Patent Publication Number: US-10760425-B2

Title: Airfoil shape for third stage compressor stator vane

Description:
BACKGROUND OF THE INVENTION 
     The subject matter disclosed herein relates to compressor stator vanes, and more specifically, to a third stage compressor stator vane. 
     Compressors are used in a variety of industries and systems to compress a gas, such as air. For example, gas turbine engines typically include a compressor to provide compressed air for combustion and cooling. Compressors typically include a rotor assembly and a stator assembly. In multi-stage compressors, the rotor assembly may include multiple rows (e.g., rotor stages) each row having multiple rotor blades. Likewise, the stator assembly may include multiple rows (e.g., stator stages) each row having multiple stator vanes. The rotor assembly is designed to rotate with respect to the stator assembly, compressing an intake fluid as the fluid traverses the compressor. 
     BRIEF DESCRIPTION OF THE INVENTION 
     Certain embodiments commensurate in scope with the originally claimed subject matter are summarized below. These embodiments are not intended to limit the scope of the claimed invention, but rather these embodiments are intended only to provide a brief summary of possible forms of the subject matter. Indeed, the invention may encompass a variety of forms that may be similar to or different from the embodiments set forth below. 
     In a first embodiment, a system includes an airfoil. The airfoil includes a first suction portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the first suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the first suction portion of the nominal airfoil profile are coupled together to define the first suction portion, the airfoil includes an airfoil length along a Z axis, the first suction portion comprises a first portion length along the Z axis, the first portion length is less than or equal to the airfoil length, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances. 
     In a second embodiment, a system includes an airfoil. The airfoil includes a suction side of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the suction side of the nominal airfoil profile at each Z coordinate value, the suction side sections of the suction side of the nominal airfoil profile are coupled together to define the suction side, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances. 
     In a third embodiment, a system includes an airfoil. The airfoil includes a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values are coordinate values that couple together to define airfoil sections of the nominal airfoil profile at each Z coordinate value, the airfoil sections of the nominal airfoil profile are coupled together to define an entirety of the airfoil, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features, aspects, and advantages of the present subject matter will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is a block diagram of an embodiment of a gas turbine system having a multi-stage axial compressor; 
         FIG. 2  is a cross-sectional side view of an embodiment of the gas turbine engine of  FIG. 1 , illustrating stages of blades and vanes of the multi-stage axial compressor; 
         FIG. 3  is side view of an embodiment of an airfoil of a compressor rotor blade or a compressor stator vane; 
         FIG. 4  is side view of an embodiment of an airfoil of a compressor rotor blade or a compressor stator vane; 
         FIG. 5  is a side view of an embodiment of an airfoil of the compressor rotor blade or a compressor stator vane; and 
         FIG. 6  is an axial view of an embodiment of the airfoil of the compressor rotor blade or compressor stator vane of  FIGS. 3-5 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     One or more specific embodiments of the present subject matter will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     When introducing elements of various embodiments of the present subject matter, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. 
     The disclosed embodiments include a multi-stage axial compressor, which may be a standalone unit or part of a multi-stage rotary machine such as a gas turbine system. In certain embodiments, the multi-stage axial compressor includes a plurality of rotor stages and corresponding stator stages, each rotor stage and stator stage including a plurality of airfoils (e.g., blades or vanes) with a specific airfoil profile. During operation, a compressible fluid (e.g., gas such as air, oxygen, oxygen enriched air, oxygen reduced air, exhaust gas, nitrogen, etc.) may enter the multi-stage axial compressor through an inlet system, and each stage of the multi-stage axial compressor will generally increase the pressure and temperature of the compressible fluid by a certain amount. In a gas turbine system, a compressed fluid may then be delivered, for example, via an outlet system, to a combustor for combustion with a fuel. The amount of pressure and temperature increase at each stage of the multi-stage axial compressor may depend on particular operating conditions, such as speed, inlet boundary conditions (e.g., flow, pressure, temperature, composition, and so forth), outlet boundary conditions (e.g., flow resistance, and so forth), and stage efficiency. 
     During compression, an energy level of the compressible fluid may increase as the compressible fluid flows through the multi-stage axial compressor due to the exertion of a torque on the fluid by the rotating rotor blades. The stator&#39;s stationary vanes slow the compressible fluid, converting a circumferential component of the flow into pressure. An airfoil profile or design of the airfoil (e.g., rotor blades and/or stator vanes) may directly affect compression of the compressible fluid. Airfoil profiles described herein may be more optimized and matched for specific velocities and turning speeds. Further, the airfoil profiles described herein may be more optimized for specific stages of the multi-stage axial compressor with a specific total number of stages. Additionally, the airfoil profiles described herein may be designed for compressor rotor blades, compressor stator vanes, or any combination thereof. In certain embodiments, the airfoil profiles described herein may be designed for compressor rotor blades and/or compressor stator vanes in any one or more stages of a multi-stage axial compressor with 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 stages. More specifically, in certain embodiments, the airfoil profiles described herein may be designed for compressor rotor blades and/or compressor stator vanes in stage 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and/or 14 of a 14 stage axial compressor. For example, in certain embodiments, the airfoil profiles described herein may be more optimized for a third stage airfoil (e.g., a rotor blade or stator vane) of a 14 stage axial compressor. The airfoils (e.g., blades or vanes) described herein may be described in terms of X, Y, and Z values set forth in certain table(s) described herein that define airfoil sections of the airfoils. In certain embodiments the X, Y, and Z values may describe suction side airfoil surfaces, pressure side airfoil surfaces, or a combination thereof. The X, Y, and Z values may include coordinate values in a Cartesian coordinate system, including negative and positive values denoting sides that are opposite to each other from a certain axis (e.g., X, Y, Z axis). 
     Turning now to  FIG. 1 , the figure is a block diagram of an embodiment of a turbine system  10  that includes a gas turbine engine  12  and a controller  14  (e.g., electronic and/or processor-based controller). The controller  14  may be communicatively coupled to a variety of sensors  16  and actuators  18  disposed in various components of the gas turbine engine  12 . Signals received via the sensors  16  may be used to derive control actions executable via the actuators  18 . The illustrated gas turbine engine  12  includes a compressor  20  (e.g., a multi-stage axial compressor or compressor section), a turbine  22  (e.g., a multi-stage turbine or turbine section), and fuel nozzles  24  coupled to one or more combustors  26  (e.g., compressor section). The compressor  20  and turbine  22  each may have any number of rows stages of rotor blades and stator vanes (e.g., 1 to 20). As discussed in detail below, an embodiment of an airfoil profile is provided for use with airfoils (e.g., rotor blades or stator vanes) in one or more stages of the compressor  20 . However, before presenting details of the airfoil profile, the following discussion provides a brief description of the gas turbine engine  12  and its operation. 
     In operation, the compressor  20  is configured to compress a compressible fluid (e.g., gas such as air, oxygen, and/or exhaust gas), and deliver the compressed fluid to the fuel nozzles  24  and/or combustors  26 . Although the compressible fluid may include any suitable gas, the following discussion may generally refer to the compressible fluid as an oxidant (e.g., air) as one non-limiting example. The fuel nozzles  24  are configured to supply fuel (e.g., from one or more fuel supplies) into the one or more combustors  26  (e.g., in combustion chambers), which combust the fuel with the oxidant (e.g., air) to generate hot combustion gases to drive the turbine  22 . The fuel nozzles  24  may be designed as pre-mix fuel nozzles  24  and/or diffusion fuel nozzles  24 . Pre-mix fuel nozzles  24  mix the fuel with the oxidant (e.g., air) to create pre-mix type flames. Diffusion fuel nozzles  24  do not premix the fuel with the oxidant, and thus create diffusion type flames. Regardless of the type of flames, the hot combustion gas flows from the combustors  26  into the turbine  22 , thereby driving rotation of one or more stages of turbine blades coupled to a turbine rotor and shaft  30  along an axis  32 . Eventually, the hot combustion gas exits the turbine  22  through an exhaust outlet  28  (e.g., exhaust stack, exhaust end). In the illustrated embodiment, the shaft  30  is coupled to the compressor  20  and a load  36 , such that rotation of the shaft  30  also drives rotation of the compressor  20  and the load  36 . The compressor  20  may intake the oxidant (e.g., air) through an air intake  34 , which may include filters, thermal control systems, or any other preconditioning systems. The load  36  may include an electrical generator, a rotary machine, a propulsion system of a vehicle, or any other suitable device. 
     The airfoil profile described in further detail below may be used in any stage of the compressor  20  (e.g., multi-stage axial compressor with any number of stages of rotor blades and stator vanes). The compressor  20  may include rotating blades and stationary vanes (e.g., airfoils) that may be disposed in rows or stages, described in more detail below. The oxidant (e.g., air) may be progressively compressed in stages or rows of rotating blades and corresponding stator vanes as the air moves downstream in the compressor  20 . In the depicted embodiment, the compressor  20  is a multi-stage axial compressor  20  having at least two rows or stages of blades and vanes. For example, in certain embodiments, the multi-stage axial compressor  20  may have 14 rows or stages of compressor blades and vanes. 
     It may be beneficial to illustrate a more detailed view of certain components of the gas turbine engine  12 . Accordingly,  FIG. 2  is a cross-sectional side view of an embodiment of the compressor  20  of the gas turbine engine  12  of  FIG. 1 . Throughout the discussion of  FIG. 2 , a set of axes will be referenced. These axes are based on a cylindrical coordinate system and point in an axial direction  38  (e.g., downstream), a radial direction  40 , and a circumferential direction  42 . For example, the axial direction  38  extends downstream through the compressor  20  generally parallel to the axis  32 , the radial direction  40  extends away from the axis  32 , and the circumferential direction  42  extends around the axis  32 . 
     In operation, air enters the compressor  20  in the axial direction  38  through the air intake  34  and may be pressurized in the multi-stage axial compressor  20 . The compressed air may then be mixed with fuel for combustion within the combustor  26  to drive the turbine  22  to rotate the shaft  30  in the circumferential direction  42  and, thus, the multi-stage axial compressor  20  and the load  36 . The rotation of the shaft  30  also causes one or more blades  44  (e.g., compressor rotor blades) within the multi-stage axial compressor  20  to draw in and pressurize the air received by the air intake  34 . 
     The multi-stage axial compressor  20  may include a rotor assembly  46  having multiple rotor blades  44  surrounded by a static casing  48  having multiple stator vanes  50  (e.g., variable stator vanes and/or fixed stator vanes). In some embodiments, the static casing  48  of the compressor  20  or the air intake  34  may have one or more sets of inlet guide vanes  52  (IGVs) (e.g., variable IGV stator vanes) that may control flows into the compressor  20 . Each variable stator vane  50  (including each variable IGV stator vane  52 ) may be configured to vary its vane angle relative to the gas flow (e.g. air flow) by rotating the vane  50 ,  52  about an axis of rotation (e.g., radially oriented vane shaft). However, each variable stator vane  50  may be otherwise stationary relative to the rotor blades  44 . In certain embodiments, each variable stator vane  50  may be coupled to an actuator  18  (e.g., electric drive, pneumatic drive, or hydraulic drive), which is coupled to a controller  14  configured to vary the vane angle in response to feedback from sensors  16 . Each fixed stator vane  50  may be configured to remain in a fixed angular position, such that the vane angle does not vary. The compressor  20  may include a plurality of rows or stages  54 , such as between 2 to 30, 2 to 25, 2 to 20, 2 to 14, or 2 to 10 rows or stages, or any specific number or range therebetween. In each stage, the multi-stage axial compressor  20  may include 2 to 1000, 5 to 500, or 10 to 100 rotor blades  44 , and 2 to 1000, 5 to 500, or 10 to 100 stator vanes  50 . In particular, the illustrated embodiment of the multi-stage axial compressor  20  includes 14 stages. It may be appreciated that each stage  54  has a set of rotor blades  44  disposed at a first axial position and a set of stator vanes  50  disposed at a second axial position along the length of the compressor  20 . In other words, each stage  54  has the rotor blades  44  and stator vanes  50  axially offset from one another, such that the compressor  20  has an alternating arrangement of rotor blades  44  and stator vanes  50  one set after another along the length of the compressor  20 . Each set of rotor blades  44  extends (e.g., in a spaced arrangement) in the circumferential direction  42  about the shaft  30 , and each set of stator vanes  50  extends (e.g., in a spaced arrangement) in the circumferential direction  42  within the static casing  48 . While the compressor  20  may include greater or fewer stages  54  than 14,  FIG. 2  illustrates an embodiment of the compressor  20  with 14 stages  54  identified as follows: first stage  54   a , second stage  54   b , third stage  54   c , fourth stage  54   d , fifth stage  54   e , sixth stage  54   f , seventh stage  54   g , eighth stage  54   h , ninth stage  54   i , tenth stage  54   j , eleventh stage  54   k , twelfth stage  541 , thirteenth stage  54   m , and fourteenth stage  54   n . In certain embodiments, each stage  54  may include rotor blades  44  and stator vanes  50  (e.g., fixed stator vanes  50  and/or variable stator vanes  50 ). For example, in certain embodiments, earlier stages  54  (e.g.,  54   a ,  54   b ,  54   c , etc.) may include variable stator vanes  50 , while later stages  54  may include fixed stator vanes  50 . 
     The airfoil described in the TABLE I below may describe either a rotor blade  44  or a stator vane  50  of the compressor  20 . For example, the airfoil described in the TABLE I below may be placed as a stator vane  50  of the third stage  54   c . In use, the rotor blades  44  may rotate circumferentially about the static casing  48  and the stator vanes  50 . Rotation of the rotor blades  44  may result in air entering the air intake  34 . The air is then subsequently compressed as it traverses the various stages  54  (e.g., third stage  54   c  to fourteenth stage  54   n ) of the compressor  20  and moves in the axial direction  38  downstream of the multi-stage axial compressor  20 . The compressed air may then exit through an outlet  56  of the multi-stage axial compressor  20 . The outlet  56  may have a set of exit guide vanes  58  (EGVs). The compressed air that exits the compressor  20  may be mixed with fuel, directed to the combustor  26 , directed to the turbine  22 , or elsewhere in the turbine system  10 . 
     Certain designs of the rotor blades  44  and stator vanes  50  (e.g., airfoils) provide for a more efficient multi-stage axial compressor  20  system. For example, certain rotor blade and/or stator vane (e.g., airfoil) designs may improve compressor  20  efficiency and enable improved operations for the turbine system  10 . Referring now to  FIG. 3 , the figure is a side view of an embodiment of an airfoil  82  that may be included in the multi-stage axial compressor  20  as a rotor blade  44  or stator vane  50 . In the particular embodiment, the airfoil  82  may be included in the third stage  54   c  of the multi-stage axial compressor  20  as a stator vane  50 . In the depicted embodiment, the airfoil  82  is disposed on a base  60 , which may, in certain embodiments, be removably coupled as a rotor blade  44  to the rotor assembly  46 . That is, the base  60  having the airfoil  82  may be removed from the rotor assembly  46 , for example, to inspect, repair, and/or replace the airfoil  82 . Additionally, or in the alternative, the airfoil  82  may be removably coupled as a stator vane  50  to the static casing  48 . That is, the base  60  having the airfoil  82  may be removed from the static casing  48 , for example, to inspect, repair, and/or replace the airfoil  82 . The base  60  may include a removable mount or coupling  59 , such as a dovetail joint. For example, the coupling  59  may include a T-shaped structure, a hook, one or more lateral protrusions, one or more lateral slots, or any combination thereof. The coupling  59  (e.g., dovetail joint) may be configured to mount into the rotor assembly  46  or the static casing  48  in an axial direction  38 , a radial direction  40 , and/or a circumferential direction  42  (e.g., into an axial slot or opening, a radial slot or opening, and/or a circumferential slot or opening). 
     As further described herein, the airfoil  82  includes a suction side  62  and a pressure side  64  disposed opposite from one another on the airfoil  82  (i.e., opposite faces). The airfoil  82  also includes leading and trailing edges  61  and  63  disposed opposite from one another on the airfoil  82  (e.g., opposite upstream and downstream edges). The suction side  62 , the pressure side  64 , the leading edge  61 , and the trailing edge  63  generally extend from the base  60  to a tip  68  of the airfoil  82 . The leading and trailing edges,  61  and  63  respectively, may be described as the dividing or intersecting lines between the suction side  62  and the pressure side  64 . In other words, the suction side  62  and the pressure sides  64  couple together with one another along the leading edge  61  and the trailing edge  63 , thereby defining an airfoil shaped cross-section that gradually changes lengthwise along the airfoil  82 . The airfoil profile described in further detail below may be utilized along any portion or the entirety of the airfoil  82  between the base  60  and the tip  68 . For example, the portion having the disclosed airfoil profile may include all or part of the suction side  62 , all or part of the pressure side  64 , or a combination thereof. 
     In operation, the rotor blades  44  rotate about an axis  66  exerting a torque on a working fluid, such as air, thus increasing energy levels of the fluid as the working fluid traverses the various stages  54  of the multi-stage axial compressor  20  on its way to the combustor  26 . The suction side  62  creates and/or increases a suction force on the working fluid, while the pressure side  64  creates and/or increases a pressure bias on the working fluid. The rotor blades  44  may be adjacent (e.g., upstream and/or downstream) to the one or more stationary stator vanes  50 . The stator vanes  50  slow the working fluid during rotation of the rotor blades  44 , converting a circumferential component of movement of the working fluid flow into pressure. Accordingly, continuous rotation of the rotor blade  44  creates a continuous flow of compressed working fluid, suitable for combustion via the combustor  26 . 
     The airfoil  82  (e.g., rotor blade  44 , stator vane  50 ) includes an airfoil length L measured from the tip  68  of the airfoil  82  to a bottom region  70  of the airfoil  82  adjacent the base  60  (e.g., at an intersection of the airfoil  82  with the base  60 ). An X axis  72  lies parallel to the base  60  and to the rotational axis  66 . The rotational axis  66  may be parallel to the axis  32  or the shaft  30 . The X axis  72  is orthogonal to a Z axis  74  which bisects the airfoil  82 . A Y axis  76  (shown coming out of the plane of the drawing) is orthogonal to both the X axis  72  and the Z axis  74 . The X axis  72  and the Y axis  76  may be used to define an airfoil profile, shape, or section, for example, taken through line  6 - 6  at a point along the Z axis  74 . That is, the airfoil profile may include an outline of the surface (e.g., section) of the airfoil  82  (e.g., rotor blade  44 , stator vane  50 ) at a point along the Z axis  74 . The airfoil profile may include X, Y, and Z values for the suction side  62 , and X, Y, and Z values for the pressure side  64 . A Cartesian coordinate system point  78  (e.g., origin) may be used to define a zero point for the X axis  72 , the Z axis  74 , and the Y axis  76  of the respective airfoil  82 . TABLE I below lists various non-dimensionalized airfoil shapes for the suction side  62  and the corresponding pressure side  64  disposed at locations along the Z axis  74  from the bottom region  70  to the tip  68  of the airfoil  82 . 
     The airfoil  82  may be described in terms of certain airfoil sections containing various air foil shapes and corresponding rows of the TABLE I. For example, as illustrated in  FIG. 4 , the airfoil  82  may be described via airfoil shapes disposed on one or more portions  80 . In certain embodiments, the portion  80  of the airfoil  82  may be described as an area of interest, an area of greater importance, or a sweet spot, wherein the particular airfoil profile may have a greater impact on the performance, efficiency, and other attributes of the airfoil  82  as compared with other areas of the airfoil  82 . However, the portion  80  may include any area of the airfoil  82 , regardless of importance. The one or more portions  80  may include a suction side portion of the suction side  62 , a pressure side portion of the pressure side  64 , or any combination thereof. For example, the one or more portions  80  may include suction side portions  62  and pressure side portions  64  that are offset from one another without any overlap along the Z axis  74 , suction side portions  62  and pressure side portions  64  that partially overlap along the Z axis  74 , or suction side portions  62  and pressure side portions  64  that completely overlap along the Z axis  74 . Portion  80  is shown as a rectangle in dashed lines. More specifically,  FIG. 4  is a side view of an embodiment of the airfoil  82  illustrating the portion  80 . As described above, the airfoil  82  may be the rotor blade  44  or the stator vane  50 , such as the stator vane  50  of the third stage  54   c . Because the figure depicts like elements to  FIG. 3 , the like elements are illustrated with like numbers. In the depicted embodiment, the airfoil  82  includes the length L (e.g., total length), as mentioned previously, measured along the Z axis  74  (e.g., in the radial direction  40 ) from the tip  68  of the airfoil  82  to the bottom region  70  of the airfoil  82 . 
     The portion  80  may begin at a distance or position d and include a length l extending away from the base  60  in the Z direction along the Z axis  74 . As appreciated, in embodiments having one or more suction side portions  80  on the suction side  62  and/or one or more pressure side portions  80  on the pressure side  64 , each portion  80  may be defined by a length l and a position d. A zero value of the position d corresponds to the bottom region  70  of the airfoil  82  adjacent the base  60  (e.g., at an intersection of the airfoil  82  with the base  60 ), which also corresponds to the coordinate origin  78 . When d is zero and l is equal to L, the portion  80  includes the entirety of the airfoil  82  from the bottom region  70  to the tip  68  of the airfoil  82 . By varying values for d and l, portions  80  having varying lengths and start locations from the coordinate origin  78  may be provided for defining the area of interest (e.g., sweet spot) along the airfoil  82 . Each portion  80  may include one or more adjacent airfoil shapes (e.g., airfoil sections or airfoil shapes  110 ) “stacked” on top of each other along the Z axis  74 , described in more detail below with respect to  FIG. 6  and TABLE I below. Each airfoil section or airfoil shape  110  corresponds to Cartesian coordinate values of X, Y, and Z for a common Cartesian coordinate value of Z in TABLE I. Furthermore, adjacent airfoil sections or airfoil shapes  110  correspond to the Cartesian coordinate values of X, Y, and Z for adjacent Cartesian coordinate values of Z in the TABLE I. 
     With reference to TABLE I, the position d may be used to define a start position (e.g., first Cartesian coordinate value of Z) of the portion  80  in the Z direction along the Z axis  74 , while a sum of the position d and the length l may be used to define an end position (e.g., last Cartesian coordinate value of Z) of the portion  80  in the Z direction along the Z axis  74 . In certain embodiments, the position d (e.g., start position) may be selected directly from one of the Cartesian coordinate values of Z in TABLE I, and the sum of the position d and the length l (e.g., end position) may be selected directly from one of the Cartesian coordinate values of Z in TABLE I. In other embodiments, the desired values of the position d and the length l may be initially selected without referencing TABLE I, and then TABLE I may be subsequently analyzed to select best fits of the Cartesian coordinate values of Z in TABLE I based on the desired values of d and l. For example, with reference to TABLE I, the start position of the portion  80  may correspond to the Cartesian coordinate value of Z equal to or nearest to the value of the position d (e.g., start Z value). If the position d is midway between adjacent Cartesian coordinate values of Z in TABLE I, then the lesser or greater Cartesian coordinate value of Z may be selected for the start position of the portion  80  (e.g., start Z value). Alternatively, in some embodiments, if a specific value of the position d is desired but does not match the specific Cartesian coordinate values of Z in TABLE I, then regression analysis and/or curve fitting may be used to analyze the data in TABLE I and interpolate new Cartesian coordinate values of X, Y, Z to enable use of the desired d value. Similarly, with reference to TABLE I, the end position (e.g., end Z value) may correspond to the Cartesian coordinate value of Z equal to or nearest to the sum of the position d and the length l. If the sum of the position d and the length l is midway between adjacent Cartesian coordinate values of Z in TABLE I, then the lesser or greater Cartesian coordinate value of Z may be selected for the end position (e.g., end Z value). Alternatively, in some embodiments, if a specific value of the length l is desired but the sum of the position d and the length l does not match the specific Cartesian coordinate values of Z in TABLE I, then regression analysis and/or curve fitting may be used to analyze the data in TABLE I and interpolate new Cartesian coordinate values of X, Y, Z to enable use of the desired l value. 
     In certain embodiments, the portion  80  may be defined by the Cartesian coordinate values of X, Y, and Z corresponding to the start Z value, the end Z value, and all intermediate Z values in TABLE I. However, in some embodiments, if the Z values do not match the desired start and end positions, then the portion  80  may be defined by the Cartesian coordinate values of X, Y, and Z in TABLE I in the Z direction between the start and end positions (e.g., based on the position d and length l). Furthermore, as discussed herein, the portion  80  may include the Cartesian coordinate values of X, Y, and Z for the suction side  62  (e.g., suction side profile  112 —see  FIG. 6 ), the pressure side  64  (e.g., pressure side profile—see  FIG. 6 ), or a combination thereof. 
     In certain embodiments, the portion  80  may include the airfoil profile of TABLE I only for the suction side  62  according to the position d and length l, only for the pressure side  64  according to the position d and length l, or for both the suction and pressure sides  62  and  64  according to the position d and length l. The position d of the portion  80  may be greater than or equal to approximately 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, or 75 percent of the length L of the airfoil  82 . Furthermore, the length l of the portion  80  may be greater than or equal to approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, or 100 percent of the length L of the airfoil  82 . For example, the portion  80  selected from TABLE I may be the suction side  62  of the outer third of the airfoil  82 . In another example, the portion  80  selected from TABLE I may be both the suction side  62  and the pressure side  64  of an interior portion  80  of the airfoil  82 , where d is greater than 0 and l is less than L (e.g., l=0.3 L). 
     Additionally or alternatively, a portion of the airfoil  82 , such as portion  80 , may be described in terms of a start height (e.g., first position) and a stop height (e.g., second position) along the Z axis  74  (e.g., in the radial direction  40 ) as illustrated in  FIG. 5 . Collectively, the start and stop heights (e.g., first and second positions) define a range along the Z axis  74 . Again, the portion (e.g.,  80 ) of the airfoil  82  may be described as an area of interest, an area of greater importance, or a sweet spot, wherein the particular airfoil profile may have a greater impact on the performance, efficiency, and other attributes of the airfoil  82  as compared with other areas of the airfoil  82 . However, the portion (e.g.,  80 ) may include any area of the airfoil  82 , regardless of importance. For example, as shown in  FIG. 5 , an embodiment of the airfoil  82  is illustrated with multiple defined heights  90 ,  92 ,  94 ,  96 ,  98 , and  100  along the Z axis  74 . The heights  90 ,  92 ,  94 ,  96 ,  98 , and  100  may divide the airfoil  82  into a plurality of portions along the Z axis  74 , wherein the plurality of portions may have equal lengths along the Z axis  74  (e.g., five portions each being 20 percent of the total length L of the airfoil  82 ). However, in some embodiments, the plurality of portions defined by the heights  90 ,  92 ,  94 ,  96 ,  98 , and  100  may have different lengths along the Z axis  74 . Although the illustrated embodiment includes 6 heights (e.g.,  90 ,  92 ,  94 ,  96 ,  98 , and  100 ) defining 5 portions, certain embodiments may include any number of heights (e.g., 2 to 100 or more) defining any number of portions (e.g., 2 to 100 or more) with equal or different lengths along the Z axis  74 . 
     For example, certain embodiments may include 11 heights to define 10 portions with equal or different lengths along the Z axis  74  (e.g., 10 portions each being 10 percent of the total length L of the airfoil  82 ). By further example, certain embodiments may include 101 heights to define 100 portions with equal or different lengths along the Z axis  74  (e.g., 100 portions each being 1 percent of the total length L of the airfoil  82 ). In this manner, the heights may be used to define a specific portion (e.g.,  80 ) of the airfoil  82 , wherein the specific portion (e.g., area of interest) may track the airfoil profile described below in TABLE I. Again, similar to the discussion of  FIG. 4 , the specific portion (e.g.,  80 ) defined by the heights in  FIG. 5  may track the airfoil profile of TABLE I along only the suction side  62 , only the pressure side  64 , or both the suction and pressure sides  62  and  64 . Because  FIG. 5  depicts like elements to  FIG. 4 , the like elements are illustrated with like numbers. 
     In the illustrated embodiment, the portion (e.g.,  80 ) may be defined by the start height and the stop height, wherein the start height is closer to the bottom region  70  than the stop height, and each of the start and stop heights may be selected from one of the heights  90 ,  92 ,  94 ,  96 ,  98 , or  100 . Multiple start and stop heights  90 ,  92 ,  94 ,  96 ,  98 ,  100  may be defined to divide the airfoil  82  and define the portion (e.g.,  80 ). For example, a first start height  92  and a first stop height  90  may describe a first section or segment  102  (e.g., portion  80 ) of the airfoil  82 , a second start height  96  and a second stop height  92  may describe a second section or segment  104  (e.g., portion  80 ) of the airfoil  82 , and a third start height  96  and a third stop height  94  may describe a third section or segment  106  (e.g., portion  80 ) of the airfoil  82 . As shown in  FIG. 5 , each height  90 ,  92 ,  94 ,  96 ,  98 ,  100  may define a start height for a segment, a stop height for the segment, or a start height for one segment and a stop height for another segment. Each of the heights  90 ,  92 ,  94 ,  96 ,  98 ,  100  may be selected to correspond to a different Cartesian coordinate value of Z in TABLE I. In certain embodiments, each of the heights  90 ,  92 ,  94 ,  96 ,  98 ,  100  may be selected directly from one of the Cartesian coordinate values of Z in TABLE I. In other embodiments, the desired values of the heights  90 ,  92 ,  94 ,  96 ,  98 ,  100  may be initially selected without referencing TABLE I, and then TABLE I may be subsequently analyzed to select best fits of the Cartesian coordinate values of Z in TABLE I based on the desired values of the heights  90 ,  92 ,  94 ,  96 ,  98 ,  100 . For example, each of the heights  90 ,  92 ,  94 ,  96 ,  98 ,  100  may correspond to the Cartesian coordinate value of Z equal to or nearest to the value of the particular height  90 ,  92 ,  94 ,  96 ,  98 , or  100 . If the height  90 ,  92 ,  94 ,  96 ,  98 , or  100  is midway between adjacent Cartesian coordinate values of Z in TABLE I, then the lesser or greater Cartesian coordinate value of Z may be selected for the particular height  90 ,  92 ,  94 ,  96 ,  98 , or  100 . Alternatively, in some embodiments, if specific heights are desired but do not match the specific Cartesian coordinate values of Z in TABLE I, then regression analysis and/or curve fitting may be used to analyze the data in TABLE I and interpolate new Cartesian coordinate values of X, Y, Z to enable use of the desired heights. In some embodiments, if the Z values do not match the desired heights, then the portion  80  may be defined by the Cartesian coordinate values of X, Y, and Z in TABLE I in the Z direction between the start and stop heights. Furthermore, with reference to TABLE I, the overall height dimension of each segment (e.g.,  102 ,  104 ,  106 ) may be equal to an absolute value of the difference between the start and stop heights (e.g., Cartesian coordinate values of Z) for the particular segment. In certain embodiments, an offset or correction value may be used to account for negative values in TABLE I. For example, certain components of the airfoil  82 , such as the bottom region  70 , may be disposed below the origin point  78  by a distance  108 , and thus certain Z values may be negative denoting sections of airfoil  82  below the origin point  78 . Accordingly, the offset may be equal to an absolute value of the smallest negative value given in TABLE I. 
     As mentioned earlier with respect to the portion  80  of  FIG. 4 , the sections  102 ,  104 , and  106  (e.g., portion  80 ) of  FIG. 5  may include one or more airfoil shapes, profiles, or sections, such as an airfoil shape shown in  FIG. 6 . More specifically,  FIG. 6  is a cross-sectional top view depicting an embodiment of an airfoil shape  110  taken through line  6 - 6  of  FIGS. 3, 4, and 5 , wherein the airfoil shape  110  may be included, for example, in the portion  80  of the airfoil  82  (e.g., rotor blade  44 , stator vane  50 ). As mentioned earlier, the airfoil  82  may be described in terms of one or more airfoil shapes (e.g., sections) “stacked” on top of each other along the Z axis  74 , such as the depicted airfoil shape  110 . To define the airfoil shape  110 , a unique set or loci of points in space are provided in TABLE I. 
     A Cartesian coordinate system of X, Y, and Z values given in TABLE I below defines a suction side profile  112  and a pressure side profile  114  of the airfoil shape  110  at various locations along the airfoil  82 . For example, point  116  defines a first pair of suction side X and Y values at the Z value of line  6 - 6  of  FIGS. 3-5 , while point  118  defines a second pair of pressure side X and Y values at the same Z value of  FIGS. 3-5 . The X, Y, and Z values of TABLE I are set forth in non-dimensionalized units, and thus a variety of units of dimensions may be used when the values are appropriately scaled by a scale factor F. The scale factor F may be substantially equal to 1, greater than 1, or less than 1. For example, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.) or a mixed number (e.g., 1½, 10¼, etc.). The dimensional distances may be any suitable format (e.g., inches, feet, millimeters, centimeters, etc.) These values exclude a coated region or coatings  120  of the airfoil  82 . In other words, these values correspond to the bare surface of the airfoil  82 . The coated region  120  may include one or more coating layers, surface treatments, or a combination thereof, over the bare surface of the airfoil  82 . The Cartesian coordinate system of  FIG. 6  utilizes the same orthogonally-related X axis  72 , Y axis  76 , and Z  74  as the Cartesian coordinate system of  FIGS. 3-5  to define locations on the airfoil shape  110  for both the suction side profile  112  and the pressure side profile  114  along the length L of the airfoil  82 . 
     The X axis  72  and the Y axis  76  lie parallel to the base  60 , as illustrated in the previous figures. In some embodiments, a positive X coordinate value is axial in the downstream axial direction  38  toward the aft, for example the exhaust outlet  28  of the multi-stage axial compressor  20 . In some embodiments, a positive Y coordinate value is directed normal to the X axis  72 . A positive Z coordinate value is directed radially from the X axis  72  and the Y axis  76  outward toward tip  68  of the airfoil  82 , which is towards the static casing  48  of the multi-stage axial compressor  20  for rotor blades  44 , and directed radially inward towards the shaft  30  of the multi-stage axial compressor  20  for stator vanes  50 . 
     By defining X and Y coordinate values at selected locations in a Z direction normal to the X-Y plane, the airfoil shape  110 , with its suction side profile  112  and pressure side profile  114 , may be defined, for example, by connecting each X and Y coordinate value to adjacent X and Y coordinate values with smooth continuing arcs. The suction side profile  112  is joined to the pressure side profile  114 , as shown in  FIG. 6 , to define the airfoil shape  110 . The airfoil shapes  110  (e.g., sections) of the airfoil  82  at various surface locations (e.g., heights) between the Z coordinate values may be determined by smoothly connecting the adjacent (e.g., “stacked”) airfoil shapes  110  to one another, thus forming the airfoil  82 . It may be appreciated that the airfoil shape  110  of the airfoil  82  may change from the base  60  to the tip  68 . For example, adjacent airfoil shapes  110  may taper or expand in one or more directions (e.g., X axis  72 , Y axis  76 ), adjacent airfoil shapes  110  may rotate about an axis (e.g., Z axis  74 ) in a clockwise direction or a counter-clockwise direction, or any combination thereof. It is also to be noted that TABLE I values represent the Cartesian coordinate values for the airfoil  82  at ambient, non-operating or non-hot conditions. Additionally, TABLE I values represent the Cartesian coordinate values for an uncoated airfoil (i.e., without coatings  120 ). For a coated airfoil, a thickness t of the coating  120  may be added to each of the X, Y values of TABLE I below. 
     The X, Y, and Z coordinate values of TABLE I below are non-dimensional values convertible to dimensional distances with the scale factor F. That is, the X, Y, and Z values of TABLE I may be scaled as a function of the same scale factor F (e.g., constant or number) to provide a scaled-up or a scaled-down airfoil. Thus, TABLE I defines the relationships between the X, Y, and Z coordinate values without specifying the units of measure (e.g., dimensional units) for an embodiment of the airfoil  82 . Accordingly, while different scale factors F may be applied to the X, Y, and Z coordinate values of TABLE I to define different embodiments of the airfoil  82 , each embodiment of the airfoil  82  regardless of the particular scale factor F is considered to be defined by the X, Y, and Z coordinate values of TABLE I. For example, the X, Y, and Z coordinate values of TABLE I define a first embodiment of the airfoil  82  formed with a 1:1 inch scale factor F, a second embodiment of the airfoil  82  formed with a 1:2 inch scale factor F, and a third embodiment of the airfoil  82  formed with a 1:1 cm scale factor F. It may be appreciated that any scale factor F may be used with the X, Y, and Z coordinate values of TABLE I, according to the design considerations of a particular embodiment. 
     The TABLE I values below are computer-generated and shown to five decimal places. However, certain values in TABLE I may be shown to less than five decimal places (e.g., 0, 1, 2, 3, or 4 decimal places), because the values are rounded to significant figures, the additional decimal places would merely show trailing zeroes, or a combination thereof. Accordingly, in certain embodiments, any values having less than five decimal places may be shown with trailing zeroes out to 1, 2, 3, 4, or 5 decimal places. Furthermore, in some embodiments and in view of manufacturing constraints, actual values useful for forming the airfoil  82  are may be considered valid to fewer (e.g., one, two, three, or four) decimal places for determining the airfoil shape  110  of the airfoil  82 . Further, there are typical manufacturing tolerances which may be accounted for in the airfoil shape  110 . Accordingly, the X, Y, and Z values given in TABLE I are for the airfoil shape  110  of a nominal airfoil. It will therefore be appreciated that plus or minus typical manufacturing tolerances are applicable to these X, Y, and Z values and that an airfoil  82  having a profile substantially in accordance with those values includes such tolerances. For example, in certain embodiments, a manufacturing tolerance of about ±between 0.001 to 0.20 inches (e.g., between 0.025 to 5 mm) is within design limits for the airfoil  82 , and a manufacturing tolerance of about ±0.0008 to 0.1 inches (e.g., 0.02 to 2.5 mm) may be maintained during manufacturing. Accordingly, the values of X and Y carried to three decimal places and having a manufacturing tolerance about ±0.010 inches (0.25 mm) and preferably about ±0.008 inches (0.20 mm) is acceptable to define the airfoil shape  110  of the airfoil  82  at each radial position (e.g., Z coordinate, height) throughout its entire length. As used herein, any reference to Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of N decimal places is intended to include: (1) values to N decimal places if shown in TABLE I with N or greater decimal places, and (2) values to less than N decimal places if shown in TABLE 1 with less than N decimal places, wherein N may be 0, 1, 2, 3, 4, or 5. For example, any reference to Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of three (3) decimal places is intended to include: (1) values to three (3) decimal places if shown in TABLE I with three (3) or greater decimal places, and (2) values to less than three (3) decimal places if shown in TABLE 1 with less than three (3) decimal places (e.g., 0, 1, or 2 decimal places). Furthermore, any reference to Cartesian coordinate values of X, Y, and Z as set forth in TABLE I all carried to N decimal places is intended to include: (1) values to N decimal places if shown in TABLE I with N or greater decimal places, and (2) values with trailing zeros to N decimal places if shown in TABLE 1 with less than N decimal places, wherein N may be 0, 1, 2, 3, 4, or 5. 
     As noted previously, the airfoil  82  may also be coated for protection against corrosion, erosion, wear, and oxidation after the airfoil  82  is manufactured, according to the values of TABLE I and within the tolerances explained above. For example, the coating region  120  may include one or more corrosion resistant layers, erosion resistant layers, wear resistant layers, oxidation resistant or anti-oxidation layers, or any combination thereof. An anti-corrosion coating may be provided with an average thickness t of 0.008 inches (0.20 mm), between 0.001 and 0.1 inches (between 0.25 and 2.5 mm), between, 0.0001 and 1 inches or more (between 0.0025 and 2.5 mm or more). For example, in certain embodiments, the coating  120  may increase X and Y values of a suction side in TABLE I by no greater than approximately 3.5 mm along a first suction portion, a first pressure portion, or both. It is to be noted that additional anti-oxidation coatings  120  may be provided, such as overcoats. 
     
       
         
           
               
               
             
               
                 TABLE I 
               
             
            
               
                   
               
               
                 Pressure Surface 
                 Suction Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 −1.78786 
                 1.14424 
                 0.00000 
                 1.84031 
                 −1.48822 
                 0.00000 
               
               
                 −1.78708 
                 1.14469 
                 0.00000 
                 1.83990 
                 −1.48957 
                 0.00000 
               
               
                 −1.78543 
                 1.14545 
                 0.00000 
                 1.83901 
                 −1.49174 
                 0.00000 
               
               
                 −1.78193 
                 1.14634 
                 0.00000 
                 1.83574 
                 −1.49632 
                 0.00000 
               
               
                 −1.77473 
                 1.14615 
                 0.00000 
                 1.82761 
                 −1.50082 
                 0.00000 
               
               
                 −1.76398 
                 1.14271 
                 0.00000 
                 1.81148 
                 −1.49855 
                 0.00000 
               
               
                 −1.74645 
                 1.13241 
                 0.00000 
                 1.79099 
                 −1.49319 
                 0.00000 
               
               
                 −1.72544 
                 1.11525 
                 0.00000 
                 1.76369 
                 −1.48600 
                 0.00000 
               
               
                 −1.69973 
                 1.08977 
                 0.00000 
                 1.72731 
                 −1.47629 
                 0.00000 
               
               
                 −1.66912 
                 1.05645 
                 0.00000 
                 1.68191 
                 −1.46390 
                 0.00000 
               
               
                 −1.62971 
                 1.01278 
                 0.00000 
                 1.62299 
                 −1.44742 
                 0.00000 
               
               
                 −1.58413 
                 0.96249 
                 0.00000 
                 1.55515 
                 −1.42787 
                 0.00000 
               
               
                 −1.53534 
                 0.90900 
                 0.00000 
                 1.48298 
                 −1.40639 
                 0.00000 
               
               
                 −1.47994 
                 0.84930 
                 0.00000 
                 1.40651 
                 −1.38287 
                 0.00000 
               
               
                 −1.41790 
                 0.78341 
                 0.00000 
                 1.32131 
                 −1.35575 
                 0.00000 
               
               
                 −1.34919 
                 0.71138 
                 0.00000 
                 1.22301 
                 −1.32321 
                 0.00000 
               
               
                 −1.27659 
                 0.63682 
                 0.00000 
                 1.12070 
                 −1.28787 
                 0.00000 
               
               
                 −1.19982 
                 0.56001 
                 0.00000 
                 1.01445 
                 −1.24956 
                 0.00000 
               
               
                 −1.11861 
                 0.48126 
                 0.00000 
                 0.90433 
                 −1.20814 
                 0.00000 
               
               
                 −1.03275 
                 0.40083 
                 0.00000 
                 0.79043 
                 −1.16343 
                 0.00000 
               
               
                 −0.94213 
                 0.31890 
                 0.00000 
                 0.67283 
                 −1.11528 
                 0.00000 
               
               
                 −0.84664 
                 0.23564 
                 0.00000 
                 0.55162 
                 −1.06359 
                 0.00000 
               
               
                 −0.74618 
                 0.15122 
                 0.00000 
                 0.42685 
                 −1.00827 
                 0.00000 
               
               
                 −0.64065 
                 0.06583 
                 0.00000 
                 0.29869 
                 −0.94904 
                 0.00000 
               
               
                 −0.53363 
                 −0.01767 
                 0.00000 
                 0.17170 
                 −0.88734 
                 0.00000 
               
               
                 −0.42533 
                 −0.09951 
                 0.00000 
                 0.04616 
                 −0.82274 
                 0.00000 
               
               
                 −0.31596 
                 −0.17992 
                 0.00000 
                 −0.07768 
                 −0.75494 
                 0.00000 
               
               
                 −0.20574 
                 −0.25916 
                 0.00000 
                 −0.19960 
                 −0.68376 
                 0.00000 
               
               
                 −0.09494 
                 −0.33758 
                 0.00000 
                 −0.31935 
                 −0.60897 
                 0.00000 
               
               
                 0.01620 
                 −0.41552 
                 0.00000 
                 −0.43675 
                 −0.53056 
                 0.00000 
               
               
                 0.12760 
                 −0.49309 
                 0.00000 
                 −0.55170 
                 −0.44858 
                 0.00000 
               
               
                 0.23939 
                 −0.57010 
                 0.00000 
                 −0.66408 
                 −0.36312 
                 0.00000 
               
               
                 0.35169 
                 −0.64635 
                 0.00000 
                 −0.77378 
                 −0.27424 
                 0.00000 
               
               
                 0.46469 
                 −0.72158 
                 0.00000 
                 −0.88064 
                 −0.18198 
                 0.00000 
               
               
                 0.57858 
                 −0.79543 
                 0.00000 
                 −0.98452 
                 −0.08637 
                 0.00000 
               
               
                 0.68972 
                 −0.86520 
                 0.00000 
                 −1.08191 
                 0.00924 
                 0.00000 
               
               
                 0.79798 
                 −0.93101 
                 0.00000 
                 −1.17289 
                 0.10455 
                 0.00000 
               
               
                 0.90321 
                 −0.99308 
                 0.00000 
                 −1.25761 
                 0.19925 
                 0.00000 
               
               
                 1.00526 
                 −1.05161 
                 0.00000 
                 −1.33628 
                 0.29297 
                 0.00000 
               
               
                 1.10407 
                 −1.10669 
                 0.00000 
                 −1.40912 
                 0.38537 
                 0.00000 
               
               
                 1.19956 
                 −1.15841 
                 0.00000 
                 −1.47628 
                 0.47618 
                 0.00000 
               
               
                 1.29164 
                 −1.20691 
                 0.00000 
                 −1.53787 
                 0.56518 
                 0.00000 
               
               
                 1.38022 
                 −1.25232 
                 0.00000 
                 −1.59398 
                 0.65219 
                 0.00000 
               
               
                 1.45711 
                 −1.29077 
                 0.00000 
                 −1.64235 
                 0.73294 
                 0.00000 
               
               
                 1.52621 
                 −1.32458 
                 0.00000 
                 −1.68365 
                 0.80690 
                 0.00000 
               
               
                 1.59149 
                 −1.35588 
                 0.00000 
                 −1.71861 
                 0.87359 
                 0.00000 
               
               
                 1.65289 
                 −1.38480 
                 0.00000 
                 −1.74976 
                 0.93693 
                 0.00000 
               
               
                 1.70628 
                 −1.40951 
                 0.00000 
                 −1.77456 
                 0.99286 
                 0.00000 
               
               
                 1.74745 
                 −1.42828 
                 0.00000 
                 −1.79061 
                 1.03708 
                 0.00000 
               
               
                 1.78045 
                 −1.44316 
                 0.00000 
                 −1.79973 
                 1.07358 
                 0.00000 
               
               
                 1.80524 
                 −1.45423 
                 0.00000 
                 −1.80273 
                 1.10163 
                 0.00000 
               
               
                 1.82385 
                 −1.46249 
                 0.00000 
                 −1.80092 
                 1.12268 
                 0.00000 
               
               
                 1.83690 
                 −1.47105 
                 0.00000 
                 −1.79706 
                 1.13377 
                 0.00000 
               
               
                 1.84054 
                 −1.47925 
                 0.00000 
                 −1.79287 
                 1.14000 
                 0.00000 
               
               
                 1.84090 
                 −1.48465 
                 0.00000 
                 −1.79015 
                 1.14260 
                 0.00000 
               
               
                 1.84061 
                 −1.48690 
                 0.00000 
                 −1.78865 
                 1.14372 
                 0.00000 
               
               
                 −1.78525 
                 1.13305 
                 0.08046 
                 1.83750 
                 −1.43029 
                 0.08046 
               
               
                 −1.78448 
                 1.13352 
                 0.08046 
                 1.83709 
                 −1.43162 
                 0.08046 
               
               
                 −1.78288 
                 1.13430 
                 0.08046 
                 1.83621 
                 −1.43377 
                 0.08046 
               
               
                 −1.77943 
                 1.13525 
                 0.08046 
                 1.83297 
                 −1.43828 
                 0.08046 
               
               
                 −1.77230 
                 1.13522 
                 0.08046 
                 1.82492 
                 −1.44270 
                 0.08046 
               
               
                 −1.76158 
                 1.13208 
                 0.08046 
                 1.80898 
                 −1.44048 
                 0.08046 
               
               
                 −1.74401 
                 1.12230 
                 0.08046 
                 1.78872 
                 −1.43524 
                 0.08046 
               
               
                 −1.72282 
                 1.10581 
                 0.08046 
                 1.76171 
                 −1.42820 
                 0.08046 
               
               
                 −1.69680 
                 1.08120 
                 0.08046 
                 1.72574 
                 −1.41869 
                 0.08046 
               
               
                 −1.66577 
                 1.04893 
                 0.08046 
                 1.68084 
                 −1.40657 
                 0.08046 
               
               
                 −1.62583 
                 1.00659 
                 0.08046 
                 1.62258 
                 −1.39042 
                 0.08046 
               
               
                 −1.57966 
                 0.95782 
                 0.08046 
                 1.55550 
                 −1.37127 
                 0.08046 
               
               
                 −1.53027 
                 0.90594 
                 0.08046 
                 1.48413 
                 −1.35022 
                 0.08046 
               
               
                 −1.47424 
                 0.84800 
                 0.08046 
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                 0.58680 
                 4.58510 
               
               
                   
               
            
           
         
       
     
     It is noted that the first column of TABLE I lists X coordinate values of the pressure side at each respective Z coordinate value of the third column, the second column lists Y coordinate values of the pressure side at each respective Z coordinate value of the third column, the fourth column lists X coordinate values of the suction side at each respective Z coordinate value of the sixth column, and the fifth column lists Y coordinate values of the suction side at each respective Z coordinate value of the sixth column. The Z coordinate values of the third column and the sixth column are equal to each other for each respective row. As set forth in TABLE I, at each respective Z coordinate value, the airfoil shape  110  of the airfoil  82  (e.g., a cross-sectional profile taken through line  6 - 6  of  FIGS. 3, 4, and 5 ) is defined by multiple sets of Cartesian coordinate values of X, Y, and Z for both the suction side  62  (e.g., suction side profile  112 ) and the pressure side  64  (e.g., pressure side profile  114 ). For example, at each respective Z coordinate value, the suction side profile  112  of the suction side  62  may be defined by at least equal to or greater than 10, 15, 20, 25, 30, 35, 40, 45, 50, or 55 (e.g.,  56 ) sets of Cartesian coordinate values of X, Y, and Z. Similarly, at each respective Z coordinate value, the pressure side profile  114  of the pressure side  64  may be defined by at least equal to or greater than 10, 15, 20, 25, 30, 35, 40, 45, 50, or 55 (e.g., 56) sets of Cartesian coordinate values of X, Y, and Z. Furthermore, in the Z direction along the Z axis  74 , the airfoil profile of the airfoil  82  may be defined by multiple sets of Cartesian coordinate values of X, Y, and Z at multiple Cartesian coordinate values of Z, such as at least equal to or greater than 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z. 
     As noted above, the Cartesian coordinate values of X, Y, and Z as set forth in TABLE I may be non-dimensional values convertible to dimensional distances. For example, the Cartesian coordinate values of X, Y, and Z may be multiplied by a scale factor F (e.g., F equal to 1, greater than 1, or less than 1) to obtain the desired dimensional distances. In certain embodiments, a nominal airfoil profile of the airfoil  82  may be partially or entirely (e.g., all or part of the suction side  62 , all or part of the pressure side  64 , or a combination thereof) defined by the Cartesian coordinate values of X, Y, and Z as set forth in TABLE I. The nominal airfoil profile of the airfoil  82  also may be covered by the coating  120 , which increases the X and Y values as set forth in TABLE I. 
     For example, the airfoil  82  may include a first suction portion (e.g.,  80 ) of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side  62  as set forth in TABLE I, wherein the X and Y values of the suction side  62  are coordinate values that couple together (e.g., in a smooth continuous and/or curved manner) to define suction side sections of the first suction portion (e.g.,  80 ) of the nominal airfoil profile at each Z coordinate value, and the suction side sections of the first suction portion (e.g.,  80 ) of the nominal airfoil profile are coupled together (e.g., in a smooth continuous and/or curved manner) to define the first suction portion (e.g.,  80 ). In such an embodiment, the airfoil  82  has an airfoil length L along the Z axis  74 , and the first suction portion (e.g.,  80 ) comprises a first portion length l along the Z axis as illustrated and described above with reference to  FIG. 4 . The first portion length l is less than or equal to the airfoil length L. The first portion length l may include greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z (e.g., consecutive values of Z) in TABLE I. The first portion length l may be equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 percent of the airfoil length L. 
     By further example, the airfoil  82  may include a second suction portion (e.g.,  80 ) of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the suction side  62  as set forth in TABLE I, wherein the X and Y values of the suction side  62  are coordinate values that couple together (e.g., in a smooth continuous and/or curved manner) to define suction side sections of the second suction portion (e.g.,  80 ) of the nominal airfoil profile at each Z coordinate value, the suction side sections of the second suction portion (e.g.,  80 ) of the nominal airfoil profile are coupled together (e.g., in a smooth continuous and/or curved manner) to define the second suction portion (e.g.,  80 ). In such an embodiment, the second suction portion (e.g.,  80 ) has a second portion length l along the Z axis, the second portion length l is less than or equal to the airfoil length L, and the first and second suction portions (e.g.,  80 ,  102 ,  104 ,  106 ) are offset from one another along the Z axis as illustrated and described above with reference to  FIGS. 4 and 5 . Again, the second portion length l may include greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z (e.g., consecutive values of Z) in TABLE I. The second portion length l may be equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 percent of the airfoil length L. Furthermore, the first and second suction portions (e.g.,  80 ,  102 ,  104 ,  106 ) may be separated by an offset distance of equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, or 90 percent of the airfoil length L. 
     By further example, the airfoil  82  may include a first pressure portion (e.g.,  80 ) of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the pressure side  64  as set forth in TABLE I, wherein the X and Y values of the pressure side  64  are coordinate values that couple together (e.g., in a smooth continuous and/or curved manner) to define pressure side sections of the first pressure portion (e.g.,  80 ) of the nominal airfoil profile at each Z coordinate value, the pressure side sections of the first pressure portion (e.g.,  80 ) of the nominal airfoil profile are coupled together (e.g., in a smooth continuous and/or curved manner) to define the first pressure portion (e.g.,  80 ). In such an embodiment, the first pressure portion (e.g.,  80 ) comprises a second portion length l along the Z axis, and the second portion length l is less than or equal to the airfoil length L as illustrated and described above with reference to  FIG. 4 . Similar to the first suction portion (e.g.,  80 ), the second portion length l of the first pressure portion (e.g.,  80 ) may include greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z (e.g., consecutive values of Z) in TABLE I. The second portion length l of the first pressure portion (e.g.,  80 ) may be equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 percent of the airfoil length L. In certain embodiments, the first suction portion (e.g.,  80 ) and the first pressure portion (e.g.,  80 ) at least partially overlap with one another along the Z axis. 
     For example, in certain embodiments, the first and second portion lengths l may be substantially the same, and the first and second portion lengths l may start at a common distance d relative to the base  60  of the airfoil  82  and extend toward the tip  68  of the airfoil  82 . However, in some embodiments, the first and second portion lengths l may be different from one another, the first and second portion lengths l may start at different distances d relative to the base  60  of the airfoil  82 , or a combination thereof. Additionally, the airfoil  82  may include a second pressure portion (e.g.,  80 ) of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the pressure side  64  as set forth in TABLE I, wherein the first and second pressure portions (e.g.,  80 ,  102 ,  104 ,  106 ) are offset from one another along the Z axis  74 . 
     Technical effects of the disclosed embodiments include an airfoil having a first suction portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in TABLE I, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the first suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the first suction portion of the nominal airfoil profile are coupled together to define the first suction portion, the airfoil includes an airfoil length along a Z axis, the first suction portion comprises a first portion length along the Z axis, the first portion length is less than or equal to the airfoil length, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances (e.g., instances in inches or mm). 
     This written description uses examples to disclose the subject matter, including the best mode, and also to enable any person skilled in the art to practice the subject matter, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter 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 have 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 language of the claims.