Handbook of Turbomachinery Second Edition Revised - Ventech!

For turbine airfoil-cooling applications, it is recommended that two
basic correlations be used to characterize cylindrical pin fin heat transfer.
Separate correlations should be used for short and long pin fins. Short pin
fin ðH=d43Þ heat-transfer performance can be predicted using an equation
defined by Metzger et al. [79]. This correlation should cover the majority of
trailing-edge applications and is given by
where
Nud ¼ 0:135Re 0:69
d ðSL=dÞ 0:34
ðRefer to the figure for nomenclatureÞ
Red ¼ Wd=ðAminmÞ:
Amin ¼minimum flow area of pin fin array for the ranges
Red from 10 3
to 10 5 ;
H=d from 0:5 to 3:0;
SL=d from 1:5 to 5;
ST=d from 2:0 to 4:0:
For long pin fin ðH=d > 3Þ applications, the heat-transfer performance
should be predicted using a correlation established by Faulkner [80].
The use of pin fins to cool turbine airfoils is generally not limited to the
simple uniform arrays in a constant flow area duct discussed earlier, but may
require more complex geometries. Complex pin fin arrays might include
various strategies for manipulation of the local row by row heat transfer to
obtain a desired distribution, such as interarray changes in pin diameter or
spacing and interruptions in the pin pattern. Such arrays may also be
located in ducts that converge in the mean flow direction.
For the situation where the pin fin array is located in a converging
channel, the measured Nusselt numbers were found to be consistently lower
than predicted by applying the constant flow area results using the local row
value of Reynolds number. This degradation was thought to be due to
accelerating flow effects. To account for this, a multiplying factor of 2.28
Re 0:096
d to the average heat-transfer coefficient was proposed for converging
channels.
In certain airfoil-cooling applications, such as in the trailing-edge
region of blades, air enters at the root of the blade and flows radially
through a pin fin channel, with some of the flow exhausting through holes in
the tip of the blade while the rest of the air is ejected through slots in the
trailing edge. The gradually decreasing mass flow due to the lateral ejection
Copyright © 2003 Marcel Dekker, Inc.