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A core tie having a varying cross sectional diameter, a component including such a core tie, and a method of casting a hot gas path component for a turbomachine are provided herein. In an embodiment, the core tie includes a tie member having an axial length; and a cross sectional diameter which vari

A core tie having a varying cross sectional diameter, a component including such a core tie, and a method of casting a hot gas path component for a turbomachine are provided herein. In an embodiment, the core tie includes a tie member having an axial length; and a cross sectional diameter which varies along the axial length of the tie member. A variation in the cross sectional diameter of the tie member positively secures a position of the core tie relative to the core.

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1. A component comprising: a body;a first cooling passageway disposed within the body, the first cooling passageway including a first hole therein; anda core tie disposed in the first hole, such that the core tie occludes the first hole,the core tie comprising:a tie member having an axial length, an

1. A component comprising: a body;a first cooling passageway disposed within the body, the first cooling passageway including a first hole therein; anda core tie disposed in the first hole, such that the core tie occludes the first hole,the core tie comprising:a tie member having an axial length, anda substantially rectangular cross sectional area which varies along the axial length of the tie member, wherein a variation in the cross sectional area of the tie member positively secures a position of the core tie relative to the first hole,wherein the tie member includes:a first cross sectional area at each of a first end, a second end, and a point approximately midway along the axial length of the tie member, anda second cross sectional area at each of a point between the first end and the point approximately midway along the axial length of the tie member, and a point between the second end and the point approximately midway along the axial length of the tie member,wherein the first cross sectional area is greater than the second cross sectional area, andwherein the first cross sectional area is greater than a diameter of the first hole. 2. The component of claim 1, wherein the core tie further comprises a ceramic, alumina, or quartz. 3. The component of claim 1, wherein the core tie further comprises a metal. 4. The component of claim 1, wherein the component is a hot gas path component of a turbo-machine. 5. The component of claim 4, wherein the hot gas path component includes a nozzle or a shroud. 6. The component of claim 4, wherein the hot gas path component includes a bucket. 7. The component of claim 1, further comprising: a second cooling passageway having a second hole thereinwherein the second hole is aligned with the first hole such that core tie passes through both of the first hole and the second hole. 8. The component of claim 1, wherein a geometry of the core tie, including a variation in the cross sectional area of the tie member, positively locks the core tie in place. 9. A component comprising: a body;a first cooling passageway disposed within the body, the first cooling passageway including a first hole therein; anda core tie disposed in the first hole, such that the core tie occludes the first hole,the core tie comprising:a tie member having an axial length; anda cross sectional area which varies along the axial length of the tie member, wherein a variation in the cross sectional area of the tie member positively secures a position of the core tie relative to the first hole, and the tie member includes:a first cross sectional area at each of a first end, a second end, and a point approximately midway along the axial length of the tie member, anda second cross sectional area at each of a point between the first end and the point approximately midway along the axial length of the tie member, and a point between the second end and the point approximately midway along the axial length of the tie member,wherein the first cross sectional area is greater than the second cross sectional area, andwherein the first cross sectional area is greater than an area of the first hole. 10. The component of claim 9, wherein the cross sectional area of the tie member is substantially circular, substantially ovoid, or substantially rectangular. 11. The component of claim 9, wherein the core tie further comprises a ceramic, alumina, or quartz. 12. The component of claim 9, wherein the core tie further comprises a metal. 13. The component of claim 9, wherein the component is a hot gas path component of a turbo-machine. 14. The component of claim 13, wherein the hot gas path component includes a nozzle or a shroud. 15. The component of claim 13, wherein the hot gas path component includes a bucket. 16. The component of claim 9, further comprising: a second cooling passageway having a second hole thereinwherein the second hole is aligned with the first hole such that core tie passes through both of the first hole and the second hole. 17. The component of claim 9, wherein a geometry of the core tie, including a variation in the cross sectional area of the tie member positively locks the core tie in place. 18. A component comprising: a body;a first cooling passageway disposed within the body, the first cooling passageway including a first hole therein; anda core tie disposed in the first hole, such that the core tie occludes the first hole,the core tie comprising:a tie member having an axial length, anda cross sectional area which varies along the axial length of the tie member, wherein a variation in the cross sectional area of the tie member positively secures a position of the core tie relative to the first hole,wherein the tie member includes, in order of axial position, a first, second, third, fourth, and fifth cross sectional area along the axial length of the tie member, andeach of the second and fourth cross sectional areas is smaller than each of the first, third, and fifth cross sectional areas, andwherein the first and fifth cross sectional areas are each greater than a diameter of the first hole. 19. The component of claim 18, wherein the cross sectional area of the tie member is substantially circular, substantially ovoid, or substantially rectangular. 20. The component of claim 18, wherein the core tie further comprises a ceramic, alumina, quartz, or a metal.