Thermodynamic cycles can be divided into two general categories: power cycles, which produce a net power output, and refrigeration and heat pump cycles, which consume a net power input. The thermodynamic power cycles can be categorized as gas cycles and vapor cycles. In gas cycles, the working fluid remains in the gas phase throughout the entire cycle. In vapor cycles, the working fluid exits as vapor phase during one part of the cycle and as liquid phase during another part of the cycle. Internal combustion engines and gas turbines undergo gas power cycle.

Internal combustion engines, which are commonly used in automobiles, have two principal types: spark-ignition engines and compression-ignition engines. This section will introduce the compression-ignition engines and the ideal cycle for compression-ignition engines - Diesel Cycle.

Four-stroke Compression Cycle
for CI Engine

In compression-ignition engines, air is compressed to a high pressure and temperature which is above the auto ignition temperature of the fuel. When the fuel is injected, the combustion occurs spontaneously. Compression-ignition engines are suited for heavy trucks, buses, and ships which require large amount of power.

In spark-ignition engine, compression ratio is limited because of engine knock. In CI engine, only air is compressed during the compression stroke. Therefore, CI engine can be designed to operate at a much higher compression ratio.

The four strokes for a CI engine is the same as SI engine. They are

• Intake stroke:
  The piston starts at the top dead center, the intake valve opens, and the piston moves down to let the engine take in a cylinder-full of air
• Compression stroke:
  The piston moves back up to compress air to a temperature which is higher than the auto ignition temperature of the fuel.
• Combustion stroke (power stroke):
  When the piston approaches the top of its stroke, fuel starts to be injected from the fuel injector and the combustion occurs spontaneously, driving the piston down. Fuel is injected during the first part of the power stroke, resulting in a longer combustion interval.
• Exhaust stroke:
  Once the piston hits the bottom of its stroke, the exhaust valve opens and the exhaust leaves the cylinder to go out through the tail pipe.

A new cycle can begin again.

Isentropic Compression (1-2)

The only difference between ideal Otto cycle and ideal Diesel cycle is the heat addition process. Instead of constant volume heat addition process in SI engine, heat is added to the air in the Diesel engine at constant pressure. The four processes are:

• 1-2 Isentropic compression
• 2-3 Constant pressure heat addition
• 3-4 Isentropic expansion
• 4-1 Constant volume heat rejection

Isentropic Expansion (3-4)

Constant Volume Heat Rejection (4-1)

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:

      -w₁₂ = u₂ - u₁

      -w₃₄ = u₄ - u₃

w₁₂ is negative since work is needed to compress the air in the cylinder and w₃₄ 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

      w₂₃ = P₂(v₃ - v₂)

The energy balances for this process is:

      q₂₃ = u₃ - u₂ + w₂₃ = h₃ - h₂

In the constant volume heat rejection process, no work interaction is involved since no volume change occurs. The energy balances for this process is:      

      q₄₁ = u₁ - u₄

q₂₃ is positive since heat is added to the air and q₄₁ 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,

      q₂₃ + q₄₁ - w₁₂ - w₃₄ = 0

The thermal efficiency of an ideal Otto cycle is

      η_th,Diesel = w_net/q_in

According to the analysis above, the net work output is

      w_net = w₃₄ + w₁₂ = q₂₃ + q₄₁

      q_in = q₂₃

      η_{th, Diesel} = 1+ q₄₁/q₂₃

Under the cold air-standard assumption, the thermal efficiency of an ideal Diesel cycle is

In order to simplify the above equation, the cutoff ratio r_c is defined as

r_c = v₃/v₂

Process 1-2 and process 3-4 are isentropic. Thus,

The thermal efficiency relation reduces to