# Patent

## Title
Bucket for the last stage of a steam turbine

## Abstract

A turbine bucket including a bucket airfoil having an airfoil shape is provided. The airfoil shape has a nominal profile according to the tables set forth in the specification. The X and Y coordinate are smoothly joined by an arc of radius R defining airfoil profile sections at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.

## Background
BACKGROUND OF THE INVENTION
The present invention relates to turbines, particularly steam turbines, and more particularly relates to last-stage steam turbine buckets having improved aerodynamic, thermodynamic and mechanical properties.
Last-stage buckets for turbines have for some time been the subject of substantial developmental work. It is highly desirable to optimize the performance of these last-stage buckets to reduce aerodynamic losses and to improve the thermodynamic performance of the turbine. Last-stage buckets are exposed to a wide range of flows, loads and strong dynamic forces. Factors that affect the final bucket profile design include the active length of the bucket, the pitch diameter and the high operating speed in both supersonic and subsonic flow regions. Damping and bucket fatigue are factors which must also be considered in the mechanical design of the bucket and its profile. These mechanical and dynamic response properties of the buckets, as well as others, such as aero-thermodynamic properties or material selection, all influence the optimum bucket profile. The last-stage steam turbine buckets require, therefore, a precisely defined bucket profile for optimal performance with minimal losses over a wide operating range.
Adjacent rotor buckets are typically connected together by some form of cover bands or shroud bands around the periphery to confine the working fluid within a well-defined path and to increase the rigidity of the buckets. Grouped buckets, however, can be stimulated by a number of stimuli known to exist in the working fluid to vibrate at the natural frequencies of the bucket-cover assembly. If the vibration is sufficiently large, fatigue damage to the bucket material can occur and lead to crack initiation and eventual failure of the bucket components. Also, last-stage buckets operate in a wet steam environment and are subject to potential erosion by water droplets. A method of erosion protection sometimes used, is to either weld or braze a protective shield to the leading edge of each bucket at its upper active length. These shields, however, may be subject to stress corrosion cracking or departure from the buckets due to deterioration of the bonding material as in the case of a brazed shield.
BRIEF DESCRIPTION OF THE INVENTION
In one aspect of the present invention, a turbine bucket including a bucket airfoil having an airfoil shape is provided. The airfoil has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R as set forth in Tables 1-19. The X, Y, Z and R distances are in inches, and an arc of radius R smoothly joins the X and Y coordinate values. The airfoil profile sections are defined at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.
In another aspect of the present invention, a turbine wheel having a plurality of buckets is provided. The buckets include an airfoil having an airfoil shape defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R as set forth in Tables 1-19. The X, Y, Z and R distances are in inches, and an arc of radius R smoothly joins the X and Y coordinate values. The airfoil profile sections are defined at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.
In yet another aspect of the present invention, a turbine including a turbine wheel having a plurality of buckets is provided. The buckets include an airfoil having an airfoil shape defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R as set forth in Tables 1-19. The X, Y, Z and R distances are in inches, and an arc of radius R smoothly joins the X and Y coordinate values. The airfoil profile sections are defined at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective partial cut away illustration of a steam turbine.
FIG. 2 is a perspective illustration of a turbine bucket that may be used with the steam turbine shown in FIG. 1.
FIG. 3 is a graph illustrating a representative airfoil section of the bucket profile as defined by the tables set forth in the following specification.



DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a perspective partial cut away view of a steam turbine 10 including a rotor 12 that includes a shaft 14 and a low-pressure (LP) turbine 16. LP turbine 16 includes a plurality of axially spaced rotor wheels 18. A plurality of buckets 20 are mechanically coupled to each rotor wheel 18. More specifically, buckets 20 are arranged in rows that extend circumferentially around each rotor wheel 18. A plurality of stationary nozzles 22 extend circumferentially around shaft 14 and are axially positioned between adjacent rows of buckets 20. Nozzles 22 cooperate with buckets 20 to form a turbine stage and to define a portion of a steam flow path through turbine 10.
In operation, steam 24 enters an inlet 26 of turbine 10 and is channeled through nozzles 22. Nozzles 22 direct steam 24 downstream against buckets 20. Steam 24 passes through the remaining stages imparting a force on buckets 20 causing rotor 12 to rotate. At least one end of turbine 10 may extend axially away from rotor 12 and may be attached to a load or machinery (not shown), such as, but not limited, to, a generator, and/or another turbine. Accordingly, a large steam turbine unit may actually include several turbines that are all co-axially coupled to the same shaft 14. Such a unit may, for example, include a high-pressure turbine coupled to an intermediate-pressure turbine, which is coupled to a low-pressure turbine.
FIG. 2 is a perspective view of a turbine bucket 20 that may be used with turbine 10. Bucket 20 includes a blade portion 102 that includes a trailing edge 104 and a leading edge 106, wherein steam flows generally from leading edge 106 to trailing edge 104. Bucket 20 also includes a first concave sidewall 108 and a second convex sidewall 110. First sidewall 108 and second sidewall 110 are connected axially at trailing edge 104 and leading edge 106, and extend radially between a rotor blade root 112 and a rotor blade tip 114. A blade chord distance 116 is a distance measured from trailing edge 104 to leading edge 106 at any point along a radial length 118 of blade 102. In the exemplary embodiment, radial length 118 is approximately forty-five inches. Although radial length 118 is described herein as being equal to approximately forty-five inches, it will be understood that radial length 118 may be any suitable length depending on the desired application. Root 112 includes a dovetail 121 used for coupling bucket 20 to a rotor disc 122 along shaft 14, and a blade platform 124 that determines a portion of a flow path through each bucket 20. In the exemplary embodiment, dovetail 121 is a curved axial entry dovetail that engages a mating slot 125 defined in rotor disc 122. However, in other embodiments, dovetail 121 could also be a straight axial entry dovetail, angled-axial entry dovetail, or any other suitable type of dovetail configuration.
In the exemplary embodiment, first and second sidewalls, 108 and 110, each include a mid-blade connection point 126 positioned between blade root 112 and blade tip 114 and used to couple adjacent buckets 20 together. In one embodiment, mid-blade connection point 126 is used to couple adjacent buckets 20 together with tie wires (not shown) to facilitate improving a vibratory response of buckets 20 in a mid region between root 112 and tip 114. The mid-blade connection point can also be referred to as the mid-span or part-span shroud. The part-span shroud can be located at about 45% to about 65% of the radial length 118, as measured from the blade platform 124.
An extension 128 is formed on a portion of blade 102 to alter the vibratory response of blade 102. Extension 128 may be formed on blade 102 after a design of blade 102 has been fabricated, and has undergone production testing. At a particular point along radial length 118, a chord distance 116 defines a shape of blade 102. In one embodiment, extension 128 is formed by adding blade material to blade 102 such that at radial distance 118 where the blade material is added, chord distance 116 is extended past leading edge 106 and/or trailing edge 104 of blade 102 as originally formed. In another embodiment, blade material is removed from blade 102 such that at radial distance 118 where blade material has not been removed, chord distance 116 extends past leading edge 106 and/or trailing edge 104 of blade 102 as modified by removing material. In a further embodiment, extension 128 is formed integrally and material at extension 128 may be removed to tune each bucket as dictated by testing. Extension 128 is formed to coincide with an aerodynamic shape of blade 102 so as to facilitate minimizing a flow disturbance of steam 24 as it passes extension 128.
During design and manufacture of bucket 20, a profile of blade 102 is determined and implemented. A profile is a cross-sectional view of blade 102 taken at radial distance 118. A series of profiles of blade 102 taken at subdivisions of radial distance 118 define a shape of blade 102. The shape of blade 102 is a component of an aerodynamic performance of blade 102. After blade 102 has been manufactured the shape of blade 102 is relatively fixed, in that altering the shape of blade 102 may alter the vibratory response in an undesired way. In some known instances, it may be desirable to alter the vibratory response of blade 102 after blade 102 has been manufactured, such as during a post-manufacturing testing process. In order to maintain a predetermined performance of blade 102, the shape of blade 102 may be modified in such a way, as determined by analysis, such as by computer analysis or by empirical study to add mass to blade 102 that alters the vibratory response of blade 102. The analysis determines an optimum amount of mass needed to achieve a desired alteration of the vibratory response of blade 102. Modifying blade 102 with extension 128 to add mass to blade 102, tends to decrease the natural frequency of blade 102. Modifying blade 102 with extension 128 to remove mass from blade 102, tends to increase the natural frequency of blade 102. Extension 128 may also be crafted to alter an aeromechanical characteristic of blade 102 such that an aerodynamic response of blade 102 to a flow of steam 24 past extension 128 will create a desirable change in the vibratory response of blade 102. Thus, the addition of extension 128 may alter the vibratory response of blade 102 in at least two ways, a change of mass of blade 102 and a modification of the airfoil shape of blade 102. Extension 128 may be designed to utilize both aspects of adding mass and changing airfoil shape to effect a change in the vibratory response of blade 102.
In operation, blade 102 undergoes a testing process to validate design requirements were met during the manufacturing process. One known test indicates a natural frequency of blade 102. Modern design and manufacturing techniques are tending toward buckets 20 that are thinner in profile. A thinner profile tends to lower the overall natural frequencies of blade 102. Lowering the natural frequency of blade 102 into the domain of the vibratory forces present in turbine 10, may cause a resonance condition in any number or in an increased number of system modes that each will be de-tuned. To modify the natural frequency of blade 102, mass may be added to or removed from blade 102. To facilitate limiting lowering the natural frequency of blade 102 into the domain of the vibratory forces present in turbine 10, a minimum amount of mass is added to blade 102. In the exemplary embodiment, extension 128 is machined from a forged material envelope of leading edge 106 of blade 102. In other embodiments, extension 128 may be coupled to blade 102 using other processes. In the exemplary embodiment, extension 128 is coupled to blade 102 between connection point 126 and blade tip 114. In other embodiments, extension 128 may be coupled to leading edge 106 between blade root 112 and blade tip 114, to trailing edge 104 between blade root 112 and blade tip 114, or may be added to sidewalls 108 and/or 110.
The above-described turbine rotor blade extension is cost effective and highly reliable. The turbine rotor blade includes a first and second sidewall coupled to each other at their respective leading edge and trailing edge. An extension coupled to the blade, or removed from the blade forged material envelope alters the blade natural frequency and improves reliability. The amount of material in the extension is facilitated to be minimized by analysis or testing of the rotor blade. Minimizing this mass addition reduces to total weight of the blade, thus minimizing both blade and disk stress and improves reliability. As a result, the turbine rotor blade extension facilitates operating a steam turbine in a cost effective and reliable manner.
Referring now to FIG. 3, there is illustrated a representative bucket section profile at a predetermined distance “Z” (in inches) or radial distance 118 from surface 124. Each profile section at that radial distance is defined in X-Y coordinates by adjacent points identified by representative numerals, for example, the illustrated numerals 1 through 15, and which adjacent points are connected one to the other along the arcs of circles having radii R. Thus, the arc connecting points 10 and 11 constitutes a portion of a circle having a radius R at a center 310 as illustrated. Values of the X-Y coordinates and the radii R for each bucket section profile taken at specific radial locations or heights “Z” from the blade platform 124 are tabulated in the following tables numbered 1 through 19. The tables identify the various points along a profile section at the given heights “Z” from the blade platform 124 by their X-Y coordinates and it will be seen that the tables have anywhere from 13 to 27 representative X-Y coordinate points, depending upon the profile section height from the datum line. These values are given in inches and represent actual bucket configurations at ambient, non-operating conditions (with the exception of the coordinate points noted below for the theoretical blade profiles at the root, mid-point and tip of the bucket). The value for each radius R provides the length of the radius defining the arc of the circle between two of the adjacent points identified by the X-Y coordinates. The sign convention assigns a positive value to the radius R when the adjacent two points are connected in a clockwise direction and a negative value to the radius R when the two adjacent points are connected in a counterclockwise direction. By providing X-Y coordinates for spaced points about the blade profile at selected radial positions or heights Z from blade platform 124 and defining the radii R of circles connecting adjacent points, the profile of the bucket is defined at each radial position and thus the bucket profile is defined throughout its entire length.
Table 1 represents the theoretical profile of the bucket at the blade platform 124 (i.e., Z=0). The actual profile at that location includes the fillets in the root section connecting the airfoil and dovetail sections, the fillets fairing the profiled bucket into the structural base of the bucket. The actual profile of the bucket at the blade platform 124 is not given but the theoretical profile of the bucket at the blade platform 124 is given in Table 1. Similarly, the profile given in Table 19 is also a theoretical profile, as this section is joined to the tip shroud. The actual profile includes the fillets in the tip section connecting the airfoil and tip-shroud sections. In the middle portion of the blade, a part-span shroud may also be incorporated into the bucket. The tables below do not define the shape of the part-span shroud.
It will be appreciated that having defined the profile of the bucket at various selected heights from the root, properties of the bucket such as the maximum and minimum moments of inertia, the area of the bucket at each section, the twist, torsional stiffness, shear centers and vane width can be ascertained. Accordingly, Tables 2-18 identify the actual profile of a bucket; Tables 1 and 19 identify the theoretical profiles of a bucket at the designated locations therealong.
Also, in one preferred embodiment, the turbine includes 49 buckets, each of the profiles provided by the Tables 2-18 and having the theoretical profile given by the X, Y and R values at the radial distances of Tables 1 and 19. However, it is to be understood that any number of buckets (e.g., more or less than 49) could be employed and the X, Y and R values would be appropriately scaled to obtain the desired bucket profile.







TABLE NO. 1







Z = 0′′












POINT NO.
X
Y
R
















1
8.14269
−5.20398
0



2
8.05234
−5.07557
−16.2182



3
6.88009
−3.59989
0



4
6.79455
−3.50419
−12.0433



5
5.46936
−2.23195
−10.2247



6
4.00875
−1.22859
−11.486



7
2.36161
−0.46126
−10.6965



8
0.71906
0.00551
−12.9835



9
−0.76065
0.21312
−11.3455



10
−2.66242
0.20915
−12.0758



11
−4.40123
−0.06964
−9.38671



12
−6.75505
−0.9736
−6.95049



13
−8.05266
−1.89219
0.14286



14
−8.27779
−1.72609
1.90355



15
−8.02488
−1.32011
8.87163



16
−6.84361
−0.12142
7.90759



17
−5.7334
0.65761
8.50374



18
−3.27442
1.61214
9.94464



19
−0.50286
1.81863
9.35978



20
2.70352
1.02294
8.56383



21
4.18539
0.1734
8.94235



22
6.17556
−1.78429
11.93268



23
6.58317
−2.37131
61.30643



24
7.34792
−3.57674
141.7845



25
7.69087
−4.13434
0



26
8.28597
−5.11004
0.08572



27
8.14269
−5.20398
0

















TABLE NO. 2







Z = 4.552′′












POINT NO.
X
Y
R
















1
6.86668
−5.96371
−14.0609



2
5.47222
−3.91188
−20.4525



3
3.4143
−1.73999
−8.60622



4
1.24007
−0.29415
−7.37985



5
−1.09022
0.35078
−7.68903



6
−3.2812
0.26831
−8.90384



7
−5.52553
−0.45946
−4.54205



8
−5.849
−0.63065
−10.2262



9
−6.25351
−0.87879
0.54072



10
−6.39112
−0.94237
0.15144



11
−6.58268
−0.76502
0.54072



12
−6.52934
−0.62194
4.49951



13
−5.1571
0.91336
6.429



14
−2.91267
1.91118
7.1473



15
−0.99193
2.08605
4.61171



16
0.52219
1.75807
8.01567



17
2.66566
0.4777
11.41873



18
4.68621
−1.71265
17.92081



19
5.45598
−2.90119
16.79805



20
5.99933
−3.89214
0



21
7.0082
−5.88854
0.08015



22
6.86668
−5.96371
11.93268

















TABLE NO. 3







Z = 9.1028′′












POINT NO.
X
Y
R
















1
5.26358
−6.07395
−0.72114



2
5.20983
−5.9376
−40.2462



3
4.69365
−4.97198
−14.6591



4
2.34221
−1.80943
−7.38262



5
0.04359
−0.21632
−5.12742



6
−1.24096
0.15948
−8.71006



7
−2.98287
0.25262
−8.1828



8
−3.83361
0.16799
−18.9473



9
−5.02122
−0.05216
0.71644



10
−5.18645
−0.06858
0.18234



11
−5.33788
0.21051
0.71644



12
−5.23152
0.34254
6.18288



13
−3.78337
1.39581
5.71719



14
−2.0806
1.97082
5.12201



15
−0.51004
1.99265
3.3534



16
0.69203
1.57999
4.60877



17
1.83358
0.65404
10.65731



18
3.13974
−1.15978
27.97914



19
3.97105
−2.72845
22.23978



20
4.54028
−3.98787
0



21
5.38821
−6.03076
0.06608



22
5.26358
−6.07395
11.93268

















TABLE NO. 4







Z = 11.3776′′












POINT NO.
X
Y
R
















1
4.48709
−6.06174
0



2
4.40741
−5.89542
−19.0432



3
4.18165
−5.43992
−32.6737



4
3.47323
−4.13153
−15.0586



5
2.74312
−2.9782
−10.9154



6
1.5228
−1.52024
−7.98608



7
0.22255
−0.46521
−5.82226



8
−0.28202
−0.17194
−7.2406



9
−1.62911
0.36013
−9.98687



10
−3.26816
0.67925
−14.3215



11
−4.62007
0.7622
0.22265



12
−4.77165
1.14497
0.59033



13
−4.64949
1.23571
7.98942



14
−3.28705
1.83803
6.15608



15
−2.03335
2.11627
4.60122



16
−0.88106
2.10286
3.51239



17
0.34231
1.69496
3.27678



18
0.80173
1.38672
4.52434



19
1.50883
0.67831
7.59899



20
2.13789
−0.24063
15.16049



21
2.75458
−1.41608
32.16122



22
3.53705
−3.22258
55.39263



23
3.86564
−4.06988
0



24
4.59621
−6.01523
0.05938



25
4.48709
−6.06174
0

















TABLE NO. 5







Z = 13.6522′′












POINT NO.
X
Y
R
















1
3.77201
−5.97958
−56.57



2
2.2127
−3.09834
−10.9567



3
1.4095
−1.90098
−9.75049



4
0.05471
−0.46967
−8.82884



5
−1.48754
0.59729
−11.1118



6
−1.99767
0.85836
−39.815



7
−2.98203
1.31411
0



8
−3.55102
1.56681
73.40256



9
−3.87176
1.71185
16.35228



10
−4.02287
1.78156
0.15137



11
−4.03202
2.05114
3.41315



12
−2.79565
2.45215
4.46469



13
−1.31032
2.38493
3.96666



14
0.02726
1.82519
4.44377



15
1.14632
0.77496
5.21119



16
1.57629
0.09917
11.48497



17
2.08053
−0.9777
42.38902



18
2.56189
−2.21708
79.22593



19
3.13967
−3.83014
0



20
3.86922
−5.93846
0.05291



21
3.77201
−5.97958
32.16122

















TABLE NO. 6







Z = 15.9221′′












POINT NO.
X
Y
R
















1
3.20634
−5.94189
0



2
2.3248
−4.33582
16.8259



3
2.04392
−3.79165
−16.8259



4
1.38492
−2.58312
−14.0679



5
0.29629
−1.01864
−12.9619



6
−0.94587
0.32452
−22.2454



7
−1.84901
1.12731
22.24539



8
−3.00019
2.16658
8.94741



9
−3.13559
2.30049
13.50015



10
−3.29841
2.46786
0.14302



11
−3.24651
2.70013
2.47322



12
−2.1218
2.85473
3.43836



13
−0.83989
2.47108
3.69043



14
0.03854
1.82382
5.62144



15
0.87199
0.76604
6.03234



16
1.22537
0.09439
13.84047



17
1.65159
−0.97328
12.52819



18
1.72337
−1.1832
107.7916



19
1.92655
−1.80142
0



20
2.67719
−4.09716
37.75222



21
2.73307
−4.26423
−37.7522



22
2.81755
−4.51586
0



23
3.28953
−5.90528
0.04563



24
3.20634
−5.94189
0.05938

















TABLE NO. 7







Z = 18.2012′′












POINT NO.
X
Y
R
















1
2.72769
−5.84753
0



2
1.96568
−4.63648
3.91954



3
1.87284
−4.47872
0



4
0.60228
−2.15846
−64.8003



5
−0.28818
−0.60873
−16.8873



6
−0.77465
0.16319
−35.8688



7
−1.53008
1.24913
35.86876



8
−2.0302
1.95843
6.45422



9
−2.58539
2.93782
0.18456



10
−2.43795
3.19791
2.23922



11
−1.3505
3.04842
3.04942



12
−0.29159
2.3309
2.86304



13
0.09546
1.82427
6.52936



14
0.52895
0.96455
6.03718



15
0.68048
0.55872
71.58372



16
1.13699
−0.86141
6.38032



17
1.16995
−0.97125
−6.38032



18
1.1988
−1.0677
0



19
1.50673
−2.09944
−84.7491



20
1.98755
−3.59073
−19.412



21
2.18539
−4.15615
0



22
2.79457
−5.81467
0.03747



23
2.72769
−5.84753
0.04563

















TABLE NO. 8







Z = 20.4775′′












POINT NO.
X
Y
R
















1
2.30728
−5.82104
0



2
1.87407
−5.11416
4.06378



3
1.75979
−4.91494
10.80126



4
1.58846
−4.58198
0



5
0.78939
−2.93817
−9.10586



6
0.70437
−2.76957
0



7
−0.17713
−1.02349
37.38615



8
−1.28734
1.34369
26.74437



9
−2.07022
3.40951
0.20171



10
−1.86439
3.67435
1.12707



11
−1.45991
3.56748
2.16793



12
−0.97706
3.25227
2.6963



13
−0.51512
2.73639
6.86141



14
0.03467
1.77828
5.26443



15
0.21824
1.33803
23.56335



16
0.54362
0.38279
19.69941



17
0.76215
−0.35674
−19.6994



18
0.86791
−0.72794
0



19
1.49937
−2.9549
17.51244



20
1.5854
−3.25112
−17.5124



21
1.71651
−3.69524
0



22
2.36646
−5.79424
0.03275



23
2.30728
−5.82104
0.04563

















TABLE NO. 9







Z = 22.7558′′












POINT NO.
X
Y
R
















1
2.01086
−5.78492
0



2
1.77127
−5.39305
6.83794



3
1.4921
−4.89008
9.57775



4
1.24813
−4.36421
0



5
1.19473
−4.23931
6.59464



6
1.12336
−4.06564
0



7
0.57085
−2.66454
−10.3976



8
0.475
−2.42989
0



9
0.3274
−2.08079
−10.244



10
0.27183
−1.95185
0



11
−0.31059
−0.62528
59.9572



12
−0.67265
0.21681
22.75803



13
−1.20831
1.61659
11.7057



14
−1.57838
2.93257
6.99237



15
−1.71226
3.80234
0.22265



16
−1.37201
4.0108
1.88442



17
−1.01684
3.72181
2.93469



18
−0.59502
3.16271
5.29042



19
−0.26772
2.49626
9.96354



20
0.03956
1.62768
33.73321



21
0.35761
0.50693
0



22
2.0648
−5.76153
0.02969



23
2.01086
−5.78492
0.04563

















TABLE NO. 10







Z = 25.0338′′












POINT NO.
X
Y
R
















1
1.81505
−5.76825
15.72298



2
1.56739
−5.27717
30



3
0.65763
−3.19351
75



4
−0.44402
−0.1988
26.63003



5
−1.04084
1.78431
13.81459



6
−1.43114
4.06229
0.74728



7
−1.43357
4.14851
0.14272



8
−1.20162
4.25562
0.74728



9
−1.12652
4.18644
2.2833



10
−0.72156
3.59509
12



11
0.07255
1.38392
0



12
1.86883
−5.74766
0.02901



13
1.81505
−5.76825
11.7057

















TABLE NO. 11







Z = 27.3109′′












POINT NO.
X
Y
R
















1
1.66692
−5.74133
0



2
1.12277
−4.61262
4.11497



3
1.03508
−4.40816
23.74997



4
0.84338
−3.90929
0



5
0.63975
−3.35834
0.57106



6
0.63603
−3.34754
5.45871



7
0.62496
−3.31401
0



8
−0.24726
−0.6132
32.48476



9
−0.86584
1.6598
18.25371



10
−1.1838
3.39676
21.93099



11
−1.23945
3.84972
24.92753



12
−1.28904
4.33374
0.14286



13
−1.03331
4.43369
2.5686



14
−0.68907
3.82809
12.43525



15
−0.2081
2.37275
36.57981



16
−0.03539
1.69041
134.69



17
0.27682
0.37637
0



18
1.04382
−2.94283
−147.62399



19
1.16922
−3.46869
−108.15



20
1.28126
−3.9302
0



21
1.72041
−5.72213
0.02858



22
1.66692
−5.74133
0.02969

















TABLE NO. 12







Z = 29.5884′′












POINT NO.
X
Y
R
















1
1.51597
−5.71912
139.3053



2
0.98183
−4.5066
3.01844



3
0.90988
−4.32532
10.77397



4
0.75283
−3.85543
34.20319



5
0.44357
−2.79355
0



6
−0.0857
−0.86034
48.60234



7
−0.87365
2.47549
17.30307



8
−1.15438
4.50507
0.44337



9
−1.15225
4.59529
0.08468



10
−1.00934
4.64551
0.44337



11
−0.94996
4.57459
2.57476



12
−0.628
3.90406
29.46461



13
−0.00641
1.58567
70



14
0.1233
0.99714
0



15
1.56932
−5.70167
0.02823



16
1.51597
−5.71912
134.69

















TABLE NO. 13







Z = 31.8659′′












POINT NO.
X
Y
R
















1
1.37725
−5.69672
137.6895



2
0.91796
−4.60379
1.70029



3
0.8722
−4.48025
3.4118



4
0.79678
−4.21332
97.0057



5
0.47157
−2.80704
0



6
−0.74575
2.64135
83.91212



7
−0.92003
3.4396
14.02929



8
−1.0334
4.03385
6.44655



9
−1.11124
4.71531
0.32572



10
−1.10944
4.77442
0.06221



11
−1.00462
4.81177
0.32572



12
−0.96456
4.76533
1.96955



13
−0.74312
4.35991
7.94476



14
−0.47464
3.57668
29.54417



15
−0.17891
2.45839
23.99381



16
0.04576
1.44045
143.30981



17
0.1273
1.02548
185.80972



18
0.14862
0.91597
0



19
1.40035
−5.52483
136.64554



20
1.4305
−5.68046
0.02801



21
1.37725
−5.69672
0.02858

















TABLE NO. 14







Z = 34.1435′′












POINT NO.
X
Y
R
















1
1.30024
−5.68367
0



2
0.81215
−4.56682
1.07849



3
0.76343
−4.43132
3.20433



4
0.72698
−4.29204
7.61968



5
0.67477
−4.05592
0



6
−0.8365
3.33401
16.85328



7
−0.99746
4.24892
7.90627



8
−1.07009
4.9652
0.06857



9
−0.9417
5.00231
2.94371



10
−0.7577
4.60396
6.35831



11
−0.52553
3.84073
−94.7678



12
−0.4565
3.55126
0



13
−0.31732
2.97168
17.86547



14
−0.12419
2.06424
0



15
0.73398
−2.55376
−54.4051



16
0.81808
−2.99614
0



17
1.00508
−3.95802
−27.1624



18
1.05339
−4.20062
0



19
1.35238
−5.66716
0.02751



20
1.30024
−5.68367
0.02801

















TABLE NO. 15







Z = 36.4218′′












POINT NO.
X
Y
R
















1
1.28721
−5.67147
0



2
0.69127
−4.42436
0.48204



3
0.65442
−4.31543
103.2697



4
0.55332
−3.8273
−500



5
−0.02683
−1.03264
0



6
−0.4485
0.96985
38.35151



7
−0.9102
3.62048
17.3778



8
−1.05546
5.1998
0.06857



9
−0.9233
5.22842
4.89375



10
−0.72457
4.6179
17.18319



11
−0.46267
3.40691
0



12
−0.33716
2.70483
−176.212



13
0.00372
0.85533
0



14
0.35192
−0.97896
−134.032



15
0.98865
−4.12693
−55.9761



16
1.31427
−5.55208
0



17
1.33874
−5.65313
0.02751



18
1.28721
−5.67147
0

















TABLE NO. 16







Z = 38.7016′′












POINT NO.
X
Y
R
















1
1.25913
−5.65294
87.53835



2
0.72125
−4.54406
1.47705



3
0.66033
−4.39601
5.91333



4
0.47172
−3.73516
82.38358



5
−0.04808
−1.22655
10



6
−0.08499
−1.0218
0



7
−0.51202
1.49661
48.40389



8
−0.82787
3.6529
23.04195



9
−0.97661
5.40196
0.2199



10
−0.97071
5.46383
0.042



11
−0.89751
5.48072
0.2199



12
−0.86487
5.42716
2.54425



13
−0.72316
4.99061
24.25494



14
−0.43944
3.53951
0



15
0.11067
0.18612
−76.8724



16
0.71254
−3.04795
−59.549



17
1.31162
−5.63353
0.02814



18
1.25913
−5.65294
0

















TABLE NO. 17







Z = 40.9827′′












POINT NO.
X
Y
R
















1
1.21987
−5.65479
0



2
0.7985
−4.87148
31.42264



3
0.741
−4.7641
1.23199



4
0.65349
−4.5559
5.5107



5
0.61644
−4.43375
16.09645



6
0.39827
−3.60087
38.31746



7
0.08847
−2.14769
0



8
−0.0106
−1.6344
25



9
−0.21776
−0.39414
0



10
−0.55542
1.99575
57.90813



11
−0.81637
4.12741
28.68988



12
−0.93501
5.68442
0.05714



13
−0.83534
5.7253
0.1515



14
−0.80286
5.66679
6.44268



15
−0.65091
5.02648
0



16
−0.54839
4.46912
18.5916



17
−0.44348
3.83789
0



18
0.2358
−0.73448
−9.19071



19
0.2683
−0.93753
0



20
0.35889
−1.46572
−33.5814



21
0.47515
−2.10628
0



22
0.52937
−2.38933
−43.2909



23
0.98054
−4.46727
−60.9649



24
1.11309
−5.00222
0



25
1.27274
−5.63426
0.02858



26
1.21987
−5.65479
0.08572

















TABLE NO. 18







Z = 43.2654′′












POINT NO.
X
Y
R
















1
1.18126
−5.67467
0



2
0.84884
−5.13531
2.77432



3
0.49882
−4.26532
70.5369



4
−0.07838
−1.2827
38.55754



5
−0.23221
−0.30999
63.44528



6
−0.40931
1.00769
0



7
−0.59561
2.51326
59.53784



8
−0.79907
4.40491
30.89333



9
−0.90043
5.92769
0.20122



10
−0.89467
5.98457
0.03843



11
−0.82759
5.99959
0.20122



12
−0.79756
5.94926
1.6985



13
−0.69912
5.61953
34.69339



14
−0.41738
3.91472
0



15
0.16104
−0.22347
−44.6866



16
0.57547
−2.68486
−60.1787



17
1.04914
−4.87144
0



18
1.23371
−5.65298
0.02876



19
1.18126
−5.67467
0

















TABLE NO. 19







Z = 45.55′′












POINT NO.
X
Y
R
















1
1.12747
−5.71414
0



2
0.57999
−4.88189
0.38633



3
0.54175
−4.80717
0.60926



4
0.5103
−4.69162
0



5
0.28237
−3.34203
58.05177



6
0.23511
−3.05787
0



7
−0.05661
−1.27676
45.25879



8
−0.08987
−1.07069
0



9
−0.33632
0.47871
10



10
−0.3961
0.91688
0



11
−0.61081
2.80034
71.57434



12
−0.79431
4.61535
33.18385



13
−0.89791
6.24806
0.05714



14
−0.78605
6.26656
6.16388



15
−0.64595
5.69765
17.56455



16
−0.56598
5.26131
4.03085



17
−0.54606
5.13154
0



18
0.26807
−0.8145
−7.68995



19
0.29713
−1.00833
0



20
0.40029
−1.6413
−23.6684



21
0.45034
−1.93659
0



22
0.55916
−2.55494
−25.0416



23
0.61114
−2.84055
0



24
0.74545
−3.55509
−15.7037



25
0.7916
−3.79061
0



26
1.17933
−5.69274
0.02858



27
1.12747
−5.71414
0










Exemplary embodiments of turbine rotor buckets are described above in detail. The turbine rotor buckets are not limited to the specific embodiments described herein, but rather, components of the turbine rotor bucket may be utilized independently and separately from other components described herein. Each turbine rotor bucket component can also be used in combination with other turbine rotor bucket components.
While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.

## Claims

1. A turbine bucket including a bucket airfoil having an airfoil shape, said airfoil comprising a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R set forth in Tables 1-19 wherein the X, Y, Z and R distances are in inches, the X and Y coordinate values being smoothly joined by an arc of radius R defining airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.

2. The turbine bucket according to claim 1 forming part of a last stage bucket of a turbine.

3. The turbine bucket according to claim 1, wherein said airfoil shape lies in an envelope within about +/−0.25 inches in a direction normal to any airfoil surface location.

4. The turbine bucket according to claim 1, wherein the height of the airfoil is about 45 inches.

5. The turbine bucket according to claim 1, wherein a part-span shroud is superimposed on the nominal profile of the airfoil.

6. The turbine bucket according to claim 1, wherein the nominal profile for the airfoil applies in a cold, non-operating condition.

7. The turbine bucket according to claim 1, wherein the nominal profile for the airfoil comprises an uncoated nominal profile.

8. A turbine wheel comprising a plurality of buckets, each of said buckets including an airfoil having an airfoil shape, said airfoil comprising a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R set forth in Tables 1-19 wherein the X, Y, Z and R distances are in inches, the X and Y coordinate values being smoothly joined by an arc of radius R defining airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.

9. The turbine wheel according to claim 8, wherein said airfoil shape lies in an envelope within about +/−0.25 inches in a direction normal to any airfoil surface location.

10. The turbine wheel according to claim 8, wherein the nominal profile for the airfoil applies in a cold, non-operating condition.

11. The turbine wheel according to claim 8, wherein the nominal profile for the airfoil comprises an uncoated nominal profile.

12. The turbine wheel according to claim 8, wherein the turbine wheel comprises a last stage of the turbine.

13. The turbine wheel according to claim 8, wherein the turbine wheel has about 49 buckets.

14. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets including an airfoil comprising a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R set forth in Tables 1-19 wherein the X, Y, Z and R distances are in inches, the X and Y coordinate values being smoothly joined by an arc of radius R defining airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.

15. The turbine according to claim 14, wherein said airfoil shape lies in an envelope within about +/−0.25 inches in a direction normal to any airfoil surface location.

16. The turbine according to claim 14, wherein the nominal profile for the airfoil applies in a cold, non-operating condition.

17. The turbine according to claim 14, wherein the nominal profile for the airfoil comprises an uncoated nominal profile.

18. The turbine according to claim 14, wherein the turbine wheel comprises a last stage of the turbine.

19. A turbine according to claim 14, wherein the turbine wheel has about 49 buckets.

20. A turbine according to claim 19 further comprising:
a bucket having a part-span shroud, said part-span shroud located at a distance of about 45% to about 65% of a total airfoil length from a base of said airfoil.