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Prediction of Adiabatic Effectiveness of Various Cratered Film Hole Configurations: Sensitivity Analysis for the

Rectangle Shaped Mask

Nghia T. Tran1, Cuong Q. Nguyen2, Son H. Ho3, and Jayanta S. Kapat4 Center for Advanced Turbines and Energy Research (CATER)

University of Central Florida, Orlando, Florida, 32816

Over the past few years, trench film cooling has taken a massive leap in the film cooling technology by helping the coolant flow spread out to cover more down-stream area. This advancement improved the performance of film cooling in terms of effectiveness. However, there are instances in which a trench cannot be employed due to the repairing and refurbishing process of the thermal barrier coating (TBC). In these cases, crater film cooling is used. The effectiveness of crater film cooling is not as adequate as the trench film cooling, but it is a far better method than basic film cooling method as shown in previous study. Crater film cooling method (or so-called masked film cooling hole) is a non-continuous type of traverse slot film cooling. There are several geometrical masks that have been employed in gas turbines, which will be investigated in a series of studies. However, for the current work, only rectangular masks will be considered. Basic sensitivity analysis will be conducted to find out the optimum combination of geometrical parameters conjugated with the flow conditions that will provide the maximum spatially averaged film cooling effectiveness and to determine the uniformity of the temperature distribution on downstream area of a flat plate. Since the above topic is the primary purpose of this particular study, a cylindrical coolant pipe will be employed in this work for simplicity purposes. A numerical model is used to analyze the geometric variation and the results are compared to data from literature.

Nomenclature a = width of the crater (horizontal edge) b = length of the crater (vertical edge) d = coolant pipe diameter L = coolant pipe length l = distance of the crater leading edge to the cylindrical pipe’s center P = pressure p = pitch (distance between 2 neighboring film holes) T = temperature s = crater’s depth x = distance downstream (from the trailing edge of coolant outlet) z = lateral distance (from the trailing edge of coolant outlet)

BR = blowing ratio, �����

����

Greek symbols α = angle of hole-axis inclination

1 Graduate Research Assistant, Dept. of Mechanical, Materials and Aerospace Engineering, AIAA Student Member 2 Graduate Research Assistant, Dept. of Mechanical, Materials and Aerospace Engineering, AIAA Student Member 3 Postdoctoral Research Associate, Dept. of Mechanical, Materials and Aerospace Engineering, AIAA Member 4 Professor, Dept. of Mechanical, Materials and Aerospace Engineering, AIAA Associate Fellow

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

AIAA 2010-404

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

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η = adiabatic film cooling effectiveness �������

�����

ρ = density Subscripts and Superscripts aw = adiabatic wall c = coolant k = numerical of factor in the factorial design m = main flow r = recovery temperature of the main flow

I. Introduction

Crater film cooling is a comparative alternate film cooling method to trench film cooling. The idea of disrupting the coolant stream at the exit and spreading out the coolant downstream from the trench to increase the cooling effectiveness is not new. The advancement in gas turbine engines has led to very high turbine inlet temperatures. As the outlet temperature of the combustor has been raised higher and higher over the years, cooling the first turbine stage has become an extremely important task. Film cooling is one of the most effective ways to protect the surface from the incoming hot flow. Examples include end-wall cooling, blade cooling, tip cooling, combustor chamber cooling, etc. By forming a blanket of coolant flow on the top of the metal surface, unsafe temperature in the component can be prevented. Slot or trenched film cooling provides a continuous and uniform protection blanket to the downstream application area. Although it seems to be an ideal configuration, it weakens the structure at the high combustion temperatures of modern gas turbine engines. This issue with slot film cooling can be avoided by employing a continuous trench imposed on the top of the discrete film cooling holes shown in Fig. 1. However, trench can still be affected by the same structural degradation as the slot. Crater can resolve this problem by increasing the structural integrity. The strength of the crater varies with different geometric mask. With the invention of the crater in the last few years, its comparison with trench film cooling had become a new area of research.

Fric and Campbell [1], the inventor of the crater, did only a basic comparison between the craters versus the flat plate with straight hole film cooling. Even though they showed crater film cooling has a 100% better effectiveness than the flat plate at blowing ratio of 5.0, they did not show any other data processing for the study, like heat transfer coefficient enhancement. The crater’s geometry in the study was also a very simple cylindrical mask with three variations of relative location between the mask and the coolant elliptical outlet. Lu [2] did some further comparison of the basic crater geometry with baseline film cooling (straight hole for the flat surface), trench film cooling, and converging slot film cooling. They also found that crater’s cooling effectiveness was much higher than that of the baseline film cooling. Also, they claimed that depending on the relative location of the crater with respect to the coolant outlet; it could further improve the effectiveness of the cooling. However, the trench film cooling results displayed a better performance at higher blowing ratio. As predicted, the converging slot film cooling tops out the baseline, crater cases and even the trench case. Lu [2] commented that converging slot (shape hole) was not an adequate comparison for the crater case, due to the fact that real applications can cause a crater in shaped hole.

In this study, crater geometric differences are the primary parameters. The baseline is basic film cooling with cylindrical hole. The geometry of the crater is in the form of a rectangular shape, varying from horizontal rectangle to square and vertical rectangle. Adiabatic film cooling effectiveness η is used to evaluate the performance of any film cooling design. It can be presented as

���, �� ����

��,����������

(1)

Two frequently used averaged effectiveness, laterally-averaged effectiveness and area-averaged effectiveness, are respectively presented in Equations 2 and 3 as

���� ����,���

�� (2)

����� ����,����

����� (3)

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II. Problem formulation and methodology

A. Studied parameter Seven different crater geometries were investigated in the Center for Advanced Turbines and Energy Research

(CATER) at the University of Central Florida (UCF) as shown in Table 1, but only the rectangular shapes in the dashed box is presented in this paper. In addition to the shape of the crater, the location of the crater relative to the cylindrical hole and the depth of crater are also set as geometric parameters in this study. The blowing ratio is the other parameter and it is the only flow factor. There are other factors that can affect the final result, but based on past experience and literature reviews, these four parameters are the foundation in determining the ideal case for crater film cooling. The values for the other factors were chosen due to their high performance and set as a control in this study. The result will be compared to two baseline cases, which already have already been carried out both experimentally and numerically:

• Crater film cooling, Fric and Campbell [1] • Regular cylindrical film cooling on a flat plate , Fric and Campbell[1] • Trenched film cooling, Nguyen et. al [3, 4]

Table 1. Diagram of all crafted geometries and their variations.

Location: nominal Location: variety 1 Location: variety 2 Circle

Ellipse (a)

Ellipse (b)

Square

Rectangle (a)

Rectangle (b)

Triangle

Trapezoidal

In addition to Table 1, the geometric parameter can be clearly identified by Fig. 1 and Fig. 2. The first parameter that was consider is “b/a”. If the pitch is kept constant, as “b/a” increases it gradually converts into trench film cooling. Again, Lu’s paper states that trench film cooling has higher film cooling effectiveness than crater film cooling. This parameter will determine when the geometry will act like a trench and if it still keep its structural integrity as a crater. “b/a” is varied from 0.75 to 1.25. When “b/a” is equal 1, the rectangle becomes a square.

FLOW

FLOW

FLOW

FLOW

FLOW

FLOW

FLOW

FLOW

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“ l/a” determines the position of the crater relative to the cylindrical hole. As “l/a” increases from 0.25 to 0.75,

the cooling hole move from the leading side to the trailing side of the crater. The step at the trailing edge, depict in Fig. 1, can have a very important effect on the performance of the cooling film. If the cooling hole is in the middle of the crater or near the leading side, the crater may act as a buffer zone for high blowing ratio case. This buffer zone may prove to resist coolant lift off effects as the blowing ratio increase. As the cooling-hole moves closer to the trailing edge, the step may trip the coolant fluid, causing it to spread the flow laterally. With the flow spreading laterally, the uniformity can help cool the hot surface evenly. The last geometry parameter is “s/d”. This is the most important factor that deals with film cooling by trench or crater. The value of “s/d” is directly related to the step of the crater. All other flow parameters (blowing ratio, momentum ratio, etc) and geometric parameters (compound angle, “p/d”, “ L/d”, etc) were ignored to keep the comparison. The following table 2 lists all the parameter use in the current paper.

Coolant pipe

Hot Flow

b

p/d

p/d

Vertical ellipse (1) Vertical ellipse (0) Vertical ellipse (-1)

a

L

L

L

P-b

a

L

L

L

a

L

L

L

Figure 1. Crater geometry diagram.

Figure 2. Positioning of crater diagram.

Coolant flow

L

Hot main flow

S

b

a

D

α

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Table 2. Input variable ranges.

Main Coded Factors

Range of Natural Factors Range of Coded Factors

Low Middle High Low Middle High

b/a X1 0.75 1 1.25 -1 0 1

l/a X2 0.25 0.5 0.75 -1 0 1

Blowing ratio, BR X3 0.5 1 1.5 -1 0 1

s/d X4 0.1 0.55 1 -1 0 1

B. Computational modeling and solution A simplified 3D model was utilized to take advantage of the vertical symmetry surface crossing the film hole

centerline. Also, the supply coolant plenum is removed to reduce the number of numerical elements. At this point, a CFD model has completely been built for the rectangle mask film cooling hole, and the typical models are shown in Fig.3.

The GAMBIT mesh generation software [5] was utilized to create a mesh using all hexahedral topologies. In order to limit the needed size of the mesh, a symmetry boundary condition was applied 10 diameters above the surface. At the no-slip walls, y+ values less than 20 were used to set the boundary layer mesh size. Only the one half-pitch was modeled, with symmetric boundary conditions on both sides in the lateral direction. Refined element layers were assigned around inlet, outlet, and solid surfaces to capture the high rates of change of momentum and heat transfer that exist there. Figure 3 clearly shows the different in cell size between the area near the cooling hole and the area near the trailing edge of the model. The coolant holes entrance had an inclination angle of 35°. The space considered in the meshed model included 10 diameters upstream of the hole, in order to prevent the boundary layer to develop, and 50 diameters downstream of the hole, in order to capture temperature data up to “x/d” = 50. The meshed model was imported into Fluent [6] for flow analysis which took about 5-6 hours per run to get the numerical solution to converge. 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 given tolerance of 1E-6. The numerical solution includes the values of three velocity components, pressure and temperature. Temperature is the only component used for cooling effectiveness in this paper.

Figure 3. Typical mesh grid structure At the inlet and outlet for the hot mainstream, a pressure boundary condition was set to imitate the actual

experimental operating conditions. The pressure at the inlet to the coolant plenum was then set in order to produce

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the desired blowing ratios. Table. 3 list all the pressure and boundary condition for all cases. The temperatures of the mainstream and coolant inlets were 340 K and 260 K, respectively.

Table 3. Flow boundary conditions for numerical simulation.

Mainstream temperature, Tm [K] 340

Cool-stream temperature, Tc [K] 260

Mainstream total pressure, Pt_inlet 102,303

Mainstream pressure, Ps_inlet [Pa] 100,450

Cool-stream Pressure for low BR [Pa] 102,000

Cool-stream Pressure for nominal BR [Pa] 104,750

Cool-stream Pressure for high BR [Pa] 109,500

C. Grid independent study and validation A grid convergence study was performed over five mesh sizes, from 100,000 to 600,000 volumes. The different

mesh sizes were generated by systematically refining the size of the individual elements in the fluid zones of the model. Fig. 4 shows temperature values over the different mesh sizes at five set points. Temperature change between grid sizes at the points analyzed was less than 1 K after the 300,000-volumes model. Therefore, all of the later solutions in this study were obtained from meshes of 302,534 hexahedral cells and typical mesh structure is shown in Fig. 3.

Figure 4. Grid independent study for the 3D numerical model on cylindrical hole.

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(a) (b)

(c) (d) Figure 5. a) Temperature distribution on the adiabatic wall, b) Distribution of velocity, c) Path-line colored

by velocity and d) Path-line colored by static temperature. Numerical model validation is very important to a computational model analysis. Unfortunately, experimental and

numerical data on crater is very sparse, let alone data on a rectangular crater. There were many numerical analysis and experimental testing done on basic film cooling and trench film cooling in CATER lab. The baseline data of these studies were compared directly to literature and were found to be accurate. Since the model on this paper only has a small deviation (crater) from the basic cylindrical film cooling model, it is reasonably safe to move on for the DOE study.

III. RESULTS Four factors (effects), which include the flow and geometrical parameters, were considered in this study. Again, Table. 2 summarize the ranges of those factors. They were also coded so that each factor has three levels: low/mid/high that corresponds to -1 / 0 / +1, respectively. The coding system was used to simplify future work in sensitivity analysis. This study can only determine the final result from value in each parameter. The interaction effect from multiple parameters is still unknown. Sensitivity analysis can clearly show the first, second and third order interaction from all of the parameter. This knowledge will improve the process to determine what type of crater is needed. The final area averaged η is presented in Table. 4. The laterally averaged η value of this current study is plotted against trench film cooling with 2 different blowing ratios, Nguyen [4], and basic film cooling and circular mask film cooling with blowing ratio of 1, Fric and Campbell [1]. As indicated before, both trench curves are higher than the rest of the data, which agree with both Fric and Campbell [1] and Lu [2]. The basic cylindrical film cooling is near the bottom. Looking at the data, not all crater film cooling has higher film cooling performance than the basic film cooling. This may be due to other parameters that were set as a constant. “p/d” from this study is higher than most of the literature. Due to this high value of “p/d”, η decreases by a certain level. This is greatly documented by the literature. This leaves a lot of room for further investigation by including “p/d” as one of the variable. With the blowing ratio of 1.5, the curve jump down to the bottom of the pile. This result matches with the literature. As the blowing ration increases in Fig. 8a, the chance of cooling fluid lifts off the surface increases, therefore decreasing the film cooling effectiveness greatly.

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Figure 6. Rectangular crater result of laterally averagedηηηη.

Table 4. Area average film cooling effectiveness

Case number X1 X2 X3 X4 η=

1 0 0 0 0 0.074

2 1 0 0 0 0.101

3 -1 0 0 0 0.069

4 0 1 0 0 0.167

5 0 -1 0 0 0.084

6 0 0 1 0 0.033

7 0 0 -1 0 0.122

8 0 0 0 1 0.174

9 0 0 0 -1 0.071

The laterally averaged eta is matched up with the area averaged eta. Parameter “b/a” shows very little

interesting result. As “b/a” varies between the values, cooling effectiveness doesn’t improve much. Even thought the results from the parameter “b/a” are consistently low, it only mean the holes are still too far apart to have a

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uniform film cooling across the hot surface. The reason “p/d” was set at 5 is to clearly identify the parameter “b/a”. With shorter pitch distance, high value “b/a” might not be needed in future study of other crater geometry.

(a)

(b) Figure 7. ηηηη vs. coded factor a) Parameter "l/a" b) Parameter "b/a"

From Fig. 6 and Fig. 7a, high value “l/a” clearly result in higherη. Lower “p/d” might even increases higherη, due to more coverage in a same amount of area. Even with high blowing ratio, case 4 and case 8 have the highest cooling effectiveness compare to the rest of the cases in this study. These two cases have the same value as crater hole from Fric and Campbell paper. Case 4 refers to high “l/a” value and case 8 refers to high “s/d” value. From Fig. 7a and Fig. 8b, it is shown that as “l/d” and “s/d” increase, the overall area average cooling effectiveness is more than double the nominal value. This does not mean that the increase is linearly. More data is needed to determine how cooling effective behave as the function of “l/a” and “s/d”. As BR deceases, η decreases. This matches with the literature, that stated that highest η resulted from BR between 0.5 to 1.0. Again, the graph below does not infer linear relationship. The two factors that have the most impact in this study is “s/d” and “l/d”

(a)

(b) Figure 8. ηηηη vs. coded factor a) Parameter "BR" b) Parameter "s/d"

IV. CONCLUSION Numerical analysis was done on rectangular shape craters. The numerical model went through independent study

to significantly reduce the number of cells. There are the totals of 3 geometric parameters along with one flow parameter in this study. The results of this study seem to match with the literature and show some interesting results. The results from this study confirm Lu’s statement that trench outperform crater film cooling. But due to

0.03

0.08

0.13

0.18

-1 0 1

FCE

Coded factor

0.03

0.08

0.13

0.18

-1 0 1

FCE

Coded factor

0.03

0.08

0.13

0.18

-1 0 1

FCE

Coded factor

0.03

0.08

0.13

0.18

-1 0 1

FCE

Coded factor

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structural integrity, crater is still needed to replace trench in many case. In order to select the best parameter for crater film cooling, this paper and its future study will show the important of each parameter.

The position of the crater relative to the cooling hole is very important, Even though this study shows higher values of “l/a” have higher result, it might not be the case for other crater mask. Same can be said for high value “s/d”. Cooling uniformity coefficient is another factor that needs to be calculated and examined along withη. In the future study, this parameter will be changed according to this result to obtain the best geometric crater case. Along with cooling uniformity coefficient, extensive sensitivity analysis will be performed to see the whole picture of crater film cooling. Other cratered film hole shapes will also be investigated in future works in CATER.

ACKNOWLEDGMENTS Special thanks go to Ms. Thao Tran and Mr. Bryan Bernier for her support in review comments and proofreading this manuscript. Last, the authors would like to thank the Florida Center for Advanced Aero-Propulsion (FCAAP) for the financial support.

References [1] Fric, T. F., and Campbell, R. P., “Method for improving the Cooling Effectiveness of a Gaseous Coolant Stream which Flows Through a Substrate and Related Articles of Manufacture”, US Patent No.6,383,602, filed 7 May. 2002. [2] Lu, Y., “Effect of hole configurations on film cooling from cylindrical inclined holes for the application to gas turbine blades”, Ph.D. Dissertation, Louisiana State University, Dec 2007. [3] Nguyen, C. Q., Rodriguez, S., Zuniga, H., Ho, S. H., and Kapat, J. S., “Sensitivity Analysis of Flow Conditions and Geometric Parameters on the Film Cooling Effectiveness for a Flat Test Plate, Part 1: Single Row of Cylindrical Holes Film Cooling”, ASME Proceedings of Summer Heat Transfer 2009, San Francisco, Ca, USA Paper HT-88141, 2009. [4] Nguyen, C. Q., Tran, N. V. T., Bernier C. B., Ho, S. H., and Kapat, J. S., “Sensitivity analysis for film effectiveness on a round film hole embedded in a trench using conjugate heat transfer numerical model” Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea and Air, GT2010 June 14-18, 2010 Scottish Exhibition & Conference Center, Glasgow, UK, 2010. [5] GAMBIT, Mesh Generation Software, Ver. 2.3.16, ANSYS Inc, Pa, 2008. [6] FLUENT, Flow Modeling Software, Ver. 6.3.26, ANSYS Inc, Pa, 2008.