Page 362 - Advanced thermodynamics for engineers

16.2 FURTHER CONSIDERATIONS OF BASIC ENGINE CYCLES 351

(a) (b)
3 3
p 2 Incremental cycle
Pressure, Pressure, p

Incremental
cycle
2 4 4

1 1
Volume, V Volume, V
FIGURE 16.2
p–V diagrams comparing realistic cycles with air-standard cycles (a) Otto cycle; (b) diesel cycle.

1
h ¼ 1 k 1
th
r e
but now r e is not the nominal compression ratio but is an effective compression ratio, or more
accurately the expansion ratio, for that incremental cycle.
The incremental cycle can be considered to be brought about by addition of dq units of energy and
hence the work output of the whole engine cycle is
1
X
W ¼ dq 1 k 1 (16.11)
r e
whilst the energy addition is
X
Q ¼ dq (16.12)
So the efficiency is

1
P
dq 1 k 1
r e
h ¼ P (16.13)
th
dq
1

which results in h th being less than the maximum value of 1 and depending on the
r k 1
‘roundness’ of the diagram. It is possible to take this into account using a diagram factor (h d ) such that
the actual efficiency (and work output) can be related to the ideal cycle by
1
h ¼ h h ¼ h d 1 (16.14)
d th
r k 1
h d is usually about 0.7.