Turbine Firing Temperature
900
Gas Turbine Exhaust Temperature
700
500
300
Figure 20-1.. Effect of the .lant load on turbine firing tem.erature and the turbine e.haust.
The gasifier turbine efficiency (ηgt)
Htit Hpita
ηgt = Htit Hpiti 100匹20-30)
where Hpita = is the enthalpy of the gas based on the actual temperature at the exit of the gasifier turbine; Hpiti is the enthalpy of the gas based on the ideal temperature at the exit of the gasifier turbine. To obtain this idealenthalpy， the pressure ratio across the gasifier turbine must be known.
The pressure ratio (pgrt) across the turbine depends on the pressure drop (.pcb) through the combustor. This varies in various combustor designs where a pressure drop of between 1-3% of the compressor discharge pressure.
pgrt = pdc匹1 .pcb)匹20-31)pdgt
where pdgtis the pressure at the gasifier turbine exit.Thus， the ideal enthalpy at the gasifier turbine exit is given by
Htit
Hpiti = ( 1 )匹20-32)
cptit
pgrt
cppit
0.00 20.00 40.00 60.00 80.00 100.00 120.00 Plant load (%)
where is based on an average temperature across the gasifier turbine based on equation (20-24). The power turbine efficiency can be computed using equations (20-30) and (20-32).
The overall thermal efficiency of the gas turbine in a simple cycle (varies between 2 -4 % depending on the turbine) is computed to determine dete-rioration of the turbine:
powg
ηmt
ηovt = mjLH旦 100匹20-33)
The heat rate can now be easily computed
2 44 Btu 3600 .J
H. = ηth Hp hr = ηth .. hr 匹20-34)
100 100
Gas Turbine Performance .alculations
The performance of the gas turbine is based on the basic equations in the prior section. To relate these relationships to the turbine in concern and tocalculate the deterioration of different sections of the gas turbine， the values obtained must be corrected to design conditions and in some cases values would have to be transposed from off-design conditions to the design con-ditions. The corrected values define the engine corrected performancevalues. Geometric similarity such as blade characteristics， clearances， nozzleareas， and guide vane settings do not change when geometric similarity isconstant. Dynamic similarity， which relates to such parameters as gas vel-ocities， and turbine speeds， when maintained together with the geometric similarity ensures that these corrected parameters will maintain the engine performance at all operating conditions.
Corrected mass flow
........
Tinlet
m
Tstd macorr =匹20-3 )
pinlet
pstd
where macorr is the corrected mass flow of the air entering the gas turbine inlet. These corrections are from the ambient conditions to usually the ISOconditions (14.7psia， 60 0F， RH =60%)， (1.01 Bar， 1 0C， RH = 60%).
.18 Gas Turbine Engineering Handbook
The corrected speed for both the gasifier and power turbine defines the corrected engine performance. Corrected speed
.act
.corr =............ 匹20-36)
.T
匹.T)std
Corrected temperature
Tcorr = TT inlet 匹20-37)
Tstd
Corrected fuel flow
mfcorr = . mj ........ 匹20-38)
pinlet Tinlet
pstd Tstd
Corrected power
Tinlet
Hpact
Hpcorr = Tstd 匹20-39)
pinlet
pstd
The above relationship has to be further modified to take into account the pressuredrop in the inlet ducting， the increase in back pressure due toexhaust ducting， the off-design operation due to decrease in turbine firing temperature and decrease in speed of the power turbine. These modifications are used to calculate the transposed power (Hppt) by transposing from the off-design output power at operating conditions of the turbine to the design conditions.
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