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Experimental investigation on the effects of rotation and the blowing ratio on the leading-edge film cooling of a twist turbine blade
International Journal of Heat and Mass Transfer 129 (2019) 47–58
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Experimental investigation on the effects of rotation and the blowing ratio on the leading-edge film cooling of a twist turbine blade Hai-wang Li, Feng Han, Yi-wen Ma, Hai-chao Wang, Zhi-yu Zhou, Zhi Tao ⇑ National Key Laboratory of Science and Technology on Aero Engines Aero-thermodynamics, The Collaborative Innovation Middle for Advanced Aero-Engine of China, School of Energy and Power Engineering, Beihang University, Beijing 100191, China
a r t i c l e
i n f o
Article history: Received 22 December 2017 Received in revised form 18 August 2018 Accepted 2 September 2018
Keywords: Film cooling Leading edge Rotating blade Effectiveness Blowing ratio
a b s t r a c t An experimental investigation has been performed to investigate the effects of the rotation and blowing ratio on the film cooling effectiveness distributions of the leading-edge regions of a twist gas turbine blade using a thermochromic liquid crystal (TLC) technique. The experiments were carried out at three rotating speeds, including 400 rpm (positive incidence angle), 550 rpm (zero incidence angle), and 700 rpm (negative incidence angle). The averaged blowing ratio ranged from 0.5 to 2.0. CO2 was used as the coolant to ensure that the coolant-to-mainstream ratio was equal to 1.56. The Reynolds number, based on the mainstream velocity of the turbine outlet and the rotor blade chord length, was 6.08 104. The effects of the rotating speed and the blowing ratio were analyzed based on the film cooling effectiveness distribution. The results show that rotating speed plays an indispensable role in determining the film cooling effectiveness of distributions on the leading edge. The position of the stagnation line moves from the pressure side (PS) to the suction side (SS) via an increase in rotating speed. Under the same blowing ratio, the area-averaged film cooling effectiveness increases monotonously with an increase in rotating speed. Under the same rotating speed, the area-averaged film cooling effectiveness increases with the increase in blowing ratio. More details about the effects of the rotation speed and blowing ratio on the spanwise averaged film cooling effectiveness of the leading-edge region are shown in this study. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction In the design of the modern gas turbine engine, the inlet temperature of the turbine has been increased continuously to obtain a higher thermal efficiency. However, the higher inlet temperature exceeds the melting point of the currently used heat resistant alloys, which can greatly reduce both the reliability and the lifetime of the turbine. Therefore, a variety of cooling techniques are employed to ensure that the turbine operating temperature remains in a safe range. Film cooling, an efficient cooling technique, has been widely accepted as a method of preventing the turbine components from experiencing high-temperature thermal deterioration. In this technique, a relatively cooler coolant penetrates the film hole or gap in the end face of the turbine blade surface and forms a shielded film between the turbine components and the hot temperature gases. Over the past 5 decades, a considerable number of researchers have sought a deeper understanding of the physical process of film cooling to optimize a design configuration that can achieve more efficient protection with less cooling ⇑ Corresponding author. E-mail address: [email protected] (Z. Tao). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.005 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
gas. The various aspects of the heat exchange mechanism and the cooling process of the turbine blade were described by Han et al. [1]. The leading-edge region of the turbine blade often withstands higher heat loads than any part of the blade surface due to the highest heat-transfer rate. Many investigations into the film cooling process of the leading edge of a turbine blade have been carried out with the blade in a stationary state. A detailed study of the heat transfer characteristics and film cooling effectiveness on a circular leading-edge model was performed by Mick and Mayle [2]. Those researchers reported that the maximum values of the heat exchange coefficient and film effectiveness do not occur in the same region. More recently, Cruse et al. [3] analyzed the effect of a stagnation line position on the adiabatic effectiveness of the film cooling of a leading-edge model. The results from their experiments showed that the stagnation line position is a very important factor in changing the cooling flow direction. A thermochromic liquid crystal (TLC) technique was used by Ekkad et al. [4] to study the effects of mainstream turbulence and coolant density on the effectiveness of film distribution over a leading-edge test model. The mainstream Reynolds number was Re = 1.009 105 and the blowing ratio was maintained at 0.4, 0.8 and 1.2. Their results
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Nomenclature C d DR M Ma Re p X T v s R k
blade chord length (mm) film hole diameter (mm) density ratio, qc =qg blowing ratio, M ¼ qc mc =qg mg Mach number (Ma ¼ v =s) Reynolds number, Re ¼ qg mout C=l hole spacing in the spanwise direction (mm) distance from the stagnation line (mm) temperature (K) velocity (m/s) pffiffiffiffiffiffiffiffiffi sound velocity (m/s) (s ¼ kRT ) gas constant [J/(kgK)] specific heat ratio
Abbreviations TLC thermochromic liquid crystal RGB Pixel Red, Green and Blue values HSV hue, saturation, value PS pressure side
showed that film effectiveness decreases as mainstream turbulence increases at a low blowing ratio. The highest film cooling effectiveness was measured at M = 0.4 and M = 0.8 for air and CO2 coolants, respectively. Ou et al. [5] conducted a film cooling investigation in which film effectiveness was measured on a circular leading-edge model. The mainstream Reynolds number varied from 3.0 104 to 6.0 104, and the blowing ratio was set to 1.0, 1.5, 2.0 and 2.5. Those researchers noted that under high turbulence conditions, the film effectiveness increases as the blowing ratio increases from 1.0 to 2.0 for both Reynolds numbers. Film effectiveness increases as the Reynolds number rises, except for the M = 2.5 case for higher turbulence. Kim and Kim [6] used infrared thermography technology to experimentally study the influence of five different structures of the film hole on the blade’s leading-edge film cooling characteristic. The blowing ratio was maintained at 0.7, 1.0, 1.3 and 1.7, respectively. Their results demonstrated that traditional cylindrical holes show the lowest level of film cooling performance. Those researchers also found that the shape of the holes can effectively improve the film cooling characteristic. Rozati and Tafti [7] studied the effect of the blowing ratio on leading-edge area film cooling via contributions from a large eddy simulation (LES) method. They reported that film cooling effectiveness decreases with an increase in the blowing ratio. Johnson et al. [8] studied the influence of a fluctuating flow on the film cooling characteristics of a turbine blade leading-edge model. They found the film cooling effectiveness with an oscillating stagnation line was degraded by as much as 25% compared to the effectiveness of a steady flow with the stagnation line aligned with the roe of holes at the leading edge. Li et al. [9] presented the film cooling characteristics of the leading edge using the Pressure Sensitive Paint (PSP) technique. Their results showed that shaped holes can provide better protection than cylindrical holes at a higher blowing ratio. Radial angle-shaped holes can provide the highest cooling effectiveness at a higher density ratio. In Chowdhury et al. [10], an experimental study was conducted in a wind-tunnel facility to consider the effect of turbine blade leading-edge shape on film cooling. 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 2.0R with an after body. That study’s results suggest that a 1.5R leading-edge model can provide better cooling performance than the other two models.
SS CCS SCS SCM
suction side camera control system strobe control system single-chip microcomputer
Greek symbols adiabatic film cooling effectiveness, g ¼ ðT g T w Þ=ðT g T c Þ q density (kg/m3) X rotating speed (rpm) l dynamic viscosity of the mainstream, kg/(ms)
g
Subscripts w adiabatic wall g mainstream c coolant out turbine outlet
Although there have been numerous studies of film cooling characteristics, most of those studies were conducted in the stationary state. Only a few useful results use experimental investigation to study film cooling under rotating conditions because of the great difficulty in conducting such experiments. The film cooling performance of a blade under rotating conditions was first studied by Dring et al. [11]. Film coolant was injected from cooling holes on both the pressure side (PS) and the suction side (SS). According to the obtained results, the radial component of the jet trajectory has an indispensable influence on the distribution of cooling effectiveness. On the SS, the radial deviation of the jet is small, which is consistent with a previous research result taken on a flat plate. An obvious radial deviation caused by the radial component of the main flow on the PS results in lower cooling effectiveness. A heat-mass transfer analogy was used by Takeishi et al. [12] to measure the film cooling effectiveness of a low-speed cascade under the stationary state and under the rotating conditions of the blade, in turn. Those researchers reported that film cooling effectiveness on the SS of the rotating blade is consistent with the result of the stationary cascade and is only 30% lower downstream. The cooling effectiveness of the PS is lower because of the radial flow of the concave surface and the strong mix between the coolant jets and mainstream fuel. Ahn et al. [13] presented an experimental investigation in which film cooling effectiveness was measured on the blade’s leading edge in a 3-stage turbine under rotating conditions via a PSP method. All their experiments were carried out at rotational speeds of 2400 (positive incidence angle), 2550 (zero incidence angle) and 3000 (negative incidence angle) r/min. Their results demonstrate that rotation is the most important factor in determining the distribution of film cooling effectiveness. Under the same blowing ratio, the average film effectiveness shows a decreasing trend with an increase in rotating speed. The average film effectiveness shows a decreasing trend with an increase in the blow ratio at X = 3000 r/min, whereas it is not sensitive to a blowing ratio at 2400 and 2550 r/min cases. Subsequent research by Ahn et al. [14] involved a further study on the blade’s leading edge under rotating conditions. They reported that the rotating speed changes the direction of the coolant traces. For the three rotational speed conditions, the average film effectiveness increases slightly as the blowing ratio rises. An experiment on the film cooling performance of the blade under rotating
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49
Fig. 1. Simplified schematic of the experimental apparatus.
conditions in a 1–1/2 stage turbine was provided by Tao et al. [15]. All those researchers’ tests were carried out at rotational speeds of 600, 667 and 702 r/min, and the blowing ratio changed in a range from 0.3 to 3.0. They noted that on the PS, film cooling efficiency shows an increasing trend with an increase in the blowing ratio and a decrease associated with an increase in the rotation number. On the SS, optimal film cooling efficiency is measured as the blowing ratio is set to the medium value, and both film coverage and efficiency decrease as the rotating number increases. Recently, Li et al. [16] reported the influence of the free stream turbulence and Reynolds number on the film cooling characteristics of a blade under rotating conditions in a 1–1/2 stage turbine. Both the experimental and the numerical simulations showed that the film cooling effectiveness level was improved when increasing the mainstream Reynolds number on both the PS and the SS. Based on the above discussions, there have been investigations with the TLC technique available on film cooling in rotating conditions, but those investigations have studied only the blades’ pressure and the SS, not the leading edge. Furthermore, there have been only two experimental investigations [13,14] of film cooling performance on the leading-edge region of a turbine blade under rotating conditions published in the literature, but the authors of those studies used the PSP technique measurement instead. And they used the straight blade instead of the three-dimensional twist blade. However, Zeng et al. [17] recently studied the effect of simplification on the film cooling performance of a turbine blade. They noted that simplification of the blade’s form from twist to straight has a noticeable effect on film cooling effectiveness and leads to a change in the stagnation line on the leading-edge region under rotating conditions. They also noted that the film cooling performance of the twist blade should be considered in the design. In addition, Yang et al. [18] used numerical simulations to predict the film cooling effectiveness on the leading edge of a rotating blade in a 1.5-stage turbine. They indicated the flow stagnation line on the leading edge of the present two-dimensional rotor blade tilted from the pressure side root region to the suction side tip region under rotating conditions. They pointed out that a welldesigned three-dimensional twisted blade will be able to provide more uniform film coolant coverage and improve the aerodynamic performance. The uniformity of the film cooling distribution on the leading-edge of a twisted turbine blade is directly related to the
position of the stagnation line. Therefore, it is necessary to study the effects of rotation and blowing ratio on the leading-edge film cooling of a twist turbine blade. Based on these studies, the objective of this paper is to apply a TLC technique to investigate the effects of the rotating speed and blowing ratio on the film cooling characteristics in the leading-edge region of a twist turbine blade in a low-speed 1-stage turbine. The Reynolds number based on the mainstream velocity of the turbine outlet and the rotor blade chord length was fixed at 6.08 104. CO2 worked as the coolant to achieve a coolant-to-mainstream density ratio of 1.56. All the measurements were made at three different rotating speeds: 400 rpm (positive incidence angle), 550 rpm (zero incidence angle), and 700 rpm (negative incidence angle). The average blowing ratio varies from 0.5 to 2.0. The influence of rotation and blowing ratio on film cooling effectiveness were studied. The experimental results will be beneficial to explain the heat transfer process with respect to leading-edge film cooling and will help design a more efficient turbine rotor blade structure. 2. Experimental apparatus Fig. 1 shows the simplified schematic of the experimental apparatus (8300 mm long 4400 mm wide 3000 mm high) used in conducting this investigation at the National Key Laboratory of Science and Technology of Aero-Engines in Beihang University in China. The experimental apparatus consists of two parts: the mainstream path (1red arrow) and the coolant flow path (blue arrow). The centrifugal blowing compressor used to supply the mainstream air is KF3-95 No6.3E and the maximum rotational speed is 2300 rpm. 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 was employed to heat the mainstream air temperature to the experimental request. The compressed and heated mainstream air passes through the inlet cone and honeycomb and enters the 1-stage turbine. A honeycomb is placed at the rear of the inlet cone to ensure axial uniformity in the mainstream air entering the annular channel with inner and outer diameters of 600 and 1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
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H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58 Table 1 1-stage turbine dimension. Item
1st Stator stage
1st Rotor stage
Stagger angle (degree) Tip diameter (mm) Hub diameter (mm) Chord length (mm) Height (mm) Blade No.
45 782 612 77 85 42
60 780 646 40 67 73
Fig. 2. The diagrammatic drawing of the turbine.
Fig. 4. The test blade. Fig. 3. The position of the test blade.
800 mm, respectively. The annular channel was equipped with four pitot tubes and two static pressure holes to measure the mainstream total and static upstream pressure in the turbine. Moreover, based on the values of the total and static pressures measured by a differential pressure transmitter (Type, Rosemount3051), the mainstream flow rate through the turbine component can be calculated. The 1stage turbine is a core component of the experiment apparatus. A helicoid collector is placed in the back of the turbine section to collect and stabilize the exhaust air, which is transported to the heater to complete the circle. The turbine shaft is connected through a synchronous belt with the rear end of a 22-kW dynamometer (Type, Z4132-1) that has a rated rotational speed of 3090 rpm. A torque meter (Type, TI-1) is connected to the dynamometer via a flexible coupler that is employed to output the turbine torque and power. The coolant flow, supplied by a dedicated gas cylinder, passes through valves, the filter, the air pressurizer tank, the flow meter and the insulation tube installed in the hollow shaft before entering the test blade. A labyrinth seal and a mechanical seal are adapted to prevent leakage of the mainstream and coolant parts, respectively. Three ranges of glass rotor flow-meters (Type, LZB-6, LZB-10 and LZB-15) were employed to meet the various requirements of coolant flow. The rotating speed of the 1-stage turbine is measured via a digital tachometer. The static and dynamic conversion of the electrical signal is accomplished via a carbon brush-copper collar system. As seen in Fig. 1, the data-acquisition system mounted on the extended shaft is used to transmit the temperature signal to the computer. Fig. 2 provides the diagrammatic drawing of the 1-stage turbine and Fig. 3 shows the position of the test blade. Table 1 lists the detailed dimensions of the 1-stage turbine. Forty-two blades with a staggered 45° angle were mounted on the first-stage stator and
73 blades with a staggered 60° angle were mounted on the firststage rotor. The stator blade tip diameter, hub diameter, height and chord length are 782 mm, 612 mm, 85 mm and 77 mm, respectively. The rotor blade tip diameter, hub diameter, height and chord length are 780 mm, 646 mm, 67 mm and 40 mm, respectively. The test blade model is composed of engineering plastic (Type, RGD525), which has a low thermal conductivity of 0.22 W/(mK), to reduce the effect of heat conduction. The other 114 blades were made of aluminum alloy. One hundred sixty-five film holes with a diameter (d) of 0.4 mm are arranged in the leading edge in three rows: the PS row, the stagnation line row and the SS row (See Fig. 4). Three rows of film holes are located at 30°, 0° and 30°, respectively, with respect to the stagnation line. The injection angle of the film cooling hole is 45° in the spanwise direction. Each row has 55 film holes, and the film holes in the stagnation line row are staggered with the film holes of the PS and SS rows. On the measurement area, each row has a hole-to-hole spacing (p) of 2.5-d in the spanwise direction. The coolant passes through the pipe installed in the hollow shaft into the gas-collecting chamber inside the blade, then flows out through the film holes on the blade’s leading edge.
3. Experimental methods 3.1. Image-acquisition system Fig. 5 shows a diagrammatic of the image-acquisition system that includes a computer, a camera control system (CCS), a singlechip microcomputer (Type, STM32F103RCT6) (SCM), a stator blade, a photoelectric sensor (Type, P+F OBT200-18GM60-E5), LED lights, a rotor blade and strobe control system (SCS) components. The SCM
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Real-time image
LED lights control signal
Exposure time control signal
CCS
SCS
Camera control signal Rotation signal
Ω
SCM Strobe control signal
Computer
Camera control system
Photoelectric sensor
LED lights
Single chip microcomputer Rotor blade
Stator blade
Strobe control system
Fig. 5. Image capture system.
is the core control unit to realize the image collection. The photoelectric sensor interface is wired to the SCM input terminal, and both the SCS and the CCS are wired to the SCM output terminal. The test blade leading-edge surface is coated with TLC and is illuminated by LED lights installed inside the casing. A CCD camera (Type, MU9Px-MH) with resolution of 2592 1944 pixels mounted on one of the stator blades is employed to capture temperature distributions. The dimensions of the CCD camera are 15 15 8.5 mm. A smooth transition on both sides of the lens should be ensured to reduce the interference of the lens to flow field as much as possible. The CCD camera is set to an external trigger mode and needs to control the exposure time. For instance, the CCD camera exposure time must be set to less than 15-ls to ensure that the captured images are clear when the rotating speed is 1400 rpm. By using the highspeed optical coupling isolation circuit, the CCS can achieve fast and precise control of the CCD camera exposure time. To receive the signal sent by the photoelectric sensor, the SCM input terminal is set to receive the interrupt signal triggered by a rising edge. The SCM interrupt handler is triggered by a signal from the photoelectric sensor when the test blade goes to the initial position. At the same time, the pulse signal is timed. After an appropriate delay, the SCM will output two different square wave pulse signals to the SCS and the CCS, respectively. The time delay of the square wave pulse signal is a key factor in determining whether the CCD camera can perform accurate positioning and operate in synchronization with the strobe lights when the turbine is in a high-speed rotation condition. Moreover, there is a one-to-one relationship between the
Interrupt signal The time of acquiring image
time delay of the square wave pulse signal and the rotating speed. To ensure that the CCD camera can perform an accurate positioning, the time delay of the square wave pulse signal changes with the change in rotating speed. The CCD camera exposure and the strobe starter can be precisely controlled according to the pulse width of the signal. Fig. 6 shows the timing diagram of the experimental control signal. Finally, the images taken by the CCD camera are transmitted to the computer to convert the RGB elements to HSV format. 3.2. Calibration of TLC A steady-state, hue-capturing method was applied in the current experiment for the temperature measurements. A wideband liquid crystal (Type, SPN/R30C20 W) ranging from 303 K to 323 K was used to measure the adiabatic wall temperature Taw. Before the calibration experiment, black paint and TLC were sprayed uniformly onto the leading-edge region using a spray gun. The temperature of the mainstream air changed from 303 K to 323 K as a result of the heater used during the calibration experiment, and the TLC color changed from red to green to blue. The CCD camera was used to capture and transfer the TLC images. And the CCD camera used for the calibration was the same one used in the formal experiments. Illumination angles, camera view angles and the shooting method were consistent with the subsequent formal experiments. To obtain the calibration curve between hue values and the temperature for the leading edge, as shown in Fig. 7, the TLC images were recorded and transmitted to the computer for each 1.0 K increase. 3.3. Film cooling effectiveness The film cooling effectiveness (g) is defined as follows
Strobe control signal
Camera control signal Fig. 6. Timing diagram of the experimental control signal.
g ¼ Tg Tw = Tg Tc
ð1Þ
where Tg and Tc are the abbreviation of the temperature of the mainstream air and coolant jet, respectively. Tw denotes the temperature of the measurement area on the leading-edge surface. In this paper, Tg and Tc were obtained via the T-type thermocouples with the accuracy of ±0.5 K mounted in the annular channel and
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thermocouple. Therefore, when Tw = 308 K, the uncertainty of the calculated adiabatic film cooling effectiveness was 6.9%. The uncertainty of the rotating speed measured by the intelligent tachometer (Type, YK-23) was ±1 rpm. The uncertainty of the mass flow rate and blowing ratio was ±3% and ±2%, respectively.
50
Temperature/°C
45
4. Discussion of results
40
In this work, the film cooling effectiveness level, spanwise averaged film cooling effectiveness and area-averaged film cooling effectiveness were experimentally analyzed to study the effects of the blowing ratio and rotating speed on the leading-edge region of a twist turbine blade in a 1-stage turbine.
35
30
0
20
40
60
80
100
120
140
160
180
200
Hue Fig. 7. Calibration for TLC.
the thermosensitive resistor (Type, TH-44034-40-T) with the accuracy of ±0.2 K installed in the blade cooling chamber, respectively. Table 2 lists the operating conditions of the current experiment. The mainstream mass flow rate measured by the differential pressure transmitter (Type, Rosemount3051) was 3.21 kg/s. The mainstream turbulence intensity was 5% and was obtained via a hotwire anemometer (Type, TSI1213-20 and IFA100). The turbine inlet and outlet velocity were 12.5 m/s and 26 m/s, respectively. The mainstream Reynolds number (Re), based on the turbine outlet velocity and the rotor blade chord length, was fixed at 6.08 104. All measurements were carried out at three different rotating speeds: 400, 550, and 700 rpm. The average blowing ratio varies from 0.5 to 2.0. The coolant-to-mainstream density ratio (DR) was chosen to be 1.56 with CO2 injection. 3.4. Uncertainty calculations An uncertainty analysis is needed to evaluate the effect of the experimental parameters on the measurement of the adiabatic film cooling effectiveness. According to the method suggested by Moffat [19], the uncertainty of the film cooling effectiveness could be calculated by
ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # " #2 u" 2 u T w T c 2 2 1 T g T w 2 2 t Dg ¼ DT g þ ðDT w Þ þ 2 2 ð DT c Þ T g T c T g T c T g T c
ð2Þ For the current experiment, Tg was kept at 315 K and Tc was kept at 298 K. The uncertainty of Tg and Tc were set to ±0.5 K and ±0.2 K, respectively. The uncertainly of Tw measured using a liquid crystal was controlled via ±0.5 K, the same as the T-type
Table 2 Operating conditions. Parameter
Value
Mainstream mass flow rate (kg/s) Mainstream turbulence intensity Turbine inlet velocity (m/s) Relative velocity at rotor blade inlet (m/s) Turbine outlet velocity (m/s) Re Mainstream Mach number at rotor blade inlet X (rpm) M DR Tg (K) Tc (K)
3.08 5% 12.5 20.4 26 6.08 104 0.059 400, 550, 700 0.5–2.0 1.56 315 298
4.1. Film cooling effectiveness level 4.1.1. Effects of the blowing ratio Figs. 8–10 show the effect of the blowing ratio on the film cooling effectiveness distributions under different rotating speeds. The horizontal ordinate s/smax represents the non-dimensional distance, where s is the distance measured along blade surface from the measurement area centerline and the negative value indicates the area from the measurement area centerline to the PS and the positive value indicates the area from the measurement area centerline to the SS. The vertical coordinate Y/H represents the nondimensional 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 general, despite the rotating speed, the film cooling effectiveness level increases monotonously with an increase in blowing ratio in the leadingedge region. As the rotating speed became constant, increasing the blowing ratio meant increasing the velocity of the coolant jets, which is beneficial to the coolant jet spread. We take the case of 550 rpm as an example. Fig. 9 shows the film cooling effectiveness distributions at 550 rpm with different blowing ratios. Under M = 0.5, there is almost no film protection in the middle of the leading edge, which may be due to the back-flow phenomenon occurs here. This is because the pressure gradient in the coolant gas chamber reduces along the spanwise direction. As the blowing ratio increases to 1.0, we can see that part of the coolant jets flow out from the upper half of the leading edge, which happens now and didn’t happen before. When the blowing ratio increases to 1.5, the film cooling effectiveness level significantly increases in the entire region and the film cooling effectiveness level, under larger blowing ratios of 1.5 and 2.0, are clearly higher than for the smaller blowing ratios. A film cooling effectiveness level under M = 2.0 shows little difference from the effectiveness level under M = 1.5. 4.1.2. Effects of rotating speed To understand and correctly interpret the experimental results for film cooling effectiveness, we need to investigate the following turbine aerodynamic aspects in advance (for detailed discussion see Schobeiri et al.) [20,21]. When the turbine is operated at the lower rpm condition, the mainstream flow impinges on the blade’s leading edge with a positive incidence angle and results in the stagnation line moving to the PS. Consequently, part of the coolant jets ejected from the PS row are deflected toward the SS. In the same way, when the turbine is operated at a high rpm condition, the main stream flow impinges on the blade’s leading edge with a negative incidence angle, causing the stagnation line to move to the SS and the coolant jets to be deflected toward the PS. This phenomenon is explained in Fig. 11. The experimental results for film cooling effectiveness at 400 rpm, 550 rpm and 700 rpm are presented in Figs. 8–10, respec-
H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58
Fig. 8. Film cooling effectiveness distributions for 400 rpm under different blowing ratios.
Fig. 9. Film cooling effectiveness distributions for 550 rpm under different blowing ratios.
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Fig. 10. Film cooling effectiveness distributions for 700 rpm under different blowing ratios.
Fig. 11. Flow path inside and outside the blade for (a) positive incidence angle, (b) zero incidence angle, and (c) negative incidence angle conditions [22].
tively. To study the effect of rotating speed, we take the case of M = 1.5 as an example [Fig. 8(c), Figs. 9(c) and 10(c)]. In general, based on the distributions of film cooling effectiveness, the stagnation line clearly moves from the PS to the leading edge, and then to the SS with an increase in rotating speed. At 400 rpm, the effectiveness level near the SS row is slightly higher than near the PS row. In this case, it seems that the stagnation line lies between the PS and the stagnation line rows. As a result, some of the coolant jets ejected from the PS row and the coolant traces ejected from the stagnation line row are deflected toward the SS of the blade. At 550 rpm, the stagnation line lies near the stagnation line row and the coolant jets are divided into the PS and the SS. Thus, the film coverage becomes the largest and most uniform over the entire region compared to the positive incidence angle and negative incidence angle conditions. At 700 rpm, the stagnation line lies on the
SS. Because the coolant jets are deflected toward the PS of the blade, the film cooling effectiveness level near the PS row is higher than that near the SS row. Thus, the highest level of film cooling effectiveness reaches 0.65 in the area between the PS and the stagnation line rows. Accordingly, the rotating speed is the most crucial factor in determining the distribution of film cooling effectiveness. 4.2. Spanwise averaged film cooling effectiveness 4.2.1. Effects of the blowing ratio In this work, the average blowing ratio was controlled at 0.5, 1.0, 1.5 and 2.0 at a constant rotating speed. Figs. 12–14 show the effects of the blowing ratio on spanwise average film cooling effectiveness under different rotation speeds. It should be pointed out that the coordinate X used to report results (see Figs. 8–10)
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0.60
M=0.5 M=1.0 M=1.5 M=2.0
0.55 0.50
η
0.45
0.55
0.45 0.40
0.35
0.35
η
0.40
0.30
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10 -4
-3
0.10
SS
PS
0.05
-2
-1
0
1
2
M=0.5 M=1.0 M=1.5 M=2.0
0.50
3
SS
PS
0.05 4
-4
-3
-2
-1
X/D
2
3
4
Fig. 13. Effect of the blowing ratio on the spanwise average film cooling effectiveness for 550 rpm.
0.60
M=0.5 M=1.0 M=1.5 M=2.0
0.55 0.50 0.45 0.40 0.35
η
appears to be the apparent coordinate related to the view angle of the camera and not the geometric distance. Therefore, we have fixed the coordinate X with certain geometric transformation to ensure that the pitch between the PS and middle rows is equal with that between the middle and SS rows in Figs. 12–18. The vertical coordinate g indicates the value of film cooling effectiveness. The horizontal coordinate X/D is the non-dimensional distance and X indicates the stream-wise distance from the stagnation line row. The vertical coordinate g indicates average film cooling effectiveness in the spanwise direction, which is calculated from the average value: 4.3 < X/D < 3.75. Note that the entire interval (4.3D, 3.75D) in the spanwise direction is the leading edge interval of our study. Three black arrows are used to indicate the position of the three rows of holes. For all blowing ratio cases, at a constant rotating speed, there are three clear peaks in the downstream of each row film hole caused by the high film cooling effectiveness in the downstream direction of the coolant jet outlet. The four hundred rpm (positive incidence angle) case is shown in Fig. 12. In general, average cooling effectiveness increases with an increase in the blowing ratio in the interval (4.3D, 1.5D). However, with the blowing ratio increasing to 2.0, there is an obvious decrease in the interval (1.5D, 3.75D) near the SS row, which means that the lift-off phenomena occur here, as shown in Fig. 11(a). The M = 1.5 case shows that the highest level of film cooling effectiveness is in the interval (1.5D, 3.75D) near the SS row. The five-hundred and fifty rpm (zero incidence angle) case is shown in Fig. 13. Average cooling effectiveness increases with an increase in the blowing ratio at the leading edge. The average cooling effectiveness in the interval (4.3D, 0D) is 0.21, 0.27, 0.31 and 0.35 at M = 0.5, 1.0, 1.5 and 2.0, respectively. And the average cooling effectiveness in the interval (0D, 3.75D) is 0.18, 0.26, 0.30 and 0.34 at M = 0.5, 1.0, 1.5 and 2.0, respectively. Therefore, for the zero incidence angle condition, at a constant blowing ratio, cooling effectiveness is higher on the PS than on the SS in the leadingedge region, which is consistent with the results found by Ahn et al. [13] and Zhang et al. [23]. Furthermore, both the peak positions near the PS and the SS rows show a tendency toward the stagnation line when the blowing ratio is between 0.5 and 2.0. This is caused by the coolant jet momentum. With the increase in blowing ratio, the momentum of the coolant jet increases and is gradually comparable to the momentum of the mainstream. Therefore, the coolant jet traces are better able to withstand the pressure of the mainstream and flow further along the coolant ejection
1
X/D
0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
4
X/D Fig. 14. Effect of the blowing ratio on the spanwise average film cooling effectiveness for 700 rpm.
0.60 0.55
400 rpm 550 rpm 700 rpm
0.50 0.45 0.40 0.35
η
Fig. 12. Effect of the blowing ratio on the spanwise average film cooling effectiveness for 400 rpm.
0
0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
4
X/D Fig. 15. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 0.5.
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H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58 0.60
400 rpm 550 rpm 700 rpm
0.55 0.50 0.45 0.40
η
0.35 0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
4
X/D Fig. 16. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 1.0.
0.60
400 rpm 550 rpm 700 rpm
0.55 0.50 0.45 0.40
η
0.35 0.30 0.25 0.20 0.15 0.10 -4
-3
4.3. Effects of rotating speed
SS
PS
0.05
-2
-1
0
1
2
3
4
X/D Fig. 17. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 1.5.
0.60
400 rpm 550 rpm 700 rpm
0.55 0.50 0.45
η
0.40 0.35 0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
3D) near the PS row is 0.28, 0.35, 0.40 and 0.45 at M = 0.5, 1.0, 1.5 and 2.0, respectively. The average cooling effectiveness in the interval (1D, 1D) near the stagnation line row is 0.20, 0.25, 0.29 and 0.31 at M = 0.5, 1.0, 1.5 and 2.0, respectively. And the average cooling effectiveness in the interval (2.75D, 3.75D) near the SS row is 0.26, 0.35, 0.41 and 0.43 at M = 0.5, 1.0, 1.5 and 2.0, respectively. In general, the increase rate of cooling effectiveness gradually decreases with a blowing ratio ranging from 0.5 to 2.0. One reason is that there is more intense mixing between the coolant jets and the mainstream at high blowing ratios, which is caused by the increased interaction. Therefore, the coolant jet traces decay faster along the direction of the coolant ejection than in the lower blowing ratio case. Another reason is that the lift-off phenomena occur at high blowing ratios. The seven hundred rpm (negative incidence angle) case is shown in Fig. 14. Our results show that the average cooling effectiveness increases with an increase in the blowing ratio, whereas a slight increase occurs when the blowing ratio exceeds 1.5. By comparing the film cooling effectiveness distribution in the interval (4.3D, 3D) on the PS row under the M = 1.0, 1.5 and 2.0 conditions, we can clearly see that the film cooling effectiveness values are almost at the same level. This is because of the stagnation line location and lift-off phenomena. Thus, the high rpm (negative incidence angle) condition and the stagnation line lies on the SS and the coolant jets from the stagnation line row and SS row shift to the PS to fill the spaces between the PS film cooling holes, which explains the higher level of cooling effectiveness on the PS row when the blowing ratio is 1.0. In addition, lift-off occurs when the blowing ratio increases to 1.5, which explains why the average film cooling effectiveness distributions are almost the same. In this case, the stagnation line lies near the SS row, and the coolant jets from the SS row film holes are suppressed by the mainstream flow. Therefore, the averaged film cooling effectiveness near the SS row is more insensitive to the blowing ratio than near the other rows.
4
X/D Fig. 18. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 2.0.
direction. According to the profile of average cooling effectiveness, all blowing ratio cases show similar behavior for cooling effectiveness. The average cooling effectiveness in the interval (4.3D,
To study the effect of rotating speed, spanwise averaged film cooling effectiveness is re-arranged under different blowing ratios (Figs. 15–18). In general, regardless of the blowing ratio, the averaged film cooling effectiveness increases with rotating speed ranging from 400 rpm to 700 rpm on the PS row. Cooling effectiveness on the stagnation line row is more insensitive to rotating speed than it is on the other rows. On the SS row, the 700-rpm case shows the lowest cooling effectiveness level at each blowing ratio. As mentioned above, different rotating speeds change the incidence angle and determine the direction of the coolant traces. As shown in Fig. 15, under M = 0.5, the averaged cooling effectiveness slightly increases with an increase in rotating speed near the PS row. It seems that the rotating speed does not change the averaged cooling effectiveness on the SS row, which is probably because of the back-flow phenomenon mentioned in the previous section. We take the moderate blowing ratio case with M = 1.0 to discuss the effect of rotating speed in detail. As shown in Fig. 16, the 400-rpm case shows the lowest cooling effectiveness level near the PS row. For the low rpm (positive incidence angle) condition, the stagnation line lies on the PS, which means that the coolant jets are ejected from the three-row flow to the SS. Consequently, the SS row benefits from the stagnation line and the PS row, which results in the highest cooling effectiveness level near the SS row. In the interval (4.3D, 3D) near the PS row, the difference in the average cooling effectiveness between the 400-rpm case and the 550rpm case is marginally within the experimental uncertainty of 6.9%. For the 550-rpm (zero incidence angle) case, the stagnation line lies on the stagnation line row, which means that the coolant
H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58
jets ejected from the stagnation line row flow to the PS and the SS, respectively. As a result, the PS row benefits from the stagnation line row, which explains the 550-rpm case that shows a higher cooling effectiveness level than the 400-rpm case in the vicinity of the PS row. The cooling effectiveness level on the SS row remains almost unchanged when the rotating speed increases from 400 rpm to 550 rpm. However, when compared to the 400-rpm case, the SS row does not benefit from the PS row and the benefit from the stagnation line row is also reduced for the 550-rpm case. This may be because the 550-rpm case can provide a more uniform film distribution on the SS row. The rotation speed increases to 700 rpm, where there is an obvious improvement in the cooling effectiveness near the PS row. In addition, average film cooling effectiveness increases 0.19 in the interval (4.3D, 3D) near the PS row compared to the 400-rpm case. For the high rpm (negative incidence angle) condition, the stagnation line lies on the SS and the coolant jets from the stagnation line row and the SS row shift to the PS row to fill the spaces between the PS film cooling holes. Consequently, the PS row benefits from the stagnation line and the SS rows, resulting in the highest cooling effectiveness level near the PS row. In contrast, a part of the coolant jet ejected from the SS row does not have enough momentum to overcome the suppression of the stagnation line, which explains why the 700 rpm shows the lowest cooling effectiveness level on the SS row. As shown in Fig. 17, as the rotating speed increases, the M = 1.5 experimental case shows a similar trend with the case of M = 1.0 in the entire region. As shown in Fig. 18, under M = 2.0, average cooling effectiveness increases with an increase in rotating speed near the PS row. In the interval (2.75D, 3.75D) near the SS row, the average cooling effectiveness is 0.34, 0.43 and 0.27 at 400 rpm, 550 rpm and 700 rpm, respectively. Therefore, the average cooling effectiveness near the SS row firstly increases then decreases with rotating speed ranging from 400 rpm to 700 rpm. On the SS row, the 400-rpm case shows the lowest cooling effectiveness level. This is likely because the coolant jets are ejected from the SS row lift-off and penetrates the mainstream.
4.4. Area-averaged film cooling effectiveness To better analyze the effects of the blowing ratio and rotating speed, Table 3 lists the averaged cooling effectiveness of the measurement area at Re = 6.08 104, with different rotating speeds and different blowing ratios. From Table 3, for all rotating speed cases, the value of the area-averaged film cooling effectiveness increases monotonically with the increase in the blowing ratio, which is consistent with the experimental results found by Ahn et al. [14]. For all blowing ratio cases, the value of the area-averaged film cooling effectiveness increases with the increase in rotating speed, which is consistent with the experimental result under the condition of M = 2.0 given by Ahn et al. [14]. As can be seen from Table 3, compared to the effect of bowling ratio, the rotating speed plays an indispensable role in determining film cooling effectiveness distributions on the leading edge. This is because the rotating speed can change the mainstream incidence angle to the leading edge and affect the film cooling flow path direction. However, Ahn’s
Table 3 Averaged cooling effectiveness on the measurement area. Item
M = 0.5
M = 1.0
M = 1.5
M = 2.0
400 rpm 550 rpm 700 rpm
0.1877 0.1970 0.2703
0.2726 0.2929 0.3447
0.3050 0.3339 0.3925
0.3177 0.3671 0.4116
57
investigation found that the averaged film cooling effectiveness on the area of interest first decreases and then increases with increased rotating speed for M = 0.5 and 1.0 cases. This may be related to the geometry of the turbine blade used in the experiments. The tests by Ahn et al. [14] were carried out on the leading edge of a straight blade, whereas a twist blade was used in this work. For the zero incidence angle condition, there is an inclination between the stagnation line and the centerline of the stagnation line row film holes for the straight blade case, whereas there is an overlap between the stagnation line and the centerline of the stagnation line row film holes for the twist blade case.
5. Conclusions The effects of rotating speed and blowing ratio on film cooling characteristics on the leading-edge region of a twist turbine blade have been experimentally investigated under rotating conditions in this paper. Experiments have been performed using a constant Reynolds number (6.08 104) with a rotating speed ranging from 400 to 700 rpm and a blowing ratio ranging from 0.5 to 2.0. CO2 worked as the coolant to maintain a coolant-to-mainstream DR of 1.56. The major conclusions of this study are as follows: (1) Rotating speed plays an indispensable role in determining film cooling effectiveness distributions on the leading edge. The position of the stagnation line moves from the PS to the SS when rotational speed changes from 400 to 700 rpm. (2) The film cooling effectiveness level increases monotonously with an increase in the blowing ratio in the leading-edge region, for any rotating speed. (3) In general, regardless of the blowing ratio, the spanwise averaged film cooling effectiveness increases with rotating speed ranging from 400 to 700 rpm on the PS row. In addition, the spanwise average film cooling effectiveness on the stagnation line row is insensitive to rotating speed when compared to the other rows. On the SS row, the 700-rpm case shows the lowest level of spanwise film cooling effectiveness at each blowing ratio, which might be linked to the shift of the stagnation line. (4) For all rotating speed cases, the value of the area-averaged film cooling effectiveness increases monotonically with the blowing ratio ranging from 0.5 to 2.0. For all blowing ratio cases, the value of the area-averaged film cooling effectiveness on the leading edge increases slightly with rotating speed when ranging from 400 to 700 rpm. Conflict of interest statement We declare that we have no conflict of interest. References [1] J.C. Han, S. Dutta, S.V. Ekkad, Gas turbine heat transfer and cooling technology, Epfl 9 (2014) 82. [2] W.J. Mick, R.E. Mayle, Stagnation film cooling and heat transfer, including its effect within the hole pattern, J. Turbomach. 110 (1) (1988) 66–72. [3] Michael W. Cruse, Ushio M. Yuki, David G. Bogard, Investigation of various parametric influences on leading edge film cooling, in: ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, 1997, pp. V003T09A058–V003T09A058. [4] 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) (1998) 799–807. [5] D. Lakehal, G.S. Theodoridis, W. Rodi, Three-dimensional flow and heat transfer calculations of film cooling at the leading edge of a symmetrical turbine blade model, Int. J. Heat Fluid Flow 22 (2) (2001) 113–122. [6] 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.
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[7] A. Rozati, D.K. Tafti, Effect of coolant–mainstream blowing ratio on leading edge film cooling flow and heat transfer – LES investigation, Int. J. Heat Fluid Flow 29 (4) (2008) 857–873. [8] R. Johnson, J. Maikell, D. Bogard et al. Experimental study of the effects of an oscillating approach flow on overall cooling performance of a simulated turbine blade leading edge, in: ASME Turbo Expo 2009: Power for Land, Sea, and Air., 2009, pp. 1009–1016. [9] 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. [10] 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. [11] 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. [12] K. Takeishi, S. Aoki, T. Sato, et al., Film cooling on a gas turbine rotor blade, J. Turbomach. 114 (4) (1992) 828–834. [13] J. Ahn, M.T. Schobeiri, J.C. Han, et al., 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 Transfer 128 (9) (2006) 879–888. [14] J. Ahn, M.T. Schobeiri, J.C. Han, et al., 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. [15] Z. Tao, G. Li, H. Deng, et al., Film cooling performance in a low-speed 1.5-stage turbine: effects of blowing ratio and rotation, J. Enhanced Heat Transfer 18 (5) (2011) 419–432.
[16] 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. [17] L. Zeng, P. Chen, X. Li, et al., Influence of simplifications of blade in gas turbine on film cooling performance, Appl. Therm. Eng 128 (5) (2018) 877–886. [18] H. Yang, H.C. Chen, J.C. Han, et al., Film-cooling prediction on rotor blade leading edge in 1–1/2 turbine stage, J. Thermophys. Heat Transfer 22 (2) (2015) 201–209. [19] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1) (1988) 3–17. [20] M.T. Schobeiri, J.L. Gilarranz, E.S. Johansen, Aerodynamic and performance studies of a three-stage high pressure research turbine with 3-D - blades, design point and off-design experimental investigations, in: ASME Turbo Expo 2000: Power for Land, Sea, and Air, 2000. [21] M.T. Schobeiri, A. Suryanarayanan, C. Jermann et al., A comparative aerodynamic and performance study of a three-stage high pressure turbine with 3-D bowed blades and cylindrical blades, in: ASME Turbo Expo 2004: Power for Land, Sea, and Air, 2004, pp. 1237–1246. [22] J. Ahn, M.T. Schobeiri, J.C. Han et al., Film cooling effectiveness on the leading edge of a rotating film-cooled blade using pressure sensitive paint, in: ASME Turbo Expo 2005: Power for Land, Sea, and Air, 2005, pp. 375–384. [23] C.X.-Z. Zhang, I. Hassan, Rotational effects on film cooling performance, Int. J. Numerical Methods Heats Fluid Flow 22 (5) (2012) 622–640.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation on the effects of rotation and the blowing ratio on the leading-edge film cooling of a twist turbine blade Hai-wang Li, Feng Han, Yi-wen Ma, Hai-chao Wang, Zhi-yu Zhou, Zhi Tao ⇑ National Key Laboratory of Science and Technology on Aero Engines Aero-thermodynamics, The Collaborative Innovation Middle for Advanced Aero-Engine of China, School of Energy and Power Engineering, Beihang University, Beijing 100191, China
a r t i c l e
i n f o
Article history: Received 22 December 2017 Received in revised form 18 August 2018 Accepted 2 September 2018
Keywords: Film cooling Leading edge Rotating blade Effectiveness Blowing ratio
a b s t r a c t An experimental investigation has been performed to investigate the effects of the rotation and blowing ratio on the film cooling effectiveness distributions of the leading-edge regions of a twist gas turbine blade using a thermochromic liquid crystal (TLC) technique. The experiments were carried out at three rotating speeds, including 400 rpm (positive incidence angle), 550 rpm (zero incidence angle), and 700 rpm (negative incidence angle). The averaged blowing ratio ranged from 0.5 to 2.0. CO2 was used as the coolant to ensure that the coolant-to-mainstream ratio was equal to 1.56. The Reynolds number, based on the mainstream velocity of the turbine outlet and the rotor blade chord length, was 6.08 104. The effects of the rotating speed and the blowing ratio were analyzed based on the film cooling effectiveness distribution. The results show that rotating speed plays an indispensable role in determining the film cooling effectiveness of distributions on the leading edge. The position of the stagnation line moves from the pressure side (PS) to the suction side (SS) via an increase in rotating speed. Under the same blowing ratio, the area-averaged film cooling effectiveness increases monotonously with an increase in rotating speed. Under the same rotating speed, the area-averaged film cooling effectiveness increases with the increase in blowing ratio. More details about the effects of the rotation speed and blowing ratio on the spanwise averaged film cooling effectiveness of the leading-edge region are shown in this study. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction In the design of the modern gas turbine engine, the inlet temperature of the turbine has been increased continuously to obtain a higher thermal efficiency. However, the higher inlet temperature exceeds the melting point of the currently used heat resistant alloys, which can greatly reduce both the reliability and the lifetime of the turbine. Therefore, a variety of cooling techniques are employed to ensure that the turbine operating temperature remains in a safe range. Film cooling, an efficient cooling technique, has been widely accepted as a method of preventing the turbine components from experiencing high-temperature thermal deterioration. In this technique, a relatively cooler coolant penetrates the film hole or gap in the end face of the turbine blade surface and forms a shielded film between the turbine components and the hot temperature gases. Over the past 5 decades, a considerable number of researchers have sought a deeper understanding of the physical process of film cooling to optimize a design configuration that can achieve more efficient protection with less cooling ⇑ Corresponding author. E-mail address: [email protected] (Z. Tao). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.005 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
gas. The various aspects of the heat exchange mechanism and the cooling process of the turbine blade were described by Han et al. [1]. The leading-edge region of the turbine blade often withstands higher heat loads than any part of the blade surface due to the highest heat-transfer rate. Many investigations into the film cooling process of the leading edge of a turbine blade have been carried out with the blade in a stationary state. A detailed study of the heat transfer characteristics and film cooling effectiveness on a circular leading-edge model was performed by Mick and Mayle [2]. Those researchers reported that the maximum values of the heat exchange coefficient and film effectiveness do not occur in the same region. More recently, Cruse et al. [3] analyzed the effect of a stagnation line position on the adiabatic effectiveness of the film cooling of a leading-edge model. The results from their experiments showed that the stagnation line position is a very important factor in changing the cooling flow direction. A thermochromic liquid crystal (TLC) technique was used by Ekkad et al. [4] to study the effects of mainstream turbulence and coolant density on the effectiveness of film distribution over a leading-edge test model. The mainstream Reynolds number was Re = 1.009 105 and the blowing ratio was maintained at 0.4, 0.8 and 1.2. Their results
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Nomenclature C d DR M Ma Re p X T v s R k
blade chord length (mm) film hole diameter (mm) density ratio, qc =qg blowing ratio, M ¼ qc mc =qg mg Mach number (Ma ¼ v =s) Reynolds number, Re ¼ qg mout C=l hole spacing in the spanwise direction (mm) distance from the stagnation line (mm) temperature (K) velocity (m/s) pffiffiffiffiffiffiffiffiffi sound velocity (m/s) (s ¼ kRT ) gas constant [J/(kgK)] specific heat ratio
Abbreviations TLC thermochromic liquid crystal RGB Pixel Red, Green and Blue values HSV hue, saturation, value PS pressure side
showed that film effectiveness decreases as mainstream turbulence increases at a low blowing ratio. The highest film cooling effectiveness was measured at M = 0.4 and M = 0.8 for air and CO2 coolants, respectively. Ou et al. [5] conducted a film cooling investigation in which film effectiveness was measured on a circular leading-edge model. The mainstream Reynolds number varied from 3.0 104 to 6.0 104, and the blowing ratio was set to 1.0, 1.5, 2.0 and 2.5. Those researchers noted that under high turbulence conditions, the film effectiveness increases as the blowing ratio increases from 1.0 to 2.0 for both Reynolds numbers. Film effectiveness increases as the Reynolds number rises, except for the M = 2.5 case for higher turbulence. Kim and Kim [6] used infrared thermography technology to experimentally study the influence of five different structures of the film hole on the blade’s leading-edge film cooling characteristic. The blowing ratio was maintained at 0.7, 1.0, 1.3 and 1.7, respectively. Their results demonstrated that traditional cylindrical holes show the lowest level of film cooling performance. Those researchers also found that the shape of the holes can effectively improve the film cooling characteristic. Rozati and Tafti [7] studied the effect of the blowing ratio on leading-edge area film cooling via contributions from a large eddy simulation (LES) method. They reported that film cooling effectiveness decreases with an increase in the blowing ratio. Johnson et al. [8] studied the influence of a fluctuating flow on the film cooling characteristics of a turbine blade leading-edge model. They found the film cooling effectiveness with an oscillating stagnation line was degraded by as much as 25% compared to the effectiveness of a steady flow with the stagnation line aligned with the roe of holes at the leading edge. Li et al. [9] presented the film cooling characteristics of the leading edge using the Pressure Sensitive Paint (PSP) technique. Their results showed that shaped holes can provide better protection than cylindrical holes at a higher blowing ratio. Radial angle-shaped holes can provide the highest cooling effectiveness at a higher density ratio. In Chowdhury et al. [10], an experimental study was conducted in a wind-tunnel facility to consider the effect of turbine blade leading-edge shape on film cooling. 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 2.0R with an after body. That study’s results suggest that a 1.5R leading-edge model can provide better cooling performance than the other two models.
SS CCS SCS SCM
suction side camera control system strobe control system single-chip microcomputer
Greek symbols adiabatic film cooling effectiveness, g ¼ ðT g T w Þ=ðT g T c Þ q density (kg/m3) X rotating speed (rpm) l dynamic viscosity of the mainstream, kg/(ms)
g
Subscripts w adiabatic wall g mainstream c coolant out turbine outlet
Although there have been numerous studies of film cooling characteristics, most of those studies were conducted in the stationary state. Only a few useful results use experimental investigation to study film cooling under rotating conditions because of the great difficulty in conducting such experiments. The film cooling performance of a blade under rotating conditions was first studied by Dring et al. [11]. Film coolant was injected from cooling holes on both the pressure side (PS) and the suction side (SS). According to the obtained results, the radial component of the jet trajectory has an indispensable influence on the distribution of cooling effectiveness. On the SS, the radial deviation of the jet is small, which is consistent with a previous research result taken on a flat plate. An obvious radial deviation caused by the radial component of the main flow on the PS results in lower cooling effectiveness. A heat-mass transfer analogy was used by Takeishi et al. [12] to measure the film cooling effectiveness of a low-speed cascade under the stationary state and under the rotating conditions of the blade, in turn. Those researchers reported that film cooling effectiveness on the SS of the rotating blade is consistent with the result of the stationary cascade and is only 30% lower downstream. The cooling effectiveness of the PS is lower because of the radial flow of the concave surface and the strong mix between the coolant jets and mainstream fuel. Ahn et al. [13] presented an experimental investigation in which film cooling effectiveness was measured on the blade’s leading edge in a 3-stage turbine under rotating conditions via a PSP method. All their experiments were carried out at rotational speeds of 2400 (positive incidence angle), 2550 (zero incidence angle) and 3000 (negative incidence angle) r/min. Their results demonstrate that rotation is the most important factor in determining the distribution of film cooling effectiveness. Under the same blowing ratio, the average film effectiveness shows a decreasing trend with an increase in rotating speed. The average film effectiveness shows a decreasing trend with an increase in the blow ratio at X = 3000 r/min, whereas it is not sensitive to a blowing ratio at 2400 and 2550 r/min cases. Subsequent research by Ahn et al. [14] involved a further study on the blade’s leading edge under rotating conditions. They reported that the rotating speed changes the direction of the coolant traces. For the three rotational speed conditions, the average film effectiveness increases slightly as the blowing ratio rises. An experiment on the film cooling performance of the blade under rotating
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49
Fig. 1. Simplified schematic of the experimental apparatus.
conditions in a 1–1/2 stage turbine was provided by Tao et al. [15]. All those researchers’ tests were carried out at rotational speeds of 600, 667 and 702 r/min, and the blowing ratio changed in a range from 0.3 to 3.0. They noted that on the PS, film cooling efficiency shows an increasing trend with an increase in the blowing ratio and a decrease associated with an increase in the rotation number. On the SS, optimal film cooling efficiency is measured as the blowing ratio is set to the medium value, and both film coverage and efficiency decrease as the rotating number increases. Recently, Li et al. [16] reported the influence of the free stream turbulence and Reynolds number on the film cooling characteristics of a blade under rotating conditions in a 1–1/2 stage turbine. Both the experimental and the numerical simulations showed that the film cooling effectiveness level was improved when increasing the mainstream Reynolds number on both the PS and the SS. Based on the above discussions, there have been investigations with the TLC technique available on film cooling in rotating conditions, but those investigations have studied only the blades’ pressure and the SS, not the leading edge. Furthermore, there have been only two experimental investigations [13,14] of film cooling performance on the leading-edge region of a turbine blade under rotating conditions published in the literature, but the authors of those studies used the PSP technique measurement instead. And they used the straight blade instead of the three-dimensional twist blade. However, Zeng et al. [17] recently studied the effect of simplification on the film cooling performance of a turbine blade. They noted that simplification of the blade’s form from twist to straight has a noticeable effect on film cooling effectiveness and leads to a change in the stagnation line on the leading-edge region under rotating conditions. They also noted that the film cooling performance of the twist blade should be considered in the design. In addition, Yang et al. [18] used numerical simulations to predict the film cooling effectiveness on the leading edge of a rotating blade in a 1.5-stage turbine. They indicated the flow stagnation line on the leading edge of the present two-dimensional rotor blade tilted from the pressure side root region to the suction side tip region under rotating conditions. They pointed out that a welldesigned three-dimensional twisted blade will be able to provide more uniform film coolant coverage and improve the aerodynamic performance. The uniformity of the film cooling distribution on the leading-edge of a twisted turbine blade is directly related to the
position of the stagnation line. Therefore, it is necessary to study the effects of rotation and blowing ratio on the leading-edge film cooling of a twist turbine blade. Based on these studies, the objective of this paper is to apply a TLC technique to investigate the effects of the rotating speed and blowing ratio on the film cooling characteristics in the leading-edge region of a twist turbine blade in a low-speed 1-stage turbine. The Reynolds number based on the mainstream velocity of the turbine outlet and the rotor blade chord length was fixed at 6.08 104. CO2 worked as the coolant to achieve a coolant-to-mainstream density ratio of 1.56. All the measurements were made at three different rotating speeds: 400 rpm (positive incidence angle), 550 rpm (zero incidence angle), and 700 rpm (negative incidence angle). The average blowing ratio varies from 0.5 to 2.0. The influence of rotation and blowing ratio on film cooling effectiveness were studied. The experimental results will be beneficial to explain the heat transfer process with respect to leading-edge film cooling and will help design a more efficient turbine rotor blade structure. 2. Experimental apparatus Fig. 1 shows the simplified schematic of the experimental apparatus (8300 mm long 4400 mm wide 3000 mm high) used in conducting this investigation at the National Key Laboratory of Science and Technology of Aero-Engines in Beihang University in China. The experimental apparatus consists of two parts: the mainstream path (1red arrow) and the coolant flow path (blue arrow). The centrifugal blowing compressor used to supply the mainstream air is KF3-95 No6.3E and the maximum rotational speed is 2300 rpm. 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 was employed to heat the mainstream air temperature to the experimental request. The compressed and heated mainstream air passes through the inlet cone and honeycomb and enters the 1-stage turbine. A honeycomb is placed at the rear of the inlet cone to ensure axial uniformity in the mainstream air entering the annular channel with inner and outer diameters of 600 and 1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
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H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58 Table 1 1-stage turbine dimension. Item
1st Stator stage
1st Rotor stage
Stagger angle (degree) Tip diameter (mm) Hub diameter (mm) Chord length (mm) Height (mm) Blade No.
45 782 612 77 85 42
60 780 646 40 67 73
Fig. 2. The diagrammatic drawing of the turbine.
Fig. 4. The test blade. Fig. 3. The position of the test blade.
800 mm, respectively. The annular channel was equipped with four pitot tubes and two static pressure holes to measure the mainstream total and static upstream pressure in the turbine. Moreover, based on the values of the total and static pressures measured by a differential pressure transmitter (Type, Rosemount3051), the mainstream flow rate through the turbine component can be calculated. The 1stage turbine is a core component of the experiment apparatus. A helicoid collector is placed in the back of the turbine section to collect and stabilize the exhaust air, which is transported to the heater to complete the circle. The turbine shaft is connected through a synchronous belt with the rear end of a 22-kW dynamometer (Type, Z4132-1) that has a rated rotational speed of 3090 rpm. A torque meter (Type, TI-1) is connected to the dynamometer via a flexible coupler that is employed to output the turbine torque and power. The coolant flow, supplied by a dedicated gas cylinder, passes through valves, the filter, the air pressurizer tank, the flow meter and the insulation tube installed in the hollow shaft before entering the test blade. A labyrinth seal and a mechanical seal are adapted to prevent leakage of the mainstream and coolant parts, respectively. Three ranges of glass rotor flow-meters (Type, LZB-6, LZB-10 and LZB-15) were employed to meet the various requirements of coolant flow. The rotating speed of the 1-stage turbine is measured via a digital tachometer. The static and dynamic conversion of the electrical signal is accomplished via a carbon brush-copper collar system. As seen in Fig. 1, the data-acquisition system mounted on the extended shaft is used to transmit the temperature signal to the computer. Fig. 2 provides the diagrammatic drawing of the 1-stage turbine and Fig. 3 shows the position of the test blade. Table 1 lists the detailed dimensions of the 1-stage turbine. Forty-two blades with a staggered 45° angle were mounted on the first-stage stator and
73 blades with a staggered 60° angle were mounted on the firststage rotor. The stator blade tip diameter, hub diameter, height and chord length are 782 mm, 612 mm, 85 mm and 77 mm, respectively. The rotor blade tip diameter, hub diameter, height and chord length are 780 mm, 646 mm, 67 mm and 40 mm, respectively. The test blade model is composed of engineering plastic (Type, RGD525), which has a low thermal conductivity of 0.22 W/(mK), to reduce the effect of heat conduction. The other 114 blades were made of aluminum alloy. One hundred sixty-five film holes with a diameter (d) of 0.4 mm are arranged in the leading edge in three rows: the PS row, the stagnation line row and the SS row (See Fig. 4). Three rows of film holes are located at 30°, 0° and 30°, respectively, with respect to the stagnation line. The injection angle of the film cooling hole is 45° in the spanwise direction. Each row has 55 film holes, and the film holes in the stagnation line row are staggered with the film holes of the PS and SS rows. On the measurement area, each row has a hole-to-hole spacing (p) of 2.5-d in the spanwise direction. The coolant passes through the pipe installed in the hollow shaft into the gas-collecting chamber inside the blade, then flows out through the film holes on the blade’s leading edge.
3. Experimental methods 3.1. Image-acquisition system Fig. 5 shows a diagrammatic of the image-acquisition system that includes a computer, a camera control system (CCS), a singlechip microcomputer (Type, STM32F103RCT6) (SCM), a stator blade, a photoelectric sensor (Type, P+F OBT200-18GM60-E5), LED lights, a rotor blade and strobe control system (SCS) components. The SCM
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Real-time image
LED lights control signal
Exposure time control signal
CCS
SCS
Camera control signal Rotation signal
Ω
SCM Strobe control signal
Computer
Camera control system
Photoelectric sensor
LED lights
Single chip microcomputer Rotor blade
Stator blade
Strobe control system
Fig. 5. Image capture system.
is the core control unit to realize the image collection. The photoelectric sensor interface is wired to the SCM input terminal, and both the SCS and the CCS are wired to the SCM output terminal. The test blade leading-edge surface is coated with TLC and is illuminated by LED lights installed inside the casing. A CCD camera (Type, MU9Px-MH) with resolution of 2592 1944 pixels mounted on one of the stator blades is employed to capture temperature distributions. The dimensions of the CCD camera are 15 15 8.5 mm. A smooth transition on both sides of the lens should be ensured to reduce the interference of the lens to flow field as much as possible. The CCD camera is set to an external trigger mode and needs to control the exposure time. For instance, the CCD camera exposure time must be set to less than 15-ls to ensure that the captured images are clear when the rotating speed is 1400 rpm. By using the highspeed optical coupling isolation circuit, the CCS can achieve fast and precise control of the CCD camera exposure time. To receive the signal sent by the photoelectric sensor, the SCM input terminal is set to receive the interrupt signal triggered by a rising edge. The SCM interrupt handler is triggered by a signal from the photoelectric sensor when the test blade goes to the initial position. At the same time, the pulse signal is timed. After an appropriate delay, the SCM will output two different square wave pulse signals to the SCS and the CCS, respectively. The time delay of the square wave pulse signal is a key factor in determining whether the CCD camera can perform accurate positioning and operate in synchronization with the strobe lights when the turbine is in a high-speed rotation condition. Moreover, there is a one-to-one relationship between the
Interrupt signal The time of acquiring image
time delay of the square wave pulse signal and the rotating speed. To ensure that the CCD camera can perform an accurate positioning, the time delay of the square wave pulse signal changes with the change in rotating speed. The CCD camera exposure and the strobe starter can be precisely controlled according to the pulse width of the signal. Fig. 6 shows the timing diagram of the experimental control signal. Finally, the images taken by the CCD camera are transmitted to the computer to convert the RGB elements to HSV format. 3.2. Calibration of TLC A steady-state, hue-capturing method was applied in the current experiment for the temperature measurements. A wideband liquid crystal (Type, SPN/R30C20 W) ranging from 303 K to 323 K was used to measure the adiabatic wall temperature Taw. Before the calibration experiment, black paint and TLC were sprayed uniformly onto the leading-edge region using a spray gun. The temperature of the mainstream air changed from 303 K to 323 K as a result of the heater used during the calibration experiment, and the TLC color changed from red to green to blue. The CCD camera was used to capture and transfer the TLC images. And the CCD camera used for the calibration was the same one used in the formal experiments. Illumination angles, camera view angles and the shooting method were consistent with the subsequent formal experiments. To obtain the calibration curve between hue values and the temperature for the leading edge, as shown in Fig. 7, the TLC images were recorded and transmitted to the computer for each 1.0 K increase. 3.3. Film cooling effectiveness The film cooling effectiveness (g) is defined as follows
Strobe control signal
Camera control signal Fig. 6. Timing diagram of the experimental control signal.
g ¼ Tg Tw = Tg Tc
ð1Þ
where Tg and Tc are the abbreviation of the temperature of the mainstream air and coolant jet, respectively. Tw denotes the temperature of the measurement area on the leading-edge surface. In this paper, Tg and Tc were obtained via the T-type thermocouples with the accuracy of ±0.5 K mounted in the annular channel and
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thermocouple. Therefore, when Tw = 308 K, the uncertainty of the calculated adiabatic film cooling effectiveness was 6.9%. The uncertainty of the rotating speed measured by the intelligent tachometer (Type, YK-23) was ±1 rpm. The uncertainty of the mass flow rate and blowing ratio was ±3% and ±2%, respectively.
50
Temperature/°C
45
4. Discussion of results
40
In this work, the film cooling effectiveness level, spanwise averaged film cooling effectiveness and area-averaged film cooling effectiveness were experimentally analyzed to study the effects of the blowing ratio and rotating speed on the leading-edge region of a twist turbine blade in a 1-stage turbine.
35
30
0
20
40
60
80
100
120
140
160
180
200
Hue Fig. 7. Calibration for TLC.
the thermosensitive resistor (Type, TH-44034-40-T) with the accuracy of ±0.2 K installed in the blade cooling chamber, respectively. Table 2 lists the operating conditions of the current experiment. The mainstream mass flow rate measured by the differential pressure transmitter (Type, Rosemount3051) was 3.21 kg/s. The mainstream turbulence intensity was 5% and was obtained via a hotwire anemometer (Type, TSI1213-20 and IFA100). The turbine inlet and outlet velocity were 12.5 m/s and 26 m/s, respectively. The mainstream Reynolds number (Re), based on the turbine outlet velocity and the rotor blade chord length, was fixed at 6.08 104. All measurements were carried out at three different rotating speeds: 400, 550, and 700 rpm. The average blowing ratio varies from 0.5 to 2.0. The coolant-to-mainstream density ratio (DR) was chosen to be 1.56 with CO2 injection. 3.4. Uncertainty calculations An uncertainty analysis is needed to evaluate the effect of the experimental parameters on the measurement of the adiabatic film cooling effectiveness. According to the method suggested by Moffat [19], the uncertainty of the film cooling effectiveness could be calculated by
ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # " #2 u" 2 u T w T c 2 2 1 T g T w 2 2 t Dg ¼ DT g þ ðDT w Þ þ 2 2 ð DT c Þ T g T c T g T c T g T c
ð2Þ For the current experiment, Tg was kept at 315 K and Tc was kept at 298 K. The uncertainty of Tg and Tc were set to ±0.5 K and ±0.2 K, respectively. The uncertainly of Tw measured using a liquid crystal was controlled via ±0.5 K, the same as the T-type
Table 2 Operating conditions. Parameter
Value
Mainstream mass flow rate (kg/s) Mainstream turbulence intensity Turbine inlet velocity (m/s) Relative velocity at rotor blade inlet (m/s) Turbine outlet velocity (m/s) Re Mainstream Mach number at rotor blade inlet X (rpm) M DR Tg (K) Tc (K)
3.08 5% 12.5 20.4 26 6.08 104 0.059 400, 550, 700 0.5–2.0 1.56 315 298
4.1. Film cooling effectiveness level 4.1.1. Effects of the blowing ratio Figs. 8–10 show the effect of the blowing ratio on the film cooling effectiveness distributions under different rotating speeds. The horizontal ordinate s/smax represents the non-dimensional distance, where s is the distance measured along blade surface from the measurement area centerline and the negative value indicates the area from the measurement area centerline to the PS and the positive value indicates the area from the measurement area centerline to the SS. The vertical coordinate Y/H represents the nondimensional 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 general, despite the rotating speed, the film cooling effectiveness level increases monotonously with an increase in blowing ratio in the leadingedge region. As the rotating speed became constant, increasing the blowing ratio meant increasing the velocity of the coolant jets, which is beneficial to the coolant jet spread. We take the case of 550 rpm as an example. Fig. 9 shows the film cooling effectiveness distributions at 550 rpm with different blowing ratios. Under M = 0.5, there is almost no film protection in the middle of the leading edge, which may be due to the back-flow phenomenon occurs here. This is because the pressure gradient in the coolant gas chamber reduces along the spanwise direction. As the blowing ratio increases to 1.0, we can see that part of the coolant jets flow out from the upper half of the leading edge, which happens now and didn’t happen before. When the blowing ratio increases to 1.5, the film cooling effectiveness level significantly increases in the entire region and the film cooling effectiveness level, under larger blowing ratios of 1.5 and 2.0, are clearly higher than for the smaller blowing ratios. A film cooling effectiveness level under M = 2.0 shows little difference from the effectiveness level under M = 1.5. 4.1.2. Effects of rotating speed To understand and correctly interpret the experimental results for film cooling effectiveness, we need to investigate the following turbine aerodynamic aspects in advance (for detailed discussion see Schobeiri et al.) [20,21]. When the turbine is operated at the lower rpm condition, the mainstream flow impinges on the blade’s leading edge with a positive incidence angle and results in the stagnation line moving to the PS. Consequently, part of the coolant jets ejected from the PS row are deflected toward the SS. In the same way, when the turbine is operated at a high rpm condition, the main stream flow impinges on the blade’s leading edge with a negative incidence angle, causing the stagnation line to move to the SS and the coolant jets to be deflected toward the PS. This phenomenon is explained in Fig. 11. The experimental results for film cooling effectiveness at 400 rpm, 550 rpm and 700 rpm are presented in Figs. 8–10, respec-
H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58
Fig. 8. Film cooling effectiveness distributions for 400 rpm under different blowing ratios.
Fig. 9. Film cooling effectiveness distributions for 550 rpm under different blowing ratios.
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Fig. 10. Film cooling effectiveness distributions for 700 rpm under different blowing ratios.
Fig. 11. Flow path inside and outside the blade for (a) positive incidence angle, (b) zero incidence angle, and (c) negative incidence angle conditions [22].
tively. To study the effect of rotating speed, we take the case of M = 1.5 as an example [Fig. 8(c), Figs. 9(c) and 10(c)]. In general, based on the distributions of film cooling effectiveness, the stagnation line clearly moves from the PS to the leading edge, and then to the SS with an increase in rotating speed. At 400 rpm, the effectiveness level near the SS row is slightly higher than near the PS row. In this case, it seems that the stagnation line lies between the PS and the stagnation line rows. As a result, some of the coolant jets ejected from the PS row and the coolant traces ejected from the stagnation line row are deflected toward the SS of the blade. At 550 rpm, the stagnation line lies near the stagnation line row and the coolant jets are divided into the PS and the SS. Thus, the film coverage becomes the largest and most uniform over the entire region compared to the positive incidence angle and negative incidence angle conditions. At 700 rpm, the stagnation line lies on the
SS. Because the coolant jets are deflected toward the PS of the blade, the film cooling effectiveness level near the PS row is higher than that near the SS row. Thus, the highest level of film cooling effectiveness reaches 0.65 in the area between the PS and the stagnation line rows. Accordingly, the rotating speed is the most crucial factor in determining the distribution of film cooling effectiveness. 4.2. Spanwise averaged film cooling effectiveness 4.2.1. Effects of the blowing ratio In this work, the average blowing ratio was controlled at 0.5, 1.0, 1.5 and 2.0 at a constant rotating speed. Figs. 12–14 show the effects of the blowing ratio on spanwise average film cooling effectiveness under different rotation speeds. It should be pointed out that the coordinate X used to report results (see Figs. 8–10)
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H.-w. Li et al. / International Journal of Heat and Mass Transfer 129 (2019) 47–58 0.60
0.60
M=0.5 M=1.0 M=1.5 M=2.0
0.55 0.50
η
0.45
0.55
0.45 0.40
0.35
0.35
η
0.40
0.30
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10 -4
-3
0.10
SS
PS
0.05
-2
-1
0
1
2
M=0.5 M=1.0 M=1.5 M=2.0
0.50
3
SS
PS
0.05 4
-4
-3
-2
-1
X/D
2
3
4
Fig. 13. Effect of the blowing ratio on the spanwise average film cooling effectiveness for 550 rpm.
0.60
M=0.5 M=1.0 M=1.5 M=2.0
0.55 0.50 0.45 0.40 0.35
η
appears to be the apparent coordinate related to the view angle of the camera and not the geometric distance. Therefore, we have fixed the coordinate X with certain geometric transformation to ensure that the pitch between the PS and middle rows is equal with that between the middle and SS rows in Figs. 12–18. The vertical coordinate g indicates the value of film cooling effectiveness. The horizontal coordinate X/D is the non-dimensional distance and X indicates the stream-wise distance from the stagnation line row. The vertical coordinate g indicates average film cooling effectiveness in the spanwise direction, which is calculated from the average value: 4.3 < X/D < 3.75. Note that the entire interval (4.3D, 3.75D) in the spanwise direction is the leading edge interval of our study. Three black arrows are used to indicate the position of the three rows of holes. For all blowing ratio cases, at a constant rotating speed, there are three clear peaks in the downstream of each row film hole caused by the high film cooling effectiveness in the downstream direction of the coolant jet outlet. The four hundred rpm (positive incidence angle) case is shown in Fig. 12. In general, average cooling effectiveness increases with an increase in the blowing ratio in the interval (4.3D, 1.5D). However, with the blowing ratio increasing to 2.0, there is an obvious decrease in the interval (1.5D, 3.75D) near the SS row, which means that the lift-off phenomena occur here, as shown in Fig. 11(a). The M = 1.5 case shows that the highest level of film cooling effectiveness is in the interval (1.5D, 3.75D) near the SS row. The five-hundred and fifty rpm (zero incidence angle) case is shown in Fig. 13. Average cooling effectiveness increases with an increase in the blowing ratio at the leading edge. The average cooling effectiveness in the interval (4.3D, 0D) is 0.21, 0.27, 0.31 and 0.35 at M = 0.5, 1.0, 1.5 and 2.0, respectively. And the average cooling effectiveness in the interval (0D, 3.75D) is 0.18, 0.26, 0.30 and 0.34 at M = 0.5, 1.0, 1.5 and 2.0, respectively. Therefore, for the zero incidence angle condition, at a constant blowing ratio, cooling effectiveness is higher on the PS than on the SS in the leadingedge region, which is consistent with the results found by Ahn et al. [13] and Zhang et al. [23]. Furthermore, both the peak positions near the PS and the SS rows show a tendency toward the stagnation line when the blowing ratio is between 0.5 and 2.0. This is caused by the coolant jet momentum. With the increase in blowing ratio, the momentum of the coolant jet increases and is gradually comparable to the momentum of the mainstream. Therefore, the coolant jet traces are better able to withstand the pressure of the mainstream and flow further along the coolant ejection
1
X/D
0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
4
X/D Fig. 14. Effect of the blowing ratio on the spanwise average film cooling effectiveness for 700 rpm.
0.60 0.55
400 rpm 550 rpm 700 rpm
0.50 0.45 0.40 0.35
η
Fig. 12. Effect of the blowing ratio on the spanwise average film cooling effectiveness for 400 rpm.
0
0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
4
X/D Fig. 15. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 0.5.
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400 rpm 550 rpm 700 rpm
0.55 0.50 0.45 0.40
η
0.35 0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
4
X/D Fig. 16. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 1.0.
0.60
400 rpm 550 rpm 700 rpm
0.55 0.50 0.45 0.40
η
0.35 0.30 0.25 0.20 0.15 0.10 -4
-3
4.3. Effects of rotating speed
SS
PS
0.05
-2
-1
0
1
2
3
4
X/D Fig. 17. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 1.5.
0.60
400 rpm 550 rpm 700 rpm
0.55 0.50 0.45
η
0.40 0.35 0.30 0.25 0.20 0.15 0.10
SS
PS
0.05 -4
-3
-2
-1
0
1
2
3
3D) near the PS row is 0.28, 0.35, 0.40 and 0.45 at M = 0.5, 1.0, 1.5 and 2.0, respectively. The average cooling effectiveness in the interval (1D, 1D) near the stagnation line row is 0.20, 0.25, 0.29 and 0.31 at M = 0.5, 1.0, 1.5 and 2.0, respectively. And the average cooling effectiveness in the interval (2.75D, 3.75D) near the SS row is 0.26, 0.35, 0.41 and 0.43 at M = 0.5, 1.0, 1.5 and 2.0, respectively. In general, the increase rate of cooling effectiveness gradually decreases with a blowing ratio ranging from 0.5 to 2.0. One reason is that there is more intense mixing between the coolant jets and the mainstream at high blowing ratios, which is caused by the increased interaction. Therefore, the coolant jet traces decay faster along the direction of the coolant ejection than in the lower blowing ratio case. Another reason is that the lift-off phenomena occur at high blowing ratios. The seven hundred rpm (negative incidence angle) case is shown in Fig. 14. Our results show that the average cooling effectiveness increases with an increase in the blowing ratio, whereas a slight increase occurs when the blowing ratio exceeds 1.5. By comparing the film cooling effectiveness distribution in the interval (4.3D, 3D) on the PS row under the M = 1.0, 1.5 and 2.0 conditions, we can clearly see that the film cooling effectiveness values are almost at the same level. This is because of the stagnation line location and lift-off phenomena. Thus, the high rpm (negative incidence angle) condition and the stagnation line lies on the SS and the coolant jets from the stagnation line row and SS row shift to the PS to fill the spaces between the PS film cooling holes, which explains the higher level of cooling effectiveness on the PS row when the blowing ratio is 1.0. In addition, lift-off occurs when the blowing ratio increases to 1.5, which explains why the average film cooling effectiveness distributions are almost the same. In this case, the stagnation line lies near the SS row, and the coolant jets from the SS row film holes are suppressed by the mainstream flow. Therefore, the averaged film cooling effectiveness near the SS row is more insensitive to the blowing ratio than near the other rows.
4
X/D Fig. 18. Effect of rotating speed on the spanwise average film cooling effectiveness for M = 2.0.
direction. According to the profile of average cooling effectiveness, all blowing ratio cases show similar behavior for cooling effectiveness. The average cooling effectiveness in the interval (4.3D,
To study the effect of rotating speed, spanwise averaged film cooling effectiveness is re-arranged under different blowing ratios (Figs. 15–18). In general, regardless of the blowing ratio, the averaged film cooling effectiveness increases with rotating speed ranging from 400 rpm to 700 rpm on the PS row. Cooling effectiveness on the stagnation line row is more insensitive to rotating speed than it is on the other rows. On the SS row, the 700-rpm case shows the lowest cooling effectiveness level at each blowing ratio. As mentioned above, different rotating speeds change the incidence angle and determine the direction of the coolant traces. As shown in Fig. 15, under M = 0.5, the averaged cooling effectiveness slightly increases with an increase in rotating speed near the PS row. It seems that the rotating speed does not change the averaged cooling effectiveness on the SS row, which is probably because of the back-flow phenomenon mentioned in the previous section. We take the moderate blowing ratio case with M = 1.0 to discuss the effect of rotating speed in detail. As shown in Fig. 16, the 400-rpm case shows the lowest cooling effectiveness level near the PS row. For the low rpm (positive incidence angle) condition, the stagnation line lies on the PS, which means that the coolant jets are ejected from the three-row flow to the SS. Consequently, the SS row benefits from the stagnation line and the PS row, which results in the highest cooling effectiveness level near the SS row. In the interval (4.3D, 3D) near the PS row, the difference in the average cooling effectiveness between the 400-rpm case and the 550rpm case is marginally within the experimental uncertainty of 6.9%. For the 550-rpm (zero incidence angle) case, the stagnation line lies on the stagnation line row, which means that the coolant
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jets ejected from the stagnation line row flow to the PS and the SS, respectively. As a result, the PS row benefits from the stagnation line row, which explains the 550-rpm case that shows a higher cooling effectiveness level than the 400-rpm case in the vicinity of the PS row. The cooling effectiveness level on the SS row remains almost unchanged when the rotating speed increases from 400 rpm to 550 rpm. However, when compared to the 400-rpm case, the SS row does not benefit from the PS row and the benefit from the stagnation line row is also reduced for the 550-rpm case. This may be because the 550-rpm case can provide a more uniform film distribution on the SS row. The rotation speed increases to 700 rpm, where there is an obvious improvement in the cooling effectiveness near the PS row. In addition, average film cooling effectiveness increases 0.19 in the interval (4.3D, 3D) near the PS row compared to the 400-rpm case. For the high rpm (negative incidence angle) condition, the stagnation line lies on the SS and the coolant jets from the stagnation line row and the SS row shift to the PS row to fill the spaces between the PS film cooling holes. Consequently, the PS row benefits from the stagnation line and the SS rows, resulting in the highest cooling effectiveness level near the PS row. In contrast, a part of the coolant jet ejected from the SS row does not have enough momentum to overcome the suppression of the stagnation line, which explains why the 700 rpm shows the lowest cooling effectiveness level on the SS row. As shown in Fig. 17, as the rotating speed increases, the M = 1.5 experimental case shows a similar trend with the case of M = 1.0 in the entire region. As shown in Fig. 18, under M = 2.0, average cooling effectiveness increases with an increase in rotating speed near the PS row. In the interval (2.75D, 3.75D) near the SS row, the average cooling effectiveness is 0.34, 0.43 and 0.27 at 400 rpm, 550 rpm and 700 rpm, respectively. Therefore, the average cooling effectiveness near the SS row firstly increases then decreases with rotating speed ranging from 400 rpm to 700 rpm. On the SS row, the 400-rpm case shows the lowest cooling effectiveness level. This is likely because the coolant jets are ejected from the SS row lift-off and penetrates the mainstream.
4.4. Area-averaged film cooling effectiveness To better analyze the effects of the blowing ratio and rotating speed, Table 3 lists the averaged cooling effectiveness of the measurement area at Re = 6.08 104, with different rotating speeds and different blowing ratios. From Table 3, for all rotating speed cases, the value of the area-averaged film cooling effectiveness increases monotonically with the increase in the blowing ratio, which is consistent with the experimental results found by Ahn et al. [14]. For all blowing ratio cases, the value of the area-averaged film cooling effectiveness increases with the increase in rotating speed, which is consistent with the experimental result under the condition of M = 2.0 given by Ahn et al. [14]. As can be seen from Table 3, compared to the effect of bowling ratio, the rotating speed plays an indispensable role in determining film cooling effectiveness distributions on the leading edge. This is because the rotating speed can change the mainstream incidence angle to the leading edge and affect the film cooling flow path direction. However, Ahn’s
Table 3 Averaged cooling effectiveness on the measurement area. Item
M = 0.5
M = 1.0
M = 1.5
M = 2.0
400 rpm 550 rpm 700 rpm
0.1877 0.1970 0.2703
0.2726 0.2929 0.3447
0.3050 0.3339 0.3925
0.3177 0.3671 0.4116
57
investigation found that the averaged film cooling effectiveness on the area of interest first decreases and then increases with increased rotating speed for M = 0.5 and 1.0 cases. This may be related to the geometry of the turbine blade used in the experiments. The tests by Ahn et al. [14] were carried out on the leading edge of a straight blade, whereas a twist blade was used in this work. For the zero incidence angle condition, there is an inclination between the stagnation line and the centerline of the stagnation line row film holes for the straight blade case, whereas there is an overlap between the stagnation line and the centerline of the stagnation line row film holes for the twist blade case.
5. Conclusions The effects of rotating speed and blowing ratio on film cooling characteristics on the leading-edge region of a twist turbine blade have been experimentally investigated under rotating conditions in this paper. Experiments have been performed using a constant Reynolds number (6.08 104) with a rotating speed ranging from 400 to 700 rpm and a blowing ratio ranging from 0.5 to 2.0. CO2 worked as the coolant to maintain a coolant-to-mainstream DR of 1.56. The major conclusions of this study are as follows: (1) Rotating speed plays an indispensable role in determining film cooling effectiveness distributions on the leading edge. The position of the stagnation line moves from the PS to the SS when rotational speed changes from 400 to 700 rpm. (2) The film cooling effectiveness level increases monotonously with an increase in the blowing ratio in the leading-edge region, for any rotating speed. (3) In general, regardless of the blowing ratio, the spanwise averaged film cooling effectiveness increases with rotating speed ranging from 400 to 700 rpm on the PS row. In addition, the spanwise average film cooling effectiveness on the stagnation line row is insensitive to rotating speed when compared to the other rows. On the SS row, the 700-rpm case shows the lowest level of spanwise film cooling effectiveness at each blowing ratio, which might be linked to the shift of the stagnation line. (4) For all rotating speed cases, the value of the area-averaged film cooling effectiveness increases monotonically with the blowing ratio ranging from 0.5 to 2.0. For all blowing ratio cases, the value of the area-averaged film cooling effectiveness on the leading edge increases slightly with rotating speed when ranging from 400 to 700 rpm. Conflict of interest statement We declare that we have no conflict of interest. References [1] J.C. Han, S. Dutta, S.V. Ekkad, Gas turbine heat transfer and cooling technology, Epfl 9 (2014) 82. [2] W.J. Mick, R.E. Mayle, Stagnation film cooling and heat transfer, including its effect within the hole pattern, J. Turbomach. 110 (1) (1988) 66–72. [3] Michael W. Cruse, Ushio M. Yuki, David G. Bogard, Investigation of various parametric influences on leading edge film cooling, in: ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, 1997, pp. V003T09A058–V003T09A058. [4] 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) (1998) 799–807. [5] D. Lakehal, G.S. Theodoridis, W. Rodi, Three-dimensional flow and heat transfer calculations of film cooling at the leading edge of a symmetrical turbine blade model, Int. J. Heat Fluid Flow 22 (2) (2001) 113–122. [6] 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.
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