(2) Determine the thermal efficiency and
compression ratio using Diesel-cycle model
The P-v and T-s 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: T1 = 15oC,
P1 = 100 kPa (given)
State 2: T2 = 343.3oC
State 3: T3 = 1800oC
State 4: T4 = 695.7oC
The heat input to the cycle is:
qin,Otto = cv23 (T3 -
T2) = 0.718(1800 - 343.3)
In Diesel cycle, with the temperature limit is the same as In Otto cycle,
temperature at state 1 and state 3 are:
T1 = 15oC
T3 = 1800oC
Also, heat input is the same as in the ideal Otto cycle. In Diesel cycle,
heat is input from the constant pressure cycle.
qin,Diesel = cP23 (T3 -
T2) = 1.005 (1800 - T2)
The temperature at state 2 can be determined from the above expression.
T2 = 759.3oC
= 1032.3 K
The thermal efficiency of the ideal Diesel cycle is:
where r is the compression ratio and rc is the cutoff ratio.
r = v1/v2
rc = v3/v2
In Diesel cycle, process 1-2 is isentropic compression process. It gives,
Hence, the compression ratio of an ideal Diesel-cycle is 24.3, which
is much higher than the compression ratio of an ideal Otto-cycle, which
Process 2-3 in an ideal Diesel cycle is an constant pressure cycle.
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 Diesel-cycle is much higher
than the ideal Otto-cycle, which is 53.3%.