Maybe such a thing cannot be done - it would be in the software packages otherwise right!
– Jon
Jul 6, 2015 at 4:13
• @Jon Kolmogorov is the best reference for Probability Theory and Turbulence Modelling. You can dedicate your life trying to understand one of those beasts. I modified the answer adding more details. Jul 6, 2015 at 8:56
• @Jon in my world we usually don't look for 'probability of exceedance', but we do look for peak and critical loads. usually we'll just use a rans solution with a safety factor. we occasionally will go with an unsteady solution, which you could try if you have the additional computing resources. if you have lots to spare, you might look into des, which would add les to certain regions of your domain. Jul 6, 2015 at 9:47