Page 116 - Entrophy Analysis in Thermal Engineering Systems

Irreversible engines—Open cycles 109

The two values obtained using Eqs. (8.21) and (8.23) are very close. Thus,
from Eq. (8.23), one may conclude that T 0 C 2 L ¼ 0. Eq. (8.22) may
w
0
finally be expressed as
w rev ¼C + F Λ (8.24)
ðÞ
where

(8.25)
C¼ HHV + T 0 C 1
2 3
Λ
3:76Λ
a a
y y
6 O 2 N 2 7
F ΛðÞ ¼ T 0 R ln 6 7 (8.26)
4 y z 5
3:76Λ Λ x +
4 2

p p x p
y y y
N 2 CO 2 O 2
It can be deduced from Eqs. (8.20) and (8.25) that C 1 ,and therefore C are
constant parameters for a specified fuel at the ambient temperature and pres-
sure. So, w rev can be represented as a function of fuel-air equivalence ratio, ϕ:
w rev ¼w rev (ϕ), where ϕ¼Λ/Λ min .
The numerical values of w rev are calculated and given in Table 8.1 for 13
different fuels over a range of equivalence ratios. The last column, Δw rev , lists
the percentage increase in w rev as ϕ is raised from 1 to 5. These results indicate
that a fivefold increase in ϕ only raises w rev by 1.7% on average. Thus, w rev
appears to be a very weak function of ϕ. Note that for hydrogen and carbon
monoxide, w rev is less than the lower heating value (LHV), whereas for other
fuels it is between the lower and higher heating values.
The trend observed in Table 8.1 can be written as

w rev ϕð ð (8.27)
1 Þ w rev ϕ Þ… w rev ϕðÞ 1 ϕ 5 i ¼ 1,2,…,n
2
n
i
It can be implied from Eq. (8.27) that the numerical value of F ΛðÞ is neg-
ligible compared to constant C in Eq. (8.24) whereby w rev ffiC. Alternatively,
w rev may be expressed in terms of any ϕ within the range 1 ϕ i 5. For the
sake of simplicity, ϕ min ¼1 is selected. Noting the definition of thermal effi-
ciency η ¼ w net , Eq. (8.5) results in the following inverse relationship between
HV
η and SEG.
w rev Λ min Þ T o SEG
ð
η ¼ (8.28)
HV
where w rev (Λ min ) is evaluated using Eqs. (8.24)–(8.26). Note that both η and
SEG are dependent on several process parameters such as the highest tem-
perature/pressure of the working fluid. Because w rev (Λ min ) is constant for a