阅读说明：本技术 带有具有可变椭圆后缘的翼型件的涡轮机转子叶片 (Turbine rotor blade with airfoil having variable elliptical trailing edge ) 是由 马里奥斯·卡拉卡西斯 罗伯特·彼得·布伊尼基 亚当·约翰·弗雷德蒙斯基 于 2020-11-20 设计创作，主要内容包括：本发明公开了一种涡轮机(10)的转子叶片(100),该转子叶片包括翼型件(114)。该翼型件(114)包括在其间限定该翼型件(114)的翼展(128)的根部(118)和尖端(115)。该翼型件(114)还包括前缘(124)以及沿着流动方向在该前缘(124)下游的后缘(126)。前缘(124)和后缘(126)各自在翼型件(114)的翼展(128)上从根部(118)延伸到尖端(115)。该翼型件(114)还包括压力侧表面(120)和吸力侧表面(122)。压力侧表面(120)和吸力侧表面(122)围绕后缘(126)是连续的,并且共同限定居中在后缘(126)上的弧(210)。该弧(210)具有半长轴(206)和半短轴(204)。该弧(210)的半长轴(206)和半短轴(204)限定轴比,并且轴比在翼型件(114)的翼展(128)上变化。(A rotor blade (100) of a turbomachine (10) includes an airfoil (114). The airfoil (114) includes a root (118) and a tip (115) defining a span (128) of the airfoil (114) therebetween. The airfoil (114) also includes a leading edge (124) and a trailing edge (126) downstream from the leading edge (124) in the flow direction. The leading edge (124) and the trailing edge (126) each extend from the root (118) to the tip (115) over a span (128) of the airfoil (114). The airfoil (114) also includes a pressure side surface (120) and a suction side surface (122). The pressure side surface (120) and the suction side surface (122) are continuous about the trailing edge (126) and collectively define an arc (210) centered on the trailing edge (126). The arc (210) has a semi-major axis (206) and a semi-minor axis (204). The semi-major axis (206) and the semi-minor axis (204) of the arc (210) define an axis ratio, and the axis ratio varies over the span (128) of the airfoil (114).)

1. An airfoil (114) for a rotor blade (100) of a turbomachine (10), the airfoil (114) comprising:

a root (118);

a tip (115) spaced radially outward from the root (118), the root (118) and the tip (115) defining a span (128) of the airfoil (114) therebetween;

a leading edge (124) extending from the root (118) to the tip (115) over the span (128) of the airfoil (114);

a trailing edge (126) downstream of the leading edge (124) in a flow direction, the trailing edge (126) extending from the root (118) to the tip (115) over the span (128) of the airfoil (114);

a pressure side surface (120) extending between the root (118) and the tip (115) and between the leading edge (124) and the trailing edge (126);

a suction side surface (122) extending between the root (118) and the tip (115) and between the leading edge (124) and the trailing edge (126), the suction side surface (122) opposing the pressure side surface (120), the pressure side surface (120) and the suction side surface (122) being continuous around the trailing edge (126); and

an arc (210) centered on the trailing edge (126) and collectively defined by a portion of the pressure side surface (120) and a portion of the suction side surface (122), the arc (210) having a semi-major axis (206) and a semi-minor axis (204);

wherein the semi-major axis (206) and the semi-minor axis (204) of the arc (210) define an axis ratio, and the axis ratio varies over the span of the airfoil (114).

2. The airfoil (114) according to claim 1, wherein the axial ratio is greater at a midpoint of the span (128) than at the root (118) or the tip (115).

3. The airfoil (114) according to claim 1, wherein the axial ratio varies symmetrically across the span (128).

4. The airfoil (114) according to claim 1, wherein the axial ratio is constant over a mid-span portion (156) of the airfoil (114).

5. The airfoil (114) according to claim 4, wherein the mid-span portion (156) of the airfoil (114) comprises about two-thirds of the span (128) of the airfoil (114).

6. The airfoil (114) according to claim 1, wherein the axial ratio is greatest in a mid-span portion (156) of the airfoil (114); and wherein the semi-major axis (206) is about three times the semi-minor axis (204) in the mid-span portion (156) of the airfoil (114).

7. The airfoil (114) according to claim 6, wherein the axial ratio is constant over the mid-span portion (156) of the airfoil (114).

8. The airfoil (114) according to claim 7, wherein the mid-span portion (156) of the airfoil (114) comprises about two-thirds of the span (128) of the airfoil (114).

9. The airfoil (114) according to claim 1, wherein the arc (210) is an elliptical arc defined in a constant span cross section of the airfoil (114).

10. A turbine (10), comprising:

a compressor (14);

a combustor (16) disposed downstream of the compressor (14); and

a turbine (18) disposed downstream of the combustor (16), the turbine (18) comprising a rotor shaft (24) extending through the turbine (18) along an axial direction and rotor blades (100) connected to the rotor shaft (24), an airfoil (114) of the rotor blades (100) being defined according to any one of claims 1 to 9.

Technical Field

The present disclosure relates generally to turbomachines. More specifically, the present disclosure relates to rotor blades for turbomachinery.

Background

Gas turbine engines typically include a compressor section, a combustion section, a turbine section, and an exhaust section. The compressor section gradually increases the pressure of the working fluid entering the gas turbine engine and supplies the compressed working fluid to the combustion section. The compressed working fluid and a fuel (e.g., natural gas) are mixed within the combustion section and combusted in the combustion chamber to generate high pressure and temperature combustion gases. The combustion gases flow from the combustion section into a turbine section where the combustion gases expand to produce work. For example, expansion of the combustion gases in the turbine section may rotate a rotor shaft connected to, for example, an electrical generator to produce electricity. The combustion gases then exit the gas turbine via an exhaust section.

The turbine section generally includes a plurality of rotor blades. Each rotor blade includes an airfoil positioned within the flow of combustion gases. In this regard, the rotor blades extract kinetic and/or thermal energy from the combustion gases flowing through the turbine section. The airfoils of the rotor blades typically extend radially outward from the platform to a tip at a radially outer end of the airfoil. Certain rotor blades may include a tip shroud coupled to a radially outer end of an airfoil. The tip shroud reduces the amount of combustion gases that leak past the rotor blades. Fillets may be provided at the transition between the airfoil and the platform and at the transition between the airfoil and the tip shroud.

The airfoil may extend from a leading edge to a trailing edge downstream from the leading edge, and may define aerodynamic surfaces therebetween, such as a pressure side surface and a suction side surface. In conventional airfoils, the aerodynamic surface near the trailing edge of the airfoil may be optimized for aerodynamic properties or may be optimized for structural properties, but typically optimization of one set of properties is at the expense of another set of properties.

Accordingly, an airfoil for a rotor blade that provides both robust structural features and effective aerodynamic performance would be useful.

Disclosure of Invention

Aspects and advantages of the present technology will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the present technology.

According to one embodiment, an airfoil for a rotor blade is provided. The airfoil includes a root and a tip spaced radially outward from the root. The span of the airfoil is defined between a root and a tip. The airfoil also includes a leading edge extending from the root to the tip over a span of the airfoil and a trailing edge downstream from the leading edge in the flow direction. The trailing edge also extends from the root to the tip over the span of the airfoil. The airfoil also includes a pressure side surface extending between the root and the tip and extending between the leading edge and the trailing edge, and a suction side surface extending between the root and the tip and extending between the leading edge and the trailing edge. The suction side surface is opposite the pressure side surface. The pressure side surface and the suction side surface are continuous around the trailing edge. The airfoil also includes an arc centered on the trailing edge and collectively defined by a portion of the pressure side surface and a portion of the suction side surface. The arc has a semi-major axis and a semi-minor axis. The major and minor half-axes of the arc define an axial ratio, and the axial ratio varies over the span of the airfoil.

According to another embodiment, a turbine is provided. The turbomachine includes a compressor, a combustor disposed downstream of the compressor, and a turbine disposed downstream of the combustor. The turbine includes a rotor shaft extending through the turbine in an axial direction and rotor blades connected to the rotor shaft. An airfoil of the rotor blade includes a root and a tip spaced radially outward from the root. The span of the airfoil is defined between a root and a tip. The airfoil also includes a leading edge extending from the root to the tip over a span of the airfoil and a trailing edge downstream from the leading edge in the flow direction. The trailing edge also extends from the root to the tip over the span of the airfoil. The airfoil also includes a pressure side surface extending between the root and the tip and extending between the leading edge and the trailing edge, and a suction side surface extending between the root and the tip and extending between the leading edge and the trailing edge. The suction side surface is opposite the pressure side surface. The pressure side surface and the suction side surface are continuous around the trailing edge. The airfoil also includes an arc centered on the trailing edge and collectively defined by a portion of the pressure side surface and a portion of the suction side surface. The arc has a semi-major axis and a semi-minor axis. The major and minor half-axes of the arc define an axial ratio, and the axial ratio varies over the span of the airfoil.

These and other features, aspects, and advantages of the present technology will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the technology and together with the description, serve to explain the principles of the technology.

Drawings

A full and enabling disclosure of the present technology, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:

FIG. 1 is a schematic illustration of an exemplary gas turbine engine, according to an embodiment of the present disclosure;

FIG. 2 is a side view of an exemplary rotor blade according to an embodiment of the present disclosure;

FIG. 3 is a cross-sectional view of the airfoil of FIG. 2 taken along line 3-3 in FIG. 2;

FIG. 4 is an enlarged view of a portion of the airfoil shown in FIG. 3;

FIG. 5 is a cross-sectional view of a portion of the airfoil of FIG. 2 taken along line 5-5 in FIG. 2;

FIG. 6 is a cross-sectional view of a portion of the airfoil of FIG. 2 taken along line 6-6 in FIG. 2;

FIG. 7 is a cross-sectional view of a portion of the airfoil of FIG. 2 taken along line 5-5 in FIG. 2, according to one or more additional exemplary embodiments; and is

FIG. 8 is a cross-sectional view of a portion of the airfoil of FIG. 2 taken along line 5-5 in FIG. 2, according to one or more additional exemplary embodiments.

Repeat use of reference characters in the present specification and drawings is intended to represent same or analogous features or elements of the present technology.

Detailed Description

Reference now will be made in detail to embodiments of the present technology, one or more examples of which are illustrated in the drawings. Detailed description the detailed description uses numerical and letter designations to refer to features in the drawings. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the technology. As used herein, the terms "first," "second," and "third" may be used interchangeably to distinguish one element from another and are not intended to denote the position or importance of the various elements. The terms "upstream" and "downstream" refer to relative directions with respect to fluid flow in a fluid pathway. For example, "upstream" refers to the direction from which the fluid flows, and "downstream" refers to the direction to which the fluid flows.

As used herein, an approximation such as "substantially" or "about" includes values within ten percent of the stated value or less. When used in the context of an angle or direction, such terms include values within ten degrees of greater or less than the angle or direction. For example, "generally vertical" includes directions within ten degrees of vertical in any direction (e.g., clockwise or counterclockwise).

Each example is provided by way of explanation of the present technology, not limitation of the present technology. In fact, it will be apparent to those skilled in the art that modifications and variations can be made in the present technology without departing from the scope or spirit of the technology. For instance, features illustrated or described as part of one embodiment, can be used on another embodiment to yield a still further embodiment. Thus, it is intended that the present technology cover the modifications and variations of this technology provided they come within the scope of the appended claims and their equivalents.

Although an industrial or land-based gas turbine is shown and described herein, the present techniques as shown and described herein are not limited to land-based and/or industrial gas turbines unless otherwise specified in the claims. For example, the techniques as described herein may be used in any type of turbomachine, including but not limited to aviation gas turbines (e.g., turbofan, etc.), steam turbines, and marine gas turbines.

Referring now to the drawings, in which like numerals refer to like elements throughout the several views, FIG. 1 schematically illustrates a gas turbine engine 10. It should be understood that the gas turbine engine 10 of the present disclosure need not be a gas turbine engine, but may be any suitable turbine, such as a steam turbine engine or other suitable engine. The gas turbine engine 10 may include an inlet section 12, a compressor section 14, a combustion section 16, a turbine section 18, and an exhaust section 20. Compressor section 14 and turbine section 18 may be coupled by a shaft 22. The shaft 22 may be a single shaft or a plurality of shaft segments coupled together to form the shaft 22.

Turbine section 18 may generally include a rotor shaft 24 having a plurality of rotor disks 26 (one of which is shown) and a plurality of rotor blades 28 extending radially outward from rotor disks 26 and interconnected to rotor disks 26. Each rotor disk 26, in turn, may be coupled to or may form a portion of rotor shaft 24 that extends through turbine section 18. Turbine section 18 also includes an outer casing 30 that circumferentially surrounds rotor shaft portion 24 and rotor blades 28, at least partially defining a hot gas path 32 through turbine section 18.

During operation, air or another working fluid flows through inlet section 12 and into compressor section 14, where the air is progressively compressed to provide pressurized air to a combustor (not shown) in combustion section 16. The pressurized air is mixed with fuel and combusted within each combustor to produce combustion gases 34. Combustion gases 34 flow from the combustion section 16 into the turbine section 18 along the hot gas path 32. In the turbine section, rotor blades 28 extract kinetic and/or thermal energy from combustion gases 34, thereby rotating rotor shaft 24. The mechanical rotational energy of rotor shaft 24 may then be used to power compressor section 14 and/or generate electricity. The combustion gases 34 exiting the turbine section 18 may then be exhausted from the gas turbine engine 10 via the exhaust section 20.

FIG. 2 is a view of an exemplary rotor blade 100 that may be incorporated into turbine section 18 of gas turbine engine 10 in place of rotor blade 28. As shown, the rotor blade 100 defines an axial direction A, a radial direction R, and a circumferential direction C. Generally, axial direction a extends parallel to an axial centerline 102 of shaft 24 (fig. 1), radial direction R extends generally orthogonal to axial centerline 102, and circumferential direction C extends generally concentrically about axial centerline 102. The rotor blades 100 may also be incorporated into the compressor section 14 of the gas turbine engine 10 (FIG. 1).

As shown in FIG. 2, rotor blade 100 may include a dovetail 104, a shank portion 106, and a platform 108. More specifically, the dovetail 104 secures the rotor blade 100 to the rotor disk 26 (FIG. 1). Shank portion 106 is coupled to dovetail 104 and extends radially outward from dovetail 104. Platform 108 is coupled to shank portion 106 and extends radially outward from shank portion 106. Platform 108 includes a radially outer surface 110 that generally serves as a radially inward flow boundary for combustion gases 34 flowing through hot gas path 32 of turbine section 18 (FIG. 1). Dovetail 104, shank portion 106, and platform 108 may define an air inlet 112 that allows cooling fluid (e.g., exhaust air from compressor section 14) to enter rotor blade 100. In the embodiment shown in FIG. 2, the dovetail 104 is an axial entry fir-tree type dovetail. Alternatively, the dovetail 104 may be any suitable type of dovetail. Indeed, dovetail 104, shank portion 106, and/or platform 108 may have any suitable configuration.

Referring now to fig. 2 and 3, the rotor blade 100 also includes an airfoil 114. Specifically, the airfoils 114 extend radially outward from the radially outer surface 110 of the platform 108 to a tip 115, with a tip shroud 116 disposed at the tip 115. Opposite the tip shroud 116, the airfoil 114 is coupled to the platform 108 at a root 118 (i.e., the intersection between the airfoil 114 and the platform 108). The airfoil 114 includes a pressure side surface 120 and an opposite suction side surface 122 (FIG. 3). The pressure side surface 120 and the suction side surface 122 are joined together or interconnected at a leading edge 124 of the airfoil 114 that is oriented to enter the flow of combustion gases 34 (FIG. 1). The pressure side surface 120 and the suction side surface 122 are also joined together or interconnected at a trailing edge 126 of the airfoil 114 spaced downstream from the leading edge 124. The pressure side surface 120 and the suction side surface 122 are continuous about a leading edge 124 and a trailing edge 126. The pressure side surface 120 is generally concave and the suction side surface 122 is generally convex.

Referring specifically to FIG. 2, airfoil 114 defines a span 128 extending from root 118 to tip 115. Specifically, the root 118 is positioned at zero percent (0%) of the span 128 and the tip 115 is positioned at one-hundred percent (100%) of the span 128. As shown in FIG. 2, zero percent (0%) of the span 128 is identified by 130 and one hundred percent (100%) of the span 128 is identified by 132. Further, points at about ninety percent of the span 126 are identified by 134 and points at about fifteen percent of the span 126 are identified by 133. Other locations along the span 128 may also be defined. As noted above, "about" is used herein to encompass ranges within plus or minus ten percent of the stated value. In terms of percentage values, the range is intended to be included within plus or minus ten percentage points, for example, about ninety percent may include eighty percent to one hundred percent, and about fifteen percent may include five to twenty-five percent.

Referring now to FIG. 3, airfoil 114 defines a camber curve 136. More specifically, camber curve 136 extends from leading edge 124 to trailing edge 126. Cambered curve 136 is also positioned between and equidistant from pressure side surface 120 and suction side surface 122. As shown, the airfoil 114, and more generally, the rotor blade 100, includes a pressure side 138 positioned on one side of the camber line 136 and a suction side 140 positioned on the other side of the camber line 136.

As discussed above, the rotor blade 100 includes the tip shroud 116. As shown in FIG. 2, a tip shroud 116 is coupled to a radially outer end (e.g., tip 115) of the airfoil 114 and generally defines a radially outermost portion of the rotor blade 100. Functionally, the tip shroud 116 reduces the amount of combustion gases 34 (FIG. 1) escaping past the rotor blade 100. In the embodiment shown in FIG. 2, the tip shroud 116 includes a seal rail 152 extending radially outward from the radially outer surface 146. However, alternative embodiments may include more seal rails 152 (e.g., two seal rails 152, three seal rails 152, etc.) or no seal rails 152 at all.

As can be seen in FIG. 2, the section along line 3-3 is taken through the mid-span portion 156 of the airfoil 114. That is, the span 128 of the airfoil 114 may generally encompass three different portions that differ at least with respect to the shape of the aerodynamic surface at and around the trailing edge 126, as will be described in more detail below, and the line 3-3 is taken through the middle of the three portions. An intermediate span portion 156 may be defined between points 133 and 134, an inner span portion 154 of airfoil 114 may be defined from platform 108 to point 133, and an outer span portion 158 of airfoil 114 may be defined from point 134 to tip 115 and/or tip shroud 116.

The intermediate span portion may extend over a majority of the span 128, such as between about two-thirds of the span and about three-quarters of the span 128. Thus, in some exemplary embodiments, the point 133 may be at about twelve and one-half percent (12.5%) of the span 128, and the point 134 may be at about eighty-seven and one-half percent (87.5%) of the span 128 (e.g., where the intermediate span portion 156 extends over about seventy-five percent (75%) of the span 128, and where the span lengths of the inner and outer portions 154, 158 are equal). In additional exemplary embodiments, the point 133 may be at about sixteen and one-half percent (16.5%) of the span 128 and the point 134 may be at about eighty-three and one-half percent (83.5%) of the span 128, for example, where the intermediate span portion 156 of the airfoil 114 extends over about two-thirds or sixty-seven percent (67%) of the span 128.

It should be noted that each of the cross-sectional views in figures 3 to 6 is a constant span segment. For example, FIG. 3 may be taken at about fifty percent (50%) of the span 128, and as shown in FIG. 3, the entire section through the airfoil 114 is located at the same location along the span 128, for example, at about fifty percent (50%) of the span 128. In other words, each of the cross-sectional views in fig. 3 to 6 may be taken in a plane perpendicular to the radial direction R.

As can be seen in fig. 3-6 (and particularly fig. 4-6), portions of the pressure and suction side surfaces 120, 122 proximate the trailing edge 126 are generally arcuate, e.g., the pressure and suction side surfaces 120, 122 collectively define an arc 210 centered at the trailing edge 126. In some implementations, arc 210 may be substantially circular, e.g., the ratio of the major axis of arc 210 to the minor axis of arc 210 may be about one-to-one (1: 1). In other embodiments, arc 210 may be elliptical, e.g., the major axis may be larger than the minor axis.

In further exemplary embodiments, the shape (e.g., ratio of axes) of the arcs 210 may vary across the span 128 of the airfoil 114. For example, the arc 210 may be elliptical at and around the middle of the span 128, and may be substantially circular or nearly circular at the root 118 and tip 115 (e.g., at about zero percent (0%) and about one-hundred percent (100%) of the span 128). For example, the shape of the arc 210 in the mid-span portion 156 may be different from the shape of the arc 210 in the inner-span portion 154 and the outer-span portion 158, and the shape of the arc 210 may vary within span portions, such as at least the inner-span portion 154 and the outer-span portion 158. Such embodiments may maximize aerodynamic performance by providing an elliptical shape of arc 210 over a majority of span 128, while also maximizing durability by providing a circular (or nearly circular) shape of arc 210 at or around root 118 and tip 115/tip shroud 116.

As seen in fig. 4-6, an arc 210 may be centered at the trailing edge 126 and may extend from a first endpoint 202 on the suction side surface 122 to a second endpoint 200 on the pressure side surface 120. Arc 210 may be semi-circular or semi-elliptical. For example, first endpoint 202 and second endpoint 200 may be located at opposite ends of line segment 203, and line segment 203 may define a minor diameter (or minor axis) of arc 210 and/or the ellipse of which arc 210 is a segment, e.g., arc 210 may be half of an ellipse having major and minor axes of different lengths. The curved curve 136 may intersect the minor diameter 203 at a midpoint 208 of the minor diameter 203, the midpoint 203 defining a center of the ellipse.

The semi-major axis 206 of arc 210 may be defined from the intersection of arc curve 136 and minor diameter 203 (e.g., from the midpoint 208 of minor diameter 203) to trailing edge 126, and semi-major axis 206 may be the major diameter or half of the major axis of the ellipse of which arc 210 is a segment. Semi-major axis 206 may be defined along major axis 205, which is an extension or portion of arcuate curve 136 and may be perpendicular to minor diameter 203. As shown in fig. 4-6, the minor diameter 203 may define a minor axis 204 (e.g., a minor radius) and the major axis 205 may define a major axis 206.

Turning now specifically to FIG. 4, an elliptical arc 210 is shown. It should be noted that fig. 4 is a portion of fig. 3 taken along the constant span line 3-3 in fig. 2, e.g., the segments in fig. 4 are taken in a plane perpendicular to the radial direction R. Accordingly, it should be understood that the elliptical shape of the arc 210 in the cross-sections described herein with reference to fig. 4 (as well as fig. 5 and 6) is an elliptical shape in the constant span cross-section of the airfoil 114. FIG. 4 depicts an elliptical arc 210 that may be disposed in the mid-span portion 156 of the airfoil 114, for example, between the point 133 and the point 134 in FIG. 2. As noted above, the intermediate span portion 156 may extend over between about two-thirds and about three-quarters of the span 128.

As shown in FIG. 4, the elliptical arc 210 may have an axial ratio of about four to one (4: 1). For example, the axis ratio may be the ratio of the semi-major axis 206 to the semi-minor axis 204 such that when the axis ratio is about four to one (4: 1), the semi-major axis 206 is about four times the semi-minor axis 204. In various embodiments, the trailing edge arcs 210 may have an axial ratio of about two to one (2: 1) or higher, such as about three to one (3: 1) or higher, throughout the mid-span portion 156 of the airfoil 114.

The arcs 210 may maintain the same axial ratio throughout the mid-span portion 156 of the airfoil 114. Thus, the mid-span portion 156 of the airfoil 114 may have a constant axial ratio at the trailing edge 126 and may have a higher axial ratio than the rest of the airfoil 114. The axial ratio of the arcs 210 may vary outside of the mid-span portion 156 of the airfoil 114, e.g., may smoothly transition or blend from the high axial ratio shape of fig. 4 into a generally circular shape having a generally equal axis (e.g., "generally" equal means that the semi-major axis 206 may be equal to the semi-minor axis 204 or up to ten percent greater than the semi-minor axis 204), or a nearly circular shape in which the semi-major axis 206 is up to about twenty-five percent greater than the semi-minor axis 204.

Fig. 5 and 6 illustrate the varying elliptical shape of the arc 210 in a constant span cross-section taken about the trailing edge 126 as the shape of the arc 210 is varied by the outer span portion 158. It should be appreciated that the change in the arc 210 at the trailing edge 126 may be generally span-wise symmetric such that, for example, where FIG. 5 represents a cross-section at point 134 (e.g., 87.5% of the span 128), the same cross-sectional shape would be provided at the trailing edge 126 at point 133 (e.g., 12.5% of the span 128). Thus, the exemplary arcs shown in FIGS. 5 and 6 may be disposed in corresponding locations in the outer-span portion 158 (as shown in FIG. 2) and in the inner-span portion 154.

FIG. 5 shows a cross-section at the beginning of the transition from the highest axial ratio in the mid-span portion 156 to the lowest axial ratio at the root 118 and tip 115. Thus, as shown in FIG. 5, the axial ratio at point 134 (FIG. 2) may be relatively close to the axial ratio in the mid-span portion 156 of the airfoil 114. For example, as shown in FIG. 5, the axial ratio may be about three to one (3: 1), e.g., the semi-major axis 206 may be about three times the semi-minor axis 204. In various embodiments, the axial ratio at the point 134 may be between about one and one-half to one (1.5: 1) and about three and one-half to one (3.5: 1), for example, the semi-major axis 206 may be between about one and one-half times and about three and one-half times the semi-minor axis 204 in the mid-span portion 156.

FIG. 6 illustrates the shape of an arc 210 in a constant span cross-section taken about the trailing edge 126 at or near the end of the airfoil 114, such as at or near one or both of the root 118 and tip 115 (e.g., at line 6-6 of FIG. 2). In various embodiments, the shape of the arc 210 may approximate a circular shape at the end of the airfoil 114, as described above. Thus, as shown in FIG. 6, the axial ratio may be about one and one-quarter to one (1.25: 1). In various embodiments, the axial ratio at the location shown in FIG. 6 may be between about one and one-half to one (1.5: 1) and about one to one (1: 1).

In additional embodiments, the trailing edge 126 portion may be square (as shown in FIG. 7) or blunt (as shown in FIG. 8). Fig. 7 and 8 each show the shape of the airfoil in a constant span cross-section taken around the trailing edge 126 at or around the mid-span portion 156.

This written description uses examples to disclose the technology, including the best mode, and also to enable any person skilled in the art to practice the technology, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the technology is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they include structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.