springer handbook of experimental fluid mechanics · 2013. 7. 19. · department of applied...
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Springer Handbookof Experimental Fluid Mechanics
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Springer Handbooks providea concise compilation of approvedkey information on methods ofresearch, general principles, andfunctional relationships in physi-cal sciences and engineering. Theworld’s leading experts in the fieldsof physics and engineering will beassigned by one or several renownededitors to write the chapters com-prising each volume. The contentis selected by these experts fromSpringer sources (books, journals,online content) and other systematicand approved recent publications ofphysical and technical information.
The volumes are designed to beuseful as readable desk referencebooks to give a fast and comprehen-sive overview and easy retrieval ofessential reliable key information,including tables, graphs, and bibli-ographies. References to extensivesources are provided.
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123
HandbookSpringerof Experimental Fluid
MechanicsCameron Tropea, Alexander L. Yarin, John F. Foss
(Eds.)
With DVD-ROM, 1240 Figures and 123 Tables
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Editors:
Cameron TropeaFachgebiet Strömungslehre und AerodynamikTechnische Universität DarmstadtPetersenstraße 30,64287 Darmstadt, Germany
Alexander YarinDepartment of Mechanical and Industrial EngineeringUniversity of Illinois at Chicago842 W. Taylor St.,Chicago, IL 60607-7022, USA
John F. FossMechanical EngineeringMichigan State UniversityA118 Engineering Research Complex,East Lansing, MI 48824-1326, USA
Library of Congress Control Number: 2007931998
ISBN: 978-3-540-25141-5 e-ISBN: 978-3-540-30299-5
This work is subject to copyright. All rights reserved, whether the wholeor part of the material is concerned, specifically the rights of translation,reprinting, reuse of illustrations, recitation, broadcasting, reproduction onmicrofilm or in any other way, and storage in data banks. Duplication ofthis publication or parts thereof is permitted only under the provisions ofthe German Copyright Law of September, 9, 1965, in its current version,and permission for use must always be obtained from Springer-Verlag.Violations are liable for prosecution under the German Copyright Law.
Springer is a part of Springer Science+Business Media
springer.com
c© Springer-Verlag Berlin Heidelberg 2007The use of designations, trademarks, etc. in this publication does not imply,even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for generaluse.
Product liability: The publisher cannot guarantee the accuracy of anyinformation about dosage and application contained in this book. In everyindividual case the user must check such information by consulting therelevant literature.
Typesetting and production:LE-TEX Jelonek, Schmidt&Vöckler GbR, LeipzigSenior Manager Springer Handbook: Dr. W. Skolaut, HeidelbergTypography and layout: schreiberVIS, SeeheimIllustrations: Hippmann GbR, SchwarzenbruckCover design: eStudio Calamar Steinen, BarcelonaCover production: WMXDesign GmbH, HeidelbergPrinting and binding: Stürtz GmbH, Würzburg
Printed on acid free paper
SPIN 10934340 89/3180/YL 5 4 3 2 1 0
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V
Preface
Cameron Tropea
John Foss
Alexander Yarin
The purpose of this Springer Handbook is to provide comprehensive support to theexperimental fluid mechanics community, for planning, executing, and interpretingexperiments. This purpose is addressed by organizing the handbook into four parts:Part A (Chaps. 1 and 2) addresses the motivation for experiments and the equationsthat build the foundations for experimental work; Part B (Chaps. 3–8) examines themeasurement of, and measurement techniques used for, all primary quantities appearingexplicitly in the governing equations; Part C (Chaps. 9–21) presents topics related toa specific application area or technique and; Part D (Chaps. 22–25) is meant to serveas a reference in questions regarding signal and data acquisition and processing.
Experimental fluid mechanics comprises a very large number of topics and specialapplication areas and in undertaking such a handbook project a selection must necessar-ily be made. In making this selection the editors have attempted to cover as completelyas possible the most fundamental concepts and most frequently employed measure-ment techniques and fluid behaviors. Those topics that have not been included in thisfirst edition will perhaps find a place in a future edition.
The editors of this Springer Handbook would like to heartily thank the contributingauthors, who have all captured the spirit of this handbook and made significant improve-ments to our original concept. Furthermore, a special thanks goes to Dr. Werner Skolautat Springer for his untiring efforts in assembling the final version of all the manuscriptsand coordinating the production process. And finally, thanks go to Ms. Claudia Rauand her team at LE-TeX Jelonek, Schmidt & Vöckler GbR for their skillful preparationof manuscripts into final production form.
Inevitably there will be misprints in this handbook and readers are invited to bringthese to the attention of the Editors via e-mail. Similarly, suggestions for improvementsin a second edition are also very welcome.
July 2007 Cam TropeaJohn Foss
Alex Yarin
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VII
List of Authors
David M. AdmiraalUniversity of Nebraska-LincolnDepartment of Civil EngineeringNebraska Hall W348Lincoln, NE 68588-0531, USAe-mail: [email protected]
Ronald J. AdrianArizona State UniversityIra A. Fulton School of Mechanicaland Aerospace EngineeringP.O. Box 876106Tempe, AZ 85210, USAe-mail: [email protected]
Nuri AkselUniversität BayreuthDepartment of Applied Mechanicsand Fluid DynamicsUniversitätsstr.95440 Bayreuth, Germanye-mail: [email protected]
Yiannis AndreopoulosThe City College of the City University of New YorkDepartment of Mechanical EngineeringNew York, NY 10031, USAe-mail: [email protected]
Roger E.A. ArndtUniversity of MinnesotaSaint Anthony Falls Laboratory2 Third Ave. SE,Minneapolis, MN 55414, USAe-mail: [email protected]
Marc J. AssaelAristotle UniversityChemical Engineering DepartmentThessaloniki, 54124, Greecee-mail: [email protected]
Howard A. BarnesUniversity of Wales AberystwythInstitute of Mathematical and Physical SciencesPenglais AberystwythCeredigion, SY23 3BZ, UKe-mail: [email protected]
Terry D. Blake8 HazelyTring, HP23 5JH, UKe-mail: [email protected]
Eberhard BodenschatzMax Planck Institute for Dynamicsand Self-OrganizationLaboratory of Fluid Dynamics, Pattern Formationand Nanobiocomplexity (LFPN)Am Faßberg 1137077 Göttingen, Germanye-mail: [email protected]
Jean-Paul BonnetUniversité de Poitiers, ENSMA, CNRSLaboratoire d’Etudes Aérodynamiques43 rue de l’aérodrome86036 Poitiers, Francee-mail: [email protected]
Michael P. BrennerHarvard UniversitySchool of Engineering and Applied Science29 Oxford StreetCambridge, MA 02139, USAe-mail: [email protected]
Ronald J. CalhounArizona State UniversityMechanical and Aerospace EngineeringP.O. Box 876106Tempe, AZ 85287-6106, USAe-mail: [email protected]
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VIII List of Authors
Antonio CastellanosUniversidad de SevillaAvda. Reina Mercedes s/nSevilla, 41013, Spaine-mail: [email protected]
Angelo A. CavoneNASA Langley Research CenterATK Space Systems, Inc.Mail Stop 493Hampton, VA 23681, USAe-mail: [email protected]
Teresa K. ChereskinUniversity of California-San DiegoScripps Institution of Oceanography9500 Gilman DriveLa Jolla, CA 92093-0230, USAe-mail: [email protected]
Geneviève Comte-BellotEcole Centrale de LyonCentre Acoustique36 avenue Guy de Collongue69134 Ecully, Francee-mail: [email protected]
Joël De ConinckUniversité de Mons-HainautCentre for Research in Molecular Modelling20 Place du Parc7000 Mons, Belgiume-mail: [email protected]
Laurent CordierCNRS, Université de PoitiersLaboratoire d’Etudes Aérodynamiques43, route de l’aérodrome86036 Poitiers, Francee-mail: [email protected]
Alvaro CuervaUniversidad Politécnica de MadridInstituto Universitario de Microgravedad,AeronáuticosPlaza del Cardenal Cisneros 3Madrid, 28040, Spaine-mail: [email protected]
Werner J.A. DahmThe University of MichiganDepartment of Aerospace Engineering3056 FXB 2140Ann Arbor, MI 48109-2140, USAe-mail: [email protected]
Joël DelvilleCNRS, Université de Poitiers – CEATLaboratoire d’Etudes Aérodynamiques47, route de l’Aérodrome86036 Poitiers, Francee-mail: [email protected]
Andreas DreizlerTechnische Universität DarmstadtFachgebiet für Energie- und KraftwerkstechnikPetersenstraße 3064287 Darmstadt, Germanye-mail: [email protected]
John K. EatonStanford UniversityDepartment of Mechanical EngineeringBuilding 500Stanford, CA 94305, USAe-mail: [email protected]
Volker EbertUniversität HeidelbergPhysikalisch Chemisches InstitutIm Neuenheimer Feld 25369120 Heidelberg, Germanye-mail: [email protected]
Yasuhiro EgamiInstitute of Aerodynamics and Flow TechnologyGerman Aerospace CenterBunsenstr. 1037073 Göttingen, Germanye-mail: [email protected]
Rolf H. EnglerInstitute of Aerodynamics and Flow TechnologyGerman Aerospace Center, Experimental MethodsBunsenstr. 1037073 Göttingen, Germanye-mail: [email protected]
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List of Authors IX
Marie FargeEcole Normale SupérieureLaboratoire de Météorologie Dynamique(IPSL-CNRS)24, rue Lhomond75231 Paris, Francee-mail: [email protected]
Harindra J.S. FernandoArizona State UniversityMechanical and Aerospace EngineeringTempe, AZ 85287-9809, USAe-mail: [email protected]
Uwe FeyInstitute of Aerodynamics and Flow TechnologyGerman Aerospace CenterBunsenstr. 1037073 Göttingen, Germanye-mail: [email protected]
John F. FossMichigan State UniversityMechanical EngineeringA118 Engineering Research ComplexEast Lansing, MI 48824-1326, USAe-mail: [email protected]
Marcelo H. GarcíaUniversity of Illinois at Urbana-ChampaignVen Te Chow Hydrosystems Laboratory, Departmentof Civil and Environmental Engineering205 North Mathews AvenueUrbana, IL 61801-2352, USAe-mail: [email protected]
Klaus HannemannGerman Aerospace Center (DLR)Institute of Aerodynamics and Flow Technology,Spacecraft SectionBunsenstraße 1037073 Göttingen, Germanye-mail: [email protected]
Lutz HeymannUniversität BayreuthLehrstuhl für Technische Mechanikund Strömungsmechanik, Fakultätfür Angewandte Naturwissenschaften95440 Bayreuth, Germanye-mail: [email protected]
Bruce HoweUniversity of WashingtonApplied Physics Laboratory1013 NE 40th StreetSeattle, WA 98105-6698, USAe-mail: [email protected]
Wolf-Heinrich HuchoGärtnereiweg 386938 Schondorf, Germanye-mail: [email protected]
Klaus HufnagelTechnische Universität DarmstadtFluid Mechanics and AerodynamicsPetersenstr. 3064287 Darmstadt, Germanye-mail: [email protected]
Bernd JähneUniversity of HeidelbergResearch Group Image Processing,Interdisciplinary Center for Scientific ComputingIm Neuenheimer Feld 36869120 Heidelberg, Germanye-mail: [email protected]
Markus JehleUniversity of HeidelbergResearch Group Image Processing,Interdisciplinary Center for Scientific ComputingIm Neuenheimer Feld 36869120 Heidelberg, Germanye-mail: [email protected]
Joseph KatzThe Johns Hopkins UniversityDepartment of Mechanical Engineering3400 N. Charles St.Baltimore, MD 21218, USAe-mail: [email protected]
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X List of Authors
Damien KawakamiUniversity of MinnesotaMechanical Engineering10550 Nicollet Ave S.Bloomington, MN 55420, USAe-mail: [email protected]
Saeid KheirandishUniversität Karlsruhe (TH)Institut für Mechanische Verfahrenstechnik undMechanikBauing. Kolleg. III, Fasanengarten,Gotthard-Franz-Straße 376131 Karlsruhe, Germanye-mail:[email protected]
Michael KlarUniversity of HeidelbergResearch Group Image Processing,Interdisciplinary Center for Scientific ComputingIm Neuenheimer Feld 36869120 Heidelberg, Germanye-mail: [email protected]
Joseph C. KlewickiUniversity of New HampshireDepartment of Mechanical EngineeringDurham, NH 03824, USAe-mail: [email protected]
Manoochehr M. KoochesfahaniMichigan State UniversityDepartment of Mechanical EngineeringA131, Engineering Research ComplexEast Lansing, MI 48824, USAe-mail: [email protected]
Tomasz A. KowalewskiPolish Academy of SciencesInstitute of Fundamental Technological Research(IPPT PAN), Department of Mechanics and Physicsof FluidsSwietokrzyska 21Warszawa, 00-049, Polande-mail: [email protected]
Eric LaugaMassachusetts Institute of TechnologyDepartment of Mathematics77 Massachusetts AvenueCambridge, MA 02139-4307, USAe-mail: [email protected]
Joseph W. LeeNASA Langley Research CenterAdvanced Sensing and Optical MeasurementsBranchMail Stop 493Hampton, VA 23681, USAe-mail: [email protected]
Jacques LewalleSyracuse UniversityMechanical Engineering149 Link HallSyracuse, NY 13244, USAe-mail: [email protected]
Phillip LigraniUniversity of OxfordDepartment of Engineering ScienceParks RoadOxford, OX1 3PJ, UKe-mail: [email protected]
Abraham MarmurTechnion-Israel Institute of TechnologyDepartment of Chemical EngineeringHaifa 32000, Israele-mail: [email protected]
Jan Martinez SchrammInstitute of Aerodynamics and Flow TechnologyDepartment SpacecraftBunsenstraße 1037073 Göttingen, Germanye-mail: [email protected]
Ivan MarusicUniversity of MelbourneVictoria, Australiae-mail: [email protected]
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List of Authors XI
Beverley J. McKeonCalifornia Institute of TechnologyGraduate Aeronautical Laboratories,Division of Engineering and Applied Science1200 E. California Blvd. MC 301–46Pasadena, CA 91125-4600, USAe-mail: [email protected]
Gareth H. McKinleyMassachusetts Institute of TechnologyDepartment of Mechanical Engineering77 Massachusetts AvenueCambridge, MA 02139, USAe-mail: [email protected]
Charles MeneveauThe Johns Hopkins UniversityDepartment of Mechanical Engineering3400 N. Charles StreetBaltimore, MD 21218, USAe-mail: [email protected]
Wolfgang MerzkirchUniversität EssenLehrstuhl für StrömungslehreUniversitätsstraße 245141 Essen, Germanye-mail: [email protected]
James F. MeyersNASA Langley Research CenterAdvanced Sensing and Optical MeasurementsBranchMail Stop 493Hampton, VA 23681, USAe-mail: [email protected]
Scott C. MorrisUniversity of Notre DameDepartment of Aerospace and MechanicalEngineering109 Hessert LaboratoryNotre Dame, IN 46556, USAe-mail: [email protected]
John A. MullinNorthrop Grumman Space TechnologyOne Space ParkRedondo Beach, CA 90278, USAe-mail: [email protected]
Klaas te NijenhuisDelft University of TechnologyDepartment of Polymer Materialsand Polymer EngineeringJulianalaan 1362628 BL, Delft, The Netherlandse-mail: [email protected]
Holger NobachMax Planck Institute for Dynamicsand Self-OrganizationAm Faßberg 1737077 Göttingen, Germanye-mail: [email protected]
Jeffrey A. OdellUniversity of BristolDepartment of PhysicsTyndall AvenueBristol, BS8 1TH, UKe-mail: [email protected]
Nicholas T. OuelletteMax Planck Institute for Dynamicsand Self-OrganizationLaboratory of Fluid Dynamics, Pattern Formationand Nanobiocomplexity (LFPN)Am Faßberg 1137077 Göttingen, Germanye-mail: [email protected]
Ronald L. PantonThe University of TexasMechanical Engineering Department1 University Station C2200Austin, TX 78712-0292, USAe-mail: [email protected]
Eric R. PardyjakUniversity of UtahDepartment of Mechanical EngineeringSalt Lake City, UT 8411, USAe-mail: [email protected]
Marc PerlinUniversity of MichiganNaval Architecture and Marine Engineering2600 Draper Rd.Ann Arbor, MI 48109-2145, USAe-mail: [email protected]
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XII List of Authors
Marko PrincevacUniversity of California RiversideDepartment of Mechanical EngineeringBourns Hall A315Riverside, CA 92521, USAe-mail: [email protected]
Alberto T. PérezUniversidad de SevillaDepartamento de Electrónicay Electromagnetismo, Facultad de FísicaAvda. Reina Mercedes s/nSevilla, 41012, Spaine-mail: [email protected]
Giovanni Paolo RomanoUniversity of Roma “La Sapienza”Department Mechanics and AeronauticsVia Eudossiana 1800184 Rome, Italye-mail: [email protected]
William S. SaricTexas A&M UniversityAerospace EngineeringCollege Station, TX 77843-3141, USAe-mail: [email protected]
Fulvio ScaranoDelft University of TechnologyAerospace Engineering DepartmentKluyverweg 12627 HS, Delft, The Netherlandse-mail: [email protected]
Günter ScheweGerman Aerospace Center (DLR)Institut für AeroelastikBunsenstraße 1037073 Göttingen, Germanye-mail: [email protected]
Kai SchneiderUniversité de ProvenceCentre de Mathématiques et d’Informatique39, rue F. Joliot-Curie13453 Cedex 13 Marseille, Francee-mail: [email protected]
Richard SchodlGerman Aerospace Center (DLR)Institute of Propulsion TechnologyEngine Measurement SystemsLinder Höhe51147 Köln, Germanye-mail: [email protected]
Christof SchulzUniversität Duisburg-EssenInstitut für Verbrennung und GasdynamikLotharstrasse 147057 Duisburg, Germanye-mail: [email protected]
Stephen SpiegelbergCambridge Polymer Group52-R Roland StreetBoston, MA 02129-1234, USAe-mail: [email protected]
Victor SteinbergWeizmann Institute of ScienceDepartment of Physics of Complex SystemsRehovot 76100, Israele-mail: [email protected]
Howard A. StoneHarvard UniversityDivision of Engineering and Applied SciencesCambridge, MA , USAe-mail: [email protected]
Stephanus A. TheronTechnion – Israel Institute of TechnologyDepartment of Mechanical EngineeringHaifa 3200, Israele-mail: [email protected]
Cameron TropeaTechnische Universität DarmstadtFachgebiet Strömungslehre und AerodynamikPetersenstraße 3064287 Darmstadt, Germanye-mail: [email protected]
Oğuz UzolMiddle East Technical UniversityDepartment of Aerospace EngineeringAnkara, 06531, Turkeye-mail: [email protected]
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List of Authors XIII
Petar V. VukoslavčevićUniversity of MontenegroDepartment of Mechanical EngineeringCetinjski put bbPodgorica, 8100, Montenegroe-mail: [email protected]
Manfred H. WagnerTechnische Universität BerlinPolymertechnik/PolymerphysikFasanenstr. 9010623 Berlin, Germanye-mail: [email protected]
William A. WakehamUniversity of SouthamptonHighfieldSouthampton, SO17 1BJ, UKe-mail: [email protected]
James M. WallaceUniversity of MarylandDepartment of Mechanical EngineeringCollege Park, MD 20742, USAe-mail: [email protected]
Jerry WesterweelDelft University of TechnologyDepartment of Mechanical EngineeringLeeghwaterstraat 212628 CA, Delft, The Netherlandse-mail: [email protected]
Charles H.K. WilliamsonCornell UniversityMechanical and Aerospace Engineering144 Upson HallIthaca, NY 14853, USAe-mail: [email protected]
Jürgen WolfrumRuprecht-Karls-Universität HeidelbergPhysikalisch-Chemisches InstitutIm Neuenheimer Feld 25369120 Heidelberg, Germanye-mail: [email protected]
Martin WosnikAlden Research Laboratory30 Shrewsbury St.Holden, MA 01520, USAe-mail: [email protected]
Haitao XuMax Planck Institute for Dynamicsand Self-OrganizationDepartment of Fluid Dynamics, Pattern Formation,and NanobiocomplexityAm Faßberg 11/Turm 237077 Göttingen, Germanye-mail: [email protected]
Alexander L. YarinUniversity of Illinois at ChicagoDepartment of Mechanicaland Industrial Engineering842 W. Taylor St.Chicago, IL 60607-7022, USAe-mail: [email protected]
Eyal ZussmanTechnion – Israel Institute of TechnologyDepartment of Mechanical EngineeringHaifa 3200, Israele-mail: [email protected]
James H. DuncanUniversity of MarylandDepartment of Mechanical Engineering3181 Martin HallCollege Park, MD 207, USAe-mail: [email protected]
Daniel G. NoceraMassachusetts Institute of TechnologyDepartment of Chemistry77 Massachusetts Ave.Cambridge, MA 02139-4307, USAe-mail: [email protected]
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XV
Contents
The authors of the different Sections can be identified by consulting the DetailedContents or the About the Authors part.
List of Abbreviations ................................................................................. XXINomenclature ............................................................................................ XXV
Part A Experiments in Fluid Mechanics
1 Experiment as a Boundary-Value ProblemRonald L. Panton, Saeid Kheirandish, Manfred H. Wagner......................... 31.1 Thermodynamic Equations............................................................. 31.2 Kinematic Equations ..................................................................... 51.3 Balance Laws and Local Governing Equations ................................. 61.4 Balance Laws and Global Governing Equations ............................... 81.5 Constitutive Equations ................................................................... 101.6 Navier–Stokes Equations ............................................................... 111.7 Discontinuities in Density .............................................................. 111.8 Constitutive Equations and Nonlinear Rheology of Polymer Melts .... 13References .............................................................................................. 30
2 Nondimensional Representation of the Boundary-Value ProblemJohn F. Foss, Ronald L. Panton, Alexander L. Yarin .................................... 332.1 Similitude, the Nondimensional Prototype and Model Flow Fields ... 342.2 Dimensional Analysis and Data Organization .................................. 422.3 Self-Similarity ............................................................................... 57References .............................................................................................. 82
Part B Measurement of Primary Quantities
3 Material Properties: Measurement and DataWilliam A. Wakeham, Marc J. Assael, Abraham Marmur, Joël De Coninck,Terry D. Blake, Stephanus A. Theron, Eyal Zussman.................................... 853.1 Density ......................................................................................... 853.2 Surface Tension and Interfacial Tension of Liquids .......................... 963.3 Contact Angle ................................................................................ 1063.4 Viscosity ........................................................................................ 1193.5 Thermal Conductivity and Thermal Diffusivity ................................. 1333.6 Diffusion ....................................................................................... 1473.7 Electric and Magnetic Parameters of Liquids and Gases ................... 158References .............................................................................................. 169
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XVI Contents
4 Pressure Measurement SystemsBeverley J. McKeon, Rolf H. Engler ............................................................ 1794.1 Measurement of Pressure with Wall Tappings ................................. 1804.2 Measurement of Pressure with Static Tubes .................................... 1854.3 Hardware and Other Considerations ............................................... 1874.4 Pressure-Sensitive Paint (PSP) ........................................................ 188References .............................................................................................. 209
5 Velocity, Vorticity, and Mach NumberBeverley J. McKeon, Geneviève Comte-Bellot, John F. Foss,Jerry Westerweel, Fulvio Scarano, Cameron Tropea, James F. Meyers,Joseph W. Lee, Angelo A. Cavone, Richard Schodl,Manoochehr M. Koochesfahani, Daniel G. Nocera, Yiannis Andreopoulos,Werner J.A. Dahm, John A. Mullin, James M. Wallace,Petar V. Vukoslavčević, Scott C. Morris, Eric R. Pardyjak, Alvaro Cuerva ....... 2155.1 Pressure-Based Velocity Measurements .......................................... 2165.2 Thermal Anemometry .................................................................... 2295.3 Particle-Based Techniques ............................................................. 2875.4 Molecular Tagging Velocimetry (MTV) .............................................. 3625.5 Vorticity ........................................................................................ 3825.6 Thermal Transient Anemometer (TTA) .............................................. 4345.7 Sonic Anemometry/Thermometry .................................................... 436References .............................................................................................. 446
6 Density-Based TechniquesWolfgang Merzkirch ................................................................................. 4736.1 Density, Refractive Index, and Optical Flow Visualization ................ 4736.2 Shadowgraphy .............................................................................. 4746.3 Schlieren Method .......................................................................... 4766.4 Moiré Deflectometry ...................................................................... 4786.5 Interferometry .............................................................................. 4806.6 Optical Tomography ....................................................................... 485References .............................................................................................. 485
7 Temperature and Heat FluxTomasz A. Kowalewski, Phillip Ligrani, Andreas Dreizler, Christof Schulz,Uwe Fey, Yasuhiro Egami ......................................................................... 4877.1 Thermochromic Liquid Crystals ....................................................... 4887.2 Measurements of Surface Heat Transfer Characteristics
Using Infrared Imaging .................................................................. 5007.3 Temperature Measurement via Absorption, Light Scattering
and Laser-Induced Fluorescence .................................................... 5157.4 Transition Detection by Temperature-Sensitive Paint ...................... 537References .............................................................................................. 553
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Contents XVII
8 Force and Moment MeasurementKlaus Hufnagel, Günter Schewe ................................................................ 5638.1 Steady and Quasi-Steady Measurement .......................................... 5648.2 Force and Moment Measurements in Aerodynamics
and Aeroelasticity Using Piezoelectric Transducers........................... 596References .............................................................................................. 615
Part C Specific Experimental Environments and Techniques
9 Non-Newtonian FlowsKlaas te Nijenhuis, Gareth H. McKinley, Stephen Spiegelberg,Howard A. Barnes, Nuri Aksel, Lutz Heymann, Jeffrey A. Odell .................... 6199.1 Viscoelastic Polymeric Fluids .......................................................... 6199.2 Thixotropy, Rheopexy, Yield Stress ................................................. 6619.3 Rheology of Suspensions and Emulsions ......................................... 6809.4 Entrance Correction and Extrudate Swell ........................................ 7209.5 Birefringence in Non-Newtonian Flows .......................................... 724References .............................................................................................. 732
10 Measurements of Turbulent FlowsGiovanni Paolo Romano, Nicholas T. Ouellette, Haitao Xu,Eberhard Bodenschatz, Victor Steinberg, Charles Meneveau, Joseph Katz.... 74510.1 Statistical Eulerian Description of Turbulent Flows .......................... 74610.2 Measuring Lagrangian Statistics in Intense Turbulence .................... 78910.3 Elastic Turbulence in Viscoelastic Flows .......................................... 79910.4 Measurements for Large-Eddy Simulations ..................................... 830References .............................................................................................. 849
11 Flow VisualizationWolfgang Merzkirch ................................................................................. 85711.1 Aims and Principles of Flow Visualization ....................................... 85711.2 Visualizations of Flow Structures and Flow Direction ....................... 85911.3 Visualization of Free Surface Flows ................................................. 868References .............................................................................................. 869
12 Wall-Bounded FlowsJoseph C. Klewicki, William S. Saric, Ivan Marusic, John K. Eaton ............... 87112.1 Introductory Concepts .................................................................... 87112.2 Measurement of Wall Shear Stress .................................................. 87512.3 Boundary-Layer Stability and Transition ......................................... 88612.4 Measurements Considerations in Non-Canonical Flows ................... 896References .............................................................................................. 902
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XVIII Contents
13 Topological Considerations in Fluid Mechanics MeasurementsJohn F. Foss ............................................................................................. 90913.1 A Companion Document ................................................................ 90913.2 Utilization of Topological Considerations for Flow Field Analyses ..... 910References .............................................................................................. 918
14 Flow Measurement Techniques in TurbomachineryOğuz Uzol, Joseph Katz ............................................................................ 91914.1 Background On Turbomachinery Flows ........................................... 91914.2 Non-Optical Measurement Techniques ........................................... 92114.3 Optical Measurement Techniques ................................................... 93314.4 Concluding Remarks ...................................................................... 950References .............................................................................................. 951
15 HydraulicsRoger E.A. Arndt, Damien Kawakami, Martin Wosnik, Marc Perlin,James H. Duncan, David M. Admiraal, Marcelo H. García ........................... 95915.1 Measurements in Cavitating Flows ................................................. 95915.2 Wave Height and Slope .................................................................. 100915.3 Sediment Transport Measurements ................................................ 1020References .............................................................................................. 1033
16 AerodynamicsWolf-H. Hucho, Klaus Hannemann, Jan Martinez Schramm,Charles H.K. Williamson ........................................................................... 104316.1 Ground Vehicle Aerodynamics ........................................................ 104316.2 Short-Duration Testing
of High Enthalpy, High Pressure, Hypersonic Flows ......................... 108116.3 Bluff Body Aerodynamics ............................................................... 1125References .............................................................................................. 1146
17 Atmospheric MeasurementsHarindra J.S. Fernando, Marko Princevac, Ronald J. Calhoun ..................... 115717.1 Point Measurements ...................................................................... 115917.2 Dispersion Measurements .............................................................. 116717.3 Remote Sensing ............................................................................ 116917.4 Satellite Measurements ................................................................. 1175References .............................................................................................. 1178
18 Oceanographic MeasurementsBruce Howe, Teresa K. Chereskin ............................................................... 117918.1 Oceanography ............................................................................... 117918.2 Point Measurements ...................................................................... 118218.3 Lagrangian Techniques .................................................................. 118818.4 Remote Sensing ............................................................................ 1192
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Contents XIX
18.5 Measurement Systems ................................................................... 120318.6 Experiment Case Studies ................................................................ 1208References .............................................................................................. 1214
19 Microfluidics: The No-Slip Boundary ConditionEric Lauga, Michael P. Brenner, Howard A. Stone ...................................... 121919.1 History of the No-Slip Condition..................................................... 122019.2 Experimental Methods ................................................................... 122219.3 Molecular Dynamics Simulations .................................................... 122619.4 Discussion: Dependence on Physical Parameters ............................. 122819.5 Perspective ................................................................................... 1234References .............................................................................................. 1235
20 Combustion DiagnosticsChristof Schulz, Andreas Dreizler, Volker Ebert, Jürgen Wolfrum .................. 124120.1 Basics ........................................................................................... 124220.2 Laser-Based Combustion Diagnostics .............................................. 124320.3 Experimental Data Devoted to Validation
of Numerical Simulations and Modeling ......................................... 124420.4 Application of Laser-Based Techniques .......................................... 124720.5 Conclusions ................................................................................... 1299References .............................................................................................. 1300
21 Electrohydrodynamic SystemsAntonio Castellanos, Alberto T. Pérez ........................................................ 131721.1 Equations ..................................................................................... 131821.2 Fluid Statics and Dynamics in EHD .................................................. 132021.3 Experimental Methods in EHD ........................................................ 132221.4 Conductivity .................................................................................. 132321.5 Mobility ........................................................................................ 132721.6 Electric Field Measurement: Kerr Effect ........................................... 132821.7 Velocity ......................................................................................... 132921.8 Visualization ................................................................................. 1330References .............................................................................................. 1331
Part D Analysis and Post-Processing of Data
22 Review of Some Fundamentals of Data ProcessingHolger Nobach, Cameron Tropea, Laurent Cordier, Jean-Paul Bonnet,Joël Delville, Jacques Lewalle, Marie Farge, Kai Schneider, Ronald J. Adrian 133722.1 Fourier Transform .......................................................................... 133722.2 Correlation Function ...................................................................... 134222.3 Hilbert Transform .......................................................................... 134422.4 Proper Orthogonal Decomposition: POD .......................................... 1346
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XX Contents
22.5 Conditional Averages and Stochastic Estimation .............................. 137022.6 Wavelet Transforms ....................................................................... 1378References .............................................................................................. 1395
23 Fundamentals of Data ProcessingHolger Nobach, Cameron Tropea............................................................... 139923.1 Statistical Principles ...................................................................... 139923.2 Stationary Random Processes ......................................................... 140123.3 Estimator Expectation and Variance ............................................... 140223.4 Signal Noise .................................................................................. 140623.5 Cramér–Rao Lower Bound (CRLB) .................................................... 140823.6 Propagation of Errors..................................................................... 1416References .............................................................................................. 1417
24 Data Acquisition by Imaging DetectorsBernd Jähne ............................................................................................ 141924.1 Definitions .................................................................................... 141924.2 Types of Detectors ......................................................................... 142024.3 Imaging Detectors ......................................................................... 142124.4 Performance of Imaging Sensors .................................................... 142624.5 Camera Selection ........................................................................... 1435References .............................................................................................. 1436
25 Data AnalysisBernd Jähne, Michael Klar, Markus Jehle .................................................. 143725.1 Image Processing .......................................................................... 143725.2 Motion Analysis ............................................................................. 1464References .............................................................................................. 1488
Acknowledgements ................................................................................... 1493About the Authors ..................................................................................... 1495Detailed Contents ...................................................................................... 1513Subject Index ............................................................................................. 1531
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XXI
List of Abbreviations
3-D three-dimensional4-D MRV 4-D magnetic resonance velocimetry
A
A/D analog-to-digitalABS acoustic bubble spectrometerABS acoustic backscatteracac acetylacetonateACF autocorrelation functionACN acetonitrileADC analog-to-digital converterADCP acoustic Doppler current profilerAFM atomic force microscopyAFTRF axial flow turbine research facilityAGW adaptive Gaussian windowingAMODE-MST acoustic mid-ocean dynamics
experiment-moving ship tomographyAPE-HKE available potential energy-to-horizontal
kinetic energyARD atmospheric re-entry demonstratorASFM acoustic scintillation flow meterASTM American Society for Testing and
MaterialsATK–GASL Alliant Techsystems Inc. – General
Applied Science LaboratoriesAUV autonomous undersea vehiclesAVHRR advanced very high-resolution radiometerAVP absolute velocity profilerAXBT air-expendable bathythermograph
B
BBO Basset–Boussinesq–OseenBC boundary conditionBCCE brightness change constraint equationBL boundary layerBT bathythermograph
C
CAD crank angle degreeCARS coherent anti-Stokes Raman
spectroscopyCARS coherent anti-Stokes Raman scatteringCCA constant current anemometerCCD charge-coupled deviceCD cyclodextrinCFD computational fluid dynamicCFK carbon-fiber-reinforced plasticCFT continuous Fourier transform
CLSM confocal laser scanning microscopyCMC critical micelle concentrationCMD count median diameterCMD count mean diameterCMOS complementary metal oxide
semiconductorCP cone-and-plateCR constraint releaseCRDLAS cavity-ring-down laser-absorption
spectroscopyCRLAS cavity ring-down laser absorption
spectroscopyCRLB Cramér–Rao lower boundCRV crew return vehicleCS coherent structuresCSM cavitation susceptibility metersCSR controlled-shear-rateCSS controlled-shear-stressCT Couette–TaylorCTA constant temperature anemometerCTAB cetyltrimethyl ammonium bromideCTD conductivity–temperature–depth/pressureCUBRC Calspan - University at Buffalo Research
CenterCVA constant voltage anemometer
D
DAS direct absorption spectroscopyDBP di-n-butyl phthalateDBR distributed Bragg reflectorDE Doi and EdwardsDEHS di-ethyl-hexyl-sebacatDFB distributed feedbackDFG difference-frequency generationDFT discrete Fourier transformDFWM degenerate four-wave mixingDGV Doppler global velocimetryDIDSON dual frequency identification sonarDIN Deutsches Institut für NormungDL diode laserDLR German Aerospace CenterDMF dimethylformamideDMSO dimethylsulfoxideDNS direct numerical simulationDOE diffractive optical elementDPIV digital PIVDPV Doppler picture velocimetryDR dynamic rangeDSNU dark signal nonuniformityDSPIV dual-plane particle image velocimetry
-
XXII List of Abbreviations
E
EAST Electric Arc Shock TunnelEBCCE extended brightness change constraint
equationEDM electric discharge machiningEGR exhaust gas recirculationELAC elliptical aerodynamic configurationELIF excimer-laser-induced fragmentationEM-CCD electron-multiplying CCDEMI electromagnetic interferenceEMVA European Machine Vision AssociationESA European Space AgencyESTEC European Space Research and
Technology CenterETW European transonic wind tunnel
F
FARLIF fuel–air ratio by laser-inducedfluorescence
FBRM focused beam reflectance measurementFFT fast Fourier transformFFW finite fringe widthFIR far-infraredFITCD fluorescent-conjugated dextranFMS frequency modulation spectroscopyFOBS fiber-optic backscatterFPN fixed pattern noiseFTR Fourier-transform rheology
G
GBCCE generalized brightness change constraintequation
GEO geostationary Earth orbitGIFTS geosynchronous imaging
Fourier-transform spectrometerGOES geostationary operational environmental
satellitesGPS global positioning systemGUM guide of uncertainties in measurement
H
HDG high-pressure windtunnelHEG High Enthalpy Shock Tunnel GöttingenHEM horizontal electrometerHF high-frequencyHIEST high enthalpy shock tunnelHITRAN high-resolution transmission molecular
absorptionHPIV holographic particle image velocimetryHPR heave–pitch–rollHTV hydroxyl tagging velocimetryHWA hot-wire anemometry
I
IAPWS International Association for theProperties of Water and Steam
IC initial conditionIC internal combustionICCD intensified CCDICET international cavitation erosion testIEP isoelectric pointIES inverted echosounderIFW infinite fringe widthIGV inlet guide vanesIMET improved meteorological packagesIRT infrared thermographyISC intersystem crossingISL Institute of Saint LouisISO International Organization for StandardsISS International Space StationITTC international towing tank conferenceIVC iodine vapor cellIVK Institut für Verbrennungsmotoren und
Kraftfahrwesen
J
JAXA Japanese Aeronautics ExplorationAgency
JFTA joint frequency–time analysisJIS Japanese Industrial Standards
L
L2F laser two-focus velocimetryLAOS large-amplitude oscillatory shearLAS laser absorption spectroscopyLCO limit-cycle oscillationLD laser DopplerLDA laser Doppler anemometryLDPE low-density polyethyleneLDV laser Doppler velocimetryLED light-emitting diodesLEI laser-enhanced ionizationLENS large energy national shockLES large-eddy simulationLFM laser frequency monitorLIF laser-induced fluorescenceLII laser-induced incandescenceLIM local intermittency measureLIPA laser-induced photochemical anemometryLISST laser in situ scattering and
transmissometryLPT Lagrangian particle trackingLSS laser speckle strophometryLT laser transitLTV laser transit velocimetryLWIR long-wavelength infrared
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List of Abbreviations XXIII
M
MARIN Maritime Research Institute NetherlandsMC modulus-compensatingMC methylene chlorideMDA minimum detectable absorptionMDPR mean depth of erosion penetration rateMEMS microelectromachined sensorsMFI melt flow indexMHT multiple hypothesis trackerML maximum-likelihoodMLE maximum-likelihood estimatorMMH mixed metal hydroxideMRA multiresolution analysisMRI magnetic resonance imagingMSACA most stable apparent contact angleMSF molecular stress functionMT montmorilloniteMTV molecular tagging velocimetryMW Maxwell–WiechertMWIR mid-wavelength infraredMZI Mach–Zehnder interferometer
N
NACA National Advisory Committee forAeronautics
NAL National Aeronautics LaboratoryNASA National Aeronautics and Space
AdministrationNd:YAG neodymium-doped yttrium aluminum
garnetNEE noise-equivalent exposureNETD noise equivalent temperature differenceNIR near-infraredNMA monomethylacetamideNMR nuclear magnetic resonanceNMT monomethyltryptamineNO nitric oxide
O
OBS optical backscatterODE ordinary differential equationsOH hydroxide,wegOPG optical parametric generationOPO optical parametric oscillatorOTV ozone tagging velocimetry
P
PAA polyacrylic acidPAA polyacrylamidePACA practical advancing contact anglePAH polycyclic aromatic hydrocarbonPBS phosphate buffer solution
PCI peripheral component interfacePCL polycaprolactonePDA phase Doppler anemometryPDE partial differential equationsPDF probability density functionPDI polydispersity indexPDMS polydimethylsiloxanePDV planar Doppler velocimetryPET poly(ethyleneterephthalate)PETW pilot facility of ETWPHANTOMM photoactivated non-intrusive tracking
of molecular motionPIB polyisobuthylenePIT phase inversion temperaturePIV particle image velocimetryPLIF planar laser-induced fluorescencePM polarization modulationPMMA polymethylmethacrylatePOCS projection onto convex setsPOD proper orthogonal decompositionPP plate–platePPI plan–position indicatorPRCA practical receding contact anglePRNU photoresponse nonuniformityPS polarization spectroscopyPSD particle size distributionPSD power spectral densityPSF point spread functionPSP pressure-sensitive paintPTV particle tracking velocimetryPU polyurethanePUV pressure and two components of
horizontal currentPVA polyvinyl alcoholPVDF polyvinylidene fluoridePWM-CTA pulse-width-modulated
constant-temperature anemometer
R
RANS Reynolds-averaged Navier–Stokesequations
RASS radio acoustic sounding systemsRELIEF Raman excitation plus laser-induced
electronic fluorescenceREMPI resonance-enhanced multiphoton
ionizationREMUS remote environmental monitorung
unitsRET rotational energy transferRFI radio frequency interferenceRH relative humidityRHI range–height indicatorRIC relative information contentRMS root-mean-square
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XXIV List of Abbreviations
S
S+H sample-and-holdSAOS small-amplitude oscillatory shearSAR synthetic aperture radarSAT sonic anemometer/thermometerSCR selective catalytic reductionSEE saturation-equivalent exposureSER sentmanat extension rheometerSFA surface force apparatusSFG sum-frequency generationSG specific gravitySGS subgrid-scale stressSHG second-harmonic generationSI spark ignitionSNCR selective non-catalytic reductionSNR signal-to-noise ratioSODAR sound detection and rangingSOFAR sound fixing and rangingSPL sound-pressure levelSR spatial resolutionSSD sum-of-squared differencesSVD singular value decompositionSWIR short-wavelength infrared
T
TACA theoretical advancing contact angleTCFB two-color flow birefringenceTDC top dead centerTDLAS tunable diode laser absorption
TEM transmission electron microscopyTHF tetrahydrofuranTLC thermochromic liquid crystalsTOPEX topography experimentTPT thermographic phosphor thermographyTR time resolutionTRCA theoretical receding contact angleTS Tollmien–SchlichtingTSP temperature-sensitive paintTWG transonic wind tunnel Göttingen
U
UV ultravioletUVW three components of velocity
V
VAO Versuchsanstalt für Wasserbau ObernachVCSEL vertical-cavity surface-emitting laserVET vibrational energy transferVPI Virginia Polytechnic Institute
W
WMS wavelength modulation spectroscopy
X
XBT expendable bathythermographXPP extended pom-pom
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XXV
Nomenclature
Experimental fluid mechanics draws on numerous dis-ciplines in addition to fluid mechanics itself: rheology,physics, electromagnetic theory, optics, electronics, sig-nal processing, data processing, etc. Each disciplineand community has developed its own nomenclatureand conventions and inevitably there exist many con-flicting designations when one attempts to assembleall of these conventions into one handbook. There-fore, we have instructed authors to adhere as closelyas possible to the skeleton nomenclature given belowand to note explicitly in their respective articles any
deviations or extensions thereof. Authors of articlesdealing with constitutive equations, material proper-ties and non-Newtonian flows were asked to follow, asfar as possible, the nomenclature given in J.M. Dealy:Official nomenclature for material functions describ-ing the response of a viscoelastic fluid to variousshearing and extensional deformations, J. Rheol. 39(1),253–265 (1995). Furthermore, all authors were askedto prepare their manuscripts using SI units, a reviewof which is provided below, following the nomencla-ture.
List of Symbols
Vectors and tensors are written boldComplex quantities carry an underscore
f Frequency (Hertz)
m Mass
ṁ Mass flux
n Outer unit normal vector
p Pressure
t Time
T Temperature
u or v Velocity vector
x1 or x Cartesian position coordinate
x2 or y Cartesian position coordinate
x3 or z Cartesian position coordinate
γ Ratio of specific heats (CP/CV)
δ Boundary-layer thickness
μ Dynamic viscosity
ν Kinematic viscosity
ρ Density
σ Surface tension
σ or σij Stress tensor
τ Deviatoric stress
τw Wall shear stress
ω Circular frequency (rad/s)
ω Vorticity vector
Λ Circulation
Ψ Stream function
Operators
Average of ensembles, time average
〈 〉 Spatial averageIm {} Imaginary partRe {} Real part�{} Fourier transformˆ EstimatorE[] Expectation
b2[] Biasvar[] Variance∇ Nablagrad Gradient of scalar: ∇div Divergence of vector; ∇·curl or rot Rotation vector: ∇×Δ Laplace: ∇2
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XXVI
International System of Units (SI)
Base and Supplementary SI Units
Quantity Name of Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic temperature kelvin K
Luminous intensity candela cd
Amount of substance mole mol
Supplementary units
Plane angle radian rad
Solid angle steradian sr
Derived SI Units
Quantity Name(s) of unit Unit symbol or abbreviationwhere differing from basicform
Unit expressed in terms ofbasic or supplementary units
Area square meter m2
Volume cubic meter m3
Frequency hertz, cycle per second Hz s−1
Density, concentration kilogram per cubic meter kg/m3
Velocity meter per second m/s
Angular velocity radian per second rad/s
Acceleration meter per second squared m/s2
Angular acceleration radian per second squared rad/s2
Volumetric flow rate cubic meter per second m3/s
Force newton N kg m/s2
Surface tension newton per meter, joule persquare meter
N/m, J/m2 kg/s2
Pressure newton per square meter,pascal
N/m2, Pa kg/ms2
Viscosity, dynamic newton-second per squaremeter
N s/m2, PI kg/ms
Viscosity, kinematic poisseuil m2/s
Thermal and mass diffusivity meter square per second m2/s
Work, torque, energy, quantityof heat
joule, newton-meter, watt-second
J, N m, W s kg m2/s2
Power, heat flux watt, joule per second W, J/s kg m2/s3
Heat flux density watt per square meter W/m2 kg/s3
Volumetric heat release rate watt per cubic meter W/m2 kg/ms−3
Multiplying Factors
Multiple and submultiple Prefix Symbol
1018 exa E1015 peta P1012 tera T109 giga G106 mega M103 kilo k102 hecto h10 deka da10−1 deci d10−2 centi c10−3 milli m10−6 micro μ10−9 nano n10−12 pico p10−15 femto f10−18 atto a
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XXVII
Quantity Name(s) of unit Unit symbol or abbreviationwhere differing from basicform
Unit expressed in terms ofbasic or supplementary units
Heat transfer coefficient watt per square meter degree W/m2deg kg/s2deg
Latent heat, enthalpy (specific) joule per kilogram J/kg m2/s2
Capacity rate watt per degree W/deg kg m2/s3deg
Thermal conductivity watter per meter degree, W/m degJ m/s m2 deg
kg m/s3 deg
Mass flux, mass flow rate kilogram per second kg/s
Mass flux density, mass flowrate per unit area
kilogram per square metersecond
kg/m2s
Mass-transfer coefficient meter per second m/s
Quantity of electricity coulomb C A s
Electromotive force volt V, W/A kg m2/A s3
Electric resistance ohm Ω, V/A kg m2/A2 s3
Electric conductivity ampere per volt meter A/V m A2 s3/kg m3
Electric capacitance farad F, A s/V A3 s4/kg m2
Magnetic flux weber Wb, V s kg m2/A s2
Inductance henry H, V s/A kg m3/A2 s2
Magnetic permeability henry per meter H/m kg m/A2 s2
Magnetic flux density tesla, weber per square meter T, Wb/m2 kg/A s2
Magnetic field strength ampere per meter A/m
Manetomotive force ampere A
Luminous flux lumen lm cd sr
Luminance candela per square meter cd/m2
Illuination lux, lumen per square meter lx, lm/m2 cd sr/m2
Non-Dimensional Numbers
Re Reynolds number
Ma Mach number
Pr Prandtl number
St Strouhal number
Fr Froude number
Nu Nusselt number
Subscripts
max maximum
min minimum
x or 1 Cartesian coordinates
y or 2 Cartesian coordinates
z or 3 Cartesian coordinates
⊥ Perpendicularly polarized‖ Parallel polarized
Superscripts
′ Fluctuating quantity in time∗ Complex conjugateT Transpose
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XXVIII
Physical and Mathematical Constants
c Speed of light
e 2.718281828 . . .
h Planck’s constant
g Gravity
i Imaginary unit
π 3.141592653 . . .
Functions
arg Argument
cos Cosine function
cosh Hyperbolic cosine function
exp Exponential function
int Integer
ln Logarithmis function, base e
log Logarithmic function, base 10
max Maximum
min Minimum
sin Sine function
sinh Hyperbolic sine function
sgn Signum function
tan Tangent function
tanh Hyperbolic tangent function
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1
ExperimePart APart A Experiments in Fluid Mechanics
1 Experiment as a Boundary-Value ProblemRonald L. Panton, Austin, USASaeid Kheirandish, Karlsruhe, GermanyManfred H. Wagner, Berlin, Germany
2 Nondimensional Representationof the Boundary-Value ProblemJohn F. Foss, East Lansing, USARonald L. Panton, Austin, USAAlexander L. Yarin, Chicago, USA
-
2
The objective of Part A is to establish the fundamentalconcepts and equations that underlie experimental fluidmechanics. The first chapter, Sects. 1.1 through 1.8,addresses both the governing equations and the con-stitutive equations for Newtonian and non-Newtonianfluids. Chapter 2 provides the systematic bases formodel testing and the scaling of experimental results.Sections 2.1.1 through 2.1.6 derive similarity param-eters (Reynolds number, Froude number, etc.) fromthe governing equations and the boundary conditions.
Dimensional analysis (Sect. 2.2) provides a rationalapproach for the organization and interpretation of ex-perimental data. Section 2.3, covering self-similarity,documents known flow fields that exhibit this con-dition (for example, an axisymmetric jet in whichū/uc = f (r/r1/2) and ucrc = constant) and providesguidance on what other flows may exhibit this be-havior. The encyclopedic presentation of exampleswill allow the reader to comprehend the universalfeatures of both complete and incomplete self-similarity.
-
3
Experiment a1. Experimentas a Boundary-Value ProblemA fluid flow experiment is an attempt to iso-late a part of the world and measure flow andthermodynamic properties. A fluid is defined asa material that deforms continuously if a shearstress is applied. An internal flow situation haswalls bounding the flow, but an inflow and out-flow position must be controlled. An external flowproblem has a uniform flow far from the body ofinterest. In both situations the state of flow at theboundary is controlled. In the mathematical rep-resentation of the flow, the flow conditions onthe boundary are specified. This is the nature ofthe governing physics. If the boundary conditionsdepend on time the flow situation in the entireregion must be specified at the initial time.
In what follows the major physical laws areoutlined. In most cases tensor calculus in sym-bolic form is employed. Scalars are lightface type,vectors are boldface type, and tensors are bold-face capitals. However, in cases where confusionis possible with tensor multiplications, index no-tation is employed. Scalars are then without anindex, vectors have one index and tensors havetwo or more indices.
1.1 Thermodynamic Equations .................... 31.1.1 Thermodynamics .......................... 4
1.2 Kinematic Equations ............................. 5
1.3 Balance Lawsand Local Governing Equations .............. 61.3.1 Continuity ................................... 6
1.3.2 Linear Momentumand Related Equations.................. 6
1.3.3 Angular Momentum...................... 71.3.4 Energy ........................................ 71.3.5 Entropy ....................................... 7
1.4 Balance Lawsand Global Governing Equations ............ 81.4.1 Regions....................................... 81.4.2 Leibnitz and Gauss Theorems......... 81.4.3 Volume ....................................... 81.4.4 Mass ........................................... 81.4.5 Linear Momentum ........................ 81.4.6 Total Energy ................................ 91.4.7 Thermal Energy ............................ 101.4.8 Mechanical Energy ....................... 101.4.9 Entropy ....................................... 10
1.5 Constitutive Equations .......................... 10
1.6 Navier–Stokes Equations ....................... 111.6.1 Incompressible Flows ................... 11
1.7 Discontinuities in Density ...................... 111.7.1 Normal Surface Discontinuity ......... 111.7.2 Fluid–Solid Boundary ................... 121.7.3 Interfaces with Surface Tension...... 12
1.8 Constitutive Equationsand Nonlinear Rheologyof Polymer Melts .................................. 131.8.1 Classical Theories ......................... 131.8.2 Convected Derivatives
and Differential Equations ............ 161.8.3 Microstructural Theories ................ 171.8.4 Conclusions ................................. 29
References .................................................. 30
1.1 Thermodynamic Equations
The properties of a continuum are defined by an imag-inary experiment where a region of volume V withcharacteristic length L is imagined to contain molecules.At a given position the volume is reduced around thatposition as indicated by the limit process L→ 0. A typ-ical molecule, denoted by the subscript i, has a mass miand an instantaneous velocity vi . The density is the sumof mass over all molecules in the region divided by the
volume as the limit is taken. Although L→ 0 is indi-cated, it cannot become so small that fluctuations occurbecause only a few molecules are present.
ρ = limL→0
∑mi
V. (1.1)
The mass-averaged velocity is a vector average ofthe molecular velocities and mass. This is appropriate to
PartA
1
-
4 Part A Experiments in Fluid Mechanics
measure the momentum:
v= limL→0
∑mivi
∑mi
. (1.2)
If the substance has several chemical species, n(k)
moles in the region, a molar averaged velocity for eachspecies k is
V (k) = limL→0
∑v
(k)i
n(k). (1.3)
Such a velocity is useful in diffusion problems. Theinternal energy (per unit mass) due to random transla-tional motions of the molecules is
e= limL→0
∑ 12 mi (vi −v) · (vi −v)∑
mi. (1.4)
The total internal energy includes other molecularmotions such as vibrations, and configuration energies.The properties above are well defined whether or not thesubstance is in thermodynamic equilibrium.
1.1.1 Thermodynamics
It is assumed that the bulk motion of the substancedoes not affect the thermodynamic state. All thermo-dynamic variables of a simple compressible substanceare described by a fundamental law that gives the en-tropy s = s(ρ, e) or in another form e= e(s, ρ). Eachsubstance has its own entropy function, however, allfunctions obey the fundamental differential equation ofthermodynamics.
e= e(s, ρ) (1.5)de= T ds− pd(ρ−1) , (1.6)
the thermodynamic pressure is defined by
p(s, ρ)≡ ∂e∂(ρ−1)
∣∣∣∣s, (1.7)
and the temperature is given by
T (s, ρ)≡ ∂e∂s
∣∣∣∣ρ
. (1.8)
Other thermodynamic properties follow from theirdefinitions, for example the enthalpy h = e+ p/ρ.
Two equations of state are equivalent to the funda-mental law of a substance. The first equation of state isof the form
p= p(ρ, T ) (1.9)
or
ρ = ρ(p, T ) . (1.10)It is equivalent to specify the compressibility coefficientfunctions:
α(p, T )≡ 1ρ
∂ρ
∂p
∣∣∣∣T, (1.11)
β(p, T )≡ − 1ρ
∂ρ
∂T
∣∣∣∣
p. (1.12)
Integration of these functions will reproduce ρ =ρ(p, T ).
The second equation of state is that for energy:
e= e(ρ, T ) . (1.13)The important derivative function here is the specific
heat (per unit mass) at constant volume:
cv(ρ, T )≡ ∂e∂T
∣∣∣∣ρ
. (1.14)
The other function ∂e/∂ρ|T is related to the stateequation ρ = ρ(p, T ) by thermodynamic theory. Insummary, the functions p= p(ρ, T ) and cv = cv(ρ, T )describe the thermodynamics of a substance.
Often the enthalpy h = e+ p/ρ is used in preferenceto the internal energy. The important derivative func-tion here is the specific heat (per unit mass) at constantpressure:
cp(p, T )≡ ∂h∂T
∣∣∣∣
p. (1.15)
The other function ∂h/∂p|T is related to the stateequation ρ = ρ(p, T ) by thermodynamic theory. Alter-natively, the functions p= p(ρ, T ) and cp = cp(p, T )describe the thermodynamics of a substance.
There are special approximations of importance: theperfect gas, ideal gas, and incompressible fluid. Fora perfect gas the state equations are:
p= ρRT , (1.16)e= cv(ρ, T )T . (1.17)Alternatively, h = cp(ρ, T )T . A further restriction to
an ideal gas gives simpler forms,
e= cv(T )T (1.18)h = cv(T )T + p/ρ (1.19)
cp(T )= cv(T )+ R (1.20)where R is the specific gas constant.
PartA
1.1
Schaltfläche: