Fluid-structure interactions and uncertainties : Ansys and fluent tools

279 Pages·2017·14.96 MB·English

by  El Hami

Fluid-Structure Interactions and Uncertainties
Reliability of Multiphysical Systems Set
coordinated by
Abdelkhalak El Hami
Volume 6
Fluid-Structure Interactions
and Uncertainties

Ansys and Fluent Tools

Abdelkhalak El Hami
Bouchaib Radi
First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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The rights of Abdelkhalak El Hami and Bouchaib Radi to be identified as the authors of this work have
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Library of Congress Control Number: 2016960066

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ISBN 978-1-84821-939-7
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Chapter1.Fluid–StructureInteraction . . . . . . . . . . . . . . . 1
1.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.Fluid–structureinteractionproblem . . . . . . . . . . . . . . . . 2
1.2.1.Fluid–structurecouplingmethods . . . . . . . . . . . . . . . 5
1.2.2.Temporalcoupling. . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3.Spatialcoupling . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.Vibroacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1.Vibrationsofthree-dimensionalsolids . . . . . . . . . . . . 15
1.3.2.Acousticsoffluids . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.3.Numericalmethodsforcalculatingastructure
coupledwithastagnantfluid . . . . . . . . . . . . . . . . . . . . . 18
1.4.Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.1.Aeroelasticproblems . . . . . . . . . . . . . . . . . . . . . . 23
1.4.2.Aerodynamicloads . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.3.Problemequations . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter2.Fluid–StructureInteractionwithAnsys/Fluent . . . 35
2.1.PresentationofAnsys . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.CouplingwithAnsys . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.1.Typesofcouplinganalysis . . . . . . . . . . . . . . . . . . . 38
2.3.Exampleoffluid–structureinteractionusingthe“physics”
environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.1.Fluidinmotion . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.2.Stagnantfluid . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.ExampleofinteractionusingFluent . . . . . . . . . . . . . . . . 54
vi Fluid–StructureInteractionsandUncertainties
Chapter3.Vibroacoustics . . . . . . . . . . . . . . . . . . . . . . . 59
3.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.Equationsoftheacousticandstructureproblems . . . . . . . . 60
3.2.1.Equationoftheacousticproblem . . . . . . . . . . . . . . . 60
3.2.2.Boundaryconditionsoftheacousticproblem . . . . . . . . 61
3.2.3.Equationofthestructureproblem . . . . . . . . . . . . . . . 62
3.2.4.Boundaryconditionsofthestructureproblem . . . . . . . . 62
3.3.Vibroacousticproblem . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.1.Problemstatement . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.2.Boundaryconditionsattheinterface. . . . . . . . . . . . . . 65
3.3.3.Finiteelementapproximation . . . . . . . . . . . . . . . . . 66
3.4.Studyofanelasticplatecoupledwithafluidcavity . . . . . . . 86
3.4.1.Equationsofthecoupledfluid–structureproblem . . . . . . 87
3.4.2.Variationalformulationofthefluid . . . . . . . . . . . . . . 88
3.4.3.Variationalformulationoftheplate . . . . . . . . . . . . . . 92
3.4.4.Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . 94
3.5.Studyofthepropellerofaboat. . . . . . . . . . . . . . . . . . . 97
3.5.1.Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . 99
Chapter4.Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . 103
4.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.Computationalmethod . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.1.Conformalmesh . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.2.Immersedboundarymethods . . . . . . . . . . . . . . . . . . 105
4.2.3.Volume-basedfictitiousdomainmethods . . . . . . . . . . . 106
4.3.Aerodynamicproblem’sresolution . . . . . . . . . . . . . . . . 107
4.3.1.Mobiledomain. . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.3.2.Weakformulation . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.3.Evaluatingtheenergyofthesystem . . . . . . . . . . . . . . 111
4.3.4.Numericallysolvingthesystem . . . . . . . . . . . . . . . . 116
4.3.5.Discretizationbyfiniteelements . . . . . . . . . . . . . . . . 120
4.4.Finiteelementmethodforthesolid . . . . . . . . . . . . . . . . 123
4.4.1.Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4.2.Assemblingthesystem . . . . . . . . . . . . . . . . . . . . . 126
4.4.3.Solvingthesystemofalgebraicequations . . . . . . . . . . 126
4.4.4.IntegrationbyGaussianquadrature . . . . . . . . . . . . . . 126
4.4.5.Advancingthetimestepusingthe
Hilbert–Hugues–Tayloralgorithm . . . . . . . . . . . . . . . . . . 127
4.4.6.LinearizationusingtheNewton–Raphsonalgorithm. . . . . 129
4.5.Finitevolumesforthefluid . . . . . . . . . . . . . . . . . . . . . 130
4.5.1.Generictransportequation . . . . . . . . . . . . . . . . . . . 130
Contents vii
4.5.2.Conservationpropertyofthemethod . . . . . . . . . . . . . 131
4.5.3.Thedifferentstepsinthemethod . . . . . . . . . . . . . . . 131
4.5.4.Integratingthemodelequation . . . . . . . . . . . . . . . . . 132
4.5.5.Controlvolumes . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.5.6.Physicalinterpolation . . . . . . . . . . . . . . . . . . . . . . 135
4.5.7.Evaluatingthefluxthroughthefaces . . . . . . . . . . . . . 135
4.5.8.Centeredscheme. . . . . . . . . . . . . . . . . . . . . . . . . 136
4.5.9.Upwindscheme . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5.10.Hybridscheme . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.5.11.Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.6.Couplingprocedures . . . . . . . . . . . . . . . . . . . . . . . . 141
4.6.1.Couplingstrategies . . . . . . . . . . . . . . . . . . . . . . . 141
4.6.2.Implicitpartitionedcoupling . . . . . . . . . . . . . . . . . . 142
4.7.Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.7.1.Staticanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.8.Studyofa3Dairplanewing . . . . . . . . . . . . . . . . . . . . 150
4.8.1.Modalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.9.Transientanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Chapter5.ModalReductionforFSI . . . . . . . . . . . . . . . . . 163
5.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.2.Dynamicsubstructuringmethods . . . . . . . . . . . . . . . . . 164
5.2.1.Linearproblems . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.2.2.Nonlinearproblems . . . . . . . . . . . . . . . . . . . . . . . 167
5.3.Nonlinearsubstructuringmethod . . . . . . . . . . . . . . . . . 169
5.3.1.Vibrationalequationsofasubstructure . . . . . . . . . . . . 170
5.3.2.Fixed-interfaceproblem. . . . . . . . . . . . . . . . . . . . . 171
5.3.3.Staticbearingproblem . . . . . . . . . . . . . . . . . . . . . 172
5.3.4.Representingthesystemwiththelinear
Craig–Bamptonbasis. . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.3.5.ModelreductionusingtheapproachofShawandPierre . . 174
5.3.6.Assemblingthesubstructures . . . . . . . . . . . . . . . . . 176
5.4.Properorthogonaldecompositionforflows . . . . . . . . . . . . 178
5.4.1.PropertiesofPODmodes . . . . . . . . . . . . . . . . . . . . 179
5.4.2.SnapshotPOD . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.4.3.Findinglow-orderexpressionsfordynamicsystems . . . . . 180
5.5.Dynamicsubstructure/acousticsubdomaincoupling . . . . . . . 185
5.5.1.Basicequations . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.5.2.Variationalformulations . . . . . . . . . . . . . . . . . . . . 190
5.5.3.Discretizationbyfiniteelements . . . . . . . . . . . . . . . . 191
5.5.4.Calculatingthelocalmodes . . . . . . . . . . . . . . . . . . 194
viii Fluid–StructureInteractionsandUncertainties
5.5.5.Modalsynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.6.Numericalsimulation . . . . . . . . . . . . . . . . . . . . . . . . 199
5.6.1.Elasticring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
5.6.2.Boatpropeller . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Chapter6.Reliability-basedOptimizationforFSI . . . . . . . . 211
6.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.2.Reliabilityinmechanics. . . . . . . . . . . . . . . . . . . . . . . 212
6.2.1.Randomvariables . . . . . . . . . . . . . . . . . . . . . . . . 212
6.2.2.Reliabilityfunction . . . . . . . . . . . . . . . . . . . . . . . 214
6.3.Failureinmechanics. . . . . . . . . . . . . . . . . . . . . . . . . 215
6.3.1.Failurescenarios . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.3.2.Expressionofthefailureprobability. . . . . . . . . . . . . . 217
6.4.Reliabilityindex . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.4.1.Rjanitzyne–Cornellindex . . . . . . . . . . . . . . . . . . . . 217
6.4.2.Hasofer–Lindindex . . . . . . . . . . . . . . . . . . . . . . . 218
6.5.Mechanoreliabilitycoupling . . . . . . . . . . . . . . . . . . . . 218
6.5.1.Reliability-basedcalculationmethods . . . . . . . . . . . . . 219
6.5.2.MonteCarlomethod . . . . . . . . . . . . . . . . . . . . . . 220
6.5.3.FORM/SORMapproximationmethods . . . . . . . . . . . . 221
6.6.Reliability-basedoptimizationinmechanics . . . . . . . . . . . 224
6.6.1.Deterministicoptimization . . . . . . . . . . . . . . . . . . . 225
6.6.2.DifferentapproachestoRBDO. . . . . . . . . . . . . . . . . 226
6.6.3.Classicalapproach. . . . . . . . . . . . . . . . . . . . . . . . 228
6.6.4.Hybridapproach . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.6.5.Frequency-basedhybridapproach . . . . . . . . . . . . . . . 231
6.7.SPmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.7.1.Formulationoftheproblem. . . . . . . . . . . . . . . . . . . 234
6.8.Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6.8.1.Reliabilitycalculationforanairplanewing . . . . . . . . . . 237
6.8.2.ApplicationofRBDOtotheairplanewing . . . . . . . . . . 239
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Preface
The progress achieved by digital and software tools in the past 40 years
has allowed scientists to dramatically improve their understanding of the
world. The development of mathematical models has allowed us to work on
increasingly sophisticated problems in a wide range of fields: predicting the
behavior of production tools, transportation, the environment, etc. Managing
thesecomplexproblemshasbeenfacilitatedwithineachdisciplineseparately
but also from a cross-disciplinary perspective, allowing more general
phenomenatobetackled.
Thefieldoffluid–structureinteractionsunitesthestudyofallphenomena
involving a coupling between the motion of a structure and the motion of a
fluid.Therangeofstudiedphenomenaisverybroad,fromvibratingcylinders
in flows, such as in the nuclear industry, to vibrating structures in turbulent
flowsandfree-surfacephenomenainreservoirs.Onewell-knownexampleof
fluid–structureinteractionandthecomplexityofthecouplingsinvolvedisthe
collapseoftheTacomabridgein1940, whichbeganvibratingtothepointof
resonance frequency under the effect of violent winds, causing it to be
completely destroyed. This shows just how important it is to prepare reliable
models in advance of any project so that this kind of behavior may be
predicted.
Wind tunnels, such as in aeronautics, allow us to inspect the behavior of
the structure on the ground without needing to perform tests in flight. The
EulerandNavier–Stokesequationshavemadeitpossibletorigorouslydefine
a physical framework for characterizing the behavior of the aircraft in terms
of a set of different parameters such as the velocity or Mach number. Finite
elementmodelshavegreatlysimplifiedtheprocessofrepresentinganaircraft
modelanditsstructure,aswellasthewaythattheaircraftrespondstostress.
x Fluid–StructureInteractionsandUncertainties
However, the complexity of the studied phenomena is reflected in the
prohibitive computational costs, which motivates us to search for reduced
modelswithmorerealisticcomputationtimes.Byareducedmodel,wemean
a description as a low-dimensional system obtained by analyzing classical
numerical formulations. Acheiving this reduction incurs an initial cost, but
this cost is largely offset if the reduced model is later found to be applicable
forconfigurationsofparametersotherthanthoseoftheinitialformulation.
Thus, just like in other areas of the industry, optimization research is
extremelyactivewithintheaviationsector.Onesignificantdevelopmentsince
the late 1980s has been the introduction of uncertainty parameters into
numerical models. Optimization techniques in the presence of uncertainty in
aerodynamics have only been studied more recently, beginning in the early
2000s. Their introduction was motivated by the need to account for specific
typesofsituationsthatmakeittoodifficulttopreciselyevaluatetheaircraft’s
behavior. For example, during the aircraft design phase, in order to meet the
various different criteria or eliminate certain problems encountered by the
model, the model is able to adjust itself to more effectively meet the
requirements and needs that it is designed to satisfy. The initial drafts of the
modelarenotfixed,butforsafetyreasonsitisnecessarytoensurethroughout
the development process that the structure is capable of withstanding the
stresses that it is likely to encounter in operating conditions. One way of
accounting for these potential changes is to introduce uncertainty into the
model.
Furthermore, when designing aircraft, manufacturers are naturally
interestedinmaximizingtheperformanceofeachvehicle: reducingpollution,
noise, drag, increasing the range, maximizing stability, etc. Minimizing the
structural mass is an important objective for manufacturers as it allows other
optimization criteria such as reducing pollution or extending the range to be
satisfied.Butlessmasswillalsohavenegativerepercussionsonothercriteria,
including the stability of the aircraft in flight, for example by rendering it
susceptibletothephenomenonof“fluttering”.
Manufacturers must therefore perform constrained optimization:
minimizingtheweightofthewingwhileensuringthatflutteringcannotaffect
the airplane within its flight envelope. In such a case, optimization problems
have a cross-disciplinary character, since they exhibit behaviors that include
bothstructuralandaerodynamicaspects.
Thegoalisnowtointegratetheaspectofuncertaintymentionedaboveinto
theoptimizationprocess.However,todothis,wemustfirstidentifythenature
Preface xi
oftheseuncertainties,anddecidehowweshouldrepresentthem.Severaltypes
ofuncertaintyhavebeenidentifiedandclassifiedaccordingtotheirnature.
Accountingforuncertaintyhasbeenstudiedinanumberofresearchareas,
but, until recently, in aeronautics research it was not possible to account for
orquantifystructuraluncertaintieswithintheoptimizationproceduresdueto
the limitations of numerical tools and a lack of theoretical understanding of
their impact within reliability studies. Engineers have therefore been forced
to implement alternative procedures to simplify the integration of structural
uncertainties into model development. The first studies on this topic in the
aviationsectorwereonlyconductedinthe1990s, atwhichpointthisfieldof
researchbegantoproducetangibleresults.
In the case of optimization problems with probabilistic constraints,
reliability-based optimization, which is extremely common in industrial
contexts, replaces these probabilistic constraints with another deterministic
optimization problem derived by techniques of approximation. The primary
difficulty lies in evaluating the reliability of the structure, which is itself the
result of another given optimization procedure. Reliability analysis is
performed at the optimal point in order to determine the reliability index of
thelimitingstatethatisbeingconsidered.
This book presents the different aspects of fluid–structure interaction:
vibroacousticsandaerodynamics,andthevariousnumericalmethodsusedto
simulatethemnumerically.
One chapter is devoted to the question of model reduction in
fluid–structure interaction problems. We begin by presenting dynamic
substructuring methods in linear and nonlinear cases. We then give a
descriptionofthemethodofproperorthogonaldecompositionforfluidflows.
Finally,wepresentamodalsynthesismethodforsolvinglarge-scalecoupled
fluid-structure problems. This method couples a dynamic substructuring
method of the type proposed by Craig and Bampton with an acoustic
subdomainmethodbasedonanacousticformulationofthevelocitypotential.
To account for uncertainty, one chapter presents concepts associated with
reliability and its objectives and benefits in mechanics, methods for
calculating the probability of failure, simulation methods such as the Monte
Carloandresponsesurfacemethods,andapproximatemethodsforanalyzing
thereliabilityandcalculatingthereliabilityindexbythefirst-orderreliability
method (FORM) and the second-order reliability method (SORM). We then
giveadetailedpresentationoftheimplementationofthelatterapproachinthe