Civil Engineering Reference
In-Depth Information
Figure 5.19 shows the distribution [5.51] for a typical QSV
with
. We can see a significant adverse
pressure gradient on the ejection side of the structure, which
causes an unsteady local separation - a phenomenon which
was mentioned at the start of this chapter. We expect to see
the creation of two clusters of negative and positive vorticity,
respectively, on the left (ejection side) and on the right
(sweep side) of the mother structure. Indeed, equation [5.52]
suggests that the near-wall vorticity at a distance
y
+
comparable to the thickness of the viscous sublayer is
governed, primarily, by
and
a
+
Re
=
22
=
20
T
⎛
⎞
∝+
∂ω
+
∂
p
x
0
[5.53]
ωω
y
=+
ω
y
⎜
⎝ ⎠
x
x
0
x
0
∂
y
∂
z
+
Although the near-wall value of
depends on its initial
ω
x
value
, it is not inconceivable for two layers of vorticity of
opposite signs to form under the mother structure, as the
observations in [BRO 93] suggest. The layer
ω
x
0
on the
left-hand side (Figure 5.19) may dominate the phenomenon,
under the destabilizing influence of the adverse pressure
gradient, unlike
ω <
0
x
which is more inclined to diffuse and
disappear. These arguments provide a qualitative
explanation for the generation of a generic vortex in the
opposite direction to the mother structure. However, they
need to be considered with caution, because the pre-existing
background turbulence inevitably has a bearing on the
effects caused by
ω >
0
x
∂
+ +
. Initially, the pockets of positive
and negative vorticity shown in Figure 5.19 diffuse, and local
dependency in the streamwise direction is crucial for their
growth, because all the production terms of
pz
ω
in equation
x
[5.48] depend implicitly on
. The diffusion may cause a
material line of null vorticity, which encourages unsteady
separation according to [ATI 04], as discussed in
section 5.3.3.
∂∂
x
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