An experimental investigation of film cooling performance of louver scheme

International Journal of Heat and Mass Transfer 54 (2011) 1387–1399

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

An experimental investigation of film cooling performance of louver scheme M.G. Ghorab a, I.G. Hassan a,⇑, T. Lucas b a b

Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC, Canada H3G1M8 Pratt and Whitney Canada, Longueil, QC, Canada J4G 1A1

a r t i c l e

i n f o

Article history: Received 21 August 2010 Received in revised form 18 November 2010 Accepted 18 November 2010 Available online 7 January 2011 Keywords: Film cooling effectiveness Heat transfer coefficient ratio Louver TLC NHFR

a b s t r a c t An experimental investigation of the film cooling performance of louver schemes using Thermochromic Liquid Crystal technique is presented in this paper. The louver scheme allows the cooling flow to pass through a bend and encroach with the blade material (impingement effect), then exit to the outer surface of the aerofoil through the film cooling hole. The cooling performance of the louver scheme was analyzed for blowing ratios ranging from 0.5 to 1.5 and for a density ratio of 0.94. The results showed that the louver scheme enhances the local and the average film cooling effectiveness, and the net heat flux reduction better than other published film hole configurations. The louver scheme also provides a wide extensive spread of the secondary flow over the outer surface, thus enhancing the lateral film cooling performance over the downstream surface area. Moreover, the louver scheme produces a lower heat transfer ratio than other film hole geometries at low and high blowing ratios. As a result, the louver scheme is expected to reduce the gas turbine airfoil’s outer surface temperature by provide superior cooling performance than other film cooling schemes hence increasing the airfoil life time. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Many experimental and computational studies were dedicated to understanding the complex flow and heat processes involved in film cooling of gas turbine airfoils in order to ultimately devise the best cooling schemes possible. Film hole geometry is one of the most influential parameters in film cooling performance. Fig. 1 presents schematics of several advanced film hole configurations: fanshaped film hole [1], laterally diffused holes [2], forward and lateral shaped holes [3], console film hole [4], laidback fanshaped [5], straight fan-shaped holes [6], compound angle fanshaped holes (CAFSH) [7] and fan-shaped with trench holes [8]. Eriksen and Goldstein [1] experimentally investigated the effect of the blowing ratio on the centerline film cooling effectiveness for injection film holes having a 35° inclination angle and a lateral expansion angle of 10° at a distance of 1d from the entrance of the film hole as shown in Fig. 1a. The film cooling effectiveness along the centerline was shown to increase with increasing blowing ratio until a peak value is reached, at a particular downstream location, after which, the film cooling effectiveness decreased with any further increase in blowing ratio. Film holes having 10° lateral expansion angles significantly enhance the spreading of the secondary flow downstream of the film hole injections. The fan shaped hole also decreased the exit velocity of the secondary flow thereby reducing its penetration into the main stream.

⇑ Corresponding author. E-mail address: [email protected] (I.G. Hassan). 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.12.002

Cho et al. [2] studied the effect of the film hole geometry on heat transfer characteristics and the film cooling effectiveness. The holes had a 30° inclination angle and 0°, 45° and 90° compound angles. The first geometry analyzed was a circular hole. The second one was conical at a 4° angle. The third configuration used a film hole that was tilted 4° along its center and conically shaped with an 8° angle downstream at L/d = 5.4. The three different film hole geometries were investigated for blowing ratios equal to 0.5, 1.0, and 2, and a density ratio of 1.0. Higher film cooling effectiveness was obtained by increasing the lateral injection angle. It was also found that the film hole with a 4° conical angle as shown in Fig. 1b provided the best cooling performance under all conditions. Film cooling performance of three different film hole configurations were analyzed experimentally by Yu et al. [3]. The first configuration was circular and coolant was injected at a 30° angle in the streamwise direction and L/d = 10. The second film cooling hole analyzed had a shape was similar to the baseline circular, but a 10° forward diffusion angle start at distance of 0.8d below the test surfaces. The third hole was obtained by adding an extra 10° diffusion angle in the lateral direction to the previous hole. The three configurations were tested for two blowing ratios (Br = 0.5 and 1.0), at a Reynolds number ranging between 2300 and 4300, based on the hole diameter. They observed that the third configuration (Fig. 1c) provided the highest film cooling effectiveness. However, its heat transfer coefficient was close to that obtained with the second configuration and lower than the one of the circular scheme. Sargison et al. [4] investigated experimentally the film cooling performance and the aerodynamic losses for a converging slot-hole

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Nomenclature Symbols Br Cp D Dh Dr Fn H Hue I K L Nu p q Re T t Tw Um x, y, z a

g gav h

blowing ratio (qjuj/qmum) specific heat hydraulic diameter of film hole (m) hydraulic diameter of the main duct density ratio (qj/qm) p Frossling number = Nu/ Re heat transfer coefficient (W/m2 K) hue color component momentum flux ðqj u2j =qm u2m Þ thermal conductivity of plate (W/m K) length of film hole (m) Nusselt number (hDh/k) film hole pitch (m) heat transfer flux (W/m2) Reynolds number (qDhUm/l) temperature (K) time (s) average wall temperature (K) normal main stream velocity in x direction (m/s) coordinates thermal diffusivity (m2/s), = (k/qCp) local film cooling effectiveness ((Tf  Tm)/(Tj  Tm)) span wise averaged film cooling effectiveness ðT w  T m Þ=ðT j  T m ÞÞ non-dimension surface temperature ((Tm  Tj)/ (Tm  Tw))

(Console) as shown in Fig. 1d, over a flat plate. The console cross section was changed from circular shaped at the hole inlet to slot shaped at the hole exit. The hole’s wall was convergent in the streamwise direction and divergent in the lateral direction. The cross section area decreased from the inlet to the exit so that the flow accelerated toward the exit. The accelerated flow was less turbulent and yielded a more stable jet, which reduced secondary and mainstream penetration. Reynolds number, based on the slot height, was 144,000 with a main stream momentum flux ratio of 1.1. The console film hole provided an adiabatic effectiveness that was laterally uniform. The console’s laterally averaged heat transfer coefficient was also similar to that produced by the slot hole. The console film hole yielded less aerodynamic losses than circular and fan shaped holes, but induced higher thermal stress concentrations, particularly at the exit area. Dittmar et al. [6] investigated the film cooling performance of four different film hole configurations using infrared thermography. Double rows of cylindrical injection holes and discrete slots were used along with a single straight fanshaped hole and compound angle fanshaped holes. The results showed that the four film holes provided the same film cooling effectiveness at low blowing ratios. However, the fanshaped hole, with a compound angle as shown in Fig. 1g, provided the highest film cooling effectiveness at high blowing ratios. Taslim and Khanicheh [7] analyzed the effects of two different compound hole angles on the film cooling performance. The setup involved a single row of 90° compound angle circular film holes (d = 7.5 mm), and 45° for shaped film holes, with a 25° inclination angle in the downstream direction. The two film hole schemes were tested for blowing ratios ranging from 0.7 to 4.0. The highest overall film cooling effectiveness was achieved with the diffuser shaped holes, as shown in Fig. 1f. It was concluded that increasing the exit cross-sectional area decreased the jet penetration into the main flow because it reduced the momentum flux, consequently producing a higher cooling effectiveness.

q s u

e

density (kg/m3) color change time (s) over all film cooling effectiveness in the practical engine (1/h) least square error

Subscripts and superscripts av average c centerline f film i initial j refers to jet m main stream o without film s solid w wall conditions Abbreviations CHT conjugate heat transfer HSV hue, saturation, value HTC heat transfer coefficient NHFR net heat flux reduction RGB red, green, blue TIFF Tagged Image File Format TLC Thermochromic Liquid Crystal

Baheri et al. [8] numerically studied the effect of a trench at the exit of circular and fan shaped film holes at two blowing ratios, 0.6 and 1.25. The holes were inclined by 35°; the trench dimensions were 0.43d in depth and 2d in width. Jet lift off was eradicated at high blowing ratios in the case of the trenched fanshaped hole (Fig. 1h), and the coolant spread more in the streamwise direction. However, the trench film hole included sharp areas, which may result in vortex formation, and hence, high thermal stresses inside the film hole and an increase in the aerodynamic losses. Goldstein and Taylor [9] investigated regions of high and low heat transfer coefficients around the injection hole. The heat transfer coefficient was high in regions between two contiguous holes at high blowing ratios, and decreased with decreasing blowing ratios. It was also high at exit regions along the film hole sides, as the interaction between the main-stream flow and the injection flow creates eddies and high shear stresses. At high blowing ratios, the heat transfer coefficient increased as the cooling jet partially reattaches to the airfoil surface, and decreased further downstream of the film hole (x/d > 10). Makki and Jakubowski [10] and Kohli and Bogard, [11] found that forward-and-laterally positioned film holes have lower heat transfer coefficients and higher film cooling effectiveness when compared to round holes. Makki and Jakubowski’s [10] conclusion arose after comparing the cooling performance for forward-andlaterally expended holes with circular film hole geometries using a 35° inclination angle and a pitch to diameter ratio of 3. The effect of film hole spacing arrangements, staggered and in line, was studied by Ligrani et al. [12] They reported that the arrangement of the film hole rows did not significantly influence the heat transfer coefficient at low blowing ratios, while at high blowing ratios, the heat transfer coefficient increased with increasing number of film rows. Schmidt et al. [13] investigated the effect of three different compound angles (CA) on the heat transfer coefficient. The first case was a circular hole with a 0° CA, the second hole had a 60°

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d

10°

y

β

Flow

1389

x 4° 4°

6.1 d 4d

α

35°

d

(a) Eriksen and Goldstein [1]

(b) Cho et al. [2]

10°

d

0.2d d

0.79 d

1.75d 3d 10d

30°

35o

(c)Yu et al. [3]

(d) Sargison et al. [4] Console film hole. x/d 14°

10o

Flow

d 45o

15° 4.4d d

L/d=8 P/d=5.56

o 25o 10

d

3d 2d

(e) Saumweber et al. [10] Laidback fanshaped

(f) Taslim and Khanicheh [7]

x/d 0.43d

o

35

z/d

2d d

o

14

4d

2d

(g) Dittmar et al. [6]

(h) Baheri et al. [8] CAFSH

Fig. 1. Different advanced published film hole configurations (reproduced from the referred references).

CA in the lateral direction, and the third hole had a 15° forward expansion with a 60° CA. They reported that the heat transfer coefficient increases with increasing momentum flux for 0° CA and 60° CA. Furthermore, the forward expansion augmented the lateral mixing, such as the heat transfer coefficient further increased with increasing momentum flux. Ekkad et al. [14] used a TLC technique to investigate the effect of a 45° and a 90° compound angle in the span wise direction on the heat transfer coefficient of holes having a 35° inclination angle in the stream-wise direction. The compound angle provided high

mixing between the main and the jet streams, which increased the heat transfer coefficient as the flow over the surface was turbulent. Liu et al. [15] investigated the effect of the console film hole exit–entry area ratios of 0.67 and 1.33 on the film cooling performance. They noted that, a smaller exit–entry area ratio provided a better thermal protection and a higher film cooling effectiveness at a minimum discharge coefficient. A small exit–entry area promoted flow acceleration at low-turbulence, providing a stable film cooling over the wall surfaces.

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Saumweber et al. [16] used fanshaped, laidback fan shaped, and circular holes to study the film cooling performance experimentally using turbulence ratios of 3.5, 7.5, and 11%. Both fanshaped holes were expanded 14° laterally, and the laidback fanshaped hole was expanded 15° in the streamwise direction as presented in Fig. 1e. A length to diameter ratio of 6 was used and the film hole geometries were analyzed at blowing ratios of 0.5, 0.75, 1.0, 1.25 and 1.5. The authors noted that the shaped holes provided similar cooling and heat transfer characteristics and reported that no benefit was drawn from using the layback configuration. Zuniga et al. [17] investigated experimentally the effect of pitch-to-diameter ratio (P/d) on film cooling effectiveness. They used three different ratios, namely, 4, 8 and 12, for circular and shaped holes embedded in tranches. They observed that, by increasing P/d from 4 to 8, the film cooling effectiveness remained constant for the cylindrical holes with a trench. But the film cooling effectiveness of the trenched fanshaped holes decreased with increasing P/d at low and high blowing ratios. Immarigeon and Hassan [18] investigated numerically the film cooling performance of the louver scheme. They inspected four different geometries using different numbers of pedestals. The operating conditions consisted of blowing ratios ranging from 0.87 to 5.22, 3% turbulence intensity and a density ratio of 1.73. They reported that at high blowing ratios, the pedestals have negligible effects on the laterally averaged film cooling effectiveness near the hole exits (x/d < 2), yet the coolant spread well downstream. Zhang and Hassan [19] continued that numerical investigation and compared the louver scheme performance to that of traditional circular and shaped film holes using single and multiple rows in staggered and inline arrangements. They noted that the louver scheme provided the highest average and local film cooling effectiveness at lower heat transfer ratio. The above literature review can be summarized as follows: hole geometries affect the film cooling performance. Laterally and forward expanded film holes provide higher values of spanwise averaged effectiveness and lower values of heat transfer coefficients than round holes, moreover, they reduce jet lift-off and hence increase film cooling performance downstream of the film cooling holes. A compound injection angle increases the spanwise averaged effectiveness. However, compound jet angles generally produce higher values of heat transfer coefficient due to an increase in the turbulence over the surface. 1.1. Louver film cooling scheme Fig. 2 shows a schematic of the louver scheme on a flat plate. Numerical investigations of the louver scheme film cooling performance were done by Immarigeon and Hassan [18] and Zhang and Hassan [19] over a flat plate. The scheme was designed to combine the advantages of the traditional film cooling and the impingement effect. The secondary flow passes through a bend that impacts the inner blade material (impingement effect) then exits to the outer surface of the aerofoil through the film cooling holes with less jet lift-off. The present experimental study compares the film cooling performance of the louver scheme to that of the circular hole on a flat plat using TLC sheets for different blowing ratios and a density ratio of 0.94. A uniform velocity of 23 m/s and a temperature of 22 °C are applied at the inlet. 10% mainstream turbulence intensity was measured using Particle Image Velocimetry (PIV). The secondary turbulence intensity was estimated to be 3%. The turbulent length scales of the main and secondary flows are 0.001 m and 0.0015 m, respectively. The secondary flow, having a temperature ranging from 42 °C–45 °C, passes through a plenum, and then moves through the louver scheme to spread over the downstream surface. The main Reynolds number, based on the hydraulic diameter of the main duct, is 1.14  105 for all experi-

y

2.9d

x

Impingement on material 35° 0.5d

Bend

25°

1d d Plenum

1.4d

3d x

Jet exit

d

z 10° 3d

1.4d

Fig. 2. Louver film hole geometry.

mental tests. Table 1 lists the test conditions and geometrical parameters of the circular and louver schemes. The main and secondary stream Reynolds numbers are calculated based on the hydraulic diameter of the main duct, and the film hole diameter respectively. The manufacturing process of the louver scheme consisted of a regular machining process to create individual parts of the scheme that are later assembled together. Prototyping methods can be used to manufacture the louver scheme over either flat plate or airfoils. 2. Test facility setup and experimental methodology Fig. 3 presents a schematic diagram of a new open loop film cooling test rig. The air supplied to the test rig is provided by a compressed air tank at a regulated pressure of 7 atm. The test rig consists of mechanical and thermography systems. The thermography system includes a Data Acquisitions System (DAQ), light sources, a camera, and a computing workstation. The mechanical system consists of main and secondary flow loops. The secondary air was heated while the main stream was kept at a temperature equal to that of the supply. Each loop includes a pressure controller to maintain a steady operating pressure. A Rosemount MultiVariable Mass Flow Meter (3095MV) was used to measure the main flow, and a rotameter (FL-1502A) was used for the secondary flow. The flow rate in each loop was adjusted manually through gate and needle control valves. The main flow meter records the load pressure and temperature to correct for density variations in measuring the flow rate. A divergent–convergent nozzle was designed to settle down the main flow before entering the test section. A honeycomb was installed at the exit of the convergent nozzle to create a more uniform velocity distribution for the main flow entering the mainstream duct. The divergent–convergent

Table 1 Measurement conditions. Parameters

Circular hole

Louver scheme

d (cm) p/d Br Dr I ReD (duct) Red (hole)

1.39 3 0.5, 1.0 0.94 0.27, 1.085 1.14E+07 1.25E+04, 2.50E+04

1.27 3 0.5, 1.0, 1.5 0.94 0.27, 1.071, 2.385 1.24E+07 1.23E+04, 2.47E+04, 3.68E+04

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1391

Fig. 3. A schematic diagram of designed film cooling test rig.

nozzles and the main duct were made from cast acrylic sheets, 1.27 cm thick, with 91% light transmittance. The main duct cross section has dimensions of 11 cm  5 cm and a total length of 150 cm, measured from the converging exit area. Numerical work was conducted to investigate the effects of end wall geometry on the film cooling results. A height of 2.5d was found suitable for small Reynolds numbers. Regarding the width, further experimental work had been done using a test section provided with holes at distance of 1.5d from the wall. Processing of these holes results gave the same results as the centerline one. This means that holes that are away from the wall by 2.5d are completely insensitive to end wall effects. The plenum is made from cast acrylic, and is insulated to reduce heat losses to the surroundings. The thermocouples used to measure the secondary stream temperature were positioned just before the holes to eliminate any influence of the plenum volume on the secondary stream temperature. An electrical variable power air heater with a maximum capacity of 1200 Watt was installed upstream of the plenum to heat the secondary flow. A fast acting two-way solenoid valve routes the flow through a bypass until steady state conditions are achieved, then the secondary flow is allowed to pass to the test section through the plenum. 2.1. Instrumentation and measurement techniques Pressure transducers, air flow meters, and thermocouples were selected and installed at specific locations in the test rig to measure the pressure, flow rate, and temperature of the main and secondary flows. Type-T thermocouples with a fine precision were used to measure the temperatures in the plenum and Type-E were used to measure the main flow temperatures. In addition, a Type-E thermocouple was used to measure the secondary flow temperature after the air heater. Two pressure transducers (0–5.2 bar) were installed in the main duct and the plenum to measure the pressure of the main and the secondary flows, respectively. A Rosemount multi-variable mass flow transmitter (3095MV) was used to measure the main flow rate. The two output signals from the pressure transducers and the multi-variable mass flow transmitter were a

digital display and an analog signal of 4–20 mA. Additionally, PGH-45L-100 Omega pressure gauges were also placed in each loop in order to monitor the pressure. The output signals from the instruments were connected to an M series NI data acquisition system (DAQ) and then monitored using Labview software. An inhouse Labview code was developed for this study in order to monitor and save a variety of signals from pressure, flow, and temperature instruments. The solenoid valves were also controlled through the Labview software. A digital 3CCD IK-TF7C Toshiba camera was used to capture the Thermochromic Liquid Crystal (TLC) images over the downstream surface area of the film holes at a rate of 10 fps. The acquired simultaneous images were transferred to the computing workstation through a NI PCIE-1340 dual frame grabber, which can work up to two base Camera Link configurations using the Labview program. The image quality depends on the adjustment of the lens and the light distribution, and intensity. The light intensity was adjusted with a variable light source. A color calibration target was used as an objective to adjust the resolution. The captured, Red– Green–Blue (RGB) images were saved in Tagged Image File Format (TIFF) with a size of 1024  768 pixels. An in-house image processing code was created using MATLAB software. The RGB images were converted to hue values through the image processing code, then to temperature values, using TLC calibration curves. 2.2. Thermochromic Liquid Crystal measurements The unencapsulated Thermochromic Liquid Crystal (TLC) sheet used in this study has a fine resolution and uniform TLC coating, and produces a clear RGB color with minimal uncertainty in measurements. The TLC sheet consists of a 125 lm clear polyester layer that is colored black on one side and coated with microunencapsulated TLC. The other side of the sheet is covered with an adhesive backing (pressure-sensitive adhesive) that is used to adhere to the desired surface. The R25C5W TLC sheet was used throughout this study. The TLC sheets retain color play characteristics for many months under normal handling conditions. The Hue angle method was used to quantify the observed color to

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ðT f  T m Þ ðT j  T m Þ

the material temperature. The Hue is described in Eq. (1) by Hay and Hollingsworth [20].

g¼

" pffiffiffi # 1 3ðG  BÞ Hue ðHÞ ¼ arctan 2p ð2R  G  BÞ

Inserting this definition into Eq. (4) gives,

ð1Þ

or; T f ¼ gT j þ T m ð1  gÞ

" T w  T i ¼ 1  exp

In Eq. (1), R, G, and B are digital values of color signals and the Hue (H) value ranges from 0 to 1 or from 0 to 360°. The color analysis for HSV (hue-saturation-value) was used in the image processing and its value ranges from 0 to 255 (8-bit scale). An aluminum flat plate, having a 2 mm thickness, was used for the TLC calibration and for measuring the heat transfer coefficient without film cooling. Two identical flat electrical heaters (KH 608/2.5-P) were installed underneath the plate. The two heaters were connected to a variable direct-current DC power supply, which was used to control the input power to the heaters. The TLC sheet was installed on top of the plate. The bottom surface of the plate was insulated with a 1.27 cm thick polystyrene layer in order to reduce the heat transfer from the heaters to the surrounding. Four flat sticky thermocouples (SA1XL-T) were installed on the flat plate near the TLC sheet from both sides in order to record the surface temperatures during the calibration process. This method preserved the image measurement conditions, such as camera focus and lighting for the actual tests. The target image area was divided into regions of interest (ROIs) of 5  5 pixels (0.81  0.81 mm) in size, and each region has a unique calibration curve. Calibration was achieved by correlating the thermocouple reading to the corresponding hue values at steady state measurements. A 3rd order polynomial was fit through the calibration data points and was appropriate for most of ROIs, while a 5th order fit was better in some other regions of interest. Therefore, combinations of 3rd and 5th order polynomial fits were used over the target surface. Dividing the target area into ROIs provided good quality data points to cover the entire color range.

The local heat transfer coefficient (hf) and film cooling effectiveness (g) were determined by assuming one-dimensional transient heat conduction over a semi-infinite solid. Cast acrylic has low thermal conductivity (k = 0.19 W/m K), and a thickness of 3.2 cm, and the transient test duration was 30 s, which allowed the use of semi-infinite solid assumption. The one dimensional unsteady heat conduction equation, without heat generation, can be written as,

qC p

  @T @ @T ¼ k @t @y @y

ð2Þ

The initial and boundary conditions are;

t ¼ 0;

T ¼ Ti

y ¼ 0;

hðT f  T w Þ ¼ k @T @y

y ¼ 1; T ¼ T i

9 > = > ;

ð3Þ

According to the initial and boundary conditions in Eq. (3), the solution for Eq. (2) is obtained as follows:

! pffiffiffiffiffi! 2 t t Tw  T h a h a erfc ¼ 1  exp 2 Tf  Ti k k

ð4Þ

 is the thermal diffusivity of the wall material. where, a The film temperature (Tf), jet temperature (Tj), and main stream temperature (Tm) are used to determine the film cooling effectiveness (g) as,

k

2

!

pffiffiffiffiffi!# h at  ½gðT j  T m Þ þ T m  T i  erfc k ð6Þ

A single transient test of 30 s was conducted to calculate the two unknown variables, h and g using, a non-linear least square regression method. In Eq. (6), Tw, Tj, and Tm are time-dependent. The best fit was achieved when the summation of squared residuals was minimal. The non-linear least square regression method was used to solve Eq. (6) for every ROI over the target surface. The regression method was preferred in transient tests at high flow temperatures response over Duhamel’s superposition method [21]. The regression analysis technique was also used to solve Eq. (6), and reduce the experimental error [5,21]. In the present study the secondary flow temperatures were difficult to control during the experiments, therefore the non-linear least square regression method was used. The surface temperatures of each ROI over the target surface were measured using TLC technique at each time step (s) during transient measurements as,

T wðROIÞ ðh; gÞjt¼s ¼ T TLC jt¼s

ð7Þ

A total of 300 images (N) were captured during experimental tests. In the first few images (n), no TLC response was recorded over the entire target area. As a result, N–n equations were applied in Eq. (6) to calculate the two parameters (h and g) using nonlinear least square regression method. The optimum solution was achieved by minimizing the least square error (e) for each ROI over the downstream film cooling surface as follows:

eðh; gÞ ¼ 2.3. Heat transfer data reduction

2 h at

ð5Þ

N  2  1X T wðROIÞ ðh; gÞt¼s  T TLC jt¼s 2 i¼n

ð8Þ

The number of unused images (n) influences the final solution of h and g. The ‘‘n’’ is dependent on the time response of the secondary flow over the downstream TLC surface. Each ROI, had a different n value, based on the flow conditions. For every test, different regions of interest were selected downstream of the film holes to determine the proper ‘‘n’’ values that would provide the minimum least square error (e), in Eq. (8). A linear profile of ‘‘n’’ with x/d, was used to calculate the two parameters, h and g, for the entire downstream surface. The ‘‘n’’ value increased in the downstream direction. The heat transfer coefficient without film cooling (ho) is measured using an aluminum flat plate. The heat flux from the two flat heaters to the plate surface is adjusted using a power supply. The main flow passes over the aluminum plate, which is positioned similarly to the test section. After achieving the steady state condition, an image is captured. For every ROI, the heat transfer coefficient without film cooling (ho) was calculated as follows:

ho ¼ q=ðT w  T m Þ

ð9Þ

An error analysis was conducted to determine the data accuracy of measured heat transfer coefficient, film cooling effectiveness, Frossling number, net heat flux reduction (NHFR), and blowing ratio. The film cooling heat transfer coefficient over the flat plate can be expressed as follows:

 ; kÞ h ¼ f ðT w ; T m ; T j ; T i ; t; a

ð10Þ

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 , and k are dTw, dTm, dTj, dTi, dt, The variations in Tw, Tm, Tj, Ti, t, a  , and dk, respectively, which yields the following uncertainty in da heat transfer coefficient :

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2 Uh T w @h @T w T m @h @T m k @h @k þ þ ......þ ¼ h h @h k h @T w T w h @T m T m ð11Þ Eq. (11) is complex, and calculating the uncertainty can be difficult. Therefore, for simplification purposes, only the square root of the summation of the squares of the relative uncertainty is used, as shown in Eq. (12). s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  2  2  2  2  2  2ffi  @T w @T m @T j @T i @t @a @k þ þ þ þ þ þ a t k Tw Tm Tj Ti

Uh ¼ 

ð12Þ And the uncertainty in film cooling effectiveness is;

0.9

ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2  2  2  2  2  @T w @T m @T j @T i @t @a @k 2 Ug ¼  þ þ þ þ þ þ þðUhÞ a Tw Tm Tj Ti t k

ð13Þ

The average uncertainty in the heat transfer ratio (hf/ho), film cooling effectiveness, Frossling number, net heat flux reduction, and blowing ratio were estimated to be ±11%, ±8%, ±14%, ±15%, and ±11%, respectively.

3. Results and discussion The film cooling effectiveness and heat transfer coefficient of the circular film hole were compared with previously published data in order to validate the current experimental technique and methodology. The cylindrical film geometry was selected as it is the most frequently used baseline geometry in previous research.

0.7

Present study (circular) Br = 0.5 Russin et al. [22] Br = 0.4 Russin et al. [22] Br = 0.6

0.8 0.7

*

Present study (circular) Br = 1.0 Ekkad et al. [23]

0.6

Coulthard et al. [24] Br = 1.0

Ekkad et al. [23] Br = 0.5

0.5

0.6 0.4

ηc

ηc

0.5 0.4 0.3

*

*

*

0.3

*

*

*

*

*

*

0.2

*

*

0.2

*

0.1

0.1 0

0

2

4

6

8

10

0

12

0

2

4

6

x/d

8

10

12

10

12

x/d

(a) Film cooling effectiveness 2

Present study (circular) Br = 0.5

1.75 1.5

Sen et al. [25] Circular Br = 1.0 1.5 1.25

hf / ho

hf /ho

Sargison et al. [4] Br = 0.82 Gritsch et al. [26] Br = 1.0

Gritsch et al. [26] Br = 0.5

1.25 1

1

0.75

0.75

0.5

0.5

0.25

0.25

0

Present study (circular) Br = 1.0

1.75

Sen et al. [25] Circular Br = 0.5 Ekkad et al. [14] Br = 0.5

0

2

4

6

8

10

12

0

0

2

4

6

8

x/d

x/d

(b) Heat transfer coefficient ratio Fig. 4. Validation centerline film cooling effectiveness and heat transfer ratio for circular film hole with published data.

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Film cooling holes of 1.39 cm in diameter, an inclination angle of 35°, and a compound angle of 0° were used for validation. The local centerline film cooling effectiveness of the circular hole at Br = 0.5 and 1.0 is compared with published data in Fig. 4a, and an agreement of more than 90% is found. The published data used for comparison at Br = 0.5 and for x/d > 6 was taken from [22,23], and at Br = 1.0, data was taken from [23]. However, a distinct discrepancy is noted between the results and published data near the injection hole at low and high blowing ratios. It is probably due to the 3D nature of the flow structure in the region, which subsequently increases the error in image processing. The film cooling effectiveness in [24] is the highest because it was calculated based on adiabatic wall conditions (Tf = Tw). Fig. 4b compares the centerline heat transfer coefficient ratio of the circular hole to that in published data at blowing ratios of 0.5 and 1.0. Good agreement is found at x/d > 3 with data from [14,25,26] at Br = 0.5. The disparity error between the predicted results and the published data decreases along the downstream direction and increases near the injection hole, as shown in Fig. 4b. At a high blowing ratio, the heat transfer coefficient ratio obtained was in agreement with [25,26], within experimental

uncertainty (±12%). The centerline heat transfer ratio obtained here was in agreement with [4] at x/d > 5 (Fig. 4b). Some discrepancy was recorded in the region near the exit hole (x/d < 5). The agreement found between published literature and the present results validate the current experimental technique and methodology. Fig. 5 provides historical temperature profiles at Br = 1.5, downstream of the trailing edge of the louver scheme at two different span-wise locations: z/d = 0.0 and 1.0. The secondary flow is heated, while the main flow is kept at supply air temperature. The secondary flow spreads widely over the target surface after it is expelled from the louver hole, consequently changing the TLC colors with time from black to red then to green followed by blue, as illustrated in Fig. 5a. The temperature profile is high at z/d = 0.0. It diminishes faintly along the downstream and span-wise directions and increases with time as shown in Fig. 5b. The centerline temperature profiles for x/d < 3 do not vary with time after 10 s as the secondary flow starts to spread further downstream as shown in Fig. 5b. The temperature profiles increase with time for

1 0.9

Louver Br=0.5

0.8

Present Circular Br=0.5 Yu et al. Shaped [3] Br=0.5

0.7

ηc

0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8

10

12

x/d

(a) Br = 0.5 1.5

Louver, Present study (Exp.), Br = 1.0 Present circular Br = 1.0

1.4 1.3

Yu et al. shaped [3] Br = 1.0

1.2

∗

1.1

Eriksen et al. [1] Circular Br = 1.0 Eriksen et al. [1] Shaped Br = 1.0

1

ηc

0.9 0.8 0.7 0.6 0.5 0.4 0.3

∗

∗

0.2

∗

∗

∗

0.1 0

0

2

4

6

∗ 8

10

12

x/d

(b) Br = 1.0 Fig. 5. Historical downstream TLC images and temperature profiles for louver scheme at different span-wise locations (Br = 1.5).

Fig. 6. Centerline film cooling effectiveness performance for louver scheme with other published data at low and high blowing ratios.

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x/d P 3 in the streamwise direction, near the hole center, and for z/ d > 0 in the span-wise direction. 3.1. Film cooling effectiveness performance Fig. 6a and b compare the centerline film cooling effectiveness of the louver scheme at a blowing ratio of 0.5 and 1.0 with those of circular and shaped film holes. At a low blowing ratio (Br = 0.5), the secondary flow exits the circular film hole then spreads over the surface and provides better film cooling performance along the centerline than that of the shaped hole [3]. The louver scheme enhances more the film cooling effectiveness over the surface when compared to the circular and shaped film holes, especially close to the jet holes. In the case of a circular hole, at a high blowing ratio [27], the secondary flow jet lifts off, penetrates the main stream, and does not re-attach to the downstream surface after it exits the jet holes, yielding a reduction in film cooling effectiveness. Film cooling holes with large exit areas enhance the film cooling performance [7]; the reduction in the secondary flow momentum and the more uniform jet at exit reduce the jet liftoff. Consequently, fanshaped holes provide higher film cooling 1

Present Louver Br = 1.0 Present circular Br = 1.0 Yu et al. Shaped [3] Br = 1.0

0.9 0.8 0.7

ηav

0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8

10

12

x/d

effectiveness at high blowing ratios [1,3] than circular holes, as shown in Fig. 6b. The present results show however, that the louver scheme provides the highest film cooling effectiveness at high blowing ratios. The louver scheme film cooling effectiveness is high because of the impingement effect which reduces the secondary flow momentum and the jet lift-off. As the secondary flow momentum is more uniform at the film hole exit [28], it re-attaches to the downstream surfaces, resulting in the highest film cooling effectiveness. The film cooling effectiveness decreases gradually in the streamwise direction as the secondary flow momentum decreases. Fig. 6b compares experimental data of the louver scheme to numerical results by [29], at Br = 1.0. The centerline film cooling effectiveness obtained numerically is 10% higher than that obtained experimentally. This discrepancy is partly due to the fact that the density ratio used in the numerical investigation is 2.13 times that used in the experimental study; the film cooling effectiveness increases with increasing density ratio [23]. Higher density ratio can be achieved inside the lab by using gases other than air for secondary flow. The discrepancy is also due to the fact that the numerical investigation assumed adiabatic downstream boundary conditions, while heat losses could not be avoided in the experiments. The laterally averaged film cooling effectiveness of the louver scheme is compared to that of other traditional and advanced published film hole geometries at blowing ratios of 1.0 and 1.5, in Fig. 7. A wider film hole exit area produces higher lateral average film cooling effectiveness close to the hole exit. At high blowing ratio (Br = 1.0), the louver scheme directs the jet flow in the horizontal direction as seen from the downstream velocity profiles presented in [28,29], hence, improving film cooling performance downstream the film holes (Fig. 7a). The louver scheme lateral average film cooling effectiveness is higher than that of traditional circular hole, forward and lateral shaped hole [3], and compound angle fan-shaped holes (CAFSH) [7]. It provides film cooling performance similar to that of the console film hole [4] for x/d > 4. The jet lift-off increases with increasing blowing ratio for traditional film holes [27]. The louver scheme adjusts the coolant momentum in the horizontal direction at high blowing ratios [28], hence, providing the highest lateral average film cooling effectiveness at Br = 1.5, as shown in Fig. 7b, which compares experimental data obtained with the straight fanshaped holes [6], and fanshaped hole [30].

(a) Br = 1.0 1

1 0.9

0.9

Lu et al. [30] Br = 1.5

0.8

0.7

0.7

0.6

0.6

0.5

0.5

η

ηav

0.8

Louver Br = 1.5 Dittmar et al. [6] Br = 1.5

0.4

0.4

0.3

Br = 0.5

0.3

Br = 1.0

0.2 0.2

0.1 0

Central

Br = 1.5 Br = 0.5

0.1

0

2

4

6

8

10

12

x/d

(b) Br = 1.5 Fig. 7. Laterally averaged film cooling effectiveness performance of the louver scheme at a high blowing ratio.

Br = 1.0

Average

Br = 1.5

0

0

2

4

6

8

10

12

x/d Fig. 8. Effect of blowing ratio on downstream centerline and laterally averaged film cooling effectiveness for louver scheme.

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One of the advantages of shaped holes over circular holes is that film cooling effectiveness increases with increasing blowing ratio due to the absence of the jet lift off. The horizontal slot inside the louver scheme promotes the reattachment of the jet to the wall, thus enhancing the effectiveness in the stream wise direction. The shaped hole exit allows the spreading of the jet in the span wise direction. In Fig. 8, the louver scheme centerline and laterally averaged film cooling effectiveness downstream the film holes increases with increasing blowing ratio, because of the increase in the amount of coolant injected. The latter contributes to the effectiveness in the stream wise direction in two ways, Firstly, it increases the covered length, and secondly, it increases the local effectiveness value by providing more insulation to the surface. Fig. 8 shows that the length covered by the coolant is larger for Br = 1 and 1.5 than for Br = 0.5. Increasing the amount of coolant also contributes to increasing the effectiveness in the span wise directions, as the area covered by the jet is larger.

3.2. Heat transfer performance Streamwise variations in the centerline heat transfer coefficient ratio (hf/ho) of the louver scheme and other film holes are illustrated in Fig. 9a and b at 0.5 and 1.0 blowing ratios respectively. At low blowing ratio, near the injection hole, the louver scheme produces variations in the heat transfer ratio similar to those of the present circular hole and of [25], but it provides higher values far downstream as shown in Fig. 9a. The heat transfer coefficient ratio increases with increasing blowing ratio for traditional film cooling holes, but is unvarying for the louver scheme as shown in Fig. 9b (Br = 1.0). The heat transfer coefficient ratio for the present circular film hole, [1,25,26] is higher than that of the louver scheme, as shown in Fig. 9b at high blowing ratio. The louver scheme creates a thin layer of secondary flow over the surface which reduces the turbulent vortices downstream of the film holes, according to [19,28], therefore the ratio of hf/ho is independent of the blowing ratio downstream. Good conformity is found at Br = 1.0 between the experimental and numerical [28] heat transfer ratio of the louver scheme as displayed in Fig. 9b.

2

Present circular Br=0.5 Present Louver, Br=0.5

1.75

2

Sen et al. [25] Circular Br=0.5

1.8

1.5

Yu et al. [3] Shaped hole, Br = 0.5 Dittmar et al. [6] SFSH hole Br = 0.5 Saumweber et al. [16] Fan-shaped Br = 0.5 Jubran and Maiteh [31] Circular two rows, Br = 0.6

1.6 1.25

(hf /ho)av

hc /ho

Present Louver Br = 0.5 Present circular Br = 0.5

1

1.4

Ligrani et al. [32] Circular two rows, Br = 0.5

1.2 1

0.75

0.8 0.5

0

1

2

3

4

5

6

7

8

9

10

11

12

0.6

x/d 0

(a) Br = 0.5 2

4

X

Present circular, Br = 1.0 Sen et al. [25] Circular Br = 1.0

1.8

Louver Br = 1.0 Present circular Br = 1.0

Eriksen et al. [1] Circular Br = 1.0 Gritsch et al. [26] Br = 1.0

1.6

Yu et al. [3] shaped hole Br = 1.0 Yuen et al. [33] two rows, Br = 1.0

1.25

X

1

10

X

X

12

2

(hf /ho)av

1.5

8

(a) Br = 0.5

Louver, Present study (Exp.), Br = 1.0

1.75

6

x/d

Zhang [28], Louver, (Num.), Br = 1.0

hc/ho

2

X

1.4 1.2 1 0.8

0.75

0.6 0.5

0

1

2

3

4

5

6

7

8

9

10

11

12

0

2

4

6

x/d

x/d

(b) Br = 1.0

(b) Br = 1.0

Fig. 9. Comparison centerline heat transfer ratio for louver scheme with other film hole configurations at low blowing ratio.

8

10

12

Fig. 10. Comparison lateral average heat transfer ratio of louver scheme with other film hole configurations at low and high blowing ratios.

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3.3. Net heat flux reduction The film cooling effectiveness and heat transfer coefficient are combined in order to evaluate the film cooling performance of the film hole geometries using the net heat flux reduction (NHFR). The NHFR is presented in Eq. (18), and is used by Sen [25] and Gritsch et al. [26] to calculate the heat transfer reduction of an airfoil with film cooling as compared to an airfoil without film cooling. The NHFR can involve a negative effect (NHFR < 0.0) when the film cooling effectiveness is relatively low and the heat transfer coefficient ratio (hf/ho) is high. In this case, a hot spot may occur over the airfoil surface. The NHFR has a value between 0 and 1.0 when film cooling has a positive effect. When the surface is uncovered with coolant flow (g = 0.0 and ho/hf = 1.0), the NHFR is equal to zero; this occurs far downstream of the jet exit holes. The NHFR is also equal to zero when the heat fluxes with and without film cooling are equal, or at ho/hf = 1  g  h. When the film cooling

2

Present Louver, Br = 0.5 1.75

Present circular, Br=0.5 Yu et al. [3] Shaped hole Br=0.5

1.5 1.25

NHFR

The laterally averaged heat transfer coefficient ratio (hf/ho) profiles in the streamwise direction for the louver scheme and other published film hole geometries, at low and high blowing ratios, are presented in Fig. 10a and b, respectively. The laterally averaged value of hf/ho for the straight fanshaped holes used by [6] is equal to 1.2 at a blowing ratio of 0.5 along the downstream direction. Straight fanshaped holes [6] produced a higher heat transfer ratio than other film hole geometries; such as fanshaped [3,16], the present circular study, circular hole [31,32] for two rows, and the louver holes. The laterally averaged hf/ho obtained with the louver scheme is similar to that obtained with the fanshaped geometry by Yu et al. [3]. The heat transfer ratio (hf/ho) is highest for the fanshaped holes [33] close to the injection hole, and the solution trend is similar trend to that of [23] for x/d > 2.5 as shown in Fig. 10a. At Br = 1.0, the shaped hole [33] results in a heat transfer ratio higher than that of [3] and of the louver scheme as presented in Fig. 10b. The laterally averaged hf/ho increases more with blowing ratio for the two rows arrangement. The ratio of hf/ho for the louver scheme increases gradually in the downstream direction until it reaches unity, as the heat transfer coefficient increases far downstream with decreasing film cooling effectiveness. The main flow velocity and film hole geometry have significant effects on the heat transfer ratio. The effect of the Frossling number is investigated for the circular hole and the louver scheme. The p dimensionless number (Nu/ Re) combines the effects of the main flow velocity, heat transfer coefficient, and film hole exit area. The Reynolds number is calculated based on the main stream velocity and the hydraulic diameter of the film hole exit. Fig. 11 presents the effect of the blowing ratio on the laterally averaged Frossling number at two downstream locations (x/d = 2.0 and 6.0) for the circular hole and the louver scheme. The circular film hole Frossling number decreases with increasing blowing ratio due to the jet lift-off near the film hole area only. The louver scheme Frossling number increases from 0.9 to 1.0 as the blowing ratio increases from 0.5 to 1.0. After unity is reached, the Frossling number decreases with increasing blowing ratio since the heat transfer decreases for blowing ratio greater than unity. Frossling number is not significantly affected by blowing ratio variations in the downstream direction.

1 0.75 0.5 0.25 0

0

2

4

6

8

10

12

x/d

(a) Br = 0.5 2

Present Louver, Br = 1.0

1.2 1.75

1.1

Yu et al. [3] Shaped hole Br=1.0 1.5

1 0.9

NHFR

1.25

0.8

Fn av

Present circular, Br=1.0

0.7

1 0.75

0.6

0.5

Present circular x/d = 2

0.5

Louver x/d = 2

0.4

Present circular x/d = 6

0.25

Louver x/d = 6

0.3 0.2

0

0.5

0.75

1

1.25

1.5

Br Fig. 11. Lateral average Frossling number variations for louver scheme and circular hole with blowing ratio at different downstream locations.

0

2

4

6

8

10

12

x/d

(b) Br = 1.0 Fig. 12. Comparison centerline NHFR of louver scheme with other film hole configurations at low and high blowing ratios.

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effectiveness is equal to a typical overall value of cooling effectiveness for gas turbines (g = u), the NHFR value is equal to unity for all values of heat transfer ratio, according to Eq. (18). In addition, for NHFR > 1, the film cooling effectiveness (g) produced by the film hole geometry is greater than the typical overall film cooling effectiveness (u). As a result, there are three different overall film cooling performance regions for h = 1.5 (h = 1/u): negative film cooling (NHFR < 0), positive film cooling (0 < NHFR < 1), and hyper film cooling (NHFR > 1). The heat flux with and without film cooling can be presented as;

qf ¼ hf ðT f  T w Þ

ð14Þ

qo ¼ ho ðT m  T w Þ

ð15Þ

Therefore, the heat flux ratio is:

qf hf ðT f  T w Þ ¼ qo ho ðT m  T w Þ ðT T Þ

For h ¼ ðT mmT wj Þ and g ¼ Thus,

ð16Þ ðT f T m Þ ðT j T m Þ

qf hf ¼ ð1  g  hÞ q o ho NHFR ¼ 1 

  qf hf ¼1 ð1  g  hÞ ; qo ho

ð17Þ

and h ¼ 1=/:

ð18Þ

where u is the overall cooling effectiveness and is equal to 0.5–0.7 for a typical airfoil cooling system.

/¼

b  gcov þ gf ð1  gcov Þ 1 þ gcov ðb  gf Þ

The louver scheme centerline and lateral average heat transfer coefficients were lower over the downstream surface than those obtained with the circular hole but very close to those of the shaped hole. Moreover, the louver scheme heat transfer ratio is not significantly affected by the blowing ratio. The louver scheme Frossling number increases with increasing blowing ratio until it reaches a peak point then starts decreasing with any further increase in blowing ratio. It is constant along the downstream jet holes of the louver. The net heat flux reduction was presented to illustrate the overall film cooling performance by combining the film cooling effectiveness and heat transfer coefficient ratio. The dimensionless reference temperature, h = 1.5, was used to calculate the NHFR. The louver scheme provided a high film cooling effectiveness with relatively low heat transfer coefficient ratio therefore it yielded the highest NHFR in the streamwise and lateral average directions compared to circular and fan shaped holes. In conclusion, the louver scheme could increase the airfoil’s life time and allow an increase in the gas turbine inlet temperature, hence improving the overall gas turbine efficiency. The present study was focused on investigating the film cooling performance of the louver scheme. However, the proposed scheme was designed to include an impingement effect which could significantly influence the conjugate heat transfer (CHT). Therefore, further experimental and numerical work is required to investigate both the conjugate effect and the film cooling effect over an airfoil.

ð19Þ

The convective efficiency and film effectiveness are represented by gcov and gf, respectively, while b is the heat load to the part. The NHFR is investigated for the louver scheme to further evaluate the overall film cooling performance using Eq. (18). Fig. 12a and b show the centerline NHFR performance of the louver scheme and other film hole geometries at low and high blowing ratios respectively. The results show that the louver scheme produces a higher NHFR than the traditional circular and fan-shaped holes [28] at a blowing ratio of 0.5 as shown in Fig. 12a. Near the film hole exit, the louver scheme NHFR is significantly enhanced compared to other film hole geometries, and the NHFR decrease gradually in the streamwise direction. For x/d > 4, the louver scheme NHFR is approximately 15% higher than the one of the circular hole. And, the shaped hole provides the lowest NHFR at low blowing ratio, as shown in Fig. 12a. Fig. 12b shows that the louver scheme provides a high NHFR at high blowing ratio (Br = 1.0) over the downstream surface. At high blowing ratio, the jet lift-off increases in the case of a circular hole, thus producing lower NHFR, as shown in Fig. 12b. For x/d > 10, the effect of the reattached secondary flow can be detected and the NHFR results of the circular hole are nearly the same as those of the shaped hole. 4. Conclusions and recommendations The film cooling performance of the louver scheme was presented and compared with other traditional and advanced published film hole geometries. The film cooling performance of the louver scheme was investigated for blowing ratios ranging from 0.5 to 1.5 and for a density ratio of 0.94. The results showed that the louver scheme has a superior centerline and lateral film cooling effectiveness. Also, its film cooling effectiveness is enhanced with increasing blowing ratio.

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