Fundamentals of Aeroacoustics with Applications to Aeropropulsion Systems

558 Pages·2020·38.505 MB·English

by  Xiaofeng Sun, Xiaoyu Wang

FUNDAMENTALS OF
AEROACOUSTICS WITH
APPLICATIONS TO
AEROPROPULSION SYSTEMS
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FUNDAMENTALS OF
AEROACOUSTICS WITH
APPLICATIONS TO
AEROPROPULSION SYSTEMS
Elsevier and Shanghai Jiao Tong
University Press Aerospace Series
XIAOFENG SUN
Fluid and Acoustic Engineering Laboratory,
School of Energy and PowerEngineering,
Beihang University, Beijing, China
XIAOYU WANG
Fluid and Acoustic Engineering Laboratory,
Research Institute of Aero-Engine,
Beihang University, Beijing, China
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Contents
Preface vii
1. Basic equations of aeroacoustics 1
1.1 Soundsourcesinmovingmedia 3
1.2 GeneralizedGreen’sformula 17
1.3 Lighthillequation 20
1.4 FfowcsWilliams-Hawkingsequation 24
1.5 GeneralizedLighthill’sequation 29
References 32
2. Propellernoise: Prediction andcontrol 33
2.1 Noisesourcesofpropeller 33
2.2 Propellernoisepredictioninfrequencydomain 41
2.3 Propellernoisepredictionintimedomain 57
References 70
3. Noise prediction in aeroengine 73
3.1 Noisesourcesinaeroengine 73
3.2 Tonenoisebyrotor/statorinteractioninfan/compressor 78
3.3 Shockwavenoiseinfan/compressor 98
3.4 Combustionnoise 117
3.5 Jetnoise 119
References 130
4. Linearized unsteady aerodynamicsfor aeroacoustic
applications 135
4.1 Introduction 135
4.2 Basiclinearizedunsteadyaerodynamicequations 136
4.3 Unsteadyloadingfortwo-dimensionalsupersoniccascadeswith
subsonicleading-edgelocus 143
4.4 Liftingsurfacetheoryforunsteadyanalysisoffan/compressor
cascade 165
References 203
v
vi Contents
5. Vortex soundtheory 207
5.1 Introductiontosoundgenerationinducedbyvortexflow 207
5.2 Basicequationsofvortexsound 208
5.3 Vortexsoundmodeloftrailingedgenoise 217
5.4 Vortexsoundmodeloflinerimpedance 223
5.5 Effectofgrazingflowonvortexsoundinteractionofperforated
plates 231
5.6 Nonlinearmodelofvortexsoundinteraction 242
References 257
6. Sound generation, propagation, andradiation in/from an
aeroengine nacelle 261
6.1 Introduction 261
6.2 Basictheoryofsoundpropagationinducts 262
6.3 Computationalapproachesforductacoustics 265
6.4 Fannoisesourcemodeling 346
6.5 Interactioneffect 391
References 410
7. Thermoacoustic instability 415
7.1 Basicconceptsofthermoacoustics 415
7.2 One-dimensionalcalculationmethod 417
7.3 Three-dimensionallinearcombustioninstabilityanalysismethod 421
7.4 ControlofthermoacousticinstabilityinaRijketube 467
AppendixA Coefficientsofthematchingconditions 486
AppendixB Coefficientsofthematchingconditionsforvariable
cross-sectionscases 488
AppendixC CoefficientsinEq.(7.149) 495
AppendixD CoefficientsinEq.(7.169) 497
References 498
8. Impedance eduction for acoustic liners 501
8.1 Introduction 501
8.2 Straightforwardmethodofacousticimpedanceeduction 504
8.3 Shearfloweffectontheimpedanceeduction 511
8.4 3-Dstraightforwardmethodofacousticimpedanceeduction 517
References 530
Index 533
Preface
Aeroacousticshaditsbeginningsintheearly1950sthankstothepioneering
work of SirJames Lighthillabout aerodynamic sound. Sincethen, thisdis-
ciplinehasconcentratedonunderstandingnoisegenerationbyeitherturbu-
lent fluid motion or aerodynamic forces interacting with surfaces. In
particular, emphasis has also been placed on aeronautical applications for
noise reduction of both aircraft and aeropropulsion systems. At present,
there are already several books available that introduce basic knowledge
andprogressinitsvariousaspects.Itisnoted,however,thatthemostprom-
inent noise sources of modern aircrafts originate from the aeropropulsion
system in many situations; meanwhile, the thermoacoustic oscillations
occurringin the combustion chamberof the aeroengine hasreceived great
attention on its prediction and control, which is equally related to aeroa-
coustics. Therefore, it is necessary to have a book dedicated to aeroengine
acoustic problems.
Asiswellknown,therearevariousscales,suchasdifferentvortexstruc-
tures,entropy,andpressurefluctuationsinmovingflowmedia,whichmake
itextremelydifficulttoaccuratelycalculateandanalyzeallflowandacoustic
fielddetailsundertheconditionofmultiscales.Therearethustwowaysto
getworkdone.OnemethodisLighthill’sacousticanalogytheory,whichis
stillwidelyappliedinvariousaerodynamicnoisecalculations,especiallyfor
rotating source prediction. The other method is numerical techniques like
computational aeroacoustics (CAA), which suppresses both dissipation and
dispersion on the basis of the differential schemes. There is no doubt that
CAA has shown great potential for the study of jet noise and other flow-
induced acoustic problems. Still, given the limits of current computational
capabilities, acoustic computation for a problem of practical interest is still
out of reach by directly solving Navier-Stokes equations, particularly for
anumericalsimulationofrotatingormovingsoundsourceproblemsinasso-
ciation with aeroengine noise generation.
Withreferencetothecontext,theaimofthisbookistodevelopaunified
frameworktohandletheacousticproblemofaeropropulsionsystemsforthe
design phase of an aeroengine; meanwhile, it is also intended for scientists,
engineers,andgraduateswhoareinterestedinmodelinganddoingitright.
Therefore,thecorepartsofthisbookarestillbasedontheacousticanalogy
theoryortheunifiedsolutionapproachofflowandacousticfieldsunderthe
vii
viii Preface
linearizing assumption. More importantly, the theoretical work described
herein is substantially a compilation of our research publications, except
thebasicknowledgeofaeroacousticequations.Inaddition,itisworthnot-
ing that understanding the mechanism of the aeroengine noise generation
andwhatmethodscanbeusedtopredictorsuppresstheresultingnoisehave
beenthecoreproblemofaeroacousticresearch.Thisbookwillfocusonpre-
senting our research results and other important progress in these regards.
The outline of the bookis as follows: Chapter1 consistsof a colloquial
introduction to basic equations of aeroacoustics with an emphasis on the
application of Green’sfunctionmethod.Advancedpropeller noisegenera-
tionandpredictionaregiveninChapter2,accompaniedbythesolutionof
Ffowcs Williams-Hawkings equation using both frequency and time
domain methods. This is followed in Chapter 3 by a brief introduction of
various aerodynamic noise sources in the aeroengine. This chapter also
involvescertainalgorithmdetailsforbothrotor/statorinteractionandshock
noise predictions. Chapter 4 is composed of a detailed description of
unsteadyaerodynamicsof compressorcascade,whichshowshowto calcu-
lateaerodynamicbladeloadingunderlinearizingassumption.Adescription
of vortex sound theory is providedin Chapter 5, which introduces discus-
sion and analysis on how to use the discrete vortex method to study the
energy exchange between vortex and acoustic waves. Then in Chapter 6,
the Transfer Element Method (TEM) and its applications are introduced
indetail.TheTEMcanbeappliedtostudyvariousinteractingproblemslike
theinteractionbetweenasoundsourceandacoustictreatmentinflowducts.
Thisisalsooneofthecorepartsofourresearchworkpresentedinthisbook.
Chapter7dealswiththethermoacousticproblemorcombustioninstabilities
in an aeropropulsion system. This chapter is particularly devoted to the
recent progress, both algorithmical and theoretical, in applying the three-
dimensionalthermoacousticmodel,includingacoustictreatment,toamore
complexcombustionsystem.Finally,Chapter8touchesupontheeduction
ofwallacousticimpedance,whichisconsideredoneofthemostimportant
aeroacoustictests.Thestraightforwardimpedanceeductionmethodandits
latest developments are expounded along with the relevant experimental
and computational results.
Thewritingofthisbooktremendouslybenefitsfromtheexistingtheo-
ries and various research results openly published in this discipline. We are
particularlygratefultotheseauthorsfortheirvaluablecontributionstogether
withvariouscitationsmarkedinthisbook.ProfessorVigorYangintroduced
ustothefieldofthermoacoustics,andsomejointresearchwithhishelphas
Preface ix
beenreflectedinChapter7.Hispreciouscontributionisverymuchappre-
ciated. Moreover, the core contents of this book originate from the work
of our faculty and graduates in different periods of time at the Fluid and
Acoustic Engineering Laboratory, BUAA. Accordingly, we would like to
takethisopportunitytothankthesepeoplewhopartlycontributedandread
the manuscript and suggested definite improvements, including Professor
Xiaodong Jing, Dr. Zhiliang Hong, Mr. Guangyu Zhang, Mr. Lingfeng
Chen,Dr.AnLiang,Dr.WeiguangZhang,Ms.YuSun,Mr.ZhuoWang,
Dr. Lin Du, Dr. Lei Li, Dr. Xiwen Dai, Mr. Wei Dai, Ms. Lei Qin, and
Mr. Shuo Tian.
Furthermore,weareindebtedtothecontinuoussupportofourresearch
bytheNationalNatural ScienceFoundationofChina(NSFC),andbythe
973 projects of the Ministry of Science and Technology, China.
Finally,wewishtoexpressourgratitudetoDr.FangzhenQianofShang-
hai Jiao Tong University Press for her indispensable enthusiasm, patience,
and care throughout this project.
Xiaofeng Sun
Xiaoyu Wang
Beihang University
Beijing, China
February 2020