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NomenclatureCAD Computer Aided Design

CFD Computational Fluid Dynamics

NSGA Non-dominated Sorting Genetic Algorithm

RANS Reynolds Averaged Navier Stokes

RMS Root Mean Squared

SST Shear Stress Transport

Symbolsβ Bladeangle

D Characteristic Linear Dimension

ε Turbulencedissipationrate

∅ Variableofthegeneraltransportequation

k Kineticturbulenceenergy

M Machnumber

μ Dynamicviscosity

μt Turbulenteddyviscosity

ρ Density

Re Reynoldsnumber

t Time

v Velocity

y+ Dimensionless wall distance

ω Specificturbulencedissipationrate

IntroductionTheaeronauticalindustryanditscompetitivenessinthemarketof

increasinglyefficientaircraft,constantlyseekthroughalotofresearchand technological development, an increasingly safe and cheapsolutiontothefinalconsumerwhoisthepassenger.Thesesurveyscanfollowdifferentgoalssuchas:dragreduction,liftimprovement,fueleconomy, noise reduction, improved thermal comfort, greater easeofmanufacturing,robustpartsdesigntoincreaseyourlife,increasedpropulsion and reduced costs generally. For each of these fields,severalstudieswererequired.

Inthepresentwork,theaxialturbineusedtosupplypowertothecompressor in the propulsion system of an aircraft, known as gasturbineengine,wasstudiedandamethodologywascreated for theoptimizationofthisturbomachineinitsearlydesignphase.Asuitabledesign of an axial turbine is aimed at generating power, efficiencyand a good compromisewith its performance. One of the greatestchallengesisundoubtedlytheadequacyandgooddimensioningofitsaxialchannel,fromtheinlettotheoutletoftheturbomachine.Becauseit isa time-consumingandcomplextasktochangeandanalyzetheflowateachgeometricchangeintheturbine,theuseofsupporttoolsiscertainlyveryinterestingtothedesigner.Oneoftheseresourcesistheuseofoptimizationalgorithmscoupledwiththedesigntools.

Amethodologyhasbeendevelopedtousethesetoolsinacoupledwaywiththeaimofprovidinginterestingresultstothedesigner,whocan analyze different solutions for a given problem.The choice ofthemostappropriatedesign,at theendof theoptimizationprocess,isstronglydependentonwhat isdesiredfor the turbomachine.Theoptimizationtechniqueperformssearchesthroughobjectivefunctionsandconstraints,adoptedbytheuser,withtheuseofspecificalgorithms.Thus,thecomputationaltoolsofthecompressibleandturbulentflowthrough the turbine were coupled with optimization models. Theflow was calculated using Computational Fluid Dynamics (CFD)techniques.Withthesolutionsofthecharacteristicsoftheflow,itispossibletodeterminetheoperationalcharacteristicsoftheturbine.

Aeron Aero Open Access J. 2019;3(4):198‒211. 198©2019 Amaral et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine

Volume 3 Issue 4 - 2019

Luiz Gustavo Franco Amaral,1,2 Rubén Bruno Diaz,1 Jesuino Takachi Tomita,1 Cleverson Bringhenti,1 Izabela Batista Henriques1

1Aeronautics Institute of Technology, Turbomachines Department, São José dos Campos, Brazil2ESSS-ANSYS,423 Rocio St., ITC e International Trade Center, Brazil

Correspondence: Luiz Gustavo Franco Amaral, Aeronautics Institute of Technology, Turbomachines Department, São José dos Campos, Brazil, Email

Received: October 14, 2019 | Published: December 05, 2019

Abstract

The internalflow in turbomachines is extremelycomplexdue to the levelofdetailsoftheblades,withdifferentanglesanddifferentlevelsofcurvatureandthickness,aswellasthecharacteristicsofthechannelbetweenbladesthatisadirectreflectionofthegeometryemployed, added to the phenomena caused by high speed rotation. In the literaturewecan find several studies that aim to improve the performance of aeronautical turbines,an arduous but necessary task, to enable the maximization of efficiency and power,thus leading to evenmore complex projects.Among the various possible strategies, anengineeringbranchspecializesincomputationaltechniquesduetotheagilityandversatilitytheyprovide.Throughavirtualprototype,itbecomespossibletoobservethephenomenainvolvedandchangesincontourandgeometryconditionstocomparetheresults.ThisstudyseekstheoptimizationofanaxialturbinefromasmallgasturbineenginedevelopedbyITAusingComputationalFluidDynamics(CFD)andMulti-ObjectiveOptimizationtechniquesfocusedongeometrychangestomaximizetheturbineperformance.ThesimulationprocesswillbedonethroughtheuseofthecommercialsoftwareANSYS®.

Keywords: turbo-machinery,optimization,CFD,ANSYS,multi-objective,modefrontier

Aeronautics and Aerospace Open Access Journal

Research Article Open Access

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 199Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Axial turbine fundamental concepts

Turbines are components that transform thermal and pressureenergyintomechanicalenergythroughthekineticenergyoftheflowthrough the grid of the rotating system.The generatedmechanicalenergycanbeusedinseveralways,suchastriggeringanotherdevice(e.g. a compressor or a pump) or tomove a generator.Essentially,the twomost common types of turbines are: the radial turbine andthe axial turbine. There are mechanisms to determine which typeismost suitable for aparticular application, for example,using thespeedor specific rotationdiagram. Ingeneral, for lowflowvalues,radialturbinesaremoreindicated.Becauseofthegreaterdeflectionsintheflow,theradialmachinestransfermoreenergyperrotor,whencomparedtotheaxialmachines.Asabasicoperatingprinciple,thehotgasfromthecombustionchamberpassingthroughtheaxialturbineissubjectedtovaryingtheamountofmovement,raisingthekineticenergyoftherelativeflowandasaconsequencegeneratingmovement(rotation) of the rotor. This rotor grille then acquires mechanicalpowerthroughtheshaftthatisabsorbedbythecompressor.

Computational fluid dynamics

Computational Fluid Dynamics is the area of engineering thatdetermines the general equations of fluid mechanics (continuity,momentum and energy) through approximate numerical solutions.Theinitialdevelopmentofthistechniquedatesbacktothelate1960s,when Brian Spalding worked with his students to transform CFDfromamathematicalsciencetoarichresourceforengineerstosolvereal problems.1 From established theoretical concepts, numericalandcomputationalmethodsareusedtocalculatecomplexproblemsthat would be difficult to solve by means of analytical methods.This technique uses the transport theory, heat transfer, chemicalreactionsandotherfluiddynamicsphenomenatoassisttheindustryintheresearchanddevelopmentofprojects.CFDprovidesdetailedandaccurateflowandfluidbehavior information, suchaspressure,velocity and temperature distributions, forces and torques, phasedistributions,flowpaths,recirculationflowzones,amongothers.

Itsapplication takesplace inawide rangeof segments, suchasaerospace, automotive, biomedical, energy, chemical processes,electroniccomponents,andcanbeusedinallstagesoftheengineeringprocess, from concept and design of new products to optimizationphase, fault handling and re-design. Fundamentally, the methodcontainsthreebasicsteps:

a. Pre-processing: in which the CAD drawing of the proposalequipment is prepared, discretized (in computational domain)and has its boundary conditions assigned. Hypotheses andsimplificationsaremadeatthisstage;

b. Processing: stage in which the computer program of highperformancesolvesthetransportequations(fluidmechanics)andother equations that model the physics and phenomena of theproblemtobesolved;

c. Post-processing:wherephenomena involved in thecasecanbeevaluatedwith the responseof thecalculatednumericalmodel.At this point the user evaluates the numerical results to discuss possibledesignimprovementsandanalyzethecharacteristicsoftheflow,heattransferandmassasawholetoeachengineeringproblem.

Governing equations

ThelawsofconservationrespectLavoisier’sobservationsofmorethan200years:Inachemicalreactiondoneinaclosedvessel,thesumofthemassesofthereactantsisequaltothesumofthemassesoftheproducts.Fromhisremark,thefamousphrase“In nature nothing is created and nothing is lost, everything is transformed” wascreated.Inmathematicaltermswecanprovethisbymeansofacontrolvolume,showninFigure1.

Figure 1 Space defined system.2

Through the balance in this control system and the use of thedivergencetheoremitispossibletoarriveatthedifferentialformofthetransportequation,asinEquation1.

0 v

tρ ρ∂

= +∇ ⋅∂

(1)

The equation can be presented in terms of mass, momentumand energy after the imbalance on the control system.After somerearrangementitispossibletoexpressthegeneraltransportequation,presentinEquation2,orgeneraltransportequationof∅ variable:

.

V VA A

dV dA dA S dVtρ ρ ∅ ∅ ∅

∂∅ + ∅ = Γ ∇ ⋅ +

∂ ∫ ∫∮ ∮v

(2)

The structure of this equation is the basis of all CFDmethodsandshowsatransienttermfollowedbyaconvective,adiffusiveandfinally thesource term.On thisequation thecontinuity,momentumand energy equations can be expressed after the∅ variable isrespectively changed by the mass, velocity and temperature. Fora discrete domain, each cell volumewill need to have all of theseexpressionssolved.

Turbulence

ThestudyofturbulenceremarksthetimeofthenotableLeonardoDaVinci,around500yearsago.Inaverycleverway,hewasabletounderstandtheeffectsofturbulencebycomparingthisphenomenontothemovementofhumanhair.3 Nowadays it is well known that a flowcanbeclassifiedinthreedifferentways:laminar,turbulentandtransitional.TheReynoldsnumber,fromEquation3,isusedtohelpinthisclassification.

vDRe ρµ

=

(3)

Theturbulenceisacharacteristicoftheflowandnotofthefluid,

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 200Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

and as a consequence the general characteristics of the turbulencearerespectedforallfluids.4Duetothis,theturbulencebehaviorcanbemodeledtosavethetroubleofcalculationalltheturbulentscalesassociatedtotheproblem(Figure2).

Figure 2 Velocity fluctuation.5

There are several turbulence models common to both researchlabs and industry. For this paper the chosen method is RANS, orReynolds Averaged Navier Stokes. This methodology models allturbulentstructuresonthedomaininordertoprovidegoodstationaryresolutionformostengineeringapplications.6ThisprojectsolvesthecompressibleflowequationsbytheuseoftheSSTturbulencemodel,whichwasproposedbyMenterin1993andrepresentsanenhancedk-ωmodel.7 Previous works have shown that this is an appropriate model for solving 3D turbulent flow simulations applied toturbomachinery.8-11Themainreasonforthesuccessofthismodelisitsabilitytoworkasak-ωmodelnearthewallsandasak-εmodelawayfromthewalls.Thisbehavioraddsversatilitytothecalculation,asthemodel can automatically change to the most interesting methodology tocapturethemainmanifestationsineachdomainregion.5

( ) ( )2 2 1 ctk

FDP k

Dt kω ω

ρω µ ωµ ω α βρω ρ ωσ σ ω

− = ∇ + ∇ + − + ∇ ∇

(4)

Optimization

Theoptimizationprocessentersintothetraditionaldesignflowbysuggestingthat,afterproofofperformanceofthestudyequipmentisrealized,modificationsareproposedand studied inorder to furtherimprove the operation of this project. The cycle of a project isexpressedbelowinFigure3.

The concept stage aims to raise market needs, technologicalpossibilitiesforimplementationintheprojectandeconomicfeasibilityof the investment.After this study, planning is performed for thepurpose ofmapping the user to the product being developed, theirtechnicalrequirements,requiredresearch,theiruseandoperationaswellasspecification.Finally,inthestageofproductengineering,issuessuch as design, design calculations, simulations and optimizations,validationsandprototypingarediscussedtoallowthisproducttobemade.12After this step, design begins, atwhich point the objectiveestheticisdefined.Thentheprojectstarts,whenthenecessaryitemsaredefined,sizedandspecified.Theanalysisstagebegins,inwhichsimulationswillbeperformedtoestimatetheproductbehavior.Ifit

isfoundthattheoperationwiththecurrentprojectiscompromised,improvementsareproposed.Afterthis,thestudyoptimizationcanbecontemplated,processinwhichobjectivesandgoalsareestablishedandmodificationsarerealizedinthemodelwiththeaimofimprovingitsperformance.Asthisprocessleadstomodifications,newanalyzesmustbeperformedandonlyattheendofthiscycleshouldtheproductbereferredtothegenerationofaprototype,forvalidationandfinallyproduction,savingunnecessarycostswithintermediateprototypes.13

Figure 3 Cycle of general engineering projects.12

Thiscycle fromFigure4can lead toanuncountablenumberofmodifications, which consequently require a countless number ofsimulations. To avoid infinite possibilities, cases are elaboratedusing optimization methods. In these methods the variables to beworkedaredefined,thatistosay,whichparametersaresusceptibleofmodificationsinthemodel,alongwiththeobjectivesofthisprocess.At the end of these definitions one must choose an optimizationmethod,which isnothingmore thana search technique inwhichafinitenumberofcaseswillbestudiedandacurveorresponsesurfaceisgeneratedinordertoestimateapossibleoptimalpointofdesign,or even a point of improvement.After applying these techniques,the analysis of the points obtained for validation of the estimateddatawiththedataobtainedbysimulationshouldbeperformed.Thisprocessallowstheresponsetobeobtainedwithareducednumberofsimulationsandconsequently,lesstime(savingcomputationaleffort).

Figure 4 Product life cycle development.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 201Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Mostengineeringrealproblemscannotbeexpressedinsinglegoaloptimization.Formultiple-objectivecasesitisusualthattheobjectivesareconflicting,inorderthatitisnotpossibletodetermineonesingleoptimized configuration.14 To solve this kind of problem geneticalgorithmsweredevelopedaround1970.15 Genetic Algorithms start theirsearchfromarandomlycreatedinitialpopulation.Fromthissetofindividuals,theadaptationorindividualqualityofeachisanalyzedandonlyafewindividualsarepreservedforthenextgeneration.Thedecisioncriterion is thenon-dominatedorPareto-optimalsolutions,that is, solutions that cannot be improved independently of theobjectiveunlesstheworseningofanotherobjectiveoccurs.16Withthesolutionsofthepopulation,calledtheparents,crossingandmutationoperatorsareappliedinordertogenerateanewpopulation,calledadescendant,thatwillbeclosertothefinalresponsethanthepreviousgeneration.Theprocesscontinuesinthiscycleuntilthestopconditionisreached,asshownintheflowchartshowninFigure5elaboratedbyDebetal.17

Figure 5 Flowchart of genetic algorithms.17

The NSGA method, proposed by Professor Deb and hiscolleagues17 is a method of regular accuracy and low convergencerate.18However,itisfastandrobust,beingabletooperatecontinuousand discrete variables and creating new populations in regionsstatisticallymoreinterestingforthecalculation.19 Another advantage ofthisalgorithmisitsabilitytoallowdifferentscenariostobestudiedin parallel. For computers with adequate configuration this featurecan be a differential to get the problem response in reduced time.This algorithmwas developed to overcome themain criticisms ofthemodelsthatexisteduntilthen,includingtheNSGAmodel,whichpresents high computational cost, the need for an operator, calleda sharing parameter, that raises the level of difficulty of using thetechnology,andthelackofelitistreproduction,whichshowsitselfasagreatperformanceacceleratorofgeneticalgorithms.17

This model discards the need to use the sharing operator when usingapopulationcomparisonapproach, thus eliminating theneedforuserinterventiontodefinethisparameter.Inaddition,Debandhis

colleagueshavedemonstratedseveralcasesinwhichthebenefitsofusingthisalgorithmareclear.WhiletheNSGAmodelcompareseachindividualtoallothers,theimprovedmodelanalyzestheindividualandseparatesthemintoaselectedgroup,andthenextsolutionwillbecomparedtothisparticulargroup.Withthis,theconceptofelitismisused,inwhichthealgorithmestablishesrelationstodeterminethebestindividualsforthecalculationofthenextgenerations.Becauseofthisfeature,itsconvergencerateishighquality,althoughslow.

In Figure 6, an outline of the proceedings of the NSGA-IIalgorithmisshown.Themainoperationstartswithapopulation 0P.Foreachsolutionobtained,arankingisassignedinascendingorder,inwhichlevel1isthebest,followedbylevel2andsoon.Afterthemutationandcrossingoperations,thepopulation 0Q isobtained.Fromthecombinedpopulationof 0P and 0Q ,solutionsFareobtainedfromthedistancesDofeachsolutionfortheobjectives.Thoseindividualswho present the longest distance are rejected while those of theshortestdistancearepreservedforthenextgeneration.ThisprocessisgivenbytheEquation5:

1 1i iD F F+ −= − (5)

TheelitismconceptusedintheNSGA-IIalgorithmisresponsiblefor thedisposalof lessable individualsonbehalfof thepopulationthat shows itselfmoreadapted to surviveuntil thenextgeneration,inwhichitwillbecombinedwithotherelementsgivingrisetoanewelitistprocess.Throughtheseoperationsitbecomespossibletoselectthemostsuitableindividualsfortheobjectivescontemplated.Finally,inadditiontoallthequalitiespresentedabove,thismodelwaschosenfor thecurrent researchbecauseof itsgreat expression in themostrecentworksofoptimizationofturbomachinery,showingthecurrenttrend of the application of optimization algorithms in this specificbranchofknowledge.As an example, theworksofZhuet al.,20 ofPatraoet al.,21 ofTorabi et al.,22 ofZhuet al.,23Wanget al.,24 and Wangetal.,25andAmaraletal.26

Figure 6 NSGA-II algorithm proceedings.17

Computational procedureThepresentworkmakesuseoftheprojectdevelopedinprevious

work,27inwhichpreliminarydataofanaxialturbinewithgeneratedpowerof1,722MW,adiabaticefficiencyof88.5%andthetorqueintheaxisof584.092Nmforthespecifiedgasturbine.Thepresentprojectstartedatthisstage.Fromthedataprovidedasboundaryconditionsand the virtual prototype of the turbine (Figure 7), themodelwaselaborated in the computational solutions using other software forthedeterminationof turbulent3Dflowandoptimization.Thestepsofmodifyingthegeometry,meshgeneration,calculationandanalysisoftheresultswereperformedatANSYStools,whiletheoptimizationtool used was Esteco’s ModeFRONTIER.We chose to use a fewdifferenttoolstoensuretherobustnessoftheprocessdevelopedhereandthemainadvantageofworkingwithonlytwosoftwaresuppliers

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 202Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

wastheeaseofcouplingthesetools.TheentirestudymodelwasmadeinANSYSWorkbench,whichmadeitpossibletogeneratethemodelsetupinanautomatedway.EachdistinctprojectthatwasproposedbyModeFRONTIERwasimportedbyANSYS,whichinturnwasabletoreproducealldiscretizationdefinitions,physicalproblemdefinitionsand post-processing capabilities for each situation.This robustnessisofgreatimportancebecauseitallowsalargenumberofdifferentgeometriestobestudiedinanautomatedwaywithouttoolsconflictsofcommunicationandwithoutthenecessityofmanualscriptscreatedbytheuser.

Figure 7 CAD model of the rotor and stator of the machine stage.27

The use of computational tools

InitiallytheCADmodelwaseditedinANSYSSpaceClaimv18.0software,anadvancedCADmodelingtooltopreparethemodelfora simulation analysis inwhichgeometric elements unnecessary forthe study were eliminated. Then the design was created on BladeModelersoftware,amodulecapableofextractingmathematicallythetopologyofcurvatureofhighcomplexityofthefacesoftheprofile.Referenceaxesmustberespectedandthedomainentryandexitmustbeproperlydelimited.Themainbenefitof this tool is its ability torecreatethedesignoftheturbinewithparameterizableform.Thisisa commonprocedure in turbomachineryoptimization studies, sincethe researcher has more access to the geometric variables of thecase for future optimization studies and avoids the use ofmultipleplatformsfromdifferentsuppliers,whichapproachmayprovetobeless,especiallywhenworkingwithoptimizationtools.

Thegenerationofthefluiddomainiscreatedinthisstep,startingfrom the geometry of the blades that were properly worked andrecreatedwith theuseofparameters.Thedomaincreated is showninFigure8, and it is composedof the followingparts: an inlet; anoutlet; an interface region between the stator and rotor domains;walls representing the blades, the hub and the shroud and faces ofperiodicity,becausethecreatedmathematicaldomainconsidersonlyastatorbladeandabladeoftherotorinordertosavecomputationaleffort.

The parameterizable model extracted by the Blade Modelersoftware has another advantage: it can be easily coupled to theTurbogridsoftware(bothof themoftheANSYSWorkbenchv.18.0platform),a tool thathasadvancedmeshgenerationcapabilitiesforturbomachinery and allows the generation of hexahedralmesh andof good quality with due refinement, especially in the regions of

theleadingandtrailingedgesofbothblades.Withthis,thediscretemathematicalmodeliscreated.Themeshgenerated,showninFigure9, is then exported toANSYSCFXv.18.0 software, a commercialtool in the academic and industrial sector for three-dimensionalcalculationofcomputationalfluiddynamics(CFD)ofturbomachineryandvariousotherengineeringproblems.Thedomainofstudyhasaninlet,anoutlet,twoperiodicinterfacesandaninterfacetorealizethecommunication of the stator domain with the rotor domain of therotor.Furtherdetailson themeshwillbepresented insubsequenceparagraphs.

Figure 8 CAD model of the rotor and stator of the machine stage.27

Figure 9 Discrete model of the study domain.

Mesh independence study

Whenmodelingagivenproblem,itisnecessarytoensurethatthemodel represents the real case reliably. In this sense, an importantanalysis is the resolution of the mesh used, since the numericalmethodsarestronglydependentonthequalityofthecomputationalmesh.Itiseasilyobservedthattheresultofasimulationisremarkablysensitivetothenumberofelementsinuse.Ingeneral,thegreaterthenumberofmeshelementsthatdiscretizethedomain,thegreaterthelevel of accuracy of the results obtained. However, overly refinedmeshesrequirea lotofcomputationalpowerforcalculationanddonotnecessarilyprovidemoreaccuracy.Thus,astrategyisneededtoanalyzetheindependenceoftheresultsinrelationtothemeshused,sothatthemeshlessrefinedand,thatisabletocapturethephenomenaofinterest,isusedinthenumericalstudies.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 203Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Inthisway,itbecomesnecessarytostudymeshconvergence(andindependence).A studywas carried out comparing the results of aphysicalmodelvariablefordifferentmeshsizessothatitiseasytovisualizethepointatwhichwehavetheidealmesh,refinedenoughtocaptureallthedesiredphenomenainvolved,butnotoverlyrefineddelaythestudy.InthiscasethevalueoftheMachnumberinaregionoftheextradoszoneofthebladesandthepowergeneratedbythemachineismeasured.Thesedatawerechosenbecausethepowerisarelevantdataandofinterestforthestudyasawhole,whilethemonitoringofapointvariablelikeMachisidealtobettermapfluctuationsthatoccurin the domain, since parameter-weightedmonitoring such as areas,floworvolumestendtoamortizethischaracteristic.InTable1, theresultsofthemeshconvergencestudyarepresented.

Table 1 Mesh convergence study

Number of elements Mach ε % Power [W] ε %

45,658 1.154 6.63 1.67588E+06 5.09

50,466 1.186 4.04 1.75423E+06 0.66

2,292,168 1.222 1.13 1.76489E+06 0.06

7,716,375 1.236 0 1.76588E+06 0.00

10,216,473 1.236 0 1.76588E+06 0.00

Figure10,showstheevolutionofpowerandMachnumberwiththenumberofelementsofthemesh.

Figure 10 Evolution of the results of the mesh study.

The study presented above is common for several CFDapplications,however it is littleused in turbomachinerydesigndueto its inability toshow inamoredetailedway theevolutionof theresults with different meshes for different points of the domain.Becauseofthehighcomplexitytopologyofthebladesitisinterestingtosurveymorecomprehensively,monitoringotherpropertiesthataremodifiedduetothediscretizationemployed.Thus, thedistributionsofpressure,temperature,totalpressure,totaltemperatureandMachfromthebladehubtoitstopwerealsoevaluated.Thevaluesofy+anditsdistributiononthewallsofthedomainshouldalsobeevaluated.Themesh independencestudyexhibits thepointatwhich themeshconvergedandthecasewasnolongerdependentonthemeshrefininglevel. Possible uncertainties regarding the level of accuracy due todiscretizationareeliminatedbythisstrategy.

Themeshwithabout7.7millionelementsisabletorepresentthemodelusedforbothvariablesthatweremonitoredduringtheprocess,butneverthelesspresentsthemaximumy+valueof4inthewalls.Thevalueisabovethatrecommendedbytheliteraturefortheturbulence

modelusedinthepresentwork.However,themeshthatrespectstherecommendedvalueofy+<1presentsmorethan10millionelementsanddidnotpresentsignificantdifferencesinthevariablesmonitored.

Asthedifferenceinthesimulationtimebetweenthesetwomeshesisrelevantandthesamecannotbesaidinrelationtothedifferencesofthecapturedresults,themeshparametersof7.7millionelementswereusedasreferencethroughoutthework.Thetechnicallibraryofthetoolinformsthatforvaluesof2<y+>30intheturbulencemodelused (k-ω SST), the scalablewall law is applied, that is, althoughnosignificantdifferencesinresultswereobtainedforthemeshesof7,7million and 10million elements, there is a relevant differencewithrespecttotheformthatthecalculationintheboundarylayerisobtained.Meshesthatpresentthevalueofy+>2modeltheturbulencein theboundary layer,whilemeshes that respect thevalueofy+<2effectivelycalculate theflowphenomenapresent in theboundarylayer.

ThemeshindependencestudyispresentedbyFigure11.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 204Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Figure 11 Comparison of the distribution of properties of interest from the base to the top of the blade at the leading edge of the stator for different meshes.

In these images, there are severalpoints inwhich the resultsofthesetwomeshesoverlap,makingpossibletoobservethatthereisnorelevantvariationofperformance.Table2showsindetailsthelevelofdifferencebetweenthemeshesof7,7millioncellsvs.10millioncells.

Table 2 Comparative between refined meshes

Performance data 7,7 E+06 cells 1E+07 cells

Torque [(kg m^2) / s^2] 599,038 599,038

Power [W] 1.766E+09 1.766E+09

Total-total isentropic efficiency 14,412 14,412

Total-total polytropic efficiency 7,097 7,097

Inthepossessionofall theabovedataitwasdecidedtousethe7.7millionelementsmeshasreferenceforthepresentstudy,sinceitdemonstratesgoodreliabilitywiththeresultsandashortercalculationtimewhencomparedwiththemostrefinedmeshes.

Results from the original axial turbine

Thisstudyconsidered the responseasconverged from thepointofviewof theresidualswhentheresultsreachedthe levelofRMS<10E-6,which isbelow thestandard residualvalues thataremostcommonlyused in thisCFDsoftware,RMS<10E-4.Also,physicsstabilization and numerical balance were also evaluated to ensureconvergence. The pressure contour calculated can be observed atFigure12.Thepressuredistributiondemonstratestheevolutionofthispropertyinthedirectionoftheflowandallowsthevisualizationofthehighpressurezoneattheentranceofthedomainandthereductionofitsmagnitudeinthedownstream(stator-rotor)direction.Furthermore,itispossibletoviewlowpressurezonesafterthetrailingedgeoftherotorblade.

Performance data comparing the CFD study with the previoustheoreticalvaluesispresentedthroughTable3.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 205Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Figure 13 shows the good correlation between the values determined in thepreliminarydesignof the axial turbineusing1Dmodelingwiththeresultsofthesolutionofthecalculationofthe3Dflowusing the techniqueofCFD. In the regionsnear thehuborattheshroud,aslightchangeofvalues isobserved,asa resultof the

variationofthekineticenergyoftheflowduetotheexistenceoftheboundarylayer.Also,itiscleartheabsenceofhotspotsthatprejudicethemachineoperation.Therearedistinctionsoftheresultsattherotorblades,whichmeansthatthereisanindicativethatthedesigncouldberecalibrated.

Figure 12 Pressure contour at the flow path.

Figure 13 Comparison of variables distribution along the height of the rotor blade.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 206Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Table 3 Comparison of the performance data of the preliminary design with the model used in the CFD study

Performance Design CFD Original ׀Δ׀ ε (%)

Power [MW] 1.722 1.766 0.044 2.544

Efficiency (%) 88.5 89.8 1.347 1.522

Total pressure ratio

2.16 2.153 0.007 0.338

Torque [Nm] 584.092 599.038 14.946 2.559

ResultsFortheoptimizationprocess,differentvariationswereconsidered

forthebladeangles,whichwereproperlyparameterizedtobeusedbythegeneticalgorithmintheevolutionaryprocess.Theseangleswereconsideredatdifferentheightsforeachblade.Fiveheightswereused:thehub,thetopandthreemoreintermediateandequidistantheightsoftheblade.Foreachoftheheightsdescribedabove,sevenvaluesofβwereusedtomodeltheanglesofeachblade,traversingitsleadingedge geometry to the trailing edge. Fromfive distinct heights, andsevenparametersdefinedbyheightthereare35inputparametersforthestudyofaspade.Sincethestageconsistsofastatorbladeandanimpellerblade,thereare70inputparameterstobeevaluated.

A multiobjective optimization study, a problem with the levelof complexity as described above, and the mesh quality alreadypresented considering seventy different parameters, is not feasibleto be solved. Because of this reality, different techniques wereconsideredtosimplifytheproposedproblemandthustoobtaindatainashorter time. Itwasconsidered thepossibilityofworkingwithcurvatureadjustmentorresponsesurfacetechniques,aspresentedbyLiuetal.,28inwhichacorrelationbetweentheparametersbasedontheoriginalproblemtobestudiedwascreated.Thesestrategieswererejectedtoincreasethereliabilityof thestudyhere,reducingerrorswith oversimplifications of themathematicalmodel.However, duetothedifficultyofcarryingoutsuchacomplexstudywithsomanyinputparameters, a solutionalreadyused inother studies thathaveencounteredthissamelimitationhasbeenadopted,aspublishedbyKammereretal.29Sensitivityanalysis(Figure14)wereperformedtostudywhich angles aremost relevant to the expected objectives-toincreasepowerandefficiency,andtoallowtheoptimizationprocessto disregard input parameters that cause less impact on responses in favorofothermoreinterestingparameters.

Beforetheoptimizationprocess,asensitivitystudywasproposedtohelpinunderstandingtherelevanceofalltheparametersinvolvedandtoenablethemostinterestingonestobechosenforthedefinedobjectives. For the elaboration of the sensitivity analysis onemustcreatevariationsof theoriginaldesignandsolveeachoneof thesedifferent simulations. With this, the optimization tool is able tocorrelatethechangesoccurringineachnewprojectandtoworkwithelection criteria to determine which ones are most pertinent to beworkedon.Usingthenativetoolofgeneratingprojectswithrandomvariations of the originalmodel, respecting a range of possibilitiespreviouslydefinedbytheuser,morethan1,400differentsimulationswere performed. This methodology and procedure allowed theunderstandingthattherootandtopanglesofthestatorandrotorhadverylowimpactonthedeterminedtargets,whencomparedwiththeotherparameterscreatedatintermediateheightsofbothblades.Due

totheloweffectofthesevariables,thedecisionwasmade,basedonthegoodpracticesofturbomachineryprojects,todiscardthemfromtheoptimizationprocess.Thefactthattheseparametershavenotbeenchosen to remain in the optimization process does not mean that they havenoimpactontheresults.Theconclusionofthisstepisthattherearemorerelevantparametersinwhichgreaterdedicationisjustifiedalongtheheuristicgoalprocess.

Figure 14 Power and efficiency sensitivity charts.

The objective of the optimization study is to maximize powerandefficiencyinturbineoperatingconditions.Theinitialpopulationgiven was achieved by random initialization, taking advantage ofindividualscreatedforthesensitivitystudy,sothatalargespectrumcouldbestudied.Bythisapproach,thenumberofparameterscouldbereducedfrom70to49.ThenalltheprojectsusedforthisstudywereusedtofeedtheheuristicmodelandserveasthestartingpointfortheoptimizationprocessusingtheNSGAmodel-II.

Results from the original axial turbine

The optimization algorithm based on genetic code has as acharacteristictheevolutionfromgenerationtogenerationandallowsthe construction of the Pareto Front, which expresses the varioussolutions that canbe used for the project.As expected, there are alargenumberofsolutionspresentintheParetoFront.Asingle,perfectand idealsolution isnotpossible formultiobjectiveproblemssinceanysolutionobtainedfromParetoBorder isunable to improveonegoal without harming others. There is no single possibility to beusedtoachievetherequiredobjectives,buttheimplementedgeneticalgorithmhasbeenabletofindseveraldistinctdesignpointsthatareequivalent,inadditiontosurpassingtheoriginaldesignobtainedbythemidlinetheory.Thegeneticalgorithmworkedwith35evolutionarygenerationsuntilitsconvergencecriterionwasreached.Theprocesscalculated more than 8700 distinct individuals, each individualpresentingadifferentdesignofthisturbine.ForthecalculationofalltheseanalyzesaclusterwithIntelXeonprocessorsof3.0GHzand32nodeswasused.Thetotalsimulationtimewas2920hours,whichisequivalenttoabout4monthsofcalculation.

Thegenetic code applied itsmechanismsof evolution (crossingand mutation) until the criteria of numerical convergence wasreached. Remembering that the decision to stop in the numericalsolution is function of the user experience about the engineeringproblembeing analyzed. Several individualswere determined overthe35evolutionarygenerations,whichwerenecessaryfor thecodeto reach its convergence. Figure 15 shows all the individuals thatweresimulatedthroughouttheprocess.Itscolorpatternisinfunctionofthenumberofgenerations,beingdarkbluetheresultsofthefirstgenerationsandredtheprojectsobtainedinthelastgenerationoftheprocess.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 207Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Figure 15 Individuals calculated by the genetic algorithm.

TheParetoFrontobtained,expressestheseveralpossibleprojectsof this machine so that the proposed objectives are reached. ThePareto Frontier demonstrated by Figure 16 shows all the differentprojects that were obtained from modifications in the originalmachine,tothedetrimentofimprovingeachoneoftheobjectivesofstudy.Intheverticalaxisisexpressedtheefficiencyofthesetwhilein thehorizontal axis is thepowergenerated.Asexpected, there isnosingleproject thatmeets theproposedobjectivesand theParetoFrontier has the function of demonstrating possible modificationsthatareequivalenttoeachother,sinceeachprojectpresentsgreaterimprovementforoneobjectivetothedetrimentoftheother.

Figure 16 Pareto front.

Inordertocomparedifferentresultsof thisParetoBorder, threedifferentprojectswerechosentoanalyzetheresults.Theseprojectswere named as: Optimized 1: the Pareto Border higher efficiencypoint;Optimized2: the“global”point inwhichaprojectwas triedthatbenefitsbothefficiencyandpowergenerated;Optimized3: thehighest Pareto border power point. For the decision of what thesepointswere,agraphinFigure17wasdrawnfromtheParetoFrontierwith thepurposeofdimensioning theobtaineddataandfacilitatingthevisualizationoftheproposedprojectsforanalysisofresults.

Forthesethreedifferentprojects,thedistributionofthepropertiesand thecharacteristicsof theflowwereevaluated, inasimilarwaytowhatwas already demonstrated in themesh convergence study.Fortheleadingandtrailingedgesofthestatorandrotorblades,therelative Mach number distributions, static pressure, relative total

pressure,statictemperatureandrelativetotaltemperaturewereraised,ascanbeobservedatFigure18.

Figure 17 Gain of the Pareto Frontier.

Table 4 presents the comparison between the original turbinedesignandthethreeoptimizeddesigns,whichwereselectedforpost-processing.

Itisnoticedthat,asindicatedbytheParetoFrontier,theanswersobtained are equivalent to each other, but they may privilegeone objective over another, which is common in the design ofthesemachines, since there is a distinctionbetweenwhat is a highperformanceandwhatisahighefficiency.Thus, it isobservedthatthe optimized design 1 presents values of efficiency much higherthantheoriginalone,withanincreaseofabout1.5%inthemeasuredefficiency, while the generated power was impaired and presentedlowervalues than theoriginalmachine.Theoptimizeddesign3, inturn,presentshighervaluesofgeneratedpower(7.7%higher),butitsefficiencywasalsoimpairedwhencomparedtotheoriginalmachine.Thischaracteristicwasexpected,sincetheoutputparameters(PowerandEfficiency)areconflictingwitheachother.Forthisreason,itisproposedtheoptimizationanalysisbygeneticalgorithmtoinvestigatedifferentprojectsthatcouldbenefitbothobjectives.

ThedesignOptimized2isintherangeofpossibilitiesoftheParetoFrontierthatsurpasstheperformanceoftheoriginalprojectforbothobjectives,withanincreaseof0.8%inefficiencyandmorethana3%increaseinthepowergenerated.Amongthepossibilitiesselectedhere,thisprojectwasmoreinterestingbecauseitprivilegedbothobjectivesandwas selected tobe compared inotherpost processingwith theoriginal design. The blade-to-blade view is an interesting resourcefor flow analysis along the domain of turbocharged engines. In ananalogouswaytothatusedtopresentthepartialresults,itwasoptedfortheanalysisoftheresultsinthesolution2.Whenanalyzingthepressuregradientsinacomparativeoftheoriginalmodelinrelationtothemodelobtainedthroughthegeneticalgorithmitbecomesclearthe greater smoothing and homogenization of the disturbance.Thereductionoftheshocksfoundintherotorbladesisalsoclear,throughFigure19.

In general, part of the flow presents the same aspect as thatobserved in theoriginalmodel, as regionofgreatervelocity in thedorsal of the blade, zones of stagnation and mat characteristic ofthe profile. However, the contours above present smoother results,makingtheflowmoreefficient.Fromisosurfaces,theregioninwhichthepresenceofzoneswithM>1occursisclearandhowthatregionwasattenuatedat theendoftheoptimizationprocess.Intheregion

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 208Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

closetotherotortherearesmallareasofMach>1anditisclearthatthiswastheregionofgreatestbenefitofthischaracteristicthroughthegeneticcode.Theimprovementthatisobservedintheperformance

ofthisequipmentistheresultofthisreductionofshockzones,whichimposelossesonthesystem,asshowninFigure20.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 209Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Figure 18 Distribution of absolute properties: Mach number, Pressure, Total Pressure, Temperature and Total Temperature for both NGV and Rotor.

Figure 19 Comparison of the static pressure gradient in the original model vs optimized for the blade height of 50%.

Figure 20 Isosurfaces of value M = 1.

In order to understand the modifications between these twoprojects, an overlap of both geometries-Original and Optimized2-is presented in Figure 21, with the original blades being in thetranslucent gray color and the optimized in the opaque blue color.It isobserved that thegeometrypresentedherewasobtainedunderasingleanalysisoftheeffectsofcomputationalfluiddynamics,and

theperformanceimprovementwasduetothereductionofthebubblezone,orclogging,thatoccursinthemachineinregionsofhighMachvalues. No manufacturing limitations, as internal cooling of theblades,materialsandalloys,wereconsideredatthepresentstudynoranalyzesofstructuralfatigueandthermalfatigue.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 210Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

Table 4 Comparison of the different projects presented

Design Original Optimized 1 Optimized 2 Optimized 3

Power [W] 1.72E+06 1.76E+06 1.73E+06 1.82E+06 1.90E+06

Efficiency [%] 88.5 89.85 91.4 90.6 87.5

Figure 21 Comparison of original and optimized 2 blade geometries.

ConclusionsThe results of the original machine analysis enabled the

identificationofthepropertydistributionsalongthedomainofstudy.Itwasobservedtheevolutionofthestaticpressureandtotalpressurein theaxialdirectionof theflow,withreductionin thedownstreamdirection as expected. It was also identified the presence of shockwaves, a common phenomenon in axial turbines due to the highvelocity values involved. There was little variation in the thermalloadastheflowflowsbetweenthechannelsofthestatorbladestothechannelsoftherotorblades,whichfollowswithasitwasexpectedsince this energy is not used for theworkgeneration.A sensitivitystudy was carried out to determine the relevance of the variousparameters thatwere created from the original angles of the statorandrotorbladesforthemodificationsoftheexpectedresponsestothestudy:theimprovementofthepowerandefficiencyofthisstage.Thesensitivity study developed allowed to understand which parameters arethemostrelevanttoachievetheseobjectives,andtheimpactoftheintermediatesectionanglesofthebladeswasclearwhencomparedtotheanglespresentattherootandatthetop.Thismethodologyallowedto reduce the number of input parameters of this problem from70to 49, whose benefit was explored in the elitist heuristic processperformedinthesequence.Oneoftheprojectsobtainedwaschosenfor study - the project titledOptimized 2.This project presented a0.8%increaseinefficiencyandmorethan3%inthepowergenerated.

Theresultsobtainedfromthismethodologyprovidedtheobtainmentofprojectsoptimizedinrelationtotheoriginalmachineandverifiedthattheuseofmethodologiesbasedongeneticalgorithmiseffectivetoimproveturbomachineryprojects.ThemethodologypresentedherewasabletocoupleCFDandmultiobjectiveoptimizationtechniqueswithgeneticalgorithmeffectivelyandprovidedadequateresultsfor

the improvement of the originalmachine.With the Pareto frontierobtained,itisuptothedesignertodefinewhichdistinctdesignwillbe used based on the various possibilities obtained, in which oneoutputparameteristhemostbenefitedwhencomparedtotheother.Inthisway,thechoicewillbedependentontheengineeringdecisiontoworkwithamoreefficientormorepowerfulmachine.Theproposedmethodologycanbereproducedinotherstagesof thesameturbineand even in other projects, whether turbomachinery or not. TheassociationofCFDtechniqueswithgeneticalgorithmdemonstratesaviablepathforobtainingbetterengineeringprojects.Thetechnologyis recent, if studied in a timelineof engineering techniques, but itseffectivenessandgainsensureamplespacetobeevenmoreusedinvariousindustrysectors.

Multiobjective optimization studies are increasingly present inseveral sectors of the industry and are present in the most recentresearches offluiddynamics improvement of turbomachinery.Thistechnology makes it possible to obtain relevant data in a timelymanner.Theprocessofdevelopinganewaxialturbinetakestimeandoptimization algorithms proposes to increase productivity and even to obtain non-intuitive designs in attractive time, especially in thehighlycompetitivescenarioofthisindustry.Asasuggestionforfuturestudies,anaturalevolutionforthisstudywouldbeanewoptimizationprocessfromtheconsiderationofallinputparameters.Thesensitivitystudyproposedhereaimedatreducingthetotalnumberofparametersthatwouldbeusedintheanalysistoacceleratetheresults,sothatnewstudiescouldcontemplatealltheseparameterstoverifyifthisdecisionwould lead tomodifications in theParetoFrontieranduntilevenifthereisthepossibilityofanewParetoFrontiertechnicallysuperiortotheonefoundhere.Also,fluidstructureinteractionsimulationscouldalsobeperformedtostudyheatexchange,flutterandotherpertinentphenomena.

Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine 211Copyright:

©2019 Amaral et al.

Citation: Amaral LGF, Diaz RB, Tomita JT, et al. Optimization based on 3D CFD simulations of an axial turbine from a small gas turbine engine. Aeron Aero Open Access J. 2019;3(4):198‒211. DOI: 10.15406/aaoaj.2019.03.00098

AcknowledgmentsNone.

Conflicts of interestAuthorsdeclarethatthereisnoconflictofinterest.

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