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Title:
GAS TURBINE ENGINE AIRFOIL
Document Type and Number:
WIPO Patent Application WO/2015/175073
Kind Code:
A2
Abstract:
A gas turbine engine includes a fan section, a compressor section and a turbine section, one of which includes an airfoil. The airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a maximum chord length projection that is not in an axial view.

Inventors:
GALLAGHER EDWARD J (US)
MONZON BYRON R (US)
LIU LING (US)
LI LINDA S (US)
WHITLOW DARRYL (US)
FORD BARRY M (US)
Application Number:
PCT/US2015/016584
Publication Date:
November 19, 2015
Filing Date:
February 19, 2015
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
UNITED TECHNOLOGIES CORP (US)
International Classes:
F04D29/38; F01D5/14
Other References:
See references of EP 3108118A4
Attorney, Agent or Firm:
GOTTSCHALK, William S. (Gaskey & Olds/Pratt & Whitneyc/o CPA Global,P.O. Box 5205, Minneapolis Minnesota, US)
Download PDF:
Claims:
CLAIMS

What is claimed is:

1. A gas turbine engine comprising:

a combustor section arranged between a compressor section and a turbine section; a fan section arranged upstream from the compressor section; and

an airfoil that is arranged in one of the fan section, the compressor section and the turbine section, the airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip, wherein the airfoil has a maximum chord length projection that is not in an axial view.

2. The gas turbine engine according to claim 1, wherein the maximum chord length projection is in a 20° to 60° view.

3. The gas turbine engine according to claim 2, wherein the maximum chord length projection is in a 30° to 50° view.

4. The gas turbine engine according to claim 3, wherein the maximum chord length projection is in an about 40° view.

5. The gas turbine engine according to claim 4, wherein the maximum chord length projection in the about 40° view is in a range of 60% to 70% span position.

6. The gas turbine engine according to claim 3, wherein the maximum chord length projection is in an about 50° view.

7. The gas turbine engine according to claim 6, wherein the maximum chord length projection in the about 50° view is at the 100% span position.

8. The gas turbine engine according to claim 3, wherein the maximum chord length projection is in an about 30° view.

9. The gas turbine engine according to claim 1, wherein the airfoil is a fan blade in the fan section.

10. The gas turbine engine according to claim 9, wherein the fan blade is a composite blade.

11. The gas turbine engine according to claim 10, wherein the composite blade is a swept blade.

12. The gas turbine engine according to claim 1, wherein the fan section has a fan pressure ratio of less than or equal to 1.5.

13. The gas turbine engine according to claim 1, wherein the engine has a bypass ratio of greater than 6.

14. A gas turbine engine comprising:

a combustor section arranged between a compressor section and a turbine section; a fan section arranged upstream from the compressor section; and

an airfoil that is arranged in one of the fan section, the compressor section and the turbine section, the airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip, wherein the airfoil has a maximum leading edge projection in a 20° to 40° view.

15. The gas turbine engine according to claim 14, wherein the maximum leading edge projection is in an about 30° view.

16. The gas turbine engine according to claim 15, wherein the maximum leading edge projection is in a range of 35% to 55% span position.

17. The gas turbine engine according to claim 14, wherein the airfoil is a fan blade in the fan section.

18. The gas turbine engine according to claim 17, wherein the fan blade is a composite blade.

19. The gas turbine engine according to claim 18, wherein the composite blade is a swept blade.

20. The gas turbine engine according to claim 14, wherein the fan section has a fan pressure ratio of less than or equal to 1.5.

21. The gas turbine engine according to claim 14, wherein the engine has a bypass ratio of greater than 6.

22. A gas turbine engine comprising:

a combustor section arranged between a compressor section and a turbine section; a fan section arranged upstream from the compressor section; and

an airfoil that is arranged in one of the fan section, the compressor section and the turbine section, the airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip, wherein the airfoil has a maximum trailing edge projection in a 50° to 70° view.

23. The gas turbine engine according to claim 22, wherein the maximum trailing edge projection is at the 100% span position.

24. The gas turbine engine according to claim 23, wherein the maximum trailing edge projection is in about 60° view.

25. The gas turbine engine according to claim 22, wherein the airfoil is a fan blade in the fan section.

26. The gas turbine engine according to claim 25, wherein the fan blade is a composite blade.

27. The gas turbine engine according to claim 26, wherein the composite blade is a swept blade.

28. The gas turbine engine according to claim 22, wherein the fan section has a fan pressure ratio of less than or equal to 1.5.

29. The gas turbine engine according to claim 22, wherein the engine has a bypass ratio of greater than 6.

30. A gas turbine engine comprising:

a combustor section arranged between a compressor section and a turbine section; a fan section having an array of twenty-six or fewer fan blades, wherein the fan section has a fan pressure ratio of less than 1.55;

a geared architecture coupling the fan section to the turbine section or the compressor section; and

wherein the fan blades include an airfoil having pressure and suction sides, the airfoil extends in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip, wherein the airfoil has a maximum chord length projection in a 20° to 60° view the airfoil has a maximum leading edge projection in a 20° to 40° view and the airfoil has a maximum trailing edge projection in a 50° to 70° view.

Description:
GAS TURBINE ENGINE AIRFOIL

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to United States Provisional Application No. 61/941,871 filed on February 19, 2014.

BACKGROUND

[0002] This disclosure relates generally to an airfoil for gas turbine engines, and more particularly to a fan or compressor blade's profile, including leading and trailing edges and chord length, projected onto a series of planes.

[0003] A turbine engine such as a gas turbine engine typically includes a fan section, a compressor section, a combustor section and a turbine section. Air entering the compressor section is compressed and delivered into the combustor section where it is mixed with fuel and ignited to generate a high-speed exhaust gas flow. The high-speed exhaust gas flow expands through the turbine section to drive the compressor and the fan section. The compressor section typically includes low and high pressure compressors, and the turbine section includes low and high pressure turbines.

[0004] The propulsive efficiency of a gas turbine engine depends on many different factors, such as the design of the engine and the resulting performance debits on the fan that propels the engine. As an example, the fan may rotate at a high rate of speed such that air passes over the fan airfoils at transonic or supersonic speeds. The fast-moving air creates flow discontinuities or shocks that result in irreversible propulsive losses. Additionally, physical interaction between the fan and the air causes downstream turbulence and further losses. Although some basic principles behind such losses are understood, identifying and changing appropriate design factors to reduce such losses for a given engine architecture has proven to be a complex and elusive task.

SUMMARY

[0005] In one exemplary embodiment, a gas turbine engine includes a combustion section arranged between a compressor section and a turbine section. A fan section is arranged upstream from the compressor section. An airfoil is arranged in one of the fan section, the compressor section and the turbine section. The airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a maximum chord length projection that is not in an axial view.

[0006] In a further embodiment of the above engine, the airfoil has a maximum chord length projection in a 20° to 60° view.

[0007] In a further embodiment of any of the above engines, the maximum chord length projection is in a 30° to 50° view.

[0008] In a further embodiment of any of the above engines, the maximum chord length projection is in an about 40° view.

[0009] In a further embodiment of any of the above engines, the maximum chord length projection in the about 40° view is in a range of 60% to 70% span position.

[0010] In a further embodiment of any of the above engines, the maximum chord length projection is in an about 50° view.

[0011] In a further embodiment of any of the above engines, the maximum chord length projection in the about 50° view is at the 100% span position.

[0012] In a further embodiment of any of the above engines, the maximum chord length projection is in an about 30° view.

[0013] In a further embodiment of any of the above engines, the airfoil is a fan blade in the fan section.

[0014] In a further embodiment of any of the above engines, the fan blade is a composite blade.

[0015] In a further embodiment of any of the above engines, the composite blade is a swept blade.

[0016] In a further embodiment of any of the above engines, the fan section has a fan pressure ratio of less than or equal to about 1.5.

[0017] In a further embodiment of any of the above engines, the engine has a bypass ratio of greater than 6.

[0018] In one exemplary embodiment, a gas turbine engine includes a combustion section arranged between a compressor section and a turbine section. A fan section is arranged upstream from the compressor section. An airfoil is arranged in one of the fan section, the compressor section and the turbine section. The airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a maximum leading edge projection in a 20° to 40° view.

[0019] In a further embodiment of the above engine, the maximum leading edge projection is in an about 30° view.

[0020] In a further embodiment of any of the above engines, the maximum leading edge projection is in a range of 35% to 55% span position.

[0021] In a further embodiment of any of the above engines, the airfoil is a fan blade in the fan section.

[0022] In a further embodiment of any of the above engines, the fan blade is a composite blade.

[0023] In a further embodiment of any of the above engines, the composite blade is a swept blade.

[0024] In a further embodiment of any of the above engines, the fan section has a fan pressure ratio of less than or equal to about 1.5.

[0025] In one exemplary embodiment, a gas turbine engine includes a combustion section arranged between a compressor section and a turbine section. A fan section is arranged upstream from the compressor section. An airfoil is arranged in one of the fan section, the compressor section and the turbine section. The airfoil includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a maximum trailing edge projection in a 50° to 70° view.

[0026] In a further embodiment of the above engine, the maximum trailing edge projection is at the 100% span position.

[0027] In a further embodiment of any of the above engines, the maximum trailing edge projection is in about 60° view.

[0028] In a further embodiment of any of the above engines, the maximum trailing edge projection is in about 50° view.

[0029] In a further embodiment of any of the above engines, the airfoil is a fan blade in the fan section. [0030] In a further embodiment of any of the above engines, the fan blade is a composite blade.

[0031] In a further embodiment of any of the above engines, the composite blade is a swept blade.

[0032] In a further embodiment of any of the above engines, the fan section has a fan pressure ratio of less than or equal to about 1.5.

[0033] In one exemplary embodiment, a gas turbine engine includes a combustor section arranged between a compressor section and a turbine section. A fan section has an array of twenty-six or fewer fan blades. The fan section has a fan pressure ratio of less than 1.55. A geared architecture couples the fan section to the turbine section or the compressor section. The fan blades include an airfoil having pressure and suction sides. The airfoil extends in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a maximum chord length projection in a 20° to 60° view the airfoil has a maximum leading edge projection in a 20° to 40° view and the airfoil has a maximum trailing edge projection in a 50° to 70° view.

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The disclosure can be further understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:

[0035] Figure 1 schematically illustrates a gas turbine engine embodiment.

[0036] Figure 2A is a perspective view of a portion of a fan section.

[0037] Figure 2B is a schematic cross-sectional view of the fan section.

[0038] Figure 2C is a cross-sectional view a fan blade taken along line 2C-2C in Figure 2B.

[0039] Figure 3A is a schematic view of fan blade span positions.

[0040] Figure 3B is a schematic view of a fan blade's leading and trailing edges and chord length projected onto an axial plane.

[0041] Figure 4A illustrates a first example airfoil chord length projected onto a series of planes defined between the axial and tangential directions. [0042] Figure 4B illustrates a second example airfoil chord length projected onto a series of planes defined between the axial and tangential directions.

[0043] Figure 5 A illustrates a first example airfoil leading edge projected onto a series of planes defined between the axial and tangential directions.

[0044] Figure 5B illustrates a second example airfoil leading edge projected onto a series of planes defined between the axial and tangential directions.

[0045] Figure 6A illustrates a first example airfoil trailing edge projected onto a series of planes defined between the axial and tangential directions.

[0046] Figure 6B illustrates a second example airfoil trailing edge projected onto a series of planes defined between the axial and tangential directions.

[0047] Figure 6C illustrates a third example airfoil trailing edge projected onto a series of planes defined between the axial and tangential directions.

[0048] The embodiments, examples and alternatives of the preceding paragraphs, the claims, or the following description and drawings, including any of their various aspects or respective individual features, may be taken independently or in any combination. Features described in connection with one embodiment are applicable to all embodiments, unless such features are incompatible.

DETAILED DESCRIPTION

[0049] Figure 1 schematically illustrates a gas turbine engine 20. The gas turbine engine 20 is disclosed herein as a two-spool turbofan that generally incorporates a fan section 22, a compressor section 24, a combustor section 26 and a turbine section 28. Alternative engines might include an augmenter section (not shown) among other systems or features. The fan section 22 drives air along a bypass flow path B in a bypass duct defined within a nacelle 15, while the compressor section 24 drives air along a core flow path C for compression and communication into the combustor section 26 then expansion through the turbine section 28. Although depicted as a two-spool turbofan gas turbine engine in the disclosed non-limiting embodiment, it should be understood that the concepts described herein are not limited to use with two-spool turbofans as the teachings may be applied to other types of turbine engines including three-spool architectures. That is, the disclosed airfoils may be used for engine configurations such as, for example, direct fan drives, or two- or three-spool engines with a speed change mechanism coupling the fan with a compressor or a turbine sections.

[0050] The exemplary engine 20 generally includes a low speed spool 30 and a high speed spool 32 mounted for rotation about an engine central longitudinal axis X relative to an engine static structure 36 via several bearing systems 38. It should be understood that various bearing systems 38 at various locations may alternatively or additionally be provided, and the location of bearing systems 38 may be varied as appropriate to the application.

[0051] The low speed spool 30 generally includes an inner shaft 40 that interconnects a fan 42, a first (or low) pressure compressor 44 and a first (or low) pressure turbine 46. The inner shaft 40 is connected to the fan 42 through a speed change mechanism, which in exemplary gas turbine engine 20 is illustrated as a geared architecture 48 to drive the fan 42 at a lower speed than the low speed spool 30. The high speed spool 32 includes an outer shaft 50 that interconnects a second (or high) pressure compressor 52 and a second (or high) pressure turbine 54. A combustor 56 is arranged in exemplary gas turbine 20 between the high pressure compressor 52 and the high pressure turbine 54. A mid-turbine frame 57 of the engine static structure 36 is arranged generally between the high pressure turbine 54 and the low pressure turbine 46. The mid-turbine frame 57 further supports bearing systems 38 in the turbine section 28. The inner shaft 40 and the outer shaft 50 are concentric and rotate via bearing systems 38 about the engine central longitudinal axis X which is collinear with their longitudinal axes.

[0052] The core airflow is compressed by the low pressure compressor 44 then the high pressure compressor 52, mixed and burned with fuel in the combustor 56, then expanded over the high pressure turbine 54 and low pressure turbine 46. The mid-turbine frame 57 includes airfoils 59 which are in the core airflow path C. The turbines 46, 54 rotationally drive the respective low speed spool 30 and high speed spool 32 in response to the expansion. It will be appreciated that each of the positions of the fan section 22, compressor section 24, combustor section 26, turbine section 28, and fan drive gear system 48 may be varied. For example, gear system 48 may be located aft of combustor section 26 or even aft of turbine section 28, and fan section 22 may be positioned forward or aft of the location of gear system 48. [0053] The engine 20 in one example is a high-bypass geared aircraft engine. In a further example, the engine 20 bypass ratio is greater than about six (6), with an example embodiment being greater than about ten (10). In another example, the bypass ratio between about ten (10) and about eighteen (18). In yet another example, the bypass ratio is less than about nine (9), for example, about seven (7) to about nine (9). In one example, the geared architecture 48 is an epicyclic gear train, such as a planetary gear system or other gear system, with a gear reduction ratio of greater than about 2.3 and the low pressure turbine 46 has a pressure ratio that is greater than about five. In one disclosed embodiment, the engine 20 bypass ratio is greater than about ten (10: 1), the fan diameter is significantly larger than that of the low pressure compressor 44, and the low pressure turbine 46 has a pressure ratio that is greater than about five (5: 1). Low pressure turbine 46 pressure ratio is pressure measured prior to inlet of low pressure turbine 46 as related to the pressure at the outlet of the low pressure turbine 46 prior to an exhaust nozzle. The geared architecture 48 may be an epicyclic gear train, such as a planetary gear system or other gear system, with a gear reduction ratio of greater than about 2.3: 1. It should be understood, however, that the above parameters are only exemplary of one embodiment of a geared architecture engine and that the present invention is applicable to other gas turbine engines including direct drive turbofans.

[0054] The example gas turbine engine includes the fan 42 that comprises in one non-limiting embodiment less than about twenty-six (26) fan blades. In another non-limiting embodiment, the fan section 22 includes less than about twenty (20) fan blades. Moreover, in one disclosed embodiment the low pressure turbine 46 includes no more than about six (6) turbine rotors schematically indicated at 34. In another non-limiting example embodiment the low pressure turbine 46 includes about three (3) turbine rotors. A ratio between the number of fan blades 42 and the number of low pressure turbine rotors is between about 3.3 and about 8.6. The example low pressure turbine 46 provides the driving power to rotate the fan section 22 and therefore the relationship between the number of turbine rotors 34 in the low pressure turbine 46 and the number of blades 42 in the fan section 22 disclose an example gas turbine engine 20 with increased power transfer efficiency.

[0055] A significant amount of thrust is provided by the bypass flow B due to the high bypass ratio. The fan section 22 of the engine 20 is designed for a particular flight condition - typically cruise at about 0.8 Mach and about 35,000 feet. The flight condition of 0.8 Mach and 35,000 ft, with the engine at its best fuel consumption - also known as "bucket cruise Thrust Specific Fuel Consumption ('TSFC')" - is the industry standard parameter of lbm of fuel being burned divided by lbf of thrust the engine produces at that minimum point. "Low fan pressure ratio" is the pressure ratio across the fan blade alone, without a Fan Exit Guide Vane ("FEGV") system. The low fan pressure ratio as disclosed herein according to one non-limiting embodiment is less than about 1.55. In another non-limiting embodiment the low fan pressure ratio is less than or equal to about 1.7, for example, from about 1.2 to about 1.7. In another example, the low fan pressure ratio is less than or equal to about 1.5, for example, from about 1.4 to about 1.5, and, for example, about 1.45. In another non- limiting embodiment the low fan pressure ratio is from 1.1 to 1.45. "Low corrected fan tip speed" is the actual fan tip speed in ft/sec divided by an industry standard temperature correction of [(Tram °R) / (518.7 °R)] 0'5 . The "Low corrected fan tip speed" as disclosed herein according to one non-limiting embodiment is less than about 1150 ft / second.

[0056] Referring to Figure 2A-2C, the fan blade 42 is supported by a fan hub 60 that is rotatable about the axis X. Each fan blade 42 includes an airfoil 64 extending in a radial span direction R from a root 62 to a tip 66. A 0% span position corresponds to a section of the airfoil 64 at the inner flow path (e.g., a platform), and a 100% span position corresponds to a section of the airfoil 64 at the tip 66. The airfoil 64 may also be used for other sections of the engine 20, for example, the compressor section 24 or the turbine section 28.

[0057] The root 62 is received in a correspondingly shaped slot in the fan hub 60. The airfoil 64 extends radially outward of the platform, which provides the inner flow path. The platform may be integral with the fan blade or separately secured to the fan hub, for example. A spinner 66 is supported relative to the fan hub 60 to provide an aerodynamic inner flow path into the fan section 22.

[0058] The airfoil 64 has an exterior surface 76 providing a contour that extends from a leading edge 68 aftward in a chord-wise direction H to a trailing edge 70, as shown in Figure 2C. Pressure and suction sides 72, 74 join one another at the leading and trailing edges 68, 70 and are spaced apart from one another in an airfoil thickness direction T. An array of the fan blades 42 are positioned about the axis X in a circumferential or tangential direction Y. Any suitable number of fan blades may be used in a given application.

[0059] The exterior surface 76 of the airfoil 64 generates lift based upon its geometry and directs flow along the core flow path C. The fan blade 42 may be constructed from a composite material, or an aluminum alloy or titanium alloy, or a combination of one or more of these. Abrasion-resistant coatings or other protective coatings may be applied to the fan blade 42. In one example, the fan blade 42 is a composite that has a swept configuration.

[0060] One characteristic of fan blade performance relates to the fan blade's leading and trailing edge locations and chord length relative to a particular span position (R direction) as projected onto a series of planes defined between the axial and tangential directions. In addition to varying with span, the projections vary between a hot, running condition and a cold, static ("on the bench") condition.

[0061] Referring to Figure 3A, span positions are schematically illustrated from 0% to 100% in 10% increments. Each section at a given span position is provided by a conical cut that corresponds to the shape of the core flow path, as shown by the large dashed lines. In the case of a fan blade with an integral platform, the 0% span position corresponds to the radially innermost location where the airfoil meets the fillet joining the airfoil to the platform. In the case of a fan blade without an integral platform, the 0% span position corresponds to the radially innermost location where the discrete platform meets the exterior surface of the airfoil.

[0062] R d is the radial distance from hub's rotational axis X to the tip of the leading edge 68. R d as disclosed herein according to one non- limiting embodiment is about 35-37 inches (0.89 - 0.94 meters). In another non-limiting embodiment R d is about 27-29 inches (0.69 - 0.74 meters). In another non-limiting embodiment R d is about 39 - 41 inches (0.99 - 1.04 meters).

[0063] Referring to Figure 3B, the airfoil 64 includes a reference point 80 that is the axial and tangential center of the root, which corresponds to 0, 0 in the X and Y directions. The airfoil 64 extends a chord length B from the leading edge 68 to the trailing edge 70. The chord length B varies and the airfoil twists along the span. Al plane P is parallel with the X direction at a viewing angle of 0°. The profile of the airfoil 64, for example, the leading edge 68, trailing edge 70 and chord length B, can be projected (dashed arrows) onto a plane P from various views and the plane will be perpendicular to the viewing direction. This profile relates to the aerodynamic design and efficiency of the airfoil. The views are taken in 10° increments from 0° to 90°, where 0° projects into the axial plane or X direction and 90° projects into the tangential plane or Y direction. Each 10° increment view is represented by a curve in Figures 4A-6C.

[0064] Example projections for the chord length relative to the span positions are shown in Figures 4A-4B for several example fan blades, each represented by a curve. Only one curve in each graph is discussed for simplicity. Example projections for the leading edge relative to the span positions are shown in Figures 5A-5B for several fan blades. Example projections for the trailing edge relative to the span positions are shown in Figures 6A-6C for three fan blades.

[0065] The airfoil has a maximum chord length projection that is not in an axial view, for example, in a 20° to 60° view. Said another way, the chord when viewed from 20° to 60° appears to be greater in length than when viewed at other projections from 0° to 90°. In one example, the maximum chord length projection is in a 30° to 50° view. Referring to Figure 4A, the maximum chord length projection is in an about 40° view. The maximum chord length projection in the about 40° view is in a range of 60% to 70% span position. Referring to Figure 4B, the maximum chord length projection is in an about 50° view, and the maximum chord length projection in the about 50° view is at the 100% span position.

[0066] The airfoil has a maximum leading edge projection in a 20° to 40° view. Referring to Figure 5 A, the maximum leading edge projection (distance with respect to 0 position) is in an about 30° view. Referring to Figure 5B, the maximum leading edge projection (distance with respect to 0 position) is in a range of 35% to 55% span position.

[0067] The airfoil has a maximum trailing edge projection in a 50° to 70° view. Referring to Figures 6A and 6B, the maximum trailing edge projection is at the 100% span position, and the maximum trailing edge projection is in about 60° view. Referring to Figures 6C, illustrates another example maximum trailing edge projection in about the 50° view.

[0068] The leading and trailing edges and chord length, as projected onto a series of planes in a hot, running condition along the span of the airfoil 64, relate to the contour of the airfoil and provide necessary fan operation in cruise at the lower, preferential speeds enabled by the geared architecture 48 in ordered to enhance aerodynamic functionality and thermal efficiency. As used herein, the hot, running condition is the condition during cruise of the gas turbine engine 20. For example, the leading and trailing edges and chord length as projected onto a series of planes in the hot, running condition can be determined in a known manner using numerical analysis, such as finite element analysis.

[0069] It should also be understood that although a particular component arrangement is disclosed in the illustrated embodiment, other arrangements will benefit herefrom. Although particular step sequences are shown, described, and claimed, it should be understood that steps may be performed in any order, separated or combined unless otherwise indicated and will still benefit from the present invention.

[0070] Although the different examples have specific components shown in the illustrations, embodiments of this invention are not limited to those particular combinations. It is possible to use some of the components or features from one of the examples in combination with features or components from another one of the examples.

[0071] Although an example embodiment has been disclosed, a worker of ordinary skill in this art would recognize that certain modifications would come within the scope of the claims. For that reason, the following claims should be studied to determine their true scope and content.