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maxj March 4, 2013 21:17

Question regarding Reynolds Number and Turbulent Intensity

I have a question regarding Reynolds numbers.

As I understand, the higher a Reynolds number, the more turbulent a flow becomes, with Re>4000 considered turbulent.

I have a model where I've calculated a Reynolds number of 10^7, and when going to set my model boundary conditions I'm asked for a 'Turbulent Intensity' parameter, so I do some research and find the following equation:


So my question is, why does the turbulent intensity decrease as the Reynolds number increases, when a higher Reynolds number flow is meant to become more turbulent?

For my calculations I got a turbulent intensity of around 2%, which seemed far too low..

RodriguezFatz March 5, 2013 03:43

Saying that a flow for Re>4000 is considered to be turbulent is not correct. The Reynolds number always depends on a typical length scale. Normally you have multiple conclusive length scales you can use. In a pipe you can use the radius or the diameter (what people normally do) -> you get Re differences of a factor of 2 for identical cases. Also the critical Reynolds number strongly depends on the shape, roughness,... of your setup. Therefore they can differ from case to case by orders of magnitude.

I don't know where that formula is from, but I would try to find a similar case in the literature / a paper and look for the intensity they used.

By the way: A decreasing turbulent intensity does not mean, that the flow becomes less turbulent. It just says that the velocity fluctuations divided by the mean velocity decreases. If both values increase, but the mean velocity increases even more, than the intensity decreases.

maxj March 5, 2013 05:53

Hi there RodriguezFatz, and thank you for your response!

Your insight into Re numbers is appreciated, so thank you! I did use the pipe diameter to calculate my Re number, the model I have is reasonably simple, and has allowed me to make several assumptions in order to treat it as more of an academic exercise :)

I find it hard to understand how the mean velocity can increase more, when the Re number is also inversely proportional to it.. surely both values will change at the exact same rate, am I not correct?

I will search through some more reputable literature today, however here are my sources so far:

RodriguezFatz March 5, 2013 06:15


I did not expect the turbulent intensity to decrease for increasing Re in a pipe... but: If you look at different Re, you will see, that the turbulent intensity does not change too much for a wide range of Re. Also a value of about 4% can't be very wrong. You can also have a look how your results change when you change the inlet intesity from 3% to 4% and I guess that you won't see any change at all. But try it!

maxj March 5, 2013 07:16

Ahaa that's exactly what I mean! The equation works perfectly, and is an more than efficient approximation equation for the purposes I'm using it for, and as you say, it did come out fine when modeling.

I'm just worried, as this is part of my final year dissertation, and it's one of the few aspects of my project that I don't completely understand, and it's exactly the kind of question I feel that I could be asked in my dissertation defense :( I guess it's back to the books, unless anyone else could share some insight!

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