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About the Reynolds Stress Model input parameter of OpenFOAM in 2D turbulent flow. 

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June 16, 2022, 09:17 
About the Reynolds Stress Model input parameter of OpenFOAM in 2D turbulent flow.

#1 
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Xingguang Zhou
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Hello everyone, this is watermelon, a new FOAMer.
When I used the LRR model in OpenFOAM v9, I found that the input parameter of R is a symmetric tensor. I think when i use LRR to calculate the 2D turbulent flow problem, the component Rzz need to be zero. But when I check my results, i found the component Rzz also has been calculated in 2D turbulent flow, why? Any suggestion is helpful, thank you! Best regards, watermelon 

June 18, 2022, 08:18 

#2 
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Turbulence is a 3D phenomenon ... hence even if you zero out one of the normal stresses, the pressure strain terms will repartition the turbulence energy amongst the different Reynolds stresses, including the one that you zero'd out.
Your mean flow may be two dimensional (e.g. a planar shear flow), with zero mean flow in the third direction, but the turbulence will always be three dimensional. 

June 18, 2022, 08:28 

#3  
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Xingguang Zhou
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Quote:
Yes, you are right, turbulent flow is 3D. What i do not understand is when i calculate a 2D case in LRR, the component of Reynolds Stress in ZZ (Rzz) is not zero. Because i think in 2D case, the Reynolds Stress should be : Rxx, Rxy, Ryx and Ryy. But when i use the LRR to calculate the 2D case, i found Rzz also be calculated, but the Rxz, Ryz, Rzx, Rzy are not be calculated. So why the Rzz be calculated in 2D case? 

June 18, 2022, 08:32 

#4 
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Umm ... not sure how I can say this differently, my friend. Rzz should NOT be zero, even in a 2D case.


June 18, 2022, 08:48 

#5  
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Xingguang Zhou
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Quote:
Actually, i think when i calculate the 2D case, only the X and Y direction should be calculated. But i found OpenFOAM and Fluent are also have been calculate the Rzz when i use LRR model. I do not understand how the Rzz was calculated in a 2D case, maybe i should to get more knowledge about turbulence. Thanks again. Yours. 

June 18, 2022, 08:56 

#6 
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Exactly  this is the key point. In a 2D case, the mean velocity in the direction, W, is not solved for and it is assumed that mean flow variables are homogeneous in the zdirection. However, the LRR closure model still solves for the full Reynolds stress tensor, since even in a 2D case Rzz is not zero. The physical reason is that the pressure strain still redistributes energy to all three normal stresses. Definitely worth reading up on turbulence modelling, esp. second order closure models. Good luck my friend.


June 18, 2022, 09:24 

#7  
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Xingguang Zhou
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Quote:
Actually, turbulent flow is 3D, so the turbulent kinetic energy should be calculated as :. So, the Boussinesq Hypothesis of eddy viscosity model can write the Reynolds Stress as: So, can I consider in 2D case, the turbulent kinetic energy can be calculated as :, and the Reynolds Stress be written as : ? Thanks a lot! 

June 18, 2022, 09:27 

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Nope. Last time of saying this. Even in a "2D case", as I explained above, the turbulence remains 3D. So the turbulence energy is the sum of ALL 3 normal stresses, and Rzz = w'w' is not zero.


June 18, 2022, 09:30 

#9 
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Xingguang Zhou
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Ok, thanks a lot~~
Wish you good health and success in your career. Best Regards. 

June 19, 2022, 08:44 

#10 
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Xingguang Zhou
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OK, thank you guys.
I think I have known this problem. In Turbulent Flows, which is written by Pope, in section 4.2, prof. Pope has interpret the 2D case in turbulent flow, and the Reynolds Stress is , this is the 2D3C (twodimensional, 3 components) case. And what i have suppose the 2D case, the Reynolds Stress is :, this is the 2D2C (twodimensional, 2 components) case, and the 2D2C is the "upper boundary" of the Lumley triangle. So, the 2D2C is a special case of 2D3C, and 2D2C is usually in the nearwall turbulence condition (Pope Chapter 9). And I also derived the secondorder equation in 2D case, the can be calculated. Thanks! Best Regards, watermelon 

Tags 
2d turbulent flow, lrr, openfoam v9, reynolds stress tensor 
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