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#1 |
Senior Member
luca mirtanini
Join Date: Apr 2018
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Looking here for the theory of the k-epsilon model I have a question:
If k is the mean turbulent kinetic energy, so not dependent on the time, how it is possible to do the derivative in time? Thanks |
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#2 | |
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Filippo Maria Denaro
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Quote:
This topic is quite debated also in other forum |
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#3 |
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Lucky
Join Date: Apr 2011
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A triple decomposition allows you to treat temporal variation of statistical variables easily. When you do this you can recognize a coherent part and random part. Most people don't distinguish the time-averaged and unsteady parts of the coherent term because they don't formally use a triple decomposition, but there is also no need to. You can get away with a bit of notational hand-waving and just allow k to be unsteady and it will still be a proper Reynolds-average. Temporal dependence of k is not the issue, you just need to recalibrate your thinking a little bit.
The debate mentioned is what is happening in URANS when you apply an otherwise time-averaged model and try to use it. This topic is indeed contested. |
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#4 |
Senior Member
luca mirtanini
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#5 | |
Senior Member
luca mirtanini
Join Date: Apr 2018
Posts: 165
Rep Power: 8 ![]() |
Quote:
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#6 | |
Senior Member
Filippo Maria Denaro
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Quote:
https://www.researchgate.net/post/UR...ompared-to-LES https://www.linkedin.com/posts/bhara...medium=ios_app |
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#7 |
Senior Member
Lucky
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The kinetic energy is
![]() ![]() You don't have to go to triple decomposition, just the normal double decomposition is enough. Triple is just for explaining physically what a time-dependent k means. |
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#8 |
Senior Member
luca mirtanini
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Quote:
k= ![]() have angle bracket which I believe means time averaging and this is what I found also in the link in the OP. |
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#9 |
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Filippo Maria Denaro
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I suppose that <*> stands for the ensemble averaging, the result being an unsteady function. But the devil is in …
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#10 |
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luca mirtanini
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Ok Thanks! Now it makes sense. Sometimes in my opinion it is better to specify this details
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#11 |
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Lucky
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Any Reynolds-average will result in the exact same governing equations (i.e URANS) regardless of average you intend or want it to be in your dreams Nothing tells the solver that a time-average or ensemble average was used in this transport equation... And it's not limited to just a time-average or ensemble average either. Since all Reynolds averages will lead to the same outcome, the meaning of rho,u, and phi is therefore open to interpretation at the theoretical level and what spatio-temporal characteristics actually existing in your numerical solution depends on all the details of the numerical methods and underlying closure models used. You can write whatever you want on paper in any document of you think rho, u, and phi are; but solvers work backwards (they solve linear systems to give you rho, u, and phi), they don't go forward (they don't use your interpretation of rho, u, and phi to come up with a transport equation). You can write down time-averages and ensemble-averages and cowabunga-averages all day, numerical solvers don't work that way. If you want to filter DNS data or experimental measurements to recover the appropriate Reynolds-averaged quantity then it matters what averaging you use, but for numerical URANS solvers it does not.
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#12 | |
Senior Member
Filippo Maria Denaro
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Quote:
Yes! And that is one of the issues I highlighted previously! Actually, the type of mean should be implied by a proper turbulence model, that is a model that acts differently for time or ensemble averaging. But that is one of the lack in URANS formulations. |
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Tags |
turbulent kinetic energy |
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