US20100303627A1

US20100303627A1 - Turbine stage

Info

Publication number: US20100303627A1
Application number: US12/792,352
Authority: US
Inventors: Benjamin Megerle; Thomas MOKULYS; Said Havakechian
Original assignee: Alstom Technology AG
Current assignee: General Electric Technology GmbH
Priority date: 2009-06-02
Filing date: 2010-06-02
Publication date: 2010-12-02
Also published as: CN101922311A; EP2261462A1; JP2010281320A

Abstract

A turbine stage includes a circumferentially distributed row of adjacent airfoils between which there is a flow passage. The passage has a surface, which in its unmodified form, defines a datum plane. A channel, located in the passage, extends in the direction of an airfoil pressure face from a point towards a leading edge line to a point towards a trailing edge line. The channel includes two channel walls angled relative to the datum plane. Relative to the datum plane, the channel has a low point, two high points, and a channel height, which is measured between the low point and the highest one of the high points. The channel provides a means to reduce secondary flow losses.

Description

RELATED APPLICATION

This application claims priority under 35 U.S.C. §119 to European Patent Application No. 09161706.8 filed in Europe on Jun. 2, 2009, the entire content of which is hereby incorporated by reference in its entirety.

FIELD

The present disclosure relates generally to axial gas and steam turbines in which there are one or more rows of generally radially extending airfoils of non rotating vanes and rotating blades. More particularly, the present disclosure relates to configurations of end walls joined to radial ends of airfoils with improved aerodynamic behaviour.
Within this specification, the term “pitchwise” is used to mean a circumferential direction between two adjacent airfoils, vanes or blades. Further, the term “end wall” is broadly defined to encompass any surface at a radial end of an airfoil, and any surface from which the airfoil radially extends. End walls thus include, but are not limited to, airfoil platforms and shrouds.

BACKGROUND INFORMATION

The ideal flow through a turbine is termed the “primary flow”. The difference between the primary flow and the actual flow is termed the “secondary flow”. The secondary flow represents, to a large extent, a loss that has an impact on axial turbine efficiency.
The development of secondary flow in a turbine cascade starts with the end wall boundary layer interacting with a leading edge of the airfoil. As the flow impinges on the leading edge of the airfoil, radial variation in the stagnation pressure creates flow along the stagnation line of the airfoil towards the end wall. When this flow reaches the end wall, the flow travels locally upstream along the end wall. A separation occurs where the incoming boundary layer meets this flow, and a so-called horseshoe vortex is formed around the leading edge of the airfoil. The strength of this vortex is dependent on the thickness of the leading edge and the variation of the radial static pressure gradient along the leading edge, which is, among other things, linked to the end wall boundary layer thickness and quality.
The pressure side leg of the vortex is influenced by the airfoil-to-airfoil pressure gradient as it enters the flow passage and travels towards the suction side. The resulting cross-passage flow along the end wall imposes vortex motion in the cascade. These vortices may commonly be referred to as passage vortices that include horseshoe vortices in their core. These vortices can be present in any flow channel with a curved shape and a boundary layer. The strength of this secondary flow in a cascade is dependent on a number of other factors, including the amount of turning and the shape of the incoming boundary layer.
The end wall vortex generation negatively affects turbine efficiency, contributing up to approximately 35% of the total losses for a typical high-pressure turbine. The key cause for the additional loss generation is the passage vortex that grows downstream of the cascade. The kinetic energy stored in this vortex is lost for further use as the kinetic energy is mostly mixed out downstream. The passage vortex can be easily detected as a high loss core existing away from the suction surface close to the center of the passage vortex.
Besides loss generation, secondary flow perturbs the exit flow distribution downstream of the cascade. Since the low momentum boundary layer fluid is deflected substantially more than the main flow close to the end wall, the low momentum boundary layer fluid sees the same blade to blade pressure gradient but has less impulse and thus causes overturning of the exit flow close to the end wall. Further away from the end wall, the rotation of the passage vortex comes into play and thus less turning occurs, which, due to the passage vortex driving the fluid in an opposite direction, results in so-called under turning.
The inhomogeneous flow field after the cascade is responsible for additional losses in the following cascade. This is partly due to the overturned flow close to the end wall leading to more secondary flow in the next blade row.
As the passage vortex lifts off the end wall and grows in size, the flow channel is increasingly influenced by secondary flow. It is known to be beneficial if the passage vortex is closer to the end wall as this increases the region of undisturbed primary flow. One method of inferring this is through the measurement of peak radial helicity.
Airfoil design has evolved to reduce secondary flow by optimizing the three-dimensional shape of airfoils and, more recently, by contouring of the end walls. This technology, which is referred to as Tangential End Wall Contouring (TEWC), involves adjusting end wall surfaces to reduce secondary flow, resulting, for example, in a modified airfoil face pressure profile.
US Patent Application Publication No. US 2007/0059177 A1 describes such an end wall non-axisymmetric profile. This solution includes forming circumferentially extending sinusoids at a number of axial positions, wherein corresponding points on successive sinusoids are joined by spline curves so that the curvature of the end wall is smooth.
Another alternative solution involves providing the end wall with a fence that lifts the vortex up off the end wall and into the main flow, which has the effect of washing out the vortices. The fence, of which an example is described in ASME Turbo Expo 2000 “Secondary flow measurements in a turbine passage with end wall flow modification”, 2000-GT-0212, has a leading edge at the center of a line connecting the leading edges of the pressure and suction side airfoils. While such walls can reduce aerodynamic losses, practical problems can arise due to the need to cool the fence.
An alternative method of reducing the affects of secondary flow involves using non-axisymmetric profiling to reduce cross flow instead of adjusting the pressure profile. EP 1 995 410 A1, for example, provides a solution in which an end wall of a turbine stage cascade includes a first projection having a ridge extending downward from the trailing edge of a turbine blade toward the downstream side, gently at the beginning and steeply at the end, and along the suction side of an adjacent turbine blade. Such an arrangement is, however, limited by the fact that downstream axial space is required, and therefore, such a solution may not always be applicable.

SUMMARY

An exemplary embodiment provides a turbine stage, which includes a circumferentially distributed row of adjacent airfoils. Each of the airfoils respectively has a pressure face, a suction face, and at least one end wall from which the airfoils radially extend, respectively. The exemplary turbine stage also includes a flow passage, which is defined by a region between a pressure face of a first one of the airfoils, a suction face of a second one of the airfoils adjacent to the first airfoil, a leading edge line extending between lead edges of adjacent airfoils, and a trailing edge line extending between trailing edges of adjacent airfoils. The flow passage has a defined datum plane extending between a base of the pressure face and a base of the suction face of adjacent airfoils. The exemplary turbine stage also includes a channel, in the flow passage, adjacent to the pressure face and extending in the direction of the pressure face from a point towards the leading edge line to a point towards the trailing edge line, the channel including two angled and joined channels walls that, relative to the datum plane, form a low point at the joined channel walls, two high points, and a channel height, the channel height defining the radial distance between the low point and highest one of the high points.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional refinements, advantages and features of the present disclosure are described in more detail below with reference to exemplary embodiments illustrated in the drawings, in which:

FIG. 1 is a top view of two adjacent airfoils of a turbine stage according to an exemplary embodiment of the present disclosure;

FIG. 2 is a perspective view of the adjacent airfoils of FIG. 1;

FIG. 3 is a perspective view of the two adjacent airfoils of a turbine stage with exemplary channels of the disclosure in end walls according to an exemplary embodiment of the disclosure;

FIG. 4 is a pitchwise sectional view of a turbine stage showing adjacent airfoils and an end wall of an exemplary embodiment of the present disclosure;

FIGS. 5 and 6 are expanded views of channel wall sections V and VI of FIG. 4, respectively;

FIG. 7 is a pitchwise profile of a channel of FIG. 3 or 4;

FIG. 8 is a height profile of a channel of FIG. 3 or 4;

FIG. 9 is a perspective view of an exemplary embodiment with an extended region;

FIG. 10 is a top view of FIG. 9 showing secondary flow lines; and

FIGS. 11-14 are exemplary performance graphs of exemplary embodiments.

Other aspects and advantages will become apparent from the following description, when taken in connection with the accompanying drawings, which, by way of illustration and example, illustrate exemplary embodiments of the present disclosure.

DETAILED DESCRIPTION

Exemplary embodiments of the present disclosure are directed towards correcting the problem, in a turbine, of over- and under-turning capability and/or reduced helicity losses as a result of secondary flows caused by cross flow that flows in the pitchwise direction from a pressure face of an airfoil towards the suction face of an adjacent airfoil across an end wall surface.
Exemplary embodiments of the present disclosure address this problem by providing a turbine stage as described herein.
According to an exemplary embodiment, the turbine stage includes one or more adjacent channels formed in end walls in flow passages between adjacent airfoils. Each channel extends in the primary flow direction and can be located adjacent to airfoil pressure faces, for example. The channels each have two angled walls, which, in conjunction with the configuration and location of the channels, are configured to reduce the potential for secondary flow formation in the channels.
An exemplary embodiment provides a turbine stage that includes a circumferentially distributed row of adjacent airfoils. Each of the airfoils includes a pressure face, a suction face, and at least one end wall, from which the airfoils radially extend, respectively. One or more of the airfoils can also include two end walls between which the airfoils extend. The turbine stage also includes a flow passage defined by a region between a pressure face of a first airfoil, a suction face of a second airfoil adjacent to the first airfoil, a leading edge line, which is defined as a line extending between the lead edges of adjacent airfoils, and a trailing edge line, which is defined as a line extending between the trailing edges of adjacent airfoils. The flow passage has a surface, which, in its unmodified form, defines a datum plane. The turbine stage, in each flow passage has at least one adjacent channel(s), adjacent a pressure face, that modify the surface and extend in the direction of primary flow lines from a point towards the leading edge line to a point towards the trailing edge line. Each channel includes two channels walls angled relative to the datum plane that provide the channels with a low point, two high points, and a channel height which is the radial distance between the low point and a highest one of the high points. The location of the channels adjacent the pressure face reduces the extent of influence of cross flow pitchwise across the flow passage and thereby reduce the influence of secondary flow. The closer the channel is to the pressure face, the more pronounced this effect is. In this way, any negative effect on aerodynamic performance is more than offset by the benefit of reduced secondary cross flow.
In accordance with an exemplary embodiment, the high points of each channel do not extend above the datum plane, thereby reducing the impact of the channels on primary flow and reducing scraping losses. In accordance with an exemplary embodiment, the low point of each channel is substantially in the midpoint, pitchwise, between high points of each channel. In accordance with another exemplary embodiment, the angle of the walls of each channel closer to the pressure face is less, relative to the datum plane, than channel walls closer to the suction face.
According to an exemplary embodiment, the channel height, in the primary flow direction, increases to a maximum at a relative channel length, in the direction of primary flow lines, of between approximately 0.35-0.55, for example, at which point the channel height decreases. In the last fifth of the length of the channel, this rate of decrease may be less. In this way, the channel depth provides a balance between scraping losses, which change with the velocity profile in the flow passage, and cross flow presence.
In accordance with an exemplary embodiment, the channel height of each successive adjacent channel, adjacent in the pitch wise direction extending from the pressure face to the suction face, remains the same or decreases. For example, the channel height of the channel adjacent the pressure face is at least twice that of the channel furthest, in the pitch wise direction, from the pressure face. In this way, channels are configured to reduce cross flow where its affect is strongest, e.g., adjacent the pressure face.
In accordance with an exemplary embodiment, in each flow passage, the point of extension of each adjacent channel is the same or further from the leading edge line the closer the channel is to the suction face thus defining an extended region, adjacent the suction face, which is free of channels. The extended region can be generally defined as a region, that in operation, is configured in a region that is essentially free of secondary flow vortices caused by cross flow originating from the pressure face.
Exemplary embodiments of the present disclosure are now described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the disclosure. It may be evident, however, that the disclosure may be practiced without these specific details.
FIGS. 1 and 2 respectively show top and perspective views of two adjacent airfoils 10 of a turbine stage, in which airfoils 10 are adjacently and circumferentially distributed in rows. Each airfoil 10 is integrally joined at one or both radial ends to corresponding end walls 12, which are partially shown as grid lines. The area between the pressure face 14 and suction face 16 of adjacent airfoils 10 defines a flow passage 18 that is further bound by a region extending between a leading edge line 20, which is defined as a line extending between the lead edges 21 of adjacent airfoils 10, and a trailing edge line 22, which is defined as a line extending between the trailing edge 23 of adjacent airfoils 10. The flow passage 18 has a surface common with a surface of the end walls 12. In its unmodified form, the surface defines a datum plane DR (see FIG. 4), wherein “unmodified form” means the contour that the passage surface would take if the surfaces were not changed, for example, by TEWCs, thus forming a plane extending between bases of the pressure face 14 and suction face 16 of adjacent airfoils 10. The grid lines in FIGS. 1 and 2 representing an unmodified surface include primary flow lines PFL that represent ideal lines of flow unaffected by secondary flow, and pitch wise sections A-D.
FIG. 3 shows an exemplary embodiment applied to the turbine stage shown in FIGS. 1 and 2. The exemplary embodiment illustrated in FIG. 3 includes channels 30 formed in the passage surfaces of end walls 12, at one or both radial ends of adjacent airfoils 10. The channels 30 extend in the direction of primary flow lines PFL (e.g., essentially in the direction of the pressure face 14) of an airfoil 10, resulting in the channels 30 being substantially parallel to each other. The extension of the channels 30 is from a point towards the leading edge line 20 to a point towards the trailing edge line 22. Each channel 30 includes two channel walls 32 that angle relative to the datum plane DR, which is shown in more detail in FIGS. 5 and 6, and join to define a low point LP of the channel 30 relative to the datum plane DR.
FIG. 4 shows an exemplary cross section through a pitch wise section A-D extending between the pressure face 14 of one airfoil 10 to the suction face 16 of another adjacent airfoil 10. As shown in the exemplary embodiment illustrated in FIG. 4, channels 30 are formed in end walls 12 between the adjacent airfoils 10. Each channel 30 has two channel walls 32, one closer to the pressure face 14 and the other closer to the suction face 16. The channel height CH is the radial height, that is, the height measured perpendicular to the datum plane DR, between the channel's low points LP and the highest one of the high points HP. As used herein, “low” and “high” are defined relative to the datum plane DR, wherein “low” refers to a negative extension from the datum plane DR into the end wall 12, while “high” refers to a positive extension in the direction away from the end wall 12. The indication is independent of absolute location. That is, even though the high point HP extends in a direction away from the end wall 12, the high point HP, as shown in FIG. 7, for example, may or may not extend above the height of the datum plane DR
The “channel wall angle” θ, as shown in the exemplary embodiments illustrated in FIGS. 5 and 6, is the angle of a nominal channel wall 33 relative to the datum plane DR. The nominal channel wall 33, without curvature, approximates the actual channel wall 32. For example, with reference to the exemplary embodiment illustrated in FIG. 5, an expanded view of V of FIG. 4 is shown, in which the channel wall angle θ of a bowed channel wall 32 is illustrated. The wall angle θ is taken to be the angle of the nominal channel wall 33, which is the average angle of the nominal channel wall 32. In another example shown in FIG. 6, which is an expanded view of VI of FIG. 4, a channel wall 32 is shown with a rounded-off end section that is otherwise straight. In this case, the nominal channel wall 33 corresponds to the channel wall 32 straight portion, disregarding the rounded end section.
One purpose of the channels 30 is to reduce cross flow and thereby reduce secondary flow and resulting losses. The desired channel height CH and desired number of channels 30 is dependent on the degree of cross flow, estimatable using known techniques, described, for example, in Harvey, N. W. et al, 2000 “Nonaxisymmetric Turbine End Wall Design: Part I”, ASME J. Turbomach., 122, pp. 278-285, and Hartland, J. C. et al, 2000 “Nonaxisymmetric Turbine End Wall Design: Part II”, ASME 122 J. Turbomach, 122, pp. 286-293. With increasing channel height CH and number of channels 30 (and hence an increased number of channel walls 32), passage surface area increases, which, in the absences of secondary flow, results in increased scraping losses. Where the effect of scraping losses may be higher than the beneficial effect of channels 30, it may be advantageous to minimise both channel height CH and/or the number of channels 30. An embodiment in its simplest form suitable for turbine stages with minimal cross flow therefore comprises one channel 30 located adjacent to the pressure surface 14, which is the region with the most significant cross flow.
The channel depth CH, shown in detail in FIG. 4, is a function of the number of channels 30 and the degree of cross flow. If the channel depth CH is too great, further secondary flow can be created resulting in additional losses. If the channel depth CH is too low, the ability of the channel 30 to limit cross flow will be limited. A further consideration is the channel wall angle θ. If the channel wall angle θ is too steep, additional secondary flow may be created. Channel design is therefore a compromise between at least these factors and so is dependent on airfoil design and operation conditions. In consideration of these factors, an optimum design can be derived by simulation using known methods.
In accordance with an exemplary embodiment of the present disclosure, the low point LP of each channel 30 is at the pitchwise midpoint between the high points HP of the channel, as shown in FIG. 4, for example.
In accordance with an exemplary embodiment of the present disclosure, the channel height CH of each successive adjacent channel 30 in the pitchwise direction from the pressure face 14 to the suction face 16 remains the same or decreases. In accordance with another exemplary embodiment, the channel height CH of the channel 30 adjacent the pressure face 14 is at least twice that of the channel 30 furthest from the pressure face 14, as can be seen in FIG. 4, for example. As cross flow is typically greatest towards the pressure face 14, the benefit of channels 30 may decrease towards the suction face 16.
In accordance with another exemplary embodiment of the present disclosure, the low point LP is closer to the suction face 16, represented as the pitchwise position “1” in FIG. 7 than the pressure face 14, which is represented as “0”. This arrangement can result in the channel wall angle θ of the channel wall 32 closer the suction face 16 being greater than the channel wall angle θ of the channel wall 32 closer the pressure face 14. In this way, a smooth transition into the channel 30 is provided for cross flow originating from the pressure face 14, which minimizes the formation of additional losses, while cross flow suppression can be promoted by the steeper channel wall angle θ of the channel wall 32 located closer to the suction face 16. The channel wall angle θ of the channel wall 32 located closer to the suction face 16 can be less than less than 90 degrees, since an angle approaching 90 degrees or greater may create additional vortices resulting in additional losses.
In accordance with an exemplary embodiment of the present disclosure, the channel walls 32 are configured such that the channels 30 do not extend above the datum plane DR, as shown in FIG. 7, for example, wherein “0” is the channel height CH at the datum plane DR. By this means, it was found that scraping losses of the primary flow can be further reduced while still maintaining good cross flow suppression performance.
Through a turbine cascade, the flow is accelerated significantly. Scraping losses, which have a squared relationship with velocity, are of greatest significance in the region of highest velocity. The highest velocity may correspond to a region where the separation distance measured in the pitchwise direction, between adjacent airfoils 10, is smallest. In such a region, overall efficiency may be optimized if the channel height CH is limited so as to be lower than would optimally be designed in view only of predicted cross flow. Therefore, in accordance with an exemplary embodiment of the present disclosure, in the direction of primary flow lines PFL extending from towards the leading edge line 20 to the trailing edge line 20, the channel height initially increases to a maximum at a relative channel length of between approximately 0.35-0.55, for example, after which it decreases. In accordance with another exemplary embodiment of the present disclosure, the decrease is not as pronounced in the last fifth of the relative channel length. The relative channel length is the length point along a channel 30 measured relative to the total length of the channel 30. FIG. 8 shows an example of a configuration of an exemplary embodiment in which it was found that for one set of operating conditions not only can scraping losses be reduced but also over- and under-turning performance can be improved without detrimentally affecting helicity.
FIG. 9 shows an exemplary embodiment in which the channels 30 towards the suction face 16 start further from the leading edge line 20 than the channels 30 closer to the pressure face 14. That is, their point of extension from the leading edge line 20 is further. This results in the formation of an extended region ER adjacent the suction face 16, towards the leading edge line 20, which is free of channels 30. The extended region ER may be bounded by a midpoint on the leading edge line 20, a point along the suction face 16, and/or a point on the suction face 16 at which the suction face 16 and leading edge line 20 join, as shown in both FIGS. 9 and 10. Such an arrangement is beneficial when the flow across the extended region ER is essentially free of secondary flow, as shown in FIG. 10, and as such the loss in this region primarily includes scraping losses. In accordance with another exemplary embodiment of the present disclosure, the extended region ER is the region adjacent the suction face 16 towards the leading edge line 20 that is essentially free of secondary flow, as shown by the flow lines FL in FIG. 10. As the size and shape of the extended region ER is dependent not only on turbine stage configuration but also the operating conditions of the turbine stage, the optimum location of the extended region ER is unique for each turbine configuration. Accordingly, the extended region ER is defined by a region derived and determined by known flow simulation methods.
FIGS. 11-14 show examples of the performance that can be achieved with a combination of various exemplary embodiments described herein. Improvements include over- and under-turning, shown in FIGS. 11 and 12 for both a stator and a rotor, and helicity, shown in FIGS. 13 and 14 also for a stator and rotor.
Although the disclosure has been herein shown and described in what is conceived to be practical exemplary embodiments, it will be appreciated by those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The presently disclosed embodiments are therefore considered in all respects to be illustrative and not restricted. The scope of the invention is indicated by the appended claims rather that the foregoing description and all changes that come within the meaning and range and equivalences thereof are intended to be embraced therein.

REFERENCE NUMBERS

- 10 Airfoil
- 12 End wall
- 14 Pressure face
- 16 Suction face
- 18 Flow passage
- 20 Leading edge line
- 21 Leading edge
- 22 Trailing edge line
- 23 Trailing edge
- 30 Channel
- 32 Channel wall
- 33 Nominal channel wall
- A-D Pitchwise sections
- CH Channel height
- DR Datum plane
- ER Extended region
- FL Flow lines
- PFL Primary flow lines
- LP Low point (of a channel)
- HP High point (of a channel)
- RD Radial direction
- θ Channel wall angle

Claims

1. A turbine stage comprising:

a circumferentially distributed row of adjacent airfoils, each of the airfoils respectively having

a pressure face,

a suction face, and

at least one end wall from which the airfoils radially extend, respectively; and

a flow passage defined by a region between

a pressure face of a first one of the airfoils,

a suction face of a second one of the airfoils adjacent to the first airfoil,

a leading edge line extending between lead edges of adjacent airfoils, and

a trailing edge line extending between trailing edges of adjacent airfoils,

wherein the flow passage has a defined datum plane extending between a base of the pressure face and a base of the suction face of adjacent airfoils, and

wherein the turbine stage further comprises a channel, in the flow passage, adjacent to the pressure face and extending in the direction of the pressure face from a point towards the leading edge line to a point towards the trailing edge line, the channel including two angled and joined channels walls that, relative to the datum plane, form a low point at the joined channel walls, two high points, and a channel height, the channel height defining the radial distance between the low point and highest one of the high points.

2. The turbine stage of claim 1, wherein each flow passage includes at least two adjacent channels.

3. The turbine stage of claim 1, wherein the high points of the channel do not extend above the datum plane.

4. The turbine stage of claim 1, wherein the low point of the channel in each flow passage is substantially in the midpoint, in the pitchwise direction, between the high points of each channel.

5. The turbine stage of claim 1, wherein in each flow passage, an angle of the channel wall closer to the pressure face is less, relative to the datum plane, than an angle of the channel wall closer to the suction face.

6. The turbine stage of claim 1, wherein in each flow passage, the channel height in the primary flow direction increases to a maximum, at a relative channel length measured in the direction from the leading edge line to the trailing edge line, of between approximately 0.35-0.55, at which point the channel height decreases.

7. The turbine stage of claim 2, wherein in the pitchwise direction from the pressure face to the suction face, the channel height of each successive adjacent channel one of remains the same and decreases.

8. The turbine stage of claim 7, wherein, in each flow passage, the channel height of the channel adjacent the pressure face is at least twice that of the channel furthest, in the pitchwise direction, from the pressure face.

9. The turbine stage of claim 2, wherein, in each flow passage, in the pitchwise direction from the pressure face to the suction face, each successive adjacent channel extends from a point that is one of the same and further from the leading edge line to form an extended region, adjacent the suction face, free of channels.

10. The turbine stage of claim 9, wherein the extended region is a region that, in operation, encompasses a region essentially free of secondary flow vortices caused by cross flow originating from the pressure face.

11. The turbine stage of claim 2, wherein the high points of the channel do not extend above the datum plane.

12. The turbine stage of claim 11, wherein in the pitchwise direction from the pressure face to the suction face, the channel height of each successive adjacent channel one of remains the same and decreases.

13. The turbine stage of claim 12, wherein, in each flow passage, the channel height of the channel adjacent the pressure face is at least twice that of the channel furthest, in the pitchwise direction, from the pressure face.

14. The turbine stage of claim 11, wherein, in each flow passage, in the pitchwise direction from the pressure face to the suction face, each successive adjacent channel extends from a point that is one of the same and further from the leading edge line to form an extended region, adjacent the suction face, free of channels.

15. The turbine stage of claim 14, wherein the extended region is a region that, in operation, encompasses a region essentially free of secondary flow vortices caused by cross flow originating from the pressure face.

16. The turbine stage of claim 2, wherein the low point of the channel in each flow passage is substantially in the midpoint, in the pitchwise direction, between the high points of each channel.

17. The turbine stage of claim 2, wherein in each flow passage, an angle of the channel wall closer to the pressure face is less, relative to the datum plane, than an angle of the channel wall closer to the suction face.

18. The turbine stage of claim 2, wherein in each flow passage, the channel height in the primary flow direction increases to a maximum, at a relative channel length measured in the direction from the leading edge line to the trailing edge line, of between approximately 0.35-0.55, at which point the channel height decreases.

19. The turbine stage of claim 3, wherein the low point of the channel in each flow passage is substantially in the midpoint, in the pitchwise direction, between the high points of each channel.

20. The turbine stage of claim 3, wherein in each flow passage, an angle of the channel wall closer to the pressure face is less, relative to the datum plane, than an angle of the channel wall closer to the suction face.

21. The turbine stage of claim 3, wherein in each flow passage, the channel height in the primary flow direction increases to a maximum, at a relative channel length measured in the direction from the leading edge line to the trailing edge line, of between approximately 0.35-0.55, at which point the channel height decreases.

22. The turbine stage of claim 4, wherein in each flow passage, an angle of the channel wall closer to the pressure face is less, relative to the datum plane, than an angle of the channel wall closer to the suction face.

23. The turbine stage of claim 4, wherein in each flow passage, the channel height in the primary flow direction increases to a maximum, at a relative channel length measured in the direction from the leading edge line to the trailing edge line, of between approximately 0.35-0.55, at which point the channel height decreases.

24. The turbine stage of claim 1, wherein each airfoil respectively has two end walls between which the airfoils respectively extend.