Precessing vortex rope (PVR) plays a key role in inducing hydraulic resonance in Francis turbines operating at partial load, possibly degrading power plant stability and availability. Air injection into the runner cone is a suitable mitigating alternative; however, the influence mechanism of air injection on PVR remains unclear. The principal objective of this study was to establish response relationships between the characteristic parameters and air injection by the method of computational fluid dynamics (CFD) considering the fluid components of water, water vapour and air. The findings show that cavitation flow can be completely suppressed by slight air injection; however, the helical vortex structures are persisted at 1.0% and 2.0% air volume fractions, and the static pressure recovery is improved together with a slight increase in the hydraulic loss. At 3.0% air volume fraction, the vortex structure completely disappears, leaving an umbrella-shaped structure, with no pressure vibration arising in the turbine. Moreover, the physical mechanism of reducing the pressure amplitudes is clarified. This results clarify the influence mechanism of air injection on PVR, and contribute to steadily extending the flexibility of the operating range of the turbine during the engineering application.

进动涡流绳 (PVR) 在引起部分负荷运行的混流式水轮机的水力共振方面起着关键作用，这可能会降低发电厂的稳定性和可用性。将空气注入流道锥体是一种合适的缓解方案；然而，空气注入对PVR的影响机制仍不清楚。本研究的主要目的是通过计算流体动力学 (CFD) 方法考虑水、水蒸气和空气的流体成分，建立特征参数与空气注入之间的响应关系。研究结果表明，通过轻微的空气注入可以完全抑制空化流；然而，螺旋涡结构持续存在于 1.0% 和 2.0% 的空气体积分数，静压恢复得到改善，水力损失略有增加。在空气体积分数为3.0%时，涡结构完全消失，留下伞状结构，涡轮内不产生压力振动。此外，阐明了降低压力幅度的物理机制。该结果阐明了注气对PVR的影响机理，有助于在工程应用中稳步扩展涡轮运行范围的灵活性。