# Patent

## Title
Gas turbine with optimized airfoil element angles

## Abstract

A turbine airfoil assembly for installation in a gas turbine engine. The airfoil assembly includes an endwall and an airfoil extending radially outwardly from the endwall. The airfoil includes pressure and suction sidewalls defining chordally spaced apart leading and trailing edges of the airfoil. An airfoil mean line is defined located centrally between the pressure and suction sidewalls. An angle between the mean line and a line parallel to the engine axis at the leading and trailing edges defines gas flow entry angles, α, and exit angles, β. Airfoil inlet and exit angles are substantially in accordance with pairs of inlet angle values, α, and exit angle values, β, set forth in one of Tables 1, 3, 5 and 7.

## Background
CROSS REFERENCE TO RELATED APPLICATION
This application claims the benefit of U.S. Provisional Patent Application Ser. No. 61/543,850, filed Oct. 6, 2011, entitled “GAS TURBINE WITH OPTIMIZED AIRFOIL ELEMENT ANGLES”, the entire disclosure of which is incorporated by reference herein.


FIELD OF THE INVENTION
The present invention relates to a turbine vanes and blades for a gas turbine stage and, more particularly, to third and fourth stage turbine vane and blade airfoil configurations.
BACKGROUND OF THE INVENTION
In a turbomachine, such as a gas turbine engine, air is pressurized in a compressor then mixed with fuel and burned in a combustor to generate hot combustion gases. The hot combustion gases are expanded within the turbine section where energy is extracted to power the compressor and to produce useful work, such as turning a generator to produce electricity. The hot combustion gas travels through a series of turbine stages. A turbine stage may include a row of stationary vanes followed by a row of rotating turbine blades, where the turbine blades extract energy from the hot combustion gas for powering the compressor, and may additionally provide an output power.
The overall work output from the turbine is distributed into all of the stages. The stationary vanes are provided to accelerate the flow and turn the flow to feed into the downstream rotating blades to generate torque to drive the upstream compressor. The flow turning in each rotating blade creates a reaction force on the blade to produce the torque. The work transformation from the gas flow to the rotor disk is directly related to the engine efficiency, and the distribution of the work split for each stage may be controlled by the vane and blade design for each stage.
SUMMARY OF THE INVENTION
In accordance with an aspect of the invention, a turbine airfoil assembly is provided for installation in a gas turbine engine having a longitudinal axis. The turbine airfoil assembly includes an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall. The airfoil has an outer wall comprising a pressure sidewall and a suction sidewall joined together at chordally spaced apart leading and trailing edges of the airfoil. An airfoil mean line is defined extending chordally and located centrally between the pressure and suction sidewalls. Airfoil inlet and exit angles are defined at the airfoil leading and trailing edges that are substantially in accordance with pairs of inlet angle values, α, and exit angle values, β, set forth in one of Tables 1, 3, 5 and 7. The inlet and exit angle values are generally defined as angles between a line parallel to the longitudinal axis and the airfoil mean line lying in an X-Y plane of an X, Y, Z Cartesian coordinate system in which Z is a dimension perpendicular to the X-Y plane and extends radially relative to the longitudinal axis, and wherein each pair of inlet and exit angle values is defined with respect to a distance from the endwall corresponding to a Z value that is a percentage of the total span of the airfoil from the endwall. A predetermined difference between each pair of the airfoil inlet and exit angles is defined by a delta value, Δ, in the Table, and a difference between any pair of the airfoil inlet and exit angles varies from the delta values, Δ, in the Table by at most 5%.
In accordance with another aspect of the invention, third and fourth stage vane and blade airfoil assemblies are provided in a gas turbine engine having a longitudinal axis. Each airfoil assembly includes an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall. The airfoil has an outer wall comprising a pressure sidewall and a suction sidewall joined together at chordally spaced apart leading and trailing edges of the airfoil. An airfoil mean line is defined extending chordally and located centrally between the pressure and suction sidewalls. Airfoil inlet and exit angles are defined at the airfoil leading and trailing edges that are substantially in accordance with pairs of inlet angle values, α, and exit angle values, β. The inlet and exit angle values are generally defined as angles between a line parallel to the longitudinal axis and the airfoil mean line lying in an X-Y plane of an X, Y, Z Cartesian coordinate system in which Z is a dimension perpendicular to the X-Y plane and extends radially relative to the longitudinal axis. Each pair of inlet and exit angle values is defined with respect to a distance from the endwall corresponding to a Z value that is a percentage of the total span of the airfoil from the endwall, wherein:

    
    
        a) the pairs of inlet angle values, α, and exit angle values, β, for the third stage vane are as set forth in Table 1;
        b) the pairs of inlet angle values, α, and exit angle values, β, for the third stage blade are as set forth in Table 3;
        c) the pairs of inlet angle values, α, and exit angle values, β, for the fourth stage vane are as set forth in Table 5;
        d) the pairs of inlet angle values, α, and exit angle values, β, for the fourth stage blade are as set forth in Table 7; and
    
    


wherein a predetermined difference between each pair of the airfoil inlet and exit angles is defined by a delta value, Δ, in the Table, and a difference between any pair of the airfoil inlet and exit angles varies from the delta values, Δ, in a respective Table by at most 5%.
In accordance with a further aspect of the invention, a turbine airfoil assembly is provided for installation in a gas turbine engine having a longitudinal axis. The turbine airfoil assembly includes an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall. The airfoil has an outer wall comprising a pressure sidewall and a suction sidewall joined together at chordally spaced apart leading and trailing edges of the airfoil. An airfoil mean line is defined extending chordally and located centrally between the pressure and suction sidewalls. Airfoil exit angles are defined at the airfoil trailing edge that are substantially in accordance with exit angle values, β, set forth in one of Tables 1, 3, 5 and 7, where the exit angle values are generally defined as angles between a line parallel to the longitudinal axis and the airfoil mean line lying in an X-Y plane of an X, Y, Z Cartesian coordinate system in which Z is a dimension perpendicular to the X-Y plane and extends radially relative to the longitudinal axis. Each exit angle value is defined with respect to a distance from the endwall corresponding to a Z value that is a percentage of the total span of the airfoil from the endwall, and wherein each airfoil exit angle is within about 1% of a respective value set forth in the Table.



BRIEF DESCRIPTION OF THE DRAWINGS
While the specification concludes with claims particularly pointing out and distinctly claiming the present invention, it is believed that the present invention will be better understood from the following description in conjunction with the accompanying Drawing Figures, in which like reference numerals identify like elements, and wherein:
FIG. 1 is a cross sectional view of a turbine section for a gas turbine engine;
FIG. 2 is a side elevational view of a third stage vane assembly formed in accordance with aspects of the present invention;
FIG. 3 is a perspective view of the vane assembly of FIG. 2;
FIG. 4 is a cross sectional plan view of an airfoil of the vane assembly of FIG. 2;
FIG. 5 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the vane assembly of FIG. 2;
FIG. 6 is a side elevational view of a third stage blade assembly formed in accordance with aspects of the present invention;
FIG. 7 is a perspective view of the blade assembly of FIG. 6;
FIG. 8 is a cross sectional plan view of an airfoil of the blade assembly of FIG. 6;
FIG. 9 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the blade assembly of FIG. 6;
FIG. 10 is a side elevational view of a fourth stage vane assembly formed in accordance with aspects of the present invention;
FIG. 11 is a perspective view of the vane assembly of FIG. 10;
FIG. 12 is a cross sectional plan view of an airfoil of the vane assembly of FIG. 10;
FIG. 13 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the vane assembly of FIG. 10;
FIG. 14 is a side elevational view of a fourth stage blade assembly formed in accordance with aspects of the present invention;
FIG. 15 is a perspective view of the blade assembly of FIG. 14;
FIG. 16 is a cross sectional plan view of an airfoil of the blade assembly of FIG. 14; and
FIG. 17 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the blade assembly of FIG. 14.



DETAILED DESCRIPTION OF THE INVENTION
In the following detailed description of the preferred embodiment, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration, and not by way of limitation, a specific preferred embodiment in which the invention may be practiced. It is to be understood that other embodiments may be utilized and that changes may be made without departing from the spirit and scope of the present invention.
Referring to FIG. 1, a turbine section 12 for a gas turbine engine is illustrated. The turbine section 12 comprises alternating rows of stationary vanes and rotating blades extending radially into an axial flow path 13 extending through the turbine section 12. In particular, the turbine section 12 includes a first stage formed by a first row of stationary vanes 14 and a first row of rotating blades 16, a second stage formed by a second row of stationary vanes 18 and a second row of rotating blades 20, a third stage formed by a third row of stationary vanes 22 and a third row of rotating blades 24, and a fourth stage formed by a fourth row of stationary vanes 26 and a fourth row of rotating blades 28.
During operation of the gas turbine engine, a compressor (not shown) of the engine supplies compressed air to a combustor (not shown) where the air is mixed with a fuel, and the mixture is ignited creating combustion products comprising a hot working gas defining a working fluid. The working fluid travels through the stages of the turbine section 12 where it expands and causes the blades 16, 20, 24, 28 to rotate. The overall work output from the turbine section 12 is distributed into all of the stages, where the stationary vanes 14, 18, 22, 26 are provided for accelerating the gas flow and turn the gas flow to feed into the respective downstream blades 16, 20, 24, 28 to generate torque on a rotor 30 supporting the blades 16, 20, 24, 28, producing a rotational output about a longitudinal axis 32 of the engine, such as to drive the upstream compressor.
The flow turning occurring at each rotating blade 16, 20, 24, 28 creates a reaction force on the blade 16, 20, 24, 28 to produce the output torque. The work split between the stages may be controlled by the angular changes in flow direction effected by each of the vanes 14, 18, 22, 26 and respective blades 16, 20, 24, 28, which work split has an effect on the efficiency of the engine. In accordance with an aspect of the invention, a design for the third and fourth stage vanes 22, 26 and blades 24, 28 is provided to optimize or improve the flow angle changes through the third and fourth stages. Specifically, the design of the third and fourth stage vanes 22, 26 and blades 24, 28, as described below, provide a radial variation in inlet and exit flow angles to produce optimized flow profiles into an exhaust diffuser 34 downstream from the turbine section 12. Optimized flow profiles through the third and fourth stages of the turbine section 12 may facilitate a reduction in the average Mach number for flows exiting the fourth stage vanes 26, with an associated improvement in engine efficiency, since flow loss tends to be proportional to the square of the Mach number.
Referring to FIGS. 2-5, a configuration for the third stage vane 22 is described. In particular, referring initially to FIGS. 2 and 3, a third stage vane airfoil structure 36 is shown including three of the airfoils or vanes 22 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 4, the vanes 22 each include an outer wall comprising a generally concave pressure sidewall 38, and include an opposing generally convex suction sidewall 40. The sidewalls 38, 40 extend radially between an inner diameter endwall 42 and an outer diameter endwall 44, and extend generally axially in a chordal direction between a leading edge 46 and a trailing edge 48 of each of the vanes 22. The endwalls 42, 44 are located at opposing ends of the vanes 22 and are positioned at locations where they form a boundary, i.e., inner and outer boundaries, defining a portion of the flow path 13 for the working fluid. Opposing radially inner matefaces 45a, 47a and radially outer matefaces 45b, 47b are defined by the respective inner and outer diameter endwalls 42, 44 of the airfoil structure 36.
FIG. 4 illustrates a cross section of one of the vanes 22 at a radial location of about 50% of the span, SV3 (FIG. 2), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 3), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, SV3, of the airfoil for the vane 22. It should be noted that the matefaces 45a, 47a and 45b, 47b are shown herein as extending at an angle relative to the direction of the longitudinal axis 32.
The cross section of FIG. 4 lies in the X-Y plane. As seen in FIG. 4, the vane 22 defines an airfoil mean line, CV3, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 38, 40. At the leading edge 46, a blade metal angle of each of the surfaces of the pressure and suction sides 38, 40 adjacent to the leading edge 46 is provided for directing incoming flow to the vane 22 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CV3, at the leading edge 46, i.e., tangential to the line CV3 at the airfoil leading edge 46.
At the trailing edge 48, a blade metal angle of the surfaces of the pressure and suction sides 38, 40 adjacent to the trailing edge 48 is provided for directing flow exiting from the vane 22 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CV3, at the trailing edge 48, i.e., tangential to the line CV3 at the airfoil trailing edge 48.
The inlet angles, α, and exit angles, β, for the airfoil of the vane 22 are as described in Table 1 below. The Z coordinate locations are presented as a percentage of the total span of the vane 22. The values for the inlet angles, α, and exit angles, β, are defined at selected Z locations spaced at 10% increments along the span of the vane 22, where 0% is located adjacent to the inner endwall 42 and 100% is located adjacent to the outer endwall 44. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 5.










TABLE 1





Z - Span %
α - LE Angle
β - TE Angle
Δ - Delta Value


















0
40.10
−57.86
97.96


10
38.16
−58.12
96.28


20
35.01
−58.48
93.49


30
33.66
−58.31
91.97


40
33.58
−58.00
91.58


50
33.51
−57.91
91.42


60
32.35
−60.01
92.36


70
31.01
−62.12
93.13


80
28.28
−64.26
92.54


90
22.61
−66.44
89.05


100
21.00
−65.34
86.34









Table 1 further describes a predetermined difference between each pair of the airfoil inlet and exit angles, at any given span location, as defined by a delta value, Δ, presented as the absolute value of the difference between the leading edge or inlet angle, α, and the trailing edge or exit angle, β. The delta value, Δ, is representative of an amount of flow turning that occurs from the inlet to the exit of the third stage vane 22. The inlet angle, α, is selected with reference to the flow direction coming from the second row blades 20, and the exit angle, β, is preferably selected to provide a predetermined direction of flow into the third stage blades 24.
It should be noted that the difference between any pair of airfoil inlet and exit angles, α, β, at any given span location, SV3, may vary from the delta value, Δ, listed in Table 1 due to various conditions, such as manufacturing tolerances or other conditions. In particular, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SV3, may generally vary from the delta value, Δ, listed in Table 1 by at most 5%. More preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SV3, may vary from the delta value, Δ, listed in Table 1 by at most 3%. Most preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SV3, may vary from the delta value, Δ, listed in Table 1 by at most 1%. In other words, the amount of flow turning may vary slightly from the given predetermined delta value, Δ, within a percentage range of, for example, 5% to 1%. However, an optimal configuration for the airfoil of the vane 22 is believed to be provided by a configuration having a minimal variation from the given predetermined delta values, Δ.
Portions of sections of the airfoil for the vane 22 are described below in Table 2 (end of specification), generally located at the noted selected Z or spanwise locations described above for Table 1. It may be noted that the description provided by Table 2 comprises an exemplary, non-limiting description of leading edge and trailing edge airfoil sections forming the inlet and exit angles α, β.
The portions of the airfoil for the vane 22 described in Table 2 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 3) 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, and generally parallel to the span, SV3, of the airfoil for the vane 22. The Z coordinate values in Table 2 have an origin or zero value at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the vane 22, i.e., adjacent the inner endwall 42, and are presented as a percentage of the total span of the vane 22. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. Exemplary profiles for leading edge sections and trailing edge sections of the airfoil for the vane 22 are defined by the X and Y coordinate values, located at point locations, N, at selected locations in the Z direction normal to the X, Y plane. Each leading edge and trailing edge profile section at each selected radial Z location is determined by connecting the X and Y values at the point locations, N, with smooth, continuous arcs. Similarly, the surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the leading edge section and trailing edge section of the airfoil.
The leading edge section 50 at each Z location is described by successive data points N=1 to N=30 defining the leading edge section 50 as extending from the suction sidewall 40, around the leading edge 46, and along a portion of the pressure sidewall 38.
The trailing edge section 52 at each Z location is described in two parts. In particular, a first part of the trailing edge section 52 is described along the suction sidewall 40 by data points N=31 to N=40, and a second part of the trailing edge section 52 is described along the pressure sidewall 38 by data points N=41 to N=60. It may be noted that the data points N=31 and N=60 have the same X and Y coordinate values for continuity in presenting the data in Table 2, and are both located at or near the trailing edge 48 of the vane 22.
Referring to FIGS. 6-9, a configuration for the third stage blade 24 is described. In particular, referring initially to FIGS. 6 and 7, a third stage blade airfoil structure 56 is shown including one of the airfoils or blades 24 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 8, the blades 24 each include an outer wall comprising a generally concave pressure sidewall 58, and include an opposing generally convex suction sidewall 60. The sidewalls 58, 60 extend radially outwardly from an inner diameter endwall 62 to a blade tip 64, and extend generally axially in a chordal direction between a leading edge 66 and a trailing edge 68 of each of the blades 24. A blade root is defined by a dovetail 65 extending radially inwardly from the endwall 62 for mounting the blade 24 to the rotor 30. The endwall 62 is positioned at a location where it forms a boundary, i.e., an inner boundary, defining a portion of the flow path 13 for the working fluid.
FIG. 8 illustrates a cross section of the blade 24 at a radial location of about 50% of the span, SB3 (FIG. 6), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 7), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, SB3, of the airfoil for the blade 24. It should be noted that a central lengthwise axis 67 of the dovetail 65 is shown herein as extending at an angle relative to the direction of the longitudinal axis 32.
The cross section of FIG. 8 lies in the X-Y plane. As seen in FIG. 8, the blade 24 defines an airfoil mean line, CB3, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 58, 60. At the leading edge 66, a blade metal angle of each of the surfaces of the pressure and suction sides 58, 60 adjacent to the leading edge 66 is provided for directing incoming flow to the blade 24 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CB3, at the leading edge 66, i.e., tangential to the line CB3 at the airfoil leading edge 66.
At the trailing edge 68, a blade metal angle of the surfaces of the pressure and suction sides 58, 60 adjacent to the trailing edge 68 is provided for directing flow exiting from the blade 24 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, α, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CB3, at the trailing edge 68, i.e., tangential to the line CB3 at the airfoil trailing edge 68.
The inlet angles, α, and exit angles, β, for the airfoil of the blade 24 are as described in Table 3 below. The Z coordinate locations are presented as a percentage of the total span of the blade 24. The values for the inlet angles, α, and exit angles, β, are defined at selected locations spaced at 10% increments along the span of the blade 24, where 0% is located adjacent to the inner endwall 62 and 100% is located adjacent to the blade tip 64. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 9.










TABLE 3





Z - Span %
α - LE Angle
β - TE Angle
Δ - Delta Value


















0
−36.65
51.98
88.63


10
−34.53
52.57
87.10


20
−31.93
53.34
85.27


30
−28.72
53.68
82.40


40
−25.24
53.61
78.85


50
−21.76
53.54
75.30


60
−16.64
53.26
69.90


70
−11.48
52.88
64.36


80
−7.86
52.46
60.32


90
−6.65
50.34
56.99


100
−4.56
49.84
54.40









Table 3 further describes a predetermined difference between each pair of the airfoil inlet and exit angles, at any given span location, as defined by a delta value, Δ, presented as the absolute value of the difference between the leading edge or inlet angle, α, and the trailing edge or exit angle, β. The delta value, Δ, is representative of a change of direction of the flow between the leading edge 66 and trailing edge 68, where it may be understood that the amount of work extracted from the working gas is related to the difference between the inlet angle, α, and exit angle, β, of the flow. For example, increasing the delta value, Δ, may increase the amount of work extracted from the flow.
It should be noted that the difference between any pair of airfoil inlet and exit angles, α, β, at any given span location, SB3, may vary from the delta value, Δ, listed in Table 3 due to various conditions, such as manufacturing tolerances or other conditions. In particular, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SB3, may generally vary from the delta value, Δ, listed in Table 3 by at most 5%. More preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SB3, may vary from the delta value, Δ, listed in Table 3 by at most 3%. Most preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SB3, may vary from the delta value, Δ, listed in Table 3 by at most 1%. In other words, the amount of flow turning may vary slightly from the given predetermined delta value, Δ, within a percentage range of, for example, 5% to 1%. However, an optimal configuration for the airfoil of the blade 24 is believed to be provided by a configuration having a minimal variation from the given predetermined delta values, Δ.
Portions of sections of the airfoil for the blade 24 are described below in Table 4 (end of specification), generally located at the noted selected Z or spanwise locations described above for Table 3. It may be noted that the description provided by Table 4 comprises an exemplary, non-limiting description of leading edge and trailing edge airfoil sections forming the inlet and exit angles α, β.
The portions of the airfoil for the blade 24 described in Table 4 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 7) 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, and generally parallel to the span, SB3, of the airfoil for the blade 24. The Z coordinate values in Table 4 have an origin or zero value at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the blade 24, i.e., adjacent the inner endwall 62, and are presented as a percentage of the total span of the blade 24. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. Exemplary profiles for leading edge sections and trailing edge sections of the airfoil for the blade 24 are defined by the X and Y coordinate values, located at point locations, N, at selected locations in the Z direction normal to the X, Y plane. Each leading edge and trailing edge profile section at each selected radial Z location is determined by connecting the X and Y values at the point locations, N, with smooth, continuous arcs. Similarly, the surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the leading edge section and trailing edge section of the airfoil.
The leading edge section 70 at each Z location is described by successive data points N=1 to N=30 defining the leading edge section 70 as extending from the pressure sidewall 58, around the leading edge 66, and along a portion of the suction sidewall 60.
The trailing edge section 72 at each Z location is described in two parts. In particular, a first part of the trailing edge section 72 is described along the pressure sidewall 58 by data points N=31 to N=40, and a second part of the trailing edge section 52 is described along the suction sidewall 60 by data points N=41 to N=60. It may be noted that the data points N=31 and N=60 have the same X and Y coordinate values for continuity in presenting the data in Table 4, and are both located at or near the trailing edge 68 of the blade 24.
Referring to FIGS. 10-13, a configuration for the fourth stage vane 26 is described. In particular, referring initially to FIGS. 10 and 11, a fourth stage vane airfoil structure 76 is shown including four of the airfoils or vanes 26 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 12, the vanes 26 each include an outer wall comprising a generally concave pressure sidewall 78, and include an opposing generally convex suction sidewall 80. The sidewalls 78, 80 extend radially between an inner diameter endwall 82 and an outer diameter endwall 84, and extend generally axially in a chordal direction between a leading edge 86 and a trailing edge 88 of each of the vanes 26. The endwalls 82, 84 are located at opposing ends of the vanes 26 and are positioned at locations where they form a boundary, i.e., inner and outer boundaries, defining a portion of the flow path 13 for the working fluid. Opposing radially inner matefaces 85a, 87a and radially outer matefaces 85b, 87b are defined by the respective inner and outer diameter endwalls 82, 84 of the airfoil structure 76.
FIG. 12 illustrates a cross section of one of the vanes 26 at a radial location of about 50% of the span, SV4 (FIG. 10), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 11), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, SV4, of the airfoil for the vane 26. It should be noted that the matefaces 85a, 87a and 85b, 87b are shown herein as extending at an angle relative to the direction of the longitudinal axis 32.
The cross section of FIG. 12 lies in the X-Y plane. As seen in FIG. 12, the vane 26 defines an airfoil mean line, CV4, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 78, 80. At the leading edge 86, a blade metal angle of each of the surfaces of the pressure and suction sides 78, 80 adjacent to the leading edge 86 is provided for directing incoming flow to the vane 26 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CV4, at the leading edge 86, i.e., tangential to the line CV4 at the airfoil leading edge 86.
At the trailing edge 88, a blade metal angle of the surfaces of the pressure and suction sides 78, 80 adjacent to the trailing edge 88 is provided for directing flow exiting from the vane 26 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CV4, at the trailing edge 88, i.e., tangential to the line CV4 at the airfoil trailing edge 88.
The inlet angles, α, and exit angles, β, for the airfoil of the vane 26 are as described in Table 5 below. The Z coordinate locations are presented as a percentage of the total span of the vane 26. The values for the inlet angles, α, and exit angles, β, are defined at selected locations spaced at 10% increments along the span of the vane 26, where 0% is located adjacent to the inner endwall 82 and 100% is located adjacent to the outer endwall 84. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 13.










TABLE 5





Z - Span %
α - LE Angle
β - TE Angle
Δ - Delta Value


















0
33.41
−53.19
86.60


10
31.92
−53.03
84.95


20
28.03
−53.51
81.54


30
26.00
−53.25
79.25


40
26.01
−52.10
78.11


50
26.02
−50.95
76.97


60
22.61
−50.09
72.70


70
17.99
−49.26
67.25


80
15.22
−49.04
64.26


90
20.19
−50.28
70.47


100
18.51
−56.65
75.16









Table 5 further describes a predetermined difference between each pair of the airfoil inlet and exit angles, at any given span location, as defined by a delta value, Δ, presented as the absolute value of the difference between the leading edge or inlet angle, α, and the trailing edge or exit angle, β. The delta value, Δ, is representative of an amount of flow turning that occurs from the inlet to the exit of the fourth stage vane 26. The inlet angle, α, is selected with reference to the flow direction coming from the third row blades 24, and the exit angle, β, is preferably selected to provide a predetermined direction of flow into the fourth stage blades 28.
It should be noted that the difference between any pair of airfoil inlet and exit angles, α, β, at any given span location, SV4, may vary from the delta value, Δ, listed in Table 5 due to various conditions, such as manufacturing tolerances or other conditions. In particular, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SV4, may generally vary from the delta value, Δ, listed in Table 5 by at most 5%. More preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SV4, may vary from the delta value, Δ, listed in Table 5 by at most 3%. Most preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SV4, may vary from the delta value, Δ, listed in Table 5 by at most 1%. In other words, the amount of flow turning may vary slightly from the given predetermined delta value, Δ, within a percentage range of, for example, 5% to 1%. However, an optimal configuration for the airfoil of the vane 26 is believed to be provided by a configuration having a minimal variation from the given predetermined delta values, Δ.
Portions of sections of the airfoil for the vane 26 are described below in Table 6 (end of specification), generally located at the noted selected Z or spanwise locations described above for Table 5. It may be noted that the description provided by Table 6 comprises an exemplary, non-limiting description of leading edge and trailing edge airfoil sections forming the inlet and exit angles α, β.
The portions of the airfoil for the vane 26 described in Table 6 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 11) 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, and generally parallel to the span, SV4, of the airfoil for the vane 26. The Z coordinate values in Table 6 have an origin or zero value at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the vane 26, i.e., adjacent the inner endwall 82, and are presented as a percentage of the total span of the vane 26, and are presented as a percentage of the total span of the blade 28. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. Exemplary profiles for leading edge sections and trailing edge sections of the airfoil for the vane 26 are defined by the X and Y coordinate values, located at point locations, N, at selected locations in the Z direction normal to the X, Y plane. Each leading edge and trailing edge profile section at each selected radial Z location is determined by connecting the X and Y values at the point locations, N, with smooth, continuous arcs. Similarly, the surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the leading edge section and trailing edge section of the airfoil.
The leading edge section 90 at each Z location is described by successive data points N=1 to N=30 defining the leading edge section 90 as extending from the suction sidewall 80, around the leading edge 86, and along a portion of the pressure sidewall 78.
The trailing edge section 92 at each Z location is described in two parts. In particular, a first part of the trailing edge section 92 is described along the suction sidewall 80 by data points N=31 to N=40, and a second part of the trailing edge section 92 is described along the pressure sidewall 78 by data points N=41 to N=60. It may be noted that the data points N=31 and N=60 have the same X and Y coordinate values for continuity in presenting the data in Table 6, and are both located at or near the trailing edge 88 of the vane 26.
Referring to FIGS. 14-17, a configuration for the fourth stage blade 28 is described. In particular, referring initially to FIGS. 14 and 15, a fourth stage blade airfoil structure 96 is shown including one of the airfoils or blades 28 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 16, the blades 28 each include an outer wall comprising a generally concave pressure sidewall 98, and include an opposing generally convex suction sidewall 100. The sidewalls 98, 100 extend radially outwardly from an inner diameter endwall 102 to a blade tip 104, and extend generally axially in a chordal direction between a leading edge 106 and a trailing edge 108 of each of the blades 28. A blade root is defined by a dovetail 105 extending radially inwardly from the endwall 102 for mounting the blade 28 to the rotor 30. The endwall 102 is positioned at a location where it forms a boundary, i.e., an inner boundary, defining a portion of the flow path 13 for the working fluid.
FIG. 16 illustrates a cross section of the blade 28 at a radial location of about 50% of the span, SB4 (FIG. 14), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 15), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, SB4, of the airfoil for the blade 28. It should be noted that a central lengthwise axis 107 of the dovetail 105 is shown herein as extending at an angle relative to the direction of the longitudinal axis 32.
The cross section of FIG. 16 lies in the X-Y plane. As seen in FIG. 16, the blade 28 defines an airfoil mean line, CB4, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 98, 100. At the leading edge 106, a blade metal angle of each of the surfaces of the pressure and suction sides 98, 100 adjacent to the leading edge 106 is provided for directing incoming flow to the blade 28 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CB4, at the leading edge 106, i.e., tangential to the line CB4 at the airfoil leading edge 106.
At the trailing edge 108, a blade metal angle of the surfaces of the pressure and suction sides 98, 100 adjacent to the trailing edge 108 is provided for directing flow exiting from the blade 28 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, CB4, at the trailing edge 108, i.e., tangential to the line CB4 at the airfoil trailing edge 108.
The inlet angles, α, and exit angles, β, for the airfoil of the blade 28 are as described in Table 7 below. The Z coordinate locations are presented as a percentage of the total span of the blade 28. The values for the inlet angles, α, and exit angles, β, are defined at selected locations spaced at 10% increments along the span of the blade 28, where 0% is located adjacent to the inner endwall 102 and 100% is located adjacent to the blade tip 104. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 17.










TABLE 7





Z - Span %
α - LE Angle
β - TE Angle
Δ - Delta Value


















0
−28.00
39.00
67.00


10
−27.15
43.66
70.81


20
−25.18
40.17
65.35


30
−26.54
39.65
66.19


40
−25.46
40.56
66.02


50
−22.80
40.83
63.63


60
−19.17
41.93
61.10


70
−14.48
44.50
58.98


80
−8.66
47.56
56.22


90
−1.59
49.68
51.27


100
7.88
51.42
43.54









Table 7 further describes a predetermined difference between each pair of the airfoil inlet and exit angles, at any given span location, as defined by a delta value, Δ, presented as the absolute value of the difference between the leading edge or inlet angle, α, and the trailing edge or exit angle, β. The delta value, Δ, is representative of a change of direction of the flow between the leading edge 106 and trailing edge 108, where it may be understood that the amount of work extracted from the working gas is related to the difference between the inlet angle, α, and exit angle, β, of the flow. For example, increasing the delta value, Δ, may increase the amount of work extracted from the flow.
It should be noted that the difference between any pair of airfoil inlet and exit angles, α, β, at any given span location, SB4, may vary from the delta value, Δ, listed in Table 7 due to various conditions, such as manufacturing tolerances or other conditions. In particular, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SB4, may generally vary from the delta value, Δ, listed in Table 7 by at most 5%. More preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SB4, may vary from the delta value, Δ, listed in Table 7 by at most 3%. Most preferably, the difference between the airfoil inlet and exit angles, α, β, at any given span location, SB4, may vary from the delta value, Δ, listed in Table 7 by at most 1%. In other words, the amount of flow turning may vary slightly from the given predetermined delta value, Δ, within a percentage range of, for example, 5% to 1%. However, an optimal configuration for the airfoil of the blade 28 is believed to be provided by a configuration having a minimal variation from the given predetermined delta values, Δ.
Portions of sections of the airfoil for the blade 28 are described below in Table 8 (end of specification), generally located at the noted selected Z or spanwise locations described above for Table 7. It may be noted that the description provided by Table 8 comprises an exemplary, non-limiting description of leading edge and trailing edge airfoil sections forming the inlet and exit angles α, β.
The portions of the airfoil for the blade 28 described in Table 8 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 7) 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, and generally parallel to the span, SB4, of the airfoil for the blade 28. The Z coordinate values in Table 8 have an origin or zero value at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the blade 28, i.e., adjacent the inner endwall 102. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. Exemplary profiles for leading edge sections and trailing edge sections of the airfoil for the blade 28 are defined by the X and Y coordinate values, located at point locations, N, at selected locations in the Z direction normal to the X, Y plane. Each leading edge and trailing edge profile section at each selected radial Z location is determined by connecting the X and Y values at the point locations, N, with smooth, continuous arcs. Similarly, the surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the leading edge section and trailing edge section of the airfoil.
The leading edge section 110 at each Z location is described by successive data points N=1 to N=30 defining the leading edge section 106 as extending from the pressure sidewall 98, around the leading edge 106, and along a portion of the suction sidewall 100.
The trailing edge section 112 at each Z location is described in two parts. In particular, a first part of the trailing edge section 112 is described along the pressure sidewall 98 by data points N=31 to N=40, and a second part of the trailing edge section 112 is described along the suction sidewall 100 by data points N=41 to N=60. It may be noted that the data points N=31 and N=60 have the same X and Y coordinate values for continuity in presenting the data in Table 8, and are both located at or near the trailing edge 108 of the blade 28.
Tables 2, 4, 6 and 8
The tabular values given in Tables 2, 4, 6 and 8 below are in millimeters and represent leading edge section and trailing edge section 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 are determined relative to an origin of the coordinate system, as is typical of a Cartesian coordinate system.
The values presented in Tables 2, 4, 6 and 8 are generated and shown for determining the leading edge and trailing edge profile sections of the airfoil for the vane 22, blade 24, vane 26, and blade 28, respectively. Further, there are typical manufacturing tolerances as well as coatings which are typically accounted for in the actual profile of the airfoil for the vane 22, blade 24, vane 26, and blade 28. Accordingly, the values for the airfoil section profiles given in Tables 2, 4, 6 and 8 correspond to nominal dimensional values for uncoated airfoils. 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 Tables 2, 4, 6 and 8 below. Accordingly, a distance of approximately ±1% of a maximum airfoil height, in a direction normal to any surface location along the leading edge and trailing edge profile sections of the airfoils, defines an airfoil profile envelope for the leading edge and trailing edge profile sections of the airfoils described herein.
The coordinate values given in Tables 2, 4, 6 and 8 below in millimeters provide an exemplary, non-limiting, preferred nominal profile envelope for the leading and trailing edge profile sections of the respective third stage vane 22, third stage blade 24, fourth stage vane 26 and fourth stage blade 28. Further, the average Z value at 100% span for each of the airfoils may be approximately the following values: third stage vane 22=1145 mm; third stage blade 24=1191.7 mm; fourth stage vane 26=1268.5 mm; and fourth stage blade 28=1366.9 mm.









TABLE 2





N
X
Y















Third Stage Vane LE and TE at Z = 0%









1
596.2648
26.9033


2
590.7822
24.6028


3
586.0492
22.0131


4
583.2977
20.2043


5
579.7508
17.4640


6
577.7539
15.6668


7
575.2701
13.0861


8
573.4066
10.6876


9
572.5051
9.2178


10
571.6058
7.2832


11
571.2641
6.2166


12
571.0638
5.1478


13
571.0189
4.1549


14
571.1202
3.1517


15
571.3854
2.1680


16
571.8811
1.1281


17
572.4909
0.3042


18
573.2425
−0.3922


19
574.1054
−0.9375


20
575.1667
−1.3640


21
576.1508
−1.5788


22
577.1388
−1.6479


23
578.1001
−1.5879


24
579.5191
−1.3215


25
581.3417
−0.8171


26
582.7806
−0.3762


27
585.2828
0.4041


28
588.2156
1.2934


29
590.4211
1.9273


30
594.1185
2.8908


31
713.5055
−69.7089


32
712.6509
−68.1276


33
711.5355
−66.0592


34
710.6472
−64.4097


35
709.0968
−61.5306


36
707.2812
−58.1682


37
705.9196
−55.6607


38
703.6408
−51.5063


39
701.9556
−48.4797


40
699.1598
−43.5661


41
699.2449
−57.1262


42
701.0559
−59.1821


43
703.4869
−62.0163


44
704.9191
−63.7368


45
706.7917
−66.0574


46
708.3448
−68.0553


47
709.2102
−69.2011


48
710.2644
−70.6310


49
710.8103
−71.3872


50
711.1004
−71.6938


51
711.4806
−71.9307


52
711.9202
−72.0576


53
712.3720
−72.0517


54
712.7844
−71.9303


55
713.1268
−71.7171


56
713.4173
−71.4008


57
713.6213
−70.9985


58
713.7002
−70.5486


59
713.6540
−70.1037


60
713.5055
−69.7089







Third Stage Vane LE and TE at Z = 10%









1
597.2343
24.5387


2
591.5963
22.6658


3
586.6911
20.4113


4
583.8246
18.7786


5
580.1131
16.2419


6
578.0164
14.5469


7
575.4018
12.0809


8
573.4201
9.7664


9
572.4429
8.3406


10
571.4446
6.4512


11
571.0533
5.4001


12
570.8069
4.3438


13
570.7188
3.3566


14
570.7758
2.3531


15
570.9968
1.3619


16
571.4449
0.3051


17
572.016
−0.5418


18
572.7337
−1.2678


19
573.569
−1.8485


20
574.607
−2.3197


21
575.5778
−2.5769


22
576.559
−2.6895


23
577.5197
−2.6724


24
578.9671
−2.4791


25
580.8411
−2.0969


26
582.3269
−1.7505


27
584.9152
−1.1314


28
587.9494
−0.4578


29
590.2269
−0.0031


30
594.0284
0.6467


31
715.6596
−74.8040


32
714.8119
−73.2064


33
713.6936
−71.1230


34
712.7944
−69.4660


35
711.2109
−66.5815


36
709.3402
−63.2217


37
707.9302
−60.7201


38
705.5636
−56.5796


39
703.8134
−53.5639


40
700.9182
−48.6641


41
701.1117
−62.0388


42
702.9780
−64.1043


43
705.4785
−66.9583


44
706.9490
−68.6942


45
708.8679
−71.0396


46
710.4553
−73.0627


47
711.3362
−74.2258


48
712.4026
−75.6821


49
712.9507
−76.4550


50
713.2384
−76.7658


51
713.6166
−77.0076


52
714.0550
−77.1399


53
714.5067
−77.1391


54
714.9199
−77.0222


55
715.2641
−76.8124


56
715.5571
−76.4988


57
715.7644
−76.0978


58
715.8471
−75.6479


59
715.8047
−75.2015


60
715.6596
−74.8040







Third Stage Vane LE and TE at Z = 20%









1
598.5124
22.2312


2
592.6984
20.8232


3
587.6047
18.9181


4
584.6177
17.4581


5
580.7434
15.1052


6
578.5546
13.4933


7
575.8266
11.1118


8
573.733
8.8645


9
572.6702
7.4835


10
571.541
5.6490


11
571.0753
4.6193


12
570.7591
3.5804


13
570.6054
2.6009


14
570.5954
1.5960


15
570.7498
0.5932


16
571.1264
−0.4897


17
571.6398
−1.3710


18
572.3077
−2.1413


19
573.1029
−2.7744


20
574.1082
−3.3113


21
575.0609
−3.6304


22
576.0342
−3.8058


23
576.996
−3.8503


24
578.4802
−3.7459


25
580.4073
−3.4663


26
581.9323
−3.1719


27
584.5865
−2.6182


28
587.7041
−2.0581


29
590.0463
−1.7260


30
593.9526
−1.3373


31
717.7578
−80.2348


32
716.9089
−78.6221


33
715.7833
−76.5219


34
714.8744
−74.8538


35
713.2661
−71.9543


36
711.3574
−68.5824


37
709.9148
−66.0746


38
707.4902
−61.9268


39
705.6975
−58.9061


40
702.7394
−53.9957


41
703.0133
−67.2639


42
704.9154
−69.3534


43
707.4592
−72.2454


44
708.9537
−74.0062


45
710.9035
−76.3857


46
712.5166
−78.4382


47
713.4109
−79.6188


48
714.4913
−81.0984


49
715.0453
−81.8847


50
715.3312
−82.1956


51
715.7078
−82.4377


52
716.1450
−82.5702


53
716.5960
−82.5697


54
717.0091
−82.4529


55
717.3537
−82.2432


56
717.6477
−81.9297


57
717.8564
−81.5289


58
717.9410
−81.0790


59
717.9008
−80.6325


60
717.7578
−80.2348







Third Stage Vane LE and TE at Z = 30%









1
593.5317
19.6581


2
588.2588
17.8480


3
585.1682
16.4125


4
581.1687
14.0515


5
578.9158
12.4143


6
576.1160
9.9817


7
573.9552
7.6922


8
572.8399
6.2954


9
571.6248
4.4478


10
571.1059
3.4099


11
570.7472
2.3784


12
570.5540
1.4007


13
570.5044
0.3924


14
570.6200
−0.6194


15
570.9558
−1.7191


16
571.4372
−2.6210


17
572.0782
−3.4166


18
572.8525
−4.0785


19
573.8416
−4.6507


20
574.7862
−5.0025


21
575.7567
−5.2106


22
576.7206
−5.2870


23
578.2466
−5.2236


24
580.2287
−4.9708


25
581.7933
−4.6757


26
584.5088
−4.0877


27
587.6940
−3.4762


28
590.0897
−3.1254


29
594.0979
−2.7628


30
597.0399
−2.6675


31
719.7108
−85.5849


32
718.8380
−83.9475


33
717.6859
−81.8126


34
716.7591
−80.1153


35
715.1257
−77.1620


36
713.1949
−73.7243


37
711.7399
−71.1658


38
709.3008
−66.9318


39
707.5013
−63.8469


40
704.5374
−58.8303


41
704.8449
−72.3017


42
706.7635
−74.4470


43
709.3262
−77.4176


44
710.8320
−79.2254


45
712.7993
−81.6655


46
714.4317
−83.7658


47
715.3397
−84.9714


48
716.4423
−86.4782


49
717.0114
−87.2761


50
717.2987
−87.5832


51
717.6762
−87.8199


52
718.1134
−87.9462


53
718.5638
−87.9389


54
718.9756
−87.8160


55
719.3184
−87.6011


56
719.6101
−87.2830


57
719.8163
−86.8787


58
719.8983
−86.4272


59
719.8557
−85.9809


60
719.7108
−85.5849







Third Stage Vane LE and TE at Z = 40%









1
593.9380
19.2543


2
588.5117
17.2625


3
585.3394
15.7066


4
581.2477
13.1695


5
578.9497
11.4206


6
576.1016
8.8343


7
573.9080
6.4149


8
572.7749
4.9477


9
571.5321
3.0198


10
570.9942
1.9430


11
570.6328
0.9088


12
570.4378
−0.0719


13
570.3874
−1.0836


14
570.5034
−2.0989


15
570.8411
−3.2018


16
571.3254
−4.1057


17
571.9706
−4.9020


18
572.7496
−5.5632


19
573.7442
−6.1331


20
574.6933
−6.4815


21
575.6677
−6.6853


22
576.6346
−6.7569


23
578.2084
−6.6797


24
580.2517
−6.3896


25
581.8646
−6.0654


26
584.6566
−5.3999


27
587.9148
−4.6284


28
590.3639
−4.1393


29
594.4772
−3.5651


30
597.5047
−3.3331


31
721.4481
−90.7790


32
720.5383
−89.1035


33
719.3499
−86.9121


34
718.4029
−85.1649


35
716.7497
−82.1160


36
714.8152
−78.5560


37
713.3673
−75.9007


38
710.9534
−71.4983


39
709.1786
−68.2866


40
706.2590
−63.0597


41
706.4934
−77.0511


42
708.4131
−79.2863


43
710.9783
−82.3767


44
712.4878
−84.2534


45
714.4659
−86.7797


46
716.1155
−88.9463


47
717.0388
−90.1852


48
718.1700
−91.7262


49
718.7599
−92.5378


50
719.0509
−92.8403


51
719.4314
−93.0702


52
719.8708
−93.1876


53
720.3220
−93.1706


54
720.7333
−93.0382


55
721.0747
−92.8147


56
721.3638
−92.4886


57
721.5665
−92.0777


58
721.6442
−91.6220


59
721.5972
−91.1741


60
721.4481
−90.7790







Third Stage Vane LE and TE at Z = 50%









1
594.3024
19.1197


2
588.7155
16.9904


3
585.4483
15.3519


4
581.2305
12.6982


5
578.8606
10.8749


6
575.9261
8.1810


7
573.6765
5.6580


8
572.5222
4.1262


9
571.2573
2.1189


10
570.7121
0.9996


11
570.3615
−0.0352


12
570.1767
−1.0158


13
570.1368
−2.0262


14
570.2638
−3.0392


15
570.6139
−4.1384


16
571.1089
−5.0376


17
571.7637
−5.8278


18
572.5511
−6.4817


19
573.5533
−7.0420


20
574.5073
−7.3814


21
575.4849
−7.5759


22
576.4530
−7.6381


23
578.0823
−7.5356


24
580.1949
−7.2090


25
581.8648
−6.8708


26
584.7549
−6.1733


27
588.1141
−5.2966


28
590.6317
−4.6900


29
594.8530
−3.8997


30
597.9691
−3.5356


31
722.8869
−95.9146


32
721.9544
−94.1905


33
720.7485
−91.9290


34
719.7960
−90.1213


35
718.1479
−86.9585


36
716.2361
−83.2556


37
714.8128
−80.4889


38
712.4483
−75.8955


39
710.7128
−72.5414


40
707.8551
−67.0810


41
707.8061
−81.6850


42
709.7202
−84.0223


43
712.2856
−87.2430


44
713.8005
−89.1925


45
715.7937
−91.8084


46
717.4650
−94.0434


47
718.4058
−95.3170


48
719.5639
−96.8973


49
720.1698
−97.7280


50
720.4636
−98.0311


51
720.8480
−98.2594


52
721.2918
−98.3733


53
721.7477
−98.3508


54
722.1634
−98.2118


55
722.5084
−97.9815


56
722.8007
−97.6477


57
723.0057
−97.2290


58
723.0845
−96.7664


59
723.0373
−96.3131


60
722.8869
−95.9146







Third Stage Vane LE and TE at Z = 60%









1
594.9078
19.0580


2
589.1302
17.0270


3
585.7366
15.4427


4
581.3289
12.8450


5
578.8413
11.0408


6
575.7576
8.3491


7
573.4013
5.7987


8
572.1995
4.2373


9
570.8829
2.1860


10
570.3212
1.0368


11
569.9754
0.0167


12
569.7929
−0.9506


13
569.7526
−1.9479


14
569.8770
−2.9493


15
570.2216
−4.0384


16
570.7088
−4.9319


17
571.3534
−5.7198


18
572.1292
−6.3751


19
573.1177
−6.9411


20
574.0599
−7.2887


21
575.0264
−7.4938


22
575.9849
−7.5678


23
577.6755
−7.4690


24
579.8649
−7.1459


25
581.5979
−6.8232


26
584.6030
−6.1642


27
588.0934
−5.3088


28
590.6975
−4.6819


29
595.0270
−3.8207


30
598.2299
−3.4549


31
723.9476
−101.0275


32
723.0299
−99.2470


33
721.8492
−96.9093


34
720.9205
−95.0391


35
719.3185
−91.7650


36
717.4623
−87.9307


37
716.0785
−85.0664


38
713.7743
−80.3129


39
712.0776
−76.8438


40
709.2722
−71.2010


41
708.6668
−86.2958


42
710.5751
−88.7275


43
713.1486
−92.0629


44
714.6765
−94.0743


45
716.6955
−96.7657


46
718.3957
−99.0591


47
719.3549
−100.3643


48
720.5295
−101.9881


49
721.1376
−102.8465


50
721.4303
−103.1594


51
721.8170
−103.3971


52
722.2669
−103.5186


53
722.7321
−103.5011


54
723.1589
−103.3641


55
723.5157
−103.1330


56
723.8211
−102.7957


57
724.0393
−102.3707


58
724.1299
−101.8994


59
724.0919
−101.4361


60
723.9476
−101.0275







Third Stage Vane LE and TE at Z = 70%









1
595.7258
19.7156


2
589.7641
17.7809


3
586.2549
16.2386


4
581.6816
13.6722


5
579.0915
11.8707


6
575.8712
9.1604


7
573.4025
6.5727


8
572.1385
4.9824


9
570.7384
2.894


10
570.1272
1.7259


11
569.7694
0.7591


12
569.5683
−0.1626


13
569.5009
−1.119


14
569.5883
−2.0863


15
569.8801
−3.1482


16
570.3121
−4.0303


17
570.8962
−4.8207


18
571.6090
−5.4927


19
572.5272
−6.0927


20
573.4106
−6.4816


21
574.3240
−6.736


22
575.2367
−6.8647


23
576.9887
−6.8532


24
579.2676
−6.568


25
581.0676
−6.2421


26
584.1857
−5.5636


27
587.8049
−4.6869


28
590.4943
−4.0296


29
594.9371
−3.1074


30
598.2319
−2.7433


31
724.7393
−106.1285


32
723.8659
−104.2804


33
722.7420
−101.8556


34
721.8573
−99.9170


35
720.3277
−96.5265


36
718.5461
−92.5613


37
717.2100
−89.6032


38
714.9715
−84.7004


39
713.3133
−81.1269


40
710.5568
−75.3207


41
709.3112
−90.7604


42
711.2150
−93.2892


43
713.7960
−96.7456


44
715.3344
−98.8244


45
717.3719
−101.6019


46
719.0897
−103.9665


47
720.0577
−105.3129


48
721.2312
−106.9961


49
721.8287
−107.8929


50
722.1137
−108.2187


51
722.4965
−108.4710


52
722.9475
−108.6074


53
723.4190
−108.6031


54
723.8561
−108.4766


55
724.2257
−108.2525


56
724.5471
−107.9191


57
724.7834
−107.4942


58
724.8922
−107.0186


59
724.8705
−106.5474


60
724.7393
−106.1285







Third Stage Vane LE and TE at Z = 80%









1
596.6447
21.6899


2
590.5380
19.6041


3
586.9611
17.9464


4
582.3246
15.2076


5
579.7033
13.2965


6
576.4329
10.4354


7
573.8972
7.7273


8
572.5751
6.0791


9
571.0717
3.9345


10
570.3680
2.7552


11
569.9785
1.8907


12
569.7341
1.0554


13
569.6082
0.1747


14
569.6171
−0.7298


15
569.7977
−1.7412


16
570.1157
−2.6023


17
570.5762
−3.3981


18
571.1609
−4.1025


19
571.9360
−4.7678


20
572.6983
−5.2354


21
573.5009
−5.5836


22
574.3168
−5.8178


23
576.1214
−6.0091


24
578.5001
−5.7882


25
580.3656
−5.403


26
583.5725
−4.5433


27
587.2815
−3.456


28
590.0336
−2.6599


29
594.5908
−1.5464


30
597.9836
−1.0538


31
725.4432
−111.1990


32
724.6232
−109.2665


33
723.5627
−106.7348


34
722.7238
−104.7137


35
721.2655
−101.1836


36
719.5556
−97.0611


37
718.2664
−93.9885


38
716.0960
−88.9000


39
714.4818
−85.1930


40
711.7898
−79.1711


41
710.0909
−94.8710


42
711.9927
−97.5192


43
714.5682
−101.1391


44
716.1004
−103.3171


45
718.1242
−106.2294


46
719.8236
−108.7122


47
720.7774
−110.1278


48
721.9259
−111.9010


49
722.5053
−112.8485


50
722.7739
−113.1806


51
723.1417
−113.4433


52
723.5812
−113.5936


53
724.0463
−113.6054


54
724.4821
−113.4950


55
724.8553
−113.2857


56
725.1852
−112.9665


57
725.4346
−112.5536


58
725.5601
−112.0861


59
725.5568
−111.6185


60
725.4432
−111.1990







Third Stage Vane LE and TE at Z = 90%









1
597.4244
24.4103


2
591.1925
22.0496


3
587.5676
20.2064


4
582.9066
17.2161


5
580.2828
15.1584


6
577.0043
12.1108


7
574.4377
9.2661


8
573.0772
7.5566


9
571.4955
5.3547


10
570.7109
4.1656


11
570.2944
3.3948


12
570.0125
2.6384


13
569.8356
1.8269


14
569.7753
0.9804


15
569.8569
0.0171


16
570.0723
−0.8222


17
570.4209
−1.6194


18
570.8884
−2.3496


19
571.5306
−3.0700


20
572.1788
−3.6057


21
572.8752
−4.0366


22
573.5964
−4.3651


23
575.4333
−4.7586


24
577.8883
−4.6116


25
579.8014
−4.1652


26
583.0600
−3.0933


27
586.8127
−1.7441


28
589.6013
−0.7815


29
594.2568
0.5441


30
597.7376
1.1898


31
726.1397
−116.0867


32
725.3656
−114.0569


33
724.3566
−111.4022


34
723.5531
−109.2855


35
722.1483
−105.5923


36
720.4948
−101.2819


37
719.2471
−98.0691


38
717.1460
−92.7466


39
715.5839
−88.8669


40
712.9807
−82.5590


41
711.0878
−98.4837


42
712.9924
−101.2744


43
715.5505
−105.1025


44
717.0600
−107.4134


45
719.0380
−110.5120


46
720.6838
−113.1614


47
721.6019
−114.6745


48
722.7077
−116.5661


49
723.2681
−117.5726


50
723.5139
−117.9007


51
723.8571
−118.1656


52
724.2727
−118.3250


53
724.7177
−118.3522


54
725.1391
−118.2611


55
725.5039
−118.0726


56
725.8310
−117.7771


57
726.0844
−117.3888


58
726.2210
−116.9436


59
726.2340
−116.4939


60
726.1397
−116.0867







Third Stage Vane LE and TE at Z = 100%









1
597.8976
27.1052


2
591.5444
24.5466


3
587.8646
22.5690


4
583.1563
19.3954


5
580.5157
17.2329


6
577.2226
14.0567


7
574.6419
11.1188


8
573.2677
9.3658


9
571.6590
7.1198


10
570.8441
5.9163


11
570.4230
5.1880


12
570.1311
4.4684


13
569.9379
3.6902


14
569.8528
2.8730


15
569.8961
1.9364


16
570.0697
1.1126


17
570.3707
0.3214


18
570.7866
−0.4130


19
571.3680
−1.1497


20
571.9619
−1.7088


21
572.6060
−2.1703


22
573.2787
−2.5356


23
575.1321
−3.0310


24
577.6269
−2.9446


25
579.5670
−2.4783


26
582.8498
−1.2834


27
586.6199
0.2376


28
589.4324
1.3076


29
594.1764
2.7316


30
597.7334
3.4113


31
726.7519
−120.5058


32
726.0066
−118.3830


33
725.0298
−115.6086


34
724.2490
−113.3979


35
722.8811
−109.5415


36
721.2734
−105.0389


37
720.0653
−101.6797


38
718.0401
−96.1086


39
716.5412
−92.0425


40
714.0527
−85.4224


41
712.0662
−101.5573


42
713.9726
−104.4968


43
716.5082
−108.5452


44
717.9898
−110.9974


45
719.9139
−114.2945


46
721.4987
−117.1210


47
722.3777
−118.7368


48
723.4428
−120.7487


49
723.9904
−121.8115


50
724.2141
−122.1302


51
724.5318
−122.3925


52
724.9210
−122.5575


53
725.3416
−122.5986


54
725.7432
−122.5270


55
726.0939
−122.3615


56
726.4120
−122.0935


57
726.6628
−121.7351


58
726.8047
−121.3190


59
726.8297
−120.8942


60
726.7519
−120.5058


















TABLE 4





N
X
Y















Third Stage Blade LE and TE at Z = 0%









1
777.2090
−11.2552


2
773.7695
−9.4742


3
771.7330
−8.2691


4
769.0597
−6.4649


5
767.5310
−5.2796


6
765.6184
−3.5540


7
764.1601
−1.9273


8
763.4399
−0.9198


9
762.7334
0.4330


10
762.5082
1.1982


11
762.4437
1.7103


12
762.4419
2.1665


13
762.4964
2.6150


14
762.6109
3.0473


15
762.8107
3.5039


16
763.0494
3.8741


17
763.3430
4.2023


18
763.6859
4.4833


19
764.1201
4.7392


20
764.5395
4.9111


21
764.9811
5.0317


22
765.4356
5.1020


23
766.5195
5.0931


24
767.9273
4.9162


25
769.0422
4.7272


26
770.9828
4.3631


27
773.2465
3.9127


28
774.9361
3.5716


29
777.7435
3.0106


30
779.7982
2.6110


31
877.7744
32.2651


32
877.0831
31.2042


33
876.1688
29.8234


34
875.4316
28.7275


35
874.1275
26.8254


36
872.5764
24.6195


37
871.3995
22.9842


38
869.4108
20.2911


39
867.9292
18.3412


40
865.4576
15.1975


41
866.2242
24.3089


42
867.7254
25.6578


43
869.7366
27.5321


44
870.9236
28.6744


45
872.4834
30.2160


46
873.7882
31.5408


47
874.5212
32.2988


48
875.4209
33.2428


49
875.8900
33.7410


50
876.1287
33.9343


51
876.4252
34.0673


52
876.7536
34.1142


53
877.0837
34.0685


54
877.3801
33.9471


55
877.6167
33.7618


56
877.8057
33.5031


57
877.9293
33.1935


58
877.9626
32.8633


59
877.9047
32.5434


60
877.7744
32.2651







Third Stage Blade LE and TE at Z = 10%









1
784.7477
−14.3864


2
781.0620
−12.8740


3
777.8247
−11.2550


4
775.9113
−10.1465


5
773.3969
−8.4844


6
771.9499
−7.4006


7
770.1162
−5.8411


8
768.6683
−4.3955


9
767.9182
−3.5054


10
767.1460
−2.2847


11
766.8941
−1.5747


12
766.8169
−1.1671


13
766.7933
−0.8032


14
766.8159
−0.4451


15
766.8881
−0.0995


16
767.0286
0.2657


17
767.2045
0.5620


18
767.4268
0.8247


19
767.6907
1.0493


20
768.0293
1.2526


21
768.3594
1.3878


22
768.7089
1.4815


23
769.0702
1.5352


24
770.0938
1.5420


25
771.4282
1.3576


26
772.4837
1.1549


27
774.3209
0.7794


28
776.4672
0.3428


29
778.0726
0.0304


30
780.7459
−0.4555


31
874.9987
32.4133


32
874.3507
31.4119


33
873.4935
30.1084


34
872.8020
29.0739


35
871.5776
27.2789


36
870.1185
25.1988


37
869.0088
23.6584


38
867.1279
21.1257


39
865.7231
19.2945


40
863.3772
16.3445


41
864.1151
24.6228


42
865.5171
25.9445


43
867.3960
27.7770


44
868.5050
28.8922


45
869.9622
30.3955


46
871.1813
31.6863


47
871.8659
32.4246


48
872.7061
33.3437


49
873.1442
33.8286


50
873.3737
34.0222


51
873.6614
34.1576


52
873.9821
34.2087


53
874.3061
34.1687


54
874.5981
34.0538


55
874.8320
33.8754


56
875.0199
33.6241


57
875.1441
33.3221


58
875.1795
32.9992


59
875.1248
32.6859


60
874.9987
32.4133







Third Stage Blade LE and TE at Z = 20%









1
784.1823
−13.2656


2
781.0625
−11.9217


3
779.2094
−10.9896


4
776.7629
−9.5732


5
775.3489
−8.6373


6
773.5560
−7.2658


7
772.1513
−5.9595


8
771.4410
−5.1312


9
770.7720
−3.9590


10
770.6076
−3.2728


11
770.5884
−2.9708


12
770.6004
−2.7006


13
770.6405
−2.4327


14
770.7094
−2.1712


15
770.8210
−1.8893


16
770.9501
−1.6540


17
771.1066
−1.4370


18
771.2882
−1.2409


19
771.5181
−1.0474


20
771.7411
−0.9010


21
771.9775
−0.7795


22
772.2235
−0.6836


23
773.1720
−0.4856


24
774.4469
−0.4919


25
775.4602
−0.6003


26
777.2199
−0.8627


27
779.2713
−1.2059


28
780.8042
−1.4612


29
783.3552
−1.8656


30
785.2253
−2.1401


31
871.9412
32.5122


32
871.3330
31.5599


33
870.5276
30.3209


34
869.8773
29.3382


35
868.7246
27.6337


36
867.3499
25.6594


37
866.3041
24.1977


38
864.5316
21.7941


39
863.2084
20.0558


40
861.0014
17.2531


41
861.7633
24.7356


42
863.0497
26.0615


43
864.7784
27.8909


44
865.8019
28.9990


45
867.1509
30.4871


46
868.2834
31.7596


47
868.9212
32.4852


48
869.7057
33.3863


49
870.1157
33.8607


50
870.3359
34.0544


51
870.6145
34.1923


52
870.9271
34.2482


53
871.2447
34.2146


54
871.5320
34.1071


55
871.7631
33.9365


56
871.9501
33.6937


57
872.0751
33.4003


58
872.1131
33.0855


59
872.0624
32.7791


60
871.9412
32.5122







Third Stage Blade LE and TE at Z = 30%









1
785.8363
−13.8272


2
782.8010
−12.6386


3
780.9949
−11.8022


4
778.6096
−10.5124


5
777.2330
−9.6461


6
775.4975
−8.3555


7
774.1616
−7.1015


8
773.5062
−6.2939


9
772.9367
−5.1433


10
772.8357
−4.4738


11
772.8556
−4.2377


12
772.8920
−4.0253


13
772.9447
−3.8126


14
773.0127
−3.6015


15
773.1071
−3.3686


16
773.2070
−3.1678


17
773.3221
−2.9750


18
773.4513
−2.7913


19
773.6115
−2.5970


20
773.7653
−2.4365


21
773.9284
−2.2900


22
774.0996
−2.1597


23
774.9863
−1.8069


24
776.2180
−1.6726


25
777.2034
−1.7082


26
778.9085
−1.8893


27
780.8911
−2.1758


28
782.3701
−2.4006


29
784.8288
−2.7606


30
786.6296
−3.0053


31
868.7737
32.5288


32
868.1916
31.6164


33
867.4202
30.4301


34
866.7970
29.4896


35
865.6922
27.8589


36
864.3751
25.9701


37
863.3741
24.5713


38
861.6805
22.2695


39
860.4189
20.6030


40
858.3195
17.9121


41
859.1508
24.8207


42
860.3482
26.1405


43
861.9617
27.9546


44
862.9198
29.0498


45
864.1863
30.5161


46
865.2531
31.7659


47
865.8554
32.4770


48
866.5980
33.3584


49
866.9867
33.8217


50
867.1991
34.0135


51
867.4696
34.1516


52
867.7744
34.2098


53
868.0851
34.1805


54
868.3668
34.0786


55
868.5937
33.9144


56
868.7780
33.6792


57
868.9018
33.3942


58
868.9402
33.0876


59
868.8915
32.7890


60
868.7737
32.5288







Third Stage Blade LE and TE at Z = 40%









1
789.7414
−16.1873


2
786.4276
−15.1433


3
783.5017
−13.9623


4
781.7674
−13.1241


5
779.4876
−11.8248


6
778.1798
−10.9490


7
776.5404
−9.6471


8
775.2909
−8.3908


9
774.6811
−7.5910


10
774.1423
−6.4738


11
774.0330
−5.8289


12
774.0430
−5.6148


13
774.0681
−5.4206


14
774.1076
−5.2245


15
774.1609
−5.0284


16
774.2370
−4.8100


17
774.3191
−4.6198


18
774.4149
−4.4351


19
774.5233
−4.2573


20
774.6588
−4.0669


21
774.7895
−3.9079


22
774.9290
−3.7607


23
775.0760
−3.6276


24
775.9066
−3.2248


25
777.0894
−3.0512


26
778.0432
−3.0710


27
779.6906
−3.2372


28
781.6051
−3.5158


29
783.0332
−3.7356


30
785.4075
−4.0771


31
865.6421
32.3974


32
865.0705
31.5187


33
864.3136
30.3761


34
863.7029
29.4701


35
862.6216
27.8988


36
861.3350
26.0780


37
860.3589
24.7288


38
858.7113
22.5066


39
857.4869
20.8960


40
855.4547
18.2918


41
856.3580
24.9125


42
857.5099
26.1950


43
859.0632
27.9570


44
859.9862
29.0203


45
861.2068
30.4436


46
862.2353
31.6565


47
862.8162
32.3466


48
863.5324
33.2019


49
863.9073
33.6516


50
864.1139
33.8388


51
864.3773
33.9739


52
864.6747
34.0311


53
864.9779
34.0029


54
865.2526
33.9039


55
865.4736
33.7442


56
865.6526
33.5152


57
865.7723
33.2377


58
865.8082
32.9395


59
865.7589
32.6496


60
865.6421
32.3974







Third Stage Blade LE and TE at Z = 50%









1
787.6933
−16.8435


2
784.9087
−15.7595


3
783.2613
−14.9770


4
781.1004
−13.7522


5
779.8639
−12.9210


6
778.3156
−11.6788


7
777.1396
−10.4701


8
776.5643
−9.7004


9
776.0287
−8.6407


10
775.8843
−8.0319


11
775.8683
−7.8276


12
775.8699
−7.6407


13
775.8867
−7.4511


14
775.9189
−7.2608


15
775.9737
−7.0485


16
776.0386
−6.8636


17
776.1186
−6.6844


18
776.2127
−6.5126


19
776.3332
−6.3300


20
776.4517
−6.1789


21
776.5792
−6.0402


22
776.7143
−5.9153


23
777.4642
−5.4847


24
778.5662
−5.2677


25
779.4685
−5.2605


26
781.0325
−5.3772


27
782.8546
−5.5881


28
784.2158
−5.7575


29
786.4813
−6.0197


30
788.1420
−6.1876


31
862.5971
31.9946


32
862.0357
31.1513


33
861.2948
30.0533


34
860.6988
29.1816


35
859.6474
27.6678


36
858.4014
25.9108


37
857.4593
24.6070


38
855.8736
22.4570


39
854.6983
20.8969


40
852.7521
18.3717


41
853.6172
24.8015


42
854.7338
26.0323


43
856.2387
27.7251


44
857.1324
28.7477


45
858.3136
30.1175


46
859.3081
31.2859


47
859.8694
31.9510


48
860.5611
32.7759


49
860.9231
33.2098


50
861.1236
33.3914


51
861.3796
33.5226


52
861.6686
33.5780


53
861.9631
33.5505


54
862.2296
33.4542


55
862.4434
33.2990


56
862.6161
33.0766


57
862.7306
32.8072


58
862.7633
32.5182


59
862.7129
32.2378


60
862.5971
31.9946







Third Stage Blade LE and TE at Z = 60%









1
790.8423
−18.5730


2
788.2101
−17.8389


3
786.6433
−17.2720


4
784.5773
−16.3439


5
783.3889
−15.6927


6
781.8917
−14.6769


7
780.7523
−13.6240


8
780.1977
−12.9247


9
779.6676
−11.9492


10
779.4981
−11.3883


11
779.4668
−11.2049


12
779.4526
−11.0362


13
779.4517
−10.8641


14
779.4648
−10.6905


15
779.4962
−10.4957


16
779.5390
−10.3250


17
779.5956
−10.1585


18
779.6650
−9.9979


19
779.7569
−9.8261


20
779.8494
−9.6828


21
779.9506
−9.5499


22
780.0593
−9.4286


23
780.6944
−8.9372


24
781.6779
−8.6039


25
782.5046
−8.5133


26
783.9563
−8.4823


27
785.6580
−8.5042


28
786.9328
−8.5383


29
789.0567
−8.6106


30
790.6147
−8.6629


31
859.6988
31.1803


32
859.1630
30.3822


33
858.4604
29.3400


34
857.8984
28.5105


35
856.9128
27.0657


36
855.7529
25.3832


37
854.8803
24.1315


38
853.4175
22.0633


39
852.3362
20.5603


40
850.5486
18.1260


41
851.1694
24.2588


42
852.2268
25.4415


43
853.6514
27.0692


44
854.4970
28.0527


45
855.6147
29.3699


46
856.5561
30.4930


47
857.0878
31.1320


48
857.7433
31.9240


49
858.0865
32.3402


50
858.2788
32.5171


51
858.5253
32.6456


52
858.8041
32.7012


53
859.0887
32.6764


54
859.3463
32.5851


55
859.5528
32.4365


56
859.7196
32.2227


57
859.8300
31.9633


58
859.8610
31.6848


59
859.8115
31.4145


60
859.6988
31.1803







Third Stage Blade LE and TE at Z = 70%









1
794.6279
−20.3073


2
792.1465
−19.9546


3
790.6592
−19.6128


4
788.6884
−18.9803


5
787.5497
−18.5007


6
786.1091
−17.6965


7
785.0128
−16.7950


8
784.4829
−16.1701


9
783.9688
−15.2853


10
783.7880
−14.7769


11
783.7521
−14.6200


12
783.7306
−14.4750


13
783.7194
−14.3261


14
783.7189
−14.1749


15
783.7315
−14.0038


16
783.7542
−13.8524


17
783.7880
−13.7029


18
783.8324
−13.5569


19
783.8937
−13.3984


20
783.9576
−13.2639


21
784.0293
−13.1367


22
784.1082
−13.0182


23
784.6332
−12.4776


24
785.4961
−12.0322


25
786.2429
−11.8525


26
787.5752
−11.6713


27
789.1465
−11.5185


28
790.3255
−11.4285


29
792.2897
−11.3134


30
793.7301
−11.2407


31
856.7725
29.6890


32
856.2726
28.9481


33
855.6205
27.9783


34
855.1012
27.2045


35
854.1954
25.8536


36
853.1355
24.2759


37
852.3416
23.0996


38
851.0151
21.1527


39
850.0366
19.7362


40
848.4206
17.4407


41
848.7470
23.1611


42
849.7372
24.2776


43
851.0709
25.8148


44
851.8624
26.7437


45
852.9083
27.9881


46
853.7892
29.0490


47
854.2866
29.6524


48
854.9001
30.4003


49
855.2213
30.7933


50
855.4060
30.9650


51
855.6432
31.0906


52
855.9119
31.1461


53
856.1863
31.1241


54
856.4348
31.0378


55
856.6339
30.8960


56
856.7946
30.6911


57
856.9008
30.4421


58
856.9302
30.1744







Third Stage Blade LE and TE at Z = 80%









1
797.3742
−22.0119


2
795.0547
−21.7984


3
793.6666
−21.5141


4
791.8357
−20.9258


5
790.7847
−20.4558


6
789.4644
−19.6619


7
788.4666
−18.7956


8
787.9833
−18.2132


9
787.4977
−17.4074


10
787.3155
−16.9478


11
787.2792
−16.8120


12
787.2554
−16.6858


13
787.2400
−16.5555


14
787.2334
−16.4226


15
787.2369
−16.2712


16
787.2498
−16.1365


17
787.2721
−16.0027


18
787.3035
−15.8711


19
787.3489
−15.7272


20
787.3975
−15.6041


21
787.4531
−15.4870


22
787.5153
−15.3769


23
787.9728
−14.8505


24
788.7457
−14.3844


25
789.4249
−14.1671


26
790.6472
−13.9377


27
792.0902
−13.7702


28
793.1702
−13.6704


29
794.9655
−13.4969


30
796.2791
−13.3484


31
853.4873
27.1206


32
853.0153
26.4478


33
852.3967
25.5696


34
851.9021
24.8706


35
851.0358
23.6535


36
850.0178
22.2361


37
849.2534
21.1814


38
847.9754
19.4377


39
847.0338
18.1693


40
845.4835
16.1113


41
845.7746
21.4065


42
846.7316
22.3922


43
848.0219
23.7508


44
848.7869
24.5743


45
849.7951
25.6818


46
850.6403
26.6315


47
851.1153
27.1745


48
851.6985
27.8505


49
852.0025
28.2072


50
852.1855
28.3706


51
852.4183
28.4888


52
852.6803
28.5389


53
852.9461
28.5143


54
853.1854
28.4279


55
853.3758
28.2886


56
853.5277
28.0888


57
853.6260
27.8470


58
853.6495
27.5880


59
853.5976
27.3373


60
853.4873
27.1206







Third Stage Blade LE and TE at Z = 90%









1
799.0323
−22.7321


2
796.9002
−22.5431


3
795.6267
−22.2668


4
793.9513
−21.6829


5
792.9933
−21.2136


6
791.7914
−20.4396


7
790.8749
−19.6352


8
790.4213
−19.1125


9
789.9501
−18.3956


10
789.7709
−17.9819


11
789.7352
−17.8587


12
789.7113
−17.7441


13
789.6951
−17.6259


14
789.6871
−17.5051


15
789.6880
−17.3676


16
789.6979
−17.2451


17
789.7166
−17.1234


18
789.7437
−17.0035


19
789.7835
−16.8724


20
789.8265
−16.7601


21
789.8762
−16.6531


22
789.9320
−16.5524


23
790.3515
−16.0756


24
791.0636
−15.6527


25
791.6883
−15.4382


26
792.8128
−15.2179


27
794.1389
−15.0959


28
795.1276
−15.0273


29
796.7663
−14.8554


30
797.9610
−14.6701


31
849.6736
23.5436


32
849.2233
22.9472


33
848.6255
22.1749


34
848.1424
21.5650


35
847.2866
20.5111


36
846.2697
19.2945


37
845.5010
18.3946


38
844.2126
16.9122


39
843.2652
15.8347


40
841.7151
14.0821


41
842.1383
18.9979


42
843.0821
19.8058


43
844.3587
20.9200


44
845.1161
21.5985


45
846.1110
22.5182


46
846.9393
23.3161


47
847.4014
23.7770


48
847.9644
24.3566


49
848.2557
24.6652


50
848.4428
24.8169


51
848.6763
24.9226


52
848.9349
24.9610


53
849.1940
24.9267


54
849.4248
24.8332


55
849.6058
24.6902


56
849.7469
24.4897


57
849.8341
24.2502


58
849.8479
23.9963


59
849.7887
23.7525


60
849.6736
23.5436







Third Stage Blade LE and TE at Z = 100%









1
800.4316
−21.0530


2
798.4947
−21.1569


3
797.3160
−21.1225


4
795.7258
−20.9386


5
794.7884
−20.7404


6
793.5724
−20.3491


7
792.5986
−19.8609


8
792.1013
−19.4918


9
791.5980
−18.9105


10
791.4213
−18.5438


11
791.3858
−18.4257


12
791.3618
−18.3174


13
791.3451
−18.2065


14
791.3357
−18.0940


15
791.3340
−17.9663


16
791.3403
−17.8526


17
791.3541
−17.7394


18
791.3751
−17.6276


19
791.4072
−17.5042


20
791.4431
−17.3976


21
791.4856
−17.2944


22
791.5346
−17.1956


23
791.9135
−16.7505


24
792.5820
−16.3710


25
793.1639
−16.1695


26
794.2055
−15.9198


27
795.4339
−15.7059


28
796.3509
−15.5577


29
797.8714
−15.2815


30
798.9795
−15.0463


31
845.4099
19.9393


32
845.0170
19.4184


33
844.4970
18.7424


34
844.0779
18.2071


35
843.3379
17.2797


36
842.4614
16.2055


37
841.8005
15.4087


38
840.6944
14.0929


39
839.8814
13.1348


40
838.5505
11.5747


41
838.4809
16.1266


42
839.3313
16.8432


43
840.4855
17.8259


44
841.1721
18.4215


45
842.0761
19.2262


46
842.8305
19.9223


47
843.2522
20.3239


48
843.7664
20.8282


49
844.0328
21.0966


50
844.2189
21.2404


51
844.4489
21.3371


52
844.7018
21.3668


53
844.9537
21.3249


54
845.1772
21.2256


55
845.3520
21.0787


56
845.4874
20.8765


57
845.5701
20.6372


58
845.5817
20.3852


59
845.5228
20.1447


60
845.4099
19.9393


















TABLE 6





N
X
Y















Fourth Stage Vane LE and TE at Z = 0%









1
955.3360
77.1040


2
950.4639
75.5440


3
946.2269
73.6424


4
943.7587
72.2480


5
940.5857
70.0540


6
938.8211
68.5671


7
936.6871
66.3716


8
935.1726
64.2880


9
934.5118
62.9993


10
934.1500
61.2512


11
934.2667
60.3062


12
934.3427
60.0348


13
934.4296
59.7913


14
934.5342
59.5485


15
934.6557
59.3094


16
934.8117
59.0489


17
934.9664
58.8284


18
935.1345
58.6208


19
935.3141
58.4278


20
935.5272
58.2297


21
935.7239
58.0723


22
935.9248
57.9337


23
936.1273
57.8152


24
937.2634
57.2066


25
938.8294
56.5362


26
940.1111
56.0886


27
942.3800
55.4328


28
945.0569
54.8071


29
947.0658
54.4131


30
950.4119
53.8619


31
1062.9791
−2.8893


32
1062.0864
−1.6190


33
1060.9262
0.0462


34
1060.0060
1.3759


35
1058.4075
3.7000


36
1056.5467
6.4182


37
1055.1580
8.4472


38
1052.8457
11.8102


39
1051.1460
14.2611


40
1047.2356
10.7228


41
1049.9659
7.8110


42
1051.6088
6.0047


43
1053.8189
3.5122


44
1055.1287
2.0022


45
1056.8563
−0.0254


46
1058.3076
−1.7587


47
1059.1255
−2.7467


48
1060.1320
−3.9731


49
1060.6580
−4.6186


50
1060.9438
−4.8851


51
1061.3128
−5.0796


52
1061.7298
−5.1683


53
1062.1467
−5.1330


54
1062.5192
−4.9905


55
1062.8187
−4.7673


56
1063.0610
−4.4515


57
1063.2143
−4.0623


58
1063.2446
−3.6404


59
1063.1573
−3.2358


60
1062.9791
−2.8893







Fourth Stage Vane LE and TE at Z = 10%









1
953.6903
66.8497


2
948.4698
65.0659


3
943.9129
62.9782


4
941.2399
61.4890


5
937.7603
59.2011


6
935.7829
57.6831


7
933.3091
55.4788


8
931.4259
53.4073


9
930.5090
52.1154


10
929.8061
50.3087


11
929.7571
49.2924


12
929.8030
48.9427


13
929.8731
48.6264


14
929.9700
48.3094


15
930.0929
47.9960


16
930.2614
47.6534


17
930.4374
47.3627


18
930.6361
47.0887


19
930.8546
46.8339


20
931.1202
46.5732


21
931.3702
46.3670


22
931.6294
46.1869


23
931.8940
46.0348


24
933.1796
45.4876


25
934.9350
44.9607


26
936.3588
44.6280


27
938.8692
44.1688


28
941.8246
43.7729


29
944.0403
43.5526


30
947.7293
43.2951


31
1067.4776
−19.0251


32
1066.5528
−17.6426


33
1065.3502
−15.8314


34
1064.3958
−14.3850


35
1062.7367
−11.8569


36
1060.8042
−8.8998


37
1059.3617
−6.6923


38
1056.9595
−3.0328


39
1055.1933
−0.3652


40
1052.2829
3.9678


41
1053.7713
−7.1442


42
1055.4837
−9.1610


43
1057.8039
−11.9223


44
1059.1891
−13.5832


45
1061.0294
−15.7996


46
1062.5882
−17.6825


47
1063.4720
−18.7511


48
1064.5654
−20.0731


49
1065.1395
−20.7669


50
1065.4269
−21.0298


51
1065.7951
−21.2202


52
1066.2095
−21.3057


53
1066.6235
−21.2688


54
1066.9940
−21.1260


55
1067.2930
−20.9031


56
1067.5360
−20.5886


57
1067.6920
−20.2012


58
1067.7279
−19.7802


59
1067.6480
−19.3748


60
1067.4776
−19.0251







Fourth Stage Vane LE and TE at Z = 20%









1
946.9009
55.6857


2
941.9933
53.7221


3
939.0884
52.3013


4
935.2734
50.0878


5
933.0867
48.5977


6
930.3317
46.3985


7
928.2152
44.2882


8
927.1725
42.9541


9
926.2229
41.1039


10
925.9860
40.0447


11
925.9661
39.6233


12
925.9869
39.2417


13
926.0439
38.8585


14
926.1369
38.4786


15
926.2851
38.0614


16
926.4558
37.7049


17
926.6616
37.3663


18
926.8990
37.0492


19
927.1992
36.7224


20
927.4910
36.4618


21
927.8018
36.2316


22
928.1270
36.0336


23
929.5211
35.5650


24
931.4359
35.2879


25
932.9751
35.1492


26
935.6706
34.9706


27
938.8263
34.8084


28
941.1843
34.7042


29
945.1003
34.5477


30
947.9622
34.4371


31
1071.1063
−32.7422


32
1070.1623
−31.2920


33
1068.9228
−29.3998


34
1067.9302
−27.8944


35
1066.1880
−25.2733


36
1064.1363
−22.2215


37
1062.5929
−19.9509


38
1060.0074
−16.1969


39
1058.0992
−13.4657


40
1054.9516
−9.0331


41
1056.7252
−20.3647


42
1058.5505
−22.4470


43
1061.0195
−25.3006


44
1062.4899
−27.0198


45
1064.4371
−29.3188


46
1066.0797
−31.2773


47
1067.0077
−32.3918


48
1068.1521
−33.7737


49
1068.7512
−34.5005


50
1069.0361
−34.7615


51
1069.4014
−34.9495


52
1069.8134
−35.0324


53
1070.2258
−34.9934


54
1070.5961
−34.8488


55
1070.8964
−34.6245


56
1071.1420
−34.3090


57
1071.3022
−33.9209


58
1071.3438
−33.4993


59
1071.2704
−33.0931


60
1071.1063
−32.7422







Fourth Stage Vane LE and TE at Z = 30%









1
945.1332
47.4783


2
939.9186
45.6563


3
936.8115
44.3092


4
932.7094
42.1735


5
930.3471
40.7147


6
927.3598
38.5341


7
925.0543
36.4093


8
923.9077
35.0555


9
922.7472
33.1941


10
922.3474
32.1109


11
922.2357
31.5961


12
922.1882
31.1288


13
922.1929
30.6595


14
922.2528
30.1954


15
922.3882
29.6885


16
922.5702
29.2597


17
922.8079
28.8580


18
923.0955
28.4886


19
923.4715
28.1179


20
923.8451
27.8324


21
924.2478
27.5893


22
924.6720
27.3891


23
926.1616
27.0167


24
928.1929
26.8635


25
929.8183
26.8081


26
932.6553
26.7379


27
935.9672
26.6502


28
938.4376
26.5700


29
942.5340
26.4016


30
945.5235
26.2465


31
1074.5521
−43.6928


32
1073.5820
−42.1961


33
1072.3006
−40.2476


34
1071.2690
−38.7012


35
1069.4478
−36.0161


36
1067.2879
−32.9000


37
1065.6540
−30.5875


38
1062.9043
−26.7726


39
1060.8676
−24.0023


40
1057.5020
−19.5120


41
1059.6399
−30.8805


42
1061.5541
−33.0237


43
1064.1389
−35.9651


44
1065.6757
−37.7396


45
1067.7082
−40.1146


46
1069.4202
−42.1393


47
1070.3866
−43.2915


48
1071.5774
−44.7202


49
1072.2005
−45.4715


50
1072.4837
−45.7294


51
1072.8471
−45.9136


52
1073.2569
−45.9926


53
1073.6674
−45.9500


54
1074.0362
−45.8024


55
1074.3357
−45.5757


56
1074.5811
−45.2585


57
1074.7419
−44.8694


58
1074.7850
−44.4479


59
1074.7138
−44.0424


60
1074.5521
−43.6928







Fourth Stage Vane LE and TE at Z = 40%









1
942.8949
40.3010


2
937.4696
38.4685


3
934.2262
37.1160


4
929.9271
34.9817


5
927.4348
33.5346


6
924.2482
31.3918


7
921.7354
29.3191


8
920.4401
28.0013


9
919.0564
26.1757


10
918.5244
25.0917


11
918.3143
24.4829


12
918.1951
23.9278


13
918.1484
23.3702


14
918.1817
22.8207


15
918.3189
22.2267


16
918.5309
21.7336


17
918.8237
21.2837


18
919.1883
20.8840


19
919.6723
20.5033


20
920.1565
20.2308


21
920.6781
20.0196


22
921.2240
19.8682


23
922.8182
19.5929


24
924.9387
19.3672


25
926.6345
19.2262


26
929.5970
19.0139


27
933.0600
18.7960


28
935.6451
18.6457


29
939.9341
18.4061


30
943.0655
18.2300


31
1078.2240
−51.5951


32
1077.2091
−50.0619


33
1075.8746
−48.0604


34
1074.8052
−46.4692


35
1072.9257
−43.7017


36
1070.7056
−40.4843


37
1069.0287
−38.0940


38
1066.2062
−34.1489


39
1064.1136
−31.2844


40
1060.6467
−26.6460


41
1062.9903
−38.0805


42
1064.9305
−40.3607


43
1067.5575
−43.4824


44
1069.1270
−45.3584


45
1071.2159
−47.8566


46
1072.9908
−49.9710


47
1074.0002
−51.1664


48
1075.2526
−52.6395


49
1075.9121
−53.4097


50
1076.1975
−53.6603


51
1076.5610
−53.8362


52
1076.9686
−53.9070


53
1077.3751
−53.8569


54
1077.7389
−53.7033


55
1078.0329
−53.4724


56
1078.2720
−53.1523


57
1078.4264
−52.7626


58
1078.4640
−52.3427


59
1078.3885
−51.9405


60
1078.2240
−51.5951







Fourth Stage Vane LE and TE at Z = 50%









1
940.7092
33.8252


2
935.1315
32.0235


3
931.7920
30.7034


4
927.3415
28.6369


5
924.7396
27.2444


6
921.3701
25.1970


7
918.6468
23.2377


8
917.1929
22.0007


9
915.5704
20.2862


10
914.8744
19.2686


11
914.5864
18.6708


12
914.4035
18.1225


13
914.3006
17.5701


14
914.2874
17.0247


15
914.3858
16.4357


16
914.5762
15.9490


17
914.8601
15.5083


18
915.2273
15.1215


19
915.7272
14.7604


20
916.2351
14.5104


21
916.7873
14.3262


22
917.3681
14.2060


23
919.0691
13.9942


24
921.2960
13.7389


25
923.0730
13.5464


26
926.1754
13.2334


27
929.7997
12.8998


28
932.5045
12.6692


29
936.9913
12.3127


30
940.2671
12.0662


31
1081.8443
−57.7572


32
1080.7710
−56.2022


33
1079.3708
−54.1647


34
1078.2567
−52.5392


35
1076.3129
−49.7019


36
1074.0349
−46.3903


37
1072.3231
−43.9236


38
1069.4510
−39.8454


39
1067.3242
−36.8819


40
1063.7960
−32.0859


41
1066.1958
−43.6667


42
1068.1753
−46.0716


43
1070.8649
−49.3544


44
1072.4806
−51.3187


45
1074.6460
−53.9205


46
1076.5028
−56.1063


47
1077.5671
−57.3343


48
1078.8971
−58.8387


49
1079.6018
−59.6210


50
1079.8900
−59.8599


51
1080.2532
−60.0226


52
1080.6572
−60.0802


53
1081.0572
−60.0186


54
1081.4126
−59.8561


55
1081.6974
−59.6193


56
1081.9260
−59.2960


57
1082.0695
−58.9064


58
1082.0973
−58.4902


59
1082.0141
−58.0945


60
1081.8443
−57.7572







Fourth Stage Vane LE and TE at Z = 60%









1
938.9244
27.9008


2
933.1968
26.2768


3
929.7644
25.0811


4
925.1566
23.1984


5
922.4393
21.9150


6
918.8843
20.0056


7
915.9581
18.1783


8
914.3628
17.0321


9
912.5059
15.4677


10
911.6175
14.5604


11
911.2965
14.0977


12
911.0749
13.6709


13
910.9220
13.2381


14
910.8454
12.8080


15
910.8573
12.3388


16
910.9594
11.9455


17
911.1465
11.5828


18
911.4113
11.2572


19
911.7927
10.9431


20
912.1957
10.7150


21
912.6462
10.5352


22
913.1316
10.4032


23
914.9178
10.2070


24
917.2671
10.0850


25
919.1347
9.9907


26
922.3838
9.8105


27
926.1660
9.5619


28
928.9814
9.3471


29
933.6426
8.9405


30
937.0398
8.6058


31
1084.9325
−63.9792


32
1083.7979
−62.4250


33
1082.3198
−60.3899


34
1081.1433
−58.7636


35
1079.0909
−55.9190


36
1076.6900
−52.5921


37
1074.8915
−50.1111


38
1071.8847
−46.0058


39
1069.6648
−43.0212


40
1065.9900
−38.1914


41
1068.3893
−49.9741


42
1070.5266
−52.3636


43
1073.4262
−55.6285


44
1075.1642
−57.5835


45
1077.4882
−60.1751


46
1079.4757
−62.3562


47
1080.6123
−63.5842


48
1082.0298
−65.0922


49
1082.7796
−65.8782


50
1083.0668
−66.1026


51
1083.4255
−66.2498


52
1083.8222
−66.2921


53
1084.2123
−66.2182


54
1084.5564
−66.0475


55
1084.8297
−65.8064


56
1085.0465
−65.4831


57
1085.1783
−65.0971


58
1085.1960
−64.6885


59
1085.1059
−64.3039


60
1084.9325
−63.9792







Fourth Stage Vane LE and TE at Z = 70%









1
937.2070
22.8412


2
931.3183
21.2761


3
927.7749
20.1336


4
922.9875
18.3378


5
920.1462
17.1098


6
916.4089
15.2721


7
913.3069
13.5082


8
911.6039
12.3973


9
909.6013
10.8649


10
908.6477
9.9436


11
908.3662
9.5810


12
908.1676
9.2493


13
908.0222
8.9144


14
907.9344
8.5817


15
907.9098
8.2166


16
907.9586
7.9063


17
908.0742
7.6143


18
908.2525
7.3448


19
908.5228
7.0738


20
908.8188
6.8649


21
909.1592
6.6874


22
909.5359
6.5418


23
911.3499
6.2726


24
913.7608
6.1772


25
915.6816
6.1364


26
919.0260
6.0766


27
922.9202
5.9818


28
925.8182
5.8770


29
930.6129
5.6265


30
934.1042
5.3772


31
1087.3326
−70.1783


32
1086.1477
−68.6202


33
1084.5980
−66.5881


34
1083.3577
−64.9647


35
1081.1831
−62.1249


36
1078.6302
−58.8038


37
1076.7181
−56.3276


38
1073.5284
−52.2292


39
1071.1805
−49.2480


40
1067.3093
−44.4185


41
1069.6551
−56.5168


42
1072.0149
−58.8211


43
1075.2050
−61.9795


44
1077.1060
−63.8776


45
1079.6305
−66.4056


46
1081.7701
−68.5483


47
1082.9844
−69.7634


48
1084.4882
−71.2663


49
1085.2788
−72.0552


50
1085.5598
−72.2659


51
1085.9083
−72.4007


52
1086.2930
−72.4322


53
1086.6693
−72.3524


54
1086.9992
−72.1808


55
1087.2598
−71.9430


56
1087.4649
−71.6276


57
1087.5865
−71.2528


58
1087.5973
−70.8580


59
1087.5046
−70.4885


60
1087.3326
−70.1783







Fourth Stage Vane LE and TE at Z = 80%









1
935.3480
19.1716


2
929.3339
17.3621


3
925.6899
16.0993


4
920.7589
14.1758


5
917.8298
12.8984


6
913.9803
11.0232


7
910.7953
9.2255


8
909.0569
8.0738


9
907.0736
6.4002


10
906.2604
5.2869


11
906.0800
4.8905


12
905.9661
4.5376


13
905.8979
4.1887


14
905.8773
3.8480


15
905.9135
3.4799


16
906.0007
3.1707


17
906.1393
2.8824


18
906.3263
2.6178


19
906.5910
2.3520


20
906.8704
2.1465


21
907.1859
1.9707


22
907.5324
1.8253


23
909.2999
1.3689


24
911.6630
1.0055


25
913.5666
0.8142


26
916.9097
0.6097


27
920.8340
0.5090


28
923.7688
0.4910


29
928.6404
0.5073


30
932.1965
0.5258


31
1089.2150
−74.6846


32
1088.0057
−73.0738


33
1086.4221
−70.9733


34
1085.1528
−69.2957


35
1082.9241
−66.3622


36
1080.3035
−62.9324


37
1078.3390
−60.3749


38
1075.0611
−56.1399


39
1072.6491
−53.0562


40
1068.6773
−48.0523


41
1070.8550
−60.6869


42
1073.3340
−63.0347


43
1076.6844
−66.2517


44
1078.6797
−68.1842


45
1081.3285
−70.7553


46
1083.5726
−72.9310


47
1084.8458
−74.1632


48
1086.4220
−75.6859


49
1087.2502
−76.4845


50
1087.5222
−76.6836


51
1087.8572
−76.8101


52
1088.2260
−76.8378


53
1088.5858
−76.7602


54
1088.9004
−76.5962


55
1089.1483
−76.3694


56
1089.3426
−76.0687


57
1089.4575
−75.7120


58
1089.4675
−75.3358


59
1089.3791
−74.9826


60
1089.2150
−74.6846







Fourth Stage Vane LE and TE at Z = 90%









1
933.8471
17.2423


2
927.7977
15.0955


3
924.1183
13.6493


4
919.1572
11.5108


5
916.2241
10.1330


6
912.3942
8.1559


7
909.2577
6.2736


8
907.5639
5.0584


9
905.6937
3.2393


10
905.0361
1.9652


11
904.9242
1.4962


12
904.8713
1.0837


13
904.8637
0.6799


14
904.9023
0.2888


15
905.0014
−0.1300


16
905.1389
−0.4786


17
905.3213
−0.8010


18
905.5460
−1.0948


19
905.8456
−1.3878


20
906.1498
−1.6131


21
906.4854
−1.8048


22
906.8483
−1.9627


23
908.5577
−2.6050


24
910.8505
−3.2681


25
912.7149
−3.6559


26
916.0141
−4.1103


27
919.9169
−4.3591


28
922.8510
−4.3961


29
927.7410
−4.2676


30
931.3233
−4.0668


31
1090.7582
−76.7408


32
1089.5570
−75.0218


33
1087.9923
−72.7704


34
1086.7454
−70.9697


35
1084.5665
−67.8184


36
1082.0114
−64.1312


37
1080.0926
−61.3814


38
1076.8786
−56.8293


39
1074.5041
−53.5158


40
1070.5770
−48.1407


41
1072.4421
−61.5353


42
1074.8773
−64.0991


43
1078.1781
−67.6003


44
1080.1552
−69.6926


45
1082.8014
−72.4536


46
1085.0703
−74.7593


47
1086.3712
−76.0485


48
1087.9973
−77.6216


49
1088.8593
−78.4367


50
1089.1212
−78.6252


51
1089.4410
−78.7455


52
1089.7918
−78.7734


53
1090.1337
−78.7029


54
1090.4330
−78.5514


55
1090.6697
−78.3396


56
1090.8551
−78.0568


57
1090.9679
−77.7217


58
1090.9842
−77.3672


59
1090.9075
−77.0297


60
1090.7582
−76.7408







Fourth Stage Vane LE and TE at Z = 100%









1
933.0516
16.8308


2
927.0247
14.4095


3
923.3668
12.7933


4
918.4665
10.4249


5
915.5913
8.9147


6
911.8673
6.7700


7
908.8484
4.7508


8
907.2304
3.4618


9
905.4602
1.5610


10
904.8476
0.2553


11
904.7305
−0.2529


12
904.6763
−0.7008


13
904.6704
−1.1407


14
904.7142
−1.5680


15
904.8227
−2.0278


16
904.9714
−2.4126


17
905.1674
−2.7706


18
905.4079
−3.0993


19
905.7279
−3.4307


20
906.0525
−3.6889


21
906.4105
−3.9124


22
906.7978
−4.1008


23
908.4854
−4.8229


24
910.7585
−5.5842


25
912.6090
−6.0446


26
915.8870
−6.6142


27
919.7707
−6.9728


28
922.6946
−7.0697


29
927.5753
−6.9935


30
931.1574
−6.7890


31
1092.0654
−76.9895


32
1090.9057
−75.1337


33
1089.4074
−72.6910


34
1088.2243
−70.7337


35
1086.1731
−67.3039


36
1083.7767
−63.2881


37
1081.9706
−60.2952


38
1078.9227
−55.3488


39
1076.6521
−51.7554


40
1072.8630
−45.9407


41
1074.2410
−60.2292


42
1076.5497
−63.0621


43
1079.6873
−66.9239


44
1081.5805
−69.2223


45
1084.1432
−72.2316


46
1086.3769
−74.7108


47
1087.6764
−76.0772


48
1089.3227
−77.7198


49
1090.2059
−78.5584


50
1090.4560
−78.7383


51
1090.7593
−78.8554


52
1091.0910
−78.8874


53
1091.4152
−78.8284


54
1091.7010
−78.6931


55
1091.9290
−78.4995


56
1092.1088
−78.2365


57
1092.2245
−77.9251


58
1092.2535
−77.5938


59
1092.1946
−77.2715


60
1092.0654
−76.9895


















TABLE 8





N
X
Y















Fourth Stage Blade LE and TE at Z = 0%









1
1138.0006
−9.1243


2
1132.3216
−6.8397


3
1128.9111
−5.3108


4
1124.3525
−3.0421


5
1121.6794
−1.5666


6
1118.2128
0.5588


7
1115.3859
2.5366


8
1113.8507
3.7495


9
1112.0633
5.3768


10
1111.2024
6.3094


11
1110.8346
6.8314


12
1110.5905
7.3244


13
1110.4411
7.8243


14
1110.3962
8.3116


15
1110.4644
8.8209


16
1110.6233
9.2190


17
1110.8775
9.5673


18
1111.2252
9.8666


19
1111.7135
10.1248


20
1112.2190
10.2688


21
1112.7687
10.3302


22
1113.3370
10.3118


23
1115.1750
10.0143


24
1117.5543
9.5178


25
1119.4407
9.0776


26
1122.7192
8.2493


27
1126.5391
7.2338


28
1129.3890
6.4629


29
1134.1251
5.1899


30
1137.5952
4.2832


31
1312.0170
40.3937


32
1310.4720
39.1011


33
1308.4520
37.4141


34
1306.8440
36.0692


35
1304.0380
33.7243


36
1300.7530
30.9945


37
1298.2900
28.9682


38
1294.1730
25.6357


39
1291.1350
23.2315


40
1286.1220
19.3752


41
1289.7278
31.4464


42
1292.6686
33.2706


43
1296.6278
35.8318


44
1298.9763
37.4048


45
1302.0801
39.5346


46
1304.6988
41.3614


47
1306.1815
42.4014


48
1308.0178
43.6850


49
1308.9851
44.3544


50
1309.5706
44.6481


51
1310.2542
44.7885


52
1310.9687
44.7319


53
1311.6310
44.4703


54
1312.1727
44.0596


55
1312.5611
43.5527


56
1312.8169
42.9226


57
1312.8976
42.2145


58
1312.7666
41.5088


59
1312.4532
40.8839


60
1312.0168
40.3937







Fourth Stage Blade LE and TE at Z = 10%









1
1139.0653
−8.6078


2
1133.4984
−6.3431


3
1130.1575
−4.8206


4
1125.7046
−2.5388


5
1123.1095
−1.0355


6
1119.7704
1.1555


7
1117.0797
3.2160


8
1115.6341
4.4822


9
1113.9468
6.1539


10
1113.1026
7.0767


11
1112.8031
7.4771


12
1112.6016
7.8345


13
1112.4712
8.1824


14
1112.4136
8.5113


15
1112.4344
8.8477


16
1112.5285
9.1076


17
1112.6955
9.3309


18
1112.9341
9.5180


19
1113.2800
9.6780


20
1113.6487
9.7691


21
1114.0634
9.8105


22
1114.5114
9.8019


23
1116.3276
9.5625


24
1118.6665
9.0652


25
1120.5128
8.5830


26
1123.7111
7.6398


27
1127.4285
6.4677


28
1130.2018
5.5833


29
1134.8167
4.1452


30
1138.2070
3.1498


31
1309.9036
38.2801


32
1308.6126
36.8269


33
1306.8722
34.9757


34
1305.4409
33.5410


35
1302.8622
31.1147


36
1299.7445
28.3857


37
1297.3576
26.4105


38
1293.3118
23.2230


39
1290.3048
20.9496


40
1285.3278
17.3210


41
1288.3136
28.5947


42
1291.2554
30.2623


43
1295.2236
32.5974


44
1297.5744
34.0402


45
1300.6594
36.0286


46
1303.2164
37.7985


47
1304.6345
38.8456


48
1306.3462
40.1957


49
1307.2211
40.9339


50
1307.6300
41.2009


51
1308.1235
41.3639


52
1308.6567
41.3864


53
1309.1709
41.2554


54
1309.6119
41.0046


55
1309.9511
40.6689


56
1310.2062
40.2307


57
1310.3421
39.7183


58
1310.3248
39.1855


59
1310.1666
38.6911


60
1309.9036
38.2801







Fourth Stage Blade LE and TE at Z = 20%









1
1142.2787
−6.5175


2
1137.0133
−4.3357


3
1133.8426
−2.9043


4
1129.5905
−0.8128


5
1127.0889
0.5326


6
1123.8299
2.4553


7
1121.1583
4.2396


8
1119.7069
5.3435


9
1118.0780
6.9044


10
1117.5170
7.9288


11
1117.4740
8.1074


12
1117.4539
8.2683


13
1117.4525
8.4286


14
1117.4702
8.5857


15
1117.5128
8.7556


16
1117.5705
8.8980


17
1117.6468
9.0315


18
1117.7407
9.1553


19
1117.8655
9.2810


20
1117.9914
9.3787


21
1118.1290
9.4621


22
1118.2756
9.5306


23
1119.9898
9.7419


24
1122.2690
9.4079


25
1124.0666
9.0238


26
1127.1805
8.2539


27
1130.7976
7.2650


28
1133.4912
6.4966


29
1137.9597
5.1969


30
1141.2280
4.2435


31
1306.5232
35.9615


32
1305.1196
34.6974


33
1303.2764
33.0531


34
1301.7962
31.7543


35
1299.1840
29.5205


36
1296.0810
26.9691


37
1293.7314
25.1028


38
1289.7761
22.0690


39
1286.8520
19.8909


40
1282.0396
16.3848


41
1286.0793
26.0326


42
1288.8955
27.7859


43
1292.7028
30.2226


44
1294.9660
31.7123


45
1297.9540
33.7342


46
1300.4621
35.4859


47
1301.8728
36.4952


48
1303.6064
37.7582


49
1304.5122
38.4265


50
1304.8800
38.6254


51
1305.3140
38.7284


52
1305.7718
38.7062


53
1306.2005
38.5520


54
1306.5548
38.3004


55
1306.8130
37.9846


56
1306.9887
37.5875


57
1307.0537
37.1374


58
1306.9829
36.6851


59
1306.7937
36.2813


60
1306.5232
35.9615







Fourth Stage Blade LE and TE at Z = 30%









1
1146.8276
−7.3036


2
1142.0421
−5.3959


3
1139.1617
−4.1417


4
1135.3042
−2.2983


5
1133.0420
−1.0994


6
1130.1075
0.6340


7
1127.7221
2.2664


8
1126.4374
3.2884


9
1125.0178
4.7443


10
1124.5392
5.7004


11
1124.5548
5.8247


12
1124.5780
5.9460


13
1124.6094
6.0753


14
1124.6493
6.2104


15
1124.7062
6.3664


16
1124.7692
6.5059


17
1124.8423
6.6413


18
1124.9218
6.7687


19
1125.0155
6.9006


20
1125.0996
7.0061


21
1125.1825
7.1000


22
1125.2627
7.1822


23
1126.8137
7.5032


24
1128.8845
7.3940


25
1130.5226
7.1749


26
1133.3597
6.6567


27
1136.6486
5.9126


28
1139.0917
5.2952


29
1143.1349
4.1938


30
1146.0860
3.3484


31
1298.3468
34.2298


32
1297.0707
33.0020


33
1295.4229
31.3722


34
1294.1044
30.0756


35
1291.7607
27.8534


36
1288.9373
25.3443


37
1286.7786
23.5251


38
1283.1222
20.5846


39
1280.4114
18.4775


40
1275.9542
15.0731


41
1279.1941
24.5813


42
1281.7986
26.3258


43
1285.3340
28.7163


44
1287.4465
30.1556


45
1290.2519
32.0794


46
1292.6247
33.7191


47
1293.9678
34.6530


48
1295.6248
35.8143


49
1296.4914
36.4280


50
1296.8221
36.6011


51
1297.2102
36.6893


52
1297.6189
36.6681


53
1298.0021
36.5319


54
1298.3209
36.3104


55
1298.5559
36.0318


56
1298.7191
35.6818


57
1298.7859
35.2843


58
1298.7341
34.8827


59
1298.5774
34.5208


60
1298.3468
34.2298







Fourth Stage Blade LE and TE at Z = 40%









1
1154.4195
−10.4967


2
1150.2173
−8.9081


3
1147.6956
−7.8434


4
1144.3263
−6.2665


5
1142.3534
−5.2395


6
1139.7972
−3.7548


7
1137.7249
−2.3494


8
1136.6161
−1.4628


9
1135.3544
−0.2422


10
1134.7689
0.4855


11
1134.6530
0.7128


12
1134.5817
0.9374


13
1134.5446
1.1750


14
1134.5447
1.4180


15
1134.5923
1.6883


16
1134.6788
1.9174


17
1134.8059
2.1280


18
1134.9675
2.3139


19
1135.1818
2.4866


20
1135.3928
2.6026


21
1135.6145
2.6826


22
1135.8380
2.7273


23
1137.1878
2.7114


24
1138.9353
2.5027


25
1140.3239
2.2596


26
1142.7390
1.7506


27
1145.5565
1.0718


28
1147.6608
0.5304


29
1151.1616
−0.3995


30
1153.7294
−1.0830


31
1286.7941
33.1268


32
1285.6381
32.0146


33
1284.1426
30.5451


34
1282.9473
29.3774


35
1280.8172
27.3871


36
1278.2508
25.1489


37
1276.2982
23.5203


38
1273.0277
20.8537


39
1270.6321
18.9134


40
1266.7274
15.7455


41
1269.6178
24.4164


42
1271.9496
25.9527


43
1275.1010
28.0923


44
1276.9751
29.4004


45
1279.4535
31.1711


46
1281.5404
32.6975


47
1282.7180
33.5727


48
1284.1690
34.6636


49
1284.9284
35.2394


50
1285.2518
35.4199


51
1285.6358
35.5181


52
1286.0438
35.5080


53
1286.4289
35.3826


54
1286.7508
35.1709


55
1286.9892
34.9010


56
1287.1568
34.5588


57
1287.2278
34.1678


58
1287.1789
33.7714


59
1287.0238
33.4138


60
1286.7941
33.1268







Fourth Stage Blade LE and TE at Z = 50%









1
1163.1804
−13.7540


2
1159.4137
−12.4322


3
1157.1622
−11.5255


4
1154.1622
−10.1671


5
1152.4062
−9.2817


6
1150.1220
−8.0139


7
1148.2445
−6.8416


8
1147.2177
−6.1164


9
1146.0179
−5.1176


10
1145.4858
−4.4824


11
1145.3922
−4.2935


12
1145.3324
−4.1058


13
1145.2980
−3.9055


14
1145.2920
−3.6984


15
1145.3225
−3.4645


16
1145.3856
−3.2624


17
1145.4819
−3.0736


18
1145.6065
−2.9041


19
1145.7730
−2.7410


20
1145.9379
−2.6242


21
1146.1120
−2.5351


22
1146.2886
−2.4741


23
1147.4782
−2.3717


24
1149.0390
−2.4769


25
1150.2806
−2.6300


26
1152.4441
−2.9685


27
1154.9753
−3.4312


28
1156.8711
−3.8002


29
1160.0336
−4.4312


30
1162.3583
−4.8940


31
1278.6669
33.6789


32
1277.6319
32.7066


33
1276.2803
31.4352


34
1275.1999
30.4259


35
1273.2943
28.6867


36
1271.0364
26.6909


37
1269.3375
25.2168


38
1266.5107
22.7791


39
1264.4465
20.9970


40
1261.0842
18.0859


41
1263.5934
25.8218


42
1265.6005
27.2578


43
1268.3239
29.2374


44
1269.9496
30.4371


45
1272.1060
32.0500


46
1273.9276
33.4311


47
1274.9578
34.2194


48
1276.2297
35.1984


49
1276.8966
35.7134


50
1277.2053
35.8879


51
1277.5723
35.9829


52
1277.9626
35.9733


53
1278.3309
35.8518


54
1278.6380
35.6469


55
1278.8650
35.3862


56
1279.0239
35.0559


57
1279.0898
34.6786


58
1279.0402
34.2967


59
1278.8890
33.9533


60
1278.6669
33.6789







Fourth Stage Blade LE and TE at Z = 60%









1
1170.7303
−17.1334


2
1167.3230
−16.3534


3
1165.2679
−15.7807


4
1162.5088
−14.8678


5
1160.8855
−14.2371


6
1158.7775
−13.2830


7
1157.0705
−12.3403


8
1156.1594
−11.7319


9
1155.1374
−10.8534


10
1154.7202
−10.2609


11
1154.6628
−10.1102


12
1154.6275
−9.9645


13
1154.6084
−9.8113


14
1154.6072
−9.6539


15
1154.6297
−9.4761


16
1154.6731
−9.3209


17
1154.7379
−9.1734


18
1154.8210
−9.0377


19
1154.9320
−8.9019


20
1155.0425
−8.7984


21
1155.1604
−8.7120


22
1155.2822
−8.6433


23
1156.2879
−8.3640


24
1157.6548
−8.2178


25
1158.7629
−8.1673


26
1160.7190
−8.1738


27
1163.0136
−8.2834


28
1164.7252
−8.4091


29
1167.5656
−8.6644


30
1169.6449
−8.8676


31
1271.7509
34.4016


32
1270.8219
33.5150


33
1269.6046
32.3591


34
1268.6327
31.4395


35
1266.9356
29.8361


36
1264.9517
27.9646


37
1263.4688
26.5698


38
1261.0013
24.2609


39
1259.1928
22.5797


40
1256.2338
19.8484


41
1258.1736
26.9471


42
1259.9289
28.3545


43
1262.3268
30.2678


44
1263.7676
31.4122


45
1265.6895
32.9337


46
1267.3225
34.2227


47
1268.2497
34.9534


48
1269.3974
35.8570


49
1270.0000
36.3314


50
1270.2966
36.5043


51
1270.6508
36.6016


52
1271.0290
36.5983


53
1271.3879
36.4875


54
1271.6892
36.2955


55
1271.9135
36.0484


56
1272.0726
35.7327


57
1272.1428
35.3706


58
1272.1016
35.0026


59
1271.9612
34.6696


60
1271.7509
34.4016







Fourth Stage Blade LE and TE at Z = 70%









1
1170.7303
−17.1334


2
1167.3230
−16.3534


3
1165.2679
−15.7807


4
1162.5088
−14.8678


5
1160.8855
−14.2371


6
1158.7775
−13.2830


7
1157.0705
−12.3403


8
1156.1594
−11.7319


9
1155.1374
−10.8534


10
1154.7202
−10.2609


11
1154.6628
−10.1102


12
1154.6275
−9.9645


13
1154.6084
−9.8113


14
1154.6072
−9.6539


15
1154.6297
−9.4761


16
1154.6731
−9.3209


17
1154.7379
−9.1734


18
1154.8210
−9.0377


19
1154.9320
−8.9019


20
1155.0425
−8.7984


21
1155.1604
−8.7120


22
1155.2822
−8.6433


23
1156.2879
−8.3640


24
1157.6548
−8.2178


25
1158.7629
−8.1673


26
1160.7190
−8.1738


27
1163.0136
−8.2834


28
1164.7252
−8.4091


29
1167.5656
−8.6644


30
1169.6449
−8.8676


31
1271.7509
34.4016


32
1270.8219
33.5150


33
1269.6046
32.3591


34
1268.6327
31.4395


35
1266.9356
29.8361


36
1264.9517
27.9646


37
1263.4688
26.5698


38
1261.0013
24.2609


39
1259.1928
22.5797


40
1256.2338
19.8484


41
1258.1736
26.9471


42
1259.9289
28.3545


43
1262.3268
30.2678


44
1263.7676
31.4122


45
1265.6895
32.9337


46
1267.3225
34.2227


47
1268.2497
34.9534


48
1269.3974
35.8570


49
1270.0000
36.3314


50
1270.2966
36.5043


51
1270.6508
36.6016


52
1271.0290
36.5983


53
1271.3879
36.4875


54
1271.6892
36.2955


55
1271.9135
36.0484


56
1272.0726
35.7327


57
1272.1428
35.3706


58
1272.1016
35.0026


59
1271.9612
34.6696


60
1271.7509
34.4016







Fourth Stage Blade LE and TE at Z = 80%









1
1180.3804
−24.6815


2
1177.3791
−24.8914


3
1175.5632
−24.9172


4
1173.1107
−24.8344


5
1171.6484
−24.7197


6
1169.7029
−24.4878


7
1168.0497
−24.2029


8
1167.1145
−23.9783


9
1165.9914
−23.5681


10
1165.4996
−23.1717


11
1165.4244
−23.0387


12
1165.3705
−22.9108


13
1165.3301
−22.7761


14
1165.3047
−22.6368


15
1165.2974
−22.4764


16
1165.3131
−22.3321


17
1165.3496
−22.1906


18
1165.4041
−22.0560


19
1165.4836
−21.9148


20
1165.5674
−21.8002


21
1165.6612
−21.6971


22
1165.7633
−21.6067


23
1166.6031
−21.0773


24
1167.7486
−20.5349


25
1168.6809
−20.1816


26
1170.3309
−19.6699


27
1172.2834
−19.1856


28
1173.7550
−18.8770


29
1176.2176
−18.4199


30
1178.0287
−18.1035


31
1258.5329
37.0949


32
1257.8126
36.2685


33
1256.8690
35.1904


34
1256.1152
34.3329


35
1254.7964
32.8401


36
1253.2505
31.1018


37
1252.0930
29.8078


38
1250.1656
27.6659


39
1248.7527
26.1054


40
1246.4398
23.5688


41
1247.4783
29.6580


42
1248.8550
31.0119


43
1250.7358
32.8550


44
1251.8659
33.9586


45
1253.3744
35.4264


46
1254.6572
36.6697


47
1255.3862
37.3741


48
1256.2894
38.2446


49
1256.7640
38.7012


50
1257.0173
38.8835


51
1257.3307
39.0019


52
1257.6756
39.0310


53
1258.0129
38.9601


54
1258.3049
38.8103


55
1258.5320
38.6041


56
1258.7063
38.3305


57
1258.8033
38.0071


58
1258.7987
37.6689


59
1258.7006
37.3549


60
1258.5329
37.0949







Fourth Stage Blade LE and TE at Z = 90%









1
1183.5300
−27.0726


2
1180.8201
−27.8239


3
1179.1601
−28.1657


4
1176.9086
−28.4664


5
1175.5720
−28.5444


6
1173.8101
−28.5025


7
1172.3306
−28.2950


8
1171.4985
−28.0849


9
1170.4859
−27.7072


10
1169.9826
−27.4368


11
1169.7900
−27.2919


12
1169.6400
−27.1363


13
1169.5172
−26.9597


14
1169.4267
−26.7673


15
1169.3658
−26.5415


16
1169.3492
−26.3407


17
1169.3685
−26.1392


18
1169.4229
−25.9373


19
1169.5250
−25.7195


20
1169.6500
−25.5423


21
1169.8018
−25.3862


22
1169.9734
−25.2553


23
1170.7251
−24.8640


24
1171.7407
−24.4185


25
1172.5647
−24.0990


26
1174.0280
−23.5913


27
1175.7688
−23.0463


28
1177.0841
−22.6540


29
1179.2852
−21.9942


30
1180.9006
−21.4855


31
1252.8269
37.8733


32
1252.1670
37.0609


33
1251.3017
36.0018


34
1250.6098
35.1600


35
1249.3982
33.6956


36
1247.9767
31.9917


37
1246.9118
30.7243


38
1245.1380
28.6283


39
1243.8375
27.1022


40
1241.7103
24.6225


41
1242.5363
30.2245


42
1243.7961
31.5850


43
1245.5197
33.4370


44
1246.5574
34.5455


45
1247.9452
36.0189


46
1249.1284
37.2656


47
1249.8021
37.9712


48
1250.6384
38.8424


49
1251.0787
39.2988


50
1251.3137
39.4823


51
1251.6072
39.6074


52
1251.9323
39.6481


53
1252.2573
39.5980


54
1252.5456
39.4749


55
1252.7703
39.2919


56
1252.9436
39.0387


57
1253.0479
38.7388


58
1253.0588
38.4241


59
1252.9776
38.1256


60
1252.8269
37.8733







Fourth Stage Blade LE and TE at Z = 100%









1
1186.8945
−24.8858


2
1184.7558
−26.0712


3
1183.3986
−26.7029


4
1181.4780
−27.4113


5
1180.2913
−27.7290


6
1178.6876
−27.9847


7
1177.3347
−27.9953


8
1176.5795
−27.9069


9
1175.6529
−27.7292


10
1175.1700
−27.6076


11
1174.8617
−27.4945


12
1174.6056
−27.3444


13
1174.3819
−27.1513


14
1174.2027
−26.9221


15
1174.0613
−26.6377


16
1173.9944
−26.3765


17
1173.9846
−26.1062


18
1174.0305
−25.8284


19
1174.1480
−25.5254


20
1174.3089
−25.2806


21
1174.5124
−25.0687


22
1174.7450
−24.8976


23
1175.4116
−24.5032


24
1176.3083
−24.0351


25
1177.0282
−23.6712


26
1178.2881
−23.0422


27
1179.7567
−22.3015


28
1180.8480
−21.7394


29
1182.6476
−20.7833


30
1183.9526
−20.0628


31
1243.9637
33.1655


32
1243.4248
32.4447


33
1242.7175
31.5061


34
1242.1514
30.7608


35
1241.1584
29.4667


36
1239.9901
27.9654


37
1239.1118
26.8524


38
1237.6420
25.0198


39
1236.5578
23.6930


40
1234.7698
21.5526


41
1235.4154
26.2150


42
1236.4734
27.3943


43
1237.9126
29.0105


44
1238.7748
29.9837


45
1239.9234
31.2842


46
1240.8986
32.3908


47
1241.4525
33.0196


48
1242.1383
33.7986


49
1242.4987
34.2078


50
1242.6848
34.3691


51
1242.9204
34.4872


52
1243.1842
34.5392


53
1243.4507
34.5182


54
1243.6895
34.4365


55
1243.8780
34.3027


56
1244.0266
34.1093


57
1244.1202
33.8743


58
1244.1379
33.6219


59
1244.0798
33.3771


60
1243.9637
33.1655









It may be appreciated that the leading and trailing edge sections for the airfoils of the vane 22, blade 24, vane 26 and blade 28, as disclosed in the above Tables 2, 4, 6 and 8, may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Tables 2, 4, 6 and 8 may be scaled upwardly or downwardly such that the airfoil section shapes remain unchanged. A scaled version of the coordinates in Tables 2, 4, 6 and 8 could be represented by X, Y and Z coordinate values multiplied or divided by the same constant or number.
It is believed that the vane 22, blade 24, vane 26 and blade 28, constructed with the described average angle changes, provide and improved or optimized flow of working gases passing from the turbine section 12 to the diffuser 34, with improved Mach numbers for the flow passing through the third and fourth stages of the turbine. In particular, the design for the airfoil angles of the third and fourth stages are configured provide a better balance between the Mach numbers for the third and fourth stages, which is believed to provide an improved performance through these stages, since losses are generally proportional to the square of the Mach number.
While particular embodiments of the present invention have been illustrated and described, it would be obvious to those skilled in the art that various other changes and modifications can be made without departing from the spirit and scope of the invention. It is therefore intended to cover in the appended claims all such changes and modifications that are within the scope of this invention.

## Claims

1. A turbine airfoil assembly for installation in a gas turbine engine having a longitudinal axis, the turbine airfoil assembly including an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall, said airfoil having an outer wall comprising a pressure sidewall and a suction sidewall joined together at chordally spaced apart leading and trailing edges of said airfoil, an airfoil mean line is defined extending chordally and located centrally between said pressure and suction sidewalls, airfoil inlet and exit angles are defined at said airfoil leading and trailing edges that are in accordance with pairs of inlet angle values, α, and exit angle values, β, set forth in one of Tables 1, 3, 5 and 7, where said inlet and exit angle values are defined as angles between a line parallel to the longitudinal axis and the airfoil mean line lying in an X-Y plane of an X, Y, Z Cartesian coordinate system in which Z is a dimension perpendicular to the X-Y plane and extends radially relative to the longitudinal axis, and wherein each pair of inlet and exit angle values is defined with respect to a distance from said endwall corresponding to a Z value that is a percentage of a total span of said airfoil from said endwall, and wherein a predetermined difference between each pair of said airfoil inlet and exit angles is defined by a delta value, Δ, in said one of Tables 1, 3, 5 and 7, and a measured difference between any pair of said airfoil inlet and exit angles varies from the corresponding delta values, Δ, in said one of Tables 1, 3, 5 and 7 by at most 5%.

2. The turbine airfoil assembly of claim 1, wherein said airfoil comprises an airfoil for a third stage vane in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil inlet and exit angles is Table 1.

3. The turbine airfoil assembly of claim 1, wherein said airfoil comprises an airfoil for a third stage blade in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil inlet and exit angles is Table 3.

4. The turbine airfoil assembly of claim 1, wherein said airfoil comprises an airfoil for a fourth stage vane in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil inlet and exit angles is Table 5.

5. The turbine airfoil assembly of claim 1, wherein said airfoil comprises an airfoil for a fourth stage blade in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil inlet and exit angles is Table 7.

6. The turbine airfoil assembly of claim 1, including four airfoils comprising, in succession, an airfoil for a third stage vane having said airfoil inlet and exit angles defined by Table 1, an airfoil for a third stage blade having said airfoil inlet and exit angles defined by Table 3, an airfoil for a fourth stage vane having said airfoil inlet and exit angles defined by Table 5 and an airfoil for a fourth stage blade having said airfoil inlet and exit angles defined by Table 7.

7. The turbine airfoil assembly of claim 6, wherein said measured difference between any pair of said airfoil inlet and exit angles varies from the corresponding delta values, Δ, in a respective Table by at most 3%.

8. The turbine airfoil assembly of claim 6, wherein said measured difference between any pair of said airfoil inlet and exit angles varies from the corresponding delta values, Δ, in a respective Table by at most 1%.

9. Third and fourth stage vane and blade airfoil assemblies in a gas turbine engine having a longitudinal axis, each airfoil assembly including:
an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall, said airfoil having an outer wall comprising a pressure sidewall and a suction sidewall joined together at chordally spaced apart leading and trailing edges of said airfoil, an airfoil mean line is defined extending chordally and located centrally between said pressure and suction sidewalls, airfoil inlet and exit angles are defined at said airfoil leading and trailing edges that are in accordance with pairs of inlet angle values, α, and exit angle values, β, where said inlet and exit angle values are defined as angles between a line parallel to the longitudinal axis and the airfoil mean line lying in an X-Y plane of an X, Y, Z Cartesian coordinate system in which Z is a dimension perpendicular to the X-Y plane and extends radially relative to the longitudinal axis, and wherein each pair of inlet and exit angle values is defined with respect to a distance from said endwall corresponding to a Z value that is a percentage of a total span of said airfoil from said endwall, wherein:
a) said pairs of inlet angle values, α, and exit angle values, β, for said third stage vane are as set forth in Table 1;
b) said pairs of inlet angle values, α, and exit angle values, β, for said third stage blade are as set forth in Table 3;
c) said pairs of inlet angle values, α, and exit angle values, β, for said fourth stage vane are as set forth in Table 5;
d) said pairs of inlet angle values, α, and exit angle values, β, for said fourth stage blade are as set forth in Table 7; and

wherein a predetermined difference between each pair of said airfoil inlet and exit angles is defined by a delta value, Δ, in said Tables 1, 3, 5 and 7 associated with said third stage vane, said third stage blade, said fourth stage vane, and said fourth stage blade, respectively, and a measured difference between any pair of said airfoil inlet and exit angles varies from the corresponding delta values, Δ, in a respective one of said Tables 1, 3, 5 and 7 by at most 5%.

10. The turbine airfoil assembly of claim 9, wherein said measured difference between any pair of said airfoil inlet and exit angles varies from the corresponding delta values, Δ, in a respective one of said Tables 1, 3, 5 and 7 by at most 3%.

11. The turbine airfoil assembly of claim 9, wherein said measured difference between any pair of said airfoil inlet and exit angles varies from the corresponding delta values, Δ, in a respective one of said Tables 1, 3, 5 and 7 by at most 1%.

12. A turbine airfoil assembly for installation in a gas turbine engine having a longitudinal axis, the turbine airfoil assembly including an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall, said airfoil having an outer wall comprising a pressure sidewall and a suction sidewall joined together at chordally spaced apart leading and trailing edges of said airfoil, an airfoil mean line is defined extending chordally and located centrally between said pressure and suction sidewalls, airfoil exit angles are defined at said airfoil trailing edge that are in accordance with exit angle values, β, set forth in one of Tables 1, 3, 5 and 7, where said exit angle values are defined as angles between a line parallel to the longitudinal axis and the airfoil mean line lying in an X-Y plane of an X, Y, Z Cartesian coordinate system in which Z is a dimension perpendicular to the X-Y plane and extends radially relative to the longitudinal axis, wherein each said exit angle value is defined with respect to a distance from said endwall corresponding to a Z value that is a percentage of a total span of said airfoil from said endwall, and wherein each said airfoil exit angle is within about 1% of a respective value set forth in said one of Tables 1, 3, 5 and 7.

13. The turbine airfoil assembly of claim 12, wherein said airfoil comprises an airfoil for a third stage vane in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil exit angles is Table 1.

14. The turbine airfoil assembly of claim 12, wherein said airfoil comprises an airfoil for a third stage blade in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil exit angles is Table 3.

15. The turbine airfoil assembly of claim 12, wherein said airfoil comprises an airfoil for a fourth stage vane in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil exit angles is Table 5.

16. The turbine airfoil assembly of claim 12, wherein said airfoil comprises an airfoil for a fourth stage blade in a turbine engine, and said one of Tables 1, 3, 5 and 7 defining said airfoil exit angles is Table 7.

17. The turbine airfoil assembly of claim 12, including four of said airfoils comprising, in succession, an airfoil for a third stage vane having airfoil exit angles defined by Table 1, an airfoil for a third stage blade having airfoil exit angles defined by Table 3, an airfoil for a fourth stage vane having airfoil exit angles defined by Table 5 and an airfoil for a fourth stage blade having airfoil exit angles defined by Table 7.

18. The turbine airfoil assembly of claim 12, including at least two of said airfoils comprising, in succession, an airfoil for a third stage blade having airfoil exit angles defined by Table 3, and an airfoil for a fourth stage vane having airfoil exit angles defined by Table 5.