Dynamics of compressible fluids : a textbook / Oleksandr Girin.

Format:

Book

Author/Creator:

Girin, Oleksandr, author.

Language:

English

Subjects (All):

Fluid dynamics.

Compressibility.

Genre:

Electronic books.

Physical Description:

1 online resource (xxii, 304 pages) : illustrations (some color)

Place of Publication:

Cham : Springer, [2022]

Summary:

Compressibility is a property inherent in any material, but it does not always manifest itself. Experience suggests that it affects the medium motion only at velocities comparable to the speed of sound. Why do we study compressibility? It turns out that in order to calculate the aircraft streamlining or the internal flow in its engine, or the shell muzzle velocity, or the dynamic load of a shock wave from an accidental blast on a structural element, and in many other cases it is necessary to know and understand the laws of the Dynamics of Compressible Media (DCM) and be able to apply them in practice. This textbook is designed to help readers achieve this goal and learn the basics of DCM. This field of knowledge is high-tech and always focuses on the future: modern developments of hypersonic aircraft, designing more advanced structural elements for airplanes and helicopters, calculating the car aerodynamics, etc. Paradoxes have always given impetus to the search for new technological devices. Unusual effects in DCM include the flow chocking in supersonic outflow from reservoirs (Sect.2.2); the shock wave formation inside an initially smooth flow (Sect.5.3); the generation of a "spallation saucer" of armor inside a tank when a shell hits it (Sect.5.5); the dog-leg of a plane discontinuity surface at shockwave reflection from a rigid wall (Sec.8.1). The way to understand these and other effects is through the creation of quantitative models of a moving compressible fluid.

Contents:

Intro

Preface

Contents

About the Author

Introduction

1. Scope of the Dynamics of Compressible Fluids

2. The Subject Matter of Dynamics of Compressible Fluids

1 General Equations of Gas Motion

1.1 The Thermodynamic Model of a Perfect Gas

Adiabatic Formulae

1.1.1 Internal State of a Gas Particle

Thermodynamic Variables

1.1.2 Perfect Gas Model

Polytropic Gas

1.1.3 Adiabatic Formulae

1.2 Governing Equations of Gas Motion

Mathematical Model ...

1.3 Speed of Propagation of Small Disturbances in Ideal Gas

Sound Speed

1.4 Thermodynamics of a Moving Gas

1.4.1 Bernoulli-Saint-Venant Equation

Enthalpy

1.4.2 Stagnation Gas State

Isentropic Formulae

1.4.3 Laval's Number

Other Characteristic States of a Moving Gas

References

2 Continuous Flows

2.1 Equations of One-Dimensional Steady Gas Flow

Rule of a Stream Reversal

2.2 Gas Outflow from Reservoir

Saint-Venant-Vantzel Formula

2.3 Supersonic Outflow Mode

Laval's Nozzle

3 Discontinuity in a Gas Flow

3.1 Conservation Laws at a Strong Discontinuity Surface

3.2 Classification of Strong Discontinuities

Shocks

3.3 Normal Shock Theory

3.4 Normal Shock Regularities

3.4.1 Velocity Jump

3.4.2 Pressure Jump

3.4.3 Density Jump

3.4.4 Entropy Jump

3.5 Shock Adiabatic Curve and Its Properties

3.5.1 Equation of Shock Adiabatic Curve

3.5.2 ``Asterisk'' Property

3.5.3 Limiting Degree of Gas Compression in Shock Waves

3.5.4 Approximation of Strong Shocks

3.5.5 Approximation of Weak Shocks

4 Governing Equations and Initial-Boundary-Value Problems

4.1 Geometry of One-Dimensional Flows

4.2 Equations of Motion in Euler's Form

Initial and Boundary Conditions

4.2.1 Euler's Equations of Motion

4.2.2 Initial Conditions

4.2.3 Boundary Conditions

4.3 Equations of Motion in Lagrange's Form

4.4 Equations of Motion in Characteristic Form

the Characteristic ...

4.5 The Method of Characteristics

4.6 Generalized Cauchy Problem (Type I Problem) ...

4.7 The Goursat Problem (Type II Problem)

4.8 Combined Problem of a Special Type (Type III Problem)

4.9 Characteristics as Trajectories of a Possible Weak Discontinuity of a Solution

4.9.1 Relationships Along the Weak Discontinuity Trajectory

4.9.2 Breakup of Arbitrary Weak Discontinuity

5 Isentropic Gas Flows with Plane Waves

5.1 Riemann Method

5.1.1 Riemann Invariants

5.1.2 Riemann Variables

Riemann Method

5.1.3 The Euler-Poisson Equation

5.1.4 The Remarkable Case γ= 3

5.2 The Riemann Waves

5.2.1 Simple Waves

5.2.2 Adjoining Theorem

5.2.3 Simple Wave Equations

5.2.4 Properties of Simple Waves

5.3 Gradient Catastrophe

5.4 The Piston Problem

5.4.1 Case When the Piston Is Pulled Out from Gas

5.4.2 Case of Piston Moving with Constant Velocity

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed November 22, 2022).

ISBN:

9783031112621

3031112628

OCLC:

1350617667

Access Restriction:

Restricted for use by site license.