IntroductiontoFluidMechanicsAE225IncompressibleFluidMechanicsAniruddhaSinhaDepartmentofAerospaceEngineeringIITBombayPreview Fluidmechanicsisaveryvisual(andmathematical)subject Equationsaresometimestoocomplicatedtogetafeel SeveralowvariablestokeeptrackofoverlargedomainsCavitationonship-propelleraWing-tipvorticesb Lookupgalleryofuidmotion: http://gfm.aps.org2 / 16aAppliedresearchlab,PennStatebwww.sunlakesaeroclub.orgPreviewAnexampleofLeonardodaVincissketchesofturbulentow3 / 16Whystudyuidmechanics? Itisanimportantsubjectinphysics Itdominatesphysicalphenomena,onallmacroscopic(non-quantum)lengthscalesoftheknownuniverse Inphysicalandnaturalscience Fluidisresponsibleforenvironment,i.e. weather Lifecannotexistwithoutuids: webreatheair(auid),drinkwater(auid);wearemostlyuid Intechnology Fluidisusefulinenergyconversion Fluidmattersfortransportation Itaectsrecreation(swimming) Itaectsentertainment(music) Fluidmechanics(aerodynamics)rulesAerospaceEngineering4 / 16Fluidmechanicsinpuresciences Atmosphericsciences&oceanography Globalcirculation(e.g. Monsoon) Large-scaleweatherpatterns(predictionoftornado,hurricane,pollutantionlevels) Climatechangemodels Geophysics Understandingofearthquakes,volcanoes(thermally-drivenuidmotion) UnderstandingofEarthsmagneticeld(motionofEarthsmoltencore) Astrophysics Galacticstructureandclustering Formationanddeathofcelestialbodies5 / 16Example: weatherphenomenoninthelab6 / 16LodovicaIllari,MIT(https://www.youtube.com/watch?v=uWdKVpQ94Ns)Fluidmechanicsinpuresciences(contd.) Biologicalsciences Bloodcirculation Eyefunction Fishswimming Kidneyfunction Cellularprocesses7 / 16Example: uidmechanicsofshswimming8 / 16Borazjani etal.,U.Minn. (https://www.youtube.com/watch?v=emiBYMLNR7Y)Fluidmechanicsintechnology Internal/externalcombustionengines: steamturbines,gasturbines,scramjet,rocketengines Wastedisposalandpollutiondisposal: chemicaltreatment,incineration,sewagetransportandtreatment Renewableenergy: Waterturbines,windturbines,solarpower Transportofuidsandgases: Pipelinesforcrudeoil,naturalgas,irrigation Transportation: aircraft,roadvehicles,highspeedtrains,spacevehicles Comfort: Heating,ventilatingandair-conditioning(HVAC)systems Articialorgans: articialhearts,kidneydialysismachines,insulinpumps Chemicals: dyes,paints,drugs9 / 16LecturenotesofProf. G.R.ShevareExample: gasturbineanimation10 / 16https://www.youtube.com/watch?v=qJlj7OyhpfcBriefhistory: TheancientsArchimedesEureka(3rdcenturyBC)Romanaqueducts(1stcenturyBC)Intuitivelyuidisanythingwhichows.Withthisasanunderstanding,plentyofempiricalinformationexistedovercenturies11 / 16Briefhistory: ThegiantsTherstuidmechanicsequation: Bernoullisequation(introducedbyL.EulerandtheBernoullis)Modernuidmechanics: duetocontributionsbyNewton,Cauchy,Euler,Navier,Stokes,Reynolds,Prandtl,Taylor12 / 16MethodsofstudyinguidmechanicsInthelasttwocenturies,uidmechanics,likeanyotherscience,wasstudiedusingonlytwoapproaches: theoreticalandexperimental Theoreticaluidmechanics(thencalledhydrodynamics)waspursuedbymathematiciansusinganalyticalmethods Experimentaluidmechanics(thencalledhydraulics)wasmostlyexperimentalstudyofwaterThetheoreticaluidmechanicsandexperimentaltheoriessometimesproducedcontradictoryresults.Theoreticstudynowmeansexploringtheimportantphenomenaandarrivingatthemathematicalcorrelationsbetweenfactorsaectinguidow E.g.,whatistheessentialphysics(outoftheentiretyofmind-bogglingdetails)thatgivesrisetothenoiseheardfromjetengines?13 / 16Experimentaluidmechanics Experimentaluidmechanicsreliesonsensingandmeasuringtheowquantitiesratherthanthemathematicalexpressionsforthem Experimentalmethodshavematuredwithadvancesinaccuratetransducers,dataacquisitionanddataarchivalmethodologies Thereareinstrumentswhichcanmeasuree.g., 3-componentsofvelocityatapointat100sofkHzrate 3-componentsofvelocityoveravolumetricdomainatkHzrate Pressureonasurfaceasanimageusingpressure-sensitivepaint3-Chot-wireaParticle image velocimetrybPressure-sensitivepaintc14 / 16adantecdynamics.comben.wikipedia.org/wiki/ParticleimagevelocimetrycGregory,AIAA2004-0294Computationaluiddynamics Asthecomputingpowerincreased,limitationsofdataprocessingofhumanbeingscouldbeovercome. Lawsofphysicscanbeappliedwithalmostnoassumptions. Largenumberofmathematicaloperationscanbecarriedoutsystematically. Eectsofvariousparameterscanbeveriedwithexistingcorrelations. ExperimentalvalidationofCFDresultsisstillveryveryimportantComparisonofCFDofsupersonicjetwithexperimentsaComputedvorticitymagnitude Experimentalowvisualization15 / 16aGaitonde&Samimy,PoF,2011ApproachtosolvingproblemsinuidmechanicsRealityComponentsWings,turbinebladepassageFluidm/c:engine,aircraftIdealizedproblems:pipes,platesExperimentaluidmechanicsMathmodelsforuidmotionAnalyticaluidmechanicsComputationaluiddynamics(CFD)16 / 16LecturenotesofProf. G.R.Shevare