ANSYS FLUENT 12.0 Theory Guide - 4.9.2 Reynolds Stress Transport Equations

4.9.2 Reynolds Stress Transport Equations

The exact transport equations for the transport of the Reynolds stresses, $\rho \overline{u'_i u'_j}$ , may be written as follows:

$\underbrace{\frac{\partial}{\partial t} (\rho \; \overline{u... ...ght)} \right]}_ {\mbox{$D_{T,ij} \equiv$ Turbulent Diffusion}}$

$\; \; + \underbrace{\frac{\partial}{\partial x_{k}} \left[ \... ...{u'_{i} \theta})}_{\mbox{$G_{ij} \equiv$ Buoyancy Production}}$

$+ \underbrace{\overline{ p \left (\frac{\partial u'_{i}}{\pa... ...j}}{\partial x_k}}}_{\mbox{$\epsilon_{ij} \equiv$ Dissipation}}$

$\underbrace{- 2 \rho \Omega_k \left(\overline{u'_j u'_m} \e... ... + \underbrace{S_{\rm user}}_{\mbox{User-Defined Source Term}}$

(4.9-1)

Of the various terms in these exact equations, $C_{ij}$ , $D_{L,ij}$ , $P_{ij}$ , and $F_{ij}$ do not require any modeling. However, $D_{T,ij}$ , $G_{ij}$ , $\phi_{ij}$ , and $\epsilon_{ij}$ need to be modeled to close the equations. The following sections describe the modeling assumptions required to close the equation set.

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