[kepler123]

Hi, I'm working on a turbulent inflow simulation and I want to calculate the Reynolds stress budget normal to the airfoil wall at different locations and of different terms, the normal stress, for example.

To do this I need the fluctuating value of the three cardinal velocities, u' for instance in the flow direction. I am confused as to what this means? Is u' calculated from the instantaneous velocity, that is: u' = U (instantaneous) - Umean (over a certain time period).

I am confused because if I were to record data over the chosen time period, I would be able to generate a time series of u' as I have a time series of U. How do I know which value of u' I need to use? As of now, I am planning on considering u' from the last recorded reading at the end of my chosen time frame. Any thoughts on this?

Here are some reference papers that talk about Reynolds budgets:
file:///C:/Users/lobob/Desktop/voke1997.pdf
https://www.jstage.jst.go.jp/article.../_pdf/-char/en

Thanks.

[FMDenaro]

Originally Posted by kepler123

Hi, I'm working on a turbulent inflow simulation and I want to calculate the Reynolds stress budget normal to the airfoil wall at different locations and of different terms, the normal stress, for example.

To do this I need the fluctuating value of the three cardinal velocities, u' for instance in the flow direction. I am confused as to what this means? Is u' calculated from the instantaneous velocity, that is: u' = U (instantaneous) - Umean (over a certain time period).

I am confused because if I were to record data over the chosen time period, I would be able to generate a time series of u' as I have a time series of U. How do I know which value of u' I need to use? As of now, I am planning on considering u' from the last recorded reading at the end of my chosen time frame. Any thoughts on this?

Here are some reference papers that talk about Reynolds budgets:
file:///C:/Users/lobob/Desktop/voke1997.pdf
https://www.jstage.jst.go.jp/article.../_pdf/-char/en

Thanks.

Of course if you perform a DNS run there is no problem in computing the mean and the fluctuation for each component in a classical way defined by the Reynolds averaging.
Conversely in RANS you have no way to compute the fluctuation part.
Then, for LES or URANS you should be aware that the fluctuations can be computed after the time averaging over a long period is performed. the mean is a statistically steady field and you cna compute the fluctuation from that. Be aware that what you compute is different from the DNS fluctuation and LES and URANS produce different fluctuation fields.

[kepler123]

Originally Posted by FMDenaro

Of course if you perform a DNS run there is no problem in computing the mean and the fluctuation for each component in a classical way defined by the Reynolds averaging.
Conversely in RANS you have no way to compute the fluctuation part.
Then, for LES or URANS you should be aware that the fluctuations can be computed after the time averaging over a long period is performed. the mean is a statistically steady field and you cna compute the fluctuation from that. Be aware that what you compute is different from the DNS fluctuation and LES and URANS produce different fluctuation fields.

Thanks for the reply Prof. Denaro, your replies to the topic on Research Gate were very helpful in me understanding some of this stuff (Stress budget) a few weeks ago.

I am running a wall resolved LES. I understand that this would not be something possible with a RANS, I should have mentioned that I am performing an LES simulation in my first post.

I run the computation without added turbulence (Klein et al. method for isotropic turbulence generation) such that the mean velocities and pressure at monitoring points are statistically steady before I add the inflow turbulence.

The idea is to study the effects of turbulence by observing the budget terms at different locations along the chord, something that many have done on flatplates.

What I am confused about is this:

I introduce the inflow turbulence for a sufficiently long time such that the statistics converge satisfactorily. Let's say I run it for 100k time-steps. I then record my output and calculate the fluctuation using the instantaneous values of the velocity subtracted from the statistically steady time-averaged quantity.

I am confused, however, because if I run the simulation for a few more time steps, the fluctuation is going to differ (within a small standard deviation of the mean, of course). This could result in slightly different stress budgets (which I believe will all be statically equivalent, but something I do not have the possibility to confirm due to computational budgets).

My question is this and if I understood right it's just me confirming what you have already said: Do people consider this instantaneous value of fluctuation (at any random time step after a statistically steady mean is reached) as their required u', etc.? It definitely is not an averaged u' of sorts over multiple time steps because that would end up becoming 0 over a statistically long enough time frame.

[FMDenaro]

The standard way of doing is:
1) let the solution forget the arbitrary initial condition, that is reach a statistically steady energy equilibrium
2) Start collecting the velocity fields and do the time integral mean for a sufficiently long period.
3) for each one of the collected velocity field, subtract the ontained mean velocity field. At each time you have a sample of the velocity you get also the fluctuation u',v',w'.


After that you can do the statistical analysis you want

[kepler123]

Originally Posted by FMDenaro

The standard way of doing is:
1) let the solution forget the arbitrary initial condition, that is reach a statistically steady energy equilibrium
2) Start collecting the velocity fields and do the time integral mean for a sufficiently long period.
3) for each one of the collected velocity field, subtract the ontained mean velocity field. At each time you have a sample of the velocity you get also the fluctuation u',v',w'.


After that you can do the statistical analysis you want

Thank you for all the help.

[LuckyTran]

The average of u',v', and w' should be 0 over sufficiently long averaging duration (but practically it will be slightly non-zero due to sampling error).


But the Reynolds stresses are not u',v', or w', they are products of fluctuations u'u', u'v', u'w', v'v', v'w', w'w' which are in general non-zero.