Mark K. Harrington1
e-mail: [email protected]
Marcus A. McWaters2
e-mail: [email protected]
David G. Bogard
e-mail: [email protected]
Mechanical Engineering Department,
University of Texas at Austin,
Austin, TX 78712
Christopher A. Lemmon3
Mechanical Engineering Department,
University of Wisconsin-Madison,
Madison, WI 53706
e-mail: [email protected]
Karen A. Thole
Mechanical Engineering Department,
Virginia Polytechnic Institute and State
University,
Blacksburg, VA 24061
e-mail: [email protected]
Full-Coverage Film Cooling With
Short Normal Injection Holes
An experimental and computational investigation was conducted on the film cooling adiabatic effectiveness of a flat plate with full coverage film cooling. The full coverage film
cooling array was comprised of ten rows of coolant holes, arranged in a staggered
pattern, with short L/D ⫽ 1, normal coolant holes. A single row of cooland holes was also
examined to determine the accuracy of a superposition prediction of the full coverage
adiabatic effectiveness performance. Large density coolant jets and high mainstream turbulence conditions were utilized to simulate realistic engine conditions. High-resolution
adiabatic effectiveness measurements were obtained using infrared imaging techniques
and a large-scale flat plate model. Optimum adiabatic effectiveness was found to occur
for a blowing ratio of M ⫽ 0.65. At this blowing ratio separation of the coolant jet
immediately downstream of the hole was observed. For M ⫽ 0.65, the high mainstream
turbulence decreased the spatially averaged effectiveness level by 12 percent. The high
mainstream turbulence produced a larger effect for lower blowing ratios. The superposition model based on single row effectiveness results over-predicted the full coverage
effectiveness levels. 关DOI: 10.1115/1.1400111兴
Introduction
Film cooling is used in the turbine section of modern jet engines as a means of protecting the surface of the turbine airfoils
from the hot gases entering the turbine section from the combustion chamber. Most film cooling studies have focused on single
row configurations, but recently there has been renewed interest in
the performance of full coverage film cooling. Full coverage cooling incorporates rows of coolant holes located over the entire area
that is to be cooled. Previously there have been relatively few
studies of adiabatic effectiveness performance for full coverage
film cooling as indicated in Table 1.
Listed in Table 1 are summaries of the geometries and operating conditions for these previous studies. Because of the differences in geometric configurations among these studies, it is difficult to determine a consensus of the expected performance for full
coverage cooling. For normal hole injection, Cho and Goldstein
关1兴 found a maximum average adiabatic effectiveness of ␩ញ ⬇0.4
共␩ញ is spatially averaged adiabatic effectiveness兲 at a blowing ratio
of M ⫽0.22, with decreased adiabatic effectiveness for M ⫽0.36.
However, with larger spacing between holes. Metzger et al. 关2兴
found a maximum adiabatic effectiveness of ␩ញ ⬇0.3 for M ⫽0.2.
It is important to recognize that none of these previous studies
investigated short holes, large density ratios, or high mainstream
turbulence. Large density ratio and high mainstream turbulence
represent the conditions present within an actual gas turbine
engine.
Objectives
The primary objective of this study was to evaluate the film
cooling performance of a full coverage configuration of film cool1
Currently at General Electric Aircraft Engines.
Currently at Ford Motor Co.
3
Currently at Johns Hopkins University.
Contributed by the International Gas Turbine Institute and presented at the 46th
International Gas Turbine and Aeroengine Congress and Exhibition, New Orleans,
Louisiana, June 4 –7, 2001. Manuscript received by the International Gas Turbine
Institute February 2001. Paper No. 2001-GT-130. Review Chair: R. Natole.
2
798 Õ Vol. 123, OCTOBER 2001
ing holes. The film cooling holes were short, L/D⫽1.0, and had a
normal injection angle. Experiments were conducted using low
and high mainstream turbulence conditions. CFD predictions were
also made for a single row of holes.
The film cooling performance was evaluated using spatial
variations of adiabatic effectiveness, including determining the
optimum blowing ratio. Sellers’ 关6兴 superposition model was used
to determine if full coverage film cooling effectiveness is predictable using single row experimental measurements or single row
CFD predictions. Detailing the spatial variation in the adiabatic
effectiveness is useful for understanding the complexities of the
Table 1 Previous full coverage film cooling studies with adiabatic effectiveness measurements
Authors
Hole
Arrangement
Row
Spacing
(S/D)
Hole
Spacing
(P/D)
Hole Length
(L/D)
Injection
Angle
Density
Ratio (DR)
Blowing
Ratio (M )
Mainstream
Turbulence
Cho &
Goldstein 关1兴
Mayle &
Camarata
关3兴
in-line
Metzger
et al. 关2兴
Metzger
et al. 关4兴
Sasaki
et al. 关5兴
staggered
in-line &
staggered
in-line &
staggered
staggered
3
8, 10, &
14
4.8
4.8
5 & 10
⫽S/D
⫽0.866⫻
S/D
⫽S/D
⫽S/D
3
long
long
⬎10
⬎10
4.12
90
compound
angle
1.0
90
90
45
1.0
1.0
0.94
0.5-1.5
0.1, 0.2
0.1-0.5
low
low
low
0.150.5
low
1.0
0.22,
0.36
low
Copyright © 2001 by ASME
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interaction between the mainstream and coolant jets, as well as
providing a benchmarking database for CFD validation.
Several aspects of the present study were unique. The present
study was the first full coverage film cooling study that incorporated a large density ratio and high mainstream turbulence effects.
It is also one of only two studies 共including experimental and
computational efforts兲 that examined short, normal holes; the only
other being Hale et al. 关7兴 who used unit density ratio and low
mainstream turbulence.
Experimental Facilities and Techniques
Details of the facility and techniques are presented in Harrington 关8兴. The following is an overview of essential components.
Adiabatic effectiveness tests were performed in a closed-loop
wind tunnel. The mainstream flow was accelerated through a 9:1
contraction into the test section. Figure 1 shows a schematic representation of the test section and the secondary flow loop. The
secondary loop provided the coolant flow for the adiabatic effectiveness tests. A density ratio of DR⫽1.7 was achieved by cooling the secondary flow, using liquid nitrogen in the heat exchanger, to about T j ⫽⫺90°C. Downstream of the heat exchanger
before entering an insulated plenum, the total flow rate of the
coolant was measured with an orifice flow meter.
A jets-in-cross-flow turbulence generator produced the high
mainstream turbulence required for the present study. Figure 2
presents a schematic of the turbulence generator and shows its
relative position to the test plate. The basic configuration of this
turbulence generator was developed by Thole et al. 关9兴 and later
modified to obtain more uniform flow as described by Johnston
et al. 关10兴.
The turbulence generator produced a mainstream turbulence intensity Tu⫽0.18 and an integral length scale ⌳ f ⫽3.5D at the first
row of coolant holes in the test plates used in the present study. By
the ninth row of coolant holes of the full coverage test plate, the
turbulence intensity decayed to Tu⫽0.11 and the integral length
scale increased to ⌳ f ⫽4.5D. Vertical uniformity of the turbulence
field was checked and the turbulence intensity was found to be
uniform within ⫾6 percent of the average turbulence intensity.
Figure 3 gives a schematic representation of the primary test
plate. The coordinate system used throughout the study is also
presented in this figure. The primary test plate had coolant holes
of diameter D⫽6 mm. The 55 cm long⫻61 cm wide test plate
had ten rows of coolant holes with nine holes in each row. The
rows were arranged in a staggered pattern. The row-to-row spacing was S/D⫽7.14. The hole-to-hole pitch within each row was
P/D⫽7.14. The hole injection angle was normal to the surface.
The plate thickness matched the hole diameter in order to obtain a
Fig. 1 Test facility including turbulence generator and coolant
flow loop
Journal of Turbomachinery
Fig. 2 Schematic of jets-in-crossflow turbulence generator
hole length to diameter ratio L/D⫽1.0. This test plate was constructed of low conductivity polyurethane foam, with a thermal
conductivity k⫽0.048 W/m•K.
A second coolant hole test plate was constructed specifically to
evaluate conduction effects on measured adiabatic wall temperatures. This test plate was scaled 2.6 larger than the primary test
plate, and was constructed of polystyrene with a thermal conductivity k⫽0.024 W/m•K. This test plate had the same row and hole
spacing ratios and the same injection angle, but the array of coolant holes only contained four rows with three or four holes in the
rows. Consequently, the coolant hole diameter of the scaled-up
test plate was D⫽15.8 mm.
The plenum for the coolant flow was located directly below the
test plate and contained two flow conditioning screens that redistributed the in-flow to the plenum resulting in a uniform supply of
air to all the film cooling holes. Velocity measurements at the hole
exits verified that coolant flow from the holes was uniform. Furthermore, the lateral distribution adiabatic effectiveness with film
cooling for 7.14⭐z/D⭐57.2 共i.e., 7 holes in the center of a
row兲 was also examined, and verified to have a regular periodic
distribution.
Test plate surface temperatures were measured with an Inframetrics Model 600L infrared 共IR兲 camera. A sodium chloride window was located on the adjustable roof of the test section. A thin
cellophane window was located on the outer roof of the test section. The IR camera resolution was a function of the distance
between the camera and the test plate surface. The minimum resolution of the camera in the present study was 4.5 mm⫻4.5 mm
(0.75D⫻0.75D). This value represents the area over which the
IR camera averages to produce a temperature value for a single
pixel, although the pixel resolution was finer than this.
Since the IR camera was not designed to operate at the very low
temperatures encountered in these experiments, ⫺20°C to ⫺90°C,
the internal camera calibration could not be used. Consequently
the IR camera grayscale video output was calibrated externally.
These grayscale-temperature calibrations were nonlinear at low
temperatures, and separate calibrations were performed for each
experiment to maximize accuracy.
Fig. 3 Schematic of test plate with D Ä6 mm holes
OCTOBER 2001, Vol. 123 Õ 799
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The mainstream temperature was monitored with thermocouples located upstream of the test plate. Several thermocouples
were used in the coolant plenum to verify the uniformity of the
coolant temperature throughout the plenum. Measurements
through the coolant hole showed that the measured plenum temperature was an accurate measure of the coolant temperature at the
hole entrance. Temperature profile measurements were made with
a miniature thermocouple probe. The thermocouple sensor used in
this probe was approximately 0.5 mm in diameter.
Test Conditions
Full coverage adiabatic effectiveness tests were performed for
both low mainstream turbulence intensity, Tu⬍0.005, and high
mainstream turbulence intensity, Tu⫽0.18. The mainstream velocity was U⫽10 m/s, giving a Reynolds number based on coolant hole diameter of ReD⫽4,000. A two-dimensional, 1.6 mm diameter boundary layer trip was located 12 cm downstream of the
leading edge, which was 14.5 cm upstream of the first row of
coolant holes. The trip induced a turbulent boundary layer over
the coolant hole section of the test plate with a momentum thickness of ␪ /D⫽0.075 and Reynolds number of Re␪⫽300 at the first
row of coolant holes.
A density ratio of DR⫽1.7 was used with the blowing ratio
ranging from M ⫽0.25 to M ⫽1.0. The corresponding momentum
flux range was I⫽0.04 to I⫽0.59.
The test plate with D⫽15.8 mm holes was mainly used to
evaluate the conduction correction used for the measured adiabatic wall temperatures for the test plate with D⫽6 mm holes.
The thermal resistance of the test plate with D⫽15.8 mm holes
was five times that of the test plate with D⫽6 mm holes, significantly reducing the conduction error for this plate compared to the
primary test plate. One-dimensional conduction corrections were
applied to the measurements from the primary test plate. A measure of the conduction error was obtained from measurements
between the holes in the first row where actual adiabatic effectiveness should have been zero. Comparison of these corrected results
with results from the high-thermal-resistance test plate 共which had
negligible conduction errors兲 confirmed the reliability of the conduction corrections.
The mainstream velocity for the D⫽15.8 mm test plate was
also U ⬁ ⫽10 m/s. The resulting Reynolds number was ReD
⫽10,500. Computation predictions were done for the film cooling
performance for a range of ReD . Little effect of ReD on the film
cooling performance was found 共see Lemmon 关11兴兲.
Spanwise Uniformity, Repeatability, and Uncertainty
The overall precision uncertainty in the effectiveness measurements was determined with repeatability tests, where the same test
conditions were investigated on separate days. Based on the repeatability tests, precision uncertainty for local adiabatic effectiveness was ␦␩⫽⫾0.025, for a 95 percent confidence interval.
Results from repeated laterally averaged effectiveness tests indi¯ ⫽⫾0.01. For the primary test
cated a precision uncertainty of ␦␩
plate, conduction corrections of ⌬ ¯␩ ⫽0.06 to 0.10 were applied,
depending on the blowing ratio. The uncertainty of this correction
¯ ⫽⫾0.015. Consequently, overall uncerwas estimated to be ␦␩
tainty for the laterally averaged adiabatic effectiveness measure¯ ⫽⫾0.02.
ments on the primary test plate was ␦␩
The uncertainty of the superposition prediction examined in the
present study was determined using the sequential perturbation
technique 关12兴 incorporating the uncertainty for the single row.
¯ ⫽⫾0.07
The uncertainty in the superposition prediction was ␦␩
by the ninth row of holes. The uncertainty in the superposition
prediction for M ⫽0.25 was the same magnitude as the M ⫽0.65
prediction. The increase in uncertainty with row number was
caused by the propagation of the uncertainty inherent with the
superposition model.
800 Õ Vol. 123, OCTOBER 2001
Computational Methodology
Two test cases were computationally simulated for this study,
which included the blowing ratios of M⫽0.25 and M⫽0.65 at low
mainstream turbulence conditions. For the simulations, the computational domain included the supply chamber, a single half filmcooling hole, and the external flat plate were modeled. Appropriate symmetry boundary conditions for the film-cooling hole were
applied at the hole centerline and mid-pitch locations. The inlet
boundary condition for the external flow was set at 20 hole diameters upstream of injection while an outflow boundary condition
was placed at 30 hole diameters downstream of injection.
The Reynolds-Averaged Navier–Stokes 共RANS兲 equations and
energy equations were discretized using a second-order upwind
scheme and solved using Fluent, V5. The mesh consisted of quadrilateral cells near the wall and tetrahedral cells throughout the
remainder of the domain. The turbulence model used was the
RNG k⫺ ⑀ model with a two-layer zonal method for the near-wall
treatment. The two-layer zonal model resolves the near-wall region whereby the average location of the first cell was at a y ⫹
⫽1.8 for the studies reported in this paper. Note that all of the
turbulence modeling coefficients remained as the model-specified
values.
A number of computational studies were conducted to determine grid sensitivity with the final mesh requiring 1.2⫻106 cells.
Nominally 2100 iterations were required for convergence, which
was determined based on a decrease of the energy equation residuals by three orders of magnitude. Performing 500 iterations
beyond the 2100 iterations resulted in changes of the centerline
effectiveness levels by ␦␩⫽0.001.
Results
In the following results, experimental and computationally predicted single row performance are presented first. These data were
the baseline for superpositions predictions. Following this, experimental results for full coverage film cooling are presented for low
and high mainstream turbulence levels. Finally, superposition
predictions are compared with actual full coverage film cooling
performance.
Single Row, Low Mainstream Turbulence. Single row adiabatic effectiveness tests were performed on the D⫽15.8 mm test
plate to minimize the conduction correction 共essentially negligible兲 and thereby increase accuracy. Adiabatic effectiveness measurements were made for x/D⭐44. These single row measurements were made primarily to provide a baseline for use with
superposition predictions, and for comparison with computational
predictions. Laterally averaged adiabatic effectiveness, ¯␩ , results
are presented in Fig. 4 for blowing ratios of M ⫽0.25 and M
⫽0.65. Preliminary tests had shown that the blowing ratio of M
⫽0.65 provided the maximum adiabatic effectiveness. The low
laterally averaged adiabatic effectiveness, ¯␩ , levels downstream
of the row of coolant holes can be attributed to the large hole-tohole spacing within the row, P/D⫽7.14. For distances greater
than 20D downstream, ¯␩ levels were less than 0.08 which required extreme precision for accurate measurement. Although
these levels might be considered low enough to be inconsequential, the cumulative effects when using superposition for full coverage film cooling predictions requires that these low levels be
accurately determined.
For both blowing ratios, M ⫽0.25 and M ⫽0.65, the computational results under-predicted the effectiveness levels for x/D
⬍20. But the computationally predicted ¯␩ levels decayed at a
slower rate than the experimentally measured levels so that ¯␩
level for experiments and computations were comparable in the
range 20⬍x/D⬍40.
Differences between the experimental measurements and computational predictions were clarified by the spatial distribution of
adiabatic effectiveness downstream of the holes. Figure 5 presents
the measured and predicted two-dimensional adiabatic effectiveTransactions of the ASME
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Fig. 4 Single row laterally averaged adiabatic effectiveness;
experimental measurements and CFD predictions
ness contours for the blowing ratios M ⫽0.25 and M ⫽0.65. At
both blowing ratios the computationally predicted distribution of
␩ was distinctly narrower than the measured distribution. Also,
centerline values of ␩ for the computational predictions were
larger than experimental measurements. Both these differences
suggest that the lateral dispersion of the coolant for the computational prediction was less than actually occurred.
For both blowing ratios, experiments showed the maximum local ␩ level immediately downstream of the hole was ␩⬇0.5. This
relatively low level suggested the possibility of jet separation. The
computational results also indicate a distinct double peak in the
near hole region for the M⫽0.65 case indicating a jet lift-off in
this region. To investigate this possibility, thermal field measurements were made above the surface.
The measured and predicted thermal profiles of the coolant jet
above the surface of the test plate and along the centerline of the
jet are shown in Fig. 6 for blowing ratios of M ⫽0.25 and M
⫽0.65, respectively. The thermal profiles shown are in terms of
non-dimensional temperature, ⌰. These coolant jet profiles show
that the computational predictions of the jet lift-off were in good
agreement with experimental measurements. For M ⫽0.25, experiments and computations showed the coolant jet positioned
very close to the wall, indicating negligible separation. However,
for M ⫽0.65 the core of the coolant jet, identified by maximum ⌰
values, is distinctly above the surface, indicating a significant
separation. Although the ⌰ levels predicted by the computations
were larger than the experimentally measured ⌰ levels, the predicted penetration height of the separated coolant jet was very
similar to the measured height.
The coolant jet separation is most clearly evident from the computational velocity field predictions. Figure 7 shows a large reverse flow region which occurs for the M ⫽0.65 blowing ratio.
For M ⫽0.25 the computationally predicted velocity field showed
a very slight separation region close to the wall 共not shown兲.
Although the low ␩ levels downstream from the hole can be
attributed to jet separation for M ⫽0.65, for M ⫽0.25 the experimental measurements indicate the decreased ␩ levels are due to
smaller ⌰ levels at the exit of the hole. The maximum nondimensional temperature measured at the hole exit was ⌰⫽0.8,
and the coolant appears to exit from the downstream part of the
hole. These measurements suggest ingestion of mainstream fluid
into the hole 共there is insignificant heating of the coolant as it
passes through the hole due to the very low conductivity polystyrene material兲. The computational results give a maximum value
of ⌰⬎0.9 indicating less ingestion into the hole as compared with
the experiments.
Full Coverage, Low Mainstream Turbulence. Figure 8
shows the build-up of laterally averaged adiabatic effectiveness
Journal of Turbomachinery
Fig. 5 Single row adiabatic effectiveness contours; experimental measurements and CFD predictions
for the full coverage operation with blowing ratios of M ⫽0.25
and M ⫽0.65. The data shown in the figure were taken at multiple
IR camera positions, which include rows 1, 2, 3, 4, 5, 8, and 9.
The average adiabatic effectiveness was just slightly less for M
⫽0.25 compared to M ⫽0.65 for the first several rows of holes.
However, downstream of the fourth row of holes the performance
gap between the two blowing ratios widened, and by the eighth
row the difference in laterally averaged effectiveness for the blowing ratios of M ⫽0.25 and M ⫽0.65 was ⌬ ¯␩ ⬇0.10.
Adiabatic effectiveness for M ⫽0.25 injection appeared to
reach an asymptotic fully developed level by the fourth row of
holes. For M ⫽0.65, the fully developed level was reached by the
eighth row of holes 共no images were made for the sixth and seventh rows of holes兲.
Figure 9 shows the effect of blowing ratio for rows eight and
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Fig. 8 Full coverage adiabatic effectiveness with low mainstream turbulence, Tu Ä0.005
Fig. 9 Effect of blowing ratio on full coverage performance for
the fully developed region „rows 8 and 9… with low mainstream
turbulence, Tu Ä0.005
Fig. 6 Thermal profiles along the centerline of the coolant jet
for M Ä0.25 and 0.65
high blowing ratio, M ⫽1.0, produce nominally the same laterally
averaged effectiveness levels, so operation at M ⫽1.0 would be of
little benefit.
Full Coverage, High Mainstream Turbulence. Figure 10
shows the effect of mainstream turbulence on laterally averaged
nine, which may be regarded as the fully developed effectiveness
region for the full coverage operation. All three blowing ratios,
M ⫽0.25, M ⫽0.65, and M ⫽1.0, exhibited no variation in laterally averaged effectiveness levels between the eighth and ninth
row of holes. The intermediate blowing ratio, M ⫽0.65, and the
Fig. 7 CFD prediction of velocity field for M Ä0.65 coolant jet
injection
802 Õ Vol. 123, OCTOBER 2001
Fig. 10 Comparison of full coverage adiabatic effectiveness
with low and high mainstream turbulence, Tu Ä0.005 and 0.18
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Table 2 Spatially averaged adiabatic effectiveness levels, ␩ញ ,
for the fully developed region with full coverage film cooling
M
Tu⫽0.5
Tu⫽18
Percent change
0.25
0.65
1.0
0.23
0.34
0.35
0.16
0.30
0.30
30
12
14
adiabatic effectiveness for the eighth and ninth rows of the full
array. These results are summarized in Table 2 in terms of the
spatially averaged effectiveness, ␩ញ , which is an overall area average of the adiabatic effectiveness 共excluding the coolant holes兲.
For low blowing ratio, M ⫽0.25, there was a 30 percent decrease
in the spatially averaged effectiveness with high mainstream turbulence. The intermediate blowing ratio, M ⫽0.65, showed a 12
percent decrease and the high blowing ratio, M ⫽1.0, showed a 14
percent decrease.
Spatial distributions of adiabatic effectiveness in the fully developed region are presented in Figs. 11 and 12 for low and intermediate blowing ratios, respectively. In each case the general pattern of the effectiveness distribution downstream of the holes was
similar for low and high mainstream turbulence. However, the
high mainstream turbulence caused a relatively uniform decrease
of ⌬␩⫽0.05 in local effectiveness levels. The much narrower distribution of effectiveness, and sharper decrease in effectiveness
Fig. 12 Effect of high mainstream turbulence on full coverage
adiabatic effectiveness distribution for M Ä0.65
for the M ⫽0.65 case compared to the M ⫽0.25 case is another
indication of the significant separation which occurs for M
⫽0.65.
Fig. 11 Effect of high mainstream turbulence on full coverage
adiabatic effectiveness distribution for M Ä0.25
Journal of Turbomachinery
Superposition Predictions. The superposition model developed by Sellers 关6兴 was used to predict the performance of the
multiple rows of holes for full coverage performance. These predictions require the use of a baseline database for a single row of
holes. Consequently, predictions were made using the experimental measurements for single row operation 共as presented in Fig. 4兲,
and the computational prediction for a single row of holes.
As part of the computational study, full coverage with seven
rows was simulated using a coolant with density ratio DR⫽1.1
and a blowing ratio of M ⫽0.25. The results of this study indicated good agreement between the CFD single row simulations
using superposition and the CFD multiple row simulations.
Superposition predictions, experimental and computational, are
compared with the measured ¯␩ values for full coverage film cooling with a blowing ratio of M ⫽0.25. The superposition prediction
based on the experimental single row data showed good agreement with measurements over the first four rows of holes, but
over-predicted the effectiveness level at the eighth and ninth rows.
The superposition based on the computational results underpredicted the effectiveness level over the first several rows of the
array, but showed good agreement with measured levels at the
eighth and ninth rows.
For the full coverage measurements, the ¯␩ level downstream of
the fourth row of holes was essentially the same level as that
downstream of the eighth and ninth rows. This suggests that for
OCTOBER 2001, Vol. 123 Õ 803
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in the full array. For the M ⫽0.65, the prediction only produced
good agreement over the first three rows of holes.
Conclusions
Fig. 13 Superposition predictions using experimental and
CFD single row baselines. Low mainstream turbulence, Tu
Ä0.005
M ⫽0.25 a fully developed condition was achieved by the fourth
row of holes. Furthermore, this indicates that the coolant from the
first rows of holes must interact with the coolant jets of the second
through fourth rows of holes in such a way as to eliminate any
cooling effect from the first row of holes by the fifth row.
Figure 13 shows a comparison of the predicted and measured
full coverage ¯␩ values for a blowing ratio of M ⫽0.65. The experimental superposition prediction showed good agreement with
the measured effectiveness levels for the first three rows of holes.
After the fourth row, the experimental superposition prediction
over-predicted the effectiveness levels and the discrepancy increased with increasing streamwise position. The computational
superposition prediction was similar to the experimental superposition prediction, with the exception of poorer agreement with the
measured effectiveness levels over the first three rows of holes.
Since there was no difference in the measured ¯␩ levels evident
between the eighth and ninth rows of holes, it was apparent that a
fully developed condition had been achieved by the eighth row.
This indicates that the effect of the coolant from the first row of
holes was eliminated by the interaction of the jets from the second
to eighth rows of holes.
When the superposition predictions were extended beyond the
nine rows of holes as shown in Fig. 13 共see Harrington 关8兴兲, a
continuing increase in laterally averaged adiabatic effectiveness
was predicted up to 20 rows. These predictions were clearly contrary to the experimental measurements of the full coverage film
cooling showing that fully developed levels were established
within four and eight rows of holes for M ⫽0.25 and M ⫽0.65,
respectively.
The main deficiency of the superposition model proposed by
Sellers 关6兴 was an inability to account for the degradation of the
coolant jet caused by the interaction with coolant from downstream rows of holes. The prediction for M⫽0.25 produced good
agreement with the measurement over the first four rows of holes
804 Õ Vol. 123, OCTOBER 2001
There were several unique aspects of this full coverage film
cooling study compared to previous studies. Large density coolant
was used, the effects of very high mainstream turbulence were
investigated, and relatively short, normal holes were used. For the
full coverage configuration studied, as many as eight rows of
holes were required to reach an asymptotic ‘‘fully developed’’
adiabatic effectiveness level. Maximum spatially averaged adiabatic effectiveness of 0.35 was found to occur for a blowing ratio
of M ⫽0.65. Increasing the blowing ratio to M ⫽1.0 resulted in
essentially the same average adiabatic effectiveness.
Particular attention was placed on jet separation. The coolant jet
remained attached to the surface of the test plate for M ⫽0.25.
Significant separation of the coolant jet from the surface, both
measured and predicted, was evident for M ⭓0.65.
The high mainstream turbulence reduced the spatially averaged
effectiveness by 30 percent for the blowing ratio of M ⫽0.25. The
reduction in spatially averaged effectiveness for the blowing ratios
of M ⫽0.65 and M ⫽1.0 was not as severe, only about a 14 percent reduction. The smaller reduction in adiabatic effectiveness at
higher blowing ratios might be attributed to the coolant jet being
separated from the surface at higher blowing ratios. For separated
coolant jets, the increased dispersion caused by a highly turbulent
mainstream can have a beneficial effect of returning coolant to the
surface of the test plate.
The superposition prediction of the full coverage laterally averaged effectiveness levels based on the single row effectiveness
measurements tended to overpredict adiabatic effectiveness. Superposition predicted increasing adiabatic effectiveness performance beyond nine rows of holes, whereas the experiments
showed maximum adiabatic effectiveness was reached within four
to eight rows, depending on blowing ratio. These results indicate
that there are row-to-row interactions, which limit the maximum
adiabatic effectiveness, and these interaction are not accounted for
by the superposition model.
Acknowledgments
Our sincere thanks to Pratt and Whitney, the sponsors of this
research, for their continued support. In particular, we appreciate
the support and guidance of William Kvasnak, Fred Soechting,
and Joel Wagner.
Nomenclature
D ⫽ film cooling hole diameter
DR ⫽ density ratio of coolant to mainstream⫽␳ j / ␳ ⬁
I ⫽ momentum flux ratio of coolant to mainstream⫽
␳ j U 2j / ␳ ⬁ U ⬁2
k ⫽ thermal conductivity
L ⫽ hole length
M ⫽ mass flux ratio of coolant to mainstream⫽␳ j U j / ␳ ⬁ U ⬁
P ⫽ lateral hole pitch
Re ⫽ Reynolds number
S ⫽ streamwise row spacing
T ⫽ temperature
Tu ⫽ turbulence intensity⫽u rms /U⫻100 percent
U ⫽ mean velocity
x ⫽ streamwise coordinate originating at centerline of cooling hole in the first row
y ⫽ vertical coordinate originating at test surface
z ⫽ spanwise coordinate originating at centerline of central
hole
␩ ⫽ adiabatic effectiveness⫽(T aw ⫺T ⬁ )/(T j ⫺T ⬁ )
⌳ f ⫽ turbulence integral length scale
␳ ⫽ density
Transactions of the ASME
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␪ ⫽ momentum thickness
⌰ ⫽ nondimensional temperature⫽(T⫺T ⬁ )/(T j ⫺T ⬁ )
Subscripts
aw ⫽ adiabatic wall
j ⫽ coolant jet
⬁ ⫽ mainstream
Superscripts
¯ ⫽ lateral average
ញ ⫽ spatial average
References
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