One-Dimensional Compressible Flow

One-Dimensional Compressible Flow explores the physical behavior of one-dimensional compressible flow. Various types of flow in one dimension are considered, including isentropic flow, flow through a convergent or a convergent-divergent duct with varying back pressure, flow with friction or heat transfer, and unsteady flow. This text consists of five chapters and begins with an overview of the main concepts from thermodynamics and fluid mechanics, with particular emphasis on the basic conservation equations for mass, momentum, and energy that are derived for time-dependent flow through a control volume. The chapters that follow provide a basis for understanding steady flow with area change, friction, or heat transfer. A method for solving unsteady flow problems is described in the final chapter, which also discusses the propagation of small disturbances and unsteady flow with finite changes in fluid properties. This book will be useful to senior students pursuing a degree course in mechanical engineering and to engineers in industry.

Preface

Notation

1 Concepts from Thermodynamics and Fluid Mechanics

1.1 System, Control Volume and Control Surface

1.2 The One-Dimensional Approximation

1.3 Conservation of Mass: Continuity Equation

1.4 Newton's Second Law of Motion: Momentum Equation

1.5 The First Law of Thermodynamics

1.6 The Second Law of Thermodynamics

1.7 Stagnation States

1.8 Compressibility and Speed of Sound

1.9 Classification of Compressible Flows: Mach Number

1.10 One-Dimensional Steady Flow Equations in Terms of Mach Number

1.11 Shock Waves

Exercises

2 Isentropic Flow

2.1 General Features of Steady, Inviscid Isentropic Flow

2.2 Applications of Isentropic Flow Assumption

2.3 Isentropic Flow of a Perfect Gas

2.4 Mass Flow Rate and Choking in Isentropic Flow

2.5 Thrust

2.6 Tables for Isentropic Flow

Exercises

3 Flow in a Duct of Variable Cross-Sectional Area

3.1 Convergent Duct

3.2 Convergent-Divergent Duct

3.3 Calculation of Flow in Ducts of Varying Cross-Sectional Area

3.4 Supersonic Diffusers

3.5 Instability of a Normal Shock in a Convergent Passage

Exercises

4 Flow with Friction or Heat Transfer

4.1 Introduction

4.2 Adiabatic Flow in a Duct of Constant Cross-Sectional Area with Friction

4.3 Flow in a Duct of Constant Cross-Sectional Area with Heat Transfer

Exercises

5 One-Dimensional Unsteady Flow

5.1 Propagation of Small Disturbances

5.2 Unsteady Flow with Finite changes in Fluid Properties

5.3 Mathematical Theory of One-Dimensional Homentropic Unsteady Flow

Exercises

Table 1. One-Dimensional Normal Shock in a Perfect Gas

Table 2. One-Dimensional Isentropic Flow of a Perfect Gas

Table 3. Fanno Flow of a Perfect Gas - One-Dimensional Adiabatic Flow of a Perfect Gas in a Duct of Constant Cross-Sectional Area with Friction

Table 4. Rayleigh Flow of a Perfect Gas - One-Dimensional, Frictionless Flow of a Perfect Gas in a Duct of Constant Cross-sectional Area with Stagnation Temperature Change

Table 5. The Standard Atmosphere

Table 6 Specific Heat Data

References

Index