Gas dynamic compressible flow

File : pdf, 4.0 MB, 264 pages

by Dr. Genick Bar-Meir (www.potto.org)

TABLE OF CONTENTS

0.1 GNU Free Documentation License
1. APPLICABILITY AND DEFINITIONS
2. VERBATIM COPYING
3. COPYING IN QUANTITY
4. MODIFICATIONS
5. COMBINING DOCUMENTS
6. COLLECTIONS OF DOCUMENTS
7. AGGREGATION WITH INDEPENDENT WORKS
8. TRANSLATION
9. TERMINATION
10. FUTURE REVISIONS OF THIS LICENSE
ADDENDUM: How to use this License for your documents
0.2 Potto Project License
0.1 Version 0.4.3
0.2 Version 0.4.2
0.3 Version 0.4
0.4 Version 0.3
0.1 The new version
0.0.1 Speed of Sound
0.0.2 Stagnation effects
0.0.3 Nozzle
0.0.4 Isothermal Flow
0.0.5 Fanno Flow
0.0.6 Rayleigh Flow
0.0.7 Evacuation and filling semi rigid Chambers
0.0.8 Evacuating and filling chambers under external forces
0.0.9 Oblique shock
0.0.10 Prandtl–Meyer
0.0.11 Transient problem

1 Introduction 1
1.1 What is Compressible Flow ?
1.2 Why Compressible Flow is Important?
1.3 Historical Background
1.3.1 Early Developments
1.3.2 The shock wave puzzle
1.3.3 Choking Flow
1.3.4 External flow
1.3.5 Biographies of Major Figures
2 Fundamentals of Basic Fluid Mechanics
2.1 Introduction
2.2 Fluid Properties
2.3 Control Volume
2.4 Reynold’s Transport Theorem
3 Speed of Sound
3.1 Motivation
3.2 Introduction
3.3 Speed of sound in ideal and perfect gases
3.4 Speed of Sound in Real Gas
3.5 Speed of Sound in Almost Incompressible Liquid
3.6 Speed of Sound in Solids
3.7 Sound Speed in Two Phase Medium
4 Isentropic Variable Area Flow 39
4.1 Stagnation State for Ideal Gas Model
4.1.1 General Relationship
4.1.2 Relationships for Small Mach Number
4.2 Isentropic Converging-Diverging Flow in Cross Section
4.2.1 The Properties in The Adiabatic Nozzle
4.2.2 Examples
4.2.3 Mass Flow Rate (Number)
4.3 Isentropic Tables
4.4 Isentropic Isothermal Flow Nozzle
4.4.1 General Relationship
4.5 The Impulse Function
4.5.1 Impulse in Isentropic Adiabatic Nozzle
4.5.2 The Impulse Function in Isothermal Nozzle
4.6 Isothermal Table
4.7 The effects of Real Gases
5 Normal Shock 73
5.1 Solution of the Governing Equations
5.1.1 Informal model
5.1.2 Formal Model
5.1.3 Speed of Sound Definition
5.1.4 Prandtl’s condition
5.2 Operating Equations and Analysis
5.2.1 The Limitations of The Shock Wave
5.2.2 Small Perturbation Solution
5.2.3 Shock Thickness
5.3 The Moving Shocks
5.3.1 Shock Result From A Sudden and Complete Stop
5.3.2 Moving Shock Into Stationary Medium
5.4 Shock Tube
5.5 Shock with Real Gases
5.6 Shock in Wet Steam
5.7 Normal Shock in Ducts
5.8 Tables of Normal shocks,
Ideal Gas
6 Normal Shock in Variable Duct Areas 105
6.1 Nozzle efficiency
6.1.1 Diffuser Efficiency
7 Nozzle Flow With External Forces 115
7.1 Isentropic Nozzle
7.2 Isothermal Nozzle
8 Isothermal Flow 119
8.1 The Control Volume Analysis/Governing equations
8.2 Dimensionless Representation
8.3 The Entrance Limitation Of Supersonic Brach
8.4 Comparison with Incompressible Flow
8.5 Supersonic Branch
8.6 Figures and Tables
8.7 Examples
8.8 Unchoked situation
9 Fanno Flow 137
9.1 Introduction
9.2 Model
9.2.1 Dimensionalization of the equations .
9.3 The Mechanics and Why The Flow is Chock?
9.4 The working equations
9.4.1 Example
9.5 Supersonic Branch
9.6 Maximum length for the supersonic flow
9.7 Working Conditions
9.7.1 Variations of the tube length
9.7.2 The Pressure Ratio,effects
9.7.3 Entrance Mach number
9.8 The Approximation of the Fanno flow by Isothermal Flow
9.9 More Examples
10 RAYLEIGH FLOW 171
10.1 Introduction
10.2 Governing Equation
11 Evacuating and Filling a Semi Rigid Chambers 183
11.1 Governing Equations and Assumptions
11.2 General Model and Non-dimensioned
11.2.1 Isentropic process
11.2.2 Isothermal Process in the Chamber
11.2.3 A Note on the entrance Mach number
11.3 Rigid Tank with Nozzle
11.3.1 Adiabatic Isentropic Nozzle Attached
11.3.2 Isothermal Nozzle Attached .
11.4 Rapid evacuating of a rigid tank
11.4.1 With Fanno Flow
11.4.2 Filling process
11.4.3 The Isothermal Process
11.4.4 Simple Semi Rigid Chamber
11.4.5 The “Simple” General Case
11.5 Advance Topics
12 Evacuating/Filing Chambers under External Volume Control 199
12.1 Model .
12.1.1 Rapid Process
12.1.2 Examples
12.1.3 Direct Connection
12.2 Summary
13 Oblique-Shock 207
13.1 Preface to Oblique Shock
13.2 Introduction
13.2.1 Introduction to Oblique Shock
13.2.2 Introduction to Prandtl–Meyer Function
13.2.3 Introduction to zero inclination
13.3 Oblique Shock
13.4 Solution of Mach Angle
13.4.1 Upstream Mach number,and deflection angle,
13.4.2 In What Situations No Oblique Shock Exist or When
13.4.3 Upstream Mach Number, and Shock Angle,
13.4.4 For Given Two Angles,
13.4.5 Flow in a Semi–2D Shape
13.4.6 Small “Weak Oblique shock”
13.4.7 Close and Far Views of The Oblique Shock
13.4.8 Maximum value of of Oblique shock
13.4.9 Detached shock
13.4.10Issues related to the Maximum Deflection Angle
13.4.11Examples
13.4.12Application of oblique shock
13.4.13Optimization of Suction Section Design
13.5 Summary
13.6 Appendix: Oblique Shock Stability Analysis
14 Prandtl-Meyer Function 245
14.1 Introduction
14.2 Geometrical Explanation
14.2.1 Alternative Approach to Governing equations
14.2.2 Comparison Between The Two Approaches, And Limitations
14.3 The Maximum Turning Angle
14.4 The Working Equations For Prandtl-Meyer Function
14.5 d’Alembert’s Paradox
14.6 Flat Body with angle of Attack
14.7 Examples
14.8 Combination of The Oblique Shock and Isentropic Expansion
15 Topics in Steady state Two Dimensional flow
A Computer Program
A.1 About the Program
A.2 Usage
A.3 Program listings

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