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

1. A gas turbine engine comprising:

a turbine section operative to impart rotational energy to a compressor section, wherein the turbine section includes at least a low-pressure turbine and a high-pressure turbine, and a ratio of a number of stages in the low-pressure turbine to a number of stages in the high-pressure turbine is 2, wherein the turbine section has a first set of vanes positioned adjacent a combustion section and a first set of rotatable blades positioned downstream of and adjacent to the first set of vanes, and a number of vanes of the first set of vanes exceeds a number of blades of the first set of blades.

2. The gas turbine engine of claim 1 , wherein the low-pressure turbine has exactly four stages.

3. The gas turbine engine of claim 1 , wherein the high-pressure turbine has exactly two stages.

4. The gas turbine engine of claim 1 , wherein a first stage of the high-pressure turbine comprises the first set of vanes and the first set of blades.

5. A gas turbine engine comprising:

a turbine section operative to impart rotational energy to a compressor section, wherein the turbine section includes at least a high-pressure turbine having exactly two stages and a low-pressure turbine having exactly four stages, wherein the high-pressure turbine has a first set of vanes positioned adjacent a combustion section and a first set of rotatable blades positioned downstream of and adjacent to the first set of vanes, wherein a number of vanes of the first set of vanes exceeds a number of blades of the first set of blades.

6. A method for manufacturing a gas turbine engine comprising:

providing a gas turbine engine having a combustion section and a turbine section, providing the turbine section with a first set of vanes and a first set of blades, the first set of blades being located downstream from and adjacent to the first set of vanes, wherein the turbine section includes a high-pressure turbine and a low-pressure turbine, the low-pressure turbine having four stages, wherein the high-pressure turbine has the first set of vanes positioned adjacent the combustion section wherein a number of vanes of the first set of vanes exceeds a number of blades of the first set of blades.

7. A method of operating a gas turbine engine comprising: providing a gas turbine engine having a combustion section and a turbine section, the turbine section having a first set of vanes and a first set of blades, the first set of blades being located downstream from and adjacent to the first set of vanes, wherein the turbine section includes a high-pressure turbine and a low-pressure turbine, the low-pressure turbine having four stages, wherein the high-pressure turbine has the first set of vanes positioned adjacent the combustion section, wherein a number of vanes of the first set of vanes exceeds a 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.

8. The method of claim 7 , wherein:

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

9. The method of claim 7 , 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.

10. The method of claim 7 , further comprising film-cooling the vanes of the first set of vanes.

11. The method of claim 10 , 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.