[ari003]

Hello everyone, my query is related to the Turbulent intensity of a channel flow. It might sound very basic but the solution is not properly available anywhere so if anyone is intended to help it will be my pleasure.
The TI is defined as the ratio of standard deviation of the fluctuation to the mean velocity.

TI=u'rms/U(mean)

Method 1

t(sec) U(m/s) V W
1 12.1 2.5 1.5
2 10.5 2.2 1.7
3 11.4 2.8 1.5
....
10 10.8 2.6 1.9

If the above just represents a probe data for each velocity component I can find the TI by calculating the fluctuation(U-U(mean)) and then do the rms of the fluctuation and then putting in the above equation. From there I can find the TI(u-comp), TI(v-comp) and TI(w-comp). Does this makes sense?

Method 2

TI=sqrt(2/3k)/U

k=1/3[( u_x'^2 + u_y'^2 + u_z'^2 )] where these are the Reynolds Normal stress.
I also have the values of these stresses from OpenFoam from where I can calculate the k and eventually the TI where U here are three mean velocity components U_x, U_y and U_z.
U =sqrt{U_x^2 + U_y^2 + U_z^2}

So from the method 2 I can find the overall TI and not for each component right?
How can I validate that the TI generated through method 2 is completely accurate and that even through method 1?

[LuckyTran]

Originally Posted by ari003

How can I validate that the TI generated through method 2 is completely accurate and that even through method 1?

Just use algebra and you can establish the equivalency between 1 and 2. All you need to do is write out u'rms, v'rms, and w'rms and just look and see that the same terms are appearing in the other formula.

But k should be half the trace of the Reynolds stresses. I'm not sure why you have 1/3, maybe a typo.