Entropy Production Analysis for Hump Characteristics of a Pump Turbine Model

The hump characteristic is one of the main problems for the stable operation of pump turbines in pump mode.However,traditional methods cannot reflect directly the energy dissipation in the hump region.In this paper,3D simulations are carried out using the SST k-ω turbulence model in pump mode under different guide vane openings.The numerical results agree with the experimental data.The entropy production theory is introduced to determine the flow losses in the whole passage,based on the numerical simulation.The variation of entropy production under different guide vane openings is presented.The results show that entropy production appears to be a wave,with peaks under different guide vane openings,which correspond to wave troughs in the external characteristic curves.Entropy production mainly happens in the runner,guide vanes and stay vanes for a pump turbine in pump mode.Finally,entropy production rate distribution in the runner,guide vanes and stay vanes is analyzed for four points under the 18 mm guide vane opening in the hump region.The analysis indicates that the losses of the runner and guide vanes lead to hump characteristics.In addition,the losses mainly occur in the runner inlet near the band and on the suction surface of the blades.In the guide vanes and stay vanes,the losses come from pressure surface of the guide vanes and the wake effects of the vanes.A new insight-entropy production analysis is carried out in this paper in order to find the causes of hump characteristics in a pump turbine,and it could provide some basic theoretical guidance for the loss analysis of hydraulic machinery.

Flow excitation mechanisms of unbalanced impeller forces after pump power-trip of ultra-high head pump-turbines

To elucidate the dynamic mechanisms of unbalanced impellers in ultra-high head pump-turbines(PTs),this study employed a one-and three-dimensional coupled method to simulate the pump power-trip(PPT)process of an ultra-high head PT.The investigation revealed two novel pulsation frequency components,denoted as fDVand fINFT,associated with impeller forces.The pulsation intensities of these components were markedly higher than those of rotor-stator interaction frequency components in ultra-high head PTs.Notably,the fDVcomponents exhibited pulsations at 1–2 times the rated rotation frequency of the impeller,spanning the entire transition period.Meanwhile,the fINFTcomponents constituted a complex frequency band with various frequency values,primarily occurring near conditions(Q=0,n=0,M=0,and d M/dt=0).These two pulsation frequency components were predominantly linked to the unsteady evolution of dean vortices inside the volute and complex transitions of the flow pattern within the impeller,respectively.It is crucial to note that these unbalanced flow-induced impeller axial forces can elevate the risk of accidents where the rotor is subjected to significant upwind axial forces.These findings offer valuable insights into mitigating the risk of rotor lifting due to axial forces during PT events in ultra-high head PTs.

High-amplitude pressure fluctuations of a pump-turbine with large head variable ratio during the turbine load rejection process

Large-head variable-amplitude pump turbines(PTs) encounter serious transient hydraulic instability issues. To explore the evolution mechanisms of pressure fluctuations(PFs) and flow patterns inside large-head variable-amplitude PTs, the load rejection process(LRP) was investigated using a one-and three-dimensional coupled flow simulation approach. The temporal,spatial, and frequency characteristics of the fluctuating pressures were analyzed for four monitoring points using a combined time-frequency analysis approach. The results indicated that PFs during the LRP of large-head variable-amplitude PTs had a new fluctuation frequency component related to Dean vortices(DVs) in the volute, in addition to the common fluctuation frequency components related to rotor-stator interaction phenomena and local backflow vortices near the impeller inlet. The PF frequency component existed throughout the LRP and had a significant influence on the transient maximum pressure at the volute end. This study provides a useful theoretical guide for the design and optimization of large-head variable-amplitude PTs.

Numerical analyses of pressure fluctuations induced by interblade vortices in a model Francis turbine

Interblade vortices can greatly influence the stable operations of Francis turbines. As visible interblade vortices are essentially cavitating flows, i.e., the ones to cause interblade vortex cavitations, an unsteady simulation with a method using the RNG k- ？ turbulence model and the Zwart-Gerber-Belamri（ZGB） cavitation model is carried out to predict the pressure fluctuations induced. Modifications of the turbulence viscosity are made to improve the resolutions. The interblade vortices of two different appearances are observed from the numerical results, namely, the columnar and streamwise vortices, as is consistent with the experimental results. The pressure fluctuations of different frequencies are found to be induced by the interblade vortices on incipient and developed interblade vortex lines, respectively, on the Hill diagram of the model runner＇s parameters. From the centrifugal Rayleigh instability criterion, it follows that the columnar interblade vortices are stable and the streamwise interblade vortices are unstable in the model Francis turbine.

Dynamic analysis on pressure fluctuation in vaneless region of a pump turbine

As the pump turbine tends to be operated with high head and high rotational speed, the study of stability problems becomes more important. The pump turbine usually works at operating conditions where the guide vanes experience strong vibrations. However, most traditional studies were carried out based on constant GVO(guide vane opening) simulations. In this work, dynamic analysis on pressure fluctuation in the vaneless region of a pump turbine model was conducted using a dynamic mesh method in turbine mode. 3D unsteady simulations were conducted where GVO was closed and opened by 1° from the initial 18°. Detailed time domain and frequency domain characteristics on pressure fluctuation in the vaneless region under different guide vane rotational states compared with constant GVO simulations were investigated. Results show that, during the guide vanes oscillating process, the low and intermediate frequency components in the vaneless region are significantly different. The amplitudes of pressure fluctuation are higher than those with constant GVO simulations, which agree better with the experimental data. In addition, the pressure fluctuation increases when GVO is opened, and vice versa. It can be concluded that pressure fluctuation in the vaneless region is strongly influenced by the oscillating of the guide vanes.

Dynamic instability of a pump-turbine in load rejection transient process

Load rejection is one of the most crucial transient processes in pump-turbines. However, only a few achievements on the internal flow mechanism of pump-turbines in load rejection processes have been presented. In this study, firstly, the load rejection process in a pump-turbine was simulated with a three-dimensional unsteady turbulent numerical method using the technology of dynamic mesh and the user-defined functions in the FLUENT software. The rotational speed predicted through numerical simulation agrees well with experimental data. Secondly, based on numerical simulations, a dynamic instability in the load rejection process was found and presented that the pressure and performance characteristics, including hydraulic torque on the runner and the discharge, fluctuate in the overall trend. Meanwhile, all the performance characteristics and the pressure fluctuate sharply near the operating condition points, where hydraulic torque on the runner is equal to zero or reverse flow is maximum at reverse pump conditions. Finally, the time-frequency features and formation mechanism of the dynamic instability were analyzed emphatically. The analysis of the internal flow in the pump-turbine reveals that dynamic instability in the load rejection process are mainly caused by the vortex flow in the tandem cascades regions. Furthermore, the possible methods to improve the dynamic instability in the load rejection process were recommended.

Hydraulic fluctuations during the pump power-off runaway transient process of a pump turbine with consideration of cavitation effects

A runaway transition after the pump power interruption and the simultaneous guide vane servomotor failure is one of the most dangerous and complex transitions for a pumped storage power system(PSPS).This paper analyzes the fluctuation behavior and mechanism of a PSPS during a runaway transition caused by the pump power interruption.The transient cavitation flow in the PSPS is simulated by using a one-dimensional and three-dimensional coupling flow simulation method for the runaway transition.Subsequently,the effects of the transient fluctuation of the radial hydraulic thrust on the runner and transient pressures are analyzed using the short-time Fourier transform method.Finally,the mechanisms are analyzed based on the analysis of the internal flow field.This study suggests that the extreme fluctuation generally occurs near the critical transformation points between the two operation modes.In addition,the extreme fluctuation behavior is primarily related to the local backflow near the runner inlet and the unstable cavitation phenomena in the runner and the draft tube.This finding helps for optimizing the runner design to resolve the instability problems of a PSPS.

Investigation on the relationship between hydraulic loss and vortex evolution in pump mode of a pump-turbine

Hydraulic loss and vorticity are two most common methods in analyzing the flow characteristics in hydro-machine,i.e.,centrifugal pump,Francis turbine,etc.While the relationship and correlation between hydraulic loss and vortex evolution are not uncovered yet.In this study,hydraulic loss is regarded as the combination of dissipation effect and transportation effect in flow domains.Meanwhile,vorticityωcan be decomposed into two parts,namely the Liutex partω_(R),the shear partωs,of whichω_(R)is regarded as the third-generation vortex identification method for its precise and rigorous definition of local rigid rotation part of fluid.Based on the dimensional analysis,two new physical quantities related to vorticity(ω,ω_(R)andωS),namely enstrophyΩ,vorticity transport intensity T are adopted to express the energy characteristic in vortex evolution process.Finally,operating points at pump mode of an ultra-high head reversible pump-turbine are selected as the research object and the numerical results calculated using SST k-ωturbulence model are consistent well with the experimental data.Pearson correlation coefficient is adopted to evaluate the correlation between hydraulic loss and vortex evolution in main flow regions.Results show that apart from the spiral casing domain,the enstrophy of shear partΩs has very strong correlation with dissipation effect and Liutex transport intensity TR has stronger correlation with transportation effect when compared with other forms of vorticity.The correlation between Liutex transport intensity TR and transportation effect is strong in stay/guide vanes(SGVs)while reduce to medium level in runner and draft tube domains.In spiral casing domain,all forms of vorticity show weak or very weak correlation with transportation effect.Based on the proposed method,we believe that the relationship and correlation between hydraulic loss and vortex evolution in other hydraulic machineries can also be clearly investigated.

Numerical predictions and stability analysis of cavitating draft tube vortices at high head in a model Francis turbine

Draft tube vortex is one of the main causes of hydraulic instability in hydraulic reaction turbines,in particular Francis turbines.A method of cavitation calculations was proposed to predict the pressure fluctuations induced by draft tube vortices in a model Francis turbine,by solving RANS equations with RNG k-turbulence model and ZGB cavitation model,with modified turbulence viscosity.Three cases with different flow rates at high head were studied.In the study case of part load,two modes of revolutions with the same rotating direction,revolution around the axis of the draft tube cone,and revolution around the core of the vortex rope,can be recognized.The elliptical shaped vortex rope causes anisotropic characteristics of pressure fluctuations around the centerline of the draft tube cone.By analyzing the phase angles of the pressure fluctuations,the role of the vortex rope as an exciter in the oscillating case can be recognized.An analysis of Batchelor instability,i.e.instability in q-vortex like flow structure,has been carried out on the draft tube vortices in these three cases.It can be concluded that the trajectory for study case with part load lies in the region of absolute instability(AI),and it lies in the region of convective instability(CI)for study case with design flow rate.Trajectory for study case with over load lies in the AI region at the inlet of the draft tube,and enters CI region near the end of the elbow.

给定活动导叶开口水泵水轮机模型泵工况驼峰现象流动分析（英文）

目的:探索水泵水轮机泵工况在超负荷工况(1.24φBEP)、最优工况(1.00φBEP)、靠近最优工况(0.90φBEP)、驼峰区工况(0.65φBEP)以及低负荷工况(0.45φBEP)的流动特性,期望获得流动特性变化规律,揭示驼峰特性形成机理。方法:对某一水泵水轮机模型,采用剪切压力传输(SST)k-ω湍流模型进行三维定常数值模拟,在实验验证的基础上:1.在曲面坐标系中,分析由叶片形状所引起的各个工况叶片进出口边在周向和叶片方向上的分布规律;2.运用经典欧拉理论分析叶片进出口边液流角变化对各个工况的欧拉水头的影响;3.通过水力损失分析,获得不同部件各个工况损失变化规律。结论:1.转轮叶片进出水边的液流角随着叶片方向在不同流量工况分布下具有明显差异,导致转轮流道不同程度流动分离;2.运用经典欧拉理论得出驼峰区工况点出口角液流的减小与入口液流的增加是驼峰特性产生的主要原因之一;3.通过损失分析,确定泵工况损失主要在转轮和双列叶栅中,得出转轮部分损失是驼峰特性形成的主要原因之一;4.综合分析,驼峰特性是由该工况欧拉动量的减小和转轮部分损失的增加共同作用的结果。

Runner cone optimization to reduce vortex rope-induced pressure fluctuations in a Francis turbine

Pressure fluctuations induced by a vortex rope are the major causes of hydraulic turbine vibration in partial load operating conditions. Hence, an effective control strategy should be adopted to improve rotating characteristics of the vortex rope and reduce the corresponding pressure fluctuation. In this study, two new types of runner cones(i.e., abnormally shaped and long straight cones) were proposed to optimize the pressure distribution in the draft tube, and unsteady numerical simulations were performed to determine their mechanism of action. Numerical results were validated using flow observation and pressure fluctuation experiments. Detailed analyses were conducted to understand the effects of the helical vortex rope operating conditions. The results indicated that pressure fluctuations in the draft tube at partial load operation result primarily from low frequency fluctuations induced by the rotation of the helical vortex rope, whose amplitudes are related to the rotating radius of the helical vortex rope. Both runner cone types could effectively reduce the pressure-fluctuation amplitude. The long straight type could reduce the amplitude of low-frequency fluctuation induced by vortex rope to a maximum of 74.08% and the abnormalshape type to 38.31%. Thus, the effective optimization of the runner cone can potentially reduce pressure-fluctuation amplitudes.Our research findings were applied to a real hydraulic plant in China.