Closed gas turbine cycle components; thermal efficiency

A closed gas turbine cycle uses a gas (air, helium) that circulates in a closed loop. Heat is added and rejected through heat exchangers instead of by internal combustion and exhaust. It corresponds to the ideal Brayton cycle.

Major components

        Heat source (Q_in)
        +----[ Heater ]----+
        |                  |
   2    |                  |   3
  [Compressor] ==shaft== [Turbine] ---> Generator
        |                  |
   1    |                  |   4
        +---[ Cooler ]-----+
          Heat sink (Q_out)

1. Compressor: raises the gas pressure (1-2, isentropic).
2. Heater (heat exchanger): adds heat from an external source at constant pressure (2-3).
3. Turbine: expands the gas and delivers work (3-4, isentropic); part of the work drives the compressor.
4. Cooler (pre-cooler): rejects heat to cooling water or air at constant pressure (4-1).
5. A generator or load on the shaft takes the net power.

Thermal efficiency

Per kg of working gas with constant cp:

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

η = 1 − q_out/q_in = 1 − (T₄ − T₁)/(T₃ − T₂)

With r_p = P₂/P₁ = P₃/P₄, the isentropic processes give

T₂/T₁ = r_p^((γ−1)/γ) = T₃/T₄

so T₄/T₁ = T₃/T₂ and (T₄ − T₁)/(T₃ − T₂) = T₁/T₂. Therefore

η = 1 − T₁/T₂ = 1 − 1/r_p^((γ−1)/γ)

The efficiency increases with the pressure ratio. A closed cycle has the advantages of using any gas, high pressure throughout (compact machines) and a clean working fluid, and it can use any heat source (such as a nuclear reactor).