Abstract A precessing vortex core in the draft tube of Francis turbine is considered as unstable flow conditions and the cause of many undesirable system instabilities for hydraulic power stations. The feature of vortex rope, pressure fluctuations and runner outlet velocity at part-load conditions are investigated experimentally and numerically in this paper. An obvious vortex rope could be observed at 0.88Q11BEP point and produces the most intensive periodic pressure fluctuation at the vortex rotation frequency fv along the whole passage of Francis turbine. At other conditions away from this point, the vortex rope becomes unobvious or even invisible, and the associated pressure fluctuation amplitude also reduces. This trend could be well represented by the new parameters G and Vs, which could be used to determine the strength of helical vortex field based on the gradient of time-averaged velocity on horizontal section of the draft tube cone. Transient simulations using VLES turbulence model could obtain satisfying results by comparing with experimental data, especially in terms of the time-averaged axial velocity profile resolution. Therefore, this new method enables the designers to evaluate vortex strength in engineering applications.

中文翻译：

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一种评价混流式水轮机尾水管涡绳强度的方法

摘要 混流式水轮机尾水管中的进动涡核被认为是不稳定的流动条件，是造成水电站许多不良系统不稳定的原因。本文通过实验和数值方法研究了部分负载条件下涡绳的特性、压力波动和转轮出口速度。在 0.88Q11BEP 点可观察到明显的涡绳，在涡旋频率 fv 处沿混流式水轮机整个通道产生最强烈的周期性压力波动。在远离该点的其他条件下，涡绳变得不明显甚至不可见，相关的压力波动幅度也减小。新参数 G 和 Vs 可以很好地代表这种趋势，可用于根据尾水管锥体水平截面时均速度梯度确定螺旋涡场强度。使用VLES湍流模型进行瞬态模拟，与实验数据进行比较，特别是在时均轴向速度剖面分辨率方面，可以获得令人满意的结果。因此，这种新方法使设计人员能够评估工程应用中的涡流强度。