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-co 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 fn.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 fn-0.23 fn 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.