Influence of circulation distribution on the optimization results of mixed-flow pump based on inverse design

Abstract: To quantitatively study the influence of the impeller outlet circulation distribution on the optimization results of the mixed flow pump, the mixed flow pump with a specific speed of 511 was selected as the baseline model. A comprehensive optimization system was used to optimize under two different conditions, and the performance of the optimization results were compared with the baseline model. In the first case, the influence of the distribution form of the impeller outlet circulation on the optimization result of the mixed flow pump impeller was not considered, that is, the free vortex design (constant distribution of impeller outlet spanwise circulation) was adopted, while in the second case, the effect of circulation distribution was considered, and the forced vortex design (linear distribution of impeller outlet spanwise circulation) was adopted. The optimization system consists of an inverse design method, an optimal latin hypercube sampling method, a radial basis function neural network model and a multi-island genetic algorithm. The optimization objective is the weighted efficiency at 0.8Qdes, 1.0Qdes and 1.2Qdes with weighting factors of 0.2, 0.5, and 0.3 (Qdes means design flow rate). The constraints are the head change of the optimized mixed flow pump at 1.0Qdes less than 3% compared to the baseline model design point, and the pump section efficiency at 0.8Qdes, 1.0Qdes and 1.2Qdes is greater than the baseline model. The research results showed that in the forced vortex design, when the circulation value at the hub was selected as the design parameter, it is feasible to combinedly use the continuity equation, the energy conservation equation and the radial balance equation to calculate the spanwise distribution of impeller outlet circulation. Which can ensure that the pump section head changes of the sampling points under the design condition are within a reasonable range (the range of head variation is less than 10% of the baseline model design head), and there is no need to add new sample points. In addition, the comparison of the predicted head and calculated head of the optimal solution also shows the same result. The results of local sensitivity analysis showed that the impeller outlet spanwise circulation distribution control parameters has a greater impact on the pump section weighted efficiency, and it can influence the other design parameters effect on the weighted efficiency. Therefore, it is necessary to consider the influence of the impeller outlet circulation in the optimal design of the mixed flow pump. The internal flow analysis showed that the forced vortex design can more effectively control the flow regime near the impeller outlet than the free vortex design. This is not only conductive to the improvement of the efficiency of the impeller, but also to the reduction of the hydraulic loss of the downstream components of the impeller, thereby further improving the overall optimization effect of the mixed flow pump. In the free vortex design, the weighted efficiency of the optimization result is 84.14%, while in the forced vortex design, the weighted efficiency of the optimization result is 85.08%, and the heads of both all meet the constraint conditions. This study can provide reference for the optimization design of turbomachinery, so as to maximize the optimization effect.