Abstract
The main concern of this paper is fundamental research into an acute problem arising in the operation of hydraulic turbines, namely, the formation of a vortex core downstream of the impeller. It is noted that, at present, the operating range of these machines has to be extended due to the change in power network loads in daily and seasonal cycles, thereby increasing the time of hydraulic turbines' operation under off-design or undesirable conditions, including those involving the risk of formation of a vortex of varying intensity. To describe this complex fluid flow, a mathematical model of the vortex core flow downstream of the hydraulic turbine’s impeller was developed. This paper focuses on the fundamental issues encountered in developing the mathematical model. The methods are presented for simplifying the formulation of equations describing the structure of vortex rope formed in the flowpath. In this case, the equations of mathematical physics containing a dependent variable and taking the form of the Navier–Stokes equations when applied fluids flows were employed. They describe the time changes of the selected parameters in a controlled volume induced by the flow through the volume boundaries. The boundary conditions have been demonstrated to considerably affect the unsteady vortex structures. A special case is formulated for a potential force field using the stress tensor that governs the equilibrium. This makes it possible to describe complex motion in liquids without using an intricate form of the Navier–Stokes equations for vortex structures.
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ACKNOWLEDGMENTS
This work was supported by the project “Computer Simulation of Efficient Energy with Low Emissions,” funded as project no. CZ.02.1.01/0.0/0.0/16_026/0008392 under the applicable research, development, and education program with the priority direction 1: “Enhancing Capabilities for High-Quality Research,” and the project “Study of the Flow and Interaction of Two-Component Fluids with Solids under an External Magnetic Field” funded as project no. GA101/19-06666S by the Grant Agency of the Czech Republic.
The presented results were also obtained with the financial support of the Ministry of Science and Higher Education of the Russian Federation under the work assignment no. FSWF-2020-0021, “Development of Scientific and Engineering Fundamentals for Enhancement of Condensation Heat Transfer and Improvement of Thermohydrodynamic Characteristics and Wear Resistance of Power Equipment Through Modification of Functional Surfaces.”
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Translated by T. Krasnoshchekova
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Fialová, S., Pochylý, F., Volkov, A.V. et al. Methods for Simplification of the Mathematical Model for the Calculation of Flows in the Flow Path of Hydraulic Turbines. Therm. Eng. 68, 906–915 (2021). https://doi.org/10.1134/S004060152112003X
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DOI: https://doi.org/10.1134/S004060152112003X