Numerical analysis of flow-induced vibration of vanes in a giant Francis turbine

Francis turbines play a crucial role in converting hydropower into electricity, addressing concerns associated with traditional energy sources. Flow instabilities around stay and guide vanes contribute to turbine vibration and significantly reduce energy harvesting efficiency. This study utilizes a highly accurate spectral element method and fluid-structure interaction algorithm to investigate the physical mechanisms behind vortex-induced vibrational phenomena around the cascades of a high-head prototype Francis turbine. The results reveal that favorable pressure gradients occur on the suction side of the guide vanes and stretch incoming small-scale vortices into elongated vortical structures that cause high-amplitude low-frequency fluctuation (f <= 10 Hz). Conversely, adverse pressure gradients on the pressure side induce numerous stochastic flow separations and small-scale vortices, resulting in a wide range of low-amplitude high-frequency pulsations. Additionally, the guide vanes exhibit higher magnitudes and vibrational amplitudes of the force coefficients compared to the stay vanes. Due to the substantial pressure difference between the upstream and downstream of the guide vanes, the operating condition with the high head and small attack angle demonstrates the most robust vibrational characteristics. The likelihood of resonance occurring in both vane and vaneless space is reduced since the frequencies of force coefficients concentrate at f <= 40 Hz, which are lower than the cascade natural frequencies. However, vortex shedding at the trailing edge of the guide vanes with a wide range of deterministic and irregular frequencies contributes to the highest amplitude of pressure pulsation, reaching 0.17 with a frequency of 230 Hz, potentially inducing turbine resonance. The study provides an in-depth explanation of the hydrodynamic characteristics of the cascades and thoroughly explains the physical mechanisms behind vortex-induced vibration in Francis turbines.