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Numerical and Experimental Study of Trenched Film Hole Cooling for a Realistic Cascade in an Annular Endwall, Phase 1: Test Rig Construction and Preliminary Data

Cuong Q. Nguyen1, Jimmy Kullberg2, William McDonald, Son H. Ho3, and Jayanta S. Kapat4

Center for Advanced Turbine Energy Research (CATER)

University of Central Florida, Orlando, Florida, 32816

This is a preliminary numerical and experimental study on the film cooling effectiveness. Film cooling holes will be employed in the stagnation region (inner-diameter endwall or hub endwall) of GE-E3 first stage rotor blades of a high pressure turbine in a subsonic commercial aircraft. For deeper understanding of interaction behavior between film cooling jets and secondary flows inside the cascade passage, a realistic (0.8 Mach number) annular test rig has been built and completed in the CATER laboratory. Five (four and two halves) 3D profile airfoils are used to gain a periodic flow for the middle passage. The experimental test rig is a 3X scaled of the real engine geometry. It has an inner diameter surface of 970 mm and outer diameter surface of 1098 mm. It is the middle passage where all the measurement has been measured. A RANS numerical model has been simulated and is used to validate the experimental data and the existing open literature. The computational fluid dynamic simulation models a steady annular cascade with five realistic airfoils (4 and 2 halves). The computational fluid dynamic model is simulated using a commercial package. It is the computational fluid dynamic model will also be used to extract all the necessary data for the sensitivity analysis while certain cases will be parallel validated against with experimental data. Preliminary pressure and velocity data have been mapped and will be presented at this phase. The obtained data are useful and help the current investigation move forward. Detail study of interaction characteristic between trenched film cooling jets and the main stream will be reported in the next phase and parameter sensitivities analysis on the film cooling effectiveness and cooling uniformity coefficient using response surface methodology will also explicitly introduced.

Nomenclature T = temperature, K P = pressure, Nm-2

U = velocity, ms-1

D = coolant pipe diameter, mm K = coolant pipe length, mm d = approximation tip diameter, mm p = pitch (distance between 2 neighbor film holes, mm z = axial coordinate (from the trailing edge of the purge-flow slot), mm r = radial coordinate (from the engine axis toward the annular endwall), mm C = chord length of the blade hub profile, mm

1 Graduate Research Assistant, Department of Mechanical, Materials and Aerospace Engineering, UCF 2 Undergraduate Research Assistant, Department of Mechanical, Materials and Aerospace Engineering, UCF 3 Post Doctoral Research Associate, Department of Mechanical, Materials and Aerospace Engineering, UCF 4 Professor, Material Mechanical and Aerospace Engineering Department, UCF

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-405

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Z = length between two points in the z (axial or chord) direction, mm S = total circumferential arc length between 2 points on surface with radius r, mm ds = differentially circumferential arc length, mm h = trench depth, mm i = incidence angle of the main flow, degree BR = blowing ratio between the coolant jet to the mains stream, ( ) (c c m mU U )ρ ρ DR = density ratio between the coolant jet to the mains stream, c mρ ρ MR = momentum flux ratio between the coolant jet to the mains stream, 2 2( ) (c c m mU Uρ ρ ) Greek symbols α = angle of coolant pipe inclination β = angle of coolant pipe orientation θ = tangential coordinate Ω = mid-span (MS) inlet blade angle, relative to the axial direction Ψ = MS outlet blade angle, relative to the axial direction η = adiabatic film cooling effectiveness (FCE) ρ = density δ = distance between the trench trailing edge to the leading edge of the blade Subscripts and Superscripts aw = adiabatic wall c = coolant k = numerical of factor in the factorial design m = main flow - = laterally average = = spatially average

I. Introduction ilm cooling technique is an advanced technology, which has been employed in the modern gas turbines to protect the surface of the airfoil endwall. Hence, it allows higher temperature at the outlet of the turbine

combustion chamber without damaging the downstream components. It subsequently plays an important role on improving the engine cycle efficiency nowadays.

F However, the thermal performance of a basic film cooling is still not very high. In 2001, with the Pattern No.

6,234,755 B1 [1], Bunker et al. initially invented trenched film cooling in which a trench is cratered on a discrete hole film cooling. Trenched film cooling (as depicted in Fig. 1) provides a perfect way to transform discrete hole film cooling into a film cooling characteristic of a slot film cooling. Trench is usually made at the time of repair/maintenance procedure when thermal barrier coating is repaired. As a result, trenched film cooling has been exercised to whenever area it could be employed. Trenched film cooling has been therefore an interesting topic in the current film cooling research activities. This method was actually create a big jump in gas turbine film cooling technology, since it helps the coolant flow spread out uniformity onto the downstream area, and hence reduce thermal stress which is always associated with temperature distribution.

Sundaram and Thole [2] studied the film cooling embedded in a trench on the stagnation region of a straight endwall. They confirm that film cooling holes in a trench resulted in enhancing the adiabatic effectiveness levels at all blowing ratios compared to the one without trenches. The trench helps to spread out the coolant uniformity on both the suction and pressure sides of the airfoil and at the result it helps to increasing the overall endwall effectiveness.

It is obviously that endwall film cooling has been studied for many years, but majority of all the work are about straight cascades with two-dimensional (2D) extrusion airfoil vanes or blades. It is obviously ignoring the effect of this simplification assumption. At the result, Burd and Simon [1] pointed out that there has been little appreciation for the role of, and added complexity imposed by, reduced aspect ratios. The flow which is small disturbance (traverse components) on the main flow is named a secondary flow; the secondary flow can be of the same order of magnitude as the primary flow. Figure 2 reviews briefly some studies on the secondary flows from the existing open literature [3-8].

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ward the suc on side is covered with coolant before the film blanket is up-washed and entrained into the cross flow.

ry, at high blowing rates, the jet momentum overcomes the flow field yielding to a higher effe

laterally-averaged FCE and spatially-averaged FCE are usually defi d as in the Equation 1, 2 and 3 respectively:

It is the secondary flows that make it more difficult to film-cool the endwall because of the horse-shoe vortex, the passage vortex, etc. In gas turbine, film cooling on the airfoil endwall is the method that relative cool air, coming from the compressor, gets injected into the main flow by rows of coolant tubes. These coolant tubes are located at an inclination angle, α with respect to the engine axis and at an orientation angle, β with respect to the incident main flow. In 2001, Kost and Nicklas [9] noted that the endwall flow patents are uncertain at the result the distribution of the coolant flow are unflavored distributed on the endwall regions. The flow on the airfoil endwall is a highly three-dimension (3D) region unlike the one on the airfoil surface as stated in Colban et et al. [10]. From [9], the authors also claimed that most of the past studies are about film cooling with the cylindrical coolant hole. Kunze et al. [11] conducted a shaped film cooling at elevated density ratio on the linear endwall test plate; they found that secondary flow is intensified with higher incidence inlet flow. They also claimed that strong interaction between the near-wall flow field and the ejected film layer at higher incidence angle due o the intensified secondary flow. As the result, less endwall area to

ti Nicklas [12] studied the effect of Mach number and blowing ratio on endwall heat transfer and film-cooling

effectiveness. Three rows of holes and a slot were investigated and found that the interaction of coolant air and the secondary flow field greatly influenced heat transfer and film effectiveness. It was observed that a decrease in intensity of the horseshoe vortex near the endwall results in a reduction in heat transfer. Similarly, Zhang and Jaiswal [13] studied film cooling effectiveness (FCE) on a flat turbine nozzle endwall. It was reported that for low blowing ratios, the secondary flows dominate over the momentum of the jet, resulting in a decrease in effectiveness. On the contra

ctiveness. In literatures, adiabatic wall FCE, adiabatic ne

( , )T Taw mzT Tc m

η θ−

=−

(1)

( , )

( )z s ds

zds

ηη

×−=∫

∫ (2)

( )z dsdz

dsdz

ηη

−==∫ ∫∫ ∫

(3)

in center of advanced turbines and energy

x/D

L

D

α

s

P

Figure 1. A typical trenched film cooling coupon used for a experimental test research facility.

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(a)

(b)

(d)

(c)

(f)

(e)

Fig. 2. Previous Secondary Flow Studies: (a) Langston [3], (b) Sieverding et al. [4], (c) Sharma and Butler [5], (d) Kawai et al. [6], (e) Sauer et al. [7], and (f) Vogt and Zippel [8]

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The pitch-to-diameter ratio, p/D of a flat plate was studied by Nguyen et. al [14]. They found that this effect contribute the most among the other factors (BR, DR, s/D). They also found that the smaller the p/D the higher spatially-averaged FCE and this correlation is absolutely non-linear, since the rate of spatially-averaged FCE increase when p/D go from low (1.5) to mid level (4) is stiffer compared to the rate when p/D go from the mid level to high (6.5). The Dorrington and Bogard [15] also varied pitch-to-diameter ratio from 2.78, 4, and 5, and it was concluded that the optimal pitch-to-diameter ratio was 2.78. They also proved that p/D is a significant parameter.. A computational fluid dynamic (CFD) simulation was carried by Harrison and Bogard [16] and has agreed that the jet interaction is the driving mechanism behind the improvement shown by trenched film cooling holes. However, as the pitch decreased, more coolant is ejected to the main flow per unit length and the added interaction between close jets led to a behavior approaching that of a trench.

The trench depth-to-diameter ratio of the trench was studied Nguyen [14]. Their result showed that there was a big improvement in term of thermal performance when the trench depth, trench depth increases from 0.1D to 0.55D. And, it turned out that not much of am increasing in film cooling levels when trench depth keeps increasing up to 1D. Their result matched to the study by Dorrington and Bogard [15] where they varied the trench depth from 0.5D, 0.75D, and 1.0D and found that the trench configurations were discovered to have an optimum depth of 0.75D, with a little improvement in performance for trench depths greater than 0.75D. Also, it is good to note here that the trench was primarily initiated from the prepare purpose, it means that the trench depth is about the thickness of the thermal barrier coating, which is in the order of 1 mm.

II. Problem Formulation and Methodology

A. A Parameter Study The current study presents six three-dimensional (3D) airfoils, which so-called NASA/GE-E3, sitting inside an

annular endwalls to form five annular cascades. The scaled factor of three (3X) was selected to fit the existing close-loop wind tunnel inside the CATER Lab. We also decided to employ cylindrical film hole locating inside a trench (traverse slot). The experimental test setup has been built, but CFD simulation had been conducted to guide the experimental work. So, this sensitivity analysis in this paper will be based on a numerical model.

Design of experiment study using Response Surface Methodology (RSM) will be employed to perform sensitivity analysis of involved variables in the performance of the FCE in a 3D transonic cascade. Obviously, thermal performance of the film cooling hole on the endwall depends on many factors, as discussed in the above, in this particular sensitivity analysis work, the author decides to examine five parameters as the input factors. Those factors are depicted in Fig. 3 and listed as follow for the sake of convenient:

1. Blowing ratio of the coolant over the main stream, BR 2. Distance between the stagnation-region coolant row (SR) to the leading edge, δ/D 3. Trench depth-to-diameter ratio, p/D 4. Film hole inclination angle, α 5. Film hole orientation angle, β

B. Selection of the Parameter Ranges Film hole diameter in real aircraft engines is in the order of 1mm, therefore for the 3X scale testing model, it is

reasonable to adopt 2.5 mm as a diameter of the coolant hole. There are totally 72 blades in the first rotor stage of the aircraft engine. The pitch-to-diameter ratio, p/D = 3.38 to yield 10 coolant holes in the stagnation region row. Coolant hole length-to-diameter also fixed with a value of 10. Five factors which include the flow and the geometrical parameter are taken into consideration (DOE input variables) as shown in Table 3 and will be described in the following:

Sensitivity to the flow condition: • Blowing ratio, BR: blowing ratio is normally chosen in the range from 1.0 up to 7.0. For the sake of

comparison with available literature, the authors decided to vary blowing ratio from 1.0 to 1.5 Sensitivity to the geometrical factors as shown in Fig. 8 • The trench-depth-to-hole-diameter ratio, s/D: the trench depth usually less than or equal to the BTC

thickness which leads to the studied range for s/D from 0..2 to 1.2 • Relative film cooling hole location, δ: is the distance from the trailing edge of the trench to the blade

leading edge. As shown in Fig 8c, it is practical in gas turbine engine that δ/D is about 1d-2d upstream relative to the blade leading edge. Hence, δ will be varied from 1d to 2d with d ~12.7 mm

• Orientation angle, β: is the relative angle with respect to the incoming flow. This parameters will be varied +/- 10o

• Inclination angle, α: is the pitch angle with respect to the blade platform. In literature, most popular injection angle is 30o

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-35o o, therefore for the current study α will be varied from 25 to 45o Again, there are 5 factors (or effects) will be investigated in this study, and there levels of values are assigned for each factor for catching the nonlinear behavior of FCE. Table 1 is an explanation how to code those involved factors and its corresponding levels before it can be used for the sensitivity analysis.

Hot main flow

s

0.1D

W

Coolant flow

α

β

0.1D

GE-E3 blade

δ

OD surface

ID surface

d ~ 1/8 C =1/8x4in = 0.5in (12.7 mm)

C

(c)

(b)

(a)

D

Figure 3. Diagram depicts 4 geometrical parameters α, β, s, δ in the sensitivity analysis (not draw to scale), (b) a side view of the rotor blade and (c) an approximation of the tip diameter sketched on the root profile of the blade.

Table 1. The input variable ranges. Main Range of Natural Factors Range of Coded Factors

Coded Factors Low Middle High Low Middle High

Blowing ratio, BR X 1.0 1.5 2.0 -1 0 1 1

Trench depth-to-hole-diameter, s/D X 0.2 0.7 1.2 -1 0 1 2

Relative location ratio, δ/D 1.0d 1.5d 2.0d -1 0 1 X3

Inclination angle, α [degree] X 25 35 45 -1 0 1 4

Orientation angle, β [degree] X 33 43 53 -1 0 1 5

k=5If one wishes to use a classical full factorial 3 design, we will need to run an excessive number of design

points which is impracticable (243 cases or runs). That would also cost a lot of time and is definitely a very inefficient way of studying of parameters. Central Composite Design (CCD) would be an ideal selection since it does not required knowledge of safety operation zone (known safety range of each factor). With the CCD, one can reduce the number of runs from 243 cases down to 40 cases, but one needs to have two or more replicates for the axial point (central point). Unfortunately, with a numerical simulation tool, we can not generate more than one result for any specific problem. In 1960, Box and Behnken generated a very creative and special design for the three-level designs. It is so-called Box-Behnken design, Myers et al. [17]. This design is used for studying second-order response surfaces that is based on the balanced incomplete block designs. As a result, for the 34 factorial designs, the Box-Behnken design matrix is given in the Table 2.

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Table 2. The Box-Behnken Design Matrix and Output Variable, spatially-averaged FCE.

Standard Order X1 X2 X3 X4 X5 Standard

Order X1 X2 X3 X4 X5

1 -1 -1 0 0 0 22 0 1 -1 0 0 2 1 -1 0 0 0 23 0 -1 1 0 0 3 -1 1 0 0 0 24 0 1 1 0 0 4 1 1 0 0 0 25 -1 0 0 -1 0 5 0 0 -1 -1 0 26 1 0 0 -1 0 6 0 0 1 -1 0 27 -1 0 0 1 0 7 0 0 -1 1 0 28 1 0 0 1 0 8 0 0 1 1 0 29 0 0 -1 0 -1 9 0 -1 0 0 -1 30 0 0 1 0 -1 10 0 1 0 0 -1 31 0 0 -1 0 1 11 0 -1 0 0 1 32 0 0 1 0 1 12 0 1 0 0 1 33 -1 0 0 0 -1 13 -1 0 -1 0 0 34 1 0 0 0 -1 14 1 0 -1 0 0 35 -1 0 0 0 1 15 -1 0 1 0 0 36 1 0 0 0 1 16 1 0 1 0 0 37 0 -1 0 -1 0 17 0 0 0 -1 -1 38 0 1 0 -1 0 18 0 0 0 1 -1 39 0 -1 0 1 0 19 0 0 0 -1 1 40 0 1 0 1 0 20 0 0 0 1 1 41 0 0 0 0 0 21 0 -1 -1 0 0

A Reynolds Averaged Navier-Stoke Simulation (RANS) CFD model will be built which will provide all above

41 cases. Script files will be made for both in Gambit [18] and Fluent [19] to produce spatially-averaged FCE automatically for time saving purpose. Then, commercial statistical software, Minitab [20] will be employed to carry on the sensitivity analysis of spatially-averaged FCE on those studied effects.

III. Experimental E3 Test Rig Set Up

A. Design Constraints and Solution For a sake of completeness, the following section will describe the E3 test rig has been successfully built and

integrated in a close-loop tunnel in CATER lab. Fig. 4 shows the overall view of the 350HP transonic wind tunnel with an explored view of the E3 test section and cross sections of the GE-E3 blades from Timko [21]. The new rig must be designed to interface with an existing wind tunnel at the Laboratory for Turbine Heat Transfer and Aerodynamics (a part of CATER facility). This imposes more design constraints, like the potency of the blower and locations of the new ductwork’s inlet and outlet. The wind tunnel is meant to be closed-loop, as opposed to open-loop, meaning that it constantly circulates the same air which will approximately produce hot main flow of around 80o Celsius. Furthermore, it is transonic wind tunnel; therefore it is capable of having flow speeds near Mach 1.0 (the speed of sound). In summary, the GE-E3 test section is has been designed to compromise with floor space already occupied by rooms and other wind tunnels in the building. Equipped with a 350 HP blower, whose function is to generate the movement of air in the direction also shown in the Fig. 4. Heat exchanger, which removes some of the heat added to the flow by the blower and maintains the flow at a desired temperature (about 80° Celsius, in our case). The heat exchanger’s outlet is to connect to the inlet of our new rig which is 70 degree turning duct. There are splitters inside this duct for flow uniform distribution. The blower’s diffuser (in blue color), which is used to slow down the flow before it again passes through the blower. This will be where the test section’s exit reconnects to the pre-existing rig.

A close up view of the test section is plotted in Fig. 5 where four and two half airfoil blades ware manufactured by stereolithography (SLA) method to create a periodic condition. The flow measurements has been measured in the middle passage. The same figure also shows the place where film cooling will also be employed and temperature distribution will be captured using temperature sensitive paint technique (TSP). Detail of TSP technique can be referenced to Liu [22].

Heat exchanger (a) (b) Inner diameter (ID) surface

Turning

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Figure 4. (a) Overall view of the GE-E3 transonic wind tunnel in CATER facility, a close-look on the testing cascade, and (c) the GE-E3 blade profiles [reproduced from Timko [21] (Note: pitch profile in (c) represents MS in this study where all the flow angles will be satisfied).

Figure 5. (a) Blade angles, a look on the ID surface where film cooling jets are injected and (b) an explored view of the test section assembly (no film cooling segment).

Table 2 lists all intended values for testing parameters which is also the values as an input for the numerical

simulation and sensitivity analysis.

duct Supporting steel core 350HP blower

Diffuser

Flow direction

(c)

st1 GE-E3 Outer diameter turbine blade (OD) surface

ΦMS= 43.2o

ΨMS= 66.9o

Incoming flow

Outflow

Injected film cooling from the SR row

(b)

(a)

Table 2. The experimental parameters. Mainstream Condition Mach number at the LE surface 0.3 Mach number at the exit 0.65

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Temperature, Tm [oC | K] 80 | 353 Test section inlet total pressure, P [Pa] 101,506 t_inlet Test section inlet static pressure, P [Pa] 91,376 s_inlet Test section outlet static pressure, P [Pa] 70,090 s_outlet Mass flow rate, ms [kg/s] 3.9 (0.77 each passage) Hole Geometrical Parameters (intended) Hole shape Round (cylindrical hole) Diameter, D [ mm] 2 Number of film hole per passage 10 Pitch-to-diameter, p/D 3.4 Trench depth-to-diametr, s/D 0.7 Film hole distance, from LE δ 1.5d (d =13 mm) Film jet Inclination angle, α [degree] 35 Film jet compound angle, β [degree] 0 Coolant Flow Condition (intended) Temperature, Tc [oC | K] 25 | 298 Density ratio, DR 1.4 (1.37/0.95) Blowing ratio, BR 2 Coolant plenum mass flow rate, mc [kg/s] 0.025

B. Current E3 Test Rig and Flow Measurements The majority of the E3 rig has been built and shown in the Fig. 6. To check the periodicity of the flow fed into

each passage, static pressure taps were installed at the upstream and downstream on both ID and OD surfaces. Static pressure distributions are plotted in Fig. 7. It is reasonably to state that the periodic condition was established for the middle passage. A five hole probe was used to measure the static pressure as well as Mach number at several cross location: 0% chord, 50% chord and 75% chord surfaces. Obtained data are displayed in Fig. 8.

(a) (b) (c) Figure 6. Photographs of the current E3 rig: a view from the (a) upstream, (b) downstream, and (c) overall.

IV. A Numerical E3 Model

A. The Problem Domains and Boundary Conditions A commercial meshing software, Gambit [18] was used to generated a mesh model which is shown in the Fig. 9.

Hexahedral elements will be used to fill most parts of the domain while properly refined element layers are assigned around inlet, outlet, and solid surfaces to capture the high rates of change of momentum and heat transfer that exist there. In each element, velocity components, pressure, and temperature are approximated leading to a set of algebraic equations defining the discretized continuum. A segregated algorithm is used to solve the nonlinear system of finite algebraic equations. The iterative procedure for the solution is considered converged when the norm of the relative errors of the solution between iterative steps is less than a tolerance of 1e-6. The numerical solution includes the values of three velocity components, pressure and temperature at every nodal point of the computational domain.

90000

95000

100000

passage 1passage 2passage 3

85,000

90,000

95,000

100,000

passage 1passage 2passage 3

(b) (a)

65000

70000

75000

80000

85000

90000

passage 1

passage 3

65000

70000

75000

80000

passage 1

passage 2passage 3

(c) (d)

Figure 7. Static pressure distribution on the walls at: (a) inlet ID surface, (b) inlet OD surface, (c) outlet ID surface and (d) outlet OD surface (note: horizontal axis is a pitch distance; unit: Nm-2 in absolute scale).

75000

80000

85000

90000

95000

0 25 50 75 100

Percentage Chord Length [%]

Sta

tic P

ress

ure

[Pa]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mac

h N

umbe

r

Ps

Ma

Figure 8. Static pressure and Ma number at several streamline locations obtained from five hole probe measurement.

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(a) (b)

Figure 9. (a) Overall view of the whole meshed domain (wire-fire mode plot) and (b) close up view of the cooling holes (shaded mode plot).

Again, it is the secondary flows that promote the coolant jet lifting from the OD endwall. This can be seen from

Fig. 10, where the cooling jets get integrated into the horse-shoes vortex and passage vortex. Typical pressure and endwall temperature distributions are plotted in Fig. 11which shows reasonable result obtained from this preliminary numerical analysis.

(a) (b)

(d) (c)

Figure 10. Static pressure contour on the (a) pressure contour on the ID surface and (b) pressure contour on the OD surface, (c) velocity distribution and (d) path-line colored by velocity magnitude.

B. Preliminary CFD Results and Validation A commercial CFD packet, Fluent [19] was chosen for the flow analysis. The Spalart-Allmaras (S-A) turbulent

model was adopted for this phase of study. The advanced of this specific turbulence model is time consumption saving while it still gives a very reasonable result to validate against the data taken from experimental testing. Figure

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11 is served as a comparison on the endwall static pressure between the S-A CFD numerical solution and experimental data which obtained from static pressure taps. From there, we can see that the CFD relatively agree with data obtained from experimental test rig. Hence, in term of order of magnitude, the authors are confident to move on to next phase which will be report in the near future.

70000

75000

80000

85000

90000

95000

0 25 50 75 100

Percentage Chord Length [%]

Sta

tic P

ress

ure

[Pa]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mac

h N

umbe

r

Ps, ExperimentPs, S-A CFDMa, ExperimentMa, S-A CFD

Figure 8. Spalart-Allmaras and experimental comparison on static pressure and Ma number at several streamline locations.

Acknowledgments The first author would like to thank Dr. Sylvette Rodriguez for valuable discussion on computational modeling

for film cooling simulation and Dr. Humberto Zuniga some of his lab work in the past. We also like to thank Florida Center for Advanced Aero-Propulsion (FCAAP) for the financial support.

References [1] Bunker, R. S., Bailay, J.C., Lee, C.P., and Abuaf, N., 2001, “Method for Improving the Cooling Effectiveness of

a Gaseous Coolant Stream, and related Articles of Manufacturer”, US Patent 6,234,755 [2] Sundaram, N. and Thole, K. A., 2008, “Bump and Trench Modifications to Film-Cooling Holes at the Vane-

Endwall Junction”, J. of Turbomachinery, Vol. 130, pp. 41013-41022 [3] Langston, L.S., 1980, “Cross Flow in a Turbine Cascade Passage”, Gas Turbine Conference and Products Show,

New Orleans, Louisiana, USA [4] Sieverding, , 1985, “Recent progress in the understanding of basic aspects of secondary flows in turbine blade

passages”, Journal of Engineering for Gas Turbines and Power, Vol. 107, No. 2, pp. 248-257 [5] Sharma, O. P. and Butler, T. L., 1986, “Predictions of endwall losses and secondary flows in axial flow turbine

cascades”, Journal of Turbomachinery, Vol. 109, No. 2, pp. 229-236 [6] Kawai, T., Adachi, T. and Akashita, K., 1985, “Structure and decay of secondary flow in the downstream of a

cascade”, Japan Society of Mechanical Engineers, Vol. 28, No. 242, pp. 1642-1650 [7] Sauer, H., Müller, R., Vogeler, K., 2001, “Reduction of Secondary Flow Losses in Turbine Cascades by Leading

Edge Modifications at the Endwall”, J. of Turbomachinery, Vol. 123, pp. 207-213 [8] Vogt, H.F. and Zippel, M., 1996, “Sekundärströmungen in Turbinengittern mit geraden und gekrümmten

Schaufeln; Visualisierung im ebenen Wasserkanal”, Forschung im Ingenieurwesen, Vol. 62, pp. 247-253 [9] Kost, F.and Nicklas, M., 2001, “Film-Cooled Turbine Endwall in a Transonic Flow Field: Part I—Aerodynamic

Measurements”, Journal of Turbomachinery, Vol. 123, pp. 709-720 [10] Colban, W., Gratton, A., Thole, K.A. and Haendler, M., 2006, “Heat Transfer and Film-Cooling Measurements

on a Stator Vane With Fan-Shaped Cooling Holes”, Journal of Turbomachinery, Vol. 158, pp. 53-62

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[12] Nicklas, M, 2001, “Film-Cooled Turbine Endwall in a Transonic Flow Field: Part II—Heat Transfer and Film-Cooling Effectiveness”, Journal of Turbomachinery, vol. 123, pp. 720-729

[13] Zhang, L.J. and Jaiswal, R.S., 2001, “Turbine Nozzle Endwall Film Cooling Study Using Pressure-Sensitive Paint”, Journal of Turbomachinery, Vol. 123, pp. 730-739

[14] Nguyen, C.Q., Tran, N.T.V., Bernier, B.C., Ho, S.H., and Kapat, J. S., 2009. “Sensitivity Analysis for Film Effectiveness on a Round Film Hole Embedded in a Trench Using Conjugate Heat Transfer Numerical Model” ASME Proceedings of Turbo Expo 2010, Glasgow, UK, Paper GT2010-22120

[15] Dorrington, J.R. and Bogard, D.G., 2007, “Film Effectiveness Performance for Coolant Holes Embedded inVarious Shallow Trench and Crater Depressions,” ASME paper GT-2007-27992

[16] Harrison, K.L. and Bogard, D.G., 2007, “CFD Predictions of Film Cooling Adiabatic Effectiveness for Cylindrical Holes Embedded in Narrow and Wide Tranverse Trenches,” Paper No. GT-2007-28005, IGTI Turbo Expo, Montreal, Canada

[17] Myers, R. H., Montgomery, D.C., and Anderson-Coo, C.M., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd ed., John Wiley & Sons, New Jersey, 2009, Chaps. 7

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