US20030021680A1 - Second-stage turbine nozzle airfoil - Google Patents
Second-stage turbine nozzle airfoil Download PDFInfo
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- US20030021680A1 US20030021680A1 US09/903,853 US90385301A US2003021680A1 US 20030021680 A1 US20030021680 A1 US 20030021680A1 US 90385301 A US90385301 A US 90385301A US 2003021680 A1 US2003021680 A1 US 2003021680A1
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- airfoil
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- 239000007789 gas Substances 0.000 description 5
- 238000000576 coating method Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 239000011248 coating agent Substances 0.000 description 2
- 238000001816 cooling Methods 0.000 description 2
- 239000000654 additive Substances 0.000 description 1
- 230000000996 additive effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 239000002826 coolant Substances 0.000 description 1
- 230000006735 deficit Effects 0.000 description 1
- 238000010304 firing Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
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Classifications
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
- F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
- F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
- F01D5/12—Blades
- F01D5/14—Form or construction
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
- F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
- F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
- F01D5/12—Blades
- F01D5/14—Form or construction
- F01D5/141—Shape, i.e. outer, aerodynamic form
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2240/00—Components
- F05D2240/20—Rotors
- F05D2240/30—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor
- F05D2240/301—Cross-sectional characteristics
Definitions
- the present invention relates to a turbine nozzle for a gas turbine stage and particularly relates to a second-stage turbine nozzle airfoil profile.
- a unique turbine nozzle airfoil profile for a turbine stage preferably the second stage, which may be defined by a unique loci of points to achieve the necessary efficiency in loading requirements whereby improved turbine performance is obtained.
- the nominal profile given by the X, Y, Z coordinates of Table I which follows, define this unique loci of points.
- the coordinates given in inches in Table I are for a cold, i.e., room-temperature profile for each cross-section of the nozzle vane.
- Each defined cross-section is joined smoothly with adjacent cross-sections to form the complete airfoil shape.
- the profile of the nozzle vane will change as a result of stress and temperature.
- the cold or room-temperature profile is given by the X, Y and Z coordinates for manufacturing purposes.
- a distance of ⁇ 0.100 inches from the nominal profile in a direction normal to any surface location along the nominal profile and which includes any coating defines the profile envelope for this design. The design is robust to this variation without impairment of the mechanical and aerodynamic functions.
- the airfoil can be scaled-up or scaled-down geometrically for introduction into other similar turbine designs. Consequently, the X, Y and Z coordinates 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 given in the Table may be multiplied or divided by the same constant or number to provide a scaled-up or scaled-down version of the nozzle airfoil profile, while retaining the airfoil section shape.
- a turbine nozzle having a nozzle vane in the shape of an airfoil in an envelope within ⁇ 0.100 inches in a direction normal to any airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at a radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
- a turbine nozzle having a nozzle vane in the shape of an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at a radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate values, the profiles at the z distances being joined smoothly with one another to form the complete airfoil profile, the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down nozzle airfoil.
- a turbine comprising a turbine nozzle having a plurality of vanes, each of said vanes being in the shape of an airfoil in an envelope within ⁇ 0.100 inches in a direction normal to any nozzle airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at a radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
- a turbine comprising a turbine nozzle having a plurality of vanes, each of said vanes being in the shape of an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at the radially innermost aerodynamic section of the airfoil and the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down nozzle airfoil.
- FIG. 1 is a schematic illustration of a turbine having a second-stage nozzle employing the airfoil or vane profile hereof;
- FIG. 2 is a perspective view of a nozzle vane thereof
- FIG. 3 is an end view of the nozzle vane illustrated in FIG. 2;
- FIG. 4 is a perspective view thereof similar to FIG. 1;
- FIG. 5 is a perspective view of the nozzle vane of FIG. 4 illustrating various airfoil profiles along the length of the vane.
- FIG. 6 is a view similar to FIG. 3 illustrating the profile sections at various Z coordinate locations along the vane.
- Nozzle 12 includes a plurality of vanes 14 having an airfoil shape or profile spaced circumferentially one from the other.
- the illustrated turbine 10 includes three stages, a first stage 16 having a plurality of circumferentially spaced nozzle vanes 18 and buckets 20 circumferentially spaced about a rotatable turbine wheel 22 ; the second stage nozzle 12 comprising a plurality of circumferentially space d nozzle vanes 14 and a plurality of circumferentially spaced buckets 24 mounted on a second-stage wheel 26 and a third-stage 28 mounting nozzle vanes 30 and a plurality of circumferentially spaced buckets 32 mounted on a third-stage wheel 34 .
- the nozzle vanes and buckets lie in the hot gas path of the turbine and which gases flow through the turbine in the direction of the arrow 36 .
- the nozzle vanes 14 of the second stage 12 are disposed between inner and outer bands 38 and 40 , respectively, by which the nozzles form an annulus about the rotor axis.
- the nozzle vanes 14 have leading and trailing edges 42 and 44 , respectively, with hooks 46 and 48 for securing the nozzle vane segments to the non-rotatable casing of the turbine.
- the nozzle vanes have various passages therethrough for flowing a cooling medium through the vanes.
- FIG. 2 there is illustrated a nozzle vane 14 for the second-stage having airfoil profiles defined by a Cartesian coordinate system for X, Y and Z values.
- the coordinate values are set forth in inches in Table I which follows.
- the Cartesian coordinate system has orthogonally-related X, Y and Z axes with the X, Y and Z values commencing at a radially innermost aerodynamic section 50 of the airfoil and then made relative to that section for the Z coordinate.
- X and Y coordinate values at selected locations in a Z direction, the profile of airfoil 14 can be ascertained.
- each profile section at each distance Z is fixed.
- the surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the airfoil.
- the tabular values given in Table I below are in inches and represent airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil.
- the sign convention assigns a positive value to the value Z and positive and negative values for the X and Y coordinate values, as typically used in a Cartesian coordinate system.
- Table I values are generated and shown to four decimal places for determining the profiles of the airfoil. Where the values are carried out to less than four decimal places, zeros are added to the right to complete the value to four decimal places. Further, 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., plus or minus values and coating thicknesses, are additive to the X and Y values given in Table I below.
- a distance of ⁇ 0.100 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular nozzle vane design and turbine.
- the nozzle vane profiles given in Table I below are for the second stage of the turbine. Sixty nozzle vanes having such profiles are equally spaced from one another about the rotor axis and thus comprise the second stage.
- FIGS. 3 and 4 the radially outermost profile 52 is illustrated with various other profile sections illustrated in FIG. 4 along the length of the airfoil.
- the various profiles are also illustrated in FIG. 6 with the profiles being superposed one over the other.
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- Mechanical Engineering (AREA)
- General Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
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- Non-Silver Salt Photosensitive Materials And Non-Silver Salt Photography (AREA)
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- Materials For Photolithography (AREA)
Abstract
Description
- The present invention relates to a turbine nozzle for a gas turbine stage and particularly relates to a second-stage turbine nozzle airfoil profile.
- In recent years, advanced gas turbines have trended toward increasing firing temperatures and efforts to improve cooling of the various turbine components. In a particular gas turbine design of the assignee, a high output turbine that uses air cooling is undergoing development. It will be appreciated that the design and construction of the turbine buckets and nozzles require optimized aerodynamic efficiency, as well as aerodynamic and mechanical loading.
- In accordance with an embodiment of the present invention, there is provided a unique turbine nozzle airfoil profile for a turbine stage, preferably the second stage, which may be defined by a unique loci of points to achieve the necessary efficiency in loading requirements whereby improved turbine performance is obtained. It will be appreciated that the nominal profile given by the X, Y, Z coordinates of Table I, which follows, define this unique loci of points. The coordinates given in inches in Table I are for a cold, i.e., room-temperature profile for each cross-section of the nozzle vane. Each defined cross-section is joined smoothly with adjacent cross-sections to form the complete airfoil shape. It will also be appreciated that as the nozzle heats up in use, the profile of the nozzle vane 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 nozzle airfoil profile may be different than the nominal airfoil profile given in the following table, a distance of ±0.100 inches from the nominal profile in a direction normal to any surface location along the nominal profile and which includes any coating, defines the profile envelope for this design. The design is robust to this variation without impairment of the mechanical and aerodynamic functions.
- It will also be appreciated that the airfoil can be scaled-up or scaled-down geometrically for introduction into other similar turbine designs. Consequently, the X, Y and Z coordinates 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 given in the Table may be multiplied or divided by the same constant or number to provide a scaled-up or scaled-down version of the nozzle airfoil profile, while retaining the airfoil section shape.
- In a preferred embodiment according to the present invention, there is provided a turbine nozzle having a nozzle vane in the shape of an airfoil in an envelope within ±0.100 inches in a direction normal to any airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at a radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
- In a further preferred embodiment according to the present invention, there is provided a turbine nozzle having a nozzle vane in the shape of an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at a radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate values, the profiles at the z distances being joined smoothly with one another to form the complete airfoil profile, the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down nozzle airfoil.
- In a further preferred embodiment according to the present invention, there is provided a turbine comprising a turbine nozzle having a plurality of vanes, each of said vanes being in the shape of an airfoil in an envelope within ±0.100 inches in a direction normal to any nozzle airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at a radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
- In a further preferred embodiment according to the present invention, there is provided a turbine comprising a turbine nozzle having a plurality of vanes, each of said vanes being in the shape of an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at the radially innermost aerodynamic section of the airfoil and the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down nozzle airfoil.
- FIG. 1 is a schematic illustration of a turbine having a second-stage nozzle employing the airfoil or vane profile hereof;
- FIG. 2 is a perspective view of a nozzle vane thereof;
- FIG. 3 is an end view of the nozzle vane illustrated in FIG. 2;
- FIG. 4 is a perspective view thereof similar to FIG. 1;
- FIG. 5 is a perspective view of the nozzle vane of FIG. 4 illustrating various airfoil profiles along the length of the vane; and
- FIG. 6 is a view similar to FIG. 3 illustrating the profile sections at various Z coordinate locations along the vane.
- Referring now to FIG. 1, there is illustrated a portion of a turbine, generally designated10, having a second-stage nozzle, generally designated 12.
Nozzle 12 includes a plurality ofvanes 14 having an airfoil shape or profile spaced circumferentially one from the other. The illustratedturbine 10 includes three stages, afirst stage 16 having a plurality of circumferentially spaced nozzle vanes 18 andbuckets 20 circumferentially spaced about arotatable turbine wheel 22; thesecond stage nozzle 12 comprising a plurality of circumferentially spaced nozzle vanes 14 and a plurality of circumferentially spacedbuckets 24 mounted on a second-stage wheel 26 and a third-stage 28 mounting nozzle vanes 30 and a plurality of circumferentially spacedbuckets 32 mounted on a third-stage wheel 34. it will be appreciated that the nozzle vanes and buckets lie in the hot gas path of the turbine and which gases flow through the turbine in the direction of thearrow 36. As illustrated, the nozzle vanes 14 of thesecond stage 12 are disposed between inner andouter bands - Referring to FIG. 2, the nozzle vanes14 have leading and
trailing edges hooks - Referring now to drawing FIG. 2, there is illustrated a
nozzle vane 14 for the second-stage having airfoil profiles defined by a Cartesian coordinate system for X, Y and Z values. The coordinate values are set forth in inches in Table I which follows. The Cartesian coordinate system has orthogonally-related X, Y and Z axes with the X, Y and Z values commencing at a radially innermostaerodynamic section 50 of the airfoil and then made relative to that section for the Z coordinate. By defining X and Y coordinate values at selected locations in a Z direction, the profile ofairfoil 14 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 at the various surface locations between the distances Z are connected smoothly to one another to form the airfoil. The tabular values given in Table I below are in inches and represent airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil. The sign convention assigns a positive value to the value Z and positive and negative values for the X and Y coordinate values, as typically used in a Cartesian coordinate system. - The Table I values are generated and shown to four decimal places for determining the profiles of the airfoil. Where the values are carried out to less than four decimal places, zeros are added to the right to complete the value to four decimal places. Further, 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., plus or minus values and coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of ±0.100 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular nozzle vane design and turbine. In a preferred embodiment, the nozzle vane profiles given in Table I below are for the second stage of the turbine. Sixty nozzle vanes having such profiles are equally spaced from one another about the rotor axis and thus comprise the second stage.
- The coordinate values given in Table I below in inches provide the preferred nominal profile envelope.
TABLE I X Y Z Coordinate Coordinate Coordinate 0.0096 −1.34 13.5512 0.5594 −1.4939 12.4258 0.9047 −1.5942 11.3272 0.0541 −1.3432 12.4922 0.1887 −1.3822 11.4214 −0.0733 −1.4217 13.5621 −0.0691 −1.3783 12.5084 −0.0565 −1.3573 11.4536 0.1447 −1.5533 13.5335 0.0095 −1.4907 12.4981 −0.0617 −1.4447 11.4543 0.9513 −1.6079 13.4274 0.2123 −1.5838 11.4183 0.201 −1.389 13.5261 −0.0565 −1.3582 13.5599 0.2943 −1.4154 12.4607 0.5449 −1.4882 11.3745 −0.0312 −1.3386 12.5034 0.0512 −1.341 11.4394 −0.0314 −1.4726 13.5566 −0.0729 −1.4197 12.5089 −0.0686 −1.3776 11.4552 0.1367 −1.5493 12.4814 0.0056 −1.4883 11.4454 0.574 −1.4995 13.477 0.0571 −1.3455 13.545 0.7283 −1.5431 12.4036 −0.0696 −1.3791 13.5617 0.1153 −1.3617 12.4842 0.2859 −1.4112 11.4086 −0.0744 −1.3972 13.5623 −0.0691 −1.3783 12.5084 −0.0321 −1.3382 11.4504 0.0718 −1.5199 13.5431 −0.0337 −1.4702 12.5038 −0.0725 −1.4178 11.4557 0.129 −1.5452 11.4292 0.3027 −1.4195 13.5127 −0.0302 −1.3391 13.5565 0.4152 −1.4515 12.4448 0.7098 −1.5368 11.3529 0.0076 −1.3325 12.4983 0.111 −1.3589 11.4316 −0.0603 −1.4496 13.5604 −0.0738 −1.396 12.509 −0.0686 −1.3776 11.4552 0.2332 −1.5941 13.5218 0.066 −1.5167 12.4907 −0.036 −1.4678 11.4509 0.7469 −1.5492 13.4543 0.1196 −1.3644 13.5368 0.9279 −1.6012 12.3774 −0.0696 −1.3791 13.5617 0.1948 −1.3856 12.4737 0.4041 −1.4465 11.393 −0.0565 −1.3578 12.5068 0.0056 −1.331 11.4454 0.0134 −1.4932 13.5507 −0.061 −1.4472 12.5074 −0.0731 −1.3947 11.4558 0.2226 −1.5889 12.4701 0.0605 −1.5135 11.4382 0.4265 −1.4564 13.4964 8.6367 −5.1815 12.4172 2.771 −2.882 13.1882 2.1294 −2.5304 12.2194 1.5553 −2.2361 11.2417 6.6906 −3.6984 12.673 4.2524 −3.9336 12.9935 8.7328 −5.467 11.3514 3.5559 −3.4153 12.0319 8.9307 −6.2124 10.2722 2.8732 −2.9772 11.0685 4.4628 −2.7098 12.9658 5.5365 −5.2716 12.8247 6.9618 −3.8661 11.5842 4.9181 −4.5906 11.8528 7.5766 −4.3299 10.4502 4.2723 −4.0002 10.8846 2.444 −2.0409 13.2312 4.7975 −2.8339 11.8687 5.9341 −6.0731 11.7193 5.5578 −3.1448 10.7156 5.4333 −5.3023 10.7319 2.7532 −2.1396 12.1374 0.4443 −1.692 12.4409 3.4482 −2.3617 10.9929 9.3299 −6.4743 12.326 1.9286 −2.4132 13.299 1.1582 −1.6682 12.3471 1.3627 −2.1335 12.3202 1.6693 −1.8193 11.2267 0.8995 −1.9092 11.3279 7.9247 −4.503 12.5108 3.3645 −3.262 13.1102 2.6819 −2.8449 12.1468 2.0588 −2.503 11.1755 5.8109 −3.2613 12.7886 4.8021 −4.4333 12.9212 8.112 −4.7325 11.433 4.1275 −3.8537 11.9568 8.5338 −5.3606 10.3244 3.4463 −3.3556 10.9931 3.6139 −2.4109 13.0774 5.9368 −5.8988 12.7721 6.1189 −3.4056 11.695 5.3828 −5.1423 11.7917 6.8079 −3.7908 10.5512 4.7777 −4.4834 10.8181 1.7532 −1.8383 13.322 0.3386 −1.6428 13.508 3.9403 −2.5232 11.9814 4.689 −2.7911 10.8298 5.7718 −5.9156 10.6874 1.1765 −2.0386 13.3978 2.0333 −1.9235 12.232 0.7479 −1.8352 12.401 2.6875 −2.1237 11.0929 0.4272 −1.6839 11.39 8.9331 −5.5753 12.3782 2.4827 −2.7137 13.2261 1.8649 −2.3893 12.2542 1.1296 −1.6604 11.2977 1.3167 −2.1149 11.2731 7.1166 −3.9434 12.617 3.964 −3.6997 13.0314 8.9669 −5.8883 11.3206 3.2599 −3.2103 12.0708 2.5948 −2.808 11.1051 4.9062 −2.879 12.9075 5.3063 −4.9794 12.855 7.3648 −4.128 11.5312 4.6652 −4.3336 11.8861 4.0048 −3.7753 10.9197 2.8195 −2.1555 13.1819 5.2433 −3.0118 11.8101 5.7747 −5.7486 11.7402 5.9836 −3.3421 10.6596 5.2314 −5.0161 10.7585 1.1872 −1.6757 13.3964 0.6073 −1.7681 13.4727 3.135 −2.2584 12.0872 0.3248 −1.6363 12.4566 3.8492 −2.4934 10.9402 1.6645 −2.2783 13.3337 1.4193 −1.7441 12.3128 1.1368 −2.0223 12.3499 1.984 −1.9124 11.1854 0.7214 −1.8233 11.3513 8.2966 −4.8253 12.4619 3.0652 −3.0645 13.1496 2.4019 −2.682 12.1836 1.8027 −2.3653 11.2092 6.2547 −3.4718 12.7303 4.5321 −4.178 12.9567 8.4432 −5.0819 11.3894 3.8454 −3.6296 11.9938 8.7648 −5.7711 10.294 3.1574 −3.1593 11.0311 4.0318 −2.5542 13.0225 5.748 −5.5778 12.7969 6.5455 −3.6264 11.6389 0.775 −1.8471 13.4506 5.1581 −4.8599 11.8213 7.2012 −4.0474 10.4995 4.5305 −4.236 10.8506 2.0831 −1.9342 13.2787 4.3627 −2.672 11.9258 5.1258 −2.9619 10.7724 5.6145 −5.6022 10.7081 7.929 −4.6412 10.4039 0.9647 −1.9372 13.4257 2.3859 −2.0281 12.1857 0.5854 −1.7582 12.4224 3.0609 −2.2388 11.0438 0.3113 −1.6298 11.4053 9.1701 −6.0076 12.347 2.2017 −2.5577 13.2631 1.6092 −2.2572 12.2878 1.3844 −1.7355 11.2642 1.0981 −2.0062 11.3018 7.5296 −4.2103 12.5627 3.6678 −3.476 13.0704 9.13 −6.3422 11.2991 2.9681 −3.0207 12.1092 2.323 −2.6503 11.1408 5.3609 −3.0643 12.8478 5.0608 −4.7002 12.8872 7.75 −4.4157 11.4806 4.4011 −4.0881 11.9208 8.2512 −4.984 10.3615 3.729 −3.5607 10.956 3.2097 −2.2783 13.1306 6.0981 −6.2346 12.7509 5.6843 −3.2017 11.7521 5.5896 −5.4384 11.7646 6.4009 −3.5567 10.6047 5.0121 −4.7433 10.7873 1.4545 −1.7525 13.3613 0.4618 −1.7001 13.4918 3.5308 −2.3859 12.0352 4.263 −2.636 10.8858 5.9015 −6.2415 10.6704 1.4098 −2.1521 13.3672 1.711 −1.829 12.2744 0.9317 −1.9232 12.3769 2.3285 −2.0151 11.1401 0.564 −1.7483 11.372 9.1287 −7.681 11.2993 8.6888 −8.2716 10.304 6.0142 −9.0131 10.6556 6.3137 −6.9342 12.7225 8.9625 −8.6141 12.3743 6.2514 −8.5387 12.7307 6.2292 −7.72 11.6805 6.062 −6.888 10.6493 8.6253 −8.7717 11.3655 6.0632 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8.7335 −6.0863 9.2449 7.4004 −4.2537 9.4202 7.8688 −4.8019 8.3044 5.2786 −5.1696 9.6991 4.7306 −4.5186 8.717 5.5828 −5.9219 8.605 8.3376 −5.2581 9.297 8.54 −5.9594 8.2162 4.6407 −4.377 9.783 7.2177 −4.1876 8.39 5.6112 −5.7621 9.6554 5.1271 −5.0449 8.6649 7.7453 −4.5568 9.3748 8.1434 −5.1565 8.2683 5.0819 −4.8926 9.725 4.51 −4.2741 8.746 5.4519 −5.6188 8.6222 8.5658 −5.6576 9.267 8.639 −6.3824 8.2032 4.4003 −4.1376 9.8146 7.5573 −4.4796 8.3454 5.456 −5.4595 9.6758 4.9369 −4.7755 8.6899 4.333 −2.7237 7.7161 2.4838 −2.0781 7.9592 0.382 −1.6577 8.2355 1.1961 −2.0513 8.1285 3.6725 −3.5426 7.8029 5.5339 −3.2373 7.5582 3.5567 −2.4382 7.8181 1.8336 −1.8726 8.0446 0.6514 −1.7848 8.2001 1.6411 −2.2794 8.07 2.8881 −2.9924 7.906 6.6736 −3.8758 7.4084 4.1586 −3.9578 7.739 4.7374 −2.8849 7.6629 2.8286 −2.1905 7.9138 1.2788 −1.7024 8.1176 0.996 −1.9519 8.1548 2.1187 −2.537 8.0072 3.4171 −3.3505 7.8365 5.923 −3.433 7.5071 3.939 −2.5756 7.7679 2.152 −1.9723 8.0028 0.5072 −1.7164 8.219 1.4144 −2.1619 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−7.097 8.568 6.7808 −9.1294 7.3943 8.6992 −7.7493 9.2494 8.2313 −8.2464 8.2568 5.9076 −8.3304 8.5623 7.6995 −8.5696 7.2735 5.8187 −7.6797 7.5208 6.0348 −9.0343 8.5455 8.4635 −7.0415 7.1731 5.9014 −8.5852 7.5099 6.2172 −9.2589 8.5216 6.3532 −9.3326 8.5037 6.2112 −9.0646 7.4692 6.1926 −9.0532 7.4716 6.7432 −9.3694 8.4524 0.0637 −1.4345 7.2409 0.1768 −1.5615 7.2093 0.4845 −1.4653 7.1688 0.0387 −1.3323 7.2274 0.0672 −1.3739 7.2414 0.0076 −1.4777 7.2335 1.0112 −1.6252 7.0996 0.2508 −1.3953 7.1996 0.0361 −1.3364 7.2373 0.0714 −1.4097 7.2419 0.1025 −1.5276 7.219 0.6332 −1.51 7.1493 0.0927 −1.3483 7.2203 0.0672 −1.3739 7.2414 0.0436 −1.4576 7.2382 0.2651 −1.6021 7.1977 0.3575 −1.4272 7.1855 0.0029 −1.3255 7.2329 0.0712 −1.3892 7.2419 0.0414 −1.4998 7.2271 0.8088 −1.5632 7.1262 0.163 −1.3691 7.2111 0.0568 −1.3552 7.24 4.9849 −3.043 6.5772 3.0906 −2.3056 6.8262 0.7894 −1.8492 7.1288 5.7492 −3.4091 6.4768 1.8223 −2.3753 6.993 3.0651 −3.121 6.8296 6.1211 −3.6127 6.4279 4.2027 −2.7175 6.6801 0.3685 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−8.3652 6.4669 6.0093 −8.733 6.4426 6.1291 −8.8322 6.4268 6.1114 −8.8206 6.4291 6.3476 −8.9172 6.3981 6.9994 −8.7952 6.3124 5.6217 −6.743 6.4935 7.9531 −7.8711 6.187 5.7491 −7.9028 6.4768 5.896 −8.5645 6.4575 6.0618 −8.7831 6.4357 6.1846 −8.8632 6.4195 6.55 −8.9274 6.3715 7.3769 −8.5476 6.2628 5.6899 −7.249 6.4846 8.2283 −7.2337 6.1509 5.794 −8.2331 6.4709 5.9743 −8.6918 6.4472 6.1114 −8.8206 6.4291 6.0986 −8.8117 6.4308 6.2764 −8.8996 6.4074 6.8304 −3.8666 6.3346 5.5697 −6.4772 6.5003 7.7695 −8.1406 6.2112 5.7311 −7.7056 6.4791 8.3202 −6.4884 6.1388 5.858 −8.4745 6.4625 6.0385 −8.7624 6.4387 6.1534 −8.8467 6.4236 6.4386 −8.9283 6.3861 7.1832 −8.69 6.2882 5.6607 −7.0006 6.4884 8.1088 −7.5681 6.1666 5.7695 −8.0788 6.4741 7.5746 −8.3653 6.2368 5.9357 −8.6364 6.4522 6.082 −8.7993 6.433 5.5617 −3.3762 5.4482 0.071 −1.3873 6.1887 6.0581 −3.7184 4.3298 0.0668 −1.371 5.135 3.6965 −2.5499 5.6934 0.0363 −1.4968 6.1746 4.2888 −2.8178 4.5624 0.0479 −1.452 5.1325 2.0206 −1.951 5.9137 0.472 −1.7001 6.1173 2.5629 −2.1432 4.7893 0.7814 −1.5566 6.0766 1.1565 −1.6752 4.9742 0.9024 −1.913 5.0076 2.4733 −2.7585 5.8542 0.3299 −1.4191 5.0828 0.057 −1.3543 6.1868 3.6981 −3.6243 5.6932 0.0076 −1.3236 5.1272 3.1231 −3.2112 4.7156 4.8218 −3.0182 5.5455 0.0645 −1.4315 6.1878 5.3666 −3.3264 4.4207 0.0708 −1.3854 5.1355 2.9911 −2.2864 5.7862 0.1677 −1.5575 6.1573 3.5669 −2.5195 4.6573 0.0314 −1.4937 5.1221 1.4477 −1.765 5.989 0.7623 −1.8395 6.0792 1.9497 −1.932 4.8699 0.454 −1.6938 5.0665 0.7523 −1.5488 5.0273 0.4671 −1.4607 6.1179 1.7658 −2.3529 5.9472 1.2865 −2.1077 4.9571 0.0353 −1.3301 6.1747 2.9734 −3.0794 5.7885 0.1479 −1.3634 5.1068 2.3973 −2.7286 4.8111 5.9226 −3.5731 5.4008 0.067 −1.3725 6.1882 0.0572 −1.3534 5.1337 3.5862 −3.5736 4.6548 4.0659 −2.696 5.6449 0.0112 −1.475 6.1808 4.6519 −2.979 4.5147 0.0652 −1.4285 5.1348 1.3296 −2.1227 6.0046 2.332 −2.0557 5.8728 0.3537 −1.6442 6.1329 2.8866 −2.2602 4.7467 0.1588 −1.5535 5.1053 0.1557 −1.3664 6.1589 0.9775 −1.6172 6.0509 1.1232 −2.0178 6.0317 1.3962 −1.7512 4.9427 0.7356 −1.8307 5.0295 0.2407 −1.3921 6.1477 2.2311 −2.6142 5.8861 1.0861 −2.0052 4.9834 0.4487 −1.4555 5.0672 1.7102 −2.3326 4.9014 0.0371 −1.3359 6.1842 3.463 −3.4341 5.7241 0.0316 −1.3279 5.122 2.8828 −3.042 4.7472 0.23 −1.3885 5.096 5.1943 −3.1918 5.4965 0.0714 −1.4073 6.1887 5.7161 −3.5157 4.3748 0.0668 −1.371 5.135 0.2419 −1.5927 5.0944 0.0956 −1.5241 6.1668 3.9229 −2.6632 4.6105 0.0147 −1.4723 5.1281 1.7214 −1.853 5.9531 0.6082 −1.7651 6.0994 2.2505 −2.0341 4.8303 0.3392 −1.6389 5.0816 0.6112 −1.5045 6.099 1.5439 −2.2342 5.9764 0.9419 −1.6077 5.0024 0.0876 −1.3459 6.1678 2.7211 −2.9131 5.8216 2.162 −2.5877 4.842 6.2749 −3.7853 5.3545 0.067 −1.3725 6.1882 0.0382 −1.3353 5.1312 3.358 −3.3881 4.6848 4.4454 −2.8534 5.595 0.0458 −1.4548 6.1854 5.0115 −3.148 4.4674 0.0715 −1.4048 5.1356 1.9328 −2.456 4.8721 3.807 −3.768 4.6257 2.6556 −2.1672 5.8303 0.2534 −1.5973 6.146 3.2214 −2.3854 4.7027 0.0889 −1.5206 5.1145 1.1997 −1.6866 6.0217 0.934 −1.9236 6.. 0566 1.6606 −1.8366 4.9079 0.5861 −1.7576 5.0491 1.995 −2.4793 5.9171 0.3441 −1.4234 6.1341 0.5879 −1.4981 5.0489 1.4946 −2.2167 4.9297 3.3382 −2.4137 5.7405 0.0051 −1.3245 6.18 3.221 −3.2528 5.7559 0.0822 −1.3433 5.1154 2.6379 −2.8796 4.7794 5.1716 −5.5218 5.4995 4.752 −4.892 4.5015 5.3151 −6.187 4.4275 7.9531 −5.5511 5.1339 7.9262 −6.1153 4.0842 4.3506 −4.2546 5.6074 6.6156 −4.0158 5.3097 7.0099 −4.4359 4.2047 4.7264 −4.7297 5.558 4.2207 −4.1866 4.5714 5.3705 −6.0631 5.4734 5.0323 −5.4109 4.4647 7.5234 −4.8493 5.1904 7.724 −5.387 4.1108 4.1434 −4.0339 5.6347 6.3901 −3.9372 4.2862 5.0406 −5.2481 5.5167 4.5886 −4.6466 4.523 5.238 −5.9326 4.4376 8.0783 −5.9301 5.1174 6.9412 −4.2677 5.2669 7.2858 −4.7231 4.1684 4.5454 −4.4866 5.5818 4.019 −3.9722 4.5979 5.281 −5.7942 5.4851 4.9001 −5.1471 4.482 7.7629 −5.1849 5.1589 7.8582 −5.7487 4.0932 3.9254 −3.8239 5.6633 6.709 −4.1752 4.2443 4.8918 −4.9837 5.5363 4.4111 −4.4114 4.5463 5.4425 −6.3269 5.4639 5.1444 −5.6733 4.4499 8.1358 −6.3114 5.1099 7.2463 −4.5443 5.2268 7.5276 −5.0398 4.1366 6.0729 −8.6192 5.381 5.9576 −8.3731 4.343 5.9455 −8.3648 4.3446 6.3487 −8.7009 5.3448 6.112 −8.4479 4.3227 5.5438 −6.8334 5.4506 6.6287 −8.4046 4.2548 7.9519 −7.3617 5.134 5.6818 −7.8781 5.4324 5.5365 −7.3375 4.3984 5.8604 −8.4152 5.409 6.004 −8.5726 5.3901 5.8879 −8.319 4.3522 6.1404 −8.6528 5.3722 5.5789 −7.0741 5.446 5.997 −8.3976 4.3379 6.5837 −8.6807 5.3139 6.2641 −8.4748 4.3027 7.4421 −8.1404 5.2011 5.6078 −7.3053 5.4422 6.9506 −8.222 4.2125 5.4287 −6.6763 4.4126 7.0672 −8.461 5.2503 8.1282 −6.6835 5.1109 5.7442 −8.1545 5.4242 7.7762 −7.1347 4.104 5.596 −7.6871 4.3906 5.9332 −8.5081 5.3994 5.7864 −8.2035 4.3655 6.0495 −8.6049 5.3841 6.0324 −8.5934 5.3864 5.9296 −8.3533 4.3467 6.2605 −8.6896 5.3564 6.0624 −8.4297 4.3293 6.8907 −8.5661 5.2735 5.4993 −6.5841 5.4564 6.4907 −8.4502 4.273 7.804 −7.657 5.1535 5.6563 −7.7077 5.4358 7.3029 −7.9004 4.1662 5.5058 −7.1329 4.4024 7.4772 −7.6825 4.1433 5.8202 −8.3462 5.4143 7.9297 −6.4749 4.0838 5.6655 −7.9538 4.3814 5.9844 −8.5567 5.3927 5.8595 −8.292 4.3559 6.103 −8.6355 5.3771 5.9743 −8.384 4.3408 5.9576 −8.3731 4.343 6.4567 −8.6999 5.3306 6.1787 −8.4648 4.314 7.2528 −8.3198 5.2259 6.7835 −8.3296 4.2345 5.3778 −6.4353 4.4192 8.0634 −7.0358 5.1194 5.7109 −8.0272 5.4286 7.6402 −7.4237 4.1218 5.5658 −7.5224 4.3945 5.8988 −8.4684 5.4039 5.7454 −8.1376 4.3709 6.0324 −8.5934 5.3864 6.0201 −8.5847 5.388 5.9103 −8.3382 4.3492 6.1916 −8.6718 5.3654 6.0262 −8.4132 4.334 6.7279 −8.6381 5.2949 6.3684 −8.472 4.289 7.6286 −7.9202 5.1765 5.6325 −7.5167 5.4389 5.4704 −6.909 4.4071 5.7044 −8.0548 4.3763 5.7808 −8.2597 5.4194 7.8762 −6.8172 4.0908 5.6291 −7.8311 4.3862 5.9618 −8.5366 5.3956 5.8252 −8.2543 4.3604 7.1253 −8.0796 4.1895 0.0393 −1.3348 4.0772 3.2585 −3.3486 3.6437 5.5129 −3.4386 3.3473 0.5643 −1.4911 3.9979 4.8303 −3.0891 3.4371 0.0714 −1.4025 4.0814 3.1028 −2.354 3.6642 0.0833 −1.5165 4.0611 1.4509 −2.1968 3.8813 1.5984 −1.8203 3.8619 0.5675 −1.7474 3.9974 0.0766 −1.3406 4.062 2.5598 −2.8497 3.7355 5.8451 −3.6302 3.3037 0.0666 −1.3695 4.0808 3.6953 −3.7191 3.5863 1.2487 −2.0898 3.9079 4.1322 −2.7724 3.5288 0.0496 −1.4491 4.0785 0.2323 −1.5868 4.0415 1.1125 −1.6632 3.9258 0.8752 −1.8991 3.957 0.3155 −1.4143 4.0306 0.01 −1.3227 4.0733 3.0305 −3.1754 3.6737 0.0705 −1.3836 4.0813 2.4681 −2.1187 3.7476 3.4359 −2.4841 3.6204 0.0273 −1.4903 4.0684 1.8771 −1.9131 3.8253 0.4338 −1.6851 4.0144 0.2192 −1.3846 4.0432 0.7228 −1.5403 3.977 0.14 −1.3602 4.0535 2.3265 −2.7011 3.7662 6.1685 −3.8365 3.2611 0.0574 −1.3525 4.0796 3.4803 −3.5296 3.6145 4.4828 −2.9273 3.4827 0.0657 −1.4256 4.0807 2.7801 −2.2324 3.7066 0.1514 −1.5485 4.0521 1.3435 −1.7372 3.8954 0.713 −1.8186 3.9783 0.43 −1.4497 4.0155 1.6601 −2.3108 3.8538 0.0279 −1.3257 4.0684 2.7973 −3.0094 3.7043 0.0666 −1.3695 4.0808 5.174 −3.259 3.3919 3.7792 −2.6232 3.5752 0.0175 −1.4693 4.0743 2.167 −2.0125 3.7872 0.327 −1.6317 4.029 1.8761 −2.4324 3.8254 0.9055 −1.5976 3.953 1.0538 −1.9893 3.9335 2.0984 −2.5623 3.7962 6.4801 −4.0607 3.2202 4.2862 −4.3431 3.5086 5.0171 −5.5621 3.4125 7.2862 −4.879 3.1142 4.6231 −4.8075 3.4643 5.1921 −6.0593 3.3895 6.7751 −4.3066 3.1814 4.0993 −4.1255 3.5331 4.9036 −5.3085 3.4274 7.4823 −5.2099 3.0884 7.693 −5.9081 3.0607 4.4612 −4.5705 3.4856 7.7063 −6.255 3.059 5.1127 −5.8129 3.3999 7.0467 −4.5782 3.1457 3.902 −3.9175 3.5591 4.7708 −5.0537 3.4449 5.2575 −6.2999 3.3809 7.6191 −5.5561 3.0705 0.0242 −1.3236 3.0157 0.0711 −1.3379 3.0095 0.0664 −1.3679 3.0276 0.2083 −1.3804 2.9915 0.0411 −1.3336 1.9711 0.0403 −1.3343 3.0242 0.0124 −1.322 3.0205 0.0658 −1.3351 1.9571 0.0702 −1.3816 3.0281 0.0661 −1.3659 1.9744 0.0711 −1.3379 3.0095 0.1321 −1.3568 3.0015 0.0664 −1.3679 3.0276 0.0575 −1.3515 3.0264 0.0144 −1.3213 1.9676 0.0699 −1.3793 1.9749 0.0403 −1.3343 3.0242 0.0124 −1.322 3.0205 0.0242 −1.3236 3.0157 0.1243 −1.3533 1.9494 0.0575 −1.3502 1.9733 0.0206 −1.322 1.963 0.1321 −1.3568 3.0015 0.2083 −1.3804 2.9915 0.0575 −1.3515 3.0264 0.0661 −1.3659 1.9744 0.1975 −1.3761 1.9397 0.0664 −1.3679 3.0276 2.9452 −3.1357 2.6317 1.4102 −2.1758 2.8335 2.4875 −2.8172 2.6919 5.3086 −3.3521 2.321 5.631 −3.5321 2.2786 0.4251 −1.6755 2.963 3.593 −3.6653 2.5465 3.0946 −3.2421 1.5589 3.6337 −2.5795 2.5412 3.974 −2.722 2.4965 0.0509 −1.446 3.0256 4.4596 −2.9596 1.3795 0.0711 −1.3972 1.975 1.1797 −2.055 1.8106 2.0817 −1.9908 2.7452 2.3713 −2.0937 2.7071 1.9885 −2.5013 1.7043 0.2237 −1.5802 2.9895 2.8576 −2.2909 1.5901 0.8686 −1.5872 2.9047 0.8503 −1.8839 2.9071 1.4695 −1.7893 1.7725 0.5333 −1.7279 1.8956 1.2137 −2.0706 2.8593 0.3009 −1.4092 2.9793 1.8233 −2.4075 2.7792 0.516 −1.4764 1.8979 1.3718 −2.1566 1.7854 2.3713 −2.0937 2.7071 2.4287 −2.7713 1.6464 5.4102 −3.4359 1.2545 3.1671 −3.3046 2.6025 2.9821 −2.3209 2.6268 0.0238 −1.4865 3.0157 3.8106 −2.6748 1.4648 0.0518 −1.4423 1.9725 0.2153 −1.5744 1.9374 4.1362 −2.8148 1.422 1.5349 −1.804 2.8171 1.8029 −1.8943 2.7819 2.2715 −2.0714 1.6671 1.0676 −1.6509 2.8785 6.0097 −3.8148 1.1757 0.5403 −1.4837 2.9478 0.6928 −1.5315 2.9278 1.0216 −1.6397 1.8314 0.8252 −1.873 1.8572 3.3834 −3.481 2.5741 2.2608 −2.6715 2.7217 3.3029 −2.446 2.5847 5.631 −3.5321 2.2786 5.9455 −3.7257 2.2373 2.8776 −3.0782 1.5874 3.974 −2.722 2.4965 4.3123 −2.8695 2.452 0.066 −1.4227 3.0275 4.7806 −3.1101 1.3373 2.6715 −2.2037 2.6677 0.1448 −1.543 2.9998 3.1656 −2.4111 1.5496 0.0207 −1.4823 1.963 1.0676 −1.6509 2.8785 1.2898 −1.723 2.8493 0.6923 −1.8053 2.9279 1.7263 −1.8775 1.7388 0.4112 −1.6684 1.9116 1.7766 −2.3792 1.7322 4.6479 −3.0229 2.4079 3.5101 −3.5936 1.5043 0.2864 −1.404 1.9281 0.3009 −1.4092 2.9793 0.4112 −1.4436 2.9648 1.6135 −2.2879 2.8068 0.6622 −1.523 1.8787 4.6479 −3.0229 2.4079 2.7184 −2.9734 2.6615 2.2061 −2.6317 1.6757 0.0712 −1.4 3.0282 5.3086 −3.3521 2.321 5.7153 −3.6168 1.2144 3.3058 −3.4138 1.5311 0.3922 −1.4373 1.9142 3.3029 −2.446 2.5847 3.6337 −2.5795 2.5412 0.0199 −1.4662 3.0215 0.0662 −1.4193 1.9744 1.8029 −1.8943 2.7819 2.0817 −1.9908 2.7452 0.3161 −1.6237 2.9773 2.5595 −2.1778 1.6292 0.1385 −1.5379 1.9475 4.9803 −3.1833 2.3642 0.0785 −1.5119 3.0086 0.6928 −1.5315 2.9278 0.8686 −1.5872 2.9047 1.0241 −1.9721 2.8842 1.2345 −1.7101 1.8034 0.6713 −1.796 1.8775 4.9803 −3.1833 2.3642 2.0392 −2.5352 2.7508 1.5709 −2.2645 1.7592 5.9455 −3.7257 2.2373 2.6553 −2.9216 1.6166 4.3123 −2.8695 2.452 5.098 −3.268 1.2955 3.7066 −3.782 1.4784 0.0739 −1.5074 1.956 2.6715 −2.2037 2.6677 2.9821 −2.3209 2.6268 0.0218 −1.4624 1.9686 1.2898 −1.723 2.8493 1.5349 −1.804 2.8171 0.5505 −1.736 2.9465 1.9937 −1.9714 1.7036 0.3052 −1.6173 1.9256 3.4834 −2.5389 1.5078 0.4112 −1.4436 2.9648 0.5403 −1.4837 2.9478 0.8308 −1.5774 1.8565 0.9947 −1.9592 1.8349 6.8009 −4.4274 2.1249 7.0338 −4.715 2.0942 7.0799 −5.182 1.035 4.5042 −4.7197 2.4268 4.0731 −4.185 1.4303 5.0754 −5.9314 2.3517 4.7871 −5.3319 1.3364 7.3595 −5.3645 2.0514 7.4367 −5.7022 2.0413 7.1904 −6.1331 1.0205 6.2489 −3.9366 2.1974 6.5363 −4.1691 2.1596 6.7669 −4.5581 1.0762 3.9882 −4.0597 2.4946 4.7839 −5.2041 2.39 4.3979 −4.6228 1.3876 4.9651 −5.7998 1.313 7.4358 −6.3566 2.0414 7.0338 −4.715 2.0942 7.2248 −5.0324 2.0691 7.1603 −5.5049 1.0244 6.2882 −4.0349 1.1391 4.344 −4.4905 2.4478 3.8946 −3.9791 1.4537 4.6735 −5.0936 1.3513 5.0878 −6.2479 1.2969 7.4367 −5.7022 2.0413 7.4599 −6.0356 2.0382 6.5363 −4.1691 2.1596 6.8009 −4.4274 2.1249 6.9493 −4.8634 1.0522 4.9947 −5.6925 2.3623 3.795 −3.858 2.52 4.6511 −4.9577 2.4074 4.2412 −4.3996 1.4082 5.1421 −6.165 2.3429 4.8839 −5.5677 1.3237 7.2248 −5.0324 2.0691 7.3595 −5.3645 2.0514 7.1953 −5.824 1.0198 6.2489 −3.9366 2.1974 6.5434 −4.2817 1.1055 4.1716 −4.2705 2.4705 4.898 −5.4496 2.375 4.5423 −4.8543 1.3686 5.0324 −6.0269 1.3042 7.4599 −6.0356 2.0382 7.4358 −6.3566 2.0414 6.0214 −8.0209 2.2273 5.8376 −8.1301 3.3046 6.4655 −7.628 1.1158 5.6741 −7.8509 2.273 5.5011 −7.5577 1.2426 5.8106 −7.9502 2.255 5.8268 −7.959 2.2529 5.7985 −7.9433 2.2566 5.687 −7.7098 1.2181 6.284 −8.245 3.246 5.9587 −8.0091 2.2356 5.5958 −7.6475 1.2301 6.9985 −7.838 3.152 5.3562 −6.7594 3.3679 6.5734 −7.8596 2.1548 6.4352 −7.9398 2.1729 6.1093 −7.7894 1.1626 7.6662 −6.5868 3.0643 5.5373 −7.652 3.3441 7.2761 −6.9403 2.0624 5.321 −7.0153 2.3194 6.7359 −7.3639 1.0802 5.1342 −6.4616 1.2908 5.7509 −8.0524 3.316 5.5358 −7.6784 2.2912 5.342 −7.3004 1.2635 5.8848 −8.1624 3.2984 5.8728 −8.1547 3.3 5.7401 −7.9052 2.2643 5.877 −7.9823 2.2463 6.0361 −8.2297 3.2786 5.8488 −7.9699 2.25 5.7228 −7.7294 1.2134 6.5328 −8.1713 3.2133 6.1978 −8.0175 2.2041 6.1012 −8.0256 2.2168 5.8795 −7.7861 1.1928 5.9115 −7.9953 2.2418 7.3191 −7.4388 3.1099 5.43 −7.175 3.3582 6.8685 −7.5993 2.116 6.7196 −7.7467 2.1355 5.1971 −6.392 2.3357 6.3355 −7.7096 1.1329 7.3722 −6.6594 2.0497 5.6315 −7.8078 2.2786 5.6223 −7.8654 3.333 5.3972 −7.3429 2.3094 6.9815 −6.9589 1.0479 5.2129 −6.8549 1.2804 7.3722 −6.6594 2.0497 7.1532 −7.1967 2.0785 5.815 −8.1124 3.3076 5.4478 −7.4909 1.2496 5.8001 −7.7632 1.2032 5.9236 −8.1847 3.2933 5.8106 −7.9502 2.255 5.7825 −7.9337 2.2587 5.6638 −7.6958 1.2212 6.1835 −8.251 3.2592 5.9587 −8.0091 2.2356 6.3099 −7.9905 2.1894 5.7726 −7.7525 1.2069 6.8361 −7.9829 3.1734 5.3113 −6.5336 3.3738 6.4352 −7.9398 2.1729 6.3099 −7.9905 2.1894 7.5823 −6.897 3.0753 5.4991 −7.5133 3.3491 7.1532 −7.1967 2.0785 6.6008 −7.5132 1.098 7.0151 −7.4163 2.0967 5.7105 −8.0052 3.3213 5.4873 −7.588 2.2975 7.1505 −6.4277 1.0257 5.2942 −7.1725 1.2697 5.1752 −6.6672 1.2854 5.9523 −8.1988 3.2896 5.8569 −8.1441 3.3021 5.7106 −7.3826 2.2682 5.5511 −7.609 1.236 5.9877 −8.2137 3.2849 5.8488 −7.9699 2.25 5.8268 −7.959 2.2529 5.8106 −7.9502 2.255 5.7068 −7.7209 1.2155 6.4012 −8.22 3.2306 6.1012 −8.0256 2.2168 6.0214 −8.0209 2.2273 5.8338 −7.7743 1.1988 6.0167 −7.7988 1.1748 7.1614 −7.6571 3.1306 5.3952 −6.9766 3.3628 6.7196 −7.7467 2.1355 6.5734 −7.8596 2.1548 6.2165 −7.7614 1.1485 5.5789 −7.7694 3.3387 7.2761 −6.9403 2.0624 5.3579 −7.189 2.3145 6.8647 −7.1791 1.0633 5.7862 −8.0874 3.3114 5.5847 −7.7511 2.2847 5.3943 −7.4065 1.2566 5.9013 −8.1723 3.2963 5.8848 −8.1624 3.2984 5.763 −7.9211 2.2613 5.6336 −7.6757 1.2251 6.1009 −8.2439 3.27 5.9115 −7.9953 2.2418 5.877 −7.9823 2.2463 5.751 −7.7431 1.2097 5.735 −7.7355 1.2118 6.6793 −8.0933 3.194 6.1978 −8.0175 2.2041 5.94 −7.7958 1.1848 7.464 −7.1816 3.0908 5.4638 −7.3541 3.3538 7.0151 −7.4163 2.0967 6.8686 −7.5993 2.116 5.2434 −6.6115 2.3296 5.735 −7.7355 1.2118 5.6669 −7.9435 3.3271 5.284 −6.8226 2.3243 5.4404 −7.4761 2.3037 7.0798 −6.704 1.035 5.2516 −7.0236 1.2753 0.0174 −1.3204 0.9103 0.0658 −1.3636 0.9212 0.1872 −1.3719 0.8879 0.0416 −1.3326 0.918 0.0609 −1.3325 0.9045 0.0658 −1.3636 0.9212 0.0696 −1.3766 0.9217 0.0162 −1.3205 0.9147 0.117 −1.3499 0.8972 0.0574 −1.3486 0.9201 0.3738 −1.431 0.8634 1.5298 −2.2409 0.7114 2.5964 −2.866 0.5712 3.6224 −3.7039 0.4364 5.4888 −3.5113 0.191 3.3358 −2.5003 0.474 0.0235 −1.4582 0.9156 1.9072 −1.9536 0.6618 0.2943 −1.6116 0.8739 0.9656 −1.9475 0.7856 1.9405 −2.4654 0.6574 5.7743 −3.6968 0.1535 3.0267 −3.1761 0.5147 0.0664 −1.4157 0.9213 4.2748 −2.8986 0.3506 0.0709 −1.3941 0.9219 0.0696 −1.5027 0.9034 0.4924 −1.4693 0.8478 1.3345 −2.1379 0.7371 2.3738 −2.7221 0.6005 3.4315 −3.5193 0.4614 3.6502 −2.6297 0.4327 0.0525 −1.4383 0.9194 2.7352 −2.2626 0.553 2.1733 −2.0507 0.6268 0.207 −1.569 0.8853 0.9765 −1.6292 0.7842 0.8002 −1.8636 0.8073 2.8144 −3.0171 0.5426 0.2724 −1.3988 0.8767 1.732 −2.3497 0.6849 1.4052 −1.7758 0.7278 4.5843 −3.0396 0.3099 0.516 −1.7211 0.8447 3.0307 −2.3781 0.5141 5.1931 −3.3429 0.2299 4.8909 −3.1868 0.2696 1.6511 −1.8621 0.6955 0.0179 −1.4779 0.9102 0.6324 −1.5149 0.8294 1.1463 −2.0403 0.7619 2.1547 −2.5891 0.6293 3.2327 −3.3434 0.4876 0.3973 −1.6623 0.8603 3.9633 −2.7622 0.3915 2.4493 −2.1536 0.5906 0.1324 −1.5329 0.8951 0.7938 −1.5681 0.8082 1.1803 −1.6983 0.7574 0.6503 −1.7881 0.827 6.2895 −4.1408 0.0858 4.4354 −4.7515 0.3295 4.9234 −5.891 0.2653 6.8003 −5.0072 0.0186 3.9779 −4.0986 0.3896 4.8558 −5.6701 0.2742 4.6774 −5.2156 0.2977 5.0257 −6.3142 0.2519 6.9416 −5.917 0 6.5028 −4.4068 0.0577 4.294 −4.5261 0.3481 6.9279 −5.6206 0.0018 6.8822 −5.3159 0.0078 4.1413 −4.3084 0.3681 6.0437 −3.9049 0.1181 3.8048 −3.897 0.4124 4.5647 −4.9842 0.3125 4.9791 −6.1061 0.258 6.9256 −6.2018 0.0021 6.6756 −4.7012 0.035 4.7742 −5.4446 0.2849 5.3029 −7.2267 0.2154 5.6751 −7.5271 0.1665 5.6593 −7.5207 0.1686 5.8585 −7.5708 0.1424 6.3575 −7.3966 0.0768 5.6311 −7.5082 0.1723 6.8808 −6.4719 0.008 5.1462 −6.8609 0.236 5.4188 −7.3648 0.2002 5.6112 −7.4985 0.1749 6.1231 −7.5325 0.1076 5.7232 −7.5441 0.1602 6.0208 −7.5615 0.1211 5.1924 −7.0047 0.23 6.6025 −7.1293 0.0446 5.2451 −7.1269 0.223 5.5182 −7.4443 0.1871 5.6593 −7.5207 0.1686 5.6472 −7.5155 0.1702 5.8001 −7.563 0.1501 5.932 −7.5721 0.1327 6.2358 −7.4797 0.0928 6.8079 −6.7238 0.0176 5.1055 −6.6971 0.2414 5.6963 −7.5351 0.1637 5.3615 −7.3045 0.2077 5.557 −7.4689 0.182 5.5877 −7.4863 0.178 6.4818 −7.2802 0.0605 5.4717 −7.4104 0.1932 5.7559 −7.5533 0.1559 6.7131 −6.9435 0.0301 5.0668 −6.5145 0.2465 0.0096 −1.334 13.5512 0.5594 −1.4939 12.4258 0.9047 −1.5942 11.3272 0.0541 −1.3432 12.4922 0.1887 −1.3322 11.4214 0.0733 −1.4217 13.5621 0.0691 −1.3783 12.5084 0.0565 −1.3573 11.4536 0.1447 −1.5533 13.5335 0.0095 −1.4907 12.4981 0.0617 −1.4447 11.4543 0.9513 −1.6079 13.4274 0.2123 −1.5838 11.4183 0.201 −1.389 13.5261 0.0565 −1.3582 13.5599 0.2943 −1.4154 12.4607 0.5449 −1.4882 11.3745 0.0312 −1.3386 12.5034 0.0512 −1.341 11.4394 0.0314 −1.4726 13.5566 0.0729 −1.4197 12.5089 0.0686 −1.3776 11.4552 0.1367 −1.5493 12.4814 0.0056 −1.4883 11.4454 0.574 −1.4995 13.477 0.0571 −1.3455 13.545 0.7283 −1.5431 12.4036 0.0696 −1.3791 13.5617 0.1153 −1.3617 12.4842 0.2859 −1.4112 11.4086 0.0744 −1.3972 13.5623 0.0691 −1.3783 12.5084 0.0321 −1.3382 11.4504 0.0718 −1.5199 13.5431 0.0337 −1.4702 12.5038 0.0725 −1.4178 11.4557 0.129 −1.5452 11.4292 0.3027 −1.4195 13.5127 0.0302 −1.3391 13.5565 0.4152 −1.4515 12.4448 0.7098 −1.5368 11.3529 0.0076 −1.3325 12.4983 0.111 −1.3589 11.4316 0.0603 −1.4496 13.5604 0.0738 −1.396 12.509 0.0686 −1.3776 11.4552 0.2332 −1.5941 13.5218 0.066 −1.5167 12.4907 0.036 −1.4678 11.4509 0.7469 −1.5492 13.4543 0.1196 −1.3644 13.5368 0.9279 −1.6012 12.3774 0.0696 −1.3791 13.5617 0.1948 −1.3856 12.4737 0.4041 −1.4465 11.393 0.0565 −1.3578 12.5068 0.0056 −1.331 11.4454 0.0134 −1.4932 13.5507 0.061 −1.4472 12.5074 0.0731 −1.3947 11.4558 0.2226 −1.5889 12.4701 0.0605 −1.5135 11.4382 0.4265 −1.4564 13.4964 8.6367 −5.1815 12.4172 2.771 −2.882 13.1882 2.1294 −2.5304 12.2194 1.5553 −2.2361 11.2417 6.6906 −3.6984 12.673 4.2524 −3.9336 12.9935 8.7328 −5.467 11.3514 3.5559 −3.4153 12.0319 8.9307 −6.2124 10.2722 2.8732 −2.9772 11.0685 4.4628 −2.7098 12.9658 5.5365 −5.2716 12.8247 6.9618 −3.8661 11.5842 4.9181 −4.5906 11.8528 7.5766 −4.3299 10.4502 4.2723 −4.0002 10.8846 2.444 −2.0409 13.2312 4.7975 −2.8339 11.8687 5.9341 −6.0731 11.7193 5.5578 −3.1448 10.7156 5.4333 −5.3023 10.7319 2.7532 −2.1396 12.1374 0.4443 −1.692 12.4409 3.4482 −2.3617 10.9929 9.3299 −6.4743 12.326 1.9286 −2.4132 13.299 1.1582 −1.6682 12.3471 - 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 Z coordinate values multiplied or divided by the same constant or number.
- In FIGS. 3 and 4, the radially
outermost profile 52 is illustrated with various other profile sections illustrated in FIG. 4 along the length of the airfoil. The various profiles are also illustrated in FIG. 6 with the profiles being superposed one over the other. - 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.
Claims (10)
Priority Applications (5)
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US09/903,853 US6503054B1 (en) | 2001-07-13 | 2001-07-13 | Second-stage turbine nozzle airfoil |
CNB028174224A CN1329631C (en) | 2001-07-13 | 2002-07-09 | Second-stage turbine nozzle airfoil |
KR1020047000462A KR100871196B1 (en) | 2001-07-13 | 2002-07-09 | Second-stage turbine nozzle airfoil |
EP02749918A EP1409846A1 (en) | 2001-07-13 | 2002-07-09 | Second-stage turbine nozzle airfoil |
JP2003512537A JP2004534921A (en) | 2001-07-13 | 2002-07-09 | Second stage turbine nozzle airfoil |
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US09/903,853 US6503054B1 (en) | 2001-07-13 | 2001-07-13 | Second-stage turbine nozzle airfoil |
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US20030021680A1 true US20030021680A1 (en) | 2003-01-30 |
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US09/903,853 Expired - Lifetime US6503054B1 (en) | 2001-07-13 | 2001-07-13 | Second-stage turbine nozzle airfoil |
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US (1) | US6503054B1 (en) |
EP (1) | EP1409846A1 (en) |
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Also Published As
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US6503054B1 (en) | 2003-01-07 |
JP2004534921A (en) | 2004-11-18 |
CN1329631C (en) | 2007-08-01 |
KR20040018453A (en) | 2004-03-03 |
KR100871196B1 (en) | 2008-12-01 |
EP1409846A1 (en) | 2004-04-21 |
CN1568396A (en) | 2005-01-19 |
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