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

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

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

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

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

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

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

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

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

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

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

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

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.

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

Value of critial pressure ratio dS=0  Adiabatic ,

Value of critical pressure ratio Critical value  u=c

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

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

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

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

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

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)

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

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

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

Compressors Compressor efficiency : 0.7 to 0.8

Compressors H Adiabatic compression process S