Fluid Dynamics

Part 2: Asymptotic Problems of Fluid Dynamics

Author: Anatoly I. Ruban

Publisher: OUP Oxford

ISBN: 0191503975

Category: Science

Page: 320

View: 368

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

Asymptotic Problems of Fluid Dynamics

Author: Anatoly I. Ruban

Publisher: Oxford University Press, USA

ISBN: 0199681740

Category: Fluid mechanics

Page: 320

View: 7992

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 1: Classical Fluid Dynamics

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

Publisher: OUP Oxford

ISBN: 0191503967

Category: Science

Page: 336

View: 8315

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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Asymptotic Modelling of Fluid Flow Phenomena

Author: Radyadour Kh. Zeytounian

Publisher: Springer Science & Business Media

ISBN: 140200432X

Category: Science

Page: 550

View: 7851

for the fluctuations around the means but rather fluctuations, and appearing in the following incompressible system of equations: on any wall; at initial time, and are assumed known. This contribution arose from discussion with J. P. Guiraud on attempts to push forward our last co-signed paper (1986) and the main idea is to put a stochastic structure on fluctuations and to identify the large eddies with a part of the probability space. The Reynolds stresses are derived from a kind of Monte-Carlo process on equations for fluctuations. Those are themselves modelled against a technique, using the Guiraud and Zeytounian (1986). The scheme consists in a set of like equations, considered as random, because they mimic the large eddy fluctuations. The Reynolds stresses are got from stochastic averaging over a family of their solutions. Asymptotics underlies the scheme, but in a rather loose hidden way. We explain this in relation with homogenizati- localization processes (described within the §3. 4 ofChapter 3). Ofcourse the mathematical well posedness of the scheme is not known and the numerics would be formidable! Whether this attempt will inspire researchers in the field of highly complex turbulent flows is not foreseeable and we have hope that the idea will prove useful.
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Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances

Author: Herbert Steinrück

Publisher: Springer Science & Business Media

ISBN: 3709104084

Category: Technology & Engineering

Page: 420

View: 7228

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.
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Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Author: Hans G. Kaper,Marc Garbey

Publisher: CRC Press

ISBN: 1482277069

Category: Mathematics

Page: 286

View: 1691

Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
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The High Temperature Aspects of Hypersonic Flow

Proceedings of the AGARD–NATO Specialists' Meeting Sponsored by the Fluid Dynamics Panel of Agard Held at the Technical Centre for Experimental Aerodynamics, Rhode-Saint-Genèse, Belgium, 3–6 April 1962

Author: Wilbur C. Nelson

Publisher: Elsevier

ISBN: 1483223310

Category: Science

Page: 800

View: 682

The High Temperature Aspects of Hypersonic Flow is a record of the proceedings of the AGARD-NATO Specialists' Meeting, held at the Technical Centre for Experimental Aerodynamics, Rhode-Saint-Genese, Belgium in April 1962. The book contains the papers presented during the meeting that tackled a broad range of topics in the aspects of hypersonic flow. The subjects covered during the meeting include pressure measurements, interference effects, the use of wind tunnels in aircraft development testing, high temperature gas characteristics, boundary layer research, stability and control and the use of rocket vehicles in flight research. Aerospace engineers and aeronautical engineers will find the book invaluable.
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Analytical Fluid Dynamics, Second Edition

Author: George Emanuel

Publisher: CRC Press

ISBN: 1420036599

Category: Technology & Engineering

Page: 808

View: 5539

The second edition of Analytical Fluid Dynamics presents an expanded and updated treatment of inviscid and laminar viscous compressible flows from a theoretical viewpoint. It emphasizes basic assumptions, the physical aspects of flow, and the appropriate formulations of the governing equations for subsequent analytical treatment. Topics covered include Basic concepts A novel approach to linking complicated thermodynamics to the equations of motion Shockwave dynamics Calorically imperfect gas flows Supersonic sweep Shock-expansion interference Unsteady, one-dimensional flows First- and second-order boundary-layer theory Particularly noteworthy is a new, general treatment of forces and moments. The one-dimension flow chapter also discusses internal ballistics and the Riemann function method for solving hyperbolic equations. These two chapters, along with those dealing with thermodynamics, sweep, interference, imperfect gas glows, and several of the appendices are new to this edition. Analytical Fluid Dynamics: Second Edition answers the continued need for fluid dynamic books that combine physical insight with careful development of the corresponding mathematics. With his focus on the development of analytical skills for dealing with inviscid and viscous flow, the author achieves this goal and provides a text valuable as a research reference or a graduate-level text.
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Asymptotic Theory of Supersonic Viscous Gas Flows

Author: Vladimir Neyland

Publisher: Butterworth-Heinemann

ISBN: 0080555772

Category: Science

Page: 560

View: 4004

This is the first book in English devoted to the latest developments in fluid mechanics and aerodynamics. Written by the leading authors in the field, based at the renowned Central Aerohydrodynamic Institute in Moscow, it deals with viscous gas flow problems that arise from supersonic flows. These complex problems are central to the work of researchers and engineers dealing with new aircraft and turbomachinery development (jet engines, compressors and other turbine equipment). The book presents the latest asymptotical models, simplified Navier-Stokes equations and viscous-inviscid interaction theroies and will be of critical interest to researchers, engineers, academics and advanced graduate students in the areas of fluid mechanics, compressible flows, aerodynamics and aircraft design, applied mathematics and computational fluid dynamics. The first book in English to cover the latest methodology for incopressible flow analysis of high speed aerodynamics, an essential topic for those working on new generation aircraft and turbomachinery Authors are internationally recognised as the leading figures in the field Includes a chapter introducing asymptotical methods to enable advanced level students to use the book
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Advances in Mechanics and Mathematics

Author: David Yang Gao,Ray W. Ogden

Publisher: Springer Science & Business Media

ISBN: 9781402008177

Category: Science

Page: 302

View: 8766

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.
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Laminar Flow and Convective Transport Processes

Scaling Principles and Asymptotic Analysis

Author: Howard Brenner

Publisher: Elsevier

ISBN: 1483292223

Category: Science

Page: 760

View: 5864

Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered. A unique feature of this book is its emphasis on scaling principles and the use of asymptotic methods, both as a means of solution and as a basis for qualitative understanding of the correlations that exist between independent and dependent dimensionless parameters in transport processes. Laminar Flow and Convective Transport Processes is suitable for use as a textbook for graduate courses in fluid mechanics and transport phenomena and also as a reference for researchers in the field.
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Scaling Phenomena in Fluid Mechanics

Author: G. I. Barenblatt

Publisher: CUP Archive

ISBN: 9780521469203

Category: Mathematics

Page: 50

View: 1419

This book presents the text of the inaugural lecture of Professor G. I. Barenblatt which deals with a study of scaling phenomena in several topics studied by G. I. Taylor throughout his varied career.
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Selected Topics of Computational and Experimental Fluid Mechanics

Author: Jaime Klapp,Gerardo Ruíz Chavarría,Abraham Medina Ovando,Abel López Villa,Leonardo Di G. Sigalotti

Publisher: Springer

ISBN: 3319114875

Category: Science

Page: 548

View: 631

This book contains invited lectures and selected contributions presented at the Enzo Levi and XIX Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2013. It is aimed at fourth year undergraduate and graduate students, and scientists in the fields of physics, engineering and chemistry who are interested in fluid dynamics from an experimental and theoretical point of view. The invited lectures are introductory and avoid the use of complicated mathematics. 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 suitable for both teaching and research.
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Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

Author: Hamid Bellout,Frederick Bloom

Publisher: Springer Science & Business Media

ISBN: 3319008919

Category: Science

Page: 569

View: 9165

The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
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Free Boundary Problems in Fluid Flow with Applications

Author: J M Chadam,Helen Rasmussen

Publisher: CRC Press

ISBN: 9780582215672

Category: Mathematics

Page: 268

View: 1555

This is the third of three volumes containing the proceedings of the International Colloquium 'Free Boundary problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main part of this volume studies the flow of fluids, an area which has led to many of the classical free boundary problems. The first two sections contain the papers on various problems in fluid mechanics. The types of problems vary fromthe collision of two jets to the growth of a sand wave. In the next two sections porous flow is considered. This has important practical applications in fields such as petroleum engineering and groundwater pollution. Some new and interesting free boundary problems in geology and engineering are treated in the final section.
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Advanced Transport Phenomena

Fluid Mechanics and Convective Transport Processes

Author: L. Gary Leal

Publisher: Cambridge University Press

ISBN: 9781139462068

Category: Technology & Engineering

Page: N.A

View: 9424

Advanced Transport Phenomena is ideal as a graduate textbook. It contains a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems, focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory. Also covered are unidirectional flows, lubrication and thin-film theory, creeping flows, boundary layer theory, and convective heat and mass transport at high and low Reynolds numbers. The emphasis is on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain solutions that are due either to geometric simplifications, or large or small values of dimensionless parameters. The author emphasizes setting up problems and extracting as much information as possible short of obtaining detailed solutions of differential equations. The book also focuses on the solutions of representative problems. This reflects the book's goal of teaching readers to think about the solution of transport problems.
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