Page 114 - Entrophy Analysis in Thermal Engineering Systems

Irreversible engines—Open cycles 107

1
f p
a ¼ HHV n v L w (8.11)
0
0
H + H H 0 0
_ n f
Eq. (8.11) expresses the first right-hand-side term from Eq. (8.6) as a simple
function of HHV and the enthalpy of water evaporation. Next, the second
right-hand-side term from Eq. (8.6) is determined as follows.

1 h i p
p f y z
a + Λ x +
0
0
4 2 0
S S S 0 ¼ xs CO 2 + n v s H 2 O vðÞ s O 2 +3:76Λs N 2
_ n f

y
ð Þ s f ,0 +
a
Λs O 2 +3:76Λs N 2 0 n v s H 2 O lðÞ,0
2
(8.12)
Rearranging Eq. (8.12) to group similar species together yields
1
p f p a p a
a ð ð ð ð
0
0
Þ s O 2 0
Þ s N 2 0
S S S 0 ¼ Λ s O 2 0 Þ +3:76Λ s N 2 0 Þ s f ,0
_ n f
h i
p
y
y
z
+ n v s H 2 O lðÞ,0 + xs CO 2 + x + s O 2
2 + n v s H 2 O vðÞ 4 2 0
(8.13)
where
!
a
y O 2
a
ð s O 2 0 p ð Þ ¼ R ln (8.14)
Þ s O 2 0
p
y
O 2

a
y N 2
ð s N 2 0 p ð Þ ¼ R ln (8.15)
a
Þ s N 2 0
p
y
N 2

p p
ð s CO 2 0 (8.16)
Þ ¼ s CO 2 ,0 R ln y
CO 2

ð

p sat T 0 Þ
p
¼ s H 2 O vðÞ ,0 R ln (8.17)
p
¼ s H 2 O vðÞ ,0 R ln y H 2 O vðÞ
s H 2 O vðÞ
0 p 0

p p
ð s O 2 0 (8.18)
Þ ¼ s O 2 ,0 R ln y
O 2
where y denotes the mole fraction of species i (O 2 ,N 2 ,CO 2 ,H 2 O) in mix-
j
i
ture j (air, combustion products), R is the universal gas constant, and s i,0 is the
standard entropy of species i.
Substituting Eqs. (8.14)–(8.18) into Eq. (8.13) and rearranging yields