High resolution measurements of film cooling performance of simple and compound angle cylindrical holes with varying hole length-to-diameter ratio—Part I: Adiabatic film effectiveness

International Journal of Thermal Sciences 124 (2018) 146–161

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High resolution measurements of film cooling performance of simple and compound angle cylindrical holes with varying hole length-to-diameter ratio—Part I: Adiabatic film effectiveness

MARK

Weihong Li∗, Xunfeng Lu, Xueying Li, Jing Ren, Hongde Jiang Gas Turbine Institute, Department of Thermal Engineering, Tsinghua University, Beijing, China

A B S T R A C T Adiabatic film cooling effectiveness on a flat plate surface downstream a row of simple and compound angle holes was investigated using high-resolution pressure sensitive paint (PSP) technique. A variation of flow parameters including density ratio and blowing ratio, and geometry parameters including compound angle and length-to-diameter ratio were examined. Blowing ratios (M) ranging from 0.3 to 2, density ratio (DR) are 1.0 and 1.5, length to diameter ratios (L/D) from 0.5 to 5 and two compound angle (β: 0°, 45°) were employed composing a test matrix of 140 test cases. Discharge coefficient was measured with varied blowing ratio and L/D values for simple and compound angle hole. Detailed local, laterally averaged, and area averaged film effectiveness are presented to illustrate the effect of length-to-diameter ratio and compound angle. It was found that the effect of density ratio on the film cooling effectiveness was associated with the blowing ratio. Increasing density ratio provides a negative effect when the M ≤ 0.5 for simple and compound angle hole, which a positive effect when the M > 0.5. Also found was that the film effectiveness was highest when L/D = 0.5 and 1, regardless of blowing ratio and compound angle. The film cooling effectiveness of simple angle hole increased as L/D increased from 2 to 5 when M ≤ 1, while showed a minimum value at L/D = 3.5 when M ≥ 1. The film cooling effectiveness of compound angle hole showed a minimum value at L/D = 3.5 regardless of blowing ratio. The scaling methods of film effectiveness with velocity ratio, blowing ratio, and momentum flux ratio were also discussed for simple angle and compound angle holes with varying L/D.

1. Introduction

cooling effectiveness η, which is defined as

Modern heavy-duty gas turbines or aero-engines are requiring higher turbine inlet temperature to achieve more power generation and higher thermal efficiencies. Typical turbine inlet temperature has increased up to 2100 K for aero-engines which generates higher demand of turbine cooling to lower the turbine metal temperature. Common cooling techniques includes internal cooling and film cooling. Coolant passes internal channels with different turbulent features and then injects through discrete holes to form a protective film on the turbine blade surface. Recently, some new blade concepts are proposed, for example, double wall airfoil [1] shown in Fig. 1, where the small cooling cavity requires impingement with low distance [2–4] and thinwall outer foil requires discrete film holes with short length-to-diameter ratio. Due to manufacture limitations, shaped hole are difficult to use on the thin-wall airfoils, whereas simple angle hole and compound angle hole are suitable. A common method to evaluate the film cooling is the adiabatic film

η=

∗

T∞ − Taw T∞ − Tc

(1)

where T∞ is the mainstream temperature, Tc is the coolant jet temperature exiting the film hole, and Taw is the adiabatic wall temperature. The adiabatic film effectiveness describes how well the coolant covers the metal surface and how the coolant mix with the crossflow along the flow direction. Table 1 shows the comparison of the present study to previous experimental work on simple and compound angle cylindrical hole. Experimental work on the effect of length-to-diameter ratio have been conducted on simple angle hole [5–11]. Sinha et al. [5] measured the adiabatic film effectiveness of a row of simple angle hole. The length-todiameter ratio is 1.75. Burd et al. [6,7] measured the adiabatic film effectiveness of short and long simple angle holes with L/D being 2.3 and 7.0. They also provided hydrodynamic measurements for simple angle hole. It was reported that Short-L/D holes have a “jetting” of

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

http://dx.doi.org/10.1016/j.ijthermalsci.2017.10.013 Received 17 April 2017; Received in revised form 10 October 2017; Accepted 10 October 2017 1290-0729/ © 2017 Published by Elsevier Masson SAS.

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injection angle [15], internal crossflow [22] and so on. Ekkad et al. [14,15] used the transient liquid crystal method to measure the adiabatic film effectiveness and heat transfer coefficient downstream of simple angle and compound angle holes. Results with different density ratio and compound angle were compared. Goldstein et al. [16] used naphthalene sublimation technique to measure the adiabatic film effectiveness and heat transfer coefficient downstream a row of holes with 35 deg inclination angle and 45 deg compound angle. They found that the laterally averaged heat transfer coefficient of compound angle hole is close to that of simple angle hole at low blowing ratios, while the heat transfer coefficient drastically increases 10D downstream of injection hole at high blowing ratios due to the asymmetric vortex motion under the jets. Schmidt et al. [18] and Sen et al. [19] examined the effect of blowing ratio, hole spacing, and hole shape on the adiabatic film effectiveness and heat transfer coefficient with compound angle injection film hole. They showed that the film cooling effectiveness and the heat transfer level were increased as compound angle increased. Thus they recommended that the combination of adiabatic effectiveness and heat transfer coefficient favors the performance evaluation of compound angle injection hole. As mentioned above, double wall airfoil with thin-outer metal sheet requires simple angle hole or compound angle hole, so heat transfer characteristics of simple and compound angle hole with short length-todiameter will be necessary. However, according to the authors' knowledge, no work exit on the effect of L/D on the heat transfer coefficient of simple angle cylindrical hole. Also no work has been done to investigate the effect of L/D on adiabatic film effectiveness and heat transfer coefficient compound angle hole, especially the two dimensional distributions. This paper reported the experimental measurements on film cooling effectiveness of simple and compound angle hole with varying length-to-diameter ratio by pressure sensitive paint (PSP). The unique contribution of the paper was that it was the first time to show the film cooling effectiveness data considering length-to-diameter ratio effect on compound angle hole. The companion Paper II will discuss the heat transfer coefficient measurements.

Fig. 1. Double wall cooling vane with short film holes.

coolant into freestream and enhance mixing. Baldauf et al. [8] measured the adiabatic film effectiveness and heat transfer coefficient of a row of simple angle cylindrical hole with L/D = 6. The main focus of the study was on the effect of density ratio, blowing ratio, and hole pitch-to-diameter ratio. Lutum et al. [9] conducted the first experiment to investigate the effect of length-to-diameter ratio on the adiabatic film effectiveness of simple angle hole. The varied the L/D from 1.75 to 18. Their results indicated that decreased film effectiveness was obtained for short hole and film effectiveness remained almost unchanged for L/ D > 5. Hale et al. [10] measured the film cooling effectiveness from a row of short holes (L/D ≤ 3) fed by a narrow plenum. The plenum feed configuration was also considered. Their results indicated that similar or improved film effectiveness was achieved with 90 deg holes compared with 35 deg holes under certain conditions, which was a useful recommendation for thin-walled film cooled blade. Compound angle hole has superiority on simple angle hole by enhancing lateral diffusion especially in high blowing ratio conditions. Experimental work on compound angle film cooling [13–20] have mainly concentrate on compound angle effect [13], density ratio [14],

2. Experimental apparatus and procedures 2.1. Low speed wind tunnel All the film cooling effectiveness experiments were performed in the

Table 1 Summary of simple and compound angle film cooling work. Authors

Hole shape

L/D

DR

BR

P/D

α (°)

β (°)

Data obtained

Sinha et al. [5] Burd et al. [6,7]

Simple Simple

1.75 2.3/7.0

1.2–2.0 0.96

0.25–1.0 0.5–1

3 3

35 35

0 0

Baldauf et al. [8]

Simple

6

1.2–1.8

0.2–2.5

2,3,5

0

Lutum et al. [9] Hale et al. [10] Waye et al. [11] Saumweber et al. [12]

Simple Simple Simple Simple

1.75–18 1.16/2.91 6.7 6

1.15 0.90 1.3–1.5 1.7

0.52–1.56 0.5–1.5 0.2–1.4 0.5–1.5

2.86 3 2.78/5.5 4

30, 60, 90 35 35 30 30

0 45 0 0

Jung et al. [13] Ekkad et al. [14,15]

Compound Compound

4 4.6

0.93 0.98–1.46

0.5–2.0 0.5–2.0

3 3

35 35

30,60,90 45

Goldstein et al. [16]

Compound

6.3

1.0

0.5–2.0

3

35

45

Nasir et al. [17]

Compound

4.9

1.0

0.5–1.5

3

55

60

Schmidt et al. [18] and Sen et al. [19] Rallabandi et al. [20] Gritsch et al. [21] Present Study

Compound

4

1.6

0.5–2.5

3

35

45

Compound Shaped Simple/ Compound

7.5–10 7.5–11.5 0.5–5

1.0 1.7 1.0–1.5

0.3–1.5 0.5–2.5 0.3–2.0

3 4–6 5

30 30 35

45 0 45

Adiabatic film Adiabatic film measurements Adiabatic film coefficient Adiabatic film Adiabatic film Adiabatic film Adiabatic film coefficient Adiabatic film Adiabatic film coefficient Adiabatic film coefficient Adiabatic film coefficient Adiabatic film coefficient Adiabatic film Adiabatic film Adiabatic film coefficient

147

effectiveness effectiveness and flow field effectiveness and heat transfer effectiveness effectiveness effectiveness effectiveness and heat transfer effectiveness effectiveness and heat transfer effectiveness and heat transfer effectiveness and heat transfer effectiveness and heat transfer effectiveness effectiveness effectiveness and heat transfer

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Fig. 2. Schematic view of the low speed wind tunnel. Fig. 4. Film hole configurations: (a) simple angle hole, (b) compound angle hole.

low speed wind tunnel shown in Fig. 2. Film cooling measurements in this tunnel have been reported by Li et al. [23] for vane endwall and Chi et al. [24] for tripod holes. The test section had an inlet cross section of 0.24 × 0.16 m2, and the mainstream velocity was set to 25 m/s measured by a five-hole probe. Air was supplied to the test section from a variable speed blower, and the rectifier was used to obtain uniform mainstream. An air compressor and high pressure gas tank was used to provide the coolant gas, i.e. air or N2/CO2, respectively. The coolant massflow rate was controlled and measured by electric mass flowmeters. The coolant temperature was adjusted by a heat exchanger prior to entering the mainstream and a difference within 0.5°C to mainstream temperature was ensured due to pressure sensitive paint requirement. The coolant temperature in the cavity was measured by thermocouples. The approaching boundary layer and level of freestream turbulence were measured by a constant temperature anemometer system (DANTEC90N10) with hot-wire probe from Dantec Inc. The probe was installed in the center of the wind tunnel and locates 10D in front of the film cooling holes. The measured voltages were converted to velocities using a polynomial fit from calibration. The approaching boundary layer was shown in Fig. 3. The streamwise mean velocity was in good agreement with the near-wall log-law and the viscous sublayer trends (u+=y+). The boundary layer characteristics were shown in Table 1. The boundary layer had a thickness of δ/D = 1.89, a displacement thickness of δ*/D = 0.25, a momentum thickness of κ/D = 0.2, and a shape factor H = 1.23 typical for turbulent boundary layers.

2.2. Film cooling configurations and test conditions Two different film cooling configurations were studied in the experiments, as shown in Fig. 4. The injection angle (α) was 35° for both the simple and compound angle holes. The compound angle (β) was 45° for the compound angle hole. Both the film cooling configurations had the same pitch-to-diameter ratio (P/D) of 5. The length-to-diameter ratio (L/D) was varied from 0.5 to 5 as shown in Table 2. For each geometry, there were five holes in one row on the test plate to provide good periodicity (see Table 3). The mainstream was set to 25 m/s and the Reynolds number based on hole diameter was around 6000. The mainstream was around 298 K in the experiments, and coolant gas temperature was adjusted to fall within a 0.5 °C difference. Seven blowing ratios (M) were chosen to obtain film cooling effectiveness data from 0.3 to 2 as shown in Table 2. Hence there were in total 70 sets of experiments performed for the simple angle hole and compound angle hole. 2.3. Film cooling measurement techniques Pressure sensitive paint (PSP) has been widely used in measuring film cooling effectiveness such as Russin et al. [25], Zhang et al. [26], and Ahn et al. [27]. Recently detailed uncertainty analysis work has been conducted by Natsui et al. [28] and Johnson et al. [29]. It is proved that the PSP technology is a powerful tool for film cooling effectiveness measurements due to its high precision, stability, and repeatability. Film cooling effectiveness measured using PSP is based on heat/ mass analogy and thus can be expressed by oxygen concentration as [26]:

η=

T∞ − Tmix C − Cmix →η= ∞ T∞ − Tc C∞ − Cc

(2)

in which the C∞ is the oxygen mass concentration of mainstream gas, Cc is the oxygen mass concentration of coolant gas, and Cmix is the oxygen mass concentration of the gas mixture on the test surface. Oxygen mass concentration can be converted to oxygen partial pressure and the expression of film cooling effectiveness is reorganized as:

η = 1−

1 (P ) ⎡ (P O2) air ⎣ O2 mix

M

− 1⎤ M c + 1 ⎦ air

(3)

in which the (PO2)air is the oxygen partial pressure of mainstream gas, Table 2 Approaching boundary layer characteristics.

Fig. 3. Approach boundary layers measured at x/D = −10 for film cooling measurements.

148

δ/D

δ*/D

κ/D

Reθ

H

1.89

0.25

0.2

1032

1.23

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were quite similar to the present study. Some small differences were primarily attributed to inlet boundary conditions, like turbulence intensity and boundary layer state. However, the agreement was generally quite good, which indicated the high quality of the PSP measurement technique.

Table 3 Geometry configuration and test conditions. Parameter

Value

Um Tm, Tc DR M L/D

25 m/s 298 K 1.0 (N2), 1.5 (CO2) 0.3, 0.5, 0.8, 1.0, 1.2, 1.5, 2.0 0.5, 1, 2, 3.5, 5

3.2. Discharge coefficient The discharge coefficient Cd was the ratio of actual mass flow rate to ideal mass flow rate through the film cooling hole. The ideal mass flow rate was calculated by assuming an isentropic one dimensional expansion from the coolant plenum total pressure p1t to the crossflow static pressure p2s. The definition is expressed in Eq. (4):

(PO2)mix is the oxygen partial pressure of coolant gas, Mc is the average molecular weight of air, and Mair is the molecular weight of coolant. PSP is an oxygen-quenching photo-luminescent material which emits light when excited. The emitted light intensity is reduced with the existence of oxygen. Currently, the Uni-FIB PSP (UF470-750) from ISSI Inc. was used in the experiments. LED light with a wavelength of 470 nm excited the PSP and the emitted light was recorded by a CCD camera with a filer to shield the excitation light [19]. Four different kinds of images were recorded during the experiments: image with mainflow and N2/CO2, image with mainflow and air, image without mainflow and coolant (reference image), and background image (to remove noise). The light intensity was subtracted from these images and normalized in a manner to get light intensity ratio. The light intensity ratio was converted to pressure ratio using a calibration curve shown in Fig. 5 which was obtained using a calibration device similar to Li et al. [23]. The pressure was normalized with the room pressure (P0), while the intensity data were normalized with three different reference conditions recorded at room pressure and at the same temperature of the correspondent curve (I0). The typical uncertainty of adiabatic film cooling effectiveness measurements variedwith different coolant gas, i.e. CO2 or N2. The uncertainty was estimated to be 4.5% for η around 0.3, and 9% for η around 0.1 if N2 was used, while the uncertainty was estimated to be 6% for η around 0.3, and 11% for η around 0.1 if CO2 was used [24]. The uncertainty in the values of Cd was found to be less than 2.5% in most of the cases, increasing up to 4.0% for very low pressure ratios. All the uncertainty analysis was based on 95% confidence.

m˙

Cd = π 2 D p1t 4

( ) p1t

p2s

(κ + 1)/2κ

2κ (κ − 1) RT1t

⎛ ⎝

⎜

p2s (κ − 1)/ κ

( ) p1t

− 1⎞ ⎠ ⎟

(4)

The total pressure and temperature in the coolant supply plenum and the static pressure in the crossflow were measured using a threehole probe. Since the coolant supply plenum was significantly large compared with the hole diameter, the velocity head was negligible. Fig. 7 shows the discharge coefficient for simple angle hole with varying L/D. Apprarently, Cd increaseed as p1t/p2s increased, with it asymptotically reached a constant as p1t/p2s is high. Note that the three longest L/D holes showed nominally the same magnitudes for almost all preesure ratios. When L/D was decreased to 1 or 0.5, the Cd increased dramatically to a much higher magnitude, indicating the high throughflow capacity of the short hole. It was also observed that the Cd of compound angle hole was a little bit smaller than that of simple angle hole. 3.3. Adiabatic effectiveness The results followed the objectives with discussion on the effect of density ratio, compound angle and length-to-diameter ratio. Detailed film cooling effectiveness distribution, laterally averaged data, and area averaged data were shown.

3. Results and discussions

3.3.1. Effect of density ratio Detailed film cooling effectiveness distributions for simple angle hole with varied density ratio for L/D = 0.5 and L/D = 5 have been shown in Fig. 8. Results with blowing ratio of 0.3, 0.8 and 1.5 were shown in the figure. Like previous studies, the effect of increasing blowing ratio was clearly seen in Fig. 8a: the coolant lifted off from the surface as the M increased, and the film cooling effectiveness decreased. Blown-off phenomena happened when M was larger than 0.5, and reattachment could be seen when M = 0.8. It could also be observed that the film effectiveness in L/D = 0.5 were much higher than the corresponding cases in L/D = 5. The reason was associated with the high turbulence intensity in the coolant jet core, which was indicated by the accompanying large eddy simulation study. The high turbulence intensity in jet core enhanced the dissipation of counter rotating vortex pair, which attenuated the entrainment of high temperature gas into the bottom wall. The high turbulence intensity also enhanced the lateral spread of coolant to achieve a better lateral cooling coverage. This was contrary to the effect of high turbulence intensity in the mainstream [30], which decreased the film cooling effectiveness. The effect of density ratio was also shown in Fig. 8. When the density ratio was increased at M = 0.3, the film effectiveness showed an enhanced lateral spread but a weakened streamwise coolant convection for both L/D = 0.5 and L/D = 5. The reason was that the jet momentum was decreased when density ratio was increased, causing an enhanced lateral mixing with crossflow and a faster coolant dissipation in streamwise direction. Hence, jet with DR = 1.0 showed higher film effectiveness than jet with DR = 1.5. Fig. 8a shows the coolant jet still

3.1. Comparison with other investigations Fig. 6 shows the laterally averaged film cooling effectiveness comparison between present data and published data from Waye et al. [11], Saumweber et al. [12], and Schmidt et al. [18]. The pitch-to-diameter ratio, length-to-diameter ratio, and density ratio in the published data

Fig. 5. PSP calibration curves under different temperature conditions.

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Fig. 6. Laterally averaged film cooling effectiveness comparison with published data: (a) simple angle hole, (b) compound angle hole.

Fig. 7. Discharge coefficient for holes with varying L/D, (a) simple angle hole, (b) compound angle hole.

3.3.2. Effect of compound angle Fig. 10 shows the film cooling effectiveness distribution for simple angle hole and compound angle hole with L/D = 0.5 and L/D = 3.5. In Fig. 10a, when the L/D was 0.5, the film cooling effectiveness distribution for simple angle hole and compound angle hole were basically the same, because the compound angle did not exert typical influence on the jet and the exit jet direction was almost non-changed. When M = 1.5, the blown-off phenomenon occurred for the simple angle hole in the downstream area of the hole, while no blown-off phenomenon occurred in the compound angle hole, indicating that the compound angle had the effect of suppressing jet blown-off at the low L/D and high blowing ratio. In Fig. 10b, when the L/D was 3.5, the effect of deflecting jets by compound angle became obvious. At the low blowing ratio M = 0.3, the film cooling effectiveness distribution for simple angle hole and compound angle hole were different downstream the hole, though the compound angle hole did not show much priority. When the blowing ratio was increased to 0.8, the asymmetry in film effectiveness became quite obvious due to the transformation of a counter rotating vortex pair in simple angle hole to a single main vortex in compound angle hole. The high film cooling effectiveness area downstream the compound angle hole was significantly larger than that of simple angle hole, since the compound angle had the effect to suppress the jet lift-off. In simple angle hole, the regions between holes had low film effectiveness

attached the wall and showed an enhanced streamwise coverage due to small length-to-diameter ratio when the density ratio was increased at M = 0.8. The film cooling effectiveness in DR = 1.0 was still higher than DR = 1.5. However, the trend was reversed for cases with M = 1.5 in L/D = 0.5, M = 0.8 and 1.5 in L/D = 5. The coolant lifted off and the slowed momentum jet brought about two benefits: enhanced lateral coolant spread and counteraction of coolant lift-off. Therefore, the film effectiveness was higher with DR = 1.5. When M = 1.5 in L/ D = 5, the coolant lift-off was severe and the density ratio effect was marginal where decreasing the coolant jet momentum was not sufficient to prevent the jet lift-off. Fig. 9 shows the laterally averaged film cooling effectiveness for simple angle hole with varied density ratio for L/D = 0.5 and L/D = 5. Fig. 9a shows that the laterally averaged data of DR = 1 were higher than that of DR = 1.5 when M = 0.3 and 0.8, Higher jet momentum caused longer film coverage, since the jet still attached the wall. But when M = 1.5, the jet lifted off and the low momentum jet in DR = 1.5 showed better lateral and streamwise film coverage. Fig. 9b shows that the jet with low momentum had higher film coverage when M = 0.8, and the jet started to lift off at M = 0.8 when L/D = 5. Hence, a jet with high density ratio showed higher film effectiveness from M = 0.8 when L/D = 5, which was consistent with the findings of Wright et al. [30].

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Fig. 8. Film cooling effectiveness distribution for simple angle hole with varied density ratio for, (a) L/D = 0.5 and (b) L/D = 5.

Fig. 12 shows the local lateral film effectiveness distributions for simple angle hole and compound angle hole at four streamwise locations: x/D = 5, 10, 20, 30. The lateral distributions of film effectiveness of simple and compound angle hole almost collapsed when L/D = 0.5, indicating that the compound angle was of no effect in short length-todiameter ratio regardless of blowing ratio. Fig. 12b shows the typical distinction of simple and compound angle hole, where the film effectiveness peak of compound angle moved to positive y direction and showed higher values for high blowing ratio M = 1.5. Note that in Fig. 12b there were regions where the film effectiveness was zero at x/ D = 5 and 10 even for compound angle hole, indicating the coolant jet no longer merged at this region. However, the merging of coolant from different holes existed for L/D = 0.5 due to strong lateral spread, so there was no zero film effectiveness region in Fig. 12a. Also note that, the film effectiveness was much higher for L/D = 0.5 than L/D = 3.5 at x/D = 20 and 30 when M = 1.5, regardless of compound angle. This was caused by two reasons: one was the jet lift-off in L/D = 3.5 which prevents the coolant covering the bottom wall, the other was the fast dissipation of the counter rotating vortex pair due to high coolant core

due to jet entrainment effect. However, when the compound angle was imposed, the jet showed enhanced lateral spread and the film effectiveness between the hole was increased, causing a more uniform lateral distribution. When the blowing ratio was further increased to 1.5, the jet had been completely blown off for simple angle hole, but the compound angle hole still maintained a high film effectiveness downstream the hole till 10D. Therefore, when the length-to-diameter ratio was small, the compound angle had little effect on enhancing film cooling effectiveness. When the length-to-diameter ratio was large, the compound angle could enhance film cooling effectiveness especially when the blowing ratio was comparatively high. Fig. 11 shows the laterally averaged film cooling effectiveness distribution for simple angle hole and compound angle hole with L/ D = 0.5 and L/D = 3.5. It was shown that the effect of compound angle in L/D = 0.5 was slight on the film cooling effectiveness in Fig. 11a. The laterally averaged data for compound angle was slightly higher than the simple angle hole in the near hole region. However, in Fig. 11b the compound angle hole showed higher film effectiveness, especially at M = 0.8 and 1.5.

Fig. 9. Laterally averaged film cooling effectiveness for simple angle hole with varied density ratio for, (a) L/D = 0.5 and (b) L/D = 5.

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Fig. 10. Film cooling effectiveness distribution for simple angle hole and compound angle hole with (a) L/D = 0.5 and (b) L/D = 3.5 with varied blowing ratio, DR = 1.5.

phenomenon was obvious, and the coolant core showed a striped shape, leading to a worse lateral diffusion and film coverage. When the L/D was 5, the jet blowed off first and then reattached in the region of x/ D = 3–5. This phenomenon was typical for film jet flow. In general, the length-to-diameter ratio effect of simple angle hole on film jet mainly happened in region before x/D = 10–15. Behind that the jet was fully mixed with the crossflow and the film coverage was almost the same. Fig. 13b shows the film cooling effectiveness for the compound angle hole. Generally, there was no jet blown-off phenomenon in the downstream of the hole due to the compound angle. When the L/D was 0.5, the jet did not appear skewed because the length-to-diameter ratio was too small. Like the simple angle hole, the compound angle hole also showed significant lateral diffusion and even higher film cooling effectiveness. When the L/D was 2, the jet deflection was obvious due to compound angle. As the L/D increased to 5, the high film effectiveness region downstream the hole gradually became narrower and shorter, though not particularly noticeable. Generally, the film effectiveness increased gradually as the L/D

turbulence intensity which weakened the entrainment of crossflow on the wall.

3.3.3. Effect of length-to-hole diameter ratio Fig. 13 shows the Film cooling effectiveness distribution for simple angle hole and compound angle hole at M = 0.8 with varied length-todiameter ratio. Fig. 13a shows the film cooling effectiveness for the simple angle hole. Generally, the film cooling effectiveness showed a decreasing and then increasing trend as the length-to-diameter ratio increases. When the L/D was 0.5, the film cooling showed the highest values and the film jet did not show blown-off phenomena. Coolant showed good coverage till 5D downstream the hole and the effectiveness was very high. The coolant showed strong lateral diffusion and the high effectiveness region resembled an oval shape. The high film cooling effectiveness was attributed to strong mixing between jet and crossflow and enhanced dissipation of counter rotating vortex pair, caused by the skewed velocity profile and high turbulence intensity of the not-fully-developed jet. When the L/D was 2, the blown-off

Fig. 11. Laterally averaged film cooling effectiveness distribution for simple angle hole and compound angle hole with (a) L/D = 0.5 and (b) L/D = 3.5 with varied blowing ratio, DR = 1.5.

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Fig. 12. Local lateral film effectiveness distributions for simple angle hole and compound angle hole with (a) L/D = 0.5 and (b) L/D = 3.5, DR = 1.5.

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Fig. 13. Film cooling effectiveness distribution for (a) simple angle hole and (b) compound angle hole at M = 0.8 with varied length-to-diameter ratio, DR = 1.5.

simple angle hole and compound angle hole with varied length-todiameter ratio and blowing ratio. Fig. 14a and b shows that the effect of L/D on film cooling effectiveness was mainly concentrated in the downstream region of the hole till 5D, and it was more obvious for simple angle hole at low blow ratio. However, at the high blow ratio, the length-to-diameter ratio effect were significant. Film hole with L/ D = 0.5 showed highest film effectiveness. Meanwhile, the simple angle hole and compound angle hole both showed lowest film cooling effectiveness when L/D = 3.5.

increased when the L/D was greater than 2, especially the high effectiveness region downstream the hole. This was consistent with the results of Lutum et al. [9]. However, the film effectiveness decreased gradually in the region downstream the hole till 7D. The reason was related to the hole shape and length-to-diameter ratio. Larger length-todiameter ratio leaded to more fully development of intube flow, and the mixing with crossflow resulted in different behaviors in simple angle hole and compound angle hole. Fig. 14 shows the laterally averaged film cooling effectiveness of

Fig. 14. Laterally averaged film cooling effectiveness with varied length-to-diameter ratio and blowing ratio: (a) simple angle hole, M = 0.5, (b) compound hole, M = 0.5, (c) simple angle hole, M = 1.5, (d) compound hole, M = 1.5. DR = 1.5.

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distribution with M of 0.5 and 1.2. The film effectiveness for L/D = 0.5 in low and high blowing ratios were comparable to that for L/D = 5. In low blowing ratio, the lateral coolant diffusion and coolant coverage were comparable for L/D = 0.5 and 5. In high blowing ratio, the film effectiveness for L/D = 5 were enhanced due to compound angle and thus were comparable to that for L/D = 0.5. Fig. 17 shows the local lateral film effectiveness distributions for simple and compound angle hole at x/D = 5 and 20 with M = 1.5 and DR = 1.5. In Fig. 17a, L/D = 0.5 showed the highest film effectiveness while the L/D = 2 showed the lowest film effectiveness. Hole with L/ D = 0.5 showed higher peak value and better lateral coverage than L/ D = 2 and 5. In Fig. 17b, the film effectiveness for L/D = 0.5 showed wider coverage than L/D = 2 and 5 at x/D = 5. However, the film effectiveness for L/D = 0.5 showed much higher values than L/D = 2 and 5 at x/D = 20. The film effectiveness distribution almost collapsed for L/D = 2 and 5. Also observed was that the peak point deflected from x/D = 0 for L/D = 2 and 5. 4. Overall estimation of density ratio, compound angle, and length-to-hole diameter ratio Fig. 18 shows the area averaged film cooling effectiveness for simple angle hole and compound angle hole for DR = 1.5. the averaged region of x/D ranged from 0 to 30. Each figure combined the effect of blowing ratio M and length-to-diameter ratio L/D. It was shown that film cooling effectiveness was the highest when L/D = 0.5. when the blowing ratio was below unity, the area averaged film cooling effectiveness increased with the increase of L/D for the simple angle hole with 2 ≤ L/D ≤ 5, which was consistent with Lutum et al. [9]; For the compound angle hole, the area averaged film cooling effectiveness of compound angle hole in Fig. 18b showed slight reduction trend when L/D increased from 0.5 to 3.5. When the blowing ratio was above unity, the averaged effectiveness showed a decreasing trend when the L/D increased from 0.5 to 3.5, while an increasing trend when the L/D increased from 3.5 to 5 for simple angle hole and compound angle hole, leading to a minimum effectiveness when L/D = 3.5. This phenomenon was attributed to the intube flow state and the jet-crossflow interaction which was highly associated with length to diameter and blowing ratio. The effect of density ratio was also evaluated in the form of area averaged data. Fig. 19 shows the area averaged film cooling effectiveness difference due to density ratio: Δ = DR(1.5)−DR(1.0) for simple angle hole and compound angle hole. Obviously the effect of density ratio was varied with blowing ratio and hole length-to-diameter ratio. Increasing the density ratio provided a negative effect when the M ≤ 0.5 for simple and compound angle hole. The negative effect was most significant when the L/D = 0.5 and decreased as the L/D increased. When the M > 0.5, increasing the density ratio generally provided a positive effect. The film effectiveness increment was up to 0.04 when the L/D is 0.5. Note that in the compound angle hole, when the blowing ratio was up to 2, the positive effect of increasing density ratio was attenuated, since the jet lift-off became significant even with compound angle (see Fig. 19). The effect of compound angle was also assessed in area averaged data in Fig. 20. Generally, the compound angle enhanced the film effectiveness at all L/D values and blowing ratios, regardless of density ratio. In Fig. 20, four regions were noteworthy: A, B, C, and D. The first region A was the region with L/D = 0.5, where the compound angle showed very slight positive effect on film effectiveness. The reason was that the short L/D exerted little influence on the jet direction even with compound angle. The second region B was the region with L/D = 1 and 0.5 ≤ M ≤ 1.5, where the jet lift-off was severe in simple angle hole and the compound angle could suppress the jet by enhancing lateral spread. The third region was region C with M ≤ 0.6, where the jet still attached to the wall and thus the compound angle made little difference. The fourth region D was the region where L/D = 3 and L/

Fig. 15. Film cooling effectiveness distribution for simple angle hole with varied blowing ratio and length-to-diameter ratio, DR = 1.5.

Fig. 15 shows the film cooling effectiveness distribution for simple angle hole with varied blowing ratio and length-to-diameter ratio. The density ratio was 1.5. Here the L/D of 0.5 and 5 were selected to illustrate the effect of L/D on film cooling distribution with M of 0.5 and 1.2. When the blowing ratio was 0.5, the oval-shaped film effectiveness pattern of L/D = 0.5 showed a wider film coverage than the L/D = 5. However, the streamwise coolant diffusion and dissipation was more severe for L/D = 0.5 and the film effectiveness downstream of x/ D = 10 was lower than L/D = 5. When the blowing ratio was 1.2, the film effectiveness of L/D = 0.5 was much higher than L/D = 5. The jet momentum was low and the coolant still attached to the wall surface for L/D = 0.5, while strong jet lift-off happened for L/D = 5. The simple angle hole with short L/D showed significant superiority over long L/D when the blowing ratio was high. Fig. 16 shows the film cooling effectiveness distribution for compound angle hole with varied blowing ratio and length-to-diameter ratio. The density ratio was 1.5. Here the L/D of 0.5 and 5 were selected to illustrate the effect of L/D on compound angle hole film cooling

Fig. 16. Film cooling effectiveness distribution for compound angle hole with varied blowing ratio and length-to-diameter ratio, DR = 1.5.

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Fig. 17. Local lateral film effectiveness distributions for (a) simple angle hole and (b) compound angle hole at x/D = 5 and 20 with M = 1.5 and DR = 1.5.

5. Discussion of the coolant-to-mainstream scaling parameters

D = 1.5. The effect of compound angle showed different behaviors with different density ratios at this region, i.e. film effectiveness enhancement was large when DR = 1.0 while small when DR = 1.5. The jet momentum of DR = 1.0 and DR = 1.5 when M = 2.0 was 4 and 2.67, respectively. The jet momentum of low density ratio was much higher than that of high density ratio. Therefore, the compound angle could have more significant enhancement on film effectiveness under higher jet momentum conditions.

It is very important to obtain an effective scaling parameter to correlate film effectiveness since it is a function of downstream distance and momentum thickness Reynolds number. Goldstein et al. [31] proposed a parameter ξ which is a function of X/(MS). The correlation works well when ξ is larger than 10, since the film effectiveness is more 2-D in this regime. However, the correlation grossly overpredicts when ξ is smaller than 10, since the regime is more 3-D. Cutbirth et al. [32]

Fig. 18. Area averaged film cooling effectiveness for (a) simple angle hole, DR = 1.5, (b) compound angle hole, DR = 1.5.

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Fig. 19. Area averaged film cooling effectiveness difference due to density ratio: Δ = DR(1.5)-DR(1.0), (a) simple angle hole, (b) compound angle hole.

experimentally found that the momentum flux ratio scaled the film effectiveness from compound angle holes on a turbine vane pressure side. Sinha et al. [33] proved that the film effectiveness is better scaled based on the momentum flux ratio (I) than the blowing ratio. The data for high and low density ratio almost collapsed on a single line when plotted against I. The reason is that the momentum flux ratio combines the effect of density ratio and blowing ratio (I = M2/DR), which can scale the film effectiveness better than either individual parameter. Anderson et al. [34] recently experimentally investigated the scaling parameters with simple holes. They concluded that the use of momentum flux ratio and velocity ratio results in a better collapse of film effectiveness data. Vinton et al. [35] also confirmed that I is a proper scaling parameter of film effectiveness by measuring simple film effectiveness with varying density ratio from 1.0 to 4.0. The present study firstly examines the three scaling parameters, i.e., velocity ratio, blowing ratio, and momentum flux ratio in scaling film effectiveness with varying length-to-hole diameters. Fig. 21 shows the area averaged film cooling effectiveness scaling with three parameters. The scaling with velocity ratio VR was shown in

Fig. 21a. It was seen that the velocity ratio was not capable to collapse the film effectiveness values for the full range of coolant flow rates. The film effectiveness peak was noticed to occur at VR = 0.7 for L/D = 0.5 and VR = 0.4 for L/D = 3.5, regardless of coolant density and compound angle. The results of L/D = 3.5 were consistent with the results of Pederson et al. [36] and Anderson et al. [34], where film effectiveness peak occurred at a relatively constant velocity ratio of VR = 0.4 to 0.5. Reducing the hole length shifted the peak to higher VR, indicating increased coolant attachment ability to the wall. In Fig. 21b, the film effectiveness data distributed irregularly, which demonstrated that the blowing ratio was not successful in scaling the film effectiveness data at all range of coolant flow rates for both L/D, simple angle and compound angle holes. Therefore, it was stated that the blowing ratio was the least choice for scaling film effectiveness data with varied density ratio. Comparing Fig. 21a and b, it was found that the film effectiveness was lower for higher density ratio at any given coolant flow rate when scaling with VR, while the trend was reversed when scaling with M. This implied that the jet with higher density ratio was prone to lift off as the VR increases. When it comed to momentum flux ratio in Fig. 21c, it

Fig. 20. Area averaged film cooling effectiveness difference due to compound angle: Δ = β(45°)-β(0°), (a) DR = 1.0, (b) DR = 1.5.

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Fig. 21. Area averaged film cooling effectiveness scaling with three parameters for L/D = 0.5 and L/D = 3.5, (a) velocity ratio VR, (b) blowing ratio M, and (c) momentum flux ratio I.

was found that the momentum flux ratio provided a much better collapse of the data than VR and M. The collapse even became better as the L/D increases. Clearly, it was stated that the momentum flux ratio should be used to scale the coolant flow rates for simple and compound angle holes with varied L/D values. Close inspection of Fig. 21a and c, one would notice that the VR was superior to I in scaling the coolant flow rates at VR < 0.4 or I < 0.2, while the I was better for higher VR or momentum flux ratio. The jet was still attaching the wall for VR < 0.4 or I < 0.2, while the jet lifted off when the coolant flow rate increased. Therefore, it might be stated that the film effectiveness scaled well with the velocity ratio when the jets were attached to the wall, while the momentum flux ratio was more favorable if the jets were detached from the wall. The scaling capacity of velocity ratio and momentum flux ratio was further illuminated in Fig. 22 and Fig. 23 by the film effectiveness contours. Fig. 22 shows the film cooling effectiveness distribution with low and high velocity ratio VR. It was clearly noticed that at low velocity ratio of VR = 0.3, the film pattern was quite similar for DR = 1 and DR = 1.5. The intensified cooled area for both cases were quite

similar. At high velocity ratio of VR = 1, the jet showed better adherence to the wall and the film effectiveness was higher for DR = 1, which was consistent with Fig. 21a. However, the trend was reversed when the data was scaled with momentum flux ratio, as shown in Fig. 23. For low momentum flux ratio of I = 0.09, the jet showed an elongated jet footprint and the intensified cooled area was slightly narrower for DR = 1, while the jet showed slightly stronger lateral diffusion and better lateral coolant coverage for DR = 1.5. As the momentum flux ratio increased to 1, the film effectiveness contours were quite similar to each other for DR = 1 and DR = 1.5, which was consistent with Fig. 21c. Fig. 24 shows additional information about the scaling of film effectiveness with momentum flux ratio for L/D = 1 and L/D = 2. Generally, the holes of L/D = 1 and L/D = 2 showed a better collapse of the data with momentum flux ratio than hole with L/D = 0.5. Also observed was that the scaling was performed better for compound angle hole than the simple angle hole. It was concluded that the scaling of film effectiveness with momentum flux ratio becomes better as the L/D increases. Here it might be considered a L/D value between 1 and 2 as a 158

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Fig. 22. Film cooling effectiveness distribution with low and high velocity ratio VR.

Fig. 23. Film cooling effectiveness distribution with low and high momentum flux ratio I.

point beyond which the scaling with momentum flux ratio was satisfying.

(1) Discharge coefficient increased as coolant-crossflow pressure ratio increased, reaching a constant as p1t/p2s was high. The three longest L/D hole showed similar magnitudes of Cd, while much higher values for L/D = 0.5 and 1. Also compound angle hole showed lower discharge coefficient than simple angle hole. (2) Effect of density ratio on the film cooling effectiveness was associated with the blowing ratio. Increasing density ratio provided a negative effect when the M ≤ 0.5 for simple and compound angle hole, which a positive effect when the M > 0.5. As with the effect of compound angle, it generally enhanced the film effectiveness at all L/D values and blowing ratios, regardless of density ratio. Furthermore, compound angle positive effect was maximized when

6. Conclusions The present study investigated the adiabatic film cooling effectiveness on a flat plate surface downstream a row of simple and compound angle holes using pressure sensitive paint (PSP) technique. Effect of density ratio, blowing ratio, compound angle and length-to-diameter ratio were indicated by detailed local, laterally averaged, and area averaged film effectiveness data. The main conclusions were listed as follows:

Fig. 24. Area averaged film cooling effectiveness scaling with momentum flux ratio I for L/D = 1 and L/D = 2.

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L/D = 1 and 0.5 ≤ M ≤ 1.5, since the jet lift-off was severe in simple angle hole and the compound angle could suppress the jet by enhancing lateral spread. (3) Effect of length-to-diameter ratio was influenced by the blowing ratio. Film effectiveness was highest when L/D = 0.5 and 1, regardless of blowing ratio and compound angle. This was because the counter rotating vortex pair or the single asymmetric vortex dissipation was much enhanced due to high turbulence intensity in the jet core, resulting in attenuated entrainment of high temperature gas into the surface. The film cooling effectiveness of simple angle hole increased as L/D increased from 2 to 5 when M ≤ 1, while showed a minimum value at L/D = 3.5 when M ≥ 1. On the contrary, the film cooling effectiveness of compound angle hole showed a minimum value at L/D = 3.5 regardless of blowing ratio. (4) The scaling methods of film effectiveness with velocity ratio, blowing ratio, and momentum flux ratio were discussed. The velocity ratio was superior to momentum flux ratio in scaling the coolant flow rates at VR < 0.4 or I < 0.2, while the momentum flux ratio was better for higher VR or momentum flux ratio. Also found was that the scaling of film effectiveness with momentum flux ratio became better as the L/D increases. A L/D value between 1 and 2 might be considered as a point beyond which the scaling with momentum flux ratio was satisfying.

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Acknowledgement The authors would like to acknowledge the financial supports from National Natural Science Foundation of China (No. 51676106 and No. U1613204). Nomenclature Latin Cd D DR H I L M P P T Tu U U' X Y Z Θ Η ω δ δ* κ Subscripts

discharge coefficient film hole diameter (m) density ratio (ρc/ρm) boundary layer shape factor momentum flux ratio film hole length (m) blowing ratio (ρcVc/ρmVm) pressure (Pa) lateral hole pitch (m) temperature (K) turbulence intensity mean velocity components fluctuating velocity components streamwise coordinate (m) lateral coordinate (m) wall-normal coordinate (m) Dimensionless temperature, (Tm− T)/(Tm−Tc) film cooling effectiveness vorticity boundary layer thickness (m) boundary layer displacement thickness (m) boundary layer momentum thickness (m)

c j m n

coolant jet mainstream axis direction

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effectiveness of round and shaped holes on a flat plate, ASME paper No. GT201656210, 2016. [36] D. Pedersen, E. Eckert, R. Goldstein, Film cooling with large density differences between the mainstream and the secondary fluid measured by the heat-mass transfer analogy, ASME J Heat Transf 99 (1977) 620–627.

[34] J. Anderson, E. Boyd, D. Bogard, Experimental investigation of coolant-t-mainstream scaling parameters with cylindrical and shaped film cooling holes, ASME paper No. GT2015–43072, 2015. [35] K.R. Vinton, T.B. Watson, L.M. Wright, D.C. Crites, M.C. Morris, A. Riahi, Combined effects of freestream pressure gradient and density ratio on the film cooling

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