Numerical Study on the Internal Flow Field of a Reversible Turbine during Continuous Guide Vane Closing
The unsteady flow field in a reversible pump-turbine is investigated during the continuous load rejection using a 3D computational fluid dynamic analysis. Numerical calculations are carried out using the detached eddy simulation (DES) turbulence model and a new approach involving automatic mesh motion. In this way, the instability of the flow field is analyzed by continuously changing the guide vane openings from the best efficiency point (BEP). Unsteady flow characteristics are described by
... are described by post-processing signals for several monitoring points including mass flow, torque, head and pressure in the frequency and time-frequency domains. The formation of vortices of different scales is observed from the origin to further enlargement and stabilization; the effect of the rotating structures on the flow passage is analyzed, and the influence of unsteady flow development on the performance of the turbine is investigated. Finally, the evolution during the period of load rejection is characterized in order to determine the hydrodynamic conditions causing the vibrations in the machine. Reversible turbines are more popular compared to other forms of turbomachinery in the new generation of RPHES, due to the considerable cost effectiveness and high efficiency range. Furthermore, they gain a competitive advantage and have efficient switch connections between electricity production and consumption (Beevers et al.  and Fisher et al.  ). A Reversible Pump Turbine (RPT) can deal with problems related to the conversion and input of energy into the grid, due to the need for switching between pump and turbine mode. However, during periods of changing conditions between pump and turbine modes, starting up and stopping of the unit and load rejection, there is the need to change the speed and high frequency to compensate the off-design conditions, as shown in the S-shaped characteristic curves. As a consequence, the unit performance, regulation capacity and efficiency are affected, and both cavitation and instability phenomena could appear. The change in load, together with frequent starts and stops, represents one of the most important characteristics of a pump-turbine: it allows one to counter the increased need for leveling the peak demand of electrical energy and to better balance the system. For these reasons, pump-turbines' working conditions are particularly suitable to be investigated using unsteady analyses [4, 5] . RPTs need to be quickly disconnected from the power system when load changes or unpredictable situations occur; in order to reduce the unit damage, caused by the sudden increment of rotating speed, the guide vane must be rapidly closed accordingly. In addition, pump-turbines are synchronized with the electrical grid during load rejection; however, the procedure could be slowed down by system oscillations caused by the unstable behavior: longer times greatly contribute to unit damage. The oscillatory phenomena had been originally studied by Yamabe : the pronounced hysteretic behavior of oscillations in the values of pressure was observed and its interaction with unsteady cavitation patterns analyzed. Several authors carried out an in-depth study of the unsteady flow phenomena: Klemm  gave a simple solution of the instability of the flow by detuning some guide vanes; Martin  made a linear stability analysis to predict the occurrence of the oscillations. Afterwards, Dörfler et al.  studied how stable operations on the machine could be achieved even in the presence of the instability at no load. In addition, several studies of Nicolet et al. in [10, 11] investigated the severe problems of unstable behavior, which is induced by positive gradients of the pump turbine characteristic and also represented the time evolution of the damping for both the rigid and elastic water column modes. They finally demonstrated the higher instability of the elastic mode compared to the rigid mode. However, the above-mentioned analyses are not complete, and the requirements to limit the instability are not met: many RPHES also need to improve the stability in the period of rejecting and accepting load, in order to eliminate vibrations, to improve the S-curve characteristics and to cut down the surge pressure rises. Recent studies have shown that the S-induced instabilities can be ascribed to flow phenomena, such as stationary vortex formation and rotating stall in the runner (Yin et al. , Zeng et al.  and Hasmatuchi et al. ). However, other aspects regarding unstable behavior in the load rejection phase should be further investigated: the onset and development of the vortices in the runner channels and the reasons for the further enlargement and stabilization. On the other hand, it is necessary to find the cause of vibration and propose effective control measures to reduce the instability phenomena in order to ensure the safety of the unit in a long-term operation. In order to illustrate the accuracy of the analysis, the test case adopted for the validation of the numerical model is represented by the pump-turbine of the Xiangshuijian pumped storage plant  , and it has been widely studied by several authors    . However, the analyses of the unsteady phenomena in pump-turbines are not simple, and often experimental and numerical results differ; furthermore, the inner flow in the machine is difficult to investigate, and studies of unsteady processes have many limitations. In previous works, a linear closing law has been applied to various power plants characterized by adverse flow field effects [19, 20] . In fact, the suggested closing laws did not completely reduce the instabilities, and the flow field characteristics still need to be improved. On the other hand, several authors adopted some fixed guide vane positions in order to simulate the closing process, which cannot accurately reproduce the entire dynamic process [19, 21] .