Ideal Rankine Cycle T 1 2

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Cathleen Cannon
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1 Vapor Poer Cycle We kno that the Carnot cycle i mot efficient cycle operatg beteen to pecified temperature limit. Hoever; the Carnot cycle i not a uitable model for team poer cycle ce: he turbe ha to handle team ith lo quality hich ill caue eroion and ear turbe blade. It i impractical to deign a compreor that handle to phae. It i difficult to control the condenation proce that preciely a to end up ith the deired at pot. Fig. : - diagram for to Carnot vapor cycle. Other iue clude: ientropic compreion to extremely high preure and iothermal heat tranfer at variable preure. hu, the Carnot cycle cannot be approximated actual device and i not a realitic model for vapor poer cycle. Ideal Ranke Cycle he Ranke cycle i the ideal cycle for vapor poer plant; it clude the follog four reverible procee: -: Ientropic compreion Water enter the pump a tate a aturated liquid and i compreed ientropically to the operatg preure of the boiler. -: Cont P heat addition Saturated ater enter the boiler and leave it a uperheated vapor at tate -: Ientropic expanion Superheated vapor expand ientropically turbe and produce ork. -: Cont P heat rejection High quality team i condened the condener M. Bahrami ENSC (S ) Vapor Poer Cycle

It i impractical to deign a compreor that handle to phae. It i difficult to control the condenation proce that preciely a to end up ith the deired at pot. Fig. : - diagram for to Carnot vapor cycle.

2 Q Boiler Q urbe W out W W out Pump W Q out Condener Q out Energy Analyi for the Cycle Fig. : he ideal Ranke cycle. All four component of the Ranke cycle are teady-tate teady-flo device. he potential and ketic energy effect can be neglected. he firt la per unit ma of team can be ritten a: Pump q = 0 pump, = h h Boiler = 0 q = h h urbe q = 0 turbe,out = h h Condener = 0 q out = h h he thermal efficiency of the cycle i determed from: net qout th q q here net q q out turbe, out pump, If e conider the fluid to be compreible, the ork put to the pump ill be: (h h ) = v(p P ) here h = h f@p & v = v = v f@p Deviation of Actual Vapor Poer Cycle from Ideal Cycle A a reult of irreveribilitie variou component uch a fluid friction and heat lo to the urroundg, the actual cycle deviate from the ideal Ranke cycle. he deviation of actual pump and turbe from the ientropic one can be accounted for by utilizg ientropic efficiencie defed a: P a h h a h h a h h h h a M. Bahrami ENSC (S ) Vapor Poer Cycle

he firt la per unit ma of team can be ritten a: Pump q = 0 pump, = h h Boiler = 0 q = h h urbe q = 0 turbe,out = h h Condener = 0 q out = h h he thermal efficiency of the cycle i determed from: net

3 Fig. : Deviation from ideal Ranke cycle. Increag the Efficiency of Ranke Cycle We kno that the efficiency i proportional to: th L H hat i, to creae the efficiency one hould creae the average temperature at hich heat i tranferred to the orkg fluid the boiler, and/or decreae the average temperature at hich heat i rejected from the orkg fluid the condener. Decreag the of Condener Preure (Loer L ) Loerg the condener preure ill creae the area encloed by the cycle on a - diagram hich dicate that the net ork ill creae. hu, the thermal efficiency of the cycle ill be creaed. Increae net P < P Fig. : Effect of loerg the condener preure on ideal Ranke cycle. M. Bahrami ENSC (S ) Vapor Poer Cycle

heat i tranferred to the orkg fluid the boiler, and/or decreae the average temperature at hich heat i rejected from the orkg fluid the condener.

4 he condener preure cannot be loered than the aturated preure correpondg to the temperature of the coolg medium. We are generally limited by the thermal reervoir temperature uch a lake, river, etc. Allo a temperature difference of 0 C for effective heat tranfer the condener. For tance C + (0 C) = C. he team aturation preure (or the condener preure) then ill be P at =. kpa. Superheatg the Steam to High emperature (Increae H ) Superheatg the team ill creae the net ork output and the efficiency of the cycle. It alo decreae the moiture content of the team at the turbe exit. he temperature to hich team can be uperheated i limited by metallurgical conideration (~ 0 C). Increae net Fig. : he effect of creag the boiler preure on the ideal Ranke cycle. Increag the Boiler Preure (Increae H ) Increag the operatg preure of the boiler lead to an creae the temperature at hich heat i tranferred to the team and thu raie the efficiency of the cycle. Increae net max Decreae net Fig.: he effect of creag the boiler preure on the ideal cycle. M. Bahrami ENSC (S ) Vapor Poer Cycle

Superheatg the Steam to High emperature (Increae H ) Superheatg the team ill creae the net ork output and the efficiency of the cycle. It alo decreae the moiture content of the team at the turbe exit.

5 Note that for a fixed turbe let temperature, the cycle hift to the left and the moiture content of the team at the turbe exit creae. hi undeirable ide effect can be corrected by reheatg the team. he Ideal Reheat Ranke Cycle o take advantage of the creaed efficiencie at higher boiler preure ithout facg the exceive moiture at the fal tage of the turbe, reheatg i ued. In the ideal reheatg cycle, the expanion proce take place to tage, i.e., the high-preure and lo-preure turbe. High-preure turbe Lo-preure turbe Boiler High-P urbe Lo-P urbe P = P = P reheat Condener Pump Fig. : he ideal reheat Ranke cycle. he total heat put and total turbe ork output for a reheat cycle become: q q turbe, out primary q reheat H P turbe h h h h h h h h LP turbe he corporation of the gle reheat a modern poer plant improve the cycle efficiency by to percent by creag the average temperature at hich heat i tranferred to the team. he Ideal Regenerative Ranke Cycle he regeneration proce team poer plant i accomplihed by extractg (or bleedg) team from turbe at variou tage and feed that team heat exchanger here the feedater i heated. hee heat exchanger are called regenerator or feedater heater (FWH). FWH alo help removg the air that leak at the condener (deaeratg the feedater). here are to type of FWH, open and cloed. M. Bahrami ENSC (S ) Vapor Poer Cycle

In the ideal reheatg cycle, the expanion proce take place to tage, i.e., the high-preure and lo-preure turbe.

6 Open (Direct Contact) Feedater Heater An open FWH i baically a mixg chamber here the team extracted from the turbe mixe ith the feedater exitg the pump. Ideally, the mixture leave the heater a a aturated liquid at the heater preure. Boiler Pump II Open FWH Pump I y Condener Fig. 8: he ideal regenerative Ranke cycle ith an open FWH. Ug Fig. 8, the heat and ork teraction of a regenerative Ranke cycle ith one FWH can be expreed per unit ma of team flog through the boiler a: q q pump, here y m out h turbe PumpI yh h, out h h yh h y h / m v P P v P P PumpI PumpII PumpII hermal efficiency of the Ranke cycle creae a a reult of regeneration ce FWH raie the average temperature of the ater before it enter the boiler. Many large poer plant have a many a 8 FWH. Cloed Feedater Heater In cloed FWH, heat i tranferred from the extracted team to the feedater ithout any mixg takg place. hu; to tream can be at different preure, ce they don t mix. In an ideal cloed FWH, the feedater i heated to the exit temperature of the extracted team, hich ideally leave the heater a a aturated liquid at the extraction preure. M. Bahrami ENSC (S ) Vapor Poer Cycle

8, the heat and ork teraction of a regenerative Ranke cycle ith one FWH can be expreed per unit ma of team flog through the boiler a: q q pump, here y m out h turbe PumpI yh h, out h h yh h y h / m v

7 9 8 Boiler Mixg chamber 9 Cloed FWH urbe 8 Condener Pump II Pump I Fig.9: Ideal regenerative Ranke cycle ith a cloed FWH. Open FWH Cloed FWH imple expenive good heat tranfer characteritic brg feedater to the aturation tate a pump i required for each FWH more complex (ternal tubg) le effective (no mixg) do not require a pump for each FWH M. Bahrami ENSC (S ) Vapor Poer Cycle

Open FWH Cloed FWH imple expenive good heat tranfer characteritic brg feedater to the

8 Cogeneration Many ytem and dutrie require energy put the form of heat, called proce heat. Some dutrie uch a chemical, pulp and paper rely heavily on proce heat. he proce heat i typically upplied by team at to atm and 0 to 00 C. hee plant alo require large amount of electric poer. herefore, it make economical and engeerg ene to ue the already-exitg ork potential ( the team enterg the condener) to ue a proce heat. hi i called cogeneration. urbe Boiler Expanion valve Pump II Proce heater Condener 8 Pump I Fig. 0: A cogeneration plant ith adjutable load. In the cogeneration cycle hon the above figure, at time of high demand for proce heat, all the team i routed to the proce heatg unit and none to the condener. Combed Ga Vapor Poer Cycle Ga-turbe cycle typically operate at coniderably higher temperature than team cycle. he maximum fluid temperature at the turbe let i about 0C for modern team poer plant, but over C for ga-turbe poer plant. It i over 00C at the burner exit of turbojet enge. It make engeerg ene to take advantage of the very deirable characteritic of the ga-turbe cycle at high-temperature and to ue the high temperature exhaut gae a the energy ource for the bottomg cycle a a team poer cycle. hi i called combed cycle. Combed cycle can achieve high thermal efficiencie, ome of recent one have η about 0%. M. Bahrami ENSC (S ) Vapor Poer Cycle 8

herefore, it make economical and engeerg ene to ue the already-exitg ork potential ( the team enterg the condener) to ue a proce heat. hi i called cogeneration.

Combustion chamber. Fig.1: Schematic for an open gas-turbine cycle.

Combustion chamber. Fig.1: Schematic for an open gas-turbine cycle. Open Ga urbine Cycle Fuel Combution camber urbine Saft Compreor W net Air Combution product Woring rincipal Fig.: Scematic for an open ga-turbine cycle. Fre air enter te compreor at ambient temperature