Cebeci-Smith model
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where <math>y_{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_{inner}</math> is equal to <math>{\mu_t}_{outer}</math>: | where <math>y_{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_{inner}</math> is equal to <math>{\mu_t}_{outer}</math>: | ||
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:<math> | :<math> | ||
y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer} | y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer} | ||
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The inner region is given | The inner region is given | ||
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:<math> | :<math> | ||
{\mu_t}_{inner} = \rho l^2 l \left[\left( | {\mu_t}_{inner} = \rho l^2 l \left[\left( | ||
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where | where | ||
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:<math> | :<math> | ||
l = \kappa y \left( 1 - e^{\frac{-y^+}{A^+}} \right) | l = \kappa y \left( 1 - e^{\frac{-y^+}{A^+}} \right) | ||
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with the constant <math>\kappa = 0.4</math> and | with the constant <math>\kappa = 0.4</math> and | ||
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:<math> | :<math> | ||
A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}. | A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}. | ||
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The outer region is given by: | The outer region is given by: | ||
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:<math> | :<math> | ||
{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta), | {\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta), | ||
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where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given by | where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given by | ||
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:<math> | :<math> | ||
\delta_v^* = \int_0^\delta (1-U/U_e)dy, | \delta_v^* = \int_0^\delta (1-U/U_e)dy, | ||
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[[Category:Turbulence models]] | [[Category:Turbulence models]] | ||
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Revision as of 09:41, 12 June 2007
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 , is the velocity thickness given by
| (7) |
and 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..