U.S. patent application number 10/246689 was filed with the patent office on 2004-03-25 for first stage turbine bucket airfoil.
Invention is credited to Arness, Brian Peter, Enrique Paz, Eduardo, Jones, Andrew JR., Perry, Jacob Charles II, Siden, Gunnar Leif, Timko, Lawrence Paul.
Application Number | 20040057833 10/246689 |
Document ID | / |
Family ID | 31946424 |
Filed Date | 2004-03-25 |
United States Patent
Application |
20040057833 |
Kind Code |
A1 |
Arness, Brian Peter ; et
al. |
March 25, 2004 |
FIRST STAGE TURBINE BUCKET AIRFOIL
Abstract
The first stage buckets have airfoil profiles substantially in
accordance with Cartesian coordinate values of X, Y and Z set forth
Table I wherein X and Y values are in inches and the Z value is
non-dimensional along the bucket centerline coincident with a
turbine radius and convertible to a Z distance in inches from the
turbine axis by multiplying the Z value by the height of the
airfoil and adding the root radius to the result. The X and Y
distances may be scalable as a function of the same constant or
number to provide a scaled up or scaled down airfoil section for
the bucket. The nominal airfoil given by the X, Y and Z distances
lies within an envelop of .+-.0.160 inches.
Inventors: |
Arness, Brian Peter;
(Simpsonville, SC) ; Enrique Paz, Eduardo;
(Albany, NY) ; Perry, Jacob Charles II; (Taylors,
SC) ; Siden, Gunnar Leif; (Greenville, SC) ;
Jones, Andrew JR.; (Greenville, SC) ; Timko, Lawrence
Paul; (Fairfield, OH) |
Correspondence
Address: |
NIXON & VANDERHYE P.C.
8th Floor
1100 North Glebe Road
Arlington
VA
22201-4714
US
|
Family ID: |
31946424 |
Appl. No.: |
10/246689 |
Filed: |
September 19, 2002 |
Current U.S.
Class: |
416/243 ; 416/2;
416/223A |
Current CPC
Class: |
F01D 5/141 20130101;
F05D 2250/70 20130101; Y10S 416/02 20130101; F05D 2220/3212
20130101; F05D 2240/301 20130101; F05D 2250/20 20130101 |
Class at
Publication: |
416/243 ;
416/223.00A; 416/002 |
International
Class: |
F01D 005/14 |
Claims
What is claimed is:
1. A turbine bucket having a bucket airfoil shape in an envelope
within .+-.0.160 inches in a direction normal to any airfoil
surface location wherein the airfoil has a nominal profile
substantially in accordance with Cartesian coordinate values of X,
Y and Z set forth in Table I wherein Z is a non-dimensional value
along a bucket centerline coincident with a radius from a turbine
axis of rotation convertible to a Z distance in inches from said
turbine axis by multiplying the Z value by a height of the airfoil
and adding that product to a root radius of the bucket and wherein
X and Y are distances in inches defining the airfoil profile at
each distance Z, the profiles at the Z distances being joined
smoothly with one another to form a complete airfoil shape.
2. A turbine bucket according to claim 1 forming part of a first
stage of a turbine.
3. A turbine bucket according to claim 1 wherein the Z value is
measured from an intersection of the bucket centerline along a
radius from the turbine axis and the root radius of a flowpath
through the turbine.
4. A turbine bucket according to claim 1 wherein the root radius of
the airfoil is 49.400 inches and a height of the airfoil bucket
from the root radius is 6.815 inches, said bucket comprising part
of a first stage of a turbine.
5. A turbine bucket having an uncoated nominal airfoil profile
substantially in accordance with Cartesian coordinate values of X,
Y and Z set forth in Table I wherein Z is a non-dimensional value
along a bucket centerline coincident with a radius from a turbine
axis of rotation convertible to a Z distance in inches from said
turbine axis by multiplying the Z value by a height of the airfoil
and adding that product to a root radius of the bucket and wherein
X and Y are distances in inches defining the airfoil profile at
each distance Z, the profiles at the Z distances being joined
smoothly with one another to form a complete airfoil shape, the X
and Y distances being scalable as a function of the same constant
or number to provide a scaled-up or scaled-down bucket airfoil.
6. A turbine bucket according to claim 5 forming part of a first
stage of a turbine.
7. A turbine bucket according to claim 5 wherein the root radius of
the airfoil is 49.400 inches and a height of the airfoil bucket
from the root radius is 6.815 inches, said bucket comprising part
of a first stage of a turbine.
8. A turbine comprising a turbine wheel having a plurality of
buckets, each of said buckets having an airfoil shape in an
envelope within .+-.0.160 inches in a direction normal to any
airfoil surface location wherein the airfoil has a nominal profile
substantially in accordance with Cartesian coordinate values of X,
Y and Z set forth in Table I wherein Z is a non-dimensional value
along a bucket centerline coincident with a radius from a turbine
axis of rotation convertible to a Z distance in inches from said
turbine axis by multiplying the Z value by a height of the airfoil
and adding that product to a root radius of the bucket and wherein
X and Y are distances in inches defining the airfoil profile at
each distance Z, the profiles at the Z distances being joined
smoothly with one another to form a complete airfoil shape.
9. A turbine according to claim 8 wherein the turbine wheel
comprises a first stage turbine.
10. A turbine according to claim 8 wherein the turbine wheel has 92
buckets and Y represents a distance parallel to the turbine axis of
rotation.
11. A turbine bucket according to claim 8 wherein each of the
airfoil buckets has a root radius of 49.400 inches and a height
from the root radius of 6.815 inches, said turbine wheel comprising
a first stage of the turbine.
12. A turbine comprising a turbine wheel having a plurality of
buckets, each of said buckets having an uncoated nominal airfoil
profile substantially in accordance with Cartesian coordinate
values of X, Y and Z set forth in Table I wherein Z is a
non-dimensional value along a bucket centerline coincident with a
radius from a turbine axis of rotation convertible to a Z distance
in inches from said turbine axis of rotation by multiplying the Z
value by a height of the airfoil and adding that product to a root
radius of the bucket and wherein X and Y are distances in inches
defining the airfoil profile at each distance Z, the profiles at
the Z distances being joined smoothly with one another to form a
complete airfoil shape, the X and Y distances being scalable as a
function of the same constant or number to provide a scaled-up or
scaled-down bucket airfoil.
13. A turbine according to claim 12 wherein the turbine wheel
comprises a first stage of the turbine.
14. A turbine according to claim 12 wherein the turbine wheel has
92 buckets and Y represents a distance parallel to the turbine axis
of rotation.
15. A turbine bucket according to claim 12 wherein each of the
airfoil buckets has a root radius of 49.400 inches and a height
from the root radius of 6.815 inches, said turbine wheel comprising
a first stage of the turbine.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates to a turbine bucket for a gas
turbine stage and particularly relates to a first stage turbine
bucket airfoil profile.
[0002] In recent years, advanced gas turbines have trended toward
increasing firing temperatures in order to meet system requirements
of efficiency and loading. Consequently, efforts have been made to
improve the cooling of the various turbine stages. It will also be
appreciated that the design and construction of turbine buckets and
in particular, air-cooled buckets for a first turbine stage,
require optimized aerodynamic efficiency as well as optimized
aerodynamic and mechanical bucket loading.
BRIEF DESCRIPTION OF THE INVENTION
[0003] In accordance with a preferred embodiment of the present
invention, there is provided a unique turbine bucket airfoil
profile for the buckets of a turbine stage, preferably the first
stage of a gas turbine. The bucket airfoil profile is defined by a
unique loci of points to achieve the necessary efficiency and
loading requirements whereby improved turbine performance is
obtained. These unique loci of points define the nominal airfoil
profile and are identified by the X, Y and Z Cartesian coordinates
of Table I which follows. The 3600 points for the coordinate values
shown in Table I are for a cold, i.e., room temperature profile at
various cross-sections of the bucket airfoil along its length. The
X and Y coordinates are given in distance dimensions, e.g., units
of inches, and are joined smoothly at each Z location to form a
smooth continuous airfoil cross-section. The Z coordinates are
given in non-dimensionalized form from 0 to 1 along a bucket
centerline coincident with a radius from the axis of rotation. By
multiplying the airfoil height dimension, e.g., in inches, by the
non-dimensional Z value of Table I and adding that value to the
root radius of the bucket, the actual Z distance from the
rotational axis, e.g., in inches, is obtained. Each defined
cross-section is joined smoothly with adjacent cross-sections to
form the complete airfoil shape.
[0004] It will be appreciated that as each bucket airfoil heats up
in use, the profile will change as a result of stress and
temperature. Thus, the cold or room temperature profile is given by
the X, Y and Z coordinates for manufacturing purposes. Because a
manufactured bucket airfoil profile may be different from the
nominal airfoil profile given by the following table, a distance of
plus or minus 0.160 inches from the nominal profile in a direction
normal to any surface location along the nominal profile and which
includes any coating process, defines the profile envelope for this
bucket airfoil. The design is robust to this variation without
impairment of the mechanical and aerodynamic functions.
[0005] It will also be appreciated that the airfoil can be scaled
up or scaled down geometrically for introduction into similar
turbine designs. Consequently, the X and Y coordinates in inches
and the Z coordinates, when converted to inches, of the nominal
airfoil profile given below are a function of the same constant or
number. That is, the X, Y and Z coordinate values in inches may be
multiplied or divided by the same constant or number to provide a
scaled up or scaled down version of the bucket airfoil profile
while retaining the airfoil section shape.
[0006] In a preferred embodiment according to the present
invention, there is provided a turbine bucket having a bucket
airfoil shape in an envelope within .+-.0.160 inches in a direction
normal to any airfoil surface location wherein the airfoil has a
nominal profile substantially in accordance with Cartesian
coordinate values of X, Y and Z set forth in Table I wherein Z is a
non-dimensional value along a bucket centerline coincident with a
radius from a turbine axis of rotation convertible to a Z distance
in inches from said turbine axis by multiplying the Z value by a
height of the airfoil and adding that product to a root radius of
the bucket and wherein X and Y are distances in inches defining the
airfoil profile at each distance Z, the profiles at the Z distances
being joined smoothly with one another to form a complete airfoil
shape.
[0007] In a further preferred embodiment according to the present
invention, there is provided a turbine bucket having an uncoated
nominal airfoil profile substantially in accordance with Cartesian
coordinate values of X, Y and Z set forth in Table I wherein Z is a
non-dimensional value along a bucket centerline coincident with a
radius from a turbine axis of rotation convertible to a Z distance
in inches from said turbine axis by multiplying the Z value by a
height of the airfoil and adding that product to a root radius of
the bucket and wherein X and Y are distances in inches defining the
airfoil profile at each distance Z, the profiles at the Z distances
being joined smoothly with one another to form a complete airfoil
shape, the X and Y distances being scalable as a function of the
same constant or number to provide a scaled-up or scaled-down
bucket airfoil.
[0008] In a further preferred embodiment according to the present
invention, there is provided a turbine comprising a turbine wheel
having a plurality of buckets, each of said buckets having an
airfoil shape in an envelope within .+-.0.160 inches in a direction
normal to any airfoil surface location wherein the airfoil has a
nominal profile substantially in accordance with Cartesian
coordinate values of X, Y and Z set forth in Table I wherein Z is a
non-dimensional value along a bucket centerline coincident with a
radius from a turbine axis of rotation convertible to a Z distance
in inches from said turbine axis by multiplying the Z value by a
height of the airfoil and adding that product to a root radius of
the bucket and wherein X and Y are distances in inches defining the
airfoil profile at each distance Z, the profiles at the Z distances
being joined smoothly with one another to form a complete airfoil
shape.
[0009] In a further preferred embodiment according to the present
invention, there is provided a turbine comprising a turbine wheel
having a plurality of buckets, each of said buckets having an
uncoated nominal airfoil profile substantially in accordance with
Cartesian coordinate values of X, Y and Z set forth in Table I
wherein Z is a non-dimensional value along a bucket centerline
coincident with a radius from a turbine axis of rotation
convertible to a Z distance in inches from said turbine axis of
rotation by multiplying the Z value by a height of the airfoil and
adding that product to a root radius of the bucket and wherein X
and Y are distances in inches defining the airfoil profile at each
distance Z, the profiles at the Z distances being joined smoothly
with one another to form a complete airfoil shape, the X and Y
distances being scalable as a function of the same constant or
number to provide a scaled-up or scaled-down bucket airfoil.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a schematic illustration of a turbine having a
first stage turbine wheel employing the buckets and bucket airfoils
hereof;
[0011] FIG. 2 is a top, trailing edge and pressure side perspective
view of a first stage turbine bucket including an airfoil and a
shank in accordance with a preferred embodiment of the present
invention;
[0012] FIG. 3 is a side elevational view of the bucket including
the airfoil hereof;
[0013] FIG. 4 is a top plan view thereof; and
[0014] FIG. 5 is a rear suction side perspective view of the bucket
airfoil hereof.
DETAILED DESCRIPTION OF THE INVENTION
[0015] Referring now to FIG. 1, there is illustrated a portion of a
turbine generally designated 10 in which a first stage turbine
bucket 20 having an airfoil profile as defined herein may be
utilized. Turbine 10 includes a rotor 12 having first, second and
third stage rotor wheels 14, 16 and 18 having buckets 20, 22 and 24
in conjunction with the respective stator vanes 26, 28 and 30 of
the various stages of the rotor. It will be appreciated that a
three stage turbine is illustrated.
[0016] The first stage comprises the rotor wheel 14 on which
buckets 20 are mounted in axial opposition to the upstream stator
vanes 26. It will be appreciated that a plurality of the buckets 20
are spaced circumferentially one from the other about the first
stage wheel 14 and in this instance there are ninety-two buckets
mounted on the first stage wheel 14.
[0017] Referring now to FIG. 2, there is illustrated a turbine
bucket constructed in accordance with the present invention
including an airfoil 40 mounted on a platform 34. The turbine
bucket also includes forward and aft wheel space seals, i.e, angel
wings 36 and 38, respectively. The buckets 20 are suitably mounted
on the turbine wheel 14 by means, not shown. The airfoil 40 and
platform 34 are collectively referred to as a bucket 20. The
airfoil 40 has a profile including a compound curvature with
suction and pressure sides 42 and 44, respectively, as well as a
leading edge 46 and trailing edge 48. This first stage bucket 20 is
preferably air cooled and includes a series of internal passages,
not shown, for flowing cooling air to cool the airfoil 40, the
cooling air exiting into the hot gas path of the turbine through
apertures 50 along the trailing edge 48.
[0018] A Cartesian coordinate system of X, Y and Z values given in
Table I defines the profile of airfoil 40. The coordinate values
for the X and Y coordinates are set forth in inches in Table I
although other units of dimensions may be used. The Z values are
set forth in Table I in non-dimensional form from 0 to 1 along a
bucket centerline coincident with a radius from the axis of
rotation. To convert the Z value to a Z coordinate value, e.g., in
inches, from the turbine axis of rotation, the non-dimensional Z
value given in the table is multiplied by the height of airfoil 40
in inches and that product is added to the root radius in inches.
The airfoil height is measured from the intersection of the bucket
centerline, which is along a radius from the centerline or axis of
the turbine, and the root radius of the flowpath. The Z coordinate
value of this intersection with the root radius for each bucket of
the first stage in a preferred embodiment is 49.400 inches. The
height of the first stage airfoil bucket from the root radius in
this preferred embodiment is 6.815 inches. The Cartesian coordinate
system has orthogonally-related X, Y and Z axes with the Z axis
extending perpendicular to a plane normal to a plane containing the
X and Y values. When converted to inches, the Z distance commences
at 0 at the turbine centerline. The Y axis lies parallel to the
turbine rotor centerline, i.e., the rotary axis.
[0019] By defining X and Y coordinate values at selected locations
in a Z direction normal to the X, Y plane, the profile of airfoil
40 can be ascertained. By connecting the X and Y values with smooth
continuing arcs, each profile section at each distance Z is fixed.
The surface profiles of the various surface locations between the
distances Z are determined by smoothly connecting the adjacent
cross-sections to one another to form the airfoil. These values
represent the airfoil profiles at ambient, non-operating or non-hot
conditions and are for an uncoated airfoil. The sign convention
assigns a positive value to Z values and positive and negative
values for the X and Y coordinates as typically used in Cartesian
coordinate systems.
[0020] The Table I values are generated and shown to three decimal
places for determining the profile of the airfoil. There are
typical manufacturing tolerances as well as coatings which must be
accounted for in the actual profile of the airfoil. Accordingly,
the values for the profile given in Table I are for a nominal
airfoil. It will therefore be appreciated that .+-. typical
manufacturing tolerances, i.e., .+-.values, including any coating
thicknesses, are additive to the X and Y values given in Table I
below. Accordingly, a distance of .+-.0.160 inches in a direction
normal to any surface location along the airfoil profile defines an
airfoil profile envelope for this particular bucket airfoil design
and turbine.
[0021] The coordinate values given in Table I below provide the
preferred nominal profile envelope.
1TABLE I X Y Z' X Y Z' X Y Z' -2.106 -0.412 0.000 -1.959 -0.414
0.034 -2.296 -0.358 0.069 -2.243 -0.394 0.000 -2.217 -0.399 0.034
-2.381 -0.208 0.069 -2.398 -0.307 0.000 -2.370 -0.309 0.034 -2.340
-0.001 0.069 -2.432 -0.136 0.000 -2.405 -0.137 0.034 -2.156 0.301
0.069 -2.328 0.101 0.000 -2.306 0.104 0.034 -2.120 -0.415 0.069
-2.048 0.437 0.000 -2.035 0.448 0.034 -2.375 -0.243 0.069 -2.046
-0.413 0.000 -1.848 -0.403 0.034 -2.361 -0.060 0.069 -2.205 -0.402
0.000 -2.179 -0.407 0.034 -2.218 0.216 0.069 -2.374 -0.333 0.000
-2.347 -0.335 0.034 -1.877 0.614 0.069 -2.436 -0.173 0.000 -2.408
-0.174 0.034 -2.060 -0.419 0.069 -2.360 0.048 0.000 -2.336 0.049
0.034 -2.265 -0.376 0.069 -2.120 0.362 0.000 -2.105 0.370 0.034
-2.364 -0.277 0.069 -1.817 0.651 0.000 -2.141 -0.412 0.034 -2.372
-0.096 0.069 -1.985 -0.412 0.000 -2.319 -0.357 0.034 -2.252 0.164
0.069 -2.167 -0.407 0.000 -2.408 -0.210 0.034 -1.950 0.539 0.069
-2.346 -0.354 0.000 -2.364 -0.007 0.034 -1.999 -0.418 0.069 -2.436
-0.209 0.000 -2.173 0.290 0.034 -2.231 -0.391 0.069 -2.388 -0.008
0.000 -2.081 -0.416 0.034 -2.346 -0.308 0.069 -2.190 0.284 0.000
-2.287 -0.375 0.034 -2.379 -0.133 0.069 -1.854 -0.403 0.000 -2.401
-0.246 0.034 -2.284 0.110 0.069 -2.314 -0.371 0.000 -2.386 -0.064
0.034 -2.021 0.462 0.069 -2.430 -0.244 0.000 -2.237 0.208 0.034
-1.939 -0.414 0.069 -2.412 -0.064 0.000 -1.887 0.597 0.034 -2.195
-0.402 0.069 -2.256 0.203 0.000 -2.020 -0.416 0.034 -2.323 -0.335
0.069 -1.896 0.582 0.000 -2.253 -0.389 0.034 -2.382 -0.171 0.069
-2.279 -0.384 0.000 -2.389 -0.279 0.034 -2.313 0.055 0.069 -2.417
-0.277 0.000 -2.397 -0.100 0.034 -2.090 0.383 0.069 -2.424 -0.100
0.000 -2.273 0.156 0.034 -1.827 -0.401 0.069 -2.293 0.153 0.000
-1.962 0.524 0.034 -2.158 -0.410 0.069 -1.973 0.511 0.000 -1.596
0.842 0.034 -1.801 0.687 0.069 -1.590 -0.375 0.000 -1.284 -0.323
0.034 -1.364 1.021 0.069 -1.711 0.739 0.000 -1.369 0.995 0.034
-1.715 -0.383 0.069 -1.457 -0.361 0.000 -1.735 -0.389 0.034 -1.456
0.962 0.069 -1.325 -0.348 0.000 -1.267 1.052 0.034 -1.604 -0.362
0.069 -1.372 0.971 0.000 -1.623 -0.372 0.034 -1.546 0.898 0.069
-1.192 -0.337 0.000 -1.484 0.921 0.034 -1.491 -0.340 0.069 -1.489
0.899 0.000 -1.510 -0.355 0.034 -1.634 0.831 0.069 -1.722 -0.390
0.000 -1.809 0.667 0.034 -1.188 1.118 0.069 -1.601 0.821 0.000
-1.704 0.757 0.034 -1.379 -0.319 0.069 -1.167 1.078 0.000 -1.397
-0.338 0.034 -1.718 0.761 0.069 -0.877 -0.319 0.000 -0.280 1.286
0.034 -1.266 -0.298 0.069 -0.076 1.238 0.000 -0.542 -0.269 0.034
-0.399 -0.224 0.069 0.059 -0.382 0.000 -1.163 1.104 0.034 -0.439
1.314 0.069 -0.720 -0.316 0.000 -0.946 1.192 0.034 -1.153 -0.279
0.069 -0.724 1.227 0.000 -0.416 -0.273 0.034 -1.004 1.199 0.069
-0.563 -0.317 0.000 -1.170 -0.308 0.034 -0.273 -0.231 0.069 -0.284
1.263 0.000 -0.500 1.285 0.034 -0.997 -0.256 0.069 -0.407 -0.324
0.000 -0.291 -0.281 0.034 -0.065 1.280 0.069 -0.950 1.165 0.000
-1.014 -0.292 0.034 -0.147 -0.244 0.069 -0.251 -0.336 0.000 -0.072
1.259 0.034 -0.622 1.299 0.069 -1.034 -0.327 0.000 -0.166 -0.293
0.034 -0.841 -0.239 0.069 -0.505 1.259 0.000 -0.857 -0.279 0.034
-0.023 -0.264 0.069 -0.095 -0.356 0.000 -0.720 1.254 0.034 -0.683
-0.227 0.069 0.395 1.075 0.000 -0.041 -0.311 0.034 -0.255 1.309
0.069 0.874 0.738 0.000 -0.699 -0.271 0.034 -0.812 1.260 0.069
1.287 0.278 0.000 1.242 -0.888 0.034 -0.525 -0.222 0.069 1.236
-0.898 0.000 0.678 -0.536 0.034 0.809 -0.571 0.069 0.660 -0.566
0.000 0.082 -0.335 0.034 0.221 -0.320 0.069 0.305 1.119 0.000 0.687
0.898 0.034 1.244 -0.877 0.069 0.782 0.817 0.000 1.126 0.470 0.034
0.488 1.046 0.069 1.211 0.376 0.000 0.797 -0.596 0.034 0.957 0.654
0.069 0.781 -0.621 0.000 0.203 -0.363 0.034 0.340 -0.357 0.069
0.180 -0.408 0.000 0.122 1.208 0.034 0.870 0.742 0.069 0.212 1.157
0.000 0.588 0.970 0.034 1.273 0.272 0.069 0.687 0.893 0.000 1.045
0.563 0.034 0.457 -0.400 0.069 1.132 0.471 0.000 0.914 -0.662 0.034
0.923 -0.641 0.069 0.900 -0.683 0.000 0.322 -0.397 0.034 0.313
1.146 0.069 0.300 -0.439 0.000 0.486 1.037 0.034 0.781 0.825 0.069
0.117 1.190 0.000 0.960 0.653 0.034 1.199 0.371 0.069 0.587 0.963
0.000 1.026 -0.732 0.034 0.571 -0.448 0.069 1.049 0.563 0.000 0.440
-0.437 0.034 1.034 -0.715 0.069 1.015 -0.750 0.000 0.398 1.087
0.034 0.687 0.904 0.069 0.419 -0.475 0.000 0.872 0.740 0.034 1.121
0.468 0.069 0.484 1.027 0.000 1.280 0.275 0.034 0.692 -0.507 0.069
0.964 0.652 0.000 1.136 -0.808 0.034 0.101 -0.289 0.069 1.127
-0.821 0.000 0.556 -0.482 0.034 1.141 -0.794 0.069 0.536 -0.516
0.000 0.308 1.133 0.034 0.127 1.225 0.069 1.736 -0.413 0.000 0.781
0.821 0.034 0.590 0.978 0.069 1.701 -1.314 0.000 1.204 0.374 0.034
1.041 0.562 0.069 1.635 -0.241 0.000 1.669 -0.320 0.034 1.473
-0.021 0.069 1.808 -1.431 0.000 1.817 -1.455 0.034 1.747 -0.481
0.069 1.335 -0.974 0.000 1.577 -0.167 0.034 1.807 -1.457 0.069
1.553 -0.108 0.000 1.933 -1.599 0.034 1.376 0.127 0.069 1.910
-1.553 0.000 1.362 -0.987 0.034 1.659 -0.326 0.069 1.431 -1.054
0.000 1.482 -0.017 0.034 1.362 -0.980 0.069 1.468 0.023 0.000 1.926
-0.787 0.034 1.567 -0.173 0.069 1.928 -0.761 0.000 1.478 -1.092
0.034 1.475 -1.088 0.069 1.524 -1.137 0.000 1.383 0.131 0.034 1.915
-0.794 0.069 1.379 0.152 0.000 1.843 -0.631 0.034 1.583 -1.199
0.069 1.834 -0.587 0.000 1.589 -1.201 0.034 1.832 -0.637 0.069
1.614 -1.224 0.000 1.757 -0.475 0.034 1.921 -1.603 0.069 2.392
-2.234 0.000 1.696 -1.315 0.034 1.688 -1.315 0.069 2.192 -1.934
0.000 2.089 -1.108 0.034 2.157 -1.281 0.069 2.181 -1.266 0.000
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1.298 0.966 -2.121 1.463 1.000 -2.090 0.774 0.931 -2.239 1.097
0.966 -2.233 1.255 1.000 -1.882 0.764 0.931 -2.190 0.936 0.966
-2.217 1.076 1.000 -1.738 1.664 0.931 -2.046 0.859 0.966 -2.086
0.971 1.000 -2.056 1.373 0.931 -1.798 0.873 0.966 -1.828 0.965
1.000 -2.220 1.090 0.931 -1.877 1.624 0.966 -1.728 1.790 1.000
-2.224 0.911 0.931 -2.145 1.339 0.966 -2.088 1.504 1.000 -2.121
0.788 0.931 -2.235 1.132 0.966 -2.221 1.293 1.000 -1.930 0.758
0.931 -2.208 0.963 0.966 -2.231 1.108 1.000 -1.694 0.805 0.931
-2.080 0.867 0.966 -2.119 0.983 1.000 -1.668 1.711 0.931 -1.852
0.864 0.966 -1.891 0.958 1.000 -1.999 1.439 0.931 -1.808 1.675
0.966 -2.023 1.572 1.000 -2.199 1.146 0.931 -2.117 1.378 0.966
-2.205 1.330 1.000 -2.232 0.946 0.931 -2.227 1.168 0.966 -2.239
1.142 1.000 -2.150 0.805 0.931 -2.223 0.993 0.966 -2.149 0.999
1.000 -1.977 0.756 0.931 -2.111 0.878 0.966 -1.953 0.955 1.000
-1.741 0.793 0.931 -1.906 0.857 0.966 -1.953 1.636 1.000 -1.938
1.501 0.931 -1.738 1.722 0.966 -2.181 1.377 1.000 -2.173 1.201
0.931 -2.063 1.445 0.966 -2.242 1.177 1.000 -2.235 0.982 0.931
-2.212 1.212 0.966 -2.176 1.020 1.000 -2.175 0.826 0.931 -2.233
1.026 0.966 -2.014 0.958 1.000 -2.023 0.758 0.931 -2.141 0.893
0.966 -1.701 0.982 1.000 -1.788 0.782 0.931 -1.959 0.853 0.966
-1.501 1.891 1.000 -1.874 1.559 0.931 -1.690 0.894 0.966 -1.357
1.014 1.000 -2.143 1.253 0.931 -1.666 1.765 0.966 -1.421 1.914
1.000 -1.566 0.838 0.931 -1.357 0.952 0.966 -1.451 1.010 1.000
-1.157 0.910 0.931 -1.199 1.920 0.966 -1.341 1.932 1.000 -1.646
0.817 0.931 -1.592 1.804 0.966 -1.544 1.002 1.000 -1.241 0.904
0.931 -1.451 0.939 0.966 -1.251 1.945 1.000 -1.361 1.853 0.931
-1.515 1.838 0.966 -1.655 1.829 1.000 -1.323 0.893 0.931 -1.544
0.923 0.966 -1.637
0.991 1.000 -1.405 0.877 0.931 -1.437 1.867 0.966 -1.171 1.003
1.000 -1.204 1.890 0.931 -1.636 0.905 0.966 -1.579 1.862 1.000
-1.594 1.754 0.931 -1.169 0.959 0.966 -1.264 1.012 1.000 -1.486
0.859 0.931 -1.356 1.891 0.966 -0.219 1.538 1.000 -1.519 1.792
0.931 -1.263 0.959 0.966 -0.890 0.932 1.000 -0.281 1.613 0.931
-0.060 1.391 0.966 -0.571 1.799 1.000 -0.735 0.849 0.931 -0.428
1.716 0.966 -0.442 0.679 1.000 -1.043 1.904 0.931 -0.897 0.919
0.966 -0.982 1.940 1.000 -0.342 0.629 0.931 -0.507 0.740 0.966
-0.045 0.309 1.000 0.005 0.307 0.931 -0.090 0.386 0.966 -0.143
1.464 1.000 -0.198 1.543 0.931 0.011 1.310 0.966 -0.987 0.964 1.000
-0.568 1.796 0.931 -0.359 1.667 0.966 -0.499 1.757 1.000 -0.819
0.875 0.931 -0.981 0.939 0.966 -0.530 0.743 1.000 -0.419 0.685
0.931 -0.726 1.867 0.966 -0.893 1.923 1.000 -0.060 0.376 0.931
-0.581 0.785 0.966 -0.119 0.387 1.000 -0.119 1.468 0.931 -0.168
0.463 0.966 -0.071 1.386 1.000 -0.904 0.894 0.931 -0.292 1.615
0.966 -1.078 0.986 1.000 -0.882 1.893 0.931 -1.075 0.953 0.966
-0.430 1.711 1.000 -0.499 0.736 0.931 -0.648 1.837 0.966 -0.616
0.798 1.000 -0.127 0.443 0.931 -0.656 0.826 0.966 -0.806 1.900
1.000 -0.043 1.390 0.931 -1.039 1.926 0.966 -0.195 0.464 1.000
-0.419 1.713 0.931 -0.248 0.538 0.966 -0.001 1.306 1.000 -0.990
0.906 0.931 -0.211 1.544 0.966 -0.363 1.662 1.000 -0.575 0.778
0.931 -0.572 1.801 0.966 -0.704 0.849 1.000 -0.196 0.507 0.931
-0.734 0.863 0.966 -0.721 1.870 1.000 0.029 1.309 0.931 -0.331
0.610 0.966 -0.275 0.539 1.000 -0.349 1.665 0.931 -0.134 1.469
0.966 0.066 1.223 1.000 -1.074 0.911 0.931 -0.499 1.761 0.966
-0.298 1.609 1.000 -0.725 1.858 0.931 -0.815 0.894 0.966 -0.795
0.893 1.000 -0.654 0.816 0.931 -0.881 1.908 0.966 -0.645 1.837
1.000 -0.268 0.570 0.931 -0.417 0.677 0.966 -0.357 0.610 1.000
1.080 -0.426 0.931 -0.016 0.306 0.966 -1.071 1.949 1.000 0.547
0.572 0.931 1.139 -1.403 0.966 0.066 0.181 1.000 0.098 1.227 0.931
0.813 0.050 0.966 0.639 -0.612 1.000 0.461 -0.274 0.931 0.340 0.865
0.966 1.122 -0.636 1.000 1.046 -1.199 0.931 0.433 -0.268 0.966
0.582 0.431 1.000 0.634 0.423 0.931 1.011 -1.183 0.966 0.130 1.139
1.000 0.165 1.142 0.931 0.931 -0.181 0.966 0.521 -0.433 1.000 0.333
-0.096 0.931 0.432 0.722 0.966 1.076 -1.335 1.000 0.934 -1.011
0.931 0.306 -0.092 0.966 0.663 0.283 1.000 0.719 0.273 0.931 0.900
-0.997 0.966 0.228 1.002 1.000 0.266 1.004 0.931 1.046 -0.415 0.966
0.400 -0.257 1.000 0.255 0.008 0.931 0.520 0.576 0.966 0.974 -1.160
1.000 0.819 -0.825 0.931 0.079 1.228 0.966 0.784 0.057 1.000 0.844
0.042 0.931 0.204 0.044 0.966 0.322 0.863 1.000 0.363 0.863 0.931
0.787 -0.812 0.966 0.275 -0.083 1.000 0.175 0.110 0.931 0.606 0.428
0.966 0.865 -0.976 1.000 0.703 -0.639 0.931 0.145 1.143 0.966 0.901
-0.172 1.000 0.964 -0.191 0.931 0.096 0.177 0.966 0.411 0.721 1.000
0.456 0.718 0.931 0.672 -0.629 0.966 0.172 0.051 1.000 0.091 0.210
0.931 0.690 0.280 0.966 0.753 -0.794 1.000 0.584 -0.456 0.931 0.245
1.006 0.966 1.013 -0.404 1.000 1.714 -1.889 0.931 0.554 -0.447
0.966 0.498 0.576 1.000 1.617 -1.644 0.931 1.546 -2.090 0.966 1.503
-2.059 1.000 1.558 -2.086 0.931 1.715 -1.975 0.966 1.176 -1.510
1.000 1.677 -2.132 0.931 1.634 -1.767 0.966 1.616 -2.064 1.000
1.758 -2.048 0.931 1.367 -1.121 0.966 1.677 -1.976 1.000 1.732
-1.940 0.931 1.680 -2.080 0.966 1.631 -1.836 1.000 1.637 -1.693
0.931 1.719 -1.990 0.966 1.613 -1.788 1.000 1.193 -0.664 0.931
1.530 -2.077 0.966 1.487 -2.045 1.000 1.587 -2.118 0.931 1.635
-2.105 0.966 1.593 -2.074 1.000 1.650 -2.136 0.931 1.653 -1.815
0.966 1.674 -1.992 1.000 1.752 -2.064 0.931 1.468 -1.356 0.966
1.649 -1.886 1.000 1.750 -1.987 0.931 1.710 -2.037 0.966 1.228
-0.871 1.000 1.656 -1.742 0.931 1.516 -2.059 0.966 1.575 -1.692
1.000 1.302 -0.903 0.931 1.609 -2.108 0.966 1.567 -2.077 1.000
1.624 -2.134 0.931 1.672 -1.864 0.966 1.474 -2.028 1.000 1.739
-2.088 0.931 1.577 -1.621 0.966 1.667 -2.007 1.000 1.757 -2.002
0.931 1.659 -2.095 0.966 1.667 -1.932 1.000 1.431 -1.868 0.931
1.720 -2.005 0.966 1.330 -1.102 1.000 1.675 -1.791 0.931 1.583
-2.106 0.966 1.541 -2.075 1.000 1.406 -1.139 0.931 1.390 -1.844
0.966 1.374 -1.858 1.000 1.572 -2.104 0.931 1.691 -1.914 0.966
1.654 -2.031 1.000 1.722 -2.108 0.931 1.596 -1.670 0.966 1.673
-1.946 1.000 1.761 -2.016 0.931 1.157 -0.650 0.966 1.429 -1.335
1.000 1.304 -1.646 0.931 1.696 -2.061 0.966 1.594 -1.740 1.000
1.695 -1.840 0.931 1.563 -2.100 0.966 1.521 -2.069 1.000 1.507
-1.377 0.931 1.265 -1.624 0.966 1.275 -1.685 1.000 1.605 -2.128
0.931 1.708 -1.961 0.966 1.637 -2.050 1.000 1.701 -2.123 0.931
1.615 -1.718 0.966 1.677 -1.961 1.000 1.761 -2.032 0.931 1.264
-0.887 0.966 1.537 -1.597 1.000 1.176 -1.422 0.931 1.716 -2.021
0.966 1.556 -1.645 1.000
[0022] It will also be appreciated that the airfoil disclosed in
the above table may be scaled up or down geometrically for use in
other similar turbine designs. Consequently, the coordinate values
set forth in Table I may be scaled upwardly or downwardly such that
the airfoil section shape remains unchanged. A scaled version of
the coordinates in Table I would be represented by X, Y and,
optionally, Z coordinate values (after the Z values have been
converted to inches) multiplied or divided by the same constant or
number.
[0023] While the invention has been described in connection with
what is presently considered to be the most practical and preferred
embodiment, it is to be understood that the invention is not to be
limited to the disclosed embodiment, but on the contrary, is
intended to cover various modifications and equivalent arrangements
included within the spirit and scope of the appended claims.
* * * * *