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

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7 Investigation of the yz-plane
of the data. As the flow structures and their spatial organisation change while they are transported
downstream, the various correlation values yield information about their life history.
This is in some extent similar to the image analysis in PIV where the position, size, shape
and intensity of the signal-peak in the correlation domain yield statistical information about
the size and shape of the particle images themselves as well as information about the magnitude,
direction and homogeneity of the displacement of the particle ensemble in between the
two illuminations. The main difference lies in the fact that the fluid mechanical correlations
presented in the following are ensemble averages calculated over hundreds of realizations,
whereas in PIV the ensemble average is replaced by the spatial average of a single realization.
This implies that in our case the statistical process leading to the fluid mechanical correlation
functions must not necessarily be ergodic as required for PIV image analysis.
Intensity
Intensity
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∆ ~ x
∆τ
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FIGURE 7.2: Optimised light-sheet positioning to reduce loss-of-correlation due to unpaired particle
image pairs, induced by out-of-plane (F† " ؇mù
motion mm). Different light-sheet shadings indicate
different states of polarisation. Left: Timing diagram for measuring all components of the space-time
correlations tensor K+ Ø
for and KJ various . Right: Timing diagram for measuring all components
of the space-time correlations tensor for K‰ˆ
Ø
and various KJ .
7.2 Statistical properties of the log-law region
To ensure that the experimental arrangement was properly aligned relative to the flow direction,
the main statistical flow properties were calculated and compared with the results
presented in chapter 5. The top row of figure 7.3 shows the non-dimensional mean velocity
profile in linear and semi-logarithmic representation. It can be seen that the functional
dependence agrees fairly well with the graph from the measurements presented in chapter 5.
This demonstrates the accuracy of the stereoscopic PIV method because the mean streamwise
velocity in figure 7.3 corresponds to the out-of-plane velocity component in the present
investigation. To estimate the quality of the camera and light-sheet alignment, the statistical
properties of the fluctuations in the near-wall region were calculated. The distribution of
the velocity fluctuations and , the stream-wise vorticity a‹x and two components of the
|‹Š:Œ
Reynolds stress tensor ( Πand | ) are exactly symmetrical so that a high flow quality and
very accurate alignment of the laser and recording system can be assumed in the following.
Any misalignment of the light-sheet with respect to the wall and mean flow direction or incorrect
estimated camera positions would appear as a displacement of the distributions of certain
magnitude and direction and, thus, indicate how to improve the setup or to correct the results.
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