Fluid Dynamics

Asymptotic Problems of Fluid Dynamics

Author: Anatoly I. Ruban

Publisher: Oxford University Press, USA

ISBN: 0199681740

Category: Fluid mechanics

Page: 320

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This is the second volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. In Part 2 the reader is introduced to asymptotic methods, and their applications to fluid dynamics. Firstly, it discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The authors then consider supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. They also discuss the second order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are examined in detail. Part 2 concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered, the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stokes paradox. The authors show that this paradox can be resolved using the formalism of matched asymptotic expansions.
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Fluid Dynamics

Part 3 Boundary Layers

Author: Anatoly I. Ruban

Publisher: Oxford University Press

ISBN: 0191503983

Category: Science

Page: 382

View: 2384

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This is the third volume in a four-part series on Fluid Dynamics: PART 1: Classical Fluid Dynamics PART 2: Asymptotic Problems of Fluid Dynamics PART 3: Boundary Layers PART 4: Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. The notion of the boundary layer was introduced by Prandtl (1904) to describe thin viscous layers that form on a rigid body surface in high-Reynolds-number flows. Part 3 of this series begins with the classical theory of the boundary-layer flows, including the Blasius boundary layer on a flat plate and the Falkner-Skan solutions for the boundary layer on a wedge surface. However, the main focus is on recent results of the theory that have not been presented in texbooks before. These are based on the so-called "triple-deck theory" that have proved to be invaluable in describing various fluid-dynamic phenomena, including the boundary-layer separation from a rigid body surface.
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Fluid Dynamics

Part 1: Classical Fluid Dynamics

Author: Anatoly I. Ruban,Jitesh S. B. Gajjar

Publisher: OUP Oxford

ISBN: 0191503967

Category: Science

Page: 336

View: 5497

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This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. The present Part 1 consists of four chapters. Chapter 1 begins with a discussion of Continuum Hypothesis, which is followed by an introduction to macroscopic functions, the velocity vector, pressure, density, and enthalpy. We then analyse the forces acting inside a fluid, and deduce the Navier-Stokes equations for incompressible and compressible fluids in Cartesian and curvilinear coordinates. In Chapter 2 we study the properties of a number of flows that are presented by the so-called exact solutions of the Navier-Stokes equations, including the Couette flow between two parallel plates, Hagen-Poiseuille flow through a pipe, and Karman flow above an infinite rotating disk. Chapter 3 is devoted to the inviscid incompressible flow theory, with particular focus on two-dimensional potential flows. These can be described in terms of the "complex potential", allowing the full power of the theory of functions of complex variables to be used. We discuss in detail the method of conformal mapping, which is then used to study various flows of interest, including the flows past Joukovskii aerofoils. The final Chapter 4 is concerned with compressible flows of perfect gas, including supersonic flows. Particular attention is given to the theory of characteristics, which is used, for example, to analyse the Prandtl-Meyer flow over a body surface bend and a corner. Significant attention is also devoted to the shock waves. The chapter concludes with analysis of unsteady flows, including the theory of blast waves.
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Mathematical Fluid Dynamics, Present and Future

Tokyo, Japan, November 2014

Author: Yoshihiro Shibata,Yukihito Suzuki

Publisher: Springer

ISBN: 4431564578

Category: Mathematics

Page: 613

View: 9947

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This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.
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Elements of Fluid Dynamics

Author: Guido Buresti

Publisher: World Scientific Publishing Company

ISBN: 1908977043

Category: Technology & Engineering

Page: 604

View: 5546

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Elements of Fluid Dynamics is intended to be a basic textbook, useful for undergraduate and graduate students in different fields of engineering, as well as in physics and applied mathematics. The main objective of the book is to provide an introduction to fluid dynamics in a simultaneously rigorous and accessible way, and its approach follows the idea that both the generation mechanisms and the main features of the fluid dynamic loads can be satisfactorily understood only after the equations of fluid motion and all their physical and mathematical implications have been thoroughly assimilated. Therefore, the complete equations of motion of a compressible viscous fluid are first derived and their physical and mathematical aspects are thoroughly discussed. Subsequently, the necessity of simplified treatments is highlighted, and a detailed analysis is made of the assumptions and range of applicability of the incompressible flow model, which is then adopted for most of the rest of the book. Furthermore, the role of the generation and dynamics of vorticity on the development of different flows is emphasized, as well as its influence on the characteristics, magnitude and predictability of the fluid dynamic loads acting on moving bodies. The book is divided into two parts which differ in target and method of utilization. The first part contains the fundamentals of fluid dynamics that are essential for any student new to the subject. This part of the book is organized in a strictly sequential way, i.e. each chapter is assumed to be carefully read and studied before the next one is tackled, and its aim is to lead the reader in understanding the origin of the fluid dynamic forces on different types of bodies. The second part of the book is devoted to selected topics that may be of more specific interest to different students. In particular, some theoretical aspects of incompressible flows are first analysed and classical applications of fluid dynamics such as the aerodynamics of airfoils, wings and bluff bodies are then described. The one-dimensional treatment of compressible flows is finally considered, together with its application to the study of the motion in ducts. Sample Chapter(s) Chapter 1: Introduction (133 KB) Request Inspection Copy
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An Introduction to Theoretical Fluid Mechanics

Author: Stephen Childress

Publisher: American Mathematical Soc.

ISBN: 0821848887

Category: Science

Page: 201

View: 9177

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This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.
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Kinetic Theory and Fluid Dynamics

Author: Yoshio Sone

Publisher: Springer Science & Business Media

ISBN: 9780817642846

Category: Science

Page: 353

View: 6596

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This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit.
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Vortex Dynamics

Author: P. G. Saffman

Publisher: Cambridge University Press

ISBN: 9780521420587

Category: Mathematics

Page: 311

View: 7757

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Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.
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Topics in Fluid Mechanics

Author: René Chevray,Jean Mathieu

Publisher: Cambridge University Press

ISBN: 9780521422727

Category: Science

Page: 320

View: 1332

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This book offers a novel but unified treatment of an established subject. Rather than describe the standard topics in fluid mechanics in traditional form, the book presents each topic as part of a wider class of problems so that a unity of concepts is emphasized over a unity of material.
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