SST k-omega model

**Turbulence modeling**
	Turbulence
	RANS-based turbulence models Linear eddy viscosity models Algebraic models Cebeci-Smith model ; Baldwin-Lomax model ; Johnson-King model ; A roughness-dependent model ; ; One equation models Prandtl's one-equation model ; Baldwin-Barth model ; Spalart-Allmaras model ; ; Two equation models k-epsilon models Standard k-epsilon model ; Realisable k-epsilon model ; RNG k-epsilon model ; Near-wall treatment ; ; k-omega models Wilcox's k-omega model ; Wilcox's modified k-omega model ; SST k-omega model ; Near-wall treatment ; ; Realisability issues Kato-Launder modification ; Durbin's realizability constraint ; Yap correction ; Realisability and Schwarz' inequality ; ; ; ; Nonlinear eddy viscosity models Explicit nonlinear constitutive relation Cubic k-epsilon ; EARSM ; ; v2-f models model ; model ; ; ; Reynolds stress model (RSM) ;
	Large eddy simulation (LES) Smagorinsky-Lilly model ; Dynamic subgrid-scale model ; RNG-LES model ; Wall-adapting local eddy-viscosity (WALE) model ; Kinetic energy subgrid-scale model ; Near-wall treatment for LES models ;
	Detached eddy simulation (DES)
	Direct numerical simulation (DNS)
	Turbulence near-wall modeling
	Turbulence free-stream boundary conditions Turbulence intensity ; Turbulence length scale ;

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The SST k-omega turbulence model [Menter 1994] is a two-equation eddy-viscosity model which has become very popular. The SST formulation combines the best of two worlds. The use of a k-omega formulation in the inner parts of the boundary layer makes the model directly usable all the way down to the wall through the visous sub-layer, hence the SST k-omega model can be used as a Low-Re turbulence model without any extra damping functions. The SST formulation also switches to a k-epsilon behaviour in the free-stream and thereby avoids the common k-omega problem that the model is too sensitive to the inlet free-stream turbulence properties. Authors who use the SST k-omega model often merit it for its good behaviour in adverse pressure gradients and separating flow. The SST k-omega model does produce a bit too large turbulence levels in regions with large normal strain, like stagnation regions and regions with strong acceleration. This tendency is much less pronounced than with a normal k-epsilon model though.

Kinematic Eddy Viscosity

$\nu _T = {a_1 k \over \mbox{max}(a_1 \omega, \Omega F_2) }$

Turbulence Kinetic Energy

${{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = P_k - \beta ^* k\omega + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma_k \nu _T } \right){{\partial k} \over {\partial x_j }}} \right]$

Specific Dissipation Rate

${{\partial \omega } \over {\partial t}} + U_j {{\partial \omega } \over {\partial x_j }} = \alpha S^2 - \beta \omega ^2 + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma_{\omega} \nu _T } \right){{\partial \omega } \over {\partial x_j }}} \right] + 2( 1 - F_1 ) \sigma_{\omega 2} {1 \over \omega} {{\partial k } \over {\partial x_i}} {{\partial \omega } \over {\partial x_i}}$

Closure Coefficients and Auxilary Relations

$F_2=\mbox{tanh} \left[ \left[ \mbox{max} \left( { 2 \sqrt{k} \over \beta^* \omega y } , { 500 \nu \over y^2 \omega } \right) \right]^2 \right]$

$P_k=\mbox{min} \left(\tau _{ij} {{\partial U_i } \over {\partial x_j }} , 20\beta^* k \omega \right)$

$F_1=\mbox{tanh} \left\{ \left\{ \mbox{min} \left[ \mbox{max} \left( {\sqrt{k} \over \beta ^* \omega y}, {500 \nu \over y^2 \omega} \right) , {4 \sigma_{\omega 2} k \over CD_{k\omega} y^2} \right] \right\} ^4 \right\}$

$CD_{k\omega}=\mbox{max} \left( 2\rho\sigma_{\omega 2} {1 \over \omega} {{\partial k} \over {\partial x_i}} {{\partial \omega} \over {\partial x_i}}, 10 ^{-10} \right )$