(2) Determine the thermal efficiency and
compression ratio using Dieselcycle model
The Pv and Ts diagrams of the ideal Diesel cycle
are shown on the left. The
previous section, the properties
at the four states of an Otto cycle was determined. They are:
state 1: T_{1} = 15^{o}C,
P_{1} = 100 kPa (given)
State 2: T_{2} = 343.3^{o}C
State 3: T_{3} = 1800^{o}C
(given)
State 4: T_{4} = 695.7^{o}C
The heat input to the cycle is:
q_{in,Otto} = c_{v23} (T_{3} 
T_{2}) = 0.718(1800  343.3)
=
1045.9 kJ
In Diesel cycle, with the temperature limit is the same as In Otto cycle,
temperature at state 1 and state 3 are:
T_{1} = 15^{o}C
T_{3} = 1800^{o}C
Also, heat input is the same as in the ideal Otto cycle. In Diesel cycle,
heat is input from the constant pressure cycle.
q_{in,Diesel} = c_{P23} (T_{3} 
T_{2}) = 1.005 (1800  T_{2})
=
1045.9 kJ
The temperature at state 2 can be determined from the above expression.
That is,
T_{2} = 759.3^{o}C
= 1032.3 K
The thermal efficiency of the ideal Diesel cycle is:
where r is the compression ratio and r_{c} is the cutoff ratio.
r = v_{1}/v_{2}
r_{c} = v_{3}/v_{2}
In Diesel cycle, process 12 is isentropic compression process. It gives,
Hence, the compression ratio of an ideal Dieselcycle is 24.3, which
is much higher than the compression ratio of an ideal Ottocycle, which
is
6.7.
Process 23 in an ideal Diesel cycle is an constant pressure cycle.
Thus,
It gives that the cutoff ratio equals 2.01.
Substitute the compression ratio and cutoff ratio to the expression
of thermal efficiency yields,
Also, the thermal efficiency of the ideal Dieselcycle is much higher
than the ideal Ottocycle, which is 53.3%.
