Turbomachinery optimization is one of the most important research topics in the field of energy conversion. The velocity moment method is widely recognized for its innovative approach and high computational efficiency. However, previous studies typically assumed a constant velocity moment distribution at the impeller outlet to satisfy the constraint of constant Euler head, which restricted the optimization potential. In this study, a new full-velocity moment method was developed by parameterizing the velocity moments at the impeller outlet using the continuity, energy, and radial balance equations, building upon the traditional velocity moment method. On this basis, parameterized optimization of a mixed-flow pump impeller was conducted through coupling parameter analysis, surrogate model, and optimization algorithm. The performance of the optimized impeller was then experimentally validated. The results indicate that the velocity moment distribution at the impeller outlet significantly impacts the performance of the mixed-flow pump. The weighted efficiency of the optimized model was improved by 3.24% compared to the original model. Specifically, the efficiency at 0.8Qdes, 1.0Qdes, and 1.2Qdes increased by 1.36%, 3.84%, and 5.86%, respectively. The internal flow analysis reveals that increasing the velocity moment at the hub helps prevent boundary layer detachment caused by low-momentum fluid accumulation.
Wang et al. (2025) studied this question.