基于TBR模型的高水头混流式水轮机水力性能预测

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

    • 摘要: 叶轮机械的瞬态计算对于捕捉转子与定子之间的周期性扰动是十分必要的。为了避免共振,转子与定子数目一般是互质的,使得周期性边界条件失效,瞬态模拟必须对全通道进行计算,以保证转子与定子之间的螺距比为1,从而确保上下游信息的准确传递,因此计算资源消耗较多。该文基于k-ω SST湍流模型,分别采用传统全通道计算方法、TBR(transient blade row)模型中的单通道PT(profile transform)方法以及双通道FT(fourier transform)方法,对Francis99混流式模型水轮机进行了性能及负荷预估,并与试验值作对比。PT方法通过在交界面上按照角度比进行变量的比例缩放而保持上下游通量的守恒,FT方法采用傅里叶级数的相变周期性边界条件来解释转子与定子之间螺距比不为1的问题,对周向边界和转静边界进行求解历史的重构。数值计算采用变量边界条件(profile boundary conditions-PC)进口给定质量流量及速度方向矢量,出口给定静压。与试验值作对比,全通道计算法、PT方法以及FT方法均能较准确地预测水轮机效率、不同测点平均压力,而且3种数值方法获得的流道内压力及叶片负荷分布差别不大。FT方法计算的叶片合力及扭矩随时间变化与全通道比较一致,仅仅在变量脉动上小于全通道,而PT方法在脉动及频率上均存在较大偏差。压力脉动频谱特性方面,FT方法与全通道主频及幅值接近,且与试验结果比较吻合,而PT方法由于交界面上变量的缩放,静止域与旋转域内均捕捉到叶片通过频率,且幅值低于全通道及试验值。此外,相同计算条件下,全通道计算、PT方法以及FT方法计算所需时间比为1:0.375:0.23。综合评估分析,FT计算结果与全通道以及试验结果一致且消耗更少的计算资源,在水轮机的瞬态计算有一定的潜力和优势。

       

      Abstract: 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.

       

    /

    返回文章
    返回