Ali Abdul-Aziz

Cleveland State University, Cleveland, Ohio

Ramakrishna T. Bhatt

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Morris Girgis

Central State University, Wilberforce, Ohio

Influence of Cooling Hole Geometry and

Material Conductivity on the Thermal

Response of Cooled Silicon Nitride Plate

NASA/TM—2002-211688

November 2002
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Ali Abdul-Aziz

Cleveland State University, Cleveland, Ohio

Ramakrishna T. Bhatt

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Morris Girgis

Central State University, Wilberforce, Ohio

Influence of Cooling Hole Geometry and

Material Conductivity on the Thermal

Response of Cooled Silicon Nitride Plate

NASA/TM—2002-211688

November 2002

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

26th Annual International Conference on Advanced Ceramics and Composites

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Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2002-211688 1

Influence of Cooling Hole Geometry and Material Conductivity

on the Thermal Response of Cooled Silicon Nitride Plate

Ali Abdul-Aziz1

Department of Civil and Environmental Engineering

Cleveland State University

Cleveland, Ohio 44115

Ramakrishna T. Bhatt2

U.S. Army Research Laboratory

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Morris Girgis3

Department of Manufacturing Engineering

Central State University

Wilberforce, Ohio 45384

Summary

To complement the effectiveness of ceramic materials and their applicability to

turbine engine applications, a parametric study using the finite element method was

carried out. This study conducted thorough analyses of a thermal-barrier-coated silicon

nitride (Si3N4) plate specimen with cooling channels, where its thermal conductivity was

varied in an attempt to minimize the thermal stresses and reach an optimal state of stress.

The thermal stress profile was generated for specimens with circular and square cooling

channels. Lower stresses were reported for a higher magnitude of thermal conductivity

and in particular for the circular cooling channel arrangement. Contour plots for the

stresses and the temperature are presented and results obtained are discussed.

Introduction

Lightweight, strong, tough high-temperature materials are required to complement

efficiency improvements for next-generation gas turbine engines that can operate with

minimum cooling. Because of their low density, high-temperature strength, and thermal

conductivity, ceramic matrix composites are being investigated as potential materials for

replacing nickel-base superalloys currently used for hot-section engine components.

Ceramic structures can withstand higher operating temperatures and harsh combustion

environments. In addition, their low densities relative to metals help to reduce component

mass (refs. 1 and 2) and hence the engine weight and ultimately the fuel consumption.

1

NASA Resident Research Associate at Glenn Research Center, Telephone: 216−433−6729, Fax: 216−977−7150,

E-mail: smaziz@grc.nasa.gov. 2

Telephone: 216−433−5513, Fax: 216−433−5544, E-mail: bhatt@grc.nasa.gov. 3

Telephone: 937−376−6309, Fax: 937−376−6679, E-mail: mgirgis@csu.ces.edu.
NASA/TM—2002-211688 2

The general objectives of this research are to develop the manufacturing technology,

the thermal and environmental barrier coating (TBC/EBC) system, and the analytical

modeling capability to predict the thermomechanical stresses for testing minimally

cooled silicon nitride burner rig specimens under simulated engine conditions. These

stresses, resulting from the high temperatures in turbine engine environments, may affect

the durability of engine components. To minimize the thermal stress, this report analyzes

the effects of thermal conductivity (which varies with the temperature changes in these

environments) and cooling channel geometry on the temperature distribution for coated

silicon nitride in a burner rig environment.

Analytical Approach

Two-dimensional finite element analyses were performed in a parametric study in

which heat transfer and stress analyses were conducted under steady-state conditions to

demonstrate the feasibility of using cooled Si3N4 parts for turbine engine applications.

The calculations were made under linear elastic conditions where the behavior of the

material was defined by two material constants, Young’s modulus and Poisson’s ratio.

The geometry of a silicon nitride plate with cooling channels used for the finite element

analysis is shown in figure 1. Plate-shaped specimens were used in these analyses to

simulate conditions and environmental behavior typically experienced by vanes in turbine

engines. The test specimens consist of a square silicon nitride substrate with four coating

layers arranged in the following order: a top layer of mullite, a second layer of combined

mullite and 20 wt% barium strontium aluminosilicate (BSAS), a third layer of BSAS,

and a fourth layer of zirconia. The first three layers each have an equal thickness of

0.0765 mm, and the zirconia layer has a thickness of 0.0254 mm. Figure 1 shows the

test specimen with eight 2.03-mm-diameter cylindrical cooling channels spaced 1.02 mm

apart. The specimen with the square cooling channels has edge dimensions equal to the

diameter of the cylindrical channels in this specimen.

The analyses embraced a thermal model that closely simulated impingement heating

applied on the plate by a burner rig flame generated during previous experiments (Dennis

Fox, 2001, NASA Glenn Research Center, experimental work). The hot flame was

pointed symmetrically at the center region with the gas temperature being linearly

dissipated over the rest of the plate. Because of symmetry, only half the plate was

modeled. The steady-state temperature distributions were generated. All the finite

element calculations were conducted with ANSYS 5.7 code (ref. 3).

Finite Element Analysis

Mesh Generation

Stress and steady-state heat transfer analyses were conducted to simulate a burner rig

experimental setup that included internal cooling by air. The finite element model was

generated with MSC/PATRAN graphics (ref. 4). Figures 2 and 3 represent the twodimensional finite element models for the square and the circular channel test specimen

configurations, respectively. The models consist of 10 216 eight-node quad elements

and 31 475 nodes for the circular-channeled specimens and 9740 eight-node quad

elements and 30 145 nodes for the square-channeled specimens. The specimen was

constrained along the line of symmetry by restraining all the nodes from moving along
NASA/TM—2002-211688 3

the X-direction, and another node was constrained along the Y-direction to suppress rigid

body motion (see fig. 3).

Heat Transfer Analysis

The thermal boundary conditions applied were fundamental in evaluating the thermal

profile predicted by the analyses. Several assumptions were made to model the heat

transfer phenomena experienced by the test specimen. Furthermore, convective boundary

conditions were applied, and the corresponding heat transfer coefficients were obtained

from reference 5. Convective flame impingement was imposed over the top of the plate,

while convective cooling was applied to the bottom of the plate and inside the cooling

channels, as shown in figure 2. Also note in figure 2 that the convective heat transfer

coefficient was linearly varied from the center to the edge, simulating a decaying flame.

At the center, impingement heating conditions were imposed, and the forced-convection

state between the flame and the plate surface had a convective coefficient value of

883 W/m2 °C associated with a gas temperature of 1982 °C. This value of heat transfer

coefficient corresponds well with values of heat transfer coefficients for superheated

steam or air under forced convection (ref. 5), which are highly representative of data used

for an impingement heating environment. At the edge, a convective heat transfer

coefficient of 6 W/m2 °C was applied, representing the free-convection state considered

in the analysis. The gas temperature was linearly tapered off across the plate from a high

of 1982 °C until it reached a low of 700 °C.

The cooling channels and the specimen bottom were modeled with a convective heat

transfer coefficient of 114 W/m2 °C, a typical value for water cooling in a forcedconvection state (ref. 5) and a gas temperature of 700 °C. Air is the cooling medium

assumed in these analyses.

A symmetry boundary condition was imposed at the specimen midregion because

only half the specimen was considered for the analyses. All the coating layers were

included in the analyses; layers of elements representing the coatings in the order

described in figure 1 were generated. More details pertaining to the thermal modeling

can be found in reference 1. The material properties for the coatings and the silicon

nitride are listed in table I.

Discussion of Results

Contour plots showing the silicon nitride thermal and structural response are shown

in figures 4 to 7. The temperature and the axial stress as a function of the thermal

conductivity for the circular and square cooling channel configurations are also shown

in figures 8 and 9. The temperature and the stress results presented were generated under

cooling conditions.

Figures 4 and 5 represent the contour plots of the temperature distribution at a

silicon nitride thermal conductivity of 100 W/m °C. They indicate that the maximum

temperature is at the center section of the plate as expected. Additionally, the influence

of the cooling channel configuration is clearly exhibited by the temperature distribution

between the two channel layouts. A hotter region is recognized for the square

configuration. Figures 4 and 5 show the silicon nitride temperature predicted by the

analysis. Furthermore, temperature effects of the material properties reported in Table I
NASA/TM—2002-211688 4

were all incorporated into the analyses. Such implementation has enabled accounting

for all the thermal conductivity variations due to material properties changes with

temperature. Figures 6 and 7 illustrate the axial stresses as a result of the thermal loading

conditions applied. Similar stress distribution trends for both cooling channel shapes

are clearly indicated. However, the stresses were lower, close to 50 percent, for the

circular cooling channel plate compared with that of the square channels. High stress

concentrations are seen at the square corners and specifically near the flame area (see

fig. 6). The plate with the circular cooling channels experienced high stresses at the top

section of the channels along the 90o angle (see fig. 7); however, no stress concentrations

were noted. Thus, a circular cooling channel configuration seems to be more suitable for

intended turbine engine applications.

The data presented in figures 8 and 9 show the effects of both the shape of the

cooling channels and the thermal conductivity simultaneously. For instance, figure 8

illustrates the variation of the temperature under cooling conditions as the thermal

conductivity of the silicon nitride is increased from 2 to 100 W/m °C. This variation

range was randomly chosen in an attempt to evaluate a broader spectrum of material

conductivity data. It is obvious that the temperature is decreased as the thermal

conductivity increases. Note also that the specimens with the square and the circular

cooling channels were at nearly the same temperature over the conductivity range

considered. This is attributed to the similarity in the boundary conditions applied.

In figure 9 the maximum axial stress of the silicon nitride as a function of the thermal

conductivity decreases as the thermal conductivity increases. Furthermore, the reduction

of the stresses relative to the change in the thermal conductivity magnitude as it varied

from 2 to 100 W/m °C is about 18 percent. This leads to the conclusion that at higher

thermal conductivity the stresses become lower. However, the extent to which this

decrease in stress, resulting from the thermal conductivity variation, affects the material’s

durability may be difficult to predict. Other factors like the coating materials and the

thermal boundary conditions may have contributed to the outcome of these analyses and

affected the conductivity influence of the ceramic on the stress response.

Conclusions

A parametric study using the finite element method was conducted to investigate the

effects of varying the thermal conductivity and the cooling channel geometry on the

thermomechanical response of a prototype coated silicon nitride (Si3N4) cooling-plate

panel specimen. The analyses showed a decrease of about 18 percent in the stresses of

the silicon nitride when the thermal conductivity was increased from 2 to 100 W/m °C.

The plate specimen with circular cooling channels showed no stress concentration; in

comparison, the specimen with the square cooling channels experienced stress risers

at the channel corners. Layers of coating, as well as other factors such as boundary

conditions, may have affected the changes reported as resulting from thermal

conductivity variations. The current study offers a preliminary baseline assessment of

the effects of the thermal conductivity on the thermomechanical response of the silicon

nitride; however, more work is warranted under more realistic boundary conditions to

reach a more conclusive statement relative to gains and benefits achieved with respect

to durability. Efforts are in progress to study the effects of other key parameters such as

material surface roughness, the thermal and environmental barrier coating (TBC/EBC)

system, and the coolant pressure differential as expressed with more representative

thermal boundary conditions.
NASA/TM—2002-211688 5

References

1. Abdul-Aziz, Ali; Baaklini, George Y.; and Bhatt, Ramakrishna T.: Design Evaluation Using Finite

Element Analysis of Cooled Silicon Nitride Plates for a Turbine Blade Application. NASA/TM—

2001-210819. http://gltrs.grc.nasa.gov/ Accessed June 17, 2001.

2. Bhatt, Ramakrishna T.: Minimally Cooled Ceramics and Fiber Reinforced Ceramic Matrix Composite

Turbine Components—A Progress Report. NASA/CP—1999-208915, vol. 2, 1999. Available from

the NASA Center for Aerospace Information.

3. ANSYS 5.7 computer program, ANSYS, Inc., Canonsburg, PA, 2000.

4. MSC—Patran MSC—Nastran Preference Guide. Vols. 1 and 2, MacNeal-Schwendler Corporation,

Santa Ana, CA, 1997.

5. Wolf, Helmut: Heat Transfer. Harper & Row, New York, NY, 1983.

6. Engineering Property Data on Selected Ceramics. Metals and Ceramics Information Center Report

MCIC−HB−07, vol. 1, 1976.

7. Richerson, David W.: Modern Ceramic Engineering. Marcel Dekker, Inc., New York, NY, 1982.

8. Engineering Property Data on Selected Ceramics. Metals and Ceramics Information Center Report

MCIC−HB−07, vol. 3, 1981.

a

Ref. 6.

b

BSAS is barium strontium aluminosilicate.

c

Ref. 7.

d

Ref. 8.

Porous zirconiad

1386 0.0025 .25 28.75 .50

25 0.0025 .25 28.75 2.0

BSAS-mullite

mixturea 1386 120 ----- 18.71 .24

25 120 ----- 18.71 2.0

Mullitec

1386 145 .20 13.46 3.87

25 145 .20 13.46 5.86

TABLE I.MECHANICAL AND THERMAL PROPERTIES OF MATERIALS

Material Temperature,

°C

Elastic

modulus,

GPa

Poisson’s

ratio

Coefficient of thermal

expansion,

10−6

/°C

Thermal

conductivity,

W/m °C

BSASa, b

1386 95 ----- 23.96 .50

25 95 ----- 23.96 2.0

Silicon nitride 25 300 0.22 8.380 30.0 a

1386 250 .19 8.380 12.0
NASA/TM—2002-211688 6

Figure 1.—Monolithic silicon nitride (Si3N4) circular-channeled cooling panel cross section. BSAS

 is barium strontium aluminosilicate.

25.4 mm

Coating layers: Mullite, mullite-BSAS,

 BSAS (each 0.0765 mm thick)

 Zirconia: (0.0254 mm thick)

3.175 mm

1.02 mm

Si3N4

Cooling

channels

2.03-mm

diameter

Figure 3.—Circular configuration finite element model (10 216 eight-node quad

 elements, 31 475 nodes) and boundary conditions applied.

x

y

z

Figure 2.—Two-dimensional finite element model of square configuration (9740 eight-node quad

 elements, 30 145 nodes) and thermal boundary conditions showing applied gas temperature,

 T (°C) and heat transfer coefficients, h (W/m2 °C).

h = 6.0, T = 700

Bottom,

h = 114, T = 700

Cooling channel,

h = 114, T = 700

h = 883, T = 1982

x

y

z

Symmetry,

h = 0

h = 6.0,

T = 700

Symmetry

constraint

One node constrained in X-direction
NASA/TM—2002-211688 7

Figure 4.—Temperature distribution at thermal conductivity of 100 W/m °C for cooling with

 square channels.

Figure 5.—Temperature distribution at thermal conductivity of 100 W/m °C for cooling with

 circular channels.

Maximum temperature

x

y

z

x

y

z

Temperature,

°C

1149

1140

1132

1124

1116

1107

1099

1090

1082

1074

1065

1057

1049

1040

1032

1024

Temperature,

°C

1149

1140

1132

1124

1116

1107

1099

1090

1082

1074

1065

1057

1049

1040

1032

1024

Maximum temperature
NASA/TM—2002-211688 8

Figure 6.—Axial stress distribution at thermal conductivity of 100 W/m °C for cooling with

 square channels.

Figure 7.—Axial stress distribution at thermal conductivity of 100 W/m °C for cooling with

 circular channels.

Maximum stress

x

y

z

x

y

z

Stress,

MPa

600

554

508

462

416

370

324

278

232

186

140

94

48

2

–44

–90

Stress,

MPa

600

554

508

462

416

370

324

278

232

186

140

94

48

2

–44

–90

Maximum stress
NASA/TM—2002-211688 9

0 20 40

Thermal conductivity, W/m °C

60 80 100

Figure 9.—Axial stress for silicon nitride in X-direction as function

 of thermal conductivity for two different cooling channel con-

 figurations. Axial stress, MPa

700

600

400

500

300

200

100

Configuration

Square

Circular

Figure 8.—Temperature of silicon nitride as function of thermal

 conductivity for two different cooling channel configurations.

Temperature, °C

1600

1500

1400

1300

1200

1100

0 20 40

Thermal conductivity, W/m °C

60 80 100

Configuration

Square

Circular
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NASA TM—2002-211688

E–13417

15

Influence of Cooling Hole Geometry and Material Conductivity on the Thermal

Response of Cooled Silicon Nitride Plate

Ali Abdul-Aziz, Ramakrishna T. Bhatt, and Morris Girgis

Ceramics; Finite elements; Cooling plates; Silicon nitride, Stress analysis;

Cooling channels

Unclassified -Unlimited

Subject Categories: 01 and 39 Distribution: Nonstandard

WU–708–31–13–00

Prepared for the 26th Annual International Conference on Advanced Ceramics and Composites sponsored by the American

Ceramic Society, Cocoa Beach, Florida, January 13–18, 2002. Ali Abdul-Aziz, Cleveland State University, Cleveland, Ohio

and NASA Resident Research Associate at Glenn Research Center; Ramakrishna T. Bhatt, U.S. Army Research Laboratory,

NASA Glenn Research Center; Morris Girgis, Central State University, Wilberforce, Ohio 45384. Responsible person,

Ali Abdul-Aziz, organization code 5920, 216–433–6729.

To complement the effectiveness of ceramic materials and their applicability to turbine engine applications, a parametric

study using the finite element method was carried out. This study conducted thorough analyses of a thermal-barrier-coated

silicon nitride (Si3N4) plate specimen with cooling channels, where its thermal conductivity was varied in an attempt to

minimize the thermal stresses and reach an optimal state of stress. The thermal stress profile was generated for specimens

with circular and square cooling channels. Lower stresses were reported for a higher magnitude of thermal conductivity and

in particular for the circular cooling channel arrangement. Contour plots for the stresses and the temperature are presented

and discussed.