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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))
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