I'm reading this paper.
Article Development and Application of a Cubic Eddy-Viscosity Model ...
This paper is claiming there is a problem in k-epsilon model. Because in k-epsilon model, we assume that eddy viscosity(νT) is isotropy. But actually in real world, eddy viscosity(νT) is anisotropy for high Reynolds number and is isotropy for low Reynolds number. It means there can be error when we consider flow with high Reynolds number.
And I have a question in uploaded figure. How he can calculate fluctuation velocity?
What I know is fluctuation velocity can be calculated only when we assume that eddy viscosity(νT) is isotropy(like k-ε model).
When we use k-ε model, we can find k(Turbulence Kinetic Energy) by T.K.E transport eqation and k is same with '½(u'2+v'2+w'2)'.
Then if k(T.K.E) is found, we can calculate u', v' and w'
because u', v' and w' are same each other by assumption of isotropy.
But in this paper, author claims that we should consider flow as anisotropy and he suggests new Eddy viscosity(νT) with new Cμ. (I've uploaded expression of Cμ by picture.) So I think it is impossible to calculate fluctuation velocity because flow is considered as anisotropy.
But there is a fluctuation velocity profile that is calculated by CFD. And I think author calculated fluctation velocity using root mean square and T.K.E
Because we can find desription in figure that means he calculated fluctuation velocity by root mean square. (Figure 8: Profiles of rms velocities perpendicular (v) and parallel (u) to the wall in the impinging jet)
So it looks like contradiction to me.
How fluctuation velocity is calculated in anisotropic flow?
Actually I've thought that assumption of isotropy can be possible in the impinging jet sometimes. Because impingement occurs nearby wall, so there is a low Reynolds number nearby wall by No slip condition(dominant molecule viscosity). But, eventhough my deduction is right, I can't understand why there is a difference between v' and u'. In the case that r/D=2.5, there is a difference between v' and u' that I've marked in uploaded picture. Difference between v' and u' means this flow is anisotropy and this is contradiction against author's claim also.
Also I've infered about the one more reason why calculation of fluctuation can be possible in this paper.
I don't know well but what I've heard is
In RSM(Reynolds Stress Model) is suggested by the same claim of this paper.
I've heard RSM is suggested because flow with high Reynolds number is anisotropic in real world
and this is different with original k-ε model.
So in RSM, it is possible to calculate the each fluctuation velocities(u', v' and w') in anisotropic flow.
So RSM and this author's model has same purpose that pursue to consider anisotropic flow.
And RSM can calculate the the each fluctuation velocities(u', v' and w').
So I think this author's model can also calculate fluctuation velocity in the same reason.
Eventhough I don't know how RSM calculate each fluctuation velocities(u', v' and w'), I've tried to infer.
Summary
Anisotropic flow by using new eddy viscosity that has direction - Calculated fluctuation velocity
: I think there is a contradiction.
Left side: Anisotropic
Right Side: Should be isotropic
→ ???
Calculated fluctuation velocity - Difference between u' and v'
: I think there is a contradiction.
Left side: Isotropic
Right Side: Anisotropic(Different fluctuation velcity.)
→ ???
I'm not good at Turbulent.
I'm just Senior.
I don't have bachelor's degree yet.
But I'm interested in Turbulence.
But I'm confused now :(
Please help me.
Thanks :)
Flows with greater anisotropy in the turbulence stress tensor render standard one equation and two equation RANS models not great as they make assumptions about the turbulent shear stresses which turn out to be untrue for specific cases. This anisotropy is commonly present in flows with large separations etc. Reynolds stress models remedy this by solving transport equations for each component of the stress tensor but these too have limitations and haven't proven to be of much advantage. If high accuracy is desired, LES or DNS are the only way. But for most engineering flows of interest, one equation and two-equation eddy viscosity models provide sufficient engineering accuracy with results in a reasonable time.
Hello Rozalia
I am fine thank you I hope you are doing well too.
What I can say to Sangho Ko is that the figure represents rms of velocity fluctuations and not velocity fluctuations. I didn't understand if the question is about how to obtain rms data from experiments or about models results
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