Page 65 - Advanced Thermodynamics for Engineers, Second Edition

50 CHAPTER 3 ENGINE CYCLES AND THEIR EFFICIENCIES

k
b 1
> 1; for a diesel ðconstant pressureÞ cycle: (3.25)
C ¼
kðb 1Þ
Hence, for a given compression ratio (r) the thermal efficiencies are related by
(3.26)
th diesel
th dual comb
th Otto
ðh Þ > ðh Þ > ðh Þ
However, the situation changes if the maximum pressure is limited: in fact, if all three cycles are
compared for the same peak pressure and same work output, then
(3.27)
th diesel th dual comb th Otto
ðh Þ > ðh Þ > ðh Þ
Why is this the case? Considering first the cycles with the same compression ratio, then it is
apparent that the average expansion ratio of each of the cycles is different. The average expansion ratio
of the Otto cycle is equal to the compression ratio, r.In Fig. 3.15, V e represents a typical cycle and the
typical expansion ratio r e ¼ V 1 =V e and, since V e > V 2 , then r e < r. So if there is any constant pressure
combustion then there must be a lower mean expansion ratio than in the case of the Otto cycle.
Figure 3.16 shows a comparison of two cycles (an Otto and a Diesel cycle). These have the same
peak pressure and the same work output. It can be seen that the compression ratio of the diesel engine is
higher than that of the Otto cycle engine: in fact, the expansion ratio of the Diesel cycle throughout the
cycle is higher than the compression ratio of the Otto cycle. This means that the thermal efficiency of
each element of the Diesel cycle is more efficient than the Otto cycle, and hence this Diesel cycle is
more efficient than the Otto cycle. A similar argument applies for the dual-combustion cycle, which
lies between the Diesel and Otto cycles.
These idealised cycles enable general concepts to be understood. They have enabled us to see why a
Diesel engine cycle can be more efficient than an Otto one if the peak pressure is limited. They have
shown that expansion ratio is a more relevant parameter than compression ratio when considering the
efficiency of a cycle. However, they have not allowed us to see how the performance of real engines,
with finite rates of combustion, varies when parameters are changed. These are considered in

Maximum pressure
Pressure, p

Volume, V
FIGURE 3.16
Comparison of Otto and Diesel cycles with the same maximum pressure and work outputs.