Investigation On Evolution Characteristics Of Vortex In Francis Turbine During Operating Condition Conversions

With the implementation of the "dual carbon" strategy,in order to ensure the stability of power system,hydropower will shift from focusing on generation to emphasizing both power generation and regulation.It will inevitably lead to frequent condition conversions for hydraulic turbines to balance the grid parameters.The operating condition conversions of Francis turbine can induce complex vortex structures such as inter-blade vortex and vortex rope,which have a direct impact on hydraulic performance and can threaten the safety and stability of the turbine when severe.It is a crucial prerequisite to clarify the evolution characteristics of vortex during the operating condition conversions of Francis turbine and their impact on operational stability for expanding the operating range of hydraulic turbines and further leveraging the advantages of hydropower regulation.This paper uses a model Francis turbine and systematically investigates the evolution mechanisms of inter-blade vortex and vortex rope during the process of flow（load）reduction based on structured dynamic mesh technology,and investigates the evolution laws of the location,shape,and intensity of the inter-blade vortex during the process of head（unit speed）.The main objectives and conclusions of this paper are as follows:During the variable flow conversion process,the formation and development rules of interblade vortex are systematically analyzed.The study shows that a small amount of cavitation area exists on the back of the runner blade initially,and the inter-blade vortex gradually develops and can be observed in all flow channels as the flow rate decreases.The vortex identification method based on the Q criterion shows that at 79.1%Q_11r,a "two-stage" vortex structure,different from the typical inter-blade vortex,appears on the front of the runner blades and gradually disappears as the flow rate decreases.The analysis of flow topology shows that the formation of the interblade vortex is related to the flow separation phenomenon occurring on the hub of the runner,and its vortex motion position changes with the decrease of flow rate,showing a tendency to move toward the inlet of the blade.Loss analysis based on the energy equation shows that the complex vortex phenomena inside the runner are the main causes of energy dissipation.With the variation of flow rate,the development rules and evolution mechanisms of vortex rope are analyzed.The result shows that the vortex rope initially appears as an unstable vortex rope with a slender spiral characteristic in the transition zone,and as the flow rate decreases,the length of the vortex rope gradually shrinks and evolves into an eccentric vortex rope.As the flow rate decreases further,the vortex rope detaches from the runner cone and evolves into some scattered vortexes,which eventually disappears at 51.3%Q_11r.The number of swirls at the inlet of the draft tube increases gradually with the decrease of flow rate,with a minimum value of 0.534.However,the distribution of the circumferential velocity and axial velocity at the inlet of the draft tube required to form the vortex rope is disrupted,and the energy of the circumferential velocity cannot provide enough energy for the formation of the vortex rope,which is the reason why the vortex rope evolves into disappearance as the flow rate decreases.During the conversion process of head,the development rules of inter-blade vortex are analyzed.The study shows that the vapor volume in the runner reaches the minimum value near the design head,at which no inter-blade vortex structure exists inside the runner.When the operating head is higher than the design head,the inter-blade vortex has an A-type structure.As the operating head decreases,the A-type inter-blade vortex structure weakens gradually,and when the operating head drops below the design head,the inter-blade vortex reappears as a Btype structure.The influence range of the pressure pulsation frequency of the inter-blade vortex is about 1.0-0.75fn,and the pressure pulsation amplitude is smaller when the operating head is higher than the design head,while it is higher when the operating head is lower than the design head.