The vortex rope usually occurs in the draft tube of the Francis turbine operated under part-load conditions, to induce strong low-frequency pressure vibrations, and therefore, is very harmful to the safety of the hydropower unit. In the present work, three kinds of strategies are extensively investigated, i.e., the installations of the ventilation and the fin, as well as the hybrid strategy of the air admission through a fin, so as to effectively suppress the vortex rope oscillation and the pressure vibration in the draft tube of a Francis turbine, whose specific speed is 125 m-kW. For the unsteady flow simulation, the Reynolds averaged Navier-Stokes (RANS) method is applied coupled with the k-ω SST turbulence model and a homogeneous cavitation model. The flow analysis confirms that the low-frequency pressure vibrations are originated from the periodical oscillation of the vortex rope, and the cavitation usually enhances the vortex rope oscillation in the draft tube. Under the part-load condition, the dominant component of the pressure vibration in the draft tube has a frequency, for example, f₁, lower than the runner rotating frequency f_n. It is shown that all three strategies can be adopted to alleviate the vortex rope oscillation and the pressure vibrations in the draft tube, but their suppression mechanisms are quite different. The ventilation of an adequate amount from the turbine runner cone can change the vortex rope geometry from the spiral type to the cylindrical type, suppress the vortex rope oscillation, and consequently create the homogeneous distributions of the pressure and the pressure gradient in the draft tube. On the other hand, a fin installed at the draft tube wall can induce a small extra rope, and the interaction between the main vortex rope and the extra rope changes the flow field and alleviates the pressure vibration in the draft tube. It should be noted that a fin is much more effective to suppress the pressure vibration in the draft tube under the cavitation condition than under the non-cavitation condition. A better effect of suppressing the vortex rope oscillation can be achieved by the air admission through a fin, which is studied numerically in this paper. The result indicates that the air admission can further improve the effect of a fin for suppressing the pressure vibration in the inlet cone of the draft tube. This improvement is due to the stronger interaction between the main vortex rope and the extra air rope. However, the air admission through a fin should be carefully treated because the strong interaction may induce a larger pressure vibration in the elbow of the draft tube. Finally, it is clear that any strategy for suppressing the pressure vibration hardly changes the dominant component frequency f₁, which is in the range of 0.22 f_n-0.23 f_n due to the main vortex rope oscillation in this study. The current results may be used in various engineering applications, where the active control of the vortex oscillation and the pressure vibrations with or without the cavitation is necessary.

涡流绳通常出现在部分负载条件下运行的混流式水轮机的引流管中，以引起强烈的低频压力振动，因此对水力发电机组的安全非常有害。在本工作中，对通风和散热片的安装以及通过散热片进气的混合策略等三种策略进行了广泛研究，以有效地抑制涡流绳的振荡和压力。混流式水轮机（比速为125 m-kW）的引流管中的振动。对于非定常流动模拟，将雷诺平均Navier-Stokes（RANS）方法与k-ω耦合应用SST湍流模型和均质空化模型。流动分析证实，低频压力振动是由涡流绳的周期性振动引起的，并且空化通常会增强引流管中涡流绳的振动。在部分负载条件下，引流管中压力振动的主要成分的频率（例如f ₁）低于流道旋转频率f _n。。结果表明，可以采用全部三种策略来减轻涡流绳的振荡和引流管中的压力振动，但是它们的抑制机理却大不相同。涡轮转轮锥体的足够通风可以将涡流绳的几何形状从螺旋形改变为圆柱形，抑制涡流绳的振荡，从而在引流管中产生均匀的压力分布和压力梯度分布。另一方面，安装在引流管壁​​上的散热片会引起一条小的附加绳索，并且主涡流绳索和附加绳索之间的相互作用改变了流场并减轻了引流管中的压力振动。应当注意，在空化条件下，翅片比在非空化条件下更有效地抑制引流管中的压力振动。通过翅片的进气可以更好地抑制涡流绳振荡，本文对此进行了数值研究。结果表明，进气可以进一步提高散热片抑制引流管入口锥体中的压力振动的效果。这种改进是由于主涡流绳和额外的空气绳之间的相互作用更强。但是，由于翅片的强相互作用可能会在引流管的弯头中引起较大的压力振动，因此应谨慎对待通过散热片的空气进入。最后，f ₁，由于本研究中的主要涡流绳振荡，在0.22 f _n -0.23 f _n的范围内。当前结果可用于各种工程应用中，其中需要对有或没有空化的情况下的涡流振荡和压力振动进行主动控制。