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2 (Power Plant / Gas Turbine) 2/2547

6 4

POWER PLANT 1 - 3 2 GAS TURBINE 4 - 6 2

POWER PLANT 1. (Cogeneration Plant)

(Electricity) (Heat or Mechanical Work) (Gas Turbine) (Steam Turbine)

Extraction Turbine Back Pressure Turbine Heat Recovery Steam Generator, HRSG

1.1

Topping Cycle Bottoming Cycle Topping Cycle Bottoming Cycle

(ElectricalMatching Sizing) (Thermal Matching Sizing)

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1.2 65 %

1.3 30-36 % 7064 % () 5-10 bar 2 5 MW 10 ton/h

40 % 60 % (Jacket Cooling Water) (Exhaust Gas)

0.5 5 MW 2.5-3 ton/h

2. 3,000 kW 10 bar (179.9 oC) 5,500 kWt (Cogeneration Plant)

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Enthalpy 10 bar (179.9 oC) = 2,778 kJ/kg 5,500 kWt 5,500 /2,778 = 1.98 kg/s = 7.13 ton/h

2.1 3,000 kW (Heat Recovery Steam Generator, HRSG)

10 bar 7.5 ton/h

32 % Heat Input 3,000 / 0.32 = 9,375 kWt (3,000 + 5,500)/9375 = 90.67 %

2.2 Extraction Extraction 3,000 kW Extract

10 bar 7.5 ton/h Extraction

Biomass

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3. Superheated Rankine Cycle Power Plant (SuperheatedSteam) 40 bar, Steam Temperature 300 oC Condenser 0.10 bar (Saturated Temperature 45.8 oC) -

40 bar hf= 1,087.3 kJ/kg , h g = 2,801.4 kJ/kg ,

sf= 2.7964 kJ/kg-K , s g = 6.0701 kJ/kg-K 300 oC h = 2,963 kJ/kg , s = 6.364 kJ/kg-K

0.10 bar hf= 191.83 kJ/kg , h g = 2,584.7 kJ/kg ,sf= 0.6493 kJ/kg-K , s g = 8.1502 kJ/kg-K

. Rankine Cycle (Qin). Rankine Cycle (Qout). Rankine Cycle (Win). Rankine Cycle (Wnet). Rankine Cycle

40 bar hf= 1,087.3 kJ/kg , h g = 2,801.4 kJ/kg ,sf= 2.7964 kJ/kg-K , s g = 6.0701 kJ/kg-K

300 oC h = 2,963 kJ/kg , s = 6.364 kJ/kg-K

0.10 bar hf= 191.83 kJ/kg , h g = 2,584.7 kJ/kg ,sf= 0.6493 kJ/kg-K , s g = 8.1502 kJ/kg-K

h1 = 191.83 kJ/kgh3 = 2,963 kJ/kg

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s3 = 6.364 kJ/kg-K 2 (Power Plant / Gas Turbine) 2/2547

1W2 = -v*(P2 P1) = h1 h2= - 0.001 * (4000 10)= - 3.99 kJ/kg

h2 = h1 + Wp= 191.83 + 3.99 kJ/kg= 195.82 kJ/kg

s4 = s3 = 6.364 kJ/kg-Kx4 = (s4 - 0.6493) / (8.1502 - 0.6493)

= 0.7619h4 = hf + x4 * (hg hf)

= 191.83 + 0.7619 *(2,584.7 - 191.83)= 2,014.88 kJ/kg

Wt = h3 h4= 2,963 - 2,014.88= 948.12 kJ/kg

. Qin = h3 h2= 2,963 - 195.82= 2,767.18 kJ/kg

. Qout = h4 h1= 2,014.88 - 191.83= 1,823.05 kJ/kg

. Wp = 1W2 = - 3.99 kJ/kg. W = Wt + Wp

= 948.12 3.99= 944.13 kJ/kg

. Eff = W/Qin= 944.13 / 2,767.18

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CpCv

= 34.12 % 2 (Power Plant / Gas Turbine) 2/2547

4. gas turbine compressor 2 stages ( perfect intercooling stages ) combustion chamber turbine 1 stage, isentropic efficiency compressor stage turbine c t

() power output/mass flow 1 cycle(Rp)

Rp =

132

min

max

T

T

tc

Tmax Tmin cycle r =

() compressor stage combustion chamber turbine

2 stages reheating stages power output/mass flow 1 cycle ().

Compressor 2 stages, Turbine stage isentropic efficiency

compressor = c ( stage)turbine = t

cycle = Tmax = T5 cycle = Tmin = T1 perfect intercooling

T1 = T3 = Tmin

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. Wc

Wt

= compressor turbine work mass flow intercooler (CP)

RP = cycle = 21 cx rcr1P2Px

3P4P =

1cr 2cr compressor stage stage 2 combustion chamber P4 = P5Wc = work compressor stage stage 2

= 1cW + 2cW

= CP ( T2 T1 ) + CP ( T4 T3 ) Wc

c =1T2T1T2

T =

3T4T3T4

T

WC =cpC

1

T2

T +cpC

3

T4

T

=cpC T1

+ 13T4

T

c3TpC1

1T2

T

=cpC T1

+ 2cr

Rr 1

1-1-

11

p

c----------- (1)

Power output mass flow 1 Wt Wc Wt Wc Rp Wc stage Rp

1cr , 2cr ( Wc ) Rp

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1crcW = 0 = 1cr

+

c

1TpC2

1

c

1TpCr

c

1TpC

1

1

1

1c

cr

pR

=1

1

1

1

1cr)

1(pRc

1TpC11c

r

1c1TpC +

0 = 2-1

1

1

1crpR1cr

)1(2

1cr

=

1

pR

1cr = pR = 2cr

Wc 1cr = 2cr = pR Wc 1cr = 2cr = pR (1)

Wc min = c1TpC

+

2

pR

pR

pR 1

11

2

2

=c

1TpC 2

1p

R2

1

Wt = Cp ( T5 T6 ) = Cpt ( T5 6T )

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= Cpt

T5

1

pR

11

=

1pR

pR

5TtpC1

1

W = Wt Wc min

=

1pR

pR

5TtpC1

1

- 2

1pRc1TpC 2

1

= Cpt T5 -

1

pR

5TtpC - 2 c

1TpC

c

1TpC2pR2

1

pRW

= 0 = pR

+

21

Tt c1TpC21

pR

5pCp

R

= Cpt T5

( ) ( )

121-1

pR2

1

c1TpC

2pR

1

+

( ct1T5

T

) =)

1(

2

3

pR


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optimumpR =

)1

(32

minTmaxT

tc

----------------------------.

1tr =

4P3P

2tr =

6P5P

reheat T3 = T5 = Tmax

reheaterP4 = P5

.

Wt 1tr Rp R p = 1t

r x 2tr

Wt = Cp ( T3 T4 ) + Cp ( T5 T6 )

= Cpt T3 )3T4

T(1 + Cpt T3 )5T

6T

(1

= Cpt T3

1

1

11

1tr

12

pR

tr

----------- (2)

Wt 1t

r tW

= 0 = Cpt T31

1

1tr)1(

+

11

1 1tr)

1

(pR

3TtpC

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2-1

1tr = 1

1

pR1

tr

) 1-(2

1tr =

1-

pR

1tr = pR = 2t

r

Wt 1t

r

= 2tr

= pR

(2)

Wt = 2 Cpt T3 -pR

3TtpC

21

-

pR

3TtpC1

1-2

pR

= 2 Cpt T3 - Cpt T3)

pR1

pR1(

21

21

+

= 2 Cpt T3 - 2pR

3TtpC

21

W = 2 Cpt T3 - 2pR

3TtpC

21

-

c1TpC

( 1pR

1-

)

W pRW

= 0

= 2 Cpt T31

21

pR)21(


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+c

1TpC 1

pR)1-(

1-

tc1T3T = -2

33

pR

optimumpR =

)1

(32

mixTmaxT

tc

5. turbojet compressor 8:1 turbine 1,200 K 15 kg/s 260 m/s 7 km Nozzle specific fuelconsumption

polytropic efficiency compressor turbine = 87 % isentropic efficiency diffuser = 95 % isentropic efficiency Nozzle = 95 %

mechanical efficiency = 99 % combustion chamber = 6 %

compressorcombustion efficiency = 97 %

= 0.0187 7 km

- = 0.411

bar- =

242.7 K


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Turbojet , D = diffuser, C = compressor,

c/c = combustion chamberT = turbine , N = nozzlerc = compressor

= 8 : 1To3 = 1,200 K

m = 15 kg/sCa = 260 m/s 7 km

p = 87 % turbine compressor

i = N = 95 %

m = 99 %

Pb = 6 % P02b = 97 %

7 kmPa = 0.411 barTa = 242.7 K

(intake / diffuser)

i = aT01TaT10

T = 0.95 = 242.701T

242.710

T

T01 = T0 a = Ta + p2C2aC = 242.7 + 1,005x2

2(260)

= 242.7 + 33.6 = 276.3 K

10

T - 242.7 = 0.95 x 33.6 = 31.9 K

10T

= 274.6 K


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aP01P = 1)aT

10T

(

= 4.04.1

)242.7274.6( = 1.54

P01 = 1.54 x 0.411 = 0.633 bar

compressor,p = 0.87

01

T02

T= p

1

01P02P

= ( )8 1.4x0.87

0.4= 1.9796

T02 = 1.9796 x 276.3 = 546.97 K

P02 = 8 x 0.633 = 5.064 bar P03 = 5.064 0.06 x 5.064 = 4.76 bar

T03

= 1,200 K compressor turbine

Cpg ( T03 T04 ) m = Cpa ( T02 T01)

T03 T04 = 0.99x1.147276.3)(546.971,005

= 239.56 K

04P03P = 1-n

n

04T03T

n = polytropic

n 1n =

p1)(

n 1n = 1.3330.87x0.333 = 0.217 T04 = T03 239.56 = 1,200 239.56 = 960.44 K

04P03P = ( )960.44

1,200 0.2171 = 2.78

P04 = 2.784.76 = 1.71 bar

aP04P = 0.411

1.71 = 4.16


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cP04P = 1

)1

1-(

N

11

1

+

, Pc = critical pressure

cP04P =

4)

2.3330.333(

0.9511

1

= 1.917

Flow nozzle is choked P5 = Pc = 1.917

1.71 = 0.89 bar

T5 = Tc = ( ) 04T

12+ = 2.333

2 x 960.44

= 823.35 K , Tc = critical temperature

T04 = T05 = T5 + pg2C 25C = 960.44 K

pg2C25C = 960.44 823.35 = 137.1 K

C5 = 137.1x310x1.147x2 = 560.8 m/s

ccP

= RTc , c throat

c = 823.35x287510x0.89 = 0.377 kg/m3

m = c c

A cC = 15 = 0.377 x cA x 560.8 cA = A5 = 560.8x0.37715 = 0.0709 m

2

= throat F = m ( C5 Ca ) + ( P5 Pa ) A5

= 15 ( 560.8 260 ) + ( 0.89 0.411 ) x 0.0709 x 100= 7.907 k N

T03 T02= 1,200 546.97 = 653.03 K f = 0.0187 kgf / kga , f =

f = b0.0187

= 0.970.0187 = 0.01928 kgf / kga


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specific fuel consumption (sfc) = Ff = 310

157.907

0.01928x

= 0.03657 kgf / kN-s= 0.132 kgf / N h

6. 288K 1400 K Cp = 1.005 kJ/kg K k = 1.4 1 kg/s 1) (Maximum work)2) 3) 4) 5)

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