What is the name of the thermodynamic cycle used in gas turbines?

The thermodynamic cycle used in gas turbines is the Brayton cycle.

An ideal Brayton cycle consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection. In an open gas turbine, atmospheric air is compressed, heated—usually by burning fuel—and expanded through a turbine. Part of the turbine’s work drives the compressor; the remaining energy produces shaft power or thrust.

The cycle is also called the Joule cycle. It is named after American engineer George Brayton, whose 1872 Ready Motor used a piston compressor and expander rather than the turbine arrangement common today. John Barber had patented an earlier gas-turbine concept in 1791, but practical gas turbines emerged much later.

The Brayton cycle is often confused with the Rankine cycle. Rankine systems use a liquid–vapor working fluid, commonly water, and are typical of steam power plants. Brayton systems use gases and are fundamental to jet engines, aircraft turbines, and many electricity-generating gas turbines. Real machines depart from the ideal cycle because compression and expansion are not perfectly isentropic.