Advanced computational methods in identification of thermo-acoustic systems [Elektronische Ressource] / Krzysztof Kostrzewa. Betreuer: Manfred Aigner
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Advanced computational methods in identification of thermo-acoustic systems [Elektronische Ressource] / Krzysztof Kostrzewa. Betreuer: Manfred Aigner

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1 Advanced computational methods in identification of thermo-acoustic systems A thesis accepted by the Faculty of Aerospace Engineering and Geodesy of the Universität Stuttgart in partial fulfilment of the requirements for the degree of Doctor of Engineering Sciences (Dr.-Ing.) by Dipl.-Ing. Krzysztof Kostrzewa born in Poznan Main referee: Prof. Dr.-Ing. Manfred Aigner Co-referee: Prof. Dr.-Ing. Franz Joos thDate of defence: 17 Dezember 2010 Institute of Combustion Technology for Aerospace Engineering University of Stuttgart 2011 II 3 Acknowledgments This thesis emerged from the studies I conducted during my employment with the Institute of Combustion Technology (VT) at DLR in Stuttgart between 2003 and 2007. It is the result of an applied research, which had many contributors to its success. First of all, I would like to acknowledge the support and help of numerous people, without whom this thesis would not have been ever possible: My warmest thanks to Siemens AG from Mülheim an der Ruhr and DLR from Stuttgart for providing the funding and equipment to undertake this project. Especially I would like to mention here Dr. -Ing. Michael Huth and Dr. -Ing. Werner Krebs from Siemens AG, Prof. Dr. -Ing. Manfred Aigner and Dr. -Ing. habil.

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1

Advanced computational methods in
identification of thermo-acoustic
systems



A thesis accepted by the Faculty of Aerospace Engineering and Geodesy of the
Universität Stuttgart in partial fulfilment of the requirements for the degree of
Doctor of Engineering Sciences (Dr.-Ing.)


by

Dipl.-Ing. Krzysztof Kostrzewa

born in Poznan


Main referee: Prof. Dr.-Ing. Manfred Aigner
Co-referee: Prof. Dr.-Ing. Franz Joos
thDate of defence: 17 Dezember 2010



Institute of Combustion Technology for Aerospace Engineering
University of Stuttgart
2011
II







































3




Acknowledgments



This thesis emerged from the studies I conducted during my employment with the Institute of
Combustion Technology (VT) at DLR in Stuttgart between 2003 and 2007. It is the result of an applied
research, which had many contributors to its success.
First of all, I would like to acknowledge the support and help of numerous people, without whom this
thesis would not have been ever possible:
My warmest thanks to Siemens AG from Mülheim an der Ruhr and DLR from Stuttgart for providing
the funding and equipment to undertake this project. Especially I would like to mention here Dr. -Ing.
Michael Huth and Dr. -Ing. Werner Krebs from Siemens AG, Prof. Dr. -Ing. Manfred Aigner and Dr. -Ing.
habil. Berthold Noll from DLR who provided invaluable information and advices, which helped steer the
project in a direction leading to its successful conclusion.
Furthermore, I would like to thank to my supervisors: Dr. -Ing. Joachim Lepers, Dr. -Ing. Sven Bethke
and Dipl. -Ing. Peter Kaufmann from Siemens with whom I was honored to work. Their positive attitudes
and useful advises kept the project moving forward even when the outlook seemed grim. I appreciate
their personal character and expertise that provided the insight to overcome the many issues
encountered in this project.
Thanks also to Prof. Wolfgang Polifke and Dr. -Ing. Andreas Huber from TU München for all their
advices and assistance with regard to system identification. I also highly appreciate the possibility to
work with the Acoustic Postprocessor developed at TU München.
Many thanks go out to all persons I have had the privilege of getting to know during my time at DLR
and Siemens. Especially, I would like to thank Dipl. -Ing. Axel Widenhorn from DLR for his great
assistance during this project. He was an invaluable source for almost any questions regarding acoustic
boundary conditions.
Finally, I would like to thank my entire family. My parents and wife have always supported my
endeavors. They have been always a great source of my motivations and inspirations. Through often-
difficult situations, my wife provided me a good home environment and an understanding for me.







4


































4 i




Contents



LIST OF FIGURES .............................................................................................................. V
LIST OF TABLES ............................................................................................................. XIII
NOMENCLATURE.............................................................................................................XV
ZUSAMMENFASSUNG ....................................................................................................XXI
SUMMARY .....................................................................................................................XXIII
1 INTRODUCTION.............................................................................................................1
1.1 RESEARCH OBJECTIVE ...................................................................................................... 4
1.2 LITERATURE OVERVIEW..................................................................................................... 5
1.3 THESIS OUTLINE.................................................................................................................. 7
2 THERMO-ACOUSTICALLY INDUCED COMBUSTION INSTABILITIES......................11
2.1 MECHANISM OF COMBUSTION INSTABILITIES.............................................................. 11
2.1.1 Rayleigh’s Criterion .................................................................................................................. 12
2.2 THERMO-ACOUSTIC INSTABILITIES SOLUTIONS METHOD ......................................... 13
2.2.1 Passive means......................................................................................................................... 13
2.2.2 Active means............................................................................................................................ 14
3 ACOUSTIC MODELING ...............................................................................................15
3.1 THEORY AND BASIC CONCEPTS..................................................................................... 15
3.1.1 Wave equation ......................................................................................................................... 15
3.1.2 Validity of linearity assumptions in thermo-acoustics ............................................................... 18
3.1.3 Solution methods ..................................................................................................................... 19
3.1.3.1 One-dimensional acoustic wave propagation.................................................................... 19
3.1.3.2 Acoustic damping.............................................................................................................. 21
3.1.3.3 Acoustic Impedance.......................................................................................................... 23
3.2 ONE-DIMENSIONAL ACOUSTIC NETWORK MODELS .................................................... 24
3.2.1 Transfer matrix method ............................................................................................................ 25
3.2.1.1 Straight duct element ........................................................................................................ 26

i ii Contents

3.2.1.4 Feedback mechanism in combustion systems.................................................................. 30
3.2.1.5 Characterization of acoustic stability................................................................................. 32
3.2.1.6 Limitation of the one-dimensional acoustic network codes ............................................... 34
4 MODELING OF TURBULENT REACTIVE AND NON-REACTIVE FLOWS
USING CFD ..................................................................................................................37
4.1 THEORY AND NUMERICAL MODELING OF TURBULENCE............................................ 37
4.1.1 Numerical simulation of turbulence .......................................................................................... 38
4.1.2 RANS modeling........................................................................................................................ 39
4.1.2.1 Classical turbulence models for unclosed terms ............................................................... 41
4.1.3 Unsteady RANS modeling........................................................................................................ 43
4.1.3.1 CFL requirement ............................................................................................................... 44
4.2 COMBUSTION MODELING................................................................................................. 45
4.2.1 Turbulent premixed flames....................................................................................................... 46
4.2.2 Combustion models.................................................................................................................. 47
5 NUMERICAL SYSTEM IDENTIFICATION OF THERMO-ACOUSTIC ELEMENTS ......51
5.1 FUNDAMENTALS OF NUMERICAL SYSTEM IDENTIFICATION...................................... 51
5.1.1 Characterization of discrete time systems................................................................................ 52
5.1.2 Linear Time Invariant (LTI) Systems ........................................................................................ 53
5.1.3 Frequency response of LTI systems ........................................................................................ 54
5.1.3.1 z-Transformation............................................................................................................... 54
5.1.3.2 Inverse z-Transformation .................................................................................................. 55
5.2 MODELS OF LTI SYSTEMS................................................................................................ 55
5.3 WIENER-HOPF EQUATION................................................................................................ 56
5.3.1 Auto-correlation matrix ............................................................................................................. 57
5.3.2 Cross-correlation vector ........................................................................................................... 58
5.4 RECONSTRUCTION OF THERMO-ACOUSTIC ELEMENTS BY MEANS OF CFD/SI...... 58
5.4.1 Acoustic boundary conditions................................................................................................... 59
5.4.2 Forcing signals ......................................................................................................................... 61
5.4.2.1 Harmonic function ............................................................................................................. 61
5.4.2.2 White noise ....................................................................................................................... 62
5.4.3 Causality and choice of variables............................................................................................. 62
5.4.4 Location of the reference planes .............................................................................................. 64
5.4.5 Extraction of time series........................................................................................................... 65
5.4.6 Acoustic variables p’ and u’ and normalization......................................................................... 66
5.4.7 Optimal setting for numerical system identifications................................................................. 66

Contents iii

5.4.7.1 Filter order L and jump factor m ........................................................................................ 67
5.4.7.2 Sampling and frequency increment................................................................................... 69
5.4.7.3 First approximation for a value of L................................................................................... 69
5.4.7.4 Optimal settings for L and m ............................................................................................. 70
6 DUCT WITH A SUDDEN CHANGE OF DIMENSION....................................................73
6.1 ANALYTICAL MODEL FOR A SUDDEN CHANGE OF DIMENSION ................................. 73
6.2 CFD COUPLED WITH SYSTEM IDENTIFICATION (CFD/SI) ............................................ 74
6.2.1 Boundary conditions and CFD model....................................................................................... 75
6.2.2 Steady state solution................................................................................................................ 76
6.3 VALIDATION OF CFD/SI WITH MEASUREMENTS, FEM AND ANALYTICAL MODEL.... 77
6.4 OPTIMAL VALUES OF L AND M FOR CFD/SI ................................................................... 80
6.5 SENSITIVITY STUDY .......................................................................................................... 80
6.5.1 Spatial discretization dx............................................................................................................ 80
6.5.2 Time descritization dt ............................................................................................................... 82
6.5.3 Time scheme variations ........................................................................................................... 85
7 TRUNCATED TEARDROP SPECIMEN........................................................................89
7.1 CFD/SI APPROACH TO RECONSTRUCT ACOUSTIC TRANSFER MATRICES.............. 90
7.1.1 CFD model and Boundary Condition........................................................................................ 90
7.1.2 Steady state flow field .............................................................................................................. 92
7.2 ACOUSTIC TRANSFER MATRIX BY MEANS OF CFD/SI AND ONE-DIMENSIONAL
ACOUSTIC MODELING....................................................................................................... 93
7.3 OPTIMAL VALUES OF L AND M......................................................................................... 95
7.4 ACOUSTIC REFLECTIVITY AT BOUNDARIES.................................................................. 96
7.5 IMPEDANCE CALCULATION.............................................................................................. 98
8 ATMOSPHERIC TEST RIG WITH A GENERIC BURNER..........................................103
8.1 TEST RIG DESCRIPTION ................................................................................................. 103
8.2 URANS MODELING........................................................................................................... 105
8.3 RANS SOLUTIONS............................................................................................................ 107
8.4 VALIDATION OF THE FLAME TRANSFER FUNCTION CALCULATION ........................ 108
8.5 CFD/SI VS. TIME LAG APPROACH.................................................................................. 110
8.6 CFD/SI VS. HARMONIC FORCING .................................................................................. 111
8.7 SENSITIVITY STUDY ........................................................................................................ 113
8.7.1 Combustion modeling............................................................................................................. 113
8.7.2 Boundary conditions............................................................................................................... 117
8.7.2.1 Harmonic excitation at 60 Hz .......................................................................................... 119

iv Contents

8.7.3 Time resolution....................................................................................................................... 122
9 INDUSTRIAL TEST RIG WITH A GENERIC BURNER AT ELEVATED
PRESSURE ................................................................................................................125
9.1 URANS MODELING........................................................................................................... 126
9.1.1 Steady State Solution............................................................................................................. 128
9.2 RECONSTRUCTION OF FLAME TRANSFER FUNCTION.............................................. 129
9.3 EXPERIMENTAL PRESSURE SPECTRUM MEASUREMENTS VS. STABILITY
PREDICTION BASED ON A ONE-DIMENSIONAL ACOUSTIC NETWORK CODE ........ 130
9.3.1 CFD/SI vs. time lag approach ................................................................................................ 131
9.3.2 Stability prediction based on CFD-based transfer functions................................................... 132
10 SAS BASED FORCED RESPONSE OF AN ATMOSPHERIC TEST RIG WITH
A GENERIC BURNER ................................................................................................137
10.1 SAS MODELING ................................................................................................................ 137
10.2 SAS BASED SPACE AND TIME-RESOLVED FLOW FIELD............................................ 139
10.3 SAS WITH A HARMONIC FORCING ................................................................................ 142
11 SAS OF INDUSTRIAL TEST RIG AT ELEVATED PRESSURE .................................147
11.1 SAS MODELING ................................................................................................................ 147
11.2 SAS SPACE AND TIME-RESOLVED FLOW FIELD ......................................................... 149
12 SIMULATION OF SELF-EXCITED OSCILLATIONS ..................................................155
12.1 URANS CALCULATION OF SELF-EXCITED OSCILLATIONS ........................................ 156
12.2 VALIDATION OF CFD-BASED ACOUSTIC MODES BY MEANS OF
A ONE-DIMENSIONAL ACOUSTIC CODE....................................................................... 158
13 CONCLUSIONS AND RECOMMENDATIONS ...........................................................161
A TURBULENCE MODELS............................................................................................165
B TIME DISCRETIZATION.............................................................................................166
C ANALYTICAL TIME LAG MODELS ...........................................................................167
D SOLUTION ERROR ANALYSIS .................................................................................169
E APPROXIMATION OF IMPEDANCE BOUNDARY CONDITIONS..............................171
F HPC - COMPUTATIONAL RESOURCES ..................................................................172
LITERATURE ...................................................................................................................175


v




List of Figures



Fig. 1.1 Cross section of the SGT6-6000G gas turbine......................................................1
Fig. 1.2 NACOR Project - competence circle .....................................................................2
Fig. 2.1 A schematic of the feedback loop responsible for combustion instabilities
[5][84]..................................................................................................................12
Fig. 3.1 Acoustic wavelength in a mixture of burnt gasses as a function of temperature
and frequency.....................................................................................................19
Fig. 3.2 Sound waves traveling in a tube .........................................................................20
Fig. 3.3 Damping coefficient as a function of Mach number: red circles – thermo-
viscous effects, dark blue circles turbulence effects, green circle – sum of two
effects.................................................................................................................23
Fig. 3.4 An example of one-dimensional acoustic network model of a premixed burner...25
Fig. 3.5 Symbolic conventions for a straight duct element ...............................................27
Fig. 3.6 The acoustic wave propagation in connected ducts ............................................28
Fig. 3.7 Flame element: acoustic jump condition .............................................................29
Fig. 3.8 Simple acoustic model with a flame ....................................................................30
Fig. 3.9 A sketch of a generic partially premixed system..................................................31
Fig. 3.10 The eigenfrequency of the simple model: green triangle - interaction index
n=0.5,red rectangular n=1,5................................................................................34
Fig. 4.1 Arbitrary variable in a turbulent flow solved by DNS, LES and RANS..................38
Fig. 4.2 Periodic oscillation with superimposed turbulent fluctuations ..............................43
Fig. 4.3 Borghi turbulent combustion diagram [40]...........................................................46
Fig. 5.1 Block representation of an arbitrary system [95] .................................................52
Fig. 5.2 The system of interest: a thermo-acoustic element and reference planes [50] ....59
Fig. 5.3 Tube and wave propagation [46].........................................................................63

v vi List of Figures

Fig. 5.4 Location of the reference planes and the boundary of the black box [50]............64
Fig. 5.5 Acoustic transfer matrix of a sudden change of dimensions for the transfer
matrix element T : analytical solution (red rectangular) and CFD/SI for 11
different length of L: L=10 (green circle) and L=20 (blue triangle) .......................68
Fig. 5.6 Correlation between L, m and τ for a given filter [50]......................................68 mem
Fig. 5.7 The least square error as a function of L for a prototype burner..........................71
Fig. 5.8 Relative quadratic difference of the transfer matrix element T of the truncated 11
teardrop for a variation of m values.....................................................................72
Fig. 6.1 Geometry of a sudden change of dimension [50] ................................................73
Fig. 6.2 Acoustic element represented by the generalized CFD setup .............................74
Fig. 6.3 Simplified CFD model of a sudden change of dimensions...................................75
Fig. 6.4 Local axial velocity and pressure distributions.....................................................76
Fig. 6.5 Acoustic Transfer Matrix: Normalized Amplitude: red rectangular – analytical
model, blue rectangular – FEM, grey rectangular – measurements, green
rectangular – CFD/SI ..........................................................................................78
Fig. 6.6 Acoustic Transfer Matrix: Phase: red triangle – theory, blue triangle – FEM,
grey triangle measurements, green triangle – CFD/SI........................................79
Fig. 6.7 The Relative quadratic difference of the element T as a function of L and m ....80 11
Fig. 6.8 Spatial discretization dx variations: Normalized amplitude: green diamond –
11000 nodes, red diamond – 23000 nodes, yellow diamond 41000, grey
diamond – measurements...................................................................................81
Fig. 6.9 Spatial discretization dx variations: Phase: green diamond – 11000 nodes, red
diamond – 23000 nodes, yellow diamond 41000, grey diamond –
measurements....................................................................................................82
Fig. 6.10 Relative truncation errors as a function of number of time steps N [24]: red
rectangular – relative time derivative error, green triangle – relative absolute
error....................................................................................................................83
Fig. 6.11 Time discretization dt variations: Normalized Amplitude: green circle –
dt=2.5e-5 s, red circle dt=5e-5 s, grey circle – measurements ............................84


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