# Dual Combustion Cycle and its expression for Thermal Efficiency

Dual Combustion Cycle is a combination of Otto Cycle and Diesel Cycle.
Semi diesel engine works on this cycle, so it is also known as Semi-Diesel Cycle. This cycle is mainly used in high speed diesel engines.
In this cycle heat addition is done at constant pressure and constant volume. The efficiency of this dual combustion cycle is in between Otto and Diesel Cycle.
As compared to Otto Cycle, dual combustion cycle has more time for the fuel to completely combust because heat is added partly at constant volume and partly at constant pressure in this cycle but in Otto cycle heat is added at constant volume only.

Now, let’s see the working of this cycle using a diagram.

In dual combustion cycle, there are five processes. Two of which are isentropic processes, two are isochoric processes and one is isobaric process.
Above diagram shows a cylinder and a piston. This cyclinder is closed at one end and at other side, it is closed by piston.
In front of the cylinder, two bodies are present one is hot body and another is cold body. Air is filled in the cylinder between the piston and closed end of cylinder.

Above diagram is PV and TS diagram of different processes of Dual Combustion Cycle.
Now let’s see different processes of the above arrangement.

1) Adiabatic compression :-
At first step, piston move towards the close end of cylinder. As the cylinder is filled with air and the the piston move towards closed end of cylinder, the air present in the cylinder get compressed. Due to compression the volume of air get decreased and the pressure will increase. This process is known as adiabatic compression because no heat is added or rejected from the system. As this is an adiabatic processs entropy will remian constant and temperature will increase due to compression.

2) Isochoric heat addition:-
In this process, the hot body is brought into contact with the cylinder. As the hot body comes in contact with cylinder, heat addition will start.
In this process, the piston does not move and the process is carried at constant volume. As the heat is added, entropy will increase and temperature will also increase. As the temperature increase and voulme is constant, the pressure will increase.

3) Isobaric heat addition:-
In this process, heat is added at constant pressure i.e isobarically. As the heat is added the air expand and volume increases and the piston moves away from the closed end of cylinder. As heat is added, temperature and entropy will also increase in this process.

4) Isentropic Expansion:-
In this step, hot body is moved away from the cylinder and the air is allowed to expand.As this is isentropic process, entropy will remain constant. The volume will increase in this process and the pressure will decrease. Due to expansion without heat addition, the temperature will also decrease.

5) Isochoric heat rejection :-
In this step, the cold body is brought into contact with the cylinder. This process is an isochoric process i.e constant volume process, so the piston does not move in this process. As cold body is brought into contact with the cylinder, heat is reject from the air to the cold body. As heat is rejected, the entropy decrease and the temperature decreases.The pressure will also decrease as the heat is released at constant volume.

### Thermal Efficiency of Dual Combustion Cycle:-

Thermal Efficiency ( η ) of any thermodynamic cycle is defined as the ratio of work done (W) by it to the heat supplied to it (QH).

All heat supplied cannot be converted into Work. So the fraction of heat supplied that is converted to work is known as
Thermal Efficiency ( η ) . Since supplied heat cannot be converted to work completely, therfore the heat input (QH) is equal to work done (W) plus the heat dissipated to the environment (Qc). So the above equation becomes :-

Let, combustion ratio(r) = V1/V2
Pressure or Explosion ration (α) = P3/P2
Cut -off ratio (ρ) = V4/V3

Now,

For isentropic process (1-2) :-

For constant volume process (2-3):-

For constant pressure process (3-4):-

For isentropic process(4-5):-

Now , substituting the values of T2,T3,T4 and T5 from equation (ii), (iii), (iv) and (v) in equation (i), we get

Above equation shows efficiency of dual cycle in terms of combustion ratio (r), explosion ratio (α ) and cut-off ratio ( ρ ).