Cebeci-Smith model
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<table width="70%"><tr><td> | <table width="70%"><tr><td> | ||
:<math> | :<math> | ||
- | {\mu_t}_{inner} = \rho l^2 | + | {\mu_t}_{inner} = \rho l^2 \left[\left( |
\frac{\partial U}{\partial y}\right)^2 + | \frac{\partial U}{\partial y}\right)^2 + | ||
\left(\frac{\partial V}{\partial x}\right)^2 | \left(\frac{\partial V}{\partial x}\right)^2 | ||
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</math></td><td width="5%">(6)</td></tr></table> | </math></td><td width="5%">(6)</td></tr></table> | ||
- | where <math>\alpha=0.0168</math> | + | where <math>\alpha=0.0168</math> and <math>\delta_v^*</math> is the velocity thickness given by |
<table width="70%"><tr><td> | <table width="70%"><tr><td> | ||
:<math> | :<math> | ||
- | \delta_v^* = \int_0^\delta (1-U/U_e)dy | + | \delta_v^* = \int_0^\delta (1-U/U_e)dy. |
</math></td><td width="5%">(7)</td></tr></table> | </math></td><td width="5%">(7)</td></tr></table> | ||
- | + | <math>F_{KLEB}</math> is the Klebanoff intermittency function given by | |
<table width="100%"><tr><td> | <table width="100%"><tr><td> |
Revision as of 15:18, 11 June 2008
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.
Contents |
Equations
| (1) |
where is the smallest distance from the surface where is equal to :
| (2) |
The inner region is given
| (3) |
where
| (4) |
with the constant and
| (5) |
The outer region is given by:
| (6) |
where and is the velocity thickness given by
| (7) |
is the Klebanoff intermittency function given by
| (8) |
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..