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Abstract

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 (»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.

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Authors and Affiliations

Z. Krzemianowski
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Abstract

The optimum combination of blade angle of the runner and guide vane opening with Kaplan turbine can improve the hydroelectric generating the set operation efficiency and the suppression capability of oscillations. Due to time and cost limitations and the complex operation mechanism of the Kaplan turbine, the coordination test data is insufficient, making it challenging to obtain the whole curves at each head under the optimum coordination operation by field tests. The field test data is employed to propose a least-squares support vector machine (LSSVM)-based prediction model for Kaplan turbine coordination tests. Considering the small sample characteristics of the test data of Kaplan turbine coordination, the LSSVM parameters are optimized by an improved grey wolf optimization (IGWO) algorithm with mixed non-linear factors and static weights. The grey wolf optimization (GWO) algorithm has some deficiencies, such as the linear convergence factor, which inaccurately simulates the actual situation, and updating the position indeterminately reflects the absolute leadership of the leader wolf. The IGWO algorithm is employed to overcome the aforementioned problems. The prediction model is simulated to verify the effectiveness of the proposed IGWO-LSSVM. The results show high accuracy with small samples, a 2.59% relative error in coordination tests, and less than 1.85% relative error in non-coordination tests under different heads.
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Authors and Affiliations

Fannie Kong
1
ORCID: ORCID
Jiahui Xia
1
ORCID: ORCID
Daliang Yang
1
ORCID: ORCID
Ming Luo
1
ORCID: ORCID

  1. School of Electrical Engineering, Guangxi University, Nanning, 530000, China

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