Carnot, Otto, Diesel and Joule Cycles

The Carnot, Otto, Diesel and Joule cycles describes the processes common in combustion displacement and gas turbine engines.

Carnot Cycle

The Carnot cycle is the ideal cycle with the best possible efficiency for a machine operating between two temperature levels T_max and T_min. 

Heat addition and heat rejection occur isothermally in the cycle between point 1 and 2, and 3 and 4. 

The efficiency can be calculated as

μ = 1 - T_min / T_max          (1)

where

μ =  efficiency (0.. 1)

T_min = min. temperature (K)

T_max = max. temperature (K)

Otto Cycle

The Otto cycle is a contant-volume cycle where addition of heat or combustion takes place isochorically.

Heat addition and heat rejection occur isothermally in the cycle between point 2 and 3, and 4 and 1.

The efficiency of the Otto cycle can be calculated as

μ = 1 - ε^{(1 - κ)}        (2)

where

μ =  efficiency (0.. 1)

ε = compression ratio

κ = isentropic exponent

Diesel Cycle

The Diesel cycle is a constant-pressure cycle where the addition of heat and combustion takes place isobaric. 

Heat addition and heat rejection occur isothermic in the cycle between point 2 and 3,  and 4 and 1.

The efficiency of the Diesel cycle can be calculated as

μ = 1 - (Φ^κ - 1) / (ε^{(κ - 1)} κ (Φ - 1) )      (3)

where

μ =  efficiency (0.. 1)

ε = compression ratio

κ = isentropic exponent

Φ = injection ratio

Joule Cycle

The Joule cycle is a comparison cycle for gas turbines with continuous flow.

The efficiency can be calculated as

η = 1 - T₁ / T₂                             (4)