Thermodynamic cycles applied to gas turbines

[LaxeyT]

This is about the basic thermodynamic cycle of the gas turbine (i.e. Brayton or Joule cycle), consisting of adiabatic compression, heat addition at constant pressure, adiabatic expansion, and heat rejection at constant pressure, and the standard ways of analysing this through Pressure-Volume (P-V) and Temperature-Entropy (T-s) charts.

Real gas turbine cycles have inefficiencies in the compression and turbine expansion processes, which increase the temperatures at outlet from these components, compared with the same pressure rise (or fall) under isentropic conditions. I am trying to understand a contradiction - engineering consideration of a gas turbine would show that when the efficiencies of one or both components drops sufficiently that the turbine work output is equal to the compressor input, there is no net work output (the device would only just run).

However, if the same changes are shown on a P-V chart, there would still be positive net work output (based on the net work done around the cycle is ʃp.dv (the area under the P-V chart) around the cycle). Is it valid to use a P-V chart to show this?

Equivalently, and more straighforwardly, a Carnot cycle (a sequence of isothermal and adiabatic processes) produces positive net work output, but when analysed like a gas turbine on a T-s chart produces zero net work output..?

 

[LaxeyT]

Air standard Carnot cycle.

I would like to simplify my question:-

For the Carnot cycle:- Net work output =(ΔT)(ΔS), where ΔT = temp difference between source and sink temperatures and ΔS = entropy difference between adiabatic stages. This can be re-phrased in terms of Ps and Ts. Graphically, it is the area enclosed by the cycle on a T-S chart and also the area enclosed on a P-V chart.

In a 'real' implementation of a Carnot heat engine operating with air in a closed cycle, using turbomachinery (compressors and turbines), the net work would be extracted from the turbine, like in a Joule cycle gas turbine. However, if the net work is estimated like in a gas turbine, i.e. it is directly proportional to the difference in temperature differences across the compressor and turbine, this would be zero - no net work, but the cycle shows there is net work -can anyone explain this?

Thanks.