JP5248422B2 - Turbomachine and turbine runner - Google Patents

Description

  The present invention relates to a turbomachine and a turbine runner that obtain energy from a fluid via an impeller.

  A turbomachine that obtains energy from a fluid via an impeller includes an impeller having a plurality of moving blades attached around a shaft, and a shroud (outer casing) installed on the outer peripheral side of the impeller. Some fluids that flow in from the axial direction of the vehicle or from the oblique direction of the shaft flow out in the axial direction of the impeller.

  The moving blade in this type of turbomachine extends to the vicinity of the shroud in the radial direction of the impeller. Therefore, the circumferential speed of the moving blade during rotation increases as it goes toward the radially outer side (that is, the shroud side) of the impeller. In general, the blade is designed so that its shape follows the fluid flow so that the load is evenly distributed over the entire surface of the blade. Therefore, when a moving blade is designed based on this idea, the angle formed between the chord of the moving blade and the rotation direction (circumferential direction) of the impeller becomes smaller toward the outer side in the radial direction of the impeller. That is, the moving blade is twisted so as to follow the rotational direction of the impeller as it goes outward in the radial direction of the impeller.

  For example, Japanese Patent Laid-Open No. 7-54752 discloses a runner (impeller) that is rotatably supported as one of turbomachines having moving blades having the above-described shape, and covers the runner from the outer peripheral side of the runner. An axial turbine with a shroud is described.

Japanese Patent Laid-Open No. 7-54752

  By the way, at the shroud side end portion (tip portion) of the moving blade having the shape as described above, the speed of the fluid passing through the moving blade is high, so that it is easy to obtain a large load compared to the portion on the rotating shaft side. There is. However, on the other hand, since the fluid is fast and close to the shroud, peeling and backflow tend to occur. In addition, since there is a gap between the shroud side end of the rotor blade and the shroud, there is a risk of loss due to leakage and cavitation.

  An object of the present invention is to provide a turbomachine that is excellent in energy efficiency as a whole while suppressing separation, backflow, leakage, and cavitation at the shroud side end of a moving blade.

  In order to achieve the above object, the present invention provides an impeller having a shaft rotatably supported and a plurality of moving blades installed around the shaft, and the moving blade on the outer peripheral side of the impeller. The blade is twisted in a direction from the shaft toward the shroud, and the direction of twist of the blade in the vicinity of the shroud is the blade in the vicinity of the shaft. It is assumed that the direction of twist is reversed.

  According to the present invention, since the blade load on the shroud side of the moving blade is reduced, the overall energy efficiency of the turbomachine is improved while suppressing leakage, separation, cavitation and backflow at the shroud side end of the moving blade. Can be improved.

The water turbine which is the 1st Embodiment of this invention WHEREIN: The figure which looked at the water turbine runner periphery from the radial direction of the water turbine runner. The figure which looked at the moving blade in the 1st Embodiment of this invention from the axial direction of the water turbine runner. The figure which looked at the moving blade in the 1st Embodiment of this invention from the radial direction of the water turbine runner. Sectional drawing in the arbitrary positions of the moving blade in the 1st Embodiment of this invention. The figure which looked at the moving blade in the conventional water turbine runner from the radial direction of the water turbine runner. The pressure distribution figure of the blade surface of a moving blade in the conventional turbine runner. The figure which showed the force which acts when a fluid flows in about the cross section in the arbitrary positions of the moving blade in the 1st Embodiment of this invention. The pressure distribution figure of the blade surface of the moving blade in the 1st Embodiment of this invention. The water turbine which is the 2nd Embodiment of this invention WHEREIN: The figure which looked at the water turbine runner periphery from the radial direction of the water turbine runner. Sectional drawing in the arbitrary positions of the moving blade in the 2nd Embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. First, an axial flow turbine will be described as an example of a turbo machine for carrying out the present invention. An axial-flow water turbine is a water wheel which has a moving blade attached substantially at right angles to the axis of the water turbine runner, and causes fluid flowing in from the axial direction of the water turbine runner to flow out in the axial direction via the moving blade.

  FIG. 1 is a side view of the periphery of a water turbine runner from the radial direction of the water turbine runner in the water turbine (hydraulic machine) according to the first embodiment of the present invention. The water wheel shown in this figure is a so-called horizontal axis valve water wheel, a water wheel runner (impeller) 3, a shroud (outer casing) 4 installed on the outer peripheral side of the water wheel runner 3 with a space between the water wheel runner 3, An inner casing 5 is provided inside the shroud 4 with a space from the shroud 4.

  The water turbine runner 3 is housed in the inner casing 5, and is supported by a shaft 6 that is rotatably supported around a central shaft 40, a boss (hub) 2 that is fixed to the tip of the shaft 6, and a plurality of wheels around the boss 2. An installed moving blade 1 is provided and rotates in the direction of arrow 20 (rotation direction) in the figure. The boss 2 in the present embodiment is formed in a substantially cylindrical shape, and a plurality of blades 1 are attached to the cylindrical side surface of the boss 2 from a direction substantially perpendicular to the central axis 40. The rotor blades 1 attached to the boss 2 in this way are arranged at intervals in the circumferential direction of the boss 2, and are fixed radially to the central axis 40. The shroud side end portion (tip portion) 7 of the rotor blade 1 faces the shroud 4, and a gap (not shown) is provided between the shroud side end portion 7 and the shroud 4 so as not to contact the rotor blade 1 and the shroud 4. ) Is formed.

  FIG. 2 is a top view of the moving blade 1 according to the first embodiment of the present invention viewed from the axial direction of the turbine runner 3. In this figure, for simplicity, only one of the plurality of moving blades 1 is shown enlarged. In addition, the same code | symbol is attached | subjected to the same part as the previous figure, and description is abbreviate | omitted (the following figure is also the same).

  Here, as shown in FIG. 2, a plurality of surfaces 10, 11, 12, and 13 that are substantially parallel to the shroud 4 and have different distances from the shroud 4 are set. The radial distance to the shroud side end 7 is defined as a reference diameter R1. Since the present embodiment is directed to the axial flow turbine, the surfaces 10, 11, 12, and 13 share the shaft 6 and the central shaft 40, respectively, and are cylindrical surfaces having different distances from the shaft 6 (central shaft 40). It has become. The surface 11 is the surface closest to the shaft 6 (that is, the surface at the axial end portion of the blade 1), and the surface 13 is the surface closest to the shroud 4 (that is, the surface at the shroud side end portion 7 of the blade 1). It is. The surface 12 is located approximately at the center between the central axis 40 and the shroud side end portion 7, and when expressed using the reference diameter R1, the distance from the central axis 40 is approximately 50% of the reference diameter R1. The surface 10 is located closer to the shroud 4 than the surface 12, and the distance from the surface 10 to the central axis 40 is greater than 50% of the reference diameter R1.

  When the turbine runner 3 rotates in the rotation direction 20, the speed of the moving blade 1 due to the rotation changes according to the distance from the central axis 40, and increases as the distance from the central axis 40 increases. Therefore, considering the relative speed (inflow speed) when the fluid flows into the interblade inlet of the water turbine runner 3, the circumferential speed of the fluid increases as it approaches the shroud 4. For example, comparing the circumferential components 21, 22, and 23 of the inflow velocity on the surfaces 11, 12, and 13, the circumferential component 23 of the inflow velocity on the surface 13 is the largest, as shown in FIG. The circumferential component 21 of speed becomes the smallest.

  FIG. 3 is a side view of the moving blade 1 according to the first embodiment of the present invention viewed from the radial direction of the turbine runner 3. In this figure, cross sections (airfoil types) when the blade 1 is cut along the planes 10, 11, 12, and 13 shown in FIG. 2 are shown as cross sections 10a, 11a, 12a, and 13a, respectively. The cross section 10a cut along the plane 10 is hatched.

  The arrows 27, 28, and 29 in FIG. 3 indicate the inflow direction of the fluid on each surface 11, 12, and 13 (the direction in which the fluid flows into the water turbine runner 3) when the water turbine runner 3 rotates in the rotation direction 20. Each is shown. The inflow direction of the fluid can be obtained from the circumferential speed and the axial speed when the fluid flows into the turbine runner 3, and among these, the circumferential speed of the fluid is the central axis as described in FIG. It becomes larger as it gets closer to the shroud 4 from 40. Therefore, as shown in FIG. 3, it is assumed that the axial velocities 24, 25, and 26 of the fluids on the surfaces 11, 12, and 13 are substantially equal, and the fluid inflow directions 27, 28, and When 29 is expressed by an angle 30 with respect to the central axis 40, the fluid inflow angle 30 increases in proportion to the distance from the central axis 40. That is, the fluid flows into the moving blade 1 from the surface 11 toward the surface 13 so that the inflow angle 30 increases.

  As can be seen from the cross sections 10a, 11a, 12a, and 13a of the rotor blade 1 in FIG. 3 that do not overlap each other, the direction from the shaft 6 toward the shroud 4 (that is, the radial direction of the turbine runner 3). It is twisted over. Here, in the radial direction of the water turbine runner 3, a section from the cross section 11 a closest to the shaft 6 to the cross section 10 a toward the shroud 4 is defined as a first section, and from the cross section 10 a to the shroud 4 to the cross section 13 a. This section is the second section.

  In the first section, the rotor blade 1 is moved in the direction of the arrow 70 (upper part of FIG. Twisted counterclockwise). At this time, it is preferable to change the direction of the chord 54 so that the angle of attack 57 of the moving blade 1 is kept constant throughout the first section. Thus, if the angle of attack 57 is made constant, the blade load acting on the moving blade 1 in the first section can be made uniform.

  On the other hand, the moving blade 1 is twisted in the direction of the arrow 71 (clockwise in FIG. 3) so that the chord 54 changes in the second section in the opposite direction to the change in the fluid inflow angle 30, and the shroud 4 It is twisted so that the angle of attack 57 becomes smaller toward. That is, in the moving blade 1 of the present embodiment, with the cross section 10a as a boundary, the twist direction 71 of the second section located near the shroud 4 and the twist direction 70 of the first section located near the shaft 6 Is reversed.

  Next, the phrase “blade chord angle” is used to paraphrase the twist of the moving blade 1 in another way. FIG. 4 is a cross-sectional view at an arbitrary position of the moving blade 1 according to the first embodiment of the present invention, and the moving blade is viewed from the same direction as FIG. The cross section 15a of the moving blade 1 shown in this figure is a cross section that appears when the moving blade is cut along a plane substantially parallel to the shroud 4 as described above. In this figure, a line connecting the leading edge 8 and the trailing edge 9 of the moving blade on the cross section 15a is a chord 54, and a circle (or arc) drawn in the rotational direction 20 of the shaft 6 on the cross section 15a is a reference line 58. And an angle 60 formed by the chord 54 and the reference line 58 is a chord angle. The angle formed by the fluid inflow direction 31 to the turbine runner 3 (front edge 8) and the chord 54 is an angle of attack 57.

  If the chord angle 60 set in this way is used, the moving blade 1 shown in FIG. 3 is twisted in a direction in which the chord angle 60 gradually decreases in the first section, and the chord angle 60 in the second section. It can be said that is twisted in the direction of gradually increasing. When the moving blade 1 is formed in this way, the chord angle 60 is any one that is located in the entire section (the first section and the second section) from the axial end of the moving blade 1 to the shroud end 7. In the cross section, the minimum value in all the sections is taken. More specifically, the chord angle 60 of the moving blade 1 in FIG. 3 monotonously decreases in the first section located on the shaft 6 side, and thereafter, in the second section located on the shroud 4 side. It is increasing monotonously. That is, the chord angle 60 of the moving blade 1 has a minimum value in the cross section 10a, and the twisting direction of the moving blade 1 is reversed before and after the cross section 10a as described above. In the present embodiment, the moving blade 1 is formed so as to take the minimum value only in the cross section 10a, but the moving blade 1 is formed so as to take the same minimum value in two or more cross sections (points). Alternatively, the moving blade 1 may be formed so as to keep the minimum value over a predetermined range in the radial direction of the turbine runner 3.

Next, the effect of this embodiment will be described in comparison with the prior art.
FIG. 5 is a side view of a moving blade 100 in a general conventional turbine runner as viewed from the radial direction of the turbine runner. In this figure, similarly to FIG. 3, the sections (airfoil types) when the moving blade 100 is cut along the planes 10, 11, 12, and 13 of FIG. 2 are shown as the sections 10b, 11b, 12b, and 13b, respectively. In particular, the cross section 10b obtained by cutting the moving blade 100 along the surface 10 is hatched.

  The moving blade 100 shown in this figure is designed so that the angle of attack 57 is substantially constant over the entire blade. Therefore, the moving blade 100 is twisted only in the direction of the arrow 70 in all sections of the first section and the second section from the cross section 11b to the cross section 13b in accordance with the change of the fluid inflow angle 30. In other words, the chord angle 60 of the moving blade 100 decreases monotonously in the entire section from the cross section 11b to the cross section 13b.

  FIG. 6 is a diagram showing the pressure distribution on the blade surface after performing fluid analysis on the moving blade 100 using general-purpose software. In addition, the curve 80 attached | subjected on the moving blade 100 in a figure is an isobaric line, and a pressure is high toward the left side from the right side in a figure. The moving blade 100 is formed so as to be equally loaded at all radial positions. However, since the fluid velocity increases toward the outer periphery, the high pressure region 81 becomes larger toward the outer periphery of the blade 100 as shown in FIG. It has become. That is, when the moving blade 100 is formed as described above, there is a merit that it is easy to obtain a large load on the shroud 4 side compared to the shaft 6 side, but on the other hand, the shroud side end of the moving blade 100 is Since the fluid is fast and close to the shroud 4, there is a tendency for separation and backflow to occur easily. Further, since there is a gap between the shroud side end of the moving blade 100 and the shroud 4, there is a possibility that loss due to leakage or cavitation may occur.

  On the other hand, the rotor blade 1 in the present embodiment is twisted in the direction from the shaft 6 toward the shroud 4. In the first section located in the vicinity of the shaft 6, the arrow 70 matches the fluid inflow angle 30. The second section in the vicinity of the shroud 4 is twisted in the direction of the arrow 71 opposite to the first section. Thus, when the direction of twisting of the moving blade 1 is reversed in the second section, the attack angle 57 similar to that of the normal moving blade 100 is maintained in the first section, and in the second section, compared to the normal moving blade 100. The angle of attack 57 can be reduced. Here, the effect produced by reducing the angle of attack 57 will be described with reference to FIG.

  FIG. 7 shows the force acting on the moving blade when the fluid 51 flows in the section 50 of the moving blade 1 at an arbitrary position. In the example shown in FIG. 7A, the chord angle 60 is smaller and the angle of attack 57 is larger than the example shown in FIG. 7B.

  When the angle of attack 57 is large as shown in FIG. 7A, the flow path 52 on the suction surface side becomes longer than the flow path 53 on the pressure surface side in the moving blade 1. Therefore, the pressure difference between the suction surface side and the pressure surface side increases, and as a result, the lift force 56 increases. Further, in this case, since the flow 51 collides with the pressure surface side, the force 55 accompanying the collision also acts in the direction of increasing the lift force. On the other hand, when the angle of attack 57 is small as shown in FIG. 7B, the difference between the flow path 52 on the suction surface side and the flow path 53 on the pressure surface side becomes small. Compared to the case, the lift force 56 becomes smaller. Further, the force 55 resulting from the collision also acts in a direction substantially orthogonal to the direction of lift, and therefore does not contribute to the increase in lift 56. Therefore, if the posture of the moving blade 1 is tilted so that the angle of attack 57 becomes smaller, the lift force 56 acting on the moving blade 1 can be suppressed.

  Therefore, when the moving blade 1 is formed as in the present embodiment and the angle of attack in the second section is reduced, the lift force acting on the second section of the moving blade 1 can be suppressed. The load acting on the shroud 4 side (second section) of the moving blade 2 (second section) is reduced at the same time as the load acting on the side (first section) is kept equal to that of the normal moving blade 100. Can do.

  Further, by forming the moving blade 1 as in the present embodiment, it is also advantageous in that the collision loss at the leading edge of the second section and the loss due to separation can be reduced.

  FIG. 8 is a diagram showing the pressure distribution on the blade surface after performing fluid analysis on the moving blade 1 according to the present embodiment using general-purpose software. In the moving blade 1 according to the present embodiment, the angle of attack 57 of the blade cross section becomes smaller before reaching the shroud side end of the moving blade 1, so the load on the moving blade 1 on the shroud 4 side is reduced. As a result, as shown in this figure, the high pressure region 81 is substantially uniform from the vicinity of the center in the radial direction of the rotor blade 1 to the shroud side end. Therefore, according to the present embodiment, since the blade load on the shroud side of the moving blade 1 is reduced, the leakage, separation, cavitation and backflow at the shroud side end portion 7 of the moving blade 1 are suppressed as a whole. Energy efficiency can be improved.

  In the above, it is preferable that the cross section 10a where the chord angle 60 is minimum is set in a section within 60% to 90% of the reference diameter R1. Here, 60% or more of the reference diameter R1 is because it is preferable to obtain a blade load as much as possible near the blade center where the reference diameter R1 is 50%, and on the other hand, 90% or less of the reference diameter R1. This is because even if the angle of attack 57 is reduced on the shroud 4 side, it is difficult to obtain a substantial blade load reduction effect.

  Next, a mixed flow turbine will be described as an example of a turbo machine for carrying out the present invention. A mixed flow turbine is a turbine having a moving blade that is mounted obliquely with respect to the axis of the water turbine runner, and causes fluid flowing in from an oblique direction of the axis of the water turbine runner to flow out in the axial direction via the moving blade.

  FIG. 9 is a side view of the periphery of the water turbine runner from the radial direction of the water turbine runner in the water turbine according to the second embodiment of the present invention. The water wheel shown in this figure is a so-called vertical flow turbine (Delia water wheel), and includes a water wheel runner 3A having a substantially conical boss 2A and a moving blade 1A, and a shroud 4A. The moving blade 1A is attached substantially perpendicular to the conical surface of the boss 2A, and is attached obliquely to the central axis 40 of the water turbine runner 3A. The shroud side end portion of the moving blade 1A faces the shroud 4A, and a gap (not shown) is formed between the shroud side end portion and the shroud 4A as in the case of the axial flow turbine.

  Here, as shown in FIG. 9, a plurality of surfaces 90, 91, 92, 93 that are substantially parallel to the shroud 4 and have different distances from the shroud 4 are set, and further, the approximate center of the moving blade 1A is set. The distance on the straight line orthogonal to the passage surfaces 90, 91, 92, 93, and the distance from the central axis 40 to the shroud side end of the rotor blade 1A is defined as a reference diameter R2. Since the present embodiment is directed to a mixed flow turbine, the surfaces 90, 91, 92, and 93 are conical surfaces having apexes located on the central axis 40 of the shaft 6 and side surfaces substantially orthogonal to the rotor blade 1A, respectively. And substantially coincides with the uniform flow surface around the rotor blade 1. The surface 91 is a surface at the axial end portion of the moving blade 1A, and the surface 93 is a surface at the shroud side end portion of the moving blade 1A. If the surface 92 is expressed using the reference diameter R2, the distance from the central axis 40 is at a position about 50% of the reference diameter R2. The surface 90 is located closer to the shroud 4 than the surface 92, and the distance from the surface 90 to the central axis 40 is greater than 50% of the reference diameter R2.

  In the present embodiment, the rotor blade 1A is cut along the above-described surfaces 90, 91, 92, and 93, and the cross sections thereof are taken as the cross sections 10a, 11a, 12a, and 13a shown in FIG. By arranging in this way, the moving blade 1A is twisted in the direction from the boss 2A toward the shroud 4A (that is, in the direction of the reference diameter R2). That is, in the first section from the surface 91 to the surface 90 via the surface 92, the rotor blade 1 in the present embodiment is twisted in accordance with the change in the inflow angle of the fluid, and the second blade from the surface 90 to the surface 93. In the section, the first section is twisted in the opposite direction.

  10 is a cross-sectional view of the moving blade 1A at an arbitrary position, and the moving blade 1A is viewed from the same direction as FIG. The cross section 95a of the moving blade 1A shown in this figure is a section that appears when the moving blade 1A is cut along a plane 95 substantially parallel to the shroud 4A, like the surface 90 described above. In this figure, a circle (or arc) reference line 58 drawn in the rotation direction 20 of the shaft 6 on the cross section 95a is used, and an angle formed between the chord 54 and the reference line 58 is a chord angle 60. When the chord angle 60 defined in this way is used, the moving blade 1A in the present embodiment gradually decreases in the first section in the same manner as the moving blade 1 in the first embodiment. In other words, in the second section, it can be said that the chord angle 60 is twisted in a gradually increasing direction. That is, when the moving blade 1A is formed in this way, the chord angle 60 is any position that is located in the entire section (the first section and the second section) from the shaft side end portion to the shroud side end portion of the moving blade 1A. In the cross section, the minimum value in all the sections is taken. More specifically, the chord angle 60 of the moving blade 1A takes a minimum value in the cross section by the surface 90, and the direction of twisting of the moving blade 1A is reversed before and after the cross section by the surface 90.

  When the moving blade 1A is formed as described above, as in the first embodiment, the attack angle 57 similar to that of the normal moving blade is maintained in the first section, and in the second section, compared to the normal moving blade. The angle of attack 57 can be reduced. Accordingly, also in the present embodiment relating to the mixed flow turbine, the blade load on the shroud 4A side of the moving blade 1A is reduced, and thus the energy efficiency as a whole can be improved. In the above description, the surface 90 having the smallest chord angle 60 is preferably set in a section within 60% to 90% of the reference diameter R2 for the same reason as in the first embodiment.

DESCRIPTION OF SYMBOLS 1 Rotating blade 3 Turbine runner 4 Shroud 5 Inner casing 6 Shaft 7 Shroud type | mold edge part 8 Front edge 9 Rear edge 10, 11, 12, 13 Cylindrical surface 10b, 11b, 12b, 13b Blade cross section 20 Rotating direction of a turbine runner 30 Inflow Angle 40 Central axis (rotary axis of turbine runner)
57 Angle of attack 58 Reference line 60 Blade chord angle 70 Direction of twist of blade 1 in the first section 71 Direction of twist of blade 1 in the second section 90, 91, 92, 93 Conical surface R1, R2 Reference diameter

Claims (9)

An impeller having a shaft rotatably supported and a plurality of moving blades installed around the shaft;
A shroud installed on the outer peripheral side of the impeller with the moving blade and a space therebetween,
The blade is twisted from the shaft toward the shroud,
The direction of twisting of the moving blade near the shroud is opposite to the direction of twisting of the moving blade near the shaft ,
The direction of twisting of the rotor blade in the vicinity of the shroud is a direction in which the chord angle increases as the shroud approaches
A turbomachine characterized in that a direction of twisting of a moving blade near the shaft is a direction in which a chord angle becomes smaller as approaching the shroud . With in different surfaces of the distance from the shroud front Symbol a shroud substantially parallel to the plane, from the shaft end of the rotor blade up to the shroud side end portions cutting the rotor blade, on the each cross-section When the angle between the chord connecting the leading edge and the trailing edge of the moving blade and the circle drawn in the rotation direction of the shaft is a chord angle,
The chord angle has a minimum value in the section in any of the sections in the section from the shaft side end to the shroud side end of the rotor blade. The turbomachine according to claim 1 . A turbine runner installed on the inner circumference side of the shroud via a gap,
A shaft supported rotatably,
And a plurality of blades mounted around the shaft,
The blade is twisted from the shaft toward the shroud,
The direction of twisting of the moving blade near the shroud is opposite to the direction of twisting of the moving blade near the shaft ,
The direction of twisting of the rotor blade in the vicinity of the shroud is a direction in which the chord angle increases as it approaches the shroud,
The turbine runner according to claim 1, wherein the direction of twisting of the moving blades near the shaft is such that the chord angle becomes smaller as approaching the shroud . With a different cylindrical surface of the distance from the shroud a cylindrical surface to share the pre Symbol axis and central axis, cutting the moving blade from the shaft side end portion of the rotor blade up to the shroud side end portion, the On each cross section, when an angle formed by a chord connecting the leading edge and the trailing edge of the moving blade and a circle drawn in the rotation direction of the shaft is a chord angle,
The chord angle has a minimum value in the section in any of the sections in the section from the shaft side end portion to the shroud side end portion of the rotor blade. The turbine runner according to claim 3 . A conical surface having a pre-Symbol shaft apex and said blades substantially perpendicular to the side surface located on the central axis of, with different conical surfaces of the distance from the shroud, the shroud from the axial end of the rotor blade The blade is cut to the side end, and on each cross section, the angle formed by the chord connecting the leading edge and the trailing edge of the blade and the circle drawn in the rotation direction of the shaft is the chord. When the angle is
The chord angle has a minimum value in the section in any of the sections in the section from the shaft side end to the shroud side end of the rotor blade. The turbine runner according to claim 3 . Angle of attack before Kidotsubasa, in the section from the shaft side end portion of the rotor blade up to the cross section of the chord angle is minimized, according to claim 4 or 5, characterized in that it is held constant The turbine runner described in 1 . Before Kitsubasatsuru angle, the chord angle from the axial end of the rotor blade decreases monotonously in a section up to the cross section becomes minimum, the cross section of the chord angles is minimized of the rotor blade The turbine runner according to any one of claims 4 to 6, wherein the turbine runner increases monotonously in a section extending to the shroud side end. When the distance criterion diameter from the central axis of the front Symbol axis to the shroud side end portion in the rotor blade,
The distance from the cross section with the smallest chord angle to the shroud side end of the moving blade is smaller than the distance from the cross section with the smallest chord angle to the shaft end of the moving blade. The turbine runner according to claim 4 . Distance from the cross section before Kitsubasatsuru angle is minimum to the shroud side end portions of the blades, said chord angle is less than the distance from the section with the smallest to the shaft end of the rotor blade The water turbine runner according to claim 5, wherein

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