ME 400 Energy Conversion Systems Topic 2 Presentation 11

1. ME 400Energy Conversion SystemsTopic 2 Presentation 11 Emad Jassim & Ty NewellDepartment of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaign © 2012 University of Illinois Board of Trustees. All Rights Reserved.

2. Brayton Cycle Efficiency Enhancement • The basic Brayton cycle efficiency is lower than the reversible cycle limit due to heat transfer with temperature differences. 3 1173K “isochore” constant v T 648K “isobar” constant P 4 531K 2 293K • Note, in our example T4 (exhaust) is greater than T2 1 s

3. 3 T 2 T4 4 T2 1 s Brayton Cycle Efficiency Enhancement • The exhaust gas can be used for heating the compressor exit when the exhaust gas has a greater temperature than compressor outlet. 3 T 2 T2 T4 4 1 s • T4 > T2 • Use regeneration • T4 < T2 • Don’t use regeneration

4. Brayton Cycle Efficiency Enhancement Regenerator…heat exchanger between exhaust and compressor outlet. 4a 1173K 0.8MPa 2a 0.8MPa 531K 2 3 4 293K 0.1MPa 1 0.1MPa 648K

5. 4a 4 0.1MPa ? K 0.1MPa 648K QR 0.8MPa ? K 0.8MPa 531K 2a 2 Regenerator Analysis • The heat transfer in the regenerator reduces the amount of energy required in the combustor • The regenerator outlet temperatures must be determined (T4a, T2a ) in order to determine the regenerator heat transfer

6. Regenerator Analysis 1st Law • Using ideal gas and assuming constant specific heats: Therefore, From the 2nd Law (and common sense), the limit for heat exchange is:

7. 4a 4 0.1MPa ? K 0.1MPa 648K QR 0.8MPa ? K 0.8MPa 531K 2a 2 Regenerator Analysis Redrawing system boundaries, the heat transfer for the regenerator can be found: 1st Law: let and,

8. Regenerator Analysis Regenerator Heat Transfer: Combustor Energy: Qc 3 2a

9. Regenerator Analysis Net work for the cycle is unaffected by the regenerator: Brayton with regenerator Basic Brayton cycle Reversible cycle limit

10. Brayton Cycle Inefficiencies • Turbine, compressor and pump inefficiencies have been neglected to this point • Pump work in the Rankine cycle is generally negligible, making pump inefficiency less important • Turbine inefficiency in both Rankine and Brayton cycles directly affects overall cycle efficiency • Compressor inefficiency in Brayton is very important, and if too great, net cycle work may be negative • We will revisit the basic Brayton cycle example to examine the effect of turbine and compressor efficiency

11. 900C 1173K 0.8MPa 0.8MPa 2 3 20C 293K 0.1MPa 4 0.1MPa 1 Brayton Cycle Inefficiencies ht=0.9 hc=0.9

12. Brayton Cycle Inefficiencies Compressor Analysis: Find “actual” compressor work: Find the actual outlet temperature Note: extra work to compressor shows up in elevated outlet temperature.

13. Brayton Cycle Inefficiencies • The inefficiency increases the compressor outlet T • Oddly, the compressor inefficiency results in less energy required in the combustor Combustor 1st Law: For reversible, adiabatic compressor

14. Brayton Cycle Inefficiencies Turbine Analysis: Find “actual” turbine work: (note difference in turbine and compressor efficiency definitions) Find actual turbine outlet temperature Note reversible turbine has lower temperature, indicating greater work output.

15. Brayton Cycle Inefficiencies • Determine cycle efficiency with actual component values • Brayton cycle with reversible turbine and compressor • Reversible cycle limit

16. Summary - Brayton Cycle • The Brayton cycle is analogous in operation to the Rankine cycle except the fluid does not cross the saturation dome • SSSF analysis is a convenient way to assess the cycle operation • Brayton cycle efficiency may be improved with a regenerator when the turbine exhaust temperature exceeds the compressor outlet temperature • Inefficiencies in the turbine and compressor directly affect overall cycle efficiency