The significance of coherent flow structures for the turbulent mixing ...

: T
ž
ž
ò
5.3 Statistical properties of the flow
for the stream-wise velocity in [55] but here the velocity could be determined directly without
a sophisticated calibration procedure as required in case of the hot-wire investigation to
compensate the additional heat-loss induced by the solid wall. When the wall-normal velocity
component is considered, the first measurement point obtained with the hot-wire technique is
farther away from the wall by one order of magnitude, compared with the present PIV investigation,
due to the orientation and size of the sensor applied in [55]. The domain covered by
the PIV investigation is nearly constant when considered in outer variables :‚à[Ü 4‘“’,” (
)
because of the weak dependence of the boundary-layer Ü thickness on the Reynolds number.
However, when considered in inner variables on the other hand, it can be seen that the investigation
at &~€ رοތz roughly covers the domain from •
—–
the •Œ : T Œ range , because the log-law region increases in thickness with increasing
Reynolds number when considered in wall-units. This allows to examine the near-wall
, Reynolds number effects within the logarithmic region between
οÞzŒ
š
: T
Œ and at &~€ ؘ’,”zŒŒ
structure at Ø
&~€ and large-scale flow structures at &~€ Ø›’,”zŒŒ . The size of the region, where
Œ
h–
•Œ
v rms
/u τ w rms
/u τ u rms
/u τ
3
2
1
u +
rms
w +
rms
Re Θ
=7800 (PIV)
Re Θ
=7140 (HWA)
rms
v rms
/ u
0.8
0.6
0.4
0.2
Re θ
=7800 (PIV)
Re Θ
=7140 (HWA)
0
0
10œ
10œ
1
Ÿ +
vrms
10
2
œ
y +
10œ
3
œ
4
10
0.0
10
œ
0
10œ
1
10
2
œ
y +
œ
3
10
œ
4
10
3
0.8
v rms
/u τ w rms
/u τ u rms
/u τ
2
1
0
0
10œ
10œ
1
Re Θ
=15000 (PIV)
Re Θ
=16080 (HWA)
10
2
œ
y +
10œ
3
œ
4
10
rms
v rms
/ u
0.6
0.4
0.2
0.0
10
œ
0
10œ
1
Re θ
=15000 (PIV)
Re Θ
=16080 (HWA)
10
2
œ
y +
œ
3
10
œ
4
10
FIGURE 5.3: Left: Non-dimensional rms-profiles of the three velocity ¡N¢
fluctuations
€U£©¨
for
¡N¢ (top) and
wall coordinate in inner-law scaling for both Reynolds numbers.
vs¥s¥s (bottom). Right: Dependence of the anisotropy parameter ª «Z¬®­ ¯4¬®°²±
s¥s
¬ on the
€¤£¦¥§
77