Effects of Different Speed-Change Modes on Flow Stability and Pressure Pulsation During Variable-Speed Transients in a Francis Turbine

To improve the transient operating stability of Francis turbines under flexible regulation conditions, this study investigates the effects of different speed-change modes on the internal flow structure and pressure pulsation characteristics of a high-head Francis-99 model turbine during variable-speed transients. Three representative acceleration strategies, namely linear, quartic, and fourth-root speed-change modes, are designed. In all cases, the rotational speed increases from 333 r/min to 346.2 r/min within 4 s, corresponding to a speed increase of approximately 3.96%, thereby eliminating the influence of differences in speed-change amplitude and duration on the flow response. During this process, the main frequency induced by runner blade passing at the guide vane outlet increases from approximately 166.5 Hz to 173.1 Hz, while the main frequency induced by guide vane passing at the runner inlet increases from approximately 155.4 Hz to 161.6 Hz. Comparative analyses of the pressure distribution in the runner and guide vane regions, runner streamline evolution, time-domain pressure pulsation, and time–frequency characteristics obtained using the Hilbert–Huang transform show that the temporal distribution of the speed-change rate significantly affects pressure-field uniformity, flow-separation development, and spectral-energy distribution. The linear speed-change mode produces a continuous and relatively predictable migration of pressure and frequency. The quartic mode, characterized by a “slow-first and fast-later” strategy, delays the development of initial disturbances, yields a more balanced pressure-gradient distribution and more localized flow separation, and produces a more concentrated time–frequency energy distribution with shorter-lasting high-frequency pulsation regions. By contrast, the fourth-root mode induces excessive initial acceleration, leading to a polarized pressure distribution with high pressure at the inlet and low pressure at the outlet, large-scale separation vortices, persistent low-frequency modes, and nonlinear frequency coupling. The results indicate that, while satisfying rapid power-response requirements, avoiding excessive acceleration at the initial stage and adopting nonlinear acceleration strategies with an initial-buffering feature are effective approaches for improving the stability of variable-speed turbine transients.