Cavitation study of a pump-turbine at turbine mode with critical cavitation coefficient condition

To study the cavitation phenomenon of a pump-turbine at turbine mode when it ran at the critical cavitation coefficient condition, a high-head model pump-turbine was disperse using hexahedron grid. Three dimensional, steady cavitating flow was numerically studied using SST k-ω model. It is confirmed that ZGB cavitation model and SST k-ω model are useful ways to study the two-phase cavitation flow in pump-turbine. Mass flow inlet and pressure outlet were specified at the casing inlet and draft tube outlet, respectively. The static pressure was set according to the cavitation coefficient. The steady cavitating flows at critical cavitation coefficient condition were analysed. The cavitation area in the runner was investigated. It was found that the pressure of the suction on the blade surface was decreasing gradually with the decrease of the cavitation coefficient. In addition, the vortex flow in the draft tube was observed at the critical cavitation coefficient. It was found that the vortex flow appeared at the center of the draft tube inlet with the decreasing of the cavitation coefficient. Compared with the experimental data, the simulation results show reasonable agreement with the experimental data.


Introduction
The cavitation is one of important phenomenon in a pump-turbine at turbine model. With the development of the cavitation flow, the cavitation bubble would collapse and perish, which would cause material erosion, structure wreck, vibration and noise. But due to hydraulic machine was in low speed state, even if it had cavitation wreck, the wreck was not very critical, that trigger the short of the cavitation research [1]. In recent years, the pump-turbine develop quickly, big capacity, high head and high speed gradually become the main developing aspect gradually. Finally, the condition of the blade wreck, efficiency reduces, device destroys, noise and vibration would aggravate gradually. So the cavitation problem of the pump-turbine has become one of the important research topics of domestic and foreign academia and engineering.
With the rapid development of computing technology in recent years, the simulation by the computational fluid dynamics can get some useful results in the engineering, except experimental method [2,3]. In recent year, a lot of research about the mechanism of the cavitation form had been done. Wang Ya-yun [4] researched the unsteady hydrodynamic characteristics of a 2D cavitating hyrdrofoil and the evolution of cloud cavition, and compared the phenomenon of shedding and breakoff sheet cavitation and behaviour of cloud cavitation by using the Reynolds Averaged Navier-stokers equations, Detached Eddy Simulation and Large Eddy Simulation. The numerical results of 2D LES show that the generation and evolution of the vortex near the wake of sheet cavity in the primary reason of break-off sheet cavitation, and the reentrant jet occurs only after the break of the sheet cavity. This research about the cavitation mechanism Wu [5] studied the unsteady cavitating turbulent flow with two different models and found that the mixture model could fit the experimental data compared with the single-phase model. Nishi [6] analysed the influence of the draft tube flow and the pressure fluctuation of the draft tube caused by the different cavitation coefficient by the experiment, the pressure fluctuation frequency is almost invariant until the cavitation coefficient is less than the certain value that would magnitude the pressure fluctuation.
However, the analysis of the instability of a pump-turbine at critical cavitation coefficient hasn't yet been reported. In present paper, a two-phase cavitation model was used to predict the cavitating turbulent flow in a model Francis pump-turbine by numerical simulation. The distribution of the cavitation area in the runner was investigated.
The main parameters of the model mixed flow water turbine studied are showed in Table.1. D1 denotes the diameter of the runner outlet in turbine mode, Z denotes the number of the blades, Zs and Zg denote the number of the stay vanes and the guide vanes respectively, n denotes the velocity of the runner and H denotes the head of the test. The structure of the turbine is showed in the Figure.1.

Cavitation model
Zwart-Gerber-Belamri model was used to model cavitation in the pump-turbine. It was compatible with turbulence model well. It considered the evaporation and the condensation to control the equation. The evaporation and the condensation was included are defined as When p ≤ pb, When p > pb, Where the diameter of the bubble was 1μm, Fvap = 50 and Fcond = 0.01 which represented factors for vaporization and condensation respectively; ρv was the saturated vapour pressure; ρl was the density of the fluid; the void fraction of the nuclei was 5 × 10 -4 .

Boundary conditions
In the algorithm, the physical timescale was 0.001s. The head was specified 50m. The rotating speed of the runner was set by the function. Mass flow at casing inlet was specified at turbine mode. The outlet condition was used the value of static pressure. The outlet pressure was specified according to ICPF2015 IOP Publishing IOP Conf. Series: Materials Science and Engineering 129 (2016) 012037 doi:10.1088/1757-899X/129/1/012037 the function. The advection scheme was specified high resolution and the turbulence numeric was specified first order.
Three cavitation efficient operation conditions in the optimum operation condition and partial load condition were showed in Table.2, which were set by the cavitation coefficient.

Hydraulic performance
The steady state performances under three different rotate speed and mass flow at inlet was simulated and the results were compared with test data, as shown in Figure.2. It can be seen from the Figure.2 that the numerical results meets well with the test results and the numerical method could predict the hydraulic characteristics accurately.   Figure.3 - Figure.11 show the pressure distribution at the runner blade at different cavitation coefficient and at different load. It can be seen from the figures that, the low-pressure area is obviously exited on the suction side of the blade surface. With the decrease of the cavitation coefficient, the pressure of the low-pressure areas is decreasing gradually. And with the load decreasing, the pressure of the low-pressure areas is increasing at the same cavitation coefficient. Figure.12 - Figure.20 show the vapour volume on the runner blade at different cavitation coefficient of the optimum load and at different load. It can be learned that, the obvious cavitation area is existed when the cavitation coefficient is at 0.06. Because of the pressure decrease of the lowpressure area, the vapour occurs while the pressure of the area is lowered than the saturate pressure of the water. Compared with the condition at the same cavitation coefficient, the cavitation area at the optimum load is larger than which at the 82% load and the 70% load.

Cavitation performance
The pressure distribution at the draft tube is showed at the Figure.21 - Figure.29. Figure.21- Figure.23 shows the cavitation coefficient at 0.12, 0.08 and 0.06 when it is at the optimum load, Figure.24 - Figure.26 when at the 80% partial load and Figure.27 - Figure.29 when at the 70% partial load. It can be learned that, compared with the same load, the pressure of the center area of the draft tube inlet is decreased gradually with the decreasing of the cavitation coefficient. And when the cavitation coefficient is lowered to 0.06, whatever the load is, the vortex flow occurs at the draft tube. In addition, compared with the different load when the cavitation coefficient is at 0.06, it show that the cavitation area is bigger at the 80% partial load than which at the 72% partial load and optimum load. And it has occurred a vortex at the 80% partial load. If the vortex frequency is same with the blade rotating frequency, it would lead to the strongly vibration, which will bring about huge damage.                       In this paper, a kind of numerical method for cavitation performance prediction was presented. In order to verify the accuracy of the simulation, the hydraulic performance was compared with the experiment data. Base on the result of the analysis in the Francis turbine, the following conclusions are drawn. 1. The simulation results by cavitating flow computation based on the mixture model agree well with experimental data. 2. With the decreasing of the cavitation coefficient, the pressure of the suction on the blade surface is decreasing gradually. And when the cavitation coefficient is lowed to a certain extent, the lowpressure area will appear the vapour area. And at the same cavitation coefficient, the vapour area at the optimum condition is largest. 3. With the decreasing of the cavitation coefficient, the vortex flow is appeared at the center of the draft tube inlet.