Study On Cavitating Flows In Draft Tube Of A Francis Turbine

The vortex ropes in draft tube of Francis turbines will cause pressure pulsation and vibration, which will threaten the safety and stability of hydroturbines. Aiming at those problems, two types of cavitation vortex ropes and their correlation with the whole hydraulic system in a Francis turbine is deeply studied in this paper.Firstly, the simulation methods of cavitation simulation were compared in the simulation of a three dimensional hydrofoil. The standard RNG κ-εand LES turbulence model with the two transport equation models (Singhal full cavitation model and Zwart-Gerber-Belamri cavitation model) based on the homogeneous flow assumption had been used. The results showed that the detailed cavitation shedding characteristics like small vortex shedding are captured only by using LES turbulence model with Zwart-Gerber-Belamri cavitation model.Then the two types of vortex rope conditions in Francis turbine were simulated using verified cavitation flow computational method. The detailed vortex rope structures under these two conditions were obtained. The volume fluctuations of vortex rope will increase with the cavitation number decreases. The maximam peak to peak value of pressure pulsations occurs between the inception and critical conditions. Under swirl vortex rope conditions, the pressure pulsation aroused by swirl vortex rope have obviously phase shift. However, the pressure pulsations in axisymmetric rope conditions have no phase shift. Because the diameter of the vortex rope is related to the draft tube inlet velocity, the relationships of vortex rope with flow rate were analyzed. The diameter of vortex rope will decrease with the flowrate in swirl vortex rope conditions. To the contrary, the axisymmetrie rope diameter will increase with the flowrate.The influences of cavitation vortex on the turbine hydraulic loss were studied. When cavitation occurs, the volume fluctuations of vortex rope appears within the tube, so the greatest losses change is the draft tube for both of the two types conditions. With the decrease of cavitation number, the loss increase further. In addition, the influences of pressure fluctuation induced by vortex rope on the runner cavitaion were also analyzed. The uneven flow field caused by spiral vortex led to the asymmetric of cavitation development inside runner, which is different under axisymmetric rope conditions.The wave speed and response of the entire hydraulic system will change in the mixture flow of vapor and liquid. It is necessary to consider the cavitation effect on the whole hydraulic system analysis. Cavitation compliance and mass flow gain factor, which reflect the main characteristics of vortex rope, were injected to the transient computation. In this paper, the relationships of cavitaion number with cavitation compliance and mass flow gain factor were computed through the two phase cavitation results. And the equivalent compliance were obtaind by comprehensive consideration the water and vortex rope compliance. Finally, the wave speed was computed based on the equivalent compliance and the results agree well with experience formula’s results. The above research results provide a quantitative reference for the hydraulic system stability considering the influence of cavitation.