System and method having fluid injectors for isothermal expansion in turbine stage of gas turbine engine

A method, comprising:

• routing a combustion gas through a turbine stage along a combustion gas path disposed between a turbine shaft and a turbine casing of a gas turbine, wherein the turbine shaft is disposed along a rotational axis, the turbine casing is disposed circumferentially about the turbine shaft, the turbine stage comprises a plurality of turbine vanes disposed upstream from a plurality of turbine blades, and each of the plurality of turbine vanes has an airfoil body;
• and
• varying axial positions of combustion over an axial stage length of the plurality of turbine blades of the turbine stage to reduce temperature variations over the turbine stage via one or more variations in a plurality of fluid injectors of an isothermal expansion system coupled to the turbine stage, wherein at least one fluid injector of the plurality of fluid injectors is on the airfoil body of each of the plurality of turbine vanes, wherein the one or more variations comprise variations in an axial position of the at least one fluid injector relative to a leading edge of the airfoil body of a respective vane of the plurality of turbine vanes from one vane to another in the plurality of turbine vanes;
• wherein the at least one fluid injector of a first turbine vane of the plurality of turbine vanes is an upstream-most fluid injector of the plurality of fluid injectors and the at least one fluid injector of a second turbine vane of the plurality of turbine vanes is a downstream-most fluid injector of the plurality of fluid injectors;
• wherein the first turbine vane and the second turbine vane are diametrically opposed with respect to the turbine casing;
• wherein the axial position of the at least one fluid injector of each of a first set of turbine vanes between the first turbine vane and the second turbine vane are positioned downstream of the at least one fluid injector of a respective preceding turbine vane along a first path from the first turbine vane to the second turbine vane;
• and
• wherein the axial position of the at least one fluid injector of each of a second set of turbine vanes between the first turbine vane and the second turbine vane are positioned upstream of the at least one fluid injector of a respective preceding turbine vane along a second path from the second turbine vane to the first turbine vane.

A system, comprising:

• a controller having a processor, a memory, and instructions stored on the memory and executable by the processor to:
• control combustion in a combustor to generate a combustion gas flow that flows through a turbine stage along a combustion gas path disposed between a turbine shaft and a turbine casing of a gas turbine, wherein the turbine shaft is disposed along a rotational axis, the turbine casing is disposed circumferentially about the turbine shaft, the turbine stage comprises a plurality of turbine vanes disposed upstream from a plurality of turbine blades, and each of the plurality of turbine vanes has an airfoil body;
• and
• control an isothermal expansion system comprising a plurality of fluid injectors having one or more variations to vary axial positions of combustion over an axial stage length of the plurality of turbine blades of the turbine stage to reduce temperature variations over the turbine stage, wherein at least one fluid injector of the plurality of fluid injectors is on the airfoil body of each of the plurality of turbine vanes, wherein the one or more variations comprise variations in an axial position of the at least one fluid injector relative to a leading edge of the airfoil body of a respective vane of the plurality of turbine vanes from one vane to another in the plurality of turbine vanes;
• wherein the at least one fluid injector of a first turbine vane of the plurality of turbine vanes is an upstream-most fluid injector of the plurality of fluid injectors and the at least one fluid injector of a second turbine vane of the plurality of turbine vanes is a downstream-most fluid injector of the plurality of fluid injectors;
• wherein the first turbine vane and the second turbine vane are diametrically opposed with respect to the turbine casing;
• wherein the axial position of the at least one fluid injector of each of a first set of turbine vanes between the first turbine vane and the second turbine vane are positioned downstream of the at least one fluid injector of a respective preceding turbine vane along a first path from the first turbine vane to the second turbine vane;
• and
• wherein the axial position of the at least one fluid injector of each of a second set of turbine vanes between the first turbine vane and the second turbine vane are positioned upstream of the at least one fluid injector of a respective preceding turbine vane along a second path from the second turbine vane to the first turbine vane.