Notes 15 Chapter 5 Components of Thermodynamic Cycles

1. Notes 15Chapter 5Components of Thermodynamic Cycles

2. Components of Thermodynamic Cycles • What can be the components of thermodynamic cycles? • Turbines, valves, compressors, pumps, heat exchangers (evaporators, condensers), mixers,

3. Open Systems - Control Volume

4. Where Exactly Are They Used?

5. Vapor-cycle Power Plants

6. Inside The Household Refrigerator

7. Review of 1st Law

8. Applications to some steady state systems • Start simple • nozzles • diffusers • valves • Includes systems with power in/out • turbines • compressors/pumps • Finish with multiple inlet/outlet devices • heat exchangers • mixers

9. You will need to use all that you’ve learned to date • Conservation of mass • Conservation of energy • Property relationships • Ideal gas equation of state • Property tables • Systematic analysis approach

10. Nozzles and Diffusers • Nozzle--a device which accelerates a fluid as the pressure is decreased. V2, P2 V1, P1 This configuration is for sub-sonic flow.

11. Nozzles and Diffusers • Diffuser--a device which decelerates a fluid and increases the pressure. V2, P2 V1, P1

12. For supersonic flow, the shape of the nozzle is reversed. Nozzles

13. General shapes of nozzles and diffusers nozzle diffuser Subsonic flow nozzle diffuser Supersonic flow

14. Common assumptions we’ll make for nozzles and diffusers • Steady state, steady flow • No work - device produces or uses shaft work • Heat loss/gain is often neglected • Potential energy change is usually small

15. We start our analysis of diffusers and nozzles with the conservation of mass If we have steady state, steady flow, then: And

16. We continue with conservation of energy We can simplify by dividing by mass flow: 0 0 0 q = 0 (adiabatic) w = 0 (these are not work producing devices; neither is work done on them)

17. We can rearrange to get a much simpler expression: With a nozzle or diffuser, we are converting flow and internal energy, represented by Dh =D(u+Pv) into kinetic energy, or vice-versa.

18. System Approach to Problem Solving • State assumptions for the device • Write basic form of conservation of mass and energy equations • Apply assumptions to get to previous equation

19. Sample Problem An adiabatic diffuser is employed to reduce the velocity of a stream of air from 250 m/s to 35 m/s. The inlet pressure is 100 kPa and the inlet temperature is 300°C. Determine the required outlet area in cm2 if the mass flow rate is 7 kg/s and the final pressure is 167 kPa.

20. Sample problem: diagram and basic information INLET T1 = 300C P1 = 100 kPa V1 = 250 m/s = 7 kg/s OUTLET P2 = 167 kPa V2 = 35 m/s Diffuser

21. Sample Problem: Assumptions • SSSF (Steady state, steady flow) - no time dependent terms • adiabatic • no work • potential energy is zero • air is ideal gas

22. Sample Problem: apply basic equations Conservation of Mass Solve for A2

23. How do we get specific volumes? Remember ideal gas equation of state? or and We know T1 and P1, so v1 is simple. We know P2, but what about T2? NEED ENERGY EQUATION!!!!

24. Sample Problem:Energy Eqn V1 and V2 are given. We need h2 to get T2 and v2. If we assumed constant specific heats, we could get T2 directly

25. Sample problem - con’t However, I’m going to use variable specific heats.. we get h1 from air tables at T1 = 300 + 273 = 573K. From energy equation: This corresponds to an exit temperature of 602.2 K.

26. Now we can get solution. and

27. Throttling Devices (Valves)

28. Typical assumptions for throttling devices • No work • Potential energy changes are zero • Kinetic energy changes are usually small • Heat transfer is usually small • Two port device

29. Look at energy equation: Apply assumptions from previous page: 0 0 0 0 We obtain: or

30. Discussion Question Does the fluid temperature increase, decrease, or remain constant as it goes through an adiabatic valve?

31. h const. T P const. h const. s Look at implications: If the fluid is liquid/vapor in equilibrium: • During throattling process: • The pressure drops, • The temperature drops, • Enthalpy is constant

32. Look at implications: If fluid is an ideal gas: Cp is always a positive number, thus:

33. TEAMPLAY Refrigerant 12 enters a valve as a saturated liquid at 0.9607 Mpa and leaves at 0.1826 MPa. What is the quality and the temperature of the refrigerant at the exit of the valve?

34. TEAMPLAY Liquid + Vapor R12 Liquid R12 State (2) Liquid+vapor, x=? Psat = 0.1826 MPa Tsat = ? Hliq = ? State (1) Liquid saturated, x=0 Psat = 0.9607 MPa Tsat = ? Hliq = ?

35. Turbine • A turbine is device in which work is produced by a gas passing over and through a set of blades fixed to a shaft which is free to rotate.

40. TURBINES We’ll assume steady state, Sometimes neglected Almost always neglected

41. Turbines • We will draw turbines like this: inlet w maybe q outlet

42. Compressors, pumps, and fans • Machines developed by engineers to make life easier, decrease world anxiety, and provide exciting engineering problems from the industrial revolution for students. • Machines which do work on a fluid to raise its pressure, potential, or speed. • Mathematical analysis proceeds the same as for turbines, although the signs may differ.

43. Primary differences • Compressor - used to raise the pressure of a compressible fluid • Pump - used to raise pressure or potential of an incompressible fluid • Fan - primary purpose is to move large amounts of gas, but usually has a small pressure increase

44. Compressors, pumps, and fans Side view End view of pump of pump Compressor

49. Sample Problem Air initially at 15 psia and 60°F is compressed to 75 psia and 400°F. The power input to the air is 5 hp and a heat loss of 4 Btu/lbm occurs during the process. Determine the mass flow in lbm/min.

50. Draw Diagram 15 psia 60oF Compressor Wshaft = 5 hp 75 psia 400oF Q = 4 Btu/lb