Francis-type turbine runner and francis-type turbine

A Francis-type turbine runner comprising a crown, a band, and a plurality of vanes provided between the crown and the band, wherein

• each of the vanes has a thick root portion formed on the band side of a pressure surface to be joined to the band, and a thick root portion formed on the band side of a negative pressure surface to be joined to the band, with a thickness of each thick root portion being gradually increased toward the band,
• in a range from a first plane including a runner rotation center axis and an end point of an outlet end of the vane on the band side, up to a second plane corresponding to a position where the first plane is rotated by an angle, which is determined by dividing 360° by a value that is four times the number of vanes, in a runner rotation direction about the runner rotation center axis, when respective sections of the vane are taken at a plane including the runner rotation center axis and radially extending from the runner rotation center axis, and when a curvilinear thick-root-portion centerline, which connects a plurality center of inscribed circles inscribed in the thick root portions on the pressure surface side and the negative pressure surface side, is drawn in each of the respective sections,
• in at least one section of the respective sections, a tangent on the thick-root-portion centerline, the tangent passing through an intersection at which the thick-root-portion centerline and a flowing water surface of the band intersect, and a tangent on the flowing water surface of the band, the tangent passing through the intersection, define an acute angle on the negative pressure surface side of the vane, and define an obtuse angle on the pressure surface side thereof.

A Francis-type turbine runner comprising a crown, a band, and a plurality of vanes provided between the crown and the band, wherein

• in a range from a line passing through an end point of an outlet end of the vane on the crown side and an end point of the outlet end in a runner rotation direction excluding the end point of the outlet end on the crown side, up to 5%, with respect to a vane length from the line up to an inlet end of the vane in a chord length direction,
• when respective sections of the vane are taken at a plane extending in a runner axial direction and including line passing through reference points at which a ratio of a distance from the end point of the outlet end on the crown side up to one reference point that is set on a crown side edge within the range up to 5%, with respect to a distance of the crown side edge of the vane, the distance of the crown side edge being from the end point of the outlet end on the crown side up to an end point of the inlet end on the crown side, and a ratio of a distance from a standard point up to the other reference point that is set on a band side edge within the range up to 5%, with respect to a distance of the band side edge of the vane, the distance of the band side edge being from the standard point, which is determined at a position where the line and a flowing water surface of the band intersect, up to an end point of the inlet end on the band side, are the same,
• in at least one section of the respective sections, a tangent on a centerline of the vane, the tangent passing through an intersection at which the curvilinearly continuous centerline of the vane and the flowing water surface of the band intersect, and a tangent on the flowing water surface of the band, the tangent passing through the intersection, define an acute angle on the negative pressure surface side of the vane, and define an obtuse angle on the pressure surface side thereof.

A Francis-type turbine runner comprising a crown, a band, and a plurality of vanes provided between the crown and the band, wherein

• each of the vanes has a thick root portion formed on the band side of a pressure surface to be joined to the band, and a thick root portion formed on the band side of a negative pressure surface to be joined to the band, with a thickness of each thick root portion being gradually increased toward the band,
• in a range from a line passing through an end point of an outlet end of the vane on the crown side and an end point of the outlet end in a runner rotation direction excluding the end point of the outlet end on the crown side, up to 5%, with respect to a vane length from the line up to an inlet end of the vane in a chord length direction,
• when respective sections of the vane are taken at a plane extending in a runner axial direction and including line passing through reference points at which a ratio of a distance from the end point of the outlet end on the crown side up to one reference point that is set on a crown side edge within the range up to 5%, with respect to a distance of the crown side edge of the vane, the distance of the crown side edge being from the end point of the outlet end on the crown side up to an end point of the inlet end on the crown side, and a ratio of a distance from a standard point up to the other reference point that is set on a band side edge within the range up to 5%, with respect to a distance of the band side edge of the vane, the distance of the band side edge being from the standard point, which is determined at a position where the line and a flowing water surface of the band intersect, up to an end point of the inlet end on the band side, are the same, and when a curvilinear thick-root-portion centerline, which connects a plurality center of inscribed circles inscribed in the thick root portions on the pressure surface side and the negative pressure surface side, is drawn in each of the respective sections,
• in at least one section of the respective sections, a tangent on the thick-root-portion centerline, the tangent passing through an intersection at which the thick-root-portion centerline and the flowing water surface of the band intersect, and a tangent on the flowing water surface of the band, the tangent passing through intersection, define an acute angle on the negative pressure surface side of the vane, and define an obtuse angle on the pressure surface side thereof.