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General Go.erning ..uations
The four fundamental equations， which govern the properties of thecombined cycle are the equation of state， conservation of mass， momentum and energy equations.
Equation of state
p.
P = .M. T 匹20-4)
which can also be written as:
Momentum equation for a caloricaly and thermally perfectgas， and one in which the radial and axial velocities do not contribute to the forces generated on the rotor the Adiabatic Energy (Ead) per unit mass is given as follows (Euler Turbine Equation):
n =1， T =C (constant temperature process); n =  = CCpv， S =C (con-stant entropy process); n =∞，旦 =C (constant volume process). Conservation of mass
Where n varies from 0 →∞; n =0， p =C (constant pressure process);
Plant P
.08 Gas Turbine Engineering Handbook
pn =C匹20-4 )
P
Plant Heat Plate
Figure 20-8. Plant conditions as a function of inlet ambient tem.erature.
 
m =PA旦匹20-)
1
Ead =匹U1旦e1 U2旦e2)匹20-6)gc

1.025
1.02
1.015
1.01
1.005
1
0.995

Plant Power(%) Plant Heat Rate(%)
Energy equation for a caloricaly and thermally perfect gas the Work (.) can be written as follows:
.rad . .UE . .p旦 . ..E . .pE = .匹20-7)
where .Uis the change in the internalenergy， .p旦 is the change in the flowenergy， ..Eis the change in kinetic energy， and .pE is the change in Potential Energy. The total enthalpy is given by the following relationship:
H = U .p旦 . .E匹20-8)
neglecting the changes in potential energy (.pE) and heat losses due to radiation (.rad); the work is equal to the change in total enthalpy:
. = H2 H1匹20-9)
In the gas turbine (Brayton cycle)， the compression and expansion pro-cesses are adiabatic and isentropic processes.Thus， for an isentropic adia-
Cp
batic process = Cv ; where cp and cv are the specific heats of the gas at constant pressure and volume respectively and can be written as:
cp cv = .匹20-10)
where cp = . 1 and cv = . 1匹20-11)
values for air and products of combustion (400% theoretical air) are given in Appendix B. It is important to note that the pressure measured can be either Total orStatic however， only Total Temperature can be measured. The relationship between total and static conditions for pressure and tempera-ture are as follows:
T = Ts .旦2 匹20-12)
2cp
where Ts =static temperature， and旦 = gas stream velocity and
p = ps . P旦2 匹20-13)
2gc
.10 Gas Turbine Engineering Handbook
where ps = static pressure and the acoustic velocity in a gas is given by the following relationship
2 = ..P p 匹20-14)
s=c
for an adiabatic process (s = entropy = constant) the acoustic speed can be written as follows:
................
gc.Ts
= M. 匹20-1 )
where Ts = static Temperature. The Mach Number is defined as:
M =旦匹20-16)
it is important to note that the Mach No. is based on static temperature.
The turbine compressor efficiency and pressure ratio are closely moni-tored to ensure that the turbine compressor is not fouling. Based on these computations the turbine compressor is water washed with mineralizedwater， and if necessary adjustment of Inlet Guide Vanes (IGV) is carried out to optimize the performanceof the compressor， which amounts to between 60-6 % of the total work produced by the gas turbine.
The turbine firing temperature， which affects thelife， power output， aswell as the overall thermal efficiency of the turbine， must be calculated very accurately. To ensurethe accuracy of this calculation， the turbine firing temperature is computed using two techniques. These techniques are based firstly on the fuel heat input and secondly on the turbine heat balance. Turbine expander efficiencies are computed and deterioration noted.
　
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