System and method having isothermal combustion along set of turbine blades via varying fluid injection along set of turbine vanes

A system, comprising:

• a gas turbine, comprising:
• a turbine shaft disposed along a rotational axis;
• a turbine casing disposed circumferentially about the turbine shaft;
• a combustion gas path disposed between the turbine shaft and the turbine casing;
• a turbine stage disposed in the combustion gas path, wherein the turbine stage comprises:
• a plurality of turbine blades;
• and
• a plurality of turbine vanes disposed upstream from the plurality of turbine blades, wherein the plurality of turbine vanes comprises a plurality of fluid injectors configured to inject a fluid comprising a fuel into the combustion gas path to a plurality of combustion positions around the plurality of turbine blades, the plurality of combustion positions vary in axial positions between a leading edge and a trailing edge of the plurality of turbine blades, and the plurality of combustion positions provide a substantially isothermal combustion in the combustion gas path between the leading and trailing edges of the plurality of turbine blades of the turbine stage.