Abstract: A control volume method， named as bell-shaped curve method， was applied to make a quick assessment of the effectiveness of casing treatments， in order to reduce the cost and time-consuming design process involving enormous experiments and calculations. The advantage of this method is that the effectiveness of casing treatments can be determined quickly simply by comparing the cumulative axial momentum curves in the rotor tip region， i.e. the bell-shaped curves instead of computing the entire characteristic curves. The method was applied to slot-type casing treatments. The effectiveness of three axial-slot configurations were predicted and then verified experimentally on a large scale low-speed compressor. The results show that the predicted effectiveness of the casing treatments agrees well with the measured characteristic curves. Compared with the 3D unsteady CFD simulations， which would normally be necessary to capture the stall margin with slot casing treatments correctly， the bell-shaped curve method can significantly reduce the time for slot selection， indicating its good engineering value in the casing treatment designs.

Key words: Bell-shaped curve method；Axial-slot casing treatment；Rotor tip region；Axial momentum；Stall margin improvement

摘要： 为了降低机匣处理设计过程中的海量试验和计算成本与周期，从实际角度出发，采用了一种可快速判断不同机匣处理扩稳能力的钟形曲线法。其优势在于:不需要对机匣处理方案进行整条特性线计算，只通过比较其在光壁机匣近失速点的对应流量下动叶端区累加轴向动量，即“钟形曲线”，就可以快速判断出不同机匣处理的扩稳能力。以缝式机匣处理为示例，在低速大尺寸压气机上设计了三种不同的轴向缝方案，利用钟形曲线对其扩稳能力进行了预估，并完成了实验验证。结果表明，采用钟形曲线法预测扩稳能力与实验结果趋势一致，大幅缩减了轴向缝扩稳效果的评估周期，体现了该方法在机匣处理设计方面具有良好的工程应用价值。

关键词: 钟形曲线方法；轴向缝机匣处理；动叶叶顶端区；轴向动量；扩稳