The hump formation mechanism has not been fully understood so far, mainly because of two difficulties in analysis. The first one is how to find the most important external characteristic factor inducing humps, and the other is how to avoid too many assumptions when analysing the change in the runner’s capacity for work (the direct use of Euler’s formula makes too many assumptions). This paper proposes a new method based on the second derivative of the external characteristics to identify the most critical factor inducing humps quantitatively. The runner blades’ capacity for work is calculated and shown as a cloud diagram using as few assumptions as possible to help understand the actual relationship between flow fields and humps. Additionally, the importance of stall in affecting the runner’s capacity for work is analysed and explained. Thus, the double hump formation mechanism in pump–turbines has finally been understood.

驼峰形成机制至今尚未完全了解，主要是因为分析上存在两个困难。第一个是如何找到导致驼峰的最重要的外在特征因素，第二个是在分析跑步者的工作能力变化时如何避免过多的假设（直接使用欧拉公式做了过多的假设）。本文提出了一种基于外部特征二阶导数的新方法，用于定量识别诱发驼峰的最关键因素。使用尽可能少的假设来计算转轮叶片的工作能力并显示为云图，以帮助理解流场和驼峰之间的实际关系。此外，还分析和解释了失速在影响跑步者工作能力方面的重要性。因此，