Civil Engineering Reference
In-Depth Information
2.8. Dissipation
2.8.1.
Dissipation of kinetic energy
The dissipation equation
⎡
⎤
2
⎛
⎝
⎞
2
2
⎛
⎝
⎞
⎛
⎝
⎞
⎛
⎝
⎞
= ν
∂
u
k
∂
∂
u
i
x
k
+
∂
u
k
∂
∂
u
∂
v
∂
w
∂
⎢
⎥
ε
*
=
2
ν
+
+
+
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎢
⎥
x
i
∂
x
i
∂
x
⎠
∂
y
z
⎠
⎠
⎠
⎣
⎦
⎡
⎤
2
2
⎛
⎞
⎠
2
2
2
2
⎛
⎞
⎠
⎛
⎞
⎠
⎛
⎝
⎞
⎠
⎛
⎞
⎛
⎞
⎠
∂
u
∂
∂
v
∂
u
∂
w
∂
∂
v
∂
∂
w
∂
⎢
⎥
[2.40]
+
ν
+
+
+
+
+
+
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎥
y
⎝
∂
x
∂
z
⎝
x
⎠
⎝
z
y
⎝
⎝
⎣
⎦
⎡
⎣
⎤
⎦
∂
u
∂
∂
v
+
∂
u
∂
∂
w
∂
+
∂
v
∂
w
∂
+ 2
ν
⎢
⎥
y
∂
x
z
x
∂
z
y
contains 12 terms. Experimental measurements of these
terms are difficult or impossible to obtain at present. DNS,
although their applicability is limited to moderate Reynolds
numbers, constitute the only means of analyzing all of the
terms in equation [2.40]. Figure 2.7 shows the distribution of
ε
*+
in a developed turbulent channel flow for four Reynolds
numbers in the range
Re
180
to
.
Re
τ
=
1,100
τ
=
Figure 2.7.
Dissipation of kinetic energy in inner variables in a fully
developed turbulent channel flow for low and moderate Reynolds numbers
varying in the range
to 1,100, according to Bauer [BAU 14]
Re
=
180
τ
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