Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations

International Journal of Heat and Mass Transfer xxx (xxxx) xxx

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Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations Pingting Chen, Lang Wang, Xueying Li ⇑, Jing Ren, Hongde Jiang Department of Energy and Power Engineering, Tsinghua University, Beijing, China

a r t i c l e

i n f o

Article history: Received 8 September 2019 Received in revised form 24 October 2019 Accepted 4 November 2019 Available online xxxx Keywords: Gas turbine Non-axisymmetric contoured endwall Film cooling Adiabatic film cooling effectiveness

a b s t r a c t Non-axisymmetric endwall contouring in axial turbines are becoming popular to improve the passage aerodynamic performance or the endwall heat transfer characteristics. Meanwhile, endwall contouring changes the film cooling performance on the endwall surface by modifying the secondary flow fields and the endwall surface shapes, thus impacting the turbine efficiency and durability. Better understandings of the non-axisymmetric contoured endwall film cooling performances are in great need. In this study, adiabatic film cooling effectiveness (g) of discrete film cooling hole injections at different axial locations on an non-axisymmetric contoured endwall and a baseline endwall with different density ratios and matched averaged blowing ratios to the engine conditions are studied experimentally using Pressure Sensitivity Paint (PSP) technique. Computational fluid dynamics (CFD) simulations are also carried out to look into the local flow fields. The results show that the differences in endwall g distributions between the contoured endwall and the baseline endwall are dominated by the streamwise pressure gradients, i.e. at locations with smaller streamwise pressure gradient values on the contoured endwall than those on the flat endwall, the local g values on the contoured endwall are smaller than those on the flat endwall, and vice versa. Ó 2019 Published by Elsevier Ltd.

1. Introduction The environmental pollutions and global warming problems raise the need of clean and efficient energy sources. Gas turbine engines are relatively clean and efficient, making them to be one of the most important energy and power equipments. Thus, it is important to improve the efficiency and durability of gas turbines [1–4]. To achieve progressive higher gas turbine efficiency values, the averaged turbine inlet temperature (TIT) is raised higher with each successive engine generation [5], increasing the cooling demand of the Nozzle Guide Vane (NGV) endwall. Meanwhile, the turbine loading is continually increasing, making secondary losses in the turbine passages higher [6], which would have a bad impact on the gas turbine efficiency. Non-axisymmetric endwall contouring is becoming widely accepted as it is a way to reduce the passage secondary losses thus to increase the gas turbine efficiency [7]. However, endwall contouring can change the endwall film cooling performance on the endwall surface by modifying the secondary flow fields and the endwall surface shape [8], thus impacting the turbine efficiency and durability.

⇑ Corresponding author. E-mail address: [email protected] (X. Li).

In the conventional shaped endwall passages, i.e. the flat endwall passages in the linear cascades and the annular endwall passages in the annular cascades, Takeishi et al. [9] measured the adiabatic film cooling effectiveness (g) distributions on an endwall with three groups of discrete film cooling holes located in the fore part, the mid part and the throat of the passage on an annular endwall. They found that the coolant moves from the airfoil pressure side to the airfoil suction side by the sweeping of the passage secondary flows and covers the regions near the airfoil suction side rather than the regions near the airfoil pressure side. Friedrich [10] also found that too much coolant accumulated near the airfoil suction side but few coolant covers the region near the airfoil pressure side due to the cross flow near the endwall. He divided the endwall into several zones according to the secondary flow patterns and improved film cooling performance by rearranging the layout of the film cooling holes according to the features of each zone. Barigozzi et al. [11] located rows of shaped holes on the endwall at several axial locations and measured the g distributions on the endwall. The results show that with large coolant mass flowrates, the secondary flow are reduced, thus reducing the cross flow from the airfoil pressure side to the airfoil suction side and making the g values evenly distributed across the passage. Ornano and Povey [12] calculated the engine momentum flux ratios of discrete film cooling holes on the endwall with engine conditions and

https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995 0017-9310/Ó 2019 Published by Elsevier Ltd.

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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Nomenclature B.R. Cax Cd CFD (CO2)1 (CO2)mix (CO2)c Cp D D.R. L P Ps,m Psp PSP

blowing ratios axial chord length film cooling hole discharge coefficient computational fluid dynamics oxygen concentration of the approaching flow oxygen concentration of the mixed gas oxygen concentration of the coolant static pressure coefficient hole diameter [m] density ratios hole length film cooling hole pitch mainstream static pressure pressure at the vane stagnation point Pressure Sensitivity Paint

found the range of the momentum flux ratio to be 2–18, which is much larger than the momentum flux ratios studied in the previous investigations [12]. g distributions with several coolant momentum flux ratios were measured and the results indicates that with the increasing of the momentum flux ratio, the secondary flows are reduced and even disappeared with large momentum flux ratio values [12]. Wang el al. [13] compared two endwall film designs: the mid-chord row configuration and the downstream row configuration and found that coolant with higher MFR ratio features higher cooling effectiveness for the mid-chord row cases but may not provide the desired film cooling results for the downstream row cases. Li el al. [14] investigated film cooling performance at different axial locations on the endwall with matched blowing ratios to engine conditions. They found that due to the effect of the passage vortexes and the cross flow, there are low coolant coverages near the airfoil leading edge and the airfoil pressure side. However, film injections located in high static pressure zones with large local blowing ratios have the potential to reduce the intensity of endwall crossflow and cover these regions. A lot of efforts have been made by researchers to design nonaxisymmetric contoured endwall with reduced passage aerodynamic loss [7,15–21] or endwall heat flux [22–25]. In which Praisner et al. [19–21] combined a gradient-based optimization algorithm with computational fluid dynamics (CFD) codes to systematically vary a free-form parameterization of the endwall and found 10% total pressure loss reduction in Pack B passage by endwall contouring. Winkler [24,25] combined ice formation method with CFD methods to design endwall contouring with improved endwall heat transfer characteristics. All the contoured endwalls designed in his research achieved their heat transfer reductions at the expense of an increased total pressure loss comparing with the flat endwall case [24,25]. Most recently, Chen et al. [26,27] carried out a multi-objective optimization process to find nonaxisymmetric contoured endwall designs with both improved passage aerodynamic performance and reduced endwall total heat flux and found several improved contoured endwall designs. By endwall non-axisymmetric contouring, the film cooling performance on the endwall surface would be modified. Okita et al. [28] simulated a contoured-endwall passage and a flat endwall with full coverage film cooling configuration using CFD methods and found that with endwall contouring, the cross flow in the passage is reduced, causing the g distributions more uniform pitchwise and the pitchwise averaged g values larger than those on the flat endwall. Rezasoltani et al. [29] compared the film cooling performance of rim seal leakage on blade endwalls with a contoured endwall design and the baseline endwall design. The contoured endwall achieved larger g values than the baseline

Pt,c Pt,1 S Taw Tc Tr Tt,1 Tt,c U0 x

a

b h

g

total pressure of the coolant total pressure of the mainstream Vane height adiabatic endwall temperature coolant temperature recovery temperature of the approaching flow on the endwall total temperature of the approaching flow total temperature of the coolant velocity of the approaching flow axial coordinate film hole inclined angle film hole compound angle angle relative to the center of disk adiabatic film cooling effectiveness

endwall. However, Lynch et al. [8] measured the g distributions of a row of discrete film cooling holes located next to the airfoil pressure side on a contoured endwall and a flat endwall. The results show that due to the reduction of the cross flow by endwall contouring, the coolant migration from the airfoil pressure side to the airfoil suction side is suppressed and the pitchwise coverage area of the coolant is decreased. The conclusions by Lynch et al. [8] are discrepant from those by Okita et al. [28] or Rezasoltani et al. [29]. A main reason for this discrepancy is that the film cooling configurations are located at different locations on the endwall. Therefore, to further understand the effect of axial turbine non-axisymmetric endwall contouring on endwall film cooling, better documentation of the film cooling performance on the contoured endwall and the baseline endwall with film cooling holes at different locations is in great demand. The current study measures the g distributions of discrete film cooling hole injections at three axial locations on a nonaxisymmetric contoured endwall and a baseline endwall with different density ratios and matched averaged blowing ratios to the engine conditions using Pressure Sensitivity Paint (PSP) technique. The three axial locations are a location upstream of the passage (Row1, located at x/Cax =
0.3), a location in the fore part of the passage (Row2, located at x/Cax = 0.3) and a location in the aft part of the passage (Row3, located at x/Cax = 0.7). CFD simulations against the experimental cases are also carried out to look into the local flow field. The endwall film cooling features in the contoured endwall passage and the baseline endwall passage are analyzed and the effect of non-axisymmetric endwall contouring on film cooling at different locations are documented. The experimental methodology including the experimental facility, the test conditions and the measurement techniques are presented in Section 2. The numerical methodology are described in Section 3. The aerodynamic aspects of the contoured endwall passage and the baseline endwall passage are discussed in Section 4. In Section 5, the film cooling effectiveness on the contoured endwall and the baseline endwall are presented for (I) film cooling holes upstream of the passage, (II) film cooling holes in the fore part of the passage and (III) film cooling holes in the aft part of the passage. In Section 6, we present the conclusions.

2. Experimental methodology 2.1. Experimental facility The subsonic, open-loop type wind tunnel, shown in Fig. 1, consisted of a 15 kW blower with a frequency converter, a honeycomb,

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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a contraction nozzle, a turbulence grid, the test section and an outflow cavity. The frequency converter was able to maintain the inlet flow velocity to be 24.5 m/s. The geometry of the turbulence grid was determined according to Roach et al. [30] and placed at 1.5Cax upstream of the airfoil leading edge. By the turbulence grid, the turbulence intensity at x/Cax = 0 is 4.29% measured using a DANTEC model 55P11 hot wire. The outflow cavity was designed to manipulate the pressure fluctuation at the cascade exit. The test section was an annular sector cascade with six vanes and five passages based on a gas turbine first stage vane airfoil as shown in Fig. 2. Pressure taps were placed at the mid-span of the two adjacent vanes of the middle passage to qualify the periodicity of the passage. The measurement for endwall static pressure distributions and g distributions were carried out on the hub of the middle passage. The shroud of the cascade was made transparent to meet the requirement of the PSP measurement. The hub of the cascade consisted of three parts, the upper part (beige colored in Fig. 2), the middle passage part (white colored) and the lower part (beige colored). These three parts were replaceable in the experiment. When measuring in the contoured endwall passage, the upper and lower part were equipped by the solid contoured endwalls without film cooling configurations. The middle passage part was established by the contoured endwall with pressure taps to measure local static pressure distributions while it was equipped by the contoured endwalls with film cooling configurations to measure the g distributions. If the baseline endwall passage was measured, all the three parts of the hub were equipped by the annular endwall parts. The four vanes inside of the cascade and the middle passage hubs were made of Acrylic with low thermal conductivity by 3D printing. The shroud was made of polymethyl methacrylate by computerized numerical control (CNC) machine. The geometric and flow conditions of the cascade are listed in Table 1. 2.2. Test conditions 2.2.1. Endwall contouring configuration The non-axisymmetric endwall contouring configuration used in the current study was selected from the Pareto front of an aero-thermal objective optimization process done by Chen et al. [26]. A technique for order preference by similarity to an ideal solution (TOPSIS) [31] was employed to order all the cases in the Pareto front and to find the best design to be used for the corrent experiment. Fig. 3 shows the relative radial height distribution of the best design of the contoured endwall found by TOPSIS techinique. There is a big ‘‘valley” in the fore and mid part of the passage from the airfoil pressure side to the airfoil suction side across the passage and a small ‘‘hill” in the aft part of the passage near the airfoil suction side. The three dashed arrows in Fig. 3 are the three locations of the film cooling holes which will be described later.

Fig. 1. Wind tunnel overview.

Fig. 2. The schematic of the test section.

Table 1 Parameters of the Cascade. Parameter

Values

Cax[m] Hub radius[m] Angular pitch[°] S/Cax[–] Inlet flow angle[°] Exit flow angle [°] Inlet velocity[m/s] Inlet Re[–] Inlet Ma[–] Inlet turbulence intensity

0.078 0.614 9 0.88 0 73 24.5 1.9e5 0.069 4.29%

2.2.2. Film cooling arrangement Film cooling holes were located at three axial locations both on the contoured endwall and the baseline endwall. The three axial locations are a location upstream of the passage (Row1, located at x/Cax =
0.3), a location in the fore part of the passage (Row2, located at x/Cax = 0.3) and a location in the aft part of the passage (Row3, located at x/Cax = 0.7) as depicted in Fig. 3 and Fig. 4. The detailed parameters of the film cooling holes in each row are listed in Table 2. The diameter of each film cooling hole is 0.001 m, the thickness of the endwall is 0.003 mm and the inclined angle a is 30° resulting in the length to diameter ratio L/D = 6 for the baseline case while L/D ranging from 4 to 8 in the contoured endwall case. According to the research of the hole L/D effects on film cooling performance by Li et al. [32], adiabatic film cooling effectiveness is not sensitive to L/D with L/D larger than 2. Therefore, the effect of L/D are ignored in the current study. The pitch to diameter ratio P/D is 3. The compound angle b of the hole with the axial direction is 0 for Row1 and Row2, but 45° for Row3 as can be found in Table 2.

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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or baseline endwalls to ensure that there was only one coolant plenum in one test piece, therefore, the interactions between the coolant near the endwall surface and the fluid in the downstream film cooling plenum, which would make the measurement of the g distributions inaccurate, were eliminated. Each of the six test pieces was assembled to the middle passage hub for g measurement of each row of film cooling holes in the contoured endwall cascade or in the baseline endwall cascade. 2.2.3. Blowing ratios matched to engine condition The isentropic flow equation of ideal gas was employed to evaluate the engine condition blowing ratios of each film cooling hole with a certain range of pressure margin. The equation is:

B:R:local

¼ ðq ¼

qc U c

1 U 1 Þlocal

C d P t;c ðP s;m =P t;c Þðkþ1Þ=2k 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2k ððk
1ÞRT

ÞðPt;c =Ps;m Þðk
1Þ=k
1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P t;1 ðP s;m =Pt;1 Þðkþ1Þ=2k 

2k ððk
1ÞRT

t;c

t;1

ÞðP t;1 =P s;m Þðk
1Þ=k
1

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ C d ðPt;c =P t;1 Þðk
1Þ=2k T t;1 =T t;c rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðP =P Þðk
1Þ=k
1  ðPt;c =Pt;1 Þðk
1Þ=k þ ðP t;c=P t;1Þ
ðk
1Þ=k
1 s;m

Fig. 3. Relative radial height distribution of the contoured endwall.

ð1Þ

t;1

in which Pt,c/Pt,1 is the pressure margin with Pt,c as the total pressure at the coolant inlet and Pt,1 as the total pressure of the approaching flow. Ps,m is the local static pressure on the endwall which is obtained by a CFD simulation with typical F-class gas turbine engine conditions. Cd is the film cooling hole discharge coefficient. Tt,1 and Tt,c is the inlet total temperature of the approaching flow and the coolant temperature with the typical F-class engine condition. By Eq. (1), the local blowing ratios of film cooling holes at any location on the endwall surface can be derived with different pressure margin values. The range of the pressure margin used in the current study is 0.99 to 1.1 as the typical design value is 1.02 [33]. Fig. 5(a)–(c) plots the engine range blowing ratio distributions at each discrete film cooling hole for Row1, Row2 and Row3 on the baseline endwall with different pressure margin values. The

Table 3 Test pieces. Baseline Endwall

Contoured Endwall

Row1

Row2

Fig. 4. Schematic of the film cooling hole arrangement.

Table 2 Parameters of the film cooling holes. Parameter

Row1

Row2

Row3

Hole Number x/Cax[–] D[m] a[°] b[°]

38
0.3 0.001 30 0

17 0.3 0.001 30 0

15 0.7 0.001 30 45

Row3

Six test pieces for g measurement were manufactured in the current study as listed in Table 3. The test pieces were made respectively for each row of the film cooling holes on the contoured Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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5

Fig. 5. Engine range of blowing ratios for each discrete film cooling hole at typical engine conditions (a) blowing ratios for Row1 (b) blowing ratios for Row2 (c) blowing ratios for Row3 (d) averaged blowing ratio for Row1, Row2 and Row3.

holes in Fig. 5 is numbered from the locations near the airfoil suction side to the locations near the airfoil pressure side as also denoted in Fig. 4. For the film cooling holes upstream of the passage, i.e. the holes in Row1, the local blowing ratio values first increase, then decrease from the airfoil suction side to the airfoil pressure side when the pressure margin value is smaller than 1. However, the local blowing ratio values first decrease then increase with the pressure margin value larger than 1. Two factors determine the local blowing ratio values: the mass flux through the film cooling hole and the local mainstream velocity according to Eq. (1). With small pressure margin values, the local blowing ratio values are dominated by the mass flux through the film cooling holes. The locations with larger local Ps,m feature smaller coolant mass flow rate, thus achieving smaller local blowing ratios. On the contrary, the local blowing ratio values are dominated by the local mainstream velocity when the pressure margin is larger than 1. Therefore, the locations with larger local Ps,m get smaller local mainstream velocities, thus featuring larger local blowing ratios. This phenomenon also applies to Row2 and Row3.

Table 4 Test conditions in experiment.

Row1 Row2 Row3

D.R.

B.R.

1.0, 1.5 1.0, 1.5 1.0, 1.5

0.45, 2.89 0.93, 1.46, 1.88 1.06, 1.19, 1.32

Fig. 5(d) plots the averaged engine range blowing ratios for Row1, Row2 and Row3 with pressure margin ranging from 0.99 to 1.1. It can also be found that with the same pressure margin range, the local blowing ratio ranges are smaller when the film cooling holes located more downstream. The averaged blowing ratios in the current experiment were chosen to match with the engine conditions (shown in Fig. 5(d)) as listed in Table 4. Two density ratios (D.R.), 1.0 and 1.5, are used to study the influence of D.R. on film cooling performance. The blowing ratios (B.R.) in the contoured endwall passage and the baseline endwall passage are matched to be equal to each other in the current experiment. 2.3. Measurement techniques 2.3.1. Static pressure measurement Pressure taps were located in the mid-span of the two adjacent vanes of the middle passage and on the middle passage hub as shown in Fig. 6 to measure the local static pressure values. The pressure taps were connected with pressure transducers using silicone tubes. The pressure signals were transferred to voltage with the Honeywell HSCDRRN001PDAA pressure transducers and recorded by the computer, making the uncertainty of pressure measurement to be ±1%. 2.3.2. Adiabatic film cooling effectiveness measurement PSP technique was employed to measure the g distributions on the endwall. This technique has been widely used in the measurement of film cooling coverage over the years [34,35] which is based

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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1

0.8

Iref/I

0.6

0.4 15.5°C

0.2

29.7°C 43.2°C

0 0

0.2

0.4

0.6

0.8

1

P/Pref Fig. 7. Calibration curves for the Pressure Sensitivity Paint.

ratios to pressure ratios found by the calibration procedure is shown in Fig. 7. By recording the longer wave light intensity with/without coolant blowing, the adiabatic film cooling effectiveness can be found. In the current study, Uni-FIB PSP (UF470-750) from Innovative Scientific Solutions Incorporated (ISSI) was used. The uncertainty of the PSP measurement on film cooing effectiveness is evaluated based on the uncertainty analysis method [36] with a confidence level of 95%. With N2 as the coolant gas, the uncertainty for g is less than 5% for g larger than 0.3 and 9% for g about 0.1. While when CO2 is used, the uncertainty for g is less than 6% for g larger than 0.3 and 11.5% for g about 0.1.

Fig. 6. Static pressure taps in the passage (a) pressure taps on the mid-span of the two adjacent vanes (b) the pressure taps on the endwall surface.

on the heat/mass transfer analogy theory to find the adiabatic film cooling effectiveness:

g¼

T r
T aw ðC O2 Þ1
ðC O2 Þmix )g¼ Tr
Tc ðC O2 Þ1
ðC O2 Þc

ð2Þ

in which, Taw is the adiabatic endwall temperature, Tc is the coolant temperature and Tr is the recovery temperature of the approaching flow on the endwall. (CO2)1 is the oxygen concentration of the approaching flow, (CO2)mix is the oxygen concentration of the mixed gas near the endwall and (CO2)c is the oxygen concentration of the coolant. In the current study, the approaching flow is air while the coolant gas is N2 or CO2 to simulate the density ratios 1.0 or 1.5. Thus, (CO2)1 is around 21%, (CO2)c is 0% and (CO2)mix is between 0% and 21%. The local oxygen concentrations can be found by the PSP technique. The PSP is composed of an oxygen-sensitive fluorescent molecule embedded in an oxygen permeable binder. The fluorescent molecule can be excited by the 480 nm wavelength LED and then emits a photon of a longer wavelength (around 600 nm). When oxygen interacts with the molecule, there would be no longer wavelength emission. Thus, the intensity of the longer wavelength light is dependent on the partial pressure of oxygen at the PSP surface, i.e. the partial pressure of oxygen on the PSP surface can be found if the longer wavelength light intensity is known. To determine the relationship between the light intensity versus oxygen partial pressure, a sample of the PSP is placed in a calibration chamber. The sample is exposed to a series of pressures and temperatures and the luminescent intensities of the sample ware recorded. The calibration curves converting the light intensity

3. Numerical methodology CFD simulations were carried out against the experimental cases listed in Table 4 to look into the local flow field and to help understanding the physics behind the experimental results. Fig. 8 shows the computational domain for the contoured endwall with film cooling configuration of Row1. The mainstream cascade, the coolant plenum and the outflow cavity were included in the computational domain. The mainstream inlet was 2.5Cax upstream of the airfoil leading edge with averaged velocity and set there. Varied mass flowrates were set at the coolant inlet and averaged static pressure was given at the outlet. All the other walls were non-slip, adiabatic walls.

Fig. 8. Schematic of the computational domains.

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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Fig. 9. Static pressure coefficient (Cp) distribution in the mid-span of the two adjacent vanes of the middle passage, C represents the contoured endwall passage and B means the baseline endwall passage, EXP means the data is acquired by experiment and CFD means the data is got by CFD simulation.

Tetrahedral grids with prismatic layers on the walls were generated for the computational domains to ensure the y+＜1. The CFD problem was solved by three-dimensional finitevolume method using the numerical solver ANSYS CFX [37]. High-resolution advection and a high-resolution transient scheme using the second-order backward Euler scheme were employed. The SST c-h transition turbulence model was used in the current study. Fig. 9 shows the static pressure coefficient (Cp) distributions in the mid-span of the two adjacent vanes for the middle passage in the contoured endwall cascade and the baseline endwall cascade by experiment and CFD. Vane1 is the upper vane and Vane2 is the lower one. Cp is defined as:

Cp ¼

Ps
Psp 1 2

qU 0 2

ð3Þ

In which Ps is the local static pressure, Psp is the pressure at the vane stagnation point, q is the density of the mainstream and U0 is the velocity of the approaching flow. The Cp distributions for Vane1 and Vand2 matched both in the contoured endwall cascade and in the baseline endwall cascade, which qualifies the cascades’ periodicity. In addition, the pressure simulated by the CFD methods agrees well with the measured data, confirming that the CFD methods models the mid-span pressure distributions well. Fig. 10 plots

Fig. 10. Static pressure coefficient (Cp) distributions on the endwalls along different axial locations, C represents the contoured endwall passage and B means the baseline passage, EXP means the data is acquired by experiment and CFD means the data is got by CFD simulation.

7

Fig. 11. Static pressure coefficient (Cp) distribution on the endwall (Measured) (a) contoured endwall (b) baseline endwall.

the static pressure distributions along different axial locations from the airfoil pressure side to the airfoil suction side. The CFD data matched the experimental data well, indicating that the CFD methods models the pressure distributions near the endwall well.

4. Aerodynamic aspects of the contoured endwall passage and the baseline endwall passage Fig. 11 shows the Cp distributions on the contoured endwall and the flat endwall measured by the pressure taps on the endwall as shown in Fig. 6(b). The contoured endwall features larger Cp values in the fore part across the passage and the mid part of the passage near the airfoil pressure side than those in the baseline endwall passage, while there are smaller Cp values in the aft part of the passage near the airfoil suction side for the contoured endwall than that for the flat endwall. As shown in Fig. 10, the contoured endwall features smaller pitchwise pressure gradient in the fore part of the passage than the baseline endwall, e.g. x/Cax = 0.35, while it achieves larger pitchwise pressure gradient in the aft part of the endwall, e.g. x/ Cax = 0.75. Fig. 12 plots the Cp distributions along the inviscid streamline paths on the contoured endwall and the baseline endwall. To obtain the inviscid streamline paths, an inviscid FLUENT [38] prediction of the inviscid streamlines on the baseline endwall was done. Streamlines were released at 2.5Cax upstream of the cas-

Fig. 12. Static pressure coefficient (Cp) distribution along inviscid streamline paths (CFD predicted), C represents the contoured endwall passage and B means the baseline passage.

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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cade from three pitchwise locations, h/hpitch = 0.25, 0.50 and 0.75. These streamlines are denoted as 0.25P, 0.50P and 0.75P in this study and plotted as red, green and blue in Fig. 12. The contoured endwall features flatter pressure distributions in the fore part of the passage while they got much larger streamwise pressure gradient in the mid and aft part of the passage than the baseline case, which impacts the acceleration features of the flow near the endwall much. In the tail part of the passage, e.g. x/Cax = 0.9 for 0.75P, the contoured endwall passage features larger adverse pressure gradients than the baseline endwall passage.

5. Film cooling effectiveness on the contoured endwall and the baseline endwall The g distributions on the contoured endwall and the baseline endwall for the film cooling holes upstream of the passage (Row1, located at x/Cax =
0.3), in the fore part of the passage (Row2, located at x/Cax = 0.3) and in the aft part of the passage (Row3, located at x/Cax = 0.7) with different density ratios and matched averaged blowing ratios to the engine conditions are documented to understand the endwall film cooling features and the effect of non-axisymmetric endwall contouring on film cooling at different locations on the endwall. 5.1. Film cooling injections upstream of the passage (Row1) Fig. 13 shows the g distributions of Row1 with the B.R. equal to 0.45 and 2.89, and the D.R. equals to 1.0 and 1.5.

With B.R. = 0.45, the coolant covers the vicinity of the film cooling holes, and migrates pitchwise from the airfoil pressure side to the airfoil suction side under the effect of passage secondary flow, covering the region upstream of the lift-off line of the pressure side horseshoe vortex, i.e. covering the region near the airfoil suction side while making the regions near the airfoil pressure side and around the airfoil leading edge to be zero-coverage regions. With larger D.R., the g values are larger in the vicinity of the film hole exit, which is due to the smaller coolant momentum flux for the cases with D.R. = 1.5 than those with D.R. = 1.0, making the coolant more attached to the wall in the vicinity of the film cooling holes. The g distributions on the contoured endwall and the baseline endwall are similar but with visible differences with B.R. = 0.45: i. In the zones framed with the dashed lines which is downstream of the hole exits, the contoured endwall featured smaller g values there than the baseline endwall. According to Fig. 12, the contoured endwall features smaller local streamwise pressure gradients than the baseline endwall, which makes the coolant less attached to the contoured endwall surface than that to the baseline endwall surface. ii. In the zones framed with the dot dash lines, which is the zone around the airfoil leading edge near the airfoil suction side, the coolant coverage is better on the contoured endwall than that on the baseline endwall. Fig. 14 shows the limiting streamlines and the Cp distributions on the solid endwalls without film hole configurations. With weaker streamwise acceleration upstream of and in the fore part of the contoured endwall passage than those of the baseline endwall

Fig. 13. Adiabatic film cooling effectiveness distribution on the contoured endwall and the baseline endwall for Row1 (a) B.R. = 0.45, (b) B.R. = 2.89.

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vortices. The vortex leg near the hub directs the coolant onto the hub, resulting in a region with concentrated coolant around the airfoil leading edge. Some differences can be found in the g distributions between the contoured endwall and the baseline endwall with B.R. = 2.89. In the zones at the fore part of the passage, (e.g. the regions framed with the dashed lines in Fig. 13(b)), the contoured endwall achieved smaller g values than the baseline endwall due to weaker local streamwise acceleration thus less coolant attachment there. However, in the tail part of the passage as framed with the dot dashed lines in Fig. 13(b), the contoured endwall passage features larger streamwise acceleration than the baseline endwall passage, making more coolant to reach the tail part of the passage near the airfoil pressure side, thus achieving better cooling performance there.

Fig. 14. Limiting streamlines and Cp distributions on the solid baseline endwall and contoured endwall without film hole configurations (CFD predicted).

passage, the streamlines turn in larger angles in the fore part of the contoured endwall passage and reaches the airfoil suction side at a more upstream location as denoted in Fig. 14, which makes the coolant in the contoured endwall passage to reach the airfoil suction side at more upstream locations than that in the baseline endwall passage, making the coolant coverage around the airfoil leading edge near the airfoil suction side better on the contoured endwall than that on the baseline endwall. With larger blowing ratios, the coolant can penetrate the lift-off lines of the horseshoe vortexes and reduces the cross flow effects from the airfoil pressure side to the airfoil suction side, thus covering the regions near the airfoil pressure side and around the airfoil leading edge. As shown in Fig. 13(b) with B.R. = 2.89, the coolant covers the whole contoured endwall and the whole baseline endwall from the airfoil pressure side to the airfoil suction side except the zero-coverage region right downstream of the film cooling holes which is due to the blowing off of the injections. The regions around the airfoil leading edge achieve better cooling performance than the region in the mid-pitch of the passage at the same x/Cax location in the fore part of the passage. As depicted in Fig. 15, the coolant lifts off due to its large momentum flux and impinges onto the airfoil leading edge, forming a pair of counter-rotating

Fig. 15. Schematic of the coolant flow patterns upstream of the airfoil leading edge with large blowing ratio values.

5.2. Film cooling injections in the fore part of the passage (Row2) The film cooling performance of Row2 located at x/Cax = 0.3 with the averaged B.R. equal to 0.93, 1.46 and 1.88, and the D.R. equals to 1.0 and 1.5 are measured and compared between the contoured endwall and the baseline endwall. Fig. 16 plots the local blowing ratios for each hole of Row2 with the three averaged B.R. values under the experimental conditions. With smaller averaged B.R., e.g. B.R. = 0.93, the local B.R. differences between the contoured endwall passage and the baseline passage are small and the pitchwise B.R. distributions are relatively uniform. While with larger averaged B.R., e.g. B.R. = 1.46 and 1.88, the local B.R. values near the airfoil suction side are much smaller than those near the airfoil pressure side. In addition, the local B.R. values on the contoured endwall are larger near the airfoil suction side while smaller near the airfoil pressure side than those on the baseline endwall. Fig. 17(a) shows the g distributions on the contoured endwall and the baseline endwall with averaged B.R. = 0.93, and D.R. = 1.0 and 1.5. With such a small B.R. value, there is no obvious blowing off features in the vicinity of the hole exits, resulting in the large g values near the hole exits. However, with such small coolant momentum flux, the coolant is redirected pitchwise from the airfoil pressure side to the airfoil suction side by the pitchwise pressure gradients, resulting in an uncovered zone near the airfoil pressure side downstream. There are small zero-coverage zones in the vicinity of the film cooling holes near the airfoil suction side

Fig. 16. Local blowing ratios of film holes for Row2 (D.R. = 1.0, C represents the contoured endwall and B means the baseline endwall).

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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Fig. 17. Adiabatic film cooling effectiveness distribution on the contoured endwall and the baseline endwall for Row2 (a) B.R. = 0.93 (b) B.R. = 1.42 (c) B.R. = 1.88.

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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as denoted in Fig. 17(a) which is due to the compound angles between the coolant injections and the local mainstream flow. With larger D.R., i.e. D.R. = 1.5, the g in the vicinity of the hole exit is larger than those with D.R. = 1.0, while the coolant coverage area in the aft part of the passage (see the zones framed by the dot dash line in Fig. 17(a)) is smaller with D.R. = 1.5 than those with D.R. = 1.0. The coolant momentum flux is smaller for the D.R. = 1.5 cases than those for the D.R. = 1.0 cases, making more coolant distributes in the vicinity of the hole exit and cool there but redirects easily with the cross flow and making the lateral coverage area in the mid and aft part of the passage smaller. This phenomenon is similar with that for Row1. There are a few differences in the g distributions between the contoured endwall and the baseline endwall with B.R. = 0.93: i. In the region right downstream of the hole exits as denoted by the dashed line frames in Fig. 17(a), the g values on the contoured endwall are smaller than those on the baseline endwall, especially for the locations from the mid-pitch to the locations near the airfoil suction side. The contoured endwall features smaller local streamwise pressure gradients than the baseline endwall according to Fig. 12, which results in such differences in g distributions. The differences between the two passages in local streamwise pressure gradients are more significant in the regions near the airfoil suction side than those near the airfoil pressure side, making the g value differences between the contoured endwall and the baseline endwall more remarkable from the midpitch to the locations near the airfoil suction side. ii. In the aft part of the passage (framed by the dot dash lines), the contoured endwall achieves larger coolant coverage area and larger local g values than the baseline case due to larger local streamwise pressure gradients there in the contoured endwall passage than those in the baseline passage. iii. The contoured endwall features smaller zero coverage zones near the airfoil suction side in the vicinity of the film cooling holes than the baseline case. With smaller local streamwise pressure gradient and smaller local pitchwise pressure gradient, the local coolant streamlines redirect to the airfoil suction side more in the contoured endwall passage than those in the baseline endwall passage and covers more there, which indicates that the local streamline redirections are dominated by the effect of the streamwise pressure gradient rather than the pitchwise pressure gradient. Fig. 17(b) plots the g distributions on the contoured endwall and the baseline endwall with averaged B.R. = 1.46, while D.R. = 1.0 and 1.5. The local B.R. for each hole is larger than 1.0 with D.R. = 1.0 according to Fig. 16, resulting in the blowing off of the coolant thus the zero-coverage regions in the vicinity of the holes. The coolant reattaches to the endwall surface downstream of the zero-coverage regions, resulting in two triangular zones with poor coolant coverages near the airfoil suction side and the airfoil pressure side as denoted with the dashed lines and dot dash lines for the D.R. = 1.0 cases in Fig. 17(b). The coolant injections near the airfoil suction side lift off and reattach to the endwall with an axial distance downstream of the film cooling holes, meanwhile, the coolant in the mid-pitch of the passage redirects pitchwise gradually with the effect of the crossflow from the airfoil pressure side to the airfoil suction side, which is one reason for the low coolant coverage triangular zones near the airfoil suction side. In addition, the discrete holes near the suction side is upstream of the lift-off lines of the pressure side horseshoe vortex while the discrete holes in the mid-pitch and near the airfoil pressure side are downstream of the lift-off lines. The lift-off lines obstruct the coolant from migrating pitchwise to

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the vicinity of the suction side, making the coolant coverage upstream of the lift-off lines poor, thus causing the low coolant coverage triangular region near the airfoil suction side. The favorable coolant coverage downstream of the film cooling holes near the airfoil pressure side results in the relatively low coolant coverage triangular near the airfoil pressure side. Three reasons result in this high coolant coverage region: i. Though the coolant injects axially at the hole exits, the local mainstream is not in the axial direction. Thus, there is compound angles between the injections and the mainstream. The direction of the pitchwise flow caused by the jet compound angle is opposite to that of the endwall cross flow. A balanced point will be reached where the lateral component of the jet counteracts that of the endwall cross flow. Thus, the coolant flow will accumulate near this point, which is a location in the passage near the airfoil pressure side. This phenomenon was also observed in Li et al. [14]. ii. The coolant injections near the airfoil pressure side impinge on the airfoil pressure side surface and result in a vortex with the
x rotating sense in the corner region of the airfoil pressure side as denoted by the red semi-circled arrows in Fig. 18. This vortex makes the coolant flows from the airfoil pressure side to the locations with some distance from the airfoil pressure side as denoted by the red straight arrows, then accumulate with the coolant migrating from upstream injections, resulting in a region with large g values located by some distance from the hole exits and the airfoil pressure side. iii. according to Fig. 16, the closer to the airfoil pressure side, the larger the local blowing ratios are. With larger local blowing ratios, the coolant reattaches to the endwall at locations with longer distances from the hole exits. Therefore, the nearer to the airfoil pressure side, the longer the low coverage region is. The density ratio effects are more significant for the B.R. = 1.46 cases than those for the B.R. = 0.93 cases due to the larger momentum flux difference between different density ratios with larger B. R. values. With D.R. = 1.5, the coolant in the contoured endwall passage and the baseline passage reaches the aft part of the passage (i.e. x/Cax ＜ 0.9), while the coolant in the cases with D.R. = 1.0 reaches the tail part of the passage (i.e. x/Cax ＞ 0.9) and turns a lot with the interactions with the mainstream there as denoted with the purple dashed lines in Fig. 17(b).

Fig. 18. Vy and coolant streamlines in the pressure side corner (CFD predicted, D.R. = 1.0), C represents the contoured endwall and B means the baseline endwall.

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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Some differences can be found in the g distributions between the contoured endwall and the baseline endwall with B.R. = 1.46 as shown in Fig. 17(b): (i) The g values in the passage near the airfoil pressure side are smaller on the contoured endwall than those on the baseline endwall due to the weaker coolant impingement on the airfoil pressure side in the contoured endwall passage as shown in Fig. 18 (the red dashed lines are of the same length in Fig. 18(b)(c)(d)(e)). With smaller local blowing ratios on the contoured endwall near the airfoil pressure side than those on the baseline endwall as plotted in Fig. 16, the coolant impinges onto the vane pressure side surface at a smaller span, resulting in weaker impingement vortexes in the contoured endwall passage. Therefore, the coolant accumulating effects are weaker, resulting in smaller g values in the passage near the airfoil pressure side on the contoured endwall. (ii) With D.R. = 1.0, the coolant reaches the tail parts of the passages, and interacts with the local mainstream. According to the limiting streamline distributions shown in Fig. 14, the streamlines turn more in the aft part of the contoured endwall than those of the baseline endwall due to the larger adverse streamwise pressure gradients there in the contoured endwall passage as shown in Fig. 12 and the larger pitchwise pressure gradients there in the contoured endwall passage as shown in Fig. 10. Thus, the coolant features larger turn in the tail part of the contoured endwall passage than those of the baseline endwall passage, making the coolant coverage in the tail part of the contoured endwall worse than that of the baseline endwall. To the contrary, with D. R. = 1.5, the coolant doesn’t reach the tail part of the passage. With larger streamwise acceleration in the aft part of the contoured endwall passage, the contoured endwall features larger coolant coverage area and larger g values there than the baseline endwall. (iii) The contoured endwall features smaller no coverage region near the airfoil suction side in the vicinity of the hole exits than the baseline case, which is in accordance with the cases with B.R. = 0.93. However, as the coolant migrates to the aft part of the passage, the coolant in the contoured endwall features larger streamwise acceleration, thus, causing the zero-coverage region near the suction side in the aft part of the contoured passage larger than those of the baseline passage. With averaged B.R. = 1.88 as shown in Fig. 17(c), the coolant covers the regions near the airfoil pressure side, however, the zero coverage area near the airfoil suction side are enlarged comparing to the smaller B.R. cases. The blowing ratio values near the airfoil pressure side are much larger than those for the B.R. = 1.46 cases, causing stronger impingement vortexes (as shown in Fig. 18), thus, more coolant accumulates in the passage near the airfoil pressure side. Coolant in the cases with D.R. = 1.5 and D.R. = 1.0 all reach the tail part of the passage, and features the larger turn in the contoured endwall passage than that in the baseline endwall passage. The differences in the g distributions between the contoured endwalls and the baseline case are similar to those with the B.R. = 1.46 cases. 5.3. Film cooling injections in the aft part of the passage (Row3) Film cooling injections in the aft part of the passage locate in the regions with large mainstream velocity, which might impact the passage aerodynamic performance much. Therefore, the configuration of the film cooling holes need to be considered carefully, which makes the evaluation of the film cooling performance there

Fig. 19. Adiabatic film cooling effectiveness distribution on the contoured endwall and the baseline endwall for Row3 (a) B.R. = 1.06 (b) B.R. = 1.19 (c) B.R. = 1.32.

particularly important. The current study measured the film cooling performance of a row of film cooling holes at x/Cax = 70% (Row3) on the contoured endwall and the baseline endwall with blowing ratios matched to engine conditions equal to 1.06, 1.19 and 1.32, and density ratios equals to 1.0 and 1.5. The local g values are larger for Row3 than those for the other two rows of holes due to the large local mainstream velocity and acceleration effects. The discrete holes of Row3 are configured 45° to the axial location so that the compound angles between the film cooling holes and the mainstream are small, thus, not causing the coolant accumulating phenomenon in the passage near the airfoil pressure side as found in the cases with Row2. As shown in Fig. 19, with the increasing of the blowing ratios, more coolant reaches and covers the tail part of the passage. With the blowing ratio increasing, the coolant momentum flux

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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increases, thus, the coolant features more momentum to maintain its flow directions, resulting in a larger zero coverage gap near the airfoil suction side. While as the coolant featuring larger momentum flux, the coolant interacts more with the mainstream and manipulates the large turn effects in the tail part of the passage, thus, covers the tail part of the passage well, e.g. the cases with B.R. = 1.32 and D.R. = 1.0 features g values larger than 0.35 in the tail part of the passage. The density ratio effects on g distributions are similar to those for Row1 and Row2. The film cooling performance for the D.R. = 1.5 cases are worse than those for the D.R. = 1.0 cases. However, it is important to note that since the coolant in the cases with B.R. = 1.32 and D.R. = 1.0 penetrates the large turn mainstream in the tail part of the passage and covers there, the coolant with D.R. = 1.5 in the tail part of the passage would have a possibility to penetrate the mainstream and covers the tail part of the endwall well provided with a larger B.R. value. Thus, if further increase the local B.R., the film cooling performance in the tail part of the passage would be almost the same between the D.R. = 1.5 and D.R. = 1.0 cases. As for the comparison between the contoured endwall and the baseline endwall cases: i. According to Fig. 12, the contoured endwall features larger local streamwise pressure gradients, thus larger streamwise accelerations at and downstream of x/Cax = 70% near the airfoil pressure side, making the streamwise coolant coverage near the airfoil pressure longer in the contoured endwall passage than that in the baseline passage as denoted by the black arrows in Fig. 19. ii. The g values in the tail part of the passage are smaller in the contoured endwall passage than those in the baseline endwall passage with B.R. = 1.06 and B.R. = 1.19 due to the larger streamline turning in the tail part of the passage. However, the contoured endwall features better cooling performance in the tail part of the passage with B.R. = 1.32 and D.R. = 1.0 near the airfoil pressure side and the airfoil suction side. The coolant streamline distributions in the contoured endwall passage and the baseline endwall passage with B. R. = 1.32 and D.R. = 1.0 are shown in Fig. 20. The coolant injections at the mid-pitch of the passage experience large pitchwise pressure gradients and large adverse streamwise pressure gradients there in the contoured endwall passage,

Fig. 20. Coolant streamline distributions of the contoured endwall passage and the baseline passage with B.R. = 1.32 and D.R. = 1.0 (CFD predicted).

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Fig. 21. Static Pressure coefficient distribution in the baseline passage and the contoured endwall passage (solid endwall without film cooling configurations, CFD predicted).

Fig. 22. Local blowing ratios of each film cooling hole for Row3 (B.R. = 1.32, D.R. = 1.0).

thus turning to the suction side sharply and covers the regions near the suction side as denoted by the purple line in Fig. 20. The coolant injected near the airfoil pressure side migrates streamwise as the local favorable streamwise pressure gradient there in the contoured endwall and then redirects to the suction side near x/Cax = 1.0 due to the large adverse streamwise pressure gradient. However, in the baseline endwall passage, the coolant in the mid-pitch of the passage redirects to the suction side gradually without attaching to the airfoil suction side. The differences in streamline distributions make smaller zero-coverage zones near the airfoil suction side on the contoured endwall than those of the baseline endwall because the coolant covers the locations near the airfoil suction side by sharp streamline turnings. iii. The g values in the vicinity of the film cooling holes near the airfoil suction side on the contoured endwall are larger than those on the baseline endwall. The contoured endwall passage features larger streamwise pressure gradients there than the baseline endwall passage. Meanwhile, the contoured endwall passage achieves larger radial pressure gradients from the mid-span to the endwall surface as shown in Fig. 21 near the airfoil suction side due to the small ‘‘hill” of the endwall shape there. The larger radial pressure gradients caused the coolant there more attached to the surface, making the local g values larger there. In addition, as shown in Fig. 22, which is the local blowing ratios for each hole with B.R. = 1.32 and D.R. = 1.0 for the contoured endwall passage

Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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and the baseline passage, the film cooling holes near the suction side in the contoured endwall cascade achieve smaller local blowing ratio values than those in the baseline endwall cascade, making the coolant injection less likely to blow off, thus attaching to the endwall surface there. 6. Conclusions Three positions of a row of film cooling holes of film cooling holes upstream of the passage (Row1, located at x/Cax =
0.3), in the fore part of the passage (Row2, located at x/Cax = 0.3) and in the aft part of the passage (Row3, located at x/Cax = 0.7) with different density ratios and matched averaged blowing ratios to the engine conditions are measured by PSP technique. CFD simulations against the experimental cases are carried out to look into the local flow field and to help understanding the physics behind the experimental results. The endwall film cooling features in the contoured endwall passage and the baseline endwall passage are analyzed and the effect of non-axisymmetric endwall contouring on film cooling at different locations are documented. With averaged blowing ratio increasing, the adiabatic film cooling effectiveness in the vicinity of the film cooling holes decreases as the coolant lift-off while the film cooling performance in the aft or tail part of the passage increases with increased coolant momentum flux. The film cooling injections upstream of and in the fore part of the contoured endwall passage perform worse than those of the baseline endwall passage due to the smaller local streamwise pressure gradient in the contoured endwall passage there. While in the aft part of the passage, the adiabatic film cooling effectiveness values are larger in the contoured endwall passage due to larger local streamwise pressure gradients and larger radial pressure gradients from the mid-span to the endwall. In addition, for the regions in the tail part of the endwalls, when the blowing ratio values are relatively small, the coolant in the contoured endwall passage features larger redirections there, which makes the coolant coverage area smaller and the local film cooling effectiveness smaller in the contoured endwall passage. While with relatively large blowing ratio values, the coolant covers the region near the airfoil suction side due to the turning of the coolant streamlines, resulting in large adiabatic film cooling effectiveness there in the contoured endwall passage. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The authors would like to acknowledge the financial support by National Science and Technology Major Project of China (2017-III0009-0035) and National Natural Science Foundation of China (No. 51706116). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995. References [1] A. Mensch, K.A. Thole, Conjugate heat transfer analysis of the effects of impingement channel height for a turbine blade endwall, Int. J. Heat Mass Transf. 82 (2015) 66–77.

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Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995

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Please cite this article as: P. Chen, L. Wang, X. Li et al., Effect of axial turbine non-axisymmetric endwall contouring on film cooling at different locations, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118995