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Chapter 12 Fluid Flow

Chapter 12 Fluid Flow. 12-1 The Basic Equation of Steady-Flow. 12-1-1 The Conversation of Mass. A ： Cross section area of flow duct c ： Velocity of fluid v ： Specific volume of fluid. Differential form:. 12-1-2 The Conversation of Energy. Differential form:. 12-1-3 Process Equation.

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Chapter 12 Fluid Flow

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  1. Chapter 12Fluid Flow

  2. 12-1 The Basic Equation of Steady-Flow 12-1-1 The Conversation of Mass A：Cross section area of flow duct c ：Velocity of fluid v：Specific volume of fluid Differential form:

  3. 12-1-2 The Conversation of Energy Differential form:

  4. 12-1-3 Process Equation Usually the fluid flows too fast in a duct to exchange heat with its surroundings, so it undergoes an adiabatic process, then: pv k= const Differential form:

  5. The Velocity of Sound is denoted by 12-1-4 Velocity of Sound and Mach Number From Then

  6. Mach Number Ma is defined as：

  7. Ernst Mach was born on Feb. 18, 1838, d. Vaterstetten. He found an experimental proof for the Doppler Effect (Christian  Doppler) and by inspection of fast moving projects proposed the Mach's principle. The "Mach Number" named after him describes the relation of a body's velocity to sonic speed. His attitude was characterized by empirical thinking based on scientific findings. One of his strictest opponents and critics was M. Planck. After retiring from the University in 1901 he was appointed to the upper chamber of the Austrian Parliament, a post he held for 12 years. He died in 1916

  8. 12-2 The Fluid Flow in Duct During the fluid flow in a duct, the properties of fluid changes along the stream line. In most situations this can be treated as a one-dimensional flow 12-2-1 The Pressure and Velocity From conservation of energy dh= - cdc du +d(pv)= - cdc du+pdv+vdp= -cdc

  9. From the first law of thermodynamics: δq=du+pdv =0 Then: du+pdv+vdp= -cdc vdp= - cdc - vdp= cdc To increase the velocity of fluid(dc>0), the pressure must be decreased. This kind of duct is calledNozzle Or to decrease the velocity (dc<0) of fluid to obtain a high pressure in a duct flow. This kind of duct is calleddiffuser

  10. 12-2-2 Velocity and The Cross Section Area of Duct From conservation of mass： From the process equation

  11. Subsonic flow Subsonic flow As to a nozzle dc>0 (1)If the fluid velocity is subsonic, then (Ma2-1)<0 Therefore: dA<0 The nozzle’s shape should be as following: convergent nozzle

  12. Ultrasonic flow Ultrasonic flow (2)If the fluid velocity is ultrasonic, then (Ma2-1)>0 Therefore: dA>0 The nozzle’s shape should be as following: divergent nozzle

  13. Ultrasonic flow Subsonic flow (3)If the nozzle’s inlet velocity is subsonic, but outlet velocity ultrasonic, then: dA<0 → dA=0 → dA>0 The nozzle’s shape should be as following: throat convergent-divergent nozzle

  14. Subsonic flow Subsonic flow As to a diffuser dc<0 (1)If the fluid velocity is subsonic, then (Ma2-1)<0 Therefore: dA>0 The diffuser’s shape should be as following:

  15. Ultrasonic flow Ultrasonic flow (2)If the fluid velocity is ultrasonic, then (Ma2-1)>0 Therefore: dA<0 The diffuser’s shape should be as following:

  16. Subsonic flow Ultrasonic flow (2) If the diffuser’s inlet velocity is ultrasonic, but outlet velocity subsonic, then: dA<0 → dA=0 → dA>0 The diffuser’s shape should be as following:

  17. nozzle Diffuser(compressor) combustion chamber 12-2-3 Applications Ram-jet engine

  18. Space Shuttle Rocket

  19. 12-3 The Calculation of Nozzle 12-3-1 The Flux of Subsonic Nozzle We define P2 /P1 as compression ratio ε

  20. 12-3-2 The Critical Compression Ratio For convergent-divergent nozzle, the velocity at throat keeps as sound-velocity. This state is called critical state. The flux of this kind of nozzle is depend on that of throat. The Compression Ratio which is low enough to make the air flow at sound-velocity at the exit of nozzle is called the critical compression Ratio. It is denoted by εc

  21. 0.528 for air εc= 0.546 for saturated steam 0.577 for superheated steam

  22. The End of This Book Thank You

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