Gas turbine engine systems and related methods involving vane-blade count ratios greater than unity

1. A method for operating a gas turbine engine comprising:

providing a gas turbine engine having a combustion section and a turbine stage, the turbine stage having an inlet, a first set of vanes, and a first set of blades, the first set of vanes being located downstream and adjacent to the combustion section and downstream of the inlet, the first set of blades being located downstream from and adjacent to the first set of vanes, wherein the number of vanes of the first set of vanes exceeds the number of blades of the first set of blades; and

completing a combustion reaction along a gas flow path prior to a plane defined by downstream portions of the first set of blades;

wherein the engine exhibits a significant concentration of partially combusted products of the combustion reaction at the inlet of the turbine stage.

2. The method of claim 1 , wherein:

completing the combustion reaction comprises mixing combustion products from the combustion section using the vanes of the first set of vanes.

3. The method of claim 2 , wherein the engine is operative such that cooling air provided to the first set of vanes reacts with combustion products from the combustion section in order to complete the combustion reaction.

4. The method of claim 1 , further comprising film-cooling the vanes of the first set of vanes.

5. The method of claim 4 , wherein:

the gas turbine engine further comprises a second set of vanes located downstream from the first set of blades; and

the second set of vanes is film-cooled to a lesser extent than that provided to the first set of vanes.

6. The method of claim 5 , wherein the engine is operative to complete the combustion reaction upstream of the second set of vanes.

7. The method of claim 1 , wherein the engine is a turbofan.