Advanced Fluid Mechanics and Heat Transfer for Engineers and Scientists: For Engineers and Scientists PDF
Preview Advanced Fluid Mechanics and Heat Transfer for Engineers and Scientists: For Engineers and Scientists
Meinhard T. Schobeiri Advanced Fluid Mechanics and Heat Transfer for Engineers and Scientists Advanced Fluid Mechanics and Heat Transfer for Engineers and Scientists Meinhard T. Schobeiri Advanced Fluid Mechanics and Heat Transfer for Engineers and Scientists MeinhardT.Schobeiri DepartmentofMechanicalEngineering TexasA&MUniversity CollegeStation,TX,USA ISBN978-3-030-72924-0 ISBN978-3-030-72925-7 (eBook) https://doi.org/10.1007/978-3-030-72925-7 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The current book Advanced Fluid Mechanics and Heat Transfer is based on the author’s four decades of industrial and academic research in the area of thermo- fluid sciences including fluid mechanics, aerothermodynamics, heat transfer, and their applications to engineering systems. It unifies the fluid mechanics and heat transferinauniquemanner.Thefluidmechanicsparthasevolvedfromtwoofthe author’sgraduatefluidmechanicstextbookspublishedin2010and2014.Theessen- tialelementsofthesetextbooksarecombinedtogetherandhaveundergonearigorous update and enhancement resulting in the fluid mechanics part of the current book. Asthecontentofthefluidmechanicspartreveals,itincludesfeaturesthatarenon- existentinanyfluidmechanicstextbookavailableonthemarket.Researchfacility design for creating steady and unsteady flow environment, performing steady and unsteady flow experiments using pneumatic and hot wire anemometry, explaining indetailthedataacquisitionandanalysisandpresentingtheresultsofexperiments areafewexamples.Theheattransferpartincludesthemostadvancedfeaturesused forheattransfermeasurementincludingfilmcooling.Hereagain,researchfacility design, performing steady and unsteady heat transfer and film cooling effective- ness experiments, detailed data acquisition, and analysis using and presenting the experimental results are a few examples. To measure the surface temperature of a test object, advanced instrumentation such as infrared thermography, liquid crys- tals,andpressure-/temperature-sensitivepaintsareused.Verydetailedexplanation oftheaboveinstrumentsalongwiththeircorrespondingdataacquisitionandanal- ysisispresented.Thecontentsofthisnewbookcoverthematerialrequiredinfluid mechanics and heat transfer graduate core courses in the US universities. It also coversthemajorpartsofthePhD-levelelectivecoursesadvancedfluidmechanics andheattransferthatIhavebeenteachingatTexasA&MUniversityforthepastthree decades.Theunifiedtreatmentoffluidmechanicsandheattransferenablesstudents and novice researchers to find comprehensive answers to their specific questions withoutconsultingseveralbooks. Fluidmechanicsandheattransferareinextricablyintertwinedandbothareintegral partsofonephysicaldiscipline.Noproblemfromfluidmechanicsthatrequiresthe calculationofthetemperaturecanbesolvedusingthesystemofNavier–Stokesand continuityequationsonly.Conversely,noheattransferproblemcanbesolvedusing v vi Preface theenergyequationonlywithoutusingtheNavier–Stokesandcontinuityequations. The fact that there is no book treating this physical discipline as a unified subject inasinglebookandtheneedoftheengineeringandphysicscommunity,motivated metowritethisbook.Itisprimarilyaimedatstudentsofengineering,physics,and those practicing professionals who perform aero-thermo-heat transfer design tasks intheindustryandwouldliketodeepentheirknowledgeinthisarea. Theadvancedcharacterofthebookrequiresthatthereaderhasthebasicknowl- edgeoffluidmechanicsandheattransfer.Byreadingthroughthechapters,thereader willrealizehowhis/herlevelofunderstandingtransformsfromundergradtograduate level. An example should clarify the concept of this book: The first three chapters preparethereaderforbetterunderstandingoftheadvancedleveloffluidmechanics. Tensorsinthree-dimensionalEuclideanspacepresentedinChap.2providethereader withthemathematicalbasisthatisessentialforunderstandingthematerialtocome. Allequationsarewrittenfirstincoordinateinvariantformthatcanbedecomposed in any arbitrary coordinate system. Using the tensor analytical knowledge gained fromChap.2,itisrigorouslyappliedtothefollowingchapters.InChap.3,thatdeals withthekinematicsofflowmotion,theJacobiantransformationdescribesindetail howatime-dependentvolumeintegralisusedtosystematicallyderivetheReynolds transport theorem. This theorem is the essential tool to understand how it can be appliedtocontinuity,linearmomentum,angularmomentum,andenergyequationin integralform. InChaps.4and5,conservationlawsoffluidmechanicsandthermodynamicsare treatedindifferentialandintegralforms.InviscidflowispresentedinChap.6,where the order of magnitude of a viscosity force compared with the convective forces couldbeneglected.Thepotentialflow,aspecialcaseofinviscidflowcharacterized byzerovorticity,exhibitedamajortopicinfluidmechanicsinpre-CFDera.Inrecent years, however, its relevance has been diminished. Despite this fact, I presented it in this book for two reasons. First, despite its major shortcomings to describe the flow pattern directly close to the surface, because it does not satisfy the no-slip condition,itreflectsareasonablygoodpictureoftheflowoutsidetheboundarylayer. Second,combinedwiththeboundarylayercalculationprocedure,ithelpsacquiring areasonablyaccuratepictureoftheflowfieldoutsideandinsidetheboundarylayer. This,ofcourse,isvalidaslongastheboundarylayerisnotseparated.Itisalsoworth notingthattodaythecombinedmethodmentionedaboveisstillusedbymanyengine designersattheearlystageofdesignanddevelopmentbeforeusingCFDpackages for final design. Also, in the context of the potential flow, two topics, namely the conformaltransformationandthevorticitytheorems,arepresentedanddiscussed. Followingtheinviscidflowdiscussion,Chap.7dealswiththeparticularissuesof viscouslaminarflowthroughcurvedchannelsatnegative,zero,andpositivepressure gradients.ExactsolutionofNavier–Stokesequationdeliversthevelocitydistribution in those channels. The combination of the Navier–Stokes equations with energy equationdeliversthetemperaturedistributionwithinthesechannels.Theseexamples demonstratetheimpactofthewallcurvatureandpressuregradientonfluidmechanics and heat transfer behavior of these curved channels. Thus, the content of Chap. 7 seamlesslymergesintoChap.8thatstartswiththestabilityoflaminarflow,followed Preface vii bylaminar–turbulenttransition,itsintermittentbehavior,anditsimplementationinto Navier–Stokes equations. Averaging the Navier–Stokes equation that includes the intermittency function leading to the Reynolds-averaged Navier–Stokes equation (RANS)concludesChap.8. IndiscussingtheRANS-equations,twoquantitieshavetobeaccuratelymodeled. Oneistheintermittencyfunction,andtheotheristheReynoldsstresstensorwithits ninecomponents.Inaccuratemodelingofthesetwoquantitiesleadstoamultiplica- tiveerroroftheirproduct.ThetransitionwasalreadydiscussedinChap.8butthe Reynoldsstresstensorremainstobemodeled.This,however,requirestheknowledge andunderstandingofturbulencebeforeattemptsaremadetomodelitandthistopic istreatedinChap.9. In Chap. 9, I tried to present the quintessence of the subject turbulence that is requiredforagraduate-levelengineeringandphysicscoursesandtocriticallydiscuss severaldifferentturbulencemodels.Thetwo-equationmodels,k−g, k−Tandthe combinationofboth,thatarewidelyused,rendersatisfactoryqualitativeresultswhen theyareappliedtorelativelysimpleflowcases.However,simulatingacomplexflow situation, where different parameters are involved, leads to results, whose proper interpretations require the understanding of the model shortcomings. Efforts have beenmadetoillustratetheseshortcomingsbysimulatingmorecomplexcasesand comparethenumericalresultswiththeexperiment. While Chap. 9 predominantly deals with the wall turbulence, Chap. 10 treats differentaspectsoffreeturbulentflowsandtheirgeneralrelevanceinengineering. Amongdifferentfreeturbulentflows,theprocessofdevelopmentanddecayofwakes under positive, zero, and negative pressure gradients is of particular engineering relevance. With the aid of the characteristics developed in Chap. 10, this process of wake development and decay can be described accurately. Following Chap. 10, twochaptersdealwiththe:(a)boundarylayeraerodynamicsand(b)boundarylayer heattransfer.Thesetwochaptersareoffundamentalimportanceforfluidmechanics andheattransfer:Ontheonehand,thevelocitydistributionanditsgradientwithin the boundary are responsible for the wall friction distribution and thus the total pressurelosswithinanengineeringsystem.Ontheotherhand,thevelocityfluctuation distributionwithintheboundarylayerdeterminesthetransferofmass,momentum, andenergytotheboundarylayerandthusspecifiesthetemperaturedistributionon thewallsurface. Chapter 11 is entirely dedicated to boundary layer aerodynamics. Without the knowledgeofboundarylayerphysics,noaircraftwings,noturbineandcompressor blades,nogasturbines,andjetenginescouldbedesignedintheformweknowand usethemtoday.Theboundarylayerisathinviscouslayerveryclosetothesurface. L.Prandtlwasthefirsttorecognizethecrucialrolethatthisviscouslayerplaysin aerodynamics.Basedonhisexperimentalobservations,Prandtlfoundthattheeffect of viscosity is confined to a thin viscous layer that he called, the boundary layer. Thedistributionofthevelocityanditsfluctuationwithintheboundarydetermines thewallfriction,theheattransfercoefficient,andthefilmcoolingeffectivenessof the surface exposed to a fluid flow. Based on his thorough experiments and sound viii Preface dimensional analysis, he developed his boundary layer theory that up to today is usedintheareasmentionedabove. Conductingboundarylayerexperimentsontoday’stestobjectsaretotallydifferent fromthosebyPrantl.TheplatelengththatPrantlusedforhisboundarylayermeasure- mentwasmorethan10mlonggeneratingaboundarylayerthicknessof50cmand more.Heusedpneumaticprobeswithfishmouthgeometrywithalateraldimension ofapproximately2mmfortraversinghis50cmboundarylayer.Thetoday’sturbine orcompressorbladesgeneratemaximumboundarylayerthicknessesof3–5mmor less. To be able to traverse such boundary layer thicknesses, hot wire sensors are usedwiththesensingwirediametersof0.25–5µm.Thesesensorsareattachedto an anemometer with data acquisition frequency of 100 kHz and above detailed in Chap.11. Measurementofboundarylayerflowoccupiesafullsectionofthischapter.Two subsections detail design facilities for boundary layer research in stationary and rotating frame of references. For generation of periodic unsteady wake flows that emulatetheinteractionbetweenthestationaryandrotatingframe,twofacilitiesare introducedthatgenerateperiodicunsteadywakeflows.Instrumentation,dataacquisi- tionofsteadyandperiodicunsteadydata,sampling,andensembleaveragingexhibit another subsection in Chap. 11. More detailed data acquisition and analysis are giveninChap.13.Severalcasestudiespresentedthatshowthesteadyandunsteady boundary layer experiments. For periodic unsteady flow, distribution of the mean andthefluctuationvelocitiesasfunctionsortimedemonstratetheimportantroleof thefluctuationvelocityintransferringmass,momentum,andenergytotheboundary layer. Chapter12isfullydedicatedtoboundarylayerheattransfer.Afterabriefintro- duction, equations for heat transfer calculation are presented. The introduction is followedbythesectionthatdescribestheinstrumentationfortemperaturemeasure- ment.Tomeasurethesurfacetemperatureofatestobject,fourdifferentinstrumenta- tionsareintroduced,namelythermocouples,infraredthermography,liquidcrystals, andpressure-/temperature-sensitivepaints.Thissectionisfollowedbythecalcula- tionprocedureofindividualcontributorstoobtaintheheattransfercoefficient.This sectionisfollowedbypresentingexperimentalexamples. In selecting the material for experimental examples, I have been influenced by theneedsofmechanicalengineers.Thefirstexamplestartswithmeasuringtheheat transfercoefficientdistributionalongtheconcaveandconvexsidesofacurvedplate. Bothsidesofthecurvedplatearecoveredbyspacialliquidcrystalsheets.Toshow the effect of impinging the periodic unsteady wakes on the concave and convex surfaces,thereducedfrequencyofthewakegeneratorwasvariedfrom0.0(steady state)to5.166.Whiletheabove exampledealtwiththezero-longitudinal pressure gradient, the following case study includes the variation of pressure gradient, re- number,turbulenceintensity,andreducedfrequency. A major section treats the heat transfer problems using pressure-/temperature- sensitive paints (SP/TSP). After explaining the working principle of this method, its calibration, data acquisition, and analysis, it is applied to a rotating frame for measuringfilmcoolingeffectiveness.Tworepresentativecasesarepresented:Case Preface ix (1) measures the film cooling effectiveness on tip of turbine blades with different geometries.Case(2)presentsthefilmcoolingeffectivenessofaturbinebladethat rotatesatupto3000rpm.Themajorportionofthematerialpresentedinthischapter isquitenewandisinaccordwiththestructureofthisbook.Thediscoursediffers substantiallyfromtheconventionalheattransferbookandmaybeevennewtoexpe- rienced reader. In addition to explaining the facility design, instrumentation, data acquisition, and analysis presented in Chaps. 11 and 12, I found necessary to add twochaptersthatdealwiththeabovesubjectsinamoredetailedfashion.Chapter14 deals with fluid mechanics measurements and Chap. 15 with all aspects of heat transfermeasurementatadvancedlevel. Chapter13dealswiththecompressibleflow.Atfirstglance,thistopicseemstobe indissonancewiththerestofthebook.Despitethis,Idecidedtointegrateitintothis bookfortworeasons:(1)Duetoacompletechangeoftheflowpatternfromsubsonic to supersonic, associated with a system of oblique shocks, makes it imperative to presentthistopicinanadvancedengineeringfluidtext;(2)Unsteadycompressible flowwithmovingshockwavesoccursfrequentlyinmanyenginessuchastransonic turbines and compressors, operating in off-design, and even design conditions. A simpleexampleistheshocktube,wheretheshockfronthitsoneendofthetubeto bereflectedtotheotherend.Asetofsteady-stateconservationlawsdoesnotdescribe thisunsteadyphenomenon.Anentiresetofunsteadydifferentialequationsmustbe calleduponwhichispresentedinChap.13.Arrivingatthispoint,thestudentsneedto knowthebasicsofgasdynamics.Ihadtwooptions,eitherreferthereadertoexisting gas dynamics textbooks, or present a concise account of what is most essential in followingthischapter.Idecidedforthesecondoption. Attheendofeachchapter,thereisasectionthatentailsproblemsandprojects. Inselectingtheproblems,IcarefullyselectedthosefromthebookFluidMechanics ProblemsandSolutionsbyProf.SpurkofTechnischeUniversitätDarmstadtwhich I translated in 1997. This book contains a number of highly advanced problems followedbyverydetailedsolutions.Istronglyrecommendthisbooktothoseinstruc- torswhoareinchargeofteachinggraduatefluidmechanicsasasourceofadvanced problems.MysincerethanksgotoProf.Spurk,myformerCo-advisor,forgivingme thepermission.Besidestheproblems,anumberofdemandingprojectsarepresented thatareaimedatgettingthereadersinvolvedinsolvingCFD-typeofproblems.In typingseveralthousandequations,errorsmayoccur.Itriedhardtoeliminatetyping, spelling,andothererrors,butIhavenodoubtthatsomeremaintobefoundbyreaders. In this case, I sincerely appreciate the reader notifying me of any mistakes found; theelectronicaddressisgivenbelow.Ialsowelcomeanycommentsorsuggestions regardingtheimprovementoffutureeditionsofthebook. My sincere thanks are due to many fine individuals and institutions. First and foremost,IwouldliketothankthefacultyoftheTechnischeUniversitätDarmstadt fromwhomIreceivedmyentireengineeringeducation.Inparticular,Iowemythanks and appreciation to my deceased thesis adviser Prof. Dr.-Ing. H. Pfeil and my co- adviserProf.Dr.-Ing.J.Sprukfortheircontinuoussupport.Ifinalizedmajorchapters ofthemanuscriptofthefirstbookImentionedpreviouslyduringmysabbaticalin GermanywhereIreceivedtheAlexandervonHumboldtPrize.Iamindebtedtothe x Preface AlexandervonHumboldtFoundationforthisPrizeandthematerialsupportformy researchsabbaticalinGermany.MythanksareextendedtoProf.BerndStoffel,Prof. Ditmar Hennecke, and Dipl. Ing. Bernd Matyschok for providing me with a very congenialworkingenvironment. IamalsoindebtedtoTAMUadministrationforpartiallysupportingmysabbatical whichhelpedmeinfinalizingthebook.SpecialthanksareduetoMr.KellyMinnis whoconvertedtheWordPerfectmanuscriptintothetypesettingversionwithlatex. Last, but not least, my special thanks go to my family, Susan, and Wilfried for theirsupportthroughoutthisendeavor. CollegeStation,TX,USA MeinhardT.Schobeiri October2020 [email protected]
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