A combined approach of inverse method and direct flow analysis is presented for the hydrodynamic design of gas-liquid two-phase flow rotodynamic pump impeller. The geometry of impeller blades is designed for a specified velocity torque distribution by treating the two-phase mixture as a homogeneous fluid under the design condition. The three-dimensional flow in the designed impeller is verified by direct turbulent flow analysis, and the design specification is further modified to optimize the flow distribution. A helical axial pump of high specific speed has been developed. To obtain a favorable pressure distribution the impeller blade was back-loaded at the hub side compared to the tip side. Experimental results demonstrate that the designed pump works in a wide flow rate range until the gas volume fraction increases to over 50% and its optimum hydraulic efficiency reaches to 44.0% when the gas volume fraction of two-phase flow is about 15.6%. The validity of design computation has been proved.

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SUMMARYWith the aim of constructing a comprehensive design optimization procedure of axial ow hydraulic turbine, an improved quasi-three-dimensional inverse method has been proposed from the viewpoint of system and a set of rotational ow governing equations as well as a blade geometry design equation has been derived. The computation domain is ÿrstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and ows in di erent regions are solved simultaneously. So the in uence of wicket gate parameters on the runner blade design can be considered and the di culty to deÿne the ow condition at the runner blade inlet is surmounted. As a pre-computation of initial blade design on S 2m surface is newly adopted, the iteration of S 1 and S 2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct ow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner.

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SUMMARYThis paper is concerned with the design optimization of axial ow hydraulic turbine runner blade geometry. In order to obtain a better design plan with good performance, a new comprehensive performance optimization procedure has been presented by combining a multi-variable multi-objective constrained optimization model with a Q3D inverse computation and a performance prediction procedure. With careful analysis of the inverse design of axial hydraulic turbine runner, the total hydraulic loss and the cavitation coe cient are taken as optimization objectives and a comprehensive objective function is deÿned using the weight factors. Parameters of a newly proposed blade bound circulation distribution function and parameters describing positions of blade leading and training edges in the meridional ow passage are taken as optimization variables.The optimization procedure has been applied to the design optimization of a Kaplan runner with speciÿc speed of 440 mkW. Numerical results show that the performance of designed runner is successfully improved through optimization computation. The optimization model is found to be validated and it has the feature of good convergence. With the multi-objective optimization model, it is possible to control the performance of designed runner by adjusting the value of weight factors deÿning the comprehensive objective function.