This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier-Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H -calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier-Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier-Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier-Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier-Stokes equations.

This book offers a concise and practical survey of the principles governing compressible flows, along with selected applications. It starts with derivation of the time-dependent, three-dimensional equation of compressible potential flows, and a study of weak waves, including evaluation of the sound speed in gases. The following chapter addresses quasi-one-dimensional flows, the study of normal shock waves, and flow in ducts with constant cross section subjected to friction and/or heat transfer. It also investigates the effects of friction and heat transfer in ducts with variable cross section. The chapter ends by pointing to the analogy between one-dimensional compressible flows and open channel hydraulics. Further, the book discusses supersonic flows, including the study of oblique shock waves, and supersonic flows over corners and wedges. It also examines Riemann problems, numerical resolution of the wave equation, and of nonlinear hyperbolic problems, including propagation of strong waves. A subsequent chapter focuses on the small perturbation theory of subsonic, transonic and supersonic flows around slender bodies aligned or almost aligned to the uniform inflow. In particular, it explores subsonic and supersonic flows over a wavy wall. Lastly, an appendix with a short derivation of the Fluid Mechanics basic equations is included. The final chapter addresses the problem of transonic flows where both subsonic and supersonic are present. Lastly, an appendix with a short derivation of the Fluid Mechanics basic equations is included. Illustrated with several practical examples, this book is a valuable tool to understand the most fundamental mathematical principles of compressible flows. Graduate Mathematics, Physics and Engineering students as well as researchers with an interest in the aerospace sciences benefit from this work.

This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux. To accomplish this, some assumptions are necessary: The flux is close to homogeneous, and the initial velocity and the external force do not change too much along the axis of the cylinder. This is achieved by utilizing a sophisticated method of deriving energy type estimates for weak solutions and global estimates for regular solutions-an approach that is wholly unique within the existing literature on the Navier-Stokes equations. To demonstrate these results, three main steps are followed: first, the existence of weak solutions is shown; next, the conditions guaranteeing the regularity of weak solutions are presented; and, lastly, global regular solutions are proven. This volume is ideal for mathematicians whose work involves the Navier-Stokes equations, and, more broadly, researchers studying fluid mechanics.

The simplest way to formulate the basic equations of continuum mech- ics and the constitutive or evolutional equations of various materials is to restrict ourselves to rectangular cartesian coordinates. However, solving p- ticular problems, for instance in Chapter 5, it may be preferable to work in terms of more suitable coordinate systems and their associated bases. The- fore, Chapter 2 is also concerned with the standard techniques of tensor an- ysis in general coordinate systems. Creep mechanics is a part of continuum mechanics, like elasticity or pl- ticity. Therefore, some basic equations of continuum mechanics are put - gether in Chapter 3. These equations can apply equally to all materials and they are insuf?cient to describe the mechanical behavior of any particular material. Thus, we need additional equations characterizing the individual material and its reaction under creep condition according to Chapter 4, which is subdivided into three parts: the primary, the secondary, and the tertiary creep behavior of isotropic and anisotropic materials. The creep behavior of a thick-walled tube subjected to internal pressure is discussed in Chapter 5. The tube is partly plastic and partly elastic at time zero. The investigation is based upon the usual assumptions of incompre- ibility and zero axial creep. The creep deformations are considered to be of such magnitude that the use of ?nite-strain theory is necessary. The inner and outer radius, the stress distributions as functions of time, and the cre- failure time are calculated.

This monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer's constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable.

Dieses 1952 erstmals erschienene Standardwerk behandelt auch in seiner siebenten unverAnderten Auflage in vergleichender Weise alle verschiedenen Arten von StrAmungsmaschinen. Dieser Klassiker vereinigt Grundlagenwissen A1/4ber die StrAmungsmaschinen, das auch fA1/4r moderne Auslegungen unentbehrlich ist. Als Klassiker berA1/4cksichtigt das Buch moderne Berechnungs- und Simulationsverfahren nicht, liefert aber sehr wertvolles Grundlagenwissen mit engem Praxisbezug.

Dem Leser wird ein Buch in die Hand gegeben, das Detailwissen vertieft. Dem in der Praxis stehenden Ingenieur bietet das Buch wertvolle Anregungen bei der LAsung von Einzelproblemen und ein zuverlAssiges Repetitorium zur Erweiterung der theoretischen Grundlagen.

This book compiles a variety of experimental data on blast waves. The book begins with an introductory chapter and proceeds to the topic of blast wave phenomenology, with a discussion on Rankine-Hugoniot equations and the Friedlander equation, used to describe the pressure-time history of a blast wave. Additional topics include arrival time measurement, the initiation of detonation by exploding wires, a discussion of TNT equivalency, and small scale experiments. Gaseous and high explosive detonations are covered as well. The topics and experiments covered were chosen based on the comparison of used scale sizes, from small to large. Each characteristic parameter of blast waves is analyzed and expressed versus scaled distance in terms of energy and mass. Finally, the appendix compiles a number of polynomial laws that will prove indispensable for engineers and researchers.

This book reports on the German research initiative AeroStruct, a three-year collaborative project between universities and the aircraft industry. It describes the development of an integrated multidisciplinary simulation environment for aircraft analysis and optimization using high-fidelity methods. This system is able to run at a high level of automatism, thus representing a step forward with respect to previous ones. Its special features are: a CAD description that is independent from the disciplines involved, an automated CFD mesh generation and an automated structure model generation including a sizing process. The book also reports on test cases by both industrial partners and DLR demonstrating the advantages of the new environment and its suitability for the industry. These results were also discussed during the AeroStruct closing Symposium, which took place on 13-14 October 2015 at the DLR in Braunschweig, Germany. The book provides expert readers with a timely report on multidisciplinary aircraft design and optimization. Thanks to a good balance between theory and practice, it is expected to address an audience of both academics and professional, and to offer them new ideas for future research and development.

This book opens with a discussion of the vorticity-dynamic formulation of the low Mach number viscous flow problem. It examines the physical aspects of the velocity and the vorticity fields, their instantaneous relationship, and the transport of vorticity in viscous fluids for steady and unsteady flows. Subsequently, using classical analyses it explores the mathematical aspects of vorticity dynamics and issues of initial and boundary conditions for the viscous flow problem. It also includes the evolution of the vorticity field which surrounds and trails behind airfoils and wings, generalizations of Helmholtz' vortex theorems and the Biot-Savart Law. The book introduces a theorem that relates the aerodynamic force to the vorticity moment and reviews the applications of the theorem. Further, it presents interpretations of the Kutta-Joukowski theorem and Prandtl's lifting line theory for vorticity dynamics and discusses wake integral methods. The virtual-mass effect is shown to be the seminal event in unsteady aerodynamics and a simple approach for evaluating virtual-mass forces on the basis of vorticity dynamics is presented. The book presents a modern viewpoint on vorticity dynamics as the framework for understanding and establishing the fundamental principles of viscous and unsteady aerodynamics. It is intended for graduate-level students of classical aerodynamics and researchers exploring the frontiers of fully unsteady and non-streamlined aerodynamics.

This book offers a practical, application-oriented introduction to computational fluid dynamics (CFD), with a focus on the concepts and principles encountered when using CFD in industry. Presuming no more knowledge than college-level understanding of the core subjects, the book puts together all the necessary topics to give the reader a comprehensive introduction to CFD. It includes discussion of the derivation of equations, grid generation and solution algorithms for compressible, incompressible and hypersonic flows. The final two chapters of the book are intended for the more advanced user. In the penultimate chapter, the special difficulties that arise while solving practical problems are addressed. Distinction is made between complications arising out of geometrical complexity and those arising out of the complexity of the physics (and chemistry) of the problem. The last chapter contains a brief discussion of what can be considered as the Holy Grail of CFD, namely, finding the optimal design of a fluid flow component. A number of problems are given at the end of each chapter to reinforce the concepts and ideas discussed in that chapter. CFD has come of age and is widely used in industry as well as in academia as an analytical tool to investigate a wide range of fluid flow problems. This book is written for two groups: for those students who are encountering CFD for the first time in the form of a taught lecture course, and for those practising engineers and scientists who are already using CFD as an analysis tool in their professions but would like to deepen and broaden their understanding of the subject.

Coanda effect is a complex fluid flow phenomenon enabling the production of vertical take-off/landing aircraft. Other applications range from helicopters to road vehicles, from flow mixing to combustion, from noise reduction to pollution control, from power generation to robot operation, and so forth. Book starts with description of the effect, its history and general formulation of governing equations/simplifications used in different applications. Further, it gives an account of this effect's lift boosting potential on a wing and in non-flying vehicles including industrial applications. Finally, occurrence of the same in human body and associated adverse medical conditions are explained.

These proceedings primarily focus on advances in the theory, experiments, and numerical simulations of turbulence in the contexts of flow-induced vibration and noise, as well as their control. Fluid-related structural vibration and noise problems are often encountered in many engineering fields, increasingly making them a cause for concern. The FSSIC conference, held on 5-9 July 2015 in Perth, featured prominent keynote speakers such as John Kim, Nigel Peake, Song Fu and Colin Hansen, as well as talks on a broad range of topics: turbulence, fluid-structure interaction, fluid-related noise and the control/management aspects of these research areas, many of which are clearly interdisciplinary in nature. It provided a forum for academics, scientists and engineers working in all branches of Fluid-Structure-Sound Interactions and Control (FSSIC) to exchange and share the latest developments, ideas and advances, bringing them together researchers from East and West to push forward the frontiers of FSSIC, ensuring that the proceedings will be of interest to a broad engineering community.

The Euler and Navier-Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier-Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.

This book highlights by careful documentation of developments what led to tracking the growth of deterministic disturbances inside the shear layer from receptivity to fully developed turbulent flow stages. Associated theoretical and numerical developments are addressed from basic level so that an uninitiated reader can also follow the materials which lead to the solution of a long-standing problem. Solving Navier-Stokes equation by direct numerical simulation (DNS) from the first principle has been considered as one of the most challenging problems of understanding what causes transition to turbulence. Therefore, this book is a very useful addition to advanced CFD and advanced fluid mechanics courses.

This thesis studies the effects of superplasticizers, polyacrylate latexes and asphalt emulsions, which differ in molecular/particle size from nanometers to microns, on the rheological properties of fresh cement pastes (FCPs), as well as the action mechanisms involved. It systematically investigates the rheological properties and microstructure of cement-based materials, and elucidates the adsorption behaviors of polycarboxylate polymers with different functional groups and their effects on cement hydration. Moreover, it reveals how the working mechanism of naphthalene sulfonate formaldehyde (NSF) differs from that of polycarboxylate ether-based (PCE) superplasticizers. Lastly, it develops a conceptual microstructure model and two rheological equations. These findings lend theoretical support to the development of new chemical admixtures and new, higher-performance, cement-based composites.

This book describes the development of a new analytical, full-vehicle model with nine degrees of freedom, which uses the new modified skyhook strategy (SKDT) to control the full-vehicle vibration problem. The book addresses the incorporation of road bank angle to create a zero steady-state torque requirement when designing the direct tilt control and the dynamic model of the full car model. It also highlights the potential of the SKDT suspension system to improve cornering performance and paves the way for future work on the vehicle's integrated chassis control system. Active tilting technology to improve vehicle cornering is the focus of numerous ongoing research projects, but these don't consider the effect of road bank angle in the control system design or in the dynamic model of the tilting standard passenger vehicles. The non-incorporation of road bank angle creates a non-zero steady state torque requirement.

This edited monograph contains the proceedings of the International Shock Interaction Symposium, which emerged as an heir to both the Mach Reflection and Shock Vortex Interaction Symposia. These scientific biannual meetings provide an ideal platform to expose new developments and discuss recent challenges in the field of shock wave interaction phenomena. The goal of the symposia is to offer a forum for international interaction between young and established scientists in the field of shock and blast wave interaction phenomena. The target audience of this book comprises primarily researchers and experts in the field of shock waves, but the book may also be beneficial for young scientists and graduate students alike.

This new edition includes brand-new developments in the modeling of processes in the column apparatuses. It analyzes the radial velocity component and axial variation in the axial velocity in the column. These models are described in five new chapters. The book presents models of chemical and interphase mass transfer processes in industrial column apparatuses, using convection-diffusion and average-concentration models. It also introduces average concentration models for quantitative analysis, which use the average values of the velocity and concentration over the cross-sectional area of the column. The new models are used to analyze a broad range of processes (simple and complex chemical reactions, physical and chemical absorption, physical and chemical adsorption, catalytic reactions in the cases of physical and chemical adsorption mechanism), and make it possible to model sulfur dioxide gas purification processes.

This thesis analyzes aerodynamic forces in viscous and compressible external flows. It is unique, as the force theories discussed apply to fully viscous and compressible Navier-Stokes external flows, allowing them to be readily combined with computational fluid dynamics to form a profound basis of modern aerodynamics. This thesis makes three fundamental contributions to theoretical aerodynamics, presenting: (1) a universal far-field zonal structure that determines how disturbance flow quantities decay dynamically to the state of rest at infinity; (2) a universal and exact total-force formula for steady flow and its far-field asymptotics; and (3) a general near-field theory for the detailed diagnosis of all physical constituents of aerodynamic force and moment.

This book commemorates the 70th birthday of Eugene Morozov, the noted Russian observational oceanographer. It contains many contributions reflecting his fields of interest, including but not limited to tidal internal waves, ocean circulation, deep ocean currents, and Arctic oceanography. Special attention is paid to studies on internal waves and especially those on tidal internal waves in the Global Ocean. These papers describe the most important open problems concerning experimental studies of internal waves and their theoretical, numerical, and laboratory modeling. Further contributions investigate the physics of surface waves and their interaction with internal waves. Here, the focus is on describing interaction processes between internal waves and deep currents in the ocean, especially currents of Antarctic Bottom Water in abyssal fractures. They also touch on the problem of oceanic circulation and related processes in fjords, including those occurring under sea ice. Given its breadth of coverage, the book will appeal to anyone interested in a survey of ocean dynamics, ranging from historic perspectives to modern research topics.

The book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated: analysis of classical visco-plastic fluid models mathematical modeling of flows of visco-plastic fluids computing flows of visco-plastic fluids rheology of visco-plastic fluids and visco-plastic suspensions application of visco-plastic fluids in engineering sciences complex flows of visco-plastic fluids.

The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most importantly, provide solutions to the numerous extended exercises.

This book is a monograph on aerodynamics of aero-engine gas turbines focusing on the new progresses on flow mechanism and design methods in the recent 20 years. Starting with basic principles in aerodynamics and thermodynamics, this book systematically expounds the recent research on mechanisms of flows in axial gas turbines, including high pressure and low pressure turbines, inter-turbine ducts and turbine rear frame ducts, and introduces the classical and innovative numerical evaluation methods in different dimensions. This book also summarizes the latest research achievements in the field of gas turbine aerodynamic design and flow control, and the multidisciplinary conjugate problems involved with gas turbines. This book should be helpful for scientific and technical staffs, college teachers, graduate students, and senior college students, who are involved in research and design of gas turbines.

Encompassing both practical applications and recent research developments, this book takes the reader from fundamental physics, through cutting-edge new designs of ejectors for refrigeration. The authors' unique vision marries successful design, system optimization, and operation experience with insights on the application of cutting-edge Computational Fluid Dynamics (CFD) models. This robust treatment leads the way forward in developing improved ejector technologies. The book covers ejectors used for heat powered refrigeration and for expansion work recovery in compression refrigerators, with special emphasis on two-phase flows of "natural" fluids within the ejector, i.e. steam and carbon dioxide. It features worked examples, detailed research results, and analysis tools.

Opening with recent advances in both the theoretical and physical models for wave-seabed-structure interactions, this book provides an updated look at the mathematics behind the interactions between sea, soil and man-made structures. The main models are broken down into key equations, and their strengths and challenges are discussed. These models are then placed in context with industry-relevant examples, in both two and three dimensions. From seabed instability around offshore wind turbines, to soil conditions in response to the laying of submarine pipelines, this book takes a comprehensive look at a variety of wave-seabed-structure interactions. With important implications for the future of offshore infrastructure, this is an ideal resource for industry workers, undergraduate students, and researchers.