Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Transcription

1 Introduction to Chemical Engineering Thermodynamics Chapter 7 1

2 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum Flow processes result from pressure gradients within the fluid EOS allows computation of intensive properties at any point in the fluid 2

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4 Duct Flow of Compressible Fluids Adiabatic steady-state 1D flow of a compressible fluid without shaft work and change in potential energy Energy balance 4

5 Continuity equation Additional relation : 5

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7 Can also relate dh and dv to ds and da 7

8 As the fluid traverses a differential length, dx, of its path Irreversibilities due to fluid friction in adiabatic flow : 8

9 Pipe flow Steady-state adiabatic flow of compressible fluids in a horizontalpipe of constant cross-sectional area 9

10 Exit of pipe velocity can reach speed of sound Supersonic regime is unstable and velocity decreases to a subsonic value 10

11 Nozzles Area change in a nozzle is such that the flow is nearly frictionless 11

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13 Subsonic flow in a converging nozzle: velocity increases and pressure decreases Reach speed of sound at the exit P 2 /P 1 reaches a critical value (0.55 for steam) at which the exit velocity is sonic 13

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15 Supersonic velocities can be reached in converging/diverging nozzles with sonic velocity reached at throat where da/dx=0 Speed of sound is reached at the throat only when P 2 /P 1 is low enough 15

16 Isentropic nozzle for an ideal gas with constant heat capacities Pressure ratio at the throat 16

17 Throttling Process Fluid flows through a restriction results in a pressure drop No change in kinetic or potential energy No shaft work produced and no heat transfer H=0 For an ideal gas: no change in T occurs For real gases: T reduction results from a throttling process 17

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20 Turbines (Expanders) Expansion of a gas in a nozzle to produce a high-velocity stream This kinetic energy is converted into shaft work when the stream impinges on blades attached to a rotating shaft Overall result is conversion of internal energy of a high-pressure stream into shaft work Steam : device is called a turbine High-pressure gas (e.g., ethylene) device called expander 20

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22 Neglect potential energy, heat transfer is negligible, inlet and outlet are sized so that fluid velocities are roughly equal T 1, P 1 and P 2 are known but ignore T 2, W s and H 2 Reversible isentropic turbine (constant entropy) S 2 =S 1. Thus, one can determine H 2 and then W s. 22

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24 Compressors Rotating blades (not too high discharge pressure) or cylinders with reciprocating pistons (for high pressures) Kinetic and potential energy changes negligible. Adiabatic compression 24

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27 Pumps Need to determine enthalpy of compressed subcooled liquids 27

28 Other useful relations: Both equations are usually integrated assuming that: C P, β and V are constant 28

29 Ejectors Ejectors remove gases or vapors from an evacuated space and compress them for discharge at a higher pressure 29

30 Lower investment and maintenance costs if driving fluid allowed to mix with gases or vapors Inner converging/diverging nozzle (for driving fluid) Outer larger nozzle (for both extracted vapors/gases and driving fluid). Acts as a converging/diverging diffuser (velocity decreases and is equal, at the throat, to speed of sound) Momentum transfer from driving fluid to extracted gases/vapors 30