This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis", which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4 and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided.

Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.

This book introduces two of the most exciting heat pumping technologies, the coabsorbent and the thermal recovery (mechanical vapor) compression, characterized by a high potential in primary energy savings and environmental protection. New cycles with potential applications of nontruncated, truncated, hybrid truncated, and multi-effect coabsorbent types are introduced in this work. Thermal-to-work recovery compression (TWRC) is the first of two particular methods explored here, including how superheat is converted into work, which diminishes the compressor work input. In the second method, thermal-to-thermal recovery compression (TTRC), the superheat is converted into useful cooling and/or heating, and added to the cycle output effect via the coabsorbent technology. These and other methods of discharge gas superheat recovery are analyzed for single-, two-, three-, and multi-stage compression cooling and heating, ammonia and ammonia-water cycles, and the effectiveness results are given. The author presents absorption-related topics, including the divided-device method for mass and heat transfer analysis, and truncation as a unique method for a better source-task match. Along with advanced gax recovery, the first and second principles of COP and exergy calculation, the ideal point approaching (i.p.a.) effect and the two-point theory of mass and heat transfer, the book also addresses the new wording of the Laplace equation, the Marangoni effect true explanation, and the new mass and heat exchangers based on this effect. The work goes on to explore coabsorbent separate and combined cooling, heating, and power (CHP) production and advanced water-lithium bromide cycle air-conditioning, as well as analyzing high-efficiency ammonia-water heat-driven heating and industrial low-temperature cooling, in detail. Readers will learn how coabsorbent technology is based on classic absorption, but is more general. It is capable of offering effective solutions for all cooling and heating applications (industry, agriculture, district, household, etc.), provided that two supplying heat-sink sources with temperatures outdistanced by a minimum of 12-15C are available. This book has clear and concise presentation and illustrates the theory and applications with diagrams, tables, and flowcharts.

This short primer offers non-specialist readers a concise, yet comprehensive introduction to the field of classical fluids - providing both fundamental information and a number of selected topics to bridge the gap between the basics and ongoing research. In particular, hard-sphere systems represent a favorite playground in statistical mechanics, both in and out of equilibrium, as they represent the simplest models of many-body systems of interacting particles, and at higher temperature and densities they have proven to be very useful as reference systems for real fluids. Moreover, their usefulness in the realm of soft condensed matter has become increasingly recognized - for instance, the effective interaction among (sterically stabilized) colloidal particles can be tuned to almost perfectly match the hard-sphere model. These lecture notes present a brief, self-contained overview of equilibrium statistical mechanics of classical fluids, with special applications to both the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere potential or closely related model potentials. In particular it addresses the exact statistical-mechanical properties of one-dimensional systems, the issue of thermodynamic (in)consistency among different routes in the context of several approximate theories, and the construction of analytical or semi-analytical approximations for the structural properties. Written pedagogically at the graduate level, with many figures, tables, photographs, and guided end-of-chapter exercises, this introductory text benefits students and newcomers to the field alike.

Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. .In its fourth extended edition the successful monograph package "Multiphase Flow Daynmics" contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections. "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended," BERND PLATZER, ZAAM In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections. "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended," BERND PLATZER, ZAAM "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended," BERND PLATZER, ZAAM

The present Volume 4 of the successful monograh package "Multiphase Flow Dynamics"is devoted to selected Chapters of the multiphase fluid dynamics that are important for practical applications but did not find place in the previous volumes. The state of the art of the turbulence modeling in multiphase flows is presented. As introduction, some basics of the single phase boundary layer theory including some important scales and flow oscillation characteristics in pipes and rod bundles are presented. Then the scales characterizing the dispersed flow systems are presented. The description of the turbulence is provided at different level of complexity: simple algebraic models for eddy viscosity, simple algebraic models based on the Boussinesq hypothesis, modification of the boundary layer share due to modification of the bulk turbulence, modification of the boundary layer share due to nucleate boiling. The role of the following forces on the mathematical description of turbulent flows is discussed: the lift force, the lubrication force in the wall boundary layer, and the dispersion force. A pragmatic generalization of the k-eps models for continuous velocity field is proposed containing flows in large volumes and flows in porous structures. A Methods of how to derive source and sinks terms for multiphase k-eps models is presented. A set of 13 single- and two phase benchmarks for verification of k-eps models in system computer codes are provided and reproduced with the IVA computer code as an example of the application of the theory. This methodology is intended to help other engineers and scientists to introduce this technology step-by-step in their own engineering practice. In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described. A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided. This new second edition includes various updates, extensions, improvements and corrections. In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described. A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided. This new second edition includes various updates, extensions, improvements and corrections.

The book contains invited lectures and selected contributions presented at the Enzo Levi and XVII Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2011. It is aimed to fourth year undergraduate and graduate students, and scientists in the field of physics, engineering and chemistry that have interest in Fluid Dynamics from the experimental and theoretical point of view. The invited lectures are introductory and avoid the use of complicate mathematics. The other selected contributions are also adequate to fourth year undergraduate and graduate students. The Fluid Dynamics applications include multiphase flow, convection, diffusion, heat transfer, rheology, granular material, viscous flow, porous media flow, geophysics and astrophysics. The material contained in the book includes recent advances in experimental and theoretical fluid dynamics and is adequate for both teaching and research.

The book provides personal memories along with description of scientific works written by ex-graduate students and research associates of the late Professor Glass. The described research work covers a wide range of shock wave phenomena, resulting from seeds planted by Professor Glass. Professor Glass was born in Poland in 1918. He immigrated together with his parents to Canada at the age of 12 and received all his professional education at the University of Toronto, Canada. He became a world recognized expert in shock wave phenomena, and during his 45 years of active research he supervised more than 125 master and doctoral students, post-doctoral fellows and visiting research associates. In this book seven of his past students/research-associates describe their personal memories of Professor Glass and present some of their investigations in shock wave phenomena which sprung from their past work with Professor Glass. Specifically, these investigations include underwater shock waves, shock/bubble interaction, medical applications of shock wave, various types of shock tubes and shock tube techniques, shock wave attenuation and different types of shock wave reflections.

Based on new information obtained on free microjets, this book explains the latest phenomena in flame evolution in the presence of a transverse acoustic field with round and plane propane microjet combustion. It gives an overview of recent experimental results on instability and dynamics of jets at low Reynolds numbers and provides the reader, step by step, with the milestones and recent advances in jet flow stability and combustion. Readers will also discover a clarification of the differences between top-hat and parabolic round and plane jet instability. Chapters demonstrate features of the interaction between jet and crossflow, and how experimental data testify to similarities of the perturbed flow patterns of laminar and turbulent round jets. A similar response of the jets to external acoustic oscillations is shown, as well as the peculiarities of the effect of a transverse acoustic field on downstream evolution of round and plane macro- and microjets. Basic features of round and plane, macro and micro jets' evolution affected by initial conditions at the nozzle outlet and by environmental perturbations are highlighted. Students of fluid mechanics will gain a solid foundation in hydrodynamic stability and combustion of subsonic jet flow and researchers will value the presentation of special aspects of instability and transition. The work treats both theoretical and practical facets, and it includes supplementary material such as PowerPoint multimedia notes based on results of laboratory scientific experiments.

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.

Non-Newtonian properties on bubble dynamics and cavitation are fundamentally different from those of Newtonian fluids. The most significant effect arises from the dramatic increase in viscosity of polymer solutions in an extensional flow, such as that generated about a spherical bubble during its growth or collapse phase. In addition, many biological fluids, such as blood, synovial fluid, and saliva, have non-Newtonian properties and can display significant viscoelastic behaviour. This monograph elucidates general aspects of bubble dynamics and cavitation in non-Newtonian fluids and applies them to the fields of biomedicine and bioengineering. In addition it presents many examples from the process industries. The field is strongly interdisciplinary and the numerous disciplines involve have and will continue to overlook and reinvent each others' work. This book helps researchers to think intuitively about the diverse physics of these systems, to attempt to bridge the various communities involved, and to convey the interest, elegance, and variety of physical phenomena that manifest themselves on the micrometer and microsecond scales.

This volume comprises the communications presented at the ETC 11, the EUROMECH European Turbulence conference held in 2007 in Porto.

The scientific committee has chosen the contributions out of the following topics: Acoustics of turbulent flows; Atmospheric turbulence; Control of turbulent flows; Geophysical and astrophysical turbulence; Instability and transition; Intermittency and scaling; Large eddy simulation and related techniques; MHD turbulence; Reacting and compressible turbulence; Transport and mixing; Turbulence in multiphase and non-Newtonian flows; Vortex dynamics and structure formation; Wall bounded flows.

Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs. The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interest, time marching procedures are dealt with by briefly introducing and providing a simple, direct, and efficient method. Many examples are provided in the text as well as numerous exercises for each chapter. Several of the examples are attended by subtle points which the reader will face while working them out. Some of these points are deliberated upon in endnotes to the various chapters, others are touched upon in the book itself.

The HEDLA-08 conference was a continuation of a series of biennial conferences first held in Pleasanton, California, in 1996, and focused on progress made during recent years in designing, conducting, and analyzing the results of laboratory experiments, theoretical work, and computer simulations relevant to high-energy density (HED) astrophysics. The astrophysics aspects of HED experiments are extremely diverse and include jets, the mechanism of their generation and interaction with the ambient medium; stellar evolution with a focus on turbulence, hydrodynamic instabilities, and mixing of nuclear species; radiative supersonic flows associated with stellar explosions and jets; radiative processes in plasma; equation of state and material properties; and last but not least magnetized and relativistic plasmas. This volume contains a small but representative subset of 35 peer-reviewed papers presented at the HEDLA-08 meeting.

The second, enlarged edition of this established reference integrates many new insights into wastewater hydraulics. This work serves as a reference for researchers but also is a basis for practicing engineers. It can be used as a text book for graduate students, although it has the characteristics of a reference book. It addresses mainly the sewer hydraulician but also general hydraulic engineers who have to tackle many a problem in daily life, and who will not always find an appropriate solution. Each chapter is introduced with a summary to outline the contents. To illustrate application of the theory, examples are presented to explain the computational procedures. Further, to relate present knowledge to the history of hydraulics, some key dates on noteworthy hydraulicians are quoted. A historical note on the development of wastewater hydraulics is also added. References are given at the end of each chapter, and they are often helpful starting points for further reading. Each notation is defined when introduced, and listed alphabetically at the end of each chapter. This new edition includes in particular sideweirs with throttling pipes, drop shafts with an account on the two-phase flow features, as well as conduit choking due to direct or undular hydraulic jumps.

A survey of asymptotic methods in fluid mechanics and applications is given including high Reynolds number flows (interacting boundary layers, marginal separation, turbulence asymptotics) and low Reynolds number flows as an example of hybrid methods, waves as an example of exponential asymptotics and multiple scales methods in meteorology.

These proceedings of a well-established conference on numerical methods, calculations, and modelling in fluid dynamics concentrates on five topics: multidimensional upwinding, turbulent flows, domain decomposition methods, unstructured grids, and flow visualization, and it includes papers presented at a workshop on all-vertex schemes. All papers have been carefully refereed.

These proceedings are devoted to the most recent research in computational fluid mechanics and include a thorough analysis of the state of the art in parallel computing and the development of algorithms. The applications cover hypersonic and environmental flows, transitions in turbulence, and propulsion systems. Seven invited lectures survey the results of the recent past and point out interesting new directions of research. The contributions have been carefully selected for publication.

The author considers meteorology as a part of fluid dynamics. He tries to derive the properties of atmospheric flows from a rational analysis of the Navier-Stokes equations, at the same time analyzing various types of initial and boundary problems. This approach to simulate nature by models from fluid dynamics will be of interest to both scientists and students of physics and theoretical meteorology.

Showing marine ecologists, oceanographers and marine engineers how ocean waters interact with, influence and constrain life in the ocean, this package makes the physical processes intelligible to biologists with a modicum of mathematics. Part I of the book examines classical fluid mechanics such as laminar and turbulent flow, boundary layers, and forces induced by flow. Part II deals with large-scale flows, such as waves, large ocean currents, and tides, which are beyond the scope of classic fluid mechanics. In Part III, the link between hydrodynamics of ocean flows and marine ecology is demonstrated by examples of well-established phenomena and processes. The CD-ROM contains 12 ready-to-use computer programs on the calculation, representation and simulation of various processes.

The articles in this volume treat various problems in combustion science that are of importance in applications to technology and to environmental sciences. The authors treat turbulence in premixed and non-premixed flames as well as pressure interactions and wave phenomena. Also supersonic flows and detonations are discussed. The main emphasis, however, is on the modelling and numerical treatment of combustion phenomena. The book addresses researchers in physics and engineering, and mathematicians from scientific computing.

Using combinations of in situ and ex situ experimental methods, fundamental and relevant phenomena such as adsorption and desorption of ions and molecules, restructuring of surfaces, thin film and nanocluster growth, and electrochemical reactions on the micrometer scale are addressed. The overview includes a wide range of experimental techniques and examples of solid-liquid interfaces and aims at stimulating an expansion of this important type of interface science.

This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, from June 1-5, 2010. The subject matter ranged widely from observational data to theoretical mechanics, and reflected the broad scope of the workshop. In both the prepared presentations and in the informal discussions, the workshop engaged exchanges across disciplines and invited a lively interaction between modelers and observers. The articles in this volume were invited and fully refereed. They provide a representative if necessarily incomplete account of the field of natural locomotion during a period of rapid growth and expansion. The papers presented at the workshop, and the contributions to the present volume, can be roughly divided into those pertaining to swimming on the scale of marine organisms, swimming of microorganisms at low Reynolds numbers, animal flight, and sliding and other related examples of locomotion.

Large-scale winds and currents tend to balance Coriolis and pressure gradient forces. The time evolution of these winds and currents is the subject of the quasi-geostrophic theory. Chapter 1 presents concepts and equations of classical inertial fluid mechanics. Chapter 2 deals with the equations of thermodynamics that close the governing equations of the fluids. Then, the motion is reformulated in a uniformly rotating reference frame. Chapter 3 deals with the shallow-water model and the homogeneous model of wind-driven circulation. The chapter also describes a classical application of the Ekman layer to the atmosphere. Chapter 4 considers the two-layer model, as an introduction to baroclinic flows, together with the concept of available potential energy. Chapter 5 takes into account continuously stratified flows in the ocean and in the atmosphere.