Hydraulic performance prediction for high-head francis turbine based on TBR model

Transient simulation is indispensable for capturing the periodic disturbance between the rotor and stator for turbomachine applications. In order to avoid resonance risk, the turbomachine systems generally have prime number of components between the rotor and stator, which makes the periodic boundary conditions failed and the transient simulation must be carried out including all the passages. However, prohibitive computing resources and too much time cost are required to obtain detailed accurate simulations for the conventional methods of modeling all the passage. In this paper, 3 numerical approaches, the full passages simulation, the PT(Profile Transform) method with only 1 passage, the FT(fourier transform) method with double-passage, were respectively used to numerically predict the hydraulic performance and loading for the Francis99 turbine based on the k-ω SST turbulent model. The PT method overcame the unequal pitch problem by scaling the flow profile across the blade row interfaces. In the Fourier Transformation method, a phase-shifted boundary condition with Fourier data compression was used to account for the unequal pitch between the blade rows passages, and the solution history of circumferential boundary and rotational boundary was reasonably reconstructed. During the transient numerical simulations, the inlet and outlet boundary were given by the method of Profile Boundary Conditions. The mass flow with the velocity vector direction was prescribed on the inlet section, and the outlet was treated as a static pressure outlet where a static gauge pressure was specified. Compared with the experimental tests, the 3 simulation methods could accurately predict the hydraulic efficiency and the average pressure at different locations, and the static pressure distribution on the mid-span plane and pressure loading on runner blade were comparable. The hydraulic efficiency extracted by FT and PT methods were both higher than the result of the full passages simulation, which was attributed to the fact that the 2 simulation methods only included part of the flow passages and didn't consider the hydraulic loss of volute, fixed guide vane and draft tube. The temporal variation of blade force and torque generated by the FT method showed in good agreement with the full passages method, expect for small deviation in pulsating amplitude. However, the PT method showed larger discrepancy with the full passages results for both of pulsating frequency and amplitude. In term of spectrum characteristics of pressure fluctuation, the numerical results extracted by the FT method yielded to a very good validation with the full passages and the experimental obtainment. Due to variable scaling or stretching at the Rotor-Stator interface, the passing frequency of the blade was captured in both the static domain and the rotating domain, and the pressure amplitude of PT method was lower than that of the full passages and the experimental. In addition, the time cost ratio among the full passages, the FT method and the PT method was about 1:0.375:0.23. We concluded that the FT method was capable of predicting the hydraulic performance and pressure fluctuation well with less computing resources and was a good alternative compared to the conventional full passage method.