Francis Turbine Runner Vane Outlet Strength
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Solution Overview
Problem
Conventional Francis-type turbine runners face insufficient strength at the joint portions between the outlet end and the band, particularly on the band side, which can lead to damage under sudden impacts due to inadequate thickness and stress concentration.
Innovation Solution
The design incorporates a thick root portion on the band side with gradually increasing thickness towards the band, a convex first curved portion, and a concave second curved portion connecting it to the band, with the extreme point of the second curved portion positioned closer to the band than the crown side, ensuring sufficient thickness to withstand bending moments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of energy
If the vane thickness is gradually decreased toward the outlet end to reduce energy loss, then energy loss is reduced, but the joint portion strength between the outlet end and the band becomes insufficient
Solution Approach 1:
The vane is designed with non-uniform thickness distribution, featuring a thick root portion at the band side that gradually decreases toward the crown side. This local quality variation allows the thick root portion to provide sufficient joint strength at the band connection while the thinner portions reduce overall material usage and energy loss.
Solution Approach 2:
The outlet end incorporates curved portions with specific radii of curvature. The first curved portion has a radius R1 and the second curved portion has a radius R2, where R1 > R2. These curved transitions prevent stress concentration at sharp corners while maintaining the thickness gradient, thus preserving joint strength without increasing energy loss.
2Loss of energy
If the vane thickness is reduced at the outlet end to minimize loss, then loss is minimized, but the resistance to sudden impact on the band side becomes insufficient
Solution Approach 1:
The thick root portion is specifically positioned at the band side of the outlet end, providing localized reinforcement exactly where sudden impacts are most likely to occur. This targeted thickness distribution enhances impact resistance without requiring uniform thickness increase throughout the vane.
Solution Approach 2:
The curved portions at the outlet end, particularly the second curved portion connecting to the band, provide smooth stress transitions that prevent stress concentration during sudden impacts. The specific radius relationship (R1 > R2) ensures that the curvature geometry distributes impact forces effectively while maintaining minimal overall thickness.
Data Source
AI summary
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.