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Turbine frequency tuning, fluid dynamic efficiency, and performance can be improved using a particular airfoil profile, which can be used to determine a throat between adjacent airfoils. By shaping the throat according to the particular profile, the total pressure at an endwall can be energized, imp

Turbine frequency tuning, fluid dynamic efficiency, and performance can be improved using a particular airfoil profile, which can be used to determine a throat between adjacent airfoils. By shaping the throat according to the particular profile, the total pressure at an endwall can be energized, improving performance of the turbine.

대표청구항 ▼

1. In a turbomachine including a row of substantially identical buckets circumferentially mounted on a rotor, each bucket including a respective airfoil with opposed pressure and suction sidewalls extending chordwise between opposed leading and trailing edges and spanwise between a root and a tip, a

1. In a turbomachine including a row of substantially identical buckets circumferentially mounted on a rotor, each bucket including a respective airfoil with opposed pressure and suction sidewalls extending chordwise between opposed leading and trailing edges and spanwise between a root and a tip, a flow passage between each pair of airfoils, each flow passage comprising: a pressure sidewall of a first airfoil;a suction sidewall of a second airfoil substantially facing the pressure sidewall of the first airfoil; anda throat including an area defined at least in part by a minimum gap between the pressure sidewall of the first airfoil and the suction sidewall of the second airfoil for each corresponding chord along spans of the first and second airfoils, a width of the throat at at least one of the tips or the roots of the airfoils being no more than about 15% more than a width of the throat at a respective first or second distance from the at least one of the tips or the roots. 2. The flow passage of claim 1, wherein the first distance is no more than about 25% of the span of one of the first airfoil or the second airfoil. 3. The flow passage of claim 2, wherein the first distance is no more than about 20% of the span of the one of the first airfoil or the second airfoil. 4. The flow passage of claim 1, wherein the width of the throat increases by no more than about 10% of a width of the throat at the at least one of the first or second distance. 5. The flow passage of claim 1, wherein an absolute value of a rate of change of the width of the throat versus span increases with decreasing distance to at least one of the tips or the roots of the first and second airfoils within the first distance from the at least one of the tips or the roots. 6. The flow passage of claim 1, wherein the first distance and the second distance are no more than about 20% of a span of the first airfoil, a width of the throat at the tips is no more than about 10% wider than the width of the throat at the first distance, and a width of the throat at the roots is no more than about 10% wider than the width of the throat at the second distance. 7. The flow passage of claim 1, wherein at least one of the suction sidewall or the pressure sidewall of at least one airfoil includes a nominal profile substantially in accordance with non-dimensional Cartesian coordinate values of X, Y, and Z set forth in TABLE I, wherein the coordinate values are non-dimensionalized and convertible to distances by multiplying the coordinate values by a desired span in units of distance, and wherein X and Y values connected by smooth continuing arcs define profile sections of the at least one of the suction sidewall or the pressure sidewall at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the profile of the at least one of the suction sidewall or the pressure sidewall. 8. The flow passage of claim 1, further comprising a first end bounded at least in part by a first endwall extending between one of the roots or the tips of the first and second airfoils. 9. The flow passage of claim 8, wherein the row of substantially identical buckets is part of a diffuser of an axial turbine. 10. The flow passage of claim 1, wherein the row of substantially identical buckets is in a last stage of an axial turbine. 11. A stage of a turbine comprising: a plurality of airfoils mounted on a rotor of a turbine about an axis of rotation of the turbine in a substantially circumferential, spaced-apart fashion, each airfoil including respective opposed pressure and suction sidewalls extending chordwise between respective opposed leading and trailing edges and spanwise between opposed inner and outer endwalls, a respective root of each airfoil connected to one of the inner and outer endwalls, and at least one of the suction sidewall or the pressure sidewall including a nominal profile substantially in accordance with non-dimensional Cartesian coordinate values of X, Y, and Z set forth in TABLE I, wherein the coordinate values are non-dimensionalized and convertible to distances by multiplying the coordinate values by a desired span in units of distance, and wherein X and Y values connected by smooth continuing arcs define profile sections of the at least one of the suction sidewall or the pressure sidewall at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the profile of the at least one of the suction sidewall or the pressure sidewall; anda total throat including a component throat between adjacent airfoils of the plurality of airfoils, each component throat including a minimum gap between a pressure sidewall of a first airfoil and a suction sidewall of a second airfoil adjacent to the first airfoil for all corresponding points along spans of the first and second airfoils, a width of the component throat increasing with decreasing distance to at least one of the tips of the roots within a first distance away from the at least one of the tips or the roots. 12. The turbine nozzle of claim 11, wherein an absolute value of a rate of change of the width of the component throat with respect to span also increases with decreasing distance to the at least one of the tips of the roots within the first distance away from the at least one of the tips or the roots. 13. The turbine nozzle of claim 11, wherein the width of the component throat at at least one of the tips or the roots is no more than about 15% wider than a respective width of the component throat at the first distance away from the respective at least one of the tips or the roots. 14. The turbine nozzle of claim 13, wherein the width of the component throat at the tips is no more than about 115% of the width of the component throat at about 75% span. 15. The turbine nozzle of claim 13, wherein width of the component throat at the roots is no more than about 115% of the width of the component throat at about 25% span. 16. The turbine nozzle of claim 11, wherein the stage is a last stage of an axial turbine. 17. The turbine nozzle of claim 11, wherein both the pressure sidewall and the suction sidewall of each airfoil includes a nominal profile substantially in accordance with non-dimensional Cartesian coordinate values of X, Y, and Z set forth in TABLE I, wherein the coordinate values are convertible to distances by multiplying the values by a desired span expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile. 18. A turbine system comprising: a compressor section;a combustion section; anda turbine section, wherein a stage of the turbine section includes a plurality of substantially identical airfoils substantially circumferentially spaced apart about an axis of rotation of the turbine section, each airfoil including opposed pressure and suction sidewalls extending chordwise between opposed leading and trailing edges and spanwise between opposed respective roots and tips, and at least one of the suction sidewall or the pressure sidewall of each airfoil including a nominal profile substantially in accordance with non-dimensional Cartesian coordinate values of X, Y, and Z set forth in TABLE I, wherein the coordinate values are non-dimensionalized and convertible to distances by multiplying the coordinate values by a desired span in units of distance, and wherein X and Y values connected by smooth continuing arcs define profile sections of the at least one of the suction sidewall or the pressure sidewall at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the profile of the at least one of the suction sidewall or the pressure sidewall; anda total throat including a component throat between each pair of adjacent airfoils, each component throat including an area defined at least in part by a minimum gap between a pressure sidewall of a first airfoil and a suction sidewall of an adjacent second airfoil for all points along spans of the first and second airfoils. 19. The turbine system of claim 18, wherein a width of the component throat increases with decreasing distance to the roots of the first and second airfoils within a first distance from the roots and within a second distance from the tips, and at least one of the first distance or the second distance is no more than 25% of the spans of the first and second airfoils. 20. The turbine system of claim 18, wherein a width of the component throat at at least one of the roots or the tips is no more than about 110% of the width of the component throat at about 20% span away from the respective at least one of the roots or the tips.