Noting that the ideal Diesel cycle is executed in a closed system
and the working fluid is air according to the air-standard assumption.
Also,
changes
in kinetic
and potential energies are negligible. No heat transfer is involved in
the two isentropic processes. The energy balances for these two processes
are:
-w_{12} = u_{2} -
u_{1}
-w_{34} = u_{4} -
u_{3}
w_{12} is negative since work is needed to compress the air
in the cylinder and w_{34} is positive since air does work to
the surroundings during its expansion.
In the constant pressure heat addition process, air is expanded to keep
the pressure as constant during the heat addition. The expansion work
equals
w_{23} = P_{2}(v_{3} - v_{2})
The energy balances
for this process is:
q_{23} = u_{3} -
u_{2 }+ w_{23} = h_{3} - h_{2}
In the constant volume
heat rejection process, no work interaction is involved since no volume
change
occurs.
The energy
balances
for this process is:
q_{41} = u_{1} -
u_{4}
q_{23} is positive since heat is added to the air and q_{41} is
negative since heat is rejected to the surroundings during this process.
For the whole cycle, the energy balance can be determined by adding
the energy balance of its four processes. That is,
q_{23} + q_{41} -
w_{12} - w_{34} = 0 |