# Nonlinear eddy viscosity models

(Difference between revisions)
 Revision as of 11:39, 4 November 2009 (view source) (New page: {{Template: Turbulence modeling}} This is class of turbulence models for the RANS equations in which an [[Linear eddy viscosity ...)← Older edit Latest revision as of 14:40, 4 November 2009 (view source)m Line 4: Line 4: :$:[itex] - - \rho \left\langle u_{i} u_{j} \right\rangle = 2 \, \mu_{t} \, F_{nl} \left( S_{ij}, \Omega_{ij}, \dots \right) + - \rho \left\langle u_{i} u_{j} \right\rangle = 2 \, \mu_{t} \, \mathcal{F}_{nl} \left( S_{ij}, \Omega_{ij}, \dots \right)$ [/itex] where where - :*$F_{nl} \left( S_{ij}, \Omega_{ij}, \dots \right)$ is a nonlinear function possibly dependent on the mean strain and vorticity fields or even other turbulence variable + :*$\mathcal{F}_{nl}$ is a nonlinear function possibly dependent on the mean strain and vorticity fields or even other turbulence variable :*$\mu_{t}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity) :*$\mu_{t}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity) :*[itex]S_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}} \right] - \frac{1}{3} \frac{\partial U_{k}}{\partial x_{k}} \delta_{ij} :*[itex]S_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}} \right] - \frac{1}{3} \frac{\partial U_{k}}{\partial x_{k}} \delta_{ij}

## Latest revision as of 14:40, 4 November 2009

This is class of turbulence models for the RANS equations in which an eddy viscosity coefficient is used to relate the mean turbulence field to the mean velocity field, however in a nonlinear relationship

$- \rho \left\langle u_{i} u_{j} \right\rangle = 2 \, \mu_{t} \, \mathcal{F}_{nl} \left( S_{ij}, \Omega_{ij}, \dots \right)$

where

• $\mathcal{F}_{nl}$ is a nonlinear function possibly dependent on the mean strain and vorticity fields or even other turbulence variable
• $\mu_{t}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
• $S_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}} \right] - \frac{1}{3} \frac{\partial U_{k}}{\partial x_{k}} \delta_{ij}$ is the mean strain rate
• $\Omega_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} - \frac{\partial U_{j}}{\partial x_{i}} \right]$ is the mean vorticity