Cebeci-Smith model
From CFD-Wiki
(further clean-up, still needs work) |
Littleandy (Talk | contribs) m (Category added) |
||
| Line 81: | Line 81: | ||
* {{reference-paper|author=Smith, A.M.O. and Cebeci, T. |year=1967|title=Numerical solution of the turbulent boundary layer equations|rest=Douglas aircraft division report DAC 33735}} | * {{reference-paper|author=Smith, A.M.O. and Cebeci, T. |year=1967|title=Numerical solution of the turbulent boundary layer equations|rest=Douglas aircraft division report DAC 33735}} | ||
* {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}} | * {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}} | ||
| + | |||
| + | [[Category:Turbulence models]] | ||
Revision as of 07:51, 4 October 2006
Contents |
Introduction
The Cebeci-Smith [Smith and Cebeci (1967)] is a two-layer algebraic 0-equation model which gives the eddy viscosity, 
, 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 of a boundary layer edge.
Equations
|
| (1) |
where 
is the smallest distance from the surface where 
is equal to 
:
|
| (2) |
The inner region is given
|
| (3) |
![{\mu_t}_{inner} = \rho l^2 l \left[\left(
\frac{\partial U}{\partial y}\right)^2 +
\left(\frac{\partial V}{\partial x}\right)^2
\right]^{1/2},](/W/images/math/1/2/5/1259b699fd9a5f5544782d6b1f0cc61b.png)
where
|
| (4) |
with the constant 
and
|
| (5) |
![A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}.](/W/images/math/1/9/8/19839d857afa6c50f418ac133d894115.png)
The outer region is given by:
|
| (6) |
where 
, 
is the velocity thickness given by
|
| (7) |
and 
is the Klebanoff intermittency function given by
|
| (8) |
![F_{KLEB}(y;\delta) = \left[1 + 5.5 \left( \frac{y}{\delta} \right)^6
\right]^{-1}](/W/images/math/4/3/3/4331b74159c7e4947a91a3c15e2c8282.png)
Model variants
Performance, applicability and limitations
Implementation issues
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..
