Calculation of power output and total efficiency for a closed gas turbine cycle, one axis.

Transcription

1 alculaion of power oupu and oal efficiency for a closed as urbine cycle, one axis. In his cycle hea is ransferred o air in a closed cycle by heain fro a coal-fired boiler. he cycle has wo copressors wih iner-coolin, reeneraor and afer-cooler (before air enerin he low pressure copressor). Sar wih drawin a connecion schee for he cycle. opressor pressure raio (π) (boh). Inle eperaure each copressor º Inle eperaure urbine 0º Lowes pressure in cycle 8 bar Isenropic efficiency copressor (boh) sk 0. 8 Isenropic efficiency urbine s ressure loss boiler (air heain) % ressure loss, inercooler % ressure loss, reeneraor (boh sides) % ressure loss, afer cooler % Effeciveness of reeneraor* 80 % Generaor efficiency Mechanical efficiency Mass flow in he cycle 8 k/s he cobusion efficiency is 8% and is defined as he raio of uilized hea in he boiler o fu supply alculae he power oupu oal ecrical efficiency. *his is he sae as eperaure efficiency for hea exchaners Appendix : Specific hea raio as funcion of as conen and eperaure for flue ases Noenclaure: κ raio of specific hea ( p / V ) π pressure raio x as conen in flue ases eperaure in º eperaure in. Subscrips: s isenropic copressor urbine reeneraor ean value (averae)

2 Appendix : Specific hea raio as funcion of as conen and eperaure for flue ases abler and diara pae, version of year 998 by L. Weser, Sweden, or any oher arbirary handbook wih heral enineerin forulas and ables.

3 HINS: Hin (-p): he layou of he as urbine is shown in he fiure. 8 Boiler -: opression no -: Iner coolin -: opression no -: Air heaer fro G exhaus -: Hea exchane wih coal-fired boiler -: Expansion in urbine -8: oolin of G exhaus air- Reeneraion o copressed air 8-: Afer coolin of G exhaus before enerin he copressor Hin (-p): he power oupu is calculaed fro ( * )* where he power oupu/inpu is he assflow*he specific hea for air*eperaure difference. Hin (-p): he eperaure increase in he copressor can be calculaed as κ ( ) κ [ π ] S Reeber ha κ is a funcion of he eperaure (appendix ), hus you have o ierae beween κ and. Sar assuin ha κ is.0 for he firs copressor. he sae procedure has o be done for he urbine when calculain he eperaure decrease.

4 Soluion ) he fiure shows he layou of he closed as urbine 8 Boiler -: opression no -: Iner coolin -: opression no -: Air heaer fro G exhaus -: Hea exchane wih coal-fired boiler -: Expansion in urbine -8: oolin of G exhaus air- Reeneraion o copressed air 8-: Afer coolin of G exhaus before enerin he copressor he cycle in a -s diara is presened bow: 8 bar de 8 s

5 he power oupu fro he urbine can be calculaed as he urbine power inus he copressors power: ( * )* ower ass flow * enhalpy difference Enhalpy difference c (ean value for eperaure inerval)* eperaure difference c ( * c,, c *,? * * * c * ) eperaure increase in he copressor π + 98 S S copressorpressureraio. κ specifichearaio [ π κ ( ) κ ] copressorisenropicefficiency 0.8 In his equaion we have wo unknowns; we do no know κ or he eperaure. However κ is a funcion of he eperaure increase, so we have o sar an ieraion process (appendix ) Assue κ. (x 0, air a low ep), hen calculae and read he new κ value, ierain ill he eperaures difference is no bier han (.. ) Wih, and x 0 we find a new κ. κ.9 0 O! hen We can find he specific hea pk for air wih an averae eperaure of. as For exaple abler and diara pae, version of year 998 by L. Weser, Sweden, or any oher arbirary handbook wih heral enineerin forulas and ables.

6 008J / k,.0kj / k c, eperaure increase in urbine : Here we have o ake ino reards he pressure losses in he cycle, i.e. he urbine pressure raio is no equal o he copressor raio, as we loose pressure in he hea exchaners. S * κ ( ) κ π.* 0.9*.* 0.9* * I pressurosscoefficien S p urbineisenropicefficiency 0.90 π urbinepressureraio * π * ( ξ I ) * π * ( ξ p * * ( I ) ( I A )( ξ ) boiler ) Aain we have one equaion and unknowns, so we ierae κ for expandin flue ases (in urbine) and eperaure decrease, sarin wih assuin κ. (reeber ha he as conen x0 in his confiuraion, we are workin wih a closed air cycle) 0.90*9[ ] 8 0 / κ [ x 0,08 ]. 8 0 O! he Specific hea p for he expandin flue ases: ( x 0;0 )

7 c 09J / k,.09kj / k, Elecrical ower: ass flow 8 k/s (8*.09 * 8 * kW. MW oal efficiency: useful o fu * c cob 0.8 0? o ( *8*.0*0) * 0.98 ) * cob Hea exchaner efficiency θ + heaed air/ inle ep. difference ( 9) /, J k 00 o 0. 8*.08*(0 ) * 0.8 Low efficiency due o hih flue as eperaure and low urbine inle eperaure. he eperaure is liied because of he air coolin of boiler ubes.