Last Stage Blade Design to Reduce Turndown Vibration

Abstract

A turbine bucket includes a bucket airfoil having a cross-section in an airfoil shape. The bucket is twisted from a root end to a tip end. A degree of twist defines an accumulated angular offset of the tip end in a range of 10-15° relative to a tangential direction, thereby reducing excess negative incidence by 15-20° relative to the tangential direction.

What is claimed is: 
     
         1 . A turbine bucket including a bucket airfoil having a cross-section in an airfoil shape, the turbine bucket being twisted from a root end to a tip end, wherein a degree of twist defines an accumulated angular offset of the tip end in a range of 10-15° relative to a tangential direction, thereby reducing excess negative incidence by 15-20° relative to the tangential direction. 
     
     
         2 . A turbine bucket according to  claim 1 , wherein the degree of twist defines an accumulated angular offset of the tip end of 13°, thereby reducing excess negative incidence by 17°. 
     
     
         3 . A turbine bucket according to  claim 1 , comprising a leading edge, the leading edge being radiused to reduce positive incidence performance sensitivity. 
     
     
         4 . A turbine bucket according to  claim 1 , wherein a height dimension is defined as 0% height at the root end and 100% height at the tip end, and wherein the turbine bucket is twisted in a section between 30-60% height to a degree that is higher than other sections of the turbine bucket. 
     
     
         5 . A turbine bucket according to  claim 1 , wherein the turbine bucket is twisted at the root end to a degree that is higher than other sections of the turbine bucket. 
     
     
         6 . A turbine bucket according to  claim 1 , wherein the turbine bucket is a last stage bucket of a turbine. 
     
     
         7 . A turbine bucket according to  claim 6 , wherein at an operating speed of 3,600 RPMs, a maximum height of the turbine bucket is 35 inches. 
     
     
         8 . A turbine bucket according to  claim 6 , wherein at an operating speed of X RPMs, a maximum height of the turbine bucket is 3600/X*35. 
     
     
         9 . A turbine comprising:
 a rotor;   a rotatable shaft that rotates with the rotor; and   a turbine coupled with the rotatable shaft and the rotor, the turbine including a plurality of axially spaced rotor wheels, wherein a plurality of buckets are coupled with each rotor wheel, each of the buckets having a cross-section in an airfoil shape, wherein a last stage bucket is twisted from a root end to a tip end, and wherein a degree of twist defines an accumulated angular offset of the tip end in a range of 10-15° relative to a tangential direction, thereby reducing excess negative incidence by 15-20° relative to the tangential direction.   
     
     
         10 . A turbine according to  claim 9 , wherein the degree of twist defines an accumulated angular offset of the tip end of 13°, thereby reducing excess negative incidence by 17°. 
     
     
         11 . A turbine according to  claim 9 , wherein the last stage bucket comprises a leading edge, the leading edge being radiused to reduce positive incidence performance sensitivity. 
     
     
         12 . A turbine according to  claim 9 , wherein a height dimension of the last stage bucket is defined as 0% height at the root end and 100% height at the tip end, and wherein the last stage bucket is twisted in a section between 30-60% height to a degree that is higher than other sections of the bucket. 
     
     
         13 . A turbine according to  claim 9 , wherein the last stage bucket is twisted at the root end to a degree that is higher than other sections of the bucket. 
     
     
         14 . A turbine according to  claim 9 , wherein at an operating speed of 3,600 RPMs, a maximum height of the last stage bucket is 35 inches. 
     
     
         15 . A turbine according to  claim 9 , wherein at an operating speed of X RPMs, a maximum height of the last stage bucket is 3600/X*35. 
     
     
         16 . A method of reducing flow induced vibration in a last stage turbine bucket, the turbine bucket being twisted from a root end to a tip end, the method comprising twisting the turbine bucket to a degree that defines an accumulated angular offset of the tip end in a range of 10-15° relative to a tangential direction, thereby reducing excess negative incidence by 15-20° relative to the tangential direction. 
     
     
         17 . A method according to  claim 16 , wherein the twisting step is practiced such that the degree of twist defines an accumulated angular offset of the tip end of 13°, thereby reducing excess negative incidence by 17°. 
     
     
         18 . A method according to  claim 16 , comprising radiusing a leading edge of the turbine bucket to reduce positive incidence performance sensitivity.