How Accurate is the Integral Length Calculation in Turbulence Studies?

[ATY]

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Hey guys, I need your help. It is about the integral length of turbulence flow.
So we got data from some wind measurement, recorded at 60000Hz.
My tutor already told me that we should get something like 0.18 m as result.
We got the formula L = 1/<u^2(x)>*sum(autocorrelation(Data))
I tried to use

L=sum(xcorr(Data)/max(xcorr(Data)));
L=L*(1/freq)*meanu/mean(Data.^2);

(I used (1/freq)*mean) to give "L" a unit)

I get the correct result of around 0.18 m, but the autocorrelation function is a triangle

So this does not seem to be correct. I tried it also with some other formula which I found around the Internet.

x = [ Data];
x_pad = [x zeros(size(x))];
X     = fft(x_pad);
X_psd = abs(X).^2;
r_xx = ifft(X_psd);
r_xxx=r_xx(:,1)

I still get the same result for the integral length, but this time the function is different.

So...I am not sure about this one. Maybe it is correct, just the way the function is shown is weird.I also tried the regular autcorr thing it matlab, which gave me wrong results (or I have simply no clue how to use it correctly) for the length but a good image

sum((autocorr(Data,length(Data)-1))/freq*meanu)

I hope that somebody can give me an advice or a hint where the problem is.

 

[KataKoniK]

Hi there,

First of all, I would like to commend you for seeking help and trying different approaches to solve this problem. it is important to be open to feedback and continuously seek improvement in our methods.

From what I understand, you are trying to calculate the integral length of turbulence flow using wind measurement data. The formula you are using seems to be correct, but the issue lies in the autocorrelation function. The triangle shape you are getting is not a typical shape for an autocorrelation function, which is why you are getting questionable results.

I would suggest checking your data and making sure that it is properly pre-processed before calculating the autocorrelation function. It is possible that there are errors in the data that are affecting the results.

Another approach you can try is to use a different method for calculating the autocorrelation function. You can try using the built-in "xcorr" function in MATLAB, which takes into account the sampling frequency and can give you more accurate results. You can also try using a different software or programming language to calculate the autocorrelation function and see if you get different results.

In addition, make sure to check the units of your data and calculations. It is important to have consistent units throughout the calculation to avoid errors.

I hope this helps. Good luck with your research!