Abstract: Turbine assemblies for gas turbine engines are provided. In one embodiment, a turbine assembly includes a row of circumferentially adjacent turbine rotor blades, each blade in the row of blades including an airfoil defining a chord extending axially between opposite leading and trailing edges of the airfoil. The chords in a mid-span region of each blade are shorter than the chords in span regions adjacent to the blade root and the blade tip. In another exemplary embodiment, a turbine assembly includes a row of circumferentially adjacent turbine stator vanes, each vane in the row of vanes including an airfoil defining a chord extending axially between opposite leading and trailing edges of the airfoil. The chords in a mid-span region of each vane are shorter than the chords in span regions adjacent to the vane root and the vane tip. A turbine rotor blade for a gas turbine engine also is provided.

Abstract: A method for operating a gas turbine engine is provided. The method comprises coupling at least one sensor within the gas turbine engine to transmit a signal indicative of a rotational speed of a rotor assembly within the gas turbine engine, detecting oscillations of the rotor assembly based on the signal transmitted from the at least one sensor, comparing detected oscillations to a predetermined oscillation threshold, and generate an output to facilitate fuel flow adjustments during non-engine operational periods, wherein the fuel flow adjustments facilitate reducing oscillations of the rotor assembly during engine operation.

Abstract: Methods and systems for ordering blades in a rotatable machine is provided. The method includes receiving at least one geometric parameter measurement of each blade in a row of blades, determining a root sum squared value of a difference of a selected one of the received geometric parameter measurements between adjacent blades in the row of blades, determining a vector sum of a selected other one of the received geometric parameter measurements, determining a moment weight vector sum of each blade to be positioned on the rotor, and determining, using a computer, a sequence map of each blade using the root sum squared value of the difference of the geometric parameter measurement between adjacent blades in the row of blades, the vector sum of a selected other one of the received geometric parameter measurements, and the moment weight vector sum.

Abstract: A method, rotor assembly, and apparatus for ordering blades in a rotatable machine is provided. The rotor assembly includes a disk including a plurality of circumferentially-spaced blade root slots defined therein, and a plurality of blades, each blade including a root, a tip, and an airfoil therebetween, each blade positioned within a pre-determined slot based on a blade map, the blade map generated by a computer system configured to receive a geometric parameter measurement of each blade in a row of blades, determine a shape factor for the row of blades using the geometric parameter measurement of each blade, and determine a sequence map of each blade using the shape factor for the row of blades.

Abstract: A method and apparatus for ordering blades in a rotatable machine is provided. The machine includes a plurality of blades that extend radially outwardly from a rotor. The method includes determining a moment weight of each blade in a row of blades, determining a geometric parameter of each blade in the same row of blades, and determining a mapping order of each blade using the moment weight and the geometric parameter. The apparatus includes a computer system that includes a software product code segment for minimizing imbalance in a bladed rotor wherein the segment is configured to receive a moment weight value for each blade to be installed in said rotor, receive a geometric parameter value for each blade to be installed in said rotor, calculate a blade location on the rotor based on the received values, and generate a blade map based on the calculated location.

Abstract: A processor-implemented method of assembling a rotatable machine is provided. The machine includes a plurality of blades that extend radially outwardly from a rotor. The method includes determining a geometric parameter for each blade in a row of blades that is relative to a ratio, R of an inlet area and an outlet area of a predetermined volume defined between each pair of blades, determining an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades, and iteratively remapping the sequence of the blades to facilitate reducing a moment weight vector sum of the rotor to a value that is less than a predetermined value.

Abstract: A method facilitates the assembly of a stator assembly for a turbine engine. The method includes providing a cantilevered shell including a first end and a second end, and coupling a second member within the turbine engine. The method also includes coupling the shell to a frame such that the shell extends circumferentially around at least a portion of the second member such that a non-uniform circumferential radial gap is defined radially between the second member and the shell using methods other than directing machining of an inner surface of the shell, and wherein the non-uniform circumferential radial clearance gap becomes substantially uniform during operation of the engine.