Numerical Investigation Of Cavitating Vortex Rope Behavior In The Draft Tube Of A Francis Turbines With Splitter Blades At Off-design Conditions

In recent years in Vietnam,the need to renovate the existing hydropower stations to expand the safe operation rang of the turbine has been increasing.The Francis turbines with splitter blades runner getting more and more attention.Extending the operating range of the Francis turbine can ensure its safe and stable operation at off-design load.The flow in the draft tube of a Francis turbine operating at off-design conditions is characterized by severe flow instabilities and the appearance of a spiral/columnar vortex,which called the vortex rope.The understanding of the periodical precession of this vortex and the investigation of the vortex rope formation in the draft tube cone is necessary for preventing structural vibrations and safe and stable operation at off-design conditions.Thus,the primary objectives of the present study are to analyze the cavitating vortex rope on the draft tube of a Francis turbine with splitter blades using CFD numerical simulations.(1)The numerical of the characteristics of the cavitating flow in the draft tube of a Francis-99 turbine is presented by using the Zwart mass transfer model and Shear Stress Transport Model(SST).The shape characteristic of two types of cavitating vortex rope(spiral and columnar)and its influence on the cavitation development in the runner blades are analyzed.The result indicates that the distribution of the runner cavitation is symmetric for both types of cavitating vortex ropes,and cavitation is significantly improved when a runner with splitter blades is used.The analysis based on the vorticity transport equation further illustrates the association between the cavitation and vortex rope in the draft tube.Furthermore,the Q-criterion is difficult to accurately capture the vortex rope and periodic process,in which the “vortex breakdown” could be found for some significant threshold.In contrast,no “vortex breakdown” can be found for some smaller thresholds.(2)In order to ensure the stable operation of the turbine at off-design condition,the periodic evolution and formation mechanism of vortex must be understood.However,the vortex structure is extremely complex and is often accompanied by cavitation.Conventional vortex identification methods have a common critical shortcoming,which are the requirement of selecting a proper threshold.Liu et al.proposed the Omega method(Ω method),which is not sensitive to the threshold selection,easy to perform,and can successfully capture both strong and weak vortices simultaneously.Furthermore,the Liutex/Rortex method is introduced by Liu et al.,as the latest vortex definition.And the Liutex method is compared with the traditional Q-criterion and Omega method to analyse the periodical precession of vortex rope in the draft tube cone.Advantage of this Liutex/Rortex method over Q-criterion is shown by its enhanced ability to represent vortex rope structure.The results showed a process of vortex breakdown and evolution of vortex rope in the draft tube,which helped comprehend the development of cavitating turbulent flow in the draft tube.(3)The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent vortex rope structure with the vortex-core lines.Furthermore,since it seems to be very hard to define a sharp boundary surface for the whole vortex structure,focusing only on the vortex core line has the advantage that different vortex structures can be marked.In order to further clarify the evolution of vortex,the Liutex core line was used to give the real vortex structure to analyze the characteristics of vortex zone of the draft tube.It is easy to see the period evolution and rotation frequency of the vortex rope.The results showed that,with the unique vortex structure(threshold-free),the precession of vortex rope in the draft tube is further illustrated(4)The influence of precessing vortex rope in the draft tube on hydraulic loss is proposed in the present work.The method of entropy production is used to analyse the hydraulic loss of Francis-99 turbine and the results are compared with the vortex in the draft tune.The influence of the vortex rope in a draft tube to hydraulic loss is further clarified.The result indicates that the distribution of vorticity is almost the same as the entropy production rate.It shows that the vortex rope will cause unsteady flow and increase the hydraulic loss of the draft tube.