Civil Engineering Reference
In-Depth Information
The dissipation in isotropic homogeneous turbulence is
expressed by the simple equation
2
⎛
⎞
⎠
∂
u
(
iso
*
[2.48]
ε
K iso
= ω
i
ω
i
=
15
ν
⎜
⎟
⎝
∂
x
It is widely used by experimentalists to estimate the
dissipation by way of temporal series of
u
and Taylor's
hypothesis.
11
Turbulence achieves an approximately isotropic
homogeneous state far from the wall in the outer layer
[KIM 93]. Figure 2.10, however, shows that
*
drastically
ε
K iso
underestimates the dissipation at
y
+
≤
60
. These tendencies
still need to be confirmed with higher Reynolds numbers.
2.8.2.
Dissipation linked to the transport equations for
the Reynolds stresses
The dissipation terms in the transport equations [2.3] can
be reduced to
2
⎛
⎞
⎠
⎛
⎞
⎠
∂
u
1
∂
u
1
∂
u
ε
11,0
=−
2
ν
0
=−
2
ν
⎜
⎟
⎜
⎟
∂
x
l
∂
x
l
∂
y
⎝
⎝
0
2
⎛
⎞
⎠
⎛
⎝
⎞
⎠
∂
u
2
∂
u
2
∂
v
ε
22,0
=−
2
ν
⎜
⎟
0
=−
2
ν
0
=
0
⎜
⎟
∂
x
l
∂
x
l
∂
y
⎝
[2.49]
2
⎛
⎞
⎠
⎛
⎝
⎞
⎠
∂
u
3
∂
u
3
∂
w
∂
ε
33,0
=−
2
ν
0
=−
2
ν
⎜
⎟
⎜
⎟
∂
x
l
∂
x
l
y
⎝
0
⎛
⎝
⎞
⎠
⎛
⎝
⎞
∂
u
1
∂
u
2
∂
u
∂
v
ε
=−
2
ν
⎜
⎟
0
=−
2
ν
⎜
⎟
0
=
0
12,0
∂
x
l
∂
x
l
∂
y
∂
y
⎠
11 Remember that Taylor's hypothesis consists of neglecting all the terms
in the Navier-Stok
es
equation apart from the mean inertia terms. It is
written as
(
)
.
∂∂
/
t
=−
U
∂∂
/
x
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