Cebeci-Smith model

The Cebeci-Smith model is a 0-equation eddy viscosity model used in computational fluid dynamics analysis of turbulent boundary layer flows. The model gives eddy viscosity, $mu\_t$, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the Baldwin-Lomax model, this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the Baldwin-Lomax model, this model requires the determination of a boundary layer edge.

Equations

In a two-layer model, the boundary layer is considered to comprise two layers: inner (close to the surface) and outer. The eddy viscosity is calculated separately for each layer and combined using:

:

where $y\_\{crossover\}$ is the smallest distance from the surface where $\{mu\_t\}\_\{inner\}$ is equal to $\{mu\_t\}\_\{outer\}$.

The inner-region eddy viscosity is given by:

:$\{mu\_t\}\_\{inner\}\; =\; ho\; l^2\; l\; left\; [left(\; frac\{partial\; U\}\{partial\; y\}\; ight)^2\; +\; left(frac\{partial\; V\}\{partial\; x\}\; ight)^2\; ight]\; ^\{1/2\}$

where

:$l\; =\; kappa\; y\; left(\; 1\; -\; e^\{frac\{-y^+\}\{A^+\; ight)$

with the von Karman constant $kappa$ usually being taken as 0.4, and with

:$A^+\; =\; 26left\; [1+yfrac\{dP/dx\}\{\; ho\; u\_\; au^2\}\; ight]\; ^\{-1/2\}$

The eddy viscosity in the outer region is given by:

:$\{mu\_t\}\_\{outer\}\; =\; alpha\; ho\; U\_e\; delta\_v^*\; F\_\{K\}$

where $alpha=0.0168$, $delta\_v^*$ is the displacement thickness, given by

:$delta\_v^*\; =\; int\_0^delta\; (1-U/U\_e)dy$

and $F\_\{K\}$ is the Klebanoff intermittency function given by

:$F\_\{K\}\; =\; left\; [1\; +\; 5.5\; left(\; frac\{y\}\{delta\}\; ight)^6\; ight]\; ^\{-1\}$

References

* Smith, A.M.O. and Cebeci, T., 1967. "Numerical solution of the turbulent boundary layer equations". Douglas aircraft division report DAC 33735
* Wilcox, D.C., 1998. "Turbulence Modeling for CFD". ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.

External links

* This article was based on the [http://www.cfd-online.com/Wiki/Cebeci-Smith_model Cebeci Smith model] article in [http://www.cfd-online.com/Wiki CFD-Wiki]