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This volume is dedicated to modeling in fluid mechanics and is
divided into four chapters, which contain a significant number of
useful exercises with solutions. The authors provide relatively
complete references on relevant topics in the bibliography at the
end of each chapter.
The book is devoted to calculation methods of a
converging-diverging nozzle used in propulsion and the high
velocity flow. The algorithms and programs given in the book are
intended to help engineers and students to design and calculate the
nozzle parameters to provide optimal parameters for compressible
supersonic flows. The present monograph is a tutorial (handbook) to
calculate and determine the optimal parameters for
converging-diverging nozzles provided supersonic flow. The main
program consists from three main parts: programs for calculation
the profile of the Contraction zone, EOD code for the flow in the
Contraction zone, the program Rott-Crabtree for calculation the
pressure gradient Pohlhausen parameter, the program for the
aerodynamic design of axisymmetric and two-dimensional nozzles for
supersonic and hypersonic wind tunnels, programs for solving
laminar, transitional, or turbulent compressible boundary layer
equations for two-dimensional and axisymmetric flow, and the
program to obtain hypersonic boundary layer stability. The book is
designed to be an instrument for students and scientists interested
in study supersonic flow and high-temperature gas dynamics.
Nonlinear phenomena and instabilities arise in all fields of
physics, chemistry, biology, and engineering. The book consists of
six chapters. Chapter 1 contains preliminary topics from analysis:
elements of set theory, measure theory, integration theory,
asymptotic expansions, continued fractions and Pad'e
approximations. Chapters 2 and 3 are devoted to basic and advanced
methods of ODE's and their visualization: attractors, fractals,
bifurcations, chaos, and elements of stability theory. Chapter 4
studies analytical and geometrical aspects of perturbation theory
and contains many examples. Chapter 5 represents the basic
knowledge in turbulence theory and introduces to
Richardson-Kolmogorov concept, deals with bifurcations in
Kuramoto-Sivashinsky equation, and develops multifractal and
hierarchical (shell) models of turbulence. The main hydrodynamic
instabilities (Rayleigh-Taylor, Kelvin-Helmholtz, and
Richtmyer-Meshkov) are studied in Chapter 6. The book contains
theoretical and practical materials, examples and exercises and can
be recommended to students and specialists of mathematics and
physics, chemistry, biology and engineering.
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