# Mathematics of cyclic redundancy checks

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.

The model was developed by Tuncer Cebeci and Apollo M. O. Smith, in 1967.

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

The inner-region eddy viscosity is given by:

where

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

The eddy viscosity in the outer region is given by:

where $\alpha =0.0168$, $\delta}_{v}^{*$ is the displacement thickness, given by

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

## 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, ISBN 0-12-164650-5 - 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 Cebeci Smith model article in CFD-Wiki