51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
07 - 10 January 2013, Grapevine (Dallas/Ft. Worth Region), Texas
AIAA 2013-0603
Blake Johnson
1
, Kai Zhang
2
, Wei Tian
3
and Hui Hu
4
( )
Iowa State University, Ames, Iowa, 50011
An experimental study was conducted to investigate the performance of film cooling injection from a row of circular holes spaced laterally across a flat plate. A highresolution PIV system was used to conduct flow field measurements to reveal the tendencies of the coolant stream to remain attached to the test plate or to separate from it, and a Pressure Sensitive Paint (PSP) technique was used to map the distribution of the corresponding adiabatic cooling effectiveness on the surface of the test plate based on a mass-flux analog to traditional thermal effectiveness measurements. The effects of the density ratio between the cooling jet stream and mainstream flows, P , are investigated by performing isothermal experiments at fixed mass-flux ratios but using coolant streams of N
2
( P =0.97), air ( P =1.00), and
CO
2
( P =1.53). An accompanying analysis of alternative parametric scaling quantities, such as the momentum flux ratio I and bulk coolant-to-mainstream velocity ratio V r
, is performed to illuminate the extent to which this flow scenario can be described using purely kinematic means. It was found that those quantities that give more weight to P ( M and then I ) have more success to collapse data from varying P flows for relatively low coolant flow rates, while the bulk velocity ratio V r may be used with some success to scale the effectiveness from jets of higher bulk velocity ratio .
Introduction
There is great incentive to maximize the efficient operation of all aspects of gas turbine engines for reasons both economic and environmental. As global transportation demands lean increasingly upon the use of such engines, large savings can be attained by even marginal improvements in any of the many systems that they rely on to function. Because the greatest potential to increase fuel efficiency is realized through increasing the temperature of the combustion process, means to protect internal turbine components from high temperatures is necessary, typically through the implementation of film-cooling techniques. Optimization of film cooling systems possesses the potential for significant savings.
Understanding the effects of a variety of parameters on the coolant film behavior is necessary for such optimization.
The physics of film cooling has been studied widely through use of a number of experimental techniques, including infrared (IR) thermography of the surface to be cooled, flow measurements using particle-image velocimetry (PIV), and techniques exploiting the functionality of pressure sensitive paint (PSP) to measure the influence of the coolant on the surface. Leylek and Zerkle (1994) used numerical flow simulations to show that there is a complex coupling between the flows within the film hole, plenum, and cross-flow. Their results imply that the development of the flow within the coolant hole has strong bearing upon the coolant jet behavior.
1
Postdoctoral Research Associate, Department of Aerospace Engineering
2
Graduate Research Associate, Department of Aerospace Engineering.
3
Postdoctoral Research Associate, Department of Aerospace Engineering.
4
Associate Professor, Dept. of Aerospace Engineering, AIAA Associate Fellow, Email: huhui@iastate.edu
Copyright © 2013 by Blake Johnson, Kai Zhang, Wei Tian and Hui Hu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

IR thermography was used by Baldauf, et al (2001, 2002) to study the effects of density ratio upon film cooling from a row of inclined coolant holes set at an angle of 30˚. Their experiments required use of surface thermocouple–IR thermography temperature correlations to estimate the adiabatic wall temperature for determination of adiabatic film cooling effectiveness. However, use of techniques that measure surface temperature are inherently subject to effects of heat conduction within the solid material.
Thus, there is always some suspicion about whether such measurements truly yield adiabatic results.
Yang and Hu (2011) used PSP to study trailing-edge film cooling effectiveness using a stream of
Nitrogen (N
2
) as the coolant gas to exploit the Oxygen (O
2
)-quenching behavior of PSP. Similar approaches to studying film cooling effectiveness have been used by other researchers [Rallabandi, et al
(2011); Wright, et al (2011); for example]. Wright, et al (2011) showed the result that free stream turbulence has upon cooling effectiveness, causing a spanwise spread in the film cooling effectiveness, though for high blowing rate M , jet lift-off prevents different turbulence levels from affecting the effectiveness much whatsoever. Also through use of the PSP technique, Dhungel, et al (2009) studied the use of secondary film cooling holes to counteract coolant jet vortex development, showing that they can greatly reduce the likelihood of a jet to lift away from the surface. The PSP technique holds great promise for the study of film cooling effectiveness. Because it relies on a mass-flow analogue to measure the coolant flow, it yields a truly adiabatic measurement of the film cooling effectiveness. Use of the PSP technique in conjunction with PIV can provide great illumination of the physics of film cooling. For this study, both of these powerful experimental techniques have been employed to paint a detailed picture of the flow characteristics of film cooling.
Relatively few studies have investigated the scaling of film cooling jets [Goldstein, et al (1974), eg.], though within the community of film cooling researchers the blowing rate M =(
)
χ
/(
) is generally used to characterize the behavior of film cooling jets, where
indicates the fluid mass density, U indicates the bulk velocity, and the subscripts “c” and “ ∞ ” indicate the coolant jet and main stream flows, respectively. As such, M is the ratio of mass fluxes of the jet to the cross-flow. By rewriting M = PV r
, where P is the density ratio of the coolant gas to the mainstream gas and V r
is the ratio of bulk coolant velocity to the mainstream velocity, it is noted that for fixed M and mainstream flow conditions an increase in P requires a compensatory decrease in V r
. Similarly, the ratio of momentum fluxes I = M
2
/ P can be used to characterize the interaction between the coolant and main stream flow. Essentially, these quantities may help to discern the extent to which the interaction and mixing of the coolant and main streams occur primarily due to the kinematic conditions of the flow field or due to dynamic process that depend on the density disparity between the two fluids. Therefore it is worth investigating of the use of a few different physical parameters to describe the behavior of coolant jet flows of various P .
In this study, PSP is used to achieve high-resolution quantification of the adiabatic film cooling effectiveness of coolant jets of two different P values emitting from a row of cylindrical holes angled at
30˚ to the breakout surface of the test plate. High-resolution PIV measurements show some kinematic consequences pertaining to separation of the coolant from the surface for different values of P at a given
M . Finally, an analysis of the scaling parameters V , M , and I is made to determine whether any show promise for improved comparison of coolant flow behavior despite differences in coolant density.
Experimental Setup, Test Model, and Incoming Flow
The experimental study is conducted in a small open-circuit wind tunnel located at the Department of
Aerospace Engineering of Iowa State University. The tunnel has a test section with an 8 inch × 5 inch
(i.e., 200 mm×125 mm) cross section. The walls of the test section are optically transparent. The tunnel has a contraction section upstream of the test section with honeycombs and screen structures installed ahead of the contraction section to provide uniform low-turbulence incoming flow into the test section.

The turbulence intensity at the inlet of the test section was found to be less than 1.0% measured by using a hotwire anemometer.
Fig. 1: The test plate. (a) Upper surface; cylindrical holes inject flow at 30˚ to breakout plane of plate. (b) Lower surface, inlets are fluted to allow smooth entry of coolant into the holes.
A diagram of the flat test plate can be seen in Fig. 1. The test model is made of a hard plastic material using a rapid prototyping 3D printer that builds the model layer-by-layer with a resolution of about
25 microns. The test model is mounted to a plenum chamber via eight screws and sealed using a thin latex rubber gasket; details of the plenum geometry and interior flow can be found in Yang & Hu (2011).
Post-processing of the model includes wet-sanding with up to 2000 grit sandpaper and polishing to achieve a very smooth, glossy finish. A row of three cylindrical holes, each with diameter D =5 mm, have a spanwise pitch-to-diameter spacing of p / D =10 and are inclined at a 30˚ angle to the top plane of the model. The hole inlets are fluted to allow smooth coolant entry from the plenum and have a total axial length L =6 D , measured from the outer entrance plane of the fluted inlets to the breakout plane at the top surface of the test model. The axial centerlines of the holes intersect the breakout plane at a distance 115 mm from the leading edge of the model. Thus, from conditions emitting from the wind tunnel contraction, the boundary layer develops for a length of 22 D before the mainstream flow encounters the leading edge of the coolant hole (at x / D =-1 for the 30˚ hole used in this study).
The incoming boundary layer on the test plate was measured using PIV. Boundary layer profiles shown in Fig. 2 indicate the effect that M has upon the incoming velocity profile. For the M =0 (no coolant flow) case, the boundary layer thickness displacement thickness
99
at the leading edge of the coolant hole ( x / D =-1) is 0.98
D while the
∗
ι s 0.10
D . At this location, the profile follows very closely to a 1/7 th
power law profile. For nonzero M at x / D =-1 there is a noted distortion in the incoming velocity profile and somewhat lesser distortion noted at x / D =-2. The effect that increasing M has upon the incoming flow is to thicken the boundary layer and reduce its streamwise momentum. Further upstream, at x / D =-3 and -5, there is little or no observable effect of M upon the incoming velocity profile.
As shown in Fig. 3, a secondary system that employs a reservoir of compressed gas is used for the coolant flow; various gases (air, N
2
, or CO
2
) may be used as the coolant, depending on the desired P and the O
2 content. The mass flow rate of the coolant is measured using a mass flow meter (Omega FMA-1600).
The coolant may be diverted partially through an aerosol generator to provide PIV seeding for the jet fluid; both the seeded and unseeded streams recombine in a plenum chamber where they flow through the coolant holes in the floor of the wind tunnel test section.

Fig. 2: The incoming boundary layer for coolant jets of M =0.0, 0.4, 1.0, and 2.0 with P =1.00; the 1/7 th power-law velocity profile is also shown for reference. (a) x / D = -5, (b) x / D = -3, (c) x / D = -2,
(d) x / D = -1
Fig. 3: Schematic of experimental rig for PIV measurements.
PIV Measurements
In the present study, a high-resolution PIV system was in the present study to conduct flow field measurements to reveal the tendencies of the coolant stream to remain attached to the test plate or to separate from it. For the PIV measurements, the mainstream airflow and the cooling jet streams were seeded with ~1 µ m oil droplets by using droplet generators. Illumination was provided by a doublepulsed Nd:YAG laser (NewWave Gemini 200) adjusted on the second harmonic and emitting two pulses of 200 mJ at the wavelength of 532 nm with a repetition rate of 10 Hz. The laser beam was shaped to a

sheet by a set of mirrors, spherical and cylindrical lenses. The thickness of the laser sheet in the measurement region is about 0.50 mm. The illuminating laser sheet was aligned along the main stream flow direction bisecting the coolant hole in the middle of the test plate. A 14-bit high-resolution digital camera with a 2048x2048 pixel frame-straddling CCD array is used for the PIV acquisition with the axis of the camera perpendicular to the laser sheet. The CCD camera and the double-pulsed Nd:YAG lasers were connected to a workstation (host computer) via a Digital Delay Generator (Berkeley Nucleonics,
Model 565), which controlled the timing of the laser illumination and the image acquisition.
After PIV image acquisition, instantaneous PIV velocity vectors were obtained by a frame to frame cross-correlation technique involving successive frames of patterns of particle images in an interrogation window of 32 × 32 pixels, followed by two recursive passes of 16 × 16 pixels. An effective overlap of 50% of the interrogation windows was employed in PIV image processing. After the instantaneous velocity vectors ( u i
, v i
) are determined, the vorticity (
z
) can be derived. The distributions of the ensembleaveraged flow quantities such as the mean velocity, normalized Reynolds Stress (
= − u ' v ' / U
∞
2
) and turbulence kinetic energy ( T .
K .
E .
0 .
5 * ( u '
2
v '
2
) / U
∞
2
) were obtained from a cinema sequence of about 1,000 or more frames of the instantaneous PIV measurements. The measurement uncertainty level for the velocity vectors is estimated to be within 2%, while the uncertainties for the measurements of ensemble-averaged flow quantities such as Reynolds stress and turbulent kinetic energy distributions are about 5%.
PSP Measurements
PSP was used to determine the adiabatic film cooling effectiveness through use of a mass-flow analog to adiabatic cooling effectiveness
α w
, which is normally measured by the reduced temperature difference of the free stream T
∞
and the adiabatic wall temperature T aw
divided by the temperature difference of the freestream and the coolant fluid T c
:
ߟ
௔௪
=
ܶ
ஶ
ܶ
ஶ
− ܶ
௔௪
− ܶ
௖
.
(1)
The primary difficulty with this method is in determination of the true adiabatic temperature despite the physical reality of heat conduction within the test plate. By using a mass flow analog to measure aw
, the problem of heat conduction within the test plate can be avoided. Because PSP is sensitive to O
2
— in that the presence of O
2 serves to reduce, or “quench”, the emission of the PSP molecules — it can be used to measure the relative concentration of O
2
against the surface of the test plate. The quenching of the signal is related to the O
2
pressure against the painted surface. Therefore, since air possesses a fixed concentration of O
2
, use of an O
2 relative concentration
(ܥ
ை
మ
-free foreign gas as the coolant allows us to use PSP to measure the
) mix
of O
2
on the test plate. Technically, the reduced O
2
pressure in the presence of the foreign gas jet must be determined and compared to the O
2
pressure field created by a jet of air, as follows:
ߟ =
(ܥ
(ܥ
ை
మ
ை
మ
)
௠௔௜௡
)
௠௔௜௡
− (ܥ
− (ܥ
ை
మ
ை
మ
)
௠௜௫
)
௖௢௢௟௔௡௧
=
(ܲ
ை
మ
)
௔௜௥
(ܲ
ை
మ
− (ܲ
)
௔௜௥
ை
మ
)
௠௜௫
.
(2) where
(ܥ
ை
మ be expressed equivalently as some ratio subtracted from unity. Now, a potential pitfall arises in that the ratios
(ܥ
ை
మ
)
) coolant mix
/
(ܥ
is identically zero for choice of an O
ை
మ
) main
and P (O
2
) mix
/ P (O
2
) air
2
-free coolant gas; thus, the above expressions can
are not necessarily identical due to the differing molecular masses of the coolant gas and the main-stream flow. Charbonnier, et al (2009) showed that for the choice of a coolant gas whose molecular mass differs significantly from that of the main stream, the effectiveness as determined via use of partial pressure measurement is appropriately expressed as:

ߟ = 1 −
ଵ
ቈቆ
(ುೀమ)ೌ೔ೝ
(ುೀమ)೘೔ೣ
ቇ
ೢೌ೗೗
ିଵ቉
ಾ೎೚೚೗ೌ೙೟
ಾೌ೔ೝ
ାଵ
,
(3) where M coolant
and M air
are the molecular masses of the coolant gas and the mainstream air, respectively.
Thus, if the coolant gas has similar density to air, such as Nitrogen (N
2
, P =0.97), equation 2 will provide a reasonable approximation for the film cooling effectiveness. However, in a typical gas turbine engine the density ratio is significantly greater than unity. For this reason, use of a foreign gas that has greater density than air is sensible for the experimental study of film cooling effectiveness. In the present study, most of the experiments that were performed by using CO
2
( P =1.53) as the coolant gas, with some cases using N
2
to investigate the effects of density ratio on the film cooling effectiveness.
Each of the pressures listed in equations 2 and 3 are determined by a calibration procedure whereby normalized CCD camera image intensity is converted to relative pressure. This calibration takes the form:
ܫ
௥௘௙
ܫ = ݂ ቆ ܲ
ܲ
௥௘௙
ቇ.
(4)
However, due to experimental concerns such as the background intensity field I b
due to ambient light sources and intensity variations due to the underlying pressure field in the presence of the jet, a series of four images must be taken to achieve reliable results. These four images and their corresponding flow and illumination scenarios are given in Table 1.
Image
Table 1: PSP image parameters.
Main stream flow Jet flow Illumination
I b
I ref
I air
Off
Off
On
Off
Off
Air
Off
On
On
I gas
On Coolant Gas On
The above relation is inverted to give the necessary pressure fields to compute using equation 3 through the following relations:
൫ܲ
ை
మ
൫ܲ
ை
మ
൯
൯
௔௜௥
௥௘௙
= ݂ ିଵ ൬
ܫ
௥௘௙
ܫ
௔௜௥
− ܫ
௕
− ܫ
௕
൰,
(5) and
൫ܲ
ை
మ
൫ܲ
ை
మ
൯
௠௜௫
൯
௥௘௙
= ݂ ିଵ ൬
ܫ
௥௘௙
ܫ
௠௜௫
− ܫ
௕
− ܫ
௕
൰, where I b
, I ref
, and I air
represent the intensities of the images listed in Table 1.
(6)
In the present study, a pressure and temperature-controlled test cell was used to calibrate the PSP, as in the diagram in Fig. 4(a). The calibration cell contains two chambers separated by a solid wall into which a copper test plate is affixed. The test plate was painted with PSP. The paint that was chosen for this experimental campaign is ISSI UniFIB due to its low stated temperature sensitivity (~0.5%/˚C) and single-coat application. The paint has peak emission intensity at 650 nm upon illumination with 390 nm
UV light. Imaging of the flow is accomplished through use of a 14-bit digital 2048 x 2048 pixel CCD

array camera fitted with a long-pass filter with a 610 nm cutoff wavelength. One chamber is enclosed through which coolant fluid is circulated. An external thermal regulator was used to circulate and control the temperature of the coolant. The other chamber contains a silicon-quartz window through which the test plate was illuminated and imaged. This chamber is pressure-controlled and the pressure within the chamber was measured with a digital pressure transducer [DSA 3217 Module, Scanivalve Corp, ±0.05%
FS accuracy, FS=100 psi; shown in Fig. 3(b)]. A K-type thermocouple with 0.1˚C resolution continuously monitored the temperature of this chamber. Because the effectiveness measurements utilize a foreign gas with zero O
2
content to simulate the coolant flow, the calibration needs to be performed using vacuum pressure. A vacuum pump was employed to depressurize the cell.
(a) (b)
Fig. 4: (a) Calibration of ISSI UniFIB Pressure-Sensitive Paint. (b) Image of PSP calibration setup.
A reference pressure of 1 atm (absolute) was used, which corresponds in the wind tunnel experiments to a condition of
=0 . Because it is feasible that some effectiveness experiments might indicate a possible maximum of
=1 , corresponding to a true zero absolute O
2
pressure, it was deemed necessary to calibrate for this condition rather than rely upon calibration curve extrapolation. For this data point the cell was flushed with pure CO
2
until the PSP emission reached a steady value. Calibration was performed for a range of temperatures from 23.0˚C to 32.6˚C. For each temperature condition, all calibration points including the reference pressure were performed within the thermocouple resolution of a constant temperature. For example, all calibration data taken at 28.0˚C were likewise normalized by reference conditions of 28.0˚C as well, and so on for the other temperature conditions. In Figure 5 it can be seen that the PSP response, upon normalization by the appropriate condition, is independent of temperature.
Fig. 5: Temperature independence of the PSP calibration curve.

In the present study, the test plate is painted with the PSP and imaged with the aforementioned 14-bit digital 2048x2048 pixel CCD array camera and long-pass filtered at 610 nm to isolate emission radiation from the excitation light. To reduce effects of camera noise on the data, averaging was performed on square groups of 9x9 pixels with 50% overlap to ensure complete sampling of the data. For these measurements, the experiments typically have an image magnification of about 0.093 mm/pixel (or
10.7 pixels/mm), which results in a spatial resolution of dx = dz = 0.37 mm or 0.074
D for the PSP measurement results given in the present study.
Fig. 6: Laterally-averaged effectiveness for coolant flows of P =1.5, and p / D =3, compared with similar studies; (a) M =0.5, (b) M =1.0.
Because the use of PSP to study film cooling effectiveness is a fairly new and novel technique, comparison to similar studies in literature is made to validate its reliability as a measurement tool. For this comparison, a coolant stream of CO
2
( P =1.53) is injected through a plate of the 5 cylindrical holes and a pitch p / D =3. This geometry and experimental parameters are chosen due to an abundance of data for similar cases in the open literature. The laterally-averaged results for M =0.5 are shown in Figure 6(a),
Figure 6(b) shows the results for M =1.0. The M =0.5 results lie very close to those of Lutum & Johnson
(1999), Kunze, et al (2008), and Dhungel, et al (2009), especially through 5 < x / D < 15. The results of
Rallabandi, et al (2011) indicate somewhat lower effectiveness but were measured at P =0.97 and M =0.6, also using the PSP technique; because of their higher M and lower P it is reasonable to expect the coolant flow that they used to lift further away from the test surface than that of the present study, which would explain the reduced effectiveness that they measured. Three cases that used IR Thermography indicate

higher effectiveness than the results of the present study, including Lawson & Thole (2011), which were made at elevated mainstream turbulence intensities of 4.6% and 12.3%. Baldauf (2002) used very similar experimental conditions as the present study, including P =1.5 and mainstream Tu=1.5%, and show effectiveness levels slightly less than Lawson & Thole (2011) for most of the streamwise fetch of their test plate. A summary of the experimental conditions of these other studies is given in Table 2.
Table 2: Experimental Conditions of the Comparative Studies in Figure 6
Study M P I V r p/D Tu (%)
Measurement
Technique
Baldauf, et al (2001, 2002) 0.50 1.50 0.17 0.33 3.0 1.5 IR Thermography
Dhungel, et al (2009)
1.00 1.50 0.67 0.67 3.0 1.5 IR Thermography
0.50 1.10 0.23 0.45 3.0 2 IR Thermography
1.00 1.10 0.91 0.91 3.0 2 IR Thermography
Kunze, et al (2008) 0.50 1.37 0.18 0.36 4.0 1.5 TSP
1.00 1.37 0.73 0.73 4.0 1.5 TSP
Lawson & Thole (2011)
Lutum & Johnson (1999)
0.49 1.06 0.23 0.46 3.0 12.3 IR Thermography
1.0 1.06 0.94 0.94 3.0 12.3 IR Thermography
0.49 1.06 0.23 0.46 3.0 4.6 IR Thermography
0.52 1.15 0.24 0.45 2.9 3.5
Thermochromic
Liquid Crystals
Rallabandi, et al (2011)
Present Study
0.60
1.00
0.50
1.00
0.97
0.97
1.53
1.53
0.37
1.03
0.16
0.67
0.62
1.03
0.33
0.67
3.0
3.0
3.0
3.0
0.5
0.5
1.5
1.5
PSP
PSP
PSP
PSP
For M =1.0, the cases using PSP lie very close to one another, especially for x / D >6. The cases measured using IR thermography show excellent agreement with one another and indicate higher effectiveness than those using PSP, with the exception of Kunze, et al (2008), who used a larger hole pitch than the other cases. At this blowing rate, the results of Bauldauf, et al (2002) show fair agreement to the present case within the first five diameters and then overshoot it for x / D >5, though the results become similar once again near x / D =20; similar behavior is noted for Dhungel, et al (2009) but with poorer agreement than
Baldauf in the near field. Again, it seems that the IR Thermography method may slightly over-predict the effectiveness when compared to the mass-transfer-based PSP method, especially in the peak regions.
This over-prediction may be due to a measurement bias that is due to heat conduction within the solid boundary of the thermal-based measurements.
Furthermore, the 2D effectiveness footprint results at M =0.85 for Baldauf and the present study are shown in Figure 7. For the most part the PSP results of this study compare favorably, except for the peak effectiveness region from 3< x / D <10, for which the present study shows
to be about 0.10 lower than
Baldauf. However, in a qualitative sense the overall results are quite similar, with Baldauf’s appearing

slightly “wider” in the spanwise direction than those of the present study. This discrepancy may be attributed to the adiabatic difference between the two measurement techniques. Because PSP is based on the mass-flow analog, it is insensitive to effects of conduction — all thermal-based measurements, such as IR Thermography and TSP, are sensitive to conduction to some degree, dependent upon particulars of the experimental setup. Therefore it is within the realm of possibility that the Baldauf results indicate high effectiveness with a wider-spanning footprint due to heat conduction, particularly in the lateral direction. Their results are quoted to have accuracy within 5% while the present study is accurate to within about 3%; a difference of up to 8% between the two measurements may therefore be considered within the statistical bounds of agreement. Because most IR Thermography studies tend to indicate higher effectiveness than the cases that use the PSP method, it seems reasonable that they tend to overpredict the true adiabatic mass-flow-based measurements that are obtained using PSP.
Fig. 7: Comparison of 2D effectiveness plots between the present study and those of
Baldauf, et al (2001); M =0.85, P =1.5, Tu=1.5%.
Measurement Results and Discussion
In the present study, the effects of P on the film coolent effectiveness are investigated. As mentioned earlier, for a fixed blowing ratio of M , an increase in density ratio P necessitates a compensatory reduction in velocity ratio V r
. For constant main flow conditions, the bulk jet velocity is the only quantity that will be reduced. In Fig. 8 we can see that the consequences of this reduction of coolant flow can result in a jet that either attaches or separates from the surface of the test plate. Here PIV measurements of jets of air ( P =1.00) and CO
2
( P =1.53) show that for M =0.85 the jets remain attached to the test plate but for M =1.70 the air jet separates from the plate. By inspection of the vectors within the coolant sublayer for the M =0.85 cases, we see that there is faster flow within the P =1.00 flow scenario than that of the P =1.53 scenario. Similar comparison is difficult for the M =1.70 cases because of the qualitative difference between them but it is noted that for both P =1.53 cases, the sublayer flow is slower for the
M =0.85 case than the M =1.70 case.

Fig. 8: Effects of density ratio upon the mean flow field. For visual clarity, every 8 th
vector column is shown and every 3 rd
vector row is shown. (a) Air jet ( P =1.00) at M =0.85; (b) Air jet ( P =1.00) at M =1.70;
(c) CO
2
jet ( P =1.53) at M =0.85; (d) CO
2
jet ( P =1.53) at M =1.70.
The corresponding effectiveness footprints to the mean flows presented in Figure 8 are shown in Figure 9.
They indicate generally that flows of greater density ratio, P, provide much better film cooling at fixed M than flows of lower P . In subfigures 9(c) and 9(d), use of heavier-than-air CO
2
is seen to provide improved effectiveness over that of N
2
[subfigures 9(a) and 9(b)] at constant M . It appears to be common to all of these flows [except P =0.97, M =1.70 in subfigure 9(b)] that the effectiveness has a local maximum that occurs somewhat downstream of the injection hole. Interestingly, evidence of reverse flow can be seen upstream of the coolant holes where finite effectiveness is measured in a halo-like feature that wraps around the hole. This feature is most likely due to the presence of a horseshoe vortex that entrains some coolant from the jet hole, which is then advected within the vortex around the hole and then carried downstream. A future paper will investigate the behavior of this vortex system as it pertains to film cooling in greater detail.
Fig. 9: Effects of density ratio P upon the film cooling effectiveness. (a) N
2
( P =0.97) jet at M =0.85;
(b) N
2
( P =0.97) jet at M =1.70; (c) CO
2
( P =1.53) jet at M =0.85; (d) CO
2
( P =1.53) jet at M =1.70. Only the center hole is shown of the three-hole array.

Fig. 10: Effects of density ratio P upon film cooling effectiveness. (a) Centerline measurements ( z =0).
(b) Laterally-averaged results.
Quantitative comparison is made in the plots of Fig. 10, which show the centerline effectiveness
[subfigure 10(a)] and the laterally-averaged effectiveness [subfigure 10(b)]. Lateral averaging here is performed over the domain -5< z / D <5, or one full period of the hole spacing. Concerning the physics of the film cooling, for low M there is little difference between the coolant streams of different density, suggesting that the coolant remains well-attached to the wall at this small mass-flux ratio. However, the effectiveness clearly becomes dependent upon P for larger M , with higher density coolant resulting in increased effectiveness by the measures of both the centerline and laterally-averaged effectiveness of
M =0.85 and M =1.70.
Fig. 11: Centerline effectiveness for choice of various scaling parameters for two different coolant densities; P =0.97 and P =1.53 for N
2
and CO
2
, respectively. Dashed lines represent N
2
, solid lines represent CO
2
. (a) Matched blowing rate M , (b) matched momentum flux ratio I , (c) matched velocity ratio V r
.
To investigate the extent to which the coolant flow may be better-described by a different scaling quantity than M for flows of different P , Figure 11 gives the centerline effectiveness for P =0.97 and P =1.53 at closely-matched values of M [subfigure 11(a)], I [subfigure 11(b)], and V r
[subfigure 11(c)]. In this order, the successive subfigures represent decreasing weighting of the scaling by P or, conversely, the order of

increasing importance of flow kinematics upon the film cooling effectiveness. Here the red curves represent the slowest of the three quantities in each plot, blue curves are used for the highest, and green curves show the intermediate coolant flows. Interestingly, the red curves are little-affected by differences in P for matched M and I but significant far-field disparity is noted for V r
-matching, which suggests that influence of P is important at low M and I and those quantities successfully scale film cooling flows across differences in density (or temperature, equivalently). However, the green and blue curves indicate that increases in P result in poor matching of M and I across P differences as the coolant injection increases. This trend is reversed for velocity-matching according to V r
, for which the blue curves trend near each other for both P values but the red slow-coolant curves agree in the near-field but show disparity in the far-field, with the more-dense stream resulting in greater effectiveness than the P =0.97 case. The green curves trend closely to each other in the far-field but not in the near-field. Thus it seems that as the coolant flow increases, V r
becomes increasingly useful for the description of the effectiveness for differing P . It is worth mentioning here that the Richardson number of these flows is very small, indicating that buoyancy is not a likely culprit for the tendency of the different coolant gases to behave differently.
Summary and Conclusions
In the present study, the performance of film cooling injection from a row of three circular holes spaced laterally across a flat plate has been investigated by using PIV and PSP techniques. Focus has been placed on the effects of coolant density differences at fixed values of blowing ratio, M, due to its common usage in the film cooling community but other scaling quantities have also been investigated, such as the momentum flux ratio I and the bulk coolant velocity to bulk main-stream velocity V r
. It is evident that for low values of P , jets of M =1.70 tend to separate from the test surface, while for elevated P the coolant is likely to remain attached, offering improved cooling performance. Adiabatic PSP film cooling measurements, based on a mass-flux analog to traditional thermal effectiveness measurements, indicate that there is a corresponding increase in the effectiveness of these jets of elevated P for fixed M, and that for cases where coolant separation is observed, the effectiveness downstream of the coolant hole may be quite low in spite of the injection of large amounts of coolant.
Comparison of alternative scaling quantities indicate that those quantities that give more weight to P have more success to collapse data from varying density coolant flows for relatively low coolant flow rates, while the bulk velocity ratio V r
may be used with some success to scale the effectiveness from jets of higher velocities. The intriguing nature by which these quantities tend to have preferential success at scaling jets of different flow rates begs deeper analysis. Additionally, some observations of film cooling effectiveness patterns reminiscent of the presence of a horseshoe vortex begs a deeper analysis into the effect that closer spacing of coolant holes might have upon the jet behavior; this analysis will be performed in a future paper.
Acknowledgments
This work was funded by GE Global Research Center in Niskayuna, New York. The technical assistance of Drs. Jose Cordova, Wontae Hwang and Jonathon Slepski of GE Global Research Center and Mr. Bill
Rickard, Mr. Marc Regan of Iowa State University is greatly appreciated.

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