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Representation of Reynolds Stress Tensor

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Old   August 3, 2017, 15:48
Default Representation of Reynolds Stress Tensor
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Vedamt Chittlangia
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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,

Last edited by vcvedant; August 3, 2017 at 15:53. Reason: mathematical error
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Old   August 9, 2017, 16:54
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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.
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Old   August 9, 2017, 17:10
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Vedamt Chittlangia
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vcvedant is an unknown quantity at this point
Thank you Tobi.
Your lecture videos are also very helpful.
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reynold's stress, reynolds stress tensor, source terms, turbulence

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