Civil Engineering Reference
In-Depth Information
understand the effect of
Re
on the distributions of the terms
of transport in the inner and outer layers, and these effects
are discussed separately.
Dissipation and pressure (both local and instantaneous)
are two other quantities of prime importance in studying
turbulent flows in general, and particularly for wall
turbulence. Two detailed sections of this chapter are devoted
to the study of these values. Anisotropy and its
characterization in wall flows will be analyzed later on.
The chapter ends with a demonstration of the specific
applications of the rapid distortion theory (RDT) for wall
turbulent flows.
We will only briefly touch upon the aspects related to one-
point models and closure schemes (such as
k
or the
transport equations for the Reynolds stresses). Readers
interested in these specific aspects can consult the numerous
publications in this domain, including [SCH 07] and many
others.
,
k
− ε
− ω
2.2. Transport equations
The instantaneous equation governing the component
(
i
Ux
G
is obtained by subtracting the Navier-Stokes
equation for
)
,
from the Reynolds-averaged equation for
that component. The result is
Uu
+
i
i
∂
u
k
∂
U
k
∂
u
∂
1
ρ
∂
p
i
i
i
+
u
x
k
+
U
x
k
+
(
u
i
u
−
u
i
u
k
)
=−
x
i
+
k
∂
t
∂
∂
∂
x
k
∂
[2.1]
2
u
i
∂
ν
∂
x
∂
x
l
l
Similarly, we write the instantaneous equation for
u
j
,
which we multiply by
u
, and then we add this to the
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