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

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, and the turbine stage comprises a plurality of turbine vanes disposed upstream from a plurality of turbine blades;
• and
• control an isothermal expansion system comprising a plurality of multi-fluid injectors to vary axial positions of combustion within a turbine stage expansion of the turbine stage to reduce temperature variations over the turbine stage expansion, wherein at least one multi-fluid injector of the plurality of multi-fluid injectors is coupled to each of the plurality of turbine vanes, wherein each of the plurality of multi-fluid injectors comprises a fuel port configured to inject a fuel, an oxidant port configured to inject an oxidant, and a barrier fluid port configured to inject a barrier fluid between the fuel and the oxidant, wherein the barrier fluid is configured to delay mixing between the fuel and the oxidant.