Fluid Dynamics

Part 2: Asymptotic Problems of Fluid Dynamics

Author: Anatoly I. Ruban

Publisher: OUP Oxford

ISBN: 0191503975

Category: Science

Page: 320

View: 2078

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

Classical Fluid Dynamics

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

Publisher: Oxford University Press, USA

ISBN: 0199681732

Category: Science

Page: 317

View: 571

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 isfollowed 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 forincompressible 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. We discussin 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 compressibleflows 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.
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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: 4508

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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Meteorological Fluid Dynamics

Asymptotic Modelling, Stability and Chaotic Atmospheric Motion

Author: Radyadour K. Zeytounian

Publisher: Springer Science & Business Media

ISBN: 3540383867

Category: Science

Page: 348

View: 1011

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.
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Applications of Pad‚ Approximation Theory in Fluid Dynamics

Author: Amilcare Pozzi

Publisher: World Scientific

ISBN: 9810214146

Category: Science

Page: 236

View: 9445

Although Pad‚ presented his fundamental paper at the end of the last century, the studies on Pad‚'s approximants only became significant in the second part of this century.Pad‚ procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Pad‚ approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Pad‚ approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Pad‚ approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Pad‚ approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Pad‚ approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Pad‚ approximants to unsteady flows.
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Navier-Stokes-Fourier Equations

A Rational Asymptotic Modelling Point of View

Author: Radyadour Kh. Zeytounian

Publisher: Springer Science & Business Media

ISBN: 3642207464

Category: Technology & Engineering

Page: 276

View: 9784

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.
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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: 4921

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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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: 9759

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: 5149

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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Handbook of Mathematical Fluid Dynamics

Author: S. Friedlander,D. Serre

Publisher: Elsevier

ISBN: 9780080478302

Category: Science

Page: 724

View: 3370

This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.
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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: 8552

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: 8354

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: 8486

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: 3707

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: 2031

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: 8268

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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