Page 359 - Advanced thermodynamics for engineers

348 CHAPTER 16 RECIPROCATING INTERNAL COMBUSTION ENGINES

1 p 1 Q 0 v

p ¼ 1 k 1 (16.8)
i
r 1
RT 1 ε 1
r
Equation (16.8) shows that the imep is directly proportional to the trapped pressure (p 1 ), if all other
parameters remain constant. Hence the rating of an engine can be increased by pressurizing the inlet
manifold (e.g. by turbocharging) at constant air–fuel ratio – in reality, the amount of fuel added has
increased in proportion with the amount of air trapped in the cylinder.
Similar results can be evaluated for diesel and dual combustion cycles, and these will just be quoted
here
1. Diesel cycle (see Fig. 3.14)

k
W 1 ðb 1Þ
h ¼ ¼ 1 k 1 ;
th
Q 23 r kðb 1Þ
and
1 b 1 p 1 Q p
k 0
p ¼ 1 ; (16.9)
i
r k 1 kðb 1Þ 1
RT 1 ε 1
r
where Q is the negative of the enthalpy of reaction of the fuel, because the energy is added at constant
0
p
pressure.
2. Dual combustion cycle (see Fig. 3.15)
k
1 ðab 1Þ
h ¼ 1 k 1 ;
th
r ðakðb 1Þþða 1ÞÞ
and
1 ðab 1Þ p 1 Q p
k 0
p ¼ 1 k 1 (16.10)
i
r ðakðb 1Þþða 1ÞÞ 1
RT 1 ε 1
r
0
0
It has been assumed in deriving Eqn (16.10) that Q ¼ Q ; this is not unreasonable since the
p v
differences between these values are usually very small – see Chapter 10.
Example 16.2.1
Evaluate the cycle efficiency and imep of a petrol engine operating at an air–fuel ratio of 15:1 with
a trapped pressure of 1 bar and trapped temperature of 100 C. Consider compression ratios of 7 and

12:1 and evaluate the maximum cycle pressure.
Thermal efficiency of a constant volume cycle is given by:
1
h ¼ 1
th
r k 1
Thus the thermal efficiency at r ¼ 7is h ¼ 0:5408, and at r ¼ 12 is h ¼ 0:6299:
th
th