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, μ 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.
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:
μ t = { μ t inner if y ≤ y crossover μ t outer if y > y crossover where y crossover is the smallest distance from the surface where μ t inner is equal to μ t outer .
The inner-region eddy viscosity is given by:
μ t inner = ρ ℓ 2 [ ( ∂ U ∂ y ) 2 + ( ∂ V ∂ x ) 2 ] 1 / 2 where
ℓ = κ y ( 1 − e − y + / A + ) with the von Karman constant κ usually being taken as 0.4, and with
A + = 26 [ 1 + y d P / d x ρ u τ 2 ] − 1 / 2 The eddy viscosity in the outer region is given by:
μ t outer = α ρ U e δ v ∗ F K where α = 0.0168 , δ v ∗ is the displacement thickness, given by
δ v ∗ = ∫ 0 δ ( 1 − U U e ) d y and FK is the Klebanoff intermittency function given by
F K = [ 1 + 5.5 ( y δ ) 6 ] − 1 