Transonic airfoil and axial flow rotary machine

Sectional profiles close to a tip 124 and a part between a midportion 125 and a hub 123 are shifted to the upstream of an operating fluid flow in a sweep direction. Accordingly, an S shape is formed in which the tip 124 and the part between the midportion 125 and the hub 123 protrude. As a result, it is possible reduce various losses due to shook, waves, thereby forming a transonic airfoil having an excellent aerodynamic characteristic.

This application is a 371 of international application No. PCT/JP2007/067645 filed on Sep. 11, 2007, and claims priority of Japanese application No. 2006-298841, filed on Nov. 2, 2006.

TECHNICAL FIELD

The present invention relates to a transonic airfoil operating in a transonic or supersonic flow region and an axial flow rotary machine such as a turbine having the transonic airfoil, and more particularly, to a transonic airfoil having a three-dimensional shape and an axial flow rotary machine having the transonic airfoil.

BACKGROUND ART

In axial flow rotary machines such as a gas turbine, an aircraft fan engine, and an aircraft jet engine, losses generated in an airfoil cascade can be roughly classified into profile loss due to airfoil shape itself and secondary loss due to fluid flowing between the airfoil cascades. A rotor airfoil suppressing a secondary flow in a solid wall boundary layer generating in an airfoil surface by arranging a higher position of a leading edge is upstream in the axial direction from a lower position is suggested as an airfoil to reduce the secondary loss (see Patent Document 1). The axial direction in this specification represents an axial direction of a rotor around which airfoils are arranged and the radial direction represents a radial direction of the rotor. Profile loss is reduced by constructing a three-dimensional airfoil.

A transonic airfoil operating by a transonic or supersonic operating fluid may be used as the rotor airfoil. In an axial flow rotary machine having the transonic airfoils and operating by the transonic or supersonic operating fluid, a shook wave is generated due to the compressibility of the operating fluid and various losses such as profile loss and secondary loss are caused. That is, a loss due to the shock wave itself, a loss due to interference of the shock wave with the solid wall boundary layer, and a loss due to interference of the shock wave with a tip clearance leakage (a leakage from a clearance between an airfoil tip and a casing due to a pressure difference between a suction surface and a pressure surface) of the airfoil are generated.

Regarding the influence of the losses due to the shock wave, since a strong shock wave is generated in a tip101of an airfoil100(airfoil tip) as shown in a static pressure contour in air foil-suction surface ofFIG. 15, the efficiency of the tip is lowered as shown in the efficiency distribution in a radial direction of the air foil shown inFIG. 16. As shown inFIG. 17, an incidence angle (an angle difference between an inflow angle and an airfoil leading edge) of a flow decelerated by a detached shock wave110as a kind of shock wave with respect to the leading edge102of the airfoil100increases. When the angle of incidence increases, pressure loss also increases, thereby lowering the efficiency in the axialflow rotary machine.

Regarding various losses due to the shock wave, to suppress the loss due to the interference of the shock wave with the solid wall boundary layer in the rotor airfoil described in Patent Document 1, the interference position of the shock wave in the radial direction of the airfoil with the solid wall boundary layer is designed so that the higher position in the radial direction is upstream in the axial direction. That is, the leading edge in a rotor airfoil section leans forward upstream as a whole so that the higher position in the radial direction is upstream in the axial direction. Accordingly, a secondary flow of the solid wall boundary layer is suppressed and enlargement of the boundary layer before the interference of the shock wave is avoided in order to prevent separation, thereby reducing the loss.

DISCLOSURE OF THE INVENTION

Problem to be Solved by the Invention

As described above, in the rotor airfoil described in Patent Document 1, the interference of the secondary flow resulting from the tip leakage with the shock wave is alleviated and the loss of the tip is reduced, by forming the upstream of the rotor airfoil leaning forward. Accordingly, the flow is sent to the tip to enhance the efficiency of the tip, while the boundary layer of the hub (base) is thickened and thus the flow is unstable, thereby reducing the efficiency of the hub.

Means for Solving the Problem

In view of the above-mentioned problems, an object of the invention is to provide a transonic airfoil and an axial flow rotary machine that can suppress the reduction in efficiency due to the shook wave on the tip and avoid enlargement of a boundary layer of a hub, thereby preventing separation.

To accomplish the above-mentioned object, according to an aspect of the present invention, there is provided a transonic airfoil operating in a flow region of a transonic of faster operating fluid, the transonic airfoil including: a hub located dose to a connection position to a rotation shaft; a midportion located at a medium position in a radial direction which is a radial direction of the rotation shaft; a tip located farthest from the rotation shaft in the radial direction; a leading edge located on the upstream of the inflowing operating fluid; and a trailing edge located on the downstream of the operating fluid, wherein sectional profiles stacked in the radial direction of the airfoil are continuously shifted in parallel to a first direction connecting the leading edge and the trailing edge and the sectional profiles close to the tip and the sectional profiles between the midportion and the hub are shifted to the upstream of the first direction to form an S shape, and wherein the shift amount of the sectional profiles close to the tip in the first direction is greater than the shift amount of the sectional profiles between the midportion and the hub in the first direction.

That is, an S shape obtained by combining a forward swept shape in which the tip in the first direction leans to the upstream and a backward swept shape in which the part between the midportion and the hub in the first direction protrudes to the upstream, that is, a shape in which the tip protrudes to the most upstream, is obtained.

At this time, the sectional profiles stacked in the radial direction of the airfoil may be continuously shifted in a second direction perpendicular to the first direction. That is, a forward leant shape in which the tip leans to the upstream may be further combined therewith in the second direction or a backward leant shape in which the part between the midportion and the hub protrudes to the upstream may be combined therewith in the second direction.

An intersection angle of the first direction and an axial direction of the rotation shaft in the sectional profiles stacked in the radial direction of the airfoil may be continuously changed to form a three-dimensional airfoil shape.

According to another aspect of the present invention, there is provided an axial flow rotary machine including: a rotation shaft located at the center and rotating; a plurality of rotor airfoils disposed on the outer peripheral surface of the rotation shaft at equivalent intervals in a circumferential direction and an axial direction of the rotation shaft; a casing covering the rotation shaft and the rotor airfoils; and a plurality of state airfoils disposed on an inner circumferential surface of the casing to alternate with the rotor airfoils in the axial direction of the rotation shaft, wherein the plurality of rotor airfoils partially includes the transonic airfoil according to the above-mentioned aspect.

According to the above-mentioned aspect of the invention, by forming the S shape in which the tip and the part between the hub and the midportion are shifted to the upstream, the boundary layer of the hub can be decreased in thickness to enhance the separation resistance of the hub and the boundary layer of the tip can be increased in thickness to reduce the tip leakage loss. Since the tip protrudes to the upstream, it is possible to weaken the shock wave, thereby suppressing various losses due thereto. Because of the decrease in loss, it is possible to efficiently transmit rotary energy of the airfoil to the fluid. By reducing the separation of the airfoil, it is possible to enhance the stall margin.

DESCRIPTION OF REFERENCE NUMERALS AND SIGNS

BEST MODE FOR CARRYING OUT THE INVENTION

Axial Flow Rotary Machine

An axial flow rotary machine employing a transonic airfoil as a rotor airfoil will be described now. In the following description, a compressor of a gas turbine is exemplified as the axial flow rotary machine.FIG. 1is a diagram schematically illustrating a configuration of a gas turbine.

As shown inFIG. 1, a gas turbine includes a compressor1compressing air, a combustor2being supplied with the sir compressed by the compressor1and fuel and perforating a combustion operation, and a turbine3rotating by the combustion gas from the combustor2, The compressor1, the combustor2, and the turbine3are covered with a casing4and plural combustors2are arranged at equivalent intervals on the outer circumference of a rotor5connecting the compressor1and the turbine3with one shaft.

In the gas turbine, the air compressed by the compressor1is supplied to the combustor2or the rotor5through the casing4. The compressed air supplied to the combustor2is used to combust the fuel supplied to the combustor2. The compressed air supplied into the casing4close to the turbine3and the rotor5is used to cool stator airfoils31fixed to the casing4and rotor airfoils32fixed to the rotor5, which are exposed to a high temperature resulting from the combustion gas from the combustor2. The stator airfoils31and the rotor airfoils32are alternately arranged in the axial direction of the rotor5.

The combustion gas generated in the combustion operation of the combustor2is supplied to the turbine3and the combustion gas is sprayed to the rotor airfoils32and is rectified by the stator airfoils31, whereby the turbine3is rotationally driven. The rotational driving of the turbine3is transmitted to the compressor1through the rotor5, whereby the compressor1is also rotationally driven. Accordingly, the rotor airfoils12fixed to the rotor5in the compressor1rotates and thus the air flowing in the space formed by the stator airfoils11fixed to the casing4and the rotor airfoils12is compressed. The stator airfoils11and the rotor airfoils12are alternately arranged in the axial direction of the rotor5.

In the gas turbine shown inFIG. 1, the compressor1is a transonic or supersonic compressor operating by an operating fluid (air) of which the inflowing speed is a transonic speed, that is, a speed equal to or higher than the speed at which a supersonic region with a MACH number greater than 1 is generated in the operating fluid (air) flowing in the rotor airfoils. In the compressor1which is the transonic or supersonic compressor, transonic airfoils are used as the rotor airfoils12.

The transonic airfoil according to the present invention will fee described now. In the following description, the side into which the operating fluid (air) flows in the axial direction of the rotor5in the gas turbine shown inFIG. 1is called an “upstream” and the side from which the operating fluid (air) flows is called a “downstream”. In the gas turbine shown inFIG. 1, the radial direction of the rotor5, that is, the radial direction of the transonic airfoil is called a “span direction.” A plane parallel to the flow of the operating fluid in the axial direction of the rotor5is called a “meridional plane” and the sectional shape of the transonic airfoil perpendicular to the radial direction of the rotor5is called a “sectional profile.”

In the transonic airfoil, an operation of stacking the sectional profiles in the span direction is called “stacking.” In the sectional profile of the transonic airfoil12shown inFIG. 2, an edge on the side into which the operating fluid (air) flows is called a “leading edge” (indicated by reference numeral121inFIG. 2), an edge cm the side from which the operating fluid (air) flows is called a “trailing edge” (indicated by reference numeral122inFIG. 2), and an oblique direction of a straight line connecting the leading edge and the trailing edge about the shaft of the rotor5is called a “stagger direction” (indicated by arrow S inFIG. 2). The surface facing the upstream in the axial direction of the rotor5is called a “suction surface” (indicated by reference numeral126inFIG. 2) and the surface facing the downstream in the axial direction of the rotor5is called a “pressure surface” (indicated by reference numeral127inFIG. 2).

In the section in the span direction of the transonic airfoil12shown inFIG. 3, the position (corresponding to 80% to 100% in the radial direction of the transonic airfoil12) connected to the rotor5is called a “hub” (indicated by reference numeral123ofFIG. 3), the edge position (corresponding to 0% to 20% in the radial direction of the transonic airfoil12) close to the casing4is called a “tip” (indicated by reference numeral124ofFIG. 3), and the center position (corresponding to the vicinity of 50% in the radial direction of the transonic airfoil12) in the airfoil height is sailed a “midportion” (indicated by reference numeral125ofFIG. 3). The positions in the radial direction of the transonic airfoil12are expressed by percentage, but the percentage expression indicates the positions in the radial direction of the rotor5(corresponding to the radial direction of the transonic airfoil12) as positions relative to the height of the transonic airfoil12. The edge most apart from the outer circumferential surface of the rotor5is expressed at 0% and the position connected to the outer circumferential surface of the rotor5is expressed at 100%.

In the sectional profile of the transonic airfoil12, as shown inFIG. 4A, a shift direction (indicated by arrow P) is called a “sweep direction” when the sectional profile is shifted parallel to the stagger direction (indicated by arrow S) and as shown inFIG. 4B, a shift direction (indicated by arrow Q) is called a “lean direction” when the sectional profile is shifted perpendicular to the stagger direction.

Basic Configuration of Transonic Airfoil

A baste configuration of the transonic airfoil according to the present invention will be described with reference to the accompanying drawings. In the basic configuration, the center positions of the sectional profiles of the transonic airfoil in the span direction are continuously changed in the sweep direction. Configurations of three kinds of transonic airfoils12ato12cin which the center positions of the sectional profiles arc continuously changed in the sweep direction from the hub123to the tip124in the span direction are shown inFIGS. 5A to 5C.

A transonic airfoil12ashown inFIG. 5Ahas a configuration in which the centers of gravity G of the sectional profiles from the hub123to the tip124are parallel to the span direction. That is, the center of gravity G of the each sectional profile is constant in the radial direction of file rotor5, and the configuration shown inFIG. 5Ais used as a reference. This shape of the transonic airfoil12ais called a “reference shape” in the following description.

A transonic airfoil12bshown, inFIG. 5Bhas a configuration, in which the center of gravity G of the each sectional profile from the hub123to the tip124is continuously shifted from the downstream to the upstream in the sweep direction. That is, compared with the transonic airfoil12ashown inFIG. 5A, the upstream (the leading edge121) leans forward relative to the radial direction of the rotor5. This shape of the transonic airfoil12bis called a “forward swept shape” in the following description.

A transonic airfoil12cshown inFIG. 5Chas a configuration in which the center of gravity G of the each sectional profile from the tip124to the hub123is continuously shifted from the downstream to the upstream in the sweep direction. That is, compared with the transonic airfoil12ashown inFIG. 5A, the downstream (the trailing edge122) leans backward relative to the radial direction of the rotor5and the hub123protrudes to the upstream (the leading edge121). This shape of the transonic airfoil12cis called a “backward swept shape” in the following description.

Axial velocity (the speed of the operating fluid flowing into the leading edge121) distributions in the span direction of the transonic airfoils12ato12cshown inFIGS. 5A to 5Care represented by the curves X1to Z1inFIG. 6. In the axial velocity distributions in the span direction, when the transonic airfoil12ahaving the reference shape shown inFIG. 5Ais compared with the transonic airfoil12bhaving the forward swept shape shown inFIG. 5B, the axial velocity of the tip124is higher but the axial velocity of the hub123is lower in the curve Y1of the transonic airfoil12bman in the curve X1of the transonic airfoil12a. On the other hand, when the transonic airfoil12ahaving the reference shape shown inFIG. 5Ais compared with the transonic airfoil12chaving the backward swept shape shown inFIG. 5C, the axial velocity of the tip124is lower but the axial velocity of the hub123is higher in the curve Z1of the transonic airfoil12cthan in the curve X1of the transonic airfoil12a.

As can be seen from the curves X1to Z1shown inFIG. 6, the flow of the operating fluid (air) is gathered in the tip124in the forward swept shape in which the tip124is leaned forward as shown in the transonic airfoil12bofFIG. 5B. On the other hand, the flow of the operating fluid (air) is gathered in the hub123in the backward swept shape, in which the tip124is leaned backward as shown in the transonic airfoil12cofFIG. 5C.

Efficiency (energy efficiency with which the rotary power of the transonic airfoil is transmitted to the operating fluid) distributions in the span direction of the transonic airfoils12ato12cshown inFIGS. 5A to 5Care represented by the curves X2to Z2ofFIG. 7. In the efficiency distributions in the span direction, when the transonic airfoil12ahaving the reference shape shown inFIG. 5Ais compared with the transonic airfoil12bhaving the forward swept shape shown inFIG. 5B, the efficiency of the tip124is higher but the efficiency of the hub123is lower in the curve Y2of the transonic airfoil12bthan in the curve X2of the transonic airfoil12a. On the other hand, when the transonic airfoil12ahaving the reference shape shown inFIG. 5Ais compared with the transonic airfoil12chaving the forward swept shape shown inFIG. 5C, the efficiency of the tip124is lower but the efficiency of portions other than fee vicinity of the tip124is the same or higher in the curve72of the transonic airfoil12cthan in the curve X2of the transonic airfoil12a.

As can be seen from the curves X2to Z2shown inFIG. 7, in the forward swept shape in which the tip124is leaned forward as shown in the transonic airfoil12bof FIG.5B, the static pressure difference between the suction surface126and the pressure surface127in the leading edge121of the tip124, which occupies 70% or more of the airfoil height in the span direction, is reduced. On the other hand, in the backward swept shape in which the tip124is leaned backward as shown in the transonic airfoil12cofFIG. 5C, the static pressure difference between the suction surface126and the pressure surface127in the leading edge121of the hub123, which occupies 70% or less of the airfoil height in the span direction, is reduced.

In the forward swept shape shown inFIG. 5B, oblique shock waves80aand80bcolliding with the leading edge121of the tip124are generated to the suction surface126and the pressure surface127, like the sectional profiles close to the tip124of the plural transonic airfoils12barranged in the circumferential direction of the rotor5shown inFIG. 8. The flow of the operating fluid (air) is decelerated by the oblique shock wave80bgenerated on the pressure surface127of the tip124and thus a passage shock wave81generated between the adjacent transonic airfoils12bis weakened.

In view of this fact, by employing the forward swept shape shown inFIG. 5B, the flow of the operating fluid (air) can be sent to the tip124to improve the matching of the leading edge121and to weaken the shock wave. Accordingly, it is possible to reduce the loss due to the shook wave itself, the loss due to the interference of the shock wave with the solid wall boundary layer, and the loss due to the interference of the shock wave with the tip clearance leakage in the tip124.

On the other hand, by employing the backward swept shape shown inFIG. 5C, the operating fluid (air) is sent to the hub123to improve the matching of the leading edge121other than the tip124. Here, “to improve the matching” means that the inflow angle of the operating fluid into the airfoil becomes a proper value relative to an airfoil metal angle and thus the loss due to the airfoil becomes the minimum or close to the minimum. Accordingly, the solid wall boundary layer of the hub123can be reduced in thickness to enhance separation resistance. Therefore, it is possible to reduce loss due to the interference of the shock wave with the solid wall boundary layer on the hub123.

In this way, by adjusting the sectional profiles, which are stacked in the span direction, in the sweep direction, it is possible to control a three-dimensional pressure field of the downstream of the shock wave and to change the axial velocity profile of the leading edge121. Accordingly, the angle of incidence can be adjusted to reduce the profile loss and the flow can be sent to the trailing edge122to suppress the development of the boundary layer. Therefore, it is possible to reduce the separation of the hub of the stator airfoil11, which faces the rotor airfoil12as the transonic airfoil, close to the casing4and to enhance the stall margin. As described above, it is possible to suppress various losses due to the shock wave at the positions in the span direction of the rotor airfoil12employing the transonic airfoil, and to enhance the efficiency.

Examples of the transonic airfoils obtained by stacking the sectional profiles, which are adjusted in the sweep direction, in the span direction will be described now.

FIRST EMBODIMENT

A transonic airfoil according to a first embodiment in which the sectional profiles in the span direction are adjusted in the sweep direction will be described with reference to the drawings on the basis of the above-mentioned basic configuration.FIG. 9is a perspective view schematically illustrating a configuration of a transonic airfoil according to the present embodiment.FIG. 10is a diagram illustrating the shift in the sweep direction of the sectional profiles in the span direction from the hub to the tip.

As shown inFIG. 9, a transonic airfoil12xaccording to the present embodiment has a shape obtained by combining the forward swept shape of the transonic airfoil12bshown inFIG. 5Bwith the backward swept shape of the transonic airfoil12cshown inFIG. 5C. That is, the transonic airfoil12xshown inFIG. 9has a shape in which the sectional profiles close to the tip124are shifted to protrude to the upstream in the sweep direction, similarly to the forward swept shape of the transonic airfoil12bshown inFIG. 5B. Similarly to the backward swept shape of the transonic airfoil12cshown inFIG. 5C, the sectional profiles of the part between the hub123and the midportion125are also shifted to protrude to the upstream in the sweep direction.

In this way, by employing the configuration in which the sectional profiles are adjusted in position in the sweep direction, the transonic airfoil12xshown inFIG. 9has an S shape in the span direction. The adjusted the position in the sweep direction which is continuously shifted in the span direction is shown inFIG. 10. As shown inFIG. 10, in the transonic airfoil12xshown inFIG. 9, the protruding portion90protruding to the upstream in the sweep direction in the tip124(position corresponding to 100% in the span direction) more protrudes to the upstream in the sweep direction than the protruding portion91protruding to the upstream in the sweep direction in the part (position corresponding to 20% to 50% in the span direction) between the hub123and the midportion125, whereby the S shape is formed.

In this way, by forming the S shape obtained by combining the forward swept shape with the backward swept shape, it is possible to reduce fee thickness of the boundary layer of the hub123, to enhance the separation resistance of the hub123, and to reduce pressure loss by optimizing the shock wave structure of the tip124.

In addition, since the transonic airfoil12xhas a three-dimensional airfoil shape capable of reducing the profile loss, the stagger direction of the sectional profiles is changed in the span direction. The top views of the change of the stagger direction of the sectional profiles as viewed from the tip of the transonic airfoil are shown in FIGS.11A and11B.FIG. 11Bis a top view of the transonic airfoil12xaccording to this embodiment andFIG. 11Ashows the transonic airfoil12ahaving the reference shape with no displacement in the sweep direction for the purpose of the easy understanding, which is compared with the transonic airfoil12x. For the purpose of the easy understanding, the sectional profiles of the hub123, the midportion125, and the tip124of the transonic airfoils12aand12xare shown inFIGS. 12A and 12B, respectively.

As shown inFIGS. 11A,11B,12A, and12B, in both the transonic airfoils12aand12x, the stagger direction is determined so that the tip124becomes almost perpendicular to the axial direction of the rotor5and the stagger direction is determined so that the hub123becomes almost parallel to the axial direction of the rotor5. The stagger direction of the sectional profiles is determined so that the stagger direction is continuously changed from the hub123to the tip124. That is, in both the transonic airfoils12aand12x, the angle of the stagger direction of the midportion125about the axial direction of the rotor5is a middle value of the angles of the stagger directions of the tip124and the hub123about the axial direction of the rotor5.

Second Embodiment

A transonic airfoil according to a second embodiment in which the sectional profiles in the span direction are adjusted in the sweep direction will be described with reference to the drawings on the basis of the above-mentioned basic configuration. In the present embodiment, similarly to the transonic airfoil according to the first embodiment, in addition to the configuration in which the sectional profiles in the span direction are adjusted in the sweep direction, the positions of the sectional profiles are changed in the lean direction and the sectional profiles are stacked.

That is, in the transonic airfoil12yaccording to the present embodiment, similarly to the transonic airfoil12xaccording to the first embodiment, the sectional profiles in the span direction from the hub to the tip are shifted in the sweep direction so that the tip124has the forward swept shape and the hub123has the backward swept shape. In addition, the sectional profiles in the span direction from the hub to the tip are also shifted in the lean direction.

The transonic airfoil of which the positions of the sectional profiles are changed in the lean direction will be described in brief with reference toFIGS. 13A to 13C.FIGS. 13A to 13Cshow configurations of three kinds of transonic airfoils12a,12d, and12ein which the sectional profiles from the hub123to the tip124in the span direction are continuously changed in the lean direction. The transonic airfoil12ashown inFIG. 13Ais a transonic airfoil having the “reference shape” shown inFIG. 5A.

The transonic airfoil12dshown inFIG. 13Bhas a configuration in which the center of gravity G of the each sectional profile from the hub123to the tip124is continuously shifted from the downstream (the pressure surface127) to the upstream (the suction surface126) in the lean direction. That is, compared with the transonic airfoil12ashown inFIG. 13A, the upstream (the leading edge121) in the radial direction of the rotor5is leaned forward. The shape of the transonic airfoil12dis called a “forward leant shape” in the following description.

The transonic airfoil12eshown inFIG. 13Chas a configuration in which the center of gravity G of the each sectional profile from the tip124to the hub123are continuously shifted from the downstream (the pressure surface127) to the upstream (the suction surface126) in the lean direction. That is, compared with the transonic airfoil12ashown inFIG. 13A, the downstream (the trailing edge122) in the radial direction of the rotor5is leaned backward and the hub123protrudes to the upstream (the leading edge121). The shape of the transonic airfoil12eis called a “backward leant shape” in the following description.

Therefore, in the transonic airfoil12yaccording to the present embodiment, similarly to the first embodiment, the forward leant shape of the transonic airfoil12dshown inFIG. 13Band the backward leant shape of the transonic airfoil12eshown inFIG. 13Care combined in addition to the S shape in which the forward swept shape of the transonic airfoil12bshown inFIG. 5Band the backward swept shape of the transonic airfoil12cshown inFIG. 5Care combined. Accordingly, compared with the transonic airfoil12xaccording to the first embodiment, the degree of freedom in adjustment of the axial velocity profile or the matching increases, thereby improving the aerodynamic performance.

FIG. 14shows a shifted state in the lean direction of the sectional profiles in the span direction from the hub to the tip when the forward lean is combined. As shown inFIG. 14, when the forward leant shape is combined with the S shape formed by the forward swept shape and the backward swept shape, the shift amount of the upstream (the suction surface126) slowly increases from the hub123to the tip124, the variation rate in shift amount is high in the hub123and low in the tip124.

INDUSTRIAL APPLICABILITY

The present invention can be applied to a transonic airfoil used in the atmosphere of a transonic or supersonic operating fluid. The invention can be also applied to an axial flow rotary machine having the transonic airfoil as a rotor airfoil. The axial flow rotary machine can be applied to compressors of a gas turbine, an aircraft fan engine, and an aircraft jet engine.