Page 373 - Advanced thermodynamics for engineers

362 CHAPTER 16 RECIPROCATING INTERNAL COMBUSTION ENGINES

The imep, p is
i
pdV w i
Z
p ¼ ¼
i
V s 1
V 1 1
r
n o (16.27)
k 1 a
ðr 1Þ k 1
r
¼ p 1 :
1
ðk 1Þ 1
r
The imep given in Eqn (16.27) is exactly the same as in Eqn (16.8), except that the term
p 1 Q 0
v has been subsumed into the ‘shape’ of the diagram, e.g. the temperature rise.
RT 1 εð1 1=rÞ
The bmep is p ¼ p p . Let p be a constant, for example – 1 bar.
f
b
i
f
Then
a
ðr k 1 1Þ 1
r k
p ¼ 1 p i p f (16.28)
b
ðk 1Þ 1
r
The brake thermal efficiency h b ¼ w b /q 23 and w b ¼ p V S .
b
Thus
p V s
b
h ¼ n a o (16.29)
b
c v T 1 r k 1 1
r k
1

1

p i p f ðk 1Þ r
¼ k 1 n a o
p 1 p 1 r 1
r k
(16.30)
1

1
p f ðk 1Þ r
¼ h k 1 a
th
p 1 r 1
r k
Figure 16.8 shows imep, bmep and fmep on a p–V diagram. The fmep is subtracted from the imep
to give the bmep. Figure 16.9 shows that, within a given peak pressure, the ideal work output
(neglecting frictional and other losses) of the cycle varies from zero through a maximum value and
1=k
back to zero again as the compression ratio varies between 1 and ^ a ¼ð^ p=p 1 Þ : If the peak pressure of
an Otto cycle is limited, then it can be seen that there is a compression ratio that maximises the work
output of the cycle. This is depicted in Fig. 16.9, which shows a range of cycles with compression
ratios from 1 (which is equivalent to heat addition at constant volume) to the maximum value (where
an infinitesimal amount of heat can be transferred because the maximum pressure is reached during
compression). If these cycles are drawn on a T–s diagram, the one at maximum compression ratio is
equivalent to a Carnot cycle, producing no power output but achieving an efficiency of 1 T C /T H .