Based on the continuity and motion equations of fluid, the direct problem is settled by using iterative calculation for two kinds of stream surfaces to obtain the flow field of the mixed-flow pump impeller. The inverse problem of the mixed-flow pump impeller is solved by employing point-by-point integration method to draw the blade shape, thickening the blade and smoothing the leading edge of the blade by conformal mapping. The meridional velocity will not be determined until the iterative calculation of direct and inverse problems is converged. Based on the meridional velocity field, the impeller performance is predicted with loss models. Then an optimal design model of the mixed-flow pump impeller is developed. This model, which applies genetic algorithm, takes the highest efficiency and the velocity moment distribution as the optimum objective and the optimum parameter, respectively. The obtained velocity moment distribution is then used in the next iterative calculation of direct and inverse problems. The impeller will not be finally determined until the difference between the velocity moment distributions, which are obtained from two consecutive iterative calculations, can meet the set requirements. Based on SIMPLEC algorithm, the three-dimensional turbulent flow field of the mixed-flow pump impeller is obtained by solving the Reynolds averaged Navier-Stokes equation and RNG k-s turbulent model equation. The simulation results show that the impeller designed by this method has higher hydraulic efficiency, the pressure distribution is well uniform and the flow is steady without separation. The characteristic of this method is to determine blade shape by satisfying both the continuity and motion equations of fluid, so it can lead to high accuracy of impeller design. Meanwhile, the blade has the smooth surface and the complete data, which is convenient for blade manufacturing with numerical control machines.
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