Page 218 - Introduction to Computational Fluid Dynamics

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6.4 APPLICATIONS
Grimison May 25, 2005 11:10 197
1000
Zhukauskas
100

f x 10 3 Nu

10
STAGGERED ARRAY

1
10 100 1000 10000 100000 1E6
Re
Figure 6.17. Variation of f and Nu with Re for S T /D = S L /D = 1.5.

considered here. It is well known that for near-unity Prandtl numbers, turbulent
flow correlations are typically insensitive to the type of boundary condition. The
figure shows that the present turbulent-flow Nu predictions are in good agreement
with the correlations. Similar agreement is also obtained by Antonopoulos [2]. The
friction-factor data of Zhukauskas are read from an available graph and are shown
by a solid line. The presently predicted turbulent-flow friction-factor data are seen
to be substantially above the experimental data. Unfortunately, predicted friction-
factor data are not reported in [2]. In the laminar range, however, the friction-factor
data show the expected steeper slope with Re but no correlations are available for
comparison.
Figure 6.17 shows a similar comparison for the staggered array. Here again,
the turbulent-flow friction-factor data show gross overprediction but Nu data are
in excellent agreement with the correlation due to Zhukauskas. The laminar-flow
Nu shows a peculiar decline at Re ∼ 120. This is because of the change in the flow
structure at this Reynolds number, which in turn alters the temperature distribution.
For Re < 120, the maximum temperature occurs at the rear tube, whereas for
Re > 120, the maximum temperature occurs at the forward tube.
In summary, we may state that for both inline and staggered arrays, the predicted
turbulent Nu data are in good agreement with the experimental correlations but the
predicted turbulent f data are in poor agreement with the Zhukauskas correlations.
Although the latter correlations are taken as standard, it may be noted that there
are other researchers whose experimental correlations for f are in much closer
agreement with the present predictions.