Comparison of Francis Runner’s Dry/Wet Modes Analyses Results Using Full and Cyclic Symmetry Model

In order to explore the resonance conditions of the Francis runner due to the rotor-stator interaction between the runner and the guide vane, modal analyses in air or water are required mainly. However, it is substantially challenging to analyze the resonance conditions at a specific nodal diameter using the full model with an arbitrary number of bolt holes and balance holes. Hence, dry/wet mode analyses were performed based on the cyclic symmetry model without a bolt hole and with a balance hole, which is not real. The changes in the natural frequencies of the primary resonance modes due to the shape change were analyzed. In the dry mode, the difference is only within 0.9% at most, but in the wet mode, the difference is up to 6.37%. The absence of a bolt hole increases the stiffness, but a balance hole in each cyclic symmetry model decreases the stiffness. Despite their conflict with each other, the change in the dry mode does not occur significantly. However, in the wet mode, it is judged that the added mass effects are increased by increasing the balance holes more than in reality, which increases the change in natural frequencies compared to the cases of dry modes. Therefore, this change should be compensated for when analyzing the resonance conditions of the wet mode using a cyclic symmetry model with a different number of bolt holes and balance holes.