Design optimization of axial flow hydraulic turbine runner: Part I—an improved Q3D inverse method

Abstract

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.

Derivation of the Mathematical Approach to the Radial Pump’s Meridional Channel Design Based on the Controlment of the Medial Axis

“…Future Work. Peng et al [7,22] and Cao et al [23] have already proposed the inverse blade design theory controlled by the distribution of the torque velocity, and a series of pumps working in different industrial areas have been got with the blade design theory. But there is a lack of a specific meridional channel design approach to provide the skeleton and structural parameters for the inverse design of the blade.…”

“…To design the pump, two aspects, namely, the blade shape and the meridional channel, can be considered [5]. Though many inverse design methods about the blade shape have already been conducted by former studies [6][7][8], little attention has been paid to the meridional channel design. Nevertheless, the meridional shape is the foundation for the pump design, and Bing et al [9] had proven that the meridional shape has great effects on the pump performance, so that the related design method about the meridional channel should be treated seriously.…”

Design optimization of axial flow hydraulic turbine runner: Part II—multi‐objective constrained optimization method

“…As for the inverse design of turbomachinery blades, there are some useful fully three-dimensional (F3D) [4][5][6] and quasi-three-dimensional (Q3D) [7][8][9] inverse computation models, and they have been gradually used for the engineering practice. Compared with the F3D inverse model [10; 11], the improved Q3D inverse model reported in part I [12] has the feature of quick convergence. As shown in Figure 1, the ow computation is made from the far inlet of guide vanes to the far outlet of runner by solving a set of governing equations simultaneously in the Q3D method.…”

Inverse-design and optimization methods for centrifugal pump impellers

“…Since the 1950s, several two-dimensional and later quasi three-dimensional inverse-design methods have been developed. In fact, quasi three-dimensional methods are still being used for example by Peng et al [51], [52].…”

“…Peng et al [50,51,52] developed a quasi 3D inverse-design method by circumferential averaging. They employed a stream function for the inviscid flow analysis and used a prescribed mean-swirl distribution as loading function.…”