Experimental investigation on the effects of hole pitch and blowing ratio on the leading edge region film cooling of a rotating twist turbine blade

International Journal of Heat and Mass Transfer 150 (2020) 119380

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Experimental investigation on the effects of hole pitch and blowing ratio on the leading edge region film cooling of a rotating twist turbine blade Feng Han a, Hong Guo a, Xiao-feng Ding a, Da-wei Zhang b, Hai-wang Li b,∗ a

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China National Key Laboratory of Science and Technology on Aero Engines Aero-thermodynamics, School of Energy and Power Engineering Beihang University, Beijing 100191, China

b

a r t i c l e

i n f o

Article history: Received 13 October 2019 Revised 13 January 2020 Accepted 13 January 2020

Keywords: Leading edge Film cooling Rotating blade Hole pitch Effectiveness

a b s t r a c t An experimental investigation has been performed to study the effects of the hole pitch and the blowing ratio on the leading edge region film cooling performance of a twist turbine blade with three rows of film holes under rotating conditions. The experiments were accomplished in a test facility with one-stage turbine using the thermochromic liquid crystal (TLC) technique. All tests were made at a rotating speed of 574 r/min with the average blowing ratio ranging from 0.5 to 2.0. The Reynolds number based on the mainstream velocity of the turbine outlet and the rotor blade chord length was fixed at 6.4 × 104 .CO2 was used to obtain the coolant-to-mainstream density ratio of 1.56. The hole pitches tested were p = 2.5d, p = 3.75d and p = 5d, respectively. The results show that both the hole pitch and the blowing ratio play an integral role in determining the film cooling effectiveness distributions on the leading edge. Regardless of the hole pitch, the spanwise average film cooling effectiveness increases monotonously with the increase of blowing ratio on the leading edge region. For all blowing ratio cases, the spanwise average effectiveness has a decreasing trend as the hole pitch increases. When the bowing ratio is constant, the difference between the spanwise average film cooling effectiveness value obtained in the region of −4.3 < x/d < 0 and the region of 0 < x/d < 3.75 has a decreasing trend as the hole pitch increases. For all hole pitch cases, the area average film cooling effectiveness increases monotonously as the blowing ratio increases. For all blowing ratio cases, the area average film cooling effectiveness decreases monotonously as the hole pitch increases. However, the reduction is not always linear to the hole pitch change. When the coolant jet mass flow rate is constant, the p = 2.5d case provides a higher level of the area average film cooling effectiveness than the p = 3.75d and 5d cases. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction The inlet temperature of modern gas turbine engines has been increased continuously to achieve higher thermal efficiency and higher specific power output. In a gas turbine, the leading edge region of a turbine vane or blade often experiences a high heat load due to flow stagnation. Film cooling is one of the most effective technologies to protect the leading edge surface from the hot mainstream gas and reduce heat transfer rates. Increasing the film cooling effectiveness in the leading edge region will lead to significant benefits in reliability and life of the turbine blade. Goldstein [1] provided a fundamental understanding of film cooling in 1971.

∗

Corresponding author. E-mail address: [email protected] (H.-w. Li).

https://doi.org/10.1016/j.ijheatmasstransfer.2020.119380 0017-9310/© 2020 Elsevier Ltd. All rights reserved.

And a comprehensive compilation of the state-of-the-art cooling technology was documented by Han et al. [2] in their book. Many studies on the leading edge film cooling have been carried out under static conditions. Ekkad et al. [3] used the thermochromic liquid crystal (TLC) technique to study the effects of the mainstream turbulence and density ratio on the film cooling effectiveness over a cylindrical leading edge model. The blowing ratio ranged from 0.4 to 1.2 and the density ratio was controlled at 1.2 and 1.5. The distance between the film holes was 19 mm in the spanwise direction (p/d = 4). Results showed that air provides highest film cooling effectiveness at M = 0.4 and CO2 provides highest film cooling effectiveness at M = 0.8. Pratt and Whitney GESP organized a blind-test competition in the United States on the leading edge film cooling through three rows of compound angle holes with focus on physics and on the capability of computational fluid dynamics (CFD), where Cruse, Yuki and Bogard [4]

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F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

Nomenclature C d DR… M Ma m Re Rt T v s R k p x

chord length of the rotor blade (mm) film-hole diameter (mm) density ratio (ρ c /ρ m ) average blowing ratio (M = ρc vc /ρ∞ v∞ ) Mach number (Ma = v/s ) the coolant mass flow rate (g/s) Reynolds number Re = ρm vout C/μ rotation number Rt = ωd/vin temperature (K) velocity (m/s) √ sound velocity (m/s) (s = kRT ) gas constant [J/(kg · K)] specific heat ratio hole pitch (mm) the streamwise distance from the center row film holes (mm)

Greek symbols α spanwise inclination angle of the film hole (°) η film cooling effectiveness

did the experiments and Martin and Thole [5], Thakur, Wright, and Shyy [6], Chernobrovkin and Lakshminarayana [7], and Lin, Stephens and Shin [8] did the CFD simulations. The diameter of each film hole was 6.32 mm and the spacing between film holes in each row was 48.3 mm (p/d = 7.64). Noted that the experimental data were not released until all CFD simulations were carried out. The comparisons of the CFD simulations with the experiment showed good agreement for the surface adiabatic film cooling effectiveness. Ou and Rivir [9] used a transient liquid crystal technique to study the film effectiveness and the heat transfer coefficients on a circular leading edge model with three rows of film holes. The film hole configuration has a smaller injection angle of 20° and a larger hole pitch to the hole diameter ratio of 7.86. Results showed that film effectiveness increases as the Reynolds number increases at high turbulence except for the M = 2.5 case. The infrared thermography technology was used by Kim and Kim [10] to study the influence of five different structures injection holes on the blade leading edge film cooling performance. Three row of film holes were arranged in the cylindrical model which was used to model the leading edge. The film hole configuration has a larger hole pitch (p/d = 7.5). Their results showed that the shaped holes can effectively improve the film cooling performance compared to the traditional cylindrical holes. Liu et al. [11] performed an experimental investigation to consider the effect of film hole shape and hole pitch on the leading edge film cooling performances. Three row of film holes were arranged in the semi-cylinder model which was employed to model the leading edge. Their results showed that the p = 5d models can provide much larger film covering area than the p = 8d models. Compared with the p = 8d cases, the flow interaction is more intense for the p = 5d cases due to narrow hole-to-hole spacing. In subsequent research, Liu et al. [12] conducted a further study to consider the film cooling characteristics of cylindrical and laid-back film holes on a turbine blade leading edge model as well as the effect of the injection angle (30° and 45°) on the film cooling performance. They found that under the same blowing ratio, models with a small injection angle can give higher average film cooling effectiveness than models with a large injection angle. Dyson et al. [13] experimentally investigated the effects of hole pitch (7.6d,

ρ  μ ω

density, (kg/m3) rotating speed, (r/min) dynamic viscosity of the mainstream, [kg/(m•s)] rotational angular velocity (rad/s) (ω = 2π /60)

Subscripts W wall M mainstream C coolant In turbine inlet Out turbine outlet ∞ turbine stage inlet Abbreviations TLC thermochromic liquid crystal RGB red, green, blue HSV hue, saturation, value PS pressure side SS suction side CCS camera control system SCS strobe control system SCM single-chip microcomputer CFD computational fluid dynamics

8.6d, 9.6d and 11.6d) and blowing ratio on the overall effectiveness of a simulated turbine blade leading edge model. They found that although the overall effectiveness decreases with an increase in hole pitch when the blowing ratio is constant, the decrease is generally small until p = 11.6d Li et al. [14] used the PSP technique to study the density ratio effect on the film cooling on a leading edge model. They found that a larger density ratio can provide more coolant attach to the surface and improve film cooling performance for all cases. Recently, Chowdhury et al. [15] experimentally studied the effects of turbine blade leading edge shape, density ratio and blowing ratio on film cooling in a wind-tunnel facility. Three leading edge models were considered including a semi cylinder of radius R = 38.1 mm, elliptical leading edges of major radius 1.5R and 2R with an after body. There were three rows of cylindrical film holes and two rows of gill holes on each leading edge model. And each row has 15 film holes with a hole pitch of 4d in the spanwise direction. They found that the 1.5R leading edge model can provide better performance than the other two models and gill film holes benefit to improve the film coverage. Gao et al. [16] presented a numerical simulation to investigate the leading edge film cooling characteristics of cylindrical film holes with five different compound angles. Three rows of film holes were arranged in stagger pattern on the semi-cylinder leading edge model. The distance between the film holes is 15 mm in the spanwise direction and the film hole diameter is 3 mm (p/d = 5). The results showed that the film cooling effectiveness increases with an increase in the blowing ratio, while it slightly decreases when M = 2.0, and the best blowing ratio is approximately 1.4. In the past few decades, only a few experimental studies have been carried out to study the film cooling characteristics on the turbine blade under rotating conditions due to the great difficulty in conducting such experiments. Dring et al. [17] were among the earliest to investigate the film cooling performance on a rotor blade in a low-speed turbine first stage. The coolant was ejected from the single holes on the pressure side (PS) and suction side (SS) of the blade. Results indicated that the radial deviation of the coolant is small on the SS, which is in good agreement with the existing results taken on flat surfaces. On the PS, an obvious radial deviation caused by the radial component of the freestream flow

F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

over the blowing site results in very low levels of cooling effectiveness. A heat-mass transfer analogy was applied by Takeishi et al. [18] to study the film cooling effectiveness on a low-speed stationary cascade and the rotor blade in a one-stage turbine. Results showed that the film cooling effectiveness on the SS of the rotating blade is in agreement with the result of the stationary cascade and is only 30% lower downstream. The rotating results on the PS are lower than the stationary cascade results due to the radial flow on the concave surface and the strong mixing of the coolant jets with the mainstream. A pressure sensitive paint (PSP) technique was used by Ahn et al. [19] to measure the detailed distribution of film cooling effectiveness on the leading edge region of a rotor blade with two row of film holes in a three-stage axial turbine. The rotating speed was maintained at 2400, 2550 and 3000 r/min and the blowing ratio varied from 0.5 to 2.0. The film hole diameter was 1.19 mm and each row had a hole-to-hole pitch of p = 5.97d in the spanwise direction. Results indicated that the rotating speed is one of the most critical parameters in determining the leading edge film cooling effectiveness distributions. The average film effectiveness on the interested area decreases with an increase in the rotating speed. In subsequent research, Ahn et al. [20] used the same facility to study the influence of rotation on the leading edge film cooling performance of a turbine blade with three row of film holes using PSP technique. Results showed that the coolant path of the leading edge middle row heads to the SS, spanwise and PS direction at 240 0, 250 0 and 30 0 0 r/min, respectively. The average film effectiveness on the interested area slightly increases with an increase in the blowing ratio. Li et al. [21] used the TLC technique to study the effects of blowing ratio, density ratio and rotating number on the film cooling characteristics on both PS and SS of a rotor blade in a 1–1/2 stage turbine. A film hole was arranged on the PS and SS of the blade respectively. Results showed that the higher rotating number and lower blowing ratio result in more obvious film deflection. Li et al. [22] conducted a further study to consider the effects of mainstream Reynolds number and turbulence on the film cooling on both PS and SS of a rotating blade. They reported that both the film coverage and cooling effectiveness increase with an increase in mainstream Reynolds number on the PS and SS. Li et al. [23] carried out an experimental investigation to study the effects of the mainstream Reynolds number (4.42 × 104 –7.18 × 104 ), blowing ratio (0.5–2.0) and density ratio (1.04 and 1.56) on the film cooling performance on the leading edge region of a twist rotor blade in a one-stage turbine. They noted that for a fixed blowing ratio, the average film effectiveness on the measurement area increases with an increase in mainstream Reynolds number for both coolant gasses. Under the same Reynolds number and blowing ratio, the results with CO2 injection are higher than the results with N2 injection. In subsequent research, Li et al. [24,25] used the same facility to study the effects of rotating speed (400, 550 and 700 r/min) and injection angle (30°, 45° and 60°) on the film cooling characteristics on the leading edge of the twist turbine blade. Results indicated that the spanwise average film effectiveness on the center row film hole is insensitive to rotating speed compared to the other two rows. For the M = 0.5, 1.0 and 2.0 cases, the area average film cooling effectiveness decreases with an increase in the injection angle. As it can be seen from the above survey, few experimental studies [19,20,23–25] of the film cooling on the leading edge of a rotating turbine blade can be found in published literature. And experimental study on the influence of the film hole pitch on the leading edge film cooling of a rotating turbine blade has not been reported. In addition, few experimental studies [11,13] on the effect of film hole pitch on the turbine blade leading edge were conducted under static conditions. In these studies, the authors used straight blades instead of three-dimensional twist blades. However, Zeng et al. [26] recently studied the effect of the turbine blade

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simplifications on film cooling characteristics of a turbine blade. Results showed that the simplification of the blade form from twist to straight has a noticeable effect on the film cooling and results in a change in the stagnation line on the leading edge under rotating conditions. They noted that the film cooling characteristics of a twist blade should be considered in design. Therefore, the primary objective of the current study is to investigate the effect of three different film hole pitches on the leading edge film cooling effectiveness of a rotating twist turbine blade using the TLC technique. 2. Experimental facility Fig. 1 shows a schematic of the one-stage turbine test facility used to conduct the present study at Beihang University in China. The test facility is of 8300 mm length, 4400 mm width and 30 0 0 mm height. The test facility consists of two parts: a mainstream path (red arrow) and a coolant flow path (blue arrow). The centrifugal blowing compressor used to provide the mainstream air is a KF3-95 No6.3E, which has a maximum rotating speed of 2300 r/min. The flow and pressure of the entire mainstream section are regulated by the SMZD-S-165/440 digital direct-current control cabinet. An electric heater with a maximum rated power of 24 kW and a maximum rated voltage of 220 V is used to heat the mainstream air temperature to the experimental setting. The compressed and heated mainstream air passes through an inlet cone and a honeycomb before entering the one-stage turbine. The honeycomb is installed at the rear of the inlet cone to ensure that the mainstream air entering the annular channel is axially uniform. Moreover, the inner and outer diameters of the annular channel are 600 and 800 mm, respectively. Four pitot tubes and two static pressure holes are equipped on the annular channel to measure the mainstream total and static pressures upstream of the turbine. According to the values of the mainstream total and static pressures, the mainstream flow rate through the turbine component can be calculated by a differential pressure transmitter (Rosemount 3051). The one-stage turbine is the core component of the test facility. A helicoid collector is placed in the back of the turbine section to collect and stabilize the exhaust air, which is then transported to the heater to complete the circle. The turbine shaft is connected to the rear end of a 22 kW dynamometer (Z4-132–1) with a rated rotating speed of 3090 r/min through a synchronous belt. A torque meter (TI-1), connected to the dynamometer via a flexible coupler, is used to output the turbine torque and power. The coolant flow provided by the dedicated gas cylinder passes through the valves, filter, air pressurizer tank, flow meter and insulation tube installed in the hollow shaft before entering the test blade. The labyrinth seal and the mechanical seal are adopted to prevent leakage of the mainstream and coolant parts, respectively. Three ranges of glass rotor flow-meters (LZB-6, LZB-10 and LZB-15) are used to meet the requirements of different coolant flow rates. A digital tachometer is used to measure the rotating speed of the one-stage turbine. A carbon brush-copper collar system is used to complete the static and dynamic conversion of the electrical signals. A data acquisition system is mounted on the extended shaft to transmit the temperature signals to the computer, as shown in Fig. 1. Fig. 2 shows the diagrammatic drawing of the one-stage turbine. Fig. 3 presents the relative locations between the CCD camera and the rotating blade. Table 1 lists the dimensions of the onestage turbine in detail. Forty-two blades with a stagger angle of 45° are installed on the first stage stator and seventy-three blades with a stagger angle of 60° are installed on the first stage rotor. The stator blade tip diameter, hub diameter, height and chord length at stator blade tip are 782 mm, 612 mm, 85 mm and 77 mm, respectively. And the rotor blade tip diameter, hub diameter, height and chord length at rotor blade tip are 780 mm, 646 mm, 67 mm

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F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

Fig. 1. Schematic of the one-stage turbine test facility.

Table 1 Dimensions of the turbine.

Fig. 2. Diagrammatic drawing of the one-stage turbine.

Fig. 3. Relative locations between the CCD camera and the rotating blade.

and 40 mm, respectively. The test blade models are composed of an engineering plastic (RGD525), which has a low thermal conductivity of 0.22 W/(m•K), to reduce the influence of heat conduction as much as possible. All other blades are made of aluminum alloy. In the present experiment, three blade models with three different film-hole pitches (p = 2.5d, p = 3.75d and p = 5d, p is the film-hole pitch in the spanwise direction) have been studied. Except for the film hole pitch and the number of film holes, the other geometrical dimensions of the three blade models are exactly the same with each other. Fig. 4 presents one of the test blades with p = 2.5d on the measurement area and the coolant path inside the blade. For feeding the jet flows, the internal coolant channel is twisted. A total of 165 film holes with a di-

Item

1st stator stage

1st rotor stage

Stagger angle Tip diameter Hub diameter Height Chord length Blade number

45° 782 mm 612 mm 85 mm 77 mm 42

60° 780 mm 646 mm 67 mm 40 mm 73

ameter d of 0.4 mm are arranged along the leading edge in three rows: the PS row, the center row and the SS row. The three rows of film holes are located at 30°, 0° and 30° with respect to the stagnation line, respectively. The injection angle of the film hole is α = 45°, as shown in Fig. 5. Each row has 55 film holes, and those in the center row are staggered with respect to the film holes of the other two rows. In addition, the number of film holes on the leading edge of the second blade (p = 3.75d) and the third blade (p = 5d) is 126 and 105, respectively. As mentioned above, the rotor blade height h is 67 mm. The chord lengths at 0.1 h, 0.5 h and 0.9 h along the rotor blade root to the blade tip direction are 42.7 mm, 41.7 mm and 40.9 mm, respectively. As shown in Fig. 6, the inlet angles β of the rotor blade at 0.1 h, 0.5 h and 0.9 h along the rotor blade hub to the blade tip direction are 44°, 40.6° and 57.9°, respectively. And β is the angle between the airflow direction of the rotor blade inlet and the front line of the cascade. The outlet angles γ of the rotor blade at 0.1 h, 0.5 h and 0.9 h along the rotor blade hub to the blade tip direction are 26.2°, 27° and 26.2°, respectively. And γ is the angle between the airflow direction of the rotor blade outlet and the front line of the cascade. 3. Experimental methods 3.1. Image acquisition system Fig. 7 presents a schematic drawing of the image acquisition system that includes a computer, a camera control system (CCS), a single-chip microcomputer (SCM; STM32F103RCT6), a stator blade, a photoelectric sensor (P + F OBT200-18GM60-E5), LED lights, a rotor blade and a strobe control system (SCS). The CCD camera (MU9Px-MH, 15 × 15 × 8.5 mm) with a resolution of

F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

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Fig. 4. The test blade with p = 2.5d on the measurement area and the coolant path.

transmitted to the computer to convert the RGB (red, green, blue) elements into HSV (hue, saturation, value) format. 3.2. Calibration of TLC

Fig. 5. Configuration of the film holes.

2592 × 1944 pixels installed on one of the stator blades is applied to capture temperature distributions. And the CCD camera used for the calibration is the same one used in the formal experiment. A smooth transition on both sides of the CCD camera lens must be ensured to reduce the disturbance of the mainstream flow field as much as possible. It is necessary to precisely control the exposure time of the CCD camera due to the camera was set to an external trigger mode. For example, the CCD camera exposure time must be set to less than 15 μm to ensure the captured images are clear when the rotating speed is 1400 r/min. The CCS can provide fast and precise control of the CCD camera exposure time through a high speed optical coupling isolation circuit. To receive the signal from the photoelectric sensor, the SCM input terminal is set to receive the interrupt signal triggered by the rising edge. The SCM interrupt handler is triggered by a signal from the photoelectric sensor when the test blade moves to the initial position. And the pulse signal is timed at the same time. After an appropriate delay, the SCM output two different square-wave pulse signals to the SCS and the CCS, respectively. In addition, there is a one-to-one correspondence between the time delay of the square-wave pulse signal and the rotating speed. That is, the time delay of the square-wave pulse signal is correspondingly changed with change of the rotating speed to ensure the CCD camera can perform accurate positioning. The two different square-wave pulse signals from the SCM can precisely control the CCD camera exposure and strobe starter. The timing diagram of the experimental control signal is presented in Fig. 8. Finally, the captured images are

In the current experiment, the steady-state liquid crystal (SPN/R30C20 W), with a temperature range from 303 K to 323 K, was used to obtain the temperature distributions of the leading edge wall. The black paint and liquid crystal were sprayed uniformly onto the leading edge surface by a spray gun before the calibration experiment. During the calibration experiment, the temperature of the mainstream air was changed from 303 K to 323 K and the liquid crystal color changed from red to green to blue. The illumination angles, camera view angle and shooting method were consistent with the subsequent formal experiments. To obtain the calibration curves between the hue value and temperature for the leading edge, the liquid crystal images were recorded and transmitted to the computer for each increase of 1.0 K. Due to the large curvature of the blade leading edge, the actual viewing angle of the camera to different positions on the leading edge surface was different. Chan et al. [27] found that liquid crystal technique is sensitive to illumination and viewing angle and therefore limited to surfaces with only slight curvature. A pixel-level calibration method was applied to eliminate the error caused by the camera viewing angle and the temperature of the liquid crystal. The captured image of the measurement area in the leading edge has a pixel of 129 × 1928. Each pixel has a calibration curve when calibrating the relationship between the hue value and temperature, which can eliminate the error caused by difference of viewing angle. The MATLAB’s RGB2HSV function was used to calculate the hue values. The RGB2HSV function used the following algorithm to obtain the hue value. G−B if R = max, H = 6(R−min (R,G,B ) ) 2+B−R if G = max, H = 6(G−min (R,G,B)) 4+R−G if B = max, H = 6(B−min (R,G,B ) )

(1)

where R, G and B means the pixel values of red, green and blue respectively. And max and min are mathematical operators representing the maximum and minimum, respectively. Furthermore, another algorithm [28,29] has been recommended by many researchers to calculate the hue value.

√

H = arctan

3 (G − B ) 2R − G − B



(2)

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F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

3.3. Film cooling effectiveness If the blade wall is adiabatic or approximately adiabatic, the measured wall temperature is considered to be the adiabatic wall temperature, and the film cooling effectiveness is defined as follows:

ηmeas = (Tm − Tw )/(Tm − Tc )

(3)

where, Tm is the temperature of the mainstream air, which is the average value of the T-type thermocouples installed in the annular channel. Tc is the coolant temperature, which is obtained by a thermosensitive resistor (TH-44034-40-T) installed in the blade cooling chamber. Tw is the leading edge wall temperature, which can be obtained according to the relationship between calibration cure and hue value. Although the test blade was processed with a low thermally conductivity material, there was still some conduction through the test blade wall. To correct this error, the method proposed by Ethridge et al. [31] was used in this paper. The calculation formula with the correction term for the film cooling effectiveness was defined as follows:

η = (ηmeas − η0 )/(1 − η0 )

where η is the true film cooling effectiveness, ηmeas is the measured film cooling effectiveness and η0 is the conduction error. And η0 = (Tm − Tw0 )/(Tm − Tc ), here Tw0 indicates the wall temperature in the area where is not affected by the film. In this experiment, Tw0 was measured in the area between the upper boundary of the film hole rows and the blade top, where there was no film coverage. Moreover, Ethridge et al. [31] pointed out that the value of η0 was 0.02 ≤ η0 ≤ 0.07under the condition of high turbulence intensity. In the current experiment, the value of η0 was 0.06 when the mainstream turbulence intensity was equal to 5%. Table 2 presents the operating conditions of the current experimental study. The mainstream mass flow rate measured by a differential pressure transmitter (Rosemount 3051) was 3.21 kg/s. The mainstream turbulence intensity measured by a hot-wire anemometer (TSI1213-20 and IFA100) was approximately 5%. The turbine inlet velocity was 13 m/s and outlet velocity was 27.1 m/s. The mainstream Reynolds number (Re) based on the turbine outlet velocity and the rotor blade chord length was 6.34 × 104 . All tests were carried out at the rotating speed of 574 r/min and the corresponding rotation number Rt was 0.0018. The experiments were carried out for four average blowing ratios (M), viz. 0.5, 1.0, 1.5 and 2.0. The averaged blowing ratio was defined as M = ρc vc /(ρ∞ v∞ ), where ρ c , vc , ρ ∞ and v∞ are the coolant density, coolant velocity, mainstream density and relative mainstream velocity at the inlet of the rotor blade, respectively. CO2 was used as coolant gas and the corresponding coolant-to-mainstream density ratio (DR) was 1.56.

Fig. 6. the inlet angles β and outlet angles γ of the rotor blade at 0.1 h, 0.5 h and 0.9 h along the rotor blade hub to the blade tip direction.

Based on the calculated using mately equal in hue value in the



η =

experiments in the study of [30], the hue values the RGB2HSV function and Eq. (2) are approximost cases. We use the Eq. (1) to calculate the current study.

Tw − Tc

(Tm − Tc )2

2 ( Tm )2 +



1 Tm − Tc

2

 ( Tw )2 +

Tm − Tw

(Tm − Tc )2

Because of each pixel has a corresponding calibration curve and we are unable to present all the calibration curves in this paper. Therefore, we only give the calibration curves at the center position of the measurement area of the three blade models with different film hole pitches, as shown in Fig. 9.

(4)

3.4. Uncertainty analysis According to the method proposed by Moffat [32], the uncertainty of the film cooling effectiveness can be calculated by

2 ( Tc )2

(5)

In the present study, the mainstream temperature (Tm ) and the coolant temperature (Tc ) were kept at 315 K and 298 K, respectively. The uncertainty of Tm and Tc was ±0.25 K and ±0.2 K, respectively. The uncertainty of the wall temperature (Tw ) measured by the liquid crystal was maintained at ±0.25 K, which

F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

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Table 2 Operating conditions. Parameter

Value

Mainstream mass flow rate Mainstream turbulence intensity Turbine inlet velocity Relative velocity at rotor inlet Turbine outlet velocity Re Mainstream Mach numbers Rotating speed Rt M DR Tm Tc

3.21 kg/s 5% 13 m/s 21.3 m/s 27.1 m/s 6.34 × 104 0.059 (rotor blade inlet), 0.075 (rotor blade exit) 574 r/min 0.0018 0.5–2.0 1.56 315 K 298 K

Fig. 7. Schematic drawing of the image acquisition system.

Fig. 8. Timing diagram of the experimental control signal.

was the same as that of the T-type thermocouple. Consequently, when Tw was equal to 308 K, the uncertainty of the film cooling effectiveness was 6.9% calculated by Eq. (5). The uncertainty of the rotating speed given by the intelligent tachometer (YK-23) was ±1 r/min. Furthermore, the uncertainty of the mainstream mass flow rate and blowing ratio was ±3% and ±2%, respectively. Fig. 9. TLC calibration curves.

4. Results and discussion In this paper, the spanwise average film cooling effectiveness and area average film cooling effectiveness were experimentally analyzed to study the effects of the hole pitch and the blowing

ratio on the leading edge region of a twist turbine blade in a one-stage turbine. The distributions of the film cooling effectiveness for each hole pitch and blowing ratio are shown in Figs. 10–12. The horizontal

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F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

Fig. 10. Film cooling effectiveness distribution for different blowing ratios when p = 2.5d.

ordinate s/smax indicates the non-dimensional distance, where s is the distance measured along the blade surface from the measurement area centerline, with a negative value indicating the area from the measurement area centerline to the PS and a positive value indicating the area from the measurement area centerline to the SS. The vertical coordinate Y/H indicates the non-dimensional distance in the radial direction, where Y is the radial distance from the lower boundary of the measurement area and H is the radial height of the measurement area. In the present study, we used a relatively well-designed three-dimensional twist blade and all experiments were carried out in the low-speed one-stage turbine test facility. According to a given turbine inlet velocity (13 m/s), the rotating speed is calculated as 574 r/min under zero incidence angle conditions. For the zero incidence angle condition, there is an overlap between the stagnation line and the centerline of the center row film holes for the twist blade.

4.1. Spanwise average film cooling effectiveness 4.1.1. Effects of the blowing ratio In the current experiment, the average blowing ratio was maintained at 0.5, 1.0, 1.5 and 2.0 at a constant rotating speed 574 r/min. Figs. 13–15 show the effect of the blowing ratio on the spanwise average film cooling effectiveness under different film hole pitches. It is noteworthy that the coordinate s used to report the experimental results (see Figs. 10–12) appears to be the apparent coordinate related to the view angle of the camera and not the geometric distance. And we have fixed the coordinate x with a certain geometric transformation to ensure that the spacing between the PS and center rows is equal to that between the center and SS rows in Figs. 13–19. The horizontal coordinate x/d indicates the non-dimensional distance and x is the streamwise

distance from the center row. The vertical coordinateηindicates the spanwise average film cooling effectiveness, which is calculated from the average value of −4.3 < x/d < 3.75. Note that the entire region of −4.3 < x/d < 3.75 in the streamwise direction is the leading edge interval of our study. Three black arrows indicate the position of the three rows of film holes. For all hole pitch cases, the blowing ratio has a very important influence on the distributions of the spanwise average film cooling effectiveness, as shown in Figs. 13–15. And the experimental results indicate that the level of film cooling effectiveness obtained on the PS is higher than that obtained on the SS at the leading edge region, which is consistent with the previous results given by Ahn et al. [19], Li et al. [24] and Zhang andHassan [33]. And this phenomenon is more obvious for the p = 3.75 d and p = 5d cases. Fig. 13 presents the experimental results for the hole pitch p = 2.5d at different blowing ratios M from 0.5 to 2.0. For all blowing ratio cases, three clear peaks appear downstream of each row of film holes because of the high film cooling effectiveness in the region downstream from the coolant jet outlet. As can be seen from the Fig. 13, the spanwise average film cooling effectiveness increases monotonously with an increase in the blowing ratio in the entire region, with the best blowing ratio M = 2.0. With an increase in the blowing ratio, the exit momentum of the coolant jet increases and gradually becomes comparable to the momentum of the mainstream. And even at a high blowing ratio M = 2.0, no lift-off phenomenon occurs in the p = 2.5d case. In addition, the spanwise average cooling effectiveness in the region of −4.3 < x/d < 0is0.16, 0.24, 0.29 and 0.36 at M = 0.5, 1.0, 1.5 and 2.0, respectively. And the spanwise average cooling effectiveness in the region of 0 < x/d < 3.75is0.13, 0.21, 0.27 and 0.34 at M = 0.5, 1.0, 1.5 and 2.0, respectively. Therefore, for the p = 2.5d case, the spanwise average film cooling effectiveness

F. Han, H. Guo and X.-f. Ding et al. / International Journal of Heat and Mass Transfer 150 (2020) 119380

Fig. 11. Film cooling effectiveness distribution for different blowing ratios when p = 3.75d.

Fig. 12. Film cooling effectiveness distribution for different blowing ratios when p = 5d.

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Fig. 13. Effect of the blowing ratio on the spanwise average film cooling effectiveness for p = 2.5d.

Fig. 16. Spanwise average film cooling effectiveness for different hole pitches when M = 0.5.

Fig. 14. Effect of the blowing ratio on the spanwise average film cooling effectiveness for p = 3.75d.

Fig. 17. Spanwise average film cooling effectiveness for different hole pitches when M = 1.0.

Fig. 15. Effect of the blowing ratio on the spanwise average film cooling effectiveness for p = 5d.

Fig. 18. Spanwise average film cooling effectiveness for different hole pitches when M = 1.5.

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Fig. 19. Spanwise average film cooling effectiveness for different hole pitches when M = 2.0.

value obtained in the region of −4.3 < x/d < 0 is higher than that obtained in the region of 0 < x/d < 3.75 at each blowing ratio. Fig. 14 presents the experimental results for the hole pitch p = 3.75d at different blowing ratios M from 0.5 to 2.0. For all blowing ratio cases, there are no clear peaks appear downstream of each row of film cooling holes compared to the p = 2.5d case. The spanwise average film cooling effectiveness increases monotonously with an increase in the blowing ratio in the region of −4.3 < x/d < 1, with the best blowing ratio M = 2.0. In the region of 1.75 < x/d < 3.75, the spanwise average film cooling effectiveness level remains substantially unchanged when the bowling ratio is increased from M = 0.5 to M = 1.0. This is because when the blowing ratio is increased to M = 1.0, the film coverage area obtained in the region of 1.75 < x/d < 3.75 has not been greatly improved compared to the M = 0.5 case, as shown in Fig. 11(a) and 11(b). In the region of 1 < x/d < 3.75, the spanwise average film cooling effectiveness level remains substantially unchanged when the bowling ratio is increased from M = 1.5 to M = 2.0. This may be due to a more intense mixing between the coolant jet and the mainstream gas in the region of 1 < x/d < 3.75 at a high blowing ratio M = 2.0. In addition, the spanwise average cooling effectiveness in the region of −4.3 < x/d < 0is0.11, 0.14, 0.18 and 0.20 at M = 0.5, 1.0,1.5 and 2.0, respectively. And the spanwise average cooling effectiveness in the region of 0 < x/d < 3.75 is 0.05, 0.06, 0.08 and 0.09 at M = 0.5, 1.0, 1.5 and 2.0, respectively. Therefore, for the p = 3.75d case, the spanwise average film cooling effectiveness value obtained in the region of −4.3 < x/d < 0 is higher than that obtained in the region of 0 < x/d < 3.75 at each blowing ratio. Fig. 15 presents the experimental results for the hole pitch p = 5d at different blowing ratios M from 0.5 to 2.0. For the p = 5d case, there are also no clear peaks appear downstream of each row of film cooling holes at each blowing ratio. The spanwise average film cooling effectiveness increases monotonously as the blowing ratio increases in the entire region of −4.3 < x/d < 3.75, with the best blowing ratio M = 2.0. As the blowing ratio increases, the extent of the increase in spanwise average film cooling effectiveness in the region of 2.5 < x/d < 3.75 is smaller than that in the region of −4.3 < x/d < 2.5. In addition, the spanwise average cooling effectiveness in the region of −4.3 < x/d < 0 is 0.09, 0.12, 0.15 and 0.17 at M = 0.5, 1.0,1.5 and 2.0, respectively. And the spanwise average cooling effectiveness in the region of 0 < x/d < 3.75 is 0.05, 0.07, 0.09 and 0.10 at M = 0.5, 1.0, 1.5 and 2.0, respectively. Therefore, for the p = 5d case, the

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spanwise average film cooling effectiveness value obtained in the region of −4.3 < x/d < 0 is higher than that obtained in the region of 0 < x/d < 3.75 at each blowing ratio. Furthermore, for the p = 2.5d case, the spanwise average film cooling effectiveness obtained in the region of −4.3 < x/d < 0 are 0.06, 0.08, 0.10 and 0.09 higher than those in the region of 0 < x/d < 3.75 at M = 0.5, 1.0, 1.5 and 2.0, respectively. For the p = 3.75d case, the spanwise average film cooling effectiveness obtained in the region of −4.3 < x/d < 0 are 0.04, 0.05, 0.06 and 0.09 higher than those in the region of 0 < x/d < 3.75 at M = 0.5, 1.0, 1.5 and 2.0, respectively. For the p = 5d case, the spanwise average film cooling effectiveness obtained in the region of −4.3 < x/d < 0 are 0.03, 0.03, 0.02 and 0.02 higher than those in the region of 0 < x/d < 3.75 at M = 0.5, 1.0, 1.5 and 2.0, respectively. Therefore, when the bowing ratio is constant, the difference between the spanwise average film cooling effectiveness value obtained in the region of −4.3 < x/d < 0 and the region of 0 < x/d < 3.75 has a tendency to decrease as the hole pitch increases from p = 2.5d to p = 5d It is worth noting that no matter under small or large hole pitches, the film cooling effectiveness increases with the rising of the blowing ratio in the current experiment, which is consistent with the experimental result given by Ahn et al. [20] on the leading edge at design rpm and the numerical result given by Yang et al. [34] on the leading edge at design rpm and the experimental result given by Li et al. [20] on the SS of a rotating turbine blade. However, Li et al. [21] reported that on the SS of the turbine blade, the film cooling effectiveness increases with an increase in blowing ratio at low blowing ratios and the maximum magnitude occurs at a moderate blowing ratio of M = 1.2. And Cheng et al. [35] reported that the best blowing ratios on the PS and SS of a flat plate model are approximately M = 0.5 and M = 0.3, respectively. This is mainly because the presence of stagnation flow on the leading edge region makes the coolant outflow more difficult than other positions of the blade. In the current experiment, at the high blowing ratio M = 2.0, it seems that the coolant jet ejected from the leading edge film holes has enough momentum to overcome the suppression of mainstream gas to reach the wall surface, but not enough to penetrate into the mainstream gas. 4.1.2. Effects of the hole pitch To study the effect of the hole pitch, the spanwise average film cooling effectiveness is re-examined under different blowing ratios (Figs. 16–19). The experimental results show that the hole pitch has a significant effect on the spanwise average film cooling effectiveness at all blowing ratios. In general, when the blowing ratio is constant, the spanwise average effectiveness has a decreasing trend with the increase of the hole pitch, which is consistent with the experimental results given by Liu et al. [11] and Bogard et al. [13] on the leading edge under static conditions. Fig. 16 presents the spanwise average film cooling effectiveness for different hole pitches for the blowing ratio of M = 0.5. The p = 2.5d case provides the highest level of the spanwise average film cooling effectiveness in the regions of −4.3 < x/d < −2.5 and −1 < x/d < 3.75. The p = 5d case provides the lowest level of the spanwise average film cooling effectiveness in the region of −4.3 < x/d < 2. And the p = 3.75d case provides the highest level of the spanwise average film cooling effectiveness in the region of −2.5 < x/d < −1. Fig. 17 presents the spanwise average film cooling effectiveness for different hole pitches for the blowing ratio of M = 1.0. The p = 2.5d case provides the highest level of the spanwise average film cooling effectiveness in the regions of −4.3 < x/d < −2 and −1 < x/d < 3.75. The p = 5d case provides the lowest level of the spanwise average film cooling effectiveness in the region of −4.3 < x/d < 2. The p = 3.75d case provides the highest level of the spanwise average film cooling effectiveness in the region

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of −2 < x/d < −1. In addition, the spanwise average film cooling effectiveness level provided by the p = 3.75d and p = 5d cases is relatively close in the region of 2 < x/d <3.75. We take the M = 1.5 case to discuss the effect of hole pitch in detail. And the spanwise average film cooling effectiveness for different hole pitches for the blowing ratio of M = 1.5 is presented in Fig. 18. The p = 2.5d case provides the highest level of the spanwise average film cooling effectiveness in the regions of −4.3 < x/d < −1.8 and −1.3 < x/d < 3.75. The p = 3.75d case provides the highest level of the spanwise average film cooling effectiveness in the region of −1.8 < x/d < −1.3. And the p = 5d case provides the lowest level of the spanwise average film cooling effectiveness in the regions of −4.3 < x/d < 1 and 3 < x/d <3.75. The spanwise average film cooling effectiveness level provided by the p = 3.75d and p = 5d cases is basically the same in the region of 1 < x/d < 3. As the hole pitch increases from p = 2.5d to p = 5d, these regions between the coolant jets downstream of the film holes experience the largest impact due to there is a significant reduction in the film cooling effectiveness between the coolant jets when increasing the hole pitch. As shown in Fig. 10(c), Figs. 11(c) and 12(c), the level of the film cooling effectiveness shows a progressive degradation with an increase in the hole pitch in the leading edge region. Especially in the region between film cooling holes on the SS row, the film cooling effectiveness level obtained by the p = 3.75d and p = 5d cases has a large reduction in these regions between the film holes compared to the p = 2.5d case. When the blowing ratio keeps constant, the p = 2.5d case can provide a larger film coverage area than that of the p = 3.75d and p = 5d cases. This is because that both the total mass flow of the coolant and the number of film holes decrease as the hole pitch increases when the blowing ratio is constant. In addition, in the center row of the p = 2.5d case, the coolant jet ejected from the upper hole has a large pressing effect on the coolant jet ejected from the lower hole and changes its flow direction to the streamwise due to the hole pitch is small, which contributes to the coolant jet ejected from the PS and center rows and that between the center and SS rows. Fig. 19 presents the spanwise average film cooling effectiveness for different hole pitches for the blowing ratio of M = 2.0. The p = 2.5d case can provide the highest level of the spanwise average film cooling effectiveness in the entire regions of −4.3 < x/d < 3.75. The p = 5d case provides the lowest level of the spanwise average film cooling effectiveness in the region of −4.3 < x/d < 0.5. The spanwise average film cooling effectiveness level provided by the p = 3.75d and p = 5d cases is basically the same in the region of 0.5 < x/d < 2. The p = 3.75d case provides the lowest level of the spanwise average film cooling effectiveness in the region of 2 < x/d < 3.75. 4.2. Area average film cooling effectiveness To better analyze the effects of the blowing ratio and hole pitch, the average film cooling effectiveness on the measurement area for p = 2.5d, p = 3.75d and p = 5d with blowing ratios varying from 0.5 to 2.0 is listed in Table. 3. For all hole pitch cases, the effect of the blowing ratio on the film cooling performance is uniform, and the area average film cooling effectiveness increases monotonously with an increase in the blowing ratio.

Table 3 Average film cooling effectiveness on the measurement area. Item

M = 0.5

M = 1.0

M = 1.5

M = 2.0

p = 2.5d p = 3.75d p = 5d

0.1466 0.0861 0.0717

0.2281 0.1083 0.1000

0.2811 0.1402 0.1269

0.3542 0.1578 0.1422

Fig. 20. The effect of coolant mass flow rate on the area average film cooling effectiveness under different hole pitch.

For all blowing ratio cases, the value of the area average film cooling effectiveness decreases monotonously with an increase in the hole pitch. When the hole pitch increases from p = 2.5d to p = 5d, a 100% increase, the value of the area film cooling effectiveness is reduced by 51.1%, 56.2%, 54.9% and 59.9% at M = 0.5, 1.0, 1.5 and 2.0, respectively. Thus, it can be seen that the reduction is not always linear i.e. doubling the film hole pitch does not necessarily halve the value of the area average film cooling effectiveness, which is consistent with the experimental results given by Bashir et al. [36] on a flat plate using the PSP technique. This phenomenon also shows that the interaction between the coolant jets plays a very important role in the film cooling effectiveness. And when the hole pitch increases from p = 2.5d to p = 3.75d, a 50% increase, the value of the area film cooling effectiveness is reduced by 41.3%, 52.5%, 50.1% and 55.4% at M = 0.5, 1.0, 1.5 and 2.0, respectively. We can see that as the hole pitch increases from p = 2.5d to p = 3.75d, and then to p = 5d, the largest reduction occurs at the high blowing ratio of M = 2.0. Therefore, the hole pitch effect is more significant at the high blowing ratio of M = 2.0. For all experimental results presented so far, the effect of the hole pitch on the film cooling effectiveness has been analyzed under the same blowing ratio conditions. However, the total mass flow rate of the coolant also decreases with an increase in the hole pitch under the same blowing ratio conditions. Below we will analyze the effect of the hole pitch on the area average film cooling effectiveness when the total mass flow rate of the coolant is constant. And the effect of the coolant mass flow rate on the average film cooling effectiveness on the measurement area under different hole pitch is presented in Fig. 20. First, for all hole pitch cases, the area average film cooling effectiveness increases with an increase in the mass flow rate. When the coolant jet mass flow rate is within 0.21 g/s and 0.52 g/s, the p = 2.5d case provides a larger area average film cooling effectiveness value than the p = 3.75d and p = 5d cases. This is because the coolant jet exit momentum of each film hole in the case of p = 2.5 is small when the coolant jet mass flow rate is constant, which makes the film easier to adhere to the wall surface. And in the center row of the p = 2.5d case, the coolant jet ejected from the upper hole has a large pressing effect on the coolant jet ejected from the lower hole and changes its flow direction to the streamwise because the small hole pitch, which helps the coolant jet ejected from the center row to cover a large area between the PS and center rows and that between the center and SS rows. The

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area film cooling effectiveness values obtained by the hole pitches p = 3.75 d and p = 5d are relatively close, but both are much lower than those obtain by the p = 2.5d case. Compared to the p = 2.5d case, although the coolant jet exit momentum of each film hole is larger for both p = 3.75d and p = 5d cases when the coolant jet mass flow rate is constant, the proportion of the area covered by the film is small and the area between the film holes is not well protected. Moreover, the coolant jet ejected from the center row has a small pressing effect on the coolant jet ejected from the PS and SS rows because of the hole pitch is large. 5. Conclusions Film cooling performance were investigated experimentally on the leading edge region of a rotating twist blade in a one-stage turbine as the film hole pitch was varied from p = 2.5d to p = 5d using the TLC technique. All experiments were carried out with the mainstream Reynolds number Re = 6.34 × 104 and the blowing ratio M ranging from 0.5 to 2.0 at a constant rotating speed of 574 r/min. The coolant-to-mainstream density ratio was maintained at 1.56 with CO2 serving as coolant. The following conclusions can be made based on the experimental results: (1) Regardless of the hole pitch, the spanwise average film cooling effectiveness increases monotonously with the increase of blowing ratio on the leading edge region. (2) For all hole pitch cases, the spanwise average film cooling effectiveness value obtained in the region of −4.3 < x/d < 0 is higher than that obtained in the region of 0 < x/d < 3.75 on the leading edge region at each blowing ratio. And this phenomenon is more obvious for p = 3.75 d and 5d cases. When the bowing ratio keeps constant, the difference between the spanwise average film cooling effectiveness value obtained in the region of −4.3 < x/d < 0 and the region of 0 < x/d < 3.75 has a tendency to decrease as the hole pitch increases. (3) For all blowing ratio cases, the spanwise average effectiveness has a decreasing trend with the increase of the hole pitch. When M = 0.5, the p = 2.5 d case yields the highest spanwise average film cooling effectiveness in the regions of −4.3 < x/d < −2.5 and −1 < x/d <3.75 and the p = 3.75 d case yields the highest spanwise average film cooling effectiveness in the region of −2.5 < x/d < −1. When M = 1.0, the p = 2.5 d case yields the highest spanwise average film cooling effectiveness in the regions of −4.3 < x/d < −2 and −1 < x/d <3.75 and the p = 3.75 d case yields the highest spanwise average film cooling effectiveness in the region of −2 < x/d < −1. When M = 1.5, the p = 2.5 d case yields the highest spanwise average film cooling effectiveness in the regions of −4.3 < x/d < −1.8 and −1.3 < x/d <3.75 and the p = 3.75 d case yields the highest spanwise average film cooling effectiveness in the region of −1.8 < x/d < −1.3. When M = 2.0, the p = 2.5 d case yields the highest spanwise average film cooling effectiveness in the entire region. (4) For all hole pitch cases, the area average film cooling effectiveness increases monotonously as the blowing ratio increases. For all blowing ratio cases, it decreases monotonously as the hole pitch increases. However, the reduction is not always linear to the hole pitch change. The effect of the hole pitch on the area average film cooling effectiveness is more significant at the high blowing ratio of M = 2.0. (5) When the coolant jet mass flow rate is constant, the p = 2.5d case provides the highest level of the area average film cooling effectiveness. Declaration of Competing Interest None.

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CRediT authorship contribution statement Feng Han: Formal analysis, Writing - review & editing, Writing - original draft. Hong Guo: Writing - review & editing. Xiao-feng Ding: Writing - review & editing. Da-wei Zhang: Formal analysis. Hai-wang Li: Formal analysis, Funding acquisition. Acknowledgements The present work is financially supported by the National Natural Science Foundation of China (No. 51906008, No. 51822602) and the Fundamental Research Funds for the Central Universities (No. YWF-19-BJ-J-293), and National Science and Technology Major Project (2017-III-0 0 03-0 027). References [1] R.J. Goldstein, Film cooling, Adv. Heat Transf. 7 (1971) 321–379. [2] J.C. Han, Dutta, S. Ekkad, S. Gas, Turbine Heat Transfer and Cooling Technology, 2nd ed., CRC Press, Boca Raton, FL, 2012. [3] S.V. Ekkad, J.C. Han, H Du, Detailed film cooling measurements on a cylindrical leading edge model: effect of free-stream turbulence and coolant density, J. Turbomach. 120 (4) (1997) 799–807. [4] M.W. Y Cruse, U.M. Yuki, D.G Bogard, Investigation of various parametric influences on leading edge film cooling, in: Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, American Society of Mechanical Engineers Digital Collection, 1997. [5] C.A. Martin, K.A Thole, A cfd benchmark study: leading edge film-cooling with compound angle injection, in: Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, American Society of Mechanical Engineers Digital Collection, 1997. [6] S. Thakur, J. Wright, W Shyy, Computation of a leading–edge film cooling flow over an experimental geometry., in: Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, American Society of Mechanical Engineers Digital Collection, 1997. [7] A. Chernobrovkin, B Lakshminarayana, Numerical simulation and aerothermal physics of leading edge film cooling, in: Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 213, 1999, pp. 103–118. [8] Y.L. Lin, M.A. Stephens, T.I.P Shih, Computation of leading-edge film cooling with injection through rows of compound-angle holes, in: Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, American Society of Mechanical Engineers, 1997 V0 03T09A060-V0 03T09A060. [9] S. Ou, R.B Rivir, leading edge film cooling heat transfer with high free stream turbulence using a transient liquid crystal image method, Int. J. Heat Fluid Flow 22 (6) (2001) 614–623. [10] Y.J. Kim, S.M Kim, Influence of shaped injection holes on turbine blade leading edge film cooling, Int. J. Heat Mass Transf. 47 (47) (2004) 245–256. [11] C. Liu, H. Zhu, Z. Zhang, et al., Experimental investigation on the leading edge film cooling of cylindrical and laid-back holes with different hole pitches, Int. J. Heat Mass Transf. 55 (23–24) (2012) 6832–6845. [12] C.L. Liu, H.R. Zhu, X. Zhang, et al., Experimental investigation on the leading edge film cooling of cylindrical and laid-back holes with different radial angles, Int. J. Heat Mass Transf. 71 (4) (2014) 615–625. [13] T.E. Dyson, D.G. Bogard, J.D. Piggush, Overall effectiveness for a film cooled turbine blade leading edge with varying hole pitch, J. Turbomach. 135 (3) (2013) 031011. [14] S.J. Li, S.F. Yang, J.C Han, Effect of coolant density on leading edge showerhead film cooling using the pressure sensitive paint measurement technique, J. Turbomach. 136 (5) (2014) 051011. [15] N.H.K. Chowdhury, S.A. Qureshi, M. Zhang, et al., Influence of turbine blade leading edge shape on film cooling with cylindrical holes, Int. J. Heat Mass Transf. 115 (2017) 895–908. [16] W.J. Gao, Z.F. Yue, L. Li, et al., Numerical simulation on film cooling with compound angle of blade leading edge model for gas turbine, Int. J. Heat Mass Transf. 115 (2017) 839–855. [17] R.P. Dring, M.F. Blair, H.D Joslyn, An experimental investigation of film cooling on a turbine rotor blade, J. Eng. Gas Turbines Power 102 (1) (1980) 81–88. [18] K. Takeishi, S. Aoki, T. Sato, et al., Film cooling on a gas turbine rotor blade, J. Turbomach. 114 (4) (1992) 828–834. [19] J. Ahn, M.T. Schobeiri, J.C. Han, Film cooling effectiveness on the leading edge region of a rotating turbine blade with two rows of film cooling holes using pressure sensitive paint, J. Heat Transf. 128 (9) (2006) 879–888. [20] J. Ahn, M.T. Schobeiri, J.C. Han, Effect of rotation on leading edge region film cooling of a gas turbine blade with three rows of film cooling holes, Int. J. Heat Mass Transf. 50 (1) (2007) 15–25. [21] G. Li, J. Zhu, H. Deng, et al., Experimental investigation of rotating film cooling performance in a low speed 1.5-stage turbine, Int. J. Heat Mass Transf. 61 (6) (2013) 18–27. [22] G. Li, J. Zhu, K. Wang, et al., Film cooling performance in a low speed 1.5-stage turbine: effects of mainstream Reynolds number and turbulence, Heat Mass Transf. 51 (6) (2015) 795–805.

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