Special Topic: Binary Vapor Cycles

Transcription

1 0- Special opic: Bary Vapor ycle 0- Bary poer cycle i a cycle ic i actually a combation o to cycle; one te ig temperature region, and te oter te lo temperature region. It purpoe i to creae termal eiciency. 0- onider te eat excanger o a bary poer cycle. e orkg luid o te toppg cycle (cycle A enter te eat excanger at tate and leave at tate. e orkg luid o te bottomg cycle (cycle B enter at tate and leave at tate. Neglectg any cange ketic and potential energie, and aumg te eat excanger i ell-ulated, te teady-lo energy balance relation yield u, A E 0 (teady E Eytem 0 + E e B A B e E + A i i B or A ( B ( 0- Steam i not an ideal luid or vapor poer cycle becaue it critical temperature i lo, it aturation dome reemble an verted V, and it condener preure i too lo. 0- Becaue mercury a a ig critical temperature, relatively lo critical preure, but a very lo condener preure. It i alo toxic, expenive, and a a lo entalpy o vaporization. 0- In bary vapor poer cycle, bot cycle are vapor cycle. In te combed ga-team poer cycle, one o te cycle i a ga cycle.

2 0- Revie roblem 0- It i to be demontrated tat te termal eiciency o a combed ga-team poer plant cc can be expreed a cc g + g ere g W g / i n an d W / g, are te termal eiciencie o te ga and team cycle, repectively, and te eiciency o a combed cycle i to be obtaed. Analyi e termal eiciencie o ga, team, and combed cycle can be expreed a cc Wtotal Wg g g, W g, g, ere i te eat upplied to te ga cycle, ere i te eat rejected by te team cycle, and ere g, i te eat rejected rom te ga cycle and upplied to te team cycle. Ug te relation above, te expreion g + g cc g, g, g + g + g, g, g, g, g, can be expreed a ereore, te proo i complete. Ug te relation above, te termal eiciency o te given combed cycle i determed to be cc g + g g, 0- e termal eiciency o a combed ga-team poer plant cc can be expreed term o te termal eiciencie o te ga and te team turbe cycle a +. It i to be on tat te value o cc i greater tan eiter o or. Analyi By actorg term, te relation cc g + g g + ( g > g g oitive ce < or cc g + g + g ( > g oitive ce < cc g + g cc g g can be expreed a u e conclude tat te combed cycle i more eicient tan eiter o te ga turbe or team turbe cycle alone.

3 0-0- A team poer plant operatg on te ideal Ranke cycle it reeatg i conidered. e reeat preure o te cycle are to be determed or te cae o gle and double reeat. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a Sgle Reeat: From te team table (able A-, A-, and A-, x 0 ka 0. + x + x 00 0 ka (b Double Reeat : Ma 00 x and x 00 g g kj/kg K ( 0.(. ( 0.(. SINGLE Ma 0 ka. kj/kg. kj/kg K 00 DOUBL Ma 0 ka Any preure x elected beteen te limit o Ma and. Ma ill atiy te reuirement, and can be ued or te double reeat preure.

4 E A geotermal poer plant operatg on te imple Ranke cycle ug an organic luid a te orkg luid i conidered. e exit temperature o te geotermal ater rom te vaporizer, te rate o eat rejection rom te orkg luid te condener, te ma lo rate o geotermal ater at te preeater, and te termal eiciency o te Level I cycle o ti plant are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a e exit temperature o geotermal ater rom te vaporizer i determed rom te teadylo energy balance on te geotermal ater (bre, bre,0,000 Btu/ brec p ( (, lbm/(.0 Btu/lbm F(. F F (b e rate o eat rejection rom te orkg luid to te air te condener i determed rom te teady-lo energy balance on air, air airc p ( (,,00 lbm/( 0. Btu/lbm F(. MBtu/. F (c e ma lo rate o geotermal ater at te preeater i determed rom te teady-lo energy balance on te geotermal ater, geo,0,000 Btu/ geo (d e rate o eat put i and geo geo,0 c p ( (.0 Btu/lbm F( lbm/.0. F +, 0, ,, 000 vaporizer reeater, 0, 000 Btu / en, W W t 00 0 kw 0 kw. Btu 0.%,0,000 Btu/ kw

5 0-0- A team poer plant operate on te imple ideal Ranke cycle. e turbe let temperature, te poer put, te termal eiciency, and te mimum ma lo rate o te coolg ater reuired are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a From te team table (able A-, A-, and A-, (b and v v u, p, ka v ( ( m /kg( 000. ka.0 ka + p, ka ka. kj/kg m /kg kj/kg.0 kj/kg.0 kj/kg Ma. kj/kg 0. t W kj ka m... kj/kg kj/kg. 0.. kj/kg. kj/kg.%. kj/kg ( 0.( 0,000, kj/ kj/ t Ma. ka (c e ma lo rate o te coolg ater ill be mimum en it i eated to te temperature o te team te condener, ic i 0., cool c W 0,000, 0, kj/ 0, kj/ (. kj/kg ( 0.. kg/

6 0-0- A team poer plant operatg on an ideal Ranke cycle it to tage o reeat i conidered. e termal eiciency o te cycle and te ma lo rate o te team are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a From te team table (able A-, A-, and A-, en, u, (b v v ka v( ( m /kg(,000 ka.0 ka + p, Ma 00 Ma Ma Ma 00 ka x. kj/kg m /kg kj ka m kj/kg Ma 00 t 0. kj/kg.0 kj/kg K 00. kj/kg. kj/kg. kj/kg K. kj/kg. kj/kg. kj/kg K g. + x. + ( + ( + ( g.. 0. kj/kg kj/kg ka ( 0.0(.0. kj/kg Ma Ma kj/kg W. kj/kg.% 0. kj/kg 0,000 kj/. kj/kg. kg/ Ma

7 0-0- An 0-MW team poer plant operatg on a regenerative Ranke cycle it an open eedater eater i conidered. e ma lo rate o team troug te boiler, te termal eiciency o te cycle, and te irreveribility aociated it te regeneration proce are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi Boiler II Open urbe -y y ondener I 0 Ma 0. Ma y 0 ka -y (a From te team table (able A-, A-, and A-, v v ka.kj/kg v( / p kj ( 0.000m /kg( 00 0ka / ( 0. pi, 0. Ma at. liuid v v m /kg ka m 0.kJ/kg kJ/kg Ma 0.0 kj/kg 0.000m /kg v ( / p kj ( m /kg( 0, ka /( 0. ka m 0. kj/kg kj/kg pii, 0 Ma 00 x 0. Ma. kj/kg. kj/kg K g.0 + x g ( 0.( 0.0. kj/kg ( ( 0.0(.. kj/kg..

8 0- x 0 ka g. + x g.+ ( 0.(. 0. kj/kg ( ( 0.0(.. kj/kg. 0. e raction o team extracted i determed rom te teady-lo energy balance euation applied to te eedater eater. Notg tat W ke pe 0, E E E E E 0 (teady ytem 0 ( y ( i i mee m + m m y + ere y i te raction o team extracted rom te turbe ( /. Solvg or y, en, and y kj/kg ( y( ( 0.(.. W m... kj/kg 0,000 kj/. kg/. kj/kg (b e termal eiciency i determed rom Alo, t 0. Ma. 0. Ma. kj/kg.%. 0 ka. kj/kg K.0 kj/kg K 0. kj/kg K. kj/kg en te irreveribility (or exergy detruction aociated it ti regeneration proce i i regen 0gen 0 + mee mii 0 urr L [ y ( y ] ( 0 K [.0 ( 0.(. ( 0.( 0. ]. kj/kg 0

9 0-0- An 0-MW team poer plant operatg on an ideal regenerative Ranke cycle it an open eedater eater i conidered. e ma lo rate o team troug te boiler, te termal eiciency o te cycle, and te irreveribility aociated it te regeneration proce are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi Boiler II Open urbe -y y ondener I 0 Ma 0. Ma y 0 ka -y (a From te team table (able A-, A-, and A-, v v 0 0 ka. kj/kg m v ( ( m /kg( 00 0 ka + pi, 0. Ma at.liuid v v pii, /kg kj ka m Ma 0.0 kj/kg m ( ( m /kg( 0, ka v + pii, 0 Ma Ma x 0 ka x. kj/kg. kj/kg K 0.0 kj/kg /kg kj ka m kj/kg g.0 + x ( 0.( g. + x.+ g g 0. kj/kg. kj/kg ( 0.(. 0. kj/kg

10 0- e raction o team extracted i determed rom te teady-lo energy euation applied to te eedater eater. Notg tat W ke pe 0, E E E 0 (teady ytem 0 E ( y ( i i mee m + m m y + E ere y i te raction o team extracted rom te turbe ( /. Solvg or y, en, and y kj/kg ( y( ( 0.( 0.. W m...0 kj/kg 0,000 kj/. kj/kg. 0 kg/ (b e termal eiciency i determed rom Alo, t. kj/kg.0%. kj/kg. kj/kg 0. 0 ka.0 kj/kg K 0. kj/kg K. kj/kg en te irreveribility (or exergy detruction aociated it ti regeneration proce i i regen 0gen 0 + mee mii 0 urr L [ y ( y ] ( 0 K [.0 ( 0.(. ( 0.( 0. ].0 kj/kg 0

11 0-0- An ideal reeat-regenerative Ranke cycle it one open eedater eater i conidered. e raction o team extracted or regeneration and te termal eiciency o te cycle are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a From te team table (able A-, A-, and A-, v v ka. kj/kg v ( ( m /kg( 00 ka kj ka m 0. kj/kg kj/kg pi, 0. Ma at. liuid v v Ma /kg 0. kj/kg m /kg v( ( m /kg( 0, ka pii, kj ka m 0. kj/kg kj/kg pii, 0 Ma 00.0 Ma.0 Ma 00. kj/kg. kj/kg K. kj/kg. kj/kg. kj/kg K 0. Ma 0. kj/kg. 0. ka 0. x g. + x. + g Boiler II ( 0.(.. kj/kg Open 0 Ma 0. Ma ka I y Ma urbe -y onden. e raction o team extracted i determed rom te teady-lo energy balance euation applied to te eedater eater. Notg tat W ke pe 0, E E E 0 (teady ytem 0 E ( y ( i i mee m + m m y + E ere y i te raction o team extracted rom te turbe ( /. Solvg or y, y (b e termal eiciency i determed rom ( ( ( ( ( y( ( 0.0(... kj/kg. kj/kg and t.%. kj/kg. kj/kg

12 0-0- A nonideal reeat-regenerative Ranke cycle it one open eedater eater i conidered. e raction o team extracted or regeneration and te termal eiciency o te cycle are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi Boiler urbe II Open I y -y ondener y -y (a From te team table (able A-, A-, and A-, v ka. kj/kg m v ( ( m /kg( 00 ka pi, 0. Ma at. liuid v 0. Ma /kg pi, kj ka m 0. kj/kg Ma 0. kj/kg m /kg ( ( m /kg( 0, ka pii, v kj ka m 0. kj/kg kj/kg pii, 0 Ma 00.0 Ma. kj/kg. kj/kg K. kj/kg ( ( 0.(.. kj/kg..

13 0-.0 Ma Ma ka x. kj/kg. kj/kg K 0. kj/kg. kj/kg (. ( 0.( ( 0.(.. 0. (. ( 0.(.. g + x g. kj/kg. kj/kg e raction o team extracted i determed rom te teady-lo energy balance euation applied to te eedater eater. Notg tat W ke pe 0, E E E E E 0 (teady ytem 0 ( y ( i i mee m + m m y + ere y i te raction o team extracted rom te turbe ( /. Solvg or y, y (b e termal eiciency i determed rom and t ( + ( ( (... kj/kg ( y( ( 0.(.. 0. kj/kg 0. kj/kg.%. kj/kg

14 A team poer plant operate on an ideal reeat-regenerative Ranke cycle it one reeater and to eedater eater, one open and one cloed. e raction o team extracted rom te turbe or te open eedater eater, te termal eiciency o te cycle, and te poer put are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi Boiler loed II Hig- urbe (a From te team table (able A-, A-, and A-, v v pi, 0 Open I y. kj/kg z I m /kg v ( ( m /kg( 00 ka Lo- urbe -y-z ondener kj ka m 0.0 kj/kg ka pi, 0. kj/kg Ma at.liuid v 0. Ma m /kg pii, v( kj ( m /kg(, ka ka m.0 kj/kg kj/kg pii, 0. Ma at.liuid v v 0 0 Ma 00.0 Ma.0 Ma Ma. 0. Ma 0. kj/kg 0. kj/kg m /kg Ma 0. Ma ( + ( m /kg(, ka. kj/kg. kj/kg K v. kj/kg. kj/kg K Ma y 0 0. Ma z ka - y - z kj ka m

15 0-0. Ma 0 0. Ma 0 ka 0 x 0. kj/kg 000. kj/kg 0.0 g + x. +. kj/kg. 0.. g ( 0.0(.0 e raction o team extracted i determed rom te teady-lo energy balance euation applied to te eedater eater. Notg tat W ke pe 0, E 0 (teady E Eytem 0 E i i E e e ( ( y( ( ere y i te raction o team extracted rom te turbe ( /. Solvg or y, y For te open FWH, y E + E E + ( y z + z ( i i E E (teady ytem e e ere z i te raction o team extracted rom te turbe ( / at te econd tage. Solvg or z, z 0 ( y( 0.. ( 0.0( (b ( + ( 0 (.. + (. 0.. kj/kg ( y z( ( (.0. and t. 0.. kj/kg 0. kj/kg.%. kj/kg (c W m ( kg/(. kj/kg, kw kj/kg

16 0-0- A cogeneration poer plant i modiied it reeat and tat produce MW o poer and upplie MW o proce eat. e rate o eat put te boiler and te raction o team extracted or proce eatg are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a From te team table (able A-, A-, and 0 Ma 00. kj/kg 0. kj/kg. kj/kg. kj/kg K Boiler roce eater urbe Ma. kj/kg II I Ma. kj/kg 00. kj/kg K. 0. x 0. g. ka Ma + x g. + ( 0.(. Ma. kj/kg e ma lo rate troug te proce eater i proce,000 kj/. kg/ ka (. 0. kj/kg Alo, W ( + ( ( + (.( or, 000 kj/ ( ( ( It yield. kg/ and m.. 0. kg/ Mixg camber: E E E 0 (teady 0 or, en, ytem E E m m m m + m i i e e + ( 0.(. + (.( 0.. ( + ( (. kg/(. 0.0 kj/kg + ( 0. kg/(,00 kw (b e raction o team extracted or proce eatg i. kg/ y.%. kg/ total 0.0 kj/kg.. kj/kg ondener