Cebeci–Smith Model

The Cebeci–Smith model, developed by Tuncer Cebeci and Apollo M. O. Smith in 1967, is a 0-equation eddy viscosity model used in computational fluid dynamics analysis of turbulence in 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, it is not suitable for large regions of flow separation and significant curvature or rotation. 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:

:$\mu_t = \begin _\text & \mbox y \le y_\text \\ _\text & \mbox y > y_\text \end$

where $y_\text$ is the smallest distance from the surface where $_\text$ is equal to $_\text$.

The inner-region eddy viscosity is given by:

:
_\text = \rho \ell^2 \left left(
\frac\right)^2 +
\left(\frac\right)^2
\right

where

:$\ell = \kappa y \left( 1 - e^ \right)$

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

:
A^+ = 26\left +y\frac\right

The eddy viscosity in the outer region is given by:

:$_\text = \alpha \rho U_e \delta_v^* F_K$

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

:$\delta_v^* = \int_0^\delta \left(1 - \frac\right)\,dy$

and ''F''_''K'' is the Klebanoff intermittency function given by

:
F_K = \left + 5.5 \left( \frac \right)^6
\right

References

* Smith, A.M.O. and Cebeci, T., 1967. ''Numerical solution of the turbulent boundary layer equations''. Douglas aircraft division report DAC 33735
* Cebeci, T. and Smith, A.M.O., 1974. ''Analysis of turbulent boundary layers''. Academic Press,
* Wilcox, D.C., 1998. ''Turbulence Modeling for CFD''. , 2nd Ed., DCW Industries, Inc.

External links

* This article was based on th
Cebeci Smith model
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CFD-Wiki

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Turbulence models
Fluid dynamics
Mathematical modeling