Finite element simulation of flow-induced noise using Lighthill's acoustic analogy [Elektronische Ressource] / vorgelegt von Max Escobar

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• Physik

Informations

• Publié par: friedrich-alexander-universitat_erlangen-nurnberg
• Publié le: 01 janvier 2007
• Nombre de lectures: 20
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Finite Element Simulation
of Flow-Induced Noise using
Lighthill’s Acoustic Analogy
Der Technischen Fakult¨at der
Universit¨at Erlangen-Nu¨rnberg
zur Erlangung des Grades
DOKTOR - INGENIEUR
vorgelegt von
M.Sc. Max Escobar
Erlangen, 2007Als Dissertation genehmigt von
der Technischen Fakult¨at der
Universit¨at Erlangen-Nu¨rnberg
Tag der Einreichung: 23. April 2007
Tag der Promotion: 13. Juli 2007
Dekan: Prof. Dr.-Ing. A. Leipertz
Berichterstatter: PD Dr.-techn. M. Kaltenbacher
Prof. Dr. C.-D. Munz
Prof. Dr. Dr. h.c. F. DurstFinite Elemente Simulation
von str¨omungsinduziertem L¨arm nach
Lighthills akustischer Analogie
Der Technischen Fakult¨at der
Universit¨at Erlangen-Nu¨rnberg
zur Erlangung des Grades
DOKTOR - INGENIEUR
vorgelegt von
M.Sc. Max Escobar
Erlangen, 2007Als Dissertation genehmigt von
der Technischen Fakult¨at der
Universit¨at Erlangen-Nu¨rnberg
Tag der Einreichung: 23. April 2007
Tag der Promotion: 13. Juli 2007
Dekan: Prof. Dr.-Ing. A. Leipertz
Berichterstatter: PD Dr. techn. M. Kaltenbacher
Prof. Dr. C.-D. Munz
Prof. Dr. Dr. h.c. F. DurstAcknowledgements
The present work was carried out at the Department of Sensor Technology, University of
Erlangen-Nuremberg in Erlangen, Germany. It was funded at the beginning by the Com-
petence Network for Technical, Scientific High Performance Computing in Bavaria (KON-
WIHR) and since 2004 continued as part of the research project “Fluid-Struktur-L¨arm”
funded by the Bavarian Research Foundation (BFS).
This thesis was realised under the supervision of PD Dr. techn. Manfred Kaltenbacher. To
him I would like to express my deepest gratitude for his invaluable support, orientation and
constant encouragement.
Inaddition,Iwouldliketoexpress mysinceregratitudetoProf. Dr.-Ing. ReinhardLerchfor
his opportune advices and for providing the right environment for carrying out the present
work. Also,IwouldliketothankallmembersoftheDepartmentforthepleasantatmosphere
that they created and for their invaluable help in many aspects during my work, especially
concerning the german translations.
Regarding the cooperation during the project with the Institute of Fluid Mechanics LSTM,
firstofallIwouldliketothankProf. Dr. Dr. h.c. FranzDurstforhissupporttotheproject.
Besides, I express my very special gratitude to Dr. Stefan Becker and his co-workers M.Sc.
IrfanAliandDr. FrankSch¨aferfortheircloseco-operationduringtheprojectconcerningthe
computation of the unsteady flows and for the fruitful discussions concerning the numerical
simulations.
Finally, I would like to thank my family and -being consistent with the terminology used in
this work- my friends in the near and far fields for their permanent encouragement.
ia mis padres y a Esther
iiContents
Abstract vii
List of symbols ix
1 Introduction 1
1.1 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State of the art and current trends . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Current CAA approaches . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Solution approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Outline of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 CAA Methodologies 11
2.1 Hybrid approaches based on acoustic analogies . . . . . . . . . . . . . . . . . 14
2.1.1 Lighthill’s acoustic analogy. . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Volume integral formulations. . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3 Surface integral formulations . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.4 Variational formulation of Lighthill’s acoustic analogy . . . . . . . . . 22
2.1.5 Comparison of integral and variational formulations of the acoustic
analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Approaches based on perturbation quantities . . . . . . . . . . . . . . . . . . 24
2.2.1 LEE based methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.2 Acoustic Pertubation Equations . . . . . . . . . . . . . . . . . . . . . 25
2.2.3 Perturbed Compressible Equations . . . . . . . . . . . . . . . . . . . 27
2.3 Heterogeneous domain decomposition for aeroacoustics . . . . . . . . . . . . 28
3 FE formulation of Lighthill’s acoustic analogy 31
3.1 Strong Formulation of the Inhomogeneous Wave
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Weak Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Spatial Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Time discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Harmonic formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 FE evaluation of the acoustic source term . . . . . . . . . . . . . . . . . . . 38
iii4 Simulation of Unbounded Domains 41
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Absorbing Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Derivation of local ABCs . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.2 Finite Element Formulation . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.3 Evaluation of the ABC Implementation . . . . . . . . . . . . . . . . . 47
4.3 Perfectly Matched Layer - PML . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1 Basic Ideas of Matching . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 Construction of Perfectly Matched Layers . . . . . . . . . . . . . . . 53
4.3.3 Choice of Damping Functions . . . . . . . . . . . . . . . . . . . . . . 55
4.3.4 Finite Element Formulation . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.5 Evaluation of the PML Implementation . . . . . . . . . . . . . . . . . 58
5 Coupling of fluid and acoustic computations 61
5.1 Simulation schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Transfer of the coupling quantities . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.1 Neighborhood Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.2 Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.3 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Validation of the implementation 69
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Theoretical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.3 Numerical Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3.1 Validation of vortex sound propagation using the perturbation formu-
lation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3.2 Validation of vortex sound propagation following Lighthill’s acoustic
analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7 Application 79
7.1 Flow-Induced Noise from a 2D square cylinder . . . . . . . . . . . . . . . . . 79
7.1.1 Fluid Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.1.2 Investigation of the interpolated acoustic sources . . . . . . . . . . . 81
7.1.3 Acoustic Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 Flow-Induced Noise from 3D wall-mounted cylinders . . . . . . . . . . . . . 91
7.2.1 Fluid computation of wall-mounted square cylinder . . . . . . . . . . 92
7.2.2 Fluid computation of wall-mounted cylinder with elliptic profile . . . 94
7.2.3 Acoustic Computations . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8 Conclusions 105
A Turbulence modelling 109
A.1 LES approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 SAS approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Bibliography 111
ivGerman part 119
Inhaltverzeichnis 121
Kurzfassung 123
1 Einleitung 125
1.1 Problemstellung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
1.2 Stand der Technik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
1.2.1 Hintergrund . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
1.2.2 Aktuelle CAA Verfahren . . . . . . . . . . . . . . . . . . . . . . . . . 127
1.3 Lo¨sungsansatz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
¨1.4 Uberblick der Arbeit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
2 Zusammenfassung 135
vvi