Abstract: A startup method of a Francis turbine according to an embodiment includes: a bypass-valve opening step of opening the bypass valve with the inlet valve closed; an inlet-valve opening step of opening the inlet valve after the bypass-valve opening step; and a first rotation-speed increasing step of increasing a rotation speed of the runner by opening the guide vane at an opening that is 50% or more of a maximum opening before a flow velocity of a swirling flow flowing around the runner reaches 90 m/sec.

Abstract: A stress estimation method for a machine structure according to an embodiment is provided with a calculation step of calculating a relationship between the stress generated at the evaluation target position and a physical quantity including a sound pressure or vibration generated at a detection position different from the evaluation target position during vibration of the machine structure. The stress estimation method for a machine structure is provided with a detection step of detecting the physical quantity generated at the detection position during operation of the machine structure. The stress estimation method for a machine structure is provided with an estimation step of estimating the stress generated at the evaluation target position during operation of the machine structure on the basis of the relationship calculated in the calculation step and the physical quantity detected in the detection step.

Abstract: According to an embodiment, the vane 13 has a thick root portion 16P formed on the band 12 side of a pressure surface to be joined to the band 12, with a thickness of the thick root portion 16P being gradually increased toward the band 12, and a thick root portion 16N formed on the band 12 side of a negative pressure surface to be joined to the band 12, with a thickness of the thick root portion 16N being gradually increased toward the band 12. The outlet end 15 has a first curved portion 151 and a second curved portion 152. An extreme point 15B forming a bottom end of the second curved portion 152 is positioned closer to the band 12 than an end of the thick root portion 16P, 16N on the crown 11 side.

Abstract: According to the embodiment, in a range from a plane P1 including a runner rotation center axis C and an end point 15E2 of an outlet end 15 of the vane 13, up to a plane P2 corresponding to a position where the plane P1 is moved by an angle, which is determined by dividing 360° by a value that is four times the number of vanes 13, in a runner rotation direction, when respective sections of the vane 13 are taken at a plane including the axis C and radially extending, in at least one section, a tangent T1 on a centerline Cv of the vane 13 passing through an intersection X at which the centerline Cv and a flowing water surface 12f intersect, and a tangent T2 on the flowing water surface 12f passing through the intersection X, define an acute angle on a negative pressure surface.

Abstract: A startup method of a Francis turbine according to an embodiment includes: a bypass-valve opening step of opening the bypass valve with the inlet valve closed; an inlet-valve opening step of opening the inlet valve after the bypass-valve opening step; and a first rotation-speed increasing step of increasing a rotation speed of the runner by opening the guide vane at an opening that is 50% or more of a maximum opening before a flow velocity of a swirling flow flowing around the runner reaches 90 m/sec.

Abstract: According to the embodiment, in a range from a plane P1 including a runner rotation center axis C and an end point 15E2 of an outlet end 15 of the vane 13, up to a plane P2 corresponding to a position where the plane P1 is moved by an angle, which is determined by dividing 360° by a value that is four times the number of vanes 13, in a runner rotation direction, when respective sections of the vane 13 are taken at a plane including the axis C and radially extending, in at least one section, a tangent T1 on a centerline Cv of the vane 13 passing through an intersection X at which the centerline Cv and a flowing water surface 12f intersect, and a tangent T2 on the flowing water surface 12f passing through the intersection X, define an acute angle on a negative pressure surface.

Abstract: According to an embodiment, the vane 13 has a thick root portion 16P formed on the band 12 side of a pressure surface to be joined to the band 12, with a thickness of the thick root portion 16P being gradually increased toward the band 12, and a thick root portion 16N formed on the band 12 side of a negative pressure surface to be joined to the band 12, with a thickness of the thick root portion 16N being gradually increased toward the band 12. The outlet end 15 has a first curved portion 151 and a second curved portion 152. An extreme point 15B forming a bottom end of the second curved portion 152 is positioned closer to the band 12 than an end of the thick root portion 16P, 16N on the crown 11 side.