[ranxiaoran]

Hello everyone. When using the fluent, I feel confusing about the “relative velocity" and the "velocity". In my 2-dimensional case, they look like equal. But I still wonder which velocity does the "relative velocity" relate to. If I want to calculate the reynold stress with the formulation t=ρ(vx')(vy'), which velocity should i use?
Thank you in advance! I am very happy if anyone can answer this question!

[LuckyTran]

Relative velocity is for moving reference frames. Reynolds stress can be calculated using either velocity with different meanings. But unless you are doing LES or something, the velocity that you get from RANS/URANS is a statistically averaged velocity and you cannot calculate Reynolds stress this way.

[ranxiaoran]

Originally Posted by LuckyTran

Relative velocity is for moving reference frames. Reynolds stress can be calculated using either velocity with different meanings. But unless you are doing LES or something, the velocity that you get from RANS/URANS is a statistically averaged velocity and you cannot calculate Reynolds stress this way.

Thank you for your reply! Now I understand the difference between them.

Recently I find an article which uses the k-w sst model to analysis the Reynold stress. I don't know how the author calculate it. Maybe using these velocity in "transient time"? Or maybe this method can calculate Reynold stress but it is inaccurate comparing to the LES or DNS?

I have no idea on the calculation of the Reynold stress, and I am very happy to listen to your opinion.

Here is the article:
--------------------------------------------------------------
To investigate the mechanism of the Reynolds stress reduction,
the expression of τt is analyzed:
τt = −ρ(vx' vy') (3) （There is an overline above the vx'vy'）
where, ρ is the density and v' is the fluctuating velocity. Eq. (3) indicates that the combustion process may affect the Reynolds stress
in the near wall region through two ways: one is to change the
fluid density near the wall, and the other is to vary the fluctuating velocity near the wall.
--------------------------------------------------------------------
The attachments are the screenshot of original papers，and the result.

[LuckyTran]

That is indeed the definition of Reynolds stress. That's all you are showing... Show us something meaningful so that we might understand what is being done in the paper or you could figure it out and tell us!

But you don't get fluctuating velocities from kwSST. It doesn't matter how fine is your grid or how small is your time-step. You could calculate the stresses by invoking the Boussinesq eddy viscosity model and using the using the turbulent viscosity and strain rate, but that is definitely not the same as taking fluctuating velocities, finding their cross products, and taking the average.

[ranxiaoran]

Originally Posted by LuckyTran

That is indeed the definition of Reynolds stress. That's all you are showing... Show us something meaningful so that we might understand what is being done in the paper or you could figure it out and tell us!

But you don't get fluctuating velocities from kwSST. It doesn't matter how fine is your grid or how small is your time-step. You could calculate the stresses by invoking the Boussinesq eddy viscosity model and using the using the turbulent viscosity and strain rate, but that is definitely not the same as taking fluctuating velocities, finding their cross products, and taking the average.

Thank you for your reply!

I read the paper for many times, but I still can not find another model he uses. In his paper, after calculating the Reynolds stress, the author also mentions that the fluctuating velocity cannot obtain in the RANS simulations, so he uses the turbulent kinetic energy to evaluate the turbulent fluctuating velocity indirectly, and draws a conclusion that turbulent fluctuating velocity reduction is the main reason that reduces Reynolds stress . So I guess he doesn't change the turbulent models.

The attachments are relevant pictures which are related to the Reynolds stress in the paper.

I am very confused about this. Maybe I need to learn more theory about the Reynolds stress. I am very happy to get your suggestions!

[LuckyTran]

k is the sum of the normal stresses. You still cannot get the shear stresses from k.

You can calculate the Reynolds stresses if you just use the formula in the boussinesq model. You need the velocity derivatives and they are available as as field functions in Fluent.