Hydraulic instability in Francis turbines: A case study on wide operation of 175 MW prototype

Francis turbine has been operated across a wide range of load conditions to regulate renewable energy, hydraulic instability arising from off-design operation remains a central concern. This study employs numerical methods to examine the internal flow characteristics of a Francis turbine under various operating conditions, focusing on three main aspects: i) hydrodynamic characteristics, ii) flow distribution, and iii) pressure pulsations. Results indicate that the horseshoe vortex within stay vane enlarges with increasing load from the rated power (Pr) of 10% to 100% Pr, exerting a stronger stagnation effect on the flow entering the guide vane region. The formation of a columnar vortex structure within the runner is responsible for the drastic drop in efficiency from 0.94 to 0.72 when operation falls below 30% Pr. The primary challenge to stable operation remains pressure oscillation within the runner induced by the stator-rotor interaction at 14 f/fn. e.g., a maximum pressure amplitude coefficient Cp of 19.50% at 10% Pr, followed by a notable value of 13.91% at 20% Pr. Furthermore, at higher loads (40% ¾ 50% Pr), radial force rises significantly, increasing by 401% at 40% Pr compared with 100% Pr, while pressure pulsation shifts to a low frequency (0.22 f/fn), caused by draft tube vortex. In accordance with the operating criteria of the prototype Francis turbine, a feasible operating range of 70% ¾ 100% Pr can only be maintained by evaluating the pressure pulsation peak coefficient (Cpe).