Runner of hydraulic machine and hydraulic machine

Abstract

To provide a runner of a hydraulic machine capable of improving efficiency by reducing loss of flow during pump operation and hydraulic turbine operation.SOLUTION: The hydraulic machine runner 5 according to the embodiment includes a crown, a band provided on an outer peripheral side of the crown, and a plurality of runner blades provided between the crown and the band. The plurality of runner blades include a plurality of long blades and a plurality of short blades having a blade length shorter than that of the long blades. The long blades and the short blades are alternately arranged in the circumferential direction. When a dimension along the circumferential direction between the outer circumferential end portion of the long blade and the outer circumferential end portion of the short blade including the pressure surface facing the suction surface of the long blade is defined as a first chord length λ 1, and a dimension along the circumferential direction between the outer circumferential end portion of the short blade and the outer circumferential end portion of the long blade including the pressure surface facing the suction surface of the short blade is defined as a second chord length λ 2, λ 1> λ 2 is satisfied.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The embodiments relate to a runner for a hydraulic machine and a hydraulic machine. [Background technology]

[0002] A pump turbine for a pumped storage power plant is known as an example of a hydraulic machine. During turbine operation, the energy of the water is converted into rotational energy of the runner, and electricity is generated by a generator motor connected to the runner. During pump operation, the generator motor receives power, driving the runner to rotate, and the runner sucks up water to pump it up. During turbine operation, improved turbine operation efficiency is required, and during pump operation, improved pump operation efficiency is required. Below, a Francis-type pump turbine will be used as an example.

[0003] Known types of Francis pump-turbine runners include standard runners with uniform blade length and splitter runners with long blades and short blades. The number of blades in a splitter runner is greater than that of a standard runner. This prevents the flow inside the runner from becoming uneven. In particular, it is expected to reduce losses and water pressure pulsations at off-design points.

[0004] However, in a splitter runner, the presence of long and short blades makes the flow inside the runner more complex than in a conventional runner. Therefore, if the blade shape is not appropriate, it may cause increased losses inside the runner. Furthermore, if the blade angle at the outer periphery of the long blade and the blade angle at the outer periphery of the short blade are the same, the angle of the water flow entering the runner during turbine operation will differ near the outer periphery of the long blade and the outer periphery of the short blade. Similarly, even if the blade shape from the outer periphery to the inner periphery of the short blade is the same as that of the long blade, the angle of the water flow entering the runner may also differ. This can result in reduced efficiency and cavitation. To address this issue, splitter runners are known that optimize the blade shape of the short blades to improve efficiency and cavitation performance.

[0005] However, in this case, the short blades are formed with a blade shape different from that of the long blades. This results in portions where the width of the flow passage between the suction surface of the long blade and the pressure surface of the short blade suddenly increases or decreases. This causes a problem of increased flow loss during both pump and turbine operation. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent No. 3822416 Summary of the Invention [Problem to be solved by the invention]

[0007] An object of the embodiments is to provide a runner for a hydraulic machine and a hydraulic machine that can reduce flow loss during pump operation and water turbine operation, thereby improving efficiency. [Means for solving the problem]

[0008] A hydromachine runner according to an embodiment includes a crown, a band provided on the outer periphery of the crown, and a plurality of runner vanes provided between the crown and the band. The plurality of runner vanes include a plurality of long blades and a plurality of short blades each having a blade length shorter than that of the long blades. The long blades and short blades are arranged alternately in the circumferential direction. When the dimension along the circumferential direction between the outer peripheral end of a long blade and the outer peripheral end of a short blade including a pressure surface opposing the suction surface of the long blade is defined as a first chord length λ1, and the dimension along the circumferential direction between the outer peripheral end of a short blade and the outer peripheral end of a long blade including a pressure surface opposing the suction surface of the short blade is defined as a second chord length λ2,

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[0009] The hydraulic machine according to the embodiment includes the above-described hydraulic machine runner. [Effects of the Invention]

[0010] According to the embodiment, it is possible to reduce flow loss during pump operation and water turbine operation, thereby improving efficiency. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a meridian cross-sectional view showing the configuration of a Francis water turbine according to a first embodiment. [Figure 2] FIG. 2 is a meridian cross-sectional view showing the configuration of the runner shown in FIG. [Figure 3] FIG. 3 is a partial cross-sectional view taken along the flow line AA shown in FIG. [Figure 4] FIG. 4 is a partial cross-sectional view showing a runner as a comparative example of FIG. [Figure 5] FIG. 5 is a graph showing the change in flow path width of the runner shown in FIGS. [Figure 6] FIG. 6 is a graph showing the efficiency of the hydraulic machine shown in FIG. [Figure 7] FIG. 7 is a partial cross-sectional view similar to FIG. 3, showing a runner of a hydraulic machine according to a second embodiment. [Figure 8] FIG. 8 is a partial cross-sectional view showing a runner as a comparative example of FIG. [Figure 9] FIG. 9 is a graph showing the change in flow path width of the runner shown in FIGS. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, a runner for a hydraulic machine and a hydraulic machine according to an embodiment of the present invention will be described with reference to the drawings.

[0013] (First embodiment) A runner and a hydraulic machine according to a first embodiment will be described with reference to FIGS. 1 to 6. FIG.

[0014] First, the runner and hydraulic machine of the present embodiment will be described using Fig. 1. Here, a Francis pump-turbine, which is an example of a hydraulic machine, will be described using Fig. 1. In the following description, the terms upstream and downstream are used in accordance with the flow of water when the turbine is operating.

[0015] As shown in Figure 1, a Francis pump-turbine 1 comprises a spiral casing 2 into which water flows from an upper reservoir through a penstock (none of which are shown) during turbine operation, a plurality of stay vanes 3, a plurality of guide vanes 4, a runner 5, and a draft pipe 6.

[0016] The stay vanes 3 are components that guide water that has flowed into the casing 2 to the guide vanes 4 and runner 5. The stay vanes 3 are arranged on the inner periphery of the casing 2. A plurality of stay vanes 3 are arranged at intervals in the circumferential direction D of the runner 5, forming a fixed stationary blade row. A flow path through which water flows is formed between two stay vanes 3 that are adjacent in the circumferential direction D. The upper and lower ends of the stay vanes 3 are supported by stay rings 7. The stay rings 7 are made up of components provided above and below the stay vanes 3, respectively.

[0017] The guide vanes 4 are components that guide the inflowing water into the runner 5. The guide vanes 4 are arranged on the inner periphery of the stay vanes 3. A plurality of guide vanes 4 are arranged at predetermined intervals in the circumferential direction D, forming a movable stationary blade row. A flow path for water to flow is formed between two adjacent guide vanes 4 in the circumferential direction D. Each guide vane 4 is rotatably supported by an upper cover 8 and a lower cover 9. By rotating each guide vane 4 to change the opening degree, the flow rate of water flowing into the runner 5 can be adjusted. In this way, the amount of power generated by the generator, which will be described later, can be adjusted.

[0018] The runner 5 is configured to be rotatable around the rotation axis X relative to the casing 2. The runner 5 is rotationally driven by the water flowing in from the casing 2 when the turbine is operating. The runner 5 is a component that converts the pressure energy of the water flowing into the runner 5 into rotational energy to obtain power. The runner 5 is configured as a rotary impeller.

[0019] The runner 5 includes a crown 5a connected to the main shaft 10 (described later), a band 5b provided on the outer periphery of the crown 5a, and a plurality of runner blades 5c provided between the crown 5a and the band 5b. The plurality of runner blades 5c are arranged at predetermined intervals in the circumferential direction D of the runner 5. A flow path through which water flows is formed between two runner blades 5c adjacent to each other in the circumferential direction D.

[0020] A draft pipe 6 is provided downstream of the runner 5 when the turbine is in operation. The draft pipe 6 is connected to a lower pond (not shown), and the water that rotates the runner 5 recovers pressure and is released into the lower pond.

[0021] A main shaft 10 is connected to the crown 5a of the runner 5. The main shaft 10 is configured to be rotatable together with the runner 5 about a rotation axis X that extends in the vertical direction. The main shaft 10 extends along the rotation axis X.

[0022] A generator motor (not shown) is connected to the main shaft 10. During turbine operation, the generator motor generates electricity using the power of the runner 5, thereby providing electrical output. During pump operation, the runner 5 is driven to rotate by the supplied electric power. In this case, the runner 5 rotates in the opposite direction to when the turbine is operating. This allows water in the lower reservoir to be sucked up through the draft pipe 6 and discharged into the upper reservoir through the casing 2. In this way, the Francis pump-turbine 1 is capable of pumping (pumping operation). During this operation, the opening of the guide vanes 4 is adjusted to achieve an appropriate pumping amount depending on the pump head.

[0023] Next, the above-mentioned runner 5 according to this embodiment will be described with reference to FIGS.

[0024] The runner blades 5c of the runner 5 include long blades 20 and short blades 30. The short blades 30 have a blade length shorter than that of the long blades 20. The long blades 20 and short blades 30 are arranged alternately in the circumferential direction D of the runner 5. More specifically, the outer peripheral end portions 23 of the long blades 20 and the outer peripheral end portions 33 of the short blades 30 are arranged alternately in the circumferential direction D. A runner 5 configured in this manner is also called a splitter runner.

[0025] 3, the long blade 20 includes a suction surface 21 and a pressure surface 22 located on the opposite side of the suction surface 21. The suction surface 21 of the long blade 20 is located clockwise further forward than the pressure surface 22. The suction surface 21 and the pressure surface 22 of the long blade 20 are formed from an outer peripheral end 23 to an inner peripheral end 24 of the long blade 20.

[0026] The short blade 30 includes a suction surface 31 and a pressure surface 32 located opposite the suction surface 31. The suction surface 31 of the short blade 30 is located clockwise further than the pressure surface 32. The suction surface 31 of the short blade 30 faces the pressure surface 22 of the long blade 20, and the pressure surface 32 of the short blade 30 faces the suction surface 21 of the long blade 20. The suction surface 31 and the pressure surface 32 of the short blade 30 are formed from the outer peripheral end 33 to the inner peripheral end 34 of the short blade 30.

[0027] 3 shows two representative long wings 20 and one short wing 30 located between the two long wings 20. In the following description, the two long wings 20 will be referred to as a first long wing 20A and a second long wing 20B. The first long wing 20A and the second long wing 20B have the same blade shape.

[0028] As shown in Fig. 3, when viewed from above, the runner 5 rotates clockwise during turbine operation and counterclockwise during pump operation. The first long blade 20A is located at a position further forward in the rotation direction of the pump operation than the short blade 30, and counterclockwise. The second long blade 20B is located at a position further forward in the rotation direction of the turbine operation than the short blade 30, and clockwise. The first long blade 20A, short blade 30, and second long blade 20B are arranged in this order.

[0029] The suction surface 21 of the first long blade 20A faces the pressure surface 32 of the short blade 30. A first flow path 41 through which water flows is formed between the suction surface 21 of the first long blade 20A and the pressure surface 32 of the short blade 30. The suction surface 31 of the short blade 30 faces the pressure surface 22 of the second long blade 20B. A second flow path 42 through which water flows is formed between the suction surface 31 of the short blade 30 and the pressure surface 22 of the second long blade 20B.

[0030] As shown in Figure 3, the dimension along the circumferential direction D between the outer peripheral end 23 of the first long blade 20A and the outer peripheral end 33 of the short blade 30 is defined as a first chord length λ1. The dimension along the circumferential direction D between the outer peripheral end 33 of the short blade 30 and the outer peripheral end 23 of the second long blade 20B is defined as a second chord length λ2. The first chord length λ1 and the second chord length λ2 satisfy the following formula (1).

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[0031] In this embodiment, the third chord length λ3 and the fourth chord length λ4 described later may or may not satisfy the formula (4) described later, and are arbitrary.

[0032] As shown in FIG. 3, the blade angle β1 at the outer circumferential end 23 of the long blade 20 may be larger than the blade angle β2 at the outer circumferential end 33 of the short blade 30. The blade angle β1 at the outer circumferential end 23 of all the long blades 20, including the first long blade 20A and the second long blade 20B, may be larger than the blade angle β2 at the outer circumferential end 33 of the short blade 30. The blade angle means the angle of the direction in which the blade extends (e.g., the camber line) relative to the tangent to an arc centered on the rotation center (rotation axis X) of the runner 5 when viewed from above, and is defined as shown in FIG. 3. Therefore, a small blade angle means that the blade is formed so as to approach the tangential direction, and a large blade angle means that the blade is formed so as to approach the radial direction. The flow angle described below is also used in the same sense.

[0033] Next, the operation of this embodiment having such a configuration will be described.

[0034] As described above, when the first chord length λ1 and the second chord length λ2 satisfy the above-mentioned formula (1), the flow loss can be reduced and the efficiency can be improved. This will be explained below with reference to Figs. 4 to 6.

[0035] FIG. 4 shows a partial cross-sectional view of a runner 5 as a comparative example. In the runner 5 shown in FIG. 4, the first chord length λ1 is equal to the second chord length λ2. The blade angle β1 is larger than the blade angle β2. As a result, the short blades 30 are formed with a blade shape different from that of the long blades 20. In this case, a portion where the width of the first flow passage 41 formed between the suction surface 21 of the first long blade 20A and the pressure surface 32 of the short blade 30 changes suddenly is formed on the outer circumferential side of the runner 5. The portion where the width changes suddenly is a portion where the width suddenly increases during pump operation, and flow separation 50 can occur in this portion during pump operation.

[0036] FIG. 5 shows changes in the width of the first flow passage 41. The horizontal axis indicates the flow direction position, and the vertical axis indicates the flow passage width. The flow direction is the direction of water flow during pump operation, and is roughly the direction indicated by the thick arrows in FIGS. 3 and 4. The solid line indicates the width of the first flow passage 41 of the runner 5 (splitter runner) according to this embodiment shown in FIG. 3. The dashed line indicates the width of the first flow passage 41 of the runner 5 (splitter runner) according to the comparative example shown in FIG. 4. The dashed line indicates the width of the first flow passage 41 of the runner 5 (splitter runner) in which the blade shape from the outer peripheral end 33 to the inner peripheral end 34 of the short blades 30 is the same as that of the long blades 20, and the spacing between the short blades 30 and the long blades 20 in the circumferential direction D is equal.

[0037] 5, the width of the first flow passage 41 in the comparative example increases sharply at the outer circumferential side of the runner 5. This position corresponds to the position where flow separation 50 occurs as shown in FIG.

[0038] In contrast, in this embodiment, the first chord length λ1 and the second chord length λ2 satisfy the above-mentioned formula (1). This allows the short blade 30 to be closer to the first long blade 20A, and the sudden expansion of the width of the first flow passage 41 as shown in FIG. 4 can be mitigated. Therefore, the first flow passage 41 of the runner 5 shown in FIG. 3 can be formed to suppress the sudden expansion of its width, and the flow separation 50 shown in FIG. 4 can be reduced as shown in FIG. 3. During turbine operation, the width of the first flow passage 41, indicated by the dashed dotted line, decreases suddenly. However, in this embodiment, this sudden decrease in the width of the first flow passage 41 can be suppressed, and flow loss during turbine operation can be reduced.

[0039] Fig. 6 shows the efficiency of the Francis pump-turbine 1. The horizontal axis shows the chord length ratio, and the vertical axis shows the efficiency improvement. The chord length ratio is the value obtained by doubling the ratio of the first chord length λ1 to the dimension along the circumferential direction D between the outer circumferential end 23 of the first long blade 20A and the outer circumferential end 23 of the second long blade 20B, and is shown in equation (2) described below. The dashed line shows the efficiency improvement during pump operation, and the solid line shows the efficiency improvement during turbine operation.

[0040] As shown in FIG. 6, when the first chord length λ1 and the second chord length λ2 satisfy the following formula (2), efficiency can be improved during both pump operation and water turbine operation.

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[0041] The first chord length λ1 and the second chord length λ2 may satisfy the following formula (3). In this case, the width of the first flow path 41 can be prevented from becoming too small, and workability during manufacturing of the runner 5 can be ensured.

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[0042] As described above, according to this embodiment, the first chord length λ1 along the circumferential direction D between the outer peripheral end 23 of the first long blade 20A of the runner and the outer peripheral end 33 of the short blade 30 including the pressure surface 32 facing the suction surface 21 of the first long blade 20A is longer than the second chord length λ2 along the circumferential direction D between the outer peripheral end 33 of the short blade 30 and the outer peripheral end 23 of the second long blade 20B including the pressure surface 22 facing the suction surface 31 of the short blade 30. This prevents the first flow passage 41 formed between the first long blade 20A and the short blade 30 from having a portion where the width of the first flow passage 41 suddenly increases or decreases. This allows the width of the first flow passage 41 to change gradually. As a result, flow loss during pump operation and water turbine operation can be reduced, thereby improving efficiency.

[0043] (Second embodiment) Next, a runner and a hydraulic machine according to a second embodiment will be described with reference to FIGS.

[0044] The second embodiment shown in Figures 7 to 9 is different mainly in that the ratio of the first chord length λ1 to the second chord length λ2 is greater than the ratio of the third chord length λ3 to the fourth chord length λ4, and other configurations are substantially the same as those of the first embodiment shown in Figures 1 to 6. In Figures 7 to 9, the same parts as those in the first embodiment shown in Figures 1 to 6 are denoted by the same reference numerals, and detailed description thereof will be omitted.

[0045] As shown in FIG. 7, in the runner 5 according to this embodiment, the long blades 20 and the short blades 30 are defined as follows.

[0046] More specifically, as shown in FIG. 7, a circle centered on the rotation center of the runner 5 and passing through the inner circumferential end 34 of the short blade 30 is defined as an inner circumferential end circle 60. In FIG. 7, the inner circumferential end circle 60 is shown as a circle with a radius R1. The intersection of the inner circumferential end circle 60 and the suction surface 21 of the first long blade 20A, which faces the pressure surface 32 of the short blade 30, is defined as a first intersection point P1. The intersection of the inner circumferential end circle 60 and the pressure surface 22 of the second long blade 20B, which faces the suction surface 31 of the short blade 30, is defined as a second intersection point P2. The dimension along the circumferential direction D between the first intersection point P1 and the inner circumferential end 34 of the short blade 30 is defined as a third chord length λ3. The dimension along the circumferential direction D between the second intersection point P2 and the inner circumferential end 34 of the short blade 30 is defined as a fourth chord length λ4. The first chord length λ1, the second chord length λ2, the third chord length λ3, and the fourth chord length λ4 satisfy the following formula (4). That is, the ratio of the first chord length λ1 to the second chord length λ2 is greater than the ratio of the third chord length λ3 to the fourth chord length λ4.

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[0047] The third chord length λ3 may be greater than the fourth chord length λ4. However, as long as the third chord length λ3 satisfies the above formula (4), the third chord length λ3 may be equal to the fourth chord length λ4, or the third chord length λ3 may be smaller than the fourth chord length λ4.

[0048] The first chord length λ1 and the second chord length λ2 may satisfy the above-mentioned formula (1).

[0049] Fig. 8 shows a partial cross-sectional view of a runner 5 as a comparative example. In the runner 5 shown in Fig. 8, the first chord length λ1 is equal to the second chord length λ2. Meanwhile, the third chord length λ3 is smaller than the fourth chord length λ4. In this case, the ratio of the first chord length λ1 to the second chord length λ2 is greater than the ratio of the third chord length λ3 to the fourth chord length λ4.

[0050] In this way, because the third chord length λ3 is smaller than the fourth chord length λ4, a portion where the width of the first flow passage 41 formed between the suction surface 21 of the first long blade 20A and the pressure surface 32 of the short blade 30 changes abruptly is formed on the inner peripheral side of the runner 5. The portion where the width changes abruptly is a portion where the width increases abruptly during pump operation, and in this portion, flow separation 51 may occur during pump operation.

[0051] 9, like FIG. 5, shows the change in width of the first flow passage 41. The horizontal axis shows the flow direction position, and the vertical axis shows the flow passage width. The flow direction is the direction of water flow during pump operation, and is roughly the direction indicated by the thick arrows in FIGS. 7 and 8. The solid line shows the width of the first flow passage 41 of the runner 5 (splitter runner) according to this embodiment shown in FIG. 7. The dashed line shows the width of the first flow passage 41 of the runner 5 (splitter runner) according to the comparative example shown in FIG. 8. The dashed line shows the width of the first flow passage 41 of the runner 5 (splitter runner) in which the blade shape from the outer peripheral end 33 to the inner peripheral end 34 of the short blades 30 is the same as that of the long blades 20.

[0052] 9, the width of the first flow path 41 in the comparative example increases sharply at the inner circumferential side of the runner 5. This position corresponds to the position where flow separation 51 occurs as shown in FIG.

[0053] In contrast, in this embodiment, the first chord length λ1, the second chord length λ2, the third chord length λ3, and the fourth chord length λ4 satisfy the above-mentioned formula (4). This allows the short blade 30 to be closer to the pressure surface 22 of the second long blade 20B, and the sudden expansion of the width of the first flow passage 41 as shown in FIG. 8 can be mitigated. Therefore, the first flow passage 41 of the runner 5 shown in FIG. 7 can be formed to suppress the sudden expansion of the width, and the flow separation 51 shown in FIG. 8 can be reduced as shown in FIG. 7. During turbine operation, the width of the first flow passage 41, indicated by the dashed dotted line, can be suppressed from decreasing suddenly, and flow loss during turbine operation can be reduced.

[0054] As described above, according to this embodiment, the ratio of the first chord length λ1 to the second chord length λ2 is greater than the ratio of the third chord length λ3 to the fourth chord length λ4. This makes it possible to prevent the first flow passage 41 formed between the first long blade 20A and the short blade 30 from having a portion where the width of the first flow passage 41 suddenly increases or decreases. This makes it possible to gradually change the width of the first flow passage 41. As a result, flow loss during pump operation and water turbine operation can be reduced, improving efficiency.

[0055] According to each of the above-described embodiments, it is possible to reduce flow loss during pump operation and water turbine operation, thereby improving efficiency.

[0056] In the above-described embodiment, a Francis pump-turbine has been used as an example of a hydraulic machine, but the present invention is not limited to this. The hydraulic machine according to the present embodiment may be applied to a hydraulic turbine other than a Francis turbine.

[0057] Although the present invention has been described with reference to an embodiment and several modifications thereof, these embodiments and modifications are presented as examples and are not intended to limit the scope of the invention. These novel embodiments and modifications may be embodied in various other forms, and various omissions, substitutions, and modifications may be made without departing from the spirit of the invention. These embodiments and modifications are included within the scope and spirit of the invention, as well as within the scope of the invention and its equivalents as set forth in the claims. Furthermore, it is of course possible to combine these embodiments and modifications in part as appropriate within the spirit of the invention. [Explanation of symbols]

[0058] 1: Francis pump-turbine, 5: runner, 5a: crown, 5b: band, 5c: runner blade, 20: long blade, 21: suction surface, 22: pressure surface, 23: outer peripheral end, 30: short blade, 31: suction surface, 32: pressure surface, 33: outer peripheral end, 34: inner peripheral end, 60: inner peripheral end circle, D: circumferential direction

Claims

1. Crown and a band provided on an outer circumferential side of the crown; a plurality of runner vanes disposed between the crown and the band; Equipped with The plurality of runner blades include a plurality of long blades and a plurality of short blades having a blade length shorter than that of the long blades, The long blades and the short blades are arranged alternately in the circumferential direction, When the dimension along the circumferential direction between the outer peripheral end of the long blade and the outer peripheral end of the short blade including the pressure surface facing the suction surface of the long blade is defined as a first chord length λ1, and the dimension along the circumferential direction between the outer peripheral end of the short blade and the outer peripheral end of the long blade including the pressure surface facing the suction surface of the short blade is defined as a second chord length λ2, [Equation 1] That is, Runner of a hydraulic machine.

2. a blade angle at the outer peripheral end of the long blade is larger than a blade angle at the outer peripheral end of the short blade; A runner for a hydraulic machine according to claim 1.

3. an intersection between an inner circumferential end circle centered on the rotation center of the runner and passing through the inner circumferential end of the short blade and the suction surface of the long blade facing the pressure surface of the short blade is defined as a first intersection; an intersection between the inner circumferential end circle and the pressure surface of the long blade facing the suction surface of the short blade is defined as a second intersection; When the dimension along the circumferential direction between the first intersection point and the inner circumferential end of the short blade is a third chord length λ3, and the dimension along the circumferential direction between the second intersection point and the inner circumferential end of the short blade is a fourth chord length λ4, [Equation 2] That is, A runner for a hydraulic machine according to claim 1.

4. The first chord length λ1 and the second chord length λ2 are [Equation 3] fulfill, A runner for a hydraulic machine according to claim 1.

5. The first chord length λ1 and the second chord length λ2 are [Equation 4] fulfill, A runner for a hydraulic machine according to claim 1.

6. A hydraulic machine comprising a runner according to any one of claims 1 to 5. hydraulic machinery.

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