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

6 Investigation of the xz-plane
The left plot of the centre row of figure 6.7 reveals Äê Ñ¡ë3ìÌí ê Ñ¡ë3ìÌí the correlations, denoted by
êïî Ñí êïî Ñí for simplicity, and the right plot shows the associated correlation of the positive and
Ã
negative wall-normal fluctuations in the particular regions § where is negative. The coherent
velocity regions selected in this way show nearly the same functional dependence around the
maximum (down to correlation values of 0.2 à êïî Ñí êïî Ñí for and nearly zero ÃËÛË ¹ §zºðÀ¼ for ),
which indicates a high degree of coherence in wall-normal direction. When ÃËÌË ¹ §-ºñÀ¼
the
correlation is considered the value of the minimum increases with increasing wall distance.
This is completely different when only the correlations of the wall-normal fluctuations are
calculated which can be measured in regions where the stream-wise velocity fluctuations are
larger than the mean velocity, ÃËÛË ¹ §-½ðÀ¼ e.g. as shown in the lower right plot of the same
figure. In this case the value of the minimum decreases with increasing wall distance. The
symbol explanation of ÃËÛË ¹ §òºóÀ¼ the ÃËÌË ¹ §ô½¤À¼ and correlations in the figures indicates that
the distance between the minima and the maximum increases with increasing wall distance for
both functions but faster for ÃËÛË ¹ §j½õÀ¼ the , especially close to the wall. Moreover, it can be
concluded from the functional dependence of the correlations around the maximum that the
coherence of ÃËÛË ¹ §F½öÀ¼ the structures is rather weak compared to the coherent structures
represented ÃËÌË ¹ §óº÷À¢¼ by . Also, the structures which enter in the calculation à êïî Ñí êïî Ñí of
loose their identity to a large extent with increasing wall-distance as indicated by the strong
difference between the graphs. The exact value of the span-wise periodicity of the structures,
indicated by the minimum in the correlations, is still a point of discussion in the literature, especially
at high Reynolds numbers. One reason for this controversy is the dependence of this
number on the method applied for the determination of the wavelength. However, it should be
noted that the conditional correlation approach, applied here, is fully based on mathematical
grounds and yields only one well defined value for the wavelength, instead of a streak-spacing
distribution from which a mean has to be calculated in an appropriate way. Table 6.4 reveals
the values measured in air- and water-facilities at different Reynolds number by using various
detection methods. It can be seen that the exact spacing extracted from ÃËÌË$Á9ÃËÌË ¹ §éº»À¼
the
ÃËÌË ¹ §¥½#À¼ and correlation in figure 6.7, does not match with the values found in the cited
work but when ìêïî Ñí êïî Ñí the correlation is considered at ª¡À , the agreement is remarkable
­.®øÊ
with the other experiments.
TABLE 6.4: Comparison of streakspacing
and flow parameters. First
block: air, PIV, conditional correlation
method, Ó ®jÔ
Ü Ø
, [Present study]. Second
block:
water, hydrogen bubbles,
®ÕÔ×ù
, see [93]. Third block: air, probe
Ó
Ó ® Ô×Úúòû
rake, , see [25]. Forth block:
water, hydrogen Ó ®üÔþý
bubbles, , see
[92].
[m/s] [m/s] [m]
7800 3.0 0.1210 18.0 92
3160 0.390 0.0155 4.50 96
3310 0.305 0.0121 4.27 104
4180 0.387 0.0150 4.27 93
4940 0.475 0.0181 4.27 97
5830 0.582 0.0220 4.27 95
3300 – 0.2256 – 89
4700 – 0.3277 – 110
1080 0.152 0.0070 3.14 91
1325 0.152 0.0069 4.11 106
108