Method for minimizing forces acting on turbine blades in specific frequency ranges

1. A method for configuring circumferential staging in a gas turbine engine comprising:

determine resonance frequencies of a turbine blade that revolves within the gas turbine engine;

determine a frequency spectrum of unsteady forces the turbine blade is exposed to during one revolution of the turbine blade for a first configuration of lit injectors selected from a plurality of configurations of lit injectors;

determine a frequency spectrum of unsteady forces the turbine blade is exposed to during one revolution of the turbine blade for at least one other configuration of lit injectors selected from the plurality of configurations of lit injectors, wherein the at least one other configuration of lit injectors is different than the first configuration of lit injectors;

determine which configuration from the plurality of configurations of lit injectors results in minimum unsteady forces that the turbine blade will experience; and

configure the lit injectors in the combustor to match the configuration from the plurality of configurations of lit injectors that resulted in the minimum unsteady forces that the turbine blade will experience.

2. The method of claim 1 , wherein determining the resonance frequencies of the turbine blade comprises determining respective resonance frequencies of at least two stages of turbine blades of the gas turbine engine;

wherein determining the frequency spectrum of unsteady forces the turbine blade is exposed to during one revolution of the turbine blade for the first configuration of lit injectors comprises determining a sum of unsteady forces the at least two stages of turbine blades are exposed to during one revolution of the at least two turbine blade stages for the first configuration of lit injectors;

wherein determining the frequency spectrum of unsteady forces the turbine blade is exposed to during one revolution of the turbine blade for the at least one other configuration of lit injectors comprises determining a sum of unsteady forces the at least two stages of turbine blades are exposed to during one revolution of the at least two turbine blade stages for the at least one other configuration of lit injectors;

wherein determining which configuration of lit injectors results in minimum unsteady forces that the turbine blade will experience comprises determining which configuration of lit injectors results in a minimum sum of unsteady forces the at least two turbine stages will experience; and

wherein configuring the lit injectors in the combustor to match the configuration resulting in the minimum unsteady forces that the turbine blade will experience comprises configuring the lit injectors in the combustor to match the configuration resulting in the minimum sum of unsteady forces the at least two stages of turbine blades will experience.

3. The method of claim 1 , wherein the configuration from the plurality of lit injectors that results in minimum unsteady forces experienced by the turbine blade is different for turbine blades in at least two stages of the gas turbine engine.

4. The method of claim 1 , wherein the minimum unsteady forces that the turbine blade will experience is determined using the equation min (∫ fres.−Δ fres.+Δ FFT(T(t)df).

5. The method of claim 4 , wherein T(t) is a synthetic temperature profile constructed from normal distributions calibrated using computational fluid dynamic (CFD) results representing an unlit injector and t is a function of the revolutions per minute of the turbine blade.

6. The method of claim 4 , wherein T(t) includes effects of guide vane wakes.

7. The method of claim 1 , wherein the configuration of lit injectors that resulted in minimum unsteady forces that the turbine blade will experience results in unequal spacing between each lit injector.

8. The method of claim 1 , wherein both lit and unlit injectors are arranged in an annular configuration.