**Diesel Cycle – Definition, Process, PV Diagram and TS Diagram:**

Diesel Cycle was introduced by Rudolph Diesel in 1897. It is the cycle used in the Diesel (compression-ignition) engine. The heat is transferred to the working fluid at constant pressure. The Fig. 2.3 below shows the PV and T-s diagram of a Diesel cycle.

The Diesel cycle comprises of the following operations

**Process 1-2: Adiabatic compression:**

In this process, the piston moves from BDC to TDC position. The air is compressed adiabatically with a compression ratio typically between 15 and 20. The compression rises the temperature of the air and leads to ignition temperature of the fuel mixture formed by injecting fuel. The pressure rises from P_{1} to P_{2}, the volume decreases from V_{1} to V_{2}, the temperature increases from T_{1} to T_{2} and the entropy remains constant (S_{1} = S_{2}).

**Process 2-3: Addition of heat at constant pressure:**

In this process, the piston remains at TDC position for a moment. Heat is added at constant pressure (P_{2} = P_{3}) by injection of fuel and combustion. The volume of the mixture increases from V_{2} to V_{3}, the temperature increases from T_{2} to T_{3} and entropy increases from S_{2} to S_{3}.

**Process 3-4: Adiabatic expansion:**

In this process, the piston moves from TDC to BDC position. It is the power stroke of the cycle. The air expands adiabatically thus the volume increases from V_{3} to V_{4}, the temperature decreases from T_{3} to T_{4}, pressure decreases from P_{3} to P_{4} and the entropy remains constant (S_{3} = S_{4}).

**Process 4-1: Heat rejection at constant volume:**

In this process, the piston remains at the BDC position for a moment. Heat is rejected at constant volume (V_{1} = V_{4}). The pressure decreases from P_{4} to P_{1}, the temperature decreases from T_{4} to T_{1} and the entropy decreases from S_{4} to S_{1}.

In the cycle consider for unit mass

Let compression ratio

and cut off ratio

To derive η, we must derive T_{2}, T_{3} and T_{4} from the process 1 – 2, process 2 – 3 and process 3 – 4 respectively.

During adiabatic compression 1 – 2

During constant pressure 2 – 3

Substituting the value of T_{2} from equation (5)

During adiabatic expansion 3 – 4

Substituting the value of T_{3} from equation (6)

Inserting equation (5), (6) and (7) in equation (4), we get