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Cebeci-Smith model

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The Cebeci-Smith [Cebeci and Smith (1967)] is a two-layer algebraic 0-equation model which gives the 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 (see below). Unlike the Baldwin-Lomax model, this model requires the determination of of a boundary layer edge.


\mu_t =
{\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ 
{\mu_t}_{outer} & \mbox{if} y > y_{crossover}

where y_{crossover} is the smallest distance from the surface where {\mu_t}_{inner} is equal to {\mu_t}_{outer}:

y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}

The inner region is given by the Prandtl - Van Driest formula:

{\mu_t}_{inner} = \rho l^2 \left| \Omega \right|


l = \kappa y \left( 1 - e^{\frac{-y^+}{A^+}} \right)

\kappa = 0.4, A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}

\left| \Omega \right| = \sqrt{2 \Omega_{ij} \Omega_{ij}}

\Omega_{ij} = \frac{1}{2}
 \frac{\partial u_i}{\partial x_j} -
 \frac{\partial u_j}{\partial x_i}

The outer region is given by:

{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),

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

\delta_v^* = \int_0^\delta (1-U/U_e)dy,

and F_{KLEB} is the Klebanoff intermittency function given by

F_{KLEB}(y;\delta) = \left[1 + 5.5 \left( \frac{y}{\delta} \right)^6

Model variants

Performance, applicability and limitations

Implementation issues


  • Smith, A.M.O. and Cebeci, T. 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..
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