Third-stage turbine nozzle airfoil

Information

  • Patent Grant
  • 6461109
  • Patent Number
    6,461,109
  • Date Filed
    Friday, July 13, 2001
    23 years ago
  • Date Issued
    Tuesday, October 8, 2002
    21 years ago
Abstract
The third-stage nozzles have vanes comprising airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z. The X, Y and Z values may be scaled as a function of the same constant or number to provide a scaled-up or scaled-down airfoil section for each nozzle vane.
Description




BACKGROUND OF THE INVENTION




The present invention relates to a turbine nozzle for a gas turbine stage and particularly relates to a third-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.




BRIEF SUMMARY OF THE INVENTION




In accordance with an embodiment of the present invention, there is provided a unique turbine nozzle airfoil profile for a turbine stage, preferably the third 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, 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.











BRIEF DESCRIPTION OF THE DRAWINGS





FIG. 1

is a schematic illustration of a turbine having a third-stage nozzle employing the airfoil or vane profile hereof;





FIG. 2

is a perspective view of a nozzle segment illustrating the vanes thereof;





FIGS. 3 and

4 are end views from respective radially outer and inner portions of the nozzle vanes illustrated in

FIG. 2

;





FIG. 5

is a perspective view of a nozzle vane 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 radial locations along the vane.











DETAILED DESCRIPTION OF THE INVENTION




Referring now to

FIG. 1

, there is illustrated a portion of a turbine, generally designated


10


, having multiple stages including a third-stage, generally designated


12


. Third-stage


12


includes a plurality of nozzles comprising 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


; a second stage


24


comprising a plurality of circumferentially spaced nozzle vanes


26


and a plurality of circumferentially spaced buckets


28


mounted on a second-stage wheel


30


and the third-stage


12


comprising a plurality of circumferentially spaced nozzle vanes


14


and a plurality of circumferentially spaced buckets


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 the arrow


36


. As illustrated, the nozzle vanes


14


of the third stage


12


are disposed between inner and outer bands


38


and


40


, respectively, by which the nozzles form an annulus about the rotor axis.




Referring to

FIG. 2

, 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. As will be appreciated, the nozzle vanes have various passages therethrough for cooling the vanes. In the preferred and illustrated embodiment of the third-stage nozzle for this particular turbine, there are sixty nozzle vanes forming the third stage.




Referring now to drawing

FIG. 2

, there is illustrated a nozzle vane


14


for the third 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 Z axis extending perpendicular to a plane normal to a radius from the centerline of the turbine rotor, i.e., normal to a plane containing the X and Y values. The Z distance commences at zero in the X, Y plane at the radially innermost aerodynamic section. The X axis lies parallel to the turbine rotor centerline, i.e., the rotary axis. By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile of airfoil


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 third stage of the turbine. Sixty nozzle vanes having such profiles are equally spaced from one another about the rotor axis and thus comprise the third stage.




The coordinate values given in Table I below in inches provide the preferred nominal profile envelope.














TABLE I









X Coordinate




Y Coordinate




Z Coordinate

























−5.3141




10.0979




18.1342






−5.0139




9.5505




18.1342






−6.7466




9.2005




18.1342






−5.1074




10.0329




18.1342






−5.2692




10.0963




18.1342






−5.4679




10.092




18.1342






−6.8847




8.6041




18.1342






−5.9787




9.9584




18.1342






−5.3404




10.0975




18.1342






−5.0935




9.0127




18.1342






−5.2816




10.0976




18.1342






−4.9998




9.8073




18.1342






−5.8385




10.0001




18.1342






−5.195




10.0792




18.1342






−6.8322




8.9151




18.1342






−6.479




9.6519




18.1342






−5.09




8.2923




18.1342






−5.0383




9.3924




18.1342






−5.5356




10.0809




18.1342






−5.0585




9.9819




18.1342






−5.2533




10.0949




18.1342






−5.2763




10.0971




18.1342






−5.7202




10.0366




18.1342






−6.31




9.7995




18.1342






−5.1092




8.7893




18.1342






−5.0009




9.6884




18.1342






−5.3732




10.0977




18.1342






−5.1544




10.0622




18.1342






−5.2763




10.0971




18.1342






−6.6276




9.4501




18.1342






−5.0489




8.0288




15.1342






−5.2936




10.099




18.1342






−5.0657




9.2134




18.1342






−5.6196




10.0638




18.1342






−5.4147




10.0976




18.1342






−5.0181




9.9071




18.1342






−5.2271




10.0894




18.1342






−6.9111




8.2769




18.1342






−6.1383




9.8972




18.1342






−5.1094




8.5475




18.1342






−6.7764




6.8429




18.1342






−4.9856




7.7589




18.1342






−6.8502




7.2166




18.1342






−4.675




6.9198




18.1342






−4.3907




6.3509




18.1342






−6.8942




7.5816




18.1342






−4.9012




7.4836




18.1342






−6.5218




6.1025




18.1342






−6.9134




7.9355




18.1342






−4.5382




6.6347




18.1342






−4.236




6.071




18.1342






−6.6679




6.4686




18.1342






−4.7973




7.2037




13.1342






−3.1955




4.4604




18.1342






−4.0756




5.7945




18.1342






−4.3751




3.8528




18.1342






−5.6097




4.8269




18.1342






−2.5934




3.7185




18.1342






−3.5639




4.9832




18.1342






−4.7007




4.0742




18.1342






−5.8791




5.1145




18.1342






−3.0015




4.2062




18.1342






−3.9099




5.521




18.1342






−5.0168




4.309




18.1342






−6.1237




5.4233




18.1342






−5.3209




4.5592




18.1342






−3.3827




4.7197




18.1342






−6.3394




5.753




18.1342






−2.8002




3.9578




18.1342






−3.7394




5.2504




18.1342






−3.7085




3.4421




18.1342






−0.0411




1.6954




18.1342






−0.4628




1.7853




18.1342






−0.4094




1.9153




18.1342






−0.1781




1.6542




18.1342






−1.161




2.4207




18.1342






0.0274




1.5822




18.1342






−2.174




3.279




18.1342






−0.9282




2.0021




18.1342






−2.7438




2.9088




18.1342






0.0454




1.6382




18.1342






−0.1493




1.7585




18.1342






−0.6612




2.0753




18.1342






−0.0673




1.6033




18.1342






−1.5543




2.725




18.1342






−1.6023




2.3263




18.1342






0.041




1.5994




18.1342






−1.8688




2.4584




18.1342






−3.3779




3.2536




18.1342






−0.004




1.673




18.1342






−0.5954




1.8465




18.1342






−0.3081




1.8535




18.1342






−0.2559




1.69




18.1342






−0.9791




2.2902




18.1342






0.0012




1.5727




18.1342






−1.9652




3.0809




18.1342






−1.1298




2.0976




18.1342






−2.4417




2.7504




18.1342






0.0477




1.6159




18.1342






−4.0426




3.6419




18.1342






−0.0894




1.7232




18.1342






−0.5268




1.9888




18.1342






−0.1159




1.6254




18.1342






−1.3541




2.5659




18.1342






0.0378




1.5937




18.1342






−2.3837




3.4914




18.1342






−0.75




1.9185




18.1342






−3.0562




3.076




18.1342






0.0261




1.6581




18.1342






−0.2218




1.8018




18.1342






−0.3502




1.7338




18.1342






−0.8122




2.1755




18.1342






−0.0305




1.5858




18.1342






−1.7585




2.8964




18.1342






−1.3546




2.2056




18.1342






−2.1499




2.6004




18.1342






0.0436




1.604




18.1342






−5.052




9.1157




17.6211






−5.0201




9.8027




17.6211






−5.2174




9.9929




17.6211






−5.3008




10.0057




17.6211






−5.5171




9.9966




17.6211






−6.1102




9.817




17.6211






−5.0816




8.4569




17.6211






−6.8039




8.8435




17.6211






−5.011




9.4503




17.6211






−5.1023




9.9308




17.6211






−5.2586




10.0019




17.6211






−5.3593




10.0078




17.6211






−5.7002




9.9583




17.6211






−6.4403




9.5681




17.6211






−5.0732




8.9167




17.6211






−6.8989




8.2146




17.6211






−5.0029




9.7042




17.6211






−5.1862




9.9815




17.6211






−5.2813




10.0049




17.6211






−5.4501




10.005




17.6211






−5.9545




9.8826




17.6211






−5.0615




8.2048




17.6211






−6.7106




9.1272




17.6211






−5.03




9.2934




17.6211






−5.0567




9.8786




17.6211






−5.243




9.9997




17.6211






−5.3267




10.0065




17.6211






−5.6003




9.982




17.6211






−6.2764




9.7157




17.6211






−5.0843




8.6957




17.6211






−6.8651




8.5377




17.6211






−5.0013




9.5868




17.6211






−5.147




9.9629




17.6211






−5.2656




10.0029




17.6211






−5.2656




10.0029




17.6211






−5.3982




10.0084




17.6211






−5.2813




10.0049




17.6211






−5.818




9.9257




17.6211






−6.588




9.3707




17.6211






−6.9075




7.8768




17.6211






−6.5081




6.0631




17.6211






−4.7862




7.1252




17.6211






−6.8473




7.1651




17.6211






−4.4023




6.2743




17.6211






−4.9624




7.677




17.6211






−6.6578




6.4231




17.6211






−4.6715




6.8421




17.6211






−6.8912




7.5263




17.6211






−4.2542




5.9952




17.6211






−4.5835




7.4037




17.6211






−6.7712




6.796




17.6211






−4.5424




6.5575




17.6211






−5.022




7.9444




17.6211






−3.2286




4.4027




17.6211






−5.309




4.5434




17.6211






−4.0992




5.7199




17.6211






−6.1067




5.3958




17.6211






−3.5964




4.9165




17.6211






−4.6962




4.0614




17.6211






−3.034




4.1538




17.6211






−5.5951




4.8084




17.6211






−3.9378




5.4483




17.6211






−6.3234




5.7199




17.6211






−3.416




4.6572




17.6211






−5.0084




4.2951




17.6211






−2.8316




3.9112




17.6211






−5.8625




5.092




17.6211






−3.7702




5.1804




17.6211






−4.3749




3.8404




17.6211






−1.1927




2.4126




17.6211






−0.4969




1.7837




17.6211






−2.203




3.2498




17.6211






−0.1075




1.6047




17.6211






0.0006




1.6415




17.6211






−3.7133




3.4276




17.6211






−0.1913




1.761




17.6211






−2.1719




2.5893




17.6211






−0.6973




2.0737




17.6211






−0.9566




1.9972




17.6211






−1.5839




2.71




17.6211






−0.2927




1.6898




17.6211






−2.6238




3.6778




17.6211






−0.0411




1.5802




17.6211






−0.004




1.6031




17.6211






−0.048




1.6762




17.6211






−3.069




3.0619




17.6211






−0.004




1.6031




17.6211






−0.3481




1.8549




17.6211






−1.6251




2.3169




17.6211






−1.0122




2.2848




17.6211






−0.6267




1.8435




17.6211






−1.994




3.0569




17.6211






−0.1547




1.6264




17.6211






−0.004




1.6031




17.6211






0.0026




1.6194




17.6211






−4.0468




3.6297




17.6211






−0.1321




1.7259




17.6211






−2.461




2.7379




17.6211






−0.5643




1.9885




17.6211






−1.1565




2.0915




17.6211






−1.3846




2.5546




17.6211






−0.3858




1.7328




17.6211






−2.4132




3.4566




17.6211






−0.0721




1.5885




17.6211






−0.0182




1.6613




17.6211






−3.3869




3.239




17.6211






−0.2629




1.8038




17.6211






−1.8932




2.4491




17.6211






−0.8469




2.1722




17.6211






−0.78




1.9146




17.6211






−1.7875




2.8771




17.6211






−0.216




1.6546




17.6211






−0.0169




1.5888




17.6211






−0.0014




1.6077




17.6211






−0.0845




1.6984




17.6211






−2.7601




2.8952




17.6211






−0.4482




1.916




17.6211






−1.3794




2.1979




17.6211






−6.2049




9.4384




15.9099






−6.8255




8.3099




15.9099






−5.0022




8.6028




15.9099






−5.009




9.3629




15.9099






−5.235




9.69




15.9099






−5.1592




9.6532




15.9099






−5.3597




9.7172




15.9099






−5.7736




9.6737




15.9099






−6.5035




9.0969




15.9099






−4.9966




8.9672




15.9099






−5.0561




9.5323




15.9099






−5.2649




9.6987




15.9099






−5.2097




9.6806




15.9099






−5.4768




9.7226




15.9099






−6.0511




9.5492




15.9099






−6.7424




8.6011




15.9099






−4.9995




8.3902




15.9099






−4.9985




9.2506




15.9099






−5.2303




9.6883




15.9099






−5.1265




9.6282




15.9099






−5.3203




9.7112




15.9099






−5.2303




9.6883




15.9099






−5.658




9.7024




15.9099






−6.3584




9.2881




15.9099






−6.8808




7.9993




15.9099






−5




8.7951




15.9099






−5.0276




9.4567




15.9099






−5.2458




9.6935




15.9099






−5.1868




9.6697




15.9099






−5.4109




9.7216




15.9099






−5.9055




9.6252




15.9099






−6.6338




8.8659




15.9099






−4.9886




8.1609




15.9099






−4.9951




9.119




15.9099






−5.0905




9.5887




15.9099






−5.2894




9.7047




15.9099






−5.2239




9.6861




15.9099






−5.559




9.7175




15.9099






−4.8876




7.4087




15.9099






−6.7751




6.6242




15.9099






−4.6643




6.5886




15.9099






−4.9672




7.9189




15.9099






−6.9067




7.6722




15.9099






−6.4904




5.9282




15.9099






−4.8276




7.142




15.9099






−6.8575




6.9809




15.9099






−4.5612




6.3064




15.9099






−4.9339




7.6679




15.9099






−6.6519




6.2706




15.9099






−4.7533




6.8684




15.9099






−6.9001




7.3316




15.9099






−4.4452




6.0257




15.9099






−5.829




5.0088




15.9099






−3.1371




3.9894




15.9099






−4.3841




3.7951




15.9099






−4.0306




5.2147




15.9099






−5.2856




4.4829




15.9099






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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 and innermost profiles


50


and


52


are illustrated with various other profile sections also illustrated along the length of the airfoil. The various profiles are also illustrated in the perspective view of

FIG. 5

with the profiles being superposed one over the other in FIG.


6


.




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
  • 1. 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
  • 2. A turbine nozzle according to claim 1 forming part of a third stage of a turbine.
  • 3. 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, 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.
  • 4. A turbine nozzle according to claim 3 forming part of a third stage of a turbine.
  • 5. 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
  • 6. A turbine according to claim 5 wherein the turbine nozzle comprises a third stage of the turbine.
  • 7. A turbine according to claim 5 wherein the turbine nozzle has sixty vanes and X represents a distance parallel to a rotary axis of the turbine.
  • 8. 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 wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, 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.
  • 9. A turbine according to claim 8 wherein the turbine nozzle comprises a third stage of the turbine.
  • 10. A turbine according to claim 8 wherein the turbine nozzle has sixty vanes and X represents a distance parallel to a rotary axis of the turbine.
US Referenced Citations (3)
Number Name Date Kind
5267834 Dinh et al. Dec 1993 A
5299915 Dinh et al. Apr 1994 A
5980209 Barry et al. Nov 1999 A
Non-Patent Literature Citations (7)
Entry
U.S. patent application Ser. No. 09/779,226, Burdgick et al., filed Feb. 2001.
U.S. patent application Ser. No. 09/886,406, Pirolla et al., filed Jun. 2001.
U.S. patent application Ser. No. 09/892,911, Wang et al., filed Jun. 2001.
U.S. patent application Ser. No. 09/899,543, Frost et al., filed Jul. 2001.
U.S. patent application Ser. No. 09/901,594, By et al., filed Jul. 2001.
U.S. patent application Ser. No. 09/903,853, Bielek et al., filed Jul. 2001.
U.S. patent application Ser. No. 09/987,433, Xu et al., filed Nov. 2001.