4. Brayton, Ericsson, and Space Powercontents.kocw.net/KOCW/document/2015/chungnam/par… · ·...

1

에너지변환특론Advanced Energy Conversion

Chapter 4. Brayton, Ericsson, and Rankin cycles

교수 박 수 한

Fall semester, 2014

CNU Engine Research Lab.

5

브레이튼사이클 (Brayton cycle)

가스터빈기관의열역학적이상사이클로주로항공기추진이나전력생산에응용됨

1 2 (압축기): 가역단열압축 (reversible adiabatic compression, isentropic compression)

2 3 (연소실): 정압가열 (const.‐pr. heat addition)

3 4 (터빈) : 가역단열팽창 (reversible adiabatic expansion, isentropic expansion)

4 1 (배기): 정압방열 (const.‐pr. heat rejection)

Open‐cycle gas‐turbine engine. Closed‐cycle gas‐turbine engine.

Ideal Brayton cycle

브레이튼 사이클

2


6

브레이튼사이클해석

열효율 (thermal efficiency)

)( 23P23in23 TTChhqq

)/(

)/(

)(

)(,

1TTT

1TTT1

TTC

TTC1

q

q1

232

141

23P

14P

in

outOttoth

)( 14P14out41 TTChhqq

)( 12P12c12 TTChhww

)( 43P43t34 TTChhww

4

3k

1k

4

3k

1k

1

2

1

2

T

T

P

P

P

P

T

T

ratiopressureP

P

P

Pr

4

3

1

2P ;

k1kP

Braytonthr

11

/)(, 0%

20%

40%

60%

80%

0 5 10 15 20 25

Thermal efficiency (%)

Pressure ratio, rP

k = 1.4

Typical pressureratios

for gas turbineengines

브레이튼사이클


7

사이클일 (cycle work)

사이클최고온도는터빈블레이드가견딜수있는최대온도로제한되며, 이에따라사이클압력비도결정됨

사이클최고온도(Tmax )와최저온도(Tmin )사이에서압력비, rP에따라브레이튼사이클의정미일은증가하지만,

rP = (Tmax/Tmin )k/2(k‐1) 에서최대에도달한후감소함

k1kP

k

1k

1

23max r

P

PTT /)(

)()(, 12P43PctBraytonnet TTCTTCwww

1

T

TT

T

T1TC

1

21

3

43P

1P

PT

P

P1TC

k1k

1

21

k1k

3

43P

/)(/)(

1rTr

11TCw k1k

P1

k1k

P3PBraytonnet

/)(/)(

,


3


8

역일비(rbw, back work ratio): 터빈일에대한압축기일의비

사이클일 (cycle work)

브레이튼사이클최대일

0rk

1kTr

k

1kT

dr

w 1k

1k

P1

1k

1k

P3P

Braytonnet

,

1k

1k

P1

1k

1k

P3 rk

1kTr

k

1kT

k1k2P

1

3

min

max rT

T

T

T /)(

)( 1k2

k

min

maxP

T

Tr

k1k

P

k

1k

1

23max r

P

PTT /)(

turbine

comprwssorbw

w

wr



9

가스터빈의발달

터빈입구온도의증가 : 소재및코팅기술, 냉각기술

터보기계효율증가 : 터빈(turbine), 압축기(compressor)

기본사이클개선 : 중간냉각(intercooling), 재생(regeneration), 재열(reheating)

실제가스터빈사이클과의차이

터빈, 압축기의비가역성, 압력손실, 단열손실등

a21

s21compressor

hh

hh

s43

a43turbine

hh

hh


4


10

브레이튼 사이클로 작동하는 발전소가 압력비 8을 가지고 있다. 압축기와 터빈 입구에서 가스 온도는 각각 300 K,

1,300 K일때,공기표준사이클로가정할때압축기와터빈의출구에서가스온도,역일비및열효율을구하여라.

Example: 이상브레이튼사이클

Assumption : 1. Steady‐state process

2. Air‐standard cycle

3. Kinetic and potential energy changes are ignorable (KE = 0, PE = 0)4. Specific heat is not constant (CP const., k const. )

Solve : T

s

2

1

3

4

dP = 0

dP = 0

qin

qout

wt

wc

1,300 K

300 K

rP = 0

K300T1 @from Table A–17 :

3861P

kgkJ19300h

1r

1

.

/.

P1

2

1r

2r rP

P

P

P 091183861rPP P1r2r ..

from Table A–17 : K540T2

kgkJ35544h2 /.



11

kgkJ03800h3543PK780

kgkJ18778h2739PK760

r

r

/.,.

/.,.@

Solve :

K3001T3 ,@ from Table A–17 : 9330PkgkJ973951h 3r3 .,/.,

P3

4

3r

4r

r

1

P

P

P

P 3641

8

9330

r

PP

P

3r4r .

.

from Table A–17 :

K77076076078027393543

27393641T4

)()..(

)..(

kgkJ3778918778187780380027393543

27393641h4 /..)..(

)..(

)..(

Back work ratio, rbw :

kgkJ162441930035544hhw 12c /...

kgkJ660637789973951hhw 43t /...,

%).(..

.3404030

6606

16244

w

wr

t

cbw


5


12

Thermal efficiency :

kgkJ6285135544973951hhq 23in /...,

Solve :

kgkJ184891930037789hhq 14out /...

%).(..

..6424260

62851

162446606

q

ww

q

w

in

ct

in

netth

%).(..

.6424260

62851

184891

q

q1

in

outth

%).(..)(././)(

84444808

11

r

11cf

4140k1kP

th



13

압축기효율이 80 %이고,터빈효율이 85 %라고가정할때,예제 9‐5에서다룬가스터빈사이클의역일비,열효율및

가스터빈출구온도를구하여라.

Example: 실제가스터빈사이클

Solve :

T

s

2s

1

3

4s

qin

qout

1,300 K

300 K

4a2a

For compressor :

a

sc

w

w

kgkJ230580

16244ww

c

sactc /.

.

..,

kgkJ162441930035544hhw 12thc /....,

kgkJ2305hhw 1a2actc /..,

kgkJ39605230519300whh actc1a2 /....,

kgkJ02607hK600

kgkJ52596hK590

/.

/.@

from Table A–17 :

K5985905906005259602607

5259639605T a2

)()..(

)..(


6


14

Solve :

For turbine :

s

at

w

w

kgkJ615156606850ww stactt /....,

%).(..

.

.,

.,., 2595920

61515

2305

w

wr

actt

actcactbw %).(. 3404030

w

wr

t

cbw

kgkJ660637789973951hhw 43t /...,

kgkJ61515hhw a43actt /..,

kgkJ3688061515973951whh actt3a4 /...,.,

kgkJ27888hK860

kgkJ08866hK840

/.

/.@

from Table A–17 :

K8538208408600886627888

0886636880T a4

)()..(

)..(

kgkJ5879039605973951hhq a23actin /...,.,

kgkJ41210230561515www actcacttactnet /....,.,.,

%).(..

.

.,

.,., 6262660

58790

41210

q

w

actin

actnetactth %).(. 6424260

q

w

in

netth



15

재생브레이튼사이클 (regenerative Brayton cycle)

터빈출구의배기열을이용하여연소기입구의압축공기를가열하는재생기(regenerator)또는회수열교환기

(recuperate)를설치한브레이튼사이클

배기가스에너지의일부가사이클공급열에너지로재사용되기때문에동일출력에대한열효율이증가함

재생브레이튼사이클

7


16

재생브레이튼사이클해석

2

1

3

45’

56

T

s

qin

qout

qregen

qsaved = qregen

25actregen hhq .,

2425maxregen hhhhq ,

‐재생열 (regeneration heat) :

‐재생기의유용도 (effectiveness of regenerator) :

24

25regen

hh

hh

)( 45 TT

‐공급열, 방열량및정미일 :

53in hhq

)()( 1253net hhhhw

1216out hhhhq

)(%, 4545regen TTorhh100if



17

재생브레이튼사이클해석

34

12

3

1

43

12

TT1

1TT

T

T1

TT

TT1

/

/

)(

)()()()(,

43P

12P43P

43

1243

in

netB Regen.th

TTC

TTCTTC

hh

hh4h

q

w

‐이론열효율 (for regen = 100%) :

2

1

3

45

6

T

s

qin

qout

qregen

qsaved = qregen

k1kP

k1k

1

2

1

2 rP

P

T

T /)(/)(

k1k

P

k1k

3

4

3

4

r

1

P

P

T

T/)(/)(

k1kP

3

1K1k

P

k1kP

3

1 rT

T1

r11

1r

T

T1 /)(

/)(

/)(

)/(

ratiotempT

T

T

Tr

min

max

1

3T .;

k1kP

TBregenth r

r

11 /)(

., 0%

20%

40%

60%

80%

0 5 10 15 20 25

Thermal efficiency (%)

Pressure ratio, rP

k = 1.4

rT = 5

rT = 4

rT = 3

With regeneration

Without regeneration


8


18

예제 9‐6에서다룬가스터빈기관에유용도 80 %의재생기가설치할경우의열효율을구하여라.

Example:실제재생가스터빈사이클

Solve :

kgkJ657037825973951hhq 53in /...,

T

s

2s

1

3

4s

qin1,300 K

300 K

4a2a

qsaved = qregen

5

3960536880

39605h

hh

hh 5

a2a4

a25regen

..

.

kgkJ3782539605368808039605

hhhh a2a4regena25

/.)..(..

)(

%).(..

.

.,

.,., 6262660

58790

41210

q

w

actin

actnecactth

%).(..

., 9363690

6570

41210

q

w

in

netregenth



19

재열브레이튼사이클 (Brayton cycle with reheating)

터빈출력을증가시키기위해기체를단계적으로팽창시키고그사이에기체를재열시키는브레이튼사이클

Wnet

CompressorTurbine 1

(HP)

Combustionchamber

Reheater

Turbine 2(LP)

1

2 3 a b

4

2

1

3

4a

T

s

qin

qout

qin bTb T3

)()(,, 4ba3LtHtt hhhhwww

)()(

)()()(,

ab23

124ba3

in

netB Reh.th

4h4h

4hhh4h

q

w

재열브레이튼사이클

9


20

재열브레이튼사이클 (Brayton cycle with reheating)

터빈일을 최대로하는중간압력

2

1

3

4a

T

s

qin

qout

bTb = T3

)()(,, 4ba3LtHtt hhhhwww

b

4b

3

a3P

T

T1T

T

T1TC

k1k

b

43

k1k

3

a3P

P

P1T

P

P1TC

/)(/)(

b3 TT

iba PPP

0Pk

1kPP

k

1k

P

1TC

dP

w 1k

1k

ik

1k

4

1k

1k

i

k1k

33P

i

reh

)()(/)(

.

k

1k

i

4k

1k

3

i

P

P

P

P

4

b

a

3

P

P

P

P

재열브레이튼사이클


21

중간냉각브레이튼사이클 (Brayton cycle with intercooling)

압축일을감소시키기위해중간냉각이있는다단압축기를사용하는브레이튼사이클

2

1

3

4

a

T

s

qin

qoutb qout

43t hhw )()(,, b21aHcLcc hhhhwww

23in hhq )()( ba14out hhhhq

)( bab

2

1

a PPP

P

P

P

Compressor 1(LP)

Wnet

Combustionchamber

Turbine

Intercooler

Compressor 2(HP)

1 b

2 3

4a

중간냉각브레이튼사이클

10


22

중간냉각재열재생브레이튼사이클 (Brayton cycle with intercooling, reheating, and regeneration)

4

3

10

5

2

T

s

qin

qregen

qsaved = qregen

qout1

6 8

97

)()(

)()(,

7856

32110

in

outB regen.‐ehrth

4h4h

4h4h

q

q1

3

4

1

2

P

P

P

P

9

8

7

6

P

P

P

P

6491 PPPP ,

중간냉각재열재생브레이튼사이클


23

2단압축 2단팽창이상가스터빈사이클이전체압력비 8을가지고있다.공기는압축기의각단에 300 K,터빈의각

단에 1,300 K으로들어간다.재생기가없는경우와유용도 100 %의재생기가있는경우에대해이가스터빈사이클의

역일비및열효율을구하여라.

Example: 재열및중간냉각가스터빈


2. Air‐standard cycle

3. Kinetic and potential energy changes are ignorable (KE = 0, PE = 0)4. Specific heat is not constant (CV const., k const. )

Solve :

4

3

10

5

2

T

s

qin

qregen

qsaved = qregen

qout1

6 8

97

1,300 K

300 K

Pressure ratio for minimum compression work :

8328P

P

P

P

3

4

1

2 .

8PP8PPPP 111412 8PP 14 /

Pressure ratio for maximum turbine work :

8328P

P

P

P

9

8

7

6 . 8P8PPPPP 666967 /)/(


11


24

923838618PP 1r2r ..

Solve :

from Table A–17 : 3861PkgkJ19300h 1r1 .,/. K300T1 @

kgkJ12411h1534PK410

kgkJ98400h8063PK400

r

r

/..

/..@

from Table A–17 :

K34034001080631534

8063923T2 .

)..(

)..(

kgkJ3140498400984001241180631534

8063923h2 /..)..(

)..(

)..(

from Table A–17 : 9330PkgkJ973951h 6r6 .,/., K3001T6 ,@

11789330P8P 7r7r /./

kgkJ890681h4123PK0201

kgkJ040461h0114PK0001

r

r

/.,.,

/.,.,@

from Table A–17 :

K400610001201144123

114117T7 .,,

).(

)(

kgkJ3305310404610404618906811144123

114117h7 /.,.,).,.,(

).(

)(



25

Solve :

Compression & turbine work :

kgkJ2420819300314042hh2w 12c /.)..()(

kgkJ286853305319739512hh2w 76t /.).,.,()(

4

3

10

5

2

T

s

qprimary

qregen

qsaved = qregen

qout1

6 8

97

1,300 K

300 K

qreheatkgkJ044772420828685www ctnet /...

Heat addition & rejection :

)()( 7846reheatprimaryin hhhhqqq

kgkJ3334133053197395131404973951 /.,).,.,()..,(

0264931404330531hhq 45regen ...,

kgkJ286850264933341qqq regeninregenin /...,,

%).(..

.4303040

28685

24208

w

wr

t

cbw

%).(..,

., 8353580

33341

04477

q

w

in

netreheatth %).(.

.

.,, 6696960

28685

04477regenrehth


12



27

랭킨사이클 (Rankine cycle)

증기동력사이클의열역학적이상사이클

1 2 (펌프) : 가역단열(등엔트로피)압축 (reversible adiabatic compression, isentropic compression)

2 3 (보일러) : 정압가열(연소) (const.‐pr. heat addition)

3 4 (터빈) : 가역단열(등엔트로피)팽창 (reversible adiabatic expansion, isentropic expansion)

4 1 (응축기) : 정압방열 (const.‐or. heat rejection)

T

s

2

1

3

4

qin

qout

wpump

wturbine

랭킨사이클

13


28

랭킨사이클해석

: 가역단열압축 (Pump)

: 정압가열 (Boiler)

2323in hhqq

121221

221212 wzzgvv

2

1hhq )()()(

T

s

2

1

3

4

qin

qout

wpump

wturbine

1212p hhww

)()( 21121p vvPPvw

1Pf1 hh @

1Pf1 vv @

: 가역단열팽창 (Turbine)

4334t hhww

: 정압방열 (Condenser)

1441out hhwq

23

14

in

outRth

hh

hh1

q

q1

,

23

1243

in

netRth

hh

hhhh

q

w

)()(

,

랭킨사이클


29

랭킨사이클로작동하는증기원동소가있다. 수증기가 3 MPa, 350 C 상태로터빈에들어가서 75 kPa의압력으로

응축기에서응축된다. 이사이클의열효율을구하여라.

Example:이상랭킨사이클


2. Kinetic and potential energy changes are ignorable (KE = 0, PE = 0)

Solve :

kPa75P1 @from Table A–5 :

kgm0010370vv

kgkJ44384hh

3f1

f1

/.

/.

P2 = 3 MPa

P4 = 75 kPa

P3 = 3 MPa

T3 = 350 C

P1 = 75 kPa

kgkJ0337500030010370PPvw 121p /.),(.)(

kgkJ4738703344384whh p12 /...

KkgkJ7456sC350T

kgkJ11163hMPa3P

33

33

/.

/.,@from Table A–6 :

랭킨사이클

14


30

Solve :

from Table A–5 : @ P4 = 75 kPa, sg = 7.4558 kJ/kgK > s4 = s3 = 6.745 kJ/kgK Water vapor

886024266

213217456

s

ssx

fg

f44 .

.

..

T

s

2

1

3

4

qin

qout

wpump

wturbine

kgkJ02782hkgkJ44384h

KkgkJ24266sKkgkJ21321skPa75P

fgf

fgf4

/.,,/.

/.,/.@

kgkJ8402202782886044384hxhh fg4f4 /.,).,.(.

Heat and Work :

kgkJ672824738711163hhq 23in /.,..,

kgkJ401824438484022hhq 14out /.,..,

kgkJ37138402211163hhw 43t /..,.,

kgkJ0334438447387hhw 12c /...

Thermal efficiency :%).(.

.,

.., 0262600

67282

0333713

q

w

in

netRth

랭킨사이클


31

실제증기사이클과이상증기사이클의차이

보일러와응축기에서배관내에서유체마찰로인한압력강하가존재함

이러한압력강하를보상하기위해실제사이클에서펌프는이상사이클에서필요한압력보다높게가압해야함

또한터빈과펌프는마찰, 주위로의열손실등으로인한비가역성이존재함

1a2

1s2

a

sp

hh

hh

w

w

s43

a43

s

at

hh

hh

w

w

랭킨사이클

15


32

증기원동소가아래그림에나타낸사이클로작동한다. 펌프의단열효율이 85 %, 터빈의단열효율이 87 %일때이

사이클의열효율과질량유량이 15 kg/s일때정미출력을구하여라.

Example:실제증기동력사이클

For pump :

.

,

act

isenpp

w

w

P2 = 16 MPa

P5 = 15 MPa

T3 = 600 C

P1 = 9 kPa

T1 = 8 C

p = 0.85

P3 = 15.9 MPa

T1 = 35 C

P4 = 15.2 MPa

T4 = 625 C

P6 = 10 kPat = 0.87



Solve :

kgkJ019850

9000160010090

850

PPvww 121

c

isenpactp /.

.

),(.

.

)(,.,

from Table A–5 :

kgm0010100vkPa10P

kgm0010080vkPa57P

3f

3f

/.,@

/.,.@

kgm0010090

0010080001008000101005710

579v

3

1

/.

.)..().(

).(

랭킨사이클


33

Solve :

For turbine :

KkgkJ67966sC600T

kgkJ15833hMPa15P

55

55

/.



804049967

6492067966

s

ssx

fg

f66 .

.

..



fgf

fgf6

/.,,/.

/.,/.@

kgkJ1115213922804081191hxhh fg6f6 /.,).,.(.

isen

actt

w

w . kgkJ227711115215833870hh870ww s65isenttactt /.,).,.,(.)(.,.,

랭킨사이클

16


34

Solve :

For boiler :

kgkJ9397hkgkJ77180hMPa15P C20C40 /.,/.@ @@ from Table A–7 :

kgkJ116093979397771802040

2035h3 /..)..(

)(

)(

kgkJ17123hkgkJ15833hMPa15P C650C600 /.,,/.,@ @@ from Table A–6 :

kgkJ66473158331583317123600650

600625h4 /.,.,).,.,(

)(

)(

Heat and Work :

kgkJ54873116066473hhq 34in /.,..,

Thermal efficiency :

%).(..,

.,, 1363610

54873

22581

q

w

in

netRth

kgkJ2258101922771www ctnet /.,..,

MW918kgkJ22581skg15wmW netnet ./.,/

랭킨사이클


35

응축기압력을낮추는경우

응축기작동압력을낮추면방출되는열이방출되는온도가낮아지고, 정미일이증가되어열효율이증가함

그러나, 터빈출구에서수분함유량이증가(건도감소)되어터빈효율이감소하고터빈날개의부식문제가생김

사이클최고온도를높이는경우

공급열량도증가하나정미일의증가량이더크기때문에사이클의열효율은증가함

그러나, 터빈재료의기계적인성질로인하여사이클최고온도가제한됨 (약 620 C)

Increase in Wnet

Increase in Wnet

:..

..

avgH

avgLth

T

T1

:.. avgLT

corrosionx4 :

:..

..

avgH

avgLth

T

T1

:.. avgHT

4x

랭킨사이클의열효율향상방법

17


36

보일러압력을증가시키는경우

보일러 작동압력을증가시키면, 전체적으로사이클의열효율은증가하나, 터빈출구에서수분함유량이

증가(건도감소)함

Increase

in Wnet

Decrease

in Wnet

:..

..

avgH

avgLth

T

T1

:.. avgHT

4x



37

이상랭킨사이클로작동하는증기원동소가있다. 수증기가 3 MPa, 350 C의상태로터빈을들어가서 10 kPa의

압력으로응축기에서응축될때, 이원동소의열효율을구하여라. 또한증기가 3 MPa, 600 C로과열될때와 15 MPa,

600 C 로과열될때의열효을구하여라.

Example: 보일러의압력과온도가열효율에미치는영향

Solve :

T

s

2

1

3

4

qin

qout

3

4

kgkJ0231000030010100PPvw 121p /.),(.)(

from Table A–5 : kgkJ81191hhkgm0010100vvkPa10P f13

f1 /.,/.,@

kgkJ8319402381191whh p12 /...

KkgkJ7456sC350T

kgkJ11163hMPa3P

33

33

/.


KkgkJ51037sC600T

kgkJ86823hMPa3P

33

33

/.

/.,@

kgkJ141510000150010100PPvw 121p /.),(.)(

kgkJ95206141581191whh p12 /...


18


38

Solve :

KkgkJ67966sC600T

kgkJ15833hMPa15P

33

33

/.



sg = 8.1488 kJ/kgK > s4 = s3 = 7.5103 kJ/kgK Water vapor

sg = 8.1488 kJ/kgK > s4 = s3 = 6.6796 kJ/kgK Water vapor

8128049967

649207456

s

ssx

fg

f64 .

.

..



fgf

fgf6

/.,,/.

/.,/.@

kgkJ11362139228128081191h4 /.,).,.(.

from Table A–5 :

8041049967

6492067966

s

ssx

fg

f64 .

.

..

9149049967

6492051037

s

ssx

fg

f64 .

.

..

kgkJ33802139229149081191h4 /.,).,.(.

kgkJ31152139228041081191h4 /.,).,.(.



39

Solve :

P3 = 3 MPa, T3 = 350 C : kgkJ392128319411163hhq 23in /.,..,

kgkJ394418319111362hhq 14out /.,..,

%).(..,

.,, 4333340

39212

394411

q

q1

in

outRth


kgkJ518828319133802hhq 14out /.,..,

%).(..,

.,, 3373730

04883

518821

q

q1

in

outRth


kgkJ592318319131152hhq 14out /.,..,

%).(..,

.,, 0434300

23763

592311

q

q1

in

outRth


19


40

재열랭킨사이클 (reheat rankine cycle)

랭킨사이클의열효율을향상시키고터빈출구의수분을감소시키기위하여과열증기를 2단의터빈으로

팽창시키고두단사이의증기를재열(reheat)시키는사이클

)()( 4523reheatprimaryin hhhhqqq

)()(,, 6543LtHtt hhhhwww )()(,

4523

16reheatR

hhhh

hh1

재열랭킨사이클


41

이상재열랭킨사이클로작동하는증기원동소가있다. 증기는 15 MPa, 600 C의압력과온도로고압터빈에

들어가서 10 kPa의압력으로응축기에서응축된다. 저압터빈출구에서증기의수분함유량이 10.4%를초과하지않을

경우, 증기가재열되는압력, 사이클의열효율을구하여라. (단증기는고압터빈의입구온도까지재열된다)

Example:이상재열랭킨사이클



Solve :

T

s

2

1

5

6

15 MPa

3

4

10 kPa

from Table A–5 : kgm0010100vvkPa10P 3f1 /.,@

kgkJ141510000150010100PPvw 121p /.),(.)(

kgkJ95206141581191whh p12 /...

kgkJ81191hh f1 /.

KkgkJ67966sC600T

kgkJ15833hMPa15P

33

33

/.



20


42

Solve :

kgkJ13922hkgkJ81191h8960x


fgf6

fgf6

/.,,/..

/.,/.@

from Table A–5 :

kgkJ1335213922896081191h6 /.,).,.(.

KkgkJ3688749967896064920s6 /.)..(.

36687ss

C600T

65

5

.

@

from Table A–6 :

kgkJ96703hKkgkJ31277s


MPa4MPa54

MPa4MPa4

/.,,/.

/.,,/.

@.@

@@

MPa4P5 kgkJ96743h5 /.,

67966ss

MPa4P

34

4

.

@

from Table A–6 :



C400C400

C350C350

/.,,/.

/.,,/.

@@

@@

kgkJ015533093330933521435843677146

5843667966h4 /.,.,).,.,(

)..(

)..(

K53753503504005843677146

5843667966T4 .)(

)..(

)..(



43

Solve :kgkJ1896303155967439520615833hhhhq 4523in /.,)..,()..,()()(

kgkJ314328319113352hhq 16out /.,..,

%).(..,

.,, 0454500

18963

314321

q

q1

in

outReheatR

Pin, Pump = 10 kPa,

Discussion :

Pin, turbine = 15 MPa, Tin, turbine = 600 C

kgkJ237639520615833hhq 23in /.,..,

kgkJ592318319131152hhq 14out /.,..,

%).(..,

.,, 0434300

23763

592311

q

q1

in

outRth

kgkJ875213143218963qqw outinReheatnet /.,.,.,,

kgkJ745215923123763qqw outinnet /.,.,.,

8960xReheat .

8040xRankine .


21


44

재생랭킨사이클 (reheat rankine cycle)

터빈에서팽창하는증기의일부를추출하여열교환기를통해보일러입구의급수온도를상승시켜사이클의

공급열량을줄임으로써열효율을향상시키는사이클

재생기(regenerator) 또는급수가열기(feedwater heater, FWH) : 급수가재생에의해가열되는장치

개방형 급수가열기 (Open feedwater heater) 밀폐형 급수가열기 (Closed feedwater heater)

재생랭킨사이클


45

개방형 급수가열기 (open feedwater heater)

y

1 ‐ y

1

765 mmm 5

7

5

6

m

m

m

m1

5

6

m

my

5

7

m

my1

45in hhq

)()( 17out hhy1q

)()()( 7665t hhy1hhw

)()()(,, 34122p1pp hhhhy1www

)(, 1211p PPvw )(, 3432p PPvw

45

17regenR

hh

hhy11

)()(

,

)()()( 2336 hhy1hhy

26

23

hh

hhy


22


46

밀폐형 급수가열기 (closed feedwater heater)

56

18regenR

hh

hhy11

)()(

,

)()()( 2937 hhy1hhy

)()( 2937

29

hhhh

hhy

y

1 ‐ y

1



47

1개의개방형급수가열기를가지는이상재생랭킨사이클로작동하는증기원동소가있다. 증기는 15 MPa, 600

C의압력과온도로터빈에들어가서 10 kPa의압력으로응축기에서응축되며, 일부증기는 1.2 MPa의압력에서

터빈을떠나서개방형급수가열기로들어간다. 터빈으로부터추출된증기분율과사이클의열효율을구하여라.

Example:이상재생랭킨사이클



Solve :

from Table A–5 : kgm0010100vvkPa10P 3f11 /.,@

kgkJ2011020010010100PPvw 1211p /.),(.)(

kgkJ0119320181191whh 1p12 /...

kgkJ81191hh f1 /.

T

s

2

1

5

7

1

3

4 6

y

1 ‐ yfrom Table A–5 : kgm0011380vvMPa21P 3

f33 /.,.@

kgkJ33798hh f3 /.


23


48

Solve : kgkJ70152001000150011380PPvw 3432p /.),,(.)(

kgkJ03814701533798whh 2p34 /...

KkgkJ67966sC600T

kgkJ15833hMPa15P

55

55

/.


67966ss

MPa21P

56

6

.

.@

from Table A–6 :



C250C250

C200C200

/.,/.

/.,,/.

@@

@@

kgkJ286021816218162629355909683136

5909667966h6 /.,.,).,.(

)..(

)..(

K42182002002505909683136

5909667966T4 .)(

)..(

)..(

8041049967

6492067966

s

ssx

fg

f77 .

.

..

kgkJ13922hkgkJ81191h67966ss


fgf57

fgf6

/.,,/..

/.,/.@

kgkJ31152139228041081191h7 /.,).,.(.

from Table A–5 :



49

Solve :)()()( 2336 hhy1hhy %).(.

..

..72222700

0119322860

0119333798

hh

hhy

26

23

kgkJ176920381415833hhq 45in /.,..,

kgkJ948618119131152227001hhy1q 17out /.,)..,().()()(

%).(..,

.,, 3464630

17692

948611

q

q1

in

outRegenR

Pin, Pump = 10 kPa,

Discussion :

Pin, turbine = 15 MPa, Tin, turbine = 600 C

kgkJ237639520615833hhq 23in /.,..,

kgkJ592318319131152hhq 14out /.,..,

%).(..,

.,, 0434300

23763

592311

q

q1

in

outRth

kgkJ228219486117692qqw outinRegennet /.,.,.,,

kgkJ745215923123763qqw outinnet /.,.,.,

kgkJ17692q Regenin /.,,

kgkJ23763qin /.,


24


50

)()(

)()(,

6745

19regenreheatR

hhhh

hhy11

T

s

2

1

7

9

5

61

3

48

y

1 ‐ y

)()( 6745in hhhhq

)()( 19out hhy1q

)()()()( 988765t hhy1hhhhw

)()()(,, 34122p1pp hhhhy1www

)()()( 2338 hhy1hhy

28

23

hh

hhy

재열‐재생랭킨사이클 (reheat‐regenerative Rankine cycle)

재열-재생랭킨사이클


51

1개의개방형급수가열기와 1개의밀폐형급수가열기, 1개의재열기를가지는이상재열‐재생랭킨사이클로

작동하는증기원동소가있다. 증기는 15 MPa, 600 C의압력과온도로고압터빈에들어가서 4 MPa까지팽창된후,

일부증기는밀폐형급수가열기로들어가고나머지는같은압력에서 600 C까지재열된다. 한편, 저압터빈의일부

증기는 0.5 MPa의압력에서터빈을떠나서개방형급수가열기로추출되며, 나머지는 10 kPa압력으로응축기에서

응축된다. 각터빈으로부터추출된증기분율과사이클의열효율을구하여라.

Example:이상재열‐재생랭킨사이클



Solve :

kgm0010100vvkPa10P 3f11 /.,@

kgkJ490105000010100PPvw 1211p /.)(.)(

kgkJ319249081191whh 1p12 /...

kgkJ81191hh f1 /.

T

s

2

1

10

13

y

3

4

12z1 – y ‐ z

87

5 6

9 11

1 kg

1 ‐ y15 MPa

4 MPa

0.5 MPa

10 kPa


25


52

Solve :

kgm0010930vvMPa50P 3f33 /.,.@

kgkJ83350000040010930PPvw 3432p /.),(.)(

kgkJ9264383309640whh 2p34 /...

kgkJ09640hh f3 /.

kgm0012520vvMPa4P 3f66 /.,@

kgkJ78130004000150012520PPvw 6763p /.),,(.)(

kgkJ21011781340871whh 3p67 /.,..,

kgkJ40871hh f6 /.,

KkgkJ67966ssC600TMPa15P 10959 /.,@

kgkJ15833h9 /.,

52143h30933h77146s58436sMPa4P C400C350C400C35010 .,,.,,.,.,@

kgkJ015533093330933521435843677146

5843667966h10 /.,.,).,.,(

)..(

)..(



53

Solve :

KkgkJ37067sssC600TMPa4P 131211511 /.,@

kgkJ96743h11 /.,

60643h09612h46147s27257sMPa50P C300C250C300C25012 .,,.,,.,.,.@

kgkJ801430961209612606432725746147

2725737067h12 /.,.,).,.,(

)..(

)..(

13922h81191h49967s64920skPa10P fgffgf13 .,,.,..,@

kgkJ733521392249967

649203706781191h13 /.,.,

.

...

)()()( 45610 hhy1hhy

1766092643408714087101553

9264340871

hhhh

hhy

45610

45 .)..,().,.,(

..,

)()(

)()()( 23312 hhzy1hhz

13060319280143

319209640176601

hh

hhy1z

212

23 ...,

)..().()()(


26


54

Solve :

T

s

2

1

10

13

y

3

4

12z

1 – y ‐ z

87

5 6

9 11

1 kg

1 ‐ y15 MPa

4 MPa

0.5 MPa

10 kPa

)()()( 101189in hhy1hhq

kgkJ492120155396743823408089115833 /.,).,.,(.).,.,(

kgkJ8089140871823402101117660hy1yhh 578 /.,).,.().,.()(

56410 hy1yhhy1yh )()(

578 hy1yhh )(

kgkJ4087182340

9264392643408710155317660

y1

hhhhyh 445105 /.,

.

.)..,.,(.)(

)()( 113out hhzy1q

kgkJ34851811917335213060176601 /.,)..,()..(

%).(..,

.,, 2494920

49212

348511

q

q1

in

outRegen‐RehR

kgkJ40871hh 65 /.,



55

Discussion :

%).(., 2494920Regen‐RehR

%).(., 0434300Rth

%).(., 0454500ReheatR kgkJ87521w Reheatnet /.,,

kgkJ74521wnet /.,kgkJ23763qin /.,

kgkJ18963qin /.,

%).(., 3464630RegenR kgkJ22821w Regennet /.,, kgkJ17692q Regenin /.,,

kgkJ49212q Regen‐Rehin /.,, kgkJ14361w Regen‐Rehnet /.,,


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