JP4768361B2 - Francis type runner and hydraulic machine - Google Patents

Description

  The present invention relates to a Francis type runner and a hydraulic machine that are used in a hydraulic machine such as a Francis type turbine or a pump turbine.

  Generally, a Francis-type runner used in a hydraulic machine such as a Francis-type water turbine or a pump-type water wheel has a crown that can rotate around the axis of a main shaft, and a ring-shaped band provided apart from the crown and the above-mentioned crown. In between, a plurality of plate-like runner blades are provided in the circumferential direction so as to connect the crown and the band. When the turbine is in operation, water is introduced from the outside between the crown and the band, and the action of the introduced water rotates the Francis-type runner around the axis of the main shaft to drive the generator connected to the main shaft. .

  FIG. 30 is a longitudinal sectional view of the vicinity of the Francis turbine of the hydroelectric power plant where the Francis turbine is installed. During power generation operation, water passes from the upper pond (not shown) through the hydraulic iron pipe, from the casing 1 to the stay vane 2 and the guide vane. 3 flows into the runner 4, and the runner 4 is rotationally driven by the water flow, and the generator 6 is driven via the main shaft 5. On the other hand, the water that has driven the runner 4 flows out through a suction pipe 7 into a water discharge channel (not shown). During actual operation, the amount of power generation is changed by adjusting the amount of water flowing into the runner 4 by changing the opening of the guide vane 3. The Francis-type runner is formed of a crown 8 fixed to the main shaft 5, a ring-shaped band 9, and a plurality of runner blades 10 disposed so as to connect the crown 8 and the band 9. Yes.

  By the way, as described above, in order to adjust the power generation amount during operation, the opening amount of the guide vane 3 is adjusted and the water amount is changed. Therefore, the flow in the runner 4 varies greatly depending on the operation state. FIG. 31 shows a model of the meridional flow in the runner 4 due to the difference in the amount of water. That is, the meridional flow of the runner 4 is determined by the balance between the dynamic pressure 11 of the water flow that tries to push the flow toward the inner peripheral side and the centrifugal force 12 caused by the rotation of the runner 4 that pushes the flow toward the outer peripheral side. Therefore, at the operating point where the amount of water is smaller than the design point (the point where the power generation efficiency is to be maximized), as shown in FIG. 31 (b), the centrifugal force 12 becomes relatively large and the flow is biased toward the outer peripheral side. Compared to the design point shown in FIG. 31 (a), a wide dead water region 13 is formed, and at an operating point where the amount of water is larger than the design point (a point where power generation efficiency is to be maximized), as shown in FIG. 31 (c), The centrifugal force 12 becomes relatively small, the flow is biased toward the inner periphery, and a dead water region 13 is formed on the outer periphery.

The above-described flow deviation is called a secondary flow, and is a main cause of hydraulic loss occurring in the runner 4 at a non-design point. As a method of reducing the secondary flow at such a non-design point, as shown in FIG. 32, the inlet-side flow path between the crown 8 and the band 9 is shorter than the radial length of the crown 8 and the band 9. There has been proposed a method in which the rectifying blades 14 are protruded from the plurality of runner blades 10 substantially in parallel (for example, Patent Document 1). Further, as shown in FIG. 33, a method of providing an intermediate blade 15 having a blade length shorter than that of the runner blade between the runner blades 10 has been proposed (for example, Patent Document 2). Due to the rectifying effect of the rectifying blades 14 and the intermediate blades 15, the uneven flow in the meridian plane of the runner 4 is mitigated at the operation point where the water amount is smaller than the design point and the operation point where the water amount is larger than the design point. Can be reduced.
JP-A-8-296544 JP-A-57-126666

  However, in the above-described Francis type runner, in the design point flow where the secondary flow is weak, the rectifying effect by the rectifying blades 14 and the intermediate blades 15 is small, and the rectifying blades 14 and the intermediate blades 15 act strongly as frictional resistance. For this reason, the secondary flow loss at the non-design point is reduced, but the problem is that the friction loss at the design point increases.

  The present invention has been made to solve the above-described problem, and a Francis-type runner and hydraulic machine that suppress the occurrence of hydraulic loss at non-design points caused by the secondary flow without increasing the friction loss at the design points. The purpose is to provide.

The first invention of the present application is:
A Francis-type runner in which a plurality of runner blades are provided in a circumferential direction between a crown fixed to a rotating shaft and a ring-shaped band ,
Band side edge line of the trailing edge of the runner blade in a meridional section is located upstream of the line standing vertically against the inner surface of the bands Te to intersection with the edge line and the band, and the downstream in full Ranshisu shaped runners that have been formed in the concave shape toward,
The intersection point between the edge line of the runner blade trailing edge and the band at P1b and P1b is perpendicular to the inner surface of the band, and the intersection point of the edge line of the runner blade trailing edge is between P2b and P1b and P2b. LLb a straight line is formed, the maximum value of the distance between the edge line of a straight line LLb and La runner blade trailing edge When sb to,
0 <sb / LLb <0.15
It is characterized by satisfying.

Also, the second invention is
A Francis-type runner in which a plurality of runner blades are provided in a circumferential direction between a crown fixed to a rotating shaft and a ring-shaped band ,
Crown side edge line of the trailing edge of the runner blade in a meridional section is located upstream of the line standing vertically against the inner surface of the click round Te at the intersection between the edge line and click round, and on the downstream side in full Ranshisu shaped runners that have been formed in the concave shape toward,
Said runner blade trailing edge of the edge line and the intersection of P 1c and click round, the intersection of P 2c of the edge line of the lines and the runner blade trailing edge standing vertically against the inner surface of the click round Te in P 1c, P 1c and P2c a line formed between the LLc, when the sc maximum value of the distance between the edge line of the straight line L Lc and runner blade trailing edge,
0 <sc / LLc <0.15
It is characterized by satisfying.

  With the above configuration, the secondary flow in the meridian plane at the operation point having a larger water amount than the design point or the operation point having a smaller water amount than the design point is effectively reduced without increasing the friction loss at the design point, and the secondary flow. It is possible to suppress the occurrence of hydraulic loss at non-design points due to the above.

Embodiments and reference examples of Francis runners according to the present invention will be described below with reference to the drawings.

(First embodiment)
First, FIG. 1 shows a meridional section of the Francis-type turbine runner according to the first embodiment. The turbine runner is formed of a crown 8, a band 9, and a runner blade 10. In the first embodiment , as shown in FIG. 1, the band-side shape of the edge line 10 a at the trailing edge of the runner blade 10 in the meridional section is changed to the band 9 at the intersection P <b> 1 b between the edge line 10 a and the band 9. On the other hand, it is characterized in that it is on the upstream side of the vertically standing line 16 and is formed in a concave shape toward the downstream side.

In the first embodiment configured as described above, the static pressure suddenly recovers at the stagnation point 17 formed in the vicinity of the trailing edge of the runner blade, and the static pressure value increases. As shown in FIG. In the region near the band side of the runner blade outlet, a pressure gradient 18 is formed in which the pressure decreases from the inner peripheral side to the outer peripheral side. Since this pressure gradient acts to press the band side flow at the blade outlet portion toward the outer peripheral side, that is, the band side, the size of the outer dead water region 13 generated at the operating point where the amount of water is larger than the design point is reduced. Therefore, according to the first embodiment , as shown in FIG. 3, the secondary flow in the meridian plane at the operation point where the water amount is larger than the design point is reduced, and the generation of hydraulic loss can be suppressed.

In order to effectively function the invention according to the first embodiment , as shown in FIG. 4, the intersection of the edge line 10 a of the trailing edge of the runner blade and the band 9 on the meridian plane including the axis of the rotation axis is set. The intersection of the line 16 standing perpendicular to the band 9 at P1b and P1b and the edge line 10a of the trailing edge of the runner blade is P2b, and the length of the straight line Lb formed between P1b and P2b is LLb. When the maximum value of the distance between Lb and the edge line 10a at the trailing edge of the runner blade is sb, the value of sb / LLb needs to be made appropriate. That is, as the value of sb / LLb is larger than 0, the force 18 that presses the band-side meridional flow toward the outer peripheral side becomes stronger, but as shown in FIG. On the contrary, the force 19 for pressing the meridional surface flow toward the inner peripheral side also becomes stronger. For this reason, if the value of sb / LLb is extremely increased, the flow is separated 20 near the center of the blade, and the secondary flow loss is increased. FIG. 6 shows the relationship between sb / LLb and secondary flow loss calculated by flow analysis. From this figure, it can be seen that the secondary flow loss in the runner can be reduced in the region of 0 <sb / LLb <0.15. Therefore, in the first embodiment ,
0 <sb / LLb <0.15
By limiting the numerical values, the secondary flow in the meridian plane at the operating point where the amount of water is larger than the design point is effectively reduced, and the generation of hydraulic loss can be suppressed.

(Second Embodiment)
Next, a second embodiment of the Francis-type runner according to the present invention will be described with reference to FIGS. In addition, the same code | symbol is attached | subjected to the structure same as 1st Embodiment, and the overlapping description is abbreviate | omitted.

FIG. 7 shows a meridional section of the Francis turbine runner according to the second embodiment of the present invention. As shown in FIG. 7, the second embodiment is different from the conventional turbine runner in that the crown side shape of the edge line 10 a of the trailing edge of the runner blade in the meridional section is the same as the edge line 10 a and the inner surface of the crown 8. That is, the edge line 10a is formed in a concavely curved shape toward the downstream side with respect to the line 21 standing perpendicular to the crown 8 at the intersection P1c.

In the second embodiment configured as described above, the static pressure suddenly recovers at the stagnation point 17 formed in the vicinity of the trailing edge of the runner blade, and the static pressure value increases. As shown in FIG. In the region near the runner blade outlet crown side, a pressure gradient 19 is formed in which the pressure decreases from the outer peripheral side to the inner peripheral side. Since this pressure gradient acts so as to press the crown side flow at the blade outlet portion toward the inner peripheral side, the size of the dead water region 13 on the inner peripheral side generated at the operating point where the amount of water is smaller than the design point is reduced. Therefore, according to the second embodiment , the secondary flow in the meridional plane of the operation point having a smaller amount of water than the design point can be reduced and the generation of hydraulic loss can be suppressed. As shown in FIG. It is possible to improve hydraulic efficiency at an operation point with a smaller amount of water.

In order to make the invention according to the second embodiment function effectively, as shown in FIG. 10, the intersection of the trailing edge line 10a of the runner blade and the crown 8 on the meridian plane is represented by P1c and P1c. The intersection of the line 21 standing perpendicular to the inner surface of the crown 8 and the edge line 10a of the trailing edge of the runner blade is P2c, the length of the straight line Lc formed between P1c and P2c is LLc, the straight line Lc and the runner When sc is the maximum value of the distance from the trailing edge 10a of the blade, the value of sc / LLc needs to be made appropriate. That is, as the value of sc / LLc is larger than 0, the force 19 that pushes the meridional flow on the crown side toward the inner peripheral side becomes stronger. However, as shown in FIG. On the contrary, the force 18 that presses the meridional surface flow toward the outer peripheral side also increases. For this reason, when the value of sc / LLc is extremely increased, the flow is separated 20 near the center of the blade, and the secondary flow loss is increased. FIG. 12 shows the relationship between sc / LLc and secondary flow loss calculated by flow analysis. From this figure, it can be seen that the secondary flow loss in the runner can be reduced in the region of 0 <sc / LLc <0.15. Therefore, in the second embodiment ,
0 <sc / LLc <0.15
By limiting the numerical values, the secondary flow in the meridian plane at the operating point having a smaller amount of water than the design point is effectively reduced, and the generation of hydraulic loss can be suppressed.

( First Reference Example )
FIG. 13 shows a meridional section of the Francis turbine runner of the first reference example of the present invention. As shown in FIG. 13, the first reference example is different from the conventional turbine runner in that the crown side shape of the edge line 10 a of the trailing edge of the runner blade 10 in the meridional section is the inner surface of the edge line 10 a and the crown 8. The band-side shape of the edge line 10a of the trailing edge of the runner blade 10 in the meridional section is the band-side shape of the edge line 10a and the band. 9 is located on the upstream side of the line 16 standing perpendicular to the band at the intersection Pb, and the edge line 10a is formed in a concave shape in the downstream direction.

The first reference example is a combination of the first and second embodiments. Therefore, due to the synergistic effect of the two, the secondary flow in the runner at the non-design point can be reduced and the generation of hydraulic power loss can be suppressed. As shown in FIG. The hydraulic efficiency at a point can be improved.

In order to make the invention according to the first reference example function effectively, as shown in FIG. 15, the intersection of the trailing edge line 10a of the runner blade and the band 10 on the meridian plane is Pb, The length of the straight line L formed between the intersections Pc, Pb and Pc of the trailing edge 10a and the crown 8 is LL, and the maximum value of the distance between the straight line L and the trailing edge 10a of the runner blades. When s is s, it is necessary to make the value of s / LL appropriate. That is, as the value of s / LL is larger than 0, the force 19 for pressing the crown-side meridian flow toward the inner peripheral side and the force 18 for pressing the band-side meridian flow toward the outer peripheral side become stronger. However, as shown in FIG. 16, when the value of s / LL is extremely increased, the flow is separated 20 near the center of the blade, and the secondary flow loss is increased. FIG. 17 shows the relationship between s / LL and secondary flow loss calculated by flow analysis. From this figure, it is understood that the secondary flow loss in the runner can be reduced in the region of 0 <s / LL <0.15.

Therefore, in this first reference example
0 <s / LL <0.15
By limiting the numerical values, the secondary flow in the meridian plane at the non-design point can be more effectively reduced, and the generation of hydraulic loss can be suppressed.

( Second reference example )
Next, a second reference example of the Francis-type runner according to the present invention will be described with reference to FIGS. In addition, the same code | symbol is attached | subjected to the structure same as 1st and 2nd embodiment and a 1st reference example, and the overlapping description is abbreviate | omitted.

FIG. 18 shows a meridional section of the Francis turbine runner of the second reference example . As shown in FIG. 18, the second reference example is different from the conventional turbine runner in that a fillet 22 extending downstream is attached to the band root portion of the edge line 10a of the trailing edge of the runner blade 10 in the meridional section. It is being done.

In the second reference example configured as described above, the static pressure suddenly recovers at the stagnation point 17 formed in the vicinity of the trailing edge of the runner blade and the static pressure value increases. Similarly, as shown in FIG. 19, a pressure gradient 18 in which the pressure decreases from the inner peripheral side to the outer peripheral side is formed in the region near the runner blade outlet band side. And since this pressure gradient acts so as to press the band side flow at the blade outlet part to the outer peripheral side, the size of the dead water region 13 on the outer peripheral side generated at the operating point where the amount of water is larger than the design point is reduced. Therefore, according to the second reference example , since the secondary flow in the meridional plane at the operating point where the amount of water is larger than the design point is reduced, it is possible to suppress the occurrence of hydraulic loss, as shown in FIG. It is possible to improve the hydraulic efficiency at the operation point where the amount of water is larger than the design point.

In order to effectively function the second reference example , as shown in FIG. 21, the intersection of the runner blade trailing edge 10a and the band 9 on the meridian plane is Pb, and the runner blade trailing edge is When the intersection of the edge line 10a and the inner surface of the crown 8 is Pc, the length of the straight line formed between Pb and Pc is LL, and the radius of curvature of the fillet 22 at the band root portion is Rb, Rb / LL The value needs to be appropriate. That is, as the value of Rb / LL is larger than 0, the force 18 that presses the flow in the meridional surface on the band side toward the outer peripheral side becomes stronger. However, if the value of Rb / LL is extremely small, the force 18 that presses the band-side meridian plane flow toward the outer peripheral side is weak, and a clear effect of reducing the secondary flow loss does not appear. Also, if the value of Rb / LL is extremely increased, this action will affect the entire meridional flow path, and it will act to push the meridional flow on the crown side to the outer peripheral side. Although the secondary flow loss at the operating point with a large amount of water decreases, the secondary flow loss at the operating point with a smaller amount of water than the design point increases. FIG. 22 shows the relationship between Rb / LL and secondary flow loss at each operating point calculated by flow analysis. From this figure, in the region of 0.05 <Rb / LL <0.3, there is no increase in the secondary flow loss at the operation point having a smaller water amount than the design point, and the secondary flow at the operation point having a larger water amount than the design point. It can be seen that the loss can be reduced. Therefore, in this second reference example ,
0.05 <Rb / LL <0.3
By limiting the numerical values, the secondary flow in the meridian plane at the operating point where the amount of water is larger than the design point is effectively reduced, and the generation of hydraulic loss can be suppressed.

( Third reference example )
Next, a third reference example of the Francis runner according to the present invention will be described with reference to FIGS. In addition, the same code | symbol is attached | subjected to the structure same as 1st and 2nd embodiment and 1st and 2nd reference example, and the overlapping description is abbreviate | omitted.

FIG. 23 shows a meridional section of the Francis turbine runner of the third reference example . As shown in FIG. 23, the third reference example is different from the conventional turbine runner in that a fillet 23 extending downstream is attached to the crown root portion of the edge line 10a of the trailing edge of the runner blade 10 in the meridional section. That is.

In the third reference example configured as described above, the static pressure suddenly recovers at the stagnation point 17 formed in the vicinity of the trailing edge of the runner blade, and the static pressure value increases. Similarly, as shown in FIG. 24, a pressure gradient 19 in which the pressure decreases from the outer peripheral side to the inner peripheral side is formed in the region near the runner blade outlet crown side. And since this pressure gradient acts so as to press the crown side flow at the blade outlet part toward the inner peripheral side, the size of the dead water region 13 on the inner peripheral side generated at the operating point where the amount of water is smaller than the design point is reduced. . Therefore, according to the third reference example , since the secondary flow in the meridian plane at the operation point having a smaller water amount than the design point is reduced, the occurrence of hydraulic loss can be suppressed, and as shown in FIG. It is possible to improve the hydraulic efficiency at the operation point where the amount of water is smaller than the design point.

In order to make this third reference example function effectively, as shown in FIG. 26, the intersection of the edge line 10a of the trailing edge of the runner blade 10 and the band 9 on the meridian plane is Pb, and the trailing edge of the runner blade Value of Rc / LL, where Pc is the intersection of the edge line 10a and the crown 8, and LL is the length of the straight line formed between Pb and Pc, and Rc is the radius of curvature of the fillet 23 at the root of the crown. It is necessary to make it appropriate. That is, as the value of Rc / LL is larger than 0, the force 19 for pressing the crown side meridional flow toward the inner peripheral side becomes stronger. However, if the value of Rc / LL is extremely small, the force 19 for pressing the crown side meridional flow toward the inner peripheral side is weak, and a clear effect of reducing the secondary flow loss does not appear. Also, if the value of Rc / LL is extremely increased, this action will affect the entire meridional flow path, and the band side meridian flow will also be pushed to the inner circumference side. Although the secondary flow loss at the operation point with a smaller water amount decreases, the secondary flow loss at the operation point with a larger water amount than the design point increases. FIG. 27 shows the relationship between Rc / LL and secondary flow loss at each operating point calculated by flow analysis. From this figure, in the region of 0.05 <Rc / LL <0.3, there is no increase in the secondary flow loss at the operation point having a larger water volume than the design point, and the secondary flow at the operation point having a smaller water volume than the design point. It can be seen that the loss can be reduced. Therefore, in this third reference example
0.05 <Rc / LL <0.3
By limiting the numerical values, the secondary flow in the meridian plane at the operating point having a smaller amount of water than the design point is effectively reduced, and the generation of hydraulic loss can be suppressed.

( 4th reference example )
Next, a fourth reference example of the Francis runner according to the present invention will be described with reference to FIG. In addition, the same code | symbol is attached | subjected to the structure same as 1st and 2nd embodiment and the 1st thru | or 3rd reference example, and the overlapping description is abbreviate | omitted.

FIG. 28 shows a meridional section of the Francis turbine runner of the fourth reference example . The fourth reference example is different from the conventional turbine runner as shown in FIG. 28. The meridian cross section extends downstream from the crown root portion and the band root portion of the edge line 10a of the trailing edge of the runner blade 10 in the meridian section. At the same time, the fillets 23 and 22 formed in a concave shape toward the downstream side are attached.

The fourth reference example is a combination of the second and third reference examples . Therefore, due to the synergistic effect of the two, the secondary flow in the runner at the non-design point can be more effectively reduced and the generation of hydraulic power loss can be suppressed. As shown in FIG. The hydraulic efficiency at the point and the large design point can be improved.

The meridional sectional view of the Francis type turbine runner according to the first embodiment of the present invention. The internal flow schematic diagram of the Francis type turbine runner of a 1st embodiment. The figure which shows the change of the hydraulic efficiency in 1st Embodiment. Explanatory drawing of each part dimension in 1st Embodiment. The internal flow schematic diagram of the Francis type turbine runner of a 1st embodiment. The sb / LLb and secondary flow loss correlation diagram of the Francis type turbine runner of a 1st embodiment. The meridional sectional view of the Francis type turbine runner of the second embodiment. The internal flow schematic diagram of the Francis type turbine runner of a 2nd embodiment. The figure which shows the change of the hydraulic efficiency in 2nd Embodiment. Explanatory drawing of each part dimension in 2nd Embodiment. The internal flow schematic diagram of the Francis type turbine runner of a 2nd embodiment. The sc / LLc of a Francis type turbine runner of a 2nd embodiment, and a secondary flow loss correlation diagram. The meridional sectional view of the Francis type turbine runner of the first reference example . The figure which shows the change of the hydraulic efficiency in a 1st reference example . Explanatory drawing of the dimension of each part in a 1st reference example . The internal flow schematic diagram of the Francis type turbine runner of the 1st reference example . The s / LL and secondary flow loss correlation diagram of the Francis type turbine runner of the first reference example . The meridional sectional view of the Francis type turbine runner of the second reference example . The internal flow schematic diagram of the Francis type turbine runner of the 2nd reference example . The figure which shows the change of the hydraulic efficiency in a 2nd reference example . Explanatory drawing of each part dimension in a 2nd reference example . The Rb / LL and secondary flow loss correlation diagram of the Francis type turbine runner of the second reference example . The meridional sectional view of the Francis type turbine runner of the third reference example . The internal flow schematic diagram of the Francis type turbine runner of the 3rd reference example . The figure which shows the change of the hydraulic efficiency in a 3rd reference example . Explanatory drawing of each part dimension in a 3rd reference example . The Rc / LL and secondary flow loss correlation diagram of the Francis type turbine runner of the third reference example . The meridional sectional view of the Francis type turbine runner of the fourth reference example . The figure which shows the change of the hydraulic efficiency in a 4th reference example . The longitudinal cross-sectional view of the hydroelectric power plant in which the conventional Francis type turbine runner was installed. (A), (b), (c) is a schematic view of the flow in the meridional plane in the runner due to the difference in water amount. The figure which shows the conventional secondary flow reduction technique. The figure which shows the conventional secondary flow reduction technique.

DESCRIPTION OF SYMBOLS 1 Casing 3 Guide vane 4 Runner 5 Suction pipe 8 Crown 9 Band 10 Blade 10a Blade trailing edge edge line 13 Dead water area 16 Line standing perpendicular to the band surface 17 Stagnation point area 18 where static pressure recovers rapidly 18 Pressure gradient The fluid force 19 acting on the outer peripheral side by the fluid force 21 acting on the inner peripheral side due to the pressure gradient The line 22 standing perpendicular to the crown surface 22 Fillet

Claims (3)

A Francis-type runner in which a plurality of runner blades are provided in a circumferential direction between a crown fixed to a rotating shaft and a ring-shaped band ,
Band side edge line of the trailing edge of the runner blade in a meridional section is located upstream of the line standing vertically against the inner surface of the bands Te to intersection with the edge line and the band, and the downstream in full Ranshisu shaped runners that have been formed in the concave shape toward,
The intersection point between the edge line of the runner blade trailing edge and the band at P1b and P1b is perpendicular to the inner surface of the band, and the intersection point of the edge line of the runner blade trailing edge is between P2b and P1b and P2b. LLb a straight line is formed, the maximum value of the distance between the edge line of a straight line LLb and La runner blade trailing edge When sb to,
0 <sb / LLb <0.15
Off Ranshisu shaped runner you and satisfies the. A Francis-type runner in which a plurality of runner blades are provided in a circumferential direction between a crown fixed to a rotating shaft and a ring-shaped band ,
Crown side edge line of the trailing edge of the runner blade in a meridional section is located upstream of the line standing vertically against the inner surface of the click round Te at the intersection between the edge line and click round, and on the downstream side in full Ranshisu shaped runners that have been formed in the concave shape toward,
Said runner blade trailing edge of the edge line and the intersection of P 1c and click round, the intersection of P 2c of the edge line of the lines and the runner blade trailing edge standing vertically against the inner surface of the click round Te in P 1c, P 1c and P2c a line formed between the LLc, when the sc maximum value of the distance between the edge line of the straight line L Lc and runner blade trailing edge,
0 <sc / LLc <0.15
Off Ranshisu shaped runner you and satisfies the. Hydraulic machine with a Francis runner according to claim 1 or 2.

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