Entropy Production Rate Analysis In S Zone For A Pump-turbine

Francis pump-turbine,which is the core component of a pumped-storage power station,has a significant S-zone during the operation.The formation mechanism of Szone is complex,and the flow in S-zone is unstable,which makes the unit difficult to connect to the grids.The traditional CFD analysis of pump-turbine usually begins with the distribution of speed and pressure.This method does not describe the location of the hydraulic loss clearly,and the loss of head in the S-zone could not be calculated by using the pressure drop method.In this paper,we introduce the definition of thermodynamic entropy and the add energy equation into the calculation,considering the temperature change of the water,and using entropy production rate to describe the distribution of the energy loss in pump turbine.The entropy production rate is split into 3 parts according to the component items,the mainstream entropy production rate,the wall friction entropy production rate and the temperature change entropy production rate.We calculate entropy production rate in the operation zone and S zone for the pump-turbine.Also the difference between the hydraulic characteristics and the stability of the unit in the cases whether considering the runner clearance or not are compared.When the pump-turbine operating in the nominal conditions,the loss of wall friction entropy production loss accounts for 30% of the total loss,the mainstream entropy production loss accounts for 70%,and the entropy production loss caused by the temperature change is minimal.As the unit deviates from the optimal operating area,both the wall frictional entropy production loss and the mainstream entropy production loss increase,but the increase in the mainstream entropy production loss is much greater than the wall friction entropy production loss,indicating that the mainstream loss is the major loss in the partial operating conditions.The entropy production losses of different components in the operational area are ranked from large to small as follows: runner,draft tube,guide vane,stay vane,spiral casing;the losses mainly distribute around the runner blade wall and the draft tube vortex belt.With the unit gradually moves out normal conditions,the losses of the runners increases the most,followed by the guide vanes and the draft tube.The entropy production rate in the S-zone operation is significantly greater than that in the normal operation area,most of the increase is from the guide vane and the runner,which are the two largest sources of unit entropy production loss.The guide vane and runner's entropy production loss accounts for 80%-90% of the total entropy production loss in the unit for the zero flow condition which the valve is closed.The region with the strongest entropy production rate when operating in S-zone is near the high-speed “water-ring” formed near the dynamic and static interface between the guide vanes and the runner,and the entropy production rate near the wall of the “water-ring” is higher than that in the center of the channel.The maximum value of entropy production loss in the large guide vane opening of S-zone appears in the zero flow condition,while it appears in the runaway condition at the middle and small guide vane opening.The reason is that as the opening of the guide vane decreases,the circumferential velocity of water entering the runner at the same flow rate increases,causing the formation time of the “water-ring” advance.At the rated point,considering the clearance of the runner,the flow rate increases by 0.25%,the efficiency decreases by 0.71%,and the output decreases by 0.45%.The maximum entropy production rate strength of the unit occurs near the labyrinth seal in the runner clearance.Regardless of the piping system,only considering the pressure pulsation inside the unit,due to the rotor–stator interaction,the pressure pulsation amplitude at the interface between the guide vane and the runner is the largest.After considering the runner clearance,the pressure pulsation amplitude in the runner channel and vaneless area are smaller than that without considering the clearance.