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Rocket Engine System Analysis
Vinci Engine Turbines Analysis, Volvo Aero Corp.
Artyom Romanov
Division of Applied Thermodynamics and Fluid Dynamics
Linköping / Trollhättan, Sweden 2008
MASTER OF SCIENCE DEGREE PROJECT DIVISION OF MECHANICAL ENGINEERING
LIU‐IEI‐TEK‐A‐‐08/00493—SE
Major part of the
current work describes the development
of the update methodology for
one‐dimensional code (TML) currently used at Volvo Aero Corporation during turbine design process. The methodology is then applied and tried out in a general engine analysis (GESTPAN).
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ABSTRACT
During the turbine design process
different kinds of computational
tools for simulation
and optimization are widely used.
In order to perform the analysis of aerodynamic cycles as well as the optimization
for different assignments and setups,
aero‐ ant thermodynamic performances
over turbine blade rows have to be predicted as correctly as at all possible.
As the flow inside the
turbine is very complex,
the use of certain loss models
is needed
in several stages of the turbine design process. Most of the models are strictly empirical while some of them are based on experimental
results and analysis. A number of empirical models
is described in
the open literature.
The purpose of this work was to develop an update methodology of the
loss correlation by Kacker and Okapuu, currently used at Volvo Aero Corporation. The update should retain the original layout of the loss model while making it more adjusted to the given experimental data. The loss correlation has
been, and still is used in
FORTRAN90‐based one‐dimensional numerical
tool (TML)
specially developed for VAC.
The methodology has been created with a Six Sigma approach, widely using different DoE techniques and regression analysis. Main numerical tool used was Matlab v2008a. Several CFD simulations have been
performed on LH2 turbine stator
blades for a better comparison.
The use of the
obtained methodology lowers the total error as presented in Chapter 8.4.
A newer module for calculating losses in turbine exhaust duct has also been created and test‐run.
After the methodology has been developed, a newer version of TML has been used for creating LH2 and LOx turbine modules for General Engine Stationary Analysis. Several tests have been performed, varying different combinations of original and new turbine modules.
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ACKNOWLEDGMENTS
The presented work has been
carried out at Volvo Aero
Corporation site, “Turbines and
Rotors” department, Trollhättan. I would
like to express my gratitude towards Volvo Aero for giving me the possibility to perform my thesis as well as to gain the unique experience.
I would like to thank my supervisor at VAC, Sonny Andersson, for helping me to solve the problems I encountered and giving me the basic skills of Six Sigma and DoE. I would like to express my gratitude to my
examiner at LiTH, Professor Matts
Karlsson as well as to my
supervisor at LiTH,
Roland Gårdhagen for their opinions and advice. I wish to thank my bi‐supervisor Tomas Grönstedt, for his great help during the latter part of my thesis.
Special thanks go to my
colleague at VAC, Pedro
Cardoso Valente, for
sharing with me his
great programming experience as well as to Ingegerd Ljungkrona, Li Forsberg and Arne Boman who were always willing to answer my questions
Many thanks go to the entire staff of the “Turbines and Rotors” department for making my stay at Volvo Aero incredibly pleasant.
Finally, I would like to
thank my family
for giving me all their
support during my
thesis as well as during my whole life.
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NOMENCLATURE
ROMAN
Specific heat at constant pressure
Diameter Mach number
Dimensionless speed coefficient (also ,
Pressure
, Static pressure at the
plane
, Total pressure at the
plane Gas constant
Reynolds number
Temperature
Axial velocity component
Tangential velocity component
Profile loss coefficient
Secondary loss coefficient
Tip Leakage loss coefficient
Trailing Edge loss coefficient
Speed of sound
Enthalpy Mass flow
GREEK Epsilon
Total‐to‐static overall turbine efficiency
Total‐to‐total overall turbine efficiency
Density Shear stress
Rotational speed
Standard deviation Viscosity
Isentropic expansion factor
ACRONYMS BPD
Placket‐Burman Design CAD
Computer Aided Design CCD
Central Composite Design CFD
Computational Fluid Dynamics DoE
Design of Experiments DVT
Demonstration Verification Test FCCCD
Face‐Centered Central Composite design FFD
Fractional Factorial Design K&O
Kacker & Okapuu LH2
Liquid Hydrogen Turbine LOx
Liquid Oxygen Turbine TML
Turbine Mean Line VAC
Volvo Aero Corporation
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TABLE OF CONTENTS
Abstract ................................................................................................................................................... iii Acknowledgments .................................................................................................................................... v Nomenclature .......................................................................................................................................... vi List of Figures ............................................................................................................................................ x List of Tables ........................................................................................................................................... xii
1
Introduction .................................................................................................................................. 1 2
Six Sigma Basics ............................................................................................................................. 2 3
Theoretical Background: ............................................................................................................... 5
3.1
Rocket Engine Basics ............................................................................................................... 5 3.2
Expander Cycle ........................................................................................................................ 7 3.3
One‐Dimensional Program (T1D) .......................................................................................... 11 3.4
GESTPAN ................................................................................................................................ 14 3.5
DoE ........................................................................................................................................ 15 3.6
Computational Fluid Dynamics, CFD ..................................................................................... 20
4
Problem Definition ...................................................................................................................... 23 5
Measures of The Current State ................................................................................................... 24 6
Analysis and Improvement ......................................................................................................... 25
6.1
New TED‐Model Implementation.......................................................................................... 26 6.2
Modules’ Implementation ..................................................................................................... 28 6.3
TML Input Routine Update .................................................................................................... 30 6.4
DVT Data as Input and Reference ......................................................................................... 31 6.5
CFD Simulations ..................................................................................................................... 36 6.6
K&O Loss‐Model Tuning Algorithm ....................................................................................... 38
6.6.1
Strategy and Approach .................................................................................................. 38 6.6.2
Choice of The Polynomial Layout .................................................................................. 40 6.6.3
Choice of Coefficients’ Intervals .................................................................................... 40 6.6.4
Choice of The “Most Important” Coefficients ‐ Screening ............................................ 41 6.6.5
Polynomial Creation ...................................................................................................... 44 6.6.6
Randomized Coefficients ............................................................................................... 46 6.6.7
Finding The Optimal Coefficients .................................................................................. 47
7
DMAIC Control ............................................................................................................................ 48 8
Setups and Final Results .............................................................................................................. 49
8.1
Choice of Coefficients’ Values Variation Intervals................................................................. 49 8.2
Reference Data ...................................................................................................................... 50 8.3
Setups .................................................................................................................................... 51
8.3.1
Constants ....................................................................................................................... 51 8.3.2
Combinations of Constants, Linear Coupling and Quadratic Terms ............................. 51 8.3.3
Three‐Step Technique ................................................................................................... 53 8.3.4
LOx‐Turbine, Three‐Step Technique .............................................................................. 54
8.4
Results ................................................................................................................................... 55 9
GESTPAN‐Analysis of Different Turbine Modules ....................................................................... 57
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9.1
Goals And Strategies ............................................................................................................. 58 9.2
Setups .................................................................................................................................... 59
10
Discussion and Analysis of Results .............................................................................................. 61 11
Suggestions for Future Work ...................................................................................................... 63 12
References................................................................................................................................... 65
Appendix A
DVT‐data for both turbines ........................................................................................... 67 Appendix B
LH2‐results ..................................................................................................................... 69 Appendix C
LOx‐results ..................................................................................................................... 77 Appendix D
Plots of the final results, LH2 turbine ............................................................................ 79 Appendix E
Plots of the final results, Lox turbine ............................................................................. 83 Appendix F
TML change log .............................................................................................................. 85 Appendix G
CFD vs tml results, LH2 turbine ..................................................................................... 87 Appendix H
TML update routine manual .......................................................................................... 89 Appendix I
GESTPAN results ............................................................................................................ 91
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LIST OF FIGURES
2‐1, an illustration of Six Sigma effectiveness ......................................................................................................... 2 2‐2, DMAIC principle ............................................................................................................................................... 3 2‐3, Ishikawa diagram showing the problem layout ............................................................................................... 4 3‐1, Typical velocity triangles for a single turbine stage ......................................................................................... 5 3‐2, Expander‐cycle engine Vinci layout .................................................................................................................. 7 3‐3, Vinci expander cycle engine ............................................................................................................................. 8 3‐4, LH2 turbine layout ............................................................................................................................................ 9 3‐5, LOx turbine layout ............................................................................................................................................ 9 3‐6, simplified TML‐layout ..................................................................................................................................... 12 3‐7, turbine annulus geometry from TML Manual [2]........................................................................................... 12 3‐8, LH2‐indexing, simple ...................................................................................................................................... 13 3‐9, DoE part in Six Sigma ..................................................................................................................................... 15 3‐10, an illustration of a Full Factorial design ....................................................................................................... 16 3‐11, an example of Circumscribed CCD (left) and Inscribed CCD (right) .............................................................. 17 3‐12, an example of a Faced CCD .......................................................................................................................... 17 3‐13, a 1/2 Fraction Factorial Design .................................................................................................................... 18 3‐14, a Pareto‐chart example, showing how different coefficients affect the final results .................................. 19 4‐1, first DMAIC step ............................................................................................................................................. 23 5‐1, second DMAIC‐step ........................................................................................................................................ 24 6‐1, third and fourth DMAIC‐step .......................................................................................................................... 25 6‐2, TML modulation structure ............................................................................................................................. 28 6‐3, final TML modulation ..................................................................................................................................... 29 6‐4, a fragment of TML input‐file showing the buildup of operating points' array ............................................... 30 6‐5, new‐layout TML input‐file, explicit definition ................................................................................................ 30 6‐6, test rig ‐ schematic view ................................................................................................................................ 31 6‐8, DVT data for operating points, LH2 turbine ................................................................................................... 34 6‐9, DVT data for operating points, LOx turbine ................................................................................................... 35 6‐10, stator blade mesh, ICEM v4.0 ...................................................................................................................... 36 6‐11, blade mesh with boundary conditions applied, CFXpre ............................................................................... 37 6‐14, the optimal polynomial finding strategy ...................................................................................................... 39 6‐15, layout of the Matlab‐based Statistical Analyzer .......................................................................................... 42 6‐16, Pareto‐chart, showing the importance of Stator‐coefficients ...................................................................... 43 6‐17, Pareto‐chart, showing the importance of Stator‐coefficients ...................................................................... 43 6‐18, Regression Analysus, Response surfaces ...................................................................................................... 45 6‐19, output results' mean value and deviation versus number of randomizations ............................................. 46 7‐1, final step of DMAIC ........................................................................................................................................ 48
B‐2, influence of the STATOR's coefficients. Layout: (1)( )( )(4)(5)(6) .................................................................... 70 B‐3, influence of the ROTOR's coefficients. Layout: (1)( )( )(4)(5)(6) ..................................................................... 70 B‐4, influence of the STATOR's coefficients. Layout: (1)(2)(3)(4)( )( ) .................................................................... 71 B‐5, influence of the ROTOR's coefficients. Layout: (1)(2)(3)(4)( )( ) ..................................................................... 71 B‐6, influence of the STATOR's coefficients. Layout: (1)( )( )(4)(5)(6) .................................................................... 72 B‐7, influence of the ROTOR's coefficients. Layout: (1)(2)(3)(4)( )( ) ..................................................................... 72 B‐8, influence of the STATOR's coefficients. Layout: (1)(2)(3)(4)( )( ) .................................................................... 73 B‐9, influence of the ROTOR's coefficients. Layout: (1)( )( )(4)(5)(6) ..................................................................... 73 B‐10, influence of the STATOR's coefficients. Layout: (1)(2)(3)( )( )( ) ................................................................... 74
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B‐11, influence of the ROTOR's coefficients. Layout: (1)(2)(3)( )( )( ) .................................................................... 74 D‐1, Efficiency curves comparison, EXP vs TML vs TML_Orig ................................................................................ 79 D‐2, Mass flow curves comparison, EXP vs TML vs TML_Orig ............................................................................... 80 D‐3, P0/PS3 curves comparison, EXP vs TML......................................................................................................... 80 D‐4, P0/PS2 curves comparison, EXP vs TML vs TML_Orig.................................................................................... 81 E‐1, Efficiency curves comparison, EXP vs TML vs TML_Orig ................................................................................ 83 E‐2, Mass flow curves comparison, EXP vs TML vs TML_Orig ............................................................................... 83 E‐3, P0/PS3 curves comparison, EXP vs TML ......................................................................................................... 84 E‐4, P0/PS2 curves comparison, EXP vs TML vs TML_Orig .................................................................................... 84 G‐1, Flow Function comparison ............................................................................................................................. 87 G‐2, outlet angle, α, comparison ........................................................................................................................... 87 G‐3,
comparison .............................................................................................................................................. 88 G‐4, Mach Number comparison ............................................................................................................................ 88 I‐2, Torque Out, both turbines ............................................................................................................................... 91 I‐3, Power, LH2 turbine .......................................................................................................................................... 91 I‐4, Power, LOx turbine .......................................................................................................................................... 92 I‐5, Mass flow, both turbines ................................................................................................................................ 92 I‐6, calculated efficiency, both turbines ................................................................................................................ 92 I‐7, calculated pressure ratio, both turbines ......................................................................................................... 93 I‐8, N_K (same as NC), dimensionless speed coefficient, both turbines ................................................................ 93 I‐9, Thrust chamber force ...................................................................................................................................... 93 J‐2, Percentile difference for Specific Torque, TML results VS polynomial‐based, LOx turbine ............................. 93 J‐3, Percentile difference for Q_plus, TML results VS polynomial‐based, LOx turbine .......................................... 93 J‐4, Percentile difference for Specific Torque, TML results VS polynomial‐based, LH2 turbine ............................. 93 J‐5, Percentile difference for Q_plus, TML results VS polynomial‐based, LH2 turbine .......................................... 93
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LIST OF TABLES
6‐1, probe information .......................................................................................................................................... 32 8‐1, original TML results ........................................................................................................................................ 50 8‐2, first optimized TML results, LH2 ..................................................................................................................... 51 8‐3, intermediate updated TML results, LH2 ......................................................................................................... 52 8‐4, final updated TML results, second step, LH2 .................................................................................................. 53 8‐5, final updated TML results, third step, LH2 ..................................................................................................... 53 8‐6, final updated TML results, LOx ....................................................................................................................... 54 9‐1, parameters' intervals for GESTPAN‐run preparation ..................................................................................... 58 9‐2, GESTPAN‐experiments ................................................................................................................................... 59
A‐1, DVT‐data for LH2 turbine ............................................................................................................................... 67 A‐2, DVT‐data for LOx turbine ............................................................................................................................... 68 B‐1, LH2‐results ..................................................................................................................................................... 69 B‐12, LH2 three‐step technique results ................................................................................................................. 75 B‐13, LH2 turbine K&O coefficients for every DMAIC‐run ..................................................................................... 76 C‐1, LOx turbine results, three‐step technique ...................................................................................................... 77 C‐2, LH2 turbine K&O coefficients for every DMAIC‐run ....................................................................................... 78 I‐1, GESTPAN runs, results ..................................................................................................................................... 91 J‐1, GESTPAN operating temperature and pressure .............................................................................................. 91
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1 INTRODUCTION
Volvo Aero Corporation
Volvo Aero Corporation was founded
in 1930 and has a very
strong background in
developing different kinds of gas
turbines. Originally producing engines
for the Swedish Air Force,
the corporation is today involved
in several engine programs of Pratt&Whitney, General Electric, Rolls‐Royce, SNECMA and MTU.
In the area of rocket engines the role of VAC is to deliver the space engine nozzles and turbines for Ariane‐5 engines.
The Ariane‐5
second‐stage bi‐propellant expander‐cycle
space engine, Vinci, is studied
throughout the presented work. Since
the engine is still in
the development phase, different numerical
tools need to be updated
in order to deliver more
reality‐like results, namely the tools
for
solving one‐dimensional mean‐line codes.
Loss Models
In order to predict the flow inside the engines in a proper way, loss models are needed. There are a lot of several kinds of correlations that exist nowadays, both strictly empirical and experimental data‐related
[13]. The one that is
studied here is
the Ainley and Mathieson
correlation as modified by Kacker and Okapuu, which is currently used at VAC in one‐dimensional codes.
The Purpose of This Thesis Work
The main goal for every computational tool
is to deliver as close‐to‐reality results as possible, thus lowering
the need of
running expensive experiments, saving
time and costs. The presented
thesis focuses on development of the methodology for adjusting the currently used numerical tools using DVT as a reference. Reference data as well as all the intermediate results is analyzed with statistical methods. The methodology is created with a Six Sigma approach.
Once created, this methodology
follows the DMAIC process, which
is standardized within the
Six Sigma community thus finding
the areas of improvement in the
loss model for given
turbine geometry and reference data
so that the code would
deliver more exact results in
the studied operating domain. The
improved 1D‐codes are then used
to create the
turbine modules which,
in turn, are compared with the original ones in a general engine analysis.
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2 SIX SIGMA BASICS
Basic Theory
Every time a person or an organization makes a mistake a certain cost is being paid in terms of time, efficiency,
or productivity loss. Six Sigma
is a general‐purpose approach used
to minimize those mistakes
and maximize values. Six Sigma
is an integrated, disciplined and
proven approach
for improving performance, including manufacturing businesses, for any organization. Six Sigma tends to strive
for perfection. According to the
Six Sigma methodology only 3.4
defects per
million opportunities for each product are allowed.
Recalling the famous quality
definition, consisting of Long‐ and
Short term where the second
may vary 1.5σ (to reflect the
“real world” shift) the way to
reach Six Sigma may
be illustrated as at Figure 2‐1.
Figure 2‐1, an illustration of Six Sigma effectiveness1
Six Sigma approach widely uses
different quality methods, including
statistical methods.
The statistical representation of Six Sigma describes quantitatively how a process is performing.
Further information about Six Sigma can be found in numerous literature sources, for example [1].
1 The figure is borrowed from [9] where the reader is referred to for obtaining more information.
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DMAIC principle
Through the current work the problems were solved with a Six Sigma approach, a so called DMAIC principle of
solving problems. The acronym is
taken from the first letters
for each phase: Define, Measure,
Analyze, Improve, and Control. The
DMAIC methodology provides a structure
for
logic progression through a problem solving activity.
Figure 2‐2, DMAIC principle
During the whole presented work the DMAIC principle have been used as the main approach. Very short description of each of the five DMAIC key points follows, a more thorough description is being made through all this work.
According to the Figure 2‐2, the approach is divided into five main steps.
‐ DEFINE the problem. The problem
is that the customer, SNECMA,
is not satisfied with the final
results obtained from one‐dimensional
turbine mean line calculations, such
as
, , .
‐
MEASURE. Check which factors make influence on the problem, in our case
, , , 2. ‐ ANALYZE the
problem, make a certain plan for
collecting and analyzing data, design
the
experiments, etc. As our analysis
shows the main factor that
affects the problem’s improvement
is the K&O
loss correlation used
in the numerical calculation tool, TML. Once analyzed
the problem may be solved
applying some polynomial corrections
to the loss‐model.
‐ IMPROVE
the problem – using a well‐built
strategy that will implement
the best methods possible for applying the methods chosen to solve the problem. Here a special polynomial‐defining methodology is built resulting in a better K&O correlation
‐ CONTROL that the obtained
results are improving
the problem. Are they better? Are
they satisfactory? Will the customer
be satisfied with them? A
careful analysis of the
results normally leads to a new DMAIC‐loop, defining the objectives for the next step.
2 Read more about indexing in further chapters
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An
Ishikawa diagram showing the cause‐and‐effects breakdown of the studied problem
is shown in Figure 2‐3.
Figure 2‐3, Ishikawa diagram showing the problem layout
It is easy to observe the causes of the studied problem and to trace their path. What is done in the next step, after several DMAIC‐cycles, is the Final Control step, actually running the whole motor model comparing original and improved calculation results.
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3 THEORETICAL BACKGROUND:
In this chapter a brief description of the methods and strategies used through this thesis project
is given in order to provide
the background and to ease
the understanding of
the performed work. Reading of this chapter is not necessary for readers already familiar with the project theory. A more thorough description may be found in references, if needed.
3.1 ROCKET ENGINE BASICS
A rocket engine is basically
a reaction jet engine using
only the propellant mass for
forming its propulsive
jet of high speed. Several different types of Rocket Engines exist nowadays although the presented work will
focus on the pump‐fed bipropellant
engine, namely the Expander
Cycle‐type one. The engine is named Vinci and a more brief description follows.
Axial‐Flow Turbomachinery
A turbine
is any of various machines
in which
the kinetic energy of a moving
fluid is converted
to mechanical power by the impulse or reaction of the fluid with a series of buckets, paddles, or blades arrayed about the circumference of a wheel or cylinder [8].
In the presented work only one kind of turbines will be considered namely Axial‐Flow Turbines, where the flow of fluid is essentially parallel to the rotor axis.
An axial‐flow turbine
can have one or more
stages, each constituted by a
stator and a rotor, see Figure
3‐1 (where Va1 and Va2 are
the gas absolute velocities, Vr1
and Vr2 are the gas
speeds relative to the rotor and U is the rotational speed).
Figure 3‐1, Typical velocity triangles for a single turbine stage
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Turbine Efficiency
The main functional parameters are
Turbine efficiency
is a measure of the turbine performance. There are several definitions of turbine efficiency and one of them is a total‐to‐total efficiency
However for the Ideal gases
another definition is used. In
the presented work the
total‐to‐total turbine performance is presented by formula
1
Where
is the total pressure at the inlet and
is the total pressure at the outlet. Total‐to‐static performance is calculated in the same way but the outlet static pressure value,
is used instead of
.
The indexing used during this work is normally
or
for indicating static property “
” of index “ " and or
for indicating the total property.
The Flow Function
Assuming that the operating fluid is compressible and can be assumed as an ideal gas, the equation
of the mass flow parameter
is known as the Flow Function. The full equation for Flow Function
reads
11
2
In case the flow is both
adiabatic and isentropic both
and remain constant which
allows relation of the normal area of the flow.
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3.2 EXPANDER CYCLE
The Expander Cycle is used in rocket turbomachinery to deliver the fuel in a more efficient way. The main principle of an expander cycle is that fuel is being heated at first, usually using the waste heat from
the combustion chamber. As the
liquid fuel passes through the
thermoexchange passages it, cooling
the nossle, changes its phase from
liquid to gas. The gaseous fuel
then enters the turbine where it
expands to the target pressure
of combustion chamber initiating the
rotation of the turbopump.
After the turbine the fuel
is being mixed with an oxidizer, entering the combustion chamber where the mixture is being burnt, providing the necessary thrust to the vehicle.
Using an expander cycle engine gives lots of advantages. The material is not exposed to heat, but the thermal gradients are still in place.
Figure 3‐2 shows the schematic
layout of an expander cycle engine, Vinci, which
is being studied
in the presented work.
Figure 3‐2, Expander‐cycle engine Vinci layout
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Vinci
In May 1999 the development of the new rocket engine, Vinci®, was started. The engine intended to replace
the nowadays HM7B3 on
the upper stage of Ariane‐5. The Vinci‐program
is coordinated by SNECMA, leading
its team of European partners where Volvo Aero Corporation
is one of them. The work on Vinci has been performed
in two steps. The first one
started in 1999 and ended
in 2003. After that work on Vinci engine has been carried out since the end of 2005 and first two Vinci engines have already been fired.
As it was mentioned previously,
the Vinci engine will power
the Ariane‐5 ESC‐B upper stage.
The payload capability of 12t
and multiple firing capabilities will
be provided. The major
difference between ESC‐B and a
prior cryogenic upper stage ESC‐A
is increased engine performance and
a capability of a restart, which enables delivery of satellites at their respective optimal orbit.
Figure 3‐3, Vinci expander cycle engine
The Vinci engine
is a new generation cryogenic expander cycle rocket engine. Vinci
is bipropellant, fed with liquid hydrogen (also used for chilldown) and liquid oxygen.
3 Gas generator liquid oxygen / liquid hydrogen engine, powering Ariane‐5
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LH2 and LOX Turbines
Throughout the current work a
certain
study has been made on Vinci
turbines ‐ Liquid Hydrogen turbine,
LH2 and Liquid Oxygen turbine,
LOx. A picture describing LH2,
is shown in Figure
3‐4, indicating the components of most importance. A picture of the LOx turbine follows in Figure 3‐5.
Figure 3‐4, LH2 turbine layout
Figure 3‐5, LOx turbine layout
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Basically, there are four main components of interests:
‐ Inlet manifold ‐ Stator ‐ Rotor ‐
Turbine Exhaust Duct (TED)
The gas aero‐ and thermodynamic behavior at all five planes (between, before and after all four main components, mentioned above) is being studied here.
Air‐tests are needed for
validation purposes although turbines
are designed to run on
liquid Hydrogen (provision is made
for “real gases”). In
the presented work a DVT
in Air data is used
for comparison with the obtained calculations’ and/or simulations’ results.
The output‐rawdata of DVT tests gives the user a complete picture of gas condition throughout the whole turbine, flange‐to‐flange. More details about the DVT data can be found in [10].
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3.3 ONE‐DIMENSIONAL PROGRAM (T1D)
The design process of a turbine often starts at a one‐dimensional basis although there are different 2D
and 3D tools for calculating
turbine performance. During one‐dimensional
analysis only
the turbine mean radius is being considered.
The mean‐line theory can be
found in turbomachinery textbooks
[2]. The equations
considered depend a
lot on the sign conventions adopted. The studied T1D code
is based on PCA’s streamline code. More information can be adopted in [3].
All the calculations are made at every turbine plane at the root‐mean‐square radius that reads
The calculation starts from the
input‐data supplied such as total pressure, temperature, rpm, mass flow and
flow angle to the first stator,
if the inlet manifold is omitted
from the analysis. It
is also necessary to give the
correct representation of the change
in angular momentum inside
the manifold.
T1D code is
capable of handling different
kinds of gas property models such
as
Ideal Gas model, Semi‐Perfect Gas model, Real Gas model
and Wet Steam model. In the
presented work only
the ideal‐gas model has been studied since during all the calculations air has been used as an operative fluid. Gas constant and specific heat has been specified.
Loss correlations over
the turbine blade rows are being considered. The choice of a desirable
loss‐model is used during input. The following three loss‐models are available:
‐
Ainley and Mathieson correlation as modified by Kacker and Okapuu ‐
Ainley and Mathieson correlation as modified by Moustapha, Kacker and Tremblay ‐
Moustapha, Kacker and Tremblay
correlation as modified by Benner,
Sjolander and
Moustapha.
In the presented work the focus is being made on Kacker and Okapuu (further K&O) correlation.
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Turbine Mean Line Software
The numerical tool using T1D code for calculating turbine performance is called TML which stands for Turbine Mean Line. The code is written in FORTRAN90 and originally consists of 53 subroutines, rules defined by a Makefile [11]. During the presented work a Linux‐environment together with the Intel Fortran Compiler v10 has been used for TML compilation and runs. A thorough user guide and a T1D theory manual are provided [3], [7].
The overall work of TML can be described (if very simplified) by Figure 3‐6.
Figure 3‐6, simplified TML‐layout
As one may observe the principle
is quite straightforward. A TML‐run, supplied by all the necessary input data (turbine geometry, gas data, etc) followed by an array of operating points, gives out all the necessary output‐data
for all
the operating points at all
turbine planes. This is the
initial
layout of TML which has been changed during experiments, the description can be found in further chapters.
Figure 3‐7 is borrowed from
the TML user manual [3] and
shows the complete indexing
structure throughout the whole turbine including both inlet and outlet volutes. Further details can be found in the manual itself.
Figure 3‐7, turbine annulus geometry from TML Manual [3]
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To simplify indexing structure the following system has been used throughout the presented work
Figure 3‐8, LH2‐indexing, simple
The K&O correlation mentioned
above is applied between planes
1‐2 and 2‐3. The
loss‐model description follows.
The newer version of loss
model over TED has been
implemented during the experiments.
A thorough description can be
found in further chapters.
Nevertheless during the K&O
model optimization
the TED model has been omitted
and the turbine has been mostly
studied between planes 0 and 3.
K&O‐Loss Model
To design a turbomachine
system means getting
through a very complex, often
iterative, process. During modern
engineering operations of this kind
several computational tools for
simulating, optimizing and tuning are often needed. To predict thermo‐ and aerodynamic performance over the blade rows with certain accuracy
is an
important part of the whole turbomachinery system design. Due
to the turbine flow complexity
certain loss models are needed
both in the early design
and further simulations phases.
In the presented work the main focus will be on Kacker & Okapuu [1982] loss model which is mainly based on the method by Ainley & Mathieson [1951] and the modified method by Dunham & Came [1970].
The pressure loss coefficient is defined as
,
Where and
are the outlet total and static pressures relative to the blade row and
is the inlet total pressure.
The total pressure loss in a
cascade of blades expressed in
terms of outlet dynamic pressure
is assumed to be the sum of Profile, Secondary, Trailing Edge and Tip Leakage losses, where the Profile losses are corrected for the Reynolds’ number effects
The K&O loss model is
capable to predict the efficiencies
for desired design points of
current turbines. A more thorough description of the K&O loss model can be found in [4].
-
14
3.4 GESTPAN
GESTPAN, which originally stands
for General Stationary and Transient
Propulsion Analysis, is
a FORTRAN‐based program used for simulation of different kinds of gas turbines. GESTPAN has been developed by Volvo Aero Corporation
in
cooperation with Chalmers University of Technology and KTH, Royal University of Technology.
GESTPAN is a modular
code which means that every engine
component can be represented by
a module. Thus a whole engine or a single turbine simulation may be run. Both transient and stationary simulations are possible to perform using GESTPAN.
The turbines studied during the current work, LH2 and LOx are presented by separate modules [12] where two of the most important turbine parameters, Specific Torque and Mass Flow are presented by the polynomials based on the experimental data.
-
15
3.5 DOE
In the present work an important part of Six Sigma methodology – Design of Experiments – has been used widely
(further DoE). DoE is a
structured and organized method to
determine the
relations between the factors related to a process and the results of this process.
Figure 3‐9, DoE part in Six Sigma
There should be a strategy
for collecting and analyzing the
data, under controlled conditions,
to understand, and interpret the results in a correct way. There are a variety of tools that can be used for that and one of the most powerful of them is DoE.
DoE is used to make metaphysical models of the problem by investigating the variables influencing a process
in a way that as much
information as possible could be obtained from the minimum set of experiments. One of the major advantages
if using DoE
is a possibility to avoid the one‐factor‐at‐a‐time (OFAT) experiments allowing one to simultaneously
investigate the consequences of changing and/or varying several variables. The result is obvious – one may observe not only how each variable change would
affect the final result but
also the interactions between
variables. Of course,
the experiments are becoming much less time‐consuming which in the present work is a great advantage as well.
DoE usually starts with the definition of a problem that one
is willing to
investigate or solve. This is often
done using an Ishikawa‐diagram, or
Fishbone‐diagram. The objectives should
be defined clearly. After that a
certain set of experiments
is designed so that objectives are
satisfied. A well‐chosen strategy
should be used for collecting
and analyzing data – to capture
all the
required information and then to ensure that the results are properly interpreted. Further information about DoE can be found in [5].
Response Surface Methods
Response surface methods are very
effective and powerful optimization
tools among Designs
of Experiments. The main idea of Response surface methodology is to use a certain set of experiments in order
to obtain optimal response. This
is often done by using a
first‐degree polynomial model, such as
Factorial experiment or Fraction
Factorial Design. First‐order response
surfaces are
often used for screening purposes.
-
16
Factorial Experiment
An experiment which is designed
by two or more factors,
each with several possible values
and where all the variables take
all the possible combinations of
their values interactively is called
a Factorial Experiment of
“Fully‐crossed Experiment”. Such design
allows one to study not only
the influence of each factor on
the experiment’s result but also
the consequences and effects
of interactions between the factors. A simplest example would be a so‐called 2x2‐design: One may have two factors, each of them taking two values. An illustration of a 2x2x2‐design is in Figure 3‐10.
Figure 3‐10, an illustration of a Full Factorial design
Sometimes due to a high number of the factors the number of the possible combinations for a fully‐crossed
design is unfeasibly high. In
this case a certain number of
the combinations of less importance
can be omitted using a Fractional Factorial Design which
is, as described
further, also used for screening purposes.
Central Composite Design,
Central Composite Design or CCD
is a most popular
class of designs used for fitting
second‐order
models consisting generally of 2
factorial or fraction factorial. The main advantage of a CCD is that one
does not need a complete
three‐level factorial experiment
thus minimizing the amount
of experiments. CCD often
follows by a linear regression
to obtain results. There are
three
types of Central Composite Designs – Circumscribed, Inscribed and Faced, see Figure 3‐11, Figure 3‐12.
-
17
Figure 3‐11, an example of Circumscribed CCD (left) and Inscribed CCD (right)
The CCD is very useful for fitting the second‐order model. One should specify two parameters in the design; the distance
of the axial runs from design center and the number of center points.
According to Box and Hunter
(1957) a second‐order response
surface design should be
rotatable which means that the
variance of predicted points is
constant for the constant radius
from
the central point. Rotatable CCD’s are used throughout all the experiments since a response surface has been built after each and every of them. One of the advantages of using a Rotatable CCD is that the error is the same at a given distance from the center no matter of the direction.
The region of interest in the presented work is cuboidal rather than spherical which led to a special kind of CCD to be chosen, the Face‐Centered Central Composite Design (FCCCD) where
1. One of the advantages of the FCCCD
is that
it does not require that many center points, thus
lowering the amount of experiments and saving time.
Figure 3‐12, an example of a Faced CCD
-
18
Screening Designs
Sometimes the number of operands
in an experiment is so big
that even having a good design of experiments cannot help avoiding enormous numbers of experiments’
runs. To solve
this problem one may design an experiment that will show the magnitude and direction of the operands’ effects. Thus a complete picture about how each of the operands affects the final results can be obtained. This kind of experiment is called a Screening experiment, often involving Fraction Factorial or Placet‐Burman designs.
Fractional Factorial Design
Fractional Factorial Design is a design consisting of experiments which are carefully chosen from the full
Factorial Design. This is done
to obtain information about
the most important features of
an investigated problem. In the presented work a two‐level FF‐Design, or FFD has been used since it has been found sufficient to evaluate the screening experiment.
Figure 3‐13, a 1/2 Fraction Factorial Design
Placket‐Burman Design
Placket‐Burman designs are two‐level fractional factorial designs, often used for screening purposes. They
are constructed in a way that
the main effects are heavily
confounded with two‐factor interactions.
Placket‐Burman designs are very
useful when only the main
effects of the
factors studied are interesting.
-
19
Pareto‐Chart.
A Pareto‐chart, named after Vilfredo Pareto,
is a special sort of chart where the values plotted are organized in a descending order completed by a line graph representing the totals of each category, left to right.
Figure 3‐14, a Pareto‐chart example, showing how different coefficients affect the final results
The left vertical axis represents
frequency of occurrence in particularly
this case (but actually
can represent any other interesting unit of measure). The right vertical axis shows the percentage of the total numbers of chosen measure unit. The main use for Pareto‐charts in this work is to highlight the most important factors to be chosen for a future proper study.
Pareto charts are often used to plot the results of a screening experiment and are widely used in the current work.
-
20
3.6 COMPUTATIONAL FLUID DYNAMICS, CFD
A certain number of CFD experiments have been run during the described work. Since the governing equations are
too complex to be
solved analytically the
iterative approximate numerical
solutions method are used instead. In this section a very brief overview is made of the numerical CFD methods used in the presented work.
Governing Equations
The set of equations governing
the viscous flow are the
well‐known Navier‐Stokes equations
– Continuity, Momentum and Energy
equation. The derivation of these
can be found in most
fluid dynamics books, for example [6].
Navier‐Stokes equations for an incompressible flow in Cartesian 3D‐coordinates yield
Together with the Continuity equation
0
However, the real flow in the turbomachinery is unsteady and thus compressible. The Navier‐Stokes equations
for the compressible flow, comprising
the equations of mass, impulse
and
energy conservation, assuming ideal gas, yield
SzH
yG
xF
tQ
=∂∂
+∂∂
+∂∂
+∂∂
Where
( ) ( )⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
++−++−−−+
=
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
=
zxyxxxx
zx
yx
xx
wvuqupeuwuvpuu
F
ewvu
Q
ττττρτρτρ
ρ
ρρρρ
2
,
-
21
( ) ( ) ( ) ( )⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
++−++−+
−−
=
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
++−++−−+
−
=
zzyzxzz
zz
yz
xz
zyyyxyy
zy
yy
xy
wvuqwpepw
vwuww
H
wvuqvpevwpv
uvv
G
ττττρ
τρτρ
ρ
ττττρτρ
τρρ
2
2 ,
( ) ( ) ⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
Ω−Ω+Ω+ΩΩ−ΩΩ+Ω=
wvzvwyvzwyS
ρρρρρρρρ
2222
00
22
2
2
RTp ρ=
Dynamic Viscosity
To
implement dynamic viscosity assuming
ideal gas Sutherland’s law
is often used, where and
are reference values at
standard sea‐level conditions. Further
information about Sutherland’s
law can be found in [6].
110110
Turbulence
Turbulence
is a specific state of fluid motion where chaotic and random three‐dimensional vorticity presents. Turbulence
is usually dominant over all other flow phenomena which results
in
increased mixing, heat transfer, drag and energy dissipation. There are almost no fully‐laminar flows in nature.
There are several algebraic methods that turbulence can be described with. During CFD experiments applied
in the current work the “
” or K‐Epsilon
turbulence model has been used
(where “k” stands for
turbulence kinetic energy and “Epsilon”
for turbulence dissipation
thus enlarging the
‐vector a bit). This
is one of most common turbulence models, consisting of two extra equations to describe
turbulent transport properties of the
flow. For a deeper study
concerning
different turbulence models or the K‐Epsilon model in particular see [6].
-
22
-
23
4 PROBLEM DEFINITION
Figure 4‐1, first DMAIC step
According to the DMAIC principle mentioned in the beginning of this work the first step is to define the
problem. Some of the output
variables of the Vinci motor
cycle have been found not
quite
satisfactory and a certain
improvement should be implemented.
The variables are , ,
which stand for Turbine Efficiency, Flow function and axial force on the turbine shaft. This leads us to the improvement of the numerical tools currently used for one‐dimensional calculations, TML.
TML Update Methodology
During the presented work
the newest version of TML has been
studied deeply. TML
is a brilliant piece of software
to be used as a numerical tool
for one‐dimensional calculations. Although
it has some small inconveniences
in use as well as the
theoretical one‐dimensional values that
are calculated using TML are never exactly the same obtained during experiments.
As mentioned before the latest version uses an [MxN] array of operating points as input where M is the number
of angular velocities and N
is number of pressure ratios
equidistantly spread over
a chosen domain. This is not always convenient specially when comparing to experimental data.
Due to the complexity of TML routine structure the subroutines and functions had to be organized in a way that would allow easier use and access.
A proper K&O correlation improvement should give a more reality‐like output.
A TED model needed a certain update as well since its structure is now quite simplified.
-
24
5 MEASURES OF THE CURRENT
STATE
Figure 5‐1, second DMAIC‐step
Current results provided by TML have been logged with care and compared to the reference values. Certain deviations have been observed with an average error of nearly 4% (see 8.2 Reference data). As the reference values that are coming from air‐tests (keeping inlet pressures and temperatures as
constants) the studied output variables are
, , , .
and have been chosen to
take as fractions of
stagnation pressure since the last
varies
a bit through the studied domain of operating points.
-
25
6 ANALYSIS AND IMPROVEMENT
Next chapters will describe the most
important part of achieving the specified goals –
the Analysis and Improvement. Since several different moments are included in the TML‐tuning methodology and each of
them needed a bit of an own DMAIC‐approach,
those parts have been merged
to one for easier understanding.
Figure 6‐1, third and fourth DMAIC‐step
-
26
6.1 NEW TED‐MODEL IMPLEMENTATION
This section describes the TED correlations used in original TML version and the updates applied during the project work.
Original TED model
A TED‐model calculates the total
pressure at the outlet of the
turbine exhaust manifold.
Thus pressure losses occurring in TED may be obtained. As has been mentioned before,
The pressure loss coefficient is defined as
.
The previous TED‐model calculated
total outlet pressure mainly based
on CFD‐results.
Outlet pressure has been fit to a CFD‐curve, obtained from numerous simulations. This solution was difficult to use in iterative procedures due to startup issues so an update was implemented.
The CFD‐curve used for TED‐fitting reads (copied directly from code [11])
0,98231 0,86858 0,01413 0,080811 (6.1.1)
Where
‐
AMN is the Mach number at the manifold inlet ‐
ALFA is the gas angle at the manifold inlet
The original TED‐model has been constructed in a way so that the use of equation (6.1.1) mentioned above
is optional. One could manually set
the desired “hardcoded” value of
the dynamic pressure loss in the input‐file [7]. For example, one could assume TED to be completely lossless, or to assume 90% loss of dynamic pressure due to a big cross‐sectional area increase.
-
27
Updated or Rebuilt TED Model
A new TED‐model originally written
at VAC by Sonny Andersson, has
a different method of calculating
the outlet pressure. It uses the
test data to compute the overall
total‐to‐total pressure ratio of the LH2 turbine using the total‐to‐static pressure ratio between inlet and rotor‐trailing‐edge,
/
and the specific speed coefficient, ANC.
The relations between the
input data
and outlet pressure have been derived
from the DVT tests (AirData) of
the Vinci LH2. This model
appeared to give better values
of outlet pressure so
the deviation between calculated and experimental values could be reduced.
The loss model works using the following methodology:
‐
The ANC feasible domain is divided into 10 sections ‐
An array of pressure ratios for each section is defined ‐
Using the input data, the
desired pressure ratios over TED
are obtained from the
corresponding array using interpolation ‐
TED loss coefficient as well as outlet total pressure is obtained
More thorough information about the updated TED module can be found in [10].
No comparison between the Original and New TED models on the turbine
level is presented
in the current work. However, the
comparison is being made in
the GESTPAN‐cycle on the motor
level, where turbine overall total‐to‐total pressure is used instead of total‐to‐static.
-
28
6.2 MODULES’ IMPLEMENTATION
As it has already been mentioned before TML software consists of 53 subroutines, a Common block and a global variable module
(added
later) which are coupled together via complicated network of calls. This might not be convenient when modifying the structure of TML, not even mentioning that for
a new‐to‐TML user this may seem
way too complicated. Thus a
certain modeling has
been planned to be implemented.
Figure 6‐2, TML modulation structure
The main idea behind
this modulation was
to have a certain module
responsible for
some certain work. Thus
‐ PREPROCESSOR would contain everything
that was needed for reading the
input data and proceeding with the necessary setup for the calculation;
‐
SOLVER would contain all the subroutines used for calculations; ‐
LOSSMOD would be the module with loss‐models (TED and K&O); ‐
And POSTPROCESSOR would take the routines used for result plotting, creating the output
files and managing the messages in the output‐window.
The main difficulty
in creating those four modules was that all the 53 subroutines were calling each other, at a first glance, completely chaotically. After some work a certain structure in calls has been revealed
and three modules out of four
have been created successfully –
Preprocessor, Postprocessor and Loss Models.
The fourth module, SOLVER, was
impossible to create as a
separate one due to the
software’s complexity. It has appeared
that the subroutines
from other modules were calling ones
in SOLVER and vice verse. The result was the impossibility to compile four stand‐alone modules using Makefile.
-
29
Since three out of four modules have been created the TML structure has been decided to be held as is, mainly having three modules and the “rest”, acting as SOLVER. This solution is, of course, far from the best but it has provided certain easiness for future work.
Figure 6‐3, final TML modulation
The final TML configuration had the following amount of subroutines in each module:
‐ Preprocessor 10 subroutines ‐
Loss Models 4 subroutines ‐
Postprocessor 4 subroutines ‐
“rest” 34 subroutines
For further information about TML structure changes see the changelog [Appendix F] and the new TML source code [11].
-
30
6.3 TML INPUT ROUTINE UPDATE
As mentioned before, the input data for turbine operating points has normally been given to TML in a
form of [MxN] array where M
represented a number of rotational
velocities
and N number of expansion ratios.
…
STAGP STAGT 780 400
NEXP NREVS EXPMIN EXPMAX 10 5 1,1 2,6
REVREF 40000
REVS (%) 100 90 80 70 60
…
Figure 6‐4, a fragment of TML input‐file showing the buildup of operating points' array
Figure 6‐4 shows how a typical array of operating points is normally built. One may observe that the mentioned
[MxN] array has 5 rotational
speeds and 10 expansion ratios
for each thus giving
50 operating points.
The use of this method of
input is very convenient
to predict the turbine’s behavior
for different expansion ratios on N speed lines. However this input data is far from exactly equal to the one used at DVT tests and thus is not that good for comparison with real experiments.
The PREPROCESSOR module has been modified
in a way that all
the operating points are defined explicitly e.g. experimental data can now be read in. As said previously experimental values are more or less divided into several speed lines as well which has a later use in post‐processing.
… REVREF
40000
STAGP STAGT EXPRAT REVS (%) 779 400 1,1 23 781 339 2,1 43 780
401 2,6 32
… … … …
Figure 6‐5, new‐layout TML input‐file, explicit definition
-
31
6.4 DVT DATA AS INPUT AND
REFERENCE
The data mainly used as reference for TML model tuning is coming from air tests and is presented in form
of a large Excel‐file. The main
objectives of the DVT tests are
to evaluate the
turbine performance in terms of
‐
the total‐to‐total efficiency in the reference point ‐
the functional characteristics under
steady state running conditions in
the operational
domain, here named the narrow domain ‐
the functional characteristics in the wide domain, necessary to predict transients
The schematic view of a test rig is shown in Figure 6‐6.
Figure 6‐6, test rig ‐ schematic view
Several probes and sensors have
been applied to different sections
of the turbine. A
thorough description of the sensors’ type and placement as well as the purpose and function is listed in Table 6‐1.
-
32
Table 6‐1, probe information
Type of probe/location Purpose/usage
Static pressure inlet manifold, outer radius
Tangential pressure distribution in manifold.
Static pressure, at stator inlet, stator outlet and rotor exit
Internal static pressure distribution
Total pressure, static pressure and flow angles in the r‐x plane at rotor exit
Verification of blade outlet angles performed using 2D‐CFD‐calculations.
Static pressure, exhaust duct
Static pressure distribution in the exhaust duct
Stator surface temperature and Rub indicator
Rotor tip gap verification
The torque and the rotational speed are measured at the shaft, between the common interface load support
structure and the gearbox. Total
pressure and total temperature
are measured before turbine inlet
flange and after turbine outlet
flange, and mass flow will
be measured at the
inlet flange.
The final results after test runs are presented in an Excel file showing the output values from all the sensors mentioned above.
The DVT testing methodology described above has been applied on both LH2 and Lox turbines.
The DVT data has been post‐processed before using as input for TML in a following way:
•
If more than one sensor is sitting on a certain turbine plane, an average value has been taken •
If more than one measurement has
been performed during the experiment,
the average
value has been taken
•
A certain investigation has been performed to figure out cases with “broken sensors4” so that the average values would not be affected
in a negative way. “Broken sensors” values have been omitted
• The average values of
interest have been presented at the
separate Excel‐spreadsheet
for future work.
After the post‐processing raw data coming from DVT a complete array of operating points used for Input
is obtained, as well as a complete Output‐array, showing the output values corresponding to each and every operating point.
The data per operating point contained in input and output arrays is presented further
4 Broken sensors usually return unphysical values, that are omitted
-
33
Input:
•
Stagnation pressure (total pressure in [kPa]) •
Stagnation temperature (temperature in [K]) •
Overall pressure ratio total‐to‐static (dimensionless) •
Rotational speed (in % of a reference speed chosen by user)
Output:
• Overall efficiency total‐to‐static •
Mass flow •
Pressure ratio total‐to‐static
• Pressure ratio total‐to‐static
(where total‐to‐static pressure ratios are between the Stagnation pressure and static pressure at the corresponding plane, 2 – after stator, 3 – after rotor)
Stagnation pressure and temperature variation through the whole input array was almost negligible (their values held close (but not equal) to constant ones, namely 780Pa5 for stagnation pressure and 400K
for stagnation temperature). It has
been decided to keep those
values “as is” in order
to perform the experiments in
a way as close to reality
as possible. However, as described
in
later chapters of this work, the stagnation temperature variations affected the final results dramatically, so the stagnation temperature has been given a constant value, 400K.
Taking the
inlet temperature as a constant
is not the best solution and will be discussed
in further chapters.
5 Due to the confidentiality reasons the values of
and
are presented as constants. The real values are not presented in the current work. For real values see [10].
-
34
The operating points used for DVT tests of the LH2 turbine are presented in Figure 6‐7 and Figure 6‐8. The
envelope plots are showing the
scatter‐field for points used during
DVT tests. After
some research of the actual turbine operating modes several points have been omitted as not being used in reality due to the turbine design issues and thus returning the output values far from experimental when used as
input data for TML runs.
Interesting to know, for LH2 turbine the same “redundant” points
acted as most sensitive ones
when performing the tuning of
K&O loss correlation and produced
numerous crashes of TML when
trying to perform smallest changes
on the calculation routines.
Figure 6‐7, DVT data for operating points, LH2 turbine
The most convenient way to omit several points was to do it speed‐line‐wise. One may observe that the
points in envelope plots for
both LH2 and LOx turbines are
forming horizontal
lines corresponding different constant Nc’s (dimensionless speed coefficient).
The initial amount of operating points in the DVT data array for LH2 turbine was 62. After removing some irrelevant ones the final amount became 40 and has been used during the TML tuning.
omitted points
-
35
Figure 6‐8 below
is the envelope‐plot representing operating points array for LOx turbine. Omitted points are marked by the red line, leaving 56 operating points to perform experiments on.
Figure 6‐8, DVT data for operating points, LOx turbine
Complete arrays of DVT data used
as input and output‐reference for
turbines studied during
this work as well as more information about DVT can be found in [10].
DVT TO6 (0.40 mm)
382
13 18
17
16
15
14
12
11
10
9
8
4426
37 49
5051
52
53
54
55
56
57
58
59
60
61
62
63
64
65
454647
19
252422,232120
7 43 48
0.00
0.05
0.10
0.15
0.20
0.25
1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55
Total-to-total pressure ratio, π tt
Spee
d co
effic
ient
, Nc
omitted points
-
36
6.5 CFD SIMULATIONS
At the early stages of TML optimization process several CFD simulations have been made for stator blades of
the LH2 turbine.
This was mainly done
for obtaining better information about
the flow performance over
the blade rows which could in
future be used as reference
information
for TML loss‐model tuning.
Stator blade 3D‐geometry has been
originally created using
UniGraphics NX v4.0 and is the
one currently used at Volvo Aero Corporation for the CFD simulations. The surrounding domain has been meshed using ICEM v11.0.
Figure 6‐9, stator blade mesh, ICEM v4.0
Boundary conditions applied to the created mesh were fully corresponding to the operating points building a 98% of the reference‐RPM speed line [Appendix A]. Rotational symmetry has also been taken into account.
-
37
Applied boundary conditions as well as rotational symmetry can be seen in Figure 6‐10.
Figure 6‐10, blade mesh with boundary conditions applied, CFXpre
The operating points on which CFD
runs have been performed are
the ones corresponding to
the 98% of the reference‐RPM speed
line
[Appendix A]. The boundary conditions and
initial conditions have been used so that a CFD run would fully represent a corresponding DVT test or a TML‐run.
During post‐processing
the mass‐average values have been
taken and exported
to an Excel‐Chart. The
flow‐function plot has been created
for a 98% speed line CFD
results compared with a similar one based on experimental data as well as the original TML run.
Values of Flow function, ,
(outlet angle) and Mach Number at the outlet were obtained from CFD
runs and compared with the similar ones from original version of TML, as well as the experimental data, DVT. Further in this project, after the updated version of TML has been created, similar values have been obtained and compared to both CFD and original TML results.
The results may be found in [Appendix G]. Results are discussed in further chapters.
-
38
6.6 K&O LOSS‐MODEL TUNING ALGORITHM
Perhaps one of the most
important topics in this work
is the tuning of the currently‐used K&O
loss model. The aim of this tuning process
is to create a methodology that would “patch” the currently used one‐dimensional software, TML, so
that the more reality‐like
results would be obtained. This section describes in detail the process of creating this methodology.
6.6.1 STRATEGY AND APPROACH
As it has already been
mentioned the loss correlation
currently used in TML at Volvo
Aero Corporation is the Ainley and Mathieson correlation as modified by Kacker and Okapuu. The general, very simplified layout of the loss‐model equation reads.
The loss‐model
is applied on each of the turbine blade rows which for LH2 and LOx turbines means two
– stator and rotor. Performing
a rough tuning of the
loss model may provide
unpredictable results depending on the blade geometry and gas behavior on the currently studied blade row. This is why
a very flexible, operating points‐
and turbine blade row‐dependant
tuning methodology has been created.
The main principle was to
create a polynomial in front of
every loss‐model equation term.
A polynomial should be a second‐order function of NC (dimensionless speed coefficient) and PR (total‐to‐static pressure ratio, taken from input). An example layout is shown below.
· … …
…
As it can be seen from
equation above the polynomial
initially consists of six terms,
namely a constant, two linear,
two quadratic and a coupling
term, each multiplied with a certain coefficient (
). Finding optimal coefficients would provide with eight optimal polynomials, each having six constants. The polynomials would tune the output results of K&O model thus providing more reality‐like output results of TML.
Allowing all the coefficients to take different values independently of
‐ Position inside the polynomial ‐
Loss‐model term ‐ Blade row
one would obtain 24 coefficients for a single blade row or 48 coefficients for the whole LH2 or LOx turbine to be determined. The numbering starts with the first