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Old   June 10, 2005, 03:34
Default doubt about beta PDF
  #1
CH
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Hi Dear friends,

I got one probem. In non premixed LES combustion, f(mixture fraction SGS variance)) variance is assumed to be Beta distribution. I have DNS dat of the 3D reacting(non premixed) jet, I would like to compare actual PDF with the Beta PDF with my DNS data. in beta PDF calculation , I need two parameters one is f average and its variance. as i have only mixture fraction,how to get the variance? please help me Thankyou

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Old   June 10, 2005, 04:45
Default Re: doubt about beta PDF
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DES
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In DNS you may try it with statistics.
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Old   June 10, 2005, 05:05
Default Re: doubt about beta PDF
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Hi DES, can u please explain with more details
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Old   June 10, 2005, 05:30
Default Re: doubt about beta PDF
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DES
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Can you please be more specific with question? What do you want to know?
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Old   June 10, 2005, 06:30
Default Re: doubt about beta PDF
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my doubt is , I want to calculate pressumed PDF for mixture fraction..its formula is involving of mixture fraction f and its variance f',, i got f from DNS, i would like to know how to get f' in the LES cell.. i,e in DNS we are resolving the small scales,we r going to up to kolmogorov scale,then where is the question of variance again..in prior evaluation of the models for the variance, how we will get exact(DNS )variance? i hope u understood my doubt
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Old   June 10, 2005, 09:46
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DES
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I understand nothing. I am sorry.
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Old   June 10, 2005, 10:16
Default Re: doubt about beta PDF
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Salvador
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Go back to the basics lets call Z the mixture fraction. In DNS you have Z(x,t) in very point

You have to build a filter function that

<Z> filtered value of Z,

MEAN=<Z> 1)

and the variance is

VARIANCE=<Z^2>-<Z>^2 2)

The definition of the filter function is all you need. If you assumed that the filter is a box filter basically averaging inside the LES cell of width delta (usual approach, not the most correct but the most usual without doubt)

Then a function f is filtered as

<f> = SUM(f_i)/N (3)

where f_i are the DNS points inside a given LES cell. N is the number of those points. The gretaer the N the better the statistics. This is teh simplest way to do it. Use (3) to compute (1) and (2)

The beta PDF will depend on your MEAN and VARIANCE, and you will have a PDF in every LES cell.

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Old   June 10, 2005, 10:20
Default Re: doubt about beta PDF
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Salvador
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Sorry the equations did not display properly

[Z] indicates filtered value of Z

1) MEAN= [Z] 2) VARIANCE= [Z*Z]-[Z]*[Z] 3) [Z]= SUM(Z_i)/N

In doubt check Poinsot book, or paper by Jimenez et al (2001) in Physics of fluids,
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