Introduction to Fluid Mechanics Chapter 13 Compressible...

Introduction to Fluid Mechanics

Chapter 13

Compressible Flow

Main Topics

�Basic Equations for One-Dimensional Compressible Flow

� Isentropic Flow of an Ideal Gas – Area Variation

�Flow in a Constant Area Duct with Friction

�Frictionless Flow in a Constant-Area Duct with Heat Exchange

�Normal Shocks

�Supersonic Channel Flow with Shocks

�Oblique Shocks and Expansion Waves

Basic Equations for

One-Dimensional Compressible Flow

�Control Volume

Basic Equations for

�Continuity

�Momentum

Basic Equations for

�Second Law of Thermodynamics

�First Law of Thermodynamics

Basic Equations for

�Property Relations

�Equation of State

Isentropic Flow of an Ideal Gas

– Area Variation

�Basic Equations for Isentropic Flow

– Area Variation

�Isentropic Flow

– Area Variation

�Subsonic, Supersonic, and Sonic Flows

– Area Variation

�Reference Stagnation and Critical Conditions for Isentropic Flow

– Area Variation

�Property Relations

– Area Variation

�Isentropic Flow in a Converging Nozzle

– Area Variation

�Isentropic Flow in a Converging Nozzle

– Area Variation

�Isentropic Flow in a Converging-Diverging Nozzle

– Area Variation

�Isentropic Flow in a Converging-Diverging Nozzle

Flow in a Constant-Area Duct

with Friction

�Control Volume

with Friction �Basic Equations for Adiabatic Flow

with Friction

�Adiabatic Flow: The Fanno Line

with Friction �Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas

with Friction �Fanno-Line Relations

with Friction

�Fanno-Line Relations (Continued)

Frictionless Flow in a Constant-

Area Duct with Heat Exchange

�Control Volume

�Basic Equations for Flow with Heat Exchange

�Heat Exchange: The Rayleigh Line

Area Duct with Heat Exchange �Rayleigh-Line Relations

Normal Shocks

�Control Volume

Normal Shocks

�Basic Equations for a Normal Shock

Normal Shocks

� Intersection of Fanno & Rayleigh Lines

Normal Shocks

�Normal Shock Relations

Normal Shocks

�Normal Shock Relations (Continued)

Supersonic Channel Flow

with Shocks

�Flow in a Converging-Diverging Nozzle

Oblique Shocks and

Expansion Waves

�Typical Application

Oblique Shocks and

Expansion Waves

�Mach Angle and Oblique Shock Angle

Oblique Shocks and

Expansion Waves

�Oblique Shock: Control Volume

Oblique Shocks and

Expansion Waves

�Oblique Shock: Useful Formulas

Oblique Shocks and

Expansion Waves

�Oblique Shock Relations

Oblique Shocks and

Expansion Waves

�Oblique Shock Relations (Continued)

Oblique Shocks and

Expansion Waves

�Oblique Shock: Deflection Angle

Oblique Shocks and

Expansion Waves

�Oblique Shock: Deflection Angle

Oblique Shocks and

Expansion Waves

�Expansion and Compression Waves

Oblique Shocks and

Expansion Waves

�Expansion Wave: Control Volume

Oblique Shocks and

Expansion Waves

�Expansion Wave: Prandtl-Meyer Expansion Function

Oblique Shocks and

Expansion Waves

�Expansion Wave: Isentropic Relations

Introduction to Fluid Mechanics Chapter 13 Compressible...

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