aerodynamic design optimization based on multi-attribute

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

Aerodynamic design optimization based on Multi-Attribute Structured Hybrid Direct-

Search. Application to industrial problems

Author: Isaac Prada y Nogueira Director: Fernando de Cuadra

Director: Álvaro Sánchez Miralles

MadridMarch2017

Madrid

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

Optimización del diseño aerodinámico basada en Búsqueda Directa Híbrida,

Estructurada y Multiatributo. Aplicación a problemas industriales

Autor: Isaac Prada y Nogueira Director: Fernando de Cuadra

Director: Álvaro Sánchez Miralles

MadridMarzo2017

AcknowledgementIthankGodfortheenergyandmotivationtohavecompletedthisPhDThesisandforthekeypeople

inmylifewhohavemadeitpossible:mygirlfriend,myparents,mypartnerJoséMaríaCancerAbóitizandtheteamatKeelWitTechnology:Dr.IgnacioSerrano,PabloCancilloandEnriqueMartín.

AgradecimientoLedoygraciasaDiosporlaenergíaylamotivaciónparahabercompletadoestaTesisDoctoralyporhaberpuestoenmividaalaspersonasclavequelahanhechoposible:minovia,mispadres,misocioJoséMaríaCancerAbóitizyelequipodeKeelWitTechnology:elDr.IgnacioSerrano,PabloCancilloy

EnriqueMartín.

AbstractThe present Thesis tackles the problem of aerodynamic shape optimization,

particularlyinthecaseofbigchangesofgeometry.TheapproachproposedisaMulti-Objective Structured Hybrid Direct Search and this Thesis presents the MOST-HDSmodel developed for this purpose. This model is a general, automatic, flexible androbust methodology which is applicable to many different fields of aerodynamicoptimization and which combines elements of gradient, genetic and swarm search.MOST-HDS is applied to two relevant and significantly different industrial cases: thedesign of closedwind tunnels and the inlet duct design of industrial boilers used incombinedcyclepowerplants.Theresultsobtainedwiththeoptimizationmethodologyproposed show significant performance improvements over traditional designs and,moreover, innovative and non-conventional designs are obtained for certain cases,which also outperform current design guidelines. A comparison of MOST-HDS andsurrogate-based optimization (using response surfaces) is presented and theadvantages and limitations of each approach are discussed in detail. Finally, thealgorithm developed for this Thesis is also applied to a well-known and challengingmathematicaltestproblem(theWFGtestsuite)andcomparedtoapopular,advancedMulti-Objective Evolutionary Algorithm, the NSGA-II. The results are very promisingandillustratethepotentialofMOST-HDSforgeneraloptimizationpurposes,too.

ResumenLa presente Tesis aborda el problema de la optimización aerodinámica,

particularmenteenelcasodegrandescambiosdegeometría.Elenfoquepropuestoesuna búsqueda directa híbrida, estructurada y multiobjetivo y esta Tesis presenta elmodeloMOST-HDSdesarrolladoparaestepropósito.Estemodeloesunametodologíageneral, automática, flexibley robustaqueesaplicableamuchoscamposdiferentesde optimización aerodinámica y que combina elementos de búsqueda basada engradiente, genéticos y enjambre. MOST-HDS se aplica a dos casos industrialesrelevantesysignificativamentediferentes:eldiseñodetúnelesdevientocerradosyeldiseñodelconductodeentradadecalderasindustrialesutilizadasencentralesdeciclocombinado. Los resultados obtenidos con lametodología de optimizaciónpropuestamuestran mejoras significativas respecto a los diseños tradicionales y, además, seobtienen diseños innovadores y no convencionales para ciertos casos, que tambiénsuperanlasdirectricesactualesdediseño.SepresentaunacomparacióndeMOST-HDSylaoptimizaciónbasadaenmodelosaproximados(utilizandosuperficiesderespuesta)y se discuten en detalle las ventajas y limitaciones de cada enfoque. Por último, elalgoritmodesarrolladopara esta Tesis también se aplica a un conocido y desafianteproblemadepruebamatemática(elconjuntodeproblemasWFG)ysecomparaconunpopularyavanzadoalgoritmomultiobjetivoevolutivo,elNSGA-II. Los resultados sonmuyprometedorese ilustranelpotencialqueMOST-HDStiene,asimismo,para finesgeneralesdeoptimización.

Contents

CHAPTER1-INTRODUCTION.THESISMOTIVATION,OBJECTIVESANDCONTRIBUTIONS 10

1.1.INTRODUCTION 101.2.THESISMOTIVATION 161.3.THESISAPPROACH,MAINOBJECTIVESANDCONTRIBUTIONS 181.3.1.THESISOBJECTIVES 181.3.2.THESISCONTRIBUTIONS 191.4.STRUCTUREOFTHISDOCUMENT 21LISTOFFIGURES 22

CHAPTER2-PROBLEMDESCRIPTIONANDGENERALAPPROACH 24

2.1.INTRODUCTION 242.2.CHARACTERIZATIONOFTHETYPEOFPROBLEM 252.3.GENERALAPPROACH 272.4.DEFINITIONOFSMALLVERSUSBIGGEOMETRYCHANGES 272.5.FINALREMARKS 30LISTOFFIGURES 30

CHAPTER3-STATEOFTHEARTREVIEW 32

3.1.INTRODUCTIONANDCLASSIFICATIONCRITERIA 323.2.STATEOFTHEARTOFGENERALMETAHEURISTICOPTIMIZATION 343.3.STATEOFTHEARTOFGENERALAERODYNAMICSHAPEDESIGNOPTIMIZATION 413.4.STATEOFTHEARTOFAERODYNAMICSHAPEDESIGNOPTIMIZATIONFORTHEINDUSTRIALCASESANALYZED 46WINDTUNNELS 46HEATRECOVERYSTEAMGENERATORS(HRSGS) 513.5.CONCLUDINGREMARKSANDTHESISMAPPINGTOTHESTATEOFTHEART 52LISTOFFIGURES 54LISTOFTABLES 54

CHAPTER4-PROBLEMDEFINITION 56

4.1.INTRODUCTION 564.2.PROBLEMDEFINITION 57WINDTUNNELS 57INDUSTRIALBOILERS:HEATRECOVERYSTEAMGENERATORS(HRSGS) 61RECOMMENDATIONSFORANEFFICIENTVARIABLESETDEFINITION 664.3.GEOMETRYPARAMETERIZATION 67WINDTUNNELS 68INDUSTRIALBOILERS:HEATRECOVERYSTEAMGENERATORS(HRSGS) 714.4.FINALREMARKS 71LISTOFFIGURES 71LISTOFTABLES 72

CHAPTER5-THEMOST-HDSOPTIMIZATIONMODEL 74

5.1.INTRODUCTION 745.2.STRUCTUREDSEARCH:VARIABLEHIERARCHYANDOPTIMIZATIONPHASES 75

5.3.DESCRIPTIONOFTHEMOST-HDSALGORITHM 815.4.IMPLEMENTATIONOFTHEMOST-HDSALGORITHM 935.5.FINALREMARKS 95LISTOFFIGURES 96

CHAPTER6-RESULTSOBTAINED 98

6.1.INTRODUCTION 996.2.INDUSTRIALBOILERINLETDUCTSHAPEDESIGNOPTIMIZATION 99VALIDATIONCASEFORTHEANSYSCFDSOLVERFORINDUSTRIALBOILERSIMULATIONS 99RESULTSFORTHESHAPEOPTIMIZATIONOFTHEINLETDUCTOFHRSGS 101CONCLUSIONSONTHERESULTSFORTHESHAPEOPTIMIZATIONOFTHEINLETDUCTOFHRSGS 1116.3.CLOSEDWINDTUNNELSHAPEDESIGNOPTIMIZATION 113VALIDATIONCASEFORTHEANSYSCFDSOLVERFORWINDTUNNELSIMULATIONS 113RESULTSFORTHESHAPEOPTIMIZATIONOFCLOSEDWINDTUNNELS 116CONCLUSIONSONTHERESULTSFORTHESHAPEOPTIMIZATIONOFCLOSEDWINDTUNNELS 1276.4.USEOFTHEADJOINTMETHODFORFINALFINE-TUNING. 1286.5.BENCHMARKOPTIMIZATION.APPLICATIONOFMOST-HDSTOTHEWFG9OPTIMIZATIONTESTPROBLEM 1306.6.FINALREMARKS 136LISTOFFIGURES 137LISTOFTABLES 140

CHAPTER7-COMPARISONTOSURROGATEMODELS 1427.1.INTRODUCTION 1437.2.RESULTSOFASURROGATE-BASEDAPPROACHFORTHESHAPEOPTIMIZATIONOFTHEINLETDUCTOFHRSGS 144SURROGATE-BASEDEVALUATION 145SURROGATE-BASEDOPTIMIZATION 1497.3.DISCUSSIONONTHEADVANTAGESANDLIMITATIONSOFASURROGATE-BASEDAPPROACH 151LISTOFFIGURES 153LISTOFTABLES 154

CHAPTER8-CONCLUSIONS 156

8.1.CONCLUSIONSANDTHESISCONTRIBUTIONS 156OPTIMIZATIONAPPROACHANDCOMPARISONTOSURROGATE-BASEDOPTIMIZATION 157GENERALAPPLICABILITYOFMOST-HDS:REALINDUSTRIALCASES 158GENERALAPPLICABILITYOFMOST-HDS:MATHEMATICALTESTFUNCTIONOPTIMIZATION 160GENERALAPPLICABILITYOFMOST-HDS:GENERAL-PURPOSEOPTIMIZATION 1608.2.FUTURERESEARCHWORKBEYONDTHISTHESIS 161

CHAPTER9-REFERENCES 164

REFERENCES 164

APPENDIXA-ILLUSTRATIONOFTHEMOST-HDSPROCESS 176

APPENDIXB-IMPORTANTNOTESONMESHSENSITIVITYANDMESHQUALITY 186

B.1.MESHSENSITIVITY 186B.2.MESHQUALITY 187

AerodynamicdesignoptimizationbasedonMulti-AttributeStructuredHybridDirectSearch 10

Chapter1 -Introduction.Thesismotivation,objectivesandcontributions

Accordingtothetheoryofaerodynamicsandwindtunneltestingthebumblebeeisunabletofly.Howeverthebumblebeegoesaheadandfliesanyway—andmakesalittlehoneyeveryday.

SigninaGeneralMotorsCorporationfactory.

AsquotedinRalphL.Woods,TheBusinessman'sBookofQuotations(1951).

ThischapterintroducesageneraloverviewofthefieldofstudyofthisThesisandjustifies the generalmotivation for this researchwork.Moreover, it illustratesthe relevance of shape optimization, particularly aerodynamic shapeoptimization, with real-life examples. Based on this, the Thesis approach issummarized and its main objectives and contributions are presented.Furthermore, the chapter outlines the general structure of the document, tohelp the reader understand the sequence of the chapters. Firstly, Section 1.1.presentsageneralintroduction;Section1.2.putsforwardthegeneralmotivationof the Thesis; Section 1.3. presents a general summary of the objectives andmain contributions of this Thesis; finally, Section 1.4. describes the generalstructureofthedocument,to justifytheorderofthechaptersandtomotivatethereadertodelveintothewholedocument.

1.1.IntroductionComplex aerodynamic components are of paramount importance both for the

scientificcommunityandforoureverydaylives.Fromaspacerockettoahigh-speedtrain,acaroraboatofanykind,aerodynamicdesignoptimizationcanyieldimportantadvantages such as higher speeds, reduced fuel consumption, better stability or alargeroperationenvelope.

1

Chapter1–Introduction.Thesismotivation,objectivesandcontributions

11

However,aerodynamicshasnotalwaysbeenarelevantdisciplineforthedesignofthese different vehicles. Except in air and spacecraft, forwhich aerodynamics is thebasis,forthosebodiesintendedtotravelonlandorevenonwater,thedesignersdidnotrealizetheparamountimportanceofaerodynamicshapedesign.

Let us take the example of the automotive sector, highly advanced nowadays intermsofaerodynamicdesign.

Althoughduringitsveryfirststages(19thcentury),aerodynamicswasnottakenintoaccount, quite soon the automobile industry started including aerodynamicconsiderations in the design phase. However, themain objectivewas to reduce theDrag coefficient of the vehicle. A lower value of this coefficient means a betterpenetrationof thevehicle in theair, i.e. a lower resistanceand thereforea reducedfuel consumption or a higher speed. The mathematical definition for the Dragcoefficientisgiveninthefollowingequation1:

AVDCd

×××=

¥2

21 r

Equation1-1

where D represents the Drag itself, i.e. the force representing the aerodynamicresistanceactingonthevehicleorbodyalongthelongitudinalaxis,𝜌istheairdensity,𝑉#theairspeedofthefreestreamandAisareferencearea(normallythefrontalorprojected vehicle area). The Drag coefficients for a set of general body shapes aregiveninFigure1–1.Thestrongimpactofshapedesigncanbeveryclearlyunderstoodfromthesevalues.

Figure1–1-Dragcoefficientsforgeneralbodyshapes.

1Insteadof“d”,“x”issometimesusedastheindextorefertotheDragcoefficient(Cx).

AerodynamicdesignoptimizationbasedonMulti-AttributeStructuredHybridDirectSearch

12

TheaimofthedesignerswasthereforetoreducethevalueoftheDragcoefficientto decrease the value of the longitudinal force that the vehicle had to overcome inordertoadvance.

Forexample,asearlyas1916,thePeugeotthatwontheIndianapolis500thatyearhad a slightly streamlined, rather than square, rear end, to reduce the Drag of thevehicle(inFigure1–2,thiscanbeobserved,notjustinthePeugeot,car17,butalsointhecartotherightofthepicture).

Figure1–2-DaríoRestaandhismechanicinthePeugeotcar,whichwontheIndianapolis500in

1916.

Nevertheless,themaintechnicalleapoccurredwhenaerodynamicengineersbegantoworryabouttheLiftcoefficient,analoguetotheDragcoefficientbutreplacingthelongitudinalaerodynamicforcewiththeverticalaerodynamicforce.Morespecifically,thegoalofthedesignerswastoreducethevalueoftheLiftcoefficient,becauseitwasresponsiblefortheliftingforceonavehicleasitsspeedincreased,andeventomakeitnegative, especially for sports cars (since conventional road cars have positive Liftvalues,especiallyneartherearaxle).WithanegativeLiftordownforcethecorneringspeedyoucanreachcanexceedinmorethanthreetimesthevehicle'sspeedwithoutdownforce(Katz[2006]).

As an example of the importance of aerodynamics in motorsport, Figure 1–3illustrates thedifferent trends thathavebeen followedbyaerodynamicengineers inFormula 1 throughout its history. Figure 1–4 gives examples of real cars designedfollowingtheseaerodynamictrends.


13

Figure1–3-AerodynamictrendevolutioninFormula1sincethebeginningofthecompetition(1950).

Figure1–4-RealexamplesofthedifferentaerodynamictrendsinFormula1sincethebeginningof

thecompetition(1950).

ForthepurposeofthisThesis,itisveryworthhighlightingthataerodynamicshapedesignisnotonlyacaseoffine-tuning,butmanytimesofqualitativemodifications,ashavebeenshowninFigure1–3andFigure1–4,andevenradical,non-conventionalornon-intuitive designs, such as those depicted in Figure 1–5. These substantial,qualitative or even disruptive shape design modifications, here referred to as biggeometrychanges,willbetakenintoaccountintheshapeoptimizationmethodologypresentedinthisThesis,andthisisoneofthekeydifferentialelementswithrespecttomostofworksoftheStateoftheArt.


14

Figure1–5-ExamplesofdisruptivedesignsinFormula1,eitherbecauseofthewingdesign,orthe

nosedesign,oreventheintroductionofafanforincreaseddownforce.

Inthefieldofaerodynamics,streetcarshaveinheritednumerouselementsofthelessons learned in motorsport. Although in general they do not have wings or anaerodynamicbottom,theyhave incorporatedelementsanddetailswhichallowforabetterstabilityofthevehicleathighspeeds,whenaerodynamicsreallycounts.Othermodifications aim at achieving less aerodynamic noise within the passengercompartment, less accumulation of dirt in long journeys and greater efficiency inaspectssuchasventilationorcooling.

Thestrongevolutioninaerodynamicdesignisbynomeansexclusivetomotorsportor to the automotive sector. The following figures aim at showing the impact ofaerodynamicsinshapedesigninaverywiderangeofsectors.

Figure1–6-Aerodynamicdesignevolutionofanexampleroadcar,inthiscasetheBMW.


15

Figure1–7-Aerodynamicdesignevolutioninthetrainsector.Asteamhighspeedtrain,capableof

maximumspeedsof160km/handaveragespeedsof130km/h,comparedtothemostmodernTalgotrain,theAvril,capableofmaximumspeedsof363km/handaveragespeedsof330km/h.

Figure1–8-Aerodynamicdesignevolutioninthemarinesector,inparticularintheAmerica'sCup.To

theleftthe1871Defender,theColumbia/Sappho,whichwonthatyear.Totheright,the2013winner,theDefenderthatyear,the17OracleTeamUSA.

Figure1–9-Aerodynamicdesignevolutioninthecyclingsector.Asetofrepresentativemodern

racinghelmetsareshown.

Theabovefiguresillustratehowtheshapedesignchangesoverhistoryindifferentsectors have been a combination of fine-tuningwith qualitative or discrete leaps indesign, towards new, more radical or unconventional concepts. These are non-exhaustiveexamplesofwhatwillbereferredtoassmallversusbiggeometrychanges(Chapter2),aconceptofgreatimportanceforthisThesis.


16

1.2.ThesismotivationFromSection1.1.aboveitisclearthataerodynamicshapedesignishighlyrelevant

ingeneralbodydesigninmanydifferentsectors.Itisalsoevidenthowthedesignhasbeenmovingbothinsmallandinbigjumpsfromonedesignconcepttothefollowingone,upuntilthepresentday.

Havingsaidthis,itisalsoworthhighlightingthataerodynamicsisnotatrivialareaof researchand thegoverningequationsof thedifferent typesof flow fieldsare toocomplextobesolvedanalytically.Figure1–10depictsthe3Dvelocitystreamlinesforan example complex aerodynamic body geometry. Many highly complex flowphenomena(vorticity,flowdetachment,backflow,etc.)canbeobservedandillustratethecomplexityofaerodynamicanalyses.

Figure1–10-Example3Dvelocitystreamlinesforacomplexaerodynamicbody,inthiscasethefloor

ofamotorsportscar.

Aerodynamic research has three main tools to evaluate the performance of aparticularshapedesign(foradetaileddescriptionofthem,fortheautomotivesector,refertoJosephKatz[2006]):

1. Computer analysis: by means of numerical analysis (Computational FluidDynamics, CFD),which caneither followadirect approachof thehigh-fidelitymodel2 (direct simulation)or it canmakeuseof a surrogate (or approximate)model(agoodlistofthedifferentgeneralsurrogatetechniquescanbefoundinRobinsonetal.[2006]).

2. Windtunneltesting:Figure1–11showsthreeexamplesofwindtunneltestingforVolkswagencarsofdifferentyears.

3. Testing in the real environment: this can mean road testing, on-sea testing,flighttesting,dependingonthebodytobetested.

2 The so-called high-fidelity model, in any case, will also include a set of simplifications of the

governingequations,unlessperformedviaDirectNumericalSimulation,whichistootime-consuminginmostcases.


17

Figure1–11-WindtunneltestingforthreeVWcarsofdifferentyears.Velocitystreamlinesare

simulatedwithasmokegenerator.Changesintheflowfieldcanbeobservedbetweenthedifferentcarmodels.

Taking all the above into account, the motivation of this Thesis is to propose ageneral method to optimize shape design with an automatic, flexible and robustprocedurewhichcanbeappliedtomanydifferentrealindustryapplications.AstrongaspectofthisThesismotivationisthefactthatthegeneralmethoddevelopedshouldbeable tohandlenotonly small, but alsobig, changes to thebodygeometry, sincetheycanhavean important impactonperformance.Thesebigchangesarecurrentlyhandledmostlybytrialanderrorormanualprocedures,whilecomputeroptimizationhas been limited to cases of small geometry changes or to fine-tuning (refer to theStateoftheArt,inChapter3).


18

1.3.Thesisapproach,mainobjectivesandcontributionsThe problem this Thesis deals with is the multi-attribute or multi-objective

aerodynamic shapeoptimizationof real geometries indifferent fieldsof application,subjecttoasetofconstraints,andtakingintoaccountbothsmallandbigchangesofthegeometryofinterest.

Theapproachproposedfortheproblemdescribedabovewillbethedevelopmentof a general method based on aMulti-Objective Structured Hybrid Direct Searchoptimizationalgorithm(referredtoasMOST-HDS).

1.3.1.THESISOBJECTIVES

TheThesismainandsecondaryobjectivesarethefollowing:

1. Presentastructured,detailedandcommentedreviewoftheapplicableStateoftheArt.

2. Proposehowaproblemofshapedesigncanbedefinedinamostsuitablewaytoapplynotonlyadvancedoptimizationschemesingeneral,but, inparticular,multi-attribute/objective, structured, hybrid, direct search (MOST-HDS). Thisobjectiveincludesthefollowingsecondaryobjectives:

a. Definitionoftrulyindependentvariables.

b. Definitionofattributesorobjectivestobeoptimized.

3. Design theMOST-HDS algorithmarchitecture anddevelop a computer tool toapplyittorealproblemcases.

4. Validate the MOST-HDS general method presented to show its broad-scopeapplicability(notonlytoshapedesignoptimization):

a. Mathematicalvalidation:testsuitebenchmarkvalidation

b. Validatewithrealindustrycases:

i. Windtunnelcase.

ii. Industrialboilercase.

5. Comparetheproposedmethodtoothermethodsandapproachesused in theState of the Art (surrogate models and other commonly-used optimizationalgorithms).


19

1.3.2.THESISCONTRIBUTIONS

Basedonthissetofmainandsecondaryobjectives,thefollowingisadetailedlistofthis Thesis contributions, which will be presented again in the conclusions chapter(Chapter 8). They are listed in decreasing order of relevance, from the author’sperspective:

1. DevelopmentofMOST-HDS,ageneralmodelformulti-attributeoptimizationofaerodynamicshapedesignwhichisacontributionbecause:

a. It is capable of handling big geometry changes, which is very rarelyaddressedinliterature

b. It is applicable to a wide range of real life problems, both industrial(shapedesignoptimization)andmathematical(optimizationofcomplexfunctions modelling real problems). As commented below, the resultspresentedinthisThesisshowthatthemethodologyyieldsperformanceimprovements over currently used optimization algorithms andimproved geometry designs, with important reductions of objectivessuchasenergyconsumptionormaterialcost.

c. This model exploits the potential of direct search and, in particular,builds a hybrid direct search architecture, combining genetic, gradientand swarm search intelligence. This approach is novel in itself and, inparticular, in the areaof aerodynamic shapeoptimization.Once again,theimprovementshownintheresultssupportsthefactthatMOST-HDSis an interesting and valuable contribution to the current State of theArt.

d. ThesearchcarriedoutbyMOST-HDSisstructuredandthisisoneofthekeyaspectsofthemodel.ThisconstitutesanadditionalcontributionofthisThesistothefieldofaerodynamicshapeoptimizationbecausesuchafulluseofstructuredoptimizationhasnotbeenuseduptothisdate.


20

2. Full implementation of an automatic workflow for optimization of CFDproblems.MSExcelandaVBAcode(VisualBasicsforApplications)arecoupledto ANSYS FLUENT for this Thesis, although the optimizationmethodology caneasilybetranslatedtoMATLAB,C++,Pythonorotherprogramminglanguages(itwas considered that the integration with ANSYS would be easier and moreefficient usingMS Excel).MOST-HDS is thus implemented in a computer toolconnectedtoaCFDsolver(ANSYSFLUENTinthiscase,butitcanbeadifferentsolver). The MOST-HDS tool controls the optimization process, and calls thesolver every time a candidate design point has to be evaluated. This requiresfinding a smart geometry parameterization to represent body shapeswith anefficientsetof independentdesignvariables. Ineveryevaluation,thesedesignvariablesareautomaticallymappedtoothervariablesintheCFDsolver,whichare not so intuitive but are understood by the CFD program. This is acontribution to the State of the Art since the automaticworkflow is a robustmethodwhichreducesaproject’scycletimeorincreasesthenumberofdesignpointswhichcanbeevaluatedwithinafixedtime.

3. Application of the MOST-HDS model to two real-life problems: closed windtunnels, such as those used for testing and leisure, and industrial boilers forcombinedcyclepowerplants.Thiscontributes totheStateof theArtbecausetheresultsobtainedshowthatMOST-HDScanyieldsurprising,non-intuitiveandunconventionaldesignswhichperformbetterthantraditionalconcepts.

4. Regarding the industrial boiler optimization, the contribution of this Thesis istwofold: on the one hand, it shows that there is substantial room forimprovement in the shape design of the inlet ducts of Heat Recovery SteamGenerator (HRSGs), in terms of achieving a lower pressure drop, a highervelocity uniformity and an important cost reduction of the unit; on the otherhand, it showshow the application of theMOST-HDS algorithm, applicable inmany fields for aerodynamic shape optimization involving big geometrychanges, can find these improveddesigns,which canbequiteunconventionalandnon-intuitive.Theresultsobtained for twoHRSGfamiliesshowthat thereareoptimumtrade-offdesignpointswithsimultaneous reductions inpressuredropofupto20-25%,in lateralsurfaceofupto38%andin lengthofup16%,whilehavingcomparablevelocityuniformitiestotheexistingdesigns.

5. Furthermore,itisalsoshowninthisThesisthatthedoubleangledesignofHRSGinlet ducts, which is the current design trend, is not always better than thesingleangledesign,whichwasthetraditionalguidelinefollowed.


21

6. Analysis of the limitations of surrogate models (mainly response surfaces),whichareoptimizationtechniqueswidelyusedandverypopularnowadays.ThisThesis shows that MOST-HDS beats surrogate models in the aerodynamicoptimization of complex components (wings, high-speed train noses,automotive designs, etc.), especially when big changes of geometry areinvolved. A detailed comparison is carried out for the specific example of theindustrialboilercase.Itisdifficultinmanycasesforanysurrogatemodel(beitbymeans of data fits and response surfaces, or by reduced ordermodels orhierarchical or multi-fidelity models) to be an accurate approximation if theobjective function is stronglynon-linear,having to representphenomenasuchas flow separation, and combining variables of different types (discrete,continuous).This isverymuchthecasewhenbigvariablechangesareallowedin aerodynamicoptimizationproblems, andwhenawholebody (wind tunnel,forinstance)isoptimized,andnotonlycertainpartsorcomponentsofit.

7. Benchmark resultsofMOST-HDSwhenapplied toanexhaustivemathematicaloptimizationtestsuite, inordertocompare itsperformancewithotherwidelyused general-purpose optimization algorithms. Hence the potential ofMOST-HDS is shown, not only for shape design optimization, but also for otherapplications. The results show thatMOST-HDS can bemore competitive thanmodernoptimizationalgorithms.

8. Exhaustive review of the applicable State of the Art regarding designoptimization,withaneasy-to-followstructureandrelevanthighlightsoneachoftheresearchworksincluded.ThiscanbeusedinthefuturebyotherresearcherstohaveadetailedoverviewoftheStateoftheArtinthisareaofexpertise.

1.4.StructureofthisdocumentThis document aims to present the researchwork carried out for this Thesis in a

rigorous yet comprehensive and easy-to-read manner. Once Chapter 1 has set thefoundations for the Thesis, describing its motivation, main objectives andcontributions,therestofthedocumentisorganizedasfollows:

- Chapter2–Problemdescriptionandgeneralapproachdescribesinmoredetailtheproblemaddressed.

- Chapter3–StateoftheArtreviewisathoroughreviewoftheStateoftheArtofdesignoptimization,especiallyintheareaofaerodynamics.

- Chapter 4 – Problem definition presents the detailed problem definition andthe geometry parameterization proposed, for the two industrial examplespresented, to illustrate the applicability of the method for widely differentfields.


22

- Chapter5–TheMOST-HDSoptimizationmodeloffersandin-depthexplanationofthegeneralmodelandoptimizationalgorithmproposedbythisThesis.

- Chapter 6 – Results obtained presents the results section and shows theapplicabilityofMOST-HDSfortwoaerodynamicshapedesignproblems:closedwind tunnels for testing and other purposes, and industrial boilers used incombinedcyclepowerplants.Moreover,itanalysestheperformanceofMOST-HDSasageneralpurposeoptimizationalgorithm,applyingittoamathematicaltestsuiteusedforbenchmarkstudiesintheStateoftheArt.

- Chapter7–ComparisontosurrogatemodelscomparestheresultsobtainedbyMOST-HDSwithaverypopularoptimizationapproach,surrogatemodels,usedfor problems with time-consuming evaluations. This chapter will show thelimitationsofsurrogatemodelswhenappliedtoshapedesignproblemswithbiggeometrychanges.

- Chapter8–Conclusionssummarizesthemainconclusions,theresultsobtained,theThesiscontributions, the limitationsforMOST-HDSandthefutureworktobecarriedout,basedontheresultsofthisresearch.

- APPENDIXES

o A–IllustrationoftheMOST-HDSprocess

o B–Importantnotesonmeshsensitivityandmeshquality

ListofFigures

Figure1–1-Dragcoefficientsforgeneralbodyshapes.

Figure1–2-DaríoRestaandhismechanicinthePeugeotcar,whichwontheIndianapolis500in1916.

Figure1–3-AerodynamictrendevolutioninFormula1sincethebeginningofthecompetition(1950).

Figure1–4-RealexamplesofthedifferentaerodynamictrendsinFormula1sincethebeginningofthecompetition(1950).

Figure1–5-ExamplesofdisruptivedesignsinFormula1,eitherbecauseofthewingdesign,orthenosedesign,oreventheintroductionofafanforincreaseddownforce.

Figure1–6-Aerodynamicdesignevolutionofanexampleroadcar,inthiscasetheBMW.


23

Figure1–7-Aerodynamicdesignevolutioninthetrainsector.Asteamhighspeedtrain,capableofmaximumspeedsof160km/handaveragespeedsof130km/h,comparedtothemostmodernTalgotrain,theAvril,capableofmaximumspeedsof363km/handaveragespeedsof330km/h.

Figure1–8-Aerodynamicdesignevolutioninthemarinesector,inparticularintheAmerica'sCup.Totheleftthe1871Defender,theColumbia/Sappho,whichwonthatyear.Totheright,the2013winner,theDefenderthatyear,the17OracleTeamUSA.

Figure1–9-Aerodynamicdesignevolutioninthecyclingsector.Asetofrepresentativemodernracinghelmetsareshown.

Figure1–10-Example3Dvelocitystreamlinesforacomplexaerodynamicbody,inthiscasethefloorofamotorsportscar.

Figure1–11-WindtunneltestingforthreeVWcarsofdifferentyears.Velocitystreamlinesaresimulatedwithasmokegenerator.Changesintheflowfieldcanbeobservedbetweenthedifferentcarmodels.


Chapter2 -Problemdescriptionandgeneralapproach

Aerodynamicsisforthosewhodon’tmanufacturegoodengines.

EnzoFerrari.

This chapter presents the general problemof aerodynamic shape optimizationand the approach followed in this Thesis. It mentions other alternativeapproachesusedbyotherauthors(refertotheStateoftheArtinChapter3formore detail). In particular, this chapter gives an initial global overview of thehybridstructureddirectsearchapproach.Additionally, forthesakeofclarity, itdefinestheconceptofsmallv.biggeometrychange.Firstly,Section2.1.offersabrief introduction; Section 2.2. describes the main problem addressed by thisThesis;Section2.3.outlinestheproposedgeneralapproachforthiswork;Section2.4. illustratesthedifferencebetweensmallandbiggeometrychanges, for thepurpose of this Thesis, with a real example case which will be presentedthoroughlyinChapter6;andfinally,Section2.5.offersasetoffinalremarkstoconcludethechapter.

2.1.IntroductionAs Chapter 1 has introduced, the field of aerodynamic shape design in different

sectors (automotive,motorsport,aeronautics,high-speedtrains,etc.)hasundergonedifferent stages of development. At first not well understood, and with anunderestimated impact on overall body design, aerodynamics started growing inimportanceanditisnowoneofthekeyareasofengineeringdesigninmanyfields.

Trialanderrorhasbeenthecommondesigntrendformanydecades,basedonthedesigner’sexperience.Thereaftertheaerodynamicperformanceofeachdesignwasatfirst calculated using either simplified analytical equations or empirical correlationsderived from test data. Currently most designs require either Computational FluidDynamics (CFD) solvers, or costly wind tunnel tests, or even testing in the realenvironment.

2

Chapter2–Problemdescriptionandgeneralapproach

25

Shapedesignoptimizationhasgraduallygrowninusebydesignersandengineers,but, in most cases, it starts with a first stage of trial-and-error-based selection ofcandidatesandthena fine-tuningoptimizationof thebestdesigns. Ingeneral,whenoptimization is used, only small geometry changes are addressed. However, acomplete,automatic, flexibleandrobustmethodologyforaerodynamicshapedesignoptimization, able to analyze big geometry changes, has not been presented up todate,asfarasweknow.

ThisThesispresentsanoptimizationmethodologyofthiskind,whichcanbeappliedtomanyfieldsinwhichaerodynamicdesignisimportant.

Themaincontributionof this chapter is todescribe thedifferencebetweensmallandbiggeometrychanges, forthepurposeofthisThesis,becausethere isvery littlework in the literature focused on shape optimization considering big geometrychanges.

2.2.CharacterizationofthetypeofproblemThemethodologypresentedinthisThesisisamulti-attribute/objective,structured

optimizationprocedure,basedonhybriddirectsearch(MOST-HDS).Structuredrefersto the fact that the complete optimization problem will be divided into simpleroptimization sub-problems, following a structured architecture. Structuredoptimization is also referred to as sequential optimization, multi-level optimization,nestedoptimizationorhierarchicaloptimization(Cuadra[1990],Babu[2014],Heldetal.[2006],Robinsonetal.[2006],Zhouetal.[2015],LiuandZhang[2014]orNuñezetal.[2012]).

Theoptimizationarchitecturedevelopedhereisideallysuitedtoproblemswiththefollowing characteristics, as explained for example in Cuadra (1990) and Prada-Nogueiraetal.(2015):

1. Thenumberofindependentvariables(degreesoffreedom)ishigh.

2. The vector of independent variables does not have a fixed dimension; itsdimensiondependsonthevalueofcertainvariables.

3. Independent variables are of different mathematical kinds(discrete/continuous), and have a different (stronger or weaker) influence onthefinaldesign.Thesetwofactsleadtoahierarchyofvariables.

4. Thenumberofdesignconstraintsishigh.

5. There are attributes of interest to the engineer that cannot be reducedefficientlytoasingleobjectivefunctionbecausetheyaremutuallyconflictive,ornotcomparable.Hence,theproblemistrulymulti-attribute.


26

6. ComplexevaluationmethodssuchasCFDsolvers–notonlyanalyticalequations–mustbeused,sotheevaluationprocess(definedbyasetoflinkagefunctions)iscomplexandslow.

In a multi-attribute, structured optimization, the following entities must bethoroughlydefined:parameters, independentvariables,attributes, linkage functions,constraints, andevaluationprocess (refer toChapter 4 for thedetaileddefinitionoftheseelements).

Parametersarequantitiesoffixedvalue,beingthatvaluefixedeitherexternallybytheuseror internallybytheoptimizationmodelwithinaparticularsub-problem.Forexample,thelevelofdiscretizationofthegeometrymodelfortheaerodynamicbodyof interest (aswillbeexplained inmoredepth inChapter4),or thestoppingcriteria(maximumfunctionevaluations,maximumtime,etc.).Eresetal.(2014),forinstance,presentaninterestingandnovelmethodologytointroducecustomerrequirementsintheengineeringdesignprocess,appliedtotheaerospacesector.

Variablesarequantities thatcanchangetheirvalue.Theymaybe independentordependent,butonlyindependentvariablesarerelevantfromanoptimizationpointofview, since dependent variables are automatically computed inside a black-boxevaluationprocess. Independent variables (also calleddegrees of freedom) can takeanyvalueamongaparticulargroup(positivenumbers,binary,etc.);forexample,thelengthofasectionof thegeometry (continuousvariable),or thegeometry typeofaparticulartransversesectionofthemodel:circular,rectangular,square,etc.(discretevariable). Explicit constraintsmay limit their range of values a priori and, of course,otherconstraintsofanykindwillboundthefeasiblesearchspace.

Attributes, or objectives, are special dependent variables which allow for thecomparisonofonesolutiontoanother(i.e.onegeometrydesigntoadifferentdesign).Heretheycanrefertocost,size,flowquality,aerodynamicperformance,oranyothermagnitudeofinterestfortheuser.

Tocalculatethevaluesofthevariousattributesof interest fromthevaluesoftheindependent variables and the parameters, a set of equality constraints or linkagefunctionsisrequired.Thissetoffunctionsisstructuredasanevaluationprocess,i.e.ablack-boxprocessthatcomputestheattributesandconstraintsforeachcombinationofparametersand independentvariables.ThisThesis focusesonproblemsforwhichthe evaluation process is complex and time consuming, because it relies on CFDcomputations,althoughthemethodologypresentedcanbeappliedtootherproblems(refer toChapter6 foranexampleof the resultsobtainedwhen themethodology isappliedtodifferentkindsofproblems).

Finally, there will also be a body of inequality constraints, referred to simply as“constraints” in thiswork. They set the limits for certain variable combinations andhence determine how far off a particular solution is from the space of feasiblesolutions.Inourcasesofinterest,theconstraintsareusuallyvariablevaluerangesorgeometryabsurditylimitations.Itisoftenusefultodefinespecialattributestoquantifythestatusofconstraintviolations,i.e.,thedegreeoffeasibilityofasolution.


27

2.3.GeneralapproachTheapproachproposed in this Thesis is amulti-attribute, structuredoptimization

basedonhybriddirectsearch(i.e.directevaluationofeachcandidatedesignandnotapproximationofitsattributevaluesbyanyprocedure).

The optimization algorithm developed combines genetic, gradient and swarmsearch intelligence inevery iteration,aswillbeexplained indepth inChapter5.Thisnovel optimization method allows for an intelligent and efficient direct search incomplex aerodynamic problems with big geometry changes. This optimizationmethodology is applicable to advanced aerodynamic design in cars, aircraft, high-speedtrains,etc.

2.4.DefinitionofsmallversusbiggeometrychangesForthepurposeofthisThesis, it is importanttointroducethedifferencebetween

small and big geometry changes in the context of aerodynamic shape designoptimization.Asshowninthewholesetofresultspresented(Chapter6), theMOST-HDS optimization algorithm can also be applied successfully to problems of smallgeometry change, and even to other fields quite different to aerodynamic design.However, it is in problems with big geometry changes that MOST-HDS fills a gappresentintheStateoftheArt.

Theaimof this section isnot todefine the terms small andbig in a strict formalway, but rather to illustrate the differencewith example figures to help the readerhaveaclearideaofthemeaningofeachterm.

The conceptofbig geometry change includesnotonlyabigmodification inbodygeometry, but also a considerable change of position of discrete elements presentwithin the geometry (an engine in the case of an airplane wing, a fan or the testsectionofawindtunnel,etc.).

Theinterestofanalyzingbiggeometrychangesstemsfromthefactthattakingthistype of changes into account for the optimization can yield improved yet notconventional,ornon-intuitive,designs,aswillbeshowninChapter6.

Thefollowingfigureshowsanexampletransitionductforanindustrialapplication,namely the entrance to a particular kind of industrial boiler, called Heat RecoverySteamGenerator(HRSG),whichisusedincombinedcyclepowerplants.Thegeometryis quite simple and illustrative and is therefore used as an example. Figure 2–1representsapossiblebaselinedesignforthisduct’sshapeoptimization.Figure2–2isasampleofpossibledesignswhichcurrentcommonplaceshapeoptimizationtechniqueswouldconsider(beitbymeansofdirectsearch,surrogatemodels,adjoints,etc.).Thistypeofdesignchangesfallwithinthecategoryofsmallgeometrychanges.


28

Figure2–1-Illustrativeexampleofgeometrywhichrepresentsapossiblebaselinedesign,toshow

thedifferencebetweensmallandbiggeometrychangesforshapeoptimization.

Figure2–2-Exampledesignswhichareconsideredsmallgeometrychangeswithrespecttothe

baselinedesign(design"a"),showninFigure2–1.

Figure2–3 illustrates a selectionof candidatedesignpointswhichare consideredbiggeometrychanges–withrespecttothebaselinedesign–forthepurposeofthisThesis. Some of thesemore radical or unconventional designs have proved to yieldverygood,yetunexpected, results (refer toChapter6).Finally,Figure2–4shows3Dviewsofsomeoftheseexamplecandidatedesignswithbiggeometrychanges.


29

Figure2–3-Exampledesignswhichareconsideredbiggeometrychangeswithrespecttothe

baselinedesign(design"a"),showninFigure2–1.


30

Figure2–4-Sideviewsand3Dviewsofdifferentcandidatedesignsforanexampleshape-

optimizationproblemwithbiggeometrychanges.

2.5.FinalremarksThis chapter has characterized the type of problem that this Thesis addresses.

Moreover,ithaspresentedakeydistinctionforthepurposeofthisresearch,whichisthe difference between small and big geometry changes. This distinction if of highimportance for this Thesis, since one of its contributions is that it can consider biggeometrychangesinproblemsofshapeoptimizationandhenceyieldoptimumdesignswhich are non-intuitive, unconventional, and which have better performance thancurrentdesigns.

ListofFiguresFigure2–1-Illustrativeexampleofgeometrywhichrepresentsapossiblebaselinedesign,toshowthedifferencebetweensmallandbiggeometrychangesforshapeoptimization.

Figure2–2-Exampledesignswhichareconsideredsmallgeometrychangeswithrespecttothebaselinedesign(design"a"),showninFigure2–1.

Figure2–3-Exampledesignswhichareconsideredbiggeometrychangeswithrespecttothebaselinedesign(design"a"),showninFigure2–1.

Figure2–4-Sideviewsand3Dviewsofdifferentcandidatedesignsforanexampleshape-optimizationproblemwithbiggeometrychanges.


Chapter3 -StateoftheArtreviewIfsomeonetellsyouthereisarule,breakit.Itistheonlywaytomoveforward.

HansZimmer.

ThischapterpresentsathoroughreviewoftheapplicableStateoftheArt.Firstly,Section3.1.presentsthestructureandclassificationcriteriausedfortheStateofthe Art review; Sections 3.2. to 3.4. analyze the applicable State of the Art;finally,Section3.5.summarizesthemainconclusionsregardingtheStateoftheArtreview,aswellasthelocationofthisThesiscontributionswithintheStateoftheArt.

3.1.IntroductionandclassificationcriteriaThe present Thesis tackles aerodynamic design optimization using theMOST-HDS

generalmodel,whichproposesaMulti-ObjectiveStructuredHybridDirectSearchfortheoptimizationprocess.

Thischapterwillclassifytherelevant,applicableresearchworkintheexistingStateoftheArtasfollows,fromageneraltoamoreparticularfieldofstudy:

1. Metaheuristicoptimizationingeneral:thissectionwillbelessexhaustive,sinceit covers a much broader spectrum of research. It will discuss papers onoptimizationapproacheswhichwillbecompared to theapproach followedbyMOST-HDS.

2. Aerodynamicshapeordesignoptimization ingeneral: this includespapersofdifferentareasofresearchwithingeneralaerodynamicshapedesign.Aspecialemphasisismadeinthecommentstoclarifywhetherthedifferentpaperstakeintoaccountonlysmallgeometrychanges,oriftheyconsiderbothsmallandbiggeometrychanges.Inparticular,thefollowingaspectswillbereviewed:

a. Geometry parameterization techniques: Bézier curves, B-splines andFreeFormDeformation.

3

Chapter3–StateoftheArtreview

33

b. DesignofExperiments(DoE)techniqueused.

c. Advancedmeshing:structuredv.unstructuredmeshes,oversetmeshes,meshmorphing.

d. Evaluation scheme: direct search v. metamodels or surrogate models(ResponseSurfaceMethodology(RSM),ReducedOrderModels(ROM)orhierarchicalmodelling).

e. Optimization procedure: structured optimization, gradient-basedmethods (Adjoint Methods, Sequential Quadratic Programming (SQP),etc.),non-gradient-basedmethods(GeneticAlgorithms(GAs),SimulatedAnnealing(SA),etc.),hybridalgorithms.

f. General problem complexity: size of space of variables considered forsearch(i.e.bigv.smallgeometrychanges),numberofvariables,numberofconstraints,etc.

3. Aerodynamic shapeor designoptimization for the industrial cases analyzed:the different approaches in the area of aerodynamics will be described,specifically for the industrial applications for which detailed results arepresentedinthisThesis:closedwindtunnelsandindustrialboilersforcombinedcyclepowerplants.Inthissectionitisworthhighlightingiftheresearchpapersanalyzedfocusonalocaloptimizationoriftheycarryoutaglobaloptimizationofthewholeshapeofaparticularbody.

WithrespecttoallthesefieldsoftheStateoftheArt,thespecificcontributionsofthis Thesis, which are summarized again at the end of the chapter with a series ofscatterplots,arethefollowing:

1. Metaheuristic optimization in general: this Thesis presents the MOST-HDStool, which is highly competitive and can outperform other advanced andcommonly-usedgeneral-purposeoptimizationalgorithms,asshowninChapter6whenapplyingMOST-HDStoachallengingmathematicaltestproblem.

2. Aerodynamicshapeordesignoptimizationingeneral:

a. This Thesis can handle big geometry changes and can yield veryinnovativedesigns,with improvedperformance.Mostofthe literaturefocusesonlyonsmallgeometrychangesorfine-tuning.

b. The tool developed uses structured optimization,which has not beenusedsofullyuptodateinaerodynamics.


34

c. MOST-HDS follows a direct search approach, which is shown to beatsurrogate-basedoptimization(usingresponsesurfaces)forthetypesofproblemsaddressedbythisThesis.

3. Aerodynamicshapeordesignoptimizationfortheindustrialcasesanalyzed:

a. Wind tunnels: this Thesis considers a wide variety of tunnelconfigurations, not only 90° corners, rectangular ducts and multi-fandesigns. Itaimsatexploringbiggeometrychanges,whichcanimprovetheperformanceofmoretraditionaldesignconcepts.Itfocusesontrueoptimizationofthefullwindtunnelbody,andnotonlycertainpartsofit,suchascornersorthemainnozzle.Moreover, itconsidersdifferentrelative positions of the various elements of the wind tunnel (mainlytestsectionandfansystem).

b. Industrialboilers:inthisfield,theThesiscontributesbecauseitcarriesout amore extensive design exploration of possible candidate pointsthan the works found in literature. Consequently, it exploresunconventionaldesignswhich,insomecases,showbetterperformancethanboilersdesignedfollowingtraditionaltrend-lines.Finally,basedonthe extensive design exploration, MOST-HDS carries out a true andcompleteoptimization.IntheStateoftheArt,mostauthorslimittheirwork to exploring a reduced set of design candidates. This allows thisThesistoyieldimportantperformanceimprovements(refertoChapter6).

3.2. State of the Art of general metaheuristicoptimization

ThefirstsectionofthisStateoftheArtchapterisfocusedongeneraloptimizationresearchworkwhichisworthanalyzinginthecontextofthisThesis.

Because theMOST-HDSmodel developed inour researchworkproposes amulti-attribute, structured optimization based on hybrid direct search, let us analyze theStateoftheArtofthedifferentaspectsinvolvedinthefollowedapproach.

Theresearchonmulti-objectiveoptimization is tooextensiveandcoveringawiderange of fields and thuswewill not aim at presenting a review on this area in thisdocument. Instead, we will commence by focusing on research using structuredoptimization. The two main concepts of this optimization methodology are: a)hierarchy of variables and b) optimization phases. This approach, including directsearch inmost cases, has been used in other fields (Cuadra [1990]), but not yet inaerodynamics,oratleastnotasthoroughlyasproposedinthisThesis.


35

Ifweonlyfocusontheareaofoptimizationusingdifferentphases(orlevels)thereisrelevantresearchwork.Inmostcasesitiscombinedwiththeuseofhighly-detailedandlow-detailedmodelsforthedifferentstages(alsoreferredtoashigh-fidelityandlow-fidelitymodels).A firstrelevantexample isLyuetal. (2014),whichusesamulti-level approach to reduce the computational cost for their problem of optimizationappliedtotheCommonResearchModelWingBenchmark.Additionalgoodexamples,applied to airfoil shape optimization, areMarduel et al. (2006) and Robinson et al.(2006).Thislatterexplains,forinstance,differentmappingtechniquestofindthebestset of high-fidelity variables corresponding to a set of low-fidelity variables and viceversa.Theyproposeamethodologyofoptimizationcombining low-fidelityandhigh-fidelitymodelsandtheyobtain reductions in thenumberofevaluationsof thehigh-fidelitymodelofup to40%usingProperOrthogonalDecomposition (POD)mapping.ThispaperusessurrogatemodelsandreliesonpaperssuchasEldredetal.(2004)toconsidersecond-ordercorrectionsfortheirsurrogate-basedoptimization.

AnareainwhichoptimizationdividedintophasesiswidelyusedisVeryLargeScaleIntegration (VLSI) systems. Babu (2014) describes the different optimization levelswhereas Held et al. (2006) states that the traditional methods of hierarchicaloptimization (divide into optimization subproblems to reduce the search region) arenotthebestoption.Theyproposeaflatmethodology,inwhichtheyconstrainaslittleaspossiblethesearchregionoftheoptimizationalgorithms.

Otherinterestingcontributionsareincludedhere.Zhouetal.(2015),foramethodto obtain design alternatives from a pre-existing or base design and for the use ofmetamodels to switch from a nested optimization structure to a single-loopoptimization.LiuandZhang(2014), fortheuseofadecouplingstrategytoobtainanequivalent single-layer optimization model from their original nested optimizationproblem. Nunez et al. (2012), in which optimization workflows are analyzed andreformulated.

Regarding sequential – not strictly speaking multi-phase – optimization, Du andChen (2004) use a decoupling strategy to transform a double-loop optimizationproblem, typical of optimizationwith uncertainty, to a single-loop optimization, butthey do not decouple the optimization problem itself; they only separate theoptimizationandprobabilisticanalyses.

Movingontothetopicofhybridsearchstrategiesand,morespecifically,tohybriddirectsearch,itisworthhighlightingthenoveltyoftheproposedMOST-HDSapproach.This novelty stems from the fact thatMOST-HDS combines elements of all types ofalgorithms (in particular, genetic, gradient and swarm search techniques) in everyphase.Incontrast,mostotherauthorsswitchfromonetypeofalgorithmtotheotherdependingonhowtheoptimizationisadvancing,switchingforinstancefromgradient-based to non-gradient-based algorithms (relevant examples are Guliashki [2008],Hegazietal.[2002]orHsiaoetal.[2001]).


36

Asopposedtotheuseofdirectsearchordirectoptimizationtechniques(whichrelyonthedirectevaluationofa full-ordermodelof theproblemof interest), surrogate-based evaluation and optimization have become very popular in recent years toreduce the number of evaluations and/or the time consumed for these evaluations.Theydosobydevelopingsimplifiedmodelsof the full-ordermodel.Thesesimplifiedmodels,asexplainedverywellinRobinsonetal.(2006),canbeofadatafittype(suchas response surfaces) or of a Reduced Order Model (ROM) type or, finally, of ahierarchicalmodeltype.

Giventheamountofresearchcarriedoutinthisarea,andtheinterestofthedebatebetween direct search and surrogate-based optimization, Chapter 7 of this Thesis iswholly devoted to the comparison of the results of both approaches for one of theindustrialcasespresentedinthisresearch.

Washabaughetal. (2012)givenovel approaches regarding surrogate (in this casereduced order) models, for example. They rely on local instead of global ReducedOrderBases (ROBs), and theyobtainbetter time reductionsand improvedaccuracy.SchaumontandVerbauwhede(2004),ontheirside,usesimplifiedmodelsoftherealmodel.Theycalltheseabstractedmodels.Theyalsousepartialevaluation,i.e.theuseofdesignpropertiestospecializethesimulator.Theyimprovetheiroptimizationtoolsbyknowinghow thedesignworks, similarly towhat isproposed in thisThesis. Theyalsocarryoutoptimizationatdifferentlevelsandwithvariousalgorithms.

Other very relevant references in the area of surrogate-based optimization aredescribed next. Su et al. (2016) is a good example of the use of modal-basedoptimization for the wing shape of highly flexible morphing aircraft. Walton et al.(2013) is especially interesting for their focus on the use of surrogate models forunsteady simulations; in particular, they use a combination of proper orthogonaldecompositionandradialbasisfunctionsforthree-dimensionalunsteadycompressibleinviscidflowsoveranoscillatingONERAM6wing,andtheyreportlargereductionsincomputationtimewithoutsignificantlossesinaccuracy.TheworkbyKrajnovic(2007),foritsapplicationtovehicleshapeoptimization.ThepaperbyRobinsonetal.(2006),particularlyinterestingforitsapplicationtoairfoilshapedesign.

In addition, there is also very valuable work in the use of specific alternativeevaluators,notnecessarilytocarryoutacomputer-basedoptimization,butrathertomerely compare the performance of different solutions, as thework carried out forthis Thesis did in its first stages. An area of particular interest for this is gamesimulation, in particular chess evaluators. Edelkamp and Schroedl (2011) andFürnkranz and Kubat (2001) offer an interesting insight into the importance ofevaluatorsingametreesearchappliedtochess.


37

Optimizationproblemssimilartotheonepresentedinthispaper–ingeneralterms-areaddressednext.Kellyetal.(2010)introducesamethodtoquantifyuserpreferenceofaparticularshapedesignintotheobjectivefunction(quitedifferenttothemethodusedbyTakagi[2001],InteractiveEvolutionaryComputation,inwhichevaluationsarecarriedoutdirectlybyhumansbecause they relate to feelingsorpreferences,whichcannot be easily quantified). Xiao et al. (2011) or Yoshimura et al. (2013). Goit andMeyers (2015) uses a conjugate-gradient optimization method in combination withadjoint, large-eddy simulations for the determination of the gradients of the costfunctional,inordertomaximizeawindfarm’senergyextraction.Sicilia-Montalvoetal.(2015)proposesamulti-objectiveoptimizationwithantcolonymethodologiesfortheoptimum operation of long haul freight transportation. Izraelevitz and Triantafyllou(2014)presentsamodel-basedoptimizationapproach.Finally,Hoffensonetal.(2015)introduces sustainability and environmental impact quantification of designalternatives.

Moreover,thisThesispresentsthebenchmarkresultsoftheapplicationofMOST-HDS to one of the most challenging -as well as comprehensive- mathematical testproblemsfoundinliterature(Hubandetal.[2006])andthecomparisontotheresultsobtainedwithawell-knownMulti-ObjectiveEvolutionaryAlgorithm(MOEA),NSGA-II,tothissametestproblem.Very interestingobservationsaremade inChapter6.Thishelps support the potential of MOST-HDS for general-purpose optimization and itshowsitsadvantagesandlimitations,aswellasthoseofNSGA-II.

Inthefieldoftestproblems,somemajorexamplesthatcanbefoundinliteratureinclude:

1. ZDT:6real-valuedproblemsfromZitzleretal.(2000)

2. DTLZ:5unconstrained,scalablereal-valuedproblemsfromDebetal.(2001)

3. LZ:9real-valuedproblemsfromLiandZhang(2009)

4. CEC2009:13unconstrainedand10constrainedreal-valuedproblemsfromtheCongressonEvolutionaryComputation(CEC2009)competition

5. WFG:9scalable,real-valuedproblemsbyHubandetal.(2006)

6. BBOB-2016:55bi-objectiveproblemsfromtheBlackBoxOptimizationBenchmarking(BBOB)workshophostedattheGeneticandEvolutionaryComputationConference(GECCO2016)

7. Others,suchasknapsack,NK-landscapes,etc.

Among the researchers having used theWFG test frame, it is worthmentioninghere the Thesis by Zhao (2007) and the work by Bradstreet et al. (2007), for theircomparisonof theperformanceofvariousalgorithmswhenapplied to theWFGtestproblems.


38

Concerning themostmodernMOEAs that can be found in literature, one of thelargest libraries available currently, theMOEA framework3 presents Table 3–1. Thistable is included, given the great amount ofwork and the popularity ofMOEAs formany fields of optimization. It can prove a valuable review of MOEAs for authorsinterestedinthisarea.

MOEA DESCRIPTION

AbYSS MultiobjectiveScatterSearch

BorgMOEA AdaptiveMultioperatorSearchwithε-Dominanceandε-ProgressTriggeredRestarts

CellDE CellularGeneticAlgorithmwithDifferentialEvolution

CMA-ES CovarianceMatrixAdaptionEvolutionStrategy

DBEA ImprovedDecomposition-BasedEvolutionaryAlgorithm

DE DifferentialEvolution(SingleObjective)

DENSEA DuplicateEliminationNon-dominatedSortingEvolutionaryAlgorithm

ECEA Epsilon-ConstraintEvolutionaryAlgorithm

ES EvolutionStrategies(SingleObjective)

ε-MOEA ε-Dominance-basedEvolutionaryAlgorithm

ε-NSGA-II NSGA-IIwithε-Dominance,RandomizedRestarts,andAdaptivePopulationSizing

FastPGA FastParetoGeneticAlgorithm

FEMO FairEvolutionaryMulti-objectiveOptimizer

GA GeneticAlgorithmwithElitism(SingleObjective)

GDE3 GeneralizedDifferentialEvolution

HypE Hyper-volumeEstimationAlgorithmforMulti-objectiveOptimization

IBEA Indicator-BasedEvolutionaryAlgorithm

MOCell Multi-objectiveCellularGeneticAlgorithm

MOCHC Multi-objectiveCHCAlgorithm

3www.moeaframework.org(lastverifiedonFebruary2017).


39

MOEA/D Multi-objectiveEvolutionaryAlgorithmwithDecomposition

MSOPS MultipleSingle-ObjectiveParetoSampling

NSGA-II Non-dominatedSortingGeneticAlgorithmII

NSGA-III Reference-Point-BasedNon-dominatedSortingGeneticAlgorithm

OMOPSO Multio-bjectiveParticleSwarmOptimization

PAES ParetoArchivedEvolutionStrategy

PESA2 ParetoEnvelope-basedSelectionAlgorithm

Random RandomSearch

RSO RepeatedSingleObjectiveAlgorithm

RVEA ReferenceVectorGuidedEvolutionaryAlgorithm

SEMO2 SimpleEvolutionaryMulti-objectiveOptmimizer

SHV Sampling-BasedHyper-volume-OrientedAlgorithm

SIBEA SimpleIndicator-BasedEvolutionaryAlgorithm

SMPSO Speed-ConstrainedMulti-objectiveParticleSwarmOptimization

SMS-EMOA S-MetricSelectionMOEA

SPAM SetPreferenceAlgorithmforMulti-objectiveOptimization

SPEA2 Strength-basedEvolutionaryAlgorithm

VEGA Vector-EvaluatedGeneticAlgorithm

Table3–1-ListofmostrelevantMOEAsasprovidedbytheMOEAframeworklibrary(www.moeaframework.org).

Many of the authors working in optimization have also carried out extensiveresearch of performance indicators, to compare their algorithms to the State of theArt.Amongthemostimportantindicators,thefollowingcanbehighlighted(aspertheMOEAframework):Hyper-volume,GenerationalDistance(GD),InvertedGenerationalDistance (IGD), Additive ε-Indicator, Contribution, Maximum Pareto Front Error,Spacing,R1Indicator,R2IndicatorandR3Indicator.

Only a review of research using the hyper-volume will be included here, for itspopularityandpotentialinmulti-objectiveoptimization.


40

The hyper-volume indicator, as explained in Bader and Zitzler (2011), is the onlysingle set quality measure known to be strictly monotonic regarding Paretodominance. This means that when a Pareto set approximation entirely dominatesanotherone,theindicatorvalueofthedominantsetwillbebetter,too.Thispropertyishighly interestingand relevant forproblems involvinga largenumberofobjectivefunctions.

Somerelevantworksontheuseofthehyper-volumeindicatoraredescribednext,apart from thementioned Bader and Zitzler (2011). The PhD Dissertation by Bader(2009)providesathoroughtheoreticalbasisforhyper-volumeoptimization.Augeretal. (2012) presents two different approaches: one is the optimization of multipleobjectives simultaneously (traditional approach) and another is an indicator-basedoptimization, which maximizes hyper-volume (weighted, in this case), or otherindicators, for a setof underlyingobjectives. Bradstreet (2011);AzevedoandAraújo(2011),includethecomparisonamongdifferentperformanceindicators.Minellaetal.(2008) is particularly interesting for its comparison of two performance indicators:hyper-volume and unary epsilon. Two web references are also provided here, withworthwhileselectionsofhyper-volume-relatedliterature4,5.

To conclude this section of the State of the Art of general metaheuristicoptimization, ithasbeendeemedof interest todistinguishbetweenexact,heuristic,metaheuristic and hyperheuristic methods, to clarify why themethod developed inthisThesisisclassifiedasmetaheuristic.

Inthefirstplace,exactalgorithmsguaranteetheywillfindtheoptimuminafiniteamountoftime.However,formostrealoptimizationproblems,thisfiniteamountoftimeisusuallytoolengthy.

Asopposedtoexactmethods,heuristicsdonothavemathematicalproofthattheywill find the optimum. At most, they have a high probability of obtaining a goodsolutionwithinareasonabletime.Strictlyspeaking,heuristicalgorithmsareproblem-dependent,i.e.theyareadaptedtoaparticularoptimizationproblem.

Metaheuristics, on the other hand, offer problem-independent techniques,although they still have a set of parameters which must be fine-tuned for eachparticularproblem.

Finally,hyper-heuristicsgobeyondmeta-heuristics,andtheyrefertomethodsthateitherselectthebestheuristicsforaparticularproblemorgenerateadaptedheuristics(Burkeetal.[2013]).Additionalworksofinterestrelativetohyper-heuristicsarePillay(2016), which offers a recent review of hyper-heuristics applied to combinatorialoptimization, inparticular to theeducational timetablingproblem, andBrankeet al.(2016),whichoffersareviewofhyper-heuristics,inthiscaseforthefieldofproductionscheduling.

4https://ls11-www.cs.uni-dortmund.de/rudolph/hypervolume/start(lastverifiedonFebruary2017).5https://hpi.de/en/friedrich/research/hypervolume.html(lastverifiedonFebruary2017).


41

3.3. State of the Art of general aerodynamic shapedesignoptimization

For the purpose of this Thesis, and in order to serve as a general review of theresearch work in this field, it is important to highlight the most representative orinteresting work carried out in advanced aerodynamic optimization in general (notonlyforwindtunnelsandHRSGs).Moreover, it isalsousefultoputtheprobleminawider context, and so to indicate some relevant works on design optimization ingeneral.

Firstly,thereareinterestingresults,followingamoretraditionalapproach,suchas,forinstance,theworkofMontenegro-JohnsonandLauga(2015),J.Wild(2008),orthegeneraloverviewonoptimizationpresentedinKozielandYang(2011).

However,themostrecentapproachinthespecificareaofaerodynamicsconsistsofthefollowingsteps,ascanbeseeninFortiandRozza(2014),HickenandZingg(2010),Krajnovic (2007), Mengistu and Ghaly (2008), Okumura et al. (2013) or Paniagua(2014):

1. Geometryparameterization,normallyusingBéziercurves.

2. Metamodels or surrogate models, to approximate the real objectivefunction with a more simplified one, by means of Design of Experiments(DoE)andmetamodelssuchasResponseSurfaceMethodology(RSM),RadialBasisFunctions(RBF)orothers.

3. Optimization,usingeithernon-gradient-basedmethods(GeneticAlgorithms(GAs), SimulatedAnnealing (SA), etc.), or gradient-basedmethods (AdjointMethods,SequentialQuadraticProgramming(SQP),etc.).Mostoftheworkin this area carries out multi-objective optimization, for instancedeterminingParetooptimalfronts.

Consequently,wewillstructuretheStateoftheArtreviewinthissectionaccordingtotheabovesteps.

Inthefirstplace,theinitialstepdealswithgeometryparameterizationtechniques.In current literature, either Bézier curves, B-splines or Free FormDeformation (FFD)areused.

In the present Thesis, Bézier curves will be selected. These curves are chosenbecausetheyarerobust,theycaneasilybecontrolledtoavoidabsurdtunnelshapes,andtheyhavegoodmathematicalbehaviorandoptimumaerodynamicperformance.Bézier curves are used extensively in aerodynamic optimization (a good illustrativeexampleisPaniagua[2014]).


42

In other cases, B-splines are used as a generalization of Bézier curves to avoidproblemssuchastheRungephenomenon,orothereffects,whichmeanhigherorderpolynomialscanhavehigherinterpolationerrorsthanlowerorderpolynomials.Inourcase, theBéziercurvesarenotusedasanapproximationtoareal function,butasamethodofgeneratinggoodaerodynamicsurfaces.CubicBéziercurves(andnothigherorderones)arehencechosen inouranalyses. They representanoptimumtrade-offbetweenthenumberofcontrolpointsandthecapacitytorepresentaverywiderangeof geometries for the tunnel. Splines, for instance, could yield absurd geometries,whichmust be avoided; they also introducemuchmore complexmathematics, andtheyarebetter suited for casesof real functionapproximations andnot somuch inaerodynamicshapegeneration.

Leeetal. (2017)offersan interestingcomparisonontwoofthemostwidelyusedgeometryparametrizationtechniquescommented:B-splinesandFFD.B-splinesurfacecontrol is often found to result in slightly better performance. Nevertheless, bothmethods perform equallywell in general. FFD provides amore general approach toproblem setup, decoupling geometry control from parameterization. Overall, theresults presented suggest that B-spline surface control is better suited for simplegeometries such as wings, whereas FFD is better adapted for complex geometries,such as unconventional aircraft, and for implementation withmulti-start algorithmsandadaptivegeometrycontrolapproaches.

Theabove-mentionedworkbyHickenandZingg(2010)alsousesB-splines.AnotherveryrelevantworkintheareaofaerodynamicshapeoptimizationisJingetal.(2013),ontheoptimizationofthepositionofanacelleandpylonassemblyforaeronautics.Itisveryinterestingbecauseitcombinesgeometryparameterization,usingadaptedFFDand NURBS curves, mesh-morphing with Delaunay triangulation, Particle Swarm-searchOptimization (PSO) for theoptimizationandKriging for the response surface.Consequently,thispaperwillbehighlightedvarioustimesinthissectionoftheStateoftheArt.

MovingontotheDoEtechniquesused,whichwasnotoneoftheobjectivesofthepresentThesis(itwillbepartofthefuturework),weonlymentionheretheworkbyKrajnovic (2007) and its recommendation to study the use of Latin HypercubeSampling(LHS)andOrthogonalArrays(OA).

The next step to be carried out in aerodynamic shape optimization, once thegeometryhasbeenparameterizedormodelled,isthemeshingprocess.IntheStateoftheArt,workcanbe foundbothonstructuredandunstructuredmeshes,butaveryinteresting approach is the use of overset meshes (Kenway et al. [2017]), whichdevelops an overset meshing procedure that performs very well with respect tocommonstructuredorunstructuredmeshes.Otherrelevantpiecesofresearchonthetopic of advanced meshing are the already mentioned works by Hicken and Zingg(2010), onmeshmovement; and Jing et al. (2013),which usesmeshmorphingwithDelaunaytriangulation.Meshmorphingisundoubtedlyaveryrelevanttopicforshapeoptimizationandgeometrydeformations.


43

Regarding the evaluation scheme, of particular importance in problems of costlyevaluation (for example those requiring CFD evaluations), two approaches can befoundinmainstreamliterature:directsearch(originallydefinedformallyinHookeandJeeves[1961])andmeta-modelsorsurrogatemodels(ResponseSurfaceMethodology(RSM),ReducedOrderModels(ROM)orhierarchicalmodelling).Prada-Nogueiraetal.(2015),andespeciallyPrada-Nogueiraetal.(2017(a),2017(b))offergoodexamplesofdirect search applied to aerodynamic optimization. References of direct search andhybriddirectsearchappliedtootherfields,otherthanaerodynamics,areincludedinSection3.2ofthischapter.

Areviewonthemostrelevantandrecentreferencesintheareaofsurrogate-basedevaluationwillbecommentedbelow(andinSection3.2),whenreferringtoworksonsurrogate-basedoptimization.

A wide variety of approaches is found in current literature about optimizationprocedures.Itisusualtolabelthemas:

1. gradient-basedmethods, suchasAdjointMethodsorSequentialQuadraticProgramming(SQP)

2. non-gradient-basedmethods, such asGenetic Algorithms (GAs), SimulatedAnnealing(SA),orParticleSwarmOptimization(PSO)

buttherearealsootheroptimizationschemesorfeaturessuchasstructuredsearchorhybridalgorithms,whicharethecoreofthealgorithmdevelopedforthisThesis.

ThereferencesincludedaimatofferingarelevantselectionofthemostinnovativeresearchapproachesthatcanbefoundintheStateoftheArt,insteadofanexhaustivecoverageofmoretraditionaloptimizationschemes,ofwhichthereisawiderangeofexamples.

Forproblems inwhichthere isariskof theoptimizationprocessbeingtrapped inlocalminima,gradient-basedmethodsneedtoberevisedorenhancedtobeable toperformwell.Arreckxetal.(2016)offersanexampleofhowthelimitationsofgradientmethods can be overcome. It proposes a matrix-free optimization to avoid thecalculation of Jacobian and Hessian matrixes, for a close-to-gradient-basedoptimizationofengineeringproblemswith thousandsof variablesandconstraints. Ithasbeenespeciallyapplied toMultidisciplinaryDesignOptimization (MDO) foraero-structuralproblems.

Fabianoetal.(2016)useadjointsforMDOinatime-dependentsituation,applyingadjoint-based optimization to a different field of aerodynamic design, in this casehelicopterrotorblades.Thisreferenceoffersaveryvaluable insight intotheStateoftheArtoftheuseofadjointsinthefieldofunsteadyaerodynamicproblems.


44

Theauthorsstatethattherearemanyworksontheuseofadjointsforsteady-stateshape optimization, whereas there are not somany for unsteady flow problems. ItweretheworksbyManiandMavripilis(2009)andbyRumpfkeilandZingg(2010)thatinitially demonstrated unsteady discrete adjoint-based shape optimization in thecontext of two-dimensional problems. Mavripilis (2007) offered a preliminarydemonstrationofthemethod’sfeasibilityinthree-dimensionalproblems.Thereafter,afull implementation and application to large scale problems concerning helicopterrotorsandfighterjetswasperformedbyNielsenetal.(2010(a),2010(b)).

Basedontheworksofthesepapers inthefieldofadjoint-basedoptimization,thenext step is to extend the use of adjoint methods to multidisciplinary simulations,using the calculated sensitivities to perform MDO. In the domain of fixed andespeciallyrotarywindaircraft,aeroelasticcouplingeffectscanbeverysignificantandmustbeconsideredinthecontextofasuccessfuloptimizationprocedure,accordingtoFabianoetal.(2016).

To conclude on the references concerning the use of adjoints, the alreadycommentedpaperbyHickenandZingg(2010)isalsoaverygoodexample.

With respect to references regarding surrogate-based optimization, Section 3.2offersan interesting setof relevant researchworks.Worthhighlightinghereare theones described next. Once more, the work by Jing et al. (2013), which is a verycomplete example of aerodynamic shape optimization, from geometryparameterization and mesh morphing, to the use of the Kriging response surfacemethodfortheoptimization.Pooleetal.(2017)contributestotheStateoftheArtforseveral reasons: (1) its use of proper orthogonal decomposition to derive aerofoildesignvariables, (2) itsmethod toobtainanefficientand reducedsetoforthogonaldesignvariables,(3)theapplicationofaconstrainedglobaloptimizertoaerodynamics,and (4) its illustration that with only six variables an aerofoil optimization can becarried out successfully. Finally, Allen et al. (2016), for its use of modal-derivedvariablesandgradient-basedoptimization.

The last topic to be commented, concerning shape optimization in the field ofaerodynamics,isthecomplexityoftheproblemsolvedinthedifferentworksanalyzed.Someaspectsofspecialrelevancearethesizeofthespaceofvariablesconsideredforthesearchprocess(i.e.bigorsmallgeometrychanges),thenumberofvariables,andthenumberofconstraints.

GiventhatoneofthekeyaspectsofthemethoddevelopedforthisThesis,MOST-HDS,isthatitisabletohandlebiggeometrychanges,itisworthmentioningthatthereis very littleworkon the topicof trulybigdeformations inaerodynamics,whichcanlead to innovative and very new designs. Most of the papers analyzed focus onaerodynamicshapedesigninvolvingsmallfine-tuningofthegeometry,oratleastnotchangesoftheextentofthoseconsideredinthisThesis.


45

ExampleresearchonbiggeometrychangesincludestheverygoodpaperbyHickenand Zingg (2010). It is very worth describing this paper in detail here. The authorspresent an efficient gradient-based algorithm for aerodynamic shape optimization,which consists of several components, including a novel integrated geometryparameterizationandmeshmovement,aparallelNewton-Krylov flowsolver,andanadjoint-based gradient evaluation. In order to integrate geometry parameterizationandmeshmovement,theyusegeneralizedB-splinevolumestoparameterizeboththesurface and the volumemeshes. Thework shows that the volumemesh of B-splinecontrol pointsmimics a coarsemesh. Thereafter, a linear elasticitymesh-movementalgorithm is applied directly to this coarsemesh and the newmesh is regeneratedalgebraically. The authors claim mesh-movement time is reduced by two to threeordersofmagnitude relative toanode-basedmovement. They state that themesh-adjoint system also becomes smaller, and hence complex-step derivativeapproximationscanbeappliedsuccessfully.Whensolving the flow-adjointequationsusingrestartedKrylov-subspacemethods,anested-subspacestrategyisalsoshowntobe more robust than truncating the entire subspace. In this paper, optimization isaccomplishedbytheuseofasequential-quadratic-programming(SQP)algorithm.Theeffectivenessofthiscompletealgorithmisprovedusingalift-constrainedinduced-dragminimization that involves big changes in geometry. The extent of these geometrychangescanclearlybeseeninthefigurespresentedintheirwork.

The dissertation by Paniagua (2014) also considers big (or at least moderate)changesofgeometryinthecaseoftheshapeoptimizationofahigh-speedtrainnose.

Lundetal. (2003) isanothergood,yetolder,exampleof shapeoptimizationwithlargegeometrychange.Itusesgradient-basedoptimizationanditinvolvesbigchangesofgeometryinFluid-StructureInteraction(FSI)problems.

Moving on to other aspects of problem complexity, the paper by Arreckx et al.(2016) mentioned above, deals with problems involving thousands of variables andconstraints, which are handled efficiently thanks to the use of matrix-freeoptimization.

After going through all the relevant steps of shape optimization and offering aselectionofrelevantresearchworksforeachstep,thissectionwillbeconcludedwithuseful, yet more general, research examples, also of interest within the domain ofaerodynamicshapeoptimization.

First of all, there is a very considerable amount of research on CFD shapeoptimizationappliedtotheNASACommonResearchModelWing.Relevantexamplesarethefollowingpapers.

Lyuetal. (2014)usesagradient-basedoptimizationalgorithminconjunctionwithan adjoint method that computes the required derivatives. The objective is tominimize the drag coefficient, subject to lift, pitching moment, and geometricconstraints. The authors apply a multilevel technique in order to reduce thecomputational cost. In the first place, a single-point optimization is solvedwith 720shape variables using a 28.8-million-cell mesh and reducing the drag by 8.5%.Secondly,amorerealisticdesign isachievedthroughamulti-pointoptimization.Thegeometriesobtaineddifferbyonly0.4%of themeanaerodynamicchord.Moreover,theeffectofvaryingthenumberofshapedesignvariablesisexamined.


46

Liem et al. (2017) offers an interesting contribution because they use aircraftoperationaldataasbasisfortheiroptimization.Anadditionalreferenceof interest isthealreadyindicatedworkbyKenwayetal.(2017).

Otherinterestingworksaredescribednext.CourtyandDervieux(2006)usessomeof the abovementioned aspects, but applied to the so-called CAD-free aerodynamicoptimization problems. Chao et al. (2013), for their parameterization of complexgeometries (in the order of 250 variables), the use of an evaluator & optimizerarchitectureandthecomparisonofthepanelmethodandCFDassolutionevaluators.Van Rees et al. (2015) investigates solutions in the speed-energy space, laying thefoundationsforthedesignofhigh-performance,artificial-swimmingdevices.Miralbés-Buil and Ranz-Angulo (2015), for their multidisciplinary optimization of vortexgenerators,taking intoaccountaerodynamic,structural,ergonomicormanufacturingaspects. Quinn et al. (2015) employs experimental gradient-based optimization tomaximizethepropulsiveefficiencyofflexibleunderwaterpropulsors.

To conclude this section on the State of the Art of general shape designoptimization,itisimportanttomentiontheworkbyEschenaueretal.(2012),whichisaveryvaluablereferencebookforshapedesignoptimizationinvariousfields,mostlyfocusedonstructuralcomponentsofdiverseapplications.

3.4. State of the Art of aerodynamic shape designoptimizationfortheindustrialcasesanalyzed

Areviewwillbepresentedoftheresearchworkcarriedoutspecificallyfortheareasof the two industrial cases analyzed in this Thesis, which are two very differentexamples of aerodynamic shape design: closed wind tunnels for testing and leisureactivitiesandindustrialboilersforcombinedcyclepowerplants.

WINDTUNNELS

Regarding the topic of tunnel design optimization there are two differentapproachesfoundinliterature.Thefirstapproachfocusesontheoptimizeddesignofparticular sectionsof the tunnel (inmost cases thecontractionornozzle justbeforethe test section and the turning vanes and corners of thewind tunnel). The secondapproach is the general optimization of the whole tunnel design. It is this secondapproachthattheresearchpresentedinthisThesiswantstoaddress.However,bothapproacheswillbeanalyzed inthissection inordertohaveabetteroverviewoftheStateoftheArtinwindtunneldesignoptimization.

In the area of research focusing on particular tunnel sections, it is important tohighlight the work carried out by Borger (1976), on the optimization of tunnelcontractions for the subsonic range.Borger carriesoutanextensive surveyonotherworksoncontractiondesignmethods.


47

Thehomogenizationofthevelocityprofileattheexitofacontractionisshowntobe dependent on the contraction ratio and not on the contraction contour.Furthermore,hisdefinitionofthevelocity index inthetestsection(asthedifferencebetween the maximum and minimum velocity values over the average velocity) ismorestringentthanthemorecommonversionusedbyotherauthors.Regardingthedefinition of the contraction shape itself, Borger claims that the position of theinversionpointismuchmoreimportanttodeterminethecontractionlengththanthedefinitionofthecorrectiongeometryattheexitsectionofthecontraction.Aprogramcodeisincludedinhisworktocomputetheoptimumcontractionlengthandcontourforasetofgivenconstraints.Asaresult,anumberofoptimizedcontoursareshownforseveralexamplecases.

Mikhail (1979)describestheoptimumcontractionratioand lengthofwindtunnelnozzlesforanoptimumdesign.First,hestatesthattheoptimumcontractionratioisakey trade-off between tunnel shell size (this affectsmaterial cost,which is lower astunnel size is reduced) and power consumption (lower if tunnel is bigger, up to acertainpoint,becauseof lowerpowerlossesandreducedneedforflowconditioningdevices). Next, the minimum length must be determined to satisfy the contractionratio and the flow quality requirements in the test section. The length of the exitsectionofthenozzleisdeterminedonthebasisofachieving0.25%flowuniformityatapointonthetestsectioncenter-lineonelocalradiusdownstreamfromthecontractionexit. An optimum shape for the contraction curvature distribution is defined,whichpermitsthedesignofcontractionshalfaslongasthoseemployedwhenhispaperwaspublished. The contraction, as expected, can be made shorter for higher Reynoldsnumber applications. For low Reynolds number applications, a problem might beencountered regarding boundary-layer re-laminarization towards the exit endof thenozzle. It is also shown that shorter contractions can be used whenever a thinnerboundarylayerexistsatthecontractioninlet.

A more recent work by Doolan and Morgans (2007) offers a comparison ofoptimization methods applied to the design of tunnel contractions. They compareSequential Quadratic Programming (SQP), DIRECT and Efficient Global Optimization(EGO).TheyconcludethatSQPwasabletosolvetheoptimizationproblemefficiently,but not robustly; DIRECT provided a robust global optimization at the expense offunctionevaluations;andEGOisrobustandalwaysgaveacceptablesolutions,butitsefficiencydependedontheinitialrandomsampling.Insomecases,itwascompetitivewith SQP, and the authors claim that with further research it should become anattractivealgorithmforglobaloptimizationoflowspeedwindtunnelcontractions.

Other works can also be found on the topic of tunnel contraction optimization:Jordinson (1961),Morel (1975,1977),Downieetal. (1984)andVieiraandAparecido(1999). The main conclusions of these papers, as far as this Thesis research isconcerned, have already been outlined and are included mostly in Doolan andMorgans(2007),butalsoinBorger(1976)andMikhail(1979).


48

Furthermore,Hoghooghietal.(2016)offersaninterestingcontribution,astheyusethe ball-spine inverse design method to improve the performance (outlet velocityuniformity) of a nozzle of reduced contraction ratio (to reduce its cost), yieldingreasonably similar results to nozzles with higher contraction ratios. Ardekani (2013)also offers an interesting insight into the reductionof nozzle length, in this case forverticalwindtunnels.

Concerning research work carried out on wind tunnel turning vanes and cornerdesignoptimization,thefollowingareamongthemostrelevantpapersforthepurposeofthepresentresearch.

Thefirstoneisthewell-knownworkbyFriedmanandWestphal(1952).Theytestedthe performance of a diffusing bend with different boundary layers, simulating theflowthatwouldbeencounteredinabendsituateddownstreamofdifferentductsandobjects. They state that the use of diffusing corners does not have such a negativeimpactonpressure losseswhilehavingthebenefitof reducingoverall tunnel length.They highlight the key importance of boundary control systems to reduce pressurelosses.

Eckertetal. (1982)gives recommendations for thedesignand implementationofseveral flow control devices used for internal flow applications. Among the keyrecommendations,theauthorsproposechord-to-gapratiosof2.5-3forturningvanesin 45-90° corners. Theyhighlight the impactof a numberof factors on thepressureloss introduced by turning vanes: basic vane contour, total turning angle and taildeflectionangle,chord-to-gapratio (asalreadymentioned)andhinge-gapseals.Thispaper recommends thin vanes with a sealed hinge-gap, with respect to multi-arccircularvanes(eventhosewithtail).

Lindgren et al. (1998) offers an interesting and in-depth study of turning vaneperformance in expanding bends (diffusing bends, as Friedman andWestphal calledthem). These bends are of particular interest to reduce tunnel overall dimensions.AccordingtoLindgrenetal.,inclosedwindtunnelstherequirementofattachedflowin thevariousdiffusers isoftenamajor factor indetermining the total lengthof thecircuit.Therefore,theoptimumdesignofthecombinationofdiffusersandcorners(orbends)isofparamountimportancetoreduceoroptimizethetotalsizeofaparticularwind tunnel. Space restrictions can be a serious limiting factor and thus expandingcornerswithoptimizedturningvanescanbeapromisingsolution.Forinstance,vanesofanoptimizedprofilecanofferthreedimensionaltotalpressurelosscoefficientsuptofourtimessmallerthanconventional¼circle-shapedvaneswithprolongationatthetrailingedge.


49

However, it is not always the minimum pressure loss that is best, because flowquality must also be considered, especially in the corner upstream of the settlingchamber.Thewindtunneldesignproposedbytheauthorsachievesatotalcontractionratio of nine. This is achievedwith a quitemoderate need of diffusers, yetwith anexpansion ratio of about 1.32 in each corner. The results show that this can beachievedwithverysmall losses inthecorners,andagoodqualityoftheflowexitingthose corners. TheMISES code, developedby Youngren andDrela to analyze turbo-machinerydesign, is used tooptimize turning vanedesignusing an inversemethod:theuserinputsthedesiredpressure-distributionalongthevaneandtheprogramwillyield thevanedesign.Further informationon theMISEScodecanbe found in:GilesandDrela(1987),YoungrenandDrela(1991)orDrelaandYoungren(1995).

Moreover, Lindgren et al. also recommend inspecting the CP evolution along theupper and lower surfaces of the vanes to check where separation occurs and if afurtheroptimizationispossible.Finally,giventhatthetotalpressurelosscoefficientisinverselydependentonthe lift-to-dragratioof theentirecorner (not justofasinglevane), it is importanttomaximizethisratioforeverysinglevane,andalsotoreducethenumberofvanes.

Jeongetal.(2004)usetheKrigingmodelandGeneticAlgorithms(GAs)tooptimizethedesignofanairfoilandthepositionofa flaponamulti-elementairfoil,which isapplicabletowindtunnelturningvanedesign.Aspointedoutbytheauthors,itisveryinteresting that theKrigingmodel reduces thecomputation time required to findanoptimum.It iswellsuitedforaerodynamicproblems(thankstotheuseofGAs).Alsoworth highlighting in this work is the fact that a variance analysis is carried out todeterminetheinfluenceofthedifferentvariablesontheobjectivefunction(sensitivityanalysis).

Calautitetal.(2014)canalsobehighlighted,becauseitoffersadesignmethodforclosed-loopsubsonicwindtunnels,andmanyofitsconclusionsarefocusedonturningvaneandcornerdesignimprovements.However,unlikethepresentThesis,itdoesnotcarryoutafulloptimizationprocedure.

Finally,wewillpresentthemostrelevantpapersrelatingtotheoptimumdesignofthewholewindtunnelcircuit.Thefirstpaperworthhighlightingforourpurposeinthisarea is the work carried out by Eckert et al. (1976). In this case, formulae for thepressure losses in each tunnel section are presented (very similar to the impressiveempirical work by Idel’Cik [1969], where the pressure loss coefficient of mostcommonlyusedgeometriesinhydraulicsandaerodynamicscanbefound).Interestingformulae among those found in thework by Eckert et al. refer, for example, to thepressure loss inmeshes. This paperminimizes total pressure losses along thewholewind tunnel. The necessary structural strength of the tunnel walls is taken intoaccount. A computer program is hence developed to obtain the optimized tunneldesign and check its performance. Some additional interesting points are theexplanation of the impact of inaccurate estimations of pressure losses and fanefficiencyonthepowerrequiredbythetunnelandthevelocityinthetestsection,andafinaldescriptionofthemaintunneltypesconsidered.


50

AbbaspourandShojaee(2009)focusonthewhole-tunneldesign,buttheyfollowaninterestingapproach,forinstance,inthenozzledesign.Theirobjectiveistodevelopamultipurpose tunnel for the R&D department of the Islamic Azad University (Iran).Theyclaimthatonlythenozzlesectionandcertainpartsofthetestsectionhavetobemodified to be able to use the tunnel for three main applications: environmental,subsonicorclimatic tests.This isagoodexampleofamodularwindtunnelconcept.Theseauthorschangeapproximatelyhalfof thenozzle toadapt it to thesedifferentapplicationsandthusthefirsthalfisalwaysthesameandthesecondhalfisexchangeddependingon the test tobe carriedout (changing thewholenozzlewouldbemuchmoredifficult).Inthecaseofthedesignofthenozzle,theyuseafifthorderpolynomialasthosepresentedinBellandMehta(1988).

Thefinalpaperincludedinthecontextoffullwind-tunneldesignoptimizationisaveryvaluableworkbyGonzálezetal. (2013).Although itonlyoptimizesa traditionalwindtunnelconfiguration,theworkisverycompleteandinteresting,andtheauthorssuggestsomewhatnon-conventionalsolutionssuchasadiffuserupstreamofthefansystem, instead of a nozzle geometry. They also propose a further diffuser in thesection before the corner upstream of the test section and their design includes aconsiderablylongnozzle.AdetailedExcelspreadsheetisdevelopedandcanbefoundin their website6. This spreadsheet allows for the modification of many tunnelparametersand, forthe inputvalues, itwillyieldanoptimizeddesign.However, it isnotanautomatedcomputeroptimizationtool.

Furthermore,thisworkstatesthatinthecaseofwindtunnelsforcivilorindustrialapplications,acontractionratiobetweenfourandsixmaybesufficient.Withagooddesignoftheshape,theflowturbulenceandnon-uniformitylevelscanreachtheorderof 2.0%,which is acceptable formany applications. Nevertheless, the authors claimthatwithonescreenplacedinthesettlingchamberthoselevelscanbereducedupto0.5%,whichisaveryreasonablevalueevenforsomeaeronauticalpurposes.Formoredemandingaeronauticalapplications,whentheflowqualitymustbebetterthan0.1%in non-uniformity of the average speed and longitudinal turbulence level andbetterthan 0.3% in vertical and lateral turbulence level, a contraction ratio between eightandnineismoredesirable.Thisratioalsoallowsinstallingtwoorthreescreensinthesettling chamber to ensure the target flow quality without high pressure-lossesthrough them. The authors state that the old-style contraction shape with a smallradiusofcurvatureatthewideendandalargeradiusatthenarrowendtoprovideagentleentrytothetestsection isnottheoptimum.There isariskofboundary-layerseparationatthewideend,orperturbationoftheflowthroughthelastscreen.Goodpractice is tomake the ratioof the radiusof curvature to the flowwidth about thesameateachend.However,anexcessivelylargeradiusofcurvatureattheupstream-end leads to slowacceleration and therefore increased rateof growthof boundary-layerthickness,sotheboundarylayer,iflaminarasitshouldbeinasmalltunnel,maysuffer from Taylor-Goertler ‘centrifugal’ instability when the radius of curvaturedecreases.

6http://www.aero.upm.es/LSLCWT(lastverifiedonFebruary2017).


51

Regarding the power plant design or fan system, this work by González et al.proposesusingamulti-fanmatrix,insteadofamorestandardsingle-fanconfiguration,stating that this reduces the cost of this component by roughly one order ofmagnitude. The paper, however, does not optimize the location of this power plantalong the tunnel circuit and this has important effects on pressure loss and tunnelperformance.

To conclude the State of the Art review onwind tunnel design optimization, thecontributionsofourThesisinthisareaarenowcommented.

Theworkcoveredbyourresearchaimstotakeintoconsiderationalsoothertunnelconfigurations, not only 90° corners, rectangular ducts and multi-fan designs. Inparticular, itaimsatexploringbiggeometrychangesandthereforenon-conventionalor non-intuitive designs, which may improve the performance of more traditionaldesignconcepts.Itfocusesontrueoptimizationofthefullwindtunnelbody,andnotonly certainpartsof it, suchascornersor themainnozzle.Besides,different tunnelwallmaterialswillalsobeconsidered(infutureresearch),aswellasdifferentrelativepositions of the various elements of the wind tunnel, mainly test section and fansystem.

HEATRECOVERYSTEAMGENERATORS(HRSGS)

Overthedecades,thedesignofHRSGinletductshaslargelyremainedunchanged.In this Thesis we will focus on the shape design optimization of the inlet duct ofdifferent HRSG families, thanks to the application of the proposed MOST-HDSalgorithm.

Generallyspeaking,therearetwocurrentdesigntrend-linesforanHRSGinletduct:single-angle(moretraditional)anddouble-angle.Mostmanufacturershaveusedbothoverthedecades.However,somemanufacturers,suchasALSTOM,haverecentlytriedsomewhat unconventional variations of the double-angle inlet duct design, using asecond angle of close to 90°, as shown in Chapter 4. Anyhow, extensive designanalyseshavenotbeenperformed,asfarasweknow,tocomparethedifferentinletductdesignsalternativesthoroughly.

ThereareanumberofworksintheareaofCFDmodellingofanHRSG’sinletduct,but to our best knowledge, a complete shape optimization analysis of this criticalelement has never been addressed. The aim of these works is to analyze the flowdistributionof a particular design, or the effects of elements introduced in the inletducttoimprovetheflowdistribution,suchasAmeriandDorcheh(2013)andLeeetal.(2002).

The followingaregeneralworks in the fieldofCFDanalyses,of relevance for thepurpose of this Thesis, and useful for future authors working in the area of shapedesignoptimizationofHRSGs.


52

Galindoetal. (2014) isaveryvaluableworkbecause itdevelopsamorecomplexCFD model of the whole HRSG body to include an accurate model for the realgeometry of the tube bundles, moving on from the more traditional approach ofmodellingthetubebundlesasporousmedia.AslamBhuttaetal.(2012)offersareviewofCFDapplicationsinvarioustypesofheatexchangers.Galindoetal.(2012),forthedevelopmentofCFDmodelsofthewholeHRSGtoofferabettercomprehensionoftheflow inside theunitandof itsperformance forplantoperators.Shietal. (2009)andHedgeetal. (2007) for theirgeneralCFDmodellingofHRSGs.Sundén (2007) for theworkonCFDmodellingforR&Donthefieldofheatexchangersingeneral.AndfinallyDaiber(2006)forhisworkontheanalysisinparticularofthegassideofanHRSGflowdesign.

The contribution of this Thesis, regarding HRSG inlet-duct shape-designoptimization,istwofold.Ontheonehand,itshowsthatthereissubstantialroomforimprovementintheshapedesignoftheinletductsofHRSGs,intermsofachievingalowerpressuredrop,ahighervelocityuniformityandan importantcostreductionoftheunit.On theother hand, it showshow theMOST-HDS algorithm is applicable indiverse fields for aerodynamic shape optimization involving big geometry changes,finding improved designs that can be quite unconventional and non-intuitive. Theresults obtained for the two HRSG families presented illustrate the interest for theStateoftheArtoftheworkpresentedinthisThesis.

Furthermore, this Thesis performs extensive design analyses to compare thedifferent inlet-duct design alternatives thoroughly. As far as we know, this kind ofanalyseshavenotbeenperformedbefore.

3.5.ConcludingremarksandThesismappingtotheStateoftheArt

Asan important concluding remark to this chapteron theapplicable Stateof theArt, and as it will be commented further on in this Thesis, MOST-HDS has certainsimilarities with the Nelder and Mead simplex method for function minimizationpresentedinNelderandMead(1965).TheNelder-Meadalgorithm,orsimplexsearchalgorithm, is one of the best-known algorithms for multidimensional andunconstrainedoptimizationwithoutderivatives.

ThemaincontributionsoftheThesisintheareaofoptimizationingeneralincludethe use of structured optimization in the field of aerodynamic shape design, thedefinitionofanovelhybriddirectsearchtechniqueandthedevelopmentoftheMOST-HDSmodelasawhole.MOST-HDSisageneral,automatic,robustandflexibletoolforshapedesignoptimization,asitwillbeshownthroughoutthisdocument.

Theparticularmapping(orlocation)oftheThesiswithintheapplicableStateoftheArtisillustratedinthefollowingscatterplots,forabettergeneralperspective.


53

Figure3–1-ScatterplotofThesiscontributionstoStateoftheArt(SoA)ofwindtunneldesign

optimization.

Figure3–2-ScatterplotofThesiscontributionstoStateoftheArt(SoA)ofHRSGinletductdesign

optimization.


54

Figure3–3-ScatterplotofThesiscontributionstoStateoftheArt(SoA)ofgeneraldesign

optimization.

ListofFiguresFigure3–1-ScatterplotofThesiscontributionstoStateoftheArt(SoA)ofwindtunneldesignoptimization.

Figure3–2-ScatterplotofThesiscontributionstoStateoftheArt(SoA)ofHRSGinletductdesignoptimization.

Figure3–3-ScatterplotofThesiscontributionstoStateoftheArt(SoA)ofgeneraldesignoptimization.

ListofTablesTable3–1-ListofmostrelevantMOEAsasprovidedbytheMOEAframeworklibrary(www.moeaframework.org).


Chapter4 -ProblemdefinitionIfIhadanhourtosolveaproblemI'dspend55minutesthinkingabouttheproblemand5minutesthinkingaboutsolutions.

AlbertEinstein.

ThischapterdefinesthegeneralproblemaddressedbythisThesisinanefficientwayinordertoapplyautomated(i.e.computer-based)optimizationtechniques.It defines the main elements of this kind of problem statement: variables,attributes and parameters, as well as a crucial aspect for shape designoptimization:thegeometryparameterizationapproach.AllconceptsareappliedtothetwoindustrialexampleswhichwillbepresentedinChapter6:closedwindtunnels and industrial boilers for combined cycle electricity generation plants.Firstly, Section 4.1. puts forward the need for a robust problem definition;Section 4.2. defines the main elements; Section 4.3. presents the geometryparameterization scheme; and finally Section 4.4. summarizes a set of finalremarks.

4.1.IntroductionThe finalobjectiveof this Thesis is todevelopanoptimizationarchitecturewhich

canbeapplied toaerodynamic shapedesignoptimizationproblems.Oneof the firststeps is topresent a generalway todefineany,or at leastmost, of theproblemsadesignercanfaceinthefieldofshapeoptimization,sothattheoptimizationmodelcanhandletheminamoreefficientandcomprehensivemanner.Thismeansthatthewayattributes,parametersand,mainly,variablesaredefinedisnottobeunderestimated.Itwilllaythefoundationsforaneasy-to-followoptimizationprocess.

Variablesconditionthewaythegeometryisparameterizedandthishastobedonewith care to ensure the parameterization is clear and intuitive, since thiswill highlyfacilitate the development of the strategy to control the optimization algorithm.Furthermore,itwillmakeeasiertherevision,maintenanceandfuturedevelopmentsoftheprogramsource-code.

4

Chapter4–Problemdefinition

57

Consequently,thecontributionoftheThesisinthischapteristheproposalofhowaproblem of shape design can be defined in a most suitable way to apply not onlyadvancedoptimizationschemesingeneral,but,inparticular,multi-attribute/objective,structured,hybrid,directsearch(MOST-HDS).Thisisshownfortwoexamplecasesofverydifferentindustrialfields,toillustratethattheapproachandmethodaregeneral.

This contribution includes the following related contribution: definition of anefficientsetoftruly independentvariables.This includesdefiningvariableswhichareeasy to understand and are intuitive enough to let the designer check how theoptimizationproceeds.ThesevariablesmustthenbetranslatedtothevariablesusedbytheCFDsolver,whicharenormallynotaseasytohandleorinterpret.

A final contribution worth highlighting in this chapter is the geometryparameterizationproposedforthewindtunnelcase.Thereareveryrareexamplesofafullwindtunnelparameterizationsinliterature,moresousingBéziercurves(18-20areusedinthisThesisforarealfullwindtunnel).

4.2.ProblemdefinitionThissectionwillbedividedintotwoparts:onefocusedonclosedwindtunnelsand

another one focused on industrial boilers, since we will be applying the problemdefinitiontothesetworealexamplesthroughoutthisThesis.

WINDTUNNELS

In the nineteenth century, the Wright brothers started a systematic process tostudyflighttechnology,basedontheworkoftheirpredecessors,suchasDaVinci,theGermanOttoLilienthalortheAmericanSamuelLangley.Thankstotheirstrongeffort,both theWright brothers and SantosDumont bear the title of pioneers of aviation.Oneof theirmain contributionswas thedesignanddevelopmentof the first-knownwind tunnel. Since then, many bodies subject to wind are tested in wind tunnels:aircraft, vehicles, civil structures, sports goods, etc. All wind tunnels share two keyelements: the air-moving device (fan system) and a testing section to place theprototypesanalyzed.

In wind tunnels, an airflow is generated around the objects tested. The objectsthemselves are equipped with various kinds of sensors to obtain the relevantaerodynamicdata(mainlypressuredistributionsandforcesactingontheprototypes).The airflow quality itself (turbulence and velocity indexes) must also be accuratelymeasuredtoensurethetestisasclosetorealconditionsaspossible.Allofthesedataallowforthepredictionandanalysisoftheaerodynamicperformanceandtheforcesthatwillappearonthetestedobjectwhenusedinitsreal-lifeconditions.

Wind tunnels can be classified according to different criteria. One of the mostimportantclassificationsdivideswindtunnelsintoopen-loopandclosed-looptunnels.

Inopen-loopwindtunnels,ambientairissuctionedbythefan,itflowsthroughthetestsection,andthenthroughanopenoutletandintotheatmosphereagain.


58

However, inorder tohaveabetter controlof theairflow’squalityandconditions(temperature and humidity) and to reduce energy consumption, closed-loop windtunnelsweredeveloped.Inthesetunnels,thesameairisre-circulatedonceandagainthroughaclosedducting,commonlymovedbysomekindoffansystem.Theairflowsthroughthetestsectionandbacktothefanforanewcycle.Thehigherqualityairflowand reduced energy consumption, main advantages of closed-loop wind tunnels,usually outweigh their main drawbacks: considerable space requirement for theirconstructionandhighcost.Moreover,thefactthatthesetunnelsareclosedallowsfortheuseofothergases,differentfromair,andthisfactcontributestoabetterdensitycontrolandbroaderapplicabilityofthistypeofequipment.

ThisThesis focusesonclosedwindtunnels, sincetheyaremuchmoreextensivelyused,butthemodelcanbeappliedtoopenwindtunnels,too.

Figure4–1illustratesarepresentativevarietyoftypesofwindtunnels.

Figure4–1-Differenttypesofwindtunnels.Fromrighttoleftandtoptobottom:Replicaofthe

Wrightwindtunnel;ClosedwindtunnelattheFerrariFormula1Team;OpenwindtunnelatNASAAmesResearchCenter;A2openwindtunnelfortestingofvariouskinds(includingvehiclesandprofessional

cyclistsandskiers);andverticalwindtunnelsforscientifictestingofaircraftspins,helicopterblades,andparachutes:atNASALangleyResearchCenter(firsteverbuiltverticalwindtunnel,1940)andtheTsAGI

VerticalWindTunnelT-105inRussia(1941).

Foranykindofwindtunnel,anoptimumaerodynamicdesignisrequiredtoensureadequate performance and cost at all test conditions. This means minimal energyconsumption, minimal cost (including investment, operation andmaintenance), andbestpossibleemulationofrealconditions.


59

In order to reach an optimized wind tunnel design, an optimization modelarchitecturemustbebuilt.Thismodelwillneedtwotypesof inputs:parametersandvariables,anditwillhavetwomainoutputs:thevaluesofeachoftheattributesandtheso-calledstateoftheconstraintsvector(whichcanbeconsideredasaspecialtypeofattribute).

Table 4–1 and Table 4–2 show the generalized list of parameters (i.e. designerinput)andattributesproposed,respectively,forthestudyofclosedwindtunnels.Itisworthnotingthatsomeoftheparametersmaybeleftblank;forexample,coolingmaynot considered, or convection or radiation may be neglected. Attributes can begrouped into different categories for the sake of clarity, in groups such as costattributes, geometry/flowattributesand thermalattributes.Note that thegroupsofattributesdonothavetobedisjoint;forinstance,powerconsumptionshouldbepartofthecostgroup(energycost),butitmayalsobeconsideredacategorybyitself,forenvironmentalreasons.

PARAMETER Explanation

1.NWT Numberofsectionsormodulesforwindtunneldiscretization

2.ARMIN Minimumfrontalcross–sectionarearatiointestsection(i.e.ATESTSECTION/AMODEL)

3.ZMAXMODEL Maximumheightofmodelstobeintroducedintestsection

4.YMAXMODEL Maximumwidthofmodelstobeintroducedintestsection

5.DMINTS Minimumdistanceinzandydirectionsbetweenmodelandtestsectionwalls

6.LMINTS Minimumrequiredlengthfortestsection

7.HA Horizontalarrangementforhorizontalclosedwindtunnels(1:purelyhorizontal,2:recirculatingductrunsontopofmainduct)

8.DTMAX/s Maximumallowedtemperatureincreaseofairinsidewindtunnelpersecond

9.TAMB–time Ambientairtemperatureversustimeofairsurroundingtunnelforarepresentative24hday,forconvectionmodelling

10.GSOLAR–time Solarradiationversustimeforarepresentative24hday,forradiationmodelling

Table4–1-Proposedgeneralsetofparametersforclosedwindtunnels.

ATTRIBUTE Explanation

1.PTOT Totalpowerconsumption

2.CFIXED Fixedcost(i.e.investment)

3.CVAR Variablecost(operation&maintenance)

4.LTOT Totallength

5.WTOT Totalwidth

6.HTOT Totalheight

7.VTOT Totalvolume

8.𝑣TS Averagevelocityintestsection


60

9.𝑣INDEX Velocityindexintestsection

10.tINDEX Turbulenceindexintestsection

11.ZMAXREALMaximumachievedheightofmodelsthatcanbeintroducedintestsection(thevaluewillnormallybethesameasZMAXMODEL,butitmaybehigher)

12.YMAXREALMaximumachievedwidthofmodelsthatcanbeintroducedintestsection(thevaluewillnormallybethesameasYMAXMODEL,butitmaybehigher)

13.ARREALAchievedvalueofarearatiointestsection(thevaluewillnormallybethesameasARMIN,butitmaybehigher)

14.LREALTSAchievedvalueoflengthoftestsection(thevaluewillnormallybethesameasLMINTS,butitmaybehigher)

15.DTREAL/sAchievedvalueoftemperatureincreaseofairinsidewindtunnelpersecond(thevaluewillnormallybethesameasDTMAX/s,butitmaybelower)

Table4–2-Proposedgeneralsetofattributesforclosedwindtunnels.

Inthecaseofwind-tunneldesign,thefollowingindependentvariables,presentedinTable4–3,werealreadydefinedinPrada-Nogueiraetal.(2015)andtheyconstituteanefficientsetoftrulyindependentvariables(independentinastrictsense,i.e.,noneofthemcanbecomputedunivocallyfromtheothers).Thissetofvariablesiscapableofrepresenting most wind tunnel configurations, and it is appropriate to build anoptimizationtoolbasedonthem.Figure4–2explainsgraphicallythemeaningofeachof these variables. This set givesanexampleofhowvariables shouldbedefined forother aerodynamic components. Recommendations on how to define an efficientvariable set will be given at the end of this section, after the explanation on theindustrialboilercase.

VARIABLE Explanation

1.wTUNNEL Widthoftunnel

2.lTS Lengthoftestsection

3.wTS Widthoftestsection

4.𝛼F/TS Relativepositionoffanandtestsections

5.dF Fandiameter

6.geomTS Testsectiongeometry

7.profileDUCT1Profileshapeofthedifferentpartsinwhichwedividetheductworkwhichjoinsthetestsectiontothefan(duct1:itcomprisesdiffuser1,corner1,diffuser2,corner2andfannozzle).

8.profileDUCT2Profileshapeofthedifferentpartsinwhichwedividetheductworkwhichjoinsthefantothetestsection(duct2:itcomprisescorner3,diffuser3,corner4andnozzle1).

9.aDUCT1 Areadistributionforthewindtunnelsectionsalongduct1

10.aDUCT2 Areadistributionforthewindtunnelsectionsalongduct2

11.geomDUCT1 Transversegeometryforthewindtunnelsectionsalongduct1

12.geomDUCT2 Transversegeometryforthewindtunnelsectionsalongduct2

13.nFANS Numberoffans


61

14.Other Othervariablesinclude:lengthofdiffuserandnozzlesections,lengthoffansection,anglesofdiffuserandnozzlesections,offsetsincornersections

Table4–3-Proposedgeneralsetofvariablesforclosedwindtunnels7.

Figure4–2-Proposedsetofindependentvariableswhichyieldanefficientrepresentationofmost

windtunnelconfigurationsandareadequatefortheapplicationofcomputer-basedoptimizationmethodologies.

INDUSTRIALBOILERS:HEATRECOVERYSTEAMGENERATORS(HRSGS)

Heat Recovery SteamGenerators (HRSGs) for combined cycle power plants are akey industrial equipment in the power generation sector. They are designed andmanufacturedbybigengineeringcompaniesandtheyarebothexpensive,largeinsize,and crucial to the performance of the power plant. However, the design of certaincriticalcomponents,suchastheinletduct,hasremainedlargelyunchangedformanydecades.Theperformanceof the inletduct ismainlymeasured in termsofpressuredropthroughouttheunit,gasflowvelocityuniformityandheattransfercapacity.

7 Note that parameters and attributes are represented with uppercase names and variables are

representedwithlowercasenames.


62

In an HRSG, the hot exhaust gases of a gas turbine flow through a set of tubes(normally finned tubes) throughwhichwater ispumped.Theheatof thegas flow istransferredtothewaterflow,whichistransformedintosteam.Thissteamcanbeuseddirectly for industrialapplications,or forelectricitygeneration inasteamturbine,orforboth(intheso-calledco-generationplants).Figure4–3showsanexamplelayoutofacombinedcyclepowerplantandanexampleofarealHRSG.

Figure4–3-Examplecombinedcyclepowerplantlayoutandrealandrenderversionsofanexample

HRSG.

Themainchallenge in thisapplication is that theexhaustgas flowexiting thegasturbine has to flow into the HRSG, which has a much bigger cross-sectional area,throughacriticalsection,theso-calledinletduct.Thisintroducesflowdetachmentandhence turbulenceandvelocitynon-uniformity,which canbeobserved inFigure4–4.The velocity profile exiting the gas turbine greatly influences flow performancedependingonitsvelocityuniformity,swirlandothercharacteristics.

Gas turbineoutlet

Inletduct

HRSG


63

Figure4–4-Sideviewofvelocitycontoursinthemid-planeofatypicalHRSG(left).Detailedisometric

viewofvelocitymagnitudestreamlinesintheinlettransitionduct(right).

Despite this, allmanufacturers try tomake this inletduct as short aspossible, tomake theirwholeunits shorterandmore compact,whilegaspressuredropandgasvelocityprofilearemaintainedwithincertainlimits.Thisisbecausereducingthesizeoftheinletductfacilitatesitsintegrationintothepowerplantlayout,anditcanreducemanufacturingcostsconsiderably,sinceitisbuiltofverycostlystainlesssteel.

For the purpose of this Thesis, MOST-HDS will be applied to the shape designoptimizationoftheinletductofseveralHRSGfamilies,toshowitsapplicabilitytoanindustrialexampleofacompletelydifferentfieldtowindtunnels.

Theoptimizationproblemismulti-attributeormulti-objective,sincethefinalgoalisto obtain the inlet duct designs whichminimize two attributes: total pressure dropacrosstheinletductandvelocitynon-uniformityintheoutletplaneoftheinletduct8.

Thepressuredrop ismeasuredasthedifference inmassweightedaverageof thetotalpressurebetweentheinletandtheoutletoftheinletduct.

8 Theproblem is definedwith twoobjectives to be able to present theoptimization resultsmore

simply.Theproblemcanbedefinedwithahighernumberofobjectives.Magnitudesofimportancesuchasmaterialcostandtotallengtharecalculatedthroughouttheoptimization,butarenotuseddirectlyasoptimizationattributes.


64

Thevelocitynon-uniformityisdefinedasthedifferencebetweenthevelocityarea-weightedaverageandthemass-flow-weightedaverage.Thisdefinitionissimplyoneofthepossiblewaysofmeasuringvelocitynon-uniformity.Otheralternativedefinitionswould be, for example, checking thedifferencebetween themaximumvelocity, theminimum velocity and the average velocity (as is done for velocity indexes, forinstance); or comparing themaximum andminimum velocities, etc. However, thesealternativedefinitions, involving themaximumandminimumvelocity values, canbemisleading, sinceminormesh irregularities, inevitable in most CFD simulations, canyield false values of maximum or minimum velocities. These values are acceptablenumerical errors and can be easily discarded by the engineer when evaluating theresultsonebyoneandmanually, but cannotbedetectedaseasilyby theCFD codewhen launching an automatic optimization. Therefore, the indicated definition ofvelocity non-uniformity is used. Itmust be noted that, strictly speaking, by velocitynon-uniformitywearenotonlyreferringtothefactthatvelocityvaluesareuniforminthe outlet plane of the inlet duct, but to the fact that themass flowmust also bedistributed as evenly as possible and the “combination” of velocity and mass flowuniformityisgivenbythedifferencebetweenthevelocityarea-weightedaverageandthemass-flow-weightedaverage9.

Bothattributesarehandledinperunitmagnitude.Theoptimumdesignsarethosewhichminimizebothattributes.

Regarding the independent variables used for this case, the following set isproposed:twoanglesforthetopwall,twoanglesforthelateralwall(identicalonbothlateral walls), twomore for the bottomwall and the total length of the inlet duct.Thesevariablestakeintoconsiderationthedesignmodificationswhicharefeasibleintermsofmanufacturingandassemblyinrealpowerplants.Forexample,curvedwallsor more than two intermediate angles are not considered of interest and they areconsequentlynotincludedinthisanalysis.ThesevariablesarelistedinTable4–4.

VARIABLE Explanation

1.𝛼1T(A16) Firstangletopplane

2.𝛼2T(A17) Secondangletopplane

3.𝛼1B(A18) Firstanglebottomplane

4.𝛼2B(A27) Secondanglebottomplane

5.𝛼1S(A6) Firstanglesideplane

6.𝛼2S(A7) Secondanglesideplane

7.lTOT(V31) Totallength

Table4–4-ProposedgeneralsetofvariablesforHRSGs.ThenamesinbracketsrefertoANSYSnamesforthevariables.

9 Other definitions for velocity non-uniformity used by manufacturers in industry include the

determination of the percentage of velocity values which lie within a 10% of the RMS value of aparticularplane,orwithin15%.


65

Thewidth and height of the HRSG and the elevation difference between turbineand boiler floor are kept constant for all simulations and are therefore included asparameters.

The set of variables for the inlet duct is shown in Error! Reference source notfound.andanexampleinletduct3DgeometryisincludedinFigure4–6.

Figure4–5-VariablesusedtoparameterizeageneralinletductfordifferentHRSGfamilies(x-axis

andy-axisviews).


66

Figure4–6-Sideand3DviewsofanexampleHRSGinletductgeometry,generatedwiththe

proposedgeometryparameterization.

RECOMMENDATIONSFORANEFFICIENTVARIABLESETDEFINITION

This section offers a general outline on some of the observations orrecommendationstobetakenintoaccountwhendefiningavariablesetforaproblemtowhichwearegoingtoapplyautomaticoptimizationtools:

1. Check thoroughly that any variable set is truly independent, i.e. the value ofeachvariableisindependentfromthevalueoftherestofthevariables.

2. Thevariablesethastobedefinedtobeassimpleand intuitiveaspossible. Inthecaseofshapedesignoptimization,ausefulwayofthinkingistodefinethevariables you would need to sketch a drawing of the body geometry.Additionally, each variable should represent visual aspects of the geometry,suchasaparticulardimension,orcurvature,orrelativeposition.Avoidvariableswhichmaybeusedtodefinethegeometrybutwhicharenotcleargeometricalmagnitudesthatanynon-expertpersoncanunderstand.Asexplainedinpoint3,theoptimizationalgorithmandtheCADprogrammayusecompletelydifferentsetsofvariablestodefinethesamegeometry.


67

3. The CAD or CFD programs used to generate the body geometry require avariablesetusedtodefineorparameterizethatgeometry,butitmaynotbeanefficientvariable set for theoptimizationprocess. It is veryworthhighlightingthis,aswillbeexplainedindetailinChapter5.Itisusefultobearinmindthatthe variable set used for an optimization process will be more efficient ifindependent changes in eachof the variables are feasible, visual, anddirectlygenerate different design candidates. Note that all the algorithm-embeddedintelligencewillactdirectlyonthevariablevalues.Ifchangestothesevaluesareintuitive, it is more efficient for algorithm checking, maintenance orimprovement. For instance,using the relativepositionof twoelementsof thegeometry isbetterthanusingthebasepointpositionof theplanescontainingeachoftheelements.

4. The variablesused should allow for aneasy formulationof the constraints. Inthe caseof shapedesignoptimization, a very important typeof constraints isgeometry absurdity checks (negative volumes, intersecting parts, absurdcurvatures,etc.).

5. Despite all the above, there is normally nothing such as the best and uniquevariable set for a particular problem. These are merely general guidelinesapplicabletomostgeometries,forshapedesignoptimizationpurposes.

4.3.GeometryparameterizationIn order to carry out a full optimization of a body’s shape design, this body’s

geometry has to be parameterized in a CAD program (or CAD module of a CFDprogram, in our case). Although referred to as “parameterization”, this step reallydefines the variable (and not the parameter) set used by the CAD program torepresentthegeometryunivocally.

Ashasbeenhighlightedintheprevioussection,theefficientvariablesetdefinedfortheoptimizationprocesswillinmostcasesnotbethesameasthevariablesetdefinedtoparameterize thegeometry.The latterwilldependontheCADprogramusedandtheway thedesignergenerates thegeometry.Thisvariable setwill generallynotbethemostefficient, intuitive, illustrativeorhigh-levelenoughsoas tousedirectly fortheoptimizationprocess(thevariablesmaynotevenbeindependent).Throughoutthesectionanumberofconcreteexampleswillbegivensothat thereaderunderstandsthisaspectfully.Onceagain,forthesakeofclarity,thesectionwillbedividedintwo:windtunnelandHRSGgeometryparameterization.


68

WINDTUNNELS

Figure 4–7 represents a general closedwind tunnel of the traditional type (mostcurrentwindtunnelsarequalitativelyofthisdesign).Thepresentworkaimsatprovingthat alternative designs (different corner geometries, cross-section types, etc.) canproveinterestingandbetterforcertainapplications.

Figure4–7-Sectionsofageneralclosedwindtunnelofthe‘traditional’type.Section1isthetest

sectionand,followingtheairflowdirection,thesectionsare:2.diffuser,3.corner,4.diffuser,5.corner,6.straightsection,7.fansection,8.diffuser9.corner,10.corner,11.settlingchamberand12.nozzle.

Thewindtunnelgeometryparameterizationiscarriedoutbyadiscretizationofthetunnelintoanumberoftransversesections.Thenumberofthesesectionsisselectedbytheuserasoneoftheinputparameterstothemodel.Eachsectionisparameterizedwithanumberofsegmentsandangles(seeFigure4–8).Forthisworkeightsegmentsofequal lengthareused,butthiscanbegeneralizedtoanynumberwhichcreatesaclosedpolygon.


69

Figure4–8-Windtunnelgeometriesaregeneratedbymeansofadiscretizedsetoftransverse

parameterizedsections.Anexampleplanecontainingoneofthesetransversesectionsisshown.

Thepolygonforeachtransversesectioncanhaveanygeometry,thusbeingabletorepresentmostwind tunnel designs. The areaof eachof these sections can alsobevariedasoneofthemodelvariables.Forinstance,theanglesofthesegmentsofeachpolygonarevariablesusedintheCADmoduletogeneratethegeometryandarenotvery intuitive variables to be used for the optimization10. The geometry shape(rectangle, circle, regular polygon or others), which is much more visual, is usedinstead,andthevaluesoftheanglesareadjustedautomaticallybythetooldevelopedforthisThesissothattheCADmodulecangeneratethegeometry.

Finally,thesectionsaregeneratedalongthepointsofasetofBéziercurves.Thesecurves are chosen because they are robust, they can easily be controlled to avoidabsurd tunnel shapes, and they have good mathematical behavior and optimumaerodynamic performance. Bézier curves are used extensively in aerodynamicoptimisation(agoodillustrativeexampleisPaniagua[2014]).Inothercases,B-splinesare used as a generalization of Bézier curves to avoid problems such as the Rungephenomenon,orothereffects,whichmeanhigherorderpolynomialscanhavehigherinterpolationerrors than lowerorderpolynomials. Inourcase, theBéziercurvesarenotusedasanapproximationtoarealfunction,butasamethodofgeneratinggoodaerodynamic surfaces. Cubic Bézier curves (and not higher order ones) are hencechosen in our analyses. They are an optimum trade-off between number of controlpoints and capacity to represent a very wide range of geometries for the tunnel.Besides,splines,forinstance,couldyieldabsurdgeometries,whichmustbeavoided.

10Strictyspeaking,foranoctagon,onlytheangleforsixsidesmustbespecified,andnotforalleight,

inordernottoover-constrainthegeometryparameterization.


70

Depending on the complexity of the designer requirements for the wind tunnelmodel representation, more or less Bézier curves can be used for the geometrydefinition. An optimum trade-off must be reached between level of detail andcomputationalload.

A set of 18-20 Bézier curves provides a highly-detailedmodel, able to representmost wind tunnel geometries. The representation with this number of curves isdepictedinFigure4–9.

Figure4–9–Highly-detailedrepresentationofageneralizedwindtunneldesign,abletorepresent

mosttunnelgeometries(18-20Béziercurvesareneeded).

In thisThesis, thishighly-detailed representationwillbeused toapply theMOST-HDSalgorithmandobtainresultsforarealindustrialcase.However,tobetterexplaincertain aspects of the optimization process and to analyze the way the algorithmworks,asimplergeometrymodelwillbeusedaswellforthewindtunnelexample.

Thissimplerversion,showninFigure4–10,usesonlyfourBéziercurves:twofortheductworkbetweenthetestsectionandthefansection(referredtointhisworkasduct1)andtwofortheductworkfromthefansectionbacktothetestsection(duct2),alldefinedinthedirectionoftheairflow(Figure4–7).

Figure4–10-Low-detailrepresentationofawindtunneldesign,usedtobetterillustratecertain

aspectsoftheoptimizationmethodologypresentedinthiswork.OnlyfourBéziercurvesareused.Fanandtestsectionsarebothshadedinthisfigure(left).Anexampleplanecontainingoneofthetransverse

sectionsusedforthetunnelgeometrydiscretizationisalsoshown(right).


71

INDUSTRIALBOILERS:HEATRECOVERYSTEAMGENERATORS(HRSGS)

InthecaseoftheinletductofHRSGs,whichisamuchsimplergeometrythanthatof closed wind tunnels, the variables commented in Section 4.2. are used toparameterizethegeometry (Figure4–5).For this industrialexample, thegeometry isquite straightforward, and the variable set used for the optimization process is thesameasthatusedtogeneratethegeometryinCAD.

4.4.FinalremarksThis chapter has explained how this Thesis proposes to define shape design

optimizationproblemsofawiderangeoffields.Itincludesrealindustrialexamplesofa simple case in terms of number of variables, parameters and geometryparameterization (HRSGs) and an example of a complex case (wind tunnels). Veryespecially, the way variables are defined and the proposed geometryparameterizationsallowforanefficientandeasy-to-followoptimizationprocess,asisanalyzedinthefollowingchapters.

ListofFiguresFigure4–1-Differenttypesofwindtunnels.Fromrighttoleftandtoptobottom:ReplicaoftheWrightwindtunnel;ClosedwindtunnelattheFerrariFormula1Team;OpenwindtunnelatNASAAmesResearchCenter;A2openwindtunnelfortestingofvariouskinds(includingvehiclesandprofessionalcyclistsandskiers);andverticalwindtunnelsforscientifictestingofaircraftspins,helicopterblades,andparachutes:atNASALangleyResearchCenter(firsteverbuiltverticalwindtunnel,1940)andtheTsAGIVerticalWindTunnelT-105inRussia(1941).

Figure4–2-Proposedsetofindependentvariableswhichyieldanefficientrepresentationofmostwindtunnelconfigurationsandareadequatefortheapplicationofcomputer-basedoptimizationmethodologies.

Figure4–3-ExamplecombinedcyclepowerplantlayoutandrealandrenderversionsofanexampleHRSG.

Figure4–4-Sideviewofvelocitycontoursinthemid-planeofatypicalHRSG(left).Detailedisometricviewofvelocitymagnitudestreamlinesintheinlettransitionduct(right).

Figure4–5-VariablesusedtoparameterizeageneralinletductfordifferentHRSGfamilies(x-axisandy-axisviews).

Figure4–6-Sideand3DviewsofanexampleHRSGinletductgeometry,generatedwiththeproposedgeometryparameterization.


72

Figure4–7-Sectionsofageneralclosedwindtunnelofthe‘traditional’type.Section1isthetestsectionand,followingtheairflowdirection,thesectionsare:2.diffuser,3.corner,4.diffuser,5.corner,6.straightsection,7.fansection,8.diffuser9.corner,10.corner,11.settlingchamberand12.nozzle.

Figure4–8-Windtunnelgeometriesaregeneratedbymeansofadiscretizedsetoftransverseparameterizedsections.Anexampleplanecontainingoneofthesetransversesectionsisshown.

Figure4–9–Highly-detailedrepresentationofageneralizedwindtunneldesign,abletorepresentmosttunnelgeometries(18-20Béziercurvesareneeded).

Figure4–10-Low-detailrepresentationofawindtunneldesign,usedtobetterillustratecertainaspectsoftheoptimizationmethodologypresentedinthiswork.OnlyfourBéziercurvesareused.Fanandtestsectionsarebothshadedinthisfigure(left).Anexampleplanecontainingoneofthetransversesectionsusedforthetunnelgeometrydiscretizationisalsoshown(right).

ListofTablesTable4–1-Proposedgeneralsetofparametersforclosedwindtunnels.

Table4–2-Proposedgeneralsetofattributesforclosedwindtunnels.

Table4–3-Proposedgeneralsetofvariablesforclosedwindtunnels.

Table4–4-ProposedgeneralsetofvariablesforHRSGs.ThenamesinbracketsrefertoANSYSnamesforthevariables.


Chapter5 -TheMOST-HDSoptimizationmodel

Insanity:doingthesamethingoverandoveragainandexpectingdifferentresults.

AlbertEinstein.

This chapter describes in detail the MOST-HDS model and the optimizationalgorithmdevelopedforthisThesis.Ithighlightsthedifferentialaspectsbetweenthis approach and the current State of the Art. Firstly, Section 5.1. presents ageneral introduction.Section5.2.explains themainelementsof thestructuredoptimizationapproachproposedbyMOST-HDS.Thefactthatthesearchcarriedout byMOST-HDS is structured is one of the key aspects of themodel and acontribution of this Thesis to the field of aerodynamic shape optimization.Section 5.3. describes the MOST-HDS model. Section 5.4. illustrates thearchitectureof themodel implementation.Thisarchitecture contributes to theState of the Art because it carries out a full implementation of an automaticworkflow for an optimization-simulation environment based on direct search,applicabletoCFDproblemsofawiderangeoffields.Finally,Section5.5.outlinesasetoffinalremarksonMOST-HDS,tosummarizethemostimportantaspectsofthischapter.

5.1.IntroductionTheapproachproposedbythisThesisfortheaerodynamicshapedesignproblems,

abletohandlebothsmallandbiggeometrychanges,isthedevelopmentofageneralmethod based on a Multi-Objective Structured Hybrid Direct Search optimizationalgorithm(referredtoasMOST-HDS).

Extensive research has been carried out over many years in all aspects ofoptimization, applied to a very wide range of fields. This Thesis focuses on a veryparticulararea,aerodynamicdesign.Manyinterestingcontributionstooptimizationinthisfieldcanalsobefound(refertotheStateoftheArt,Chapter3).

5

Chapter5–TheMOST-HDSoptimizationmodel

75

ThenovelaspectsandcontributionsoftheMOST-HDSmodelare:

- Firstly,thatitisanautomatic,flexibleandrobustimplementationofstructuredoptimizationinanarea(aerodynamicshapedesign)towhichthisapproachhasnotbeenapplied,asfarasweknow.

- Secondly,thecontributiontotheconceptofhybriddirectsearch,usedbyotherauthors. In this regard, MOST-HDS combines genetic, gradient and swarmsearchintelligenceinawaynootherauthorweareawareofhasproposed.

- Moreover,thefactthatMOST-HDSisabletocopesmoothlywithbiggeometrychangesormodificationsof theshapedesignmeansthat itcanproducenon-conventional or non-intuitive designs. Such designs would never have beentriedmanually by the designer or explored by other optimization algorithmsfocusedonsmallgeometrychanges(seeChapters1and2fortheimportanceofbiggeometrychangesinthefieldofaerodynamicdesign).

- Therelevanceofdirectsearchforproblemsofaerodynamicshapedesignwithbig geometry changes is compared to other approaches, mainly surrogatemodels, which are shown not to perform as well for cases in which a biggeometry changemeans a qualitative change in the flow regime around thebodyofinterest(refertoChapter7).

- Finally, the applicability of the MOST-HDS model is shown for two realindustrialexamplesinChapter6(closedwindtunnelsandindustrialboilersforcombined cycle plants) to illustrate that it is a substantially generaloptimization model. Besides, its performance is also compared to anextensively used general purpose optimization algorithm by applying MOST-HDS to a relevant mathematical test suite which is commonly used forbenchmarkanalysesofoptimizationalgorithms(Hubandetal.[2006]).

5.2. Structured search: Variable hierarchy andoptimizationphases

Two of the fundamental concepts of this optimization methodology are thehierarchy of variables and the optimization phases. This approach – including directsearch inmost cases – has been used in other fields (Cuadra [1990] is a very goodreference example), but not yet in aerodynamics, or, at least, not as thoroughly asproposedinthiswork.


76

HierarchyofvariablesHierarchyofvariablesreferstothefactthattheindependentvariableswhichdefine

eachpossibledesignoftheaerodynamicbodyarenotallofthemofequalimportancein termsof their impactonattributesand constraints. This isoneof theaspects forwhichtheengineer’sknow-howisofparamountimportance.

As an example, in the particular case of wind tunnel design optimization, thefollowingmain independent variableswere already defined in Prada-Nogueira et al.(2015)andpresentedinChapter4:

1. Widthofthetunnel.

2. Lengthofthetestsection.

3. Widthofthetestsection.

4. Relativepositionoffanandtestsections.

5. Fandiameter.

6. Testsectiongeometry.

7. Profileshapeoftheso-calledducts1and2.

8. Areadistributionforthewindtunnelsections.

9. Transverseshapeforthewindtunnelsections.

10. Numberoffans.

Forthisdesignproblem,wepropose,basedonourexperience,thefollowinghierarchyofvariablesfortheoptimizationmodel:

1. Highimportancevariables:widthofthetunnel,lengthofthetestsection,widthofthetestsection,relativepositionoffanandtestsections,fandiameterandgeometryofthetestsection.

2. Mediumimportancevariables:profilesforducts1and2,areadistributionandshapeofsectionsinducts1and2.

3. Lowimportancevariables:numberoffans.

This hierarchy reflects the importance the engineer assigns to each variable.Treatingvariablesdifferently,accordingtotheirhierarchy(i.e.theirimportanceonthevalueoftheattributesconsidered),allowsforamoreefficientoptimizationprocess,aswillbeexplainedbelow.


77

Itmustbenotedthatthehierarchyofvariablesforthisparticularcase,orforanyother,isnotuniqueanditmustsuitthepurposeandexperienceofthedesigner.Thisiswheretheengineerplaysakeyroleinensuringthebestset-upfortheoptimizationproblem.Abadselectionofthehierarchycanresultinlessefficientoptimizations.

OptimizationphasesThe second key aspect of the optimization architecture presented, after variable

hierarchy, is the concept of optimization phase. Figure 5–1 summarizes theoptimizationmodel structure and introduces the concept of optimization phase fortwoexampleset-upconfigurations.

Figure5–1-Optimizationmodelstructure,illustratingtheoptimizationphases,fortwoexampleset-

upconfigurations.Thearrowsandequalsignsindicatemagnitudeofchangeforeachtypeofvariableineachphase.

Themaindifferencebetweenphases isthe levelofchangeofthevariousvariablehierarchies (as well as the search techniques employed by the model). Figure 5–1depictshowthevariablevalue-changesareconsideredinthedifferentphasesfortwoexample configurations (a big arrow stands for gross changes, a small arrow formediumchangesoreven fine tuningandanequal signmeans that variablesof thathierarchyarekeptconstantorderived fromothers).Thenumberofphasesdependsontheparticularproblemandtheaccuracyandtimeconstraints.

Figure 5–1 illustrates howMOST-HDS, after a design exploration phase (Phase 0,not included in this figure because it is not an optimization phase), will implementdifferenttypesofchangeforeachvariable,dependingonthehierarchyofthatvariableandtheoptimizationphase.


78

Fortheinitialphases,giventhatthedesignerhasareasonableideaofwhereinthesearchregiontheoptimumdesignscouldlie,acertainvariationwillbeallowedforthehighimportancevariables,thosewithastrongerimpactonthevalueoftheattributes.However, thisvariation rangeallowedwillnotbegross,otherwise thesearch regionwillbetoolargeandthetotalcomputingtimetoolong.Itisimportanttonotethat,fordiscretevariables,asmallchangemayalreadyimplyaqualitativechangeindesign.

Formedium importance variables, themodel allows the highest level of change.Thisissosinceitisnormallyforthistypeofvariablesthatthedesignercannotrelyonhis intuition or experience alone, or for which he cannot take all the mutualinteractions into account, to know beforehand which designs can be better thanothers. It is thus important that the optimization explores big changes in thesevariables.

Regardinglowimportancevariables,theyarenotmodifiedforthefirststagesoftheoptimization.Thereasonbehindthisisthattheirimpactonthevalueoftheattributesisweakandthereforeitmakesnosensetryingtofine-tunethedesignatthisveryearlystageoftheoptimization.

As the optimization proceeds, the variation of the high importance variables andmediumimportancevariablesisgraduallyreducedfromtheirinitiallevels,anditisthelowimportancevariablesthatsuffergrosschanges,becauseitisinthesefinalstagesoftheoptimizationthatthedesignshavetobefine-tuned.

Thewhole architecture and levels of change for each phase and type of variable(Figure 5–1) can of course be adapted to each particular problem if the designerwishestodoso.

A naïve example of the difference between variables of different hierarchies andbetweengrossandfinechangescanbetheselectionofavehicletopurchase.Thehighimportancevariableswouldbethetypeofvehicle,andgrosschangeswouldbeeitherselectingacaroratruck,whilealowimportancevariablewouldbevehiclecolorandasmallchangewouldbechangingthetoneofgreenchosen,forexample.ThisexampleisillustratedinFigure5–2,Figure5–3andFigure5–4.

Figure5–2-Grossandfinetuningexampleforhighimportancevariables.Inthisexamplethehigh

importancevariableisthetypeofvehicle.Intheupperline,grosschanges,andinthebottomline,fortheselectedvehicletype(car),finetuningoftheparticularmodel.


79

Figure5–3-Grossandfinetuningexampleformediumimportancevariables.Inthisexamplethe

mediumimportancevariableisthetypeoffuel:dieselorgasoline.Intheupperline,grosschanges(dieselorgasoline),andinthebottomline,fortheselectedfuel(gasoline),finetuningoftheparticulargasoline

type.

Figure5–4-Grossandfinetuningexampleforlowimportancevariables.Inthisexamplethelow

importancevariableisthecolorofthevehicle.Intheupperline,grosschanges,andinthebottomline,fortheselectedcolor(green)finetuningofthetone.

Variable hierarchy and optimization phases are at the core of a structuredoptimization model. Their importance stems from the fact that the number ofevaluationsoftheobjectivefunctioncanbereducedinarobustandefficientmannerifthe selection of variables in each hierarchy level and the particular gross and finetuninglevelsarewellselectedbytheexpertiseofthedesigner.

Furthermore, the optimization algorithms, evaluationmethods or tools used candiffer fromphase tophase tobetterexploit the typesofvariables tobemodified ineach phase (discrete/continuous), their hierarchy, or the level of change they suffer(gross, fineornone).Besides, theareasof thesearchregionto focusoncanalsobechanged during the optimization process. This is done automatically byMOST-HDS,basedonitsembeddedintelligenceandmetaheuristics,aswillbeexplainedlateroninthischapter.

Tofurtherillustratetheoptimizationphases,thedetailedoptimizationarchitectureisshowninFigure5–5,foreachproposedphase.Theexampleapplicationisthewindtunneldesignoptimization,subjecttoasetofconstraints.


80

Forthisparticularcase,theapproachofFigure5–1isfollowed,withsomespecificadaptations. Someof thehigh importance variables (widthof the tunnel and lengthandwidthofthetestsection)areleftconstantfromtheverybeginning,whiletherestofthehighimportancevariablessuffermediumchanges.Thisissotolimitthenumberofdesignsfortheexplorationphase(Phase0)toamanageablenumberof32,inordertopresentandanalyzetheresultsforthisThesiswithmoreclarity.Italsostemsfromthefactthattheexperiencedtunneldesignerwillacknowledgethatthevariablessetas constants are usually constraints of the project and so nomodifications (or onlyminorones)areallowed.

Ascommentedabove,thismethodology,withtheappropriatemodifications–itisthe job of the designer/engineer to adapt the method (variable hierarchies andnumberofphases)–canbeusedforotherproblemsofadvancedaerodynamicdesignofcomplexsystems.InthisThesisasecondexample,theapplicationofMOST-HDStotheshapeoptimizationofacriticalpartofindustrialboilers,willalsobepresented.


81

Figure5–5-Proposeddetailedoptimizationarchitecturefortheexamplecaseofawindtunnel

designoptimizationandforonepossibleproblemconfiguration.

Astheoptimizationproceeds,thealgorithmwillkeepthebestsolutionsitfinds,anditwillcalculatethenewdesignpointstakingthearchitectureshowninFigure5–5(ortheparticularonesetbythedesigner) intoaccountforeachphase.Consequently, inthe first phases it will allow for changes in the variables of higher importance but,gradually, it will focus on the areas of the search region which are yielding betterresults and, for those designs, itwill reduce themagnitude of themodifications forvariables of higher importance and it will focus on the optimization of the lowerimportancevariables.

5.3.DescriptionoftheMOST-HDSalgorithmThe optimization algorithm needs a set of embedded metaheuristic rules to

determine how to move throughout the search region, for the different variablehierarchies, variable types (discrete or continuous) and optimization phases. Thissectionwillgiveanoverviewoftheserules.

1.Phase0:Initialdesignsetevaluation(designexplorationphase)TheinitialphaseorPhase0performsaninitialevaluationofasetofdesignpoints

within the search region. Design points in this initial set will usually have variousdifferentvaluesforthehighandmediumimportancevariablesandfixedvaluesforthelow importance variables, in accordancewith Figure 5–1 and Figure 5–5, but it is aphaseprevioustothoseshowninthesefigures,sinceitisnotanoptimizationphaseinitself,butameredesignexploration.


82

Indefiningthisinitialevaluationtobeperformed,theexperienceoftheengineeriscritical,sinceitmustbebroadenoughtoexplorethewholeareaofthesearchspacewhereoptimumpointscouldbefound.Theoptimizationalgorithmwillthenrefinethesearch ineachoptimizationphase,butapoor initialevaluationset,ashappenswithmost optimization algorithms,will increase the computing time required to find theoptimum solutions ormaymake convergencemore difficult. However, using a verybroadevaluationsetisonlyrecommendedincasesinwhichthereisahighuncertaintyonwheretheoptimummaylie,becauseaveryhighnumberofinitialpointswillalsoincreasethecomputationtimeconsiderably.Theidealsituationistogenerateaninitialevaluation set which is both limited in the number of points and which covers thewholesearchspacewell,ortheareawheretheoptimaareknowntolie.Thissituationiscommontomostalgorithmscurrentlyused.

IntherealindustrialcasespresentedinChapter6wewilluseinitialevaluationsetswhich work well for this kind of problems, based on our experience. In one of theexamples,thewindtunneldesignoptimization,thissetisgeneratedasallthepossiblecombinations of all maximum and minimum variable values for the whole set ofvariablesdefined.Thusthefirstphaseexploresthevaluesoftheattributesfordesignpointson the limitsof the search spaceandwill then,basedon these results,moveintothesearchspace.Inthesecondexample,theindustrialboilerinletduct,theinitialevaluationsetisgeneratedbyDesignofExperiments(DoE).

Forcomputer-baseddesignoptimization,asisourcase,DoEschemessuchasLatinHypercubeSampling (LHS)orOrthogonalArrays (OA)are recommended in literature(refertoKrajnovic[2007]or,evenbetter,tothesurveyworkinSimpsonetal.[2001]).

However,forothercases,suchastheproblemoftheapplicationofMOST-HDStoamathematical test function (also presented in Chapter 6), the initial set is purely arandomgenerationof theminimumnumberofpointswhich isconsiderednecessarytohaveagoodcoverageofallthesearchspace.

In any case, the way MOST-HDS performs has been designed to reduce thedependencyoftheresultsandoftheconvergencerateontheinitialevaluationsetasmuchaspossible.Anyhow,extensiveworkonthistopicispartofthefutureworktobeperformed.

Let us illustrate Phase 0 for the wind tunnel example case. In this problem, theinitialevaluationsetisgeneratedaccordingtothefollowingsteps:

1. Twovaluesarechosenfortherelativepositionofthefanandtestsections.

2. Twofandiametersareselected(onebelowandoneaboveanominalrecommendeddiameter).

3. Twogeometriesforthetestsectionshapeareset(squareorcircular).

4. Twopossibleprofileshapesareusedforduct1(onenearlycircularandoneskewed).Duct1,asexplainedinChapter4,istheductwhichjoinsthetestsectionandthefanandwhichisdownstreamofthetestsection.

5. Finally,twoshapes(squareorcircular)aresetforthetransversesectionsofduct1.


83

Itisimportanttonotethatduct2iskeptconstanttoabaselinedesigngeometryforthisexamplecase,oncemoretokeepthenumberofdesignpointsforPhase0to3211.

Thisyieldsatreeof32windtunneldesignpoints(Figure5–6).ThesedesignpointsareevaluatedusingtheCFDsoftwareANSYSFLUENTv17.Thetreeisdesignedinthismanner, in order tominimize the points to be evaluated,while covering the searchregionadequately.

Figure5–6-ExampleinitialevaluationsetforPhase0(inthiscase,32windtunneldesigns).

OncetheinitialsearchissetinPhase0oftheoptimization,thedifferentcandidatedesign points are evaluated using CFD, in the case of aerodynamic optimizationproblems,orusinganyparticularevaluationfunctioninothercases.

BasedontheresultsofPhase0,whichisameredesignexploration,thealgorithmmustdecidehowtoproceedtotheoptimizationitself.Thismeansthatthealgorithmmustdecide:

1. Howtousetheinformationfromthepreviousphasetosetupthesearchproblemofthecurrentphase.

2. Howtoperformanoptimizationsearchinsuccessivesteps,seekingdesignimprovementsataminimumcomputingcost.

3. Whentostopsearchingandgivewaytothenextoptimizationphase.

The following subsections explain the general strategy proposed for theoptimization search. The scheme proposed exploits a mix of gradient, genetic andswarmsearchconcepts.

11Theindustrialboilercasewillillustrateamuchlargernumberofdesignpointsfortheexploration

phase.


84

2.ParetotolerancethresholdGivenasetofevaluatedsolutions,someofthemmustberejected,whiletherest

arekeptforfurtheranalysis.

ThefirststepistocalculatetheParetofrontforthesolutionsoftheinitialsearchontheevaluationset.TheParetofrontgroupstheoptimumsolutionsinamulti-objectiveoptimization.Anysolutiononthatfrontimprovesatleastoneobjectiveattheexpenseof sacrificing the value of at least another objective,with respect to the rest of thepointsontheParetofront.

Because the solutions on the Pareto front may not be the only designs worthconsideringforthesubsequentoptimizationphases,atolerancethresholdisdefined.AnexamplethresholdisdepictedinFigure5–7.Designswithinthisareaofthesearchregion could potentially evolve to be optimum designs, yielding even better resultsthanthosesolutionsinitiallyontheParetofront,becausethisParetofrontisonlytheresultofafirst-stepexploration.

Figure5–7-IllustrationoftheParetofrontandthetolerancethresholdforPhase0oftheMOST-HDS

optimizationalgorithm.

Thethresholdisdefinedintermsofallowedtolerancesforeachselectedattribute.Forinstance,apossiblethresholddefinitioncanbe:

𝑓',),*+,-./,012 = 𝑓',)45,*67-.80 + 𝛿',),* Equation5–1


85

where i represents the particular attribute considered, j the next phase of theoptimization,k represents each solutionon thePareto front,𝑓',)45,*67-.80 represents thevalueofattributei,forphasej-1(thecurrentphase),atpointkalongtheParetofront,𝛿',),* is the value of the particular threshold assigned and, finally, 𝑓',),*+,-./,012 is thethresholdvaluethatwillbeconsideredforattribute iandoptimizationphase jattheParetopointk.

Forcasessuchasthewindtunnel,thethresholdcansimplyreplicatetheshapeofthePareto front (refer toChapter6).The thresholdofFigure5–7,however,offersamoregeneralexample.InthiscasethethresholddoesnotreplicatetheParetofront,but is focused on a very particular area of the search space to which the designerwants to limit the optimization search from this phase onwards. This is the type ofthresholdusedfortheindustrialboilerinletduct,aswillbeexplainedinChapter6.Analternativethresholddefinition,whichcaneasilybeintroducedinthemodel,wouldbeto limit thenumberofpointsselected for thenextphasetoamaximumamount,soonlythebest10or100or1000pointswouldbekept,forinstance.

Regarding this tolerance definition, for problems which are evaluated using CFDcodes, it isworth commenting that thebest values for the toleranceoneachof theattributes depend on the number of solutions explored in the current phase, theaccuracyof theCFDsolver (the levelofprecision increases ingeneral fromphase tophase) and the trade-off between computing time and accuracy stated by thedesigner.Specialcaremustbetaken,forinstance,iftheaccuracyoftheCFDsolver(forexampleintermsofmeshcoarseness)doesnotyieldasystematicerrorintheresults.However,themoretheengineerusesthisoptimizationtool,themoreexperiencehewillhavetoselectappropriatetolerancevalues.

Once the tolerance threshold area is defined, as shown in Figure 5–7, all thesolutions that lie between this curve and the Pareto front are potential candidatesolutionskeptforthenextoptimizationphase.Neitherstrictdominancenorsignificantdominance criteria are used, to keep some additional and potentially interestingdesigns(seeCuadra[1990]andSchweppeandMerril[1986]foradiscussiononthesedominancecriteria).

However,amongallthesolutionsthatliewithinthetolerancethreshold,notallwillbe used as baseline for the following optimization phase. Given that the CFDevaluations are very time consuming, candidate solutions to be kept have to beselected efficiently. The selection methodology is explained in detail in Step 3.Selectionofsearchdirections.


86

3.Selectionofsearchdirection(s)Firstly,thealgorithmwillsearchfortheclosestsolutionsontheParetofronttoeach

candidate design. These are potentially good search directions to continue theoptimizationandit isoneofthemainnovelaspectofMOST-HDS.Thedesignermustchoosethenumberofclosestsolutionstobeusedtodeterminethesearchdirection(s)from a particular candidate design. He can select to use the closest solution on theParetofront,orthetwoclosest,ormore(thiscanalsobeselectedautomaticallybythealgorithm).Thehigherthenumberofdirectionstoconsider,thehighertheprobabilityofreachingagoodoptimum,butalsotheanalysiswillbemoretimeconsuming,soatrade-offmustbereached.

Itisworthnotingthat,fortheparticularcaseofsolutionsontheParetofrontoftheprevious optimization phase, the algorithm will follow search directions along theParetofrontitself.

Once the searchdirections for all candidate solutionshavebeendetermined, thereducedsetofsolutionsthatwillreallybeusedforthenextoptimizationphasemustbeselected.

Theselectionmethodisasfollows:

1. Thealgorithmgroupsallthecandidatesolutionsdependingontheirsearchdirection (i.e. the point(s) on the Pareto front towards which they wouldmove).

2. Among those solutions which would move towards the same Paretopoint(s),boththedistancebetweendesignsinthespaceofvariablesandinthespaceofattributesmustbedetermined.

3. Space of variables: the metric to measure the distance in the space ofvariables is the relative distance between two designs, for each variable,with respect to the maximum range of that variable in that particularoptimization phase. Then, to add up all the distances for the differentvariables, different weights are applied to the distance for each variable,dependingonthehierarchyofthatvariableandthephase.

4. Themetrictomeasurethedistanceinthespaceofattributesisanalogoustothatofthespaceofvariables,exceptthattheweightofalltheattributesisthesame(unlesstheuserwantsdifferentweights).

5. When a number of designs that would move towards the same Paretopoint(s) are close both in the space of attributes and in the space ofvariables (i.e. below certain presetmaximum distance thresholds), then arepresentative for that subset of designs will be selected, to prevent thealgorithmfromevaluatingverysimilardesigns.Thisrepresentativeselectionwill be carried out by means of a clustering algorithm (the k-meansalgorithm, in our case, as originally explained in Hartigan [1975] and ascurrentlycodedinMATLAB).Thisissimilartotheworkcarriedoutonswarmsearchmethodologies(agoodreferenceexampleofenhancedswarmsearchisShiandEberhart[1998]).


87

6. However,ifvarioussolutionsarecloseintheattributespace,butfarapartinthe variable space, all must be kept, because they represent differentdesignsandtheyenrichthesearchprocess(asimilarapproachisproposedinCuadra[1990]).

Thediscarded solutionsof intermediateoptimizationphaseswill, anyhow,notbeeliminatedcompletelyandwillbekept,incasethealgorithmdecidestheycanstillbeinterestingcandidatestoanalyzeinanyofthesubsequentoptimizationphases.

4.Selectionofsearchvariable(s)Basedonthesearchdirection(s)defined,thealgorithmwilldeterminethevariable

changes needed tomove eachmodel towards its Pareto targetmodel(s). Itwill runthroughthevariablevaluesforeachselectedpointandcomparethosevaluestothevaluesofthetargetParetopoint(s).SearchvariablesforeachcandidatepointwillbethoseforwhichthepointanditstargetParetopoint(s)havedifferentvalues.

5.CalculationoftheincrementtobeappliedtoeachvariableOncethesearchdirectionsforallpointshavebeendeterminedandthevariablesto

changehavebeenpickedup, thealgorithmwilldeterminetheamounteachvariablehastobechanged.Inordertodothis,thealgorithmwillcheckthetypeofvariable(i.e.hierarchy)and theoptimizationphaseand itwill introducevaluechanges toeachofthevariables,followingtheguidelinesofFigure5–1.Forexample,ifthevariabletobechangedisofhighimportance,foroptimizationPhaseIthechangesintroducedwouldbesmall, towards thevalueof the targetpointon thePareto front.However, this isonly the general approach followed by the algorithm. The detailed procedure isdetailedbelowandshownintheflowdiagramofFigure5–10.

Forcontinuousvariablesthechangesarecleartounderstand.Forinstance,inPhaseI, a big change can imply moving towards the target point 2/3 of the differencebetweenthevalueofeachvariable for thedesignpointconsideredandthevalueofthatsamevariableforthetargetpoint.Asmallchange,ontheotherhand,canmeanmoving 1/3 of the distance in that variable. The particular increment factors arecalculatedbythealgorithmdynamicallyasexplainedbelow.

Fordiscretevariables,however,thealgorithmwilljumpfromonediscretevaluetothe next one – for instance, from a circular to a square shape. For these variables,smallandbigchangesmaythereforecoincide,dependingontheirrangeofvalues.

Theseincrementfactorsaremodifiedbythealgorithmdependingonthehierarchyofvariables,theparticularvariable,theoptimizationphaseand,mostimportantly,theresultsof theoptimizationprocess.Thismethodof increments followsaverysimilarapproach to the extensively usedmethod developed originally in Nelder andMead(1965). The possible changes of values explained in that work (namely reflection,expansionandcontraction)arealsousedhere,withsomemodifications,andusingnotthecentroidpointofthesetofpointsdefiningthesimplex,buttheclosestpoint(s)ontheParetofront.


88

ItisworthnotingthatMOST-HDSwilluseincrementfactorsbeloworaboveunity.Hencetheexplorationmovesarebothwithinthesearchregionalreadyexploredandalsooutsideofit.

6.EvaluationofthenewdesignpointsOncesteps1-5havebeenperformedforalltheselecteddesignswithinthePareto

threshold of the previous optimization phase, the new candidate solutions will beevaluated (in our case simulated using CFD) and a new Pareto front will bedetermined.

7.FurtheroptimizationphasesTomove to furtheroptimizationphases, thealgorithmrepeatssteps1-6until the

stoppingcriteriadefinedaremet.

Theusercanselectamaximumnumberofevaluations (oralternativelymaximumcalculationtime)andthealgorithmcanestimatethenumberofphasesandsolutionstobekeptforeachphasetomatchthattimetargetascloselyaspossible,aswellasotherinternalaspectssuchasmeshrefiningcriteriaforeachphase(inthecaseofCFDevaluation),etc.AnotherpossiblestoppingcriterionisthemaximumpercentageofthecurrentsetofdesignpointsthatisinthebestParetofront(assoonastheoptimizationreachesthatthresholdvalueitwillstop).

Moreover, the algorithm is able to change mesh coarseness, for example,depending on the optimization phase. Extensive results on the impact of meshcoarseness (mesh sensitivity analyses) will be presented in future work. For thepurposeof thisThesis,meshsizehasbeenvaried ineachcaseuntilagoodtrade-offbetweenaccuracyandcomputingtimeisfound.

8.Finaloptimumdesignfine-tuning:theadjointmethodForanenhancedfine-tuningofeachsolutionontheParetofrontsfoundforthelast

optimizationphases,theuseoftheadjointmethod(agoodclassicalreferenceisGilesandPierce[2000])isproposed,asmentionedinFigure5–1.Thismethodallowsforthedetermination of the sensitivities of one or more particular attributes to localmodifications in the geometry of the body of interest. One of the most relevantresearchworksontheapplicationofadjointstoadvancedaerodynamicoptimizationisPaniagua(2014),forthecaseofhigh-speedtrainnoseoptimization.

In the following sections, important remarks on the MOST-HDS algorithm arehighlighted. For a detailed illustration of the optimization flow diagram andmetaheuristicsbehindMOST-HDS,refertoFigure5–10.

TheMOST-HDSoptimizationprocedureinshortIn the following sections, important remarks on the MOST-HDS algorithm are

highlighted. For a detailed illustration of the optimization flow diagram andmetaheuristicsbehindMOST-HDS,refertoFigure5–10.

A brief summary of how MOST-HDS proceeds is included here for the reader’scomfort.Figure5–8illustratesthemainstepsfollowed:


89

1. Phase0isthedesignexplorationphase,inwhichanumberofdesignpointsaregeneratedandcomputedtohaveaninitialrepresentationofthespaceofattributes(i.e.theperformancespace).ThesepointscanbegeneratedbymeansofanyDesignofExperiments(DoE)technique,orothermethods.

2. AfirstParetofrontcanbecomputed,torepresenttheoptimumdesignsforPhase 0. The Pareto front is a very useful tool for true multi-attributeoptimizationproblems.

3. A tolerance threshold is automatically generated, based on the expert’ssettings, to group the candidate points that will be selected for the nextphase. Clustering can be applied to select representative points among agroupofverysimilardesignpoints(bothinthespaceofvariablesandinthespaceofattributes).

4. Acrossoverisperformedbetweeneachselecteddesignpointanditsclosestpoint(s) on the Pareto front. The crossover is controlled by the so-calledincrement factors, which are automatically tuned to improve theoptimizationspeedandfinalresult.

5. Anewsetofdesignpointsishencegenerated.ThesepointsconstitutePhaseI.

6. AnewPareto front iscomputed.Theoptimizationhasprovedsuccessful ifthenewParetofrontimprovestheParetofrontofthepreviousphase.

7. This procedure can be repeated asmany times (i.e. phases) as set by theexpert, or as controlled internally by the algorithm based on a set ofstoppingorconvergencecriteria.

Figure5–8-IllustrationoftheprocedurefollowedbytheMOST-HDSoptimizationalgorithmforthe

optimizationineachphase.


90

FinalremarksontheMOST-HDSoptimizationmodelMOST-HDS aims to prove an original, general methodology based on multi-

attribute, structured optimization and following a hybrid direct search approach. Itcombinesgenetic,gradientandswarmsearchintelligenceineveryiteration,aswillbeexplainedinthissection.

Besides being multi-attribute, because it has been developed specifically forproblemswithmorethanoneobjectivetobeoptimized(althoughitcouldalsobeusedfor single-attribute optimization), MOST-HDS exploits the concept of structuredoptimization,making use of two key differential aspects: hierarchy of variables andoptimizationphases.Theseconceptshavebeenusedinotherfields(refertotheStateoftheArt inChapter3),buthavenotbeenused,asfarasweknow, inaerodynamicshapeoptimization.

Furthermore, MOST-HDS proposes a novel hybrid direct search approach. In thefirstplace,according to theextensivelycitedpaperbyHookeand Jeeves (1961), thetermdirectsearchisused,astheystate literally,“todescribesequentialexaminationoftrialsolutionsinvolvingcomparisonofeachtrialsolutionwiththe"best"obtaineduptothattimetogetherwithastrategyfordetermining(asafunctionofearlierresults)what the next trial solution will be. The phrase implies our preference, based onexperience, for straightforward search strategies which employ no techniques ofclassical analysis except where there is a demonstrable advantage in doing so.”. Inotherwords,direct searchwill implydirectevaluationofeachcandidatesolution (inourcasesusingCFD)andasearchstrategytoproceedwiththeoptimization,avoidingtheuseofanyothermethods,suchassurrogatemodelsoranykindofapproximationoralternativetothedirectevaluationofeachcandidatepoint12.

Regarding the search strategy developed for MOST-HDS, besides following astructuredoptimizationapproach, it isacombinationofgenetic,gradientandswarmsearchintelligence,henceahybriddirectsearch.Itsnoveltystemsfromthefactthat,as opposed to most other authors who have combined gradient-based and non-gradient-basedalgorithms(relevantexamplesareGuliashki[2008],Hegazietal.[2002]orHsiaoetal.[2001]),MOST-HDSdoesnotswitchfromonetypeofalgorithmtotheotherdependingonhowtheoptimizationisadvancing,butitbenefitsfromelementsofallthesetypesofalgorithmsineveryphase.

To illustrate this better, an example of the search strategy, showing the mostrelevant cases which can occur, is presented in Figure 5–9. This figure is also veryimportantbecause it clarifies thedifferencebetween the spaceof variables and thespaceofattributes,forasimplifiedexampleof2variablesand2attributes.Thetermssearch space and fitness space are alsoused to refer to the same concepts (a goodexampleemphasizingthedifferencebetweenbothspacesisHubandetal.[2006]).

12Ofcourse itcanalwaysbearguedthatCFDevaluation,unlesscomputedusingDirectNumerical

Simulation,orevenonlybecauseitusesspaceandtimediscretization,isnotadirectevaluationoftheproblemeither.Howeverwhatwemeanbydirectsearchistheuseofthemostapproximateevaluationmethodavailable,avoidingtheuseoffurthersimplificationsorapproximations.


91

Figure5–9-Conceptualexplanationshowinghowthehybridoptimizationalgorithmproposed

proceeds,combininggenetic,gradientandswarm-searchintelligenceforamulti-attribute,structuredoptimization.ThefiguredepictstheParetofrontandthresholdforthecurrentphaseandthenewPareto

frontandthresholdobtainedforthenextphase.

Afteraparticularphasehasbeencomputed,thesolutionstobeusedforthenextoptimizationphasearepickedonlyfromwithintheParetotolerancethreshold,ashasbeen explained. This is the fitness criterion (in genetic algorithm terminology).Moreover,oncethedistancebetweendesignpoints,bothinthevariableandattributespaces, is calculated (because both distances are important), clusteringmay furthereliminatedesignpointswhichareclosetoothers inbothspaces (for instancedesignpoint6,intheexampleofFigure5–9),sothisstepisalsopartofthefitnessevaluationofeachcandidatesolution.

Forthefollowingphase,thenewdesignpointsobtainedwillbethecrossoverofthedesign points selected in the current phase. The crossover process (i.e. determininghowthechildsolutionisobtainedfrombothparents)canchangefromphasetophase,anddependingonthetypeofvariableanditshierarchy.

One of the key aspects of noting the conceptual difference between space ofvariablesandspaceofattributesisthat,foranefficientsearchprocess,certainparentdesignpointscanbekeptordiscardedforthecrossoverprocess,dependingontheirrelativedistancesinbothspaces.AscanbeseeninFigure5–9,thechilddesignpointsobtainedfromthemostrelevantcrossovercombinations,comparedtotheirparents,canbe:

1. Closeinthespaceofvariablesandcloseinthespaceofattributes.Example:parentsolutions1,2andtheirchildsolutionX.Thecrossoverofthistypeofparentpointswillgenerallyyieldaverypredictabledesign, suchasX,verysimilar to itsparents.Therefore this typeof crossovercanbediscarded toreduce the number of evaluations. Clustering can obtain a representativedesignpointfromagroupofpointswhichareveryclose(i.e.belowpresetdistancethresholds) inbothspacesandonlycross themwithpointswhichare not so close in either spaces, to explore other regions of potentiallybetterdesigns.


92

2. Closeinthespaceofvariablesandfarapartinthespaceofattributes.Thisimpliesacriticalregionofdesign,inwhichperformanceisverysensitivetosmallchangesinthevariables.Example:parentsolutions7,8andtheirchildsolutionW.Thecrossoverofthistypeofparentpoints,whichareverycloseintheirvariablevaluesandyetfarapartintheirattributevaluescanproduceoriginal or non-conventional design points, such as pointW,which is alsoclose in the space of variables but in a different area of the space ofattributes. Thus the search can produce innovative or disruptive designs,showingthattheresultsarenotintuitiveandillustratingtheimportanceofapplyingautomaticoptimizationschemes.

3. Farapart in thespaceofvariablesandfarapart in thespaceofattributes.Example: parent solutions3, 4 and their child solutionY. The crossoverofthis type of parent points is worth exploring, since its result will alsonormallybefarapartinthespaceofvariablesandinthespaceofattributes,soitshouldproducequitenoveldesigns,whichcouldimprovetheattributevaluesobtaineduptothispointoftheoptimization.

4. Far apart in the space of variables and close in the space of attributes.Example: parent solutions3, 5 and their child solution Z. The crossoverofthis type of parent points is also worth exploring, because it means thatresults arenot intuitive, at least in somepartsof the search region, giventhatverydifferentdesignscanyieldverysimilarperformances.

In conclusion, theMOST-HDSoptimizationalgorithm ishybrid in the sense that ituses a gradient-based approach to define the Pareto front and tolerance threshold,andtoselectthesearchdirection;thereafter,variableincrement(crossoverstrategy)isdefineddependingonthehierarchyofthevariablestobechanged,theirtype,thecurrentphaseandtheresultsobtaineduptothispointoftheoptimization,inordertoobtainchildsolutionsfromtheirparents,soitfollowsageneticapproach(whichmayperform the crossover of very different designs or yield very original designs, ascommentedabove).Swarmsearchaspectsareused,asmentioned,mainlywheneverclustering isappliedand, toacertainextent, to focusoncertainareasof thesearchregion (either in the space of variables or in the space of attributes) based on theresultsofthesearchprocessforgroupsofdesignpointsindifferentpartsofthesearchregion.

In the proposed algorithm there is no mutation, as opposed to most geneticalgorithms, since all child solutions are obtained from two parents. It could beincluded,however,ifdeemedconvenient.

In general terms, on the one hand, the genetic approach introduces therandomnessneededtoproducesufficientlynoveldesignpointswhichcoverwellboththespaceofvariablesandthespaceofattributes.Ontheotherhand,gradientsearchis used when the movement of a design point improves and it seems to follow agradientreasoning(local improvements).Finally,swarmsearchintelligenceisusedatallmomentstocontrolhowtheglobalperformanceinthedifferentareasofthesearchregion is progressing. All these elements are key to handle the optimization ofchallengingfunctionsorreal-lifeproblems.


93

The intelligence embedded in the MOST-HDS model has proved successful, asshowninChapter6,notonlyforthetypeofproblemsitwasinitiallyaimedat,namelyaerodynamicshapedesignoptimizationwithbiggeometrychanges,butalsoformoregeneraloptimizationproblems.

Detailed flow diagram of the metaheuristics behind the MOST-HDSalgorithm

The following figure shows the detailed flow diagram of the MOST-HDSoptimizationalgorithmdevelopedinthisThesis.

Figure5–10-Flowdiagramanddetailednotesdescribingtheoptimizationprocedurefollowedbythe

MOST-HDSmodel.DPsstandsforDesignPoints.

5.4.ImplementationoftheMOST-HDSalgorithmThe architecture of the model implementation is illustrated in this section. This

architecture contributes to the State of the Art because it carries out a fullimplementationofanautomaticworkflowsimulationenvironmentforoptimizationofCFD problems, based on direct search, for a wide range of fields. In particular,MicrosoftExcelandaCFDsolver(ANSYSFLUENTinthiscase)arecoupledandaVisualBasics forApplications (VBA) code isdeveloped to implement theMOST-HDS solver,whichcontrolstheoptimizationprocessfromExcel(externallytoANSYS).TheMOST-HDSalgorithmiscodedinVBAandnotinotherprogramminglanguages(C++,Matlab,etc.) because it was considered that the integration to ANSYS would be easier andmore efficient. In any case the code can easily be adapted to these alternativeprogramminglanguages,tomaketheMOST-HDSalgorithmevenmorebroadlyusable.


94

ThemodelarchitectureispresentedinFigure5–11.ItisworthhighlightingthatthearchitecturefortheMOST-HDSmodelhasbeendesignedwiththeobjectiveofmakingthis tool as general as possible. The initial goal of themodel was the aerodynamicshapeoptimizationofcomplexgeometrieswithbiggeometrychanges(forthesecasesanexternalCFDsolver isrequired).Nevertheless,thetoolhasalsobeenappliedtoacommonlyusedbenchmarkmathematical function,notonly to show itsapplicabilityfor very different and challenging optimization purposes, but also to illustrate howgeneral the model is. To give an example, for this general purpose mathematicaloptimizationproblem(presented inChapter6), thearchitecture isvalidandtheonlydifference would be that, given that an external evaluator is not required (all theevaluations can be performed internally in Excel), and because there is no need forvariable translation, the module Translation of optimization variables to solvervariableswouldnotbecalled.


95

Figure5–11-SchematicdiagramofthemodulearchitectureoftheMOST-HDSmodelimplementationforafullyautomaticoptimizationworkflow,couplingMicrosoftExcelVBAandanexternalsolveror

evaluator,ifrequired(inthiscaseANSYSwasusedfortheCFDevaluations).

5.5.FinalremarksThis chapter has presented in detail the MOST-HDS optimization model. Before

moving on to Chapter 6 and the results of the application of this tool to industrialproblemsandtoamathematicalbenchmarkfunctionforoptimizationalgorithms,thefollowingisasummaryofthemainhighlightsofthismodel:

1. TheMOST-HDSmodel isaMulti-ObjectiveStructuredHybridDirectSearchoptimizationalgorithm.

2. A first contribution of this model is to apply a structured optimizationapproach,anditstwomainelements(variablehierarchiesandoptimizationphases),toaerodynamicdesignoptimizationproblems.

a. The structured architecture allows for a scope, level of detail andsearchschemeswhicharemodifiedoradaptedautomaticallyineachphaseoftheoptimization.


96

b. The conceptofhierarchyof variablesasamethod to feed into themodel the stronger orweaker influence of a particular variable ontheattributesisveryinterestingforindustrialoptimizationproblems,aswillbeshowninChapter6.Theoptimizationprocesshandlesthevariables differently among the various hierarchies defined. This,alongside other key features of MOST-HDS, allows for an efficientsearch process in a type of problems which is characterized byconsiderablytime-consumingdesignpointevaluations.

3. The difference between the variables used by the optimization algorithmand thevariablesusedby theevaluator (in this caseaCFD solver) isonceagainnoted(asinChapter4).Consequently,atranslationmoduleisrequiredtotransformtheoptimizer’svariablesintothoseusedintheCFDsolverforgeometryparameterization.

4. The hybrid direct search scheme proposed by MOST-HDS is an efficientapproachwhich,thankstothecombinationofgenetic,gradientandswarmsearchaspects,canmovethroughthesearchregioninasmartandadaptivemanner.

5. The model developed is a fully automatic, robust and highly flexibleoptimizationtoolwhich,onceset-upbyanexpertengineer,canbeusedbyanynon-expertperson.

6. Themodelarchitecturedeveloped,whichishighlygeneralandapplicabletoother domains of optimization, is also an important contribution of theMOST-HDStool.

7. Theconceptsofspaceofvariablesandspaceofattributes(alsoreferredtoinliteratureassearchspaceandfitnessspace)areclarified,sothatitcanbeseenthatthesearchprocesshastotakethepositionofeachdesignpointinbothspacesintoaccount.

8. Duetothewaytheoptimizationiscarriedout,theMOST-HDSmodelpavesthe way for non-intuitive and quite disruptive designs, which will oftenoutperformmoreconventionaldesigns,aswillbeseeninChapter6.

ListofFiguresFigure5–1-Optimizationmodelstructure,illustratingtheoptimizationphases,fortwoexampleset-upconfigurations.Thearrowsandequalsignsindicatemagnitudeofchangeforeachtypeofvariableineachphase.

Figure5–2-Grossandfinetuningexampleforhighimportancevariables.Inthisexamplethehighimportancevariableisthetypeofvehicle.Intheupperline,grosschanges,andinthebottomline,fortheselectedvehicletype(car),finetuningoftheparticularmodel.


97

Figure5–3-Grossandfinetuningexampleformediumimportancevariables.Inthisexamplethemediumimportancevariableisthetypeoffuel:dieselorgasoline.Intheupperline,grosschanges(dieselorgasoline),andinthebottomline,fortheselectedfuel(gasoline),finetuningoftheparticulargasolinetype.

Figure5–4-Grossandfinetuningexampleforlowimportancevariables.Inthisexamplethelowimportancevariableisthecolorofthevehicle.Intheupperline,grosschanges,andinthebottomline,fortheselectedcolor(green)finetuningofthetone.

Figure5–5-Proposeddetailedoptimizationarchitecturefortheexamplecaseofawindtunneldesignoptimizationandforonepossibleproblemconfiguration.

Figure5–6-ExampleinitialevaluationsetforPhase0(inthiscase,32windtunneldesigns).

Figure5–7-IllustrationoftheParetofrontandthetolerancethresholdforPhase0oftheMOST-HDSoptimizationalgorithm.

Figure5–8-IllustrationoftheprocedurefollowedbytheMOST-HDSoptimizationalgorithmfortheoptimizationineachphase.

Figure5–9-Conceptualexplanationshowinghowthehybridoptimizationalgorithmproposedproceeds,combininggenetic,gradientandswarm-searchintelligenceforamulti-attribute,structuredoptimization.ThefiguredepictstheParetofrontandthresholdforthecurrentphaseandthenewParetofrontandthresholdobtainedforthenextphase.

Figure5–10-FlowdiagramanddetailednotesdescribingtheoptimizationprocedurefollowedbytheMOST-HDSmodel.DPsstandsforDesignPoints.

Figure5–11-SchematicdiagramofthemodulearchitectureoftheMOST-HDSmodelimplementationforafullyautomaticoptimizationworkflow,couplingMicrosoftExcelVBAandanexternalsolverorevaluator,ifrequired(inthiscaseANSYSwasusedfortheCFDevaluations).


Chapter6 -ResultsobtainedDon'tbetrappedbydogma-whichislivingwiththeresultsofotherpeople'sthinking.

SteveJobs.

Thischapterpresentsadetailedoverviewofthemostrelevantresultsobtainedwith the application of theMOST-HDSmodel to different problems. Firstly, itanalyzestwo industrialproblemsofshapedesignoptimizationofverydifferentfields.Theresultsshownareverypositiveandareastrongcontributionto theStateof theArtof shapedesignoptimization for real, industrialproblems.Thefirst of these two problems is the shape optimization of the inlet duct toindustrial boilers (in particular Heat Recovery Steam Generators, or HRSGs)which are used in combined cycle power plants. The second case study is theshapeoptimizationofclosedwindtunnels,afacilitywhichisusedfortestingandfor leisure purposes. After both cases have been presented, a short sectionillustratestheresultsof theapplicationof theadjointmethodtothefinal fine-tuning of the optimized geometries. To conclude, and to offer a betterperspective on the applicability ofMOST-HDS, themodel is applied to a well-known mathematical test suite used for benchmark of general-purposeoptimization algorithms. Although the initial focus of MOST-HDS was theaerodynamic shape design optimization of geometries, including small and biggeometry changes, it was considered that this last benchmark section couldproverelevanttoshowthegeneralvalidityoftheproposedoptimizationsearchscheme.Section6.1.istheintroductiontothechapter.Section6.2.analyzestheresults of the case of the inlet duct of a set of HRSG families. Section 6.3.presentstheresults for theclosedwindtunnelcase.Section6.4.commentsonthe results of the application of the adjoint method to both industrial cases.Section6.5.studiestheresultsforthebenchmarkofMOST-HDSwhenappliedtotheWFGmathematicaltestsuite.Finally,Section6.6.indicatesthefinalremarkswhichsummarizethemostimportantconclusionswhichcanbedrawnfromthischapter.

6

Chapter6–Resultsobtained

99

6.1.IntroductionThe previous chapters have gradually presented how the MOST-HDS model has

beendeveloped:motivationandobjectives,problemdefinition,overviewoftheStateof theArt and a detailed description of how themodelworks. This chapter aims atshowingclearapplicationsofthemodelforrealindustrialproblemsandthusillustratethat it is a generalmodel for shapedesignoptimizationand for certainproblemsofgeneral optimization. The improvements obtained in performance for the differentcases presented are quantified and the model results are validated with realmeasurementstaken invalidationcases.Furthermore,someoftheoptimumdesignsobtainedareclearlyunconventional,go farbeyondtraditionaldesignguidelines,andwould rarelyhavebeen triedoutbymostdesigners.ThisoccursbecauseMOST-HDScanworkwithbiggeometrychanges,whichisnotthecaseformostresearchworksinthe literature. These are some of the key contributions of this Thesis, that will bepresentedthroughoutthischapter.

6.2. Industrial boiler inlet duct shape designoptimization

A particular kind of industrial boilers, referred to as Heat Recovery SteamGenerators (HRSGs),areused incombinedcyclepowerplants to recoverpartof theheat of the exhaust gases of a gas turbine, in order to generate steam for a steamturbine.Ever since theuseofHRSGs forpowerplants, the shapedesignof the inletduct at the entrance to these units, one of their most critical components, hasfollowed greatly unchangeddesign guidelines. The contributionof this Thesis in thissection is twofold. On the one hand, it shows that there is substantial room forimprovementintheshapedesignoftheinletductsofHRSGs,intermsofachievingalowerpressuredrop,ahighervelocityuniformityandan importantcostreductionofthe unit. On the other hand, it shows howMOST-HDS algorithm can find improveddesignsthatmaybequiteunconventionalandnon-intuitive,infieldslikeaerodynamicshapeoptimization involvingbiggeometrychanges.TheresultsobtainedforthetwoHRSG families presented show that there are optimum trade-off design pointswithsimultaneousreductionsinpressuredropofupto20-25%, in lateralsurfaceofupto38% and in length of up 16%,while having comparable velocity uniformities to theexistingdesigns.

VALIDATIONCASEFORTHEANSYSCFDSOLVERFORINDUSTRIALBOILERSIMULATIONS

Inthefirstplace,aswillalsobedonefortheclosedwindtunnelcase,abriefsectionispresentedonthevalidationoftheresultsoftheCFDsolverused(ANSYSv17.0)fortheevaluationofHRSGs.


100

ThefollowingtablepresentsthecomparisonofthepressurelossesprovidedbythemanufacturerandthepressurelossesobtainedfromtheCFDsimulationforeachoneofthetubebankswhicharelocatedthroughoutanHRSGandthroughwhichwaterispumpedtogeneratesteam.ThisisatypicalcomparisontovalidateanyCFDsimulationappliedtoHRSGs.Forclarity,thetubebanksareshownforanexamplesimulationinFigure6–1.

Figure6–1-Sideviewofvelocitycontoursinthemid-planeofatypicalHRSGtoillustratetheposition

ofthedifferenttubebanks.

Tubebank Error[%]

#1 9

#2 9

#3 7

#4 3

#5 5

#6 1

#7 2

#8 4

#9 5

#10 5

#11 4

#12 4

#13 4

#14 4

#15 5

#16 5

#17 5

#18 5

#19 6

#20 8

Table6–1–RelativeerrorbetweenthepressurelossesasprovidedbythemanufacturerandasobtainedfromtheCFDanalysisforthetubebanksofanexampleHRSG.


101

According to the previous table, there are certain errors between the valuesprovidedby themanufacturer for the pressure losses and the values obtained fromthe CFD simulation. These differences are mostly due to the non-uniformity of thevelocity distribution at the entrance of each one of the tube banks (simulated asporousmedia), whilst the porousmedia equations assume a homogeneous velocityprofile.Besides,thepressurelossesprovidedarepointmeasurementsandtheirvaluesareaffectedbytheexactpositionofthereadingwithineachtubebank’s inlet/outletplane(itmustbenotedthatthetubebanksareofconsiderablesize).

Inanycase,theerrorsareveryacceptable,giventheapplicationandtheabsolutepressurevalues,whichmeanthattheabsoluteerrorsareofveryfewPascals.RefiningtheCFDmeshmayhaveslightlyreducedtheerrors(ifthesensorreadingsareaccurateenough),butitwouldhaveincreasedthecomputationtimeconsiderably,soitwasnotdeemednecessary. Consequently, the CFD solver is considered reliable to use as anevaluatorfortheoptimizationprocesscarriedoutbyMOST-HDS13.

RESULTSFORTHESHAPEOPTIMIZATIONOFTHEINLETDUCTOFHRSGS

Overthedecades,HRSGinletductshavebeendesignedfollowinglargelythesamedesigntrendlines.Broadlyspeaking,thedesignofanHRSGinletducthasuptodatealwaysbeenofoneofthetwotypesshowninFigure6–2.

Figure6–2-HRSGinletductdesigntypesmostwidelyusedinindustry:singleangleinletduct(left)

anddoubleangleinletduct(right).

Certainmanufacturershavestartedusingalternative inletductdesigns,ascanbeseeninFigure6–3.However,extensivedesignanalyseshavenotbeenperformed,asfarasweknow,tocomparethedifferentinletductdesignsalternativesthoroughly.

13 Inanycase, iftheCFDerrorsweresystematic itwouldalsobevalidforanoptimizationprocess,

because the final optimum solutionswould be simulatedwith amuch higher detail. In any case it isusuallyverydifficulttoprovethatCFDerrorsaresystematicforaparticularproblem.


102

Figure6–3-HRSGinletductalternativedesigntypesthatsomemanufacturersarestartingtouse.

ThereareanumberofworksintheareaofCFDmodellingofanHRSG’sinletduct,but to our best knowledge, a complete shape optimization analysis of this criticalelement has never been addressed. The aim of these works is to analyze the flowdistributionof a particular design, or the effects of elements introduced in the inletducttoimprovetheflowdistribution,suchasAmeriandDorcheh(2013)andLeeetal.(2002).More general works in the field of CFD analyses of complete HRSGs can befound in Aslam Bhutta et al. (2012), Daiber (2006), Galindo-García et al. (2012 and2014),Hedgeetal.(2007),Shietal.(2009)andSundén(2007).

The aim of applying theMOST-HDS algorithm to the design of HRSGs is to yieldoptimizedgeometriesfortheinletductsofawiderangeofHRSGfamilies.Newdesignsordesign-trendsmayofferbetterperformancelevelsusingshorterandmorecompactunits, while having good velocity uniformity at the HRSG inlet. This is the maincontributionofthisThesis,regardingthisparticularindustrialproblem.

ItisworthnotingthatthisworkhasbeencarriedoutforvariousHRSGsfamiliesofaparticularmanufacturerandthereforesomeof theresultscannotbeshownfully forconfidentialityreasons.

TheinletductgeometryisparameterizedaswasexplainedinChapter4.Figure6–4isincludedhereagain,forthesakeofclarity.


103

Figure6–4-VariablesusedtoparameterizeageneralinletductfordifferentHRSGfamilies(x-axis

andy-axisviews).

Thevariablesusedareremindedhereagain:twoanglesforthetopwall,twoanglesforthelateralwall(identicalonbothlateralwalls),twomoreforthebottomwallandthe total lengthof the inletduct. These variables take into consideration thedesignmodificationswhicharefeasibleintermsofmanufacturingandassemblyinrealpowerplants.Forexample,curvedwallsormore intermediateanglesarenotconsideredofinterestandtheyareconsequentlynotincludedinthisanalysis.

The main concern of most HRSG manufacturers nowadays is to meet therequirements of the final client, and even improve them to be better than theircompetitors,while reducing theoverall costof theunit.Themain requirement foramodernHRSG iskeepingthepressuredropacross thewholeunitbelowamaximumallowedthreshold,whilerecoveringthemaximumheatavailablefromthegasstream.An additional and very important competitive advantage, as has been mentionedabove,isbeingabletomeettheperformancerequirementswithsmallerunits(mainlyreducingthetotallength).


104

TheapplicationoftheMOST-HDSalgorithmtothisparticularcaseofshapedesignoptimization has produced very interesting results. In the first place, to show theperformancedifferenceofvariousHRSGdesignalternatives,sothatitisclearthatitisworthapplyinganoptimizationscheme,twodifferentdesignsandtheirperformanceresultsaredepictedinthefollowingfigures.

Figure6–5-Sideandisometricviewsofafirstexampledesignalternativefortheinletductofan

HRSG(singleangletopplanefortheinletduct).ThisistherealcurrentdesignforthisHRSGfamily.

Figure6–6-SideandisometricviewsofasecondexamplealternativedesignfortheinletductofanHRSG(doubleangletopplanefortheinletduct).Thisisacommondesigntrendlinewhichhas

substituted,inmanycases,themoretraditionalsingleangleversion.

Thefirstdesignalternativewasusedfortherealpowerplant,intheparticularcaseofoneofthestudiedHRSGfamilies,and it iscurrently inoperation(singleangletopplane for the inlet duct). This is a more traditional design. The second designalternativehasadoubleangletopplanefortheinletduct,adesignfeaturethatmanymanufacturers introducedalreadyyearsago,because itsupposedlyhadan improvedperformance over the single angle design (it is also shown in this Thesis that thedoubleangledesignisnotalwaysbetterthanthesingleangledesign).


105

The performance results are shown in Figure 6–7 for both design alternatives.Performanceisexpressedintermsofpressuredropandvelocityuniformity,whicharethetwoattributesselectedbythemanufacturer,asexplainedinChapter4.

Thereisaconsiderableimprovementintermsofpressuredropwiththealternativedesign,soitisworthexploringmoredesignpointstohaveabetterviewofwheretheoptimum designs may be and if other more unconventional designs yieldimprovementsinperformance.

TheapplicationofMOST-HDShadaPhase0,ordesignexplorationphase,whichinthiscasehad120designpoints,toobtainawiderepresentationoftheinfinitespaceofsolutions.ForthepurposeofthisThesis,acustomDoEschemewasused,basedontheauthors’experience,butLatinHypercubeSampling(LHS)andothermethodswillalsobetestedinfuturework.

Of particular importance is the fact that thedesignpointsof Phase0need tobecheckedautomaticallytoavoidabsurdshapes(thisisdoneautomaticallybytheMOST-HDSalgorithm).

Once the exploration phase has been completed, MOST-HDS carries out theoptimization itself. The results of a one phase optimization for this particular HRSGfamily aredepicted in Figure6–7. This figure includes the comparison to the resultsobtainedusingapopularMulti-ObjectiveEvolutionaryAlgorithm(MOEA), inthiscaseNSGA-II,which is included in ANSYS optimizer as the best choice formulti-objectiveoptimizationbasedondirectsearch.TheNSGA-IIoptimizationwassetupsothatthenumber of direct evaluations would be equivalent to the one-phase optimizationcarriedoutwithMOST-HDS.

TheParetofrontshowsthefamilyofoptimumsolutions,takingintoaccountalltheattributes or objectives considered (in this case, total pressure drop across the inletductandvelocitynon-uniformityattheoutletplaneoftheinletduct).Allthesolutionson the Pareto front are equally optimum, since the absolute optimumwould be tohave pressure drops and velocity non-uniformities as close to zero as possible, andtherefore each of the solutions on the Pareto front are a potential optimumcombinationofpressuredropandvelocitynon-uniformity.


106

Figure6–7-ApplicationoftheMOST-HDSalgorithmtotheshapeoptimizationoftheinletductofa

firstfamilyofHRSGsforcombinedcyclepowerplants.TheresultsoftheapplicationoftheNSGA-IIevolutionaryalgorithmtothesameoptimizationproblemarealsoshown(purplediamonds).

Theresultsofthe120designpointsofPhase0(bluecircles)areshown,alongsidethe results of Phase I, which has analyzed 12 points (blue triangles). The tolerancethreshold (dotted line) was specified by the manufacturer. Two Pareto fronts areshown, as the lines joining the set of optimumdesigns after design exploration andaftertheone-phaseoptimization14.

Itcanbeobservedhowtheapplicationof theMOST-HDSalgorithmhasproducedanimprovementoftheperformanceresultofthisfamilyofHRSGs.Ifwecomparetheresults of MOST-HDS and NSGA-II, this latter performs well, but yields candidatedesignswhicharemorescattered,manyofwhichdonotmeettheconstraintofhavingavelocitynon-uniformitybelowthethresholdimposedinFigure6–7,theyaregloballyfurtherwayfromtheParetofront,andonlyoneofthecandidatedesignsimprovestheresultsofMOST-HDS.ThisparticularpointwouldveryprobablyhavebeenobtainedbyMOST-HDS if the tolerance region had been slightly expanded, to include morecandidate points of Phase 0. This emphasizes the importance of choosing anappropriatetoleranceregion.Inanycase,NSGA-IIisagoodoptimizationalgorithmfora wide variety of problems, but it is considered that MOST-HDS can be set-up toperform better for problems of aerodynamic shape optimization involving biggeometry changes. This is the main reason why the MOST-HDS algorithm wasdevelopedinthefirstplace.

14Forthisoptimization,132designpointswerecomputed,inan8-coreparallelcalculation,usinga

32GBRAMcomputer.Eachcalculationtookaround0.25-0.3hours.Thesizeofthemesheswasbetween1-2millionelements.


107

Regarding the specific optimization results ofMOST-HDS, it isworth commentingthat, althoughPhase0 selects thedesignpoints followingaprocedurewhich coverstheareaofthesearchregionthedesignerismostinterestedin,thisphaseinitselfisamere design exploration and not an optimization as such. Phase I is the first trueoptimizationphaseoftheMOST-HDSalgorithm.

Itmustbenoted, inanycase,thatthedesignexplorationprocedurebuilt intothemodeltocarryouttheanalysesforPhase0isalreadyquitegoodinmanycases,sincethedesignpointscalculatedyieldgoodperformanceresultsandcoverabroadareaofthespaceofattributes(orobjectives).HencePhase0isinitselfvaluableinthesensethat manufacturers have not performed such an extensive exploration of differentdesign points, inmost cases. It can be seen that the current design trend lines (i.e.usingasingleangledesignor,alternatively,believingadoubleangledesignisalwaysbetter) can be misleading or, at least, not optimum, and can be improved even inPhase0 (forthisparticular family).Someof thetypesofdesigns found inFigure6–7arerepresentedinFigure6–8,formoreclarity.

Moreover, unconventional and non-intuitive designs can prove to outperformtraditionaldesigns.Asanexampleofthis,Figure6–9toFigure6–12andTable6–2toTable 6–5 include the comparison between several representative design points,amongallthosesimulatedinFigure6–7.

Inthesefigures,itcanbeobservedthatdesignswhichareverysimilar(i.e.closeinthespaceofvariables)andwhichwould intuitivelybeveryclosealso inthespaceofattributes(i.e.haveaverysimilarperformance),mayreallybefarapartintheirresults,whereasquitedifferentdesignsmayperformverysimilarly.Itisworthhighlighting,inparticular, that double angle designs are not necessarily better than single angledesigns(forinstance,designpointsdandgareverycloseinperformance).Thismeansathoroughanalysisisrequiredineachcase,becausetraditionaldesigntrendlinesmaynotalwaysbethebestoption.

Furthermore,bothPhase0,asanexplorationphase,and,mostimportantly,PhaseI,mayyieldunconventionaldesignsordesignswithanon-intuitiveperformance(designpointsiand,especially,j).

AlltheresultsofFigure6–9toFigure6–12supporttheimportanceofapplyinganoptimizationmethodology, be itMOST-HDS or others, to the problem of inlet ductdesigninHRSGsforcombinedcycleplants.

Figure6–8-Exampledesignsobtainedfortheshapedesignoptimizationoftheinletductofvarious

HRSGfamilies.


108

Figure6–9-Sideviewofexampledesignpointswhichareverycloseinthespaceofvariablesandalso

verycloseinthespaceofattributes.

Designpoint Totalpressuredrop Velocitynon-uniformity

a 72% 146%

b 72% 145%

c 72% 145%

d 75% 139%

Table6–2-Comparisonbetweendifferentdesignpoints,toshowthatpointswhichareverycloseinthespaceofvariablescanalsobeverycloseinthespaceofattributes.Allresultsarewithrespecttothe

attributevaluesofthecurrentHRSGdesignofFigure6–7.

Figure6–10-Sideviewofexampledesignpointswhichareverycloseinthespaceofvariablesand

quiteapartinthespaceofattributes.


e 98% 89%

f 96% 102%

Table6–3-Comparisonbetweendifferentdesignpoints,toshowthatpointswhichareverycloseinthespaceofvariablescanalsobequiteapartinthespaceofattributes.Allresultsarewithrespecttothe



109

Figure6–11-Sideviewofexampledesignpointswhicharequiteapartinthespaceofvariablesand

verycloseinthespaceofattributes.


g 71% 139%

h 73% 141%

Table6–4-Comparisonbetweendifferentdesignpoints,toshowthatpointswhicharequiteapartinthespaceofvariablescanalsobeverycloseinthespaceofattributes.Allresultsarewithrespecttothe


Figure6–12-Sideviewofexampledesignpointswhicharequiteunconventional(becausetheyarequiteradicaldesigns)andsomewhatnon-intuitiveintheirperformance(especiallydesignpointj).


i 64% 146%

j 60% 159%

Table6–5-Comparisonbetweenexampledesignpoints,whicharequiteunconventionalandsomewhatnon-intuitiveintheirperformance.Allresultsarewithrespecttotheattributevaluesofthe

currentHRSGdesignofFigure6–7.


110

InPhaseI,ascanbeobserved,thedesignpointsimprovetheperformanceresultsofthedesignpointsstudiedinPhase0.Additionally,itcanbeseenhowtheapplicationof MOST-HDS improves the Pareto front obtained in Phase 0 and hence theperformance results of the optimumdesign points. The geometries of the optimumdesignsobtainedare,ashasbeenshownforsomesolutions,quiteunconventionalandnon-intuitive(Figure6–12).AllthishasallowedthemanufacturertohaveanewsetofdesignguidelinesforitsdifferentHRSGfamiliesforthecomingyears.

Besides, the fact that themanufacturer has received Pareto fronts similar to thisoneshown,foreachofhismainHRSGfamilies,allowsforawell-baseddesigntrade-offbetweentotalpressureandvelocitynon-uniformityineachcase.ForaparticulartypeofHRSG,designpointswith lowertotalpressuredropmaybepreferred,evenattheexpenseofahighernon-uniformity(orviceversa).Theexactgeometriesobtainedforthe optimum design points cannot be included in this document for confidentialityreasons.

To have a better insight into the true potential of MOST-HDS for shape designoptimizationinvolvingbiggeometrychanges,intheparticularcaseofinletductdesignfor HRSGs, the algorithm has been applied to a different HRSG family, and veryinterestingresultscanbeobservedinthefollowingfigure.

Figure6–13-ApplicationoftheMOST-HDSalgorithmtotheshapeoptimizationoftheinletductofa

secondfamilyofHRSGsforcombinedcyclepowerplants.Incrementfactors(asexplainedinChapter5)belowunity(candidatepointsmarkedwithtriangles)andaboveunity(candidatepointsmarkedwith

diamonds).

Phase0ofMOST-HDShasanalyzed120designpointsandPhaseIhasanalyzed10points. The tolerance threshold (dashed line)was specified by themanufacturer, toanalyze an area of design points with comparable pressure drops and velocityuniformitiestothecurrentdesign.


111

Inparticular,forthiscase,thedesignexplorationcarriedoutinPhase0(candidatepointsmarkedwithcircles)coversabroadareaofthesearchregion,butyettherealexisting design, already built and in operation for this particular HRSG family,dominates all the other candidates, i.e. it has better values for both attributes. Thismeansthatameredesignexplorationcanbeinadequateornotgoodenoughinsomecases. OnceMOST-HDS computes the points for Phase I, the simulations show thatPhase I candidatepoints improveconsiderably,notonlyoverpoints inPhase0,but,mostimportantly,withrespecttotherealcurrentdesignofthisHRSG.

ForthissecondexampleHRSGfamily,anadditional testhasbeenperformed.ThevariableincrementfactorsusedtoobtainnewcandidatedesignpointsforPhaseIfromthecrossoveroftheirparentsofPhase0aretuned.Inparticular,twosetsofvaluesareused. The first set (candidate points marked with triangles) has variable incrementvalues below unity, which means that the crossover of the parent solutions liesbetween both parents (in the space of variables). The second set (candidate pointsmarkedwithdiamonds)hasvariableincrementvaluesaboveunity,whichmeansthatthe crossover of the parent solutions lies beyond the parent point belonging to theParetofront(itisalwayscheckedthatthenewvariablevaluesliewithinthatvariable’svaluerange,asdefinedbythedesigner).

For this case, the use of increment factors above unity yields better results, ingeneral.However,thebestcandidatepointintermsoftotalpressuredropisobtainedwithanincrementfactorbelowunity.HencethebottomlineisthatbothsetsofvaluesshouldbeexploitedbyMOST-HDS(asexplainedindetailinChapter5)tohaveahigherprobabilityof reachingoptimumdesigns.Thismeansperformingsearcheswithin thedesignpointsalreadyevaluatedandbeyondthesepoints(inthespaceofvariables).

CONCLUSIONS ON THE RESULTS FOR THE SHAPE OPTIMIZATION OF THE INLET DUCT OFHRSGS

ThissectionhasappliedtheMOST-HDSalgorithmtotheproblemofinletductshapedesign optimization of HRSGs used in combined cycle power plants. The mainconclusionsdrawnfromthiswork,aswellasanoutlineoffutureresearchlines,canbesummarizedinthefollowingpoints:

1. The interest of applying anoptimizationmethodology, be itMOST-HDSoranyother,totheshapedesignoptimizationoftheinletductofHRSGs,hasbeenshowntobeveryvaluable.Theperformanceresultsofdifferent inletductdesignsmaynotbe intuitive inmanycasesandcanvaryconsiderablyamongdifferentdesigns.Exampleshavebeenshownofdesignpointswhichare very similar and yet yield different results, or different designs whichhaveaverysimilarperformance.

2. Inparticular, exampleshavebeenpresentedof single angledesignswhichare very similar in performance to double angle designs, so the currentdesign trend line some manufacturers follow of necessarily preferringdoubleangledesignsmaybemisleadinginsomecases.


112

3. Adesignexplorationphase(i.e.simulatingaconsiderablenumberofdesignpoints, based on the engineer’s experience, butwith no real optimizationbehind)canalreadyimprovetheresultsofcurrentdesigns.However,thisisnotthecaseforsomeHRSGfamilies,ashasbeenshownwiththeresultsofthesecondHRSGfamily.Therefore,thebestrecommendationistoapplyatrueoptimizationalgorithmfortheshapedesignofinletducts.

4. Improvementsinpressuredropofupto40%andinvelocityuniformityofupto 15% have been achieved, when applying MOST-HDS to two differentHRSG families. Given that both improvements cannot be reached at thesametime,optimumtrade-offdesignpointswithpressuredropreductionsof20-25%andcomparablevelocityuniformitytotheexistingdesignscanbeobtained.

5. Moreover, although pressure drop and velocity uniformity were theattributesdefinedbythemanufacturer,thetotallengthoftheinletductanditslateralsurfacewerealsocalculatedforthedifferentdesignpoints.Thesetwo are also important variables due to their strong impact on costreduction, because of material cost, and the importance of having morecompact(i.e.shorter)inletductdesigns.Improvementsinlateralsurfaceofupto53%and intotal inletduct lengthofupto48%havebeenachieved.Given that both improvements cannot be reached at the same time,optimumtrade-offdesignpointswithlateralsurfacereductionsof38%andlength reductions of 16% can be obtained, for the two HRSG familiespresented.

6. Takingintoaccounttheconsiderableperformanceimprovementsachieved,theapplicabilityofMOST-HDStootherfieldsdifferenttothatpresentedinPrada-Nogueiraetal.(2015and2017)hasbeenshown.Futureresearchwillbe focused on generalizing the applicability analyses of MOST-HDS as anoptimizationalgorithmforevenmorefieldsandapplications,suchasthosedescribedinPaniagua(2014)orZamorano-Reyetal.(2015).

7. Unconventional designs have been obtained, thanks to the application ofMOST-HDS.

8. Forfuturework,otherDesignofExperiments(DoE)techniques,suchasLatinHypercube Sampling (LHS), will be used for the design exploration phase;more HRSG families will be analyzed; and a general set of simple andpractical design guidelines for each HRSG family will be developed, toimprovecurrentdesigntrendlines.


113

To finish thesectionon the resultsof theapplicationofMOST-HDS toHRSG inletductoptimization,itisimportanttonotethatresultsofsurrogatebasedoptimization(usingresponsesurfaces),alsoforthisexamplecase,willbepresentedinChapter7.Aspecific chapter has been devoted to the comparison between MOST-HDS andsurrogatemodels, given their extended use, for the particular field of aerodynamicshapeoptimizationwithbiggeometrychanges.

6.3.ClosedwindtunnelshapedesignoptimizationThe second industrial case presented in this Thesis is the aerodynamic shape

optimization of closed wind tunnels. These facilities are used quite extensively fortesting purposes in many different fields and also for leisure activities (indoorskydiving),aswasshowninChapter4.Itisaverygeneralexampleoftheoptimizationof complex aerodynamic bodies, to show the applicability of MOST-HDS to verydifferentgeometries.

The level of complexity is far bigger than for theHRSG case presented above, interms of the number of variables and parameters required to representmost windtunnelgeometries(108variablesforthewindtunnelcaseversus7fortheHRSGcase).ThismakestheuseofmanycommercialCFDoptimizerpackagesimpossible,sincetheyare limited to 10 independent variables.Hence, for this case, an external optimizer,with theoptimizationalgorithm selectedby theuser,mustbeplugged into theCFDsolverinanycase.

Duetothiscomplexity,thecaseofasimplifiedwind-tunnelmodelwillbepresentedfirst (so that the results are better understood), and then the optimization of a fullwindtunnelmodelwillbeanalyzed.

VALIDATIONCASEFORTHEANSYSCFDSOLVERFORWINDTUNNELSIMULATIONS

Inthefirstplace,aswasalsodonefortheHRSGcase,abriefsectionispresentedonthevalidationoftheresultsoftheCFDsolverused(ANSYSv17.0)fortheevaluationofwindtunnels.

Twovalidationcaseswillbepresented;first,thepressurelossvalidationforasmallprototypewind tunnelused for testing; and secondly, thepressure lossandvelocitydistributionvalidationfora full-sizeverticalwindtunnel for indoorskydiving,built inLas Rozas deMadrid (Madrid Fly,www.madridfly.com). Both tunnelswere designedwith a very early version of the MOST-HDS algorithm, still not fully flexible orautomated.

Figure 6–14 and Figure 6–15 show the real prototype wind tunnel built and thegeneraldrawingofthishorizontalclosedwindtunnel.


114

Figure6–14–PrototypewindtunnelfortestingpurposespresentedtovalidatetheCFDsolverused.

Figure6–15-PrototypewindtunnelfortestingpurposespresentedtovalidatetheCFDsolverused

(generaldrawing,nottoscale).

Figure6–16illustratestheCFDsimulationofthenominalperformancepointforthewindtunnel,comparedtothemeasuredperformancetestoftherealfaninacertifiedtest rig. The pressure and flow deviation of the CFD solver versus the measuredperformancevalueswasbetween5-8%fordifferentsimulationsettings.


115

Figure6–16-Measuredperformancecurve(pressuredropv.airflow)forthefanoftheprototype

windtunnel,showingthemeasurednominalperformancepoint(orange)andthesimulatednominalperformancepoint(blue).

Regarding the full size verticalwind tunnelbuilt for indoor skydiving, Figure6–17depictsthefacilityandthetest/flightsection,alongsideapictureofthetypicalflightofafirsttimerwithinstructor.Theinletplanetothetestorflightsection,whichwillbethereferenceplaneforthevelocityindexreadingsshown,isalsoindicatedinFigure6–17 for clarity. Figure 6–18 shows the distribution of the points where the velocitysensor(Pitottube)wasplacedforthemeasurements(correctionsduetoairpropertiesduring the testswere accounted for) and Table 6–6presents the comparisonof themeasured versus the simulated results. Once again the accuracy of the ANSYS CFDsolver is considered very high and adequate to carry out the evaluations for theoptimizationprocess.

Figure6–17-Verticalwindtunnelforindoorskydiving(MadridFly,www.madridfly.com).Theinlet

planetothetestorflightsectionisshown(dashedredline).


116

Figure6–18-Distributionofpointsforvelocitymeasurementsintheinletplaneofthewindtunnel

testorflightsection(measurementswerecarriedoutwithaPitottube).

Measuringpoint

Fanpower[%] Velocitydeviationwithrespecttoaverage[%]

MEASURED

Velocitydeviationwithrespecttoaverage[%]

SIMULATED

#1 100% -0,3% -0,8%

#2 100% -1,2% -1,5%

#3 100% 0,2% 0,1%

#4 100% 0,4% 0,8%

#5 100% 0,4% 0,2%

#6 100% -0,1% 0,3%

#7 100% 1,0% 1,4%

#8 100% 0,0% 0,2%

#9 100% -0,7% -0,5%

Table6–6-Velocitydeviationwithrespecttotheaveragefor9relevantpoints(amongthoseshowninFigure6–18)intheinletplanetothetestorflightsectionofaverticalwindtunnel.Measuredv.CFD

simulatedresults.

RESULTSFORTHESHAPEOPTIMIZATIONOFCLOSEDWINDTUNNELS

Thissectionwillbedividedintotwoparts:inthefirstpartasimplifiedwindtunnelmodelwill be presented, to understand better how theMOST-HDS algorithmworksand the importance of certain features of the optimization; in the second part, anexampleoptimizationforafullwindtunnelmodelispresentedandanalyzed.

SimplifiedwindtunnelmodelThe simplifiedwind tunnelmodel, alreadypresented inChapter4, is represented

onceagaininFigure4–9.


117

Figure6–19-Lowdetailrepresentationofawindtunneldesign,usedtoillustratebettercertain

aspectsoftheoptimizationmethodologypresentedinthissection.FourBéziercurvesareusedonly.Fanandtestsectionsarebothshadedinthisfigure(left).Anexampleplanecontainingoneofthetransverse

sectionsusedforthetunnelgeometrydiscretizationisalsoshown(right).

ThefirststepistoobtaintheinitialsetofpointsforPhase0.Inthiscase,basedonourexperience,adesign tree is configuredwithall thepossiblecombinationsof thevaluesof a reducednumberof selected variables. The rest are left constant for thissimplifiedexample.Consequently,thetreeforPhase0willexploretheextremevaluesofeachvariable’srange.ThetreeofdesignpointsforPhase0isshowninFigure6–20.Itsetstwovaluesforeachofthevariables,takingintoaccounttheirhierarchy(exceptfor the low importance variable number of fans, which is considered constant andequalto1,inordertolimitthenumberofdesignpointsanalysed,andbecauseitdoesnotaddvaluetotheexplanation).

Figure6–20-ExampletreeofdesignpointcombinationsforPhase0optimizationofthesimplified

windtunnelmodel.32windtunneldesignsareconsidered.

Thevariablesusedforthesimplifiedcasestudypresentedare:

1. Relativepositionoffanandtestsections

2. Fandiameter

3. Geometryofthetestsection

4. Profileforduct1(i.e.Béziercurvesforduct1)

5. Shapeofsectionsinduct1


118

Aminimumandmaximumvalue isset for therelativepositionof the fanandthetestsectionandforthefandiameter.Thesevaluesarederivedfromtheuser’s inputon the required flow, the designer’s estimation for the pressure drop and the fanmanufacturer’srecommendation.

Forthegeometryofthetestsectiontherearethreetypicaloptions:circular,squareand rectangular. Other shapes can be analyzedwith theMOST-HDSmodel, such asflat-ovalorpolygonal,as it isstraightforwardtoaddtheseoptionstothemodel.Forthissimplifiedexample,onlycircularandsquaretestsectionswereconsidered.

In terms of ducts 1 and 2, it is very important to highlight that we proposedecoupling both optimizations when needed, i.e. the presented methodology willoptimizeducts1and2independentlyandthencombinethebestduct1withthebestduct2,forthosephasesinwhichthisspeedsupthewholeprocess.

Thiscanbedonebecause, for the flowquality required inamodernwindtunnel,theflowdistributionattheinletofthetestsectionmustbeveryuniform(thelevelofuniformityisdeterminedbythevelocityindexspecifiedbytheuser,butitisbelow2-3%fortypicalcommercialapplications).Thismeansthattheflowattheoutletofthetestsectionwillbeverysimilarforanyduct2whichisgoodenoughtobeconsideredapossible final design. Consequently, the optimization of duct 1 can be assumedindependent to the optimization of duct 2. Besides, at the fan inlet the flowof anygoodcandidate tobe the finalduct1willbe reasonablycomparableand,given thatthefanincreasestheflowuniformity,atitsoutlettheflowwillbeevenmoresimilar,formost duct 1 designs. This simplifies the optimization because it breaks thewindtunnelmodelintotwohalfmodelswhichcanbesimulatedmorerapidlyorwithfinermeshes.

Forthisexample,duct2isleftconstantandtwopossibleBéziercurvesareusedforduct1:onenearlycircularandoneskewed.

Finally,forthetransverseshapeofducts1and2,therearereallyonlytwooptions:circular or square/rectangular. Square and rectangular are not really two differentoptionsbecause the search region canbe simplified forcing thealgorithm to chooseonlyoneofthetwotocomparewithacirculardesign,dependingontheshapeofthetestsection(ifcircularorsquare,theonlytransverseshapesusedwillbecircularandsquare and if rectangular then the algorithm will compare circular and rectangulartransverseshapes).Onceagain,themodelallowsthissimplificationtobeeliminatedifconsidered necessary for a particular application. In the example of this Thesis,however,onlycircularandsquareshapesareconsideredanyway.

Theattributesselectedtocomparedifferentwindtunneldesignsare:a)fixedcost(which includes materials, manufacturing and assembly), and b) mass-weightedaveragetotalpressuredropfrominlettooutletofthewholewindtunnelcircuit.Totalpressuredropisawayofrepresentingmostoftheoperatingcost,sotheresultsareinessencefiguresoffixedcostversusoperatingcost.

TheresultsoftheCFDevaluationofthese32designpointsispresentedinFigure6–21andtheirattributevaluesaregroupedinFigure6–22,whichalsoshowstheParetofrontforPhase0.


119

Figure6–21-CFDevaluationresults(velocitycontourplotsformid-plane,totalpressuredrop–delta

p–andfixedcost)foreachofthe32windtunneldesignpointsforthesimplifiedwindtunnelmodel.


120

Figure6–22-Paretofront(redline)offixedcostv.totalpressuredropfor32windtunneldesign

pointsforthesimplifiedwindtunnelmodel.Tolerancethreshold(orangeline)toselectareaofsearchregionwherepotentialcandidatestooptimummaylie,forsubsequentoptimizationphases(valuesof

bothattributesareperunit).Maximumattributerangesareshownin%.

Asanexampleofhowthealgorithmperforms,letustakemodels3,9,10and12.Theyallliewithinthetolerancethreshold,sotheywouldbepotentialcandidatestoberetainedforPhaseI.Theywouldallmovetowardsmodel11.Model3isrelativelycloseinthespaceofattributes(lesssoincostthaninpressuredrop),butfurtherawayinthespaceofvariables,soitwouldbekeptforPhaseI.Amongmodels9,10and12,whichare close both in the space of variables and attributes, a representative must bechosen.Thisiswhenclusteringwouldbeused.

For example, if we focus on model 3, and its movement towards point 11 (thismovementisinfactalongtheParetofront),theonlydifferencebetweenbothdesignpointsisthefandiameter,sothisistheonlyvariablewhichwouldbechanged,forthisparticular case. Itwould be changed for design point 3 taking into account that theoptimization is calculating Phase I and that the fan diameter is a high importancevariable.

Inthisexample,18modelswouldberetained,crossedoverwiththeirtargetdesignpointson thePareto frontandCFDsimulated forPhase I. The resultsofa completeoptimizationareshownforthefullwindtunnelmodelinthenextsection.

VariablecorrelationandsensitivityanalysisAtthisstage,itisinterestingtoanalyzeabitfurtherthetrueindependencyofthe

selectedvariablesand,mostimportantly,theirimpactontheresults,sincethisisthekind of analyses that MOST-HDS performs internally. This analysis is easier tounderstandforthesimplifiedwindtunnelmodel.


121

Theoptimizationmethodologypresented inthisThesisperformsasmartersearchthankstotheselectionandhierarchyoftheindependentvariables.First,itisrelevantto check if they are truly independent and cover every relevant degree of freedom.Second, independent variables with a strong impact on the attributes should bevariablesofhigherhierarchy,whereas thosewithaweak impact shouldbe in lowerhierarchies. The process of mapping the variables and the various hierarchies ascorrectly as possible will allow for an efficient breakdown of the problem intooptimizationphases.

Inthissectionindependenceandhierarchywillbediscussedbasedontheexamplecase study here presented, but indicating how the complete full optimizationarchitecturecarriesoutthesetasksautomatically.

Regardingindependency,itisquiteclearinthisexamplethatanyofthesevariablescanbemodifiedwithoutaffecting thevaluesof theothers, so theyare independentvariables. As commented, this independency check is not as simple in complexaerodynamicproblemsandamorerigorousanalysisisrequired.CommercialpackagessuchasANSYSoffertoolstocarryoutcompletemulti-variablecorrelationanalyses.

Theimportantissuewhichisverywellillustratedbythesimplifiedexamplecaseisthe sensitivity of the two attributes chosen – fixed cost and pressure drop – withrespecttothevariablesused.Letuscommentthisinmoredetail(refertoFigure6–21andFigure6–22).

Firstly, the relative position of the fan and the test section divides the 32 windtunnel designs into two blocks of 16 models. The first 16 models have a relativeposition of 90°,whereasmodels 17-32 have a relative position of 180°. In terms ofcost,both relativepositionshavequiteawide rangeof values.With90° the span isslightlysmaller,from0.92to1withrespectto0.88to1for180°.Concerningpressuredrop, only 3 of the models with 90° of relative position have high pressure drops(above0.7).Allothermodelsyieldvaluesbelow0.32.Inthecaseof180°,thevaluesofpressurelossaremuchmorescattered.Thisshowshowthebehavioroftheattributes,especiallypressuredrop,isstronglyaffectedbytherelativepositionofthefanandthetestsection.Thereforethisvariableisofahighimportance.

Secondly,letusinspecttheimportanceoffandiameter.Bothformodelswitha90°ora180°relativeposition(thisshowstheindependencyoffandiameterandrelativeposition),thosemodelswithsmallerdiameterhavealowerfixedcost(models1-8and17-24) thanmodelswith abiggerdiameter (models 9-16 and25-32). Ifwe focusonpressure drop, one has to comparemodelswith the same value for the rest of thevariables and only different fan diameter. Thus, comparing models 1-4 with 9-12,models5-8with13-16,models17-20with25-28and21-24with29-32,itcanbeseenthat, inmostcases (especially for90°),pressuredrop isalways lower for thesmallerdiametermodels.This,however,isnotalwaysthecase,anditisimportanttohighlightmodels such asmodel 16. Thismodel is surprisingly low in terms of pressure drop,eventhoughithasabiggerdiameter.However,itsfixedcostisthehighest.Thisshowshowunconventionalornon-expecteddesigns,whichintuitivelywouldnotbechosen,canyieldoptimumdesigns(inoneormanyattributes).

Fandiameter isconsequentlyahigh importancevariable,dueto itsstrong impactontheattributevalues.


122

Regardingthenextvariable,thegeometryofthetestsection,thebestwaytocheckitsimpactiscomparingmodels1and5,2and6andsoon.Itsimpactislowintermsoffixedcostand,forcirculartestsectionsthepressuredropisgenerallysmaller,exceptforparticularcasessuchas,onceagain,model16.Formodel16,asquaretestsectioncanoffsetcirculartestsections,whichintuitivelyhavelowerpressuredrops(andthisisgenerallytrue),ifthesquaretestsectioniscoupledwithasquareduct1,asisthecaseinmodel16.ThismodeliseffectivelyveryclosetotheParetofront(Figure6–22)soitcould be a candidate for optimum (if its design is fine-tuned in further optimizationphasestoreduceitscost).

Onceagain,thegeometryofthetestsectionhasastrongimpactonthefinalvaluesof the attributes, mainly on the pressure drop (for instance, this can be seencomparingmodels 9 and 13, 27 and 31, etc.). Consequently, it is a variable of highimportance.

Thenexttwovariables,profileofduct1andshapeofthesectionsofduct1,aresetasmedium importancevariables. Letus check if this is correct,basedon the resultsobtained for this case study. It canbe seen that theprofile shapeaffectsnoticeablywhencomparingmodels5and7,14and16,21and23,25and27and26and28.Theshapeofthesectionsalongtheprofileaffectssubstantiallyinmostmodels.Formodels1-16, i.e. formodelswith90° relativepositionof the fanand the test section, thosedesignswithcirculartestsectionandcirculartransverseshapeinduct1orsquaretestsectionandsquaretransverseshapehave lowerpressuredrops,asexpected,duetothesmoothertransition.However,thistrendismaintainedfor180°modelsinthecaseof square test section and square transverse shape, but not for the case of designswith circular test section, in which the trend inverts. In models with a circular testsection, the pressure drop is lowerwhen duct 1 is a square duct. This is quite eye-catching and shows the importance of using intelligent, robust and automaticoptimizationtoolstofindoptimumdesigns,whichwouldprobablynotbefoundwhenusingtrialanderrorormanualoptimization.Itdoesnotimplythatthereisnodesignwithcirculartestsectionandcirculartransverseshape induct1whichcanbebetterthan designs with a square duct 1, but is does illustrate that considering non-conventionalornon-intuitivedesignscanbeveryfruitful.

Withrespecttocost,theimpactofthesetwolastvariables,profileandtransverseshape,islower,especiallyinthecaseof90°designs.

It canbe concluded that the last twovariables considered,profile and transverseshapeofduct1,arevariableswithaminorinfluenceonthefixedcostandmostlyonthepressuredrop.Thisinfluenceis,inanycase,notasstrongasthatofthepreviouslycommentedvariables.Therefore,thesetwoaremediumimportancevariables.

Thissectionhas illustratedtheconceptofvariablehierarchyand ithasshownthedifferentimpactavariableofhighormediumimportancehasontheselecteddesignattributesusedtocomparedifferentsolutions.Thishasbeenanalyzedforasimplifiedcase study, but themain conclusions are applicable to real,more complex systems,suchastheonepresentedinthefollowingsection.


123

FullwindtunnelmodelThe full wind tunnelmodel, already presented in Chapter 4, is represented once

againinFigure4–9.

Figure6–23-Highlydetailedrepresentationofageneralizedwindtunneldesign,abletorepresent

mosttunnelgeometries(18-20Béziercurvesareneeded).

Thedesignpoints forPhase0aredeterminedfollowingthesameapproachas forthesimplifiedmodel(Figure6–20).

The results of a full 2-phase optimization are shown in Figure 6–24 (theoptimizationislimitedto2phasesbecauseofcomputationtime15).TheimprovementoftheParetofrontthroughouttheoptimizationprocessandthesolutionsofPhases0,I and II canbeobserved. Thewidevarietyofdesign types, somemore conventionalandsomemoreunconventional,isquiteeye-catchingandisclearlyseeninthisfigure.This is oneof the relevant contributions ofMOST-HDS, i.e. being able to handle biggeometrychangesinshapedesignandproducingdisruptiveorcreativedesignpoints.

15For thisoptimization,57designpointswerecomputed, inan8-coreparallel calculation,usinga

32GBRAMcomputer.Eachcalculationtookaround0.75-1hours.Thesizeofthemesheswasbetween2-5millionelements.


124

Figure6–24-Resultsobtainedforafullwindtunnel2-phasedesignoptimizationperformedwiththeMOST-HDSalgorithm.PressuredropisinPascalsandthefixedcostisinfictitiousmonetaryunits.

AswasanalysedfortheHRSGcase,theintelligenceembeddedintoMOST-HDSwillautomaticallytunetheoptimizationtoproceedmoreefficiently,forexampleintermsof the increment factors. Figure 6–25 shows the impact of using increment factorsbelow and above unity for Phase II of this optimization. MOST-HDS automaticallyselectsthebestvaluesfortheincrementfactors,basedontheresultsofthedifferentCFDevaluations.

Figure6–25-Resultsobtainedforafullwindtunnel2-phasedesignoptimizationperformedwiththe

MOST-HDSalgorithm,comparingtheuseofdifferentincrementfactorsforPhaseII:belowunity(lightgreensquares)andaboveunity(darkgreendiamonds).PressuredropisinPascalsandthefixedcostisin

fictitiousmonetaryunits.


125

Let us analyze these results inmore detail, to illustrate important aspects of theshapedesignoptimizationprocessesincaseswithbiggeometrychanges.Ifwetakeacloser look at what is happening with the different design points, from Phase 0 toPhaseII,itisquiteinterestingtonotethatthesearchisadvancinginparticularareasofthe search region (in the space of variables) and certain other areas of the searchregionareabandoned.Ifweanalyzeoncemoretheinitialtreeofdesignpoints,Figure6–26showstheregionswhichgraduallydisappearasthesearchmovesforward.

Figure6–26-ExampletreeofdesignpointcombinationsforPhase0optimizationofthefullwind

tunnelmodel.32windtunneldesignsareconsidered.Theareasofthesearchregionwhichdisappearastheoptimizationproceedsareindicated.

InPhase0allbranchesofthetreearerepresented.InPhaseI,inall12designpointsobtained, the bigger diameter has disappeared. Furthermore, for the 180° relativepositionof fanandtestsection, thecircular testsectiondisappears,whereas for90°andforthenewpositionvaluewhichappearsinPhaseI(120°),therearestillcircularand square test sections. Finally, for Phase II, not only the circular test sectionscontinuetograduallydisappear,butalsothe90°designpoints.Outofthe8modelsofPhase II (with increment factorsbelowunity),only2keepacircular testsectionandonly 2 are 90° design points. 5 out of the 8 models have unconventional relativepositionsof fanand test section (120°and150°) so it canbe said thatonly3of themodelsinthisPhaseareofatraditionaltype.

These are already important conclusions and being able to study them as theoptimizationisongoingwillallowthedesignertotakedecisionsonhowtoproceedforfuture optimizations or phases of this same optimization. The comments made areonlyanexampleofalltheconclusionswhichcanbedrawnfromanoptimizationstudyofthiskind.

To concludewith this section, Figure 6–27 and Figure 6–28 represent the designfamilytypespresentthroughouttheoptimization,toshowinaveryillustrativemannerhowtheMOST-HDSmodelcanreallyhandlebiggeometrygeometrychanges.

Asaveryimportantparametertoassessthequalityofawindtunnelisthevelocityindex inthetestsection(which isameasureof thevelocityprofileuniformity),bothfiguresincludea2Dviewofthevelocitycontourplotsattheinlettoeachtunnel’stestsection.


126

Thevelocityindexinthetestsectionofthesimulateddesignpoints(bothforFigure6–27 and Figure 6–28) ranges between 5-7%. Without any means to improve flowuniformityandreduceturbulencelevelsatthisstageinsidethetunnel(honeycombsorscreens)thesearereasonablevelocityindexesforthisphaseoftheoptimization.

Figure 6–28 shows a very important result which puts forward the need foroptimizationschemeswhichcanhandlebiggeometrychangesformanyapplicationsinthe field of aerodynamic shape design. The Type III family of intermediate angles(which has either a 120° or a 150° relative position between the fan and the testsection)isoneoftheoptimumdesigntypesattheendofthefinaloptimizationanditwould probably have never been tried out manually by most expert designers.Therefore MOST-HDS is capable of finding unconventional designs with betterperformancethanothermoretraditionaldesigns.

Figure6–27-WindtunnelmodelfamiliesontheParetofrontforPhase0andtheirvelocitycontours

inthetunneltestsection(transverseplane).TheParetofrontforthisphasehas5designpoints,2oftypeIand3oftypeII.

Figure6–28-NewwindtunnelmodelfamilyontheParetofrontierforPhaseIanditsvelocitycontour

inthetunneltestsection.TheParetofrontforthisphasehas5designpoints,1oftypeI,3oftypeIIand1,quiteunconventionaldesign,oftypeIII.


127

CONCLUSIONSONTHERESULTSFORTHESHAPEOPTIMIZATIONOFCLOSEDWINDTUNNELS

Themainconclusionsdrawn fromthis sectiononclosedwind tunnels,alongwiththefutureresearchlines,are:

1. The MOST-HDS methodology is applicable to the design optimization ofmany kinds of complex aerodynamic bodies: vehicles, high-speed trains,aircraft,etc.ThishasbeenshownforthecaseofHRSGsand,inthissection,forthecaseofclosedwindtunnels.

2. The results obtained for a full wind tunnel 2-phase design optimizationproblemperformedwiththeMOST-HDSalgorithmhavebeenpresentedasareal industrial case study. It can clearly be seen how the design points ofPhaseIimprovetheresultsobtainedforPhase0.Furthermore,someofthedesigns which yield optimum results are substantially unconventionalsolutionswhichthedesignerwouldprobablyneverhavetriedbyhimself.

3. The importance and interest of the conceptsof hierarchyof variables andoptimization phases is shown. Thanks to these two concepts, manyproblems of aerodynamic optimization can be tackled using direct search,because the solutions computed with the CFD tool are very efficientlyselectedandtheyrepresenttherichnessofthewholesearchregion,bothinthespaceofvariablesandinthespaceofattributes.

4. Variable correlation and, most importantly, sensitivity analyses werepresented conceptually, showing how the algorithm proceeds. Thiscontributes to show the importance of identifying an efficient set of trulyindependentvariablesandofrankingthemaccordingtotheirhierarchies,totackletheoptimizationindescendingorderofvariableimportance.

5. Particularinterestisbeinggiven,incurrentresearch,totheaccelerationofthewholeprocedure,tobeabletoevaluateevenmorecandidatesolutions.Thismeans tackling concepts such asmeshmorphing andexploiting themforthefinalphasesoftheoptimization,whengeometrychangesarenotasconsiderable.ThemethodalreadymakesextensiveuseofthegeometryandmeshparameterizationcapabilitiesofcommercialCFDsoftware.

6. In future work, regarding wind tunnel design, fan systems using either asmallernumberoffansofbiggerdiameterorahighernumberofsmallfanswillbeanalyzedandcompared,becausebothoptionsarefoundintheStateof the Art, and it is very worth comparing both design trends morethoroughly.Theworkpresented inthisThesishasonlybeenperformedonsinglefanwindtunnelexamples.


128

7. Otheraspectswhichwillbecoveredinmoredetail infutureresearchworkare: mesh sensitivity analyses, and algorithm intelligence to select anefficientmesh coarseness for each optimization phase; an enhanced fine-tuning of the setup parameters in themodel (tolerance threshold values,etc.) to ensure the optimization process is more robust and efficient (forexampleyieldingsimilarrelativeerrorlevelsforeveryphase).

6.4.Useoftheadjointmethodforfinalfine-tuning.The use of the adjointmethod has become very popular inmany fields of shape

optimization.Averygoodexampleof itsapplicationtoaerodynamicshapedesign, inparticularforthenoseofhigh-speedtrains,canbefoundinPaniagua(2014).

Theadjointmethodanalyzesthesensitivityofeachoftheattributesdefinedtolocalvariationsofthegeometry.CommercialCFDsolverssuchasANSYSincludethisfeatureand allow for the computation of these sensitivities for a given body. A generalexampleofthegeometrychangescalculatedforageneralU-bendexampleisshowninFigure6–29toillustratehowtheadjointmethodworks.

Figure6–29-Exampleapplicationoftheadjointmethodforthelocalfine-tuningofaU-bend.

CommercialCFDsolversallowtheusertosetatargetforthedesiredimprovementof aparticularobjective (ormore thanone) and theadjointmethodwillmodify thegeometry(andtheunderlyingmesh)toreachthatimprovement(ifpossible)basedonthecalculatedsensitivities.


129

Theadjointmethod,which isaderivative-basedmethod, isan interestingtool forthelocalfine-tuningoftheoptimumcandidatepointsobtainedinthelastphaseofanoptimization. The MOST-HDS model makes use of the adjoint method wheneverapplicable to a particular case of shapedesign optimization. In the following figurestheresultsoftheadjointapplicationtooptimumdesignpointsarepresented,bothfortheHRSGinletductandfortheclosedwindtunnelcases.Inbothexamplesthetargethasbeen to reduce thepressuredropby10%.The resultsonce thenewgeometrieswererunintheCFDsolverprovethatthe10%reductionwasachievedinbothcases.The figures show the region selected for the fine-tuning and the results for the so-called Normal Optimal Displacement, which is the deformation the solver wouldintroduce to the geometry to achieve the target improvement set by the user (redregions indicatemaximumpositivedeformationsandblueregions indicatemaximumnegativedeformations).

Figure6–30-Exampleapplicationoftheadjointmethodforthelocalfine-tuningofoneofthe

optimumdesignpointsobtainedinthelastphaseoftheoptimizationprocessfortheHRSGcase.TheregiontobeoptimizedisshownalongsidetwoviewsoftheresultsoftheNormalOptimalDisplacement.

Figure6–31-Exampleapplicationoftheadjointmethodforthelocalfine-tuningofoneofthe

optimumdesignpointsobtainedinthelastphaseoftheoptimizationprocessforthefullwindtunnelcase.TheregiontobeoptimizedisshownalongsideaviewoftheresultsoftheNormalOptimal

Displacement.


130

Theadjointmethod is thereforean interesting tool for shapedesignoptimizationfine-tuning.However,givenitsderivative-basednature,ithasanumberoflimitations.Firstly, it is a tool for localoptimization, so it is aimedat local shapechanges in theareaswherethedesignerbelievesagreater impactonperformancecanbeachieved(the adjoint can be run for different areas in separate calculations). Secondly, andparticularly for the cases of aerodynamic shape optimization with big geometrychanges, itmustbenotedthatadjointscannotbeusedfor transientphenomenaso,forinstance,theyarenotapplicablegenerallyinareasofflowdetachment(whicharetypicalareaswherethedesignerwould liketoseek forperformance improvements).Finally, they may yield resulting geometries which are costly or infeasible tomanufacture,sotheirapplicationmustbecarriedoutwisely.

6.5.Benchmarkoptimization.ApplicationofMOST-HDStotheWFG9optimizationtestproblem

In this section, theMOST-HDSmodel is applied to a completely different type ofproblem.Uptothispoint,thecasespresentedhavebeentworealindustrialprojectsofaerodynamicshapeoptimization.NowMOST-HDSwillbeapplied toawell-knownmathematical test problem used for benchmark optimization among differentalgorithms.TheWFGtestsuitepresentedinHubandetal.(2006)isselectedoverotherexisting test suites for its challenging and yet comprehensive nature and because itfeatures non-separable problems, particularly non-separable multimodal problems,whichisafeaturerarelyfoundincommonlyusedtestsuites(otherexistingtestsuitesusedinliteraturearepresentedintheStateoftheArt–Chapter3).

All WFG problems are scalable, have no extremal nor medial variables, havedissimilar variable domains and Pareto optimal trade-off magnitudes, have knownParetooptimal sets,andcanbemade tohaveadistinctmany-to-onemapping fromthe Pareto optimal set (space of variables) to the Pareto optimal front (space ofattributes)byscalingthenumberofpositionvariables.

Inparticular, theWFG9 testproblem isused. The selectedWFG9problem is a2-objectiveoptimizationproblemwiththefollowingfeatures:non-separableobjectives,multimodalandincludingdeceptiveminima,withastrongparameterdependentbiasandaconcavegeometryoftheoptimalParetofront.

ThedetaileddescriptionoftheWFG9canbefoundinHubandetal.(2006)andthesummarytablesdescribingthemathematicaldefinitionoftheproblemcanbefoundinFigure6–32andFigure6–33.


131

Figure6–32-MathematicaldefinitionoftheWFG9testproblemusedforbenchmarkoptimizationof

theMOST-HDSmodel(takenfromHubandetal.[2006]).


132

Figure6–33–TransformationfunctionsusedbytheWFG9testproblem(takenfromHubandetal.

[2006]).

TheMOST-HDSmodel is compared to awell-knownMulti-Objective EvolutionaryAlgorithm(MOEA),NSGA-II(Debetal.[2002]),whichwasthesamealgorithmappliedtotheHRSGinletductoptimizationprobleminSection6.2.

The WFG9 problem chosen is set-up with 4 position-related variables and 20distance-related variables. NSGA-II was run in Huband et al. (2006) with real-codedparameters,amutationprobabilityof1/24,acrossoverprobabilityof0.9,acrossoverdistributionindexof10.0,andamutationdistributionindexof50.0.


133

InthecaseoftheNSGA-IIalgorithm,theprocedureusedintheworkbyHubandetal. (2006) executes 35 runs of NSGA-II, with a population size of 100, for 25000generations.Thenon-dominated frontof thepopulations is saved ineachcaseafter250, 2500, and 25000 generations. The authors state that, in the literature, apopulationsizeof100for250generationsisacommonchoice,so25000generationsshouldbemorethanenoughtoensureconvergence.

Thenextstepistocomputethe50%attainmentsurfacefromthe35frontsat250,2500and25000generations.Anattainment surface is theboundary in the spaceofattributesformedbytheobtainedfront,whichseparatestheregiondominatedbytheobtained solutions from the region that is not dominated (Fonseca and Fleming[1996]).Forinstance,the50%attainmentsurfaceidentifiestheregionofthespaceofattributes that is dominated by half of the given attainment surfaces, whereas the100%attainment surface identifies the region dominatedby every given attainmentsurface. Therefore, for the 35 runs, a 50% attainment surface will be that whichdominatesoverhalfofthefrontsobtainedandwhichisdominatedbytheotherhalf.

Tobeginwith,theresultsareshownforarandomevaluationoftheWFG9problemfor twodifferentnumbersof initial samples (1000and4600points), to illustrate thecoverageof thespaceofattributes fordifferent levelsofdetail (Figure6–34).This isincluded because MOST-HDS will select an initial set of 1000 evaluation points forPhase0,basedonarandomgenerationscheme.AnyefficientalgorithmmustrequirelessfunctionevaluationsthanamererandomsearchtofindtheParetooptimalfrontortogetascloseaspossibletoit16.

Figure6–34-RandomevaluationoftheWFG9problemforadifferentnumberofinitialsamples:

1000pointsand4600points.

16Anon-iterativesamplingmethodbasedonaquasi-randomnumbergeneratoriscalledScreening

method and is occasionally used as an alternative to real optimization algorithms. Any optimizationalgorithmmust, at least, perform better than a Screeningmethod, for the same number of functionevaluations.


134

Figure 6–35 shows the results presented in Huband et al. (2006) for the NSGA-IIoptimization of the WFG9 test problem. As can be seen, the WFG9 problem ischallenging and, at 250 generations,which is the number of generations commonlyused in literature, theNSGA-II algorithm showsa good coverageof thePareto front(i.e.thewholerangeoftheParetofrontiswellrepresented).However,convergenceisnot good in all areas of the Pareto front. For 2500 and for 25000 generations theconvergenceissuccessfulandtheParetofrontisreachedverysatisfactorily.

As explained by Huband et al. (2006), WFG9 has position related variablesdependent on distance related variables and, most importantly, WFG9 is alsomultimodal,andhasatroublesomekindofnon-separablereduction.Thismakesthisoptimizationproblemquitechallengingforanyoptimizationalgorithm.

Figure6–35-Paretooptimalfrontand50%attainmentsurfacesforNSGA-IIafter250,2500,and

25000generationsontheWFG9testproblem(takenfromHubandetal.[2006]).

TheresultsforMOST-HDSonthissameproblemarepresentedinFigure6–36,foragrowing number of function evaluations. Figure 6–36 (middle and bottom), inparticular,showstheresultsafter4600evaluations. Inthefirstplace, theresultsarefar better than with a Screening or quasi-random method (refer to Figure 6–34).Furthermore,thenumberofevaluationsrequiredtoproduceagoodcoverageoftheParetofrontandagoodconvergenceisconsiderablyreducedwithrespecttothe250generation case of NSGA-II, assuming only one run and not 35 runs (1 run, for apopulationof100andfor250generationsyields25000functionevaluations).This isnot to say that NSGA-II is not a good optimization algorithm. It certainly is a verysuccessfulalgorithm.IthastobeunderstoodthatWFG9isaverychallengingproblem.Besides,theNSGA-IIcouldpossiblybetunedtoobtainevenbetterresults.Moreover,more work is in any case required on the application of MOST-HDS to other testproblems.

The evolution of the optimization process of MOST-HDS is in itself quite eye-catching:


135

1. After 2540evaluations thepoints are still scatteredbut thebiashasbeenreducedand theirdistribution ismoreevenand theyare starting tomoveclearly towards the Pareto optimal front, with a better coverage of theParetofront;

2. In phases 11 to 15 the points are clearly progressing towards the Paretooptimalfrontandthecoverageisfurtherimproved;

3. Finally, after 4600 evaluations the coverage of the Pareto optimal front isgoodand it canbeconsidered thatMOST-HDShasconvergedsuccessfully.Onceagain,itisworthnotingthatperforming4600evaluationsfollowingasmartsearchprocedure,suchasthatproposedbyMOST-HDS,ismuchmoreefficientthantheresultsobtainedwith4600randomevaluations(Figure6–34).

From these results it can be concluded that MOST-HDS shows a promisingperformanceinthefieldofgeneralpurposeoptimization.However,amoreextensivestudyneedstobeperformedaspartofthefutureworkbeyondthisThesis.


136

Figure6–36–EvaluationresultsfortheMOST-HDSoptimizationalgorithmappliedtotheWFG9testproblem:(top)after10optimizationphases(2540evaluations);(middle)after16phases(4600

evaluations);(bottom)asummaryoftheoptimizationresultsforphases11to16.

6.6.FinalremarksThe results of the application ofMOST-HDS, the novel optimizationmethodology

presentedinthisThesis,havebeenpresentedextensively inthischapter.Asdetailedin Chapter 5,MOST-HDS proposes amulti-objective, structured hybrid direct searchoptimization approach. This approach has shown to be successful for two realindustrialcasesandforabenchmarkoptimizationtestproblem.


137

In the industrial cases addressed, which are aerodynamic shape designoptimizations inwhich big changes of the geometry are explored, the smart, robustandefficientselectionofcandidatesolutionsembeddedinMOST-HDShasmanagedtoyield solutiondesignswithhigh improvementsover currentdesigns, in a reasonabletime.Anefficientsearchschemeisessentialinanyoptimizationproblemandmoresowhentheevaluationsareastime-consumingasinthecaseofCFDproblems,inwhichonlyhundredsor,atmost,thousandsofcandidatepointscanbeevaluatedthroughoutthewholeoptimization.

TheMOST-HDS methodology has been applied to wind tunnel design and HRSGinlet duct design because these are two areas inwhich trial and error is stillwidelyused.Thepresentedapproachevaluatesanumberofcandidatesolutionswhichis1to2ordersofmagnitudethenumberofsolutionsfrequentlyevaluatedforsimilarcasesifusing trial and error. The automated nature of the method yields project timereductionsof5-10timesfortheexamplesconsidered,ascomparedtothedesigncycletimesusingmoretraditionalormanualmethods.

This methodology is flexible and can be tailored for specific optimizationapplications.Theuseofthisnoveloptimizationmodelinmanyaerodynamicfieldswillallow for the exploration of unconventional designs which can yield considerableimprovementsovermoretraditionalconcepts.

Finally, a key aspect of MOST-HDS is its emphasis on a direct search or directoptimizationapproach,even though theevaluationsare time-consuming.Theuseofsurrogateorapproximationmodels isnotconsideredthemostappropriateapproachduetothecomplexityoftheproblemsaddressed.Inparticular,transientoradvancedflow phenomena such as flow separation, vortices, etc. are not well captured bysurrogatemodels.Besides, thehighnumberof independentvariables (andthereforethesizeofthesearchregion)makesitdifficulttodevelopsurrogatemodelswhichareaccurateenough.ThiswillbeanalyzedindetailinChapter7.

ListofFiguresFigure6–1-Sideviewofvelocitycontoursinthemid-planeofatypicalHRSGtoillustratethepositionofthedifferenttubebanks.

Figure6–2-HRSGinletductdesigntypesmostwidelyusedinindustry:singleangleinletduct(left)anddoubleangleinletduct(right).

Figure6–3-HRSGinletductalternativedesigntypesthatsomemanufacturersarestartingtouse.

Figure6–4-VariablesusedtoparameterizeageneralinletductfordifferentHRSGfamilies(x-axisandy-axisviews).

Figure6–5-SideandisometricviewsofafirstexampledesignalternativefortheinletductofanHRSG(singleangletopplanefortheinletduct).ThisistherealcurrentdesignforthisHRSGfamily.


138

Figure6–6-SideandisometricviewsofasecondexamplealternativedesignfortheinletductofanHRSG(doubleangletopplanefortheinletduct).Thisisacommondesigntrendlinewhichhassubstituted,inmanycases,themoretraditionalsingleangleversion.

Figure6–7-ApplicationoftheMOST-HDSalgorithmtotheshapeoptimizationoftheinletductofafirstfamilyofHRSGsforcombinedcyclepowerplants.TheresultsoftheapplicationoftheNSGA-IIevolutionaryalgorithmtothesameoptimizationproblemarealsoshown(purplediamonds).

Figure6–8-ExampledesignsobtainedfortheshapedesignoptimizationoftheinletductofvariousHRSGfamilies.

Figure6–9-Sideviewofexampledesignpointswhichareverycloseinthespaceofvariablesandalsoverycloseinthespaceofattributes.

Figure6–10-Sideviewofexampledesignpointswhichareverycloseinthespaceofvariablesandquiteapartinthespaceofattributes.

Figure6–11-Sideviewofexampledesignpointswhicharequiteapartinthespaceofvariablesandverycloseinthespaceofattributes.

Figure6–12-Sideviewofexampledesignpointswhicharequiteunconventional(becausetheyarequiteradicaldesigns)andsomewhatnon-intuitiveintheirperformance(especiallydesignpointj).

Figure6–13-ApplicationoftheMOST-HDSalgorithmtotheshapeoptimizationoftheinletductofasecondfamilyofHRSGsforcombinedcyclepowerplants.Incrementfactors(asexplainedinChapter5)belowunity(candidatepointsmarkedwithtriangles)andaboveunity(candidatepointsmarkedwithdiamonds).

Figure6–14–PrototypewindtunnelfortestingpurposespresentedtovalidatetheCFDsolverused.

Figure6–15-PrototypewindtunnelfortestingpurposespresentedtovalidatetheCFDsolverused(generaldrawing,nottoscale).

Figure6–16-Measuredperformancecurve(pressuredropv.airflow)forthefanoftheprototypewindtunnel,showingthemeasurednominalperformancepoint(orange)andthesimulatednominalperformancepoint(blue).

Figure6–17-Verticalwindtunnelforindoorskydiving(MadridFly,www.madridfly.com).Theinletplanetothetestorflightsectionisshown(dashedredline).

Figure6–18-Distributionofpointsforvelocitymeasurementsintheinletplaneofthewindtunneltestorflightsection(measurementswerecarriedoutwithaPitottube).


139

Figure6–19-Lowdetailrepresentationofawindtunneldesign,usedtoillustratebettercertainaspectsoftheoptimizationmethodologypresentedinthissection.FourBéziercurvesareusedonly.Fanandtestsectionsarebothshadedinthisfigure(left).Anexampleplanecontainingoneofthetransversesectionsusedforthetunnelgeometrydiscretizationisalsoshown(right).

Figure6–20-ExampletreeofdesignpointcombinationsforPhase0optimizationofthesimplifiedwindtunnelmodel.32windtunneldesignsareconsidered.

Figure6–21-CFDevaluationresults(velocitycontourplotsformid-plane,totalpressuredrop–deltap–andfixedcost)foreachofthe32windtunneldesignpointsforthesimplifiedwindtunnelmodel.

Figure6–22-Paretofront(redline)offixedcostv.totalpressuredropfor32windtunneldesignpointsforthesimplifiedwindtunnelmodel.Tolerancethreshold(orangeline)toselectareaofsearchregionwherepotentialcandidatestooptimummaylie,forsubsequentoptimizationphases(valuesofbothattributesareperunit).Maximumattributerangesareshownin%.

Figure6–23-Highlydetailedrepresentationofageneralizedwindtunneldesign,abletorepresentmosttunnelgeometries(18-20Béziercurvesareneeded).

Figure6–24-Resultsobtainedforafullwindtunnel2-phasedesignoptimizationperformedwiththeMOST-HDSalgorithm.PressuredropisinPascalsandthefixedcostisinfictitiousmonetaryunits.

Figure6–25-Resultsobtainedforafullwindtunnel2-phasedesignoptimizationperformedwiththeMOST-HDSalgorithm,comparingtheuseofdifferentincrementfactorsforPhaseII:belowunity(lightgreensquares)andaboveunity(darkgreendiamonds).PressuredropisinPascalsandthefixedcostisinfictitiousmonetaryunits.

Figure6–26-ExampletreeofdesignpointcombinationsforPhase0optimizationofthefullwindtunnelmodel.32windtunneldesignsareconsidered.Theareasofthesearchregionwhichdisappearastheoptimizationproceedsareindicated.

Figure6–27-WindtunnelmodelfamiliesontheParetofrontforPhase0andtheirvelocitycontoursinthetunneltestsection(transverseplane).TheParetofrontforthisphasehas5designpoints,2oftypeIand3oftypeII.Figure6–28-NewwindtunnelmodelfamilyontheParetofrontierforPhaseIanditsvelocitycontourinthetunneltestsection.TheParetofrontforthisphasehas5designpoints,1oftypeI,3oftypeIIand1,quiteunconventionaldesign,oftypeIII.

Figure6–29-Exampleapplicationoftheadjointmethodforthelocalfine-tuningofaU-bend.

Figure6–30-Exampleapplicationoftheadjointmethodforthelocalfine-tuningofoneoftheoptimumdesignpointsobtainedinthelastphaseoftheoptimizationprocessfortheHRSGcase.TheregiontobeoptimizedisshownalongsidetwoviewsoftheresultsoftheNormalOptimalDisplacement.


140

Figure6–31-Exampleapplicationoftheadjointmethodforthelocalfine-tuningofoneoftheoptimumdesignpointsobtainedinthelastphaseoftheoptimizationprocessforthefullwindtunnelcase.TheregiontobeoptimizedisshownalongsideaviewoftheresultsoftheNormalOptimalDisplacement.

Figure6–32-MathematicaldefinitionoftheWFG9testproblemusedforbenchmarkoptimizationoftheMOST-HDSmodel(takenfromHubandetal.[2006]).

Figure6–33–TransformationfunctionsusedbytheWFG9testproblem(takenfromHubandetal.[2006]).

Figure6–34-RandomevaluationoftheWFG9problemforadifferentnumberofinitialsamples:1000pointsand4600points.

Figure6–35-Paretooptimalfrontand50%attainmentsurfacesforNSGA-IIafter250,2500,and25000generationsontheWFG9testproblem(takenfromHubandetal.[2006]).

Figure6–36–EvaluationresultsfortheMOST-HDSoptimizationalgorithmappliedtotheWFG9testproblem:(top)after10optimizationphases(2540evaluations);(middle)after16phases(4600evaluations);(bottom)asummaryoftheoptimizationresultsforphases11to16.

ListofTablesTable6–1–RelativeerrorbetweenthepressurelossesasprovidedbythemanufacturerandasobtainedfromtheCFDanalysisforthetubebanksofanexampleHRSG.

Table6–2-Comparisonbetweendifferentdesignpoints,toshowthatpointswhichareverycloseinthespaceofvariablescanalsobeverycloseinthespaceofattributes.AllresultsarewithrespecttotheattributevaluesofthecurrentHRSGdesignofFigure6–7.

Table6–3-Comparisonbetweendifferentdesignpoints,toshowthatpointswhichareverycloseinthespaceofvariablescanalsobequiteapartinthespaceofattributes.AllresultsarewithrespecttotheattributevaluesofthecurrentHRSGdesignofFigure6–7.

Table6–4-Comparisonbetweendifferentdesignpoints,toshowthatpointswhicharequiteapartinthespaceofvariablescanalsobeverycloseinthespaceofattributes.AllresultsarewithrespecttotheattributevaluesofthecurrentHRSGdesignofFigure6–7.

Table6–5-Comparisonbetweenexampledesignpoints,whicharequiteunconventionalandsomewhatnon-intuitiveintheirperformance.AllresultsarewithrespecttotheattributevaluesofthecurrentHRSGdesignofFigure6–7.

Table6–6-Velocitydeviationwithrespecttotheaveragefor9relevantpoints(amongthoseshowninFigure6–18)intheinletplanetothetestorflightsectionofaverticalwindtunnel.Measuredv.CFDsimulatedresults.

Chapter7 -Comparisontosurrogatemodels

Therearedarkshadowsontheearth,butitslightsarestrongerinthecontrast.

CharlesDickens.

ThischapterispresentedasaspecialsectionoftheresultsobtainedinthisThesiswiththeMOST-HDSalgorithmforshapedesignoptimizationwithbiggeometrychanges.Theuseofsurrogatemodelstoapproximatethefullmodel,inordertoreduce the evaluation time of the performance of complex geometries, hasbecome increasingly popular, so there is extensive research following thisapproach.Therefore, itwasconsidered interestingtodedicatea fullchaptertothe discussion on the advantages and the limitations of surrogate-basedoptimizationascomparedtodirectoptimization.Firstly,Section7.1.presentsageneral introduction. Section 7.2. includes quite eye-catching results ofsurrogate-basedevaluationsandsurrogate-basedoptimizationoftheHRSGinletductcasepresentedinChapter6.Section7.3.analyzesageneralsummaryofthemainadvantagesandlimitationsofasurrogate-basedmethodology. Inadditionto this, surrogatemethods are comparedwith direct optimization approaches,suchasthatfollowedbyMOST-HDS.

7

Chapter7–Comparisontosurrogatemodels

143

7.1.IntroductionIn the fieldofaerodynamicsand fluidmechanics ingeneral, theevaluationof the

performanceofaparticulardesignisoftenverycostlyintermsoftimeormoney.Toolsavailable, such as CFD simulations, wind tunnel testing, or testing in the realenvironment,arecomplexandfrequentlytooexpensive,atleastforthedesignphaseof a project. Furthermore, in the case of optimization, an area in which for otherapplications it is common to perform thousands or millions of evaluations of theobjective function, the situation for fluid mechanics problems is even morechallenging.Therefore,anincreasinglypopularapproachhasbeentheuseofdifferentkinds of surrogatemodels, to approximatemore complex evaluationmodels of theperformanceofthebody,geometryordeviceofinterest.

Surrogate-basedevaluation,andmoresosurrogate-basedoptimizationtechniques,are certainly very interesting and useful tools for a wide range of applications (asshowninrepresentativeandadvancedusesofthesetoolssuchasJingetal.[2013]orWalton et al. [2013]). However, it is important to realize that, at present, there arecertain limitations to theuseof thisapproach. In thesecases,directevaluationwithmore complex and realistic models may be preferable, leading to direct search ordirect optimization models. These complex and realistic models are also known ashigh-fidelitymodels.

As outlined in Robinson et al. (2006), surrogate models belong to one of thefollowingcategories:

1. Data fits. Typically using interpolation or regression of the high-fidelitymodelevaluatedatoneormoresamplepoints.Amongthistype,responsesurfaces are one of the most popular and strong tools available. A goodexample of the application of response-surfaces and a discussion on theirpotentialforaerodynamicandshapeoptimizationscanbefoundinKrajnovic(2007).

2. Reduced Order Models (ROMs). Obtained with techniques such as modalanalysis or Proper Orthogonal Decomposition (POD). The course notes byJanardhanan (2011) is a good description of modal analysis. The book byVolkwein(2013)isaverysoundmathematicalbasisforPODsandROMs,andthe work by Walton et al. (2013) offers an interesting discussion on theapplicabilityofPODandRadialBasisFunctions(RBF).

3. Hierarchical models. They are also referred to as multi-fidelity, variablefidelityorvariablecomplexitymodels.Thelow-fidelitysurrogatemaybethesame as the high-fidelity model, but converged to a higher residualtolerance.Forfinite-elementmodelsthesurrogatecanmakeuseofalowerbasisfunctionorderthanthehigh-fidelitymodel,oritcanalsobethesamemodel on a coarser grid. The surrogate model may also be a simplifiedengineering model that neglects some of the physics of the real, fullproblem.TheveryinterestingworkbyRobinsonetal.(2006),whichwehavecited to describe the different types of surrogate models, is a very goodexampleoftheuseofhierarchicalmodels.


144

Already a decade ago, in Krajnovic (2007), we can find some interestingconsiderations on the potential of surrogate-based optimization for aerodynamicproblems, in this case using response surfaces. In that work the author claims:“Although there is a number of questions that have to be answered before thesurrogate-based optimization can become a general engineering tool for theaerodynamicoptimizationof vehicles, there isnodoubt that it representsa valuabledesignstrategy.With increase incomputerpower,thesteadyCFDsimulationswillbereplacedwithmoreaccurateunsteadysimulationsandthereby increasetheaccuracyof the response surface model substantially. Despite the promising computerdevelopment,theuseofgradient-basedsearchalgorithmswillbeprohibitedformanyyearstocome(especiallyiftime-dependentsimulationsareused).Usingthesurrogate-basedoptimizationtogetherwithtime-dependentCFDsimulationsfortheconstructionof the surrogatemodelwill certainly becomean optimization tool that is capable tocompete with physical optimization in wind tunnels both in terms of cost andaccuracy”.

Krajnovic (2007) is already proposing the combination of highly complex CFDsimulations for the evaluation of the set of points used to generatemore accurateresponsesurfaces.Today, tenyearsafter thiswork, themostadvancedoptimizationsolversofferedincommercialpackages(bycompaniessuchasANSYSorSiemensCD-adapco)includehybridapproachesbetweensurrogate-basedanddirectoptimization,calledadaptivesingleormulti-objectiveoptimization.

Concerning our field of interest, aerodynamic shape design optimization, wewillfocus on the performance of response surfaces of various types. The results andobservationsmadeareapplicabletomostoftheothertypesofsurrogatetechniques(ROMsorhierarchicalmodels).

ThecontributionofthisThesisinthischapterismainlytopresentthelimitationsofsurrogate-based evaluation and surrogate-based optimization for cases ofaerodynamicshapedesigninwhichtheflowregimecanchangefromdesignpointtodesign point (for example because of the onset of flow detachment). This occurs inmost cases involving big geometry changes. In these cases, the robustness andaccuracy of direct optimization is shown as an alternative approach to surrogatemodels.

7.2.Resultsofasurrogate-basedapproachfortheshapeoptimizationoftheinletductofHRSGs

Firstly, let us compare the results of surrogate based evaluation to the resultsobtainedwithdirectevaluation.Secondly,theresultsofsurrogate-basedoptimizationanddirectsearchoptimizationwillbeconfronted.


145

Forthissection,theexamplecaseoftheHRSGinletductoptimizationwillbeused.First, because it is more simple and clear to understand and will illustrate our keyconclusions better. Second, because one of the limitations of surrogate models ingeneralisthatcasessuchasthefullwindtunnelhaveanexcessivenumberofvariablestobeanalyzedwithsurrogatetechniques.Forsurrogatemodelsingeneral(especiallyof the response surface type), variables sets in excess of 10 to 15 are complex orimpossible to handle (the wind tunnel case had 108 independent variables). Ifsurrogatemodelsaretobeusedforthesecases,itisnecessarytocarryoutareductionof the number of variables or to use variable hierarchies to address only thosevariableswithastrongerimpactontheresults.

SURROGATE-BASEDEVALUATION

In the first place, the results of surrogate based evaluation will be compared tothose obtained by direct CFD evaluation. Various response-surface models can beused.Toanalyzetheaccuracyandapplicabilityofsomeofthemostrelevant,theCFDresultswillbecomparedtotheresultsobtainedwiththefollowingtypesofresponsesurfaces:NeuralNetwork,Genetic,Non-ParametricRegressionandKriging(withauto-refinement).

SparseGridisanotherinterestingtypeofresponsesurface,whichcouldnotbeusedbecause it does not allow the sample points to be introduced by the user and itgeneratesthemautomatically17.Fortheparticularcaseof theHRSG inletduct,giventhata further limitationof responsesurfacemodules incommercialpackages is thatthe user cannot introduce any kind of constraints on the variables, the automaticsampling generates absurd geometries and this makes the use of the Sparse Gridresponse surface impossible. For theother four types of response surfaceused, thepointsweregeneratedautomaticallybytheprogramused(ANSYSinthiscase),buttheabsurd points could be corrected manually before each response surface wascomputed.

Table7–1presentstheresultsfortherelativeerrorsofthevaluescalculatedusingthe different response surfaces with respect to the values calculated using CFD. 14representativedesignpoints(i.e.quitespreadoutinthespaceofvariables)havebeenused for the comparison. Figure 7–1 shows these results graphically, so that theperformanceofeachresponsesurfaceismoreclear.

Itisimportanttonotethatthepredictionoftheresultsforaparticulardesignpoint,once the response surface has been computed, is quasi instantaneous, and thecalculationoftheresponsesurfaceinthefirstplacetakesanegligibleamountoftime(afewsecondsinani7,8-core,32GBRAMcomputer).

17 Both Kriging (with auto-refinement) and Sparse Grid are the two response surface types

recommended by ANSYS and other commercial packages for a higher accuracy. As is shown in thischapter,Krigingisnotalwaysthebestchoiceintermsofaccuracyofthepredictions(SparseGridcouldnotbeused,asexplained).Howeverknowingbeforehandwhichtypeofresponsesurfaceisbestsuitedforaparticularproblemisquitefrequentlycomplexorinfeasible.


146

RESPONSESURFACETYPE

NEURAL GENETIC NON-PARAMETRICREGRESSION

KRIGING+auto-refinement

Designpoint

Errorintotal

pressuredrop

Errorinvelocitynon-

uniformity

Errorintotal

pressuredrop

Errorinvelocitynon-

uniformity

Errorintotal

pressuredrop

Errorinvelocitynon-

uniformity

Errorintotal

pressuredrop

Errorinvelocitynon-

uniformity

#1 -2% 17% -2% 6% -7% 15% -2% 2%

#2 26% -23% 22% -17% 27% -19% 0% -17%

#3 -35% -9% -33% -1% -27% 2% -43% 2%

#4 7% -19% 9% -9% 12% -1% -11% -9%

#5 21% -17% 21% -7% 22% 4% -1% -8%

#6 24% -22% 18% -16% 27% -17% -3% -17%

#7 -6% -14% -4% -11% 9% -7% -22% -22%

#8 -6% -16% -6% -11% 8% -8% -27% -21%

#9 -8% 19% -1% 12% -7% 16% -2% 14%

#10 3% -11% 24% -1% 40% -2% -12% -29%

#11 -5% 12% -3% 5% -8% 9% -3% 16%

#12 -2% 11% -2% 3% -2% -3% -3% 15%

#13 -1% 9% -2% 2% 5% -18% -3% 11%

#14 7% -6% 4% -12% 13% -29% 5% -9%

Table7–1-RelativeerrorswithrespecttotheCFDvaluesforfourdifferenttypesofresponsesurfaceandforanumberofrepresentativedesignpoints.

Figure7–1-RelativeerrorswithrespecttotheCFDvaluesforfourdifferenttypesofresponsesurface

andforanumberofrepresentativedesignpoints.


147

Forthisparticularcase,thegenetictypebehavesbetterforbothattributes,butthiswillbedifferentforotherexamples.Theimportantobservationstomakeherearethattherelativeerrorscanreachvaluesofupto20%orhigherand,furthermore,thattheerror is not always systematic or predictable. Besides, for many points, differentresponse surfaces yield quite different errors, and not always in the same relativedirection.Thismeansthatresponsesurfaceapproximationshavetobeusedsensiblyandtheusershouldbeartheseconsiderationsinmind.

Amethodusedtochecktheaccuracyof thedata fitcarriedout togenerateeachresponsesurfaceistheGoodnessofFit(GoF).TheGoFisshowedinFigure7–2forallfour response-surfaces.As is common,Neural andGenetic arenot that close to thevalues of the points used to compute the response surface. The Non-ParametricRegressiontriestoforceallpointstobewithina+/-𝜀distanceoftheresponsesurface(this cannot be observed clearly in the graph for this case). The Kriging responsesurface matches the exact values of all sample points (including auto-refinement,whichmeans that additional sample points are generated automatically to improvethe first version of the surface). Despite the GoF figures for each response surface,KrigingandNon-ParametricRegressionarenotnecessarilythemostaccuratesurfaces,asseeninTable7–1andFigure7–1.

Figure7–2-GoodnessofFit(GoF)forthedifferentresponsesurfaces.PredictedversusCFDcomputedresultsforthefourresponsesurfacetypes:Neural(topleft),Genetic(topright),Non-Parametric

Regression(bottomleft)andKrigingwithauto-refinement(bottomright)(allvaluesarenormalized).Reddotsareforpressuredropandyellowdotsareforvelocitynon-uniformity.


148

Letusgoabitfurthertounderstandthecausesoftheseerrors.Inordertodoso,wewilluse theexampledesignpointsofFigure7–3.Thesedesignpointshavebeenselected, out of all of the points in Table 7–1, because the flow regime changesabruptlybetweenthem.OnlythevaluesofthetwoanglesofthebottomplaneoftheHRSGinletductaremodified,keepingtherestofthevariablesconstant.Theflowforpoints4and5isstillattachedtotheflooroftheinletduct,althoughitstartstohaveaminor detachment towards the end of the floor for design point 4. Design point 3,whichhasamuch steeper first angle for the floorplane (i.e. abiggeometry changewithrespecttopoints4and5),hasaclearflowdetachmentandhenceaqualitativelydifferentflowregime.ThismatchesnicelywithwhatisexpectedtohappenasthefloorangleincreasesandtheresultcanbeseenintheCFDevaluationvaluesofTable7–2.Itisinterestingtopointoutthat,whilethepressuredropisthehighestforpoint3andreducesgradually,thenon-uniformityisthelowest(i.e.thevelocityattheoutletoftheinlet duct is more uniform) because the flow detachment generates a better flowdistribution. This is reasonable and it is verywell capturedby a direct evaluationofeachdesignpoint.

However,ifweanalyzethedataofTable7–1closely,itisplaintoseethreesourcesoferror.First,thedifferentresponsesurfacesdonotmanagetoreproducethegradualreductioninthepressuredropfrompoint3topoint5atthesametimeasthechangeinvelocitynon-uniformities.Second, therelativeerrorvaluesarequiteconsiderable,especially fordesignpoint 3,where flowdetachmentoccurs. Third, theerror valuesamongthedifferentresponsesurfacesarequitedifferentinsomecases;whilesomeofthem underestimate the results, others overestimate them, and this is not alwaysconsistentorpredictable.Aswillbeconcludedinthefinalsectionofthischapter,ithasbeen shown that response surfaces, and this can be extended to most surrogatemodels,arenotaccurateenoughtopredicttheresultsofcomplexfluidproblemswithbig geometry changes and phenomena such as flow detachment. The results of theresponsesurfaceswillonlybeacceptableifthenumberofsamplepointsincreasesinthe regionofdesignpointswhere thesephenomenaoccur.This, inanycase,meansthatmoreCFDevaluationsarerequiredtocomputeanaccurateresponsesurface,sosurrogatemodelsarenotsotime-competitive.Forthesecases,directCFDevaluationcan yield better results with less evaluations and thus with a reduced computationtime. This should be the approach used for these situations, very especially if anoptimizationistobeperformed.

Figure7–3-Side-viewofthevelocitycontoursfordesignpoints#3,#4and#5ofTable7–1.


149


#3 100% 100%

#4 63% 109%

#5 57% 105%

Table7–2-CFDevaluationresultsfordesignpoints#3,#4and#5ofTable7–1.

SURROGATE-BASEDOPTIMIZATION

Oncetheresultsofsurrogate-basedevaluationwithdifferentresponsesurfaceshasbeen analyzed, this section presents the results obtained when a surrogate-basedapproach is followed for the optimization of a complex fluid problem, frequentlyinvolvingbigchangesofthebodygeometry.

The four response surface types of the previous section have been used for theshape optimization of the HRSG inlet duct presented in Chapter 6. In particularsurrogate-basedoptimizationhasbeenappliedtothefirstHRSGfamilypresented.Theresults obtained for theoptimization carriedoutwithMOST-HDS are included againhereforeasierreference(Figure6–7).

Figure7–4-ApplicationoftheMOST-HDSalgorithmtotheshapeoptimizationoftheinletductofafirstfamilyofHRSGsforcombinedcyclepowerplants.Surrogate-basedoptimizationresults:i)

Unconstrainedoptimization:surrogatepredictions(purplecircles)v.CFDevaluations(purplesquares);ii)Constrainedoptimization(velocitynon-uniformitybelowacertainvalue):surrogatepredictions(red

circles)v.CFDevaluations(redsquare).


150

As can be seen in Figure 6–7, the Phase 0 evaluation already improved theperformance of the current design quite considerably and Phase I was only able toimprovethatslightlyfurtherso,atleastbasedontheresultsobtainedwithMOST-HDS,one could presume that continuing with the optimization may not produceconsiderableimprovements.

Fourresponsesurfaceshavebeengeneratedwiththe120samplepointsofPhase0,thesamepointsusedfortheMOST-HDSoptimization.Anunconstrainedoptimizationwaslaunchedinthefirstplace.Inthiscase,ascanbeseeninFigure6–7,theresponsesurfacepredictedaconsiderable improvementover thePareto frontofPhase0.TheCFD evaluation for the predicted optimum points is also included. There aredifferencesintheresults,ascommentedinthesectiononsurrogate-basedevaluation,but still the use of surrogates for the optimization gives a clear indication of aninterestingareaofthesearchregionwhereoptimumdesignsmaylie.

However,tocomparetheresultsofasurrogate-basedoptimizationtoMOST-HDS,aconstrainedoptimizationmustbelaunched.Inthiscase,basedontheresultsshowninFigure6–7,somekeyobservationscanbemade:

1. The surrogate-based optimization yields design points that may have anabsurd geometry. This is because, at least in commercial packages, noconstraints can be imposed on the variable values when generating aresponse surface. Therefore, the optimumpoints predicted by a responsesurfacehaveoftentobecorrectediftheproblemhastheseconstraints.

2. OnlytheNeuralresponsesurfacewasabletocalculatepredictedoptimumpoints.Theotherresponsesurfacestypesindicatedthatnocandidatecouldbefound.

3. Most of the predicted optimumpoints appear tomeet all constraints andtheyappear to improve thePareto frontofPhase0.However,once thesepointsarecheckedforabsurdityonlyonerealcandidatedesignpointisleftand,afteraCFDevaluation,itcanbeseenthatitliesabovethevelocitynon-uniformitylevelimposedfortheMOST-HDSsearch.

Consequently,theresultsoftheuseofasurrogate-basedapproachforoptimizationcanbeusefulandgivestrongindicationsofwheretheoptimumdesignsmaylie,andinsome cases their resultsmaybe accurate enough.However, theyhave anumberoflimitations for complex problems, such asmany found in fluidmechanics. Surrogatemodels are not fit for big geometry changes, and they frequently miss flow-detachment critical points. These features are preciselywhat the designerwants tofocuson,inmanycases.


151

7.3. Discussion on the advantages and limitations of asurrogate-basedapproach

Thischapterhasfocusedontheuseofsurrogatemodelsbothforevaluationandforoptimizationofcomplexproblemsinfluidmechanics,particularlyaerodynamicshapedesign optimization with big geometry changes. Among all the types of surrogatemodels,thischapterhasfocusedontheperformanceofresponsesurfacesofvarioustypes.Theresultsandobservationsmadeareapplicabletomostoftheothertypesofsurrogatetechniques(ROMsorhierarchicalmodels),althoughamoreextensiveworkforeachsurrogatemodelwouldbenecessarytoproveitsatisfactorily.

Inthefirstplace,itmustbestatedthatsurrogatemodelsareaveryusefultoolandallow for faster and more accurate evaluation and optimization of many complexproblems.However,anumberoflimitationsandconsiderationsmustbekeptinmindtoexploitthepotentialofsurrogatemodelsmoreadequately:

1. Surrogatemodels in general have a limitation on the number of input orindependent variables they canhandle. This limit is typically around10-15variables, especially for response surfaces. Besides, for some techniquesused in the field of surrogatemodels, such as Radial Basis Function (RBF)interpolation,morethan100pointsforthe initialsamplesetaretootime-consumingtoprocess(Waltonetal.[2013]andFranke[1982]).Ifsurrogatemodelsaretobeusedfor thesecases, it iseithernecessarytocarryoutareductionof thenumberof variables, or tousehierarchiesof variables toaddressonlythosevariableswithastrongerimpactontheresults,ortouselowfidelitymodelswhicharesimplertohandle.

2. Some surrogate models, such as response surfaces, cannot incorporateconstraints on variables to ensure the design points are not absurdgeometries.Thismeansthatsomeofthecandidatedesignstheypredictaspotentialoptimaarenotevenfeasible.Ifresponsesurfacesaretobeused,checks for absurdgeometries shouldbe included. In theparticular caseoftheveryinterestingtypeofresponsesurfacereferredtoasSparseGrid,thismeans that it may not be possible to use because it does not allow thesample points to be introduced by the user and it generates themautomatically.FortheparticularcaseoftheHRSGinletduct,giventhattheuser cannot introduce any kind of constraints on the variables, theautomatic generation of sample points generates absurd geometries andthismakestheuseoftheSparseGridresponsesurfaceimpossible.

3. Moreover, certain surrogatemodels, such asmost response surfaces, arenotsupportedfordiscretevariables.


152

4. Theaccuracyofsurrogateevaluation,evenforcomplexfluidproblemssuchasunsteadycases,canbeadequate.However,itmustbeensuredthatthereis no change of flow-regime within the search region (i.e. points with orwithoutflowdetachment,forexample).Thisisfrequentlydifficulttoensurefor shape optimizations involving big geometry changes. This limitationmeans that approximatemodelsmay yield results that cannot be trusted.Furthermore, the designer is quite commonly interested precisely instudying when a particular flow-regime changes. Some examples are theanalysis of flow separation initiation, the change of turbulence regime, ortheonsetoffluidinducedvibrations.

5. Sincemanysurrogatemodelsrelyonsomesortofdatafitor interpolationscheme,predictionerrorsarerarelysystematic,andcanthereforebeinanydirectionwithrespecttotherealvalue.Thismeansthaterror-correctionisdifficultortoocomplextoperform.

6. In order to increase the accuracy of the surrogate models, most requiremore sample points (also referred to as snapshots) to derive a betterapproximatemodel.Thismayrequiretheevaluationofpointsinareasofthesearchregionwheretheattributevaluesmayhavestrongvariations(hencetheneed formorepoints), butwhere theoptimumpointsmaynot lie, sotime-consumingCFDevaluations arewasted anyway.Moreefficient directsearchschemes,suchasthatdevelopedfortheMOST-HDSmodel,mayyieldbetterresultswithlessCFDevaluations.

7. Given that there aremultiple surrogatemodels available, it is not alwayseasy,orevenpossible,todecidewhichwillbemoreappropriateoraccuratefor a particular problem. Regarding response surfaces, both Kriging (withauto-refinement) and Sparse Grid are the two response surface typesrecommended by ANSYS and other commercial packages for a higheraccuracy.Asisshowninthischapter,Krigingisnotalwaysthebestchoiceinterms of accuracy of the predictions (Sparse Grid could not be used, asexplained).However,knowingbeforehandwhichtypeofresponsesurfaceisbestsuitedforaparticularproblemisquitefrequentlycomplexorinfeasible.

8. The application of surrogate models for optimization of fluid-relatedproblemsalwaysrequiresafinalCFDevaluationoftheoptimumcandidatesto ensure that the predicted results are correct. Thismeans an additionalcalculation time, which must be accounted for when comparing a directversusasurrogate-basedoptimization.


153

9. Forcases inwhichtheCPUtimeofa full-orderevaluation isveryhighandthevariablespaceisnottoolarge,surrogatemodelscanproveinteresting.ForcasessuchasthoseaddressedbythisThesis(whichareverycommoninindustry and in research), direct search can be more adequate thansurrogate models. This is because the full-order evaluation, althoughcomplexandrequiringCFD,isnotextremelytime-consuming18,andbecausethevariablespacecanbelarge(morethan10-15variables),

Takingalltheselimitationsintoaccount,itisconsideredthattheworkpresentedinthis Thesis is an improvement over many other techniques for aerodynamicoptimization of complex components (wings, high-speed train noses, automotivedesigns, etc.), which rely on surrogate-based optimization. Those surrogate-basedmodelsincludedatafits,responsesurfaces,byreducedordermodels,andhierarchicalormulti-fidelitymodels,asexplainedinRobinsonetal.[2006].

Themain terms to compare the approachof this Thesis to other alternatives areaccuracy, flexibility and applicability to big geometry changes. Surrogatemodels arenot good inestimating stronglynon-linearobjective functions, includingphenomenasuchas flowseparation.Theyarealsopoor incombiningvariablesofmanydifferenttypes (discrete, continuous, etc.). This is very much the case when big variablevariationsareallowedinaerodynamicoptimizationproblemsandwhenawholebody(windtunnel,forinstance)isoptimized,andnotonlycertainpartsorcomponentsofit.

ListofFiguresFigure7–1-RelativeerrorswithrespecttotheCFDvaluesforfourdifferenttypesofresponsesurfaceandforanumberofrepresentativedesignpoints.

Figure7–2-GoodnessofFit(GoF)forthedifferentresponsesurfaces.PredictedversusCFDcomputedresultsforthefourresponsesurfacetypes:Neural(topleft),Genetic(topright),Non-ParametricRegression(bottomleft)andKrigingwithauto-refinement(bottomright)(allvaluesarenormalized).Reddotsareforpressuredropandyellowdotsareforvelocitynon-uniformity.

Figure7–3-Side-viewofthevelocitycontoursfordesignpoints#3,#4and#5ofTable7–1.

Figure7–4-ApplicationoftheMOST-HDSalgorithmtotheshapeoptimizationoftheinletductofafirstfamilyofHRSGsforcombinedcyclepowerplants.Surrogate-basedoptimizationresults:i)Unconstrainedoptimization:surrogatepredictions(purplecircles)v.CFDevaluations(purplesquares);ii)Constrainedoptimization(velocitynon-uniformitybelowacertainvalue):surrogatepredictions(redcircles)v.CFDevaluations(redsquare).

18 Theoptimizations carriedout for this Thesis (closedwind tunnel and industrialboilers -HRSGs)

wereperformed in an8-coreparallel calculation, using a 32GBRAMcomputer. Each calculation tookaround0.25-0.3hoursfortheHRSGcaseand0.75-1hoursforthefullwindtunnelcase.Thesizeofthemesheswasbetween1-2millionelementsfortheHRSGcaseand2-5millionelementsforthefullwindtunnelcase.


154

ListofTablesTable7–1-RelativeerrorswithrespecttotheCFDvaluesforfourdifferenttypesofresponsesurfaceandforanumberofrepresentativedesignpoints.

Table7–2-CFDevaluationresultsfordesignpoints#3,#4and#5ofTable7–1.

Chapter8 -ConclusionsIt’smorefuntoarriveataconclusionthantojustifyit.

MalcolmForbes.

This chapter summarizes the main conclusions and Thesis contributions, theresultsobtained,theadvantagesandlimitationsfortheapplicationoftheMOST-HDS model developed and the future work to be carried out, based on theresultsofthisresearch.Section8.1presentsanddiscussesthegeneralandmostrelevantconclusionsandcontributions.Section8.2presentsthefutureresearchworktobecarriedoutbeyondthisThesis.

8.1.ConclusionsandThesiscontributionsThe problem this Thesis has dealt with has been the multi-attribute or multi-

objective aerodynamic shape optimization of real geometries of different fields ofapplication,subjecttoasetofconstraints,andtakingintoaccountbothsmallandbigchangesofthegeometryofinterest.

The approach proposed for the problem described above has been thedevelopmentofageneralmethodbasedonaMulti-ObjectiveStructuredHybridDirectSearchoptimizationalgorithm(referredtoasMOST-HDS).

The main conclusions that can be drawn from this Thesis, alongside its keycontributions,arenowpresented,groupedintoasetofcategoriesforbetterclarity:

8

Chapter8–Conclusions

157

OPTIMIZATIONAPPROACHANDCOMPARISONTOSURROGATE-BASEDOPTIMIZATION

1. This research work has addressed optimization problems involving time-consuming objective function evaluation, in particular requiring CFDevaluation. For this kind of optimization problems, there are two generalways of approaching the search process in a smart way. One is usingtechniques that allow for a faster evaluation (surrogatemodels), becausethe full-order function is somehow simplified. The other is developingsmarter search schemes that reach the optimum solutions reducing thenumberofevaluations,butwhichintroducelittleornosimplificationtothefull-order model. This latter approach, called direct search or directoptimization,hasbeenthetechniqueselectedforthisThesis;

2. It has been shown that surrogatemodels (mainly response surfaces havebeen analyzed in this Thesis) are useful tools for faster evaluation andoptimization, but they have a number of limitations. Themost importantones,applicabletomosttypesofsurrogatemodels,are:

a. thenumberofinputorindependentvariablesshouldnotexceed10-15;

b. somesurrogatemodelscannotincorporateconstraintsonvariables,forexampletoensurethedesignpointsarenotabsurdgeometries;

c. a number of surrogate models are not supported for discretevariables;

d. theiraccuracyiscompromisedwhenthereisachangeofflowregimebetween different design points (such as the onset of flowdetachment),which are frequently cases of special interest for thedesigner;

e. errorsarenotsystematicandaredifficultortoocomplextocorrect;

f. finally, it may well happen that the number of CFD evaluationsrequired to compute an accurate surrogate model exceeds thenumberofevaluationsneededbyasmartdirectsearchprocess.

3. SurrogatemodelscanproveinterestingforcasesinwhichtheCPUtimeofafull-orderevaluationisveryhighandthespaceofvariablesisnottoolarge.However, direct search can bemore adequate than surrogatemodels forcases such as those addressed by this Thesis (which are very common inindustryandinresearch).Thisisbecausethefull-orderevaluation,althoughcomplexandrequiringCFD, isnotextremelytime-consuming,andbecausethespaceofvariablescanbelarge(morethan10-15variables).


158

4. Taking all these limitations into account, it is considered that the workpresentedinthisThesiscontributestotheStateoftheArtbecauseit isanimprovement over the use of surrogate-based models for aerodynamicoptimization of complex components (wings, high-speed train noses,automotive designs, etc.). This is especially the case in terms of accuracy,flexibility,applicabilitytobiggeometrychanges,andchangesofflowregime.The errors of surrogate-based evaluation can be non-systematic and canreach average values of 10-20% for real industrial cases, such as thoseanalyzed in thisThesis (refer toChapter7 formoredetails). In thespecificcaseofachangeofflowregimewithinthesearchregion,theerrorscanbemuchhigher.

5. Direct search is an alternative to surrogatemodels to tackle optimizationproblems that require time-consuming evaluations. Instead ofapproximating the evaluation model, direct search use algorithms withembedded intelligence to carry out an intelligent and efficient search,minimizingthenumberofevaluations.Inordertojustifythedevelopmentofthenovelalgorithm,MOST-HDS,it iscomparedtooneofthemostpopularMulti-ObjectiveEvolutionaryAlgorithms(MOEAs),theNSGA-II,fortheshapeoptimization of an HRSG inlet duct. Although the results obtained withNSGA-IIaregood,clearimprovementsareshownwithMOST-HDS.Thisisanimportant contributionof this Thesis, sinceNSGA-II is already a very goodand well-known optimization algorithm. Using MOST-HDS, the candidatesolutionsoftheoptimizationphasesaremoreconcentratedontheareaofinterestinthespaceofattributes,andthereisahigherrateofimprovementfrom phase to phase. Therefore, the optimized Pareto front after anequivalentnumberofevaluations (i.e.equivalentcomputingtime,becausetheevaluationsarethemosttimeconsumingpartoftheprocess)isbetter.However,much fine-tuningandupgradingworkneeds carryingouton theMOST-HDSalgorithm,sincethereisstillsubstantialroomforimprovement.

GENERALAPPLICABILITYOFMOST-HDS:REALINDUSTRIALCASES

6. MOST-HDShasbeenappliedsuccessfullytotworeal industrialcasestudiesof shape design optimization: the inlet duct of HRSGs for combined cyclepower plants, and closed wind tunnels. It has been shown that theoptimization results yield important improvements over current existingdesigns. This is a key contribution of this Thesis, not only becauseperformance results are improved for the optimum designs obtained, butalsobecausesomeofthesedesignsareveryunconventional.Consequently,this Thesis has allowed to develop a new set of design guidelines, veryspecifically in the case of the optimization of the industrial boiler (HRSG)inletduct.Inthisparticularcase,forinstance,itisshowninthisThesisthatthe double angle design of HRSG inlet ducts, which is the current designtrend, is not always better than the single angle design, which was thetraditionalguidelinefollowed.


159

7. Theresultsobtained for the twoHRSG familiespresentedshowthat thereare optimum trade-off designs with simultaneous reductions in pressuredropofup to20-25%, in lateral surfaceofup to38%,and in lengthofup16%,whilehavingcomparablevelocityuniformitiestotheexistingdesigns.Someoftheseresultsareobtainedwithnoticeablyunconventionaldesigns.Thelengthreductionobtainedresultsinaveragesavingsincostsofaround95k€perinletduct.

8. Regardingthefullwindtunnelcase,thepressuredropcanbeimprovedby30-40%andthecostcanbereducedby15-20%(withrespecttodesignswithalreadyagoodperformance).Again,someoftheseresultsareobtainedbyclearlydisruptiveorcreativedesigns.

9. Given that MOST-HDS is capable of addressing problems involving biggeometry changes, it canmove efficiently throughout areas of the searchregionwhichproduceunconventionalornon-intuitivedesigns,whichwouldprobably never have been tried by the designer. This is a particularlyimportantcontributionofthisThesis,sincethereareveryfewreferencesintheStateoftheArtaddressingbiggeometrychangesinshapeoptimizationproblemsandvery importantperformanceimprovementscanbeachieved.Mostresearchersfocusonsmallgeometrychangesor,evenmore,onfine-tuningofthegeometryofinterest.

10. TheMOST-HDSmethodology has been applied towind tunnel design andHRSGinletductdesignbecausethesearetwoareasinwhichtrialanderroris still widely used. The presented approach evaluates a number ofcandidate solutions that is 1 to 2 orders of magnitude higher than thenumberofsolutionsfrequentlyevaluatedinmanualtrialanderrordesigns.Theautomatednatureofthemethodyieldsprojecttimereductionsof5-10times for theexamples considered,as compared to thedesigncycle timesusingmoretraditionalormanualmethods.Thisisalsoacontributionwhichisverymuchworthhighlighting.


160

GENERALAPPLICABILITYOFMOST-HDS:MATHEMATICALTESTFUNCTIONOPTIMIZATION

11. MOST-HDS has also been applied to a very different problem: theWFG9problemoftheWFGtestsuite,achallengingtestfunctionusedinliteraturefor benchmark optimization among different algorithms. Once again, thepopularNSGA-II algorithm is used as benchmark. For a smaller number offunctionevaluations,MOST-HDSshowsgoodcoverageofthewholespanoftheParetofront,aswellasagoodconvergence.Basedonlyontheresultsofthistestproblem,theperformanceofMOST-HDSis,atleast,asgoodasthatof NSGA-II.More extensive work will be performed in further benchmarktesting in the future. Consequently, this Thesis contributes to generalpurposeoptimizationand,more specifically, tomathematical test functionoptimization,becauseitcanbeatNSGA-IIquiteclearlyforWFG9.However,more research is required to compare it tomorealgorithmsand formoretestproblems.

GENERALAPPLICABILITYOFMOST-HDS:GENERAL-PURPOSEOPTIMIZATION

12. Therefore, based on the results obtained in this Thesis, it can be claimedthat MOST-HDS has shown to perform well in many different problems,matching or improving currently existing techniques. The key aspects ofMOST-HDS are a structured optimization architecture (exploiting theconceptsofhierarchyofvariablesandoptimizationphases)andthehybriddirect-searchapproach.

13. The use of a structured optimization scheme is novel in the field ofaerodynamicshapeoptimization,asfaraswehavefoundintheStateoftheArt reviewed. Hence this Thesis contributes to the research work in thisfield, since the results obtained show either clear improvements inperformanceorcostreductions.

14. In every iteration, MOST-HDS features the combination of non-gradient-based and gradient-based techniques (i.e. genetic, gradient and swarmsearch intelligence). Other hybrid direct-search algorithms found inliteratureuseadifferentcombinationoftechniquesbut,most importantly,they do not combine them all in every iteration, using each of them fordifferent stages of the optimization process. Once again, the approachfollowedbyMOST-HDShasprovedsuccessful,forthecasesanalyzedinthisThesis.


161

15. Theconceptsofspaceofvariablesandspaceofattributes(alsoreferredtoinliteratureassearchspaceandfitnessspace)areclarified,sothatitcanbefullyunderstoodhowthesearchprocesstakesintoaccountthepositionofeach design point in both spaces. The fact that the optimization processwithinMOST-HDStakes intoaccountthedistanceofcandidatesolutions inbothspaces,andnotonlyinthespaceofattributes,asismorefrequentinliterature, is also a key contribution of this tool. The results obtained(Chapters6and7)showthepotentialandadvantagesofthisapproach.

16. Regardingoptimizationof fluidmechanicsproblems, theMOST-HDSmodelarchitecturecontributestotheStateoftheArtbecauseitcarriesoutafullimplementation of an automatic workflow simulation environment foroptimizationofCFDproblems,basedondirect search, forawide rangeoffields. A key challenging feature of the architecture, which justifies itsnovelty,isthattheoptimizertoolisexternaltotheCFDsolverandtakesfullcontroloftheoptimizationprocess.AnoptimizationarchitectureasgeneralandflexibleastheMOST-HDSmodelhasnotbeenfoundinliterature.Ashasbeenmentionedabove,thisarchitecturehasshownimportantprojecttimereductionsandanincreaseofthenumberofdesigncandidatesevaluated.

17. Themodel developed is thus a fully automatic, robust and highly flexibleoptimizationtoolwhich,onceset-upbyanexpertengineer,canbeusedbyanynon-expertperson.

18. In order to justify the novelty of the research work carried out for thisThesis, and to serveas abasis for reference for future authorsworking inthisfield,areviewoftheStateoftheArthasbeenpresented,forthevariousareasapplicabletothiswork.This isconsideredanadditionalcontribution,as it offers an exhaustive survey of the research in this area, and such asurveyhasnotbeenfoundelsewhere.

19. To conclude, it is considered that thewhole setofobjectivesdescribedatthebeginningofthisThesishavebeenmetquitesuccessfully.Moreover,itisbelieved that this Thesis has contributed to the State of the Art in manyaspects.Allofthesecontributions,whichwereexplainedinChapter1,havebeen analyzed in depth throughout the whole document and again, as asummary,inthisConclusionssection.

8.2.FutureresearchworkbeyondthisThesisApartfromthemoredetailedfuturelinesindicatedthroughoutthedocument,the

mostrelevantfutureresearchlinesareoutlinedbelow:

1. Amoreextensiveresearchontheeffectofotherinitialevaluationsets(i.e.thepoints forPhase0)onthetypeofproblemsweanalyzewillbecarriedout.InthecaseofthisThesis,acustomDoEschemewasused,basedontheauthor’sexperience,butLatinHypercubeSampling(LHS)andothermethodswillalsobetestedinfuturework.


162

2. Further developments will be carried out concerning: tolerance thresholddynamiccalculation(otherschemeswillbetested);effectofmorethanonesearch directions per point; increment factor dynamic calculation (otherschemes will be tested); use of other concepts to assess success of aparticularphaseofthesearch;evaluationofthepotentialofmeshmorphingfortheMOST-HDSgeneralmodel.

3. A more exhaustive comparison to other optimization algorithms for thetypesof industrial problemspresented in this Thesis. Basedon the resultsobtained throughout this research work, other optimization tools aresuspected to have limitations when dealing with aerodynamic shapeoptimization and involving big geometry changes. In particular, somechallenges to be checked for are the requirement of large initial set ofsamplepoints, thepoor coverageof thewholePareto front span, or slowconvergence,requiringmorefunctionevaluationsthanMOST-HDS.

4. The results and observations made concerning surrogate models areespeciallyfocusedonresponsesurfaces.Theconclusionsontheirlimitationsareapplicabletomostoftheothertypesofsurrogatetechniques(ROMsorhierarchical models), although a more extensive work for each surrogatemodelwouldbenecessarytoproveitcompletely.

5. MOST-HDS will be applied to other areas of aerodynamic shape designoptimization.PotentialareasconsideredforapplicationarethosedescribedinPaniagua(2014)(high-speedtrainnosedesign)orZamoranoetal.(2015)(vortexgeneratordesign).

6. Finally,asregardstotheresultsofthebenchmarktestofMOST-HDSwhenappliedtoacommonly-usedmathematicproblem,itcanbeconcludedthatthis algorithm shows a promising performance in the field of generalpurpose optimization. However, a more extensive study needs to beperformedaspartofthefutureworkbeyondthisThesis.

Chapter9 -ReferencesNoonecanreadwithprofitthatwhichhedoesnotlearntoreadwithpleasure.

ThomasHardy.

References1.Abbaspour,M.,andM.N.Shojaee.2009.“InnovativeApproachtoDesignaNewNationalLowSpeedWindTunnel”,InternationalJournalofEnvironmentalScienceandTechnology6(1):23–34.

2.Allen,C.B.,D.J.Poole,andT.Rendall.2016.“EfficientModalDesignVariablesAppliedtoAerodynamicOptimizationofaModernTransportWing”.Paperpresentedat the17thAIAA/ISSMOMultidisciplinaryAnalysisandOptimizationConference.

3. Ameri, M., and F.J. Dorcheh. 2013. “The CFD Modelling of Heat Recovery Steam Generator InletDuct”.InternationalJournalofEnergyEngineering3(3):74-79.doi:10.5963/IJEE0303003.

4. Ardekani, M. A. 2013. “Optimization of a vertical wind tunnel nozzle length using numerical andexperimentalmethods”.JournalofSolidandFluidMechanics3(3):137-147(inPersian).

5. Aslam Bhutta, M.M., N. Hayat, M.H. Bashir, A.R. Khan, K.N. Ahmad, and S. Khan. 2012. “CFDApplicationsinVariousHeatExchangersDesign:AReview”.AppliedThermalEngineering32:1-12.

6. Arreckx, S., A. Lambe, J.R.R.A.Martins, and D. Orban. 2016. “Amatrix-free augmented lagrangianalgorithmwithapplicationtolarge-scalestructuraldesignoptimization”.OptimizationandEngineering17(2):359-384.

7.Auger,A.,J.Bader,D.Brokhoff,andE.Ziztler.2012.“Hypervolume-basedmultiobjectiveoptimization:Theoretical foundations and practical implications”. Theoretical Computer Science 425: 75-103.http://dx.doi.org/10.1016/j.tcs.2011.03.012.

9

Chapter9-References

165

8.Azevedo, C.R.B., and A.F.R. Araújo. 2011. “Correlation between diversity and hypervolume inevolutionary multiobjective optimization”. Paper presented at the IEEE Congress on EvolutionaryComputation(CEC).doi:10.1109/CEC.2011.5949962.

9.Babu,A.2014.“PowerOptimisationTechniquesatCircuitandDeviceLevelinDigitalCMOSVLSI–AReview”.InternationalJournalofEngineeringResearchandTechnology3(11):375-379.

10.Bader,J.2009.“Hypervolume-BasedSearchforMultiobjectiveOptimization:TheoryandMethods”.PhDdiss.ETHZurich.

11. Bader, J., and E. Zitzler. 2011. “HypE: An algorithm for fast hypervolume-based many-objectiveoptimization”.JournalofEvolutionaryComputation19(1):45-76.doi:10.1162/EVCO_a_00009.

12. Bell, J.H., andR.D.Mehta. 1988. “Boundary–layer Predictions for Small Low–speedContractions”,AIAAJournal(ISSN0001–1452)27(3):372–374.

13.Borger,G.G.1976.“TheOptimisationofWindTunnelContractions for theSubsonicRange”.NASATechnicalTranslation/F–16899,NASAWashington.

14.Bradstreet,L.,L.Barone,L.While,S.Huband,andP.F.Hingston.2007.“UseoftheWFGToolkitandPISAforComparisonofMOEAs”.ProceedingsoftheIEEESymposiumonComputational Intelligence inMulti-CriteriaDecision-Making(pp.382-389),Honolulu,Hawaii,USA.

15. Bradstreet, L. 2011. “The hypervolume indicator formulti-objective optimization: calculation anduse”.PhDdiss.UniversityofWesternAustralia.

16. Branke, J., S. Nguyen, C.W. Pickardt, and M. Zhang. 2016. “Automated Design of ProductionSchedulingHeuristics:AReview”. IEEETransactionsonEvolutionaryComputation20(1):110-124.doi:10.1109/TEVC.2015.2429314.

17. Burke, E., M. Gendreau, M. Hyde, G. Kendall, G. Ochoa., E. Özcan, and R. Qu. 2013. “Hyper-heuristics:asurveyofthestateoftheart”.JournaloftheOperationalResearchSociety64(12):1695-1724.doi:10.1057/jors.2013.71.

18.Calautit,J.K.,H.N.Chaudhry,B.R.Hughes,andL.F.Sim.2014.“Avalidateddesignmethodologyforaclosed-loopsubsonicwindtunnel”.JournalofWindEngineeringandIndustrialAerodynamics125:180-194.doi:http://dx.doi.org/10.1016/j.jweia.2013.12.010.

19.Chao,T.,N.Li.,G.Gong.,andZ.Su.2013.“AParameterizedGeometryDesignMethod for InwardTurningInletCompatibleWaverider”.ChineseJournalofAeronautics26(5):1135–1146.

doi:10.1016/j.cja.2013.07.003

20.Courty, F., andA.Dervieux.2006. “Multilevel FunctionalPreconditioning for ShapeOptimisation”.International Journal of Computational Fluid Dynamics 20 (7): 481–490. doi: 10.1080 /10618560600839415.


166

21. Daiber, J. 2006. “Fluid Dynamics of the HRSG Gas Side”. Power Magazine,(http://www.powermag.com/gas/534.html).

22.deCuadra,F.1990.“Elproblemageneraldelaoptimizacióndediseñoporordenador:aplicacióndetécnicasdeingenieríadelconocimiento[TheGeneralProblemofComputer-basedDesignOptimisation:ApplicationofKnowledgeEngineeringTechniques]”.PhDdiss.,PontificiaCOMILLAS–ICAIUniversity.

23.Deb,K.,L.Thiele,M.Laumanns,andE.Zitzler.2001.“ScalableTestProblemsforEvolutionaryMulti-ObjectiveOptimization”.Kanpur, India:KanpurGeneticAlgorithmsLab.(KanGAL), IndianInst.Technol.KanGALReport2001001.

24.Doolan,C.J.,andR.C.Morgans.2007.“NumericalEvaluationandOptimisationofLowSpeedWindTunnel Contractions”. Paper presented at the 18th AIAA Computational Fluid Dynamics Conference,Miami,FL,July25–28.

25.Downie,J.H.,R.Jordinson,andF.H.Barnes.1984.“OntheDesignofThree–dimensionalWindTunnelContractions”.AeronauticalJournal88:287–295.

26. Drela, M., and H. Youngren. 1995. A Users Guide to MISES 2.1. MIT Computational AerospaceSciencesLaboratory.

27.Du,X.,andW.Chen.2004.“SequentialOptimisationandReliabilityAssessmentMethodforEfficientProbabilisticDesign”.JournalofMechanicalDesign126:225-233.

doi:10.1115/1.1649968.

28.Eça,L.,andM.Hoekstra.2014.“AprocedurefortheestimationofthenumericaluncertaintyofCFDcalculationsbasedongridrefinementstudies”.JournalofComputationalPhysics262(1):104-130.doi:http://doi.org/10.1016/j.jcp.2014.01.006.

29.Eckert,W.T.,K.W.Mort,andJ.Jope.1976.“AerodynamicDesignGuidelinesandComputerProgramfor Estimation of Subsonic Wind Tunnel Performance”. NASA Technical Note / D–8243, NASAWashington.

30.Eckert,W.T.,B.M.Wettlaufer,andK.W.Mort.1982.“TheAerodynamicPerformanceofSeveralFlowControlDevices for InternalFlowSystems”.NASATechnicalPaper1972,AVRADCOMTechnicalReport82–A–2.

31. Edelkamp, S., andS. Schroedl. 2011.Heuristic Search:TheoryandApplications. EditedbyMorganKaufmann.

PrintBookISBN:9780123725127.

eBookISBN:9780080919737.

32.Eldred,M.,S.Giunta,andS.Collis.2004.“Second-ordercorrectionsforsurrogate-basedoptimisationwith model hierarchies”. Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis andOptimisationConference,AIAA,Albany,NewYork,August30-September4.

Chapter9-References

167

33. Eres, M.H., M. Bertoni, M. Kossmann, and J. Scanlan, 2014. “Mapping Customer Needs toEngineering Characteristics: An Aerospace Perspective for Conceptual Design”. Journal of EngineeringDesign25(1–3):64-87.doi:10.1080/09544828.2014.903387.

34. Eschenauer, H., J. Koski, and A. Osyczka. 2012.Multicriteria design optimization. Procedures andapplications.EditedbySpringerVerlag.

PrintBookISBN:978-3-642-48699-9.

eBookISBN:978-3-642-48697-5.

35. Fabiano, E.,A.Mishra,D.J.Mavriplis, andK.Mani. 2016. “Time-dependentAero-acousticAdjoint-based Shape Optimization of Helicopter Rotors in Forward Flight”. Paper presented at the 57thAIAA/ASCE/AHS/ASCStructures, StructuralDynamics,andMaterialsConference,SanDiego,California,USA,4-8January.

36.Forti,D.,andG.Rozza.2014.“EfficientGeometricalParameterizationTechniquesof Interfaces forReduced–orderModelling:ApplicationtoFluid–structureInteractionCouplingProblems”.InternationalJournalofComputationalFluidDynamics28(3–4):158–169.doi:10.1080/10618562.2014.932352.

37. Franke, R. 1982. “Scattered data interpolation: tests of some methods”. Mathematics ofComputation38:181-200.doi:https://doi.org/10.1090/S0025-5718-1982-0637296-4.

38.Friedman,D.,andW.R.Westphal.1952.“ExperimentalInvestigationofa90oCascadeDiffusingBendwithanAreaRatioof1.45:1andwithSeveralInletBoundaryLayers”.NACATechnicalNote2668.

39.Fürnkranz,J.,andM.Kubat.2001.“MachineLearninginGames:ASurvey”InMachinesthatLearntoPlayGames,editedbyNovaScientificPublishers,Huntington,NY,Chapter2:11-59.

40. Galindo-García, I.F., A.K. Vázquez-Barragán, andM. Rossano-Román. 2012. “CFD Simulations of aHeat Recovery Steam Generator for the Aid of Power Plant Personnel”. Proceedings of the 20thInternational Conference on Nuclear Engineering and ASME 2012 Power Conference, Anaheim,California,USA,July30-August3.

41.Galindo-García,I.F.,A.K.Vázquez-Barragán,andM.Rossano-Román.2014.“CFDSimulationsofHeatRecoverySteamGenerators IncludingTubeBanks”.Proceedingsof theASME2014PowerConferencePOWER2014,Baltimore,Maryland,USA,July28-31.

42.Giles,M.B.,andM.Drela.1987.“Two–DimensionalTransonicAerodynamicDesignMethod”.AIAAJournal25:1199–1206.

43. Giles, M.B., and N.A. Pierce. 2000. “An Introduction to the Adjoint Approach to Design”. Flow,TurbulenceandCombustion65:393-415.

44. González, M.A., A.I. Moreno, A.A. Jarzabek, J.M. Perales, Y. Wu, and S. Xiaoxiao. 2013. “DesignMethodology for a Quick and Low–Cost Wind Tunnel” In Wind Tunnel Designs and Their DiverseEngineeringApplications,editedbyDr.NoorAhmed,ISBN:978–953–51–1047–7.doi:10.5772/54169.


168

45.Guliashki,V.2008.“AHybridDirectSearch–Quasi-NewtonMethod for the InverseEITProblem”.BulgarianAcademyofSciences.CyberneticsandInformationTechnology8(2).

46.Hartigan,J.A.1975.ClusteringAlgorithms.JohnWiley&Sons,NewYork.

47. Hegazi, H.A., A.O. Nassef, and S.Metwalli. 2002. “Shape Optimization of NURBSModeled 3D C-Frames Using Hybrid Genetic Algorithm”. Proceedings of the ASME 2002 International DesignEngineering Technical Conferences and Computers and Information in Engineering Conference. doi:http://dx.doi.org/10.6036/NT7357.

48.Hegde,N., I.Han,T.W.Lee,andR.P.Roy.2007. “FlowandHeatTransfer inHeatRecoverySteamGenerators”.JournalofEnergyResourcesTechnology129:232-242.

49.Held,S.,B.Korte,D.Rautenbach,andJ.Vygen.2006.“CombinatorialOptimisationinVLSIdesign”.Paperpresentedat the45th Sessionof the SéminairedeMathématiques Supérieures,Montréal, June19-30.

50.Hicken,J.E.,andD.W.Zingg.2010.“AerodynamicOptimisationAlgorithmwithIntegratedGeometryParameterizationandMeshMovement”,AIAAJournal48(2):February.

51.Hoffenson,S.,A.Dagman,andR.Söderberg.2015.“ToleranceOptimisationConsideringEconomicandEnvironmentalSustainability”.JournalofEngineeringDesign25(10–12):367–390.

doi:10.1080/09544828.2014.994481.

52. Hoghooghi, H., M.N. Ahmadabadi, and M.D. Manshadi. 2016. “Optimization of a subsonic windtunnelnozzlewith lowcontraction ratio viaball-spine inversedesignmethod”. JournalofMechanicalScienceandTechnology30:2059.doi:10.1007/s12206-016-0412-2.

53.Hooke,R.,andT.A.Jeeves.1961.““DirectSearch”solutionsofnumericalandstatisticalproblems”.JournaloftheACM8(2):212-229.doi:10.1145/321062.321069.

54.Hsiao,C.T.,Chahine,G.,andGumerov,N.2001.“ApplicationofaHybridGenetic/PowellAlgorithmand a Boundary Element Method to Electrical Impedance Tomography”. Journal of ComputationalPhysics173:433-454.doi:10.1006/jcph.2001.6866.

55.Huband,S.,P.Hingston,L.Barone,andL.While.2006.“AReviewofMulti-objectiveTestProblemsandaScalableTestProblemToolkit”.IEEETransactionsonEvolutionaryComputation10(5):477-506.

56.Idel’Cik,I.E.1969.Mementodespertesdecharge:Coefficientsdepertesdechargesingulièresetdepertesdechargeparfrottement[HydraulicHandbookonPressureLosses:ShapeandFrictionPressureLossCoefficients].EyrollesEditeur,Paris.

57. Janardhanan,S.2011.ModelOrderReductionandControllerDesignTechniques.Coursenotes. IITDelhi,India.

Chapter9-References

169

58. Jeong, S., M. Murayama, and K. Yamamoto. 2005. “Efficient Optimisation Design Method UsingKrigingModel”.JournalofAircraft42(2):March-April.

59. Jing, L., G. Zhenghong, H. Jiangtao, and Z. Ke. 2013. “Aerodynamic design optimization ofnacelle/pylonpositiononanaircraft”.ChineseJournalofAeronautics26(4):850-857.

60.Jordinson,R.,andD.I.C.1961.“DesignofWindTunnelContractions:AMethodBasedontheUseofthe Schwarz-Cristoffel Transformation for Incompressible Inviscid Flow”. Aircraft Engineering andAerospaceTechnology33(10):294–297.

61. Katz, J. 2006. New Directions in Race Car Aerodynamics. Designing for Speed. Edited by BentleyPublishers.

ISBN-10:0837601428.

ISBN-13:978-0837601427.

62.Kelly,J.C.,P.Maheut,J.F.Petiot,andP.Y.Papalambros.2010.“IncorporatingUserShapePreferenceinEngineeringDesignOptimisation”.JournalofEngineeringDesign22(9):627–650.

doi:10.1080/09544821003662601.

63. Kenway, G.K., A. Mishra, N.R. Secco, K. Duraisamy, and J. Martins. 2017. “An Efficient ParallelOverset Method for Aerodynamic Shape Optimization”. Paper presented at the 58thAIAA/ASCE/AHS/ASCStructures,StructuralDynamics,andMaterialsConference,Grapevine,Texas,USA,January9-13.

64. Koziel, S., and X-S. Yang. 2011. Computational Optimisation, Methods and Algorithms. Springer-VerlagBerlinHeidelberg.doi:10.1007/978-3-642-20859-1.

65.Krajnovic,S.2007.“AerodynamicOptimisationofVehiclesUsingComputationalFluidDynamicsandResponse Surface Methodology”. Paper presented at the 21st International JUMV AutomotiveConferenceSCIENCE&MOTORVEHICLES(PaperNMV0724),Beograd.

66.Lee,B.E.,S.B.Kwon,andC.S.Lee.2002.“OntheEffectofSwirlFlowofGasTurbineExhaustGasinanInletDuctofHeatRecoverySteamGenerator”.ASMEJournalofEngineeringforGasTurbinesandPower124:496-502.

67.Lee,C.,D.Koo,andD.W.Zingg.2017.“ComparisonofB-SplineSurfaceandFree-FormDeformationGeometryControlforAerodynamicOptimization”.AIAAJournal55(1):228-240.

68. Li, H., andQ. Zhang. 2009. “MultiobjectiveOptimization Problemswith Complicated Pareto Sets,MOEA/DandNSGA-II”.IEEETrans.onEvolutionaryComputation12(2):284-302.

69.Liem,R.P.,J.R.R.A.Martins,andG.K.W.Kenway.2017.“Expecteddragminimizationforaerodynamicdesignoptimizationbasedonaircraftoperationaldata”.AerospaceScienceandTechnology63:344-362.


170

70.Lindgren,B.,J.Österlund,andA.V.Johansson.1998.“MeasurementandCalculationofGuide–vanePerformanceinExpandingBendsforWind–Tunnels”.ExperimentsinFluids24:265–272.

71. Liu, X., and Z. Zhang. 2014. “A Hybrid Reliability Approach for Structure Optimisation Based onProbabilityandEllipsoidalConvexModels”.JournalofEngineeringDesign25(4–6):238–258.

doi:10.1080/09544828.2014.961060.

72.Lund,E.,H.Møller,andL.Jakobsen.2003.“Shapedesignoptimizationofstationaryfluid-structureinteraction problems with large displacements and turbulence”. Structural and MultidisciplinaryOptimization25(5):383-392.doi:10.1007/s00158-003-0288-5.

73.Lyu,Z.,G.K.W.Kenway,andJ.R.R.A.Martins.2014.“AerodynamicShapeOptimizationInvestigationsof the Common Research Model Wing Benchmark”. AIAA Journal 53 (4): 968-985. doi:10.2514/1.J053318.

74. Mani, K., and D.J. Mavripilis. 2009. “Adjoint-Based Sensitivity Formulation for Fully CoupledUnsteadyAeroelasticityProblems”.AIAAJournal47(8):1902-1915.doi:10.2514/1.40582.

75. Marduel, X., C. Tribes, and J-Y. Trépanier. 2006. “Variable-fidelity Optimisation: Efficiency andRobustness”.OptimisationandEngineering7(4):479-500.

doi:10.1007/s11081-006-0351-3.

76. Mavripilis, D.J. 2007. “A Discrete Adjoint-Based Approach for Optimization Problems on Three-DimensionalUnstructuredMeshes”.AIAAJournal45(4):740-750.doi:10.2514/1.22743.

77. Mengistu, T., and W. Ghaly. 2008. “Aerodynamic Optimisation of Turbomachinery Blades UsingEvolutionaryMethodsandANN–basedSurrogateModels”.OptimisationandEngineering9:239-255.

78.Mikhail,M.N.1979.“OptimumDesignofWindTunnelContractions”.AIAAJournal17(5):articleno.78–819.

79.Minella,G.,R.Ruiz,andM.Ciavotta.2008.“AReviewandEvaluationofMultiobjectiveAlgorithmsfor the Flowshop Scheduling Problem”. INFORMS Journal on Computing 20 (3): 451-471. doi:10.1287/ijoc.1070.0258.

80.Morel,T.1975.“ComprehensiveDesignofAxisymmetricWindTunnelContractions”ASMEJournalofFluidsEngineering97:225–233.

81.Morel, T. 1977. “Design of Two–dimensionalWind Tunnel Contractions”. ASME Journal of FluidsEngineering99:371–378.

82. Nelder, J.A., and R. Mead. 1965. “A Simplex Method for FunctionMinimization”. The ComputerJournal7(4):308-313.doi:https://doi.org/10.1093/comjnl/7.4.308.

Chapter9-References

171

83.Nielsen,E.J.,E.M.Lee-Rausch,andW.T.Jones.2010(a).“Adjoint-BasedDesignofRotorsUsingtheNavier-Stokes Equations in a Non-inertial Reference Frame”. Journal of Aircraft 47 (2). doi:10.2514/1.46044.

84. Nielsen, E.J., B. Diskin, andN. Yamleev. 2010 (b). “Discrete Adjoint-BasedDesignOptimization ofUnsteady Turbulent Flows on Dynamic Unstructured Grids”. AIAA Journal 48 (6): 1195-1206. doi:10.2514/1.J050035.

85.Nunez,M.,V.C.Datta,A.Molina-Cristobal,M.Guenov,andA.Riaz.2012.“EnablingExploration intheConceptualDesign andOptimisationof Complex Systems”. Journal of EngineeringDesign23 (10–11):852–875.

doi:10.1080/09544828.2012.706800.

86.Okumura,H.,Y.Hikino,andM.Kawahara.2013.“AShapeOptimisationMethodofaBodyLocatedinAdiabaticFlows”.InternationalJournalofComputationalFluidDynamics27(6–7):297–306.

doi:10.1080/10618562.2013.828049.

87.Paniagua,J.2014.“AerodynamicOptimisationoftheNoseShapeofaHigh–SpeedTrain”.PhDdiss.,TechnicalUniversityofMadrid.

88. Pillay, N. 2016. “A review of hyper-heuristics for educational timetabling”. Annals of OperationsResearch239(1):3-38.doi:10.1007/s10479-014-1688-1.

89.Poole,D.J.,C.B.Allen,andT.C.S.Rendall.2017.“High-fidelityaerodynamicshapeoptimizationusingefficientorthogonalmodaldesignvariableswithaconstrainedglobaloptimizer”.ComputersandFluids143:1-15.

90. Prada-Nogueira, I., F. de Cuadra, and A. Sánchez-Miralles. 2015. “Towards a general model forautomatic and flexible design of closed wind tunnels”. Internal publication. Institute for Research inTechnologyIIT-15-154A.

http://www.iit.upcomillas.es/publicaciones/mostrar_publicacion_working_paper.php.en?id=259.

91.Prada-Nogueira, I.,F.DeCuadra,andA.Sánchez-Miralles.2017(a).“GeneralModel forAutomaticDesignOptimisationofAerodynamicComponents.WindTunnelCaseStudy”.DYNA.DYNA-ACELERADO.(0):0.doi:http://dx.doi.org/10.6036/8144.

92.Prada-Nogueira, I., F.J.Álvarez,F.DeCuadra,andA.Sánchez-Miralles.2017 (b). “Boiler InletDuctShapeDesignOptimizationforCombinedCyclePowerPlants”.DYNA(approvedforpublication).

93. Roache, P.J. 1994. “Perspective: A Method for Uniform Reporting of Grid Refinement Studies”.JournalofFluidsEngineering116(3):405-413.doi:10.1115/1.2910291.


172

94. Robinson, T.D., MS. Eldred, K.E. Willcox, and R. Haimes. 2006. “Strategies for MultifidelityOptimisation with Variable Dimensional Hierarchical Models”. Paper presented at the 47thAIAA/ASME/ASCE/AHS/ASCStructures,StructuralDynamics,andMaterialsConference,Newport,RhodeIsland,May1-4.

95. Rumpfkeil, M.P., and D.W. Zingg. 2010. “The optimal control of unsteady flows with a discreteadjointmethod”.OptimizationandEngineering11(1):5-22.doi:10.1007/s11081-008-9035-5.

96.Schaumont,P.,andI.Verbauwhede.2004.“InteractiveCosimulationwithPartialEvaluation”.Paperpresentedatthe7thDesign,AutomationonTestinEuropeConference(DATE’04),Paris,France.

97.Schweppe,F.C.,andH.M.Merril.1986.“MultipleAttributeTrade-OffAnalysis”.EPRIRP2537,April.

98.Shi,Y.,andR.Eberhart.1998.“AModifiedParticleSwarmOptimizer”.IEEE:69-73.

0-7803-4869-9198.

99.Shi,X.,W.Chriswindarto,andD.Boyce.2009.“ApplicationofCFDModellinginHRSGEvaseDesign”.Proceedingsofthe2009PowerConference,ASME,Albuquerque,NewMexico,USA,July21-23.

100.Simpson,T.W.,J.D.Peplinski,P.N.Koch,andJ.K.Allen.2001.“Metamodelsforcomputer-basedengineeringdesign:Surveyandrecommendations”.EngineeringwithComputers17:129-150.

101.Su,W.,S.S-M.Swei,andG.G.Zhu.2016."OptimumWingShapeofHighlyFlexibleMorphingAircraftfor Improved Flight Performance". Journal of Aircraft 53 (5): 1305-1316. doi:http://dx.doi.org/10.2514/1.C033490.

102.Sundén,B.2007.“ComputationalFluidDynamicsinResearchandDesignofHeatExchangers”.HeatTransferEngineering28(11):898-910.

103.Takagi,H.2001.“InteractiveEvolutionaryComputation:FusionoftheCapacitiesofECOptimisationandHumanEvaluation”.ProceedingsoftheIEEE89(9):1275–1296.

104. Vieira, E.D.R., and J.B. Aparecido. 1999. “Design and Construction of Small AxisymmetricContractions”.In5ªReunióndoGrupoDeTrabajoSobreHidromecánicapublication,103–116.

105. Volkwein, S. 2013. Proper Orthogonal Decomposition: Theory and Reduced Order Modelling.Lecturenotes.UniversityofKonstanz.

106.Walton, S., O. Hassan, and K.Morgan. 2013. “Reduced ordermodelling for unsteady fluid flowusingproperorthogonaldecompositionandradialbasisfunctions”.AppliedMathematicalModelling30(20-21):8930-8945.doi:http://dx.doi.org/10.1016/j.apm.2013.04.025.

Chapter9-References

173

107.Washabaugh,K.,D.Amsallem,M.Zahr,andC.Farhat.2012.“NonlinearModelReductionforCFDProblems Using Local Reduced Order Bases”. Paper presented at the 42nd AIAA Fluid DynamicsConferenceandExhibit,NewOrleans,LA,June25-28.

108. Wild, J. 2008. “Multi–objective Constrained Optimisation in Aerodynamic Design of High–liftSystems”.InternationalJournalofComputationalFluidDynamics22(3):153–168.

doi:10.1080/10618560701868420.

109.Xiao,M.,L.Gao,X.Shao,H.Qiu,P.Jiang.2012.“AGeneralisedCollaborativeOptimisationMethodanditsCombinationwithKrigingMetamodelsforEngineeringDesign”.JournalofEngineeringDesign23(5):379–399.

doi:10.1080/09544828.2011.595706.

110.Yoshimura,M.,M.Hasuike,T.Miyashita,andH.Yamakawa.2013.“EvaluationofIndustrialMachineDesign Improvement IdeasUsingCharacteristic-basedHierarchicalOptimisationStrategies”. JournalofEngineeringDesign24(11):794–813.

doi:10.1080/09544828.2013.862226.

111. Youngren,H., andM.Drela. 1991. “Viscous/InviscidMethod for PreliminaryDesign of TransonicCascades”.Paperpresentedatthe27thAIAA,SAE,ASME,andASEEJointPropulsionConference.

112.Zamorano-Rey,G.,B.Garro,U.Fernández-Gámiz,andE.Zulueta.2015.“AComputationlStudyoftheVariationof the IncidenceAngle inaVortexGenerator”.DYNANewTechnologies2 (1):1-13.doi:http://dx.doi.org/10.6036/NT7357.

113.Zhao,L.2007.“Performanceofmulti-objectivealgorithmsonvaryingtestproblemfeaturesusingtheWFGtoolkit”.Thesis.TheUniversityofWesternAustralia.

114. Zhou, Q., X. Shao, P. Jiang, H. Zhou, L. Cao, and L. Zhang. 2015. “A Deterministic RobustOptimisationMethodUnderIntervalUncertaintyBasedontheReverseModel”.JournalofEngineeringDesign26(10-12):416-444.doi:10.1080/09544828.2015.1072763.

115. Zitzler, E., K. Deb, and L. Thiele. 2000. “Comparison of multiobjective evolutionary algorithms:Empiricalresults”.EvolutionaryComputation8(2):173-195.


174

WebreferencesmentionedthroughouttheThesis(lastverifiedonFebruary2017):

1.www.moeaframework.org:MOEAframework.UsefulresourceonMOEAs.

2. https://ls11-www.cs.uni-dortmund.de/rudolph/hypervolume/start: Very interesting summary ofhyper-volume-relatedliterature.

3.https://hpi.de/en/friedrich/research/hypervolume.html:Additionalhyper-volumeliterature.

4.http://www.aero.upm.es/LSLCWT:Access toa fullwind tunnelExceldesign spreadsheetdevelopedbyGonzálezetal.(2013).


AppendixA-IllustrationoftheMOST-HDSprocess

IllustrationoftheMOST-HDSprocessforthemostcomplexcasepresented,thewindtunnelshapeoptimization.

1. TheMOST-HDSuserinterfacehastreesimplesteps,asshowninFigure0–1

Figure0–1-MOST-HDSuserinterface.

2. Problemdesign:Thisisdoneviaa.txtfilecreatedbytheuser.Thisfileindicatesthenumberofhierarchiesofvariables,thenameandtypeofeachvariable,andtheirrangeofvalues.Italsospecifiesnumber,nameandtypeofattributes.

A

AppendixA–IllustrationoftheMOST-HDSprocess

177

Figure0–2-Problemdesigninputfile.

3. TheExceltoolcreatedtoimplementMOST-HDScangenerateaverywiderangeofclosedwindtunnelconfigurations,basedonthevalueoftheinputvariables.The geometry is generated via Bézier cubic curves and their correspondingcontrolpoints.Theprogramcarriesoutageometryabsurditychecktovalidateifthegeometryhasnegativevolumes,intersections,etc.TheexampleofFigure0–3illustratesacasewithabsurdgeometry.

Figure0–3-Geometryparameterization.


178

4. Phase0treegeneration:thedesignpointsforthedesignexplorationofPhase0are generated. Note that the variables defined by the user (Figure 0–2) aretransformed to variables used by ANSYS to generate the tunnel geometry(Figure 0–4). In ANSYS there are many more variables, hence not all areindependent, and they are far less intuitive than those defined by the user,whicharethevariablesusedfortheoptimizationprocessitself.

Figure0–4-GenerationofExceldesignpointtable.Inparticular,generationofdesignpointsfor

Phase0(designexplorationphase)andvariabletransformationtoANSYSvariables.


179

5. ANSYSworkflowforwindtunnelshapedesignoptimization.

Figure0–5-ANSYSworkflowarchitecture.


180

6. ANSYSparameterset:ANSYSreceivesthevariablevaluesforeachdesignpointfromtheExceldesignpointtable.

Figure0–6-ANSYSparametersetwithvaluesreceivedfromExcelforalltheANSYSvariables.

7. TheautomaticworkflowsetupinANSYS,basedonthevaluesofthevariablesofeach design point, creates the geometry (Figure 0–7), generates the mesh(based on the meshing configuration) (Figure 0–8), carries out the CFDsimulation for each design point (Figure 0–11) and finally feeds the valuesobtained for eachattribute automaticallyback to theExcel designpoint table(Figure 0–12). A closer view of the mesh is presented in Figure 0–9 andinformationonthemeshquality(skewness)isgiveninFigure0–10(refertothedetailedjustificationinAppendixBregardingtheoccasionaluseofmesheswithapparentlyunacceptableskewnessvalues).


181

Figure0–7-ANSYSgeometrygeneration.

Figure0–8-ANSYSmeshgeneration.


182

Figure0–9-ANSYSmeshgeneration(detail).

Figure0–10-Examplemeshqualityformostcomplexdesignpoints.


183

Figure0–11-ANSYSFLUENTCFDsimulationresults.

Figure0–12-AttributevaluesobtainedinANSYSarefedbacktotheExceldesignpointtable.


184

8. Once the results of all the design points for a particular phase have beencomputedand fedback toANSYS, thePareto front isautomatically calculatedand drawn. The optimization intelligence coded intoMOST-HDSwill generatethedesignpointstobesimulatedinthenextphaseoftheoptimization.

9. ThisprocessisrepeateduntiltheoptimizationstoppingcriteriaaremetandthefinalresultfortheoptimizedParetofrontisobtained(Figure0–15).

Figure0–13-Paretofrontautomaticcalculation.


185

Figure0–14-MOST-HDScomputationofthedesignpointsforthefollowingoptimizationphase.

Figure0–15-MOST-HDSoptimizationfinalresult.


AppendixB-Importantnotesonmeshsensitivityandmeshquality

Important remarkson themeshsizesused, thesensitivityof the results to themeshsizeandageneralcommentonmeshqualities.

B.1.MeshsensitivityForadirectsearchoptimization,itiskeytodevelopanefficientsearchprocessand

toensure thecalculation time isminimized, so that thebestminimumsetofdesigncandidatesisevaluatedintheshortesttimepossible.Inordertoachievetheobjectiveisminimizing (oroptimizing) the computation time for eachdesignpoint, given thatthe CFD simulationwas themost time consuming part of the process, an adequaterangeofmeshsizeshad tobedetermined.Averycoarsemeshwould result inpooraccuracy, whereas a very fine mesh would improve accuracy but would increasecomputation time. The determination of an adequate range of mesh sizes for thedesign configurations that were going to be considered did not aim to bemathematicallystrict,butinsteaditaimedatbeingreasonablefromanengineeringorindustrial perspective. Therefore this Thesis has not followed the classical GridConvergence Index methodology (GCI) of Roache (1994) or the more advancedmethodologiesofEçaandHoekstra(2014).Instead,thesensitivityanalysiscarriedoutinthisThesiswaslimitedtoacomparisonoftheresultsobtainedwithincreasingmeshsizes. The optimum mesh size range would be the minimum size above which theresultsobtaineddidnotvarymorethanareasonablethresholdfortherelativeerror(thiswaslimitedto3-5%).

This study was carried out for the wind tunnel case, since the mesh for theindustrialboilerswasnotaschallengingandevenveryrefinedmeshescomputedfast.

Theresultsofthisnon-exhaustivemeshsensitivityanalysisareillustratedinFigure0–1.Theconclusionwasthatmeshesintherangeof2-3millionelementsmarkedthethresholdabovewhichtheresultsshowednoconsiderablevariation.Themeshingset-upwasdonesothatmeshsizesformostwindtunnelswouldbekeptwithinthisrange.Thisdoesnotmeanthatcertaindesignpointgeometrieshavehadfinermeshes(butnotcoarser)thanthisrange.

B

AppendixB–Importantnotesonmeshsensitivityandmeshquality

187

Figure0–1-Illustrationofthenon-exhaustivemeshsensitivityanalysiscarriedoutforthisThesis.

B.2.MeshqualityAs already presented in Appendix A, a typical mesh for the wind tunnel case is

presented in Figure 0–2, a closer view of the mesh is shown in Figure 0–3 andinformationonthemeshquality(skewness)isgiveninFigure0–4.

Theskewnessforthemeshofsomedesignpointshasamaximumvaluecloseto1oreven1.Thisiscommonlyregardedasanindicatorofaninadequatemesh.Forthisparticularcase,atrade-offmustbereachedbetweenhavinganautomaticgenerationof themeshwhich is applicable to a verywide rangeof tunnel designs (therefore avery design-specific mesh set-up cannot be used) and having an adequate meshquality.Ithasbeencheckedthatthemeshelementswithunacceptableskewnessarelocatedinthetransitionfromthetunnelducttothefanand,insomecases,inaveryreducednumberofelementsinthetransitionfromthetestsectiontothetunnelduct.Reducingtheskewnesswouldeithermeanhavingadesign-specificmeshset-upwhichwouldnotworkautomatically for all generated tunnel geometries, or increasing thenumberofelementsandthusthecomputationtimetounacceptablelevels.Thereforethe skewness of these very few elements has been neglected and themesheswithsuch a high skewness have been considered acceptable. The results obtained withthesemesheshavebeenanalysedandtheyhavebeenfoundtobecoherentwiththeresultsofothertunnelgeometrieswithmeshesofmuchlowerskewness.


188

Figure0–2-ANSYSmeshgeneration.

Figure0–3-ANSYSmeshgeneration(detail).

AppendixB–Importantnotesonmeshsensitivityandmeshquality

189

Figure0–4-Examplemeshqualityformostcomplexdesignpoints.

aerodynamic design optimization based on multi-attribute

Documents