Representation of Reynolds Stress Tensor

vcvedant · August 3, 2017, 15:48

In OpenFOAM, for Newtonian incompressible fluid, the portion of momentum equation gives
$-\frac{\partial}{\partial x_i}[ \nu (\frac{\partial U_i}{\partial x_j} +\frac{\partial U_j}{\partial x_i}) - \bar{u_i u_j}] = divDevReff(U)$

using this I have defined
$\frac{\partial \bar{u_i u_j}}{\partial x_i} = divDevReff(U) + dev(nu,twoSymm(fvc::grad(U)))$

But now I need $\bar{u_i u_j}$ .
From the definition of Bousinesq's hypothesis
$\bar{u_i u_j} = \nu_t (\frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} ) - \frac{2}{3}k \delta_{ij}$ .

I think $\bar{u_i u_j}$ = nut*twoSymm(fvc::grad(U)) - (2/3)*k*tensor:

ne)

Can someone verify this and tell me if I am correct?

Thanks,

Tobi · August 9, 2017, 16:54

Dear Vedamt,

I guess you can find the answer in the book:

http://www.holzmann-cfd.de/index.php...s-and-openfoam

See page 86 to page 90. Especially 90 could be interesting for you.

vcvedant · August 9, 2017, 17:10

Thank you Tobi.
Your lecture videos are also very helpful.

August 3, 2017, 15:48	Representation of Reynolds Stress Tensor	#1
vcvedant Member Vedamt Chittlangia Join Date: Feb 2016 Posts: 64 Rep Power: 8	In OpenFOAM, for Newtonian incompressible fluid, the portion of momentum equation gives $-\frac{\partial}{\partial x_i}[ \nu (\frac{\partial U_i}{\partial x_j} +\frac{\partial U_j}{\partial x_i}) - \bar{u_i u_j}] = divDevReff(U)$ using this I have defined $\frac{\partial \bar{u_i u_j}}{\partial x_i} = divDevReff(U) + dev(nu,twoSymm(fvc::grad(U)))$ But now I need $\bar{u_i u_j}$ . From the definition of Bousinesq's hypothesis $\bar{u_i u_j} = \nu_t (\frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} ) - \frac{2}{3}k \delta_{ij}$ . I think $\bar{u_i u_j}$ = nuttwoSymm(fvc::grad(U)) - (2/3)ktensor:ne) Can someone verify this and tell me if I am correct? Thanks, Last edited by vcvedant; August 3, 2017 at 15:53. Reason: mathematical error*

August 9, 2017, 16:54		#2
Tobi Super Moderator Tobias Holzmann Join Date: Oct 2010 Location: Tussenhausen Posts: 2,694 Blog Entries: 6 Rep Power: 50	Dear Vedamt, I guess you can find the answer in the book: http://www.holzmann-cfd.de/index.php...s-and-openfoam See page 86 to page 90. Especially 90 could be interesting for you. __________________ Keep foaming, Tobias Holzmann

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August 9, 2017, 17:10		#3
vcvedant Member Vedamt Chittlangia Join Date: Feb 2016 Posts: 64 Rep Power: 8	Thank you Tobi. Your lecture videos are also very helpful.