Gas turbine with optimized airfoil element angles

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.

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.

DETAILED DESCRIPTION OF THE INVENTION

Referring toFIG. 1, a turbine section12for a gas turbine engine is illustrated. The turbine section12comprises alternating rows of stationary vanes and rotating blades extending radially into an axial flow path13extending through the turbine section12. In particular, the turbine section12includes a first stage formed by a first row of stationary vanes14and a first row of rotating blades16, a second stage formed by a second row of stationary vanes18and a second row of rotating blades20, a third stage formed by a third row of stationary vanes22and a third row of rotating blades24, and a fourth stage formed by a fourth row of stationary vanes26and a fourth row of rotating blades28.

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 section12where it expands and causes the blades16,20,24,28to rotate. The overall work output from the turbine section12is distributed into all of the stages, where the stationary vanes14,18,22,26are provided for accelerating the gas flow and turn the gas flow to feed into the respective downstream blades16,20,24,28to generate torque on a rotor30supporting the blades16,20,24,28, producing a rotational output about a longitudinal axis32of the engine, such as to drive the upstream compressor.

The flow turning occurring at each rotating blade16,20,24,28creates a reaction force on the blade16,20,24,28to 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 vanes14,18,22,26and respective blades16,20,24,28, 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 vanes22,26and blades24,28is provided to optimize or improve the flow angle changes through the third and fourth stages. Specifically, the design of the third and fourth stage vanes22,26and blades24,28, as described below, provide a radial variation in inlet and exit flow angles to produce optimized flow profiles into an exhaust diffuser34downstream from the turbine section12. Optimized flow profiles through the third and fourth stages of the turbine section12may facilitate a reduction in the average Mach number for flows exiting the fourth stage vanes26, with an associated improvement in engine efficiency, since flow loss tends to be proportional to the square of the Mach number.

Referring toFIGS. 2-5, a configuration for the third stage vane22is described. In particular, referring initially toFIGS. 2 and 3, a third stage vane airfoil structure36is shown including three of the airfoils or vanes22adapted to be supported to extend radially across the flow path13. Referring additionally toFIG. 4, the vanes22each include an outer wall comprising a generally concave pressure sidewall38, and include an opposing generally convex suction sidewall40. The sidewalls38,40extend radially between an inner diameter endwall42and an outer diameter endwall44, and extend generally axially in a chordal direction between a leading edge46and a trailing edge48of each of the vanes22. The endwalls42,44are located at opposing ends of the vanes22and are positioned at locations where they form a boundary, i.e., inner and outer boundaries, defining a portion of the flow path13for the working fluid. Opposing radially inner matefaces45a,47aand radially outer matefaces45b,47bare defined by the respective inner and outer diameter endwalls42,44of the airfoil structure36.

FIG. 4illustrates a cross section of one of the vanes22at 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 axis32of 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 vane22. It should be noted that the matefaces45a,47aand45b,47bare shown herein as extending at an angle relative to the direction of the longitudinal axis32.

The cross section ofFIG. 4lies in the X-Y plane. As seen inFIG. 4, the vane22defines an airfoil mean line, CV3, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls38,40. At the leading edge46, a blade metal angle of each of the surfaces of the pressure and suction sides38,40adjacent to the leading edge46is provided for directing incoming flow to the vane22and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CV3, at the leading edge46, i.e., tangential to the line CV3at the airfoil leading edge46.

At the trailing edge48, a blade metal angle of the surfaces of the pressure and suction sides38,40adjacent to the trailing edge48is provided for directing flow exiting from the vane22and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CV3, at the trailing edge48, i.e., tangential to the line CV3at the airfoil trailing edge48.

The inlet angles, α, and exit angles, β, for the airfoil of the vane22are as described in Table 1 below. The Z coordinate locations are presented as a percentage of the total span of the vane22. 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 vane22, where 0% is located adjacent to the inner endwall42and 100% is located adjacent to the outer endwall44. The inlet angles, α, and exit angles, β, are further graphically illustrated inFIG. 5.

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 vane22. The inlet angle, α, is selected with reference to the flow direction coming from the second row blades20, and the exit angle, β, is preferably selected to provide a predetermined direction of flow into the third stage blades24.

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 vane22is 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 vane22are 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 vane22described 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 vane22. 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 vane22, i.e., adjacent the inner endwall42, and are presented as a percentage of the total span of the vane22. The X axis lies parallel to the longitudinal axis32, 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 vane22are 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 section50at each Z location is described by successive data points N=1 to N=30 defining the leading edge section50as extending from the suction sidewall40, around the leading edge46, and along a portion of the pressure sidewall38.

The trailing edge section52at each Z location is described in two parts. In particular, a first part of the trailing edge section52is described along the suction sidewall40by data points N=31 to N=40, and a second part of the trailing edge section52is described along the pressure sidewall38by 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 edge48of the vane22.

Referring toFIGS. 6-9, a configuration for the third stage blade24is described. In particular, referring initially toFIGS. 6 and 7, a third stage blade airfoil structure56is shown including one of the airfoils or blades24adapted to be supported to extend radially across the flow path13. Referring additionally toFIG. 8, the blades24each include an outer wall comprising a generally concave pressure sidewall58, and include an opposing generally convex suction sidewall60. The sidewalls58,60extend radially outwardly from an inner diameter endwall62to a blade tip64, and extend generally axially in a chordal direction between a leading edge66and a trailing edge68of each of the blades24. A blade root is defined by a dovetail65extending radially inwardly from the endwall62for mounting the blade24to the rotor30. The endwall62is positioned at a location where it forms a boundary, i.e., an inner boundary, defining a portion of the flow path13for the working fluid.

FIG. 8illustrates a cross section of the blade24at 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 axis32of 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 blade24. It should be noted that a central lengthwise axis67of the dovetail65is shown herein as extending at an angle relative to the direction of the longitudinal axis32.

The cross section ofFIG. 8lies in the X-Y plane. As seen inFIG. 8, the blade24defines an airfoil mean line, CB3, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls58,60. At the leading edge66, a blade metal angle of each of the surfaces of the pressure and suction sides58,60adjacent to the leading edge66is provided for directing incoming flow to the blade24and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CB3, at the leading edge66, i.e., tangential to the line CB3at the airfoil leading edge66.

At the trailing edge68, a blade metal angle of the surfaces of the pressure and suction sides58,60adjacent to the trailing edge68is provided for directing flow exiting from the blade24and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, α, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CB3, at the trailing edge68, i.e., tangential to the line CB3at the airfoil trailing edge68.

The inlet angles, α, and exit angles, β, for the airfoil of the blade24are as described in Table 3 below. The Z coordinate locations are presented as a percentage of the total span of the blade24. 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 blade24, where 0% is located adjacent to the inner endwall62and 100% is located adjacent to the blade tip64. The inlet angles, α, and exit angles, β, are further graphically illustrated inFIG. 9.

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 edge66and trailing edge68, 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 blade24is 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 blade24are 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 blade24described 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 blade24. 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 blade24, i.e., adjacent the inner endwall62, and are presented as a percentage of the total span of the blade24. The X axis lies parallel to the longitudinal axis32, 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 blade24are 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 section70at each Z location is described by successive data points N=1 to N=30 defining the leading edge section70as extending from the pressure sidewall58, around the leading edge66, and along a portion of the suction sidewall60.

The trailing edge section72at each Z location is described in two parts. In particular, a first part of the trailing edge section72is described along the pressure sidewall58by data points N=31 to N=40, and a second part of the trailing edge section52is described along the suction sidewall60by 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 edge68of the blade24.

Referring toFIGS. 10-13, a configuration for the fourth stage vane26is described. In particular, referring initially toFIGS. 10 and 11, a fourth stage vane airfoil structure76is shown including four of the airfoils or vanes26adapted to be supported to extend radially across the flow path13. Referring additionally toFIG. 12, the vanes26each include an outer wall comprising a generally concave pressure sidewall78, and include an opposing generally convex suction sidewall80. The sidewalls78,80extend radially between an inner diameter endwall82and an outer diameter endwall84, and extend generally axially in a chordal direction between a leading edge86and a trailing edge88of each of the vanes26. The endwalls82,84are located at opposing ends of the vanes26and are positioned at locations where they form a boundary, i.e., inner and outer boundaries, defining a portion of the flow path13for the working fluid. Opposing radially inner matefaces85a,87aand radially outer matefaces85b,87bare defined by the respective inner and outer diameter endwalls82,84of the airfoil structure76.

FIG. 12illustrates a cross section of one of the vanes26at 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 axis32of 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 vane26. It should be noted that the matefaces85a,87aand85b,87bare shown herein as extending at an angle relative to the direction of the longitudinal axis32.

The cross section ofFIG. 12lies in the X-Y plane. As seen inFIG. 12, the vane26defines an airfoil mean line, CV4, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls78,80. At the leading edge86, a blade metal angle of each of the surfaces of the pressure and suction sides78,80adjacent to the leading edge86is provided for directing incoming flow to the vane26and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CV4, at the leading edge86, i.e., tangential to the line CV4at the airfoil leading edge86.

At the trailing edge88, a blade metal angle of the surfaces of the pressure and suction sides78,80adjacent to the trailing edge88is provided for directing flow exiting from the vane26and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CV4, at the trailing edge88, i.e., tangential to the line CV4at the airfoil trailing edge88.

The inlet angles, α, and exit angles, β, for the airfoil of the vane26are as described in Table 5 below. The Z coordinate locations are presented as a percentage of the total span of the vane26. 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 vane26, where 0% is located adjacent to the inner endwall82and 100% is located adjacent to the outer endwall84. The inlet angles, α, and exit angles, β, are further graphically illustrated inFIG. 13.

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 vane26. The inlet angle, α, is selected with reference to the flow direction coming from the third row blades24, and the exit angle, β, is preferably selected to provide a predetermined direction of flow into the fourth stage blades28.

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 vane26is 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 vane26are 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 vane26described 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 vane26. 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 vane26, i.e., adjacent the inner endwall82, and are presented as a percentage of the total span of the vane26, and are presented as a percentage of the total span of the blade28. The X axis lies parallel to the longitudinal axis32, 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 vane26are 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 section90at each Z location is described by successive data points N=1 to N=30 defining the leading edge section90as extending from the suction sidewall80, around the leading edge86, and along a portion of the pressure sidewall78.

The trailing edge section92at each Z location is described in two parts. In particular, a first part of the trailing edge section92is described along the suction sidewall80by data points N=31 to N=40, and a second part of the trailing edge section92is described along the pressure sidewall78by 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 edge88of the vane26.

Referring toFIGS. 14-17, a configuration for the fourth stage blade28is described. In particular, referring initially toFIGS. 14 and 15, a fourth stage blade airfoil structure96is shown including one of the airfoils or blades28adapted to be supported to extend radially across the flow path13. Referring additionally toFIG. 16, the blades28each include an outer wall comprising a generally concave pressure sidewall98, and include an opposing generally convex suction sidewall100. The sidewalls98,100extend radially outwardly from an inner diameter endwall102to a blade tip104, and extend generally axially in a chordal direction between a leading edge106and a trailing edge108of each of the blades28. A blade root is defined by a dovetail105extending radially inwardly from the endwall102for mounting the blade28to the rotor30. The endwall102is positioned at a location where it forms a boundary, i.e., an inner boundary, defining a portion of the flow path13for the working fluid.

FIG. 16illustrates a cross section of the blade28at 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 axis32of 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 blade28. It should be noted that a central lengthwise axis107of the dovetail105is shown herein as extending at an angle relative to the direction of the longitudinal axis32.

The cross section ofFIG. 16lies in the X-Y plane. As seen inFIG. 16, the blade28defines an airfoil mean line, CB4, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls98,100. At the leading edge106, a blade metal angle of each of the surfaces of the pressure and suction sides98,100adjacent to the leading edge106is provided for directing incoming flow to the blade28and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CB4, at the leading edge106, i.e., tangential to the line CB4at the airfoil leading edge106.

At the trailing edge108, a blade metal angle of the surfaces of the pressure and suction sides98,100adjacent to the trailing edge108is provided for directing flow exiting from the blade28and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line32Pparallel to the longitudinal axis32and an extension of the airfoil mean line, CB4, at the trailing edge108, i.e., tangential to the line CB4at the airfoil trailing edge108.

The inlet angles, α, and exit angles, β, for the airfoil of the blade28are as described in Table 7 below. The Z coordinate locations are presented as a percentage of the total span of the blade28. 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 blade28, where 0% is located adjacent to the inner endwall102and 100% is located adjacent to the blade tip104. The inlet angles, α, and exit angles, β, are further graphically illustrated inFIG. 17.

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 edge106and trailing edge108, 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 blade28is 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 blade28are 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 blade28described 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 blade28. 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 blade28, i.e., adjacent the inner endwall102. The X axis lies parallel to the longitudinal axis32, 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 blade28are 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 section110at each Z location is described by successive data points N=1 to N=30 defining the leading edge section106as extending from the pressure sidewall98, around the leading edge106, and along a portion of the suction sidewall100.

The trailing edge section112at each Z location is described in two parts. In particular, a first part of the trailing edge section112is described along the pressure sidewall98by data points N=31 to N=40, and a second part of the trailing edge section112is described along the suction sidewall100by 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 edge108of the blade28.

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 vane22, blade24, vane26, and blade28, 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 vane22, blade24, vane26, and blade28. 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 vane22, third stage blade24, fourth stage vane26and fourth stage blade28. Further, the average Z value at 100% span for each of the airfoils may be approximately the following values: third stage vane22=1145 mm; third stage blade24=1191.7 mm; fourth stage vane26=1268.5 mm; and fourth stage blade28=1366.9 mm.

TABLE 2NXYThird Stage Vane LE and TE at Z = 0%1596.264826.90332590.782224.60283586.049222.01314583.297720.20435579.750817.46406577.753915.66687575.270113.08618573.406610.68769572.50519.217810571.60587.283211571.26416.216612571.06385.147813571.01894.154914571.12023.151715571.38542.168016571.88111.128117572.49090.304218573.2425−0.392219574.1054−0.937520575.1667−1.364021576.1508−1.578822577.1388−1.647923578.1001−1.587924579.5191−1.321525581.3417−0.817126582.7806−0.376227585.28280.404128588.21561.293429590.42111.927330594.11852.890831713.5055−69.708932712.6509−68.127633711.5355−66.059234710.6472−64.409735709.0968−61.530636707.2812−58.168237705.9196−55.660738703.6408−51.506339701.9556−48.479740699.1598−43.566141699.2449−57.126242701.0559−59.182143703.4869−62.016344704.9191−63.736845706.7917−66.057446708.3448−68.055347709.2102−69.201148710.2644−70.631049710.8103−71.387250711.1004−71.693851711.4806−71.930752711.9202−72.057653712.3720−72.051754712.7844−71.930355713.1268−71.717156713.4173−71.400857713.6213−70.998558713.7002−70.548659713.6540−70.103760713.5055−69.7089Third Stage Vane LE and TE at Z = 10%1597.234324.53872591.596322.66583586.691120.41134583.824618.77865580.113116.24196578.016414.54697575.401812.08098573.42019.76649572.44298.340610571.44466.451211571.05335.400112570.80694.343813570.71883.356614570.77582.353115570.99681.361916571.44490.305117572.016−0.541818572.7337−1.267819573.569−1.848520574.607−2.319721575.5778−2.576922576.559−2.689523577.5197−2.672424578.9671−2.479125580.8411−2.096926582.3269−1.750527584.9152−1.131428587.9494−0.457829590.2269−0.003130594.02840.646731715.6596−74.804032714.8119−73.206433713.6936−71.123034712.7944−69.466035711.2109−66.581536709.3402−63.221737707.9302−60.720138705.5636−56.579639703.8134−53.563940700.9182−48.664141701.1117−62.038842702.9780−64.104343705.4785−66.958344706.9490−68.694245708.8679−71.039646710.4553−73.062747711.3362−74.225848712.4026−75.682149712.9507−76.455050713.2384−76.765851713.6166−77.007652714.0550−77.139953714.5067−77.139154714.9199−77.022255715.2641−76.812456715.5571−76.498857715.7644−76.097858715.8471−75.647959715.8047−75.201560715.6596−74.8040Third Stage Vane LE and TE at Z = 20%1598.512422.23122592.698420.82323587.604718.91814584.617717.45815580.743415.10526578.554613.49337575.826611.11188573.7338.86459572.67027.483510571.5415.649011571.07534.619312570.75913.580413570.60542.600914570.59541.596015570.74980.593216571.1264−0.489717571.6398−1.371018572.3077−2.141319573.1029−2.774420574.1082−3.311321575.0609−3.630422576.0342−3.805823576.996−3.850324578.4802−3.745925580.4073−3.466326581.9323−3.171927584.5865−2.618228587.7041−2.058129590.0463−1.726030593.9526−1.337331717.7578−80.234832716.9089−78.622133715.7833−76.521934714.8744−74.853835713.2661−71.954336711.3574−68.582437709.9148−66.074638707.4902−61.926839705.6975−58.906140702.7394−53.995741703.0133−67.263942704.9154−69.353443707.4592−72.245444708.9537−74.006245710.9035−76.385746712.5166−78.438247713.4109−79.618848714.4913−81.098449715.0453−81.884750715.3312−82.195651715.7078−82.437752716.1450−82.570253716.5960−82.569754717.0091−82.452955717.3537−82.243256717.6477−81.929757717.8564−81.528958717.9410−81.079059717.9008−80.632560717.7578−80.2348Third Stage Vane LE and TE at Z = 30%1593.531719.65812588.258817.84803585.168216.41254581.168714.05155578.915812.41436576.11609.98177573.95527.69228572.83996.29549571.62484.447810571.10593.409911570.74722.378412570.55401.400713570.50440.392414570.6200−0.619415570.9558−1.719116571.4372−2.621017572.0782−3.416618572.8525−4.078519573.8416−4.650720574.7862−5.002521575.7567−5.210622576.7206−5.287023578.2466−5.223624580.2287−4.970825581.7933−4.675726584.5088−4.087727587.6940−3.476228590.0897−3.125429594.0979−2.762830597.0399−2.667531719.7108−85.584932718.8380−83.947533717.6859−81.812634716.7591−80.115335715.1257−77.162036713.1949−73.724337711.7399−71.165838709.3008−66.931839707.5013−63.846940704.5374−58.830341704.8449−72.301742706.7635−74.447043709.3262−77.417644710.8320−79.225445712.7993−81.665546714.4317−83.765847715.3397−84.971448716.4423−86.478249717.0114−87.276150717.2987−87.583251717.6762−87.819952718.1134−87.946253718.5638−87.938954718.9756−87.816055719.3184−87.601156719.6101−87.283057719.8163−86.878758719.8983−86.427259719.8557−85.980960719.7108−85.5849Third Stage Vane LE and TE at Z = 40%1593.938019.25432588.511717.26253585.339415.70664581.247713.16955578.949711.42066576.10168.83437573.90806.41498572.77494.94779571.53213.019810570.99421.943011570.63280.908812570.4378−0.071913570.3874−1.083614570.5034−2.098915570.8411−3.201816571.3254−4.105717571.9706−4.902018572.7496−5.563219573.7442−6.133120574.6933−6.481521575.6677−6.685322576.6346−6.756923578.2084−6.679724580.2517−6.389625581.8646−6.065426584.6566−5.399927587.9148−4.628428590.3639−4.139329594.4772−3.565130597.5047−3.333131721.4481−90.779032720.5383−89.103533719.3499−86.912134718.4029−85.164935716.7497−82.116036714.8152−78.556037713.3673−75.900738710.9534−71.498339709.1786−68.286640706.2590−63.059741706.4934−77.051142708.4131−79.286343710.9783−82.376744712.4878−84.253445714.4659−86.779746716.1155−88.946347717.0388−90.185248718.1700−91.726249718.7599−92.537850719.0509−92.840351719.4314−93.070252719.8708−93.187653720.3220−93.170654720.7333−93.038255721.0747−92.814756721.3638−92.488657721.5665−92.077758721.6442−91.622059721.5972−91.174160721.4481−90.7790Third Stage Vane LE and TE at Z = 50%1594.302419.11972588.715516.99043585.448315.35194581.230512.69825578.860610.87496575.92618.18107573.67655.65808572.52224.12629571.25732.118910570.71210.999611570.3615−0.035212570.1767−1.015813570.1368−2.026214570.2638−3.039215570.6139−4.138416571.1089−5.037617571.7637−5.827818572.5511−6.481719573.5533−7.042020574.5073−7.381421575.4849−7.575922576.4530−7.638123578.0823−7.535624580.1949−7.209025581.8648−6.870826584.7549−6.173327588.1141−5.296628590.6317−4.690029594.8530−3.899730597.9691−3.535631722.8869−95.914632721.9544−94.190533720.7485−91.929034719.7960−90.121335718.1479−86.958536716.2361−83.255637714.8128−80.488938712.4483−75.895539710.7128−72.541440707.8551−67.081041707.8061−81.685042709.7202−84.022343712.2856−87.243044713.8005−89.192545715.7937−91.808446717.4650−94.043447718.4058−95.317048719.5639−96.897349720.1698−97.728050720.4636−98.031151720.8480−98.259452721.2918−98.373353721.7477−98.350854722.1634−98.211855722.5084−97.981556722.8007−97.647757723.0057−97.229058723.0845−96.766459723.0373−96.313160722.8869−95.9146Third Stage Vane LE and TE at Z = 60%1594.907819.05802589.130217.02703585.736615.44274581.328912.84505578.841311.04086575.75768.34917573.40135.79878572.19954.23739570.88292.186010570.32121.036811569.97540.016712569.7929−0.950613569.7526−1.947914569.8770−2.949315570.2216−4.038416570.7088−4.931917571.3534−5.719818572.1292−6.375119573.1177−6.941120574.0599−7.288721575.0264−7.493822575.9849−7.567823577.6755−7.469024579.8649−7.145925581.5979−6.823226584.6030−6.164227588.0934−5.308828590.6975−4.681929595.0270−3.820730598.2299−3.454931723.9476−101.027532723.0299−99.247033721.8492−96.909334720.9205−95.039135719.3185−91.765036717.4623−87.930737716.0785−85.066438713.7743−80.312939712.0776−76.843840709.2722−71.201041708.6668−86.295842710.5751−88.727543713.1486−92.062944714.6765−94.074345716.6955−96.765746718.3957−99.059147719.3549−100.364348720.5295−101.988149721.1376−102.846550721.4303−103.159451721.8170−103.397152722.2669−103.518653722.7321−103.501154723.1589−103.364155723.5157−103.133056723.8211−102.795757724.0393−102.370758724.1299−101.899459724.0919−101.436160723.9476−101.0275Third Stage Vane LE and TE at Z = 70%1595.725819.71562589.764117.78093586.254916.23864581.681613.67225579.091511.87076575.87129.16047573.40256.57278572.13854.98249570.73842.89410570.12721.725911569.76940.759112569.5683−0.162613569.5009−1.11914569.5883−2.086315569.8801−3.148216570.3121−4.030317570.8962−4.820718571.6090−5.492719572.5272−6.092720573.4106−6.481621574.3240−6.73622575.2367−6.864723576.9887−6.853224579.2676−6.56825581.0676−6.242126584.1857−5.563627587.8049−4.686928590.4943−4.029629594.9371−3.107430598.2319−2.743331724.7393−106.128532723.8659−104.280433722.7420−101.855634721.8573−99.917035720.3277−96.526536718.5461−92.561337717.2100−89.603238714.9715−84.700439713.3133−81.126940710.5568−75.320741709.3112−90.760442711.2150−93.289243713.7960−96.745644715.3344−98.824445717.3719−101.601946719.0897−103.966547720.0577−105.312948721.2312−106.996149721.8287−107.892950722.1137−108.218751722.4965−108.471052722.9475−108.607453723.4190−108.603154723.8561−108.476655724.2257−108.252556724.5471−107.919157724.7834−107.494258724.8922−107.018659724.8705−106.547460724.7393−106.1285Third Stage Vane LE and TE at Z = 80%1596.644721.68992590.538019.60413586.961117.94644582.324615.20765579.703313.29656576.432910.43547573.89727.72738572.57516.07919571.07173.934510570.36802.755211569.97851.890712569.73411.055413569.60820.174714569.6171−0.729815569.7977−1.741216570.1157−2.602317570.5762−3.398118571.1609−4.102519571.9360−4.767820572.6983−5.235421573.5009−5.583622574.3168−5.817823576.1214−6.009124578.5001−5.788225580.3656−5.40326583.5725−4.543327587.2815−3.45628590.0336−2.659929594.5908−1.546430597.9836−1.053831725.4432−111.199032724.6232−109.266533723.5627−106.734834722.7238−104.713735721.2655−101.183636719.5556−97.061137718.2664−93.988538716.0960−88.900039714.4818−85.193040711.7898−79.171141710.0909−94.871042711.9927−97.519243714.5682−101.139144716.1004−103.317145718.1242−106.229446719.8236−108.712247720.7774−110.127848721.9259−111.901049722.5053−112.848550722.7739−113.180651723.1417−113.443352723.5812−113.593653724.0463−113.605454724.4821−113.495055724.8553−113.285756725.1852−112.966557725.4346−112.553658725.5601−112.086159725.5568−111.618560725.4432−111.1990Third Stage Vane LE and TE at Z = 90%1597.424424.41032591.192522.04963587.567620.20644582.906617.21615580.282815.15846577.004312.11087574.43779.26618573.07727.55669571.49555.354710570.71094.165611570.29443.394812570.01252.638413569.83561.826914569.77530.980415569.85690.017116570.0723−0.822217570.4209−1.619418570.8884−2.349619571.5306−3.070020572.1788−3.605721572.8752−4.036622573.5964−4.365123575.4333−4.758624577.8883−4.611625579.8014−4.165226583.0600−3.093327586.8127−1.744128589.6013−0.781529594.25680.544130597.73761.189831726.1397−116.086732725.3656−114.056933724.3566−111.402234723.5531−109.285535722.1483−105.592336720.4948−101.281937719.2471−98.069138717.1460−92.746639715.5839−88.866940712.9807−82.559041711.0878−98.483742712.9924−101.274443715.5505−105.102544717.0600−107.413445719.0380−110.512046720.6838−113.161447721.6019−114.674548722.7077−116.566149723.2681−117.572650723.5139−117.900751723.8571−118.165652724.2727−118.325053724.7177−118.352254725.1391−118.261155725.5039−118.072656725.8310−117.777157726.0844−117.388858726.2210−116.943659726.2340−116.493960726.1397−116.0867Third Stage Vane LE and TE at Z = 100%1597.897627.10522591.544424.54663587.864622.56904583.156319.39545580.515717.23296577.222614.05677574.641911.11888573.26779.36589571.65907.119810570.84415.916311570.42305.188012570.13114.468413569.93793.690214569.85282.873015569.89611.936416570.06971.112617570.37070.321418570.7866−0.413019571.3680−1.149720571.9619−1.708821572.6060−2.170322573.2787−2.535623575.1321−3.031024577.6269−2.944625579.5670−2.478326582.8498−1.283427586.61990.237628589.43241.307629594.17642.731630597.73343.411331726.7519−120.505832726.0066−118.383033725.0298−115.608634724.2490−113.397935722.8811−109.541536721.2734−105.038937720.0653−101.679738718.0401−96.108639716.5412−92.042540714.0527−85.422441712.0662−101.557342713.9726−104.496843716.5082−108.545244717.9898−110.997445719.9139−114.294546721.4987−117.121047722.3777−118.736848723.4428−120.748749723.9904−121.811550724.2141−122.130251724.5318−122.392552724.9210−122.557553725.3416−122.598654725.7432−122.527055726.0939−122.361556726.4120−122.093557726.6628−121.735158726.8047−121.319059726.8297−120.894260726.7519−120.5058

TABLE 4NXYThird Stage Blade LE and TE at Z = 0%1777.2090−11.25522773.7695−9.47423771.7330−8.26914769.0597−6.46495767.5310−5.27966765.6184−3.55407764.1601−1.92738763.4399−0.91989762.73340.433010762.50821.198211762.44371.710312762.44192.166513762.49642.615014762.61093.047315762.81073.503916763.04943.874117763.34304.202318763.68594.483319764.12014.739220764.53954.911121764.98115.031722765.43565.102023766.51955.093124767.92734.916225769.04224.727226770.98284.363127773.24653.912728774.93613.571629777.74353.010630779.79822.611031877.774432.265132877.083131.204233876.168829.823434875.431628.727535874.127526.825436872.576424.619537871.399522.984238869.410820.291139867.929218.341240865.457615.197541866.224224.308942867.725425.657843869.736627.532144870.923628.674445872.483430.216046873.788231.540847874.521232.298848875.420933.242849875.890033.741050876.128733.934351876.425234.067352876.753634.114253877.083734.068554877.380133.947155877.616733.761856877.805733.503157877.929333.193558877.962632.863359877.904732.543460877.774432.2651Third Stage Blade LE and TE at Z = 10%1784.7477−14.38642781.0620−12.87403777.8247−11.25504775.9113−10.14655773.3969−8.48446771.9499−7.40067770.1162−5.84118768.6683−4.39559767.9182−3.505410767.1460−2.284711766.8941−1.574712766.8169−1.167113766.7933−0.803214766.8159−0.445115766.8881−0.099516767.02860.265717767.20450.562018767.42680.824719767.69071.049320768.02931.252621768.35941.387822768.70891.481523769.07021.535224770.09381.542025771.42821.357626772.48371.154927774.32090.779428776.46720.342829778.07260.030430780.7459−0.455531874.998732.413332874.350731.411933873.493530.108434872.802029.073935871.577627.278936870.118525.198837869.008823.658438867.127921.125739865.723119.294540863.377216.344541864.115124.622842865.517125.944543867.396027.777044868.505028.892245869.962230.395546871.181331.686347871.865932.424648872.706133.343749873.144233.828650873.373734.022251873.661434.157652873.982134.208753874.306134.168754874.598134.053855874.832033.875456875.019933.624157875.144133.322158875.179532.999259875.124832.685960874.998732.4133Third Stage Blade LE and TE at Z = 20%1784.1823−13.26562781.0625−11.92173779.2094−10.98964776.7629−9.57325775.3489−8.63736773.5560−7.26587772.1513−5.95958771.4410−5.13129770.7720−3.959010770.6076−3.272811770.5884−2.970812770.6004−2.700613770.6405−2.432714770.7094−2.171215770.8210−1.889316770.9501−1.654017771.1066−1.437018771.2882−1.240919771.5181−1.047420771.7411−0.901021771.9775−0.779522772.2235−0.683623773.1720−0.485624774.4469−0.491925775.4602−0.600326777.2199−0.862727779.2713−1.205928780.8042−1.461229783.3552−1.865630785.2253−2.140131871.941232.512232871.333031.559933870.527630.320934869.877329.338235868.724627.633736867.349925.659437866.304124.197738864.531621.794139863.208420.055840861.001417.253141861.763324.735642863.049726.061543864.778427.890944865.801928.999045867.150930.487146868.283431.759647868.921232.485248869.705733.386349870.115733.860750870.335934.054451870.614534.192352870.927134.248253871.244734.214654871.532034.107155871.763133.936556871.950133.693757872.075133.400358872.113133.085559872.062432.779160871.941232.5122Third Stage Blade LE and TE at Z = 30%1785.8363−13.82722782.8010−12.63863780.9949−11.80224778.6096−10.51245777.2330−9.64616775.4975−8.35557774.1616−7.10158773.5062−6.29399772.9367−5.143310772.8357−4.473811772.8556−4.237712772.8920−4.025313772.9447−3.812614773.0127−3.601515773.1071−3.368616773.2070−3.167817773.3221−2.975018773.4513−2.791319773.6115−2.597020773.7653−2.436521773.9284−2.290022774.0996−2.159723774.9863−1.806924776.2180−1.672625777.2034−1.708226778.9085−1.889327780.8911−2.175828782.3701−2.400629784.8288−2.760630786.6296−3.005331868.773732.528832868.191631.616433867.420230.430134866.797029.489635865.692227.858936864.375125.970137863.374124.571338861.680522.269539860.418920.603040858.319517.912141859.150824.820742860.348226.140543861.961727.954644862.919829.049845864.186330.516146865.253131.765947865.855432.477048866.598033.358449866.986733.821750867.199134.013551867.469634.151652867.774434.209853868.085134.180554868.366834.078655868.593733.914456868.778033.679257868.901833.394258868.940233.087659868.891532.789060868.773732.5288Third Stage Blade LE and TE at Z = 40%1789.7414−16.18732786.4276−15.14333783.5017−13.96234781.7674−13.12415779.4876−11.82486778.1798−10.94907776.5404−9.64718775.2909−8.39089774.6811−7.591010774.1423−6.473811774.0330−5.828912774.0430−5.614813774.0681−5.420614774.1076−5.224515774.1609−5.028416774.2370−4.810017774.3191−4.619818774.4149−4.435119774.5233−4.257320774.6588−4.066921774.7895−3.907922774.9290−3.760723775.0760−3.627624775.9066−3.224825777.0894−3.051226778.0432−3.071027779.6906−3.237228781.6051−3.515829783.0332−3.735630785.4075−4.077131865.642132.397432865.070531.518733864.313630.376134863.702929.470135862.621627.898836861.335026.078037860.358924.728838858.711322.506639857.486920.896040855.454718.291841856.358024.912542857.509926.195043859.063227.957044859.986229.020345861.206830.443646862.235331.656547862.816232.346648863.532433.201949863.907333.651650864.113933.838851864.377333.973952864.674734.031153864.977934.002954865.252633.903955865.473633.744256865.652633.515257865.772333.237758865.808232.939559865.758932.649660865.642132.3974Third Stage Blade LE and TE at Z = 50%1787.6933−16.84352784.9087−15.75953783.2613−14.97704781.1004−13.75225779.8639−12.92106778.3156−11.67887777.1396−10.47018776.5643−9.70049776.0287−8.640710775.8843−8.031911775.8683−7.827612775.8699−7.640713775.8867−7.451114775.9189−7.260815775.9737−7.048516776.0386−6.863617776.1186−6.684418776.2127−6.512619776.3332−6.330020776.4517−6.178921776.5792−6.040222776.7143−5.915323777.4642−5.484724778.5662−5.267725779.4685−5.260526781.0325−5.377227782.8546−5.588128784.2158−5.757529786.4813−6.019730788.1420−6.187631862.597131.994632862.035731.151333861.294830.053334860.698829.181635859.647427.667836858.401425.910837857.459324.607038855.873622.457039854.698320.896940852.752118.371741853.617224.801542854.733826.032343856.238727.725144857.132428.747745858.313630.117546859.308131.285947859.869431.951048860.561132.775949860.923133.209850861.123633.391451861.379633.522652861.668633.578053861.963133.550554862.229633.454255862.443433.299056862.616133.076657862.730632.807258862.763332.518259862.712932.237860862.597131.9946Third Stage Blade LE and TE at Z = 60%1790.8423−18.57302788.2101−17.83893786.6433−17.27204784.5773−16.34395783.3889−15.69276781.8917−14.67697780.7523−13.62408780.1977−12.92479779.6676−11.949210779.4981−11.388311779.4668−11.204912779.4526−11.036213779.4517−10.864114779.4648−10.690515779.4962−10.495716779.5390−10.325017779.5956−10.158518779.6650−9.997919779.7569−9.826120779.8494−9.682821779.9506−9.549922780.0593−9.428623780.6944−8.937224781.6779−8.603925782.5046−8.513326783.9563−8.482327785.6580−8.504228786.9328−8.538329789.0567−8.610630790.6147−8.662931859.698831.180332859.163030.382233858.460429.340034857.898428.510535856.912827.065736855.752925.383237854.880324.131538853.417522.063339852.336220.560340850.548618.126041851.169424.258842852.226825.441543853.651427.069244854.497028.052745855.614729.369946856.556130.493047857.087831.132048857.743331.924049858.086532.340250858.278832.517151858.525332.645652858.804132.701253859.088732.676454859.346332.585155859.552832.436556859.719632.222757859.830031.963358859.861031.684859859.811531.414560859.698831.1803Third Stage Blade LE and TE at Z = 70%1794.6279−20.30732792.1465−19.95463790.6592−19.61284788.6884−18.98035787.5497−18.50076786.1091−17.69657785.0128−16.79508784.4829−16.17019783.9688−15.285310783.7880−14.776911783.7521−14.620012783.7306−14.475013783.7194−14.326114783.7189−14.174915783.7315−14.003816783.7542−13.852417783.7880−13.702918783.8324−13.556919783.8937−13.398420783.9576−13.263921784.0293−13.136722784.1082−13.018223784.6332−12.477624785.4961−12.032225786.2429−11.852526787.5752−11.671327789.1465−11.518528790.3255−11.428529792.2897−11.313430793.7301−11.240731856.772529.689032856.272628.948133855.620527.978334855.101227.204535854.195425.853636853.135524.275937852.341623.099638851.015121.152739850.036619.736240848.420617.440741848.747023.161142849.737224.277643851.070925.814844851.862426.743745852.908327.988146853.789229.049047854.286629.652448854.900130.400349855.221330.793350855.406030.965051855.643231.090652855.911931.146153856.186331.124154856.434831.037855856.633930.896056856.794630.691157856.900830.442158856.930230.1744Third Stage Blade LE and TE at Z = 80%1797.3742−22.01192795.0547−21.79843793.6666−21.51414791.8357−20.92585790.7847−20.45586789.4644−19.66197788.4666−18.79568787.9833−18.21329787.4977−17.407410787.3155−16.947811787.2792−16.812012787.2554−16.685813787.2400−16.555514787.2334−16.422615787.2369−16.271216787.2498−16.136517787.2721−16.002718787.3035−15.871119787.3489−15.727220787.3975−15.604121787.4531−15.487022787.5153−15.376923787.9728−14.850524788.7457−14.384425789.4249−14.167126790.6472−13.937727792.0902−13.770228793.1702−13.670429794.9655−13.496930796.2791−13.348431853.487327.120632853.015326.447833852.396725.569634851.902124.870635851.035823.653536850.017822.236137849.253421.181438847.975419.437739847.033818.169340845.483516.111341845.774621.406542846.731622.392243848.021923.750844848.786924.574345849.795125.681846850.640326.631547851.115327.174548851.698527.850549852.002528.207250852.185528.370651852.418328.488852852.680328.538953852.946128.514354853.185428.427955853.375828.288656853.527728.088857853.626027.847058853.649527.588059853.597627.337360853.487327.1206Third Stage Blade LE and TE at Z = 90%1799.0323−22.73212796.9002−22.54313795.6267−22.26684793.9513−21.68295792.9933−21.21366791.7914−20.43967790.8749−19.63528790.4213−19.11259789.9501−18.395610789.7709−17.981911789.7352−17.858712789.7113−17.744113789.6951−17.625914789.6871−17.505115789.6880−17.367616789.6979−17.245117789.7166−17.123418789.7437−17.003519789.7835−16.872420789.8265−16.760121789.8762−16.653122789.9320−16.552423790.3515−16.075624791.0636−15.652725791.6883−15.438226792.8128−15.217927794.1389−15.095928795.1276−15.027329796.7663−14.855430797.9610−14.670131849.673623.543632849.223322.947233848.625522.174934848.142421.565035847.286620.511136846.269719.294537845.501018.394638844.212616.912239843.265215.834740841.715114.082141842.138318.997942843.082119.805843844.358720.920044845.116121.598545846.111022.518246846.939323.316147847.401423.777048847.964424.356649848.255724.665250848.442824.816951848.676324.922652848.934924.961053849.194024.926754849.424824.833255849.605824.690256849.746924.489757849.834124.250258849.847923.996359849.788723.752560849.673623.5436Third Stage Blade LE and TE at Z = 100%1800.4316−21.05302798.4947−21.15693797.3160−21.12254795.7258−20.93865794.7884−20.74046793.5724−20.34917792.5986−19.86098792.1013−19.49189791.5980−18.910510791.4213−18.543811791.3858−18.425712791.3618−18.317413791.3451−18.206514791.3357−18.094015791.3340−17.966316791.3403−17.852617791.3541−17.739418791.3751−17.627619791.4072−17.504220791.4431−17.397621791.4856−17.294422791.5346−17.195623791.9135−16.750524792.5820−16.371025793.1639−16.169526794.2055−15.919827795.4339−15.705928796.3509−15.557729797.8714−15.281530798.9795−15.046331845.409919.939332845.017019.418433844.497018.742434844.077918.207135843.337917.279736842.461416.205537841.800515.408738840.694414.092939839.881413.134840838.550511.574741838.480916.126642839.331316.843243840.485517.825944841.172118.421545842.076119.226246842.830519.922347843.252220.323948843.766420.828249844.032821.096650844.218921.240451844.448921.337152844.701821.366853844.953721.324954845.177221.225655845.352021.078756845.487420.876557845.570120.637258845.581720.385259845.522820.144760845.409919.9393

TABLE 6NXYFourth Stage Vane LE and TE at Z = 0%1955.336077.10402950.463975.54403946.226973.64244943.758772.24805940.585770.05406938.821168.56717936.687166.37168935.172664.28809934.511862.999310934.150061.251211934.266760.306212934.342760.034813934.429659.791314934.534259.548515934.655759.309416934.811759.048917934.966458.828418935.134558.620819935.314158.427820935.527258.229721935.723958.072322935.924857.933723936.127357.815224937.263457.206625938.829456.536226940.111156.088627942.380055.432828945.056954.807129947.065854.413130950.411953.8619311062.9791−2.8893321062.0864−1.6190331060.92620.0462341060.00601.3759351058.40753.7000361056.54676.4182371055.15808.4472381052.845711.8102391051.146014.2611401047.235610.7228411049.96597.8110421051.60886.0047431053.81893.5122441055.12872.0022451056.8563−0.0254461058.3076−1.7587471059.1255−2.7467481060.1320−3.9731491060.6580−4.6186501060.9438−4.8851511061.3128−5.0796521061.7298−5.1683531062.1467−5.1330541062.5192−4.9905551062.8187−4.7673561063.0610−4.4515571063.2143−4.0623581063.2446−3.6404591063.1573−3.2358601062.9791−2.8893Fourth Stage Vane LE and TE at Z = 10%1953.690366.84972948.469865.06593943.912962.97824941.239961.48905937.760359.20116935.782957.68317933.309155.47888931.425953.40739930.509052.115410929.806150.308711929.757149.292412929.803048.942713929.873148.626414929.970048.309415930.092947.996016930.261447.653417930.437447.362718930.636147.088719930.854646.833920931.120246.573221931.370246.367022931.629446.186923931.894046.034824933.179645.487625934.935044.960726936.358844.628027938.869244.168828941.824643.772929944.040343.552630947.729343.2951311067.4776−19.0251321066.5528−17.6426331065.3502−15.8314341064.3958−14.3850351062.7367−11.8569361060.8042−8.8998371059.3617−6.6923381056.9595−3.0328391055.1933−0.3652401052.28293.9678411053.7713−7.1442421055.4837−9.1610431057.8039−11.9223441059.1891−13.5832451061.0294−15.7996461062.5882−17.6825471063.4720−18.7511481064.5654−20.0731491065.1395−20.7669501065.4269−21.0298511065.7951−21.2202521066.2095−21.3057531066.6235−21.2688541066.9940−21.1260551067.2930−20.9031561067.5360−20.5886571067.6920−20.2012581067.7279−19.7802591067.6480−19.3748601067.4776−19.0251Fourth Stage Vane LE and TE at Z = 20%1946.900955.68572941.993353.72213939.088452.30134935.273450.08785933.086748.59776930.331746.39857928.215244.28828927.172542.95419926.222941.103910925.986040.044711925.966139.623312925.986939.241713926.043938.858514926.136938.478615926.285138.061416926.455837.704917926.661637.366318926.899037.049219927.199236.722420927.491036.461821927.801836.231622928.127036.033623929.521135.565024931.435935.287925932.975135.149226935.670634.970627938.826334.808428941.184334.704229945.100334.547730947.962234.4371311071.1063−32.7422321070.1623−31.2920331068.9228−29.3998341067.9302−27.8944351066.1880−25.2733361064.1363−22.2215371062.5929−19.9509381060.0074−16.1969391058.0992−13.4657401054.9516−9.0331411056.7252−20.3647421058.5505−22.4470431061.0195−25.3006441062.4899−27.0198451064.4371−29.3188461066.0797−31.2773471067.0077−32.3918481068.1521−33.7737491068.7512−34.5005501069.0361−34.7615511069.4014−34.9495521069.8134−35.0324531070.2258−34.9934541070.5961−34.8488551070.8964−34.6245561071.1420−34.3090571071.3022−33.9209581071.3438−33.4993591071.2704−33.0931601071.1063−32.7422Fourth Stage Vane LE and TE at Z = 30%1945.133247.47832939.918645.65633936.811544.30924932.709442.17355930.347140.71476927.359838.53417925.054336.40938923.907735.05559922.747233.194110922.347432.110911922.235731.596112922.188231.128813922.192930.659514922.252830.195415922.388229.688516922.570229.259717922.807928.858018923.095528.488619923.471528.117920923.845127.832421924.247827.589322924.672027.389123926.161627.016724928.192926.863525929.818326.808126932.655326.737927935.967226.650228938.437626.570029942.534026.401630945.523526.2465311074.5521−43.6928321073.5820−42.1961331072.3006−40.2476341071.2690−38.7012351069.4478−36.0161361067.2879−32.9000371065.6540−30.5875381062.9043−26.7726391060.8676−24.0023401057.5020−19.5120411059.6399−30.8805421061.5541−33.0237431064.1389−35.9651441065.6757−37.7396451067.7082−40.1146461069.4202−42.1393471070.3866−43.2915481071.5774−44.7202491072.2005−45.4715501072.4837−45.7294511072.8471−45.9136521073.2569−45.9926531073.6674−45.9500541074.0362−45.8024551074.3357−45.5757561074.5811−45.2585571074.7419−44.8694581074.7850−44.4479591074.7138−44.0424601074.5521−43.6928Fourth Stage Vane LE and TE at Z = 40%1942.894940.30102937.469638.46853934.226237.11604929.927134.98175927.434833.53466924.248231.39187921.735429.31918920.440128.00139919.056426.175710918.524425.091711918.314324.482912918.195123.927813918.148423.370214918.181722.820715918.318922.226716918.530921.733617918.823721.283718919.188320.884019919.672320.503320920.156520.230821920.678120.019622921.224019.868223922.818219.592924924.938719.367225926.634519.226226929.597019.013927933.060018.796028935.645118.645729939.934118.406130943.065518.2300311078.2240−51.5951321077.2091−50.0619331075.8746−48.0604341074.8052−46.4692351072.9257−43.7017361070.7056−40.4843371069.0287−38.0940381066.2062−34.1489391064.1136−31.2844401060.6467−26.6460411062.9903−38.0805421064.9305−40.3607431067.5575−43.4824441069.1270−45.3584451071.2159−47.8566461072.9908−49.9710471074.0002−51.1664481075.2526−52.6395491075.9121−53.4097501076.1975−53.6603511076.5610−53.8362521076.9686−53.9070531077.3751−53.8569541077.7389−53.7033551078.0329−53.4724561078.2720−53.1523571078.4264−52.7626581078.4640−52.3427591078.3885−51.9405601078.2240−51.5951Fourth Stage Vane LE and TE at Z = 50%1940.709233.82522935.131532.02353931.792030.70344927.341528.63695924.739627.24446921.370125.19707918.646823.23778917.192922.00079915.570420.286210914.874419.268611914.586418.670812914.403518.122513914.300617.570114914.287417.024715914.385816.435716914.576215.949017914.860115.508318915.227315.121519915.727214.760420916.235114.510421916.787314.326222917.368114.206023919.069113.994224921.296013.738925923.073013.546426926.175413.233427929.799712.899828932.504512.669229936.991312.312730940.267112.0662311081.8443−57.7572321080.7710−56.2022331079.3708−54.1647341078.2567−52.5392351076.3129−49.7019361074.0349−46.3903371072.3231−43.9236381069.4510−39.8454391067.3242−36.8819401063.7960−32.0859411066.1958−43.6667421068.1753−46.0716431070.8649−49.3544441072.4806−51.3187451074.6460−53.9205461076.5028−56.1063471077.5671−57.3343481078.8971−58.8387491079.6018−59.6210501079.8900−59.8599511080.2532−60.0226521080.6572−60.0802531081.0572−60.0186541081.4126−59.8561551081.6974−59.6193561081.9260−59.2960571082.0695−58.9064581082.0973−58.4902591082.0141−58.0945601081.8443−57.7572Fourth Stage Vane LE and TE at Z = 60%1938.924427.90082933.196826.27683929.764425.08114925.156623.19845922.439321.91506918.884320.00567915.958118.17838914.362817.03219912.505915.467710911.617514.560411911.296514.097712911.074913.670913910.922013.238114910.845412.808015910.857312.338816910.959411.945517911.146511.582818911.411311.257219911.792710.943120912.195710.715021912.646210.535222913.131610.403223914.917810.207024917.267110.085025919.13479.990726922.38389.810527926.16609.561928928.98149.347129933.64268.940530937.03988.6058311084.9325−63.9792321083.7979−62.4250331082.3198−60.3899341081.1433−58.7636351079.0909−55.9190361076.6900−52.5921371074.8915−50.1111381071.8847−46.0058391069.6648−43.0212401065.9900−38.1914411068.3893−49.9741421070.5266−52.3636431073.4262−55.6285441075.1642−57.5835451077.4882−60.1751461079.4757−62.3562471080.6123−63.5842481082.0298−65.0922491082.7796−65.8782501083.0668−66.1026511083.4255−66.2498521083.8222−66.2921531084.2123−66.2182541084.5564−66.0475551084.8297−65.8064561085.0465−65.4831571085.1783−65.0971581085.1960−64.6885591085.1059−64.3039601084.9325−63.9792Fourth Stage Vane LE and TE at Z = 70%1937.207022.84122931.318321.27613927.774920.13364922.987518.33785920.146217.10986916.408915.27217913.306913.50828911.603912.39739909.601310.864910908.64779.943611908.36629.581012908.16769.249313908.02228.914414907.93448.581715907.90988.216616907.95867.906317908.07427.614318908.25257.344819908.52287.073820908.81886.864921909.15926.687422909.53596.541823911.34996.272624913.76086.177225915.68166.136426919.02606.076627922.92025.981828925.81825.877029930.61295.626530934.10425.3772311087.3326−70.1783321086.1477−68.6202331084.5980−66.5881341083.3577−64.9647351081.1831−62.1249361078.6302−58.8038371076.7181−56.3276381073.5284−52.2292391071.1805−49.2480401067.3093−44.4185411069.6551−56.5168421072.0149−58.8211431075.2050−61.9795441077.1060−63.8776451079.6305−66.4056461081.7701−68.5483471082.9844−69.7634481084.4882−71.2663491085.2788−72.0552501085.5598−72.2659511085.9083−72.4007521086.2930−72.4322531086.6693−72.3524541086.9992−72.1808551087.2598−71.9430561087.4649−71.6276571087.5865−71.2528581087.5973−70.8580591087.5046−70.4885601087.3326−70.1783Fourth Stage Vane LE and TE at Z = 80%1935.348019.17162929.333917.36213925.689916.09934920.758914.17585917.829812.89846913.980311.02327910.79539.22558909.05698.07389907.07366.400210906.26045.286911906.08004.890512905.96614.537613905.89794.188714905.87733.848015905.91353.479916906.00073.170717906.13932.882418906.32632.617819906.59102.352020906.87042.146521907.18591.970722907.53241.825323909.29991.368924911.66301.005525913.56660.814226916.90970.609727920.83400.509028923.76880.491029928.64040.507330932.19650.5258311089.2150−74.6846321088.0057−73.0738331086.4221−70.9733341085.1528−69.2957351082.9241−66.3622361080.3035−62.9324371078.3390−60.3749381075.0611−56.1399391072.6491−53.0562401068.6773−48.0523411070.8550−60.6869421073.3340−63.0347431076.6844−66.2517441078.6797−68.1842451081.3285−70.7553461083.5726−72.9310471084.8458−74.1632481086.4220−75.6859491087.2502−76.4845501087.5222−76.6836511087.8572−76.8101521088.2260−76.8378531088.5858−76.7602541088.9004−76.5962551089.1483−76.3694561089.3426−76.0687571089.4575−75.7120581089.4675−75.3358591089.3791−74.9826601089.2150−74.6846Fourth Stage Vane LE and TE at Z = 90%1933.847117.24232927.797715.09553924.118313.64934919.157211.51085916.224110.13306912.39428.15597909.25776.27368907.56395.05849905.69373.239310905.03611.965211904.92421.496212904.87131.083713904.86370.679914904.90230.288815905.0014−0.130016905.1389−0.478617905.3213−0.801018905.5460−1.094819905.8456−1.387820906.1498−1.613121906.4854−1.804822906.8483−1.962723908.5577−2.605024910.8505−3.268125912.7149−3.655926916.0141−4.110327919.9169−4.359128922.8510−4.396129927.7410−4.267630931.3233−4.0668311090.7582−76.7408321089.5570−75.0218331087.9923−72.7704341086.7454−70.9697351084.5665−67.8184361082.0114−64.1312371080.0926−61.3814381076.8786−56.8293391074.5041−53.5158401070.5770−48.1407411072.4421−61.5353421074.8773−64.0991431078.1781−67.6003441080.1552−69.6926451082.8014−72.4536461085.0703−74.7593471086.3712−76.0485481087.9973−77.6216491088.8593−78.4367501089.1212−78.6252511089.4410−78.7455521089.7918−78.7734531090.1337−78.7029541090.4330−78.5514551090.6697−78.3396561090.8551−78.0568571090.9679−77.7217581090.9842−77.3672591090.9075−77.0297601090.7582−76.7408Fourth Stage Vane LE and TE at Z = 100%1933.051616.83082927.024714.40953923.366812.79334918.466510.42495915.59138.91476911.86736.77007908.84844.75088907.23043.46189905.46021.561010904.84760.255311904.7305−0.252912904.6763−0.700813904.6704−1.140714904.7142−1.568015904.8227−2.027816904.9714−2.412617905.1674−2.770618905.4079−3.099319905.7279−3.430720906.0525−3.688921906.4105−3.912422906.7978−4.100823908.4854−4.822924910.7585−5.584225912.6090−6.044626915.8870−6.614227919.7707−6.972828922.6946−7.069729927.5753−6.993530931.1574−6.7890311092.0654−76.9895321090.9057−75.1337331089.4074−72.6910341088.2243−70.7337351086.1731−67.3039361083.7767−63.2881371081.9706−60.2952381078.9227−55.3488391076.6521−51.7554401072.8630−45.9407411074.2410−60.2292421076.5497−63.0621431079.6873−66.9239441081.5805−69.2223451084.1432−72.2316461086.3769−74.7108471087.6764−76.0772481089.3227−77.7198491090.2059−78.5584501090.4560−78.7383511090.7593−78.8554521091.0910−78.8874531091.4152−78.8284541091.7010−78.6931551091.9290−78.4995561092.1088−78.2365571092.2245−77.9251581092.2535−77.5938591092.1946−77.2715601092.0654−76.9895

TABLE 8NXYFourth Stage Blade LE and TE at Z = 0%11138.0006−9.124321132.3216−6.839731128.9111−5.310841124.3525−3.042151121.6794−1.566661118.21280.558871115.38592.536681113.85073.749591112.06335.3768101111.20246.3094111110.83466.8314121110.59057.3244131110.44117.8243141110.39628.3116151110.46448.8209161110.62339.2190171110.87759.5673181111.22529.8666191111.713510.1248201112.219010.2688211112.768710.3302221113.337010.3118231115.175010.0143241117.55439.5178251119.44079.0776261122.71928.2493271126.53917.2338281129.38906.4629291134.12515.1899301137.59524.2832311312.017040.3937321310.472039.1011331308.452037.4141341306.844036.0692351304.038033.7243361300.753030.9945371298.290028.9682381294.173025.6357391291.135023.2315401286.122019.3752411289.727831.4464421292.668633.2706431296.627835.8318441298.976337.4048451302.080139.5346461304.698841.3614471306.181542.4014481308.017843.6850491308.985144.3544501309.570644.6481511310.254244.7885521310.968744.7319531311.631044.4703541312.172744.0596551312.561143.5527561312.816942.9226571312.897642.2145581312.766641.5088591312.453240.8839601312.016840.3937Fourth Stage Blade LE and TE at Z = 10%11139.0653−8.607821133.4984−6.343131130.1575−4.820641125.7046−2.538851123.1095−1.035561119.77041.155571117.07973.216081115.63414.482291113.94686.1539101113.10267.0767111112.80317.4771121112.60167.8345131112.47128.1824141112.41368.5113151112.43448.8477161112.52859.1076171112.69559.3309181112.93419.5180191113.28009.6780201113.64879.7691211114.06349.8105221114.51149.8019231116.32769.5625241118.66659.0652251120.51288.5830261123.71117.6398271127.42856.4677281130.20185.5833291134.81674.1452301138.20703.1498311309.903638.2801321308.612636.8269331306.872234.9757341305.440933.5410351302.862231.1147361299.744528.3857371297.357626.4105381293.311823.2230391290.304820.9496401285.327817.3210411288.313628.5947421291.255430.2623431295.223632.5974441297.574434.0402451300.659436.0286461303.216437.7985471304.634538.8456481306.346240.1957491307.221140.9339501307.630041.2009511308.123541.3639521308.656741.3864531309.170941.2554541309.611941.0046551309.951140.6689561310.206240.2307571310.342139.7183581310.324839.1855591310.166638.6911601309.903638.2801Fourth Stage Blade LE and TE at Z = 20%11142.2787−6.517521137.0133−4.335731133.8426−2.904341129.5905−0.812851127.08890.532661123.82992.455371121.15834.239681119.70695.343591118.07806.9044101117.51707.9288111117.47408.1074121117.45398.2683131117.45258.4286141117.47028.5857151117.51288.7556161117.57058.8980171117.64689.0315181117.74079.1553191117.86559.2810201117.99149.3787211118.12909.4621221118.27569.5306231119.98989.7419241122.26909.4079251124.06669.0238261127.18058.2539271130.79767.2650281133.49126.4966291137.95975.1969301141.22804.2435311306.523235.9615321305.119634.6974331303.276433.0531341301.796231.7543351299.184029.5205361296.081026.9691371293.731425.1028381289.776122.0690391286.852019.8909401282.039616.3848411286.079326.0326421288.895527.7859431292.702830.2226441294.966031.7123451297.954033.7342461300.462135.4859471301.872836.4952481303.606437.7582491304.512238.4265501304.880038.6254511305.314038.7284521305.771838.7062531306.200538.5520541306.554838.3004551306.813037.9846561306.988737.5875571307.053737.1374581306.982936.6851591306.793736.2813601306.523235.9615Fourth Stage Blade LE and TE at Z = 30%11146.8276−7.303621142.0421−5.395931139.1617−4.141741135.3042−2.298351133.0420−1.099461130.10750.634071127.72212.266481126.43743.288491125.01784.7443101124.53925.7004111124.55485.8247121124.57805.9460131124.60946.0753141124.64936.2104151124.70626.3664161124.76926.5059171124.84236.6413181124.92186.7687191125.01556.9006201125.09967.0061211125.18257.1000221125.26277.1822231126.81377.5032241128.88457.3940251130.52267.1749261133.35976.6567271136.64865.9126281139.09175.2952291143.13494.1938301146.08603.3484311298.346834.2298321297.070733.0020331295.422931.3722341294.104430.0756351291.760727.8534361288.937325.3443371286.778623.5251381283.122220.5846391280.411418.4775401275.954215.0731411279.194124.5813421281.798626.3258431285.334028.7163441287.446530.1556451290.251932.0794461292.624733.7191471293.967834.6530481295.624835.8143491296.491436.4280501296.822136.6011511297.210236.6893521297.618936.6681531298.002136.5319541298.320936.3104551298.555936.0318561298.719135.6818571298.785935.2843581298.734134.8827591298.577434.5208601298.346834.2298Fourth Stage Blade LE and TE at Z = 40%11154.4195−10.496721150.2173−8.908131147.6956−7.843441144.3263−6.266551142.3534−5.239561139.7972−3.754871137.7249−2.349481136.6161−1.462891135.3544−0.2422101134.76890.4855111134.65300.7128121134.58170.9374131134.54461.1750141134.54471.4180151134.59231.6883161134.67881.9174171134.80592.1280181134.96752.3139191135.18182.4866201135.39282.6026211135.61452.6826221135.83802.7273231137.18782.7114241138.93532.5027251140.32392.2596261142.73901.7506271145.55651.0718281147.66080.5304291151.1616−0.3995301153.7294−1.0830311286.794133.1268321285.638132.0146331284.142630.5451341282.947329.3774351280.817227.3871361278.250825.1489371276.298223.5203381273.027720.8537391270.632118.9134401266.727415.7455411269.617824.4164421271.949625.9527431275.101028.0923441276.975129.4004451279.453531.1711461281.540432.6975471282.718033.5727481284.169034.6636491284.928435.2394501285.251835.4199511285.635835.5181521286.043835.5080531286.428935.3826541286.750835.1709551286.989234.9010561287.156834.5588571287.227834.1678581287.178933.7714591287.023833.4138601286.794133.1268Fourth Stage Blade LE and TE at Z = 50%11163.1804−13.754021159.4137−12.432231157.1622−11.525541154.1622−10.167151152.4062−9.281761150.1220−8.013971148.2445−6.841681147.2177−6.116491146.0179−5.1176101145.4858−4.4824111145.3922−4.2935121145.3324−4.1058131145.2980−3.9055141145.2920−3.6984151145.3225−3.4645161145.3856−3.2624171145.4819−3.0736181145.6065−2.9041191145.7730−2.7410201145.9379−2.6242211146.1120−2.5351221146.2886−2.4741231147.4782−2.3717241149.0390−2.4769251150.2806−2.6300261152.4441−2.9685271154.9753−3.4312281156.8711−3.8002291160.0336−4.4312301162.3583−4.8940311278.666933.6789321277.631932.7066331276.280331.4352341275.199930.4259351273.294328.6867361271.036426.6909371269.337525.2168381266.510722.7791391264.446520.9970401261.084218.0859411263.593425.8218421265.600527.2578431268.323929.2374441269.949630.4371451272.106032.0500461273.927633.4311471274.957834.2194481276.229735.1984491276.896635.7134501277.205335.8879511277.572335.9829521277.962635.9733531278.330935.8518541278.638035.6469551278.865035.3862561279.023935.0559571279.089834.6786581279.040234.2967591278.889033.9533601278.666933.6789Fourth Stage Blade LE and TE at Z = 60%11170.7303−17.133421167.3230−16.353431165.2679−15.780741162.5088−14.867851160.8855−14.237161158.7775−13.283071157.0705−12.340381156.1594−11.731991155.1374−10.8534101154.7202−10.2609111154.6628−10.1102121154.6275−9.9645131154.6084−9.8113141154.6072−9.6539151154.6297−9.4761161154.6731−9.3209171154.7379−9.1734181154.8210−9.0377191154.9320−8.9019201155.0425−8.7984211155.1604−8.7120221155.2822−8.6433231156.2879−8.3640241157.6548−8.2178251158.7629−8.1673261160.7190−8.1738271163.0136−8.2834281164.7252−8.4091291167.5656−8.6644301169.6449−8.8676311271.750934.4016321270.821933.5150331269.604632.3591341268.632731.4395351266.935629.8361361264.951727.9646371263.468826.5698381261.001324.2609391259.192822.5797401256.233819.8484411258.173626.9471421259.928928.3545431262.326830.2678441263.767631.4122451265.689532.9337461267.322534.2227471268.249734.9534481269.397435.8570491270.000036.3314501270.296636.5043511270.650836.6016521271.029036.5983531271.387936.4875541271.689236.2955551271.913536.0484561272.072635.7327571272.142835.3706581272.101635.0026591271.961234.6696601271.750934.4016Fourth Stage Blade LE and TE at Z = 70%11170.7303−17.133421167.3230−16.353431165.2679−15.780741162.5088−14.867851160.8855−14.237161158.7775−13.283071157.0705−12.340381156.1594−11.731991155.1374−10.8534101154.7202−10.2609111154.6628−10.1102121154.6275−9.9645131154.6084−9.8113141154.6072−9.6539151154.6297−9.4761161154.6731−9.3209171154.7379−9.1734181154.8210−9.0377191154.9320−8.9019201155.0425−8.7984211155.1604−8.7120221155.2822−8.6433231156.2879−8.3640241157.6548−8.2178251158.7629−8.1673261160.7190−8.1738271163.0136−8.2834281164.7252−8.4091291167.5656−8.6644301169.6449−8.8676311271.750934.4016321270.821933.5150331269.604632.3591341268.632731.4395351266.935629.8361361264.951727.9646371263.468826.5698381261.001324.2609391259.192822.5797401256.233819.8484411258.173626.9471421259.928928.3545431262.326830.2678441263.767631.4122451265.689532.9337461267.322534.2227471268.249734.9534481269.397435.8570491270.000036.3314501270.296636.5043511270.650836.6016521271.029036.5983531271.387936.4875541271.689236.2955551271.913536.0484561272.072635.7327571272.142835.3706581272.101635.0026591271.961234.6696601271.750934.4016Fourth Stage Blade LE and TE at Z = 80%11180.3804−24.681521177.3791−24.891431175.5632−24.917241173.1107−24.834451171.6484−24.719761169.7029−24.487871168.0497−24.202981167.1145−23.978391165.9914−23.5681101165.4996−23.1717111165.4244−23.0387121165.3705−22.9108131165.3301−22.7761141165.3047−22.6368151165.2974−22.4764161165.3131−22.3321171165.3496−22.1906181165.4041−22.0560191165.4836−21.9148201165.5674−21.8002211165.6612−21.6971221165.7633−21.6067231166.6031−21.0773241167.7486−20.5349251168.6809−20.1816261170.3309−19.6699271172.2834−19.1856281173.7550−18.8770291176.2176−18.4199301178.0287−18.1035311258.532937.0949321257.812636.2685331256.869035.1904341256.115234.3329351254.796432.8401361253.250531.1018371252.093029.8078381250.165627.6659391248.752726.1054401246.439823.5688411247.478329.6580421248.855031.0119431250.735832.8550441251.865933.9586451253.374435.4264461254.657236.6697471255.386237.3741481256.289438.2446491256.764038.7012501257.017338.8835511257.330739.0019521257.675639.0310531258.012938.9601541258.304938.8103551258.532038.6041561258.706338.3305571258.803338.0071581258.798737.6689591258.700637.3549601258.532937.0949Fourth Stage Blade LE and TE at Z = 90%11183.5300−27.072621180.8201−27.823931179.1601−28.165741176.9086−28.466451175.5720−28.544461173.8101−28.502571172.3306−28.295081171.4985−28.084991170.4859−27.7072101169.9826−27.4368111169.7900−27.2919121169.6400−27.1363131169.5172−26.9597141169.4267−26.7673151169.3658−26.5415161169.3492−26.3407171169.3685−26.1392181169.4229−25.9373191169.5250−25.7195201169.6500−25.5423211169.8018−25.3862221169.9734−25.2553231170.7251−24.8640241171.7407−24.4185251172.5647−24.0990261174.0280−23.5913271175.7688−23.0463281177.0841−22.6540291179.2852−21.9942301180.9006−21.4855311252.826937.8733321252.167037.0609331251.301736.0018341250.609835.1600351249.398233.6956361247.976731.9917371246.911830.7243381245.138028.6283391243.837527.1022401241.710324.6225411242.536330.2245421243.796131.5850431245.519733.4370441246.557434.5455451247.945236.0189461249.128437.2656471249.802137.9712481250.638438.8424491251.078739.2988501251.313739.4823511251.607239.6074521251.932339.6481531252.257339.5980541252.545639.4749551252.770339.2919561252.943639.0387571253.047938.7388581253.058838.4241591252.977638.1256601252.826937.8733Fourth Stage Blade LE and TE at Z = 100%11186.8945−24.885821184.7558−26.071231183.3986−26.702941181.4780−27.411351180.2913−27.729061178.6876−27.984771177.3347−27.995381176.5795−27.906991175.6529−27.7292101175.1700−27.6076111174.8617−27.4945121174.6056−27.3444131174.3819−27.1513141174.2027−26.9221151174.0613−26.6377161173.9944−26.3765171173.9846−26.1062181174.0305−25.8284191174.1480−25.5254201174.3089−25.2806211174.5124−25.0687221174.7450−24.8976231175.4116−24.5032241176.3083−24.0351251177.0282−23.6712261178.2881−23.0422271179.7567−22.3015281180.8480−21.7394291182.6476−20.7833301183.9526−20.0628311243.963733.1655321243.424832.4447331242.717531.5061341242.151430.7608351241.158429.4667361239.990127.9654371239.111826.8524381237.642025.0198391236.557823.6930401234.769821.5526411235.415426.2150421236.473427.3943431237.912629.0105441238.774829.9837451239.923431.2842461240.898632.3908471241.452533.0196481242.138333.7986491242.498734.2078501242.684834.3691511242.920434.4872521243.184234.5392531243.450734.5182541243.689534.4365551243.878034.3027561244.026634.1093571244.120233.8743581244.137933.6219591244.079833.3771601243.963733.1655

It may be appreciated that the leading and trailing edge sections for the airfoils of the vane22, blade24, vane26and blade28, 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 vane22, blade24, vane26and blade28, constructed with the described average angle changes, provide and improved or optimized flow of working gases passing from the turbine section12to the diffuser34, 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.