The numerical optimization of practical applications has been an issue of major importance for the last 10 years. It allows us to explore reliable non-trivial configurations, differing widely from all known solutions. The purpose of this book is to introduce the state-of-the-art concerning this issue and many complementary applications are presented.

This book covers the whole range of today 's technology for pneumatic drives. It details drives for factory automation and automotive applications as well as describes the technology for the process industry like positioners or spring-and-diaphragm. In addition, the book examines several control strategies like binary mode cylinder drives or position controlled drives and computer aided analysis of complex systems.

This book develops a modern presentation of Continuum Mechanics, oriented towards numerical applications in the ?elds of nonlinear analysis of solids, structures and ?uids. Kinematics of the continuum deformation, including pull-back/push-forward transformations between di erent con?gurations; stress and strain measures; objective stress rate and strain rate measures; balance principles; constitutive relations, with emphasis on elasto-plasticity of metals and variational prin- ples are developed using general curvilinear coordinates. Being tensor analysis the indispensable tool for the development of the continuum theory in general coordinates, in the appendix an overview of t- soranalysisisalsopresented. Embedded in the theoretical presentation, application examples are dev- oped to deepen the understanding of the discussed concepts. Even though the mathematical presentation of the di erent topics is quite rigorous; an e ort is made to link formal developments with engineering ph- ical intuition. This book is based on two graduate courses that the authors teach at the Engineering School of the University of Buenos Aires and it is intended for graduate engineering students majoring in mechanics and for researchers in the ?elds of applied mechanics and numerical methods. VIII Preface I am grateful to Klaus-Jurgen Bathe for introducing me to Computational Mechanics, for his enthusiasm, for his encouragement to undertake challenges and for his friendship."

In order to allow the application of the theory from all the three volumes also to processes in combustion engines a systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature are provided also in Volume 3. Erlangen, October 2006 Nikolay Ivanov Kolev Table of contents 1 Some basics of the single-phase boundary layer theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Flow over plates, velocity profiles, share forces, heat transfer. . . . . . . . . . . . . . . . . . . . 1 1. 1. 1 Laminar flow over the one site of a plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1. 2 Turbulent flow parallel to plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2 Steady state flow in pipes with circular cross sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 Hydraulic smooth wall surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 2. 2 Transition region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2. 3 Complete rough region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2. 4 Heat transfer to fluid in a pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 3 Transient flow in pipes with circular cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Introduction to turbulence of multi-phase flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 1 Basic ideas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 2 Isotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2. 3 Scales, eddy viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2. 3. 1 Small scale turbulent motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2. 3. 2 Large scale turbulent motion, Kolmogorov-Pandtl expression. . . . . . . . . 42 2. 4 k-eps framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3 Sources for fine resolution outside the boundary layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1 Bulk sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1. 1 Deformation of the velocity field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1. 2 Blowing and suction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In sport disciplines such as running, ice skating, bicycling and cross-country skiing the aerodynamic drag force constitutes the major obstacle to overcome. Furthermore, in ski jumping and in various activities involving a ball the aerodynamic lift force comes in addition into action.

This book describes the various sport disciplines on the basis of aerodynamic analysis and also cover the biomechanics part by illustrative performance examples. Such treatment of the underlying physical phenomena of sport activities gives a valuable supplement to existing literature on sport. The reader will also be guided to references which exist for the various topics discussed, so she or he can go into a deeper study of the particular sport activity at wish.

C Specific heat at constant pressure p D Displacement field D Diffusion coefficient d D Orifice diameter E Electric field E Electron charge F Force G Acceleration due to gravity I Current J Current flux K Conductivity k Boltzmann constant B L Atomizer geometry: length from electrode tip to orifice plane i L Atomizer geometry : length of orifice channel o P Polarization Q Flow rate/Heat flux Q Charge r Atomizer geometry : electrode tip radius p T Time T Temperature U Velocity V Voltage W Energy X Distance Nomenclature (Greek) Thermal expansion coefficient ? Permittivity ? Permutation operator ? ijk Ion mobility ? VI Nomenclature Debye length ? D ? Dynamic viscosity ? Mass density Surface tension ? T Electrical conductivity ? ? Timescale ? Vorticity Nomenclature (Subscripts) Reference state ? o Cartesian tensor notation ? ijk Volume density (? per unit volume) ? v Surface density (? per unit area) ? s Linear density (? per unit length) ? l 'critical' state ? c Bulk mean injection ? inj Nomenclature (Superscripts) Time or ensemble averaged ? Contents Contents 1 Introduction................................................................... 1 1.1 Introduction and Scope.................................................. 1 1.2 Organization.............................................................. 3 2 Electrostatics, Electrohydrodynamic Flow, Coupling and Instability.................................................................. 5 2.1 Electrostatics.............................................................. 5 2.1.1 The Coulomb Force............................................. 5 2.1.2 Permittivity...................................................... 6 2.1.3 Conductors, Insulators, Dielectrics and Polarization........ 6 2.1.4 Gauss's Law...................................................... 8 2.2 Mobility and Charge Transport........................................ 10 2.2.1 Introduction...................................................... 10

This book brings together the quick integral approaches and advances in the field for the prediction of stall and surge problems in the compressor. The book is useful for people involved in the flow analysis, design and testing of rotating machinery. For students, it can be used as a specialized topic of senior undergraduate or graduate study. The book can also serve as self-study material.

"Systems of Commercial Turbofan Engines" gives the reader information about the operation of the engine systems, its components and the terminology used throughout the industry. The engine systems are explained by the use of examples from today's engines. So the readers, from aircraft mechanics to commercial pilot, become familiar with the current technology in this field and attains a deeper knowledge of the systems of commercial turbofan engines.

To understand the operation of gas turbine engines used in aircraft, it is not enough to understand the basic operation of a gas turbine. It is also necessary to understand the operation and the design of its auxiliary systems. This book is an introduction into the systems of modern commercial aircraft gas turbine engines. It is made for the reader who is familiar with the basic operation of aircraft gas turbine engine.

Besides turbulence, there is hardly any other scientific topic which has been considered a prominent scientific challenge for such a long time. The special interest in turbulence is not only based on it being a difficult scientific problem but also on its meaning in the technical world and our daily life. This carefully edited book comprises recent basic research as well as research related to the applications of turbulence. Therefore, both leading engineers and physicists working in the field of turbulence were invited to the iTi Conference on Turbulence held in Bad Zwischenahn, Gemany 21st - 24th of September 2003. Topics discussed include, for example, scaling laws and intermittency, thermal convection, boundary layers at large Reynolds numbers, isotropic turbulence, stochastic processes, passive and active scalars, coherent structures, numerical simulations, and related subjects.

Over the past three decades turbomachines experienced a steep increase in efficiency and performance. Based on fundamental principles of turbomachinery thermo-fluid mechanics, numerous CFD based calculation methods are being developed to simulate the complex 3-dimensional, highly unsteady turbulent flow within turbine or compressor stages. The objective of this book is to present the fundamental principals of turbomachinery fluid-thermodynamic design process of turbine and compressor components, power generation and aircraft gas turbines in a unified and compact manner. The book provides senior undergraduate students, graduate students and engineers in the turbomachinery industry with a solid background of turbomachinery flow physics and performance fundamentals that are essential for understanding turbomachinery performance and flow complexes.

The last two decades have brought two important developments for aeroth- modynamics. One is that airbreathing hypersonic flight became the topic of technology programmes and extended system studies. The other is the emergence and maturing of the discrete numerical methods of aerodyn- ics/aerothermodynamics complementary to the ground-simulation facilities, with the parallel enormous growth of computer power. Airbreathing hypersonic flight vehicles are, in contrast to aeroassisted re-entry vehicles, drag sensitive. They have, further, highly integrated lift and propulsion systems. This means that viscous eflFects, like boundary-layer development, laminar-turbulent transition, to a certain degree also strong interaction phenomena, are much more important for such vehicles than for re-entry vehicles. This holds also for the thermal state of the surface and thermal surface effects, concerning viscous and thermo-chemical phenomena (more important for re-entry vehicles) at and near the wall. The discrete numerical methods of aerodynamics/aerothermodynamics permit now - what was twenty years ago not imaginable - the simulation of high speed flows past real flight vehicle configurations with thermo-chemical and viscous effects, the description of the latter being still handicapped by in sufficient flow-physics models. The benefits of numerical simulation for flight vehicle design are enormous: much improved aerodynamic shape definition and optimization, provision of accurate and reliable aerodynamic data, and highly accurate determination of thermal and mechanical loads. Truly mul- disciplinary design and optimization methods regarding the layout of thermal protection systems, all kinds of aero-servoelasticity problems of the airframe, et cetera, begin now to emerge."

Free Convective Heat Transfer is a thorough survey of various kinds of free-convective flows and heat transfer. Reference data are accompanied by a large number of photographs originating from different optical visualization methods illustrating the different types of flow. The formulas derived from numerical and analytical investigations are valuable tools for engineering calculations. They are written in their most compact and general form in order to allow for an extensive range of different variants of boundary and initial conditions, which, in turn, leads to a wide applicability to different flow types. Some specific engineering problems are solved in the book as exemplary applications of these formulas.

Although the solution of Partial Differential Equations by numerical methods is the standard practice in industries, analytical methods are still important for the critical assessment of results derived from advanced computer simulations and the improvement of the underlying numerical techniques. Literature devoted to analytical methods, however, often focuses on theoretical and mathematical aspects and is therefore useless to most engineers. Analytical Methods for Heat Transfer and Fluid Flow Problems addresses engineers and engineering students. It describes useful analytical methods by applying them to real-world problems rather than solving the usual over-simplified classroom problems. The book demonstrates the applicability of analytical methods even for complex problems and guides the reader to a more intuitive understanding of approaches and solutions.

Flow meters measure the volumetric flow rate in a pipeline. Most meters are based on deriving a signal from the fluid flow and calibrating the signal against the volumetric flow rate. The calibration is done in fully-developed flow, and the same state of flow must exist at the meter's position when it is in practical use. Because the field of flow metering has been neglected by fluid mechanicists for a long time, this book addresses two major fluid mechanical problems in flow metering: the analysis of signal generation in turbulent pipe flow, which explains the function of the meter beyond a simple calibration, and the possible use of a meter in non-developed flows. These problems are investigated with reference to, and examples from, a variety of meters, e.g. ultrasound cross-correlation meters, vortex meters, and turbine meters. Studying these problems requires consideration of specific phenomena in turbulent non-developed pipe flow, as caused by installations, and finding special solutions with signal processing, both of which are included in the book.

The lattice Boltzmann method (LBM) is a modern numerical technique, very efficient, flexible to simulate different flows within complex/varying geome tries. It is evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the LGA. The core equation in the LBM turns out to be a special discrete form of the continuum Boltzmann equation, leading it to be self-explanatory in statistical physics. The method describes the micro scopic picture of particles movement in an extremely simplified way, and on the macroscopic level it gives a correct average description of a fluid. The av eraged particle velocities behave in time and space just as the flow velocities in a physical fluid, showing a direct link between discrete microscopic and continuum macroscopic phenomena. In contrast to the traditional computational fluid dynamics (CFD) based on a direct solution of flow equations, the lattice Boltzmann method provides an indirect way for solution of the flow equations. The method is characterized by simple calculation, parallel process and easy implementation of boundary conditions. It is these features that make the lattice Boltzmann method a very promising computational method in different areas. In recent years, it receives extensive attentions and becomes a very potential research area in computational fluid dynamics. However, most published books are limited to the lattice Boltzmann methods for the Navier-Stokes equations. On the other hand, shallow water flows exist in many practical situations such as tidal flows, waves, open channel flows and dam-break flows."

The importance of vorticity and vortex dynamics has now been well rec- nized at both fundamental and applied levels of ?uid dynamics, as already anticipatedbyTruesdellhalfcenturyagowhenhewrotethe?rstmonograph onthesubject, The Kinematics of Vorticity(1954);andasalsoevidencedby the appearance of several books on this ?eld in 1990s. The present book is characterizedbythefollowingfeatures: 1. A basic physical guide throughout the book. The material is directed by a basic observation on the splitting and coupling of two fundamental processes in ?uid motion, i.e., shearing (unique to ?uid) and compre- ing/expanding.Thevorticityplaysakeyroleintheformer, andavortex isnothingbuta?uidbodywithhighconcentrationofvorticitycompared to its surrounding ?uid. Thus, the vorticity and vortex dynamics is - cordinglyde?nedasthetheoryofshearingprocessanditscouplingwith compressing/expandingprocess. 2. A description of the vortex evolution following its entire life.Thisbegins from the generation of vorticity to the formation of thin vortex layers andtheirrolling-upintovortices, fromthevortex-corestructure, vortex motionandinteraction, totheburstofvortexlayerandvortexintosma- scalecoherentstructureswhichleadstothetransitiontoturbulence, and ?nallytothedissipationofthesmalleststructuresintoheat. 3. Wide range of topics.Inadditiontofundamentaltheoriesrelevanttothe abovesubjects, theirmostimportantapplicationsarealsopresented.This includes vortical structures in transitional and turbulent ?ows, vortical aerodynamics, and vorticity and vortices in geophysical ?ows. The last topic was suggested to be added by Late Sir James Lighthill, who read carefullyanearlydraftoftheplannedtableofcontentsofthebookin1994 andexpressedthathelikes"allthematerial"thatweproposedthere. These basic features of the present book are a continuation and - velopment of the spirit and logical structure of a Chinese monograph by the same authors, Introduction to Vorticity and Vortex Dynamics, Higher VI Preface EducationPress, Beijing,1993, butthematerialhasbeencompletelyrewr- tenandupdated.Thebookmay?tvariousneedsof?uiddynamicsscientists, educators, engineers, aswellasappliedmathematicians.Itsselectedchapters canalsobeusedastextbookforgraduatestudentsandseniorundergraduates. Thereadershouldhaveknowledgeofundergraduate?uidmechanicsand/or aerodynamicscourses.

This book presents the most up-to-date methods of three-dimensional modeling of the fluid dymanics and the solid-fluid interaction within these machines, which are still being developed. Adding modeling to the design process makes it possible not only to predict flow patterns more accurately, and also to determine distorting effects on rotors and casing of pressure and temperature distribution within the compressor. Examples outline the scope of the applied mathematical model.

This book covers the background theory of fluid power and indicates the range of concepts needed for a modern approach to condition monitoring and fault diagnosis. The theory is leavened by 15-years-worth of practical measurements by the author, working with major fluid power companies, and real industrial case studies. Heavily supported with examples drawn from real industrial plants - the methods in this book have been shown to work.

This book addresses the characterization of flow and transport in porous fractured media from experimental and modeling perspectives. It provides a comprehensive presentation of investigations performed and analyzed on different scales.

Althoughtheprinciplesofoperationofhelicalscrewmachines, ascompressors or expanders, have been well known for more than 100 years, it is only during the past 30 years that these machines have become widely used. The main reasons for the long period before they were adopted were their relatively poor e?ciency and the high cost of manufacturing their rotors. Two main developments led to a solution to these di?culties. The ?rst of these was the introduction of the asymmetric rotor pro?le in 1973. This reduced the bl- hole area, which was the main source of internal leakage by approximately 90%, and thereby raised the thermodynamic e?ciency of these machines, to roughly the same level as that of traditional reciprocating compressors. The second was the introduction of precise thread milling machine tools at - proximately the same time. This made it possible to manufacture items of complex shape, such as the rotors, both accurately and cheaply. From then on, as a result of their ever improving e?ciencies, high rel- bility and compact form, screw compressors have taken an increasing share of the compressor market, especially in the ?elds of compressed air production, and refrigeration and air conditioning, and today, a substantial proportion of compressors manufactured for industry are of this type. Despite, the now wide usage of screw compressors and the publication of many scienti?c papers on their development, only a handful of textbooks have been published to date, which give a rigorous exposition of the principles of their operation and none of these are in English

Despite dramatic advances in numerical and experimental methods of fluid mechanics, the fundamentals are still the starting point for solving flow problems. This textbook introduces the major branches of fluid mechanics of incompressible and compressible media, the basic laws governing their flow, and gas dynamics. Fluid Mechanics demonstrates how flows can be classified and how specific engineering problems can be identified, formulated and solved, using the methods of applied mathematics. The material is elaborated in special applications sections by more than 200 exercises and separately listed solutions. The final section comprises the Aerodynamics Laboratory, an introduction to experimental methods treating eleven flow experiments. This class-tested textbook offers a unique combination of introduction to the major fundamentals, many exercises, and a detailed description of experiments.

An extensive critical compilation of the wide range of manufacturing processes that involve the application of spray technology, this book covers design of atomizers as well as the performance of plant and their corresponding spray systems. The needs of practising engineers from different disciplines: project managers, and works, maintenance and design engineers are catered for. Of interest to researchers in the field of liquid sprays, the book includes outlines of the contemporary and possible future research and challenges in the different fields of application and deals with:

sprays and their production;

sprays in industrial production processes;

processes involving vaporisation and cooling or cleaning of gases;

spray-surface impact processes;

fuel sprays for fixed plant;

spraying of hot surfaces for steel making and other metals;

spraying of molten metals.

Guidance is given for the analysis and interpretation of experimental data obtained using different measurement techniques."

This is Volume 4 of the book series of the Body and Soul mathematics education reform program. It presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body and Soul computational finite element methodology in the form of General Galerkin (G2) up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. This is an outstanding textbook presenting plenty of new material with an excellent pedagogical approach.

Here, the authors present modern mathematical methods to solve problems of differential-operator inclusions and evolution variation inequalities which may occur in fields such as geophysics, aerohydrodynamics, or fluid dynamics. For the first time, they describe the detailed generalization of various approaches to the analysis of fundamentally nonlinear models and provide a toolbox of mathematical equations. These new mathematical methods can be applied to a broad spectrum of problems. Examples of these are phase changes, diffusion of electromagnetic, acoustic, vibro-, hydro- and seismoacoustic waves, or quantum mechanical effects. This is the second of two volumes dealing with the subject.

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.