Page 104 - Entrophy Analysis in Thermal Engineering Systems

Irreversible engines—Closed cycles 97

1
2
γ 1
ð CRÞ _ Φ min ¼ CRÞ _ W max π ðÞ CRÞ _ W max π ¼ 5:7Þ 5ðÞ ¼ 28:5
ð
ð
ð
The optimum compression ratio minimizing the entropy generation rate is
28.5, which could also be verified in Fig. 7.6. However, this compression
ratio is impractical since both the power and the efficiency of the engine
approach zero at a compression ratio of 18.

7.5 Diesel cycle

In Diesel cycle, the heat addition and heat removal processes take
place at constant pressure and constant volume through lines 2!3 and
4!1in Fig. 7.1. The air temperature at states 2 and 4 can be obtained using
the following relations.

γ 1 1

T 2 ¼ T 1 1+ CR (7.42)
η
com
( " #)
γ
1 γ
T 4 ¼ T 3 1 η 1 CR (7.43)
exp T R
where CR¼V 1 /V 2 .
The heat transfer rates between the thermal reservoirs and the engine are
obtained as follows.

γ 1

_ CR 1
Q ¼ _mc p T 3 T 2 Þ ¼ _mc p T 1 T R 1 (7.44)
ð
H η
com
( " #)
γ
1 γ
_ CR
Q ¼ _mc v T 4 T 1 Þ ¼ _mc v T 1 T R 1 η T R 1
ð
L exp T R
(7.45)
Thus, the expressions for the net power production and the thermal effi-
ciency read
( " # )
γ γ 1 1
1 γ
γ
CR CR
ð
_ W net ¼ _mc v T 1 η T R 1 + T R 1Þ γ 1Þ
ð
exp η
T R
com
(7.46)