Turbine bucket with endwall contour and airfoil profile

1. A turbomachine bucket comprising:

a base;

an airfoil supported by the base, the airfoil including opposed first and second ends with the first end at the base, the airfoil further including opposed pressure and suction sidewalls extending in chord between opposed leading and trailing edges and extending in span between the first and second ends of the airfoil;

an endwall on the base and connected to the first end of the airfoil, the endwall including opposed endwall leading and trailing edges extending substantially circumferentially between opposed pressure and suction splitlines, a distance between the pressure and suction splitlines being substantially equal to a pitch;

opposed leading edge and trailing edge regions of the endwall each extending from the respective endwall leading and trailing edges to about half way therebetween;

pressure side and suction side regions of the endwall extending from the respective pressure and suction sidewalls of the airfoil;

at least one pressure side feature in the endwall in the pressure side region, each respective pressure side feature including at least one of a trough or a bump relative to a nominal surface of the endwall,

wherein the at least one pressure side feature includes a first bump in the leading edge region, a second bump between the first bump and the trailing edge of the airfoil, and from the endwall leading edge to the endwall trailing edge, the pressure side region of the endwall rises into the first bump, descends to a lower level, rises into the second bump, then descends into substantially the nominal surface;

at least one suction side feature in the endwall in the suction side region, each respective suction side feature including at least one of a trough or a bump relative to the nominal surface of the endwall; and

at least one leading edge feature in the endwall including at least one of a trough or a bump relative to the nominal surface in the leading edge region.

2. The turbomachine bucket of claim 1 , wherein at least one of the suction sidewall or the pressure sidewall 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.

3. The turbomachine bucket of claim 1 , wherein the first bump has a peak at from about 5% chord to about 10% chord in the pressure side region and from about 0% to about 5% of pitch away from the pressure sidewall.

4. The turbomachine bucket of claim 1 , wherein the second bump has a peak at from about 35% chord to about 55% chord in the pressure side region and from about 10% to about 30% of pitch away from the pressure sidewall.

5. The turbomachine bucket of claim 1 , wherein the at least one suction side feature includes a trough.

6. The turbomachine bucket of claim 5 , wherein the trough has a lowest point at from about 15% chord to about 20% chord from the airfoil leading edge and at from about the suction sidewall to about 10% of pitch away from the suction sidewall.

7. The turbomachine bucket of claim 1 , wherein the at least one pressure side feature includes a bump in the leading edge region and substantially extending from the leading edge of the airfoil toward the pressure splitline, a trough in the leading edge region substantially extending from the leading edge of the airfoil toward the suction splitline, and the endwall, and from the pressure splitline to the suction splitline, the leading edge region rises into the first bump, descends into the trough, and rises to substantially the nominal surface.

8. The turbomachine bucket of claim 1 , wherein the endwall leading edge includes a bullnose profile that descends from at least one of the at least one pressure side feature, the at least one suction side feature, or the nominal surface to a substantially semi-cylindrical lip below the nominal surface.

9. An endwall of a flow passage formed by adjacent first and second substantially identical, substantially circumferentially spaced apart airfoils of adjacent buckets of a stage of a turbomachine, a spacing between adjacent airfoils being a pitch, each airfoil including respective opposed pressure and suction sidewalls extending chordwise between opposed leading and trailing edges and extending spanwise between opposed first and second ends, at least one of the suction sidewall or the pressure sidewall of at least one 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, the endwall comprising:

a nominal surface between opposed endwall leading and trailing edges and including a region between the pressure sidewall of the first airfoil and the suction sidewall of the second airfoil;

at least one pressure side feature including at least one bump relative to the nominal surface proximate the pressure sidewall of the first blade; and

at least one suction side feature including at least one trough relative to the nominal surface.

10. The endwall of claim 9 , wherein the at least one bump incudes a first bump proximate the leading edge of the first airfoil.

11. The endwall of claim 10 , wherein the first bump has a peak at from about 5% chord to about 10% chord from the leading edge and from about 0% to about 5% of pitch from the pressure sidewall.

12. The endwall of claim 9 , wherein the at least one bump includes a first bump located adjacent and at about midchord of the pressure sidewall of the first airfoil.

13. The endwall of claim 12 , wherein the first bump has a peak at from about 35% chord to about 55% chord away from the leading edge and from about 10% to about 30% of pitch from the pressure sidewall.

14. The endwall of claim 9 , wherein the at least one trough includes a first trough proximate the leading edge of the second airfoil.

15. The endwall of claim 14 , wherein the first trough has a lowest point at from about 15% chord to about 20% chord from the leading edge and from about 0% to about 10% of pitch away from the suction sidewall.

16. A turbine system comprising:

a compressor section;

a combustion section;

a turbine section including at least one stage of airfoils substantially circumferentially distributed at a pitch about an axis of rotation of the turbine section, each airfoil supported by a respective platform of a respective bucket such that adjacent airfoils form a flow passage including a pressure sidewall of a first airfoil, a suction sidewall of a second, adjacent airfoil, and an endwall formed by at least a portion of each of the respective platforms of the first and second airfoils, 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.

17. The turbine system of claim 16 , wherein the endwall includes at least one bump proximate the pressure sidewall of the first airfoil and at least one trough proximate the suction side of the second airfoil.

18. The turbine system of claim 16 , wherein the at least one bump includes a first bump proximate the leading edge of the first airfoil with a peak at from about 5% chord to about 10% chord from the leading edge and from about 0% to about 5% of pitch away from the pressure sidewall, and a second bump proximate a midchord of the second airfoil with a peak at from about 35% chord to about 55% chord away from the leading edge and from about 10% to about 30% of pitch away from the pressure sidewall, and the at least one trough includes a first trough with a lowest point at from about 15% chord to about 20% chord from the leading edge and from about 0% to about 10% of pitch away from the suction sidewall.

19. The turbine system of claim 16 , wherein for each airfoil both a respective suction sidewall and a respective pressure sidewall include 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 by a desired span 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.

20. A turbomachine bucket comprising:

a base;

an airfoil supported by the base, the airfoil including opposed first and second ends with the first end at the base, the airfoil further including opposed pressure and suction sidewalls extending in chord between opposed leading and trailing edges and extending in span between the first and second ends of the airfoil;

an endwall on the base and connected to the first end of the airfoil, the endwall including opposed endwall leading and trailing edges extending substantially circumferentially between opposed pressure and suction splitlines, a distance between the pressure and suction splitlines being substantially equal to a pitch;

opposed leading edge and trailing edge regions of the endwall each extending from the respective endwall leading and trailing edges to about half way therebetween;

pressure side and suction side regions of the endwall extending from the respective pressure and suction sidewalls of the airfoil;

at least one pressure side feature in the endwall in the pressure side region, the at least one pressure side feature including a first bump in the leading edge region, a second bump between the first bump and the trailing edge of the airfoil, and from the endwall leading edge to the endwall trailing edge, the pressure side region of the endwall rises into the first bump, descends to a lower level, rises into the second bump, then descends into substantially the nominal surface.

21. The turbomachine bucket of claim 20 , further comprising at least one suction side feature in the endwall in the suction side region, each respective suction side feature including at least one of a trough or a bump relative to the nominal surface of the endwall.

22. The turbomachine bucket of claim 20 , further comprising at least one leading edge feature in the endwall including at least one of a trough or a bump relative to the nominal surface in the leading edge region.

23. The turbomachine bucket of claim 20 , wherein the at least one pressure side feature includes a bump in the leading edge region and substantially extending from the leading edge of the airfoil toward the pressure splitline, a trough in the leading edge region substantially extending from the leading edge of the airfoil toward the suction splitline, and the endwall, and from the pressure splitline to the suction splitline, the leading edge region rises into the first bump, descends into the trough, and rises to substantially the nominal surface.