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