Engineering design of low-head Kaplan hydraulic turbine blades using the inverse problem method

The paper concerns the engineering design of guide vane and runner blades of hydraulic turbines using the inverse problem on the basis of the definition of a velocity hodograph, which is based on Wu's theory [1, 2]. The design concerns the low-head double-regulated axial Kaplan turbine model characterized by a very high specific speed. The three-dimensional surfaces of turbine blades are based on meridional geometry that is determined in advance and, additionally, the distribution of streamlines must also be defined. The principles of the method applied for the hydraulic turbine and related to its conservation equations are also presented. The conservation equations are written in a curvilinear coordinate system, which adjusts to streamlines by means of the Christoffel symbols. This leads to significant simplification of the computations and generates fast results of three-dimensional blade surfaces. Then, the solution can be found using the method of characteristics. To assess usefulness of the design and robustness of the method, numerical and experimental investigations in a wide range of operations were carried out. Afterwards, the so-called shell characteristics were determined by means of experiments, which allowed to evaluate the method for application to the low-head (1.5 m) Kaplan hydraulic turbine model with the kinematic specific speed ( similar to 260). The numerical and experimental results show the successful usage of the method and it can be concluded that it will be useful in designing other types of Kaplan and Francis turbine blades with different specific speeds.