7.9 Low-Re k-epsilon models
There are many low- turbulence models for
CFD simulations where the cells near the solid walls are sufficiently
thin to resolve the flow through the viscous sub-layer.
Among them are several low-
models based on
Eq. (7.1
) and Eq. (7.2
) with additional corrections
,
,
and
:
![]() |
(7.29) |
![]() |
(7.30) |
![eqn](img/index3194x.png)
![eqn](img/index3195x.png)
![]() |
(7.31) |
![k](img/index3197x.png)
![eqn](img/index3198x.png)
![eqn](img/index3199x.png)
![eqn](img/index3200x.png)
![](img/index3201x.png)
![eqn](img/index3202x.png)
![eqn](img/index3203x.png)
![eqn](img/index3204x.png)
![eqn](img/index3205x.png)
Launder and
Sharma subsequently presented13
the model with a modified function and the more established
coefficients listed in Eq. (7.3
).
The resulting model became known as the
Launder-Sharma model.14 It is arguably the most popular
low-
model today.
The first notable modification to the standard
model is
(sometimes denoted “
”) in
Eq. (7.29
). It is the dissipation
rate at the wall (
), see figure, Sec. 7.7
, calculated by
![]() |
(7.32) |
![--](img/index3215x.png)
![](img/index3216x.png)
![](img/index3217x.png)
![eqn](img/index3218x.png)
- fixed
value
;
- fixed
value
.
The next significant modification is the
function
![]() |
(7.33) |
![eqn](img/index3223x.png)
![eqn](img/index3224x.png)
![eqn](img/index3225x.png)
The extra term in Eq. (7.30)
is a follows, designed so that
matches its recognised
peak value within the buffer layer:
![]() |
(7.34) |
![eqn](img/index3229x.png)
![eqn](img/index3230x.png)
![eqn](img/index3231x.png)
![]() |
(7.35) |
![eqn](img/index3233x.png)