Numerical simulation of Fluid-Structure Interaction in high head Francis turbines

Abstract

Renewable energy sources are becoming an integral part of the global energy mix. As hydropower can be used to stabilize the new energy market, this calls for increased demands from Francis turbines. Accurate calculation of the dynamic loads, as well as estimation of the deflection and stresses in the turbine materials, is essential for safe and reliable operation of modern turbines. The primary objective of this work has been to investigate the phenomenon of resonance in Francis turbines. A procedure for numerically simulating this is presented, a three-step procedure consisting of calculating a fluid pressure, a damping ratio, and finally performing a coupled structural-acoustic simulation. The pressure in the runner channel is shown to be the sum of the viscous and acoustic pressure contributions, and this corresponds well with experiments. Included in structural- acoustic simulations is the effect of added mass. This effect will lower the natural frequency of the turbine runner from the frequency of freevibration in a vacuum. Added mass is crucial to include, as one of the critical points in a design process is to ensure that the load frequency is not equal to the natural frequency of the runner. Obtaining accurate viscous load from CFD was shown to be straightforward. Both full turbine models and reduced geometry models predicted pressure fluctuations within a couple of percent of experimental results. The damping ratio can be obtained by a modal work approach, a one-way CFD simulation using the mode shape and frequency of the structure as input. On a simplified blade cascade this was shown to be a very successful procedure, and easy to apply to turbine-like structures as well. Another interesting finding was a nearly linear relationship between the damping and a reduced velocity parameter. This relation could be used as a rough estimate for damping if CFD analysis is not performed. As the computational expense of performing accurate fluid and mechanical simulations are high, several model order reduction procedures have been tested. Depending on the physical domain, and solver method, different methods are used. In fluid simulations, it is seen that the most efficient way of reducing simulation time is to solve in the frequency domain. These methods are under development; however, there exist similar strategies today that can be used to reduce the geometrical domain as well. In the structural domain, the goal is to reduce the coefficient matrices in the governing second order equations. This is done in two different ways, using a modal decomposition method, and Krylov vectors as vector space. The modal decomposition method provides a way of solving a quasi-two-way coupled fluid-structure simulation. Here an interesting added stiffness effect was observed when the flow across a hydrofoil was increased. The Krylov vector approach was shown to provide almost identical results as solving the full structural model.