What's beautiful to me is that that combustion turbines have the simplest possible thermodynamic cycle in theory (a steady input flow of X fluid/sec at pressure P, and a steady output flow of Y>X fluid/sec at pressure P), yet it turns out to be one of the most complex cycles to harness in practice!
Is that really the thermodynamic cycle of the turbine? My understanding is that a cycle is something like "adiabatic compression followed by isothermic expansion, followed by ...", i.e. the details of what happens to the working fluid.
In a gas turbine, the phases of the thermodynamic cycle happen simultaneously in time, but in different places inside the turbine.
While a portion of air progresses through the turbine, it passes through the phases of the cycle.
During the first phase, the air passes through the compressor section of the turbine, where it is compressed adiabatically. During the second phase, fuel is added to the air and it burns, heating the air, which expands at an approximately constant pressure. During the third phase, the exhaust gases pass through the expander section of the turbine, being expanded adiabatically.
The last phase of the cycle, which closes the thermodynamic cycle, by reaching the ambient temperature and pressure, happens in the external atmosphere, for the exhaust gases. The meaning of this phase for an open-cycle engine is that its computation provides the value of the energy lost in the exhaust gases, which reduces the achievable efficiency.
This thermodynamic cycle, which approximates what happens in a gas turbine, is named by Americans the Brayton cycle, even if the historically-correct name is the Joule cycle.
(George B. Brayton has patented an engine using this cycle in 1872, without explaining it, but James Prescott Joule had published an article analyzing in great detail this cycle, “On the Air-Engine”, already in 1851, 21 years earlier. Moreover, already in 1859, a textbook by Rankine, “A Manual of the Steam Engine and other Prime Movers”, where all the thermodynamic cycles known at that time were discussed, attributed this cycle to Joule, 13 years before the Brayton patent. Not only the work of Joule happened much earlier than that of Brayton, but the publications of Joule and Rankine have been very important in the development of the industry of thermal engines, unlike the engines produced by Brayton, which had a very limited commercial success and which had a negligible contribution to the education of the engineers working in this domain. Therefore, the use of the term "Brayton cycle" does not appear to be based on any reason, except that Brayton was American and Joule British.)
