Evaluation of impedance boundary conditions in ANSYS Fluent

69 Pages·2017·1.8 MB·English

SEMESTERARBEIT
Evaluation of impedance boundary conditions
in ANSYS Fluent
Autor:
MichaelBertsch
Matrikel-No:
03640853
Betreuer:
AlexanderAvdonin,M.Sc.
Prof.WolfgangPolifke,Ph.D.
September29,2017
TechnischeUniversitätMünchen
FakultätfürMaschinenwesen
ProfessurfürThermofluiddynamik
Prof.WolfgangPolifke,Ph.D.

Erklärung
Hiermitversichereich,dievorliegendeArbeitselbstständigverfasstzuhaben.Ichhabekeine
anderenQuellenundHilfsmittelalsdieangegebenenverwendet.
Ort,Datum MichaelBertsch
Abstract
The application of impedance boundary conditions reduces the computational cost of CFD
(computational fluid dynamics) simulations. For example, if one is only interested in com-
bustionstability,itispossibletosimulatethecombustionchamberonly.Theremainingparts
of the engine up- and downstream of the combustion chamber are modelled by impedance
boundaryconditions.Theaimofthisthesisistoevaluatetheimpedanceboundaryconditions
implementedinANSYSFluent.Thereforeweinvestigatethenon-reflectingoutletoflaminar
andturbulentpipeflows.Inanothersetuptheinfluenceofnon-reflectingwallsectionsisex-
aminedforlaminarandturbulentpipeflows.Inaddition,weprescribeanimpedanceatthe
inletandoutletoflaminarandturbulentpipeflows.Finally,weevaluatenon-reflectingwalls
incombustionchambers.
Usingimpedanceboundaryconditionsatinletsoroutlets,onecanmodelorifices.Setting
the reflection coefficient for acoustic waves by means of imposing an impedance on an in-
oroutflowboundaryispracticableinprinciple.However,whenmeasuringtheflowvariables
on this boundary, thus determining the actual reflection coefficient, observed and imposed
reflectioncoefficientdiverge.Incontrasttotheimposedreflectioncoefficient,theboundary
shows reflecting behaviour towards low frequencies. This behaviour is observed for laminar
and turbulent test cases. The reason is an additional constraint to prevent the mean fields
fromdrifting.Non-reflectingbehaviouratlowfrequenciesimproveswhenthecharacteristic
domainlengthislarger.
Another part of this thesis is dedicated to the evaluation of the consequences when im-
posing a non-reflecting boundary condition on the walls of the domain, which can be used
to model mufflers. When changing the behaviour of a wall section from reflecting to non-
reflecting,themagnitudeofdownstreampropagatingacousticwavesdecreasesconsiderably.
Sequential combustors are prone to transverse thermal instabilities, which can be elim-
inated in a simulation using non-reflecting walls. Therefore we investigate the influence of
non-reflectingwallsonastablecombustionsimulation.Twocombustiontestcasesareused
to determine the influence of the acoustic parameters of the combustion chamber wall on
the flame. It shows that setting the combustion chamber walls to non-reflecting has only a
marginal effect on mean flow fields. The flame position does not change when using non-
reflectingwalls.
iv
Contents
Nomenclature viii
1 Introduction 1
1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Theoreticalprinciples 3
2.1 Computationalfluiddynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Navier-Stokesequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Numericalmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Characteristicvariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Characterisitcwavepropagation . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Reflectingbehaviourofanoutflowboundary . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Restrictionsfornon-reflectingboundaryconditions . . . . . . . . . . . . . 10
2.4 Impedanceboundaryconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Systemidentification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 FlowsimulationwithANSYSFluent 15
3.1 Flowsolvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Non-reflectingboundaryconditionsinFluent . . . . . . . . . . . . . . . . . . . . . 17
3.3 ImpedanceboundaryconditionsinFluent . . . . . . . . . . . . . . . . . . . . . . . 20
4 Testcases 22
4.1 Non-reflectingoutflowboundarycondition . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 Laminarpipeflowwithnon-reflectingoutflowboundary . . . . . . . . . . 22
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.2 Turbulentpipeflowwithnon-reflectingoutflowboundary . . . . . . . . . 24
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Wallimpedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.1 Laminarpipeflowwithnon-reflectingwalls . . . . . . . . . . . . . . . . . . 25
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
v
CONTENTS
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.2 Turbulentpipeflowwithnon-reflectingwalls . . . . . . . . . . . . . . . . . 27
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Imposedimpedanceboundaryconditiontestcases . . . . . . . . . . . . . . . . . . 28
4.3.1 Laminarpipeflowwithimposedimpedanceattheoutlet . . . . . . . . . . 28
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.3.2 Laminarpipeflowwithimposedimpedanceattheoutletwithnon-reflecting
boundaryconditionattheinlet . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.3 Turbulentpipeflowwithimposedimpedanceattheoutlet . . . . . . . . . 31
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3.4 Turbulentpipeflowwithimposedimpedanceattheinlet . . . . . . . . . . 32
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4 Combustiontestcases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.1 2Dauto-ignitionburner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.2 3Dswirlburner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4.3 3Dswirlburnerwithtransverseexcitation . . . . . . . . . . . . . . . . . . . 37
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Conclusionandoutlook 41
Appendices 42
A SpecifyinganimpedanceboundaryconditioninFluent 43
B DigitisationwithMatlab 44
C Post-processingofFluentdata 47
D Tentativestoimprovenon-reflectingbehaviouratlowfrequencies 49
D.1 Relaxationfactors:parameterstudy . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
D.2 Polesofimpedancefunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
D.3 CFLnumber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
D.4 Powerspectraldensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
D.5 Laminarversusturbulentflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
E Variationofductlength 55
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CONTENTS
F Operatingpressure 57
Bibliography 58
vii
Nomenclature
RomanSymbols
Rˆ complexreflectioncoefficient [1]
L characteristicwaveamplitude [m/s]
i
c speedofsound [m/s]
c specificheatcapacityatconstantpressure [J/(kgK)]
p
CFL Courant-Friedrich-Lewynumber [1]
f frequency [Hz]
f(s) characteristicwave-downstreampropagating [m/s]
g(s) characteristicwave-upstreampropagating [m/s]
M Machnumber [1]
M relativemolecularweight [1]
w
p totalpressure [Pa]
p absolutepressure [Pa]
abs
p gaugepressure [Pa]
gauge
p operatingpressure [Pa]
op
R reflectioncoefficient [1]
R universalgasconstant [J/(molK)]
univ
s specificentropy [J/(kgK)]
T temperature [K]
u flowspeed [m/s]
viii
CONTENTS
GreekSymbols
γ ratioofspecificheatcapacities [1]
λ thermalconductivity [W/(mK)]
λ characteristicspeed [m/s]
i
Ψ characteristicvariable [depends]
i
ρ density [kg/m3]
σ Cauchystresstensor [Pa]
Acronyms
ARX autoregressivewithexogenousinput
BC boundarycondition
BJ Box-Jenkins
CBSBC characteristicbasedstate-spaceboundarycondition
CFD computationalfluiddynamics
CFL Courant–Friedrichs–Lewy
FIR finiteimpulseresponse
LES largeeddysimulation
NSCBC Navier-Stokescharacteristicboundaryconditions
OE output-error
PDE partialdifferentialequation
TDABC time-domainadmittanceboundarycondition
TDIBC timedomainimpedanceboundarycondition
UDF userdefinedfunction
WALE wall-adaptinglocal-eddy-viscosity
ix
1 Introduction
1.1 Objectives
Impedance boundary conditions are of great importance for the investigation of thermoa-
cousticsystems.Inmanycases,theyallowforareductionofthesimulationdomain.Forex-
ample,insteadofsimulatinganentireengine,impedanceboundaryconditionsallowforper-
formingaLESofthecombustionchamberonly.ThepartswhicharenotincludedintheCFD
simulationaremodelledbyimpedanceboundaryconditions.Thussignificantlyreducingthe
computational costs of the simulation and simplifying the design of the combustion cham-
ber,withouthoweverneglectingtheacousticbehaviouroftherestofthesystem.Impedance
boundaryconditionsareimplementedinANSYSFluentbyconvolutioninthetimedomain.
Fig. 1.1 schematically shows a turbomachine and the simplified model of the combustion
chamber,inwhichtheinfluenceoftheothercomponentsonthermoacousticphenomenais
modelledbymeansofanappropriateacousticimpedance.
Figure 1.1: Schematic representation of the set-up of a LES of a combustion chamber while
modelling the other parts of the system by means of impedance boundary conditions.
ReprintedfromJaenschetal.[10].
Thisthesisaimstoevaluatethebuilt-inimpedanceboundaryconditionsinANSYSFluent
inlaminarandturbulentflowconditions.Acousticimpedanceisappliedontheinletandthe
outlet of the chamber. The influence of a non-reflecting wall patch is investigated for non-
reactinglaminarandturbulentflowconditionsinaductandforaturbulentswirlburner.
1