This book reflects the outcome of the 1st International Workshop on Turbulent Spray Combustion held in 2009 in Corsica (France). The focus is on reporting the progress of experimental and numerical techniques in two-phase flows, with emphasis on spray combustion. The motivation for studies in this area is that knowledge of the dominant phenomena and their interactions in such flow systems is essential for the development of predictive models and their use in combustor and gas turbine design. This necessitates the development of accurate experimental methods and numerical modelling techniques. The workshop aimed at providing an opportunity for experts and young researchers to present the state-of-the-art, discuss new developments or techniques and exchange ideas in the areas of experimentations, modelling and simulation of reactive multiphase flows. The first two papers reflect the contents of the invited lectures, given by experts in the field of turbulent spray combustion. The first concerns computational issues, while the second deals with experiments. These lectures initiated very interesting and interactive discussions among the researchers, further pursued in contributed poster presentations. Contributions 3 and 4 focus on some aspects of the impact of the interaction between fuel evaporation and combustion on spray combustion in the context of gas turbines, while the final article deals with the interaction between evaporation and turbulence.

The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability analysis, nonlinear reduced-order modelling, model-based control design as well as model-free and neural network approaches. The wake stabilization serves as unifying benchmark control problem.

The International Conference on Computational Fluid Dynamics is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid flow. The proceedings of the 2010 conference (ICCFD6) held in St Petersburg, Russia, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid dynamics.

This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.

This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.

This volume contains a collection of papers from the research program Protective Artificial Respiration (PAR) . In 2005 the German Research Association DFG launched the research program PAR which is a joint initiative of medicine and fluid mechanics. The main long-term objective of this program is the development of a more protective artificial respiratory system to reduce the physical stress of patients undergoing artificial respiration. To satisfy this goal 11 projects have been defined. In each of these projects scientists from medicine and fluid mechanics do collaborate in several experimental and numerical investigations to improve the fundamental knowledge on respiration and to develop a more individual artificial breathing concept. "

Physically correct boundary conditions on vapor-liquid interfaces are essential in order to make an analysis of flows of a liquid including bubbles or of a gas including droplets. Suitable boundary conditions do not exist at the present time. This book is concerned with the kinetic boundary condition for both the plane and curved vapor-liquid interfaces, and the fluid dynamics boundary condition for Navier-Stokes(fluid dynamics) equations. The kinetic boundary condition is formulated on the basis of molecular dynamics simulations and the fluid dynamics boundary condition is derived by a perturbation analysis of Gaussian-BGK Boltzmann equation applicable to polyatomic gases. The fluid dynamics boundary condition is applied to actual flow problems of bubbles in a liquid and droplets in a gas.

The term transport phenomena is used to describe processes in which mass, momentum, energy and entropy move about in matter. Advances in Transport Phenomena provide state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic, macroscopic or megascopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications. The annual review series intends to fill the information gap between regularly published journals and university-level textbooks by providing in-depth review articles over a broader scope than in journals. The authoritative articles, contributed by internationally-leading scientists and practitioners, establish the state of the art, disseminate the latest research discoveries, serve as a central source of reference for fundamentals and applications of transport phenomena, and provide potential textbooks to senior undergraduate and graduate students. This review book provides state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic, macroscopic or megascopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications. This new volume of the annual review "Advances in Transport Phenomena" series provides in-depth review articles covering the fields of mass transfer, fluid mechanics, heat transfer and thermodynamics. This review book provides state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic, macroscopic or megascopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications. This new volume of the annual review "Advances in Transport Phenomena" series provides in-depth review articles covering the fields of mass transfer, fluid mechanics, heat transfer and thermodynamics.

The near-field region within an order of 100 nm from the solid interface is an exciting and crucial arena where many important multiscale transport phenomena are physically characterized, such as flow mixing and drag, heat and mass transfer, near-wall behavior of nanoparticles, binding of bio-molecules, crystallization, surface deposition processes, just naming a few. This monograph presents a number of label-free experimental techniques developed and tested for near-field fluid flow characterization. Namely, these include Total Internal Reflection Microscopy (TIRM), Optical Serial Sectioning Microscopy (OSSM), Surface Plasmon Resonance Microscopy (SPRM), Interference Reflection Contrast Microscopy (IRCM), Thermal Near-Field Anemometry, Scanning Thermal Microscopy (STM), and Micro-Cantilever Near-Field Thermometry. Presentation on each of these is laid out for the working principle, how to implement the system, and its example applications, to promote the readers understanding and knowledge of the specific technique that can be applied for their own research interests.

Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as "frozen" turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.

1. Objective and Scope Bubbles, drops and rigid particles occur everywhere in life, from valuable industrial operations like gas-liquid contracting, fluidized beds and extraction to such vital natural processes as fermentation, evaporation, and sedimentation. As we become increasingly aware of their fundamental role in industrial and biological systems, we are driven to know more about these fascinating particles. It is no surprise, therefore, that their practical and theoretical implications have aroused great interest among the scientific community and have inspired a growing number of studies and publications. Over the past ten years advances in the field of small Reynolds numbers flows and their technological and biological applications have given rise to several definitive monographs and textbooks in the area. In addition, the past three decades have witnessed enormous progress in describing quantitatively the behaviour of these particles. However, to the best of our knowledge, there are still no available books that reflect such achievements in the areas of bubble and drop deformation, hydrodynamic interactions of deformable fluid particles at low and moderate Reynolds numbers and hydrodynamic interactions of particles in oscillatory flows. Indeed, only one more book is dedicated entirely to the behaviour of bubbles, drops and rigid particles ["Bubbles, Drops and Particles" by Clift et al. (1978)] and the authors state its limitations clearly in the preface: "We treat only phenomena in which particle-particle interactions are of negligible importance. Hence, direct application of the book is limited to single-particle systems of dilute suspensions.

TUrbulence modeling encounters mixed evaluation concerning its impor tance. In engineering flow, the Reynolds number is often very high, and the direct numerical simulation (DNS) based on the resolution of all spatial scales in a flow is beyond the capability of a computer available at present and in the foreseeable near future. The spatial scale of energetic parts of a turbulent flow is much larger than the energy dissipative counterpart, and they have large influence on the transport processes of momentum, heat, matters, etc. The primary subject of turbulence modeling is the proper es timate of these transport processes on the basis of a bold approximation to the energy-dissipation one. In the engineering community, the turbulence modeling is highly evaluated as a mathematical tool indispensable for the analysis of real-world turbulent flow. In the physics community, attention is paid to the study of small-scale components of turbulent flow linked with the energy-dissipation process, and much less interest is shown in the foregoing transport processes in real-world flow. This research tendency is closely related to the general belief that universal properties of turbulence can be found in small-scale phenomena. Such a study has really contributed much to the construction of statistical theoretical approaches to turbulence. The estrangement between the physics community and the turbulence modeling is further enhanced by the fact that the latter is founded on a weak theoretical basis, compared with the study of small-scale turbulence."

Modelling Fluid Flow presents invited lectures, workshop summaries and a selection of papers from a recent international conference CMFF '03 on fluid technology. The lectures follow the current evolution and the newest challenges of the computational methods and measuring techniques related to fluid flow. The workshop summaries reflect the recent trends, open questions and unsolved problems in the mutually inspiring fields of experimental and computational fluid mechanics. The papers cover a wide range of fluids engineering, including reactive flow, chemical and process engineering, environmental fluid dynamics, turbulence modelling, numerical methods, and fluid machinery.

This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.

Turbulent combustion sits at the interface of two important nonlinear, multiscale phenomena: chemistry and turbulence. Its study is extremely timely in view of the need to develop new combustion technologies in order to address challenges associated with climate change, energy source uncertainty, and air pollution. Despite the fact that modeling of turbulent combustion is a subject that has been researched for a number of years, its complexity implies that key issues are still eluding, and a theoretical description that is accurate enough to make turbulent combustion models rigorous and quantitative for industrial use is still lacking. In this book, prominent experts review most of the available approaches in modeling turbulent combustion, with particular focus on the exploding increase in computational resources that has allowed the simulation of increasingly detailed phenomena. The relevant algorithms are presented, the theoretical methods are explained, and various application examples are given. The book is intended for a relatively broad audience, including seasoned researchers and graduate students in engineering, applied mathematics and computational science, engine designers and computational fluid dynamics (CFD) practitioners, scientists at funding agencies, and anyone wishing to understand the state-of-the-art and the future directions of this scientifically challenging and practically important field.

The nuclear thermal hydraulic is the science providing knowledge about the physical processes occurring during the transferring the fission heat released in structural materials due to nuclear reactions into its environment. Along its way to the environment the thermal energy is organized to provide useful mechanical work or useful heat or both. Chapter 1 contains introductory information about the heat release in the re- tor core, the thermal power and thermal power density in the fuel, structures and moderator, the influence of the thermal power density on the coolant temperature, the spatial distribution of the thermal power density. Finally some measures are introduced for equalizing of the spatial distribution of the thermal power density. Chapter 2 gives the methods for describing of the steady and of the transient temperature fields in the fuel elements. Some information is provided regarding influence of the cladding oxidation, hydrogen diffusion and of the corrosion pr- uct deposition on the temperature fields. Didactically the nuclear thermal hydraulic needs introductions at different level of complexity by introducing step by step the new features after the previous are clearly presented. The followed two Chapters serve this purpose. Chapter 3 describes mathematically the "simple" steady boiling flow in a pipe. The steady mass-, momentum- and energy conservation equations are solved at different level of complexity by removing one after the other simplifying assu- tions. First the idea of mechanical and thermodynamic equilibrium is introduced.

This volume constitutes the Proceedings of the IUTAM Symposium on "Analytical and Computational Fracture Mechanics of Non-homogeneous Materials," held in Cardiff from 18th to 22nd June 2001. The Symposium was convened to address and place on record topical issues in analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Given the extensive range and scale of non-homogeneous materials, it had to be focussed to enhance the quality and impact of the Symposium. The range of non-homogeneous materials was limited to those that are inhomogeneous at the macroscopic level and/or exhibit strain softening. The issues of micro to macro scaling were not excluded even within this restricted range which covered materials such as rock, concrete, ceramics and composites on the one hand, and, on the other, those metallic materials whose ductile fracture is strongly influenced by the presence of inhomogeneities. The Symposium remained focussed on fundamental research issues of practical significance. These issues have many common features among seemingly disparate non-homogeneous materials.

Incompressible Fluid Dynamics is a textbook for graduate and advanced undergraduate students of engineering, applied mathematics, and geophysics. The text comprises topics that establish the broad conceptual framework of the subject, expose key phenomena, and play an important role in the myriad of applications that exist in both nature and technology. The first half of the book covers topics that include the inviscid equations of Euler and Bernoulli, the Navier-Stokes equation and some of its simpler exact solutions, laminar boundary layers and jets, potential flow theory with its various applications to aerodynamics, the theory of surface gravity waves, and flows with negligible inertia, such as suspensions, lubrication layers, and swimming micro-organisms. The second half is more specialised. Vortex dynamics, which is so essential to many natural phenomena in fluid mechanics, is developed in detail. This is followed by chapters on stratified fluids and flows subject to a strong background rotation, both topics being central to our understanding of atmospheric and oceanic flows. Fluid instabilities and the transition to turbulence are also covered, followed by two chapters on fully developed turbulence. The text is largely self-contained, and aims to combine mathematical precision with a breadth of engineering and geophysical applications. Throughout, physical insight is given priority over mathematical detail.

This is the second edition of the book "Thermodynamics of Fluids under Flow," which was published in 2000 and has now been corrected, expanded and updated. This is a companion book to our other title Extended irreversible thermodynamics (D. Jou, J. Casas-Vazquez and G. Lebon, Springer, 4th edition 2010), and of the textbook Understanding non-equilibrium thermodynamics (G. Lebon, D. Jou and J. Casas-Vazquez, Springer, 2008. The present book is more specialized than its counterpart, as it focuses its attention on the non-equilibrium thermodynamics of flowing fluids, incorporating non-trivial thermodynamic contributions of the flow, going beyond local equilibrium theories, i.e., including the effects of internal variables and of external forcing due to the flow. Whereas the book's first edition was much more focused on polymer solutions, with brief glimpses into ideal and real gases, the present edition covers a much wider variety of systems, such as: diluted and concentrated polymer solutions, polymer blends, laminar and turbulent superfluids, phonon hydrodynamics and heat transport in nanosystems, nuclear collisions, far-from-equilibrium ideal gases, and molecular solutions. It also deals with a variety of situations, emphasizing the non-equilibrium flow contribution: temperature and entropy in flowing ideal gases, shear-induced effects on phase transitions in real gases and on polymer solutions, stress-induced migration and its application to flow chromatography, Taylor dispersion, anomalous diffusion in flowing systems, the influence of the flow on chemical reactions, and polymer degradation. The new edition is not only broader in scope, but more educational in character, and with more emphasis on applications, in keeping with our times. It provides many examples of how a deeper theoretical understanding may bring new and more efficient applications, forging links between theoretical progress and practical aims. This updated version expands on the trusted content of its predecessor, making it more interesting and useful for a larger audience."

The present set of lectures and tutorial reviews deals with various topical aspects related to instabilities of interfacial processes and driven flows from both the theoretical and experimental point of views. New research has been spurred by demands for many applications in material sciences (melting, solidification, electro deposition), biomedical engineering and processing in microgravity environments. This book is intended as both a modern source of reference for researchers in the field as well as an introduction to postgraduate students and non-specialists from related areas.

The 24 papers presented at the international concluding colloquium of the German priority programme (DFG-Verbundschwerpunktprogramm) "Transition," held in April 2002 in Stuttgart.

The unique and successful programme ran six years, starting April 1996, and was sponsored mainly by the Deutsche Forschungsgemeinschaft, DFG, but also by the Deutsches Zentrum f r Luft-und Raumfahrt, DLR, the Physikalisch-Technische Bundesanstalt Braunschweig, PTB, and Airbus Deutschland. The papers summarise the results of the programme and cover transition mechanisms, transition prediction, transition control, natural transition and measurement techniques, transition - turbulence - separation, and visualisation issues. Three invited papers are devoted to mechanisms of turbulence production, to a general framework of stability, receptivity and control, and a forcing model for receptivity analysis. Almost every transition topic arising in subsonic and transonic flow is covered.

TheCarg'eseSummerSchool"Sound-?owinteractions"washeldinthe- stitutd'EtudesScienti?quesdeCarg'eseinCorsica,Francefrom19thJune to1stJuly,2000. Theunderstandingofsoundand?owinteractionshasmadesomerema- ableprogresssincethepioneeringworksoftheRussianandBritishschools, inthe1950s. Inaddition,thegrowingavailabilityduringthepast10years ofsophisticatedcomputer/electronics/materialstechniquesallowsforthe- velopmentofagrowingnumberofapplicationsaswellasthepossibilityof addressingnewfundamentalproblems. Thecouplingbetweenacousticwaves and?owmotionisbasicallynonlinear,sothatthesoundpropagationand generationismodi?edbythe?owandthe?owcanalsobemodi?edbythe sound. Asaresult,thisproblemisinvestigatedinmanydi?erentscienti?c communities,suchasappliedmathematics,acousticsand?uidmechanics, amongothers. Inouropinion,thetimehadcometotrytogatherthe- searchersinthedi?erentcommunitiestogetherinatutorialenvironemnt. So, thisschoolbroughttogetherworldwidespecialistsinordertopresentvarious aspectsofsound-?owinteractions,andshareexpertiseandmethodologiesso astopromotecross-fertilisation. ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram. Hepresentstheaeroacousticsofinternal?owinaverylivelyway withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand applicationslikemusicalinstruments,theRijketube,speechproductionetc. M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From Lighthill'sacousticanalogy,heshowshowvorticityandentropy?uctuations canbeseenassourcesofsound. Then,usingthecompactGreen'sfunctions, heshowshowtocomputethevortexsound. Asanexampleofthemethod presented,heappliesthistheorytopressuretransientsgeneratedbyhi- speedtrains. F. Lundgivesthebasicequationsofsound-?owinteractions. Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity andgivesthemostrecentresultsonultrasoundpropagationthroughadis- dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand theimportantpracticalproblemofsoundpropagationinturbulence(at- sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows. P. J. Mor- sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear ?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam- toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N. Peakepresents?uid-structureinteractionsinthepresenceofmean?ows, includingtheproblemsofinstabilityandcausality. Finally,W. Lauterborn presentsnonlinearacousticswithapplicationstosonoluminescenceandto acousticchaos. InthisCarg'eseSummerSchool,54studentsfrom12nations,and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: *?nancialsupportfromtheEuropeanUnion,theCentreNationaldela RechercheScienti?que,theMinist'eredesA?airesEtrang'eres,theM- ist'eredel'EducationNationale,delaRechercheetdelaTechnologieand theGroupementdeRecherche"Turbulence"; *the guidance of Elisabeth Dubois-Violette, director of the Institut d'EtudesScienti?quesdeCarg'ese; *thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally,wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur'egan , 2 September2001 Agn'esMaurel , 1 VincentPagneux , 3 Jean-Fran,coisPinton . 1 Laboratoired'Acoustiquedel'Universit'eduMaine,UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9,France 2 LaboratoireOndesetAcoustique,UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris,France 3 LaboratoiredePhysique,UMRCNRS1325, EcoleNormaleSup'erieuredeLyon,46all'eed'Italie,69007Lyon,France Preface VII SomeofthelecturersoftheCarg'eseSchool,fromlefttoright:M. S. Howe,A. Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCarg'eseSchool(PhotoC. Schram) TableofContents APrimitiveApproachtoAeroacoustics AvrahamHirschberg,ChristopheSchram...1 1 Introduction ...1 2 FluidDynamics ...2 3 Lighthill'sAnalogy...4 4 JetNoise ...7 5 Thermo-Acoustics ...9 6 AcousticalEnergy ...10 7 Rijke-Tube...11 8 Vortex-SoundTheory ...14 9 ChoiceoftheGreen'sFunction...17 10 Howe'?owinteractions,andshareexpertiseandmethodologiesso astopromotecross-fertilisation. ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram. Hepresentstheaeroacousticsofinternal?owinaverylivelyway withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand applicationslikemusicalinstruments,theRijketube,speechproductionetc. M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From Lighthill'sacousticanalogy,heshowshowvorticityandentropy?uctuations canbeseenassourcesofsound. Then,usingthecompactGreen'sfunctions, heshowshowtocomputethevortexsound. Asanexampleofthemethod presented,heappliesthistheorytopressuretransientsgeneratedbyhi- speedtrains. F. Lundgivesthebasicequationsofsound-?owinteractions. Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity andgivesthemostrecentresultsonultrasoundpropagationthroughadis- dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand theimportantpracticalproblemofsoundpropagationinturbulence(at- sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows. P. J. Mor- sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear ?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam- toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N. Peakepresents?uid-structureinteractionsinthepresenceofmean?ows, includingtheproblemsofinstabilityandcausality. Finally,W. Lauterborn presentsnonlinearacousticswithapplicationstosonoluminescenceandto acousticchaos. InthisCarg'eseSummerSchool,54studentsfrom12nations,and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: *?nancialsupportfromtheEuropeanUnion,theCentreNationaldela RechercheScienti?que,theMinist'eredesA?airesEtrang'eres,theM- ist'eredel'EducationNationale,delaRechercheetdelaTechnologieand theGroupementdeRecherche"Turbulence"; *the guidance of Elisabeth Dubois-Violette, director of the Institut d'EtudesScienti?quesdeCarg'ese; *thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally,wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur'egan , 2 September2001 Agn'esMaurel , 1 VincentPagneux , 3 Jean-FranccoisPinton . 1 Laboratoired'Acoustiquedel'Universit'eduMaine,UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9,France 2 LaboratoireOndesetAcoustique,UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris,France 3 LaboratoiredePhysique,UMRCNRS1325, EcoleNormaleSup'erieuredeLyon,46all'eed'Italie,69007Lyon,France Preface VII SomeofthelecturersoftheCarg'eseSchool,fromlefttoright:M. S. Howe,A. Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCarg'eseSchool(PhotoC. Schram) TableofContents APrimitiveApproachtoAeroacoustics AvrahamHirschberg,ChristopheSchram...1 1 Introduction ...1 2 FluidDynamics ...2 3 Lighthill'sAnalogy...4 4 JetNoise ...7 5 Thermo-Acoustics ...9 6 AcousticalEnergy ...10 7 Rijke-Tube...11 8 Vortex-SoundTheory ...14 9 ChoiceoftheGreen'sFunction...17 10 Howe'sEnergyCorollary ...20 11 TheOpenPipeTerminationofanUn?angedPipe ...21 12 Whistler-NozzleandHumanWhistling ...25 13 Conclusion...27 References...28 LecturesontheTheoryofVortex-Sound MichaelS. Howe...31 1 AerodynamicSound...31 1. 1 Lighthill'sAcousticAnalogy(1952)...31 1. 2 AerodynamicSoundfromLow-Mach-NumberTurbulence ofUniformMeanDensity...34 1. 3 AerodynamicSoundfromLow-Mach-NumberTurbulence ofVariableMeanDensity...35 2 VorticityandEntropyFluctuations asSourcesofSound...37 2. 1 TheRoleofVorticityinLighthill'sTheory...37 2. 2 AcousticAnalogyinTermsoftheTotalEnthalpy...39 2. 3 VorticityandEntropySources...40 3 FundamentalSolutionsoftheWaveEquation...43 3. 1 TheHelmholtzEquation...43 3. 2 TheWaveEquation...46 4 GeneralSolutionoftheInhomogeneousWaveEquation...47 4. 1 GeneralSolutionintheFrequency-Domain...47 X TableofContents 4. 2 GeneralSolutionintheTime-Domain...49 5 CompactGreen'sFunctions...

The utilization of mathematical models to numerically describe the performance of internal combustion engines is of great significance in the development of new and improved engines. Today, such simulation models can already be viewed as standard tools, and their importance is likely to increase further as available com puter power is expected to increase and the predictive quality of the models is constantly enhanced. This book describes and discusses the most widely used mathematical models for in-cylinder spray and combustion processes, which are the most important subprocesses affecting engine fuel consumption and pollutant emissions. The relevant thermodynamic, fluid dynamic and chemical principles are summarized, and then the application of these principles to the in-cylinder processes is ex plained. Different modeling approaches for the each subprocesses are compared and discussed with respect to the governing model assumptions and simplifica tions. Conclusions are drawn as to which model approach is appropriate for a specific type of problem in the development process of an engine. Hence, this book may serve both as a graduate level textbook for combustion engineering stu dents and as a reference for professionals employed in the field of combustion en gine modeling. The research necessary for this book was carried out during my employment as a postdoctoral scientist at the Institute of Technical Combustion (ITV) at the Uni versity of Hannover, Germany and at the Engine Research Center (ERC) at the University of Wisconsin-Madison, USA."

Combustion of Two-Phase Reactive Media addresses the complex phenomena involved in the burning of solid and liquid fuels. In fact, the multiplicity of phenomena characteristic of combustion of two-phase media determine the contents. The three parts deal with: the dynamics of a single particle; combustion wave propagation in two-phase reactive media; and thermal regimes of combustion reactors. The book generalizes the results of numerous investigations into the ignition and combustion of solid particles, droplets and bubbles, combustion wave propagation in heterogeneous reactive media, the stability of combustion of two-phase media, as well as the thermal regimes of high-temperature combustion reactors. It merges findings from the authors investigations into problems of two-phase flows and material from graduate-level courses they teach at Technion-Israel Institute of Technology.

This volume contains the proceedings of the 2001 DLES4 workshop. It describes and discusses state-of-the-art modeling and simulation approaches for complex flows. Fundamental turbulence and modeling issues but also elements from modern numerical analysis are at the heart of this field of interest.