Shaft Power Cycles Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible...

48
Shaft Power Cycles Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion chamber and heat exchanger are negligible. Working fluid is air. It behaves as an ideal gas Mass flow rate is constant and combustion process is replaced by heat addition process. Changes of K.E. of the working fluid between inlet and outlet of each component are negligible. Heat transfer in heat exchanger is complete (ε=100%)
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Transcript of Shaft Power Cycles Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible...

Page 1: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles Ideal cycles

Assumptions:• Both compressor and turbine are isentropic

(reversible adiabatic, η= 100 %)• Pressure losses in both of combustion chamber and

heat exchanger are negligible.• Working fluid is air. It behaves as an ideal gas• Mass flow rate is constant and combustion process

is replaced by heat addition process.• Changes of K.E. of the working fluid between inlet

and outlet of each component are negligible.• Heat transfer in heat exchanger is complete

(ε=100%)

Page 2: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles

• Description of simple cycle

• Specific work, w• Thermal efficiency, η=

w / q

Page 3: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles

• First law of thermodynamics (conservation of energy)

• q – w = Δh• Compressor

(adiabatic, q=0.)

• Turbine

)( 2121 TTchhw

hw

pc

c

)( 4334 TTchhw

hw

pt

t

Page 4: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles• Combustion chamber

)(

.0,

2323 TTchhq

whq

ph

h

ct

h

netth q

ww

q

w

/)1(/)1(

1

2

1

2 )()( thus4,-3 and 2-1 processes Isentropic rp

p

T

T

/)1(/)1(

4

3

4

3 )()( Also rp

p

T

T

23

14

23

2143 1)(

)()(

TT

TT

TTc

TTcTTc

p

ppth

Page 5: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles

)1

(1)1( /)1(

3

4 rT

T

Page 6: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles

)]()[(

)()( ww

by given is work specific

1243

1243t

TTTTcp

hhhhw

The

c

13/TT of ratio theis t where

)r1())r

1(1(t

)r1())r

1(1(

T

T

Tc

w

/)1(/)1(

/)1(/)1(

1

3

1p

,,cby dividing 1p thusT

ration compressio optimum thegivesequation theating,Differenti

Page 7: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Shaft Power Cycles

42

1

3

4

3

1

2

4

3

1

2/)1(

/)1(

2/)1(/)22(/)1(/)21(

/)1(/)21(

1p

TT

T

Tt

T

T

T

T and

T

T

T

Tr since

tr

)r(rt ,r)r(t

0r1

))r(1

(t : 0Tc

w

r

nsapplicatiocraft air 5.55

45.3

fort

turbinesgasindustrialfort

Page 8: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Simple cycle

Page 9: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Regeneration cycle (heat exchange cycle)

thus,T T cycle ideal

)(

)()(

q

w

54

53

1243

53h

net

for

TTc

TTcTTc

q

ww

p

ppct

To benefit from the exhaust, a regenerator is used to reduce the heat addition, the efficiency is improved since heat rejection is reduced.

/)1(/)1(/)1(

/)1(

/)1(

/)1(

3

4

1

2

3

1

1

1)1)(/1(

1

11

/11

1

11

)1(

)1(

1

rtrr

r

t

r

r

tT

TT

T

T

T

Page 10: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Regeneration cycle (heat exchange cycle)

Recall that .

cycle

cycle

simpleExcjangerHeat

simpleExcjangerHeat ww

Page 11: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Regeneration cycle (heat exchange cycle)

Page 12: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

In the reheat cycle, both of the heat addition and work done are increased. The thermal efficiency may increase or decrease depending on the values of T4 in comparison to T3.

Reheat Cycle

Page 13: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Reheat Cycle

)1()()(/

)()()(

1

2

1

6

1

5

1

4

1

31

126543

T

T

T

T

T

T

T

T

T

TTcw

TTcTTcTTcwwww

p

pppCLPTHPT

16235461

5

4

3 , , ),( PPPPPPP

P

P

P

For optimum conditions, i.e. maximum work, thus.

This gives

Page 14: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Reheat Cycle

c

tt

Tc

w

p

2 - 1 c - 2

1

Thus gives

11

1

2

1

4

3

4

3

3

4

1

3

3

4

1

4

1

3

6453 HPT

)(r )P

P( C

where )P

P(

T

T

T

T

T

T

T

T

T

T and

T

T t

TThen , T IF , T

CBut

tAlso

TTT LPT

Page 15: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Reheat Cycle

ctct

ctct

Tcq

Tcw

c

tct

T

T

T

T

T

T

T

T

Tc

q

TTcTTcq

ctctTcw

pin

p

p

in

ppin

p

/2

/212

)/(

)/(

2

)]()[(

)()(

/212)/(

but ,q

w

1

1

1

4

1

3

3

2

1

3

1

4523

1

in

net

The efficiency is calculated as

Page 16: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Cycle with reheat and heat exchange

8276 & TTTT

For ideal regenerator;

/)1(

1

1

1

21

in

net

where

)1()1

1(2

and /22

/212

)/(

)/(

tproven tha becan It

q

w

rc

cc

tTc

wctt

ctct

Tcq

Tcw

qq

www

p

pin

pnet

Rcc

cTT

Page 17: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Methods for accounting for component losses

• Performance of real cycles differ from ideal cycles for the following reasons:

• Velocities in turbomachinery are high thus Δ K.E. is not equal to zero.

• Compression and expansion are irreversible.• Friction losses in H.E. and CC.• H.E. effectiveness is less than 100%• Specific heat specific heat ratio are not constant through the cycle

processes• More work is required for compression process to overcome

bearings and friction in transmission between compressor and turbine

• Cycle efficiency is different from unit efficiency• Some compressed air is bled for turbine blade cooling.

Page 18: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Stagnation properties

The energy equation for a flow coming to rest is

Where

h is the static enthalpyO refers to the stagnation conditionC is the velocity

2

2chvelocityzeroho

Page 19: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Stagnation properties

• Thus:

2

2chho

po c

cTT

2

2

re temperatudynamic theis 2

2

pc

c

and re temperatustatic theis T

re, temperatu(or total) stagnation theis oTwhere

Page 20: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Stagnation properties• Thus the first law equation is

)()(

)2

()2

(

1212

21

1

22

2

oopoo TTchh

ch

chwq

)1/(12

)1/(2

2

)2

11(

,)2

11(

,2

11

M

Mp

p

MT

T

o

o

o

bygiven are process adiabatican in properties stagnation the

then,RT aby given sound of speed theawith

numberMach theis a

cM and )1/(c p

RgConsiderin

1

o1

o2

o1

o2 )T

T(

P

P

process isentropican

For

Page 21: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Compressor and turbine efficiency

workactual

workideal = efficiency

1

1)(

1

1

01

02

/)1(

01

02

01

02

01

02

0102

0102

0102

0102

'

'

'''

T

Tp

p

T

TT

T

TT

TT

TT

TT

Tc

Tc

h

h

w

w

c

op

op

o

o

actual

idealc

]1)[( /)1(

01

0201

01020102

'

p

pT

TTTT

c

c

Compressor efficiency

ediscalculatNormally o2T andgiven is

Page 22: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Compressor and turbine efficiency

workideal

workactual = efficiency

] ) ( / 11[

/)1(

04

03030403

p

pTTT

or

t

Turbine efficiency

/)1(

03

04

03

04

03

04

03

04

0403

0403

0403

0403

,

)(1

1

1

1

''

''

p

pT

T

T

TT

T

TT

TT

TT

TT

Tc

Tc

h

h

w

w

t

idealop

op

o

o

ideal

actualt

Page 23: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Polytropic efficiency

T

T

T

T

s

idealscs

',

,

Consider a compressor of different stages. The Polytropic efficiency (defined as the isentropic efficiency of an elemental stage in the process such that it is constant throughout the whole process) given by

c

cc

c

n

nor

TTpp

p

p

T

T

p

dp

T

dT

p

dp

T

dT

dppp

TdppCdT

consp

T

11

ln

ln1

or ln1

ln

1 and

1

11

tan

01

02

01

02

01

02

01

02

'

/1/)1(

/1'

/)1(

Page 24: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Polytropic efficiency

• For an expansion (such as a turbine)

idealideal,s

st,s dT

dT

T

T

ttancons

p

T/)1(

11

ln1

ln

ln1

ln

1 thus

1

03

04

03

04

03

04

03

04

t

t

t

tideal

n

nor

p

pT

T

p

p

T

T

p

dp

T

dT

p

dp

T

dT

Page 25: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Polytropic efficiency• For a compressor

]1)[(

]1)[(]1[

/)1(

01

0201

/)1(

01

0201

01

02010102

c

p

pT

P

PT

T

TTTT nn

])/(11[

])/(11[

/)1(

04

0303

/)1(

04

03030403

0403

0403

, ''

t

p

pT

p

pTTT

TT

TT

Tc

Tc

h

h

w

w

nn

idealop

op

o

o

ideal

actualt

• For a turbine

Page 26: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Pressure losses

hga ppp 04

]1[0202

02

0203

p

p

p

pp

pppp

ab

ab

Page 27: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Heat exchanger effectiveness

0204

0205

energy ideal

,

TT

TT

airbyreceivedenergyactualesseffectiven

Page 28: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Mechanical Losses and Variations in specific heats

99.0

/lossesh work wit

losseshout work wit

m

mct

m

ww

5.31

,4.1

)/(005.1

;

a

pa kgKkJc

airFor

Variations in specific heats

Mechanical Losses

41

,333.1

)/(148.1

;

a

pg kgKkJc

gasescombustionFor

Page 29: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Fuel Air ratio

C) 86.08% and H (13.92% nshydrocarbo liquid ofheat specific : )/(2

nshydrocarbo liquid ofreaction ofenthalpy : )/(43100

)298()1()298( )298( 0302

kgKkJc

kgkJH

TcfTfcHfTc

pf

c

pgfpfcpa

T given for f actual

T given for f ltheoreticab

K 298 of ture temperareferencefor ; .

.

a

f

m

mf

fm

af mm..

am

.

f11

f

Page 30: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Fuel Air ratio

Page 31: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Specific fuel consumption

net

a

net

a

fnetf wf

m

W

m

mWmsfc /3600 / .

..

.

....

HHVsfcHHVxfwnet /3600) (/

..

Page 32: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1• A heat exchange cycle having the following data:

– turbine inlet temperature 1100(K)– compressor pressure ratio 4.0 – isentropic efficiency of compressor 0.85– isentropic efficiency of turbine 0.87– combustion efficiency 0.98 – mechanical transmission efficiency 0.99– heat exchange effectiveness 0.80– ambient conditions 1(bar), 288 (k)– pressure losses

• combustion chamber 2% of compressor delivery pressure

• heat exchanger air side 3% of compressor delivery pressure

• heat exchanger gas side 0.04 (bar)

Page 33: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.102 012 1

12,

02, ( 1) / ( 1) /02 02

02, 01 01 01 0102 01 01

02 0202 01

01 01

(1.4 1) /1.4

02 01

( )( )

1 ( ) 1 ( ) 1

and 1 1

(4) 1288 164.7( )

0.851.005 164.7

0.

pactual

m m

ideal

idealc

c

c

c T Th hw

T p pT T T p p

T T TT TT TT T

T T K

Xw

167.2( / )99

kJ kg

Page 34: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1

03 04

04 04

( 1) /03 04 03 03 0403 04 03

( 1) /04, 0403 04, 03

0303

03 02 04

( )

1 1

and (1 ( ) )1 ( )1

4(1 0.03 0.02) 3.8( ) and

1 0.04 1.

t pg

t tidealideal

ha b a hg

w c T T

T T

T T T T pT T T

T pT T ppT

p p p p bar p p p

( 1) /0403 04 03

03

03 04

04( )

1 1.148( / ) and 1.333, 0.25

(1 ( ) ) 264.8( )

( ) 1.148 264.8 304.0( / )

136.8( / )

pg

t

t pg

net t c

bar

c kJ kgK

pT T T K

p

w c T T X kJ kg

w w w kJ kg

Page 35: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1

02 01 02 01

05 02

04 02

04 03 03 04

05 04 02 02

( ) 288 164.7 452.7( )

H.E. effectiveness

( ) 1100 264.8 835.2( )

effectiveness ( ) 758.7

T T T T K

T T

T T

T T T T K

T X T T T K

b

theoretical (from chart) 0.0094

theoretical f0.0096

f

f

Page 36: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1

0.00963600 0.253( / )

136.8t c

Specific fuel consumption is given by

fSFC kg kWh

w w

43100 /

3600 36000.331

0.253 43100

fuelnet

net

Q kJ kg

SFC Q X

Page 37: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1: Using EESKnown Information

Ta = 288 [K] Pa = 100 [kPa] To3 = 1100 [K] Pr = 4

Ettab = 0.98 Ettac = 0.85 Etta t = 0.87 Ettam = 0.99 Effecthe = 0.8

Ploss b = 0.02 Ploss ha = 0.03 Ploss hg = 4

cpa = 1.005 cpg = 1.148 R = 0.287 Gam a = 1.4 Gam g = 1.33333

HHV = 43100 Tf = 298 cpf = 1.2

To1 = Ta

Po1 = Pa

Po2 = Po1 · Pr

Gamra = Gam a – 1

Gam a

Gamrg = Gam g – 1

Gam g

To2d

To1 =

Po2

Po1

Gamra

Ettac = To2d – To1

To2 – To1

Wc = cpa · ( To2 – To1 )

Page 38: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1: Using EES

Wtc = Wc

Ettam

Po3 = Po2 · ( 1 – Ploss b – Ploss ha )

Po4 = Po1 + Ploss hg

Etta t = To3 – To4

To3 – To4d

To3

To4d =

Po3

Po4

Gamrg

Wt = cpg · ( To3 – To4 )

Wnet = Wt – Wtc

Effecthe = To5 – To2

To4 – To2

( 1 + f ) · cpg · ( To3 – 288 ) = f · HHV + cpa · ( To5 – 288 ) + f · cpf · ( Tf – 288 )

fact = f

Ettab

sfc = fact

Wnet · 3600

Etta = Wnet

fact · HHV

Page 39: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.1: Using EES

cpa = 1.005 cpf = 1.2 cpg = 1.148 Effecthe = 0.8 Etta = 0.2858 Ettab = 0.98 Ettac = 0.85

Ettam = 0.99 Ettat = 0.87 f = 0.01089 fact = 0.01111 Gamra = 0.2857 Gamrg = 0.25 Gama = 1.4

Gamg = 1.333 HHV = 43100 Pa = 100 [kPa] Plossb = 0.02 Plossha = 0.03 Plosshg = 4 Po1 = 100 [kPa]

Po2 = 400 Po3 = 380 Po4 = 104 Pr = 4 R = 0.287 [kJ/kgK] sfc = 0.2922 Ta = 288 [K]

Tf = 298 To1 = 288 [K] To2 = 452.7 To2d = 428 To3 = 1100 [K] To4 = 835.2 To4d = 795.6

To5 = 758.7 Wc = 165.5 Wnet = 136.8 Wt = 304 Wtc = 167.2

Page 40: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.2

• A simple gas turbine with free turbine power having the following data:– turbine inlet temperature 1350(K)– compressor pressure ratio 12.0– isentropic efficiency of compressor 0.86– isentropic efficiency of each turbine 0.89– combustion efficiency 0.99– mechanical efficiency of each shaft 0.99– ambient conditions 1(bar), 288 (k)– combustion chamber pressure loss 6%

comp. deliv. pres.– exhaust pressure loss 0.03(bar)

Page 41: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.2

02, ( 1) / ( 1) /02 02

02, 01 01 01 0102 01 01

02 0202 01

01 01

(1.4 1) /1.402 01

02 01

1 ( ) 1 ( ) 1

and 1 1

( )(12) 1 1.005 346.3288 346.3( ),

0.86 0.99

351.5( / )

ideal

idealc

c

ptc

m

T p pT T T p p

T T TT TT TT T

c T T XT T K w

kJ kg

Page 42: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.202 01 01 02

03 04

03 04 04 03 03 04

04 04

03 04 03 03

04,03 04,

03

288 346.3 634.3( )

( ), 1.148( / ), and 1.333

306.2( ) and 793.8( )

1 1

1 (1

tc pg pg

tc

pg

tidealideal

T T T K

w c T T c kJ kgK

wT T K T T T K

c

T T

T T T TTT T

T

( 1) /04

03

04

/( 1)04 03

03

03 02 04

)

1

(1 ) 3.243

12(1 0.06) 11.28( ), thus 3.478( )t

b

p

p

T

p T

p

p p p bar p bar

Page 43: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.2

05

04 05

04 05,

( 1) /0504 05 04

04

0.25

04 05

1 0.03 1.03( )

, thus,

(1 ( ) )

1.030.89 1043.8 (1 ( ) )

3.478243.7( )

( ) 277( / )

a exhaust

tideal

t

tp m pg

p p p bar

T T

T T

pT T T

p

X X

K

w c T T kJ kg

Page 44: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.2

0.02043600 0.265 /

277.9tp

fSFC kg kWh

w

3600 360031.5 %

0.265 43100netSFCXQ X

th

b

f 0.0202 and 0.0204thf f

Page 45: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.3• Reheat Cycle

– net work output 240 MW – turbine inlet temperature 1525(K)– compressor pressure ratio 30– polytropic efficiency for compressor and turbines

»0.89

– Pressure loss in first combustor is 2%– Pressure loss in second combustor 4%– exhaust pressure 1.02 (bar)– ambient conditions 288(K), 1.01(bar)

Assume that pressure ratios in HP and LP turbines are equal

Page 46: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.3

( 1) /02 0202

01 01

02 01

( 1) / ( 1) / 0.321

( ) /( 1) ( 1) / 0.2223

( ) 2.98, 858.1( )

( ) 573( / )

c

c

n n

c p

n n

n n

T pT K

T p

w c T T kJ kg

Page 47: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.3

06

0202 01 03 02 1

01

03 03 03

04 06 04

loss 04 0303 04

assume 1.02( )

30.3( ) and 29.69( )

29.695.395. Take 5.3 to consider

1.02

1 4 % P in the , , 5.602( )

/

exhaust

b

p p bar

pp p bar p p p bar

p

p p p

p p p

reheater thus p p barp p

T

( 1) /( 1) / 0.89(1.333 1) /1.33303 03 03

04 04 04

04

05 04 2

( ) ( ) 5.3 1.449

1052.6( )

5.602(1 0.04) 5.378( )

tn n

b

p p

T p p

T K

p p p bar

Page 48: Shaft Power Cycles  Ideal cycles Assumptions: Both compressor and turbine are isentropic (reversible adiabatic, η= 100 %) Pressure losses in both of combustion.

Example 2.303 04

05 06

( ) 536.9( / )

( ) 535.5( / )

499.4( / )

HP m pg

LP m pg

net HP LP c

w c T T kJ kg

w c T T kJ kg

w w w w kJ kg

.

480.6( / )net

net

Wm kg s

w

, 1theoretical 0.0197th bf

, 2

, 1 , 2

b

theoretical 0.0142

0.0342

th b

th b th b

f

f ff

33.9 %

netw

f X HHV