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Blob May 29, 2009 08:35

k-e turbulence model and energy equation

How does the k-e turbulence model affect the energy equation? I understand it affects the velocity which in turn affects the convection and dissipation terms in the energy equation. But in terms of the equation form, is it the same as in the laminar case except for the viscosity? More specifically, does it change the viscosity \mu of the dissipation term of the energy equation to the effective viscosity?

Dissipation term:
\Phi = \mu\left[2\left(\frac{\partial u}{\partial x}\right)^{2}+2\left(\frac{\partial v}{\partial y}\right)^{2}+2\left(\frac{\partial w}{\partial z}\right)^{2}\right.

+\left.\left(\frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}\right)^{2}+\left(\frac{\partial w}{\partial y}+\frac{\partial v}{\partial z}\right)^{2}+\left(\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x}\right)^{2}\right.

\left.-\frac{2}{3}\left(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}\right)^{2}\right]

And does \mu become \mu_{\mathsf{eff}} where \mu_{\mathsf{eff}} = \mu + 0.09\rho \frac{k^2}{\epsilon}?
Thanks in advance for anyone's help.

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