Solution of Transonic Flows by an Integro-differential Equation Method PDF Download

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 34

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Author: Pradip Niyogi
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 212

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Author: Carl Kaplan
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 42

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Book Description
The simplified nonlinear differential equation for transonic flow past a wavy wall is solved by the method of integration in series. The solution has been carried to the point where the question of the existence or nonexistence of a mixed potential flow can be answered by the behavior of a single power series in the transonic similarity parameter. The calculation of the coefficient of this dominant power series has been reduced to a routine computing problem by means of recursion formumlas resulting from the solution of the differential equation and the boundary condition at the surface of the wavy wall.

Author: Heinrich J. Ramm
Publisher: Oxford University Press
ISBN: 0195362950
Category : Science
Languages : en
Pages : 211

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This new book leads readers step-by-step through the complexities encountered as moving objects approach and cross the sound barrier. The problems of transonic flight were apparent with the very first experimental flights of scale-model rockets when the disastrous impact of shock waves and flow separations caused the aircraft to spin wildly out of control. Today many of these problems have been overcome, and this book offers an introduction to the transonic theory that has made possible many of these advances. The emphasis is on the most important basic approaches to the solution of transonic problems. The book also includes explanations of common pitfalls that must be avoided. An effort has been made to derive the most important equations of inviscid and viscous transonic flow in sufficient detail so that even novices may feel confident in their problem-solving ability. The use of computer approaches is reviewed, with references to the extensive literature in this area, while the critical shortcomings of an exclusive reliance on computational methods are also described. The book will be valuable to anyone who needs to acquire an understanding of transonic flow, including practicing engineers as well as students of fluid mechanics.

Author: P. Niyogi
Publisher: Springer
ISBN: 9783662195734
Category : Science
Languages : en
Pages : 193

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Author: Lazãr Dragos
Publisher: Springer Science & Business Media
ISBN: 9781402016639
Category : Mathematics
Languages : en
Pages : 626

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The book provides a solid and unitary mathematical foundation of the basic and advanced principles of aerodynamics. The densities of the fundamental solutions are determined from singular integral equations. The fundamental solutions method in aerodynamics was considered for the first time and used by the author in over 30 papers published in prestigious journals (e.g. QAM, AIAA, ZAMM, etc) in order to develop a unitary theory. The boundary element method is used for numerical approximations in compressible aerodynamics. The text incorporates several original contributions, among other traditional mathematical methods. The book also represents a comprehensive presentation of research results since the seminal books on aerodynamics of Ashley and Landahl (1965) and Katz & Plotkin (1991). A rigorous mathematical approach is used to present and explain classic and modern results in this field of science. The author has therefore conceived several appendices on the Distribution Theory, the singular Integral Equations Theory, the Finite Part, Gauss Quadrature Formulae, etc. The book is concluded by a relevant bibliographical list which is especially useful for researchers. The book is aimed primarily at applied mathematicians, aeronautical engineers and space science researchers. The text may be used also as a comprehensive introduction to the mathematical foundations fo aerodynamics, by graduate students n engineering and fluid dynamics with a strong mathematical background.

Author: John Anthony Gear
Publisher:
ISBN: 9780642111173
Category : Aerodynamics, Transonic
Languages : en
Pages : 10

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The unsteady transonic small perturbation differential equation is converted into an integrodifferential equation by application of the classical Green's function method. It is shown that no contribution form sock waves explicitly appears in this integral equation, due to the shock capturing properties of the Green's function method. After assuming that the motion consists of small infinitesimal perturbations around a thin nearly-planar body, a simplified integral equation for the streamwise velocity component is obtained, which is suitable for fast numerical computations. Keywords: Unsteady flow; Transonic flow; Three-dimensional flow. (Australia).

Author: Oscar Biblarz
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 0

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Book Description
The small disturbance equation of transonic flow is solved by a separation of variables technique. The resulting ordinary, nonlinear differential equations are studied in the phase plane where the general solution represents the behavior of the perturbation velocities. In the phase plane, the character of transonic flow is evident. An asymptotic explicit solution is given which encompasses the sonic flow solution. Numerical integration results for the implicit equations are presented and two flows are examined which are intrinsic to the form of the solution.

Author: Alexander G Kuz'min
Publisher: John Wiley & Sons
ISBN: 047085295X
Category : Technology & Engineering
Languages : en
Pages : 316

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Book Description
Transonic flow occurs around moving objects as they approach and cross the sound barrier. Serious problems can occur at this point, such as shock-induced flow separation which can cause the aircraft to spin out of control. Another important practical problem is the achievement of higher aerodynamic performance of aircraft at cruise conditions, which leads to considerable fuel savings. The success in application of numerical methods for simulation of transonic flow and aircraft design depends on developments in the underlying mathematical theory. This book presents a breakthrough in the solvability analysis of boundary value problems, which makes it possible to establish convergence of finite element approximations for shock-free flow and to provide a framework for putting the existing numerical methods on a more sound basis. Also, physical aspects concerned with patterns of formation and propagation of weak shock waves are analysed. This contributes to the understanding of the extreme sensitivity of transonic flow to perturbation of freestream conditions. The developed theoretical knowledge base yields promising concepts of the airfoil design and active flow control by airfoil/wing shape modifications or suction/blowing through a perforated surface. Boundary Value Problems for Transonic Flow * Focuses on Computational Fluid Dynamics. * Addresses practical problems, such as airfoil design and flow control. * Presents developments made in the last two decades. In essence this is a much needed monograph for researchers and engineers in applied mathematics and numerical analysis applied to aerodynamics and for algorithm developers in Computational Fluid Dynamics in the aircraft industry. It gives design engineers the underlying mathematical theory necessary for developing new concepts for airfoil/wing design and flow control.

Author: Grigorios Dimitriadis
Publisher: John Wiley & Sons
ISBN: 1119762553
Category : Technology & Engineering
Languages : en
Pages : 581

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Book Description
Unsteady Aerodynamics A comprehensive overview of unsteady aerodynamics and its applications The study of unsteady aerodynamics goes back a century and has only become more significant as aircraft become increasingly sophisticated, fly faster, and their structures are lighter and more flexible. Progress in the understanding of flow physics, computing power and techniques, and modelling technologies has led to corresponding progress in unsteady aerodynamics, with a wide range of methods currently used to predict the performance of engineering structures under unsteady conditions. Unsteady Aerodynamics offers a comprehensive and systematic overview of the application of potential and vortex methods to the subject. Beginning with an introduction to the fundamentals of unsteady flow, it then discusses the modelling of attached and separated, incompressible and compressible flows around two-dimensional and three-dimensional bodies. The result is an essential resource for design and simulation in aerospace engineering. Unsteady Aerodynamics readers will also find: MATLAB examples and exercises throughout, with codes and solutions on an accompanying website Detailed discussion of most classes of unsteady phenomena, including flapping flight, transonic flow, dynamic stall, flow around bluff bodies and more Validation of theoretical and numerical predictions using comparisons to experimental data from the literature Unsteady Aerodynamics is ideal for researchers, engineers, and advanced students in aerospace engineering.