The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube of a Francis turbine with splitter blades is not well understood, especially the vortex rope property. This letter presents a prediction of the behavior of the vortex rope in the draft tube of the Francis-99 turbine obtained by the computational fluid dynamics (CFD), where the Liutex/Rortex method, as the most recent vortex definition, is applied to analyze the periodical precession of the vortex rope in the draft tube cone. The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent the vortex rope structurewith the vortex-core lines. Furthermore, since it seems to be very hard to define a sharp boundary surface for the whole vortex structure, it is advantageousfocusing only on the vortex core line,by which different vortex structures can be clearly differentiated. The evolution of the vortex core and the process of the vortex breakdown in the draft tube are revealed, which might help to comprehend the development of the turbulent flow in the draft tube.

中文翻译：

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通过使用Liutex / Rortex方法预测非设计条件下Francis-99尾水管中的进动涡流芯

在非设计条件下工作时，混流式水轮机尾水管中的湍流非常复杂。尽管对非设计条件进行了广泛的研究，但对带有分流叶片的弗朗西斯涡轮机的引流管中的涡流芯线，尤其是涡流绳的性能尚不甚了解。这封信提出了通过计算流体力学（CFD）获得的弗朗西斯-99涡轮机尾流管中涡流绳行为的预测，其中使用Liutex / Rortex方法（作为最新的涡流定义）进行分析导流锥中涡流绳的周期性进动。Liutex / Rortex方法的优势在于其增强的用涡旋芯线表示旋涡绳结构的能力。此外，由于很难为整个旋涡结构定义清晰的边界表面，因此仅关注旋涡芯线是有利的，由此可以清楚地区分不同的旋涡结构。揭示了引流管中涡流核心的演变和涡旋破坏的过程，这可能有助于理解引流管中湍流的发展。