gt2011-45427

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: [email protected]

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 1600oC, 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]

http://www.iciba.com/increase/

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 DATA ANALYSIS

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 TC 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 CC P

η−−

= = （2）

Figure 1. CALIBRATION SYSTEM.

http://www.iciba.com/physical/

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 TT 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 TT 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.

http://www.iciba.com/vacuum/

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 ssiGiven 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= 0degZ 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


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


(a) (b)

(a) (b)

http://www.iciba.com/reflect/

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


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=0.4 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


Z G/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


-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 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

XG/Cax

η

longfillet i=0deg M=0.4longfillet i=0deg M=0.6longfillet i=0deg M=0.8longfillet i=0deg M=1longfillet i=0deg M=1.2

Figure14. LATERALLY ERAGED FILM COOLING AVEFFECTIVENESS AT DIFFERENT BLOWING RATIO.

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.320

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=0.4nofillet i=0deg M=0.6nofillet i=0deg M=0.8nofillet i=0deg M=1nofillet 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 0.320

0.05

0.45

0.1

0.15

0.2

0.25

0.3

0.35

0.4

ηpr

e

shortfillet i=0deg M=0.4shortfillet i=0deg M=0.6shortfillet i=0deg M=0.8shortfillet i=0deg M=1shortfillet 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 0.320

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

ηpr

e

mediumfillet i=0deg M=0.4mediumfillet i=0deg M=0.6mediumfillet i=0deg M=0.8mediumfillet i=0deg M=1mediumfillet 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 0.320

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

XG/Cax

η pre


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

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 0.320

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

XG/Cax

ηsu

c

nofillet i=0deg M=0.4nofillet i=0deg M=0.6nofillet i=0deg M=0.8nofillet i=0deg M=1nofillet 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 0.320

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

ηsu

c

shortfillet i=0deg M=0.4shortfillet i=0deg M=0.6shortfillet i=0deg M=0.8shortfillet i=0deg M=1shortfillet i=0deg M=1.2

XG/Cax 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 0.320

0.45

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

XG/Cax

ηsu

c

mediumfillet i=0deg M=0.4mediumfillet i=0deg M=0.6mediumfillet i=0deg M=0.8mediumfillet i=0deg M=1mediumfillet 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

ηsu

c


Figure22. LATERALLY AVERAGED FILM COOLING EFFECTIVENESS NEAR LEADING EDGE SUCTION SIDE AT DIFFERENT BLOWING RATIO (LONGFILLET).

nofillet M=0.8 i= 0deg

Z G/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


Z G/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


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


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 0.320

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

XG/Cax

ηpr

e

i=0deg M=0.4 Longfilleti=0deg M=0.4 Mediumfilleti=0deg M=0.4 Shortfilleti=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 0.320

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

XG/Cax

ηpr

e


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 0.320

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

XG/Cax

ηpr

e


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

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.320

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

XG/Cax

ηsu

c


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 0.320

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

X /C

ηsu

c

G ax


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 0.320

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

XG/Cax

ηsu

c


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 0.950

0.1

0.2

0.3

0.4

0.5

0.6

0.7

η


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 0.950

0.1

0.2

0.3

0.4

0.5

0.6

0.7

XG/Cax

η


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 0.950

0.1

0.2

0.3

0.4

0.5

0.6

0.7


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

tivein controlling horseshoe vortex at low blowing ratio, but for the high blowing ratio shortfillet and mediumfillet are better.

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 REF

Transfer,” Journal of Propulsion and 2.

[3] Fried he Design of n Im Journal of urb

[4] Wrig l, T.A., and Han, J.C., 2005. “Ass dy State PSP, TSP, and IR Measurement Tech Cooling”. In ASME 2005 Summer Heat E Paper No.HT2005–72363.

[5] han R.S., 2001. “Turbine Nozzle Endwall Film Cool nsitive Paint,” Journal of

[6] rig hihong, Yang, Huitao, and Han, J.C., 2008. “Film ctiveness Distribution on a Gas Turbine Blade

latf ed Slot Leakage and Discrete Film Hole lows , 130, pp. 071702/1-11.

[7] rig ., Rhee, Dong-Ho, and Han, J.C., 009 Wake with Vortex on Turbine Blade

Platf Purge Flow”. Journal of Turbomachinery

[8] Sury , Ozturk, B., Schobeiri, M.T., and Han, J.C., 2010. “Film-Cooling Effectiveness on a Rotating Turbine P f Paint Technique”. Journal of Tu b

and Han, J.C., ilm-Cooling Effectiveness on a Rotating Blade Platform”.

Journal of Turbomachinery, 131, pp.011014/1-12. [10] Praisner, T.J., Smith, C.R., 2006. “The Dynamics of the

Hors sociated Endwall Heat Transfer: Part I—

Temp Journal of Turbomachinery, 128, pp.74

[11 Prais ., 2006. “The Dynamics of the Hors ciated Endwall Heat Transfer: Part

Results”. Journal of Turbomachinery, 128,

r Removal”. IAA Paper

[13] , W.D., 1985. “Juncture Flow Control

[14] Boundary Layer Influence on

[15] On

Land, Sea, and Air, Vienna, ASME Paper

[21]

[22]

[25]

[26]

at the Endwall”. Journal of Turbomachinery, 123,

[27]

ERENCES [1] Bogard, D.G., Thole, K.A., 2006. “Gas Turbine Film Cooling”.

Journal of Propulsion and Power, 22, pp.249-270. 2] Simon, T.W., Piggush, J.D., 2006. “Turbine Endwall [

Aerodynamics and HeatPower, 22, pp.301-31

richs, S., Hodson, H.P., Dawes, W.N., 1999. “TaT

proved Endwall Film Cooling Configuration,” omachinery, 121, pp.772-780.

ht, L.M., Gao, Z., Varveessment of Steaniques for Flat Plate Film Transfer Conference, ASM

Z g, L., Jaiswal, ing Study Using Pressure-Se

, pp.730-738. TurbomachineryW

, 123ht, L.M., Gao, Z Cooling Effe

P orm With InclinFW

”. Journal of Turbomachineryht, L.M., Blake, Sarah A

2 . “Effect of Upstreamorm Film Cooling With Simulated Stator-Rotor

, 131, pp.021017/1-10. anarayanan, A.

latr

orm Using Pressure Sensitive omachinery, 132, pp.041001/1-13.

rayanan, A., Mhetras, S.P., Schobeiri, M.T., [9] Suryana2009. “F

eshoe Vortex and As

oral Behavior”. 7-754.

] ner, T.J., Smith, C.Reshoe Vortex and Asso

II—Time-Meanpp.755-762.

[12] Bloxham, M., Bons, J., and Hollis, R., 2008. “Horseshoe Vortex Control with Leading Edge Endwall Boundary LayeIn 4th Flow Control Conference, Seattle, ANo.AIAA-2008-4319. Kubendran, L.R., HarveyUsing Leading-Edge Fillets”. In 3rd Applied Aerodynamics Conference, Colorado Springs, AIAA Paper No.AIAA-85-4097. Sabatino, D.R., Smith, C.R., 2009. “the Unsteady Horseshoe Vortex Flow and Surface Heat Transfer”. Journal of Turbomachinery, 131, pp.011015/1-8. Satoshi Hada, Kenichiro Takeishi, Yutaka Oda, Seijiro Mori, and Yoshihiro Nuta, 2008. “The Effect of Leading Edge DiameterThe Horse Shoe Vortex And Endwall Heat Transfer”. In ASME Turbo Expo 2008: Power for Land, Sea, and Air, Berlin, ASME Paper No.GT2008-50892.

[16] Aunapu, N.V., Volino, R.J., Flack, K.A., and Stoddard, R.M., 2000. “Secondary Flow Measurements in a Turbine Passage With Endwall Flow Modification”. Journal of Turbomachinery, 122, pp.651-658.

[17] T.I-P.Shih, Y.-L.Lin, 2003. “Controlling Secondary-Flow Structure by Leading-Edge Airfoil Fillet and Inlet Swirl to Reduce Aerodynamic Loss and Surface Heat Transfer”. Journal of Turbomachinery, 125, pp.48-56.

[18] Mahmood, G.I., Gustafson, R., Acharya, S., 2005. “Experimental Investigation of Flow Structure and Nusselt Number in a Low-Speed Linear Blade Passage With and Without Leading-Edge Fillets”. Journal of Heat Transfer, 127, pp.499-512.

[19] Zess, G.A., Thole, K.A., 2002. “Computational Design and Experimental Evaluation of Using a Leading Edge Fillet on a Gas Turbine Vane”. Journal of Turbomachinery, 124, pp.167-175.

[20] Becz, S., Majewski, M.S., and Langston, L.S., 2004. “An Experimental Investigation of Contoured Leading Edges for Secondary Flow Loss Reduction”. In ASME Turbo Expo 2004: Power for No.GT2004-53964. Lethander, A.T., Thole, K.A., Zess, G. and Wagner, J., 2003. “Optimizing the Vane-Endwall Junction to Reduce Adiabatic Wall Temperatures in a Turbine Vane Passage”. In ASME Turbo Expo 2003: Power for Land, Sea, and Air, Atlanta, ASME Paper No.GT2003-38939. Lethander, A.T., Thole, K.A., Zess, G. and Wagner, J., 2004. “Vane-Endwall Junction Optimization to Reduce Turbine Vane Passage Adiabatic Wall Temperatures”. Journal of Propulsion and Power, 20, pp.1096-1104. Han, S., Goldstein, R.J., 2009. “The Heat/Mass Transfer Analog[23] y for a Simulated Turbine Endwall with Fillets”. Journal of Heat Transfer, 131, pp.012001/1-14. Han, S., Goldstein, R.J., 2006. “Influence of Blad[24] e Leading Edge Geometry on Turbine Endwall Heat (Mass) Transfer”. Journal of Turbomachinery, 128, pp.798-813. Mahmood, G.I., Acharya, S., 2007. “Experimental Investigation of Secondary Flow Structure in a Blade Passage with and without Leading Edge Fillets”. Journal of Fluids Engineering, 129, pp.253-262. Sauer, H., Müller, R., and Vogeler, K., 2001. “Reduction of Secondary Flow Losses in Turbine Cascades by Leading Edge Modificationspp.207-213. Pieringer, P., Sanz, W., 2004. “Influence of the Fillet Between Blade and Casing on the Aerodynamic Performance of a Transonic Turbine Vane”. In ASME Turbo Expo 2004: Power for Land, Sea, and Air, Vienna, ASME Paper No.GT2004-53119.