Multi-stage centrifugal pumps used as turbines (PATs) are widely applied in energy recovery. To enhance the understanding of the energy conversion characteristics of multi-stage PAT, this study proposes an energy loss evaluation method based on energy transfer, examining energy conversion within impellers and inter-stage transfer to identify energy losses and their impact on efficiency under various conditions. The method is derived from the principles of momentum conservation and flow continuity, based on key physical quantities such as pressure gradient, turbulence dissipation, and wall friction. The study reveals the first-stage impeller exhibits 66.5 % reduction of the kinetic energy at the inlet under the design flow rate. And wall friction losses in this region account for 54.5 % of the total energy losses. Energy conversion efficiency varies across the stages of the multi-stage PAT. At the design flow rate, the first-stage impeller achieves a maximum conversion efficiency of 57.4 %, while the second-stage impeller’s efficiency drops to 54.2 %. The first-stage impeller demonstrated significantly higher efficiency than the subsequent stages. Significant energy losses occur during the inter-stage transition after the fluid passes through the first-stage impeller. Therefore, when optimizing multi-stage PAT designs, it is crucial to ensure the compatibility between each impeller’s design and the fluid flow characteristics to improve overall efficiency.

中文翻译：

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多级离心泵作为涡轮的能量转换和损失预测理论模型


用作涡轮机 （PAT） 的多级离心泵广泛用于能量回收。为了加强对多级 PAT 能量转换特性的理解，本研究提出了一种基于能量转移的能量损失评估方法，检查叶轮内的能量转换和级间转移，以确定各种条件下的能量损失及其对效率的影响。该方法源自动量守恒和流动连续性原理，基于压力梯度、湍流耗散和壁面摩擦等关键物理量。研究表明，在设计流速下，第一级叶轮在入口处的动能降低了 66.5%。该区域的壁面摩擦损失占总能量损失的 54.5%。能量转换效率在多级 PAT 的各个阶段都有所不同。在设计流速下，第一级叶轮的最大转换效率为 57.4 %，而第二级叶轮的效率下降到 54.2 %。第一级叶轮的效率明显高于后续级。在流体通过第一级叶轮后的级间转换期间，会发生显著的能量损失。因此，在优化多级 PAT 设计时，确保每个叶轮的设计与流体流动特性之间的兼容性以提高整体效率至关重要。