Otto cycle, Diesel cycle and Dual cycle

Cycle: A cycle is defined as a repeated series of operations occurring in a certain order. In other words, any process or series of processes whose end states are identical termed as cycle.

Assumptions of Air Standard Cycle:

• Assume working medium as perfect gas (ideal gas).
• No change in mass of working period.
• Reversible processes.
• Supply of heat from a constant high temperature source (not from chemical reactions) and rejection of heal to a constant low temperature source.
• Not heat losses from the system to surroundings.
• Constant specific heats through the cycle.

Types of Cycles

Carnot Cycle: Carnot cycle is an ideal cycle in which all the processes constituting a reversible cycle. This cycle consists of two isothermal and two reversible adiabatic processes.

• Process 1 – 2 is isothermal compression process
• Process 2 – 3 is adiabatic process (isentropic process)
• Process 3 – 4 is isothermal expansive process
• Process 4 – 1 is adiabatic process (isentropic process)

All the processes are reversible.

where, T₁ = Temperature at process 1, and T₃ = Temperature at process 3.

Carnot cycle has a low mean effective pressure because of very low work output.

The Stirling Cycle: It is modified form of Carnot cycle with high mean effective pressure. It consists of two isothermal and two constant volume processes.

• Isothermal process:

• Constant volume process

 (same as Carnot cycle)

• In practical Stirling cycle, efficiency will be less than Carnot efficiency.
• For heat exchange efficiency:

where, E = Heat exchanger effectiveness.

The Ericsson Cycle: It consists of two isothermal and two constant pressure processes. The processes are

• Process 1-2 is reversible isothermal compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible isothermal expansion
• Process 4-1 is constant pressure heat rejection

The advantage of the Ericsson cycle is its small pressure ratio for given ratio of maximum to minimum specific volume with higher mean effective pressure. Ericsson cycle is applied by a gas turbine employing a large number of stages with heat exchangers, insulators and repeater

The thermal efficiency of Ericsson, cycle is given by,

The Otto Cycle: The Otto cycle is a set of processes used by spark ignition internal combustion engines (2-stroke or 4-stroke cycles). Petrol engine works on the Otto cycle. In petrol engine, fuel burnt by spark ignition. It consists, two isentropic processes (reversible adiabatic) and two constant volume processes.

• Process 1-2 is reversible adiabatic compression of air
• Process 2-3 is heat addition constant volume.
• Process 3-4 is reversible isothermal expansion of air
• Process 4-1 is heat rejection at constant volume.

Compression ratio 

where, Q_s = Heat supplied during the isothermal process.

Q_R = Heat rejected during the isothermal expression process

Work Output (W): It can be measures as

where, Q_s = Heat supplied, and Q_R = Heat rejected

Heat supplied:

Q_S = m C_V (T₃ – T₂)

Heat rejected:

Q_R = mC_V (T₄ – T₁)

where, γ = Specific heat ratio, and r_p = Pressure ratio

Pressure ratio: 

Value of 𝛄 (Ratio of Specific Heat):

• For monoatomic gas γ = 1.67
• For air γ = 1.40
• For exhaust gas γ = 1.30

Mean Effective Pressure: It is defined as the ratio of the net work done to the displacement volume of the piston.

Swept volume = V₁ – V₂ = V₂ (r – 1)

where, p_m = Mean effective pressure, r_p = Pressure ratio, and γ = Specific heat ratio.

The Diesel Cycle: This cycle is used in diesel engine. In diesel engine, fuel is burnt by compressing the air up to high pressure. It consists of two isentropic processes, one constant volume process and one constant pressure process.

• Process 1-2 is reversible adiabatic compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible adiabatic compression
• Process 4-1 is constant volume heat rejection

Volume ratio or cut-off ratio: 

Compression ratio: 

Work Output: Work output can be calculated by the following relation.

Where, r = Compression ratio, and r_c = Cut-off ratio.

Dual Cycle: In this cycle, heat is added partly at constant volume and partly at constant pressure. It consists of two isentropic processes, two constant volume processes and one constant pressure process.

• Process 1-2 is reversible adiabatic compression
• Process 2-3 is constant volume heat addition
• Process 3-4 is constant pressure heat addition
• Process 4-5 is reversible adiabatic expansion
• Process 5-1 is constant volume heat rejection

• Efficiency 
• Work output

• Mean effective pressure

Comparison of Efficiencies in Cycles:

For same compression ratio and heat addition

For same compression ratio and heat rejection

Same peak pressure, peak temperature and heat rejection

Same maximum pressure and heat input

Same maximum pressure and work output

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