For the same compression ratio, the Brayton cycle efficiency as compared to that of the Otto cycle is

Concept:

Brayton Cycle:

The Brayton cycle (or Joule cycle) represents the operation of a gas turbine engine.

The cycle consists of four processes

• Process a – b: Reversible adiabatic compression in the inlet and compressor
• Process b – c: Isobaric heat addition (fuel combustion)
• Process c – d: Reversible adiabatic expansion in the turbine and exhaust nozzle
• Process d – a: Cool the air at constant pressure back to its initial condition.

The efficiency of the Brayton cycle:

\({\eta _{\rm{b}}} = 1 - \;\frac{1}{{r{_p^{\frac{γ - 1}{γ}}}}}\)

Where, rp = pressure ratio = \(\frac{{{P_b}}}{{{P_a}}} = \frac{{{P_c}}}{{{P_d}}}\)

Otto cycle:

Otto cycle consists of four processes. They are as follows:

Process 1 – 2: Reversible adiabatic or Isentropic compression

Process 2 – 3: Constant Volume Heat Addition

Process 3 – 4: Isentropic (reversible adiabatic) expansion

Process 4 – 1: Constant Volume Heat Rejection

The efficiency of the Otto cycle:

\({\eta _{otto}} = 1 - \frac{1}{{{r^{γ - 1}}}}\)

Where r = compression ratio \(= \,\,\frac{{V_1}}{{V_2}}\)

We know that compression in both the Otto cycle and Brayton cycle is an isentropic process, so we may write

\(\frac{T_2}{T_1}=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}=\left(\frac{V_1}{V_2}\right)^{{γ -1}}\)

Thus for the same pressure ratio or compression ratio in Otto and Brayton, their efficiency is equal.