P10-078

Equations

Thermodynamics - An Engineering Approach (5th Ed) - Cengel, Boles - Mcgraw-Hill (2006) - pg. 598

Centrala cu cicluri combinate

Se considera o centrala electrica cu ciclu combinat gaze-abur care are o putere neta de 450 MW. Raportul decomprimare al ciclului turbinei cu gaze este 14. Aerul intra ı̂n compresor la 300 K si ı̂n turbina la 1400 K.Gazele de ardere care ies din turbina cu gaze sunt folosite pentru a ı̂ncalzi aburul la 8 MPa pâna la 400 ◦C ı̂ntr-un schimbator de caldura. Gazele de ardere ies din schimbatorul de caldura la 460 K. Un preı̂ncalzitor de apa dealimentare prin amestec (deschis) ı̂ncorporat ı̂n ciclul cu abur functioneaza la o presiune de 0.6 MPa. Presiuneade condensare este de 20 kPa. Considerând toate procesele de comprimare si destindere ca fiind izoentropice,sa se determine(a) raportul dintre debitele masice de aer si abur,(b) fluxul necesar de caldura introdusa ı̂n camera de ardere, si(c) randamentul termic al ciclului combinat.

Sa se studieze efectul raportului de comprimare al ciclului cu gaze daca acesta variaza de la 10 la 20 asupraraportului dintre debitele de gaze si abur si asupra randamentului termic al ciclului. Sa se reprezinte rezultateleı̂n functie de raportul de comprimare al ciclului cu gaze, si sa se discute rezultatele.

$UnitSystem K kPa

Marimi de intrare:T8 = 300 [K] ; P8 = 14.7 [kPa] ; Gaze (aer la intrarea in compresor) - Gas compressor inlet (1)

1

$IfNot ParametricTable=’P_ratio_gas’

Pratio,gas = 14; Raport comprimare compresor aer - Pressure ratio for gas compressor (2)

$EndIf

T10 = 1400 [K] ; Intrare turbina cu gaze - Gas turbine inlet (3)

T12 = 460 [K] ; Gas exit temperature from Gas-to-steam heat exchanger (4)

P12 = P8; Presiune iesire aer - Assumed air exit pressure (5)

Ẇnet = 450 [MW] ·∣∣∣∣∣1000 kWMW

∣∣∣∣∣; (6)$IfNot ParametricTable=’eta’

ηcomp = 1.0; Etagas,turb = 1.0; (7)

ηpump = 1.0; Etasteam,turb = 1.0; (8)

$EndIf

P5 = 8000 [kPa] ; DELTAT 5,11 = 40 [K] Diferenta de temperatura la capatul cald al HEx (9)

; Abur la intrare in turbina - Steam turbine inlet (10)

$IfNot ParametricTable=’P[6]’

P6 = 600 [kPa] ; Extraction pressure for steam open feedwater heater (11)

$EndIf

P7 = 20 [kPa] ; Presiunea de condensare a aburului - Steam condenser pressure (12)

Ciclul de forta cu gaze (aer) - GAS POWER CYCLE ANALYSIS

Gas Compressor anaysis

Starea [8]:

h8 = h (Air, T = T8) ; s8 = s (Air, T = T8, P = P8) ; (13)

Starea [9s]:

ss,9 = s8; For the ideal case the entropies are constant across the compressor (14)

P9 = Pratio,gas · P8; (15)

Ts,9 = T (Air, s = ss,9, P = P9) ; Ts9 is the isentropic value of T[9] at compressor exit (16)

2

ηcomp = wgas,comp,isen/wgas,comp compressor adiabatic efficiency, wcomp > wcomp,isen (17)

h8+wgas,comp,isen = hs,9 SSSF conservation of energy for the isentropic compressor, assuming: adiabatic, ke=pe=0 per unit gas mass flow rate in kg/s(18)

hs,9 = h (Air, T = Ts,9) ; (19)

Starea [9]:

h8+wgas,comp = h9; SSSF conservation of energy for the actual compressor, assuming: adiabatic, ke=pe=0(20)

T9 = T (Air, h = h9) ; s9 = s (Air, T = T9, P = P9) ; (21)

Gas Cycle External heat exchanger analysis

Starea [10]:

P10 = P9; Assume process 9-10 is SSSF constant pressure (22)

h10 = h (Air, T = T10) ; s10 = s (Air, T = T10, P = P10) ; (23)

h9+qin = h10; SSSF conservation of energy for the external heat exchanger, assuming W=0, ke=pe=0(24)

Q̇in = ṁgas · qin; (25)

Gas Turbine analysis

Starea [11s]:

P11 =P10

Pratio,gas; ss,11 = s10; For the ideal case the entropies are constant across the turbine (26)

hs,11 = h (Air, T = Ts,11) ; Ts,11 = T (Air, s = ss,11, P = P11) ; Ts11 is the isentropic value of T[11] at gas turbine exit(27)

Starea [11]:

h10 = wgas,turb,isen+hs,11; SSSF conservation of energy for the isentropic gas turbine, assuming: adiabatic, ke=pe=0(28)

ηgas,turb = wgas,turb/wgas,turb,isen; gas turbine adiabatic efficiency, wgas,turb,isen > wgas,turb (29)

h10 = wgas,turb+h11; SSSF conservation of energy for the actual gas turbine, assuming: adiabatic, ke=pe=0(30)

T11 = T (Air, h = h11) ; s11 = s (Air, T = T11, P = P11) ; (31)

Gas-to-Steam Heat Exchanger

Starea [12]:

h12 = h (Air, T = T12) ; s12 = s (Air, T = T12, P = P12) ; (32)

3

SSSF conservation of energy for the gas-to-steam heat exchanger, assuming: adiabatic,W=0, ke=pe=0

ṁgas · h11 + ṁsteam · h4 = ṁgas · h12 + ṁsteam · h5; ec 1/2 ec -> debitele (33)

Ciclul de forta cu abur - STEAM CYCLE ANALYSIS

Starea [1]:

Steam Condenser exit pump or Pump 1 analysis

P1 = P7; (34)

h1 = h (STEAM, P = P1, x = 0) ; v1 = v (STEAM, P = P1, x = 0) ; (35)

s1 = s (STEAM, P = P1, x = 0) ; T1 = T (STEAM, P = P1, x = 0) ; (36)

Starea [2]:

P2 = P6; (37)

wpump1,s = v1 · (P2 − P1) ; SSSF isentropic pump work assuming constant specific volume (38)

wpump1 = wpump1,s/ηpump; Definition of pump efficiency (39)

h1 + wpump1 = h2; Steady-flow conservation of energy (40)

s2 = s (STEAM, P = P2, h = h2) ; T2 = T (STEAM, P = P2, h = h2) ; (41)

Starea [3]:

P3 = P6; Condensate leaves heater as sat. liquid at P[3] (42)

h3 = h (steam, P = P3, x = 0) ; T3 = T (steam, P = P3, x = 0) ; (43)

s3 = s (STEAM, P = P3, x = 0) ; v3 = v (STEAM, P = P3, x = 0) ; (44)

Boiler condensate pump or Pump 2 analysis

P4 = P5; (45)

wpump2,s = v3 · (P4 − P3) ; SSSF isentropic pump work assuming constant specific volume (46)

wpump2 = wpump2,s/ηpump; Definition of pump efficiency (47)

h3 + wpump2 = h4; Steady-flow conservation of energy (48)

s4 = s (STEAM, P = P4, h = h4) ; T4 = T (STEAM, P = P4, h = h4) ; (49)

4

Steam Turbine analysis

T5 = T11 − ∆T 5,11; (50)h5 = h (steam, T = T5, P = P5) ; s5 = s (STEAM, P = P5, T = T5) ; (51)

Starea [6s]:

ss,6 = s5; (52)

hs,6 = h (STEAM, s = ss,6, P = P6) ; Ts,6 = T (STEAM, s = ss,6, P = P6) ; (53)

Starea [6]:

h6 = h5 − ηsteam,turb · (h5 − hs,6) Definition of steam turbine efficiency (54)T6 = T (STEAM, P = P6, h = h6) ; s6 = s (STEAM, P = P6, h = h6) ; (55)

y · h6 + (1 − y) · h2 = 1 · h3; Steady-flow conservation of energy (56)wsteam,pumps = (1 − y) · wpump1 + wpump2; Total steam pump work input/ mass steam (57)

Starea [7s]:

ss,7 = s5; (58)

hs,7 = h (STEAM, s = ss,7, P = P7) ; Ts,7 = T (STEAM, s = ss,7, P = P7) ; (59)

Starea [7]:

h7 = h5 − ηsteam,turb · (h5 − hs,7) ; Randamentul turbinei - Definition of steam turbine efficiency (60)T7 = T (STEAM, P = P7, h = h7) ; s7 = s (STEAM, P = P7, h = h7) ; (61)

SSSF conservation of energy for the steam turbine: adiabatic, neglect ke and pe

h5 = wsteam,turb + y · h6 + (1 − y) · h7; (62)

Steam Condenser analysis

(1 − y) · h7 = qout + (1 − y) · h1; SSSF conservation of energy for the Condenser per unit mass (63)Q̇out = ṁsteam · qout; (64)

Cycle Statistics

MassRatiogastosteam = ṁgas/ṁsteam; (65)

Ẇnet = ṁgas·(wgas,turb − wgas,comp)+ṁsteam·(wsteam,turb − wsteam,pumps) ; definitia puterii nete a ciclului - net cycle work(66)ηth = Ẇnet/Q̇in · 100 [%] ; Cycle thermal efficiency, in percent (67)

Bwr =ṁgas · wgas,comp + ṁsteam · wsteam,pumpsṁgas · wgas,turb + ṁsteam · wsteam,turb

; Back work ratio (68)

Ẇnet,steam = ṁsteam · (wsteam,turb − wsteam,pumps) ; (69)Ẇnet,gas = ṁgas · (wgas,turb − wgas,comp) ; (70)NetWorkRatiogastosteam = Ẇnet,gas/Ẇnet,steam; (71)

Data$ = Date$; (72)

5

Solution

Bwr = 0.3825 Data$ = ‘2015-03-09’ ∆T5,11 = 40 [K]ηcomp = 1 ηgas,turb = 1 ηpump = 1

ηsteam,turb = 1 ηth = 62.4 [%] MassRatiogastosteam = 9.069

ṁgas = 822.3 [kggas/s] ṁsteam = 90.67 [kgsteam/s] NetWorkRatiogastosteam = 4.183

Pratio,gas = 14 Q̇in = 721164 [kW] Q̇out = 138049 [kW]qin = 877 [kJ/kggas] qout = 1523 [kJ/kgsteam] v1 = 0.001017 [m

3/kg]

v3 = 0.001101 [m3/kg] Ẇnet = 450000 [kW] Ẇnet,gas = 363182 [kW]

Ẇnet,steam = 86818 [kW] wgas,comp = 338.1 [kJ/kggas] wgas,comp,isen = 338.1 [kJ/kggas]wgas,turb = 779.8 [kJ/kggas] wgas,turb,isen = 779.8 [kJ/kggas] wpump1 = 0.5899 [kJ/kgsteam]wpump1,s = 0.5899 [kJ/kgsteam] wpump2 = 8.144 [kJ/kgsteam] wpump2,s = 8.144 [kJ/kgsteam]wsteam,pumps = 8.629 [kJ/kgsteam] wsteam,turb = 966.1 [kJ/kgsteam] y = 0.1784

Arrays

Row Pi Ts,i Ti hs,i hi ss,i si[kPa] [K] [K] [kJ/kg] [kJ/kg] [kJ/kg-K] [kJ/kg-K]

1 20 333.2 251.3 0.83182 600 333.2 251.9 0.83183 600 432 670.6 1.9314 8000 432.9 678.8 1.9315 8000 680.6 3159 6.3946 600 432 432 2598 2598 6.394 6.3947 20 333.2 333.2 2105 2105 6.394 6.3948 14.7 300 300.4 6.2569 205.8 629.6 629.6 638.5 638.5 6.256 6.256

10 205.8 1400 1516 7.15711 14.7 720.6 720.6 735.8 735.8 7.157 7.15712 14.7 460 462.3 6.688

6

T-s Plot

all(pratiogas)

7

etath(P [6])

etath vs eta

8