Giljen, Z.; Nedeljković, M. Universal Form of Radial Hydraulic Machinery Four-Quadrant Equations for Calculation of Transient Processes. Energies2023, 16, 7736.
Giljen, Z.; Nedeljković, M. Universal Form of Radial Hydraulic Machinery Four-Quadrant Equations for Calculation of Transient Processes. Energies 2023, 16, 7736.
Giljen, Z.; Nedeljković, M. Universal Form of Radial Hydraulic Machinery Four-Quadrant Equations for Calculation of Transient Processes. Energies2023, 16, 7736.
Giljen, Z.; Nedeljković, M. Universal Form of Radial Hydraulic Machinery Four-Quadrant Equations for Calculation of Transient Processes. Energies 2023, 16, 7736.
Abstract
The Suter curves for Wh and Wm characteristics of collected and the first time presented Four-quadrant (4Q) diagrams of 11 radial pump-turbine models with different specific speeds (nq=24.34, nq=24.8, nq=27, nq=28.6, nq=38, nq=41.6, nq=41.9, nq=43.83, nq=50, nq=56, and nq=64.04) are given in the paper, as well as the Suter curves for 2 pump models (nq=25, and nq=41.8) which were already published in the literature. These 11+2 curves were analyzed to establish a certain universal law of behavior in dependence on the specific speed. For the determination of existing laws in behavior, the fitting procedure using the Regression and Spline methods was used. The paper presents a research plan and structures that include: data collection of four-quadrant diagrams for models of pump-turbines and pumps with different specific speeds (nq), the procedure of recalculation of Four-quadrant diagrams of the models into Suter curves for Wh and Wm characteristics, the definition of the optimal point for the pump and turbine operating mode in pump-turbine models for different specific speeds, and developing numerical models in the MATLAB program to obtain the Universal Equation for the Wh and Wm characteristics. The scientific contribution of this paper is the firstly published original mathematical curve named Universal Equation for the Wh and Wm characteristics for radial pumps and pump-turbines. Application of the equation has been demonstrated at the pumping station where two radial pumps are installed. The calculation of transient processes was performed using the numerical model developed by the authors in the mathematical program MATLAB. Comparison of the transition process results has been made for the two cases - when input data in the numerical model have been firstly used with the values of Suter curves for Wh and Wm characteristics obtained by recalculation from the Four-quadrant operating characteristics (Q11, n11, M11) of model’s specific speed, and then secondly with the values of the Suter curves for Wh and Wm characteristics obtained from the Universal Equation.
Keywords
universal equations for Wh and Wm characteristics; hydraulic transients calculation; radial hydraulic machinery; influence of the specific speed; method of characteristics
Subject
Engineering, Mechanical Engineering
Copyright:
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