EGR 334 Thermodynamics Chapter 9: Sections 5-6

1. EGR 334 ThermodynamicsChapter 9: Sections 5-6 Lecture 35: Gas Turbine modeling with the Brayton Cycle Quiz Today?

2. Today’s main concepts: • Be able to recognize Dual and Brayton Cycles • Understand what system may be modeled using Brayton Cycle. • Be able to perform a 1st Law analysis of the Brayton Cycle and determine its thermal efficiency. • Be able to explain how regeneration may be applied to a Brayton Cycle model. Reading Assignment: Read Chapter 9, Sections 7-8 Homework Assignment: Problems from Chap 9: 42, 47, 55

3. OK….Quick Matching Quiz B C a) Carnot b) Rankine c) Otto d) Diesel p . . 4 1 1’ . . 3 2’ 2 v A D

4. Today you get to add two more cycles to your cycle repertoire.Dual Cycle Brayton cycle. Used as a hybrid cycle which includes elements of both the Otto and Diesel cycles. Used to model internal combustion engines Used as a model for gas turbines (such as jet engines).

5. Sec 9.4 : Air-Standard Duel Cycle Neither the Otto or Diesel cycle describe the actual P-v diagrams of an engine Heat addition occurs in two steps • 2 – 3 : Constant volume heat addition • 3 – 4 : Constant pressure heat addition (first part of power stroke) Process 1 – 2 : Isentropic compression Process 2 – 3 : Constant volume heat transfer Process 3 – 4 : Constant pressure heat transfer Process 4 – 5 : Isentropic expansion Process 5 – 1 : Constant volume heat rejection To set state 3: Use ideal gas law with V3 = V2. and

6. Sec 9.4 : Air-Standard Duel Cycle Dual Cycle analysis process 1-2: s1 = s2 process 2-3: v2 = v3 process 3-4: p3 = p4 process 4-5: s4 = s5 process 5-1: v5 = v1

7. Example (9.38): The pressure and temperature at the beginning of compression in an air-standard dual cycle are 14 psi, 520°R. The compression ratio is 15 and the heat addition per unit mass is 800 Btu/lbm. At the end of the constant volume heat addition process the pressure is 1200 psi. Determine, • Wcycle, in BTU/lb. • Qout, in BTU/lb. • The thermal efficiency. • The cut off ratio

8. Example (9.38): Given Information: compression ratio, r = 15 Qin= Q23 + Q34 = 800 Btu Qout = - Q51 Identify State Properties State 1: p1 = 14 psi, T1 = 520 R State 2: s2 = s1 v2 = v1/r State 3: v3 = v2 and p3 = 1200 psiState 4: p4 = p3 = 1200 psi State 5: s5 =s4 and v5 = v1 Use Table A22E to fill in many of the other properties.

9. Example (9.38): • State 1: given T = 520 R • look up u, h, vr, and pr • State 2: use r to find v2 • and since 1-2 is isentropic • find vr2 • then use Table A22E to look up T2, pr2, u2, and h2: • Pressure p2, can then be calculated using

10. Example (9.38): • State 3: given v3 = v2 and • p3 = 1200 psi, use ideal • gas law: • then use Table A22E to look up u3 and h3:

11. Example (9.38): • State 4: Knowing p4=p3 and the heat in: • Qin= 800 Btu/lb • use the 1st Law: O • Use Table A-22E • to find T4 ,u4, pr4, • and v4r

12. Example (9.38): • State 5: • process 4-5 is also isentropic • Replace V’s using ideal gas. • Use Table A-22E to look up T5, u5, h5, and pr5 and then find p5:

13. Example (9.38): • Wcycle, in Btu/lb. • Qout, in Btu/lb. • The thermal eff. • The cut off ratio

14. Example (9.38): • Wcycle, in Btu/lb. • Qout, in Btu/lb. • Thermal efficiency • The cut off ratio Cut off ratio: from ideal gas equation at constant pressure:

15. Sec 9.5 : Modeling Gas Turbine Power Plants Air-Standard analysis of Gas Turbine Power plants. Gas power plants are lighter and more compact than vapor power plants. Used in aircraft propulsion & marine power plants.

16. Sec 9.5 : Modeling Gas Turbine Power Plants Air-Standard analysis: Working fluid is air Heat transfer from an external source (assumes there is no reaction) Jet engine: Suck (intake) Squeeze (compressor) Bang/Burn (combustion) Blow (turbine/exhaust) Heat Ex Process 1 – 2 : Isentropic compression of air (compressor). Process 2 – 3 : Constant pressure heat transfer to the air from an external source (combustion) Process 3 – 4 : Isentropic expansion (through turbine) Process 4 – 1 : Completes cycle by a constant volume pressure in which heat is rejected from the air

17. Sec 9.5 : Modeling Gas Turbine Power Plants Gas Turbine Analysis process 1-2: s1 = s2 process 2-3: p2 = p3 process 3-4: s3 = s4 process 4-1: p4 = p1 • For a gas turbine, the back work ratio is much larger than that in a steam cycle since vair>>vliquid • bwr for a gas turbine power cycle is typically 40-80% vs. 1-2% for a steam power cycle.

18. Sec 9.3 : Air-Standard Diesel Cycle • Gas Turbine Analysis • Given T1 & T3  use table to find h1 & h3 . Find state 2. Find state 4. Compressor pressure ratio: For Cold-Air Standard analysis: For state 2. For state 4.

19. Sec 9.3 : Air-Standard Diesel Cycle • Gas Turbine Analysis Effect of Compressor pressure on efficiency. with Max T3 is approximately 1700 K

20. Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 Btu/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate • The thermal efficiency • The back work ratio. • The net power developed.

21. Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate • The thermal efficiency • The back work ratio. • The net power developed. • Since we are given k=1.4, use a cold-air standard analysis. • Temperatures for states 1 and 3 are given. For state 2. For state 4.

22. Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate • The thermal efficiency • The back work ratio. • The net power developed.

23. Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate • The thermal efficiency • The back work ratio. • The net power developed. But need the mass flow rate.

24. Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine • The thermal efficiency • The net power developed.

25. Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine • The thermal efficiency • The net power developed. • Temperatures for states 1 and 3 are given. Relative pressure and enthalpy values from Table A-22E Find state 2. Find state 4.

26. Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine • The thermal efficiency • The net power developed.

27. Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine • The thermal efficiency • The net power developed. But need the mass flow rate.

28. End of Slides for Lecture 35