1. 1
Proceedings of ASME Turbo Expo 2011: Power for Land, Sea and Air
GT2008
June 6-10, 2011, Vancouver, Canada
GT2011-45427
FILM COOLING EFFECTIVENESS DISTRIBUTION ON FIRST-STAGE VANE ENDWALL WITH AND WITHOUT
LEADING-EDGE FILLETS PART I： EFFECT OF LEADING EDGE GEOMETRY
Yang Zhang, Xin Yuan
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education
Tsinghua University
Beijing 100084, P.R. China
Email: zhangyange436@yahoo.com.cn
ABSTRACT
The paper is focused on the effect of leading edge airfoil geometry
on endwall film cooling. Fillets placed at the junctions of the leading
edge and the endwall are used in investigation. Three types of fillet
profiles are tested, and the results are compared with baseline geometry
without fillet. The design of the fillet is based on the suggestion by
previous literature data indicating that sharp is effective in controlling
the secondary flow. Three types of sharp slope fillet with the length to
height ratio of 2.8, 1.2 and 0.5 are made using stereo lithography (SLA)
and assessed in the experiment. Distributed with the approximately
inviscid flow direction, four rows of compound angle laidback
fan-shaped holes are arranged on the endwall to form full covered
coolant film. The four rows of fanshaped holes are inclined 30 deg to
the endwall surface and held an angle of 0, 30, 45 and 60 deg to axial
direction respectively. The fanshaped holes have a lateral diffusion angle
of 10 deg from the hole-centerline and a forward expansion angle of 10
deg to the endwall surface. The Reynolds number based on the axial
chord and inlet velocity of the free-stream flow is 3.5*105
, and the
testing is done in a four-blade cascade with low Mach number condition
(0.1 at the inlet) while the blowing ratio of the coolant through the
discrete holes varies from 0.4 to 1.2. The film-cooling effectiveness
distributions are obtained using the PSP (pressure sensitive paint)
technique, by which the effect of different fillet geometry on passage
induced flow and coolant is shown. The present paper compares the film
cooling effectiveness distributions in a baseline blade cascade with three
similar blades with different leading edge by adding fillets. The results
show that with blowing ratio increasing, the film cooling effectiveness
increases on the endwall. For specific blowing ratio, the effects of
leading edge geometries could be illustrated as follows. The baseline
geometry provides the best film cooling performance near leading edge
pressure side. As for the leading edge suction side, the best leading edge
geometry depends on the blowing ratio. The longfillet is the more
effective in controlling horseshoe vortex at low blowing ratio, but for
the high blowing ratio shortfillet and mediumfillet are better.
INTRODUCTION
The efficiency of a gas turbine increases with the increase of the
turbine inlet temperature. Modern gas turbines are designed to operate at
high turbine inlet temperature which is above 1600o
C, placing high
thermal loads on turbine components. With adequate cooling, the
lifetime of components may be extended because of lower thermal
stresses on the turbine. The endwall region is considerably more
difficult to cool than the blade aerofoil surfaces due to the complex
secondary flow structure and strong pressure gradient in the passage.
Bogard, Thole [1], Simon and Piggush [2] summarized the recent
literature on turbine passage aerodynamics and hear transfer. A typical
secondary flow structure in the nozzle guide vanes could be introduced
in detail as follows. The horseshoe vortex at the leading edge is divided
to two legs. The transverse pressure gradient leads the PS leg to move
across the vane passage, while the SS leg of the horseshoe vortex moves
along the blade profile. Before impinging on the downstream half of the
suction side of the adjacent blade, the passage vortex grows in size in
the passage, meeting low momentum fluid along the endwall, and
causing high heat transfer rates locally. Then the PS leg and the SS leg
of the horseshoe vortex mix and lift off the endwall onto the blade
suction side. [1][2] Friedrichs et al.[3] had investigated novel film
cooling holes distribution to improve the film cooling effectiveness near
pressure side and leading edge.[3]
An experimental study has been performed by Wright and Gao et
al. [4] to investigate the filmcooling effectiveness measurements by
three different steady state techniques: pressure sensitive paint,
temperature sensitive paint, and infrared thermograph. They found that
detailed distributions could be obtained in the critical area around the
holes, and the true jet separation and reattachment behavior is captured
with the PSP.[4] Zhang et al. [5], Wright et al. [6] measured film cooling
effectiveness on a turbine vane endwall surface using the PSP technique.
Using PSP, it was clear that the film cooling effectiveness on the blade
platform is strongly influenced by the platform secondary flow through
the passage.[5][6] Wright and Blake et al. [7] used the PSP to
investigate the effects of the upstream wake and vortex on platform film
cooling. It was determined that the upstream wake had only a negligible
effect on the platform film cooling effectiveness. The film cooling
effectiveness could be significantly reduced with the generation of a
vortex upstream of the blade passage.[7] The effects of rotation on
platform film cooling had been investigated by Suryanarayanan et al.
[8][9] who found that secondary flow from the blade pressure surface to
the suction surface was strongly affected by the rotational motion
causing the coolant traces from the holes to clearly flow towards the
suction side surface.[8] [9]

2. As for the effects of leading edge modification, most of the papers
were focused on the aerodynamic losses and heat transfer. Praisner and
Smith [10][11] studied the transient and time mean behavior of leading
edge horse vortex, illustrating that the endwall juncture region was
dominated by a horseshoe vortex characterized by significant
quasiperiodic unsteadiness while the time-mean flow field on the
symmetry plane was characterized by the presence of a horseshoe,
secondary, tertiary, and corner vortices.[10][11] Bloxham et al. [12] and
Kubendran et al. [13] used the leading edge fillet and passive flow
control to eliminate the horseshoe vortex effects. Sabatino et al. [14]
investigated the influence of Boundary Layer on the unsteady horseshoe
vortex flow and surface heat transfer. The data presented in this
literature supported the hypothesis that the temporal behavior of the
horseshoe vortex system was driven by the temporal characteristics of
the impinging turbulent boundary layer.[14] Satoshi Hada and Kenichiro
Takeishi et al. [15] studied the effect of leading edge diameter on the
horseshoe vortex and endwall heat transfer. Inlet velocity, boundary
layer thickness and leading edge diameter of a symmetric airfoil were
investigated on the endwall heat transfer in a low speed wind tunnel
facility. [15] Aunapu et al. [16] adopted the endwall jets located in the
center of a turbine passage to alert the path of the pressure side leg of
the horseshoe vortex.[16] T. I-P. Shih and Y.-L. Lin[17] performed
computations to study the effects of inlet swirl and leading edge fillet on
aerodynamic loss and surface heat transfer.[17] Mahmood et al. [18]
explored the potential of the different fillet profiles in reducing the
secondary flow structures and Nusselt numbers on the endwall.
Instantaneous flow visualization images showed smaller horseshoe
vortex structures in the stagnation region with the leading-edge fillets
compared to the horseshoe vortex structure for the baseline case.[18]
2
Zess and Thole [19] studied on methods for reducing or eliminating
the horseshoe vortex that forms at the leading edge of a gas turbine
stator vane through computation and experiment. The results presented
in the paper indicated that the leading edge horseshoe vortex could be
eliminated. [19] Becz et al. [20] presented experimental results which
provided area averaged total pressure loss coefficient measurements for
four different turbine airfoil leading edge configurations, indicating that
it was possible to significantly reduce loss in a high turning airfoil
cascade through the use of leading edge modifications.[20] Lethander
and Thole et al. [21][22] used the commercial optimization software
package in conjunction with a computational fluid dynamics (CFD)
package in the design of the fillet. Results indicated that a significant
reduction in adiabatic wall temperatures could be achieved through
application of an optimized fillet.[21][22] Han and Goldstein[23][24]
investigated the heat/mass transfer analogy on a simulated turbine
endwall with blade fillets. Results showed that near the leading edge on
the pressure and the suction surface, higher mass transfer regions were
observed with the fillets. Apparently the corner vortices were intensified
with the leading edge modified blade.[23][24] Mahmood et al. [25]
experimentally investigated the secondary flow structure in a blade
passage with and without leading edge fillets. The results indicated that
in the early stages of the development of the secondary flows, the fillets
were effective in reducing the size and strength of the suction side leg of
the horseshoe vortex with associated reductions in the pressure loss
coefficients and pitch angles.[25] Sauer et al. [26] used a leading edge
bulb in the endwall region to intensify the suction side branch of the
horseshoe vortex.[26] Pieringer et al. [27] experimentally studied the
influence of the fillet between blade and casing on the aerodynamic
performance of a transonic turbine vane. The results showed that a fillet
radius might push the starting point of flow separation at the corner
between the suction side of blade and casing towards the trailing
edge.[27]
Past researchers have found that leading edge modifications can
result in changes to the local and mainstream flow field, which is
beneficial in controlling secondary flows and heat transfer. Many
studies have investigated the effects of leading edge fillets on the flow
field through aerodynamic measurements, indicating lower loss levels
for the modified leading edge geometry. Few studies, however, have
considered the effect of leading edge fillets on endwall film cooling. To
help fill this research gap, the current paper discusses the effect of
leading edge fillet on the endwall film cooling on a nozzle guide vane
endwall. The effect of varying the fillet geometry and the blowing ratio
are both considered. This paper is the first part of a two-part study that
also investigates the effect of incidence angle on the cooling
performance of a film cooled endwall with and without leading edge
fillets (PART II).
FILM COOLING EFFECTIVENESS MEASUREMENT
THEORY AND DATAANALYSIS
The PSP techniques are mainly based on a physical process called
oxygen quenched photoluminescence which could be generally
described as: After excited by a suitable light source the active part of
PSP will emit light, yet this process will be interrupted by collisions
with oxygen molecules. The result is that the PSP molecules may relax
back to their unexcited state without emitting visible light if the local
oxygen partial pressure is high. Given that the local oxygen partial
pressure is related to the local pressure of gas which contains oxygen,
such as air, the emitted light intensity is directly related to the local
pressure of surrounding air. A high spectral sensitivity CCD camera
and light emitting diode (LED) lights are used in the study to receive
the emitted light and to excite the Ruthenium-based paint respectively.
The paint is excited at 450 nm and the camera is fitted with a 600 nm
band pass filter. In the current study, the main stream is air containing
approximately 21% oxygen and the cooling flow is pure nitrogen in
which the partial pressure of oxygen was 0%. The film effectiveness
can be expressed by oxygen concentration, which can be measured by
the PSP:
2
mix aw
N c
C C T T
C C T T
η η∞ ∞
∞ ∞
− −
= ⇒ =
− −
（1）
Where C∞
and represents the oxygen concentration of the main
stream and the air/nitrogen mixture (0% to 21%) respectively. Therefore
the film effectiveness is between 0% (far upstream and downstream)
and 100% (inside the hole).
mixC
( ) ( )
( )
2 2
2
O Oair mix air mix
air O air
P PC C
C P
η
−−
= = （2）
Figure 1. CALIBRATION SYSTEM.

3. In order to measure the film cooling effectiveness, four images
taken at the same main stream temperature are required for the PSP film
cooling test. A dark image is taken without LED light and the main
stream flow. A reference image is taken without main stream, but with
LED light on. An air injection image and a nitrogen injection image are
taken with both the main stream flow and LED light on, while the
coolant gas is air and nitrogen respectively. The reference divided by the
nitrogen-injection image and the air-injection image could be obtained
with these four groups of images. The reference data derived from the
air-injection image contains the change in oxygen concentration due to
the change in pressure which is not the contributor to film cooling
effectiveness computation. The other reference data derived from the
nitrogen-injection image yields the absolute oxygen concentration. With
these two groups of reference ratios the film cooling effectiveness could
be obtained with the mass transfer/heat transfer analogy.
3
Figure 2. CALIBRATION CURVE FOR PSP.
Before the test, PSP should be calibrated to obtain the curves
representing relationship between light intensities and local partial
pressure of oxygen. Fig.1 shows a sketch of the PSP calibration system.
The PSP coated copper coupon was used to simulate the experimental
surface, with three thermocouples installed underneath the front surface
to measure the surface temperature during the calibration. The sample
coupon was located inside a sealed chamber where a partial or total
vacuum could be created. The sample was heated by a heater at the back
side of the coupon which could keep the sample at a desired temperature
with an accuracy of better than 0.5 K. The camera was located facing
the sample coupon through a transparent window. Given the experiment
environment was at a pressure of approximately 1atm and at a
temperature between 298 K and 308 K, the PSP was calibrated under
two temperatures 298 K and 308 K and pressures from vacuum to 1atm.
The calibration was also done at a low temperature of 276.5 K to
completely investigate the influence of temperature. The calibration
results are presented in the curves indicating the relationship between
intensity ratio and pressure ratio (Fig.2). As shown in the figure, the
three curves representing different temperature are close to each other
nearly collapsing into one curve, which indicates that the influence of
temperature is little. The dimensionless temperature downstream of the
cooling holes could be obtained using the light intensities, as defined in
Eq.(3):
c
T T
T T
∞
∞
−
Θ =
−
（3）
The adiabatic wall temperature is reflected by the film cooling
effectiveness which is used as a dimensionless parameter, defined as Eq.
(4) for low speed and constant property flows.
aw
c
T T
T T
η ∞
∞
−
=
−
（4）
Based on 95% confidence interval the uncertainties of the
dimensionless temperature and the film cooling effectiveness are
estimated as 3% at a typical value of 0.5. However, the uncertainty rises
with the effectiveness approaching zero, resulting in an uncertainty of
approximately 8% when the value is 0.05.
EXPERIMENTAL FACILITY
The schematic view of the test rig is shown in Fig. 3. and Fig.4.
The test section consisted of a four-blade linear cascade whose
geometry is typical of a first stage high pressure nozzle vane, GE-E3
,
with endwall platform. The inlet cross section of the test section was
318 mm (width) and 129 mm (height). Turbulence intensity was
recorded 100 mm upstream of the middle passage using a hot-wire
probe. Turbulence intensity at this location was found to be 9.5% due
to the presence of the grid. The bottom and sides on the test section
were machined out of 15 mm thick organic glass plate whereas a 10 mm
thick organic glass plate was used for the top for better optical access to
the endwall surface. Flow conditions in adjacent passages of the center
blade were ensured to be identical by adjusting the trailing edge
tailboards for the cascade. During the experiment, the cascade inlet air
velocity was maintained at 35 m/s for all the three fillets geometries and
baseline case, which corresponds to a Mach number of 0.1 at inlet. A
two times scaled model of the GE-E3 guide vanes was used with a blade
span of 129 mm and an axial chord length of 72.5 mm.
Figure 3. SCHEMATIC OF CASCADE TEST RIG.
Figure 4. SCHEMATIC OF THE TEST SECTION WITH
ROTATABLE CASCADE.
Figure 5. FILM COOLING HOLE CONFIGURATION ON
ENDWALL.

4. 4
OMPONENTS.
Figure 9. LONG, MEDIUM A GEOMETRIES.
ape. They found that a sharp slope fillet is found to be effective in
redu
uction side to the pressure
de (black lines in Fig.10-13) of the passage in the axial chord direction.
is very similar in the four
geom
Figure 6. THE GEOMETRY OF THE BLADE WITH THE FILLET
AND THE ENDWALL.
Past studies in the open literature have shown that the passage
cross flow sweeps the film coolant from pressure side to suction side
due to the pressure gradient in the passage. To reflect this phenomenon
more apparently, all of the film cooling holes are positioned in straight
lines. Studies on the flat plates show that coolant from compound angle
holes covers wider area due to jet deflection. Four rows of compound
angle laidback fan-shaped holes are arranged on the endwall to form full
covered coolant film. Fig.5 shows the holes configurations and the blade
geometric parameters. The first row is located upstream of the leading
edge plane. The following three rows are evenly positioned inside the
vane channel, with the last one located at 65% axial chord downstream
of the leading edge. Due to the large pressure gradient on the endwall, it
is difficult to control the local blowing ratios for every single hole with
one common coolant plenum chamber. In the current study, four coolant
cavities are used for the four rows of holes respectively, as shown in
Fig.6 (The extra coolant plenum chamber is designed to simulate the
purge flow which is not used in this experiment). The coolant supplied
to each cavity is independently controlled by a rotameter dedicated to
that cavity.
Figure7. FAN-SHAPED HOLE. Figure8. FILLET C
ND SHORT FILLET
The four rows of fanshaped holes are inclined 30 deg to the
platform surface and held an angle of 0, 30, 45 and 60 deg to axial
direction respectively. The laidback fan-shaped holes are featured with a
lateral expansion of 10 deg from the hole axis and forward expansion of
10 deg into the endwall surface, as shown in Fig.7. The hole diameter in
metering part (cylindrical part) of the shaped holes is 1.2 mm, and the
expansion starts at 4.2D. The design of the fillet is based on the
suggestion by G.A.Zess and K.A.Thole [19]. In their study, nine fillets
were tested computationally and experimentally to find an optimal
sh
cing separation on the suction side. The similar fillet geometry had
been investigated by S. Han, R. J. Goldstein[23] .Considering their
suggestion, the elliptical and sharp slope fillets (Fig. 8, Fig.9) were
made using stereo lithography (SLA) and adopted in the experiment.
Three types of fillets were investigated in the experiment. As shown in
Fig.9, the longfillet is 18.8 mm long, 9.48 mm high, resulting in an
aspect ratio of 0.5. The geometric parameters of the other two types of
fillets are also shown in Fig.9. The flat part of the fillet is 2 mm high
and fixed on the blade with several connecting geometries which makes
the assembly easy, as shown in Fig.6 (left).
RESULTS AND DISCUSSION
The film cooling effectiveness distributions at different blowing
ratios are shown in Fig.10-13, where two typical blowing ratios are
chosen M=0.4 (a) and M=1.2 (b). The same trend could be found in the
four groups of figures that the area coverage of coolant film is lager at
higher blowing ratio. Although valuable insight can be obtained from
the distribution maps (Fig.10-13), the spanwise averaged plots offer
additional insight and provide clear comparisons for large amounts of
data. The effectiveness is averaged from the s
si
Given the behavior of the coolant film
etry cases, only the longfillet case is presented in Fig.14 as a
typical one. The data inside the film-cooling holes were included in the
averaged results. The sharp peaks in the plot correspond to the row
locations. It should be noted that there might be shadow inside some
holes due to view angle and lighting, so data inside those holes is not as
accurate as that of downstream parts. Fig.14 indicates that increasing the
injection rate increases the film cooling effectiveness. The lowest film
cooling effectiveness appears at M=0.4. The average is significantly
lower because the coolant does not cover the entire passage. The
blowing ratio effect is clearly seen on the downstream half of the
channel, with the effectiveness being proportional to the blowing ratio.
nofillet M=0.4 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
nofillet M=1.2 i= 0deg
Z
G
/P
-1.2
-1
-0.8
-0.6
-0.4
0
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-0.2
0
Figure 10. FILM COOLING EFFECTIVENESS DISTRIBUTION.
shortfillet M=0.4 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
shortfillet M=1.2 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
0
-0.4
-0.2
0
Figure 11. FILM COOLING EFFECTIVENESS DISTRIBUTION.
(a) (b)
(a) (b)

5. 5
mediumfillet M=0.4 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
mediumfillet M=1.2 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
Figure 12. FILM COOLING EFFECTIVENESS DISTRIBUTION.
longfillet M=0.4 i= 0deg
Z
G
/P
XG ax
/C
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
longfillet M=1.2 i= 0deg
ZG
/P
X /CG ax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
Figure 13. FILM COOLING EFFECTIVENESS DISTRIBUTION.
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
XG
/Cax
η
longfillet i=0deg M=0.4
longfillet i=0deg M=0.6
longfillet i=0deg M=0.8
longfillet i=0deg M=1
longfillet i=0deg M=1.2
Figure14. LATERALLY ERAGED FILM COOLINGAV
EFFECTIVENESS AT DIFFERENT BLOWING RATIO.
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
XG ax
/C
η
pre
nofillet i=0deg M=0.4
nofillet i=0deg M=0.6
nofillet i=0deg M=0.8
nofillet i=0deg M=1
nofillet i=0deg M=1.2
Figure15. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SIDE AT
DIFFERENT BLOWING RATIO (NOTFILLET).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.05
0.45
0.1
0.15
0.2
0.25
0.3
0.35
0.4
η
pre
shortfillet i=0deg M=0.4
shortfillet i=0deg M=0.6
shortfillet i=0deg M=0.8
shortfillet i=0deg M=1
shortfillet i=0deg M=1.2
XG
/Cax
igure16. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SIDE AT
DIFFERENT BLOWING RATIO (SHORTFILLET).
F
0
0.45
0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
η
pre
mediumfillet i=0deg M=0.4
mediumfillet i=0deg M=0.6
mediumfillet i=0deg M=0.8
mediumfillet i=0deg M=1
mediumfillet i=0deg M=1.2
XG
/Cax
Figure17. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SIDE AT
DIFFERENT BLOWING RATIO (MEDIUMFILLET).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
XG
/Cax
η
pre
longfillet i=0deg M=0.4
longfillet i=0deg M=0.6
longfillet i=0deg M=0.8
longfillet i=0deg M=1
longfillet i=0deg M=1.2
Figure18. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SIDE AT
DIFFERENT BLOWING RATIO (LONGFILLET).
To facilitate the comparison between different fillet geometries,
areas for averaging have been defined along the near the leading edge
pressure side. It begins just at the boundary line of the guide vane and
extends in pitch direction towards the outer boundary, as shown in
Fig.10-13 (the narrow region in blue lines along the pressure side of the
blade). The lateral averages near the leading edge pressure side are
shown in Fig. 15-18. The effect of blowing ratio could be found by
(a) (b)
(a) (b)

6. 6
comparing the curves these four plots. A general trend is that with
blowing ratio increasing the film cooling effectiveness increases along
the pressure side. However, the shorter the fillet is (the extreme
condition is the baseline without fillet) the peak point in the curve is
more obvious, which could be explained by looking at the film cooling
effectiveness contours in Fig.10-13. At every blowing ratio, for the
longfillet case the injection flow moves along the fillet wall. It makes
the laterally averaged film cooling effectiveness curves flat and uniform.
For the other three geometries, the injection flow trace enters the region
near pressure side at high blowing ratio, which results in the peak
points.
To investigate the effects of blowing ratio on film cooling near
leading edge suction side, a narrow region along this area is selected to
compare the injection flow behavior. Fig.10-13 show the contours of
g
ction flow traces
could be seen with the blowing ratio increasing in every leading edge
geom
tio. The force preventing the coolant moving towards the near
leading edge pressure side is provided by the strong horseshoe vortex,
whic
ortex is eliminated successfully.
film coolin effectiveness along leading edge suction side. The
boundary of the region investigated is shown with blue lines (narrow
region along suction side in Fig.10-13). Longer inje
etry case, which indicates that the improved momentum of
injection flow could apparently limit the horseshoe vortex in this region.
No apparent uncooled area could be found at the maximum blowing
ratio, even for the baseline case.
Fig.19-22 compare the laterally averaged film cooling effectiveness
near leading edge suction side. Like the pitchwise averaged film cooling
effectiveness in the whole endwall surface, the laterally averaged film
cooling effectiveness is also performed along pitchwise direction. The
boundary of computing area is the two sides of the narrow region
investigated (blue lines near suction side in Fig.10-13) rather than the
pressure side and suction side. For all of the leading edge geometries,
the film cooling effectiveness increases with blowing ratio increasing.
Though the general trends are similar, several small differences could be
found. Firstly, in the nofillet (baseline) case, the trace of the injection
flow could not enter the region near leading edge suction side, which
makes the laterally averaged film cooling effectiveness low even at high
blowing ra
h indicates that the baseline geometry could not effectively
eliminate the horseshoe vortex. Secondly, for the longfillet case, the
injection flow is kept in the region at every blowing ratio, which makes
the averaged effectiveness high along the axial chord direction. The
same trend could be found in the mediumfillet and shortfillet cases that
the film cooling effectiveness is relatively high in the higher blowing
ratio. This phenomenon shows that the fillets could effectively limit the
influence of horseshoe vortex in near leading edge suction side.
Compared with the plots in Fig.15-18, the curves in Fig.19-22 show that
the function of fillets is more apparent near the suction side where the
suction side leg of the horseshoe v
Fig.23 shows the film cooling effectiveness distribution at blowing
ratio of M=0.8 for different geometry cases. The figure compares the
effects of fillet length on the film cooling effectiveness near the leading
edge pressure side (blue lines along pressure side) and the suction side
(blue lines along suction side). The effects of leading edge geometry at
the other blowing ratios could be studied by comparing the subplot (a)
in Fig.10-13 which indicates the trend at M=0.4, and the subplot (b) in
Fig.10-13 which indicates the trend at M=1.2. Different behaviors of
injection flow traces could be noticed in these three groups of contours
(Fig.23(a)(b)(c)(d), Fig.10(a)-Fig.13(a), Fig.10(b)-Fig.13(b)). For the
longfillet case the injection flow could not enter the region because the
strong horseshoe vortex has developed earlier upstream. On the contrary,
the high film cooling effectiveness area for the baseline case is
relatively larger where the trace of the injection flow reaches the blade
surface successfully.
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
XG
/Cax
η
suc
nofillet i=0deg M=0.4
nofillet i=0deg M=0.6
nofillet i=0deg M=0.8
nofillet i=0deg M=1
nofillet i=0deg M=1.2
Figure19. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE AT
DIFFERENT BLOWING RATIO (NOFILLET).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
η
suc
shortfillet i=0deg M=0.4
shortfillet i=0deg M=0.6
shortfillet i=0deg M=0.8
shortfillet i=0deg M=1
shortfillet i=0deg M=1.2
X
G
/C
ax
Figure20. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE AT
DIFFERENT BLOWING RATIO (SHORTFILLET).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.45
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
XG
/Cax
η
suc
mediumfillet i=0deg M=0.4
mediumfillet i=0deg M=0.6
mediumfillet i=0deg M=0.8
mediumfillet i=0deg M=1
mediumfillet i=0deg M=1.2
Figure21. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE AT
DIFFERENT BLOWING RATIO (MEDIUMFILLET).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
XG
/Cax
η
suc
longfillet i=0deg M=0.4
longfillet i=0deg M=0.6
longfillet i=0deg M=0.8
longfillet i=0deg M=1
longfillet i=0deg M=1.2
Figure22. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE AT
DIFFERENT BLOWING RATIO (LONGFILLET).

7. nofillet M=0.8 i= 0deg
ZG
/P
XG
/Cax
7
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
shortfillet M=0.8 i= 0deg
ZG
/P
X /CG ax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
mediumfillet M=0.8 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
longfillet M=0.8 i= 0deg
Z
G
/P
XG
/Cax
-0.2 0 0.2 0.4 0.6 0.8
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
Figure23. FILM COOLING EFFECTIVENESS DISTRIBUTION
ON THE ENTIRE ENDWALL (EFFECT OF LEADING EDGE
GEOMETRY, M=0.8).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
XG
/Cax
η
pre
i=0deg M=0.4 Longfillet
i=0deg M=0.4 Mediumfillet
i=0deg M=0.4 Shortfillet
i=0deg M=0.4 Nofillet
Figure24. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SID
(EFFECT OF LEADING EDGE GEOMETRY, M=0.4).
E
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
XG
/Cax
η
pre
i=0deg M=0.8 Longfillet
i=0deg M=0.8 Mediumfillet
i=0deg M=0.8 Shortfillet
i=0deg M=0.8 Nofillet
EDGE GEOMETRY, M=0.8).
Figure25. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SIDE
(EFFECT OF LEADING
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
X
G
/C
ax
η
pre
i=0deg M=1.2 Longfillet
i=0deg M=1.2 Mediumfillet
i=0deg M=1.2 Shortfillet
i=0deg M=1.2 Nofillet
Figure26. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE PRESSURE SIDE
(EFFECT OF LEADING EDGE GEOMETRY, M=1.2).
Comparisons of laterally averaged effectiveness near leading edge
pressure side among four geometries at different blowing ratio
conditions are shown in Fig. 24-26. Results show that a decrease in film
cooling effectiveness could be found near the leading edge pressure side
in the cases with fillets, especially for the longfillet case. As the blowing
ratio increasing, the advantage of fillets is not reflected near the leading
edge pressure side. In this region, at lower blowing ratios (M=0.4 and
0.8), the effectiveness for the fillets cases and the baseline case is
comparable. When the blowing ratio is M=0.8, the film cooling
effectiveness for fillets starts dropping due to the development of the
horseshoe vortex pressure side leg. When the blowing ratio is
lowing ratio
at hole exit near leading edge pressure side for baseline case is relatively
higher and the film cooling effectiveness keeps increasing at higher
blowing ratios.
Fig.23 also shows the film cooling effectiveness distributions near
leading edge suction side at M=0.8 (blue lines along suction side). Like
the pressure side study, the effects of leading edge geometry at the other
blowing ratios could be investigated by comparing the subplot (a) in
Fig.10-13 which indicates the trend at M=0.4, and the subplot (b) in Fig.
10-13 which indicates the trend at M=1.2. At low blowing ratio
condition (M=0.4), the length of the fillet has obvious effect on the
injection flow trace in this area. The coolant could reach the suction side
fil
increased
to M
(a) (b)
M=1.2,
the very low effectiveness along the pressure side shows that the
pressure side leg of horseshoe vortex has fully developed in the fillets
cases. Because the horseshoe vortex is delayed, the local b
for the long let case, while the cooled area becomes smaller when the
length of the fillet decreases. An apparent uncooled area could be found
for the baseline case where the horseshoe vortex suction side leg
ominates the main flow structure. When the blowing ratio isd
=0.8, the uncooled area could still be noticed near suction side,
which indicates that increasing the momentum of injection flow slightly
could not effectively eliminate the influence of horseshoe vortex in this
area. For the high blowing ratio cases, the traces of the injection flow
could reach the suction side for the baseline geometry, indicating that
with a lager injection flow momentum the domination effect of
horseshoe vortex could be limited. More general comparisons of all the
cases studied can be made by comparing the laterally averaged film
cooling effectiveness. As seen in Fig.27-29, the advantage of fillets is
obvious at every blowing ratio near the leading edge suction side,
though the difference among three fillet geometries is eliminated as the
blowing ratio increasing.
(c) (d)

8. 8
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
XG
/Cax
η
suc
i=0deg M=0.4 Longfillet
i=0deg M=0.4 Mediumfillet
i=0deg M=0.4 Shortfillet
i=0deg M=0.4 Nofillet
Figure27. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE
(EFFECT OF LEADING EDGE GEOMETRY, M=0.4).
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
X /C
η
suc
G ax
i=0deg M=0.8 Longfillet
i=0deg M=0.8 Mediumfillet
i=0deg M=0.8 Shortfillet
i=0deg M=0.8 Nofillet
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE
(EFFECT OF LEADING EDGE GEOMETRY, M=0.8).
Figure28. LATERALLY AVERAGED FILM COOLING
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
XG
/Cax
η
suc
i=0deg M=1.2 Longfillet
i=0deg M=1.2 Mediumfillet
i=0deg M=1.2 Shortfillet
i=0deg M=1.2 Nofillet
Figure29. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE
(EFFECT OF LEADING EDGE GEOMETRY, M=1.2).
Fig.30-32 compare the pitchwise-averaged film cooling
effectiveness along axial chord direction for different leading edge
geometries. The curves representing different cases are almost the same
at every blowing ratio, which indicates that the leading edge geometry
could not affect a large area in the passage, and their influence is limited
in a small region near leading edge suction side and pressure side.
Fig.23 compare the film cooling effectiveness distributions among four
e
ch indicates
the trend at M=0.4, and the subplot (b) in Fig. 10-13 which indicates the
trend at M=1.2. From the three groups of contours no obvious difference
could be found when the blowing ratio is fixed, which introduces a
possibility that the leading edge fillets might not have strong effect on
the whole endwall flow filed. This possibility could be proved through
latterly averaged film cooling effectiveness comparison, as shown in
Fig.30-32.
leading edg geometry cases at the fixed blowing ratio M=0.8. The
effects of leading edge geometry at the other blowing ratios could be
investigated by comparing the subplot (a) in Fig.10-13 whi
-0.4 -0.25 -0.1 0.05 0.2 0.35 0.5 0.65 0.8 0.95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
η
i=0deg M=0.4 Longfillet
i=0deg M=0.4 Mediumfillet
i=0deg M=0.4 Shortfillet
i=0deg M=0.4 Nofillet
XG
/Cax
Figure30. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS ON THE ENDWALL (EFFECT OF LEADING
DGE GEOMETRY, M=0.4).E
-0.4 -0.25 -0.1 0.05 0.2 0.35 0.5 0.65 0.8 0.95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
XG
/Cax
η
i=0deg M=0.8 Longfillet
i=0deg M=0.8 Mediumfillet
i=0deg M=0.8 Shortfillet
i=0deg M=0.8 Nofillet
Figure31. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS ON THE ENDWALL (EFFECT OF LEADING
EDGE GEOMETRY, M=0.8).
-0.4 -0.25 -0.1 0.05 0.2 0.35 0.5 0.65 0.8 0.95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
i=0deg M=1.2 Longfillet
i=0deg M=1.2 Mediumfillet
i=0deg M=1.2 Shortfillet
i=0deg M=1.2 Nofillet
XG
/Cax
η
Figure32. LATERALLY AVERAGED FILM COOLING
EFFECTIVENESS ON THE ENDWALL (EFFECT OF LEADING
ributions have been obtained on
the endwall of a high pressure turbine guide vane with and without
leading edge fillets. Three kinds of sharp slope fillets with different
axial length have been accessed with the baseline leading edge geometry.
The laterally averaged film cooling effectiveness is compared at three
regions including leading edge suction side, leading edge pressure side
and the main passage endwall surface. The results show that with
blowing ratio increasing the film cooling effectiveness increases in all of
these regions. For specific blowing ratio, the effects of leading edge
geometries could be illustrated as follows. The baseline geometry
provides the best film cooling performance near leading edge pressure
side. As for the leading edge suction side, the best leading edge
geometry depends on the blowing ratio. The longfillet is more effec
EDGE GEOMETRY, M=1.2).
CONCLUSIONS
The film cooling effectiveness dist
tive
in controlling horseshoe vortex at low blowing ratio, but for the high
blowing ratio shortfillet and mediumfillet are better.

9. 9
The work was partly supported by the National Natural Science
Foundation of China (Grant No. 50676043) and the Special Funds for
Major State Basic Research Projects (Grant No. 2007CB210108).
NOMENCLATURE
=actual chord length of scaled up blade profile
=axial chord length of the scaled up blade profile
=film hole diameter, mm
ACKNOWLEDGMENTS
C
axC
D
I =light intensity
=length of film hole, mm
=leading edge
L
LE
M = lowing ratio, ρcVc/ρ∞V∞b
Ma =Mach number
P =blade pitch
PS =pressure side
PSP =pressure sensitive paint
Rein =Reynolds number
S =span of the scaled up two-dimensional blade
SS =suction side
V =velocity, m/s
X , Z =Cartesian coordinate system
η =film cooling effectiveness
Subscripts
aw =adiabatic
c =Coolant fluid
G =global coordinate
mix =mixture condition
ref =Reference value
∞ =free stream condition
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