Regeneration Brayton cycle irreversible An actual gas turbine differs from the ideal due to inefficiencies in the turbines and compressors and pressure losses in the flow passages heat exchangers in closed cycle The T s diagram may be as shown static data for plot T s diagram 1200 temperature 1000 800 600 400 1 1 2 1 4 1 6 1 8 2 2 2 entropy reversible cycle irreversible cycle regeneration inlet temperature reversible irreversible heat exchanger maximum regeneration inlet temperature irreversible 3 6 T 7ss 5 5s 2 2s 7s 7 4 4 outlet of turbine 5s inlet to regenerator T5s T4 8 irreversible 1 start 2 irreversible compressor outlet 6 outlet of heat addition T6 Tmax 4 outlet of turbine 5 inlet to regenerator T5 T7 1 s 11 21 2005 state reversible process 1 start 2s reversible compressor outlet 3 outlet of heat addition T3 Tmax 1 irreversible processes can be described by some efficiencies and heat transfer effectiveness N B the efficiencies are defined wrt irreversible overall cycle h6 h7 t turbine efficiency compressor efficiency h 6 h 7s c h 2s h 1 h2 h1 T5 T2 T6 T7 t 0 8 T6 T7s T2s T1 c 0 78 T2 T1 heat exchanger effectiveness pressure loss in heater p H p 6 p 3 p H p 3 1 p3 delta p over p H 5 p L p 7 p 1 p L p 1 1 p1 delta p over p L 3 pressure loss increase in cooler relative to p 1 94 T7ss T2 we will combine these as follows as for efficiency only p across turbine matters p6 p7 p3 1 p H p3 p 2 1 p p1 p L p1 1 p1 this combines losses into effect on turbine for these calculations 1 4 power 1 one compressor no intercooling Nc 1 1 delta p over p H 1 delta p over p L delta p over p 1 delta p over p 7 767 taking advantage of constant c po T1 300 Tmax 1200 maximum T3 Tmax T6 Tmax start with 1 as 1 mathematically pr 1 3 1 4 5 reversible relationships are developed in brayton cycle summary mcd may be 2005 reversible T2s pr pr T4 pr irreversible power 1 pr T1 T2s 2 365 704 T2 pr T1 T2s pr T1 T2 2 384 236 c p6 over p7 pr pr 1 delta p over p power T3 T4 2 984 402 p6 over p7 2 1 845 1 reversible turbine calc in irreversible cycle T7s pr T6 p6 over p7 pr power T7 pr T6 T6 T7s pr t 11 21 2005 2 T7s 2 1007 T7 2 1046 at this point we can compute the thermal efficiency without regeneration reversible th wnet qH wt wc qH irreversible T3 T4 T2s T1 T3 T2s rev T6 T7 T2 T1 QH T3 T2s T6 T2 T6 T2 irrev so thermal efficiency becomes th basic rev pr T3 T4 pr T2s pr T1 th basic irr pr T3 T2s pr T6 T7 pr T2 pr T1 T6 T2 pr efficiency Brayton cycles 0 4 t 0 8 thermal efficiency 0 3 c 0 78 0 94 0 2 0 1 delta p over p 7 8 basic cycle irreversible basic cycle reversible 0 2 2 5 3 3 5 4 4 5 5 pressure ratio with regeneration all the states are the same with reversible regen inlet temperature irreversible T5s T4 T5 pr T2 pr T7 pr T2 pr with regeneration reversible th ic wnet qH wt wc qH th reg rev pr 1 11 21 2005 T3 T4 T2s T1 T3 T5s T4 irreversible T6 T7 T2 T1 T6 T5 T2s pr T1 1 T3 T3 pr power th reg irr pr 3 T5 2 1006 rev irrev QH T3 T5s T6 T5 T6 T7 pr T2 pr T1 T6 T5 pr efficiency regeneration irreversible 0 8 thermal efficiency ideal 0 7 0 6 0 5 0 4 0 3 0 2 0 1 with regeneration irreversible with regeneration reversible 1 1 5 2 2 5 3 3 5 4 4 5 5 pressure ratio also look at magnitude of compressor work compared to turbine say for pr 2 since these states are the same for w w o regeneration the work is also the same ratiorev workcomp workturb T2s T1 T3 T4 ratioirr T2s pr T1 ratiorev pr T3 T4 pr T2s 0 T2 0 T2 T1 T6 T7 T2 pr T1 T6 T7 pr T7 0 T7s 0 parameters from above power 0 286 T1 300 3 T6 1 2 10 T4 0 maximum reset to insure calculation for these calculations one stage intercooling two compressors t 0 8 pr 1 1 1 2 5 c 0 78 T2s pr N rc pr N power efficiencies from above delta p over p 7 767 range for pressure ratio reversible 11 21 2005 ratioirr 2 54 7 Intercooled Irreversible and reversible N 1 workturb ratioirr pr ratiorev 2 30 5 1 4 workcomp assuming equal pressure ratios across multiple compressors the ratio for each is 1 rc pr N pr N 1 temperature out of all compressors isentropic intercooling occurs along p constant to same T 1 Subsequent compressions T1 are at the same ratio so temperatures after each compression are the same 4 T2s 2 1 331 227 irreversible all compressors T2 pr N T1 T2s pr N T1 c T2 2 1 340 034 p6 over p7 pr pr 1 delta p over p 1 T4 pr T3 pr power 1 T7s pr T6 p6 over p7 pr T4 2 984 402 power 3 T7s 2 1 007 10 T7 pr T6 T6 T7s pr t reversile th ic wnet qH wt wc qH 3 irreversible T3 T4 N 1 T2s T1 T3 T2s T6 T7 N 1 T2 T1 T6 T2 th ic irr pr N th ic rev pr N T7 2 1 046 10 T6 T7 pr N 1 T2 pr N T1 T6 T2 pr N T3 T4 pr N 1 T2s pr N T1 T3 T2s pr N efficiency Brayton cycles thermal efficiency 0 4 0 3 t 0 8 0 2 c 0 78 0 1 delta p over p 7 767 0 intercooled irreversible intercooled reversible 0 1 1 1 5 2 2 5 3 3 5 4 4 5 5 pressure ratio ratiorev workcomp workturb ratiorev pr N 1 T2s T1 ratioirr T3 T4 N 1 T2s pr N T1 workcomp workturb ratioirr pr T3 T4 pr ratiorev 2 29 N 1 T2 T1 T6 T7 N 1 T2 pr N T1 T6 T7 pr ratioirr 2 52 calculations with reheat and multiple turbines are similar and will not be done here see brayton plot mcd for general calculations and plotting 11 21 2005 5