Introduction to Fluid Mechanics Chapter 12 Introduction to Compressible Flow

Main Topics Review of Thermodynamics Propagation of Sound Waves Reference State: Local Isentropic Stagnation Conditions Critical Conditions Basic Equations for One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas: Area Variation Normal Shocks Supersonic Channel Flow with Shocks Flow in a Constant-Area Duct with Friction Frictionless Flow in a Constant-Area Duct with Heat Exchange Oblique Shocks and Expansion Waves

Review of Thermodynamics Ideal Gas

Review of Thermodynamics Specific Heat Formulas

Review of Thermodynamics Internal Energy and Enthalpy

Review of Thermodynamics Entropy

Review of Thermodynamics The Second Law of Thermodynamics

Review of Thermodynamics Isentropic (Reversible Adiabatic) Processes

Propagation of Sound Waves

Propagation of Sound Waves Speed of Sound Solids and Liquids: Ideal Gas:

Propagation of Sound Waves Types of Flow – The Mach Cone

Propagation of Sound Waves Types of Flow – The Mach Cone (Continued) Mach Angle:

Reference State: Local Isentropic Stagnation Conditions

Reference State: Local Isentropic Stagnation Conditions Computing Equations

Critical Conditions A useful reference value for velocity is the critical speed —the speed V we attain when a flow is either accelerated or decelerated (actually or conceptually) isentropically until we reach M=1.

Basic Equations for One-Dimensional Compressible Flow Control Volume Steady flow. One-dimensional flow.

Basic Equations for One-Dimensional Compressible Flow Continuity Momentum Assumption: FBx =0

Basic Equations for One-Dimensional Compressible Flow First Law of Thermodynamics Ws =0 Wshear =Wother =0 Effects of gravity are negligible Second Law of Thermodynamics

Basic Equations for One-Dimensional Compressible Flow Equation of State Property Relations

Isentropic Flow of an Ideal Gas: Area Variation Basic Equations for Isentropic Flow

Isentropic Flow of an Ideal Gas: Area Variation

Isentropic Flow of an Ideal Gas: Area Variation Subsonic, Supersonic, and Sonic Flows

Isentropic Flow of an Ideal Gas: Area Variation Reference Stagnation and Critical Conditions for Isentropic Flow

Isentropic Flow of an Ideal Gas: Area Variation Property Relations

Isentropic Flow of an Ideal Gas: Area Variation A/A*

Isentropic Flow of an Ideal Gas: Area Variation Isentropic Flow in a Converging Nozzle

Isentropic Flow of an Ideal Gas: Area Variation Isentropic Flow in a Converging Nozzle

Isentropic Flow of an Ideal Gas: Area Variation Isentropic Flow in a Converging-Diverging Nozzle

Isentropic Flow of an Ideal Gas: Area Variation Isentropic Flow in a Converging-Diverging Nozzle

Normal Shocks Control Volume

Normal Shocks Basic Equations for a Normal Shock

Normal Shocks Normal Shock Relations

Normal Shocks Normal Shock Relations (Continued)

Supersonic Channel Flow with Shocks Flow in a Converging-Diverging Nozzle

Flow in a Constant-Area Duct with Friction Control Volume

Flow in a Constant-Area Duct with Friction Basic Equations for Adiabatic Flow

Flow in a Constant-Area Duct with Friction Adiabatic Flow: The Fanno Line

Flow in a Constant-Area Duct with Friction Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas

Flow in a Constant-Area Duct with Friction Fanno-Line Relations

Flow in a Constant-Area Duct with Friction Fanno-Line Relations (Continued)

Frictionless Flow in a Constant-Area Duct with Heat Exchange Control Volume

Frictionless Flow in a Constant-Area Duct with Heat Exchange Basic Equations for Flow with Heat Exchange

Frictionless Flow in a Constant-Area Duct with Heat Exchange Heat Exchange: The Rayleigh Line

Frictionless Flow in a Constant-Area Duct with Heat Exchange Rayleigh-Line Relations

Normal Shocks Fanno and Rayleigh Interpretation

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 Steady flow Negligible body forces Adiabatic flow No work terms Negligible gravitational effect

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