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