Ideal diesel cycle working principle

The ideal (air-standard) diesel cycle models the compression-ignition engine. Air is compressed so much that fuel injected at the end of compression ignites by itself. Heat is added at constant pressure while the piston moves outward, and rejected at constant volume.

Processes

1. 1-2: Isentropic compression. Air is compressed from V₁ to V₂ (compression ratio r = V₁/V₂, typically 14-22). The temperature rises above the ignition temperature of the fuel.
2. 2-3: Constant-pressure heat addition. Fuel is injected and burns while the piston starts moving down; the volume increases from V₂ to V₃. Cut-off ratio r_c = V₃/V₂.
3. 3-4: Isentropic expansion. The gas expands to V₄ = V₁ and produces the power stroke.
4. 4-1: Constant-volume heat rejection. Heat is rejected as the exhaust valve opens and the pressure falls to the initial value.

Diagrams

 P-V diagram                      T-s diagram
 P                                T
 |   2 _______ 3                  |               3
 |   |          \                 |             .'|
 |   |           '.               |           .'  |
 |   |             '.             |         .'    |
 |    \              '-.          |    2 _.'      |
 |     \                '-. 4     |    |          4
 |      '.                  |     |    |        .'
 |        '-.               |     |    |      .'
 |           '-._           |     |    |    .'
 |               '--.._     |     |    1.-'
 |                     '--- 1     |
 +-------------------------> V    +--------------------> s
    V2                      V1
 1-2 isentropic compression       2-3 constant-P heat addition
 3-4 isentropic expansion         4-1 constant-V heat rejection

Efficiency

q_in = cp (T₃ − T₂), q_out = cv (T₄ − T₁)

η = 1 − (1/r^(γ−1)) × (r_c^γ − 1)/(γ (r_c − 1))

The efficiency rises with the compression ratio and falls as the cut-off ratio increases. As r_c → 1, the diesel efficiency approaches the Otto efficiency 1 − 1/r^(γ−1).