Abstract:
The second stage buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth Table I wherein X, Y and Z values are in inches. Z represents a distance in inches from and perpendicular to a plane passing through the engine centerline. X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form the complete airfoil shape. The X and Y distances and optionally the Z distance 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 ±0.016 inches.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    The present invention relates to a turbine bucket for a gas turbine stage and particularly relates to a second stage turbine bucket airfoil profile.  
           [0002]    There are many considerations in the design and construction of turbine buckets, particularly their airfoils, including optimized aerodynamic efficiency and aerodynamic and mechanical bucket loading. Additionally, bucket airfoil design must also take into consideration the potential mismatch or engagement problems associated with bucket airfoils having tip shrouds. As will be appreciated, certain buckets in turbines are provided with bucket tip shrouds which circumferentially engage one another along leading and trailing edges in a circumferential direction. Typically, the shrouds mount a seal which cooperates with a fixed shroud to seal against hot gas bypass between high and lower pressure regions on opposite sides of the bucket airfoils. The shrouds are also provided on long and slender buckets to add stiffness to the bucket airfoils by the engagement of the shrouds with one another. However, with air-cooled buckets, differential thermal growth and twisting sometimes affords poor engagement of the shrouds with one another. That is, one edge of the shroud may be radially inwardly of the opposing edge of the adjacent shroud. Absent an ideal engagement between adjacent shrouds, adverse loading causes higher stress at points of contact. With loss or minimization of contact, the benefit of damping vibrations to avoid high cycle fatigue by using shrouds is minimized or lost. Less than optimum tip shroud engagement adversely impacts tip shroud creep life and reduces part life. It will also be appreciated that the failure of a single bucket including its airfoil causes the entire turbine to be taken offline. These are time-consuming and expensive repairs which include the cost of the outage to the user of the turbine.  
         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, preferably for air-cooled tip shrouded airfoils of the second stage of a gas turbine. The bucket airfoil profile yields substantially improved shroud-to-shroud engagement enabling significant increased part life and reduced repair costs. Additionally, the airfoil reduces local creep and affords improved HCF margin in the resulting airfoil. The bucket airfoil profile is defined by a unique loci of points to achieve the necessary efficiency, loading and tip shroud engagement requirements. These unique loci of points define the nominal airfoil profile ranging from 10-90% span of the airfoil height and are identified by the X, Y and Z Cartesian coordinates of Table I which follows. The 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 within the 10-90% span of the airfoil height. The X, Y and Z coordinates are given in distance dimensions, e.g., units of inches. The X and Y coordinate values are joined smoothly with one another at each Z location to form smooth continuous arcuate airfoil profile sections. The Z coordinates are distances from and perpendicular to a plane passing through a turbine axis of rotation. Each defined airfoil profile section at each Z distance is joined smoothly with adjacent airfoil profile 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 0.016 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 of the nominal airfoil profile given below are a function of the same constant or number. That is, the X and Y, and optionally the 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 including a bucket airfoil having an airfoil shape, the airfoil having nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distance being joined smoothly with one another to form the complete airfoil shape.  
           [0007]    In a further preferred embodiment according to the present invention, there is provided a turbine bucket including a bucket airfoil having an airfoil shape, the airfoil having an uncoated nominal airfoil profile ranging from 10-90% span. of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y distances being scalable as a function of the same constant 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 the buckets including a bucket airfoil having an airfoil shape, the airfoil having a nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine axis and wherein X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the 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 the buckets including a bucket airfoil having an airfoil shape, the airfoil having a nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y distances being scalable as a function of the same constant to provide a scaled-up or scaled-down bucket airfoil.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    [0010]FIG. 1 is a generalized schematic illustration of a turbine having a second stage turbine wheel employing the buckets and bucket airfoils hereof;  
         [0011]    [0011]FIG. 2 is an end view of the shrouds formed on the bucket airfoils as viewed looking radially inwardly;  
         [0012]    [0012]FIG. 3 is a side elevational view of a preferred embodiment of the bucket hereof;  
         [0013]    [0013]FIGS. 4A-4K are representative cross-sectional views taken generally about on the lines variously indicated in FIG. 3;  
         [0014]    [0014]FIG. 5 is an elevational view of the bucket hereof similarly as indicated in FIG. 3 and taken from the opposite side thereof;  
         [0015]    [0015]FIG. 6 is an axial view of the bucket as it would appear in the turbine wheel and viewed from the leading edge;  
         [0016]    [0016]FIG. 7 is a perspective view of the bucket hereof;  
         [0017]    [0017]FIG. 8 is a perspective view of the engagement between adjacent shrouds in a misaligned condition; and  
         [0018]    [0018]FIG. 9 is a schematic representation of misengaged shrouds, i.e., shingled shrouds.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0019]    Referring now to FIG. 1, there is illustrated a portion of a turbine generally designated  10  in which a second stage turbine bucket  22  having an airfoil profile  23  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.  
         [0020]    The second stage comprises the rotor wheel  16  on which buckets  22  are mounted in axial opposition to the upstream stator vanes  28 . It will be appreciated that a plurality of the buckets  22  are spaced circumferentially one from the other about the second stage wheel  16  and in this instance there are ninety-two buckets mounted on the second stage wheel  16 .  
         [0021]    Referring now to FIGS. 5 and 6, there are illustrated buckets  22  of the second stage. Each bucket  22  includes a bucket airfoil  30  mounted on a platform  32 , the bucket further including a shank  34  and a dovetail  36 . Adjacent the tip of the airfoil  30  is a shroud  38  mounting a seal  40  and a cutter tooth  42 . The shroud  38  lies in radial opposition to a fixed shroud forming part of the stationary casing of the turbine. The seals  40  are provided to seal between high and lower pressure regions on opposite sides of the airfoils which lie in the hot gas path of the turbine. The cutter tooth  42  on each shroud typically forms a wider groove in the fixed shroud to permit slight leakage flows past the seal  40 .  
         [0022]    Referring to FIGS. 2, 8 and  9 , the shrouds  38  have leading and trailing edges in a circumferential direction which engage the trailing and leading edges, respectively, of adjacent shrouds. The shrouds are not mechanically connected one to the other but are shaped to maintain engagement. It has been discovered that the leading and trailing edges of adjacent shrouds may have engagements which mismatch, which among other things, adversely impact the part life. For example, the shrouds may have a tendency to shingle relative to one another. That is, the trailing edge of one shroud may overlie or underlie the leading edge of an adjacent shroud, as illustrated in FIGS. 8 and 9, with adverse consequences. The bucket airfoil has particular effect on the shroud engagement and the present airfoil profile reduces local creep and increases high cycle fatigue margin in the airfoil, ultimately leading to higher part life.  
         [0023]    A Cartesian coordinate system of X, Y and Z values given in Table I defines the profile of airfoil  30 . The coordinate values for the X, Y and Z coordinates are set forth in inches in Table I although other units of dimensions may be used. The Cartesian coordinate system has orthogonally-related X, Y and Z axes. The Z axis extends perpendicular to a plane passing through the axis of rotation of the turbine rotor and normal to a plane containing the X and Y values. The coordinate values for Z in Table I represent distances in inches from and perpendicular to a plane passing through the axis of rotation of the turbine. The X axis extends in a direction parallel to the turbine rotor centerline and the Y axis extends in a tangential direction.  
         [0024]    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 profile sections to one another to form the airfoil shape. These values represent the airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil.  
         [0025]    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 ±0.016 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.  
         [0026]    The coordinate values given in Table I below provide the preferred nominal profile envelope ranging from 10-90% span of the airfoil height.  
                                                                                 TABLE I                                       X(10%)   Y(10%)   Z(10%)   X(20%)   Y(20%)   Z(20%)                       −0.4223   0.1413   40.213   −1.456   0.6117   41.4           −0.1007   0.8256   40.213   −1.5812   0.2658   41.4           −1.6189   0.0838   40.213   −0.7133   0.3439   41.4           0.2487   0.5905   40.213   −1.4023   0.2375   41.4           −1.0913   0.1732   40.213   −1.1368   0.8641   41.4           −1.4158   0.081   40.213   −0.4471   0.975   41.4           −1.6613   0.1579   40.213   −0.3129   0.2331   41.4           −1.4392   0.5352   40.213   −0.2371   0.1983   41.4           −0.9176   0.8859   40.213   −0.5478   0.9912   41.4           −0.5872   0.1774   40.213   −0.0903   0.1193   41.4           −1.1964   0.7378   40.213   −1.5727   0.4498   41.4           −0.1837   0.0569   40.213   −0.6497   0.9968   41.4           −1.6565   0.2049   40.213   −1.2234   0.8101   41.4           −0.7135   0.9382   40.213   −0.3483   0.9493   41.4           −1.2812   0.6749   40.213   −1.5211   0.533   41.4           −1.6274   0.2939   40.213   −1.2083   0.3012   41.4           −1.0078   0.1859   40.213   −0.6309   0.3313   41.4           −0.755   0.1953   40.213   −0.1592   0.8728   41.4           −0.9238   0.1939   40.213   −1.3056   0.7495   41.4           −1.6484   0.1129   40.213   0.0171   0.7701   41.4           −1.4562   0.0703   40.213   −1.2872   0.2744   41.4           −0.2619   0.0888   40.213   −1.0457   0.3381   41.4           −1.4974   0.0637   40.213   −1.6038   0.3085   41.4           −1.2556   0.1344   40.213   −0.0193   0.0756   41.4           −1.3621   0.6072   40.213   −1.5486   0.4925   41.4           −0.6708   0.1888   40.213   −0.8797   0.3525   41.4           −0.8169   0.9174   40.213   −1.6039   0.3573   41.4           −1.5392   0.062   40.213   −0.7964   0.351   41.4           0.0809   0.7183   40.213   −0.4692   0.291   41.4           −0.5042   0.1616   40.213   −0.963   0.3483   41.4           −1.5762   0.3751   40.213   −0.8524   0.9748   41.4           −0.0317   −0.0166   40.213   −0.7517   0.9914   41.4           −0.8394   0.197   40.213   −1.592   0.4048   41.4           −1.0146   0.8445   40.213   0.1004   0.711   41.4           −1.1076   0.7948   40.213   −1.3659   0.2469   41.4           −0.3986   0.9296   40.213   −1.4396   0.2316   41.4           −1.336   0.1086   40.213   −0.5494   0.3136   41.4           −0.1967   0.8691   40.213   0.0501   0.0294   41.4           −1.6018   0.3353   40.213   0.258   0.5812   41.4           −0.6085   0.9472   40.213   −0.1629   0.1603   41.4           −1.174   0.1559   40.213   0.3326   0.5115   41.4           −0.0081   0.7749   40.213   −1.0457   0.9103   41.4           −0.5031   0.9442   40.213   0.1807   0.6479   41.4           −0.3415   0.117   40.213   −0.3902   0.2641   41.4           0.1664   0.6565   40.213   −1.1276   0.3224   41.4           −1.6437   0.2505   40.213   −0.2522   0.9148   41.4           −1.5806   0.0676   40.213   −0.0694   0.8242   41.4           0.328   0.5208   40.213   −1.5147   0.2329   41.4           −0.2962   0.9042   40.213   −1.4772   0.2296   41.4           −1.5117   0.4585   40.213   −1.3832   0.6832   41.4           −0.1069   0.0218   40.213   −1.5506   0.2441   41.4           0.6185   0.215   40.213   −0.9507   0.9475   41.4           1.8176   −1.7672   40.213   1.4833   −1.5812   41.4           0.2543   −0.1957   40.213   0.9639   −0.2882   41.4           1.3994   −1.4266   40.213   0.2496   −0.1214   41.4           0.4043   0.448   40.213   1.5292   −1.6508   41.4           0.4538   −0.3517   40.213   1.2462   −1.2383   41.4           0.9321   −0.8278   40.213   0.8906   −0.7756   41.4           0.9872   −0.8917   40.213   1.4369   −1.5119   41.4           0.8755   −0.1196   40.213   1.4189   −1.0863   41.4           1.4957   −1.5654   40.213   0.4047   0.4391   41.4           1.4703   −1.1153   40.213   0.5418   0.2879   41.4           1.2686   −0.7446   40.213   0.7827   −0.6484   41.4           1.8161   −1.8444   40.213   1.7327   −1.7285   41.4           1.5429   −1.6354   40.213   1.5566   −1.3599   41.4           1.6191   −1.3946   40.213   1.3717   −0.9957   41.4           0.9356   −0.2063   40.213   1.2752   −0.8157   41.4           1.8269   −1.806   40.213   0.6707   0.1295   41.4           0.7505   0.0505   40.213   0.851   −0.1181   41.4           1.7879   −1.8727   40.213   1.1242   −0.5493   41.4           0.5494   0.2949   40.213   0.118   −0.019   41.4           0.7609   −0.6411   40.213   1.6436   −1.8123   41.4           1.0949   −1.0218   40.213   1.1478   −1.1037   41.4           0.0421   −0.0576   40.213   1.6014   −1.4517   41.4           1.2504   −1.2218   40.213   1.5112   −1.2684   41.4           1.1075   −0.4721   40.213   1.7287   −1.7901   41.4           0.8138   −0.0339   40.213   0.6142   −0.4635   41.4           1.4207   −1.0221   40.213   1.0469   −0.9709   41.4           1.6812   −1.8477   40.213   1.6892   −1.636   41.4           0.4781   0.3726   40.213   0.9081   −0.2027   41.4           0.3222   −0.2459   40.213   0.3133   −0.1752   41.4           1.5695   −1.3016   40.213   0.9434   −0.8401   41.4           1.6353   −1.7767   40.213   1.7386   −1.7598   41.4           0.819   −0.7024   40.213   0.7924   −0.0345   41.4           1.5894   −1.7059   40.213   0.4973   −0.3447   41.4           1.0514   −0.3827   40.213   1.6455   −1.5438   41.4           0.1143   −0.1013   40.213   1.7054   −1.8119   41.4           0.1851   −0.1474   40.213   1.6202   −1.7906   41.4           0.6416   −0.5216   40.213   1.0718   −0.4616   41.4           0.9942   −0.2941   40.213   0.3758   −0.2305   41.4           1.7107   −1.8746   40.213   0.7274   −0.586   41.4           1.3708   −0.9291   40.213   0.5563   −0.4036   41.4           1.3202   −0.8366   40.213   1.3899   −1.443   41.4           0.876   −0.7646   40.213   0.7323   0.0481   41.4           1.0415   −0.9564   40.213   0.6072   0.2095   41.4           1.4478   −1.4958   40.213   1.1973   −1.1708   41.4           1.7495   −1.8837   40.213   1.3239   −0.9055   41.4           1.3008   −1.2896   40.213   1.0184   −0.3745   41.4           1.7183   −1.5809   40.213   1.6745   −1.82   41.4           1.1475   −1.0879   40.213   1.2947   −1.3061   41.4           0.3887   −0.298   40.213   0.837   −0.7117   41.4           0.5802   −0.4636   40.213   0.4371   −0.2869   41.4           0.7018   −0.5808   40.213   0.1845   −0.0694   41.4           1.2159   −0.6531   40.213   0.9955   −0.9052   41.4           1.1622   −0.5622   40.213   1.5747   −1.7207   41.4           1.5198   −1.2084   40.213   0.6713   −0.5244   41.4           0.5177   −0.407   40.213   1.3426   −1.3744   41.4           1.1993   −1.1546   40.213   0.4743   0.3645   41.4           1.3504   −1.3578   40.213   1.1754   −0.6376   41.4           0.6855   0.1335   40.213   1.0977   −1.037   41.4           1.768   −1.6741   40.213   1.2258   −0.7264   41.4           1.6687   −1.4878   40.213   1.4654   −1.1772   41.4                       X(30%)   Y(30%)   Z(30%)   X(40%)   Y(40%)   Z(40%)                       −1.0013   0.4872   42.597   −1.0081   1.107   43.784           −0.6898   1.071   42.597   −1.2735   0.5551   43.784           −0.7887   1.0678   42.597   −0.6281   1.1421   43.784           −1.0826   0.4754   42.597   −1.4061   0.8458   43.784           −1.3992   0.7693   42.597   −1.4354   0.5665   43.784           −0.8867   1.0537   42.597   −1.3061   0.5503   43.784           −1.3254   0.8353   42.597   −1.0378   0.6098   43.784           −1.2467   0.8953   42.597   −1.4905   0.6248   43.784           −0.9824   1.0286   42.597   −0.9152   1.1323   43.784           −1.4653   0.6958   42.597   −1.484   0.7212   43.784           −1.0748   0.9931   42.597   −1.4045   0.5555   43.784           −1.1631   0.9483   42.597   −1.4629   0.5846   43.784           −0.3056   0.9849   42.597   −1.1951   0.5743   43.784           −0.4937   1.046   42.597   −1.4369   0.8074   43.784           0.0356   0.7857   42.597   −1.372   0.5502   43.784           −0.2186   0.2908   42.597   −1.339   0.5486   43.784           −0.9194   0.4926   42.597   −1.4635   0.766   43.784           −0.2904   0.3305   42.597   −1.0974   1.0715   43.784           −0.4392   0.3996   42.597   −0.8766   0.6173   43.784           −0.7557   0.4842   42.597   −1.495   0.6734   43.784           −0.8374   0.4915   42.597   −1.338   0.9138   43.784           −0.0799   0.2029   42.597   −0.8201   1.1465   43.784           0.3987   0.4503   42.597   −1.1824   1.0265   43.784           −0.364   0.3669   42.597   −0.724   1.1497   43.784           −0.1289   0.8958   42.597   −0.9574   0.617   43.784           0.1885   0.66   42.597   −1.1173   0.5958   43.784           0.0524   0.1057   42.597   −1.2627   0.9736   43.784           −0.6747   0.4709   42.597   −0.3511   1.064   43.784           −0.5162   0.4282   42.597   −0.264   1.023   43.784           −0.0452   0.8431   42.597   0.3943   0.4685   43.784           0.1164   0.0543   42.597   −0.638   0.5788   43.784           0.1134   0.7246   42.597   0.2652   0.6112   43.784           −0.2157   0.9434   42.597   −0.561   0.5544   43.784           −0.3984   1.0195   42.597   −0.1365   0.324   43.784           −0.1484   0.2482   42.597   −0.4122   0.4916   43.784           −0.5912   1.0635   42.597   −0.7165   0.5977   43.784           0.3309   0.5226   42.597   0.1135   0.1197   43.784           −0.5947   0.4521   42.597   −0.5335   1.1246   43.784           −0.013   0.1553   42.597   0.4559   0.3945   43.784           0.2609   0.5926   42.597   0.2306   0.0085   43.784           0.5851   −0.4048   42.597   −0.4857   0.5251   43.784           1.0307   −0.4344   42.597   −0.0718   0.2757   43.784           0.7972   −0.6556   42.597   −0.3406   0.4543   43.784           0.4642   0.3762   42.597   −0.2028   0.3701   43.784           0.5279   0.3003   42.597   0.1974   0.6795   43.784           0.9278   −0.2652   42.597   −0.0208   0.8683   43.784           0.8484   −0.7197   42.597   −0.441   1.0982   43.784           0.3594   −0.1664   42.597   −0.099   0.9244   43.784           0.4742   −0.2838   42.597   0.1727   0.0647   43.784           0.6392   −0.4666   42.597   −0.0086   0.2254   43.784           0.3004   −0.1093   42.597   −0.1801   0.9762   43.784           0.5897   0.2229   42.597   0.0531   0.1733   43.784           0.179   0.0012   42.597   0.0546   0.8084   43.784           0.5301   −0.3439   42.597   −0.7961   0.6107   43.784           0.765   −0.0168   42.597   0.3308   0.5408   43.784           0.9798   −0.3495   42.597   −0.2708   0.4136   43.784           0.8747   −0.1816   42.597   0.1273   0.7454   43.784           0.7081   0.0642   42.597   0.943   −0.3205   43.784           0.8206   −0.0987   42.597   0.5576   −0.349   43.784           0.7452   −0.5919   42.597   0.8089   −0.6651   43.784           0.6927   −0.5289   42.597   0.2875   −0.049   43.784           0.2403   −0.0534   42.597   0.9054   −0.7947   43.784           0.4172   −0.2247   42.597   0.5053   −0.2874   43.784           0.6497   0.1442   42.597   0.8574   −0.7297   43.784           1.3633   −1.0423   42.597   0.6304   0.1647   43.784           1.0806   −0.52   42.597   0.5157   0.3192   43.784           1.2252   −0.7794   42.597   0.5739   0.2425   43.784           0.949   −0.8495   42.597   0.7103   −0.5371   43.784           1.1777   −0.6925   42.597   0.9915   −0.4036   43.784           1.4082   −1.1306   42.597   0.4522   −0.2266   43.784           0.9984   −0.915   42.597   0.8937   −0.2379   43.784           1.2719   −0.8667   42.597   0.66   −0.4739   43.784           0.899   −0.7843   42.597   0.8434   −0.1559   43.784           1.1296   −0.606   42.597   0.7599   −0.6009   43.784           1.3179   −0.9543   42.597   0.3982   −0.1665   43.784           −1.3517   0.4021   42.597   0.7919   −0.0745   43.784           −1.5514   0.5122   42.597   1.039   −0.4873   43.784           −1.5115   0.4229   42.597   0.3434   −0.1073   43.784           −1.5215   0.6098   42.597   0.6856   0.0859   43.784           −1.3845   0.3981   42.597   0.7394   0.0061   43.784           −1.544   0.4618   42.597   0.6092   −0.4112   43.784           −1.4822   0.4078   42.597   1.6024   −1.6639   43.784           −1.1627   0.4575   42.597   1.1319   −0.6559   43.784           −1.4174   0.3972   42.597   1.3625   −1.4604   43.784           −1.4503   0.3998   42.597   1.0464   −0.9916   43.784           −1.241   0.4329   42.597   0.9999   −0.9257   43.784           −1.4955   0.6541   42.597   1.3534   −1.0829   43.784           −1.5412   0.5624   42.597   1.0926   −1.0579   43.784           −1.3195   0.4089   42.597   1.2289   −1.2582   43.784           1.3763   −1.4521   42.597   1.1774   −0.7407   43.784           1.5401   −1.3967   42.597   1.1839   −1.1912   43.784           1.0957   −1.0473   42.597   1.0859   −0.5714   43.784           1.1909   −1.1811   42.597   1.2221   −0.8259   43.784           1.5114   −1.658   42.597   1.5791   −1.686   43.784           1.6414   −1.7484   42.597   1.3962   −1.1691   43.784           1.4526   −1.2191   42.597   1.2738   −1.3254   43.784           1.4217   −1.5205   42.597   0.9529   −0.86   43.784           1.6685   −1.6646   42.597   1.31   −0.997   43.784           1.4966   −1.3078   42.597   1.517   −1.6861   43.784           1.2844   −1.3161   42.597   1.2664   −0.9113   43.784           1.6647   −1.7265   42.597   1.548   −1.694   43.784           1.1435   −1.1141   42.597   1.4064   −1.5282   43.784           1.2378   −1.2484   42.597   1.45   −1.5962   43.784           1.5832   −1.4859   42.597   1.6061   −1.602   43.784           1.3306   −1.3839   42.597   1.4809   −1.3419   43.784           1.4667   −1.5892   42.597   1.6122   −1.6335   43.784           1.6258   −1.5753   42.597   1.4388   −1.2554   43.784           1.556   −1.7269   42.597   1.5645   −1.5153   43.784  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46.169           −1.3252   0.6968   44.971   −1.2039   1.1922   46.169           −1.4349   0.7794   44.971   −1.1241   1.2363   46.169           −1.4111   0.7385   44.971   −1.2481   0.8402   46.169           −0.5664   1.2075   44.971   −0.5714   0.7762   46.169           −0.0057   0.2949   44.971   −0.8631   1.313   46.169           0.2207   0.0716   44.971   −1.0403   1.2719   46.169           0.2707   0.6357   44.971   −0.1778   0.5215   46.169           −0.2228   1.0629   44.971   0.1054   0.2507   46.169           0.3319   0.5649   44.971   −0.1823   1.1009   46.169           −0.4579   0.6164   44.971   −0.5009   0.7422   46.169           −0.1443   1.0119   44.971   0.2105   0.1343   46.169           0.3913   0.4926   44.971   −0.039   0.9884   46.169           0.1657   0.1291   44.971   −0.3014   0.6179   46.169           0.0042   0.8981   44.971   0.0938   0.8635   46.169           −0.6038   0.6794   44.971   −0.1093   1.0464   46.169           −0.5298   0.6501   44.971   0.3335   0.5892   46.169           −0.1266   0.398   44.971   0.3614   −0.0461   46.169           −0.389   1.1489   44.971   −0.3659   0.6624   46.169           −0.2537   0.4934   44.971   0.3889   0.5168   46.169           −0.3044   1.1088   44.971   0.5464   0.2934   46.169           0.0743   0.8362   44.971   −0.0605   0.4174   46.169           −0.1893   0.4469   44.971   0.1584   0.193   46.169           0.3274   −0.0461   44.971   0.0512   0.3074   46.169           0.1098   0.1856   44.971   0.1567   0.7976   46.169           −0.3199   0.5375   44.971   0.2764   0.6602   46.169           0.505   0.344   44.971   0.0286   0.9273   46.169           −0.0687   0.9569   44.971   −0.2582   1.1513   46.169           0.2075   0.7047   44.971   0.4952   0.3688   46.169           0.2745   0.0131   44.971   0.2615   0.0749   46.169           0.1421   0.7716   44.971   −0.4324   0.704   46.169           −0.3879   0.5786   44.971   −0.004   0.363   46.169           0.0527   0.2409   44.971   −0.1184   0.4702   46.169           −0.0654   0.3473   44.971   0.2175   0.7298   46.169           0.6287   −0.4159   44.971   0.3119   0.0147   46.169           0.8136   −0.1251   44.971   −0.2387   0.5708   46.169           1.0437   −0.5324   44.971   0.997   −0.9405   46.169           0.9992   −0.4501   44.971   0.5526   −0.2946   46.169           0.954   −0.3681   44.971   0.9619   −0.4134   46.169           0.8612   −0.2055   44.971   0.5057   −0.2318   46.169           0.531   −0.2904   44.971   0.911   −0.8094   46.169           1.0877   −0.615   44.971   1.0396   −1.0062   46.169           0.5596   0.2679   44.971   0.9541   −0.8748   46.169           0.3795   −0.1062   44.971   0.8237   −0.679   46.169           0.8173   −0.6718   44.971   0.7857   −0.0943   46.169           0.4812   −0.2284   44.971   0.8752   −0.2531   46.169           0.6766   −0.4793   44.971   1.0463   −0.575   46.169           0.9089   −0.8018   44.971   0.7398   −0.0156   46.169           0.724   −0.5431   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49.742       −0.5258   1.3628   47.357   −0.8643   1.1068   48.544   −0.8238   1.2185   49.742       −0.2887   1.2419   47.357   −0.4562   1.4208   48.544   −0.1924   1.3136   49.742       −0.9625   1.3969   47.357   −1.0433   1.4764   48.544   −1.078   1.5637   49.742       −0.6115   0.9073   47.357   −0.3863   0.8734   48.544   −0.0725   1.1944   49.742       −0.6105   1.3892   47.357   −1.0173   1.1166   48.544   −0.6146   1.1287   49.742       −1.2435   1.2629   47.357   −1.2194   1.197   48.544   −1.0336   1.5848   49.742       −0.5421   0.8728   47.357   −0.1713   1.225   48.544   −1.1691   1.4524   49.742       −1.3169   1.1429   47.357   −1.2024   1.3805   48.544   −1.1499   1.4976   49.742       −1.296   1.0529   47.357   −0.7894   1.09   48.544   −0.2569   0.8472   49.742       −0.7569   0.9608   47.357   −1.2024   1.1793   48.544   −0.7517   1.1943   49.742       −1.1704   0.9864   47.357   −0.7876   1.5135   48.544   −1.1572   1.3571   49.742       −1.1417   0.9825   47.357   −0.6458   1.0364   48.544   −1.1097   1.3022   49.742       −0.4437   1.3287   47.357   −0.6171   1.4847   48.544   −0.2559   1.3693   49.742       −1.276   1.0319   47.357   −0.3078   1.3317   48.544   −0.4268   0.9994   49.742       −1.2261   1.0025   47.357   −0.9599   1.4994   48.544   −1.0898   1.2881   49.742       −1.1987   0.9931   47.357   −1.1622   1.1515   48.544   −0.5397   1.551   49.742       −0.9094   0.9874   47.357   −1.117   1.1325   48.544   −0.3683   0.9507   49.742       −1.1296   1.3375   47.357   −0.5114   0.9621   48.544   −1.0687   1.2759   49.742       −1.3023   1.1882   47.357   −0.7015   1.5041   48.544   −0.1313   1.2552   49.742       −1.2522   1.0153   47.357   −0.9405   1.1157   48.544   −0.5497   1.089   49.742       −0.6976   1.4068   47.357   −0.8742   1.5121   48.544   −0.8979   1.2357   49.742       −0.8325   0.9779   47.357   −0.4478   0.9192   48.544   −0.3915   1.4699   49.742       −1.0642   0.9821   47.357   −1.1228   1.4419   48.544   −1.1439   1.3367   49.742       −1.2062   1.2927   47.357   −0.5774   1.0013   48.544   −0.7001   1.6033   49.742       −0.9869   0.9889   47.357   −1.2462   1.2913   48.544   −0.6819   1.164   49.742       −0.8748   1.4112   47.357   −1.0934   1.1262   48.544   −1.0465   1.2658   49.742       −0.3647   1.288   47.357   −1.243   1.2413   48.544   −1.1279   1.3183   49.742       −0.0784   1.0784   47.357   −0.2381   1.2802   48.544   −0.8681   1.6166   49.742       −0.1458   1.1364   47.357   −1.14   1.141   48.544   −1.1178   1.5348   49.742       0.2238   0.7534   47.357   −0.3805   1.3789   48.544   −0.9733   1.2457   49.742       0.6243   0.1666   47.357   0.373   0.0127   48.544   −0.464   1.5135   49.742       −0.3469   0.7464   47.357   0.4168   −0.0503   48.544   −0.3223   1.4216   49.742       −0.1128   0.5432   47.357   −0.1582   0.668   48.544   −0.2034   0.7931   49.742       0.5782   0.2427   47.357   0.6513   0.1169   48.544   0.0452   0.5053   49.742       −0.2158   1.1912   47.357   0.5032   −0.1772   48.544   0.5946   0.2206   49.742       0.2954   0.0767   47.357   −0.1049   0.6128   48.544   0.2716   0.1997   49.742       0.3318   0.6123   47.357   0.3824   0.5618   48.544   0.7145   −0.0028   49.742       0.434   0.4669   47.357   −0.0529   0.5563   48.544   0.4254   0.5132   49.742       0.1989   0.1981   47.357   0.6086   0.1923   48.544   0.3999   0.0109   49.742       0.2786   0.6834   47.357   0.1813   0.8439   48.544   0.2421   0.7973   49.742       −0.4099   0.7917   47.357   0.334   0.6337   48.544   0.5115   0.3678   49.742       −0.2267   0.6486   47.357   0.1274   0.9118   48.544   0.6351   0.1464   49.742       −0.0045   0.4322   47.357   0.4757   0.4157   48.544   0.3358   0.6566   49.742       0.1495   0.2579   47.357   0.1915   0.2604   48.544   −0.0023   0.5647   49.742       0.0992   0.3169   47.357   −0.2128   0.722   48.544   0.4688   0.4407   49.742       0.4832   0.3929   47.357   −0.0453   1.106   48.544   0.1832   0.3235   49.742       −0.0137   1.0176   47.357   −0.0021   0.4987   48.544   0.092   1.0016   49.742       0.3425   0.0151   47.357   −0.2689   0.7744   48.544   0.4832   −0.1165   49.742       0.1674   0.822   47.357   0.2378   0.1992   48.544   0.2895   0.7273   49.742       0.389   −0.047   47.357   0.2835   0.1374   48.544   0.0389   1.0673   49.742       0.3836   0.54   47.357   −0.107   1.1668   48.544   0.4417   −0.0527   49.742       0.4349   −0.1095   47.357   0.0476   0.4403   48.544   0.3149   0.1371   49.742       0.2476   0.1377   47.357   0.4296   0.489   48.544   0.1934   0.8663   49.742       0.0488   0.9545   47.357   0.4602   −0.1137   48.544   0.092   0.4453   49.742       0.1091   0.8891   47.357   0.0965   0.3809   48.544   −0.0509   0.6233   49.742       0.5312   0.3181   47.357   0.5651   0.2673   48.544   −0.1514   0.7376   49.742       −0.169   0.5967   47.357   0.0717   0.9783   48.544   0.2276   0.2617   49.742       0.0478   0.375   47.357   0.5209   0.3418   48.544   −0.1006   0.6809   49.742       −0.2859   0.6986   47.357   0.0142   1.0431   48.544   0.5648   −0.2448   49.742       −0.0581   0.4884   47.357   0.2336   0.7749   48.544   0.1434   0.9345   49.742       0.9251   −0.3778   47.357   0.3285   0.0753   48.544   0.6751   0.0719   49.742       0.7426   −0.5566   47.357   0.2845   0.7048   48.544   0.5534   0.2943   49.742       0.8002   −0.1422   47.357   0.1444   0.321   48.544   0.138   0.3847   49.742       0.884   −0.299   47.357   0.9334   −0.4201   48.544   0.3811   0.5852   49.742       0.6695   0.0901   47.357   0.5878   −0.3054   48.544   −0.0158   1.1317   49.742       0.7137   0.0131   47.357   1.0331   −1.0228   48.544   0.5242   −0.1806   49.742       0.6132   −0.3632   47.357   0.6711   −0.4344   48.544   0.3577   0.0742   49.742       0.8272   −0.6866   47.357   1.112   −1.1547   48.544   0.7639   −0.569   49.742       0.9932   −0.9487   47.357   0.6933   0.0411   48.544   1.3017   −1.2208   49.742       0.9107   −0.8174   47.357   1.0725   −1.0887   48.544   1.1491   −1.2251   49.742       0.6998   −0.492   47.357   0.9936   −0.9571   48.544   0.9784   −0.5322   49.742       0.8424   −0.2205   47.357   0.834   −0.6947   48.544   0.9417   −0.4562   49.742       1.0456   −0.6156   47.357   0.753   −0.5642   48.544   1.1589   −0.9144   49.742       0.4803   −0.1724   47.357   0.7121   −0.4992   48.544   1.1873   −1.2909   49.742       0.9657   −0.4568   47.357   1.0853   −0.7316   48.544   1.0727   −1.0935   49.742       1.0342   −1.0145   47.357   1.1226   −0.8098   48.544   1.2303   −1.0676   49.742       0.5251   −0.2357   47.357   1.0477   −0.6536   48.544   0.9962   −0.962   49.742       1.0849   −0.6953   47.357   0.8741   −0.7602   48.544   0.803   −0.6342   49.742       1.124   −0.7751   47.357   0.9718   −0.4977   48.544   1.266   −1.1442   49.742       0.7573   −0.0644   47.357   1.01   −0.5756   48.544   1.0345   −1.0277   49.742       0.869   −0.752   47.357   0.5457   −0.2412   48.544   1.0149   −0.6085   49.742       0.6567   −0.4275   47.357   0.7936   −0.6294   48.544   1.0871   −0.7613   49.742       0.952   −0.883   47.357   0.7346   −0.0351   48.544   0.8419   −0.6997   49.742       1.1628   −0.855   47.357   0.8156   −0.1883   48.544   0.6452   −0.374   49.742       1.0058   −0.5361   47.357   0.8553   −0.2654   48.544   0.9193   −0.8307   49.742       0.785   −0.6215   47.357   0.6295   −0.3698   48.544   1.1946   −0.991   49.742       1.0751   −1.0805   47.357   0.8945   −0.3427   48.544   0.6052   −0.3093   49.742               X(70%)   Y(70%)   Z(70%)   X(80%)   Y(80%)   Z(80%)   X(90%)   Y(90%)   Z(90%)               0.5694   −0.2993   47.357   0.9141   −0.8256   48.544   1.2255   −1.3567   49.742       1.3177   −1.4775   47.357   1.1598   −0.8882   48.544   0.7533   −0.0778   49.742       1.2774   −1.4112   47.357   1.1968   −0.9665   48.544   0.7246   −0.5039   49.742       1.3922   −1.3364   47.357   0.9539   −0.8913   48.544   0.8298   −0.2286   49.742       1.4365   −1.4483   47.357   0.7754   −0.1116   48.544   1.1231   −0.8378   49.742       1.3542   −1.2561   47.357   1.3075   −1.2017   48.544   0.9578   −0.8963   49.742       1.1967   −1.2787   47.357   1.3443   −1.2802   48.544   0.8806   −0.7652   49.742       1.3407   −1.5   47.357   1.2915   −1.4414   48.544   0.9047   −0.3802   49.742       1.2779   −1.0955   47.357   1.2688   −1.4186   48.544   1.111   −1.1592   49.742       1.403   −1.5009   47.357   1.3875   −1.3901   48.544   0.7918   −0.1532   49.742       1.1157   −1.1465   47.357   1.3225   −1.4501   48.544   0.6851   −0.4389   49.742       1.2013   −0.9351   47.357   1.3775   −1.4208   48.544   1.0511   −0.6849   49.742       1.2397   −1.0153   47.357   1.3539   −1.4426   48.544   0.8675   −0.3043   49.742       1.4303   −1.4167   47.357   1.1905   −1.2866   48.544   1.3339   −1.3596   49.742       1.3161   −1.1758   47.357   1.2706   −1.1233   48.544   1.248   −1.3798   49.742       1.2372   −1.345   47.357   1.2337   −1.0449   48.544   1.3102   −1.3814   49.742       1.3718   −1.5086   47.357   1.1512   −1.2206   48.544   1.2789   −1.3887   49.742       1.1563   −1.2125   47.357   1.3811   −1.3586   48.544   1.3439   −1.3289   49.742       1.4266   −1.479   47.357   1.2296   −1.3526   48.544   1.3375   −1.2974   49.742                  
 
         [0027]    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 multiplied or divided by the same constant or number.  
         [0028]    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.