Page 361 - Advanced thermodynamics for engineers
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350 CHAPTER 16 RECIPROCATING INTERNAL COMBUSTION ENGINES
Considering the case of a compression ratio r ¼ 12.
Then h th ¼ 0.6299 and
0:6299 1 43000
p ¼ ¼ 18:40 bar:
i
0:287 373 15 ð1 1=12Þ
The peak pressure is given by working around cycle
k 1:4
p 2 ¼ p 1 ðrÞ ¼ 1 ð12Þ ¼ 32:42 bar
k 1
T 2 ¼ T 1 ðrÞ ¼ 1007:8K:
The peak temperature at 3, T 3 ¼ 1007.8 þ 4009.32 ¼ 5017.1 K and the peak pressure, p 3 ,is
5017:1
p 3 ¼ 1 12 ¼ 161:4 bar:
378
This example shows that the increase of compression ratio from r ¼ 7to r ¼ 12 gives an increase in
the thermal efficiency from 54% to 63% but also results in a very large increase in the peak pressure
(from 90 to 161 bar) while only achieving an increase in output (mep) from 16.9 to 18.4 bar. Hence an
increase in compression ratio, while helping the efficiency, does bring problems in its wake. The
higher compression ratio will result in higher pressures and temperatures, which will cause increased
loadings, both mechanical and thermal on the engine structure, and significantly more dissociation
further limiting the gains achieved from the higher compression ratio.
Example 16.2.2
Consider the effect on the imep of increasing the air–fuel ratio from 15 to 20:1. There is no effect
on thermal efficiency, which is a function only of compression ratio. Consider compression ratio of
r ¼ 7 then
15
p ¼ 16:90 ¼ 12:7 bar:
i
20
If compression ratio, r ¼ 12
15
p ¼ 18:40 ¼ 13:8 bar:
i
20
Hence the imep is inversely related to the air–fuel ratio in an air-standard Otto cycle, as would be
expected because the amount of fuel burned has been reduced.
16.2.1 REALISTIC ENGINE CYCLES
In a real engine cycle, the rate at which fuel is burned, equivalent to the rate at which energy is added to
the cycle, usually referred to as the rate of heat release, cannot achieve the constant volume or constant
pressure combustion required by the Otto or diesel cycles – see Fig. 16.1. This means that the actual
p–V diagram will be rounded as shown in Fig. 16.2. Considering only the Otto cycle, this can be
considered to consist of an infinite number of infinitesimal cycles, as shown. Each of these cycles
approximates to an Otto cycle and has an efficiency of (Eqn (3.16))