Robert J. Boyle, Ankur H. Parikh, and Vinod K. Nagpal

N&R Engineering and Management Services, Parma Heights, Ohio

Design Concepts for Cooled Ceramic

Composite Turbine Vane

NASA/CR—2015-218390

February 2015
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Robert J. Boyle, Ankur H. Parikh, and Vinod K. Nagpal

N&R Engineering and Management Services, Parma Heights, Ohio

Design Concepts for Cooled Ceramic

Composite Turbine Vane

NASA/CR—2015-218390

February 2015

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Acknowledgments

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Table of Contents

Page

1.0 Summary 1

2.0 Acknowledgements 4

3.0 Introduction 5

4.0 Benefits from CMC vanes and blades 8

4.1 SFC improvement from CMC vanes 8

4.2 NOx reduction from CMC vanes 13

4.3 SFC improvement from CMC vanes and blades 16

4.4 Conclusions 18

5.0 Stress analysis of CMC vane 19

5.1 No Trailing Edge Ejection Comparisons 27

5.1.1 Effect of Rib 28

5.1.2 Effect of Non-Uniform Temperature Gradient 31

5.1.3 Effect of Differential Wall Thickness 33

5.1.4 Effect of Combined Pressure and Temperature Loads 35

5.1.5 Effect of Insulating Connecting Rib 36

5.1.6 Effect of Modifying Rib Shape 37

5.1.7 Effect of No Internal Pressure 38

5.1.8 Effect of Revised Temperature Distribution 40

5.1.9 Effect of Trailing Edge Shape 42

5.2 Trailing Edge Ejection 43

5.2.1 Effect of Centerline Trailing Edge Ejection 44

5.2.2 Effect of Pressure Side Trailing Edge Ejection 47

5.2.3 Effect of Modified Rib Shape 49

5.2.4 Effect of Single Impingement Cavity 50

5.2.5 Effect of Rectangular & Square Ejection Tube Geometry 52

5.2.6 Effect of Square & Circular Tube Geometry 54

5.2.7 Effect of Revised CMC Temperature Gradients 57

5.2.8 Effect of Reduced Tube Heat Transfer Coefficents 59

5.2.9 Effect of Insulating Fork Region 60

5.3 Property and Boundary Condition Effects 61

5.3.1 Effect of Through Thickness Stiffness Modulus 62

5.3.2 Effect of Doubling Thermal Conductivity 64

5.3.3 Effect of Reducing End Plate Stiffness 66

5.3.4 Effect of Boundary Condition Variation 67

5.4 Mesh Refinement Studies 68

5.4.1 Effect of Vane & End Plate Mesh Density 69

5.4.2 Effect of Mesh Shape for Square Ejection Tube 70

5.4.3 Effect of Mesh for Circular Ejection Tube 71

5.5 Maximum Component Stresses 72

5.6 Conclusions 77

6.0 Radial Cooling 78

6.1 Half Scale EEE Vane 81

6.1.1 Radial Cooling Tubes - No Film Cooling 82

6.1.2 Radial Cooling Tubes & Film Cooling 86

6.1.3 Single Cavity & Trailing Edge Ejection 87

6.2 NASA Vane 91

6.2.1 Radial Cooling Tubes - No Film Cooling 92

6.2.2 Radial Cooling Tubes & Film Cooling 94

6.2.3 Single Cavity & Trailing Edge Ejection 95

6.3 Conclusions 96

7.0 References 97

NASA/CR—201-218390 iii

1.0 - Summary

The objective of this work was to develop design concepts for a cooled ceramic vane to

be used in the first stage of the High Pressure Turbine(HPT). To insure that the design

concepts were relevant to the gas turbine industry needs, Honeywell International Inc. was

subcontracted to provide technical guidance for this work. The work performed under this

contract can be divided into three broad categories. The first was an analysis of the cycle

benefits arising from the higher temperature capability of Ceramic Matrix Composite(CMC)

compared with conventional metallic vane materials. The second category was a series of

structural analyses for variations in the internal configuration of first stage vane for the High

Pressure Turbine(HPT) of a CF6 class commercial airline engine. The third category was

analysis for a radial cooled turbine vanes for use in turboshaft engine applications. The size,

shape and internal configuration of the turboshaft engine vanes were selected to investigate

a cooling concept appropriate to small CMC vanes.

Cycle benefits. The benefits to the engine cycle from using CMC vanes in the HPT are

improved efficiency and reduced NOx. The higher temperature capability of CMC materials

compared to conventional metallic vane materials results in less required vane coolant when

the rotor inlet temperature is unchanged. The higher temperature capability of CMC materials provide the greatest cycle benefits when these materials are used in the first HPT stage.

In a cycle analysis most vane cooling air is non-chargeable air, in that this air is available to

do work in the first stage rotor. Even if all vane cooling air is considered as non-chargeable

air, reduced vane cooling improves vane efficiency. With the same cooling approach for

CMC and metallic vanes the calculated reduction in required cooling was nearly 5.5% of the

compressor discharge flow rate over a wide range of conditions. The 5.5% reduction in compressor discharge air represents approximately a one-third to one-half reduction in required

vane coolant. The calculated improvement in cycle efficiency due to reduced first stage vane

coolant was 0.4%. Cooling air introduced into the main gas flow path downstream of the

vane throat is sometimes considered chargeable air. Cooling air ejected from the vane trailing

edge falls into this category, since it is introduced into the main gas flow path downstream of

the vane throat. There is a reduction in trailing edge ejection air when CMC vanes replace

metallic vanes. If this air is considered to be chargeable air, the additional improvement

in cycle efficiency is 0.6% It is expected that CMC vanes can eliminate second stage HPT

vane coolant. When this is done the calculated additional improvement in cycle efficiency

was between 0.3 and 0.5%, depending on the compressor extraction location for second stage

cooling air. In summary, the calculated cycle efficiency, and thus specific fuel consumption,

improvement was as much as 1.5% due to replacing conventional metallic vanes with CMC

vanes in both stages of the HPT. The largest improvement in cycle efficiency occurs when

both vanes and rotors have higher temperature capability. The calculated improvement in

Design Concepts for Cooled Ceramic Composite Turbine Vane 

Robert J. Boyle, Ankur H. Parikh, and Vinod K. Nagpal 

N&R Engineering and Management Services 

Parma Heights, Ohio 44130 

1$6$&52 
to-air ratio decreases. If there was no vane coolant, the combustor outlet and rotor inlet

temperatures would be equal. If vane coolant is 10% of mainstream flow, the combustor

outlet temperature, and thus the fuel-to-air ratio, would increase by approximately 5%.

The 5% reduction in vane coolant was calculated to reduce combustor outlet temperature by

50◦C(90◦F). Experimental data from different sources show that this temperature reduction

yields a NOx reduction between 15 to 40%.

Replacing first stage metallic vanes and rotor blades with CMC components in order to

raise the rotor inlet temperature was calculated to improve cycle efficiency by at least 5%.

A 5% increase in efficiency would reduce CO2 emissions by 5%. However, NOx emissions

would not be reduced, since T40 increases as T41 increases.

Full size vane Steady state aerothermal and structural analyses were done for a first

stage HPT vane, and this vane was sized to be consistent with vanes in CF6 class engines.

While alternate external vane shapes were identified as likely candidates to reduce maximum

stresses, only internal modifications to the reference vane shape were structurally analyzed.

Analyses were performed for both pressure and temperature loads. Stresses were determined

when only pressure loads were applied, and when only thermal loads were applied. Stresses

were also determined when both pressure and thermal loads were simultaneously applied.

Pressure loads were determined assuming gas and coolant total pressures of 50 atm. Thermal

loads arose from temperature gradients, which varied with the cooling scheme. Even though

the total pressure was greater than in current engines, stresses from thermal loads generally

exceeded those due to pressure loads. Stresses were calculated using the ANSYS computer

code with the linear static modeling assumption, so that creep effects were not included in

the analysis. Three stress components: (1) through thickness; (2) hoop; and (3) spanwise,

are discussed for each case. While shear stresses were calculated, they are not discussed.

The material properties used in the analysis were those of the N24A SiC/SiC CMC system

developed under the NASA’s Enabling Propulsion Materials (EPM) program. The N24A

material is formed from balanced two-dimensional woven plies. The CMC fiber orientation

was assumed such that the strength of the CMC was the same in the hoop and spanwise

directions. The material strength in the through thickness direction was less than onetenth of the strength in the other two directions. The through thickness direction was

perpendicular to the plane of the weave.

Perhaps the most significant conclusion from this work is that stresses which exceeded

design goals were seen for cooling configurations which resembled those used to cool current metallic vanes. However, peak stresses were often highly localized. Significantly lower

maximum stresses were identified for configurations without trailing edge ejection, which is

a feature of current metallic vanes. However, these configurations required as much cooling

as metallic vanes, even though maximum CMC temperatures were much higher than the

maximum metal temperatures. A path was identified to reduce maximum CMC stresses,

cycle efficiency was between 5 and 6% when the first stage rotor sees an increased inlet temperature. Raising the rotor inlet temperature while still using metallic rotor blades yields

little or no efficiency benefits. Rotor cooling air rapidly increases as rotor inlet temperature

is raised, and all rotor cooling air is chargeable air.

The production of NOx in gas turbine combustion is a major concern, and NOx production is a non-linear function of the fuel-to-air ratio. As vane cooling decreases, and rotor

inlet temperature remains constant, the combustor outlet temperature, and thus the fuel1$6$&52 
moving the location of the rear of the vane impingement cooling cavity forward, maximum

stresses were reduced when trailing. edge ejection was used.

The results from the structural analysis identify where future work is needed. The highly

localized regions of maximum stresses indicate that a creep analysis is likely to show reduced

maximum stresses. This is especially true for configurations with trailing edge ejection

tubes. Maximum tensile and minimum compressive stresses were often seen within the tube,

and relatively close to each other. Internal configurations that increased radii in either the

rib or fork region showed reduced maximum stress. Alternate external vane shapes which

allow for larger radii in high stress regions, and provide acceptable aerodynamics, should be

investigated.

Radial cooled vane Current cooling schemes rely on impingement and film cooling to

achieve acceptable temperatures. Radial cooling has been proposed for small CMC vanes,

such as would be found in turboshaft engine applications. With radial cooling the impingement scheme is replaced by using several cooling tubes, oriented in the spanwise or radial

direction. Without film cooling, air flowing through the radial tubes absorbs the entire heat

flux due to the gas-to-wall temperature difference. With film cooling, air is extracted from

the tubes and is used to reduce the external heat flux by insulating the wall with a film of

cooler air. For the same coolant amount, when film cooling air is extracted from the tubes

the average tube heat transfer coefficient is lower than when no film cooling is used. Two

configurations were analyzed. One was multi-tube radial cooling. The other was a single cavity configuration. This single cavity configuration could be viewed as a single radial tube, or,

if there was enough space, as an impingement cooled vane. The single cavity configuration

always was coupled with trailing edge ejection tubes.

The thermal and aerodynamic performance was determined for two vane external configurations. One was a half scale version of the vane used for the full size vane structural

analysis. The other was a vane shape specified by Dr. Jerry Lang at the NASA Glenn

Research Center. Both had acceptable aerodynamics in that calculated vane efficiency was

consistent with the full size vane. Neither vane could be effectively cooled using only radial

cooling. Film cooling was required to be used in conjunction with multi-tube radial cooling.

With film and multi-tube radial cooling, or single cavity and trailing edge ejection cooling,

the aggressive future engine goals of NASA’s Large Civil Tilt Rotor(LCTR) program could

be achieved. These goals are a gas temperature of 1927◦C(3500◦F), and a coolant temperature of 594◦C(1100◦F). The gas temperature includes a pattern factor to account for

temperature variations at the combustor outlet. The coolant temperature is significantly

warmer than ambient due to a takeoff pressure of 30 atm.

while maintaining the 5% reduction in required vane coolant. Stress analysis comparisons

are given for twenty five pairs of cases. The initial comparisons were done for configurations

without trailing edge ejection. For these configurations a rib connecting the suction and

pressure surfaces, as well as having a minimum pressure surface wall thickness, was beneficial in terms of reduced maximum stresses. With trailing edge ejection pressure side, as

opposed to centerline, trailing edge coolant ejection resulted in lower maximum stresses. By

1$6$&52 
2.0 - Acknowledgments

We would like to acknowledge the helpful discussions we had with Michael Vinup, Kin

Poon, and Edward Zurmehly of Honeywell International Inc., and with Michael Halbig,

Ramakrishna Bhatt, James DiCarlo, and Jerry Lang of the NASA Glenn Research Center.

Michael Halbig was the contract monitor for this work.

1$6$&52 
3.0 - Introduction

Ceramic Matrix Composite(CMC) vane and rotor blades can significantly improve gas

turbine efficiency, due to their higher temperature capability compared to conventional

metallic blades. The CMC consists of Silicon Carbide(SiC) fibers in a SiC matrix. Using CMC vanes in the first stage of the High Pressure Turbine(HPT) provides the greatest

benefit in terms of reduced vane coolant. Reduced vane coolant results in improved vane

and turbine stage efficiency, which results in lower CO2 emissions. If rotor inlet temperature

is unchanged when CMC vanes are used, NOx emissions are reduced because the combustor outlet temperature is lowered. However, vane pressure and thermal loads are also at a

maximum in the first stage of the HPT. CMC materials have directionally dependent properties, as well as directionally dependent strengths or load bearing capability. CMC have

significantly lower strength in the interlaminar direction, compared to their strength in the

plane of the fibers. This report gives stress analysis results which account for directionally

dependent material properties.

To illustrate the benefits and challenges associated with CMC vanes the report is divided

into three sections. The first section addresses the benefits in terms of improved efficiency

and reduced NOx emissions from using CMC vanes and blades. The second section presents

the results of stress analyses for a vane with varying internal configurations. In this section

component stresses in the through thickness, hoop, and spanwise directions are shown. This

vane analyzed is suitable for a large engine application. The third section presents the results

of a thermal analysis of cooled small size vanes suitable for a turboshaft engine application.

This section also gives details of the thermal analysis used for both the small and large engine

size vanes.

The benefits of replacing conventional metallic vanes with CMC vanes arise from the

higher temperature capability of CMC vanes. For the same rotor inlet temperature, T41,

CMC vanes require less coolant than conventional metallic vanes. Vane efficiency increases

as the amount of cooling air decreases. Hartsel[1] gave a correlation to estimate the improvement in vane efficiency due to reduced coolant. Increasing vane efficiency increases

cycle efficiency, and thus reduces CO2 emissions and fuel consumption. From a cycle standpoint reducing cooling air ejected from the vane trailing edge may be more important than

reducing the overall amount of vane cooling air. Trailing edge ejection air is sometimes considered chargeable air. Chargeable air is unavailable to do work in the first HPT stage. NOx

emissions are reduced when the combustor outlet temperature is reduced. When T41 is held

constant, and vane cooling air is reduced, the temperature difference between T41 and the

combustor outlet temperature, T40 is reduced, since the coolant temperature, T3 is much less

than T41 A reduced temperature difference between T40 and T41 results in a lower T40, since

T41 is unchanged with reduced coolant. Reducing T40 reduces the combustor fuel-to-air ratio,

and a small change in the fuel-to-air ratio has a disproportionately large change in NOx production. The benefits analysis also includes the consequences of replacing both conventional

metallic vanes and rotor blades with CMC vanes and rotor blades. It will be shown that

replacing both vanes and rotor blades yields a much greater improvement in cycle efficiency,

and thus CO2 emissions, than just replacing metallic vanes with CMC vanes. The efficiency

improvement is achieved by raising the rotor inlet temperature, T41. Since raising T41 also

raises T40, the benefits of reduced NOx emissions are not available when CMC rotor blades

1$6$&52 
are used.

Stress analyses were done for a vane sized for a CF6 engine size application. Component

stresses were evaluated. The component directions were the through thickness or interlaminar, the hoop or circumferential, and the spanwise or radial directions. The vane internal

configuration was varied, while the external geometry was held constant for the stress analyses. Stress analyses were done for vanes with and without trailing edge ejection tubes.

Thermal analyses showed that trailing edge ejection was needed to achieve the reductions in

vane coolant. Without trailing edge ejection, excessive amounts of film cooling were needed

if film cooling rows were avoided for the aft portion of the suction surface.

The feasibility of manufacturing CMC vanes have been discussed in several references.

CMC vanes have been designed, fabricated, and tested, as discussed by Verrilli et al.[2],

Vedula et al.[3], Brewer et al.[4], Watanabe et al.[5], and Nakamura et al.[6]. Marshall

and Cox[7] discussed the use of ceramic textiles in gas turbine components. These references

discuss the desirability of using film cooling, since current design maximum gas temperatures

exceed the expected temperature capability of the Environmental Barrier Coating(EBC) used

to shield the CMC. The presence of film cooling rows was not included in the stress analysis.

This is not a short coming, since results showed that most of the vane can accommodate the

stress augmentation from film cooling rows without causing excessive stresses.

In the stress analysis section comparisons illustrating the effects of vane internal geometric

variations, property variations, and modeling assumptions are given. The vane external

geometry is that given by Halila et al.[8]. The effects of a rib connecting the pressure

and suction surfaces will be examined. The effects of using a thinner pressure surface wall

thickness will be examined, The effects of centerline and pressure side trailing edge ejection

will be examined. The effects of material property and boundary conditions, as well as the

effects of mesh refinement studies will be examined. Stresses due only to pressure loads, and

stresses due only to temperature gradients, as well as stresses due to combining these loads

will be given. Stresses due to individual loads are shown because, in a specific application,

loads different than those used for the analysis are likely to be applied. For example, if the

inlet pressure was half of the 50 atm. used, and the pressure distribution was similar, stresses

due to pressure loads would be nearly halved. Two stress components, through thickness and

hoop, will be discussed in detail. The strength of woven CMC materials in the interlaminar

or through thickness direction is substantially lower than the strength in the hoop or fiber

direction. For the majority of cases examined the maximum spanwise stress was less than

the maximum hoop stress. Detailed stress distributions are not given for spanwise stress, but

the maximum spanwise stress is given for each case. The chosen CMC material was N24A.

The properties of N24A were given by Mital et al.[9]. This material is a two dimensional

balanced weave. It was assumed that material properties in the spanwise or radial direction

were the same as those in the hoop direction.

Pressure loads were determined from the vane static pressure distribution. A pressure of

50 atm. was assumed for both the internal pressure, and the external total pressure. Thermal

loads were calculated assuming film cooling and impingement cooling for vane cavities. Heat

transfer in the trailing edge ejection tubes was calculated from a correlation.

The third section of this report discusses thermal analyses for two vane geometries suitable for the first HPT stage of a turboshaft engine. Vanes for turboshaft engines are approximately half the size of the vanes for a large commercial aircraft engine. One vane geometry

1$6$&52 
was a half scale version of the full size vane used for the stress analysis. The other vane geometry was specified by Dr. Jerry Lang of the NASA Glenn Research Center. This vane is

referred to as the NASA vane. Two cooling configurations were analyzed for each vane. The

first configuration was for radial cooling, where tubes are aligned in the spanwise direction.

Air flowing through these tubes absorbs heat from the mainstream gas. Thermal analysis

was done for radial cooling with and without film cooling. The other cooling configuration

was for a single cavity in the forward part of the vane, and trailing edge ejection tubes to

cool the aft portion of the vane. Two sets of boundary conditions were analyzed. One was

for a gas temperature of 1700◦K(2600◦F) and an inlet total pressure of 17 atm. The other

was for a gas temperature of 2200◦K(3500◦F) and an inlet total pressure of 30 atm. This

temperature and pressure are consistent with NASA’s goals for the Large Civil Tilt Rotor

Aircraft(LCTR) program[10].

One objective of this work was to determine if vane radial cooling was a viable cooling

approach. In the radial cooling approach tubes are oriented in the spanwise or radial direction. Internal cooling is provided by flow in the radial tubes, and no impingement cooling is

used. This cooling approach is relatively easy to implement, and small size vanes may not

have room for even a single impingement cooling insert. Since the vanes are smaller than

for the full size vane, thermal resistance is lower for HPT vanes of a turboshaft engine than

the thermal resistance of vanes used in a large commercial engine.. The analysis included

film cooling. It was found that radial cooling without film cooling was unable to keep vane

temperatures within acceptable limits. Another objective of this work was to determine if a

vane with a single cavity and having trailing edge ejection tubes could be sufficiently cooled

when the gas temperature was 2200◦K(3500◦F). The procedure used to determine vane

temperatures is discussed in section 4. The same procedure was used to determine vane

temperatures for both the full size vane and for the radial cooled vane.

This work addresses the benefits and challenges associated with using CMC vanes to

replace conventional metallic vanes in the high pressure turbine. The work was undertaken

in consultation with Honeywell International Inc. personnel to insure that it is relevant to

industry needs. It is recognized that the trailing edge thickness of a CMC vane may need to

be greater than the relatively thin trailing edge of this metal vane.

The purpose of this report is to comprehensively present the results of the work done

under the SBIR contract. Previous reports[11-13] covered aspects of the work, but the results

presented here cover aspects of the work not presented in any of the references.

1$6$&52 
4.0 - Benefits from CMC vanes and blades

Typical CMC materials have higher temperature capabilities than conventional metallic

vanes, and this leads to less required coolant for the same gas temperature. When only

metallic vanes are replaced by CMC vanes rotor inlet temperature, T41 is unlikely to increase.

Wilcock et al.[14] showed that raising T41 for current HPT blades is unlikely to improve

thermodynamic efficiency because the additional required rotor cooling air negates the gain

in efficiency from raising T41. Rotor cooling air is unavailable to do work in the stage for

which it is introduced. If current metallic blades are replaced by CMC blades T41, and

thus thermodynamic efficiency, can increase, since rotor cooling need not increase as T41 is

increased. Even if only current metallic vanes are replaced with CMC vanes there is an

improvement in thermodynamic efficiency, since vane efficiency increases as vane cooling

requirements decrease. Perhaps as importantly, when only the vanes are made from CMC

materials reduced vane coolant is expected to reduce NOx production, since reduced vane

coolant reduces the temperature difference between the combustor outlet, T40, and the rotor

inlet, T41. If CMC vanes and rotors are used raise cycle efficiency by raising T41, CO2

emissions are reduced, but NOx emissions are not reduced.

4.1 - SFC Improvement from CMC vanes.

Less vane coolant is required when metallic vanes are replaced by CMC vanes. Less

vane coolant improves vane aerodynamic efficiency, and stage efficiency further improves

because the amount of coolant air ejected from the vane trailing edge is also decreased.

If the trailing edge ejection air is considered to be chargeable air, a reduction in this air

increases stage output work, with no increase in fuel flow or compressor work. Figure 4.1.1

compares material properties for a selected CMC material and MA754, which is an alloy

suitable for HPT vanes(Halila et al.[8]). The MA754 properties were obtained from the

Special Metals web site[15]. The properties of the CMC material(N24A), a balanced 2D

weave, were obtained from Mital et al.[9]. As discussed by DiCarlo et al.[16] this is a fiber

reinforced SiC/SiC material with an upper use temperature of 1316◦C(2400◦F). While the

ratio of the Proportional Limit(PL) strength to the Ultimate Tensile Strength(UTS) is lower

for N24A than for MA754, N24A maintains its strength to a much higher temperature. This

figure shows that for N24A the UTS in the through thickness or interlaminar direction is

nearly a order of magnitude lower than the UTS in the plane of the weave.

Thermal properties and stiffness are given in figure 4.1.2 for both the CMC material and

the reference metallic material. At high temperatures N24A has lower thermal conductivity

and coefficient of thermal expansion than MA754. In the comparative thermal analysis a

thin EBC layer was applied over the CMC vane and was assumed to have a temperature capability of 1483◦C(2700◦F). This EBC layer had a thermal conductivity of 1W/m−K. The

EBC material was described by Lee et al.[17]. For the comparative thermal analysis a Thermal Barrier Coating(TBC) having the same thermal conductivity, but a lower temperature

capability of 1316◦C(2400◦F). was applied to the metallic vane.

Figure 4.1.3 shows typical maximum temperatures for the CMC and the protective low

conductivity EBC layer. These temperatures are the midspan outer temperatures of each

layer. A surface distance of zero corresponding to the leading edge stagnation point. Since

1$6$&52 
CMC materials require an EBC, comparisons were made assuming that both the metal and

CMC vanes had prime reliant 0.25mm(10mil) Thermal Barrier Coatings(TBC). A relatively

thick EBC or TBC layer, reduces the temperature gradients in the vane walls. The desirability of reducing the wall temperature gradient will be shown.

The calculations shown in figure 4.1.3 were done using data from Reiss and Bolcs[18] for

the leading edge region film effectiveness and heat transfer, and the correlation developed

by Boyle and Ameri[19] for film cooling effectiveness. Local film cooling effectiveness was

calculated assuming superposition from upstream cooling rows. The outer temperatures

show a saw tooth pattern, and temperature minimums indicate the location of film cooling

rows. No suction surface film cooling rows were downstream of the vane throat, since doing

so causes excessive aerodynamic losses. The relatively thick barrier coatings resulted in the

outer coatings reaching their maximum temperatures, while most of the vane temperatures

were less than their maximum values. Using a thick barrier coating lessened the vane through

thickness temperature gradients, which lowered vane thermal stresses.

Figure 4.1.4 shows calculated vane coolant fractions, (vane coolant-to-compressor discharge, (wC/w2.5) ratio) for both the metal and CMC vanes. Comparisons were made at

constant rotor inlet temperature, T41. These comparisons show that the reduction in vane

coolant when using CMC vanes is approximately 5% over a wide range of rotor inlet temperatures, T41. The calculated coolant fractions included both film cooling and cooling using

trailing edge ejection. The portion of the cooling air fraction attributable to trailing edge

ejection was found using internal heat transfer correlations and appropriate pressure losses.

The approximately 5.5% reduction in required cooling air improves cycle efficiency because vane aerodynamic efficiency increases when vane cooling is reduced. Stage output

increases when vane trailing edge ejection air is reduced. Improved cycle efficiency reduces

CO2 emissions. The improvement in vane aerodynamic efficiency due to reduced coolant

was calculated using the correlation given by Hartsel[1] Calculations using this correlation

showed that a 5.5% reduction in vane coolant air increased the total pressure at the rotor

inlet by 0.86%. Even though this increase in total pressure is less than 1%, there is a resulting increase in turbine output of 0.2%. This 0.2% increase in turbine output results in a

cycle efficiency increase of approximately 0.4%.

Most first stage HPT vane cooling air is non-chargeable air, and is available to do work

in the first stage rotor. However, air ejected from the trailing edge of the first HPT stage

vane may be considered as chargeable air. Even if this air is not considered to be chargeable

air the first stage performance is likely to decrease since trailing edge ejection air causes

increased aerodynamic loss. Assuming first stage vane trailing edge ejection cooling air is

fully chargeable air gives a significant improvement in SFC. Calculations showed that there

was a 5.5% reduction in required vane coolant from using CMC vanes. Trailing edge ejection

air was reduced by 1.2% of mainstream air, or nearly a quarter of the overall 5.5% reduction.

This 1.2% reduction in first stage vane chargeable air improved SFC by 0.6% for a highly

efficient two stage HPT with equal work splits, and an equal work split between the HPT and

Low Pressure Turbine. If trailing edge ejection air is not considered to be chargeable air, it

still benefits stage performance to reduce trailing edge ejection air. Trailing edge ejection air

only partially fills in the vane wake, and there is a large rotor incidence variation when the

rotor passes through the vane wake. The incidence variation decreases rotor, and therefore

stage, performance.

1$6$&52 
If using CMC material reduces first stage HPT coolant requirements, cooling can be

eliminated for the second stage HPT vane. This also improves SFC. In the design report

of Halila et al.[8] the second stage HPT vane cooling flow was 1.85%, of which 0.75% was

used for purge air. It is conservative to assume a 1.1% reduction in stage two vane cooling

air due to using CMC vanes. While second stage air is chargeable air, it may come from

an intermediate compressor stage, and thus is not fully chargeable air. On the other hand,

according to Honeywell International Inc. personnel, in small engine applications, it is

sometimes desirable to extract HPT cooling air for both stages from the compressor exit.

A 1.1% reduction in second stage HPT vane cooling air improves cycle efficiency by 0.55%,

when this air is compressor discharge air. It is estimated that the SFC improvement would be

about 0.3% when second stage vane cooling air is extracted from and intermediate compressor

stage. The Hartsel[1] correlation gives only a small reduction in second stage vane pressure

loss due to the elimination of cooling air.

1$6$&52 
0 500 1000 1500 2000 2500

Temperature, o

F

1

10

100

Strength, ksi

MA754

N24A - In plane - UTS

N24A - In plane - PL

N24A -Through thickness - UTS

Fig. 4.1.1 Strength properties of CMC material N24A and conventional metallic vane material MA754

0 500 1000 1500 2000 2500

Temperature, o

 F

0

10

20

30

40

Material properties

MA754

CMC Thermal conductivity, W/m/C

Thermal conductivity, W/m/C

Thermal expansion coefficient, X 106,

o

F

-1

Thermal expansion coefficient, X 106

,

 o

F

-1

Stiffness, X 10-3

, ksi

Stiffness, X 10-3, ksi

Fig. 4.1.2 Material properties for N24A and MA754

1$6$&52 
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

Surface distance, m

800

900

1000

1100

1200

1300

1400

1500

1600

Temperature, o

C

Pressure surface Suction surface

2400o

F

2700o

F

2060o

F

Max EBC temperature

Max CMC temperature Max TBC temperature

Max metal temperature

Fig. 4.1.3 Maximum vane and EBC/TBC temperatures for CMC and metallic vanes

1400 1500 1600 1700 1800 1900 2000 2100 2200

Rotor inlet temperature,T41

o

 C

0

0.04

0.08

0.12

Vane coolant fraction, w

C / w2.5

CMC vane

Metal vane

Fig. 4.1.4 Coolant fractions for CMC and metallic vanes

1$6$&52 
4.2 - NOx reduction from CMC vanes.

Because CMC vanes use less cooling air than metal vanes for the same rotor inlet temperature, T41, the combustor outlet temperature, T40, is lower when CMC vanes replace

conventional metallic vanes. Since most vane cooling air is non-chargeable air, the turbine

output is nearly the same when CMC vanes replace metallic vanes.

Data show that a small reduction in T40 significantly reduces NOx. A constant specific

heat thermal balance across the vane row gives:

T41(1 + wC/w40) = T40 + wCTC

where wC/w40 is the vane coolant fraction, and TC is the coolant temperature. While T41 and

TC vary depending on the application, a typical difference between these two temperatures

is 1000◦C(1800◦F). For this temperature difference a 5% reduction in wC/w40 results in a

50◦C(90◦F) reduction in T40.

Several references showed that the amount of NOx produced is very sensitive to T40.

Figure 4.2.1, from Tacina et al.[20], shows the amount of NOx produced per kilogram of

fuel as a function of the flame temperature. NOx is strongly dependent on the combustor

configuration, and the red line data is for the configuration with the lowest NOx at high

temperature. The peak gas temperature, TG, which corresponds to the flame temperature

is over 2000◦K(3140◦F) and is expected to be more than 200◦C(360◦F) hotter than T40.

An extrapolation of the curve shows that NOx is reduced by nearly 15% when the flame

temperature is reduced by 50◦C(90◦F).

The straight lines in figure 4.2.2, which is from Harth et al.[21] show that the relative

sensitivity of NOx to the adiabatic combustor temperature is independent of this temperature. This combustor, like the combustor tested by Tacina et al.[20], is for an aircraft

engine application, At the highest combustor pressure and inlet temperature a change of

50◦K(90◦F) in the adiabatic temperature reduces NOx by more than 40%.

1$6$&52 
x

Fig. 4.2.1 NOx as a function fo flame temperature for different combustor geometries, from

Tacina et al.[20]

Fig. 4.2.2 NOx as a function of adiabatic temperature for different combustor consitions and

fuel splits, from Harth et al.[21]

1$6$&52 
Fiure 4.2.3, from Dusing et al.[22], shows results similar to those in figure 4.2.2, but

for a combustor designed for ground power application. This figure has lines with straight

slopes, and shows that a 50◦K(90◦F) reduction in combustor outlet temperature reduces

NOx by more than 40lines are approximately parallel for two technology levels, (2006 &

2011). Therefore, it is not likely that future combustor designs will have relative NOx sensitivities significantly lower than current combustor designs. The absolute level of NOx is

expected to be lower for future combustors operating at current conditions. However, combustor outlet temperatures and pressures are expected to increase over time, and increases

in either of these parameters raises NOx levels. The benefits of lower T40 from using CMC

vanes provides a means of offsetting the adverse effects of higher temperature and pressure.

Fig. 4.2.3 NOx as a function fo flame temperature for different combustor geometries, from

Dusing et al.[22]

1$6$&52 
20 30 40 50 60 70

Overall pressure ratio

0.4

0.42

0.44

0.46

0.48

0.5

0.52

Cycle efficiency

T41=3500o F (2200o K)

T41=2600o

 F (1700o K)

T41=2780o F (1800o K)

T41=2960o

 F (1900o K)

T41=3140o

 F (2000o K)

T41=3320o

 F (2100o K)

Fig. 4.3.1 Typical cycle efficiency, constant coolant fraction, from Boyle and Jones[23]

4.3 - SFC improvements from CMC vanes and blades

The maximum SFC improvement from replacing metallic airfoils with CMC airfoils is

achieved by maintaining the cooling fraction and raising the rotor inlet temperature, T41.

Wilcock et al.[14] showed that raising T41 for conventional metallic rotor blades does not

improve SFC because of the additional cooling air required for the rotor blades. Without

penalizing the rotor for additional cooling air, raising T41 implicitly assumes both CMC

vanes and rotor blades. Figure 4.3.1, from Boyle and Jones[23], shows cycle efficiency for

a representative set of conditions, and the assumption that rotor cooling flow fractions are

independent of temperature. Higher gas temperatures are achieved by improving the temperature capability of the vane and rotor materials. In reference 24, it was shown that there

is no improvement in cycle efficiency with increasing temperature for an ideal cycle, due

to the specific heat increasing with temperature. However, this is not the case when stage

efficiencies are less than one. At the lowest T41, efficiency decreases for Overall Pressure Ratio(OPR) beyond 45, but efficiency continues to increase with OPR for higher temperatures.

Analyses were also done for the increase in T41 when using CMC vanes. Maximum

surface temperatures were 2700◦F(1756◦K) for the CMC vane and 2400◦F(1589◦K) for the

metal vane. The vane coolant fraction was held constant at 10.6% of compressor discharge

air. Coolant air temperature was also held constant. The rotor inlet temperature for the

metallic vane was calculated to be 2935◦F(1886◦K). Somewhat surprisingly, the increase in

T41 was greater than the 300◦F(167◦C) increase in the maximum surface temperature. T41

increased by 525◦F(292◦C) when the metallic vane was replaced by a CMC vane. Figure

4.3.1 shows that a 300◦(540◦F) increase in T41 produces a relative increase in cycle efficiency

of at least 3% at constant OPR when the OPR is between 40 and 50. The minimum relative

1$6$&52 
increase is at high T41 values. When the increase in T41 is accompanied by an increase in

OPR, as has been the historic trend, a 300◦ increase in T41 yields even greater efficiency

gains. Going from T41 = 1900◦K(2960◦F) and an OPR of 40 to a T41 = 2200◦K(3500◦F)

and an OPR of 50 results in a relative cycle efficiency gain of over 6%. It is conservative to

expect a gain of 5% in cycle efficiency due to replacing metallic vanes and rotor blades with

CMC components.

1$6$&52 
4.4 - Conclusions

CMC first stage HPT vanes require 5.5% less vane coolant due to the CMC vanes having

higher temperature capabilities for the same cooling configuration. Just replacing metallic

vanes with CMC vanes can improve cycle efficiency up to 1.5%. An improvement of 0.4% in

efficiency was due to increased first stage vane efficiency. Elimination of second stage vane

coolant was estimated to increase cycle efficiency between 0.3 and 0.5%. The lower increase

assumed that second stage vane cooling was extracted from an intermediate compressor stage.

The higher efficiency increase assumed that second stage vane cooling air was extracted from

the compressor exit. With CMC vanes there is a reduction in the required amount of air

ejected from the vane trailing edge. Trailing edge ejection air is sometimes considered to be

chargeable air in a cycle analysis. If the reduction in trailing edge ejection air, is treated

as chargeable air, the additional cycle efficiency improvement was estimated as 0.6% This

improvement came from replacing metallic vanes with CMC vanes.

When conventional metallic vanes are replaced with CMC vanes, and the rotor inlet

temperature, T41 remains the same, the required vane coolant is reduced by approximately

5% of mainstream air ratio. This is due to the higher temperature capability of the CMC

materials. The 5% reduction in mainstream air used for vane coolant reduces T40 by approximately 50◦K(90◦F). This has a disproportionately large reduction in NOx due to the high

sensitivity of NOx to combustor outlet temperature, T40. Experimental data from different

sources show a reduction in NOx ranging from 15% to over 40% due to just a 50◦K(90◦F)

reduction in T40.

Replacing both conventional metallic HPT vanes and rotor blades with CMC vanes and

rotors results in the highest gain in cycle efficiency. It was calculated that the rotor inlet

temperature could be raised nearly 300◦C(540◦F) when CMC vanes and rotor blades are

used. It was shown that a 300◦C increase in T41 is expected to raise cycle efficiency by at

least 5%. A 5% efficiency increase represents a 5% decrease in CO2 emissions. However,

NOx emissions will not decrease due to using CMC vanes and blades, since raising T41 raises

T40.

1$6$&52 
5.0 - Stress Analysis of CMC Vane

Steady state aerothermal and structural analyses were done to identify approaches to

achieving acceptable stress distributions for a specified vane external geometry. This section

of the report gives the effects on stress components due to changes in the vane internal

geometry, as well as other factors, such as material properties, boundary conditions, and grid

density. Figure 4.1.1 shows that allowable stresses for the CMC material are directionally

dependent. Consequently, component stresses were calculated. A somewhat arbitrary goal

of this work was to identify configurations having through thickness or interlaminar stresses

below 1.5ksi(10.5MPa), and having hoop and spanwise stresses below 17ksi(117MPa). This

goal was based on the properties of N24A material, and as shown by Engel[25] other CMC

materials have significantly higher interlaminar strengths. Detailed results are presented for

through thickness and hoop stresses. For the assumed orientation of the reference CMC

material(N24A) the allowable stresses in the spanwise or radial direction and in the hoop or

vane circumferential direction were the same. Generally, but not for all cases, the maximum

spanwise stress in the vane midspan region was lower than the maximum hoop stress in

this region. Although a detailed discussion of spanwise stresses is not given, the maximum

component stress in all three directions is discussed.

Pressure and thermal loads were determined from Navier-Stokes Computational Fluid

Dynamics analyses. Pressure and heat transfer coefficient distributions were calculated using

two and three dimensional versions of the Navier Stokes computer analysis codes described

in references 26 and 27. A single vane normalized pressure distribution was used. This distribution is for a vane exit Mach number of 0.95. Three dimensional analyses of the vane and

flow path of reference vane geometry given by Halila et al.[8] showed little spanwise variation

in either pressures or heat transfer coefficients. Consequently, midspan distributions were

used for each spanwise vane location.

Heat transfer distributions vary with vane total pressure, and were also obtained using

the Navier Stokes analysis. Boundary layer transition was accounted for in determining heat

transfer distributions, when film cooling was not used. Data show that, just the presence

of film cooling holes causes transition to fully turbulent flow immediately downstream of

the film cooling holes. Consequently, when film cooling was used, the flow was assumed to

be fully turbulent. The local heat flux is a function of both the heat transfer coefficient

and the adiabatic wall temperature. Without film cooling the adiabatic wall temperature is

nearly the gas temperature. With film cooling the adiabatic wall temperature approaches the

coolant, or compressor discharge, temperature, when the film effectiveness approaches one.

The distribution of the vane film cooling effectiveness away from the leading edge was found

using the analysis given by Boyle and Ameri[19]. In the leading edge region the film cooling

effectiveness, and the increase in the local heat transfer coefficients, were found using the

results given by Reiss and Bolcs[18] Internal cooling was either by impingement cooling or by

flow through radial cooling tubes. When impingement cooling was assumed, the correlation

of Florschuetz et al.[28] for a staggered array of impingement cooling holes was used. When

radial cooling was used, the tube heat transfer coefficient was determined by the standard

correlation for turbulent flow in a tube[29]. Tube heat transfer, which is a function of the

mass flux, was corrected to account for the change in midspan mass flux when film cooling

was used in conjunction with radial cooling.

1$6$&52 
Fig. 5.0.1 Vane with two endplates

Structural analysis was done using the ANSYS code[30]. Component stresses were

calculated using the ANSYS linear-static assumptions. CMC materials have higher strengths

in the fiber directions. At each point within the CMC material stresses were resolved into

three directions. These were the through thickness, hoop, and spanwise directions. The

through thickness direction was generally normal to the internal vane surface. Where the

vane had no internal surface, typically the aft portion of the vane, the through thickness

direction was normal to the vane external surface. The hoop direction was normal to the

through thickness direction. Component stresses were calculated using local coordinate

systems within the vane and the “as calculated” ANSYS option. Properties of the CMC

material, N24A, were also directionally dependent. Even though actual gas turbine vanes

are defined by cylindrical coordinates, Cartesian coordinates were used in the analysis. The

model vane, shown in figure 5.0.1, has all the necessary features of an actual vane. The vane

and end plates show a typical external temperature distribution, where the temperature is

in ◦F. One of the end plates is fixed, while the other end plate is free to expand in all

directions.

While film cooling was assumed to determine vane temperature distributions, film cooling

holes were not included in the structural analysis. Film cooling holes have closer spacing in

the spanwise direction than in the circumferential or hoop direction. Because of this, hoop

stresses are more sensitive than spanwise stresses to stress augmentation due to an area

reduction from film cooling holes. It will be shown that peak stresses are highly localized.

For most cases there are ample regions where rows of film cooling holes could be located

without causing excessive stresses.

The reference vane is shown in figure 5.0.2 The external vane shape is that of the

vane of Halila et al.8]. This vane was designed under contract as part of NASA’s Energy

Efficient Engine(EEE) program. This figure shows a uniform wall thickness of 2mm(80 mil).

The vane has an axial chord, CX, of 3.38cm(1.33in), and a true chord nearly twice as long at

6.3cm(2.48in). Three red circles are shown in this figure. The largest circle shows the leading

edge region curvature. While the actual leading edge is elliptical in shape, the leading edge

radius is approximately 0.3cm(118mil). A smaller circle of 0.076cm(30mil) radius is shown

where the inner CMC surfaces come together to form the fork region. Where the inner

suction and pressure walls join this radius was used in the stress analysis for the uniform

wall thickness cases.. The third circle with a radius of 0.0535cm(21mil) is at the trailing

edge. The analysis was done using this radius, even though a thicker trailing edge is likely

to be needed for a CMC vane.

1$6$&52 
-6 -5 -4 -3 -2 -1 0 1

Axial distance, cm

0

1

2

3

4

5

6

Pitchwise distance, cm

0.20cm(80mil)

True chord 6.48 cm ( 2.55 in.)

CX=3.38 cm (1.33 in.)

Fig. 5.0.2 Reference vane geometry

0 0.2 0.4 0.6 0.8 1

Axial distance, x/CX

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Static pressure ratio, P / P

T

Suction surface

Pressure surface

Fig. 5.0.3 Pressure distribution for reference vane

1$6$&52 
Pressure loads were evaluated using the external pressure distributions shown in figure

5.0.3. Except for one analysis case, there was an internal pressure equal to the external total

pressure. The largest pressure differential occurs near mid-chord, where the suction surface

pressure is only about half of the inlet total pressure.

Table 5.0.1 gives the list of cases that were analyzed. The case numbering, 1A through

13B, is somewhat arbitrary, but is used to identify cases for comparison purposes. Stresses

were calculated for pressure and temperature loads independently, and when pressure and

temperature loads were combined. The purpose of each case is given in the table. The

majority of cases had a rib connecting the pressure and suction surfaces of the vane, and

for most of these cases the rib was insulated. The majority of cases had a differential wall

thickness, where the the thickness of the pressure surface and in leading edge were half of

the 2mm(80 mil) thickness of the uniform wall thickness cases. Reducing the suction surface

wall thickness resulted in very high stresses just due to pressure loads. For most of the

cases a non-uniform temperature distribution was used. Nearly half of the cases had either

centerline or pressure side trailing edge ejection.

Figure 5.0.4 shows the vane configurations described in Table 5.0.1 This figure show the

vane configurations and temperatures for the CMC vane. Only very close to the trailing

edge does the vane temperature slightly exceed the desired maximum CMC temperature of

1316◦C(2400◦F). The region is very small, and is approximately the same in each part of the

figure. Part a shows the baseline case of single large impingement cavity. Part b shows a vane

having a differential wall thickness. The rib is uninsulated, accounting for its relatively cold

temperature. Part c shows temperatures through a slice of the vane showing the trailing

edge ejection tube. As expected, near the entrance of the tube the surface temperatures

are relatively cold. Part d shows temperatures for a single cavity configuration. The end

temperatures are shown through the solid section, rather than through the trailing edge

ejection tube. This single cavity configuration has the size cavity as the forward cavity

shown in part b of figure 5.0.4

1$6$&52 
Table 5.0.1 - List of Cases

Cases Load Purpose Rib Wall CMC T.E.

Present Insulated Thickness ΔT Ejection

1A Pres Base line case No N.A. Uniform N.A. No

1B Temp Uniform ΔT No N.A. Uniform Uniform No

1C Temp Non-Uniform ΔT No N.A. Uniform Non-Uniform No

1D Comb Combined loads No N.A. Uniform Non-Uniform No

2A Pres Connecting rib Yes N.A. Uniform N.A. No

2B Temp Connecting rib Yes No Uniform Non-Uniform No

2C Comb Combined loads Yes No Uniform Non-Uniform No

3A Pres Differential wall thickness Yes N.A. Differential N.A. No

3A2 Pres No internal pressure Yes N.A. Differential N.A. No

3B Temp Differential wall thickness Yes No Differential Non-Uniform No

3C Temp Insulating rib Yes Yes Differential Non-Uniform No

3D Comb Insulating rib Yes Yes Differential Non-Uniform No

4A Pres Centerline trailing edge ejection Yes N.A. Differential N.A. Yes/Cl

4B Temp Centerline trailing edge ejection Yes Yes Differential Non-Uniform Yes/Cl

4C Comb Centerline trailing edge ejection Yes Yes Differential Non-Uniform Yes/Cl

5A Comb Revised rib shape Yes Yes Differential Non-Uniform Yes/Cl

5B Comb Reduced coolant Yes Yes Differential Non-Uniform Yes/Cl

5C Comb Presure side trailing edge ejection Yes Yes Differential Non-Uniform Yes/P.S.

5D Pres Revised rib shape Yes N.A. Differential N.A. No

5E Pres Single impingement cavity No N.A. Differential N.A. Yes/P.S.

5F Pres Pressure side trailing edge ejection Yes N.A. Differential N.A. Yes/P.S.

5G Comb Single impingement cavity No N.A. Differential Non-Uniform Yes/P.S.

6A Comb Modulus(E33) change Yes Yes Differential Non-Uniform No

6B Comb Modulus(E33) change Yes Yes. Differential Non-Uniform No

6C Comb Revised temperatures Yes Yes Differential Non-Uniform No

6D Comb Modulus(E33) change Yes Yes Differential Non-Uniform No

6E Comb Modulus(E33) change Yes Yes Differential Non-Uniform Yes/Cl

6F Temp Revised temperatures Yes Yes Differential Non-Uniform No

6G Comb Combined loads Yes Yes Differential Non-Uniform No

7A Comb End plate thickness Yes Yes Differential Non-Uniform No

7B Comb Mesh refinement Yes Yes Differential Non-Uniform No

7C Comb Boundary conditions Yes Yes Differential Non-Uniform No

7D Comb Square trailing edge Yes Yes Differential Non-Uniform No

8A Comb Increased CMC conductivity Yes Yes Differential Non-Uniform No

10A Temp Modified leading edge shape Yes Yes Differential Non-Uniform No

10B Temp Mesh refinement Yes Yes Differential Non-Uniform No

10C Temp Hemispherical rib Yes Yes Differential Non-Uniform No

10D Temp New temperature distribution Yes Yes. Differential Non-Uniform No

11A Pres Square tube - Hemispherical fork No N.A. Differential N.A. Yes/P.S.

11B Pres Meshing variation No N.A. Differential N.A. Yes/P.S.

11C Pres Circular tube No N.A. Differential N.A. Yes/P.S.

11D Pres Circular tube - mesh refinement No N.A. Differential N.A. Yes/P.S.

11E Pres Circular tube - meshing variation No N.A. Differential N.A. Yes/P.S.

11F1 Temp Circular tube - meshing variation No N.A. Differential Non-Uniform Yes/P.S.

11F2 Comb Circular tube - meshing variation No N.A. Differential Non-Uniform Yes/P.S.

11G1 Temp Square tube - meshing variation No N.A. Differential Non-Uniform Yes/P.S.

11G2 Comb Square tube - meshing variation No N.A. Differential Non-Uniform Yes/P.S.

12A Comb E33 variation E33=157 Yes Yes Differential Non-Uniform Yes/P.S.

12B Comb E33 variation E33=77 Yes Yes Differential Non-Uniform Yes/P.S.

13A Temp Revised temperatures Yes Yes Differential Non-Uniform Yes/Cl

13B Temp Insulated fork region Yes Yes Differential Non-Uniform Yes/Cl

1$6$&52 
a) Baseline vane - no rib - no trailing edge ejection

b) Differential wall thickness - no trailing edge ejection

1$6$&52 
c) Centerline trailing edge ejection

d) Pressure side trailing edge ejection

Fig. 5.0.3 Vane internal configurations

1$6$&52 
Table 5.0.2 - List of Comparisons

Page

5.1 - No Trailing Edge Ejection 27

5.1.1 - Effect of Rib 28

5.1.2 - Effect of Non-Uniform Temperature Gradient 31

5.1.3 - Effect of Differential Wall Thickness 33

5.1.4 - Effect of Combined Pressure and Temperature Loads 35

5.1.5 - Effect of Insulating Connecting Rib 36

5.1.6 - Effect of Modifying Rib Shape 37

5.1.7 - Effect of No Internal Pressure 38

5.1.8 - Effect of Revised Temperature Distribution 40

5.1.9 - Effect of Trailing Edge Shape 42

5.2 - Trailing Edge Ejection 43

5.2.1 - Effect of Centerline Trailing Edge Ejection 44

5.2.2 - Effect of Pressure Side Trailing Edge Ejection 47

5.2.3 - Effect of Modified Rib Shape 49

5.2.4 - Effect of Single Impingement Cavity 50

5.2.5 - Effect of Rectangular & Square Ejection Tube Geometry 52

5.2.6 - Effect of Square & Circular Tube Geometry 54

5.2.7 - Effect of Revised CMC Temperature Gradients 57

5.2.8 - Effect of Reduced Tube Heat Transfer Coefficient 59

5.2.9 - Effect of Insulating Fork Region 60

5.3 - Property and Boundary Condition Effects 61

5.3.1 - Effect of Through Thickness Stiffness Modulus 62

5.3.2 - Effect of Doubling Thermal Conductivity 64

5.3.3 - Effect of Reducing End Plate Stiffness 66

5.3.4 - Effect of Boundary Condition Variation 67

5.4 - Mesh Refinement Studies 68

5.4.1 - Effect of Vane & End Plate Mesh Density 69

5.4.2 - Effect of Mesh Shape for Square Ejection Tube 70

5.4.3 - Effect of Mesh for Circular Ejection Tube 71

5.5 - Maximum Component Stresses 72

The four sections of Table 5.0.2 describe the comparisons made to illustrate the effects

on midspan region stresses due to various internal configurations. The first section lists

the comparisons made for configurations without trailing edge ejection. The second section

lists comparisons for cases with trailing edge ejection. The third section lists comparisons

that investigate the effects of CMC property configurations and boundary conditions. The

fourth section lists comparisons that involved changes to the mesh used in the analysis. Also,

included in this table are the pages in which the comparisons are discussed.

1$6$&52 
5.1 - No Trailing Edge Ejection Comparisons

There are ten comparisons for cases with no trailing edge. These are the cases listed in

the first section of Table 5.0.2. Trailing edge ejection is commonly used to cool the portion

of the vane suction surface aft of the throat. This is done to avoid large aerodynamic loss

penalties associated with having film cooling rows aft of the vane throat. On the other hand

it may be desirable to avoid trailing edge ejection tubes in CMC vanes. These tubes have

a far greater length-to-hydraulic diameter ratio than are required for film cooling holes. If

trailing edge ejection is not feasible in a particular application, suction surface film cooling

rows downstream of the throat is an alternative. The reduction in vane cooling from using

CMC vanes could still be achieved. However, the aerodynamic efficiency benefits of reduced

coolant may be overwhelmed by the additional loss from having suction surface cooling rows

downstream of the throat. Unless vane efficiency is severely degraded from aft suction surface

film cooling rows, the benefits of reduced NOx would still be achieved.

In the following figures, which show stress contours, the vane orientation may be different

in each part of the comparison. The different orientations arise because maximum stress

locations are different for cash case. The vane in each figure was rotated to show the location

of maximum stress.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

No rib - case 1A Rib - case 2A

Fig. 5.1.1.1 - Effect of rib - Pressure load only

5.1.1 - Effect of Rib. Figures 5.1.1.1 through 5.1.1.3 illustrate the effects of using a rib

to connect the suction and pressure surfaces of the vane. Without a rib there is a single hole

for an impingement tube, and with a rib two impingement tubes are needed. Comparisons

are made for just pressure loads, cases 1A and 2A, just thermal loads, cases 1C and 2B, and

when the pressure and thermal loads are simultaneously applied, cases 1D and 2C.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

No rib - case 1C Rib - case 2B

Fig. 5.1.1.2 - Effect of rib - Thermal load only

Figure 5.1.1.1 shows through thickness and hoop stresses in the vane midspan region due

only to pressure loads for the baseline cases without a rib(1A), and a case with a rib(2A).

The presence of a rib is very effective in reducing maximum stresses. Without a rib the

maximum tensile stress occurs in the fork region, where the suction and pressure surfaces

join together. With a rib the maximum through thickness and pressure stresses occurs in

the rib region, and are much lower than the maximum through thickness and hoop stresses

for the case without a rib. Although not shown, for each of the six cases the maximum

spanwise or radial stresses in the midspan region were lower than the maximum hoop stress

for pressure, thermal, and combined loads.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

No rib - case 1D Rib - case 2C

Fig. 5.1.1.3 - Effect of rib - Combined pressure and thermal loads

Figure 5.1.1.2 shows stresses due to non-uniform thermal loads. With a rib maximum

through thickness and hoop stresses are higher, and occur in the rib region. The thermal

stresses in the fork region do not significantly change due to the presence of a rib. In the

through thickness direction thermal load stresses are significantly greater than pressure load

stresses. When a rib is used the maximum through thickness stress due to thermal loads is

nearly seven times the maximum through thickness stress due to pressure loads. When a

rib is used the maximum hoop stress due to thermal loads is over twice the maximum hoop

stress due to pressure loads

Figure 5.1.1.3 shows stresses due to combined pressure and thermal loads. When no

rib is present high stresses occur in the fork region for both pressure and thermal loads.

Consequently, the maximum stress due to combining loads approaches adding the stress

for both types of loads. The results are different when a rib is present. Even though the

maximum hoop stress due to pressure loads is 17ksi(117MPa) the maximum stress due to

combined loads is only 4ksi(28MPa) greater than the maximum hoop stress due to thermal

loads.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Surface distance, s/CX

-50

0

50

100

150

200

250

300

Vane temperature difference, o F

Suction surface Pressure surface

Uniform temperature difference

50

100

150

o

C

Fig. 5.1.2.1 Temperature difference across CMC vane walls

5.1.2 - Effect of Non-Uniform Temperature Gradient. Since thermal stresses are

greater than pressure stresses, the effect of a uniform temperature gradient across the walls of

the vane were determined. This was done for the case without a rib. Figure 5.1.2.1 shows the

temperature difference across the vane walls. This figure shows the unwrapped vane midspan

temperature difference. Local minimums occur just downstream of rows of cooling holes.

(The presence of cooling hole rows was not included in the stress analysis.) The temperature

difference shown in figure 5.1.2.1 results in the stress distribution previously shown in figure

5.1.1.4. Through thickness and hoop stresses for the uniform and non-uniform temperature

difference cases are shown in figure 5.1.2.2. The uniform temperature difference across the

CMC vane was 83.3◦C(150◦F). This figure shows that a non-uniform temperature difference

increases both maximum through thickness and maximum hoop stress stress by over 50%.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Uniform ΔT - case 1B Non-uniform ΔT - case 1C

Fig. 5.1.2.2 Effect of Non-uniform temperature gradient - Thermal load

Calculations were done where the uniform temperature gradient across the vane wall was

halved. As expected, halving the gradient halves the thermal load stresses. Previous results

for cases 2A and 2B showed that thermal stress generally exceed thermal stresses. While

this comparison is for uniform differential temperatures, later comparisons for a case where

the CMC thermal conductivity was increased show similar stress reductions due to reduced

CMC vane thermal gradients.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Uniform wall thickness - case 2A Differential wall thickness - case 3A

Fig. 5.1.3.1 Effect of Non-uniform wall thickness - Pressure load

5.1.3 - Effect of Differential Wall Thickness. In an effort to reduce the thermal

gradient across the CMC vane wall a case was analyzed where the wall thickness along the

pressure surface and in leading edge region was halved. Reducing the wall thickness from

2mm(80mil) to 1mm(40mil) reduced thermal gradients across the pressure surface. It was

not practical to reduce the suction surface wall thickness below 2mm(80mil), since suction

surface stresses rose very rapidly as the suction surface wall thickness was reduced. Figure

5.1.3.1 shows that the maximum through thickness stress due to pressure loads is higher for

the thinner pressure surface wall. Fortunately, figure 5.1.3.2 shows that maximum through

thickness stress due to thermal loads is lower by nearly 20% for the thinner pressure surface

wall case.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Uniform wall thickness - case 2B Differential wall thickness - case 3B

Fig. 5.1.3.2 Effect of Non-uniform wall thickness - Thermal load

The maximum hoop stress is lowered when the pressure surface is thinner than the

suction surface. While the reduction in maximum hoop stress is only a few percent, stresses

for both pressure and thermal loads are reduced.

1$6$&52 
a) Through thickness stress, psi

a) Through thickness stress, psi

Uniform wall thickness - case 2C Differential wall thickness - case 3D

Fig. 5.1.3.3 Effect of Non-uniform wall thickness - Combined pressure and thermal loads

5.1.4 - Effect of Combined Pressure and Thermal Loads. Figures 5.1.1.1 through

5.1.1.3 illustrated the effects of combining pressure and temperature loads on stresses for

uniform wall thickness cases. Figures 5.1.3.1 through 5.1.3.3 illustrate the same effects for

the differential wall thickness case. These two sets of comparisons show behavior typical

of all cases examined. Also, the results are similar for either through thickness or hoop

stresses. The maximum stress for combined loads is significantly lower than the algebraic

sum of the maximum pressure load stress and the maximum thermal load stress. However,

at the location of the maximum tensile stress from one load, which is generally a thermal

load, there is a positive stress from the other load. The maximum stress from combined

loads is slightly greater than the maximum stress from either a pressure or thermal load.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Cooled rib - case 3B Insulated rib - case 3C

Fig. 5.1.5.1 Effect of insulating connecting rib - Thermal load

5.1.5 - Effect of Insulating Connecting Rib. The effect of insulating the rib connecting the vane pressure and suction surfaces is to reduce maximum stresses due to thermal

loads. Figures 5.1.5.1 shows that insulating the rib reduces peak through thickness stress

by nearly 20%. Both the magnitude and location of the maximum hoop stress is affected

by insulating the rib. With a cooled rib the maximum hoop stress occurs in the rib region,

while for the insulated rib the maximum hoop stress is in the fork region. The maximum

hoop stress is reduced by over 20% when the rib is insulated. For both cases internal cooling

was assumed to be done using an impingement insert. For an uncooled or insulated rib

there would be no impingement holes facing the rib. Since there are several pressure surface

film cooling rows, cross flows passing over the rib from the internal pressure surface to the

internal suction surface can be avoided.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Small rib radii - case 3A Semi-circular rib radii - case 5D

Fig. 5.1.6.1 Effect of Rib shape - Pressure load

5.1.6 - Effect of Modifying Rib Shape. Figure 5.1.6.1 shows stresses caused by

pressure loads for the reference rib geometry and a semi-circular rib geometry. In the semicircular rib case each rib surface used to form the front and rear impingement cavities has

a single radius of curvature. The rib in the other case has four corners with small radii

are only 2.3% of the axial chord, CX. The effect of larger rib radii is to reduce maximum

through thickness stress due to pressure loads by more than half. The semi-circular rib

increased the maximum hoop stress, and changed the location where the maximum hoop

stress occurred. The maximum hoop stress increased by nearly 7%, and moved from the

rib-suction surface region to the inner surface, near the leading edge. The minimum hoop

stress for the semi-circular rib occurred on the exterior surface of the vane. Unfortunately,

this rib configuration is unlikely to significantly affect thermal stresses.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Internal pressure - case 3A No internal pressure - case 3A2

Fig. 5.1.7.1 Effect of no internal pressure - Pressure load only

5.1.7 - Effect of No Internal Pressure If the vane is uncooled, which may be the

case for a HPT second stage CMC vane, there need not be an internal pressure causing

a ballooning stress. When there is no internal pressure there is still a bending load on

the vane, because the average external pressure surface pressure is higher than the average

suction surface external pressure. While a second stage vane has a much lower inlet total

pressure than the 50 atm. total pressure assumed for the first stage vane, the normalized

external pressure ratio, P/PT−IN, distribution is expected to be similar to that for the first

stage vane. Calculations showed that pressure load stresses are proportional to the inlet

total pressure, PT−IN, when the normalized pressure distribution, P/PT−IN, is constant. For

comparative purposes the analysis was done assuming the same inlet total pressure of 50

atm. as for the other cases. Figure 5.1.7.1 shows that pressure load stresses for a case with

no internal pressure are much higher than those where the internal pressure is 50 atm. Both

through thickness and hoop stresses are much higher for the case with no internal pressure.

There were no thermal loads present for the case with no internal pressure, and previous

cases showed that thermal stresses generally exceeded pressure stresses. With no internal

pressure the maximum through thickness stress shown in figure 5.1.7.1a nearly equals the

1$6$&52 
maximum through thickness combined load stress for any case previously shown. Similarly,

the maximum hoop stress shown in figure 5.1.7.1b exceeds the maximum hoop combined

load stress for any of the previous cases. These results indicate that the stresses for an

uncooled first stage HPT vane may exceed those for a cooled first stage vane. Even for an

uncooled second stage HPT vane, stresses may be as high as for a cooled first stage vane, if

the thermal gradients in the first stage vane are moderate.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Surface distance, s/CX

-50

0

50

100

150

200

250

300

Vane temperature difference, o F

Case 3D

Case 6C

Suction surface Pressure surface

50

100

150

o

C

Fig. 5.1.8.1 Two temperature differences across CMC vane walls

5.1.8 - Effect of Revised Temperature Distribution The arrangement of film cooling rows can affect the CMC temperatures to some degree without affecting the amount

of required film cooling. Figure 5.1.8.1 shows two temperature differences across the CMC

vane. Case 6C has lower temperature differences across much of the vane surface. On the

other hand, case 6C has higher streamwise temperature gradients on the suction surface

between s/CX = 1 and s/CX = 1.4. The surface distance, s, is approximately twice the axial

chord, CX.

Figure 5.1.8.2 gives the through thickness and hoop stresses for the temperature differences

shown in figure 5.1.8.1. Stresses are given for combined loads.. The results are somewhat

unexpected, in that the lower temperature difference results in higher maximum through

thickness stress. The increase in maximum through thickness stress is not large, being less

than 8%, but is associated with a smaller temperature difference. Overall through thickness

stresses, though not the maximum stress, are reduced with a lower temperature difference.

This is most evidenced in the fork region where case 3D has stresses in excess of 5000

psi(34474 MPa), and the reduced temperature difference case, 6C, has no stresses in excess

of 4500 psi(31027 MPa).

Both maximum and local hoop stresses are reduced with lower temperature difference.

The reduction in maximum is only 4%. However, figure 5.1.8.2 shows large regions of the

pressure surface with lower hoop stresses when the temperature difference across the CMC

vane walls is lower.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Original temp. dist. - case 3D Revised temp. dist. - case 6C

Fig. 5.1.8.2 Effect of revised temperature distribution - Combined loads

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Circular trailing edge - case 7B Square trailing edge - case 7D

Fig. 5.1.9.1 Effect of modified trailing edge shape - Combined loads

5.1.9 - Effect of Trailing Edge Shape Figure 5.1.9.1 shows that the effect of changing

the shape of the trailing edge from a semi-circle to a squared-off trailing edge is small. This

analysis was done to determine if this geometric modification, which required a different grid

topology, would result in a significantly changed stress distribution near the vane trailing

edge. For the case with a semi-circular trailing edge, 7B, both through thickness and hoop

stresses are low in the trailing edge region, relative to the rest of the vane.

1$6$&52 
5.2 - Trailing Edge Ejection

Typical metallic HPT first stage vane have some form of trailing edge ejection,

whether along the vane centerline or at the rear of the pressure surface. From a fabrication

point alone it would be convenient if trailing edge ejection could be avoided for CMC vanes.

However, analysis showed that to maintain the suction surface of the vane either film cooling

rows had to be placed downstream of the vane throat, or substantially more cooling air was

required. Placing film cooling rows downstream of the vane throat, which is close to the

midpoint of the vane surface, causes a substantial vane efficiency penalty. To cool the aft

portion of the suction surface without trailing edge ejection requires high film effectiveness

at a relatively long distance from the last cooling row. To achieve the high film effectiveness

substantially more cooling air is required, since film effectiveness decreases with downstream

distance from the location of the film row, but increases with increased amounts of film

cooling. Trailing edge ejection is an effective cooling approach because there is a relatively

small thermal resistance between the outer vane surface and the trailing edge ejection tube.

In effect, trailing edge ejection redirects film cooling air from the last one or two rows of

pressure side cooling holes, and uses this air in a conventional duct cooling approach before

ejecting the air at the vane trailing edge.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

No trailing edge ejection - case 3A Centerline trailing edge ejection - case 4A

Fig. 5.2.1.1 Effect of centerline trailing edge ejection - Pressure load

5.2.1 - Effect of Centerline Trailing Edge Ejection From a thermal standpoint

centerline trailing edge ejection is desirable because the distances between the trailing edge

ejection tube and the vane walls are minimized. Figures 5.2.1.1 through 5.1.1.3 show through

thickness and hoop stress when there are pressure, thermal, and combined loads. In the trailing edge ejection case the trailing edge ejection tube is a converging duct with a uniform

height in the spanwise or radial direction. For all three loading conditions there are substantial increased in maximum through thickness or hoop stress when there is a tube connecting

the aft cavity and the vane trailing edge. For pressure loads the maximum through thickness stress increased by nearly a factor of four, while the maximum hoop stress increase by

nearly a factor of 1.5. For thermal loads the maximum through thickness stress increased

by a factor of 3.5. The increase in maximum hoop stress was less, being only 20%. As

in previous cases combined load stresses were heavily influenced by thermal load stresses.

The maximum combined load through thickness stress with trailing edge ejection was over

a factor of three greater than the maximum stress without trailing edge ejection. For hoop

stresses the increase in maximum stress was nearly 30%.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

No trailing edge ejection - case 3C Centerline trailing edge ejection - case 4B

Fig. 5.2.1.2 Effect of centerline trailing edge ejection - Thermal load

While the maximum stresses are very high with trailing edge ejection, the high stresses

are confined to very small regions. For pressure load and combined load through thickness

stresses the maximum and minimum stresses are located near each other, and the maximum

thermal load stress is located near the tube exit, while the minimum through thickness stress

is on the inner pressure surface wall, close to the tube entrance. It may seem somewhat

surprising that the location for the maximum through thickness stress changes between

the thermal and combined load cases. The highly localized nature of the maximum stress

obscures the fact that there was a high, but not the highest, stress at the same location as

the maximum combined load stress.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

No trailing edge ejection - case 3D Centerline trailing edge ejection - case 4C

Fig. 5.2.1.3 Effect of centerline trailing edge ejection - Combined loads

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Centerline trailing edge ejection - case 4A Pressure side trailing edge ejection - case 5F

Fig. 5.2.2.1 Effect of pressure side trailing edge ejection - Pressure load

5.2.2 - Effect of Pressure Side Trailing Edge Ejection Because using a centerline

trailing edge ejection tube resulted in high maximum stresses, changing the location of the

trailing edge ejection tube was investigated. In this trailing edge configuration the tube

exited the vane on the its pressure side, The shape of the tube was also changed, to be easier

to fabricate. The pressure side trailing edge ejection tube had a constant rectangular cross

section, and was 0.86 mm(34 mil) high, and 0.25 mm(10 mil) wide.

Figures 5.2.2.1 and 5.2.2.2 show stresses for the centerline and pressure side trailing edge

ejection cases. While maximum through thickness stresses are still high, there was a substantial reduction in maximum stresses when pressure side trailing edge ejection is substituted

for centerline trailing edge trailing edge ejection. The maximum through thickness stress is

reduced by approximately 25% for both the pressure load and combined load cases. While

the maximum hoop stress is also reduced by nearly 25% for the pressure load case, the

maximum hoop stress is nearly the same for centerline and pressure side ejection for the

combined load case.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Centerline trailing edge ejection - case 4C Pressure side trailing edge ejection - case 5C

Fig. 5.2.2.2 Effect of pressure side trailing edge ejection - Combined loads

The locations of maximum and minimum through thickness stresses are approximately

the same for pressure side and centerline trailing edge ejection. For combined loads the

location of maximum through thickness stress is unchanged between centerline and pressure

side trailing edge ejection. For the combined load case the location of minimum through

thickness stress is near the tube entrance for centerline ejection, and near the tube exit for

pressure side ejection. The location for maximum hoop stress due to pressure loads moves

away from the tube when there is pressure side ejection. The hoop stress in the rib region

reaches almost the same level for both forms of trailing edge ejection. For combined loads

the location of maximum hoop stress is the same for both forms of trailing edge ejection.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Small rib corner radii - case 4C Semi-circular rib - case 5A

Fig. 5.2.3.1 Effect of semi-circular rib with trailing edge ejection - Combined loads

5.2.3 - Effect of Modifying Rib Shape It was hoped that modifying the rib shape

would reduce maximum stresses, even if they occur away from the rib region. Figure 5.1.6.1

showed that a semi-circular rib was beneficial for cases without trailing edge ejection. Figure

5.2.3.1 shows stresses for cases with centerline trailing edge ejection and two rib geometries.

The rib geometries are the same as those shown in figure 5.1.6.1. One is a rib with four

small radii where the rib joins the pressure and suction surfaces. The other geometry has

the rib sides formed by constant radius arcs. The radius of the rib side facing the aft cavity

is smaller than the radius of the rib side facing the forward cavity.

Because maximum through thickness and hoop stresses occur in the tube region, the

rib shape had no significant effect on maximum stresses. In the rib region the results for

combined pressure and thermal loads shown in figure 5.2.3.1 are different from the results

shown in figure 5.1.6.1 for just pressure loads. For combined loads the semi-circular rib sides

show higher through thickness stresses with a semi-circular rib, but for pressure loads the

stresses are lower for a semi-circular rib. For combined loads the semi-circular rib shows

lower hoop stresses, especially where the rib joins the vane pressure surface forming the

forward cavity. For pressure loads figure 5.1.6.1 shows only a small decrease in stresses in

the rib region for the semi-circular rib geometry.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Two impingement cavities - case 5F Single impingement cavity - case 5E

Fig. 5.2.4.1 Effect of single impingement cavity - Pressure load

5.2.4 - Effect of Single Impingement Cavity Since semi-circular ribs were generally

preferable to ribs with four small radii corners, a case was analyzed where the radius near

the trailing edge ejection tube was maximized. This resulted in a single cavity configuration.

Figure 5.2.4.1 and 5.2.4.2 shows result for two cavity and single cavity configurations. Both

cases have pressure side trailing edge ejection tubes. Figure 5.2.4.1 shows results for pressure

loads, and figure 5.2.4.2 shows results for combined loads. The single cavity configuration

reduces maximum through thickness stress by over 60% for pressure load cases, and by over

25% for the combined load cases. For maximum hoop stresses the single cavity configuration

was reduced by nearly 25% for the combined load case, but only by 5% for the pressure

load only case. Other than a lower maximum through thickness stress, which is definitely

beneficial, the through thickness stress distribution within the trailing edge ejection tube is

similar for the single and two cavity cases. The location of maximum hoop stress moves

away from the entrance to the trailing edge ejection tube for the single cavity cases. For the

pressure load case the location of maximum hoop stress moved from the suction side of the

rib to the leading edge region.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Two impingement cavities - case 5C Single impingement cavity - case 5G

Fig. 5.2.4.2 Effect of single impingement cavity - Combined loads

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Rectangular tube - case 5E Square tube - case 11A

Fig. 5.2.5.1 Effect of trailing edge ejection tube geometry - Pressure load

5.2.5 - Effect of Rectangular & Square Ejection Tube Geometry The effect of

the tube geometry was found to significantly affect stresses. The maximum through thickness

stress increased by more than a factor of four when the tube geometry was changed from a

0.86mm X 0.25 mm(34 mil X 10mil) rectangle to a 0.76mm(30mil) square. Figure 5.2.5.1 for

pressure loads shows that the maximum through thickness stress increases by more than a

factor of four when the rectangular tube is replaced by a square tube. The maximum hoop

stress increases by less than 9%, but the location of maximum hoop stress moves from the

leading edge region to the entrance of the square tube.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Square tube - case 11B Circular tube - case 11C

Fig. 5.2.6.1 Comparison of square and circular tube geometries - Pressure load

5.2.6 - Effect of Square & Circular Tube Geometry Figures 5.2.6.1 through 5.2.6.3

shows stresses for square and circular trailing edge ejection tube with pressure, thermal, and

combined loads. The diameter of the circular tube, 0.76mm(30mil), is the same as the width

of the square tube. Both have the same hydraulic diameter, but the cross sectional area of

the square tube is greater by just over 20%. The difference in maximum stresses in either the

through thickness or hoop directions between the square and circular trailing edge ejection

tubes is small. While the maximum through thickness stress is higher for the circular tube for

thermal loads, the maximum stress is lower for pressure or combined loads. The maximum

hoop stress is higher for the circular tube for pressure loads, but the maximum hoop stress

is lower for thermal or combined loads.

Comparing these results with those in figure 5.2.4.2 shows that for combined loads the

maximum through thickness or hoop stress is nearly the same for all three trailing edge tube

geometries. On the other hand figure 5.2.4.1 shows that for pressure loads the rectangular

tube geometry has a much lower maximum through thickness stress, and also a reduced

maximum hoop stress.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Square tube - case 11G1 Circular tube - case 11F1

Fig. 5.2.6.2 Comparison of square and circular tube geometries - Thernal load

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Square tube - case 11G2 Circular tube - case 11F2

Fig. 5.2.6.3 Effect of trailing edge ejection tube geometry - Thermal load

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Square tube - case 11G2 Circular tube - case 11F2

Fig. 5.2.6.3 Effect of trailing edge ejection tube geometry - Combined loads

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Surface distance, s/CX

-50

0

50

100

150

200

250

300

Vane temperature difference, o F

Case 4B

Case 13A

Pressure surface Suction surface

50

100

150

o

C

Fig. 5.2.7.1 Temperature difference across CMC vane walls

5.2.7 - Effect of Revised CMC Temperature Gradients Figure 5.2.7.1 shows two

temperature difference distributions for the vane. Case 13A has a much lower average temperature difference across the CMC vane than does case 4B. To achieve the lower temperature difference case 13A required addition vane cooling. While the multiple film cooling row

cause large variations in the temperature difference for both cases, case 13A has an average

temperature difference only about half of the average temperature difference for case 4B.

Figure 5.2.7.2 shows stresses for both cases due to thermal loads. Surprisingly, the lower

average temperature difference case, 13A, resulted in higher maximum through thickness

stress. In the rib region the lower average temperature case, 13A, shows lower through

thickness stresses. Near where the maximum through thickness stress occurs, the streamwise

temperature gradient on the pressure surface are of opposite sign. Between s/CX = −1.4 and

-1.6 on the pressure surface case 4B has a negative streamwise pressure gradient, and case

13A has a positive streamwise pressure gradient. For case 13A temperatures are increasing

with pressure surface distance, and for case 4B temperatures are decreasing with pressure

surface distance. These results imply that streamwise temperature gradients, as well as

temperature gradients across the vane significantly affect thermal stresses.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Reference case temperature gradients - case 4B Lowered CMC temperature gradients -

case 13A

Fig. 5.2.7.1 Effect of changing CMC temperature gradient - Thermal load

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

hTUBE = 8000W/m −◦ K - case 5A hTUBE = 4000W/m −◦ K - case 5B

Fig. 5.2.8.1 Effect of varying ejection tube heat transfer coefficient - Thermal load

5.2.8 - Effect of Reduced Tube Heat Transfer Coefficient The heat transfer coefficient(s) within the ejection tube can be varied in a number of ways. Reducing the amount

of trailing edge ejection coolant reduces the average tube heat transfer coefficient, and the

reduction in tube flow rate could be balanced by an increase in film cooling. Increasing the

tube cross sectional area for the same flow rate would also reduce the average tube heat

transfer coefficient. An analysis was done to determine the effects of halving the ejection

tube heat transfer coefficient. Figure 5.2.8.1 shows the results of this analysis. Maximum

through thickness stresses are reduced by 18% when the tube heat transfer coefficient is

halved. The location of maximum through thickness stress is unchanged. Hoop stresses are

not affected by reducing the average heat transfer coefficient.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Uninsulated fork region - case 13A Insulated fork region - case 13B

Fig. 5.2.9.1 Effect of insulating fork region - Thermal load

5.2.9 - Effect of Insulating Fork Region Because high stresses were often seen at

the entrance of the trailing edge ejection tube, an analysis was done to determine if these

stresses would be less if the fork region at the entrance to the trailing edge ejection tube

was insulated. Figure 5.2.9.1 shows the results of this analysis for a case with thermal loads.

The thermal boundary condition on the cavity surface in the fork region had no noticeable

effect on either through thickness or hoop stresses.

1$6$&52 
5.3 -CMC Material Property and Boundary Condition Effects

In this section four comparisons are examined. The first comparison is for the effects of

varying the through thickness stiffness modulus, E33, This parameter is expected to experience significant variations due to even small changes in material composition. The second

comparison is for variations in thermal conductivity. It is desirable to increase CMC thermal conductivity, since this decreases the thermal gradients across the vane walls. The third

comparison examines the effects of changing the stiffness of the two vane end plates. This

was done by halving the thickness of each end plate. This comparison helps to answer the

question of whether increasing the rigidity lowers stresses in the midspan region. The fourth

comparison examines the effects of changing the boundary conditions on midspan stresses.

The boundary conditions are applied to the edges of each end plate.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

E33 = 157 GPa(22.8 M psi) - case 6A E33 = 77 GPa(11.2 M psi) - case 6B

Fig. 5.3.1.1 Effect of through thickness stiffness- Combined loads

5.3.1 - Effect of Through Thickness Stiffness Modulus The through thickness

stiffness modulus, E33, was varied to determine the sensitivity of stresses to changes in this

parameter. When E33 was varied Poisson’s ratio was held constant at 0.17 for the through

thickness direction properties. Figure 5.3.1.1 and 5.3.1.2 show stresses for two values of E33

for pressure and thermal loads combined. Figure 5.3.1.1 compares cases without trailing

edge ejection, and figure 5.3.1.2 compares cases with pressure side trailing edge ejection

through a rectangular ejection tube. Stresses are reduced as E33 is reduced, but by less than

proportionately. For cases without trailing edge ejection, and when E33 is nearly halved

the maximum through thickness stress is reduced by only about 20%. Nearly halving E33

reduces the maximum hoop stress by 12%. Figure 5.3.1.2 shows similar results for trailing

edge ejection cases. Nearly halving E33 reduces the maximum through thickness stress by

28%, and reduces the maximum hoop stress by 11%.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

E33 = 157 GPa(22.8 M psi) - case 12A E33 = 77 GPa(11.2 M psi) - case 12B

Fig. 5.3.1.2 Effect of through thickness stiffness- Combined loads

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a) Through thickness stress, psi

b) Hoop stress, psi

kCMC = 20 W/m-K - case 6G kCMC = 40 W/m-K - case 8A

Fig. 5.3.2.1 Effect of doubling CMC thermal conductivity - Combined loads

5.3.2 - Effect of Doubling Thermal Conductivity Increasing the CMC thermal

conductivity decreases the temperature difference across the CMC vane. The difference is

not proportional to the increase in thermal conductivity. The overall thermal resistance is

determined by the internal and external heat transfer coefficients, the thermal resistance

of the EBC protective layer, as well as the thermal resistance of the vane itself. When the

CMC thermal conductivity is increased less vane coolant is required, so that the temperature

differences across the vane also change. Under these circumstances the chief benefit for stress

reductions may be reductions in streamwise temperature gradients. Since the analysis was

done with less cooling for the higher thermal conductivity case, there is also a cycle benefit

to higher CMC conductivity.

Figure 5.3.2.1 shows a comparison for cases with combined loads and no trailing edge

ejection. Maximum through thickness stress is reduced by more than 25% when the CMC

thermal conductivity is doubled from 20W/m−◦ K. Maximum hoop stress is reduced by less

than 9%. The location of maximum stress changed when the CMC conductivity was doubled.

When the CMC thermal conductivity doubled, the location of the maximum through

1$6$&52 
thickness stress moved from the suction side of the fork region to forward of the rib on the

pressure surface. The location of maximum hoop stress remained in the fork region, but

shifted from the suction side to the pressure side as the conductivity doubled.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Original end plate thickness- case 6G End plate thickness halved - case 7A

Fig. 5.3.3.1 Effect of reducing end plate thickness - Combined loads

5.3.3 - Effect of Reducing End Plate Stiffness The stiffness of the end plate has

a significant effect on vane stresses, even in the midspan region, away from the end plate.

Previous results were calculated where the two end plates were 4mm(160 mil) thick, and

had the same material properties as the CMC vane. Figure 5.3.3.1 shows stresses when

the thickness of both end plates is halved. Results are shown for combined loads and cases

where there is no trailing edge ejection. This allows greater vane deflections, especially in

the midspan region. The maximum through thickness stress increased by nearly 45% when

thickness of both end plates was halved, and the maximum hoop stress increased by 36%.

The location of maximum stresses also changed. The maximum through thickness stress

moved from the suction side of the fork to just forward of the rib on the pressure surface

when the end plate thicknesses were halved. The maximum hoop stress moved from the

suction side of the fork to the leading edge region when the end plate thicknesses were

halved. These results show the desirability of using stiff end plates with CMC vanes.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Original boundary condition- case 7B Modified boundary condition - case 7C

Fig. 5.3.4.1 Effect of modifying plate boundary condition - Combined loads

5.3.4 - Effect of Boundary Condition Variation The effect of changing the end

plate boundary conditions was examined. Figure 5.3.4.1 shows results for two cases with

different end plate boundary conditions. Case 7B has the standard boundary conditions,

and case 7C has the modified boundary conditions. For the standard boundary conditions

the hub end plate is held in the axial and spanwise directions, and along its leading edge in

the pitchwise direction. The other end plate is free to move in all directions. For case 7C

there is an additional constraint along the edge of the hub end plate. The hub end plate

is fixed at the pressure side corner, where the axial and pitchwise edges meet. When the

additional constraint was added to the end plate, the maximum through thickness stresses

decreased by 12%, and the location of maximum stress remained the same. The maximum

hoop stresses increased by 12%, and the maximum hoop stress location moved from the

pressure side of the fork to the leading edge region.

1$6$&52 
5.4 - Mesh Refinement Studies

This section gives the results of four comparisons for results with different computational

meshes. The first comparison examines the effects on midspan region stresses due to a

variation in the mesh density used for each end plate. The second comparison examines the

effects of changing the mesh density in the leading edge region. The last two comparisons

examine the effects on stresses for changes in the mesh used around the trailing edge ejection

tube. One case is for a square trailing edge ejection tube and the other is for a circular tube.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

“Coarse” mesh - case 7A Finer mesh - case 7B

Fig. 5.4.1.1 Effect of increasing end plate mesh density - Combined loads

5.4.1 - Effect of Vane and End Plate Mesh Density Figure 5.4.1.1 shows stresses

for two cases with different mesh density. Comparisons are for combined thermal and pressure

loads. This comparison is for thinner end plates of 2mm(80mil) thickness, and not the

standard end plate thickness of 4mm(160mil). Case 7A has typical mesh of 30000 total

elements for cases without trailing edge ejection. Case 7B has a more dense mesh of 50000

total elements. When the number of end plate elements increased, there was also an increase

in the number of vane elements. Only in the region of maximum stress does increasing the

number of elements have an effect. It is not unexpected that an increase in the number

of elements would increase the maximum stress. Since maximum stresses are so highly

localized, the magnitude of the stress gradient is very high at the location of maximum

stress. Increasing the number of elements positions nodes closer to the theoretical location

of maximum stress, and a higher maximum stress is expected as the mesh density increases.

Figure 5.1.1,1a shows that the maximum through thickness stress increased by 17%. As

expected the location of maximum through thickness stress did not change. Somewhat

unexpectedly figure 5.4.1.1b shows that the maximum hoop stress decreased by 5% as the

total number of elements increased. The response of the maximum hoop stress to the increase

in the number of elements occurred because the location of maximum hoop stress changed

as the number of elements increased. The maximum hoop stress moved from leading edge

to the pressure side of the fork region.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

Hexagonal mesh elements - case 11A Hexagonnal & tetrahedral elements - case 11B

Fig. 5.4.2.1 Effect of varying mesh type for square tube - Pressure load

5.4.2 - Effect of Mesh Shape for Square Ejection Tube Figure 5.4.2.1 shows the

effects of mesh element shape for squared tube cases. For case 11A a hexahedral mesh was

used 11A with 130,000 elements. Typically, hexahedral elements were used for the ANSYS

analysis. The number of elements was significantly increased when trailing edge ejection

was used because a mesh was needed for each of the ten trailing edge ejection tubes. Case

11B used a combination of hexahedral and tetrahedral mesh elements. Transitional pyramid

elements were used in the fork and trailing edge regions. Case 11B had 230,000 elements.

Through thickness stresses are unaffected by the shape of the mesh elements. Only the

magnitude of the maximum hoop stress is affected by the shape of the mesh elements.

While the increase of 28% in maximum hoop stress is large, the increase is confined to a

very small region. Part of the increase in maximum hoop stress may be due to a larger

number of mesh elements. Also, hexahedral elements are preferred to tetrahedral elements

for achieving accurate results, Brauer[31]. However, tetrahedral elements are required when

the trailing edge ejection tube is circular.

1$6$&52 
a) Through thickness stress, psi

b) Hoop stress, psi

“Standard” mesh density case 11C Reduced mesh density - case 11E

Fig. 5.4.3.1 Effect of varying mesh density for circular tube - Pressure load

5.4.3 - Effect of Mesh for Circular Ejection Tube Due to complexity of circular

ejection tube model, tetrahedral shaped elements were used in case 11C. This case had

720,000 elements. Case 11E had a combination of hexahedral and tetrahedral elements,

Transitional pyramid elements were used in the fork and trailing edge regions. Case 11E

had 350,000 elements. Figure 5.4.3.1 shows that the only effect of using fewer elements is a

reduction in maximum stress. The maximum through thickness stress is reduced by 19%,

but the location at the tube entrance is unchanged. The maximum hoop stress is reduced

by 27%, and the location of maximum stress changed between the two cases. For case 11C

the maximum hoop stress occurred more than half way down the ejection tube, and for case

11E the maximum hoop stress occurred in the leading edge region.

1$6$&52 
5.5 - Maximum Component Stresses

Even though maximum stresses are often confined to a very small region of the vane,

comparisons of maximum stress in the three component directions is useful. These comparisons help to show a path to reduced stresses. by different vane internal geometries, and also

the effects of modeling assumptions.. Tables IIa through IId show the maximum component

stresses, and the location where these stresses occur. The maximum through thickness or

interlaminar, the maximum hoop, and the maximum spanwise or radial stress is given for

pairs of cases. Comparisons are given for pairs of cases to illustrate the change in maximum

stresses for a specific effect. Table IIa shows results for cases without trailing edge ejection,

and Table IIb shows results for cases with centerline and pressure side trailing edge ejection. Table IIIc shows results for property and boundary condition variations, while Table

IId shows results of mesh sensitivity studies. While no figures were given for the spanwise

stresses in the midspan region, these tables include the maximum spanwise stress in the

midspan region, The location of the maximum spanwise stress is also given.

Table IIa shows that, except for one case, the maximum spanwise stress is lower than

the maximum hoop stress. The assumed orientation of the reference material, N24A, was

that the material properties in the hoop and span directions were the same. Since spanwise

maximum stresses were almost always lower than the maximum stress in the hoop direction,

hoop stresses were of greater interest. Table IIa shows that the location of maximum hoop

stress was generally different from the location of maximum spanwise stress.

Table IIa shows that the case of no internal pressure, 5.1.7, results in very high maximum

hoop and spanwise stresses. For this case the maximum through thickness stress is comparable to the maximum through thickness stress for cases with combined loads. Without an

internal pressure no vane thermal stresses are expected to occur.

Maximum thermal stresses are generally higher than maximum pressure stresses. Table

IIa shows that maximum thermal stresses are very sensitive to variations in temperature

distributions. There was over a 50% increase in maximum thermal load stresses when a

uniform CMC temperature differential was replaced by wall temperatures consistent with a

film cooled vane. There was over a 20% reduction in maximum thermal load stresses when

the rib connecting the pressure and suction surface was insulated. Table IIb shows similar

results for cases with trailing edge ejection. Changing the CMC temperature gradients

resulted in maximum through thickness and spanwise stresses increasing by more than 30%.

Table IIb shows that maximum stresses increase significantly when there is a trailing

edge ejection tube. Pressure side, as differentiated from centerline, trailing edge ejection

is sometimes favored for vane efficiency reasons, since it allows for a thinner trailing edge

thickness. The results in Table IIb show that it is also preferable from a stress standpoint.

For pressure loads and combined loads the reduction in maximum through thickness stress

is over 25%. For combined loads the reduction in maximum spanwise stress is nearly 40%.

Maximum hoop loads are less affected by going from centerline to pressure side ejection.

In contrast to the results without trailing edge ejection, maximum spanwise stresses for

several cases exceed maximum hoop stresses. However, maximum spanwise stresses vary

over a wide range. For the single impingement cavity case, which has the lowest combined

load maximum through thickness stress, the maximum spanwise stress is within 15% of

the maximum hoop stress. The 5.2.7 comparison shows that the maximum spanwise stress

1$6$&52 
decreased by over 10% when the trailing edge ejection tube was halved.

Table IIc shows that reducing the through thickness modulus of elasticity, E33, or increasing the CMC thermal conductivity is effective in reducing maximum through thickness

stresses. Using thinner end plates, which is desirable from a weight standpoint, results in

higher maximum stresses in the midspan region of the vane. Halving the thickness of the

end plates caused the maximum through stress to increase by more than 40%. The other

maximum stresses also increased.

Table IId shows that maximum stresses are somewhat sensitive to the type of mesh used.

Since all other comparisons were done with the same mesh type, the relative change between

cases is expected to be accurate. The values in Table II are maximum values, and near the

maximum values the component stresses change very rapidly. Therefore, it is not surprising

that as the number of elements in the finite element analysis increase, maximum stresses also

increase. The results for comparisons 5.4.1 and 5.4.3 show that more elements give higher

maximums in regions of high gradients. Using a mixture of hexahedral and tetrahedral mesh

element resulted in higher maximum hoop and spanwise stresses compared with just using

hexahedral elements.

1$6$&52 
Table IIa. Comparisons for midspan region maximum calculated stress, ksi,(MPa)

5.1 - No Trailing Edge Ejection

Case Load Through thickness Hoop Span

Value Location Value Location Value Location

5.1.1 - Effect of Rib

1A Press 4.62(31.9) Fork 31.4(217) Fork 13.3(92.0) T.E.

2A Press 1.57(10.8) Rib 17.0(117) Rib 13.3(92.0) T.E.

% change -66 -46 0

1C Temp 6.91(47.6) Fork 31.1(214) L.E. 28.5(197) Fork

2B Temp 10.5(72.4) Rib 41.5(286) Rib 34.3(236) P-aft of rib

% change +52 +33 +20

1D Comb 10.8(75.4) Fork 55.5(383) Fork 29.1(201) Fork

2C Comb 10.6(73.1) Rib 45.6(314) Rib 36.9(254) P-aft of rib

% change -2 -18 +27

5.1.2 - Effect of Non-Uniform Temperature Gradient

1B Temp 4.44(30.6) L.E. 20.4(141) L.E. 17.7(122) Fork

1C Temp 6.91(47.6) Fork 31.1(214) L.E. 28.5(197) Fork

% change +56 +53 +61

5.1.3 - Effect of Differential Wall Thickness

2A Pres 1.57(10.8) Rib 17.0(117) Rib 13.3(92.0) T.E.

3A Pres 2.40(16.5) Rib 16.7(115) Rib 13.8(94.8) P-L.E.

% change +53 -2 +4

2B Temp 10.5(72.4) Rib 41.5(286) Rib 34.3(236) P-aft of rib

3B Temp 8.52(58.7) Rib 38.2(263) Rib 31.2(215) Fork

% change -20 -8 -9

5.1.4 - Effect of Combining Pressure and Temperature Loads

3A Pres 2.40(16.5) Rib 16.7(115) Rib 13.8(94.8) P-L.E.

3C Temp 6.61(45.6) Rib 29.4(203) Fork 26.3((182) P-aft of rib

3D Comb 7.28(50.2) Fork 36.6(252) Fork 27.2(188) P-aft of rib

5.1.5 - Effect of Insulating Rib

3B Temp 8.52(58.7) Rib 38.2(263) Rib 31.2(215) Fork

3C Temp 6.61(45.6) Rib 29.4(203) Fork 26.3(182) P-aft of rib

% change -22 -23 -16

5.1.6 - Effect of Modified Rib Shape

3A Pres 2.40(16.5) Rib 16.7(115) Rib 13.8(94.8) P-L.E.

5D Pres 1.11(7.65) Rib 17.9(123) L.E. 15.4(106) P-for. of rib

% change -54 +7 +12

5.1.7 - Effect of No Internal Pressure

3A Pres 2.40(16.5) Rib 16.7(115) Rib 13.8(94.8) P-L.E.

3A2 Pres 10.9(75.2) Rib 115.(793) Rib 59.8(412) P-for. of rib

% change +354 +589 +333

5.1.8 - Effect of Revised Temperatures

3D Comb 7.28(50.2) Fork 36.6(252) Fork 27.2(188) P-aft of rib

6C Comb 7.82(53.9) Fork 35.1(242) Fork 40.2(277) P-for. of rib

% change +7 -4 +48

5.1.9 - Effect of Trailing Edge Shape

7B Comb 10.8(74.2) Rib 38.1(263) Fork 38.4(264) P-for. of rib

7D Comb 10.8(74.2) Rib 39.2(270) L.E. 38.4(264) R-for. of rib

% change 0 +3 0

1$6$&52 
Table IIb. Comparisons for midspan region maximum calculated stress, ksi,(MPa)

5.2 - Trailing Edge Ejection

Case Load T.E. Through thickness Hoop Span

Ejection Value Location Value Location Value Location

5.2.1 - Effect of Centerline Trailing Edge Ejection

3A Pres No 2.40(16.5) Fork 16.7(115) Fork 11.1(76.5) P-front

4A Pres Cl 9.04(62.3) Tube 20.2(139) Fork 16.5(114) Fork

% change +277 +21 +41

3C Temp No 6.61(45.6) Rib 29.4(203) Fork 26.3(181) P aft of rib

4B Temp Cl 23.1(159) Tube 35.4(244) Tube 74.4(513) Tube

% change +249 +20 +183

3D Comb No 7.28(50.2) Fork. 36.6(252) Fork 27.2(178) P aft of rib

4C Comb Cl 22.5(155) Tube. 49.3(340) Tube 83.4(575) Tube

% change +209 +35 +207

5.2.2 - Effect of Pressure Side Trailing Edge Ejection

4A Pres Cl 9.04(62.3) Tube 20.2(139) Fork 16.5(114) Fork

5F Pres PS 5.60(38.6) Tube 17.8(123) Rib 17.1(118) Fork

% change -38 -12 +4

4C Comb Cl 22.5(155) Tube 49.3(340) Tube 83.4(575) Tube

5C Comb PS 16.7(115) Tube 49.4(340) Fork 51.2(353) Fork

% change -26 0 -39

5.2.3 - Effect of Revised Rib Shape

4C Comb Cl 22.5(155) Tube 49.3(340) Tube 83.4(575) Tube

5A Comb PS 22.5(155) Tube. 48.2(333) Fork. 83.4(575) Tube

% change 0 -2 0

5.2.4 - Effect of Single Impingement Cavity

5F Pres PS 5.60(38.6) Tube 17.8(123) Rib 17.1(118) Fork

5E Pres PS 2.19(15.1) Tube 16.9(117) L.E. 15.8(109) Pres. surf.

% change -61 -5 -8

5C Comb PS 16.7(115) Tube 49.4(340) Fork 51.2(353) Fork

5G Comb PS 12.2(84.4) Tube 37.9(261) P.S. 43.5(300) Tube

% change -27 -23 -15

5.2.5 - Effect of Trailing Edge Ejection Tube Geometry

5E Pres PS 2.19(15.1) Tube 16.9(117) L.E. 15.8(109) Pres. surf.

11A Pres PS 9.29(64.1) Tube 18.4(127) Fork 18.5(128) Pres. surf.

% change +324 +9 +17

5.2.6 - Effect of Square & Circular Tube Geometry

11A Pres PS 9.29(64.1) Tube 18.4(127) Fork 18.5(128) Pres. surf.

11C Pres PS 8.94(61.6) Tube 13.8(95 ) L.E. 94.0(648) Pres. surf.

% change -3 -25 +408

11G1 Temp PS 10.3(71.0) Tube 32.9(227) P.S. 69.7(480) Tube

11F1 Temp PS 11.0(76.1) Tube 30.6(211) P.S. 74.2(512) Tube

% change +7 -7 +6

11G2 Comb PS 14.8(102) Tube. 34.4(237) P.S. 71.8(495) Tube

11F2 Comb PS 13.2(91.1) Tube 33.9(233) S.S. 75.5(521) Tube

% change -11 -1 +5

5.2.7 - Effect of Revised CMC Temperature Gradients

4B Temp Cl 23.1(159) Tube 35.4(244) Tube 74.4(513) Tube

13A Temp Cl 30.7(212) Tube 35.4(244) Tube 102(701) Tube

% change +33 0 +37

5.2.8 - Effect of Reduced Tube Heat Transfer Coefficient

5A Comb PS 22.5(155) Tube. 48.2(333) Fork. 83.4(575) Tube

5B Comb PS 18.4(127) Tube. 49.0(338) Fork. 74.2(512) Tube

% change -18 +2 -11

5.2.9 - Effect of Insulating Fork Region

13A Temp Cl 30.7(212) Tube 35.4(244) Tube 102(701) Tube

13B Temp Cl 30.7(212) Tube 34.4(244) Tube 102(701) Fork

% change 0 0 0

1$6$&52 
Table IIc. Comparisons for midspan region maximum calculated stress, ksi,(MPa)

5.3 - Property and Boundary condition effects

Case Load T.E. Through thickness Hoop Span

Ejection Value Location Value Location Value Location

5.3.1 - Effect of Through Thickness Stiffness Modulus

6A- E33 = 157 GPa Comb No 6.87(47.4) Fork 33.9(234) Fork 24.4(167) P-aft of fork

6B E33 = 77 GPa Comb No 5.40(37.2) Fork 29.9(206) Fork 24.5(169) P-L.E.

% change -22 -12 0

12A - E33 = 157 GPa Comb PS 13.7(94.9) Tube 46.6(321) Fork 47.8(329) Tube

12B - E33 = 77 GPa Comb PS 9.81(67.7) Tube 41.6(287) Fork 46.9(324) Tube

% change -29 -11 -2

5.3.2 - Effect of CMC Thermal Conductivity

6G Comb No 6.41(44.2) Fork 29.5(204) Fork 32.4(224) P-aft of fork

8A Comb No 4.73(32.6) Fork 27.0(186) Fork 29.7(205) P-for. of rib

% change -26 -8 -8

5.3.3 - Effect of End Plate Stiffness

6G Comb No 6.41(44.2) Fork 29.5(204) Fork 32.4(224) P-aft of fork

7A Comb No 9.24(63.7) Fork 40.0(276) L.E. 38.3(264) P-for. of rib

% change +44 +36 +18

5.3.4 - Boundary Conditions

7B Comb No 10.8(74.5) Rib 38.1(263) Fork 38.4(265) P-for. of rib

7C Comb No 9.49(65.4) Rib 42.5(293) L.E. 38.8(268) P-for. of rib

% change -12 +12 +1

Table IId. Comparisons for midspan region maximum calculated stress, ksi,(MPa)

5.4 - Mesh Refinement

Case Load T.E. Through thickness Hoop Span

Ejection Value Location Value Location Value Location

5.4.1 - End Plate

7A Comb No 9.24(63.7) Fork 40.0(276) L.E. 38.3(264) P-front

7B Comb No 10.8(74.5) Rib 38.1(263) Fork 38.4(265) P-front

% change +17 -5 0

5.4.2 - Square Trailing Edge Ejection Tube

11A Pres PS 9.29(64.1) Tube 18.4(127) Fork 18.5(128) Pres. surf.

11B Pres PS 9.27(64.0) Tube 23.4(161) Tube 20.3(140) Pres. surf

% change 0 +27 +10

5.4.3 - Circular Trailing Edge Ejection Tube

11C Pres PS 8.94(61.6) Tube 13.8(95 ) L.E. 94.0(648) Pres. surf.

11E Pres PS 7.22(50.0) Tube 17.5(121) L.E. 29.4(122) Pres. surf.

% change -19 +27 -69

1$6$&52 
5.6 - Conclusions

The results of the stress analysis for the full size EEE vane showed that stresses from

expected thermal loads are greater than stresses expected from pressure loads even though

the inlet total pressure was 50 atm. All components of stress, through thickness, hoop, and

spanwise, were higher due to thermal loads compared with pressure loads. Maximum stresses

occurred either in the fork region, where the pressure and suction surfaces meet, or in the

rib connecting these two surfaces. When there was trailing edge ejection, maximum stresses

often occurred in the trailing edge ejection tube. These maximum stresses often occurred in

the fork region near the tube entrance.

The reference material, N24A, was a two-dimensional woven material. The desired maximum stress in the trough thickness, or interlaminar, direction was 10.3 MPa(1.5 ksi). The

desired maximum stress in the hoop and spanwise directions was 17ksi(117 MPa). Maximum

calculated combined load through thickness stress was more than four times greater than the

desired maximum through thickness stress. The maximum combined load hoop stress and

the maximum spanwise stress were about double the desired stress for the better low stress

cases examined. Maximum stresses were very localized. In many cases close to 98% of the

vane cross section had stresses less than one half of the maximum component stress. Also, for

cases with trailing edge ejection maximum and minimum stresses were located close to each

other within the ejection tube. This suggests that a creep analysis of vane stresses, which

is expected to be more applicable in the engine environment, may result in lower maximum

component stresses. Kaufman[xx] showed a significant reduction in maximum stress for a

metal vane when creep was taken into account.

The analysis was done for thermal loads, pressure loads, and thermal and pressure loads

combined. Stresses due to thermal loads were greater than those due to pressure loads. The

location of maximum pressure load stress was not coincident with the location of maximum

thermal load stress. The maximum combined load component stress was generally only

slightly greater than the the maximum thermal load component stress.

The stress analysis results indicate that not including stress augmentation due to rows

of film cooling holes is not a short coming of the analysis. Hoop stresses are most affected

by the presence of a row of film cooling holes, due to their relatively close spacing in the

spanwise direction. Many cases showed large regions of the vane with low stresses, where

rows of film cooling holes could be placed without exceeding desired maximum hoop stress.

Stress augmentation in the spanwise direction due to rows of film cooling holes is much less

than in the hoop direction due to the wider spacing between rows than between holes in a

row.

1$6$&52 
6.0 - Radial Cooled Vane

Current cooling schemes rely on impingement and film cooling to achieve acceptable material temperatures. These schemes are well suited for commercial turbofan and military

engine applications. Impingement cooling schemes rely on an insert to distribute the vane

cooling air. For small size vanes, such as for use in turboshaft engine applications, impingement cooling may not be practical. Radial cooling has been proposed for small CMC vanes,

such as would be found in turboshaft engine applications. With radial cooling the impingement scheme is replaced by using several cooling tubes, oriented in the spanwise or radial

direction. No impingement insert is required, and the diameter of the radial cooling holes

can be small, approaching the diameter of film cooling holes if necessary. Similar to film

cooling, many small diameter radial tubes, as opposed to one or two maximum diameter

tubes, facilitate heat removal from the radial tubes. However, pressure drop considerations

favor somewhat larger diameter tubes, since radial cooling tubes are much longer than film

cooling tubes. An additional reason for investigating the feasibility of radial cooling for turboshaft engine applications is that as the vane size decreases the thermal resistance within

the vane material also decreases. Vane wall thickness decreases as the vane size decreases.

The decrease in vane size is generally coupled with an increase in freestream and coolant side

convective resistances. The convective resistances increase as the combustor outlet pressure

decreases, and historically the combustor outlet pressure is lower for smaller size engines.

It is easier to fabricate CMC vanes with radial cooling tubes and no film cooling, than

to fabricate CMC vanes with radial cooling tubes from which film cooling is extracted. On

the other hand, the heat flux absorbed by the air flowing through the tubes is less when film

cooling is used. Without film cooling, air flowing through the radial tubes absorbs the entire

heat flux due to the gas-to-wall temperature difference. With film cooling, air is extracted

from the tubes and is used to reduce the external heat flux by insulating the wall with a film

of cooler air. For the same coolant amount, when film cooling air is extracted from the tubes

the average tube heat transfer coefficient is lower than when no film cooling is used. Vane

thermal analyses were done for vanes cooled only by radial cooling, and for vanes cooled by

radial cooling coupled with film cooling. The configuration where trailing edge ejection is

used in conjunction with radial cooling is also analyzed.

The thermal and aerodynamic performance was determined for two vane external configurations. One was a half scale version of the vane used for the full size vane structural

analysis. The other was a vane shape specified by Dr. Jerry Lang at the NASA Glenn

Research Center. Both vanes had acceptable aerodynamics. The calculated profile loss was

similar for the two vanes.

The analysis showed that neither vane could be effectively cooled using only radial cooling. Film cooling or trailing edge ejection was required to be used in conjunction with radial

cooling. With film and radial cooling the aggressive future engine goals of NASA’s Large

Civil Tilt Rotor(LCTR)[10] program could be achieved. These goals are a gas temperature

of 1927◦C(3500◦F), and a coolant temperature of 594◦C(1100◦F). The gas temperature

includes a pattern factor to account for temperature variations at the combustor outlet. The

coolant temperature is significantly warmer than ambient due to a takeoff pressure of 30

atm. The thermal and aerodynamic analysis results were transmitted to Dr. Lang to be

used in his structural analysis of the LCTR vane.

1$6$&52 
Thermal and aerodynamic results will be given for the half scale vane of Halila et al.[8]

and for the NASA vane. For each vane results will be given with and without film cooling,

and when trailing edge ejection is used in conjunction with film cooling. Current engines

have lower combustor outlet temperatures, and the engine Overall Pressure Ratio(OPR)

is also lower. Results will be given for engine gas temperatures of 1427◦C(2600circF) and

1927◦C(3500◦F). For the lower gas temperature the analysis assumed a coolant temperature

of 376◦C(708◦F), which is consistent with an engine OPR of 17.. For the gas temperature of

1927◦C(3500◦F) coolant temperature is 594◦C(1100◦F), and the engine OPR was 30. Heat

transfer coefficients changed as the gas temperature changed, primarily due to changes in

the vane inlet total pressure.

Figure 6.0.1 shows the two vane shapes. The half size vane is the vane given by Halila

et al.[8] with the dimensions reduced by a factor of 2. This vane is designated as the half

scale EEE vane. The vane shape designated as the NASA vane is the one specified by NASA

personnel. The NASA vane has a longer axial chord, but its true chord-to-axial chord ratio

is lower than the true chord-to-axial chord ratio for the half scale EEE vane. The true chordto-axial chord ratio for the NASA vane is 1.727. Most of the gas turning for the NASA vane

occurs in the last half of the vane, and this results in an aft loaded pressure distribution.

Figure 6.0.2 compares the pressure distributions for the two vanes. The pressure distributions were calculated for the same axial chord-to-pitch(solidity) ratio. Since the NASA

vane has a longer chord than the half scale EEE vane, there would be fewer NASA vanes in

an engine with the same vane inner and outer diameters. The aft vane loading tends to delay suction surface transition at low Reynolds numbers. The aft loading results in favorable

pressure gradients for more of the suction surface, and this tends to reduce boundary layer

growth.

1$6$&52 
-1 0 1 2 3 4

Axial distance, cm

-4

-3

-2

-1

0

1

Tangential distance, cm

Half scale EEE vane

NASA vane

Fig. 6.0.1 Comparison of vane eometries

0 0.2 0.4 0.6 0.8 1

Axial distance, x/CX

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Static pressure ratio, P / PT

Half scale EEE vane

NASA vane

Suction surface

Pressure surface

Suction surface

Pressure surface

Fig. 6.0.2 Pressure distribution for both vanes

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

0

500

1000

1500

2000

2500

Nusselt number, hC

X / k

Transitioning

Fully turbulent

Pressure surface

PT=17 atm.

PT=30 atm.

Pressure surface Suction surface

PT=17 atm.

PT=30 atm.

Fig. 6.1.0.1 Midspan Nusselt number distributions

6.1 - Half scale EEE vane

Figure 6.1.0.1 shows four Nusselt distributions for the half scale EEE vane. These distributions are shown for vane inlet total pressures of 17 and 30 atm., and for two transition

modeling assumptions. If there is no vane film cooling, transition does not occur close to the

leading edge at these low Reynolds numbers. The Reynolds number is almost proportional

to the inlet pressure and surface distance. Both of these quantities are lower in turboshaft

engine applications than in commercial engines in the CF6 size class. The transition analysis

accounted for an inlet turbulence of 10%. Prior to the flow becoming fully turbulent, the

effective viscosity included a freestream turbulence effect. This effect is the reason that the

transitioning Nusselt numbers are higher than the fully turbulent Nusselt numbers along the

forward portion of the pressure surface. Where the suction surface heat transfer approaches

zero, at s/CX near 1.0, the boundary layer is nearly separated. This corresponds to the

adverse pressure gradient region seen in figure 6.0.2. Figure 6.1.0.1 shows that when the flow

is assumed fully turbulent, there is a heat transfer decrease in this region, but the boundary

layer does not approach separation. Data, such as Arts[32], show that flows downstream of

film cooling rows are turbulent, even at low Reynolds numbers.

1$6$&52 
2 radial holes 4 radial holes

Fig. 6.1.1.1 Two radial cooling hole configurations.

6.1.1 - Radial cooling tubes - no film cooling. Figure 6.1.1.1 shows the half scale

EEE vane with two and four cooling tubes. The two tube configuration has two 2.54mm(100mil)

diameter cooling tubes. In the four tube configuration the two forward tubes are also

2.54mm(100mil) in diameter, and the third and fourth tubes have a smaller diameter in

order to fit within the CMC shell. The third tube is 2.0mm(78mil) in diameter, and the

fourth tube is 1,27mm(50mil) in diameter. The shell for the half scale vane was assumed

to be 1mm(40mil) thick, and that the EBC protective layer was 0.127mm(5mil) thick. The

thermal analysis assumed that the space inside the CMC shell was filled with a CMC material

having the same 20W/m −◦ C thermal conductivity as the CMC shell.

Figure 6.1.1.2 through 6.1.1.5 show outer surface temperatures for both the CMC layer

and the EBC layer. Figures 6.1.1.2 and 6.1.1.3 show the effects of having four instead of

two radial cooling holes. These results are for a gas temperature, TG, of 2600◦F(1700◦K),

and a total pressure of 17 atm. Even though this relatively low gas temperature is below

the desired maximum EBC temperature, CMC temperatures exceed the maximum desired

CMC temperature of 2400◦F(1589◦K). The four tube configuration has less of the vane

seeing excessive CMC temperatures than does the two tube configuration. Aft of where

there is insufficient space for a cooling tube, heat can not be effectively removed, and CMC

temperatures are excessive.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

Tem[erature, o

F

TG=2600 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Fig. 6.1.1.2 CMC and EBC temperatures - two tubes - P=17 atm. - TG = 2600◦F - no film

cooling

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

Tem[erature, o

F

TG=2600 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Fig. 6.1.1.3 CMC and EBC temperatures - four tubes - P=17 atm. - TG = 2600◦F - no film

cooling

Figures 6.1.1.4 and 6.1.1.5 show temperatures for cases similar to that shown in figure

6.1.1.3, except that the gas temperature was increased to 3500◦F(2200◦K), and the total

pressure was increased to 30 atm. Increasing the total pressure increases both the coolant

temperature, and the internal and external heat transfer coefficients. For comparison purposes the internal heat transfer coefficient, hI, was set to 5000W/m2 −◦ K in figure 6.1.1.4.

This is the same value as was used for the lower total pressure cases. Figure 6.1.1.5 shows

results where the internal heat transfer coefficient is increased to 8000W/m2 −◦ K.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

TG=3500 o

F

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Fig. 6.1.1.4 CMC and EBC temperatures - four tubes - P=30 atm. - TG = 3500◦F -

hI = 5000W/m2 −◦ K - no film cooling

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Fig. 6.1.1.5 CMC and EBC temperatures - four tubes - P=30 atm. - TG = 3500◦F -

hI = 8000W/m2 −◦ K - no film cooling

These two figures show that, even away from the trailing edge region, radial cooling

alone is insufficient to maintain EBC and CMC temperature at acceptable values. Away

from the trailing edge region EBC temperatures are unacceptably high. While a higher

internal heat transfer coefficient allows acceptable CMC temperatures in the forward part

of the vane, EBC temperatures are unacceptably high. Reducing the EBC thickness below

0.127mm(5mil) would lower the maximum EBC temperatures. However if this was done

to lower maximum EBC temperature to acceptable levels, the maximum CMC temperature

would be unacceptable.

1$6$&52 
Figures 6.1.1.4 and 6.1.1.5 illustrate the importance of the internal film cooling heat

transfer coefficient. Because the radial tubes have a small diameter, they may not be hydraulically smooth. Tube heat transfer coefficients increase as surface roughness increases.

The penalty for increased surface roughness is increased tube pressure losses. Kays and

Crawford[26] discuss smooth and rough tube heat transfer rates in terms of Nusselt numbers, Nu. Nu = hD/k, where h is the tube heat transfer coefficient, D is is the tube

diameter, and k is the thermal conductivity. For a smooth tube with fully developed flow

Nu is given by:

Nu = 0.022P r0.5

Re0.8

P r is the Prandtl number, and Re is the tube Reynolds number. It is convenient to express

the Reynolds number in terms of the tube Mach number, M.

Re = P

RT μM



γRTD

where P is pressure, R is the gas constant, T is the absolute temperature, μ is the dynamic

viscosity, and γ is the specific heat ratio. μ and k are both proportional to T n, where n is

approximately 0.7. Consequently Nu is almost independent of temperature, but h increases

somewhat with temperature. Also, h increases slightly at the diameter, D, decreases. For P

equal to 17 atm., T equal to 650◦K(710◦F), M equal to 0.3, and D equal to 2.54mm(100mil),

Nu is 196. The tube heat transfer coefficient, h is 3725W/m2◦K.

When tubes are not hydraulically smooth, roughness can increase tube heat transfer by

up to a factor of 2.5(Kays and Crawford[26]). They also state that this increase comes at

the expense of a four fold increase in tube friction factor, and thus a four fold increase in

tube pressure drop.

The expected length-to-diameter,(L/D), ratios for radial cooling tubes is between 10

and 20. Even at an L/D = 20, the average smooth tube Nu will be somewhat greater than

the Nu for fully developed flow. This is due to an entrance effect, and the degree of heat

transfer augmentation is highly dependent on the specific entrance configuration. Overall,

the consequences of possible tube roughness and entrance effects indicate that a tube heat

transfer coefficient, hI of 5000W/m2 −◦ K for a pressure of 17 atm., and 8000W/m2 −◦ K for

a pressure of 30 atm. is conservative. However, hI will be lower when coolant is extracted

from the tubes for either film cooling or trailing edge ejection.

The amount of cooling flowing through the tubes was calculated to be approximately 7%

for the four tube configuration. This calculation assumed a coolant-to-inlet Mach number

ratio of 2, an inlet-to-coolant temperature ratio of 2.25, a span-to-axial chord ratio of 1.5,

and a vane pitch-to-axial chord ratio of 1.4.

1$6$&52 
6.1.2 - Radial cooling & film cooling. It was shown by Arts[32] that just the presence of film cooling holes causes laminar boundary layers to become turbulent. When a

laminar boundary layer is tripped and becomes turbulent there is a rapid increase in the

heat transfer coefficient. If the flow upstream of a cooling row is already turbulent, there is

only a small increase in heat transfer coefficients downstream of the film cooling row. Heat

transfer in the leading edge region is always laminar like because of strong favorable pressure

gradients, which increase as the leading edge diameter decreases. In this region heat transfer

coefficients increase dramatically in the presence of film cooling rows as shown by Reiss and

Bolcs[18], and by Ou and River[33]. Augmentation factors as great as a factor of four have

been reported. However, augmentation factors are relative to a solid leading edge with low to

moderate freestream turbulence. The high turbulence at the combustor outlet is expected to

increase solid vane leading edge region heat transfer coefficients by 50% or more. However,

because of low Reynolds numbers associated with vanes for turboshaft engine applications,

turbulence alone will not cause transition to turbulent flow in this region.

Figure 6.1.2.1 shows CMC and EBC temperatures for the vane with two assumptions

regarding transition in the leading edge region. Figure 6.1.2.2 shows the Nusselt number distributions corresponding to these two assumptions, and also shows results for a transitioning

flow model with a vane inlet turbulence intensity of 10%. The first assumption is that flows

are fully turbulent, and the second delays transition to locations downstream of the leading

edge. The second assumption was made to better account for the heat transfer augmentation

factors that are present in the Reiss and Bolcs[18] leading edge film cooling model. Figure

6.1.2.2 shows significantly different leading edge heat transfer coefficients between the fully

turbulent and delayed transition models. However, figure 6.2.2.1 shows that the effect of

these two model assumptions on both EBC and CMC temperature is relatively small. With

film cooling CMC temperatures are acceptable throughout the entire vane. However, EBC

temperatures are excessive in the leading edge region. Temperatures may be over estimated

because any heat transfer within the CMC vane to the cooling holes was neglected. Leading

edge region film holes are closely spaced, and are relatively long because these holes are

steeply angled in the spanwise direction. An indication that heat transfer into the film cooling holes should be considered in a future analysis is that the temperatures in the leading

edge region were nearly the same with and without film cooling.

Only three rows of film cooling holes were used in addition to the leading edge film

cooling. Two rows were on the pressure surface, and one on the suction surface. The coolant

fraction was calculated to be 16% of mainstream flow. Only three rows of film cooling holes

were sufficient because the minimum cooling hole size is independent of the vane size. The

smaller the vane, the fewer rows of film cooling holes are required.

1$6$&52 
6.1.3 - Single cavity & trailing edge ejection. Film cooling is very effective away

from the vane leading edge region. Nusselt numbers are lower in the leading edge region if

there is no film cooling. Trailing edge ejection was effective in the trailing edge region. A

thermal analysis was done for a solid vane with trailing edge ejection. At most there would

be room for only a single cavity in the half scale EEE vane. The configuration analyzed

here is geometrically similar to the single cavity configuration discussed in section 5.2.4.

The configuration analyzed has no film cooling. The internal heat transfer coefficients will

vary significantly, depending on the internal cooling arrangement. For comparison purposes

the internal heat transfer coefficient was assumed to be 5000W/m2◦K. The trailing edge

ejection tube heat transfer coefficient was determined based on the assumed inlet-to-exit

pressure ratio.

Figure 6.1.3.1 compares CMC and EBC outer surface temperatures for the four tube

radial cooling configuration with those for the single cavity with trailing edge ejection tube

configuration. Neither configuration employs film cooling. The single cavity configuration

has acceptable CMC temperatures over much of the vane surface. However, on both the

suction and pressure surfaces CMC temperatures exceed the temperature limit by more

than 180◦F(100◦C). EBC temperatures exceed the desired maximum EBC temperature over

much of the vane surface. The single cavity configuration yields lower EBC temperatures

than does the four radial tube configuration.

Figure 6.1.3.2 shows that decreasing the pitch-to-diameter ratio of the trailing edge ejection tube is an effective means of maintaining CMC temperatures less than the maximum

allowable CMC temperature. Unfortunately, decreasing the pitch-to-diameter ratio has little

effect on the EBC outer surface temperatures.

The outer surface temperature of the EBC can be lowered by reducing the thickness of the

EBC coating. However, reducing the EBC thickness raises the outer surface temperature

of the CMC vane. Figure 6.1.3.3 shows the effects of varying the EBC thickness. For

illustration purposes the EBC coating has a uniform thickness. These results were calculated

for a trailing edge ejection tube pitch-to-diameter ratio of 1.67. Unfortunately, near the aft

portion of the vane, where EBC temperatures are most in excess of the EBC temperature

limit, reducing the EBC thickness does not significantly reduce EBC temperatures. In the

leading edge region EBC temperatures also exceed the EBC temperature limit. In this region

reducing the EBC thickness is somewhat more effective than in the trailing edge region.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

Fully Turbulent

Delayed Forced Transition

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Fig. 6.1.2.1 CMC and EBC temperatures four tubes - P=30 atm. - TG = 3500◦F - hI =

5000W/m2 −◦ K - film cooled

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

0

500

1000

1500

2000

2500

Nusselt number, hC

X / k

Transitioning

Fully Turbulent

Delayed Forced Transition

Fully Turbulent

Transitioning

Delayed Forced

Pressure surface Suction surface

Transition

Fig. 6.1.2.2 Midspan Nusselt number distributions - P=30 atm.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

4 Radial Cooling Tubes

Single Cavity with Trailing Edge Ejection

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Fig. 6.1.3.1 Comparison of radial tube and single cavity CMC and EBC temperatures -

P=30 atm. - TG = 3500◦F - hI = 5000W/m2 −◦ K

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

Tube pitch = 5.0D

Tube pitch = 2.5D

Tube pitch = 1.67D

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Suction surface Pressure surface

Fig. 6.1.3.2 Effect of trailing edge ejection tube pitch-to-diameter ratio on CMC and EBC

temperatures - P=30 atm.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

t

EBC = 10 mil

t

EBC = 5 mil

t

EBC = 2.5 mil

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Suction surface Pressure surface

Fig. 6.1.3.3 Effect of EBC thickness on CMC and EBC temperatures - P=30 atm.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Surface distance, s/CX

0

500

1000

1500

2000

2500

Nusselt number, hC

X / k

Transitioning

Fully turbulent

Pressure surface

PT=17 atm. PT=30 atm.

Pressure surface Suction surface

PT=17 atm.

PT=30 atm.

Fig. 6.2.0.1 Midspan Nusselt number distributions - NASA vane

6.2 - NASA vane

Figure 6.2.0.1 shows Nusselt number distributions for the NASA vane. The profile and

pressure distributions for this vane were shown in figures 6.0.1 and 6.0.2. The Nusselt number

distributions for this vane can be compared with those shown in figure 6.1.0.1 for the half

scale EEE vane. The higher maximum Nusselt numbers for the NASA vane compared with

the maximum Nusselt numbers for the half scale vane do not represent higher heat transfer

coefficients. As shown in figure 6.0.1, the NASA vane has a longer axial chord, CX, and h

is proportional to Nu divided by CX. Suction surface transition is very different between

the NASA vane and the half scale EEE vane. Figure 6.1.0.1 for the half scale EEE vane

showed that increasing the inlet total pressure from 17 to 30 atm. caused suction surface to

move forward from 2/3 to 1/2 of the surface distance. Figure 6.2.0.1 shows that the NASA

vane at a pressure of 17 atm. has suction and pressure surface transition occurring close

to the trailing edge. At 30 atm., however, suction surface transition is relatively close to

the leading edge, and after transition the maximum Nusselt number exceeds the maximum

fully turbulent Nusselt number. Figure 6.0.2 shows that the NASA vane has a less favorable

suction surface pressure gradient. Consequently, at a pressure of 30 atm. suction surface

transition occurs further forward on the NASA vane compared with the half scale EEE vane.

1$6$&52 
-0.01 0 0.01 0.02 0.03 0.04

Axial distance, m

-0.04

-0.03

-0.02

-0.01

0

0.01

Tangential distance, m

-0.01 0 0.01 0.02 0.03 0.04

Axial distance, m

-0.04

-0.03

-0.02

-0.01

0

0.01

Tangential distance, m

2 radial holes 4 radial holes

Fig. 6.2.1.1 NASA vane with two radial cooling hole configurations.

6.2.1 - Radial cooling tubes - no film cooling. Figure 6.2.1.1 shows two and four

hole configurations for the NASA vane. Since cooling of the trailing edge is an issue, the two

radial tube configuration has the aft tube further aft than the two hole configuration of the

half scale EEE vane shown in figure 6.1.1.1. The radial cooling tubes are 2.54mm(100 mil)

in diameter.

Figure 6.2.1.2 shows outer EBC and CMC temperatures for the two and four radial tube

configurations. The results are for a gas temperature of 1700◦K(2600◦F), and an EBC thickness of 0.127mm(5 mil). Temperatures were calculated for a heat transfer coefficient within

the tubes of 5000W/m2◦K, which at a pressure of 17 atm. may be somewhat optimistic.

Even at this relatively low gas temperature and external heat transfer coefficients that are

mostly laminar, CMC temperatures exceed the design temperature for N24A towards the

rear of the vane. Unless the CMC temperature limit is raised, radial cooling without film

cooling is insufficient at this low gas temperature.

Figure 6.2.1.3 shows EBC and CMC temperatures for a case with four radial cooling

tubes. Here the gas temperature is 2200◦K(3500◦F), and the inlet total pressure is 30

atm. Increasing the inlet total pressure from 17 to 30 atm. causes the suction surface heat

transfer to change from mostly laminar to mostly turbulent. There is also an increase in

coolant temperature with an increase in inlet total pressure. Temperatures are shown for

two values of the tube internal heat transfer coefficient, hI. The lower value of 5000W/m2−◦

K is conservative at this pressure, since hI increases with pressure. Going from 5000 to

8000W/m2−◦K represents the expected change in hI due to the total pressure increasing from

17 to 30 atm. The EBC temperatures exceed the EBC temperature limit of 1756◦K(2700◦F)

almost everywhere, even for the higher hI value. Along the entire suction surface CMC

temperatures exceed their limit, as they do for the majority of the pressure surface.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

Tem[erature, o

F

Fore & Aft Cooling Tubes

4 Cooling Tubes

TG=2600 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Pressure surface Suction surface

Fig. 6.2.1.2 Effect of number of cooling tubes on CMC and EBC temperatures - P=17 atm.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Surface distance, s/CX

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

hI = 5000 W/m2 oK

hI = 8000 W/m2 oK

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Pressure surface Suction surface

Fig. 6.2.1.3 Effect of tube heat transfer coefficient, hI, on CMC and EBC temperatures -

P=30 atm.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

hI = 3000 W/m2 oK

hI = 5000 W/m2 oK

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Pressure surface Suction surface

Fig. 6.2.2.1 Effect of tube heat transfer coefficient, hI, on CMC and EBC temperatures -

with film cooling - P=30 atm.

6.2.2 - Radial cooling & film cooling. EBC and CMC outer surface temperatures

for the four radial cooling tube configuration with film cooling are shown in figure 6.2.2.1.

These results are for a gas temperature of 2200◦K(3500◦K), and an inlet total pressure of 30

atm. In addition to leading edge film cooling there are three film cooling rows on the pressure

surface, and one row on the suction surface. Tube heat transfer coefficients are lower when

film cooling air is extracted from the tube. Therefore, results are shown for lower tube heat

transfer coefficients of 3000 and 5000W/m2 −◦ K. The effects of changing hI are relatively

small. However, the higher value for hI is sufficient to maintain the CMC suction surface

temperatures near the leading edge within the CMC limit temperature.

1$6$&52 
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Surface distance, s/CX

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Tem[erature, o

F

Trailing edge ejection tube pitch = 5D

Trailing edge ejection tube pitch = 1.67D

TG=3500 oF

EBC Limit

CMC Limit

EBC Temp.

CMC Temp.

Pressure surface Suction surface

Fig. 6.2.3.1 Effect of trailing edge ejection tube heat transfer coefficient, hI, on CMC and

EBC temperatures - no film cooling - P=30 atm.

6.2.3 - Single cavity & trailing edge ejection. Figure 6.2.3.1 shows temperatures for

a single cavity configuration similar to the configurations discussed in sections 5.2.4 and 6.2.3.

This figure shows that acceptable CMC temperatures can be achieved with a single cavity

configurations as long as there is trailing edge ejection. Except at the rear of the pressure

surface, CMC temperatures are less than the CMC limit temperature of 1583◦K(2400◦F).

Previous results showed that only a small amount of pressure surface film cooling would

reduce CMC temperatures at the rear of this surface to acceptable values.

The difference in temperatures between results with a trailing edge ejection spanwise

pitch-to-tube diameter,D, ratio of 1.67 and 5 shows the sensitivity of temperatures to the

amount of heat removed via trailing edge ejection. The average heat transfer coefficient for

the trailing edge ejection tube was calculated from the correlation for fully developed flow

in a tube. The hydraulic diameter of the cavity is much larger than the hydraulic diameter

of the radial cooling tubes, and the average inter heat transfer coefficient decreases as the

hydraulic diameter decreases. Fortunately, the decrease is not linear, but only to the 0.2

power, because the radial flow is turbulent in either the cavity or radial tubes. While the

assumed value of 5000W/m2◦K may be somewhat optimistic, it is not excessively so. CMC

temperatures are acceptable, except near the trailing edge. However, EBC temperatures

exceed the EBC temperature limit in the forward part of the suction surface as well as the

aft portion of the pressure surface.

1$6$&52 
6.3 - Conclusions

Results were similar for both vanes analyzed for turboshaft engine applications. Pressure

distributions, and consequently the heat transfer distributions, were different between the

two vane geometries. Even so, both vane geometries required film cooling or trailing edge

ejection to achieve acceptable temperature limits. Radial cooling alone provided insufficient

cooling to avoid excessive CMC and EBC temperatures, even when the gas temperature was

only 1700◦K(2600◦F).

When the gas temperature was 2200◦K(3500◦F) film cooling and trailing edge ejection

provided sufficient cooling to keep CMC temperatures generally below 1589◦K(2400◦F).

Even when the EBC thickness was 0.127mm(5 mil), EBC temperatures were generally in

excess of their limit of 1756◦K(2700◦F) at locations where the CMC temperatures were

close to their limit value. Either raising the EBC temperature limit or increasing EBC

conductivity would help to alleviate this problem. The EBC thermal conductivity was

assumed to be 1W/m − K.

1$6$&52 
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1$6$&52