
[Sponsors] 
Confusion in calculation of u', the velocity flucation 

LinkBack  Thread Tools  Search this Thread  Display Modes 
March 16, 2022, 12:12 
Confusion in calculation of u', the velocity flucation

#1 
New Member
CPark
Join Date: Apr 2021
Posts: 11
Rep Power: 3 
Dear all,
I have a simple dataset with just the 3 components of velocity, , and , and I am trying to compute the turbulence kinetic energy, , in which the velocity fluctuations need to be computed. The velocity fluctuation is simply, , where is the time average of . The confusion is, say the dataset exists from time to with a finite number time steps and i would like to compute for each timestep. So for example for where , I need to compute the at this specific time. Then, is the time average between and or is it between and ? It is a simple base theory for CFD but I just ran into this confusion while trying to calculate by myself instead of relying on programs. 

March 16, 2022, 14:15 

#2 
Senior Member
Lucky
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 5,022
Rep Power: 60 
You should average all times. There is only one average.
Technically the answer is neither. What you are looking for is the population quantity in statistics. What you can obtain is a sample estimate of the population quantity. The real time average is from time going from negative infinity to positive infinity. 

March 16, 2022, 14:15 

#3 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,152
Rep Power: 66 
Quote:
The time averaging must be theoretically extended up to T>Infinite. Therefore, in practice you have to compute from 0 to T, but T must be enough large. 

March 17, 2022, 06:50 

#4  
New Member
CPark
Join Date: Apr 2021
Posts: 11
Rep Power: 3 
Quote:
This leads me to another question. Since k is a time varying parameter and involves the mean of the squared u' (UPrime2mean as OpenFoam calls it), does it mean that this mean is not computed as poulation average but instead just the average up until the specific time t that I am computing k for? 

March 17, 2022, 07:16 

#5  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,152
Rep Power: 66 
Quote:


March 17, 2022, 07:23 

#6  
New Member
CPark
Join Date: Apr 2021
Posts: 11
Rep Power: 3 
Quote:
So is the (u'u')_bar term a time varying parameter? 

March 17, 2022, 08:04 

#7  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,152
Rep Power: 66 
Quote:
[f_fil(x,t)]_bar = F(x) 

March 17, 2022, 08:28 

#8 
Senior Member
Lucky
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 5,022
Rep Power: 60 
UMean and UPrime2Mean are averages from 0 to T and both of these are sample estimates for population statistics. There are infinite number of possible such estimators. You only really care about the best estimator that you get in the very last time dir because it is averaged over the longest time duration. Getting the population value is not possible unless you have the entire population ensemble, which means running your simulation until T=>infinity.
Hence, it's nearly impossible to directly calculate the timevarying u' and timevarying k at runtime because you don't know (and can never know) the population statistics. You must calculate it until T=>infinity, save U at all the times you care about, and then postprocess it a posteriori. If you waned to do this manually you would run your simulation with fieldAverage option set. Go to the very last time dir and find UMean. Copy (and overwrite) this latest UMean into all previous time dirs. Then do something like: Code:
foamCalc addSubtract U subtract field UMean resultName UPrime And then calculate k. 

March 17, 2022, 09:08 

#9  
New Member
CPark
Join Date: Apr 2021
Posts: 11
Rep Power: 3 
Quote:
However, I am not sure how k can be time varying when it only depends on the 3 directional components of UPrime2Mean which are not time varying. What am I missing? 

March 17, 2022, 09:20 

#10  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,152
Rep Power: 66 
Quote:


March 17, 2022, 09:33 

#11 
New Member
CPark
Join Date: Apr 2021
Posts: 11
Rep Power: 3 
I am currently considering LES for k, the resolved k to be precise.
Apologies, I did not really get what you meant by "[f_fil(x,t)]_bar = F(x)" but thanks for helping me recall that in LES it is a filtering operation instead of averaging. I completely missed that. Anyhow, according to Sagaut's book on LES for incompressible flow, the resolved turbulence kinetic energy is simply half of the squared of filtered velocity (page 51). Since the velocity data I have is for the given grid, the filtered velocity in my case is simply this velocity data. Does this sound like a valid statement? 

March 17, 2022, 10:31 

#12  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,152
Rep Power: 66 
Quote:
Your LES database provided for sure the filtered velocity. From that you can deduce the k (unsteady) but also the approximation for the RANS (steady) velocity and the fluctuations. My previous notation means you can apply the time averaging to the filtered variable and the result is a steady field. 

March 17, 2022, 12:28 

#13 
Senior Member
Lucky
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 5,022
Rep Power: 60 
The instantaneous k depends on the three direction components of u', not uPrime2Mean. UPrime2Mean is the root mean square of u', it is a statistic like UMean. k inherits the temporal characteristics of u'.
You can get the timeaveraged k from UPrime2Mean, but not the instantaneous k. And UPrime2Mean is ,,, etc. 

March 21, 2022, 07:40 

#14  
New Member
CPark
Join Date: Apr 2021
Posts: 11
Rep Power: 3 
Quote:
Quote:
Thank you FMDenaro and LuckyTran for your kind replied. I have eventually figured it out with your help and managed to calculate the TKE of my dataset. 

Tags 
turbulence kinetic energy, velocity component, velocity fluctuation 
Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
PanelMethod, velocity calculation  mrbm  Main CFD Forum  17  August 5, 2022 11:03 
fluctuation component of velocity (Urms) calculation from RANS simulation results  atul1018  Main CFD Forum  5  February 4, 2021 10:09 
Calculation of tangential velocity  lxlylzl.123  FLUENT  4  November 18, 2020 14:13 
Time dependent angular velocity calculation UDF  shashankmechguy  Fluent UDF and Scheme Programming  1  July 26, 2018 02:23 
The problem for velocity calculation using turbulent model in openfoam.  mscheng  OpenFOAM Running, Solving & CFD  6  September 10, 2013 08:35 