1. Turbine Vane Seal Support
Finite Element Model and Analysis
Submitted to:
Mike Zoch, Repair Development Engineer
Standard Aero San Antonio, Inc.
San Antonio, Texas
Prepared by:
Yuval Doron
Christopher Holsonback, Team Leader
Sang Kyu Lee
Kris Tatsch
Mechanical Engineering Design Projects Program
The University of Texas at Austin
Austin, Texas
Fall 2004

2. i
Acknowledgements
Without the help of several individuals, this project would not have been
possible. The team wishes to acknowledge and thank the following people for their
assistance in making this project a success:
• Mike Zoch, Repair Development Engineer, our contact at Standard Aero, took the
necessary time to help us thoroughly understand our project’s details. Mr. Zoch
helped provide us with materials that made this project a success.
• David Crowley, Director Project Engineering, our project sponsor, for giving us
the opportunity to work on this project and thereby allowing us to learn a great
deal about the aerospace repair industry.
• Dr. Richard Crawford, the design class professor, for providing us with guidance
throughout the duration of the class. Dr. Crawford made himself available at all
times and was able to direct us each time our team reached an impasse.
• Julie Lindsey, our teaching assistant, who was a pleasure to work with throughout
this project. Julie made meetings a time to look forward to. She provided us with
constant guidance and helped us make decisions throughout the duration of this
project.
• Dr. Eric P. Fahrenthold, our faculty advisor, for providing guidance and insight
for this project. Dr. Fahrenthold’s great insight into FEM helped to guide us in
the proper direction for this project under the time constraints.
• Dr. Bogard, for his assistance in understanding the results of our CFD analysis, as
well as for the overall understanding of stator vane behavior in a gas turbine. Dr.
Bogard was able to meet with us at a moments notice and helped keep the project
moving ahead.
• Dr. Dolling, for providing us with first hand conceptual understanding for choked
flow behavior.
• Dr. Panton, for his assistance in helping us understand choked flow analysis, and
correlated equations.
• Dr. Traver, for his assistance in using the ANSYS FEM software.
• DongMei Zhou, for her assistance during the initial stages of the CFD analysis.

4. iii
Table of Contents
Acknowledgements…………………………………………………………………......….i
Table of Contents……………………………………………………………………....…iii
List of Figures…………………………………………………………………………..…v
List of Tables.…………………………………………………………………………...viii
Executive Summary………………………………...…………………………………….ix
I. Introduction………………………………………………………………………..1
II. Background Information…………………………………………………………..2
2.1 Background of Standard Aero…………………………………………….2
2.2 Project Motivation………………………………………………………...2
III. Problem Statement………………………………………………………………...5
IV. Requirements and Constraints…………………………………………………….5
4.1 Requirements……………………………………………………………...5
4.2 Constraints………………………………………………………………...6
V. Deliverables……………………………………………………………………….6
VI. Project Research…..………………………………………………………………7
6.1 Gas Turbine Research……………..…………...………………………….7
6.2 TVSS Material properties…………..………………...…………………...9
VII. Boundary Conditions…………………………………..………………………...11
7.1 Problem Setup……...…………………………..………………………...11
7.2 Calculation of Inlet Static Pressure…...……..…………………………...12
7.3 Calculation of Inlet Total Temperature…...……..……………………….15
7.4 Verification of Calculations Using Choked Flow Approximation…........16
VIII. CFD Model of the Combustion path...………………….…………………...…...19
8.1 Formulation of CFD Model……………...……………..………………..20
8.2 Grid Independent Study…………………...……………..………………25
8.3 CFD Analysis Results……………………...……………..……………...27

5. iv
Table of Contents
IX. Static Analysis……………………………………………………………….…..32
9.1 Motivation………………………….………………………..…………...32
9.2 Static Load Calculations…………………………………………………34
9.3 Establishment and Loading of 2-D Sections……………………………..40
X. 2-D Finite Element Modeling……………………………………………………48
10.1 Formulation of 2-D FEMs……………………………………………….48
10.2 Grid Independent Study………………………………………………….49
10.3 2-D FEM results………………………………………………………….50
XI. 3-D Finite Element Modeling……………………………………………………52
11.1 Formulation of 3-D FEM………………………………………………...52
11.2 Grid Independent Study………………………………………………….54
11.3 3-D FEM Results………………………………………………………...56
XII. Conclusions………………………………………………………………………58
XIII. Recommendations………………………………………………………………..59
XIV. References………………………………………………………………………..63
Appendix A: Solving for Ratio of Specific Heats, “k”.............................................…..A-1
Appendix B: Iterating Mach Number …...…….…………………………………...….B-1
Appendix C: CFD Problem Setups...………………………………………………..…C-1
Appendix D: CFD Grid Independent Study Data...........................................................D-1
Appendix E: CFD Parameter Studies..............................................................................E-1
Appendix F: 2-D FEM Grid Independent Study……………………............................F-1
Appendix G: 3-D FEM Grid Independent Study………………………………………G-1
Appendix H: Project Gantt Chart...................................................................................H-1

6. v
List of Figures
Figure 1. Cross-section of a gas turbine engine showing the location of the TVSS...3
Figure 2. Close-up pictures of the flange surface of the TVSS...................................4
Figure 3. Nominal Composition of A-286 in weight percent...................…………...9
Figure 4. A choked flow situation within a nozzle....................................................17
Figure 5. Location of the modeled cross-sections……………….…………………21
Figure 6. Image of a modeled gas path between two stators….……………………21
Figure 7. Image of a modeled gas path with the added inlet section ...……………22
Figure 8. Image of a meshed model showing the triangular meshing elements ......22
Figure 9. Mass flow and residual convergence for a representative case …………25
Figure 10. Force coordinate system used throughout the analysis ………………….26
Figure 11. Plot of calculated tangential force versus mesh density ……...…………26
Figure 12. Plot of calculated axial force versus mesh density ……………...………27
Figure 13. Representative contours of Mach number ……………….…………...…28
Figure 14. Representative contours of velocity magnitude ……………….……..….28
Figure 15. Representative contours of static pressure ……………….…………...…29
Figure 16. Tangential force distribution across the height of one stator vane …...…30
Figure 17. Axial force distribution across the height of one stator vane ……………31
Figure 18. Stator Vane loading, as resulted from CFD modeling…………...……....32
Figure 19. Single Stator Vane reaction forces from the T56 casing and TVSS… ….33
Figure 20. Single Stator Vane static loading condition in the axial direction…….....34
Figure 21. Stator Vane pivot and lever action reaction forces………………………35
Figure 22. TVSS reaction axial forces………………………………………………36

7. vii
List of Figures
Figure 23. Stator Vane tangential force and TVSS reaction force…………………..38
Figure 24. Stator Vane twist condition due to moment……………………………...39
Figure 25. Six cross section implementation…………………………………..…….41
Figure 26. Image of buckle condition inside TVSS slot guide ……………………..42
Figure 27. Image of twist condition inside TVSS guide slot………………………..43
Figure 28. Image of pressure affecting TVSS surfaces ……………………………..44
Figure 29. Loading on section AA……………………………....……………….….44
Figure 30. Loading on section BB…………………………..……………………….45
Figure 31. Loading on section CC…………………………..……………………….45
Figure 32. Loading on section DD………………………….……………….………46
Figure 33. Loading on section EE………………………….………………………..46
Figure 34. Loading on section FF………………………….………………………..47
Figure 35. TVSS 2-D cross-section with constraints………………………………..48
Figure 36. Grid independent study results for 2-D FEM TVSS cross-section………50
Figure 37. Contours of von Mises stress on section BB...……………………….….51
Figure 38. 3-D modeled portion of the TVSS……………………………………….53
Figure 39. 3-D TVSS subjected to section BB 2-D loading…………………...........54
Figure 40. Results of 3-D grid independent study of the modeled TVSS section.….55
Figure 41. von Misses stress contours on 3-D TVSS ….............................................56
Figure 42. Contours of von Mises stress within the flange area ................................57
Figure F.1. Locations of keypoints…... ………………………………………..…...F-2

8. vii
List of Figures
Figure G.1. Locations of keypoints…... ………………………………………..…...G-2
Figure H.1. Current project Gantt chart ………………………………………..…...H-2

9. viii
List of Tables
Table 1. Selected Temperature-Dependent Properties of A-286………………….10
Table 2. Summary of Results from FLUENT……………………………………..29
Table 3. Scaled Forces Calculated by FLUENT…………………………………..30
Table 4. Calculation of Total Force……………………………………………….31
Table C.1. FLUENT Problem Setup for Cross-Section AA………………………..C-2
Table C.2. FLUENT Problem Setup for Cross-Section CC………………………..C-3
Table C.3. FLUENT Problem Setup for Cross-Section EE………………………...C-4
Table D.1. Data for Section AA…………………………………………………....D-1
Table D.2. Data for Section CC…………………………………………………….D-2
Table D.3. Data for Section EE…………………………………………………….D-2
Table E.1. Data for Parameter Study of Inlet Turbulence-Viscosity Ratio………...E-1
Table E.2. Data for Parameter Study of Outlet Static Pressure…………………….E-2
Table E.3. Data for Parameter Study of Inlet Static Pressure……………………....E-3
Table F.1. Grid Independent Study for 2-D Model...................................................F-1
Table G.1. Grid Independent Study for 3-D Model...................................................G-1

10. ix
Executive Summary
The Senior Design Projects Program, as part of the undergraduate Mechanical
Engineering curriculum at the University of Texas at Austin, provides an opportunity for
engineering seniors to apply four years worth of training to an actual industry problem.
The project team for this project consisted of Yuval Doron, Christopher Holsonback
(team leader), Sang Kyu Lee, and Kris Tatsch.
The sponsor of this project, Standard Aero San Antonio, Inc., is a global company
that specializes in the repair and remanufacture of gas turbine engines. To keep at the
forefront of their industry, Standard Aero has pioneered repair processes for expensive
gas turbine components. They developed one such repair for a component of the Rolls-
Royce T56 turboprop engine known as the turbine vane seal support (TVSS). The TVSS
separates the combustion and turbine sections of the T56 and serves to restrain the first-
stage stator vanes. After thousands of hours of impingement by high temperature, high-
pressure combustion gasses, the stator vanes wear the flange surface of the TVSS at their
interface. This allots the stators even more freedom of movement, causing not only
additional damage to their construction but also the loss of efficiency of the turbine.
The repair developed to address this issue involves the machining of the damaged
surface of the TVSS, followed by a surface restoration process. However, the sponsor
was concerned about how much material could be removed from the contact surface
before the TVSS would plastically yield under normal loading. Therefore, Standard Aero
enlisted the help of the student project team to determine the boundary conditions of the
combustion flow and force distribution on the TVSS, develop a finite element model
(FEM) of the TVSS disk, and predict the value of the maximum machining depth that
could be used during the repair process.
The team began by determining the condition of the combustion flow at the inlet
and outlet of the first-stage stators. This information was inputted into a computational
fluid dynamics (CFD) model of the combustion gas path that calculated the forces and
moment acting on the stator surfaces. Next, the team performed a static analysis to
translate the calculated loads into forces and pressures acting on the TVSS disk itself.
This involved assuming that the TVSS accepted all of the forces from the stators; none of
the force was distributed to the casing of the T56.
The forces determined through static analysis were then applied to two-
dimensional (2-D) FEMs of critical TVSS cross-sections to determine the peak von Mises
stress within the TVSS under normal loads. The 2-D models resulted in unrealistic
behavior, including the prediction of plastic yielding of the TVSS under normal loads.
The team then resorted to a more complicated three-dimensional (3-D) FEM of a periodic
section of the TVSS disk. However, when all of the loads determined through the static
analysis were applied to the 3-D FEM, it also predicted failure of the TVSS.
The results indicated that the assumption about the distribution of load between
the TVSS and casing during the static analysis was overly conservative. Unfortunately,
due to time constraints, the project team was unable to readdress the load distribution
issue, and therefore could not recommend a maximum machining depth to use during the
repair process. However, the team did outline several potential areas for future work in
this project that may lead to a more accurate simulation of the response of the TVSS.

12. I. Introduction
Gas turbine engines have many uses in the world today. One of the most common
applications for the gas turbine is in aircraft propulsion, where they appear in several
forms. One such form is the turboprop, where the gas turbine powers a spinning
propeller [1]. One of the more common turboprop engines is the Rolls-Royce T56. This
engine, despite being designed over fifty years ago, is still widely used throughout the
commercial industry and by the U.S. military [2]. Because of the prevalence and age of
the T56, maintenance programs are in constant demand to service these engines.
Additionally, engineers at companies that provide maintenance services for the T56 are
continually designing new repair processes to prolong the life of major internal
components. This project is based on one such repair.
The team assigned to this project is composed up of senior-level undergraduate
students of Mechanical Engineering from the University of Texas at Austin. The team is
composed of Yuval Doron, Christopher Holsonback (team leader), Sang Kyu Lee, and
Kris Tatsch. The project team has technical knowledge and experience in the areas of
Thermal-Fluid Systems and Systems and Design.

13. 2
II. Background Information
2.1 Background of Standard Aero
One company that provides rebuilding and remanufacturing service for the T56 is
Standard Aero, Incorporated [3]. Standard Aero is an international company that has
over forty years of experience in the remanufacturing and refurbishing of the T56 and
prides itself on its excellence of workmanship [4]. Due to its continuing success in the
remanufacturing market, both the U.S. Air Force and Navy have awarded major contracts
to Standard Aero to maintain their fleets of T56-powered aircraft [5, 6]. The T56 engine
is currently used in the Navy’s P-3 Orion, C-130 Hercules, E-2 Hawkeye, and C-2
Greyhound aircraft [5].
In order to maintain their growth as a business, Standard Aero has recently started
designing repair processes for many major components of the T56. Standard Aero hopes
to reduce the frequency of replacing expensive internal components of the T56 by
conducting repairs that will considerably prolong the lifetime of the components [6].
2.2 Project Motivation
One major component of the T56 for which Standard Aero is designing a repair
for is the Turbine Vane Seal Support (TVSS). The TVSS performs two major roles in the
T56. Firstly, it acts as a physical barrier between the combustion can and turbine sections
of the engine. Secondly, the TVSS supports and locates the first-stage turbine stator

14. 3
vanes, which serve to direct the combustion flow onto the rotating turbine blades [7].
Figure 1 shows a schematic of a gas turbine engine and the location of the TVSS.
Figure 1. Cross-section of a gas turbine engine showing the location of the
TVSS.
After many hours of operation, the stator vanes begin to twist within their seat on
the TVSS due to the high pressure, high temperature gas impinging on them [7]. The
twisting of the stator vanes causes wear on the flange surface of the TVSS at the contact
point between the stator vanes and the TVSS, as shown in Figure 2.

15. 4
Figure 2. Close-up pictures of the flange surface of the TVSS. Note the notching of
the flange seat area resulting from the twisting of the first-stage stator vanes [8].
The project sponsor, Mike Zoch, is a repair development engineer for Standard
Aero who has developed a repair for the flange surface of the TVSS. During which the
damaged surface is machined off. However, he wants to ensure that the structural
integrity of the TVSS is not compromised by the repair process [7]. Unfortunately, the
forces, temperatures, and vibrations to which the TVSS is subjected under normal use are
predominately unknown and are difficult to ascertain [7]. Therefore, the project sponsor
has enlisted the help of the project team with modeling the TVSS, to ensure the
soundness of the repair.

16. 5
III. Problem Statement
Standard Aero commissioned the project team to generate a computer model of
the TVSS to simulate its response to physical loading. The model should be used to
determine the maximum amount of material that can be removed from the flange area of
the TVSS during the repair process before the TVSS will fail under normal loading [7].
IV. Requirements and Constraints
4.1 Requirements
For this project, the project team adhered to several requirements provided by the
sponsor. First, Standard Aero required that the team create a finite element model (FEM)
of the TVSS. The team created this FEM such that the boundary conditions, including
forces, temperatures, and vibrations, to which the model is subjected could be easily
changed. This flexibility was required so that the model could continue to be used as
engineers at Standard Aero gain more information about the true load and temperature
conditions of the TVSS [7]. Additionally, Standard Aero required that the FEM created
use the commercially available ANSYS software package.

17. 6
4.2 Constraints
To reduce the scope of the project to a more manageable level, the sponsor has
indicated that the team is to study the effects of material removal on the TVSS only.
Furthermore, the FEM will not address the repair process used in material replacement
[7].
V. Deliverables
At the conclusion of the project, the team provided Standard Aero with this
report, which outlines the results as well as methodology, decisions, and rationale used
during this analysis. Additionally, the team provided the sponsor with a copy of the FEM
of the TVSS and other materials used in this analysis. Finally, the team provided
Standard Aero with recommendations for future work in this project

18. 7
VI. Project Research
As with any project, the project team began with background research to ensure a
more full understanding of the problem and the analysis techniques that were selected. A
literature review of current gas turbine engine modeling was conducted as well as
research into the mechanical properties of the TVSS.
6.1 Gas Turbine Research
Background research into gas turbine repairs consisted of patent searches,
academic journal searches, and general internet searches. Almost no information was
found about gas turbine engine repairs, most likely due to their proprietary nature.
However, the research did uncover the fact that computer modeling of gas turbine
components is a major industry. For example, a company known as Southwest Research
Institute (SwRI) has “evaluated a substantial number of gas turbine engines to diagnose
the cause of failures, correct operating problems, or improve component life” [8]. SwRI
purports itself to be a company that applies innovative technology, including finite
element modeling, to the stress analysis of gas turbine components. In fact, SwRI
frequently uses ANSYS in its analyses [9]. SwRI also uses around other such companies,
computational fluid dynamics (CFD) software to model the flow of air and combustion
products through gas turbine engines. They indicate that “fluid dynamics, heat transfer,
and fluid-[to]-structure interaction are essential disciplines to the effective design,

19. 8
application, and performance evaluation of gas turbines” [9]. This indicates that the
analysis the project team performed during this project was both valuable and consistent
with good engineering practices.
Journal searches revealed that gas turbine modeling is also a major area of
academic research. Researchers frequently use both finite element modeling and CFD
analysis in their projects. One paper even mentioned that, “within a limited schedule and
engineering budget, the CFD model significantly increased the effectiveness of the
analysis...compared to traditional trial and error approaches” [10]. This paper went on to
couple results from a CFD analysis with an FEM to minimize the weight of an intake
manifold on a rocket engine. This reiterates the idea that the analysis methodology that
the project team selected is widely used around the world on very sophisticated projects.
Two other journal articles illustrated the use of the CFD software FLUENT [11,
12]. Here, FLUENT was used to calculate pressure distribution, streamline pattern,
temperature distribution, and velocity of several complicated flows. One author indicated
that there was “good agreement between the CFD prediction and the experimental
measurements” [12].
The project team believes that this background research has shown that FEM and
CFD modeling are used in industry and academic settings to accurately simulate
complicated physical phenomena under time and budget constraints. In addition,
ANSYS and FLUENT are both commonly selected software packages that generally
provide good agreement between simulation and experimental results.

20. 9
6.2 TVSS Material Properties
The TVSS is made from A-286, which is an austenitic stainless steel with nominal
composition shown in Figure 3 [13]. A-286 demonstrates considerable strength in high-
temperature environments, like as those found in the turbine section of a gas turbine
engine. Selected temperature-dependent mechanical properties of A-286 are shown in
Table 1 [14, 15].
Nickel (Ni) 26.0%
Aluminum (Al) 0.2%
Mangenese (Mn) 1.3%
Chromium (Cr) 15.0%
Iron (Fe) 53.6%
Molybdenum (Mo) 1.3%
Silicon (Si) 0.5%
Carbon (C) 0.05%Boron (B) 0.015%
Titanium (Ti) 2.0%
Figure 3. Nominal composition of A-286 in weight percent (wt. %).

21. 10
Table 1. Selected Temperature-Dependent Properties of A-286
Temperature
[deg. F]
Yield Strength
at 0.2% Offset
[ksi]
Modulus of
Elasticity
[psi]*10^6
70 105 29.1
400 93.5 -
800 93 -
1000 88 23.5
1100 90 22.8
1200 88 22.2
1300 86 21.1
1400 62 20.6
1500 33 18.7
1600 - 18.9
Iron-based superalloys, such as A-286, derive their strength from a closed-packed
face-centered-cubic (fcc) structure that is stabilized by a high nickel content as well as
solid-solution hardening and precipitated intermetallics. Solid-solution hardening is
accomplished primarily through alloying elements such as chromium while precipitation
strengthening occurs through intermetallics phases such as γ′ (Ni3Al), γ ′′ (Ni3Nb), and η
(Ni3Ti). Additionally, small amounts of other alloying elements, such as Boron (B),
serve to suppress grain-boundary fracture under creep rupture (high temperature)
conditions [14]. All of these mechanical properties qualify A-286 and other similar iron-
based super alloys to serve in the high-temperature, highly corrosive environment found
in gas turbine engines.

22. 11
VII. Boundary Conditions
One of the prerequisites of establishing the maximum machining depth was the
determination of the boundary conditions of the TVSS. These boundary conditions were
to be used in the FEM to determine the peak stress concentrations of the TVSS under
normal loading both before and after machining. Although the FEM can predict the peak
stresses within the model, it can only produce accurate results if the forces applied to the
model are realistic. Therefore, before work could begin on the FEM, the magnitude,
direction, and location of the loads on the TVSS had to be determined.
Forces on the TVSS, especially at the flange area, are primarily due to the
combustion gasses impinging on the first-stage stator vanes. Background research
indicated that one of the most accurate ways of determining the effects of the combustion
gasses was to create a model of the combustion gas path through the stators using CFD
software such as Fluent. However, before the CFD model could be used, the condition of
the combustion flow at the inlet and outlet of the first-stage stator vanes had to be
established.
7.1 Problem Setup
The boundary conditions of the combustion flow that were required inputs for a
CFD analysis of the combustion flow through the first stage stators were:
1. the inlet total pressure,

23. 12
2. inlet total temperature,
3. inlet static pressure, and
4. outlet static pressure of the flow.
Fortunately, the sponsor provided us with the following conditions of the combustion
flow [7]:
5. inlet total pressure, totalP , equaled 135 pounds per square inch, absolute (psia),
6. turbine inlet static temperature, staticT , equaled 1970 degrees Fahrenheit (° F),
7. mass flow rate of air through the turbine, airm& , equaled approximately fifteen
kilograms per second (kg/s), and
8. mass flow rate of fuel, fuelm& , equaled 2,460 pounds per hour, which was
equivalent to 0.31 kg/s.
Utilizing this data and several well-supported simplifications, the unknown
boundary conditions of the combustion flow, with the exception of outlet static pressure,
were determined for the inlet stator vanes as discussed below. Outlet static pressure was
determined iteratively during the CFD analysis, and is discussed in a later section.
7.2 Calculation of Inlet Static Pressure
The inlet static pressure was determined using the relation between total and static
pressure in a moving fluid. [16]:
2
2
1
VPP statictotal ⋅⋅+= ρ (1)

24. 13
where ρ is the density of the combustion gasses and V is the free-stream velocity of the
flow at the inlet to the stator vanes. Rearranging equation (1) gave:
2
2
1
VPP totalstatic ⋅⋅−= ρ (2)
However, the free-stream velocity was unknown. It was calculated via continuity using
the following equation [1]:
AVm ⋅⋅= ρ& (3)
where m& is the total mass flow rate and A is the area through which the flow travels.
Rearranging equation (3) to solve for velocity gave:
A
m
V
⋅
=
ρ
&
(4)
The total mass flow rate was simply the summation of the mass flow rates of the
air and fuel:
s
kg
s
kg
s
kg
mmm fuelair 31.1531.015 =+=+= &&&
The density of the combustion gas was calculated from the ideal gas law

25. 14
assuming that the gas has properties very similar to that of air. Although this was the
ideal gas law equation for incompressible fluids, it served as a good first approximation:
TR
P
⋅
=ρ (5)
where P is the total pressure, R is the specific gas constant for air, and T is the
temperature of the flow. Substituting the known values into equation (5) gave:
3
40.2
1350
1970895.6
1970287.0
135
m
kg
K
F
psi
kPa
F
Kkg
kJ
psia
=⋅⋅
⋅
⋅
=
o
o
ρ
The cross-sectional area of the flow was simply the area traced out by the height
of the stators all the way around the circumference of the T56. That is:
( )2222
ioioio rrrrAAA −⋅=⋅−⋅=−= πππ
where or is the outer radius of the stators from the axial centerline of T56 and ir is the
inner radius of the stators. From the engineering specifications provided to the project
team by Standard Aero, the area was:
( ) 2
2
2
2222
0395.0
550,1
0065.81417.9 m
in
m
ininA =⋅−⋅= π
Substituting in values for m& , ρ , and A into equation (4) gave:
s
ft
s
m
m
m
kg
s
kg
V 9.5295.161
0395.040.2
31.15
2
3
==
⋅
=

26. 15
Substituting this velocity and other values already determined into equation (2) gave (unit
correction factors excluded):
psia
s
ft
m
kg
psiaPstatic 5.1309.52940.2
2
1
135 2
2
2
3
=⋅⋅−=
This was the value used for the inlet static pressure required by the CFD software.
7.3 Calculation of Inlet Total Temperature
The calculation of the inlet total temperature followed that of the inlet static
pressure closely. Total temperature is defined as the temperature of the flow that would
be measured if the flow were isentropically (i.e. constant entropy) decelerated to zero
velocity. The equation that relates static to total temperature is [16]:
2
2
1
V
Cp
TT statictotal ⋅
⋅
+= (6)
where Cp is the constant-pressure specific heat of the fluid. At the static temperature
provided by Standard Aero, the specific heat of air is equal to 1.198 kJ/kg-K [17].
Substituting in this value and the value of the flow velocity previously established into
equation (6) gave:

27. 16
FK
s
m
J
Kkg
KTtotal
o
9.199113625.161
198,12
1
1350 2
2
2
==⋅
⋅
⋅+=
This was the value used for the inlet total temperature required by the CFD software.
7.4 Verification of Calculations Using Choked Flow Approximation
During the initial stages of the project, the sponsor indicated that the combustion
flow through the first stage stators was choked. Choked flow is a condition generated in
a convergent-divergent nozzle in which the velocity of the flow reaches the speed of
sound in that fluid at some location of minimum area, called the throat. Figure 4
represents such a condition, where conventionally the throat is labeled A*. The Mach
number is defined as:
C
V
M = (7)
where V is the velocity of the flow and C is the speed of sound in that flow [16]. Figure 4
shows an example of a choked flow situation.

28. 17
Figure 4. A choked flow situation within a nozzle.
Once choked flow is achieved, it implies that the flow characteristics are
independent on the outlet conditions, including the outlet static pressure [16]. In a
choked flow, the velocity of the flow cannot increase, even if the outlet static pressure is
reduced to below the critical pressure, unless the pathway is specifically designed to
create supersonic flow. However, supersonic flow is accompanied by physical
phenomena called shock waves, which are lines of extreme pressure gradients that serve
to remove energy from the flow and decelerate it [16]. Shock waves within the turbine
section of the T56 would quickly destroy the rotor blades and stator vanes, possibly
catastrophically.
The study of fluid dynamics addresses choked flow situations by assuming steady
state, 1-D, isentropic flow of an ideal gas [16]. 1-D refers to the condition where the flow
assumes a path on one axis only. Although these are very large assumptions, utilizing
choked flow correlations verified the previous boundary condition calculations.
Assuming the flow is choked through the first stage stators allowed the following
relation [16]:

29. 18
( )12
1
2
*
2
1
2
1
1
1
−
+
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎝
⎛
+
⋅
−
+
⋅=
k
k
k
M
k
MA
A
where A is the cross-sectional area of the flow anywhere upstream or downstream of the
throat, A* [figure 4], and k is the ratio of specific heat for the fluid, found using a
mathematical model of the T56 discussed in Appendix A. Inputting this equation into a
Matlab iterating program (discussed in Appendix B), and inputting the values of A at the
inlet and A* at the throat from the engineering drawings provided to us by Standard Aero,
as well as a calculated k of air at the inlet temperature and pressure [17]. The program
indicated that at the inlet to the stators, M = 0.226.
Knowing the Mach number, the inlet static pressure was solved for directly
through [16]:
1
2
2
1
1
−
⎟
⎠
⎞
⎜
⎝
⎛
⋅
−
+=
k
k
static
total
M
k
P
P
(8)
Rearranging equation (8) to solve for the inlet static pressure gave:
psia
psia
M
k
P
P
k
k
total
static 6.130
226.0
2
1314.1
1
135
2
1
1
1314.1
314.1
2
1
2
=
⎟
⎠
⎞
⎜
⎝
⎛
⋅
−
+
=
⎟
⎠
⎞
⎜
⎝
⎛
⋅
−
+
=
−−

30. 19
which was within 0.08 percent of the previously calculated value.
Total inlet temperature followed a similar calculation through [16]:
2
2
1
1 M
k
T
T
static
total
⋅
−
+= (9)
Equation (9), when solved for total temperature, gave:
KKM
k
TT statictotal 8.1360226.0
2
1314.1
11350
2
1
1 22
=⎟
⎠
⎞
⎜
⎝
⎛
⋅
−
+⋅=⎟
⎠
⎞
⎜
⎝
⎛
⋅
−
+⋅=
which was within about 0.09 percent of the previously calculated value. These choked
flow calculations verified that our previous calculations of inlet static pressure and inlet
total temperature were correct.
VIII. CFD Model of the Combustion Path
The project team decided to create a computer model of the combustion gas path
through the first-stage stator vanes for several reasons. First, we knew that the
combustion flow was a major contributor to the forces acting on the flange section of the
TVSS, but that it would be very difficult to calculate these forces accurately using
simplified flow equations from fluid mechanics without making many assumptions about

31. 20
the condition of the flow. For example, the simplified Bernoulli Equation assumes
inviscid and incompressible flow, neither of which is a characteristic of the actual flow
through the stator vanes [16]. Second, the possibility of modeling the gas path as a series
of two-dimensional cross-sections to simplify the analysis was encouraging. This idea
came about through a conversation with a professor of CFD in the Mechanical
Engineering department [18]. Two-dimensional cross-sections would allow for simpler
meshing and would require less computing time than a full three-dimensional model.
Representative data from several two-dimensional cross-sections would provide us with a
good approximation of the overall force condition of the stators. Lastly, the ability of the
computer model to simulate complex flow situations such as turbulent and transonic
flow, like those found in the actual gas path, was very powerful. The overall goal of CFD
modeling of the gas path was to determine the forces and moments acting on the stator
vanes without making major, simplifying assumptions about the condition of the flow.
8.1 Formulation of CFD Model
The CFD model began by creating solid models of cross-sections of the stator
vanes from the engineering drawings provided by Standard Aero. Three different cross-
sections were modeled: AA, CC, and EE, as shown in Figure 5. The designation for each
cross-section was taken directly from the engineering drawings. We chose to eliminate
the surfaces of the stators that did not interact with the gas path and enclosed the top and
bottom of the gas path, as shown in Figure 6. This left two-dimensional models of the
gas path with no extraneous features.

32. 21
Figure 5. Location of the modeled cross-sections.
Figure 6. Image of a modeled gas path between two stators.
Next was the importing of the solid models into the meshing program GAMBIT.
In GAMBIT, an inlet section was added onto the imported edges, as shown in Figure 7,
flow outlet
flow inlet
to model

33. 22
so that the stagnation phenomena that would occur on the nose of the stators could be
more easily captured. Additionally, the inlet section allowed us to utilize a constant inlet
velocity boundary condition, as discussed later. This idea was the result of several
discussions with a professor who specializes in turbine vane cooling within the
Mechanical Engineering department [19]. After cleaning up the connections between the
imported and created edges, the models were meshed using triangular elements to
preserve their rounded features, as shown in Figure 8.
Figure 7. Image of a modeled gas path with the added inlet section.
Figure 8. Image of a meshed model showing the triangular meshing elements.

34. 23
Next came importing the mesh into the CFD software FLUENT. Several
FLUENT tutorials addressed situations that were similar to the gas path model, and were
utilized as a general guide for the first iteration of the model. For example, we selected
the Spalart-Allmaras model for turbulent flow modeling because it was “designed
specifically for aerospace applications involving wall-bounded flows and [gives] good
results for boundary layers subject to adverse pressure gradients,” such as those found in
choked flow situations [20].
One of the assumptions that carried over from the determination of the boundary
conditions was that the effects of combustion were ignored. Consequently, the working
fluid was air for all of the CFD models. However, thermal dependency of the physical
properties was maintained, as recommended by the FLUENT tutorials [21]. For
example, constant-pressure specific heat and thermal conductivity of the air were
modeled as functions of temperature [17]. Additionally, the Sutherland law was used to
model the dynamic viscosity of air because the FLUENT tutorial indicated that “the
Sutherland law for viscosity is well suited for high-speed compressible flows” [21].
Although using temperature-dependent properties made the models more complicated, it
served to increase the veracity of the results.
As previously discussed, the boundary conditions of the flow were derived from
several sources including data provided by the sponsor, the calculations of the project
team, and iterative analysis of the CFD model. For example, the outlet static pressure
was fixed between 110.2 and 107.3 psia, depending on the cross-section, which was
determined through an iterative process of inputting a value, running the model,
determining the maximum Mach number of the flow, and then adjusting the value of the

35. 24
outlet static pressure to force a choked flow situation. This process was the result of a
discussion of preliminary results of the model, which showed supersonic flow though the
gas path, with a professor in the Mechanical Engineering department [22].
Heat transfer into the stators was modeled by assuming that the surfaces of the
stators were at a constant temperature, determined from the following correlation:
( )coolingfreestreamcoolingstators TTTT −⋅+= 90.0
where statorsT is the mean surface temperature of the stator vanes, coolingT is the
temperature of the internal cooling air, and freestreamT is the free stream temperature of the
combustion gasses [22]. Therefore, from the information provided to us by the sponsor,
the calculation becomes:
( ) KKKKTstators 65.12765.616135090.05.616 =−⋅+=
Fixing the surface temperature of the stators as constant and neglecting to model
the internal cooling represented rather large assumptions. However, these were safe
assumptions to make since the primary goal of the CFD analysis was to determine the
forces on the stators, not their temperature or heat transfer characteristics.
The upper left and right hand surfaces of the model, as shown in Figure 7, were
set as adiabatic, frictionless surfaces to minimize their interaction with the flow. The
model was then iterated until the convergence criteria were met and the mass flow at the

36. 25
exit became steady, as shown in Figure 9 for a representative case. Appendix C presents
summaries of the problem setup for each of the three cross-sections.
Figure 9. Image of mass flow and residual convergence for a representative case.
8.2 Grid Independent Study
Different mesh densities were tested for each cross-section to verify that
FLUENT’s calculations converged on the actual solution. In general, the axial and
tangential forces on the stators changed only about one percent from mesh to mesh. For
reference, Figure 10 shows the coordinate system we used to define the terms
“tangential” and “axial,” which essentially correspond to lift and drag on the stators,
respectively.

37. 26
Figure 10. Force coordinate system used throughout the analysis.
Figures 11 and 12 are plots of the net tangential and net axial forces on the stator
vane surfaces calculated by FLUENT for the three mesh densities from each cross-
section. Note that the forces calculated by FLUENT are relatively insensitive to mesh
density. The data used in the grid independent study can be found in Appendix D.
1000
1500
2000
2500
3000
3500
4000
3.0E+07 3.2E+07 3.4E+07 3.6E+07 3.8E+07 4.0E+07 4.2E+07 4.4E+07 4.6E+07 4.8E+07 5.0E+07
Mesh Density [cells/m^2]
TangentialForce[N]
Section AA, tangential
Section CC, tangential
Section EE, tangential
Figure 11. Plot of calculated tangential force versus mesh density.

38. 27
-5000
-4500
-4000
-3500
-3000
-2500
-2000
3.0E+07 3.2E+07 3.4E+07 3.6E+07 3.8E+07 4.0E+07 4.2E+07 4.4E+07 4.6E+07 4.8E+07 5.0E+07
Mesh Density [cells/m^2]
AxialForce[N]
Section AA, axial
Section CC, axial
Section EE, axial
Figure 12. Plot of calculated axial force versus mesh density.
Additionally, parameter studies were conducted to determine the effects of inlet
turbulent-viscosity ratio (a measure of turbulence), outlet static pressure, inlet static
pressure, and shape of the test section. Data and conclusions from these tests can be
found in Appendix E.
8.3 CFD Analysis Results
One of the major advantages of using commercial CFD software is the ability to
visualize flow phenomena. For example, Figures 13, 14, and 15 show representative
contours of Mach number, velocity magnitude, and static pressure throughout the gas
path. Note that in Figure 13, the maximum Mach number for the flow is approximately
unity and that the throat region is clearly visible. Figure 14 clearly shows the stagnation
of the flow at the nose of the stator vanes. Lastly, Figures 14 and 15 show that the

39. 28
constant static pressure, and therefore constant velocity, inlet boundary condition was a
reasonably accurate assumption.
Figure 13. Representative contours of Mach number.
Figure 14. Representative contours of velocity magnitude, in m/s.

40. 29
Figure 15. Representative contours of static pressure, in Pa.
Once the solution for each case had converged, several of FLUENT's calculated
parameters were recorded, including the net tangential and net axial forces on the
surfaces of the stators. Table 2 shows the results for selected meshes from each cross-
section. Note that the maximum Mach number through the gas path for each case is
approximately equal to unity, which indicates that the flow is choked through the stators.
Table 2. Summary of Results from FLUENT
Mesh ID: AA-7 CC-2 EE-7
Number of Cells [#]: 26,202 28,330 29,164
Maximum Mach Number: 1.05 1.07 1.02
Maximum Velocity [ft/s]: 2,236 2,278 2,185
Minimum Static Press [psia]: 63 62 65
Total x-force (tangential) [lbf]: 492.2 596.7 615.5
Total y-force (axial) [lbf]: -661.6 -795.0 -786.6
The values for tangential and axial forces shown in Table 2 are very large because
they represent the forces on a model having one meter (m) of depth. Even in two-
dimensional analysis, FLUENT must assume some depth through which the fluid flows.

41. 30
Table 3 shows the results of scaling the tangential and axial forces to represent a cross-
section one millimeter (mm) in depth. Once these values were calculated, a quadratic
curve was fit to the data resulting in force distributions across the entire height of the
stators, as shown in Figures 16 and 17.
Table 3. Scaled Forces Calculated by FLUENT
Section ID: AA-7 CC-2 EE-7
These forces are for 1 m of depth:
Total x-force (tangential) [lbf]: 492.2 596.7 615.5
Total y-force (axial) [lbf]: -661.6 -795.0 -786.6
So, for 1 mm of depth:
Total x-force (tangential) [lbf]: 0.49 0.60 0.62
Total y-force (axial) [lbf]: -0.66 -0.80 -0.79
0
5
10
15
20
25
30
0.40 0.45 0.50 0.55 0.60 0.65 0.70
Tangential Force [lbf]
DistancefromBottomofStator[mm]
data points
distirbution
Figure 16. Tangential force distribution across the height of one stator vane

42. 31
0
5
10
15
20
25
30
-0.90 -0.85 -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50
Axial Force [lbf]
DistancefromBottomofStators[mm]
distribution
data points
Figure 17. Axial force distribution across the height of one stator vane.
Integrating the force distribution functions from height equals zero to height
equals thirty mm produced the total forces shown in Table 4. Adding the tangential and
axial force vectors produced a total resultant force of almost twenty-nine pounds-force
(lbf) per stator. Although this appears to be a rather small force on first inspection, one
must remember that the TVSS supports thirty modules of two stators each. Therefore,
the TVSS and casing of the T56 support over 1700 lbf exerted by the combustion flow.
Table 4. Calculation of Total Force
Total calculated tangential force [lbf]: 17.42
Total calculated axial force [lbf]: -23.07
Resultant force on each stator [lbf]: 28.91
Total stator modules around the TVSS [#]: 30
Stators per module [#]: 2
Total force [lbf]: 1735

43. 32
IX. Static Analysis
9.1 Motivation
The next major step in the analysis was to determine how the forces and moment
acting on the stator vanes translated into forces acting on the TVSS. Fundamentally, the
loading on the stator vanes was three-dimensional, as shown in Figure 18 for one stator
module. Additionally, complicated reaction forces existed due to the interaction between
the stator vane, TVSS, and T56 casing, as shown in Figure 19 for a single vane. The
project team quickly realized that to the complexity of the loading condition on the TVSS
would require several simplifying assumptions to be manageable.
Figure 18. Stator Vane loading, as resulted from CFD modeling.
F Total, axial
M Total
F Total, tangential
F Total, tangential
F Total, axial
M Total

44. 33
Figure 19. Single Stator Vane reaction forces from the T56 casing and TVSS.
To simplify the load analysis, the project team decided to separate the 3-D loading
condition on the stator vanes into three 2-D static loading cases. Within each case, the
reaction forces from both the TVSS and casing were located to help simplify the analysis,
since their true point of application was unknown. To simplify the calculations further,
the connection between the stator vane and casing was reduced to a simple pivot,
providing no resistance to bending. The project team invoked this assumption to simulate
a worse case scenario, whereby the TVSS flange would be required to support all of the
forces and moments acting on the stator vanes.
F casing, axial
F TVSS, axial
F casing, tangential
F casing, radial
F TVSS, tangential
F TVSS, radial
F Total, axial
M Total
F Total, tangential

45. 34
9.2 Static Load Calculations
As mentioned before, the 3-D load condition determined through the CFD
analysis of the first-stage stators was simplified by separating the problem into three 2-D
cases. For example, viewing a single stator vane along the tangential direction gives the
loading condition shown in Figure 20. Note that Figure 20 represents a statically
indeterminate problem. That is, there are four unknown forces (Fcasing, radial, Fcasing, axial,
FTVSS, radial, and FTVSS, axial) and only three governing equations (∑ = 0axialF ,∑ = 0radialF ,
and ∑ = 0M ).
Figure 20. Single Stator Vane static loading condition in the
axial direction.
Allowing the stator vane to pivot at location A eliminates the effect of both the
radial and axial force from the casing through summation of the moments about A.
F casing, radial
F Total, axial
A
F TVSS, axial
F TVSS, radial
B
F casing, axial

46. 35
However, if the stator vane pivots at location A, an additional force is generated by the
stator tang twisting within the TVSS flange, as shown in Figure 21. The project team
termed this the “buckle” condition. This additional reaction force once again makes the
problem indeterminate due to there being only one available equation and two unknown
forces. Incorporating this force and summing the moments about A gave:
( )321,22,1,:0 LLFLFLFM axialTVSSaxialTVSSaxialTotalA +⋅=⋅+⋅=∑ (1)
Figure 21. Stator Vane pivot and lever action reaction forces.
F TVSS, axialF TVSS, radial
B
A
F Total, axial
F TVSS, axial 2
L1
L2
L3
F casing,
F casing, radial

47. 36
Approaching the problem from the point of view of the TVSS proved to be the
key to solving for both of the axial forces shown in Figure 22. Envisioning a pivot point
located on the TVSS where it bolts to the T56 provides one additional equation
(∑ = 0CM ) relating the unknown forces.
Figure 22. TVSS reaction axial forces.
F TVSS, axial 1
F TVSS, axial 2
C
B
L4
L3

48. 37
Summing the moments about location C gave:
( ) 41,432,:0 LFLLFM axialTVSSaxialTVSSC ⋅=+⋅=∑ (2)
Solving equation (2) for FTVSS, axial 2 gave:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
⋅=
43
4
1,2,
LL
L
FF axialTVSSaxialTVSS (3)
Substituting equation (3) into equation (1) and solving for FTVSS, axial 1 gave:
( )321,
43
42
1,1, LLF
LL
LL
FLF axialTVSSaxialTVSSaxialTotal +⋅=⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
⋅
⋅+⋅
( ) ⎥
⎦
⎤
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
⋅
−+⋅=⋅
43
42
321,1,
LL
LL
LLFLF axialTVSSaxialTotal
( )
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
⋅
−+
⋅=
43
42
32
1
,1,
LL
LL
LL
L
FF axialTotalaxialTVSS = 10.4 lbf
Substituting the value for FTVSS, axial 1 into equation (3) gave:

49. 38
2, axialTVSSF = 3.2 lbf
Similar to the total axial force, the total tangential force calculated by FLUENT
creates a reaction force on the TVSS. Figure 23 shows the vane when viewed along the
axis of the T56.
Figure 23. Stator Vane tangential force TVSS reaction force.
Again, summing the moments about location A eliminated the effects of the forces from
the casing, and gave:
,:0 TotalA FM∑ = tangential ,5 TVSSFL =⋅ tangential 2L⋅ (5)
Fcasing, radial
Fcasing, tangential
F Total, tangential
F TVSS, radial
F TVSS, tangential
A
L5
L2

50. 39
Rearranging equation (5) and substituting in known values gave:
,TVSSF tangential = 7.65 lbf
The total moment calculated by FLUENT creates two reaction forces on the
TVSS, as shown in Figure 24. The project team termed this the “twist” condition
because the tang of the stator vane rotates within the TVSS flange. These reaction forces,
F TVSS, axial 3 and F TVSS, axial 4, are the forces most likely to be responsible for the wear
occurring in the flange of the TVSS.
Figure 24. Stator Vane twist condition due to moment.
F TVSS, axial 3
F TVSS, axial 4
M Total
A
L6
L7

51. 40
Summing moments about A gave:
TotalaxialTVSSaxialTVSSA MLFLFM =⋅+⋅=∑ 74,63,:0 (6)
Assuming that there are no additional forces along line A, which is consistent with the
worst-case scenario formulation, and summing the forces in the axial direction gave:
4,3,:0 axialTVSSaxialTVSSaxial FFF ==∑ (7)
Substituting equation (7) into equation (6) and substituting in known values gave:
== 4,3, axialTVSSaxialTVSS FF 235.0 lbf
9.3 Establishment and Loading of 2-D Sections
Once the reaction forces acting on the TVSS were determined, the project team
sought a way to apply the loads to 2-D FEMs of the TVSS flange area. To accomplish
this, a section of the TVSS wide enough to accommodate a single stator module was
discretized into six different cross-sections, with each representing a potential location of
peak stress. Figure 25 shows the location of the selected cross-sections.

52. 41
Figure 25. Six separate cross section implementation.
The loading on each cross-section was determined by superimposing the static loads
calculated previously. However, the loads applied to the TVSS are not point loads as in
the static analysis; they are distributed lines of load and pressures. For example, FTVSS,
axial 1 and FTVSS, axial 2 are distributed along the top and bottom inside surfaces of the flange
area, as shown in Figure 26. Note that cross-sections CC and DD do not experience these
forces because of the absence of the upper flange at those locations.
E
EF
F
D
D
A
A
B
B
C
C

53. 42
Figure 26. Image of buckle condition inside TVSS slot guide.
Forces FTVSS, axial 3 and FTVSS, axial 4 are very similar except that they are distributed
along the width of the flange, as shown in Figure 27. Note that cross-sections CC and EE
do not experience these loads because of the flange cutout.
F TVSS, axial 2
F TVSS, axial 1

54. 43
Figure 27. Image of twist condition inside TVSS guide slot.
In general, we were not concerned with forces such as ,TVSSF tangential because they act along
the inside surfaces of the flange area and could not be modeled in the 2-D FEM analysis.
To address the static loading condition assuming no bending, the project team
calculated a pressure acting on the back inside face of the flange area due to the total
axial force calculated by FLUENT. Referring to Figure 20 and assuming that the casing
provides no resistance to the total axial force, then the force acting on the back inside
surface of the flange area has the same magnitude as the total axial force. However, this
reaction force is distributed over the entire surface of contact between the TVSS flange
and stator vane tang, and was labeled Paxial as shown in Figure 28. A pressure was also
established to reflect the 140-psia pressure acting on the front face of the TVSS within
the T56, also shown in Figure 28.
F TVSS, axial 3
F TVSS, axial 4

55. 44
Figure 28. Image of pressure affecting TVSS surfaces.
Finally, using the forces determined previously and the distribution schemes
discussed above, the project team determined the loading condition for each of the six
cross-sections. Figures 29 through 34 show the distributed loads and pressures applied
the inside surfaces of each cross-section.
Figure 29. Loading on section AA
Buckle Condition
Axial Pressure
140 psia
Paxial

56. 45
Figure 30. Loading on section BB
Figure 31. Loading on section CC
Buckle Condition
Axial Pressure
Twist Condition
Axial Pressure

57. 46
Figure 32. Loading on section DD
Figure 33. Loading on section EE
Axial Pressure
Twist Condition
Buckle Condition
Axial Pressure

58. 47
Figure 34. Loading on section FF

59. 48
X. 2-D Finite Element Modeling
10.1 Formulation of 2-D FEMs
With the loads on the TVSS flange and their application points determined, the
next step was to import the 2-D cross-sections into the finite element software ANSYS.
For each section, the model was constrained to have zero degrees of freedom (DOF) at a
certain location, as shown in Figure 35. This line represents the location of a bolthole
through which the actual TVSS is bolted to the T56.
Figure 35. TVSS 2-D cross-section with constraints.
Once imported and constrained, the calculated forces and pressures were applied
to each model as shown in Figures 29 through 34. The project team then meshed each
model using 10-node tetrahedral elements, as recommended by the ANSYS reference
guide [23]. The mechanical properties of the TVSS material, as shown in Table 1 were
inputted and the models were then solved in ANSYS to obtain first approximations to the
DOF constraint
TVSS
cross-section

60. 49
location and magnitude of the peak stress within each cross-section. Similar to the CFD
analysis, a grid independent study was conducted on a representative model to ensure that
the results of the FEM were independent of the mesh density used.
10.2 Grid Independent Study
Just as for the CFD analysis, a grid independent study within the FEM served two
purposes: first, it provided proof that the result of each case was converged on the true
solution, independent of the mesh density employed; secondly, it enabled the project
team to select the coarsest mesh possible while ensuring results within a specified error
tolerance. In general, a grid independent study allows the user to strike a balance
between the quality of results obtained and the amount of computer time and memory
required to solve the model. The project team focused their grid independent study on a
representative model of a 2-D cross-section of the TVSS, using keypoints in several
critical locations, such as the interior corners of the TVSS flange, to determine the stress
at those locations. Figure 36 shows stresses at selected keypoints as a function of mesh
density, where the increasing mesh number corresponds to increasing mesh density. The
data used in the 2-D grid independent study can be found in Appendix F.

61. 50
Figure 36. Results of the 2-D FEM grid independent study on a representative TVSS
cross-section
Clearly, the results are converged for meshes ten through fourteen. Therefore, the
project team selected a mesh density near mesh ten (element edge length of 0.03 in),
which they believed represented a good balance between accuracy and computational
requirements.
10.3 2-D FEM Results
Once the proper mesh density was determined, the six cross-sections were each
meshed with an element size necessary to obtain a similar density and then run through
the ANSYS solver. Figure 37 shows the results for section BB, which are representative
converged
results
un-converged
results

62. 51
of many of the 2-D cross-sections. In general, the results of 2-D analysis did not fit with
the project team’s engineering judgment.
Figure 37. Contours of von Mises stress on section BB.
One of the major concerns with the results of the 2-D analysis, like that shown in
Figure 37, was that the peak von Mises stress for the models was significantly beyond the
yield strength of the TVSS material. Maximum-distortion-energy theory contends that
when the von Mises stress (also called the “equivalent” stress, σe) exceeds the tensile
yield strength of the material, plastic yielding is predicted [24]. The 2-D FEM results
maximum von Mises
stress [psi]
constraint
location

63. 52
indicated that the TVSS would yield under the forces determined from the static analysis,
and therefore could not support the removal of any material from the flange area.
Additionally, the results showed that the maximum stresses were located near
where the model was constrained at the location of the boltholes; there appeared to be
minimal stress near the flange area. Clearly, because the wear on the actual TVSS is
occurring in the flange area, and because the TVSS is not yielding during normal use,
these results were not realistic. Therefore, the project team determined that the 2-D FEM
models were not able to simulate the reaction of the TVSS accurately. This was probably
due to the inability of the 2-D cross-sections to spread stress continuously within the
TVSS. Consequently, the project team turned to a full 3-D FEM of the TVSS.
XI. 3-D Finite Element Modeling
11.1 Formulation of 3-D FEM
Similar to the 2-D cross-sections, a twelve-degree, 3-D slice of the TVSS was
imported into the ANSYS software and constrained at the location of the boltholes.
However, the 3-D nature of the model required additional constraints on the sectioned
surfaces, as shown in Figure 38. The project team chose to apply a symmetry boundary
condition to the sectioned surfaces to simulate the influence of neighboring material.
Simply put, the symmetry boundary condition allows a slice portion of the TVSS to

64. 53
simulate the entire disk, thereby significantly reducing computational time and memory
required for the FEM.
Figure 38. 3-D modeled portion of the TVSS.
Once the 3-D model was constrained and boundary conditions assigned, the
model was meshed using 8-node brick elements, as recommended by the ANSYS
reference guide [23]. To facilitate a direct comparison between the 2-D and 3-D models,
the project team initially utilized a simple loading condition, identical to the loading
applied to section BB of the 2-D analysis (shown in Figure # 30). The initial results of
the 3-D analysis indicated that the project team’s suspicions about the shortfalls of the 2-
D model were correct. Figure 39 shows that for the section BB loading condition applied
to the 3-D FEM, the 3-D TVSS model predicted peak stresses near the flange and
symmetry
boundary condition
on sectioned surfaces
DOF constraint

65. 54
minimal stress near the constraint. This result fit more with the team’s engineering
judgment, and motivated the team to continue with the 3-D analysis.
Figure 39. 3-D TVSS subjected to section BB 2-D loading.
11.2 3-D Grid Independent Study
Similar to the CFD analysis and the 2-D FEM, the team attempted to perform a
grid independent study of the 3-D model. However, the range of element sizes available
to the team was severely limited. Too large of an element size eliminated the fine detail
within the flange area and prompted warnings from the ANSYS software; too small of an
minimal
stress near
constraint
maximum
stress in
flange area

66. 55
element size severely protracted meshing and solution, sometimes causing the model to
exceed the computational memory limits (six gigabytes) available to the project team.
Despite these complications, Figure 40 shows that over the workable range of element
sizes the peak stress at selected points in the model did not change significantly. Similar
to the 2-D grid independent study, increasing mesh number in Figure 40 signifies
decreasing element edge length and increasing mesh density. Therefore, the project team
selected an element with edge length of 0.04 in which resulted in the model containing
117,570 elements. The data used in the 3-D grid independent study can be found in
Appendix G.
Figure 40. Results of 3-D grid independent study of the modeled TVSS section.

67. 56
11.3 3-D FEM Results
After the selection of the proper element size, the team applied all of the loads
determined through the static analysis at the appropriate locations. The model was then
allowed to reach solution. Figure 41 shows contours of von Mises stress across the
modeled part. Consistent with the simplified 3-D analysis used in the grid independent
study, the final model displayed high stress concentration in the flange area and lower
stress concentration in the area of the constraint. Additionally, as shown in Figure 42, the
model exhibited a zero tang-slope at the sectioned surfaces, indicating that the symmetry
boundary condition was a proper assumption.
Figure 41. von Misses stress contours on 3-D TVSS.
minimal
stress near
constraint
maximum
stress in
flange area

68. 57
Figure 42. Contours of von Mises stress within the flange area.
While the results of the full 3-D analysis seemed more realistic, Figure 41 shows
that the peak von Mises stress predicted by ANSYS still exceeded the yield strength of
the TVSS material. This result implied that the project team’s assumption that the TVSS
supports the whole of the load from the first-stage stators was overly conservative.
Therefore, without better information about the loading condition on the TVSS, this
analysis cannot provide information of any engineering quality to determine the
maximum amount of material that can be removed from the flange surface of the TVSS.
Further, since there is no simple way of determining how the load on the stators is
zero tang-slope
maximum
von Mises
stress [psi]

69. 58
distributed between the TVSS and T56 casing, any scaling of the calculated loads (say, to
fifty percent of their current value) to prevent yielding in the FEM would be completely
arbitrary. The degree of scaling would implicitly determine the maximum machining
depth, an idea that completely undermines the validity of the FEM.
XII. Conclusion
In general, the project team feels that the preceding report represents a thorough
analysis of the TVSS, utilizing a modern and robust methodology. The project team
worked to determine the boundary conditions of the combustion gas flow through the
first stage stators. These boundary conditions were then implemented in a simplified, yet
thorough, 2-D CFD analysis of the gas path that calculated the forces acting on the stator
vanes.
The CFD analysis resulted in a distribution of axial and tangential forces, as well
as a moment, acting on a single vane. Integrating the force and moment distributions
created total effective forces, which were utilized in a static analysis of the stator
vane/TVSS interaction to determine the forces acting on the TVSS flange.
Believing a 2-D analysis would be sufficient, the project team sectioned the TVSS
flange into six different cross-sections, each representing a potential area of peak stress.
Using the principle of superposition, the forces were then applied to each section either as
point loads, distributed line loads, or pressures. The sections were then solved in

70. 59
ANSYS. The results from the ANSYS solver indicated that the TVSS was severely
plastically yielding under the applied loads. However, the project team felt that this
result was an indication of the limitation of the 2-D FEM. The team then decided to
move to a 3-D model of the TVSS, which they believed had the potential to deliver a
more realistic solution.
A 3-D model of a section of the TVSS was created, imported into the ANSYS
software, and loaded with the forces determined through the static analysis. Although
more physically realistic, the results of the 3-D FEM analysis also indicated that the
TVSS was plastically yielding under the applied loads. This result implied that the
project team’s assumption that the TVSS accepts all of the force from the first-stage
stator vanes was overly conservative. Unfortunately, due to there being no definitive way
to determine how much of the load was supported by the casing of the T56, this analysis
could not predict the amount of material available to be removed from the TVSS flange.
Therefore, the final step of the project team’s work is to recommend future work for this
project that may facilitate the creation of a more realistic and accurate model of the TVSS
XIII. Recommendations
The project team recognizes that the determination of forces acting of the TVSS,
as well as the response of the 3-D FEM, used in the preceding analysis are gross
approximations of the actual physical phenomena. Unfortunately, due to time constraints

71. 60
the project team is unable to see the project to its rightful conclusion. However, we
believe several courses of action, if implemented in future projects, will result in a much
more accurate determination of the amount of machining that can be performed on the
flange surface of the TVSS.
First, an FEM of at least one module of first stage stator vanes should be
generated, simulating not only its temperature dependent mechanical properties, but also
its structural properties such as moment of inertia. This will be a very difficult modeling
task due to complicated features of the stators, such as the internal cooling passages, that
undoubtedly affect the structural characteristics of the vanes. The 3-D FEMs of the
TVSS and stator module should then be interconnected with each other, modeling the
actual interfacing of these components. The steady-state loads calculated by the CFD
analysis of the combustion gas path could then be directly applied to the stator model.
Creating such a model would help to eliminate the need for manual-determination of the
location and magnitude of forces applied to the TVSS from the stator vanes. Contact
elements available within the ANSYS software may aid in this task.
Unfortunately, modeling the contact between the TVSS and first stage stators will
also add a series of complicated and unpredictable phenomena to an already difficult
problem. For example, the static and dynamic coefficients of friction between the TVSS
and stator materials must be determined in order to model the frictional forces created by
the tangential force imposed on the stators by the combustion flow. Similarly, friction
between the two sections of the bottom tang of the stator module due to the angular
deflection of the vane under the moment created by the flow must be more fully
understood.

72. 61
Additionally, modeling the stator-TVSS interaction will require a much more
complete determination of the extent of structural support provided to the stator module
by the casing of the T56. In fact, the project team believes that a significant portion of
the load on the stators created by the impinging flow is supported at the outer connection
between the stator module and casing. If these and the frictional effects were dealt with
in a conscientious and conservative manner, the project team believes that a very accurate
model of the stator-TVSS interaction could be created.
Another major milestone in the future of this project would be to determine the
dynamic effects of vibrational loading from both the combustion gas path. The preceding
CFD analysis assumed a steady-state flow condition for simplicity. However, even a
brief review of current gas turbine modeling research will show that the velocity of the
combustion flow through the first stage stators is inherently unsteady. In fact, recent
research has shown that the peak dynamic forces acting on the stators may be as much as
thirty percent greater than the average forces. The time-dependence of the flow is
primarily due to pressure interactions between the stators and neighboring rotor blades,
but other more complicated flow phenomena undoubtedly play a role.
Although unsteady, the flow fluctuations are periodic, and this fact could aid the
creation of a more thorough, and yet still simplified, 2-D CFD model of one complete
stator-rotor interaction. Such a model could build on the current work by incorporating
either a rotor blade passing across the outlet of the current model or by prescribing a
time-dependent static pressure at the outlet of the current gas path model. Simply
incorporating a model of a first-stage rotor blade may be simplest solution because it
would not require the amplitude of pressure fluctuation to be determined a priori.

73. 62
A significantly more thorough CFD analysis might incorporate modeling the
combustion gas path in three dimensions to eliminate estimation of the force and moment
distribution curves across the height of the stator vanes such as was used in the preceding
analysis. Additionally, a 3-D CFD model of the stator module could serve to determine
the temperature distribution across the vanes. The preceding analysis utilized a constant-
surface-temperature assumption and neglected the internal cooling of the vanes for
simplicity. Current gas turbine modeling research has shown that the temperature
gradients across the height of the first stage stators are significant and vary in all three
dimensions.
The determination of the temperature distribution across the vanes would aid the
modeling of the mechanical properties of the stator material in the FEM, as well as the
conduction heat transfer occurring into the TVSS from the stator module tang. Better
knowledge of the heat transfer phenomena would allow for a better determination of the
temperature of the flange area of the TVSS, and therefore its thermally dependent
mechanical properties used in the FEM. Unfortunately, a 3-D simulation of the
combustion gas path, especially if it incorporated unsteady loading and heat transfer
analysis, would be extremely computationally intensive.

74. 63
XIV. References
1. Moran, M.J., and Shapiro, H.N., 1999, Fundamentals of Engineering
Thermodynamics, Wiley, John & Sons, Inc., New York, New York
2. “Rolls-Royce,” www.rolls-
royce.com/defence_aerospace/downloads/tactical/t56.pdf, accessed Sept 8, 2004.
3. “Standard Aero,” http://www.standardaero.com/, accessed Sept 3, 2004.
4. “Standard Aero, Rolls-Royce T56/501D,” http://www.standardaero.com/t56.asp,
accessed Sept 19, 2004.
5. “Standard Aero Awarded Multi-Million Dollar Contract for US Navy T56 Engine
Maintenance,” http://www.standardaero.com/news/2004/t56_usn_contract.asp,
accessed Sept 3, 2004.
6. Personal Communication with Dave Crowley, Director, Project Engineering,
Standard Aero San Antonio, Inc., Sept 14, 2004.
7. Personal Communication with Mike Zoch, Repair Development Engineer,
Standard Aero San Antonio, Inc., Sept 14, 2004.
8. Simmons, H.R., “Gas Turbine Technology Experience,”
http://www.swri.edu/4org/d18/mechflu/planteng/gasturb/gtexp.htm, accessed
October 15, 2004.
9. Cheruve, S., “Gas Turbine Technology,”
http://www.swri.edu/3pubs/brochure/d04/turbn/turbn.htm#Failure%20Analysis ,
accessed October 15, 2004.
10. Holzmann, W.A. and Wagner, V.J., 1996, “Shape Optimization of a Cast Turbine
Manifold,” Paper Number 21, 1996 World Users Conference, 3.
11. Lethander, A.T., Thole, K.A., Zess, G. and Wanger, J., June 16-19, 2003,
“Optimizing the Vane-Endwall Junction to Reduce Adiabatic Wall Temperatures
in a Turbine Vane Passage,” Proceeding of ASME Turbo Expo 2003 Power for
Land, Sea, and Air, Atlanta, Georgia, pp.1,2,4-10.
12. Zess, G.A. and Thole, K.A., 2002, “Computational Design and Experimental of
Using a Leading Edge Fillet on Gas Turbine Vane,” Journal of Turbomachinery

75. 64
April 2002 by ASME, 124, pp. 167,169-174.
13. Stoloff, N.S., 1995, “Iron-Based Superalloys,” ASM Metals Handbook, 1, pp.
959-965.
14. Stoloff, N.S., 1995, “Nickel-Based Superalloys,” ASM Metals Handbook, 1, pp.
950-959.
15. “A-286 Technical Data,”
http://www.hightempmetals.com/techdata/hitempA286data.php, accessed October
29, 2004.
16. Fox, R.W., and McDonald, A.T., 1998, Introduction to Fluid Mechanics, Wiley,
John & Sons, Inc., New York, New York.
17. Incropera, F.P., and DeWitt, D.P., 2001, Fundamentals of Heat and Mass
Transfer, Wiley, John & Sons, Inc., New York, New York.
18. Personal Communication with DongMei Zhou, Lecturer, Department of
Mechanical Engineering, The University of Texas at Austin, October, 4, 2004.
19. Personal Communication with Dr. David Bogard, Professor, Department of
Mechanical Engineering, The University of Texas at Austin, October 28, 2004.
20. FLUENT, Inc., 2003, “FLUENT Tutorial 4: Modeling Unsteady Compressible
Flow,” FLUENT, Inc., New York, New York.
21. FLUENT, Inc., 2003, “FLUENT Tutorial 3: Modeling External Compressible
Flow,” FLUENT, Inc, New York, New York.
22. Personal Communication with Dr. David Bogard, Professor, Department of
Mechanical Engineering, The University of Texas at Austin, October 29, 2004.
23. ANSYS, Inc., “ANSYS Release Documentation,” accessed October 30, 2004.
24. Juvinall, C., and Marshek, K.M., 1999, Fundamentals of Machine Component
Design, Wiley, John & Sons, Inc., New York, New York

76. A-1
Appendix A
Solving for Ratio of Specific Heats “k”
For our choked flow correlated equations, the following two input variables were
required: the Mach number and the ratio of specific heats, denoted by “k.” The method
for arriving at the Mach number is discussed in Appendix B. Nominally, when dealing
with air as the working fluid at STP, k is equal to about 1.4. However, since k is a
temperature dependent variable, we decided to solve for k using a Brayton Cycle Model
of the T56 gas turbine. This model employs ideal gas and isentropic flow behavior, and
uses the compressor’s compression ratio. Therefore, the model is independent of the
number of stages in the compressor. The model also incorporates isentropic conditions,
meaning there is no entropy production. For this reason, we assumed that the compressor
has 85% thermodynamic efficiency and the turbine has 90% thermodynamic efficiency.
The efficiency was determined through an iterative process until the horsepower
generated by the model approximated the horsepower of the T56. The basic calculation
of the Brayton Cycle Model is that the total work generated by the gas turbine is equal to
the change of enthalpy across the turbine, subtracted from the change in enthalpy across
the compressor and then multiplied by the mass flow rate. The following equation
represents this calculation [1]:
( ) ( )4321 hhmhhmworknet −−−= && (1)

77. A-2
Then from the definition of the constant pressure specific heat, over small temperature
differences we have:
T
h
cp
∆
∆
= (2)
Combining equations (1) and (2) yields:
( ) ( )[ ]4321 TTTTCmwork pnet −−−= & (3)
From equation (3) we can see that the net work can be found by simply knowing the
temperature change across the compressor and turbine, and by assuming constant Cp.
However, in our model, we decided to be more accurate. Therefore, we calculated Cp as
a function of temperature. This variation of the model calculates a more accurate result.
We used the following function for Cp, where the constants were determined by assuming
air as the working fluid [1]:
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
Μ
⋅++++=
R
TTTTcp
432
εδχβα
Calculations for Cp used a different temperature for each stage. That is T1, T2, T3, and T4,
where T1 is the inlet to the compressor, T2 is the compressor outlet, T3 is inlet to the
turbine, also known as TIT, and T4 is the turbine outlet. To find the unknown

78. A-3
temperatures T2 and T4, we used the following equation for isentropic compression:
⎟
⎠
⎞
⎜
⎝
⎛ −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅=
k
k
P
P
TT
1
1
2
12 (4)
Equation (4) was similarly used to find T4. Now since:
M
R
cc pv
−= (5)
Substituting equation (5) into the definition of k gave:
M
R
k
c
c
c
c
p
p
v
p
−
==
From this equation, k was determined to be 1.31 J/kg K at the inlet to the first-stage
stators.

79. B-1
Appendix B
Iterating Mach number
As stated in Appendix A, the Mach number at the inlet to the stator vanes was a
required input for the CFD software. Assuming that the stator vanes behave as a
converging-diverging nozzle, we were able to employ the following equation, which
correlates the Mach number with the area ratios of a converging-diverging nozzle [16].
( )
( )
( )
M
M
k
k
A
A
k
k
k
k
12
1
2
12
1
*
2
1
1
2
1
−
+
−
+−
⎟
⎠
⎞
⎜
⎝
⎛
⋅
−
+
⋅⎟
⎠
⎞
⎜
⎝
⎛ +
=
Using k, which was found in Appendix A, and the area ratios taken from the engineering
drawings supplied by Standard Aero, we developed a Matlab model. The code is given
here:
A = 9.6; % inlet area
B = 3.6; % throat area
k = 1.314; % k from appendix A
M = 0.25; % inital guess
for i=1:100
C = (1/M)*((1+((k-1)/2)*M^2)/(1 + ((k-1)/2)))^((k+1)/(2*(k-1)));
if abs(C-(A/B))>0.001
M = M + 0.001;
elseif abs(C-(A/B))<0.001
M
i=100;
end
i = i+1;
end
while abs(C-(A/B))>0.001
M = M
M
The iteration yielded a Mach number of 0.266 at the inlet to the first stage stators.

80. C-1
Appendix C
CFD Problem Setups
Because of the complicated nature of CFD modeling, it is essential for the
problem setup to be presented in addition to the resulting data. All of the CFD analysis
conducted for this report was done in FLUENT, a very common software package.
Although the project team does not claim to be experts in CFD modeling and analysis, we
have had the opportunity to work on a variety of real-world problems and have had the
advantage of discussing our results with several professors within the Mechanical
Engineering department that have vast experience in CFD modeling (see references 12
and 13). Additionally, several FLUENT tutorials were utilized as models for these
problem setups (see references 14 and 15).
The following tables explain the problem setups we used in the analysis of each
cross-section of the 2D gas path. Refer to Figure 5 for the location of each cross-section
on the stator module.

81. C-2
Table C.1. FLUENT Problem Setup for Cross-Section AA

82. C-3
Table C.2. FLUENT Problem Setup for Cross-Section CC

83. C-4
Table C.3. FLUENT Problem Setup for Cross-Section EE

84. D-1
Appendix D
CFD Grid Independent Study Data
The purpose of the grid independent study is to demonstrate that the calculated
data is primarily independent of the resolution of the mesh used in the analysis.
Generally, finer meshes are desirable; however, too fine of a mesh can produce erroneous
results due to the accretion of round-off errors associated with the computer’s
calculations in each element. The following data was created by FLUENT when
analyzing the 2D gas path cross-sections with the additional inlet section discussed in this
report. This is the data used to create Figures 11 and 12. Refer to Figure 5 for the
location of each cross-section on the stator module. Note that the net forces were
computed on the left and right stator walls, as shown in Figure 6, and that forces are for a
section depth (into the page) of one meter. Below the data, the mesh identification
describes the unique mesh that was created for each case in GAMBIT.
Table D.1. Data for Section AA
Section AA Altered Meshes (big top) outlet pressure = 760kPa
Mesh ID: AA-5 AA-6 AA-7
Num of Cells [#]: 22,458 19,216 26,202
Area of section [m^2]: 0.000570 0.000570 0.000570
Cell Density [cells/m^2]: 39,406,167 33,717,255 45,975,947
Max. Mach [dim-less]: 0.95 0.92 1.05
Max Velocity Mag. [m/s]: 627.27 609.56 681.46
Min. Static Press [Pa]: 485,356.70 500,969.90 434,748.90
Min. Static Temp [K]: 1,056.60 1,056.60 1,056.60
Total x-force (1 0 0) [N]: 2,181.21 2,272.85 2,189.31
Total y-force (0 1 0) [N]: -2,952.97 -3,174.84 -2,943.02
Mesh ID: selected data
AA-5 T,B = 75; L,R = 130; TL,TR = 75
AA-6 T = 50; B = 120; L,R = 120; TL,TR = 50
AA-7 L,R = 140; T,B = 75; TL,TR = 75

85. D-2
Table D.2. Data for Section CC
Section CC Altered Meshes (big top) outlet pressure = 740kPa
Mesh ID: CC-1 CC-2 CC-3
Num of Cells [#]: 21,896 28,330 23,948
Area of section [m^2]: 0.000623 0.000623 0.000623
Cell Density [cells/m^2]: 35,119,150 45,438,980 38,410,614
Max. Mach [dim-less]: 1.04 1.07 1.10
Max Velocity Mag. [m/s]: 678.59 694.23 708.90
Min. Static Press [Pa]: 423,534.10 428,302.30 413,498.20
Min. Static Temp [K]: 1,056.60 1,056.60 1,056.60
Total x-force (1 0 0) [N]: 2,680.89 2,654.25 2,685.94
Total y-force (0 1 0) [N]: -3,580.09 -3,536.53 -3,577.88
Mesh ID: selected data
CC-1 L,R = 130; B = 120 @ 1.01 ratio; TL,TR = 50 @ 1.05 ratio; T = 50
CC-2 L,R = 140; B = 120; TL,TR = 75; T = 50
CC-3 L,R = 140; B = 120; TL,TR = 50 @ 1.05 ratio; T = 50
Table D.3. Data for Section EE
Section EE Altered Meshes (big top) outlet pressure = 750kPa
Mesh ID: EE-5 EE-6 EE-7
Num of Cells [#]: 21,853 23,996 29,164
Area of section [m^2]: 0.00067 0.00067 0.00067
Cell Density [cells/m^2]: 32,569,833 35,764,263 43,466,785
Max. Mach [dim-less]: 0.82 1.11 1.02
Max Velocity Mag. [m/s]: 556.00 714.43 665.96
Min. Static Press [Pa]: 571,148.30 391,066.20 445,091.00
Min. Static Temp [K]: 1,056.60 1,056.60 1,056.60
Total x-force (1 0 0) [N]: 2,705.65 2,739.27 2,737.67
Total y-force (0 1 0) [N]: -3,557.21 -3,486.80 -3,499.03
Mesh ID: selected data
EE-5 L,R = 120; B = 131; TL,TR = 50 @ 0.95 ratio; T = 50
EE-6 L,R = 140; B = 100; TL,TR = 50 @ 0.95 ratio; T = 50
EE-7 L,R = 140; B = 100; TL,TR = 75 @ 0.98 ratio; T = 50

86. E-1
Appendix E
CFD Parameter Studies
A thorough CFD analysis always tests the effects of parameters on the resultant
data. This is especially important in instances when the modeler is not familiar with the
meaning or importance of the parameter. For example, because of the project team’s
inexperience with turbulence theory, we were unfamiliar with the turbulence-viscosity
ratio used in the Spalart-Allmaras turbulence model. One FLUENT tutorial stated that
“for low to moderate…turbulence, a viscosity ratio of 1 is recommended” [14].
Additionally, the FLUENT user’s guide indicated that highly turbulent flows have a
turbulence-viscosity ratio closer to ten, the maximum value. Although our analysis
utilized an inlet turbulence-viscosity ratio of ten, Table E.1 shows that the effects of inlet
turbulence-viscosity ratio were negligible for the analysis.
Table E.1. Data for Parameter Study of Inlet Turbulence-Viscosity Ratio
Inlet Turbulence-Viscosity Ratio: 10 5 1
Num of Cells [#]: 9984 9984 9984
Maximum Mach [dim-less]: 1.469994 1.470723 1.471515
Maximum Velocity Magnitude [m/s]: 913.1705 913.5669 913.9566
Minimum Static Press [Pa]: 267449.3 267611.4 268367
Minimum Static Temp [K]: 995.5983 995.5393 996.0556
Total x-force (1 0 0) [N]: 4824.1305 4823.9661 4833.8856
Total y-force (0 1 0) [N]: -8127.8232 -8126.0063 -8130.6153
The effects of outlet static pressure on the model were also tested. Although it is
intuitive that the outlet static pressure would be an important parameter for non-choked
flows, we discovered that FLUENT was also dependent on the outlet static pressure

87. E-2
entered by the user for choked and supersonic flows. An initial guess at a value for outlet
static pressure produced results produced a maximum flow Mach number of about 1.5.
Clearly, this did not fit with the choked flow assumption. The data in Table E.2 is for
cross-section CC (refer to Figure 5 for section definitions) and represents the iterative
approach we used to determine the outlet static pressure that would cause a maximum
Mach number of unity in the flow. The outlet static pressure for each cross-section was
determined independently because each required a unique static pressure to produce a
choked flow situation. The final values for outlet static pressure used in the modeling are
shown in the problem setups in Appendix C.
Table E.2. Data for Parameter Study of Outlet Static Pressure
Outlet Static Pressure [Pa]: 400,000 600000 700000 737500 750000
Num of Cells [#]: 9984 9984 9984 9984 9984
Maximum Mach [dim-less]: 2.134745 1.407972 1.236832 1.03617 0.9379613
Maximum Velocity Magnitude [m/s]: 1007.8410 880.5545 795.7304 673.5861 614.7039
Minimum Static Press [Pa]: 136261.2 279801.8 328020.7 438779.4 494908.4
Minimum Static Temp [K]: 910.8413 995.6082 1055.255 1056.6 1054.285
Total x-force (1 0 0) [N]: 5415.6925 4112.6453 3224.8261 2827.9107 2669.4183
Total y-force (0 1 0) [N]: -9839.3375 -6350.5572 -4423.8013 -3740.4163 -3514.4992
After realizing the effect of the outlet static pressure had on the results, we
decided to determine whether the inlet static pressure had the same effect. Using the
same iterative approach as the tests of outlet static pressure, the project team determined
that, surprisingly, inlet static pressure (and therefore inlet velocity) had very little effect
on the results. Table E.3 presents representative data illustrating this fact for cross-
section CC.

88. E-3
Table E.3. Data for Parameter Study of Inlet Static Pressure
Inlet Static Pressure [Pa]: 925,000 915,000 902,523.7 870,000 840,000
Num of Cells [#]: 9984 9984 9984 9984 9984
Maximum Mach [dim-less]: 1.469274 1.468934 1.469994 1.469968 1.469799
Maximum Velocity Magnitude [m/s]: 912.759 912.7406 913.1705 912.8143 913.1345
Minimum Static Press [Pa]: 267438.2 267838.8 267449.3 266904.4 267620.6
Minimum Static Temp [K]: 995.7704 994.8762 995.5983 996.2906 995.816
Total x-force (1 0 0) [N]: 4825.3723 4816.2373 4824.1305 4825.8846 4826.8843
Total y-force (0 1 0) [N]: -8131.4427 -8115.8745 -8127.8232 -8142.2085 -8130.7708
Finally, we tested the effects of adding the inlet section onto the top of the 2D
model. The project team’s original models were similar to that shown in Figure 6.
However, a discussion with a professor in the Mechanical Engineering department
encouraged us to add the inlet section so that a constant velocity (or constant static
pressure) boundary condition would be a more accurate assumption [13]. The upper
walls were set as adiabatic and frictionless for all tests, and resulted in almost no change
in the axial force on the stator surfaces. However, the added inlet section did affect the
tangential force, probably due to the increased resolution of the stagnation areas at the
nose of each stator. Because of this discovery, all of the analysis for each case was
repeated. The project team did not produce very much data from this test and so present
none here.

89. F-1
Appendix F
2-D FEM Grid Independent Study
The purpose of the grid independent study is to demonstrate that the calculated
data is primarily independent of the resolution of the mesh used in the analysis.
Generally, finer meshes are desirable; however, too fine of a mesh can produce erroneous
results due to the accretion of round-off errors associated with the computer’s
calculations in each element. Table F.1 shows the data for the 2-D study conducted for
the ANSYS model. The data shows the von Mises stresses at a set of keypoints on the
mesh body, and how these stresses changed as a function of the element size.
Additionally, the data shows the number of elements for each different element edge
length, as well as an identification number used to label each mesh in increasing order
with respect to the number of elements. This identification number made it easy to plot
the data in a meaningful manner.
Table F.1. Grid Independent Study Data for 2-D Model.
von Mises stress [psi]
Mesh
Identification
Number
Element
Edge
Length
[in]
at
keypoint
44
at
keypoint
43
at
keypoint
28
at
keypoint
24
Number
of
Elements
1 0.1 53,519 37,458 23,965 16,131 73
2 0.09 57,788 43,991 35,712 12,172 83
3 0.08 50,712 53,619 39,673 15,308 117
4 0.07 46,582 47,616 33,383 13,174 139
5 0.06 53,968 52,491 47,413 14,059 160
6 0.05 45,142 47,293 32,415 19,596 243
7 0.04 45,743 45,955 32,724 19,771 317
8 0.03 48,185 47,022 34,325 20,646 594
9 0.02 46,761 45,568 30,605 28,219 1,242
10 0.01 46,168 46,554 30,954 52,306 4,697
11 0.009 47,063 47,940 31,794 60,773 5,843
12 0.008 47,723 48,042 31,589 62,255 7,515

90. F-2
The grid independent study focused on the stresses at set of keypoints. These
keypoints were selected because they are in the region of interest for the analysis. As the
mesh density was varied for the study, these keypoints remained anchored in the same
position, where as nodes for each mesh changed locations. Figure F.1 shows the
locations of the keypoints at which stress values were compared.
Figure F.1. Locations of keypoints.
Keypoint 43
Keypoint 28 Keypoint 24
Keypoint 44

91. G-1
Appendix G
3-D FEM Grid Independent Study
The purpose of the grid independent study is to demonstrate that the calculated
data is primarily independent of the resolution of the mesh used in the analysis.
Generally, finer meshes are desirable; however, too fine of a mesh can produce erroneous
results due to the accretion of round-off errors associated with the computer’s
calculations in each element. Table G.1 shows the data for the 3-D study conducted for
the ANSYS model. The data shows the von Mises stresses at a set of keypoints on the
mesh body, and how these stresses changed as a function of the element size.
Additionally, the data shows the number of elements for each different mesh element
size, as well as an identification number used to label each mesh in increasing order with
respect to the number of elements. This identification number made it easy to plot the
data in a meaningful manner.
Table G.1. Grid Independent Study Data for 3-D Model.
von Mises stress [psi]
Mesh
Identification
Number
Element
Edge
Length
[in]
at
keypoint
57
at
keypoint
58
at
keypoint
59
at
keypoint
60
Number
of
Elements
1 0.04 68076 93990 110010 118080 117570
2 0.039 58404 95614 109110 113660 125933
3 0.038 58023 95883 110200 119310 134894
4 0.037 59205 99727 100630 114560 144092

92. G-2
The grid independent study focused on the stresses at set of keypoints. These
keypoints were selected because they are in the region of interest for the analysis. As the
mesh density was varied for the study, these keypoints remained anchored in the same
position, where as nodes for each mesh changed locations. Figure G.1 shows the
locations of the keypoints at which stress values were compared.
Figure G.1. Locations of keypoints.
Keypoint 60
Keypoint 59
Keypoint 58
Keypoint 57

93. H-1
Appendix H
Project Gantt Chart
The project Gantt chart is shown below. The team’s schedule was maintained
throughout the duration of the project, but some of individual tasks varied with respect to
the original projected chart. In particular, the steps most important to establishing
boundary conditions for each the computation fluid dynamics model, as well as for the
finite element model took longer than the team had originally projected. This was due to
the constantly increasing number of assumptions required to continue from each step of
the way. Because very little was known about the conditions inside the engine during
operation, a great deal of time had to be invested in determining what assumptions were
reasonable, and verifying that those assumptions provided the team with the best
approach to the problem. Figure H.1 below shows the final project Gantt chart.

94. H-2