1

phase two 0 W phase single

0Q Phase cu t refrigeran

cs steam ch Gas Real cT f(T)c,c dy Unstea

c v cc,c Open ion Refrigeratcp Gas Ideal Closed Power

FLUID SYSTEM PROCESS G WORKIN MICTHERMODYNA CYCLE

vp

vp

=====

==

===

0Qc,hc,p phase 2 ts,RefrigeranOpen on Refrigeratn CompressioVapor 0Qc,p Air Open ion Refrigerat Brayton Reversed

on regenerati reheat superheat

cQ c,p phase 2 steam, Open Power Rankine0Qc,p Air Open Power Brayton

0Q c,vc,p Air Closed Power Dual0Qc,vc,p Air Closed Power Diesel

0Qc,v Air Closed Power Otto0Qc,vc,p Air Closed Power Lenoir

=====

====

======

=====

ENERGY SYSTEM CYCLESCONCEPTS

SystemPropertiesState PointProcessCycle

2

( )( )( )( )14out

43out

23in

12in

shaft

2

hhmQ 0, W1,4 Process,Condenser hhm W0,Q, 43 Process, Expansion hhmQ 0, W, 32 Process,Boiler hhm W0,Q 2,1 Process, Pump

Wgz)2

Vpv(umQ

Processesfor Equation Energy FlowSteady spacein region -SystemOpen Flow,Steady

−==⇒−==⇒−==⇒−==⇒

++++∆×=

boiler

condenser

pumpexpander

1

2

3

4 1

2

3

4

T

s

SIMPLE RANKINE CYCLE

in

cycle

in

netcycle

cyclecycle

cyclecycle

Q

W

QW

WQ

δWδQ

Cyclesfor LawFirst

∑

∑∑

∫∫

==η

=

=

3

T

s

CARNOT CYCLE WITH WATER

inQ

netWηη

Q

HT

LT

area maximumkJ/kg 740.W

% 41.9ηC 240T

:at maximum W

QηWΔSTQ

TT1η

net

Carnot

net

innet

Hin

H

LCarnot

==

=

×==

−=

25 C

374.1 C

4

1

2

3

4

T

s

1

2

3

4

s

5

boiler

condenser

pump

1

2

3

4

boiler

condenser

pump

1

23

4

turbines 6

5

6

SUPERHEAT RANKINE CYCLE

REHEAT RANKINE CYCLE

5

( ) ( )

( ) ( )

∫=

===

−=+−−=

++=

+=+=

==

+=+=

vdph

vdpdh0TdsQ process, adiabatican for

vdpdhTdspdvvdppdvdhTds

du,for ngsubsitiutivdppdvdudh

aldifferentiexact an ish ,definitionproperty h pvuh

pdvduTdsdw, and dqfor ngsubsitiuti

orkBoundary W pdvdwLaw Second Tdsdq

dwdudqLawFirst W ΔUQ

( )( )

mfm

f

m

f

2m

2f

3

1212

BTU/lb044.lbft 778

BTU1lb

lbft 6.34w

fluid) of(ft ,lb

lbft 6.34

ft1

ftlb62.4

ftlb2160

w

62.4lb/ft144psi/psf15psia30psiaw

ppvhhw

=×=

==

×−=

−=−=

Example: water pumpedfrom 15 psia to 30 psia

Example: water pumpedfrom 100 kPa to 300 kPa

( )( )

kJ/kg kPa,kgm .2086w

kPa 001kPa 300/kgm .0010432w

ppvw

3

312

=

−×=

−=

6

9-29 ex

1

2

4

5

6

7

8

9

T

s

10

%80=η

%95=η

A steam power plant runs on a reheat cycle and produces 80 MW. The turbine inlet conditions are 10 MPA , 500 C and 1 MPA, 500 C. The condenser operates at 10 kPa. The efficiency of the turbines is 80%. The efficiency of the pump is 95%. Determine: a) the turbine exit conditions b) the cycle efficiency and c) the mass flow rate of the steam.

3

10 MPa

1 MPa

10 kPaboiler

condenser1

35

7

turbines

8

10

79-29 ex

kPa 10 107.7642 kPa 0 1 9

7.7642 3479.1 MPa 1 500 8 MPa 1 7

6.5995 MPa 1 66.5995 3375.1 MPa 10 500 5

MPa 10 4 MPa 10 3

.6492 MPa 10 2.001010 .6492 191.81 kPa 10 45.81 1 v s h p TPt

1

2

4

5

6

7

8

9

T

s

10

%80=η

%95=η

A steam power plant runs on a reheatcycle and produces 80 MW. The turbineinlet conditions are 10 MPA , 500 C and 1 MPA,500 C. The condenser operates at 10 kPa. The efficiency of the turbines is 80%. The efficiency of the pump is 95%. Determine: a) the turbine exit conditions, b) the cycleefficiency and c) the mass flow rate of the steam.

3

10 MPa

1 MPa

10 kPa

8

9-29 exJ/kg11.2784h6.5850 2777.1 179.886.5995ss

6.6956 2828.3 200s h T

ss MPa, 1 @

kJ/kg 10.71W.95

10)(10,000.001010ηΔpvW

kJ/kg 203.95h

11.14191.81Whh

kJ/kg 11.14.95

191.81202.39W

.95hh

.95W

W

kJ/kg 202.39h.5685 176.37 40

.6492ss .8260 259.43 60

s h T 10MPap 7,-A Table water,liquid compressed

6

56

56

pump

pump

3

lpumpactura13

actual pump

12ideal pumpactual pump

2

12

2

=

==

=

=

−×=

×=

=

+=+=

=−

=

−==

=

==

=

( )( )

( )( )

C)902519.8,(h kJ/kg 2664.51h

2460.863479.1.83479.1hhh.8hh

.8hhhhη

kJ/kg 2460.862392.8x191.81h

.94877.4996

.64927.7642s

ssx

ss kPa, 10 @kJ/kg 2902.03h

2784.113373.7.83373.7hhh.8hh

hhhhη

Osat10

10

98810

98

108

9

fg

f8

89

7

7

6557

65

75

≈==

−×−=−×−=

=−−

=

=×+=

=−

=−

=

==

−×−=−×−=

−−

=

9

( ) ( )( ) ( )

( ) ( )( ) ( )( ) ( )

kg/sec 62.721275.527

ec80,000kJ/s WorkSpecific

WorkTotalm

34.05%3748.221276.38

QWη

1275.522472.73748.22WQQ

dWdQ

kJ/kg 1276.3811.28814.11472.74W11.282664.513479.12902.033375.1W

WhhhhWkJ/kg 2472.7191.812664.51hhQ

kJ/kg 3748.22 Q203.953375.12902.033479.1Q

hhhhQ

in

netcycle

netoutin

pump10875

110out

in

in

3578in

===

===

=−

=−

=

=−+=−−+−=

−−+−=

=−=−==

−+−=−+−=

∫ ∫

9-29 ex

10

EES Model

11

12

Boiler

6

8

2

7

15

1

2

5

3

8

7

6

turbine

open feedwater heater

condenser

REGENERATION RANKINE CYCLEopen feed water heater

T

s

( )( ) ( )

( ) ( ) ( )( ) ( ) ( )

( )∑∑ =

×=×+×−

−×−+−×=

−×+−×−=−×−=

−×=

cyclecycle

372

8776turbine

3512pump

18out

56in

WQh1hxhx1

BalanceEnergy Heater hhx1hh1W

hh1hhx1Whhx1Q

hh1Qx

(1-x)

3

13

A steam power plant runs on a regenerative cycle and produces 80 MW. The turbine

inlet conditions are 10 MPA , 550 C. Steam is extracted at .8 MPA to feed an open feed

water heater the rest is reheated to 500 C. The condenser operates at 10 kPa.

The efficiency of the turbines is 100%. The efficiency of the pump is 100%. Determine:

a) the turbine exit conditions, b) the cycle efficiency and c) the mass flow rate

of the steam.

14

7.8692 kPa 10 87.8692 3481.3 MPa .8 500 76.7585 66.7585 3502. MPa 10. 550 5

MPa 10 4.001115 2.0457 720.87 MPa .8 3

MPa .8 2.00101 191.81 10kPa 1

v s h p TPt

kJ/kg 731.28h Liquid Compressed 7-A Table

2.0457s and MPa 10 @kg2494.68kJ/h

2392.1.962781.191h

hxhh

.9627.64928.1488.64927.8692x

1488.8s .6492,s kPa, 10 @

8

8

fgf8

8

gf

=

=

=×+=

×+=

=−−

=

==

1

234

5550 C

6

7500 C

8

T

s

10 MPa

.8 MPa

10 kPa

9-43

m-1

m

A steam power plant runs on a regenerativecycle and produces 80 MW. The turbineinlet conditions are 10 MPA , 550 C. Steamis extracted at .8 MPA to feed an open feedwater heater the rest is reheated to 500 C.

The condenser operates at 10 kPa. The efficiency of the turbines is 100%. The efficiency of the pump is 100%. Determine: a) the turbine exit conditions, b) the cycleefficiency and c) the mass flow rate of the steam.

15

( )( )( )

%36.443304.591465.98

qwη b)

kg/sec 54.571838.613304.59

80,00m

qq80,000

WWm a)

kJ/kg 1838.61q191.812494.68.7984q

hhm1q

in

net

outinnet

out

out

181out

===

=−

=

−==

=−=

−−=

( ) ( )( )

( ) ( )( )( ) ( )

kJ/kg 3304.59533.872770.72q2812.633481.3.7984731.283502.q

hh.20161hh kg/sec 1q

.2016192.612812.63192.61720.87m

hhhhm

hhm1hhmby water gained qsteamby lost q

BalanceEnergy kJ/kg 2812.63h

6.6616 2768.3 170.416.7585 6.8177 2839.8 200

s h T MPa .8 @

kJ/kg 192.6110)(800.00101191.81h)p(pvhh

in

in

6745in

26

231

231361

6

2

23112

=+=−×+−=

−−+−=

=−−

=

−−

=

−−=−=

=

=−×+=−×+=

1

234

5

67

8

T

s

10 MPa

.8 MPa

10 kPa1m1−

1m

16

boiler

6

8

32

7

15

1

2

53

8

7

6

turbine

closed feedwater heater

condenser

REGENERATIONRANKINE CYCLEclosed feed water heater

T

s

( )( ) ( ) ( )

( )( ) ( ) ( )

( ) ( )3725

8776turbine

12pump

1318out

56in

hhxhh1BalanceEnergy Heater

hhx1hh1W

hh1Whhxhhx1Q

hh1Q

−×=−×

−×−+−×=

−×=−×+−×−=

−×= x

(1-x)

17

boiler

6

89

3 24

7

1

5

1

2954

3

8

7

6

turbine

closed feedwater heater

condenser

REGENERATIONRANKINE CYCLEclosed feed water heater

T

s

( )( ) ( )

( ) ( ) ( )( ) ( ) ( )

( ) ( ) ( )( ) 549

3729

8776turbine

3412pump

18out

56in

h1hxhx1 Mixing hhxhhx1Heater

BalancesEnergy hhx1hh1Whhhhx1W

hhx1Qhh1Q

×=×+×−−×=−×−

−×−+−×=

−×+−×−=−×−=

−×=

x

x

(1-x)

18

1

6

10

11

14

QdotRH

HPQdotSH

Wdot

Qdotout

IP

7

LP LP

13

20

LP

92

18

HP HP

16

3

15

19

17

21

8

12

4

5

Regenerative, Reheat Rankine Cycle similar to Figure 8-12, page 3742 high pressure feed water heaters, 2 low pressure feed water heaters1 open feed water heater, 1 stage of reheat

19

OPEN CYCLE ANALYSIS TOOL KIT1. Properties

Ideal GasGas TablesFluid Properties- steam, refrigerant tables

2. Processes3. Energy Balances (First Law)4. Component Performance

Turbine EfficiencyCompressor EfficiencyHeat Exchanger EffectivenessApproach Temperature

5. Cycle PerformanceCycle EfficiencyCarnot Efficiency Cycle COPCarnot COP

20

( )( )

( )

)397( ppln R)(Ts)(Tsss

vvln R)(Ts)(Tsss

50)-(7 VV

vv

vv 49)-(7 ,

pp

pp

pRTmV ,

pRTv

eTemperatur Absolute of functions as v,p,su,h,E17A ,17A TABLE, GAS

347 ppln R

TTln css

33)-(7 vvln R

TTln css

)264( TTcdTch

25)-(4 TTcdTcu

10)-(3 p

RTmV ,p

RT vGAS IDEAL

1

21

02

012

1

21

02

012

2

1

2

1

r2

r1

2

1

r2

r1

rro

1

2

1

2p12

1

2

1

2v12

12pp

12vv

−

−−=−

+−=−

===

==

−−

−

−

=−

+

=−

−−==

−==

==

∫∫

p and T of functions as s, andh,u, v, -Table Liquid Compressed

p Tand of functions as s, andh,u,v, -TableSuperheat

3)(3 mm

xquality,

sor h u, v,becan φ here w

5)-(3 φ

φφ x

)4(3 φxφφ eTemperatur of functions as Ps,h,u, v,

-Table eTemperatur Pressure of functions as Ts,h,u, v,

- Table Pressure 134aR steam, -PROPERTIESFLUID

g

fg

f

fgf

−=

−=

−×+=

−

1. PROPERTIES

21

2.PROCESSES

38)-(5 Wρgh)2

VpvΔ(u mQ

LawFirst of formEquation FlowSteady SystemsOpen

ss

44)(7 vv

pp

43)-(7 pp

TT

42)-(7 vv

TT

constantpvIReversible 0,ΔS 0,Q Adiabatic,

shaft

2

21

k

2

1

1

2

k1k

1

2

1

2

1k

2

1

1

2

k

++++×=

=

−

=

=

=

=−

==−

−

−

Gas Real

Gas deal

PROCESSISENTROPIC ( )

( ) ( )

( )

( ) ( )

in

netcycle

cyclecycle

332211

321

inhot outhot hotin coldout coldcold

fluidhot fluid cold

21outin

21outin

1221

21outin

QWη WQ

CycleFor hmhmhm

mmm Mixing

hhmhhm ΔQΔQ

ExchangersHeat hh ,HH

valvesprocess, tling throt0,Q and with W systemsOpen

hhmQ Q,HH heaters water feed

,condensersboiler, ,exchangersheat 0, with WsystemsOpen

ppvhhm W pumps

hhm W W,HH 40)-(5 scompressor es, turbin

0,Q with systems adiabaticOpen

==

=+=+

−×=−×=

==

=−×=+=

=−=−×=

−×=+=

=

∑∑

3. ENERGY BALANCES

22

4. COMPONENT PERFORMANCE

in coldouthot out coldinhot

in coldinhot

in coldout cold

in coldinhot

outhot inhot

12

isentropic 2COMPRESSOR

actual

isentropicCOMPRESSOR

isentropic 21

21TURBINE

isentropic

actualTURBINE

TT andTTETEMPERATUR APPROACH

)23(5 hhh-h

hhhhε

23)-(5 Q Maximum

Q Actualε

ESSEFFECTIVEN EXCHANGER HEAT

63)(7 hh

h-hη

62)-(7 W

Wη

EFFICIENCY PUMPAND COMPRESSOR

61)(7 hh

hhη

60)-(7 WWη

EFFICIENCY TURBINE

−−

−−

=−−

=

=

−−

=

=

−−

−=

=

T

T

Ts

s

1

22is2

2is

1

hot in

hot outcoldout cold in

distance

23

5. CYCLE PERFORMANCE

21)(6 TT

TCOP

20)(6 TT

TCOP

11)(6 QQ

QW

QCOP

9)-(6 QQ

QWQCOP

EPERFORMANC OF TCOEFFICIEN CYCLE

18)-(6 TT1

TTT η

5)(6 QQ1η

Q

QQQWη

QQWEFFICIENCY CYCLE

LH

H

pumpheat CARNOT

LH

L

ionrefrigeratCARNOT

outin

outoutheatpump

outin

ininionrefrigerat

H

L

H

LH

CYCLECARNOT

in

outCYCLE

in

outin

in

netCYCLE

outin

−−

=

−−

=

−−

==

−==

−=−

=

−−=

−==

−=

T

s

inQ

outQnetW

T

sinQ

outQ

netW