1. Chapter 7. Application of Thermodynamics to Flow Processes
고려대
화공 생명공학과

2. 7.1 Duct Flow of Compressible Fluids (1)
Adiabatic, steady state, one-dimensional flow of compressible fluid
No shaft work and no change in potential energy
Energy Balance Equation – 1st law
Steady state
Changes in enthalpy
directly go to
changes in velocity

3. 7.1 Duct Flow of Compressible Fluids (2)
Mass balance equation – Continuity Equation

4. 7.1 Duct Flow of Compressible Fluids (3)
Thermodynamic Relations
Replace V in terms of S and P
(eqn 3-2)
(eqn 6-17)

5. 7.1 Duct Flow of Compressible Fluids (4)
Relation from physics
Velocity of sound in a medium
is related with pressure
derivative w.r.t volume
with const.S

6. 7.1 Duct Flow of Compressible Fluids (5)
Variables : dH, du, dV, dA, dS, dP
Equations : four
dS, dA : independent
Can develop equations of other derivatives with
dS and dA

7. 7.1 Duct Flow of Compressible Fluids (6)
M : Mach number = u/c

8. 7.1 Duct Flow of Compressible Fluids (7)
According to second law, (dS/dx) >= 0

9. Pipe Flow Pipe Flow : constant cross sectional area (dA/dx=0)
Subsonic flow :
Implies :
Pressure drops
in the direction of flow
Velocity increases
in the direction of flow

10. Pipe flow The velocity does not increase indefinitely.
If the velocity exceeds the sonic value,
Supersonic flow
Shock wave and turbulence
Unstable flow

11. Nozzles Flow within a pipe or a duct (variable cross-sectional area)
Assume isentropic flow  reversible flow

12. Nozzles Converging Diverging Subsonic (M<1) Supersonic(M>1)
dA/dx - +
dP/dx
du/dx

13. Converging Nozzle Pressure Velocity
Maximum obtainable velocity = speed of sound
Increase in velocity requires increase in cross-sectional area in diverging section
Converging nozzle can be used to deliver constant flow into a region of variable pressure
P1  P2
As p2 decreases, velocity increases and maximum value at sonic velocity.
Further decrease in p2 has no effect on velocity.

14. Converging / Diverging Nozzle
Speed of sound is attained at the throat of converging/diverging nozzle only when the pressure at the throat is low enough that critical value of P2/P1 is reached.
See figure 7.1

15. Value of critial pressure ratio
dS=0  Adiabatic ,

16. Value of critical pressure ratio
Critical value  u=c

17. Throttling Process
Throttling Process : Orifice , Partly closed valve, porous plug, …
Primary result : pressure drop
For ideal gases, H=H(T) and no change in T
For real gases, slight change in T

18. Example 7.5 Joule-Thompson Coefficient
Temperature change resulting from a throttling a real gas.
Joule-Thompson coefficient

19. Joule/Thomson Coefficient and other properties
J-T coeff. comes from the pressure dependence of H

20. Joule/Thomson Coeff. from PVT relation
With Cp and PVT relation , any property can be predicted.

21. 7.2 Turbines (Expanders) Expansion of gas  Production of Work
Internal Energy  Kinetic Energy  Work 1 Ws 2

22. Turbines (Expanders)
Heat effects are negligible, Inlet and outlet velocity changes are small
Normally T1, P1 and P2 are given
Maximum work : isentropic process (adiabatic process)

23. Turbines (Expanders) Turbine Efficiency
Turbine efficiency of properly designed turbine : 0.7 to 0.8

24. Turbines (Expanders) H
Adiabatic expansion process in a turbine or expander S

25. 7.4 Compression Processes
Compression Devices : Rotating blades, Reciprocating pistions 2 Ws 1

26. Compressors
Compressor efficiency : 0.7 to 0.8

27. Compressors H
Adiabatic compression process S