Page 119 - Entrophy Analysis in Thermal Engineering Systems

112 Entropy Analysis in Thermal Engineering Systems

where j¼1, 2.
Within the combustor, methane is burned according to the following
reaction.

CH 4 + Λ O 2 +3:76N 2 Þ ! CO 2 +2H 2 O+ Λ 2ð ÞO 2 +3:76ΛN 2 (8.33)
ð
The thermodynamic model of the fuel compressor (FC) is like that of the air
compressor. The combustion products leave the combustor at adiabatic
flame temperature T 3 , which is the turbine inlet temperature (TIT).
The molar flowrate of the air required per unit molar flowrate of the fuel,
i.e., 4.76Λ, can be obtained by applying an energy balance to the combustor.

ð ð
h CH 4 + Λ h 2,O 2 +3:76h 2,N 2 Þ ¼ h 3,CO 2 +2h 3,H 2 O + Λ 2Þh 3,O 2 +3:76Λh 3,N 2
(8.34)

For a given T 3 , Eq. (8.34) is solved to find Λ.
The hot combustion products are expanded within the turbine to the
ambient pressure, i.e., p 4 ¼p 0 . The temperature at the outlet of the turbine
under isentropic condition is found as
γ t 1

p 4
T 4s ¼ T 3 γ t (8.35)
p 3
where γ t ¼c p,mix /(c p,mix R) and

X
c p,mix ¼ y i c p,i i ¼ CO 2 ,H 2 O,O 2 ,N 2 (8.36)

where y i is the mole fraction of component i in the combustion gases.
The outlet temperature of the turbine T 4 is determined using its isentro-
pic efficiency.

h 3 h 4
η ¼ (8.37)
t h 3 h 4s
The enthalpy and entropy of the combustion products at the entrance and
exit of the turbine are computed by

½ ð Š (8.38)
H j ¼ h CO 2 +2h H 2 O + Λ 2Þh O 2 +3:76Λh N 2 j
½ ð Š (8.39)
S j ¼ s CO 2 +2s H 2 O + Λ 2Þs O 2 +3:76Λs N 2 j
where j¼3, 4.