Turbine airfoil with optimized airfoil element angles

Abstract

A turbine airfoil assembly for installation in a gas turbine engine. The airfoil assembly includes an endwall and an airfoil extending radially outwardly from the endwall. The airfoil includes pressure and suction sidewalls defining chordally spaced apart leading and trailing edges of the airfoil. An airfoil mean line is defined located centrally between the pressure and suction sidewalls. An angle between the mean line and a line parallel to the engine axis at the leading and trailing edges defines gas flow entry angles, α, and exit angles, β. Airfoil inlet and exit angles are substantially in accordance with inlet angle values, α, and exit angle values, β, set forth in one of Tables 1, 2, 3, and 4.

Claims

1. A turbine airfoil assembly for installation in a gas turbine engine having a longitudinal axis, the turbine airfoil assembly including an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall, the airfoil having 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 inlet angle values, α, and exit angle values, β, set forth in one of Tables 1, 2, 3, and 4, where 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 place 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 of the inlet and exit angle values is defined with respect to a distance from the endwall corresponding to a Z value that is a distance of a total span of the airfoil from the endwall with the distances being joined smoothly with one another to form a complete airfoil shape.

2. The turbine airfoil assembly of claim 1, wherein the airfoil comprises an airfoil for a third stage vane in a turbine engine, and the one of Tables 1, 2, 3, and 4 defining the airfoil inlet and exit angles is Table 1.

3. The turbine airfoil assembly according to claim 1, wherein the airfoil comprises an airfoil for third stage blade in a turbine engine, and the one of Tables 1, 2, 3, and 4 defining the airfoil inlet and exit angles is Table 2.

4. The turbine airfoil assembly of claim 1, wherein the airfoil comprises an airfoil for a fourth stage vane in a turbine engine, and the one of Tables 1, 2, 3, and 4 defining the airfoil inlet and exit angles is Table 3.

5. The turbine airfoil assembly according to claim 1, wherein the airfoil comprises an airfoil for fourth stage blade in a turbine engine, and the one of Tables 1, 2, 3, and 4 defining the airfoil inlet and exit angles is Table 4.

6. The turbine airfoil assembly of claim 1, including four airfoils comprising, in succession, an airfoil for a third stage vane having the airfoil inlet and exit angles defined by Table 1, an airfoil for a third stage blade having the airfoil inlet and exit angles defined by Table 2, an airfoil for a fourth stage vane having the airfoil inlet and exit angles defined by Table 3 and an airfoil for a fourth stage blade having the airfoil inlet and exit angles defined by Table 4.

7. Third and fourth stage vane and blade airfoil assemblies in a gas turbine engine having a longitudinal axis, each airfoil assembly including: an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall, the airfoil having 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 inlet angle values, α, and exit angle values, β, where 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 of the 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 inlet angle values, α, and exit angle values, β, for the third stage vane are as set forth in Table 1; b) the inlet angle values, α, and exit angle values, β, for the third stage blade are as set forth in Table 2; c) the inlet angle values, α, and exit angle values, β, for the fourth stage vane are as set forth in Table 3; d) the inlet angle values, α, and exit angle values, β, for the fourth stage blade are as set forth in Table 4.

8. A turbine airfoil assembly for installation in a gas turbine engine having a longitudinal axis, the turbine airfoil assembly including an endwall for defining an inner boundary for an axially extending hot working gas path, and an airfoil extending radially outwardly from the endwall, the airfoil having 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, 2, 3, and 4, 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, wherein each the exit angle value is defined with respect to a distance from the endwall corresponding to a Z value that is a distance of a total span of the airfoil from the endwall with the distances being joined smoothly with one another to form a complete airfoil shape, and wherein each the airfoil exit angle is within about 1% of a respective value set forth in one of Tables 1, 2, 3, and 4.

9. The turbine airfoil assembly of claim 8, wherein the airfoil comprises an airfoil for a third stage vane in a turbine engine, and one of Tables 1, 2, 3, and 4 defining the airfoil exit angles is Table 1.

10. The turbine airfoil assembly of claim 8, wherein the airfoil comprises an airfoil for a third stage blade in a turbine engine, and one of Tables 1, 2, 3, and 4 defining the airfoil exit angles is Table 2.

11. The turbine airfoil assembly of claim 8, wherein the airfoil comprises an airfoil for a fourth stage vane in a turbine engine, and one of Tables 1, 2, 3, and 4 defining the airfoil exit angles is Table 3.

12. The turbine airfoil assembly of claim 8, wherein the airfoil comprises an airfoil for a fourth stage blade in a turbine engine, and one of Tables 1, 2, 3, and 4 defining the airfoil exit angles is Table 4.

13. The turbine airfoil assembly of claim 8, including four of the airfoils comprising, in succession, an airfoil for a third stage vane having airfoil exit angles defined by Table 1, an airfoil for a third stage blade having airfoil exit angles defined by Table 2, an airfoil for a fourth stage vane having airfoil exit angles defined by Table 3 and an airfoil for a fourth stage blade having airfoil exit angles defined by Table 4.

14. The turbine airfoil assembly of claim 8, including at least two of the airfoils comprising, in succession, an airfoil for a third stage blade having airfoil exit angles defined by Table 2, and an airfoil for a fourth stage vane having airfoil exit angles defined by Table 3.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is shown in more detail by help of figures. The figures show preferred configurations and do not limit the scope of the invention.

(2) FIG. 1 is a cross-sectional view of a turbine section for a gas turbine engine;

(3) FIG. 2 is a side elevational view of a third stage vane assembly formed in accordance with aspects of the present invention;

(4) FIG. 3 is a perspective view of the vane assembly of FIG. 2;

(5) FIG. 4 is a cross-sectional plan view of an airfoil of the vane assembly of FIG. 2;

(6) FIG. 5 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the vane assembly of FIG. 2;

(7) FIG. 6 is a side elevational view of a third stage blade assembly formed in accordance with aspects of the present invention;

(8) FIG. 7 is a perspective view of the blade assembly of FIG. 6;

(9) FIG. 8 is a cross-sectional plan view of an airfoil of the blade assembly of FIG. 6;

(10) FIG. 9 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the blade assembly of FIG. 6;

(11) FIG. 10 is a side elevational view of a fourth stage vane assembly formed in accordance with aspects of the present invention;

(12) FIG. 11 is a perspective view of the vane assembly of FIG. 10;

(13) FIG. 12 is a cross-sectional plan view of an airfoil of the vane assembly of FIG. 10;

(14) FIG. 13 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the vane assembly of FIG. 10;

(15) FIG. 14 is a side elevational view of a fourth stage blade assembly formed in accordance with aspects of the present invention;

(16) FIG. 15 is a perspective view of the blade assembly of FIG. 14;

(17) FIG. 16 is a cross-sectional plan view of an airfoil of the blade assembly of FIG. 14; and

(18) FIG. 17 is a graphical illustration of entry and exit angles defined along the span of an airfoil for the blade assembly of FIG. 14.

DETAILED DESCRIPTION

(19) In the following detailed description of the preferred embodiment, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration, and not by way of limitation, a specific embodiment in which the invention may be practiced. It is understood that other embodiments may be utilized and that changes may be made without departing from the spirit and scope of the present invention.

(20) Broadly, an embodiment of the present invention provides 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 inlet angle values, α, and exit angle values, β, set forth in one of Tables 1, 2, 3, and 4.

(21) Referring to FIG. 1, a turbine section 12 for a gas turbine engine is illustrated. The turbine section 12 includes alternating rows of stationary vanes and rotating blades extending radially into an axial flow path 13 extending through the turbine section 12. In particular, the turbine section 12 includes at least a first stage formed by a first row of stationary vanes 14 and a first row of rotating blades 16, a second stage formed by a second row of stationary vanes 18 and a second row of rotating blades 20, a third stage formed by a third row of stationary vanes 22 and third row of rotating blades 24, and a fourth stage formed by a fourth row of stationary vanes 26 and a fourth row of rotating blades 28.

(22) During operation of the gas turbine engine, a compressor (not shown) of the engine supplies compressed air to a combustor (not shown) where the air is mixed with a fuel, and the mixture is ignited creating combustion products comprising a hot working gas defining a working fluid. The working fluid travels through the stages of the turbine section 12 where it expands and causes the blades 16, 20, 24, 28 to rotate. The overall work output from the turbine section 12 is distributed into all of the stages, where the stationary vanes 14, 18, 22, 26 are provided for accelerating the gas flow and turn the gas flow to feed into the respective downstream blades 16, 20, 24, 28 to generate torque on a rotor 30 supporting the blades 16, 20, 24, 28, producing a rotational output about a longitudinal axis 32, of the engine, such as to drive the upstream compressor.

(23) The flow turning occurring at each rotating blade 16, 20, 24, 28 creates a reaction force on the blade 16, 20, 24, 28 to produce the output torque. The work split between the stages may be controlled by the angular changes in flow direction effected by each of the vanes 14, 18, 22, 26 and respective blades 16, 20, 24, 28, which work split has an effect on the efficiency of the engine. In accordance with an aspect of the invention, a design for the third and fourth stage vanes 22, 26, and blades, 24, 28, is provided to optimize or improve the flow angle changes through the third and fourth stages. Specifically, the design of the third and fourth stage vanes 22, 26 and blades 24, 28, as described below, provide a radial variation in inlet and exit flow angles to produce optimized flow profiles into an exhaust diffuser 34 downstream from the turbine section 12. Optimized flow profiles through the third and fourth stages of the turbine section 12 may facilitate a reduction in the average Mach number for flows exiting the fourth stage vanes 26, with an associated improvement in engine efficiency, since flow loss tends to be proportional to the square of the Mach number.

(24) Referring to FIGS. 2 through 4, a configuration for the third stage vane 22 is described. The vanes 22 each include an outer wall comprising a generally concave pressure sidewall 38, and include an opposing generally convex suction sidewall 40. The sidewalls 38, 40 extend radially between an inner diameter endwall 42 and an outer diameter endwall 44, and extend generally axially in a chordal direction between a leading edge 46 and a trailing edge 48 of each of the vanes 22. The endwalls 42, 44 are located at opposing ends of the vanes 22 and are positioned at locations where they form a boundary, i.e., inner and outer boundaries, defining a portion of the flow path 13 for the working fluid. Opposing radially inner matefaces 45a, 47a and radially outer matefaces 45b, 47b are defined by the respective inner and outer diameter endwalls 42, 44 of the airfoil structure 36.

(25) FIG. 4 illustrates a cross section of one of the vanes 22 at a radial location of about 50% of the span, S.sub.V3, along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y, and Z axes, wherein the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, S.sub.V3, of the airfoil for the vane 22. It should be noted that the matefaces 45a, 47a, and 45b, 47b are shown herein (in FIG. 3) as extending at an angle relative to the direction of the longitudinal axis 32.

(26) The cross section of FIG. 4 lies in the X-Y plane. As seen in FIG. 4, the vane 22 defines an airfoil mean line, C.sub.V3, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 38, 40. At the leading edge 46, a blade metal angle of each of the surfaces of the pressure and suction sides 38, 40 adjacent to the leading edge 46 is provided for directing incoming flow to the vane 22 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle α, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.V3, at the leading edge 46, i.e., tangential to the line C.sub.V3, at the airfoil leading edge 46.

(27) At the trailing edge 48, a blade metal angle of the surfaces of the pressure and suction sides 38, 40 adjacent to the trailing edge 48 is provided for directing flow exiting from the vane 22 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.V3, at the trailing edge 48, i.e., tangential to the line C.sub.V3 at the airfoil trailing edge 48.

(28) The inlet angles, α, and exit angles, β, for the airfoil of the vane 22 are as described in Table 1 below. The Z coordinate locations are presented as lengths along the total span of the vane 22. The values for the inlet angles, α, and exit angles, β, are defined at selected Z locations spaced at increments along the span of the vane 22, where 800 mm (of total value) is located adjacent to the inner endwall 42 and 1215 mm (of total value) is located adjacent to the outer endwall 44. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 5.

(29) TABLE-US-00001 TABLE 1 β-Metal Outlet α-Metal Inlet Angle Angle (deg) @ Z TE (mm) @ (deg) @LE Z LE (mm) @ LE TE TE 11.7 800 −62.79 800 17.2 840.43 −62.52 822.82 19.7 864.24 −63.06 847.22 24.7 913.25 −63.8 902.53 27.7 965.73 −64.6 963.8 27.7 1018.57 −65.9 1028.54 25.7 1068.68 −67.8 1094.99 20.7 1110.49 −69.3 1158.05 −0.3 1215 −69.58 1215

(30) The inlet angle, α, is selected with reference to the flow direction coming from the second row blades 20, and the exit angle, β, may be selected to provide a predetermined direction of flow into the third stage blades 24.

(31) The portions of the airfoil for the vane 22 described in Table 1 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, S.sub.V3, of the airfoil for the vane 22. The Z coordinate values in Table 1 have 800 mm at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the vane 22, i.e., adjacent the inner endwall 42, and are presented as lengths along the total span of the vane 22. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. 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.

(32) Referring to FIGS. 6-9, a configuration for the third stage blade 24 is described. In particular, referring initially to FIGS. 6 and 7, a third stage blade airfoil structure 56 is shown including one of the airfoils or blades 24 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 8, the blades 24 each include an outer wall comprising a generally concave pressure sidewall 58, and include an opposing generally convex suction sidewall 60. The sidewalls 58, 60 extend radially outwardly from an inner diameter endwall 62 to a blade tip 64, and extend generally axially in a chordal direction between a leading edge 66 and a trailing edge 68 of each of the blades 24. A blade root is defined by a dovetail 65 extending radially inwardly from the endwall 62 for mounting the blade 24 to the rotor 30. The endwall 62 is positioned at a location where it forms a boundary, i.e., an inner boundary, defining a portion of the flow path 13 for the working fluid.

(33) FIG. 8 illustrates a cross section of the blade 24 at a radial location of about 50% of the span, S.sub.B3 (FIG. 6), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 7), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, S.sub.B3, of the airfoil for the blade 24. It should be noted that a central lengthwise axis 67 of the dovetail 65 is shown herein as extending at an angle relative to the direction of the longitudinal axis 32.

(34) The cross section of FIG. 8 lies in the X-Y plane. As seen in FIG. 8, the blade 24 defines an airfoil mean line, C.sub.B3, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 58, 60. At the leading edge 66, a blade metal angle of each of the surfaces of the pressure and suction sides 58, 60 adjacent to the leading edge 66 is provided for directing incoming flow to the blade 24 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.B3, at the leading edge 66, i.e., tangential to the line C.sub.B3 at the airfoil leading edge 66.

(35) At the trailing edge 68, a blade metal angle of the surfaces of the pressure and suction sides 58, 60 adjacent to the trailing edge 68 is provided for directing flow exiting from the blade 24 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.B3, at the trailing edge 68, i.e., tangential to the line C.sub.B3 at the airfoil trailing edge 68.

(36) The inlet angles, α, and exit angles, β, for the airfoil of the blade 24 are as described in Table 2 below. The Z coordinate locations are presented as lengths along the total span of the blade 24. The values for the inlet angles, α, and exit angles, β, are defined at selected Z locations spaced at increments along the span of the blade 24, where 810 mm (of total value) is located adjacent to the inner endwall 62 and 1252 mm (of total value) is located adjacent to the blade tip 64. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 9.

(37) TABLE-US-00002 TABLE 2 β-Metal Outlet α-Metal Inlet Angle Angle (deg) @ Z TE (mm) @ (deg) @LE Z LE (mm) @ LE TE TE −47.5 810 55 810 −46 838.83 56.3 841.33 −45.5 854.72 56.7 861.87 −44 901.75 57.7 914.8 −40 992.5 59.05 1014.33 −27 1098.44 59.95 1125 −12 1207.24 58.9 1228.65 −6.5 1252 58.6 1252

(38) The portions of the airfoil for the blade 24 described in Table 2 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 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, S.sub.B3, of the airfoil for the blade 24. The Z coordinate values in Table 4 have 810 mm at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the blade 24, i.e., adjacent the inner endwall 62, and are presented as a percentage of the total span of the blade 24. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. 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.

(39) Referring to FIGS. 10-13, a configuration for the fourth stage vane 26 is described. In particular, referring initially to FIGS. 10 and 11, a fourth stage vane airfoil structure 76 is shown including four of the airfoils or vanes 26 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 12, the vanes 26 each include an outer wall comprising a generally concave pressure sidewall 78, and include an opposing generally convex suction sidewall 80. The sidewalls 78, 80 extend radially between an inner diameter endwall 82 and an outer diameter endwall 84, and extend generally axially in a chordal direction between a leading edge 86 and a trailing edge 88 of each of the vanes 26. The endwalls 82, 84 are located at opposing ends of the vanes 26 and are positioned at locations where they form a boundary, i.e., inner and outer boundaries, defining a portion of the flow path 13 for the working fluid. Opposing radially inner matefaces 85a, 87a and radially outer matefaces 85b, 87b are defined by the respective inner and outer diameter endwalls 82, 84 of the airfoil structure 76.

(40) FIG. 12 illustrates a cross section of one of the vanes 26 at a radial location of about 50% of the span, S.sub.V4 (FIG. 10), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 11), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, S.sub.V4, of the airfoil for the vane 26. It should be noted that the matefaces 85a, 87a and 85b, 87b are shown herein as extending at an angle relative to the direction of the longitudinal axis 32.

(41) The cross section of FIG. 12 lies in the X-Y plane. As seen in FIG. 12, the vane 26 defines an airfoil mean line, C.sub.V4, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 78, 80. At the leading edge 86, a blade metal angle of each of the surfaces of the pressure and suction sides 78, 80 adjacent to the leading edge 86 is provided for directing incoming flow to the vane 26 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.V4, at the leading edge 86, i.e., tangential to the line C.sub.V4 at the airfoil leading edge 86.

(42) At the trailing edge 88, a blade metal angle of the surfaces of the pressure and suction sides 78, 80 adjacent to the trailing edge 88 is provided for directing flow exiting from the vane 26 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.V4, at the trailing edge 88, i.e., tangential to the line C.sub.V4 at the airfoil trailing edge 88.

(43) The inlet angles, α, and exit angles, β, for the airfoil of the vane 26 are as described in Table 3 below. The Z coordinate locations are presented as lengths along the total span of the vane 26. The values for the inlet angles, α, and exit angles, β, are defined at selected Z locations spaced at increments along the span of the vane 26, where 780 mm (of total value) is located adjacent to the inner endwall 82 and 1400 mm (of total value) is located adjacent to the outer endwall 84. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 13.

(44) TABLE-US-00003 TABLE 3 β-Metal Outlet α-Metal Inlet Angle Angle (deg) @ Z TE (mm) @ (deg) @LE Z LE (mm) @ LE TE TE 32 780 −55.75 780 33.5 860.27 −55.5 850.23 34 923.17 −56.05 925.91 30.5 1039.6 −57 1061.43 15.5 1159.24 −58 1199.19 3 1239.36 −58.5 1297.69 0 1350 −58 1350 −2 1400 −57.24 1400

(45) The portions of the airfoil for the vane 26 described in Table 6 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 11) with the Z axis extending perpendicular to a plane normal to a radius from the centerline of the turbine rotor, i.e., normal to a plane containing the X and Y values, and generally parallel to the span, S.sub.V4, of the airfoil for the vane 26. The Z coordinate values in Table 6 have 780 mm at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the vane 26, i.e., adjacent the inner endwall 82, and are presented as a percentage of the total span of the vane 26, and are presented as a percentage of the total span of the blade 28. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. 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.

(46) Referring to FIGS. 14-17, a configuration for the fourth stage blade 28 is described. In particular, referring initially to FIGS. 14 and 15, a fourth stage blade airfoil structure 96 is shown including one of the airfoils or blades 28 adapted to be supported to extend radially across the flow path 13. Referring additionally to FIG. 16, the blades 28 each include an outer wall comprising a generally concave pressure sidewall 98, and include an opposing generally convex suction sidewall 100. The sidewalls 98, 100 extend radially outwardly from an inner diameter endwall 102 to a blade tip 104, and extend generally axially in a chordal direction between a leading edge 106 and a trailing edge 108 of each of the blades 28. A blade root is defined by a dovetail 105 extending radially inwardly from the endwall 102 for mounting the blade 28 to the rotor 30. The endwall 102 is positioned at a location where it forms a boundary, i.e., an inner boundary, defining a portion of the flow path 13 for the working fluid.

(47) FIG. 16 illustrates a cross section of the blade 28 at a radial location of about 50% of the span, S.sub.B4 (FIG. 14), along the Z axis of a Cartesian coordinate system that has orthogonally related X, Y and Z axes (FIG. 15), where the Z axis extends perpendicular to a plane normal to a radius from the longitudinal axis 32 of the engine i.e., normal to a plane containing the X and Y axes, and generally parallel to the span, S.sub.B4, of the airfoil for the blade 28. It should be noted that a central lengthwise axis 107 of the dovetail 105 is shown herein as extending at an angle relative to the direction of the longitudinal axis 32.

(48) The cross section of FIG. 16 lies in the X-Y plane. As seen in FIG. 16, the blade 28 defines an airfoil mean line, C.sub.B4, comprising a chordally extending line at a central or mean location between the pressure and suction sidewalls 98, 100. At the leading edge 106, a blade metal angle of each of the surfaces of the pressure and suction sides 98, 100 adjacent to the leading edge 106 is provided for directing incoming flow to the blade 28 and defines an airfoil leading edge (LE) or inlet angle, α. The airfoil inlet angle, α, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.B4, at the leading edge 106, i.e., tangential to the line C.sub.B4 at the airfoil leading edge 106.

(49) At the trailing edge 108, a blade metal angle of the surfaces of the pressure and suction sides 98, 100 adjacent to the trailing edge 108 is provided for directing flow exiting from the blade 28 and defines an airfoil trailing edge (TE) or exit angle, β. The airfoil exit angle, β, is defined as an angle between a line 32.sub.P parallel to the longitudinal axis 32 and an extension of the airfoil mean line, C.sub.B4, at the trailing edge 108, i.e., tangential to the line C.sub.B4 at the airfoil trailing edge 108.

(50) The inlet angles, α, and exit angles, β, for the airfoil of the blade 28 are as described in Table 4 below. The Z coordinate locations are presented as lengths along the total span of the blade 28. The values for the inlet angles, α, and exit angles, β, are defined at selected Z locations spaced at increments along the span of the blade 28, where 760 mm (of total value) is located adjacent to the inner endwall 102 and 1439 9 mm (of total value) is located adjacent to the blade tip 104. The inlet angles, α, and exit angles, β, are further graphically illustrated in FIG. 17.

(51) TABLE-US-00004 TABLE 4 β-Metal Outlet α-Metal Inlet Angle Angle (deg) @ Z TE (mm) @ (deg) @LE Z LE (mm) @ LE TE TE −43 760 41 760 −43 793 41 793 −35 877.61 45 870.68 −32 974.69 48.2 972.26 −24.25 1089.3 46.91 1091.9 −10 1190.36 49.93 1198.67 −0.75 1280.53 51.73 1296.59 7.5 1345.71 52.08 1364.95 8.5 1399 53.08 1399 8.5 1439.9 53.08 1439.9

(52) The portions of the airfoil for the blade 28 described in Table 8 are provided with reference to a Cartesian coordinate system, as discussed above, that has orthogonally related X, Y and Z axes (FIG. 7) with the Z axis extending perpendicular to a plane normal to a radius from the centerline of the turbine rotor, i.e., normal to a plane containing the X and Y values, and generally parallel to the span, S.sub.B4, of the airfoil for the blade 28. The Z coordinate values in Table 8 have 760 mm at a radial location coinciding with the X, Y plane at the radially innermost aerodynamic section of the airfoil for the blade 28, i.e., adjacent the inner endwall 102. The X axis lies parallel to the longitudinal axis 32, and the Y axis extends in the circumferential direction of the engine. 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.

(53) It is believed that the vane 22, blade 24, vane 26, and blade 28, constructed with the described average angle changes, provide an improved or optimized flow of working gases passing from the turbine section 12 to the diffuser 34, with improved Mach numbers for the flow passing through the third and fourth stages of the turbine. In particular, the design for the gas-path boundaries and 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.

(54) While specific embodiments have been described in detail, those with ordinary skill in the art will appreciate that various modifications and alternative to those details could be developed in light of the overall teachings of the disclosure. Accordingly, the particular arrangements disclosed are meant to be illustrative only and not limiting as to the scope of the invention, which is to be given the full breadth of the appended claims, and any and all equivalents thereof.