Principles and Applications of Dimensional Analysis and Similarity PDF
Preview Principles and Applications of Dimensional Analysis and Similarity
Mathematical Engineering Sandro G. Longo Principles and Applications of Dimensional Analysis and Similarity Mathematical Engineering SeriesEditors JörgSchröder,InstituteofMechanics,UniversityofDuisburg-Essen,Essen, Germany BernhardWeigand,InstituteofAerospaceThermodynamics,Universityof Stuttgart,Stuttgart,Germany Today,thedevelopmentofhigh-techsystemsisunthinkablewithoutmathematical modeling and analysis of system behavior. As such, many fields in the modern engineering sciences (e.g. control engineering, communications engineering, mechanicalengineering,androbotics)callforsophisticatedmathematicalmethods inordertosolvethetasksathand. The series Mathematical Engineering presents new or heretofore little-known methodstosupportengineersinfindingsuitableanswerstotheirquestions,presenting thosemethodsinsuchmannerastomakethemideallycomprehensibleandapplicable inpractice. Therefore,theprimaryfocusis—withoutneglectingmathematicalaccuracy—on comprehensibilityandreal-worldapplicability. Tosubmitaproposalorrequestfurtherinformation,pleaseusethePDFProposal Formorcontactdirectly:Dr.ThomasDitzinger([email protected]) IndexedbySCOPUS,zbMATH,SCImago. Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/8445 Sandro G. Longo Principles and Applications of Dimensional Analysis and Similarity SandroG.Longo DepartmentofEngineeringandArchitecture UniversityofParma Parma,Italy ISSN2192-4732 ISSN2192-4740 (electronic) MathematicalEngineering ISBN978-3-030-79216-9 ISBN978-3-030-79217-6 (eBook) https://doi.org/10.1007/978-3-030-79217-6 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2021 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland TomyparentsVincenzoandGilda, whohaveneverleftmealone Preface Dimensional analysis is a research tool that covers all research sectors. Much has alreadybeenwrittentosurveythegeneralconceptsortodeepensomesubtleaspects, anditisdifficulttoaddsomethingnewordifferent.Alistofthecontributionswould inevitablybeincomplete. Itisacommonopinionthatdimensionalanalysisallowsustoclarifyfactsalready known and appears not very effective for the analysis of new processes and for progress;seealsothecommentbyGibbings.1Itisworthwhiletorememberthatthe search for greater clarity in the analysis of physical processes inevitably leads to greater knowledge. The criteria of analogy between distinct processes, introduced by dimensional analysis and then developed by the theory of similarity, are very effectiveforimprovingtheaveragelevelofscientificarguments. Thediscussionoftheprinciplesandapplicationsofdimensionalanalysisleaves manyquestionsonrelevantissuesstillunanswered,althoughthediscussionsonthe fundamentals are commonly neglected while taking care of the more applicative aspects.Forexample,thequestionofthenumberandnatureoffundamentaldimen- sions,aswellasthevalidityofreducingtheirnumberonthebasisofnewphysical relationshipsoroftheirincreasebydiscriminatingthembygivingdifferentrolesto thesamedimension,isstillunanswered.Thisisnotatrivialmattersince,asdemon- stratedinthebook,anincreaseinthenumberoffundamentalquantitiesleadstoa reductioninthenumberofdimensionlessgroupsand,ultimately,toasimplification ofthestructureofphysicalequations–allthisonlyonthebasisofchoicesunjustified and not justifiable a priori. This is one of the reservations and is perhaps the most relevant. However, weremind ourselves thatclassicalmechanics isbased onprin- ciplesandaxioms(homogeneityandisotropyofthespace;stationarity;seeLandau &Lifshitz19782),assumedtobethebasisofacompletetheorythat,ultimately,has undergoneexperimentalvalidation. 1J.C.Gibbings.(1980).Ondimensionalanalysis.JournalofPhysicsA:MathematicalandGeneral 13(1),75. 2L. D. Landau & E. M. Lifshitz. (1960). Course of Theoretical Physics (Vol. 1: Mechanics). PergamonPress. vii viii Preface Practicallynonexistentarereservationsonthetheoryofsimilarityandmodels,the secondimportanttopicdiscussedhere.Currentthinkingonthescientificrepresenta- tionofrealityassumesthattheresourcesusefulforsuchrepresentationarelinguistic, considering mathematics as a specific language (Giere 20043): the language of science has its own syntax, a semantic aspect and a pragmatic one. In physical modelling,itisthepragmaticaspectthatisemphasised,withsyntaxandsemantic aspectsadaptedaccordingly. Leaving aside the issues of foundation, which are here only briefly mentioned, thepurposeofthebookistoprovidethenecessaryandappropriatetoolsforanaccu- rateandconsistentinterpretationofphysicalprocesses,boththroughmathematical analysisandthroughphysicalmodelling.Thefirstchaptersaddressthedefinitions, with few dimensional analysis theorems and similarity criteria. There is also the analysisofself-similarity,bothoffirstandsecondkind,withacoupleofcompletely solvedproblems,framedwithinthegrouptheory.Ihavedeliberatelynotdealtwith thetheoryofrenormalisedgroups,whichIconsidermorespecialised. From Chap. 5 onward, the focus is on applications in some of the engineering sectors. The number of topics is necessarily limited, but, almost always, there are details, calculations and treatment of assumptions. To avoid making the book too broad,Ihaveleftoutthedescriptionofmanyexperimentaldevicesusedforphysical modelling, such as channels and tanks with wave generators and rotary platforms forgeophysicalmodels.Ihaveincludedonlyabriefdescriptionofthecentrifugeof theshakingtable,althoughanentirechapterisdevotedtowindtunneltechnology. I have also omitted the treatment of measurement techniques and instrumentation, available, for example, in Doebelin, 20084 and in several other books focused on differentbranchesofresearch.Somemorespecificnotions,requiredbythecontext, arereportedintheAppendix,whereappearsalsothedescriptionofnumerousdimen- sionless groups, all of engineering interest, but with the exclusion of many others relatedtophysicalprocessesofelectricalnatureorphysicsofparticles.Ipreferto repeatedlyexplainthesymbolsnexttotheformulasthatusethem,ratherthanlisting them in an Appendix. As far as I could, I tried to make them uniform: a specific symbolcorrespondstothesamevariablethroughoutthebook.Theglossaryliststhe meaningofsomespecifictermsusedinthebook. Thebookisaddressedtothosetrainedinengineeringdisciplinesandnaturaland physical sciences and to graduate students and fellow researchers interested in a clarification of the methodology, of dimensional analysis and theory of similarity aimsandpurposes. Muchoftheworkinvolvedinwritingthisbookwasdoneduringmystayonsabbat- icalleaveinGranada,Spain,intheSpring-Summerof2010,hostedbyProf.Miguel A. Losada, Emeritus of the University of Granada and at that time Director of the CentroAndaluzdeMedioAmbiente(CEAMA),ajointresearchstructurebetween the Junta de Andalucia and the Universidad de Granada. At CEAMA, in addition 3R.N.Giere.(2004).Howmodelsareusedtorepresentreality,PhilosophyofScience,71,742– 752. 4E.O.Doebelin.(1990).Measurementsystems:Applicationanddesign.McGraw-HillBookCo. Preface ix to the availability of the laboratory and all the equipment to carry out my experi- mentalresearchprogram,co-monitoredbyLucaChiapponi,MaraTonelli,Simona BramatoandChristianMans,Ihadthecompleteavailabilityofwhatwasnecessary forbibliographicinvestigationsandtomeditateandtowrite.Ihadafantastictime inGranada,wherenumerousyoungresearchersandstudentsweredeeplyinvolved inwindtunnelandseagravitywavesandrelatedphenomenaresearch. The English language version, revised and extended with new sections, was completed during the COVID-19 pandemic in 2020, which is about to be finally eradicatedthankstobiomedicalresearch,withseveralvaccinesbeingdevelopedvery quickly.Thanksareduetoalltheresearchersinvolvedinthatfieldandinmemory ofthosewhodidnotsurvive. Parma,Italy SandroG.Longo April2021 Acknowledgements Muchoftheexpertiseacquiredpriortothedraftingofthismonograph,istheresultof decadesofscientificcollaborationwithMiguelA.Losada,EmeritusoftheUniversity ofGranada(Spain),MariusUngarish,EmeritusofTechnion(Israel),andVittorioDi Federico,FullProfessorattheUniversityofBologna(Italy).Iwouldliketothank them and their research groups for sharing their knowledge on some fascinating phenomenaofFluidMechanics. Igratefullyacknowledgecriticalreadingofsomechaptersbycolleagues;Andrea Maranzoni critically commented on Chap. 3, Andrea Spagnoli commented on Chap. 7, and Diana Petrolo revised and commented on all the chapters. I thank LucaChiapponi,whocreatedsomeofthemostcomplexfigureswithgreataccuracy. xi
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