The spanwise distribution of impeller exit circulation (SDIEC) has a significant effect on the impeller performance, therefore, there is a need for its consideration in the optimization design of mixed-flow pumps. In this study, a combination optimization system, including a 3D inverse design method (IDM), computational fluid dynamics (CFD), Latin hypercube sampling (LHS) method, response surface model (RSM), and non-dominated sorting genetic algorithm (NSGA-Ⅱ) was used to improve the performance of the mixed-flow pump after considering the effect of SDIEC on the performance of the impeller. The CFD results confirm the accuracy and credibility of the optimization results because of the good agreement the CFD results established with the experimental measurements. Compared with the original impeller, the pump efficiency of the preferred impeller at 0.8Qdes, 1.0Qdes, and 1.2Qdes improved by 0.63%, 3.39%, and 3.77% respectively. The low-pressure region on the blade surface reduced by 96.92% while the pump head difference was less than 1.84% at the design point. In addition, a comparison of the flow field of the preferred impeller and the original impeller revealed the effect of SDIEC on mixed-flow pump performance improvement and flow mechanism.

This study investigated the irreversible energy losses in the different sections of propeller blades. To the best of our knowledge, this is the first study to consider the properties of a shear-thinning fluid in evaluating irreversible energy losses based on the entropy generation theory. The numerical simulation results were consistent with the experimental results. The flow energy losses and the total mechanical energy loss gradient of an anaerobic digestion (AD) system were determined. The results indicated that the total mechanical energy loss occurred in the propeller region and was primarily influenced by the operation speed. The effects of rheology were neglected, although rheology notably affects the equivalent-volume velocity field within specific power characteristics, leading to an insufficient mixing field in the AD system. The energy losses primarily occurred around the propeller region, primarily in sections 3–5 under different flow rates. Viscous diffusion and velocity fluctuation are the primary factors contributing to the entropy of the system, accounting for more than 98%. According to the wall separation and friction loss on the suction and pressure surfaces of the propellers, sections 3–5 accounted for 90% of the energy loss. Energy dissipation in the propeller was mostly constituted by turbulence entropy and direct entropy. The rotation speed was the key factor causing viscous diffusion. Although the rheology effect on hydraulic loss is limited at low concentrations, the hydraulic loss in the blade tip region due to high-concentration fluids is significantly affected by rheology.